41 subsidence due to fluid withdrawal

Developments in Petroleum Science, 41

subsidence due to fluid withdrawal

This Page Intentionally Left Blank

Developments in Pet ro leum Science, 41

subsidence due to fluid withdrawal

E d i t e d by

G.V. CHILINGARIAN

School of Engineering, University of Southern California, Los Angeles, California, USA

E.C. D O N A L D S O N

Route 2, Box 52, Wynnewood, OK 73098, USA

and

T.E Y E N

School of Engineering, University of Southern California, Los Angeles, California, USA

o.

1995

E L S E V I E R S C I E N C E

A m s t e r d a m - L a u s a n n e - N e w York - O x f o r d - S h a n n o n - T o k y o

ELSEV1ER SCIENCE B.V. Sara Burgerhartstraat 25 P.O. Box 211, 1000 AE Amsterdam, The Netherlands

ISBN: 0-444-81820-0

© 1995 Elsevier Science B.V. All rights reserved.

No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Science B.V., Copyright & Permissions Department, P.O. Box 521, 1000 AM Amsterdam, The Netherlands.

Special regulations for readers in the USA - This publication has been registered with the Copyright Clearance Center Inc. (CCC), Salem, Massachusetts. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the USA. All other copyright questions, including photocopying outside of the USA, should be referred to the publisher.

No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein.

This book is printed on acid-flee paper.

Printed in The Netherlands

Dedication

This book is dedicated to

HIS E X C E L L E N C Y

H I S H A M M O H Y U D D I N N A Z E R

Minister of Petroleum and Mineral Resources, Kingdom of Saudi Arabia,

in recognition of his outstanding contributions to the petroleum industry and for his vision and leadership in the promotion of mineral, environmental and geohazard programs in Saudi Arabia.

vii

PREFACE

This book identifies and discusses the geoscience and engineering issues and effects associated with the subsurface extraction of fluids. The editors' introduction chapter focuses the reader on the universality of subsidence due to fluid withdrawal. Following chapters present the synergism of various disciplines required in interpreting and mitigating subsidence problems.

Land subsidence due to fluid withdrawal from aquifers and hydrocarbon reservoirs is an increasing worldwide geohazard directly affecting the quality of surface and subsurface environments. The results of uncontrolled subsidence economically impacts industry, commerce, and development of rural and urban areas. The reader is made aware of the conflict between the need for extracting large amounts of valuable fluids from the subsurface and land use. This conflict exasperates environmental concerns and issues.

Subsidence problems manifest themselves in various ways. The following worldwide examples portray the problems. The extraction of natural gas caused land subsidence in the Po delta of Italy and in the large Groningen gas field of the Netherlands producing infrastructure damage. Widespread harbor subsidence resulted from oil production in the Wilmington field, Los Angeles and Long Beach, California, U.S.A. Seabed subsidence occurring around the North Sea Ekofisk production platforms posed a threat to the safety of personnel, equipment, and platforms. The rapid drawdown of the groundwater table by overpumping in arid and semi-arid agricultural regions can result in abrupt ground failure. Excessive withdrawal of groundwater created large earth fissures in the farming area of Wadi al Yatimah and destruction of new tourist facilities at A1 Aflaj lakes, western and central Saudi Arabia, respectively. Widespread ground subsidence in the large metropolitan areas of Osaka, Japan, and London, England, resulted from excessive aquifer pumping. Detailed case histories of four areas explore some of these problems in depth.

The compaction process is discussed thoroughly in this book. The overburden pressure of subsurface reservoirs is supported by the grain-to-grain pressure of the formation and fluid pressure in the pores. Fluid withdrawal from the reservoirs results in the depletion of the reservoir's pore pressure. A depletion of fluid pressure is the cause of subsidence. Redistribution of subsurface formation stresses results in the rearrangement of grain contacts and the spreading of the area of compaction in the reservoir. The redistribution of stress eventually leads to surface subsidence. A computer program based on constitutive equations gives the reader the ability to analyze the amount of compaction, and loss of porosity and permeability with respect to distance from a production well.

viii PREFACE

Corrective measures such as repressurizing the oil/gas zones by injecting water or gas can control the amount and rate of subsidence over hydrocarbon reservoirs. This strategy is one of using pressure maintenance technology. Prorating the amounts of groundwater to be pumped can have beneficial results. This action will not only control the rate of subsidence but conserve groundwater, help to maintain the structural integrity of facilities and infrastructures, and prevent aquifer invasion by seawater in coastal areas. Economic development policy has to consider geohazard and environmental concerns to insure the future empowerment of industrial and agricultural benefits to a region m country's economy. Practicing petroleum engineers, geologists, civil engineers, hydrologists, environmentalists, and central planners will welcome the knowledge contained in this book.

HERMAN H. RIEKE Consultant

Morgantown, WV U.S.A.

ix

LIST OF CONTRIBUTORS

A. ABDULRAHEEM University of Petroleum and Minerals, KFUPM # 1105, Dhahran 31261, Saudi Arabia

G.C. BORGIA Istituto di Scienze Minerarie, Universitdt di Bologna, Viale Risorgimento 2, 40136 Bologna, Italy

G. BRIGHENTI Istituto di Scienze Minerarie, Universitd~ di Bologna, Viale Risorgimento 2, 40136 Bologna, Italy

G.V. CHILINGARIAN Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089-1211, U.S.A.

X.C. COLAZAS Director, Long Beach Department of Oil Properties, 333 West Ocean Boulevard, Long Beach, CA 90802, U.S.A.

E.C. DONALDSON Route 2, P.O. Box 52, Wynnewood, OK 73098, U.S.A.

W. FERTL Late President, Atlas Wireline Services, Houston, TX, U.S.A.

A.S. FINOL IVIC, Apartado 1827, Caracas, IOIOA, Venezuela

A.E. GUREVICH Consultant, 1323 N. Harvard Blvd., No. 4, Los Angeles, CA 90027, U.S.A.

E. MESINI Istituto di Scienze Minerarie, Universitdt di Bologna, Viale Risorgimento 2, 40136 Bologna, Italy

D. MOMENI Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089-1211, U.S.A.

H.H. RIEKE, III Directorate General of Mineral Resources, P.O. Box 345, Jeddah 21191, Saudi Ara- bia

J.-C. ROEGIERS Professor of Rock Mechanics, Energy Center, University of Oklahoma, Norman, OK 73019, U.S.A.

Z.A. SANCEVIC IVIC, Apartado 1827, Caracas, IOIOA, Venezuela

R.W. STREHLE Long Beach Department of Oil Properties, 333 West Ocean Boulevard, Long Beach, CA 90802, U.S.A.

T.E YEN School of Civil Engineering, University of Southern California, Los Angeles, CA 90089-1211, U.S.A.

M.M. ZAMAN Professor, School of Civil Engineering and Environmental Science, University of Oklahoma, Norman, OK 73019, U.S.A.

x i

C O N T E N T S

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii List of Con t r ibu to r s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

Chapter 1. I N T R O D U C T I O N T O C O M P A C T I O N / S U B S I D E N C E - - I N T R O D U C T I O N

T O T E C T O N I C S A N D S E D I M E N T A T I O N

E.C. Dona ldson , G.V. Chi l ingar ian and T.E Yen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

I n t r o d u c t i o n to tectonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

C o m p o s i t i o n of the globe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

M o v e m e n t of sections (plates) of the l i thosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Co n t i n en t a l marg ins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

I n t r o d u c t i o n to s e d imen ta t i on . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Source and f r a g m e n t a t i o n of rocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Classif icat ion of sands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Statist ical analyses of part icles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Part icle shape, roundness and spherici ty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

C o m p o s i t i o n and classification of sands and sands tones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Gene t i c classification of sands on the basis of grain-size d is t r ibut ions . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Physical p roper t i e s of sands and sands tones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Porosi ty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Permeabi l i ty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Specific surface a rea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Surface areas of sands and sands tones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Elast ic p roper t i es . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Compress ib i l i ty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

N o m e n c l a t u r e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Refe rences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Chapter 2. C O M P A C T I O N O F A R G I L L A C E O U S S E D I M E N T S

G.V. Chi l ingar ian , H.H. Rieke, III and E.C. D o n a l d s o n . . . . . . . . . . . . . . . . . . . . . . . . 47 In t ro d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

C o m p a c t i o n mode l d e v e l o p m e n t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

T h e Katz and Ib rah im compac t ion mode l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

B o n h a m ' s mode l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Seals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Clay mine ra l diagenesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Diagenes is . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Ear ly d iagenet ic changes of clay minera ls in sed iments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Clay minera l facies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Clay minera l dehydra t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

M a t h e m a t i c a l descr ip t ion of compac t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Ra te of compac t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

O v e r b u r d e n po ten t ia l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

Sharp ' s m o m e n t u m and energy ba lance equa t ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 E q u a t i o n of cont inui ty for m o m e n t u m t r anspor t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

E q u a t i o n of cont inui ty for energy t ranspor t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

xii CONTENTS

Parameters and constants in Sharp's model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

Restora t ion model ing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Quant i ta t ive evaluat ion of porosity in argillaceous sediments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Quant i ta t ive evaluat ion of bed thickness changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

Model ing thickness changes in sedimentary layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Flow of fluids th rough argillaceous media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

Water influx f rom overlying, overpressured shales into producing reservoirs . . . . . . . . . . . . . . . . 86

Subsidence of producing reservoirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

Diffusion-l imited model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

Chemis t ry of intersti t ial fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

Composi t ion of interstit ial solutions related to seawater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

Changes in the chemistry of solutions squeezed out at different overburden pressures . . . 102

Salinity distr ibution in sandstones and associated shales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

Fluid chemistry compact ion m diagenetic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

Compac t ion effects on the expulsion of hydrocarbons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

Exper imenta l compact ion results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Hydrocarbons m geochemical and migrat ion models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

Stresses in sediments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

Hydrostat ic stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

Resolut ion of the total stress field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

Spheric stress state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

Deviatoric stress state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

Total stress tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

Tectonic overcompact ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Compressibil i t ies of sand and clayey sediments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

Exper imenta l values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

Effect of rock compressibili ty on the est imation of pe t ro leum reserves . . . . . . . . . . . . . . . . . . . . . 146

Compac t ion of carbonates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

Derivat ion of the Ricken's carbonate compact ion equat ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

Carbonate compact ion equat ion for rocks with low porosities (Ricken, 1986, 1987) . . . . . . . . . 150

Testing of compact ion equat ion by compact ion measurements (Ricken, 1986, 1987) . . . . . . . . . 150

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

Chapter 3. STRESSES IN S E D I M E N T S

E.C. Donaldson, G.V. Chil ingarian and H.H. Rieke . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

Compac t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

Labora tory and mathemat ica l analysis of compact ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

Overburden stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

Est imat ion of the magni tude and direction of stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

P r e s s u r e - d e p t h - d e n s i t y relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

Subsidence of deposi t ional basins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

Basins and geosynclines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

Hydrogeological cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Subsidence as a result of fluid withdrawal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

Nomenc la tu re . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

R e c o m m e n d e d bibl iography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

Chapter 4. P O S S I B L E IMPACT OF S U B S I D E N C E ON GAS L E A K A G E TO T H E

S U R F A C E F R O M S U B S U R F A C E OIL A N D GAS R E S E R V O I R S

A.E. Gurevich and G.V. Chil ingarian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

In t roduct ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

Cur ren t theories of f luid-sol id force interaction: a critical review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

CONTENTS x i i i

F r ac tu r ing due to subs idence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

His to ry and causes of subs idence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

Ra te s of subs idence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

Stress and s t ra in d i s t r ibu t ion in subs id ing fo rmat ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

Sur face fissures caused by subs idence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

I m p a c t of subs idence on faults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

M e c h a n i s m s of gas s e e p a g e f rom pools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

U p w a r d diffusion of gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

M e c h a n i c a l m e c h a n i s m s of gas mig ra t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204

U p w a r d m i g r a t i o n of s e p a r a t e gas globules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204

U p w a r d mig ra t i on of the con t inuous gas p h a s e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

L e a k a g e of gas t h r o u g h o p e n f rac tures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

S u m m a r y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 R e f e r e n c e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

Chapter 5. S U B S I D E N C E S T U D I E S IN ITALY

G. Br ighent i , G.C. Borg ia and E. Mes in i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

G e n e r a l i n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

M e a s u r e m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

T h e geo techn ica l f ea tu res of s ed imen t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

S a m p l i n g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

L a b o r a t o r y tests and the in f luence of s ampl ing d i s t u rbance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

Values of the compress ib i l i ty of u n c o n s o l i d a t e d sed imen t s of the P o - V e n e t o Pla in . . . . . . . . . . 224

Var ia t ions in wa te r sal ini ty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

Mode l l i ng of the p h e n o m e n o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

Aqu i f e r s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

H y d r o c a r b o n reservoirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230

I m p a c t of subs idence on an a rea and r emed ie s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234

D a m a g e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234

R e m e d i e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235

Lega l cons ide ra t ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

Case h is tory of the Po D e l t a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238

I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238

Geo logy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238

Gas p r o d u c t i o n and subs idence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

S e d i m e n t c o m p a c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243

P r e s e n t t r end of the subs idence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

R e m e d i e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

F ina l r e m a r k s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

Venice case his tory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248

I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248

Geo logy and hydrogeo logy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248

His to ry of subs idence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

F ina l r e m a r k s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

R a v e n n a case his tory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

In t roduc t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

Geo logy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254

Wate r p r o d u c t i o n f rom u n d e r g r o u n d s t ra ta and subs idence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255

Gas p r o d u c t i o n and subs idence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

S u m m a r y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260

B o l o g n a case his tory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260

I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260

Geo logy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261

x i v C O N T E N T S

H i s t o r y o f s u b s i d e n c e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263

S u m m a r y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267

M o d e n a ca se h i s t o ry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

G e o l o g y a n d h y d r o g e o l o g y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

H i s t o r y o f s u b s i d e n c e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

S u m m a r y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

O t h e r cases o f s u b s i d e n c e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

A c k n o w l e d g e m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276

R e f e r e n c e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276

Chapter 6. S U B S I D E N C E IN T H E W I L M I N G T O N O I L F I E L D , L O N G B E A C H ,

C A L I F O R N I A , U S A

X.C. C o l a z a s a n d R.W. S t r e h l e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

G e o l o g y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286

G e n e r a l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286

S t r a t i g r a p h y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

Oi l z o n e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290

U p p e r f o u r z o n e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290

L o w e r t h r e e z o n e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

S t r u c t u r e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292

D r i l l i n g a n d c o m p l e t i o n m e t h o d s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293

D i r e c t i o n a l d r i l l ing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293

C o r i n g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293

C o m p l e t i o n m e t h o d s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293

S u b s i d e n c e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294

H i s t o r y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294

C o m p a c t i o n t h e o r y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298

L a b o r a t o r y i n v e s t i g a t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300

C o n s o l i d a t i o n tes t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301

Tr iaxia l tes ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302

R e s u l t s o f l a b o r a t o r y tes t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305

Tar Z o n e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306

R a n g e r Z o n e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310

U p p e r T e r m i n a l Z o n e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310

L o w e r T e r m i n a l Z o n e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314

Ar t i f i c ia l ly m i x e d s a m p l e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

A p p l i c a t i o n o f l a b o r a t o r y r e su l t s in e s t i m a t i n g c o m p a c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

F i e l d m e a s u r e m e n t o f c o m p a c t i o n a n d s u b s i d e n c e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

F i r s t - o r d e r leve l su rveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

P r e c i s i o n ca s ing co l l a r surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

R a d i o a c t i v e b u l l e t su rveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

S h a l l o w - c o m p a c t i o n r e c o r d e r s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

T i d a l - g a u g e r e c o r d e r s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326

S e i s m i c su rveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

R e s e r v o i r p r e s s u r e su rveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

H o r i z o n t a l - s t r a i n su rveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

P r o d u c t i o n - i n j e c t i o n b a l a n c e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

R e p r e s s u r i z a t i o n a n d r e b o u n d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

Types a n d t r e a t m e n t o f i n j e c t i o n w a t e r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

S o u r c e wel l w a t e r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

P r o d u c e d w a t e r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330

CONTENTS XV

Fresh wate r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330

O t h e r wate r sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330

Effects of wa te r inject ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330

Refe rences and b ib l iography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334

Chapter 7. S U B S I D E N C E IN V E N E Z U E L A

A. Finol and Z.A. Sancevic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337

In t roduc t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337

Venezue lan oil indust ry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337

Venezue lan heavy, extra heavy and b i tumen reserves and p roduc t ion . . . . . . . . . . . . . . . . . . . . . . . 338

Bol ivar coastal fields (Tfa Juana , Lagunil las, Bachaque ro ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340

Geologica l set t ing and d e v e l o p m e n t history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340

Subs idence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346

C o m p a c t i o n m e c h a n i s m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347

Subs idence records and moni to r ing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357

Precis ion m e a s u r e m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361

Des ign and cons t ruc t ion of coastal dikes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361

Geo techn ica l aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361

Hydrog raph ic aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362

Seismicity and seismic geology aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362

Surface cracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363

D r a i n a g e system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364

D r a i n a g e Mas te r Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364

Predic t ion of subs idence and compac t ing reservoir s imula t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365

Or inoco Belt subs idence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369

Refe rences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370

Chapter 8. R E S E R V O I R C O M P A C T I O N A N D S U R F A C E S U B S I D E N C E IN

T H E N O R T H S E A E K O F I S K F I E L D

M.M. Z a m a n , A. A b d u l r a h e e m and J.-C. Roegiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

In t roduc t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

Discovery and explora t ion in the Nor th Sea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375

P roduc t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377

Ekofisk Fie ld descr ip t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377

Fie ld d e v e l o p m e n t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378

E n h a n c e d oil recovery projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379

Pla t forms sinking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379

Causes of subs idence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380

M e a s u r e m e n t s of subs idence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381

M e a s u r e m e n t of reservoir compac t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381

Tempora ry r emedia l measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381

P e r m a n e n t remedia l measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382

Jack-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383

Protect ive barr ie r for the t ank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384

Character is t ics of the Ekofisk reservoir rocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384

Minera logy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385

Porosi ty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385

Permeabi l i ty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388

Mechanics of the Ekofisk reservoir rocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388

S t reng th tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388

Uniaxial strain tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389

Hydros ta t ic compress ion tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393

Effect of stress on porosi ty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393

xvi CONTENTS

Effect of stress on pe rmeab i l i t y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

Stress ra t io . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

L o a d i n g ra te . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397

Effect of s e a w a t e r on c o m p a c t i o n behav io r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398

Pore s a t u r a n t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399

S u m m a r y of the tes t resul ts on Ekof isk reservoi r rocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400

Cons t i tu t ive m o d e l i n g of the reservoi r rocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400

P red i c t i on of rese rvo i r c o m p a c t i o n and surface subs idence at the Ekof isk . . . . . . . . . . . . . . . . . . . . . . 404

Empi r i ca l a p p r o a c h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404

N u m e r i c a l s imu la t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406

2D s imu la t i on by Potts et al. (1987) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407

2D s imu la t ion by B a r t o n et al. (1988) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407

2D s imu la t ion by B o a d e et al. (1989) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409

2D s imu la t ion by A b d u l r a h e e m et al. (1994) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

3D n u m e r i c a l s imula t ion by Phil l ips g roup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

I m p a c t of c o m p a c t i o n on reservoi r p e r f o r m a n c e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417

Inc rea sed recovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417

Poros i ty r educ t i on . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418

Cas ing d e f o r m a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419

O v e r b u r d e n c o m p a c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419

R e f e r e n c e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419

Appendix A. S I M U L A T I O N O F C O M P A C T I O N D U E T O F L U I D W I T H D R A W A L

E.C. D o n a l d s o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425

I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425

N u m e r i c a l m o d e l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425

P re s su re c o m p u t a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425

C o m p a c t i o n c o m p u t a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428

C o m p u t a t i o n p r o c e d u r e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429

Discuss ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429

N o m e n c l a t u r e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432

C O M P A C : Reservo i r c o m p a c t i o n due to fluid w i thd rawa l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

R e f e r e n c e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438

Appendix B. S U R V E I L L A N C E T E C H N O L O G Y T O D E T E C T A N D M O N I T O R

C O M P A C T I O N A N D S U B S I D E N C E E F F E C T S

W. Fert l , G.V. Chi l ingar ian and E.C. D o n a l d s o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439

I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439

M o d e l i n g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439

Core tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440

S u b s i d e n c e surve i l lance t echn iques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441

Cas ing d e f o r m a t i o n eva lua t ion t echn iques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441

In-s i tu c o m p a c t i o n m o n i t o r i n g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443

A c k n o w l e d g e m e n t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450

R e f e r e n c e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450

Appendix C. U S E O F T H E G L O B A L P O S I T I O N I N G S Y S T E M (GPS) F O R G R O U N D

S U B S I D E N C E M O N I T O R I N G

B. E n d r e s and G.V. Ch i l ingar i an . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453

I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453

T h e global pos i t ion ing sys tem (GPS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453

U s e of d i f ferent ia l nav iga t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454

E x a m p l e s of subs idence m o n i t o r i n g using G P S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454

CONTENTS xvi i

Future applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457

Appendix D. E A R T H Q U A K E P R E D I C T I O N AS RELATED TO S U BS ID EN CE S. Katz, L. Khilyuk and G.V. Chilingarian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459

Short review and current state of the problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459 Joint study of earthquake activity and environmental impact related to oil and gas product ion . . 460 Physical and geological rationale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460 Nonfunctional relations among quantitative characteristics of upward gas mobility, ground subsidence, and earthquake activity in seismically active regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462 Nonfunctional relations between quantitative characteristics of upward gas mobility and ground subsidence in seismically passive regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463 Formulation of neural network methodology for prediction of upward gas mobility, ground subsidence, and earthquake activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463 Prediction of ground subsidence based on measurement of subsidence and gas leakage parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465 Monitoring of gas leakage and gas concentration in soils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465 Monitoring of seismic activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466 Joint monitoring of subsidence and seismic activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468 Production-induced seismic phenomena in the vicinity of petroleum producing fields . . . . . . . . . . . 468 Example of earthquake prediction based on the use of integral seismicity parameters . . . . . . . . . . 4 7 0 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472

Author index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475 Subject index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485

Subsidence due to Fluid Withdrawal. Developments in Petroleum Science, 41 edited by G.V. Chilingarian, E.C. Donaldson and T.E Yen �9 1995 Elsevier Science B.V. All rights reserved

Chapter 1

INTRODUCTION TO COMPACTION/SUBSIDENCE-- INTRODUCTION TO TECTONICS AND SEDIMENTATION

E R L E C. D O N A L D S O N , G E O R G E V. C H I L I N G A R I A N and T E H FU YEN

I N T R O D U C T I O N TO T E C T O N I C S

The compaction of subsurface geological structures and subsequent subsidence of the surface are an integral part of the entire geologic history of the sediments: the reason for their accumulation at a particular site, the source and types of sediments, the processes of erosion, transportation of the sediments, etc. The geologic record begins at the formation of the earth about 4.5 billion years ago, but the fossil record did not begin until 550-600 million years ago: the beginning of the Paleozoic era (Table 1-I). Although the Precambrian record represents more than 85% of the age-correlations of the rocks, the rocks are beyond the scope of present geophysical dating methods (relative time based on identifiable sequences of events in the geological and fossil records and radiometric time based on the decay of radioactive elements).

The continents on the earth's surface are continually moving and rearranging their positions relative to each other as the angles of the resultant vectors of the forces acting on them change. From about 500 to 415 million years ago, many of today's continents (Africa, Antarctica, Australia, India and South America) were packed together in a single landmass known as Gondwanaland. This grouping of continents was centered at the South Pole. The excess mass at the South Pole was instrumental in unbalancing the earth and causing it tumble over slowly until (after 100 million years) the mass of continents straddled the equator. A rotating body with distributed mass on its surface will stabilize only when the mass is distributed evenly around its center of rotation. As the earth's axis of rotation changed, Gondwanaland also moved north and eventually merged with landmasses in the north forming the global continent called Pangaea, which encompassed all of the great landmasses. Then, around 240 million years ago, great rifts formed in Pangaea due to stresses caused by the equatorial bulge (centrifugal forces) and convective currents within the mantle beneath the landmass. This was the beginning of the Atlantic Ocean (Decker and Decker, 1982; Link, 1982; All6gre, 1988; Gubbins, 1990).

Theories that explain the reasons behind the movements of the continents over the surface of the globe have been developed by geophysicists studying the patterns of seismic waves emanating from earthquakes. Recent developments in tomography yield new and more detailed information of the inner structure of the planet from the surface to the core. Laboratory experiments and mathematical simulations by scientists have elucidated the probable temperatures and pressures existing in the

2 E.C. DONALDSON, G.V. CHILINGARIAN AND T.E YEN

TABLE 1-I

Relative geological time scale (after Dott and Batten, 1976; Link, 1982; and Grosvenor, 1985)

Era Period Epoch Date Biological and (years, 106 ) physical events

Cenozoic Quaternary Holocene 0-2 Glacial ages Pleistocene Homo sapiens

Tertiary Pliocene 6 Colorado River begins Miocene 22 Mountains in Nevada Oligocene 36 Primitive horses Eocene 58 Yellowstone volcanism Paleocene 63 Rocky Mountains begin

Mesozoic Cretaceous 145 Climax of dinosaurs Jurassic 210 Birds Triassic 255 Rifts disintegrate Pangaea;

Atlantic Ocean begins; dinosaurs, small mammals

Paleozoic Permian 280 Mammal-like reptiles Carboniferous- 320 Coal forests, insects, reptiles, Pennsylvanian amphibians; Pangaea forming Carboniferous- 360 Amphibians Mississippian Devonian 415 Fish; Gondwanaland at the

South Pole Silurian 465 Land plants and animals Ordovician 520 Appalachian Mts. begin Cambrian 580 Marine animals abundant

Precambrian 4000

Birth of Planet 4650

Oldest dated rocks, bacteria, blue-green algae

deep subsurface (Table 1-II). These data reveal a pattern of slow moving convective currents within the mantle that are the principal conveyors of the drifting continents.

COMPOSITION OF THE GLOBE

Earthquakes produce three types of waves that are yielding information about the detailed structure of the planet: (1) Primary (P) waves that vibrate as compressions and rarefactions and travel at the highest velocity (1.0 km/s in water and 6.2 km/s in granite, at 25~ (2) secondary or shear (S) waves that vibrate perpendicular to the direction of propagation and travel at about half the velocity of the P-waves; (3) surface waves that travel at even lower velocities along the surface of the globe and are divided into Rayleigh waves that contain compressional motions and Love waves that are made up of shear motions. Table 1-II shows the increase of velocity of the P- and S-waves as a function of depth. The velocity is a function of the physical

INTRODUCTION TO COMPACTION/SUBSIDENCE

TABLE 1-II

Estimated, average physical properties of the earth as a function of deptb (after Dott and Batten, 1976; Decker and Decker, 1982; and Gubbins, 1990)

Depth Density P-velocity S-velocity Pressure Temp. (km) (g/cm 3) (km/s) (km/s) (kbar/km) (~

Crust 0- 50 2.8- 3.3 Lower lithosphere 5- 50 2.8- 3.3 Asthenosphere 100- 150 3.3- 3.4 Asthenosphere 150- 200 3.4- 3.4 Upper mantle 200- 450 3.4- 3.8 Upper mantle 450- 650 3.8- 4.1 Lower mantle 650-1500 4.1- 4.8 Lower mantle 1500-2900 4.8-10.0 Core (liquid) 2900-5000 10.0-12.0 Core (solid) 5000-6370 12.0-13.1

6.2- 7.8 3.4-4.7 0- 12 0- 500 6.4- 8.0 4.0-4.8 1.2- 12 125- 500 8.0- 7.8 4.8-4.3 28- 44 1200-1300 7.8- 8.2 4.5-4.4 44- 61 1300-1500 8.2- 9.6 4.4-5.1 61- 150 1500-2000 9.6- 9.9 5.1-5.4 150- 223 2000-2200 9.9-12.2 5.4-6.7 223- 616 2200-2500

12.2- 8.1 6.7-0.0 616-1404 2500-3500 8.1-10.3 0.0-0.0 1404-3216 4000-4200

10.3-11.3 0.0-3.6 3216-3660 4200-4400

properties of the materials through which it is traveling. The changes of velocity, especially at depths less than 1000 km, indicate boundaries where the physical properties of the mantle change. The velocities of the waves increase rapidly with depth from the surface to the Mohorovicic discontinuity at the base of the crust. The decrease of velocity in the asthenosphere (100-200 km) is due to the presence of partially melted rock acting as an interstitial fluid in the asthenosphere, which is appropriate because the lithosphere is divided into the mobile plates of the plate- tectonic model that are at the top of the asthenosphere (Fig. 1-1). At a depth of 2900 km, the shear wave velocity decreases to zero indicating that the outer core,

Fig. 1-1. Cross-section of the earth in accordance with the theories of plate tectonics. (After Wyllie, 1975, bottom p. 51" courtesy of Scientific American.)

E.C. DONALDSON, G.V. CHILINGARIAN AND T.E YEN

beginning at this boundary, is a liquid because a liquid cannot propagate a shear vibration. In addition, the P-wave velocity decreases sharply from 12.2 to about 8.0 km/s. Several other physical properties also change at this boundary: the density changes abruptly from 4.8 to 10.0 g/cm 3 and the pressure gradient changes from 0.62 to 1.40 Mbar/km as shown in Table 1-II.

The structure of the earth that emerged from the seismic data is one of a series of concentric shells superimposed on a solid sphere of iron at the center. The continental crust, composed primarily of granite or silicon-aluminum compounds (SIAL), rests on top of basaltic material made up principally of silicon-magnesium- iron (SIMA), somewhat greater in density. The ocean crusts are also composed of basaltic material and have been found to be no older than 200 million years, which is relatively young geologically. This young age for the ocean floors is explained by the current theory of plate tectonics: ocean crust is constantly being formed at rifts where upwelling magma creates new crust, whereas the older ocean crusts on either side of the rifts are consumed in subduction zones. The continental crust thus remains at the surface constantly changing by moving around (periods of mountain building) and constant erosion followed by accumulation of sediments in low areas. An understanding of these changes is fundamental to the study of compaction and subsequent subsidence. A brief, introductory discussion of plate tectonics and sedimentation, therefore, is included with references to more detailed treatment of the topics.

The approximate depths of the concentric spheres that make up the globe and their taxonomy are listed in Table 1-III. The ocean crusts are as thin as 5 km in many places and seldom exceed 10 km in thickness. The ocean crust is quite uniform, being composed of basaltic material, principally silica and magnesium (SIMA) with an average density of 3.2 g/cm 3. Deep ocean trenches at continental margins and those associated with island arcs (the Pacific islands along the coast of China, for example), are the boundaries of subduction zones where the ocean crust is subducted into the asthenosphere and melted. Generally, earthquakes only

TABLE 1-III

Various zones and their properties (after Link, 1982; and Gubbins, 1990)

Depth (km) Comment Nomenclature Subzone Zone

5- 50 Moho at base Crust Lithosphere

50- 100 Diffused transition zone at the base Upper mantle

100- 200 Low seismic velocity zone Asthenosphere

200- 450 Weak seismic discontinuity at the base

450- 650 Change of silicate structure, possibly to stiskovite

650-2900 Shear wave velocity = 0 at base Lower mantle

2900-5000 Shear wave velocity = 0 Core (liquid)

5000-6370 Shear wave velocity present again Core (solid)


occur in the upper 100 km of the lithosphere which is brittle enough to support the earthquakes, but earthquakes as deep as 700 km are recorded at the subduction zones because the subducting portion of the ocean crust remains cold and brittle enough to sustain the earthquakes at these zones. Several factors contribute to heating in the subduction zones where the ocean crust is eventually consumed by melting into the upper mantle: (1) friction and shear stress between the subducting plate and the stationary lithosphere; (2) decay of radioactive elements; (3) heat rising from the mantle; and (4) heat released from phase changes of minerals and increase of pressure.

The continental crust ranges in depth to 50 km as delineated by the Mohorovicic discontinuity (Moho), which reflects seismic waves and is a boundary at which the seismic velocity suddenly increases. The Moho is present everywhere on the globe making it a well-defined boundary at the base of the crust. The continental crust is less homogeneous than the ocean crust, but is composed principally of granite (silica and aluminum - - SIAL) yielding an average density of 2.8 g/cm 3. The continental crust, therefore, seems to float on the top of basaltic material in the lithosphere and is not consumed at the subduction zones where, instead, it is uplifted into mountain ranges such as the Andes.

At the base of the lithosphere, which includes the crust, there occurs a thermo/ mechanical boundary (wide diffused layer) that ends at the top of the asthenosphere where the seismic velocities (especially the S-wave velocity) decrease slightly (Table 1-II). The thickness of the lithosphere is determined by the depth of this boundary which is no longer sufficiently brittle to sustain earthquakes. This boundary varies considerably in depth; it is shallow in the vicinity of the ocean riffs and becomes much deeper under the continents.

The next shell that is encountered is the asthenosphere where the seismic body waves exhibit a lower velocity. This indicates that this layer is probably a weak, partially molten zone. Earthquakes cannot occur in this zone because the temperature and pressure are such that interstitial molten minerals are present, which allows the material to deform and thus accommodate motion of various types. At about 200 km, the seismic velocities increase once more marking the base of the asthenosphere. At 450 km, there is a weak seismic discontinuity that may indicate a phase change or an atomic number change of the minerals. At 650 km, there is a definite increase of seismic velocity that is the demarcation of the base of the upper mantle. Seismic velocity increases steadily with depth to the base of the lower mantel (at about 2900 km), where the shear wave velocity immediately decreases to zero at the boundary between the lower mantle and the liquid core. This is a boundary of atomic number change from silicates to ferrous metals as well as a phase change. At about 5000 km, the shear wave is evident once more as the boundary of the solid core is reached. Experiments indicate that the pressure gradient is fairly constant, but the temperature gradient apparently increases with depth and exhibits static increases at the boundaries delineated by the seismic waves.


M O V E M E N T OF SECTIONS (PLATES) OF THE LITHOSPHERE

The theories of plate tectonics propose that sections of the lithosphere, or plates, are in constant rigid motion around the globe, deforming almost exclusively at their edges as they contact each other by direct collision: (1) transverse and rotating motions produce transverse faulting; (2) hot spots, where molten magma forms an isolated path to the surface, can be traced as the plate moves over the hot spot; (3) spreading occurs at rifts and mid-ocean ridges; (4) subduction of ocean floors occurs as the less dense continental masses encounter the more dense ocean plates; and (5) accretion terrains (seamounts and other parts of crust-material) form where plates of equal density collide. These movements create trenches and basins for the accumulation of sediments arriving from erosion of higher areas.

As mentioned above, the lithosphere is sufficiently brittle to sustain earthquakes, but it rests on a zone which apparently contains interstitial molten minerals that impart mobility to the asthenosphere. Consequently, distinct plates of the fractured, brittle lithosphere are carried along at the surface of the mobile asthenosphere. One of the prevalent theories is that convective currents within the asthenosphere and the mantle cause the motions of the plates, which sometimes collide and at other times move apart from each other (Fig. 1-2). The slow movements (about 2.5 cm per year) have been detected with seismic tomograms, which show regions of ascending and descending currents in the asthenosphere and the upper mantle. The

Fig. 1-2. Convection currents in the upper and lower mantle that are the principal source of energy for movement of continental masses. (After O'Nions et al., 1980, p. 132; courtesy of Scientific American.)

I N T R O D U C T I O N TO COMPACTION/SUBSIDENCE

seismic waves passing through the currents are accelerated in the cold, descending regions and decelerated in the hot, ascending zones. Hot magma rising into the midocean ridges and continental rifts create the new basaltic crust where the plates are spreading apart. At subduction zones, the cooler descending currents pull the denser oceanic surface downward where the ocean crust collides with the continental crust. The ocean crust descends as a tongue of material until it finally melts, becoming indistinguishable within the asthenosphere. Gravity anomalies (and slight changes in the velocities of orbiting satellites) are observed at areas of rising and descending currents in the mantle. Gravitational highs are observed over the Central Pacific, Central Atlantic and East Africa where plate spreading is taking place, whereas gravity lows are observed over Antarctica and the Indian Ocean. Trenches in front of subduction zones exhibit gravity anomalies up to -275 mGal, 1 whereas positive gravity anomalies are observed over the ascending zones up to + 75 mGal. Long-lasting transgressions and regressions of the ocean also may have resulted from movement of the ocean floor over hot, rising regions of the magma, and conversely over cool descending areas. Some radioactivity may be responsible for the heat creating the currents within the mantle, but the principal source is undoubtedly an uneven distribution of heat at the surface of the core, which is estimated to range in temperature from 4000 to perhaps greater than 5000~

C O N T I N E N T A L M A R G I N S

The general picture that emerges from the theories of plate tectonics is that the surface of the earth, composed of granitic continents, resting on a layer of more dense basaltic material is constantly being rearranged at a slow rate (an average velocity of continental drift is 2.5 cm per year). The force propelling the continents is principally due to slow-moving currents within the magma. The currents rise at ocean riffs, which are elongated volcanic uplifts rising up to 3000 m above the abyssal plains of the ocean floor and forming a network across the great oceans. The movements of continents across the surface of the globe during eons of geologic time have resulted in collisions, faulting and accretions that have created enormous changes of the surface features and the sedimentary stratigraphy. Spreading of the ocean floor at the riffs widens the seafloor 20-25 cm per year at some locations. If the continents moved at this rate, even greater changes would have occurred, but the ocean plates are pulled back into the mantle at the ocean trenches and eventually melted as the plate attains great depths (> 200 km). The descending plate generates heat that results in the formation of volcanic island arcs offshore from the continental margin. The continental margin is compressed as the ocean plate moves against it and is subducted under it, forming long mountain ranges along the shoreline. A sedimentary basin forms between the shoreline and the island arc; however, the islands and other parts of crust (known as terrains) that accumulate at the edges of subduction zones, eventually collide with the continent, as they are

1 1 G a l = U n i t of g rav i t a t iona l acce le ra t ion : 1 Ga l = 1000 mi l l iGals = 1 cm/sec 2 = 10 -2 m/ sec 2.


carried along on the ocean plate. The collisions result in accretion of the islands and terrains to the continental mass producing growth of the continents (e.g., Alaska is made up of a patchwork of terrains that collided over the past 200 million years).

The collisions of continental masses result in mountain building at the colliding margins. The densities are equal and, therefore, subduction does not occur. One continent, however, may wedge under the other, which has occurred in the case of the collision of India with Eurasia where the older, slightly heavier Indian continent wedged under the Eurasian continent creating the Himalaya mountains. Other examples are the collision of Europe and Africa that resulted in the formation of the Alps.

The westward moving Philippine ocean plate is colliding with the relatively stationary Asian continental plate. In this case, however, the denser ocean plate is slipping under the continental mass carrying the islands into the Asian continental mass.

Plates also move laterally against each other creating transform faults which is occurring in the case of the San Andreas fault in California. The Pacific plate is moving in a northwest direction with respect to the American continental plate. Stress developed along the edges of the fault is released either gradually, generating thousands of light earthquakes that can only be detected with sensitive instruments, or suddenly, generating large earthquakes that can do considerable damage to surface structures.

The convolutions of crustal plates at continental margins provide uplifts that supply the sediments to basins and other depressions. Changes in the surface environment and the motions of the plates provide stratigraphic layers of different types of sediments during the long period of accumulation.

Divergent continental margins are characterized by long extensions into the abyssal plain of the ocean. Deep deposits of salt, which result from the precipitation from the nascent ocean water as the rift between two continental masses develops, occur at the edge of divergent margins. Layers of red beds (clays, etc.) are superimposed over the salt and extend further away from the continental margin. Fine sediments (clays, etc.) are carried for great distances away from the shore before finally settling to the ocean floor. See Dott and Batten, 1976; Yen and Walsh, 1980; Decker and Decker, 1982; Link, 1982; All6gre, 1988; and Gubbins, 1990.

I N T R O D U C T I O N T O S E D I M E N T A T I O N

At numerous places on the earth, rocks are being formed by a number of processes, whereas at others, rocks are breaking apart forming boulders and particles of various sizes. The processes at work are physical, chemical and biochemical. The result of rock disaggregation is the production of sedimentary particles which may be grains, minerals, or precipitates from aqueous solutions. These products of weathering are transported, sometimes for great distances, by rivers, winds, tides and currents, and change in surface attitude by tectonic events. Eventually they accumulate in depressions, bodies of water, or cover large flat landscapes. Some


of the accumulations are cemented into new rocks or buried by layers of new accumulations.

As layers of sediments are deposited in an area, they undergo compaction and other diagenetic changes. Compaction is the process of volume reduction which is more pronounced in unconsolidated sediments and occurs principally during the diagenetic stage. Diagenesis includes all of the physicochemical, biochemical, and physical processes that modify the sediments during deposition and through lithification. Epigenetic, or catagenetic, changes begin after diagenesis and continue until metamorphism. The time intervals for diagenetic and epigenetic changes vary from one extreme to another.

The factors that contribute to the formation of clastic sedimentary rocks and have a great influence on compaction of the sediments include:

(a) source and fragmentation of the rocks, (b) mode and distance of transport, (c) chemistry and energy of the depositional environment, and (d) chemical alterations and cementation. The formation of clastic rocks is not a relentless process that proceeds through

specific stages; instead, it consists of stages that are often interrelated so closely as to be inseparable, and in some instances some of these stages do not occur at all. Compaction also is a very important process in rocks that are easily soluble in groundwater, such as carbonates and evaporites.

SOURCE AND FRAGMENTATION OF ROCKS

The sedimentary rocks constitute a thin layer on the surface of the granitic crust of the earth. Although the crust contains a large variety of minerals, the sedimentary rocks are surprisingly composed of only four principal types, which are a reflection of their abundance and ease of physicochemical degradation: quartz, carbonates, clay minerals, and feldspars. These, in turn, may be divided with respect to their source as terrigenous rocks (derived from preexisting rocks) and chemical rocks (that are of chemical/biochemical origin).

Quartz is ubiquitous in terrigenous sediments because it is physically and chemically very durable. It occurs in several colors and crystalline arrangements from single to multiple crystals due to differences in molecular structure and minor mineral inclusions. Clay minerals occur as very fine particles (<1/256 mm) having specific structures that control their properties. The most common clay minerals in terrigenous sediments are illite, smectites (montmorillonite, bentonite, etc.), kaolinite, and chlorite. Illite, which is mainly a product of feldspar degradation, is by far the most abundant followed by the smectites which originate principally from volcanic materials. Montmorillonites can be diagenetically altered to illites. Feldspars, because they are easily degraded, are common only in sediments that have undergone rapid erosion and burial; for example, in canyons where sediments eroding rapidly from steep granite walls are collected and rapidly buried as dendritic granite washes.


Sedimentary ores and other minerals accumulate in certain locations due to prevailing physicochemical environmental conditions, but are minor in abundance compared to the vast collections of other terrigenous rocks.

Rocks originating from chemical and biochemical processes are the second large group, with carbonates being the principal type. Deposition of inorganic calcium carbonate from aqueous solutions is controlled by the solution pH and the amount of carbonic acid (or dissolved carbon dioxide) in the water according to the following reactions:

H 2 0 -+- CO2 ,~ ~ H 2 C O 3 (1-1)

H 2 C O 3 .~ " H + + HCO~- (carbonic acid to bicarbonate ion)

HCO~- ~ r H + + CO~- (bicarbonate to carbonate ion)

H 2 C O 3 + CaCO3 ~ - Ca 2+ + 2HCO~-

(1-2)

(1-3)

(1-4)

The release of hydrogen ions into solution by the bicarbonate ion (Eq. 1-3) decreases the pH of the solution, which results in the solution of calcium carbonate. The presence of large quantities of bicarbonate and carbonate ions in sea water produces the high alkalinity of ocean water; therefore, carbon dioxide in sea water is present as undissociated carbonic acid ( H 2 C O 3 ) which drives the reaction to the formation of calcium ions, rather than precipitation of calcium carbonate as calcite or aragonite crystals. 2 Furthermore, the presence of magnesium ions in sea water inhibits the precipitation of calcium carbonate (Berner, 1975). Consequently, the direct precipitation of inorganic crystals of calcium carbonate does not occur in sea water. Round oolites (<2 mm) and pisolites (>2 mm) form under special conditions, which consist of a high-energy environment, with calcium carbonate supersaturated sea water. Calcium carbonate (principally as aragonite) builds up over a nucleus of an organic particle or small shells in concentric layers forming spheres. The oolites are deposited evenly as in quiet zones and are eventually buried and thus preserved.

Micrite (e.g., lime mud composed of fine aragonite needles) is deposited on shallow shelves and platforms in tropical zones, e.g., by calcareous red and green algae. Algae extract calcium from sea water and use it to impart stiffness similar to a calcareous skeletal system. When the plants die, decay of the noncalcareous tissues release the needles of aragonite resulting in deposition of a lime mud in low-energy areas such as the down-wind side of islands (Stockman et al., 1967; Neumann and Land, 1975).

Biogenic limestones form from skeletal materials of small organisms such as foraminifera, 3 gastropods, and brachiopods, and those resulting from the feeding actions of parrotfish that crush the frameworks of coral reefs to extract nutrients.

2 Aragonite, which is composed of calcium carbonate, has a different crystalline structure than calcite.

3 Large order of marine rhizopods that have calcareous shells: they produce the major part of chalk and nummulitic limestone. The shells have tiny holes for protrusion of pseudopodia.

INTRODUCTION TO COMPACTION/SUBSIDENCE 11

They contribute calcium carbonate in the form of aragonite, calcite, and magnesium calcite (CaCO3 with <10% MgCO3), which are deposited in various locations during periods of favorable environmental conditions (Davis, 1983). Present formation of limestone beds at latitudes higher than 40 ~ , are from invertebrates, mollusks and foraminefera.

Inasmuch as carbonate deposits are biogenic, most are restricted to tropical-type environmental conditions (present depositions of carbonates are taking place principally in the tropical belt around the globe). The carbonate deposits originate at the place where the accumulation of sediments takes place (marine basin or platform). Terrigenous sediments, however, may originate from the erosion of preexisting rocks that are located great distances from the zones of deposition.

Coral reefs are complex structures that support various types of energy/depth dependent carbonate growths. The principal builders of reefs in deep water (>700 m) that do not require sunlight for growth are ahermatypic hexacorals, sponges and crinoids. Reefs in shallow environments (shelves, platforms, shore fringes and barrier reefs) are more complex structures. Corals in the front and crest of the reef that can tolerate the high wave energy environment consist of hemispherical, encrusting, and tubular forms; those in the low-energy back-reef environment have more delicate plate-like and branching forms. The back-reef zone is relatively quiet and contains coral-algal sands and shell fragment sands. The living corals rest on a framework, or central depositional core, that grades seaward as a slope into deeper water. A linear, barrier-type reef at the fringe of a shoreline may develop fingers that enclose a lagoon, which can result in an area of prolific swamp-type plant growth and oyster beds (James, 1983; Boggs, 1987).

CLASSIFICATION OF SANDS

The factors that contribute to the formation of clastic sedimentary particles and rocks include:

(1) fragmentation and disaggregations of the source rock, (2) mode and distance of transport, (3) dispersion and sorting during transport and deposition, (4) chemistry and energy of the depositional environment, and (5) chemical and physical alteration after deposition, such as cementation and

compaction. The term sand is commonly used to denote a granular material within a broad

range of texture and size; it is used by earth scientists as a size classification. The size classifications for aggregates, shown in Table I-IV, and the mesh sizes of screens used for separations are based on the Wentworth (1933) scale which has been adopted as the standard for size classifications. Using this scale, gravel (subdivided into granules, pebbles, cobbles and boulders) are particles which are greater than 2 mm in diameter. Sand ranges from 2 to 0.062 mm and mud, which is subdivided into silt and clay, is considered to be composed of particles smaller than 0.062 mm. The scale is a geometric progression with each size equal to one half of the succeeding size.


TABLE 1-IV

Comparison between various particle size classifications and sieve sizes (after Chilingarian et al., 1975, fig. 1-1, p. 3)

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I/25E ~ l ~ CLA

ON TO .001 11204|

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Sieve, or screen, sizes refer to the distribution of particles of sizes that will either: (a) pass through the screen, or (b) are retained by the screen. This simple distinction is frequently ignored, but in some scientific discussions of size distributions it is an important consideration. The mass of the fractions retained by a series of screen sizes also may be used as a statistical descriptor of grain sizes.

The phi-scale was introduced by Krumbein in 1934 as a simpler method for graphical presentation (because it yields even intervals) and discussion of particle- size distributions. The phi-scale contains positive and negative numbers with zero set as the largest sand size; this was done because sand, and small grains, are the most abundant components of sedimentary rocks and setting the zero at the largest sand size avoided considerable work with negative numbers (Krumbein and Pettijohn,


TABLE 1-V

Range of applicability of different techniques of size analysis (after Pettijohn et al., 1972, fig. 3-1, p. 70; in Chilingarian and Wolf, 1975, fig. 1-2, p. 6)

E L E C T R O N M I C R O S C O P E r

PIPETTE

B I N O C U L A R - " M I C R O S C O P E .r

S E D I M E N T A T I O N

T U B E

S I E V I N G

DIRECT M E A S U R E M E N T

G R A V E L ]SAND i i CLAY 256 g2 ,g ~ , ,/4 ,/,6 ,/64 ,z2~6 rag, !

I I I I I I I I J --8 - -6 - -4 --2 0 + 2 + 4 + 6 + 8 + I 0 ~ S t o l e

1938). The phi-size is the negative logarithm [base 2] of the grain-size diameter (d):

d = 2 -* (1-5)

(I) -- - log2(d ) = -3.322 lOgl0(d) (1-6)

Wentworth (1933) and Lane (1938) examined the limits of grades in terms of the physical properties involved in grain transportation. They showed that given class limits agreed well with certain distinctions between suspension and traction loads. A natural separation in nature is not really distinct, however, until the colloidal sizes are reached at about 0.002 mm, which is the clay-silt boundary used by the United States Department of Agriculture.

Several methods are used for measurement of the sizes of rocks and fine particles. Calipers are used for measurement of particles larger in size than sands (pebbles, cobbles and boulders). Unconsolidated granules or sands are commonly measured by sieve analyses and microscopic observation; direct measurement also is possible for the larger granules (Table l-V). Sieve analysis also is used for grains obtained from the physical or chemical disaggregation of consolidated sediments. A crushing machine is used for physical disaggregation rather than a grinder which will further breakdown the particles. Sandstones also may be disaggregated by saturating them with some chemical compounds such as hydrazine; the true particle-size distribution can be obtained when chemical disaggregation is used (Heath et al., 1970).

Particles ranging in phi-size from 0 to 8 also are measured by sedimentation. A calibration chart of the particle size versus settling time in a column of water at a specific temperature is prepared using either sieve analyses or a microscope. Particle shape affects the settling velocity; therefore, this procedure yields average sizes that


may be acceptable for rapid evaluations of large quantities or numerous batches of grains.

The standard method for measuring the particle size of fine silt and clay is pipette analysis. The particles are stirred vigorously into a suspension in a large settling tube and aliquots of the suspension are withdrawn at specific times and depths. The aliquots are evaporated to dryness and weighed; a table of size ranges related to the specific withdrawal depths and times is prepared for the material to be analyzed, or charts presented in books may be used (Carver, 1971). The average diameter of the particles can be calculated from:

D = (u /C) ~ (1-7)

where u = settling velocity and C = experimentally determined constant which is a function of the viscosity of the fluid and density of the particles.

Automatically recording settling tubes also are available: (1) measurement of the change in pressure of the fluid at a given depth as settling of the particles takes place; the pressure changes are automatically related to particle diameter; (2) the photohydrometer measures the intensity of a light shining through the fluid; the intensity of light passing through the settling tube increases as settling takes place because less particles are available for reflection of the light; and (3) the Coulter counter may be used for measurement of very fine particles (<1 /zm) as well as larger particles up to 1 mm in size.

In cases where analyses of consolidated samples are required without disturbance of the grains, thin slices of the consolidated sands are glued between microscopic slides and the grain-size distribution is measured using a microscope. Finally, an electron microscope may be used to evaluate fine grains of silt and clay, and also obtain an analyses of the most probable type of clay mineral under observation (Crocker et al., 1983).

Statistical analyses of particles

The large amount of data generated from the analyses of grain sizes must be processed into logical sequences for evaluation of the data. This is done by using statistical methods of analyses. The size frequency distribution is presented in graphical formats and several numerical calculations provide information about the size distributions that are important parameters for specific and general evaluation of the sediment.

A grain-size analysis is presented in Table 1-VI for illustration of the various graphical and statistical analyses that are conducted for evaluation of the sediment. The data show the phi-size and weight of the grains retained on specific screens that were used to obtain the separations. The third column is the percentage of the total weight represented by each fraction. Column 4 is the cumulative weight percentage obtained by adding the weight of each succeeding size class to the total of the preceding class. Column 5 is a list of percentiles and their corresponding phi- sizes that will be used for calculation of the various graphical statistical parameters that are listed below the table. Column 6 was obtained by linear extrapolation


TABLE 1-VI

Grain-size analysis

15

(1) (2) (3) (4) (5) (6) Phi-size Weight (g) Weight (%) Cumulative (%) Percentile Phi-size

-0 .50 1.09 1.40 1.40 5 -0 .18 0.00 4.33 5.56 6.69 16 0.43 0.50 8.18 10.51 17.47 25 0.74 1.00 12.33 15.84 33.32 50 1.46 1.50 14.04 18.04 51.36 75 2.06 2.00 16.56 21.28 72.63 84 2.41 2.50 10.82 13.90 86.53 95 2.97 3.00 8.02 9.02 95.55 3.50 3.46 4.46 100.00

78.83

Mean G - - 1.43; mode G = 2.00; median G = 1.50; standard deviation G = 0.97; skewness G - - -0.04; kurtosis G " - 1.70.

between Columns 1 and 4 to obtain the best estimates of the phi-sizes corresponding to the percentiles that are required for numerical interpretations of the graphical data.

Four different curves can immediately be prepared from the data listed in Table 1-VI. The grain-size histogram (Fig. 1-3a) is prepared by plotting the weight percent fraction (Column 3) as the ordinate with respect to the phi-size (Column 1). The histogram provides a rapid qualitative evaluation of the grain-size distribution. A continuous frequency curve (Fig. 1-3b) may be obtained by connecting the mid- points of each class on the histogram illustrated in Fig. 1-3b. These curves provide the approximate position of the mode which is the grain size that occurs most frequently (the highest point on the frequency curve). More accurate analysis is obtained from the graphical presentation using the percentile values. The cumulative frequency curve (Fig. 1-3c) is obtained by plotting the data in Columns 1 and 4 with the phi-size as the abscissa. The 50 percentile phi-size is the median of the data (the midpoint of the grain-size distribution). On the other hand the graphical arithmetic mean size is best obtained from numerical analysis. The cumulative frequency curve is an S-shaped curve whose shape represents some qualitative aspects of sorting: a steep slope of the central part of the curve indicates good sorting of the grains, whereas a gentle slope represents poor sorting. If the cumulative curve is plotted on probability paper, however, the data will approach a straight line and the percentile data (Columns 5 and 6 of Table 1-VI) may be obtained directly from a frequency probability curve.

The example calculations illustrate the methods used to obtain the parameters from graphical and numerical analysis and comparisons between the data; some differences, as expected, are apparent. The mean size is the arithmetic average of the particle sizes in the sample. A true mean of the population is not possible because the entire sediment cannot be analyzed; however, an approximation to the


Fig. 1-3. (a) Grain-size histogram prepared from the data in Table 1-IV. (b) Frequency curve from the data in Table 1-IV. (c) Particle size cumulative frequency curve from the data in Table 1-IV.

mean may be obtained from selected samples by averaging the percentile values of the samples and then calculating a numerical mean using the equations presented in Tables 1-VII and I-VIII. The standard deviation is an indication of the sorting of the grain population; it is a measure of the range, or magnitude, of the scatter of the sizes around the mean. One standard deviation encompasses the central 68% of the area under the frequency curve. Stated in another way, 68% of the grain sizes lie within plus or minus one standard deviation of the mean value. Folk (1968) assigned various degrees of sorting to the standard deviation as follows:


Degree of sorting Standard deviation (phi-units)

Very well sorted <0.35 Well sorted 0.35-0.50 Moderately well sorted 0.50-0.71 Moderately sorted 0.71-1.00 Poorly sorted 1.00-2.00 Very poorly sorted 2.00-4.00 Extremely poorly sorted >4.00

M o s t o f t h e s e d i m e n t a r y g r a i n - s i z e d i s t r i b u t i o n s d o n o t f o l l o w a n e x a c t n o r m a l

d i s t r i b u t i o n (a s y m m e t r i c a l b e l l - s h a p e d c u r v e w i t h t h e m o d e , m e d i a n a n d m e a n

v a l u e s c o i n c i d i n g ) . I n s t e a d , t h e d i s t r i b u t i o n s a r e a s y m m e t r i c , o r s k e w e d e i t h e r p o s i -

TABLE 1-VII

Formulas for the calculation of grain-size parameters

Mean G

Standard deviation G

Skewness G

Kurtosis G

((I)16 -1- (I)50-Jr- ~ 8 4 ) / 3

(~S4 -- ~ 1 6 ) / 4 + (~95 -- ~ 5 ) / 6 . 6

(r + ~84 - 2~50)/2(~84 - ~16) + (r + ~95 -- 2~50)/2(~95 - ~5)

(~95 - ~5)/2.44(~75 - ~25)

Mean N ~ f X m/n Standard deviation N v/[E.f(m - x)2/100]

Skewness N [ E f ( m -- X ) 3 / ( 1 0 0 o ' 3 ) ]

Kurtosis N [E.f(m -- X)4 / (1000"4) ]

f = weight percent in each grain-size class; m = midpoint of each grain-size grade expressed as the �9 -values; n = total number of samples (n = 100 when f is expressed in percent); x = numerical mean value; and ~r = numerical standard deviation. (See Table 1-VIII.)

TABLE 1-VIII

Values for calculation of the parameters listed in Table 1-VII

Class m .f f x m m - x (m -- X) 2 . f ( m - - X) 2 f ( m - - x) 3 f ( m - - x) 3 (m - x) 4

>0.5 -0.75 1.40 -1.05 -2.17 4.73 6.62 -10.27 -14.39 22.33 -0 .5-0 .0 -0.25 5.56 -1.39 -1.67 2.80 15.59 -4.69 -26.09 7.85

0.0-0.5 0.25 10.51 2.63 -1.17 1.38 14.48 -1.62 -17.00 1.90 0.5-1.0 0.75 15.84 11.88 -0.67 0.45 7.19 -0.31 -4.85 0.21 1.0-1.5 1.25 18.04 22.55 -0.17 0.03 0.55 -0.01 -0.09 0.00 1.5-2.0 1.75 21.28 37.23 0.33 0.11 2.26 0.03 0.74 0.01 2.0-2.5 2.25 13.90 31.28 0.83 0.68 9.49 0.56 7.84 0.47 2.5-3.0 2.75 9.02 24.80 1.33 1.76 15.86 2.33 21.04 3.09

<3.0 3.25 4.45 14.45 1.83 3.33 14.83 6.09 27.07 11.12

100.00 142.38 86.87 -5.73

Mean N(x) = 1.42; standard deviation = 0.93; skewness = -0.07; kurtosis = 2.42.


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=.1

06 I.O .I .01 .001 .000

PARTICLE SIZE, IN MM Fig. 1-4. Cumulative curves (percent finer by weight) illustrating three common grain-size distributions: I = uniformly-sorted silty sand; 2 = coarse- to medium-grained silt with one strongly predominant grain size; 3 = bimodal or skip-graded silty sand. (From Chilingarian and Wolf, 1975, p. 8, fig. 1-5.)

tively (a tail indicating a large quantity of fine particles) with the median and mean displaced toward the fine particles with respect to the mode; or negatively skewed (an excess quantity of coarse particles), the median and mean displaced toward the more coarse particles with respect to the mode. Figure 1-3b is a negatively skewed distribution (skewness c = -0.04; mode a = 2.0; median G = 1.5; mean G = 1.43; and standard deviation = 0.98), which indicates a distribution with an excess of large particles. In addition, it is a moderately sorted sample with an average grain size of 1.43 �9 (0.37 mm). The mode shows the predominance of one grain size over the others and in the example only one mode occurs making this a unimodal distribution. Bimodal distributions, however, also occur, which indicates a mixture of two size distributions. For example, sand with few fine grains mixed with silt or clay would be represented by a distribution for the sand grains and another for the silt or clay.

Grain-size distributions are descriptive properties of sedimentary rocks and, to a large extent, they are functions of the mechanisms and environmental conditions of sedimentation. Consequently, there are many variations in the size distributions of the rocks. For example, Fig. 1-4 compares a uniformly sorted silty sand (Curve 1), a coarse- to medium-grained silt with one strongly predominant grain size (Curve 2), and a bimodal silty sand (Curve 3).

The classification of mixtures of particles by named terms, such as sandy-silt, muddy-gravel, etc. is entirely empirical and must be accompanied by a guide for general interpretation. Many classification schemes have been proposed in the literature and are used for descriptive purposes in many industries where general classifications are useful working terms. Most of the classifications use some type of component chart such as those shown in Fig. 1-5. Without such charts, or diagrams, the names assigned to different mixtures by various authors are difficult to use.


Fig. 1-5. (a) Textural classification of gravel-bearing sediments and rocks. (After Folk et al., 1970, in: Chilingarian and Wolf, 1975, p. 9, fig. 1-6.) (b) Classification chart for clay-silt-sand mixtures. (After U.S. Department of Agriculture, in: Chilingarian and Wolf, 1975, p. 10, fig. 1-8.)

Particle shape, roundness and sphericity

Particle shape and roundness are two very significant factors in the mechanical compaction of sands. These two factors affect both bridging (the ability of grains to resist deformation by sliding and rearrangement) and porosity. Particles have a certain geometric form or shape (flat, disk-shaped, tabular, etc.) with varying degrees of roundness. Roundness is an independent variable, not basically related


Fig. 1-6. (a) Roundness images and classes. Columns show grains of similar roundness but different sphericity. (After Powers, 1953, as redrawn by Pettijohn et al., 1972, in: Chilingarian and Wolf, 1975, p. 15, fig. 1-1.1.) (b) Images for estimating visual roundness. (After Krumbein, 1941, in: Chilingarian and Wolf, 1975, p. 15, fig. 1-12.)

to form or shape. For example, a particle having a particular form or shape can be rounded to varying degrees.

Roundness is a measure of the sharpness of the particle edges, regardless of shape. One accepted method for determining roundness is to view the particles two-dimensionally, and determine the ratio of the average radius of curvature of the particle's corners to the radius of the largest circle that can be inscribed in that particle. The general method for estimating roundness is microscopic measurement of a number of grains and visual comparison to a standard chart (Fig. 1-6) such as those introduced by Griffiths (1967).

The degree of roundness commonly varies with size. Larger-diameter sand or gravel particles are usually more rounded than the smaller ones. Maturity and


0.97 0 0 0 0 o 0.95 O O O O 0

0.93 O 0 0 O O o.9~ 0 0 0 0 0

0.89 0 0 0 0 0 .~ 0 . 8 7 0 0 0 O O "E.

" 0 0 0 - ~ 0.85 0(~ ( / )

0.83 O 0 C)O 0

o.8, 9 0 0 0 0

o.~, 9 0 0 6 6

uO0oo o.,, o r o O SqO

0.51 O(l O

o.~ DOOO0

Fig. 1-7. Images for estimating visual sphericity. (After Rittenhouse, 1943, in: Chilingarian and Wolf, 1975, p. 16, fig. 1-13.)

degree of weathering affect this relationship. Freshly broken fragments, which tend to be angular near the source, assume a greater degree of roundness as a result of weathering and abrasion during transportation.

Sphericity is sometimes confused with roundness. Although they are related to a certain degree, roundness is primarily a measurement of the angularity of a particle's corners, whereas sphericity is a measure of the degree the shape of the particle approaches that of a sphere. Images for estimating visual sphericity visually are given in Fig. 1-7. True sphericity was defined by Wadell (1934) as the surface area of a sphere of the same volume as the particle divided by the actual surface area of the solid. A capsule-shaped object could have a roundness factor of unity, whereas if its surface area were compared to that of a sphere of the same volume, using Wadell's definition, the ratio would be far less than unity. A more practical formula for sphericity, also introduced by Wadell (1934), is to divide the nominal diameter of the particle (the diameter of a sphere of the same volume as the particle) by the diameter of the circumscribing sphere. Krumbein (1941) introduced a definition of sphericity based on volumes: he defined sphericity as the cube root of the volume of the particle divided by the volume of the circumscribing sphere.

Factors that control the shape and roundness of particles include: (a) the original shape of the fragment, (b) durability of the material (hard grains such as quartz and zircon are rounded

less during transport than soft grains composed of feldspars and pyroxenes), (c) structure of the fragment (cleavage or bedding), (d) nature of the geologic agent (wind is more effective in rounding grains than

water),

22 E.C. DONALDSON, G,V. CHILINGARIAN AND T.E YEN

(e) nature of the action to which the fragment is subjected and rigor of the action, and

(f) time or distance through which the action is extended.

Composition and classification of sands and sandstones

The mineralogic and chemical composition of terrigenous sediments vary from one extreme to another depending on numerous factors, which include source rock, climate, transportation mechanism, geologic time, depositional environment, diagenesis and epigenesis. The earth's crust is composed of rocks that contain a wide variety of minerals, but only a relatively small amount of minerals occur in abundance. These are the feldspars, pyroxenes and hornblendes (magnesium silicates), and quartz. These undergo changes in composition and are blended to form the sands and sandstones of sedimentary rocks, which constitute a thin layer on the surface of the igneous and metamorphic rocks that make up the crust. The sands and sandstones contain four principal minerals: quartz, clay minerals, carbonates and feldspars. These are supplied by: (1) plutonic rocks, which supply mostly quartz and feldspars (the feldspars generate the clay minerals); (2) volcanic rocks, which supply mostly rock fragments and glass; (3) terrigenous sediments, which supply quartz and rock fragments; and (4) carbonate rocks (originating from physicochemical or biochemical precipitation from surface waters), which supply carbonate debris (Folk et al., 1970; Chilingarian and Wolf, 1975).

The mineral and chemical compositions of terrigenous sediments are closely related to their grain-size compositions. Grains of quartz are very abundant in sands and sandstones, whereas silt and clay minerals are more abundant in rocks that progressed from shales and mudstones. This is apparent from the analyses of sand, silt and clay conducted by Grout (1925).

As indicated in Table I-IX, quartz makes up a large portion of many sands, especially the older, mature rocks that may have been reworked several times. Quartz is a hard, durable mineral that withstands weathering far better than most of the minerals with which it may have been associated in the original igneous

TABLE 1-IX

Apparent relationship between the composition of terrigenous sediments and their grain-size distributions (after Grout, 1925)

Constituent Sand Silt Clay

SiO2 71.2 61.3 48.1 A1203 10.2 13.3 18.9 CaO 3.7 5.1 5.0 FeOx 3.7 3.9 6.9 K20 2.2 2.3 2.6 MgO 1.7 3.3 3.6 Na20 0.9 1.3 ~ 1.2 Ignition loss 5.1 7.1 11.0


TABLE 1-X

Comparative elemental analysis of various sandstones (after Crocker et al., 1983)

23

Bandera Berea Coffey- Cottage Noxie Sweet- Torpedo ville Grove water

SiO2 71.4 84.6 81.5 84.6 87.6 88.7 90.5 A1203 8.7 4.5 7.7 4.7 4.9 4.2 5.1 Fe203 3.1 1.4 3.5 1.2 1.6 0.4 1.9 MgO 1.7 0.5 0.7 0.08 0.2 0.2 0.2 CaO 3.1 0.8 0.5 0.08 0.2 0.05 0.2 TiO2 0.4 0.2 1.1 0.1 0.6 0.1 0.5 SrO 0.1 0.3 0.0 0.01 0.02 0.02 0.8 K20 1.1 2.1 1.7 0.4 0.8 0.8 0.8 Na20 1.7 2.2 3.1 2.9 1.8 1.9 0.2 Mn203 0.0 0.06 0.0 0.07 0.07 0.02 0.2 Kaolinite 6.2 7.0 4.0 6.0 5.0 4.0 6.0 Chlorite 0.0 0.0 4.0 1.0 1.0 2.0 0.01 Illite/mica 0.0 4.0 6.0 6.0 7.0 8.0 7.0 Ignition loss 6.2 2.6 2.6 1.7 1.3 1.2 1.6

Permeability (mD) 12.0 302.00 62.0 284.00 421.00 0.2 94.0 Porosity (%) 17.4 19.2 22.8 26.1 27.0 5.2 24.5 Specific surface

area (m 2/g) 5.50 0.93 2.85 2.30 1.43 1.78 2.97 Cation exchange capa-

city (meq/100 g) 11.99 5.28 23.92 17.96 10.01 ND 29.27

source rock. Quartz grains differ in color due to inclusions of metals in their molecular structure and some are single crystals whereas others are polycrystalline. The absence of heavy minerals in the composition of sands may be due to the severity of weathering and the length of exposure to an oxidizing or leaching environment regardless of age and/or intrastratal solution. Crocker et al. (1983) analyzed several outcrop sandstone from Northeastern Oklahoma and one tight gas sand from Wyoming (Sweetwater Sandstone; 3790 m depth) by various methods. Their emission spectrographic analyses of the sandstones are presented in Table 1-X together with permeability, surface area and cation exchange, which were used to evaluate the differences observed in the fluid flow and other characteristics of the rocks.

According to analyses by Crocker et al. (1983), the Bandera Sandstone contains some siderite as indicated by iron in Table 1-X and by separate specific analyses. It is assumed that the presence of siderite represents secondary intrusion into the rock after its initial deposition and consolidation. The scanning electron microscopic (SEM) analyses of the surface showed a large surface concentration of alumina and iron compared to the bulk analysis by the emission spectrograph, which indicated that the clays found by X-ray are concentrated on the surfaces of the grains of silica and on the pore walls resulting in restriction of the pore to the flow of fluids. The low permeability and high specific surface area support this conclusion.


The Berea and Cottage Grove sandstones were compared by Crocker et al. (1983), because their chemical and mineral analyses are almost identical. The specific surface area and ion-exchange capacity of the Berea Sandstone are both about one-third of that of the Cottage Grove, yet their mineral analyses are almost identical. The differences were interpreted by examination of the rock with the SEM. The Berea Sandstone had most of its clay minerals between the grains, acting as cementing agents, and the pores had fairly clean silica surfaces. Clays located between the grains, present very little surface exposed to the fluids within the pores and, therefore, the ion-exchange capacity and specific surface area are considerably lower than those of rocks with clay minerals dispersed along the pore walls. The Cottage Grove Sandstone, however, had most of its clay lining the pore walls and bridging pores (as observed with the SEM) and, therefore, exhibited greater specific surface area and cation exchange capacity than the Berea Sandstone.

The properties of the Coffeyville and Torpedo sandstones were similar to those of the Cottage Grove. The physical, chemical and visual (SEM) characteristics were almost the same, except for lower permeabilities obtained for the Coffeyville and Torpedo sandstones.

The chemical and mineral analyses of the Noxie Sandstone are also similar to those of the Cottage Grove, Coffeyville, and Torpedo; however, the physical characteristics are different. The Noxie has high permeability, low density and low surface area compared to those of the other outcrop rocks. The grains in the Noxie Sandstone were found to be much larger than those of the three other rocks mentioned above. The pore sizes were much larger, accounting for the high permeability and lower density of this sandstone.

Feldspars (potassium and plagioclase) are the principal constituents of arkoses. The abundance of feldspars in many older sands indicates that the sediments were exposed to rapid erosion, a short or rapid transport and deposition, and little or no reworking, such as a granite wash where eroding granite accumulated in dendritic canyons and was rapidly buried. Another possible explanation is the predominance of mechanical processes over the chemical, because the prevailing climate (hot and dry climate) was conducive mainly to mechanical weathering with little chemical weathering (Folk, 1968).

Inasmuch as the softer, less durable, rocks are often reduced to smaller sizes and constitute small fractions of the total sand composition, their presence is reflected in the textural features of sands and the configurations of histograms and cumulative frequency curves.

Graywacke is a controversial field-term applied to tough, indurated, dark-gray rocks containing dark rock fragments or dark-colored ferro-magnesian minerals (fragments such as chert, slate, schist, carbonates and phyllites). They make up about 20% of the consolidated sand sediments. Folk (1968) replaced the term "graywacke" by "lithic arenite" (when the content of rock fragments exceeds that of feldspar, the sands are classified as lithics).

Arkoses and greywackes are composed of mineral grains and associated intergranular pore spaces, which contain silt, clays and various chemical cements. The interparticle material may be no more than a fine-grained expression of the larger


mineral grains, which may, or may not, have been mechanically and/or chemically altered into other forms such as clay. On the other hand, orthoquartzites usually contain only cement. If the interstitial material content exceeds 35%, it is termed matrix and becomes a more visible portion of the rock. There are numerous sand classifications, most of which are basically methods of determining the relative proportions and compositions of fragments and matrices.

The common minerals present in terrigenous sediments originating from muds are the clay minerals illite, kaolinite, smectite, and chlorite. Smectite is a mineral group which includes montmorillonite as a principal variety. Illite is commonly formed from mild leaching of potassium feldspar-rich granites. Diagenetic alteration of montmorillonite also yields mixed-layer clays and illite. Kaolinite originated principally in areas of severe chemical leaching that promote removal of all cations except for silicon and aluminum. Smectites are commonly the weathering products of volcanic rocks that contain plagioclase feldspars. Much of the chlorite is formed from the alteration of kaolinite and montmorillonite under more severe pressure and temperature conditions during burial (100-150~ Chlorite and illite contents increase with depth at the expense of kaolinite and montmorillonite due to diagenetic and catagenetic processes.

An interesting aspect of the distribution of clays is their occurrence in the oceans. As a rule, illite is the dominant clay mineral, and in the northern Atlantic it comprises more than 90% of the clay-mineral fraction. In the South Atlantic, montmorillonite amounts to as much as 40% of the total clay-mineral fraction, whereas in the North Atlantic area only up to 20% of the clay fraction is montmorillonite. In the southwestern area of the Indian Ocean, montmorillonite constitutes over 80% of the clay fraction, possibly because of diagenetic transformation of volcanic materials (Biscayne, 1964). The most abundant clay mineral in the South Pacific area is montmorillonite, which is associated with phillipsite. Illite, kaolinite and chlorite are less abundant. The thickness and shape of particles of various clays are shown in Table 1-XI, and the chemical analyses of various clays are presented in Table 1-XII.

There is a large increase in kaolinite content (to more than 50%) and of gibbsite

TABLE 1-XI

Physical properties and characteristics of various clay minerals (after Warner, 1964, p. 14)

Property Kaolinite Illite Montmorillonite

Thickness of cell (/~) 7 10 9.6

Thickness of clay plate (/~,) 500-20,000 >30 10-80 Surface area (m 2/g) ~15 ~90 800

Particle diameter (#m) * 0.3-4 0.1-0.3 (or larger) 0.01-0.1 Density (g/cm 3) 2.60-2.68 2.64-2.69 2.2-2.7 Cation exchange (meq/100 g) 3.15 10-40 80-150 Shape hexagonal hexagonal(?) plate-shaped(?)

plate or lath

* 1/zm = 10,000 A.


TABLE 1-XII

Emission spectrograph analyses of clays, in weight percent (after Crocker et al., 1983)

Attapulgite Dickite Halloysite Illite Kaolinite Bentonite Nontronite Pyrophyllite

SiO2 54.9 41.9 48.0 50.7 45.8 47.6 36.8 62.8 A1203 10.4 41.2 40.4 19.7 37.8 21.5 5.4 23.5 Fe203 3.9 0.04 0.1 5.0 0.2 3.6 29.1 6.2 MgO 8.4 0.02 0.01 1.8 0.2 3.4 0.7 0.07 CaO 1.1 0.1 0.04 2.5 0.2 7.6 1.8 0.07 TiO2 0.5 0.04 0.01 0.9 1.2 0.04 0.01 0.3 SrO 0.01 0.12 0.0 0.0 0.0 0.02 0.01 0.02 K20 0.9 0.0 0.0 4.9 0.0 5.8 0.3 4.3 Na20 0.1 0.2 0.1 0.4 0.3 0.0 0.0 0.0 Ignition

loss 19.5 14.4 14.6 9.3 14.5 13.4 23.4 3.6

(more than 10%) in the sediments of the Atlantic Ocean adjacent to the tropical rivers in South America and Africa. In the sediments of the Indian Ocean near Madagascar, the gibbsite content is more than 30%. The chlorite content is commonly less than 20% of the clay mineral fraction; however, large amounts are found in Antarctic regions and east of the Mid-Atlantic Ridge. The frequency of these minerals decreases from north to southwest of the Mid-Atlantic Ridge. According to Griffin and Goldberg (1963), illite, montmorillonite, chlorite, kaolinite, and to a much lesser extent, halloysite are the main clay minerals in the Pacific Ocean. Illite was found to be abundant in all samples from the North Pacific area. Kaolinite is confined to nearshore sediments. Montmorillonite is also generally more abundant in nearshore sediments. Chlorite content in nearshore sediments increases with increasing latitude.

Mudstones (which include shales, siltstones and claystones), are the most common of the sedimentary rocks. They are composed of silt- and clay-size particles resulting from chemical and physical disaggregation of many different rocks during the process of weathering and transport. Their small particle size leads to suspensions that are readily carried by moving bodies of water to be deposited in quiet zones after floods forming beds of silt/clay mixtures, and in low-energy areas of lakes and seas. Classifications of these rocks are based on particle-size distribution, types of clays, general texture, induration and the presence or absence of laminations (Lundegard and Samuels, 1980; Potter et al., 1980).

Many classification schemes have been proposed for sandstones and are currently in use. The scheme selected for use depends on the needs of the organization or individual investigator and must be defined for general discussions. A useful scheme was introduced by McBride (1963) using a ternary diagram to represent mixtures of quartz, feldspar and rock fragments, as shown in Fig. 1-8. The term "litharenite" was defined by McBride as a sandstone containing more than 25% rock particles and less than 10% feldspar (in some other schemes "greywacke" is used in place of "litharenite"). McBride also defined the useful term "lithic subarkose"


QUARTZ, QUARTZITE and CHERT

5% ~.aY~UARTZARENIT E

/ / LITH~C

FELDSPAR ~o% ~O~ ~o% ROCK FRAGMENTS

Fig. 1-8. Classification of sandstones. (After McBride, 1963, in: Chilingarian and Wolf, 1975, p. 21, fig. 1-16.)

as a sandstone or arenite containing abundant, subequal amounts of rock fragments (>10% but <25%) and detrital feldspar. McBride's "sublitharenite" contains 5- 25% rock fragments, 0-10% feldspar, and 65-95% quartz.

The Folk et al. (1970) classification includes not only mineralogic composition depicting source rocks but also textural "maturity concept": one refers to an immature, submature, mature, or supermature arkose, quartzite, or greywacke (Folk's phyllarenite, 1968, 1970) depending on the presence or absence of matrix, sorting, rounding, and mineralogic composition determined by the sedimentary environment. Textural maturity of a sediment is attained by the removal of clay-sized particles and the sorting and rounding of large grains as shown in Fig. 1-9. According to Weller (1960, p. 91), the processes of rounding, sorting and clay removal advance at different rates. The relative mineralogic maturity of sediment is indicated by the amounts of feldspar and ferro-magnesia minerals remaining in them. It is important to mention that the compressibility of sands increases with increasing content of feldspars. The changes in textural and mineralogic maturity may be independent of each other depending on numerous environmental factors (Chilingarian and Wolf, 1975).

GENETIC CLASSIFICATION OF SANDS ON THE BASIS OF GRAIN-SIZE DISTRIBUTIONS

The genetic classification of sands on the basis of grain-size distribution is still in a state of flux as changing ideas are added to the various concepts. This subject is briefly discussed here, because sands of different depositional origins compact


Fig. 1-9. Diagram illustrating the concept of textural maturity of Folk (1951, 1968). (After Weller, 1960, in" Chilingarian and Wolf, 1975, p. 22, fig. 1-18.)

Fig. 1-10. Genetic classification (energy index) of sands based upon grain-size distributions. I = sands deposited by rivers and other currents; H = near-shore sands deposited in an environment of strong water agitation; III = bottom marine or lake sands formed in weakly-agitated waters; and IV = aeolian sands. Dashed zone = area of uncertainty. (After Rukhin, 1969, in: Chilingarian and Wolf, 1975, p. 24, fig. 1-20.)

differently, probably largely because of differences in grain-size distribution and mineralogic composition.

Rukhin (1969, p. 491) prepared a genetic classification diagram for recent sands by plotting the average grain size versus the sorting coefficient (Fig. 1-10). The following depositional areas of sands can be distinguished by using his diagram, where:

I = area of river sands and sands deposited by other currents, / / = area of near-shore sands (beach and shallow water) deposited in an environ-

ment of strong water agitation,


III = area of bottom marine or lake sands formed in weakly agitated waters, and IV = area of aeolian sands. The hatched area in Fig. 1-10 represents the area of uncertainty with sandy-silty

deposits containing considerable amounts of grains less than 0.05 mm in size. Many river sediments probably would fall in this area.

Grain-size distributions are commonly made up of more than one log-normal population and can, therefore, provide information concerning the depositional processes. The distributions are commonly composed of three populations (Fig. 1-11), which can be characterized according to grain-size distributions of each of the populations making up the sediment. Referring to Fig. 1-11, (A) represents a distribution of grains transported by saltation; (B) is principally transported in suspension; and (C) transported by rolling along the surface of a stream bed (Visher, 1967).

The junction point between the saltation population (A) and the traction, or rolling, population (C) often occurs near grain size 2 �9 (0.25 mm) and its position is dependent upon the strength of the bottom current. The stronger the current, the coarser the size transported by saltation. The lower the turbulent energy, the more suspended material is included in the distribution, and the finer is the grain size at the junction between suspension (B) and saltation (A) transported populations. Thus, the strength of the current that produces saltation determines the grain-size range of saltation populations. A strong current produces a population having a large size range (1.75-2.5 ~) (Visher, 1967).

Figure 1-11C shows a curve typical of modern streams and ancient sands of fluvial origin. There is an abrupt truncation at point "t". Wind-blown deposits show a preponderance of population transported by saltation and the curve exhibits excellent sorting of that population (Fig. 1-11D).

Figure 1-11E is a sediment sample collected off the coast of North Carolina from a depth of 3.4 m (11 ft), which is the high-energy wave action zone. The figure shows the development of a size population related to rolling (C), giving a similar appearance to that of Fig. 1-11A. Effects of winnowing by wave action are also apparent.

The fourth class of distributions recognized by Visher (1967) is one related to beach processes (Fig. 1-11F). The curve presented in this figure is typical of nearly 100 samples taken from the lower swash zone from beaches along the Gulf Coast and East Coast of the United States. The inflection at point "S" represents only a slight change in the slope of the saltation population (A). Visher (1967) pointed out that the position of inflection, point "t", and percentage and sorting of population B (suspension) are similar to those found in wind-blown sand distributions, and may be in part controlled by provenance.

PHYSICAL PROPERTIES OF SANDS AND SANDSTONES

Porosity

Virtually all detrital rocks are porous to some extent. The voids are very important because they contain fluids that may be economically beneficial. Voids in a

m Fig. 1-11. Selected grain-size distributions produced by differing depositional processes. (After Visher, 1967, in: Chilingarian and Wolf, 1975, p. 16, fig. 21 1-21.)


sand are particularly important to the study of compaction, because compaction is associated with reduction in pore space. Under extremely high pressures, there also is a reduction of the volume of the solids; however, in most studies of compaction, reduction of solids volume has been ignored.

The relative volumes of voids and solids can be expressed in terms of porosity and void ratio. With few exceptions, porosity is preferred by geologists and petroleum engineers, whereas void ratio is used by soil and civil engineers. Both porosity and void ratio are related to the bulk volume of the rock. Bulk volume (Vb) is the sum of the total volume of voids or pores (Vv or Vp) and the solids (Vs):

Vb= Vv+ Vs (1-8)

Porosity, qS, is the ratio of the void space to the bulk volume expressed as a fraction or as percent:

- - V v / V b x 100 (1-9)

Void ratio, which is used extensively in the study of compaction, is the ratio of the voids volume to the solids volume:

e = V v / V s (1-10)

The relationships between porosity and void ratio are:

q5 = e(1 + e) and e = q~/(1 - ~b) (1-11)

The fractional porosity can never exceed 1.0, but the void ratio often exceeds unity for fine-grained sediments with porosities exceeding 50%.

Porosity is inversely related to the bulk volume which decreases when compaction takes place; therefore, the total volume change cannot be represented by subtracting one porosity from another because the two porosities are related to different bulk volumes. The void ratio, however, can be used for calculations because it is related to the volume of the solids which remains essentially constant during compaction.

The change of bulk volume is expressed as:

( 1 - ~bl) 3Vb = 1-- 1 ~b2 (1-12)

Inasmuch as the volume of solids remains constant, 3 Vb is equal to the change of pore volume (3 Vp) and the change of porosity (34~). The change of porosity per unit of original bulk volume may be expressed as Eq. 1-13, which is preferred when void ratios are used, because the calculations are simplified:

805 = 3e/(1 + eo) (1-13)

where eo = original void ratio.


Permeability

Permeability is a measure of the ease with which a porous medium will transmit fluids (the inverse of resistance to the flow of fluids). A general quantitative relationship between permeability and porosity cannot be achieved because the relationship depends on several independent parameters: (1) the interconnections of the pores; a rock may be porous and exhibit little or no permeability because the pores are not interconnected, as is the case with the plutonic rock generally known as pumice stone; (2) grain-size distribution; a rock with a narrow grain-size distribution will have greater porosity than a rock that contains fine particles mixed with large particles; (3) pore-size distribution; and (4) the pore path tortuosity. Empirical, exponential, relationships between permeability and porosity can be developed for specific sediments, such as those developed by Chilingar (1964) (Fig. 1-12).

Permeability (determined empirically) for a specific rock sample is a property which is related to the viscous flow of fluids through the porous medium:

k= qlzL (1-14) A x 6 p

1 8 ( 600

400 0 / ' /

�9 o ~ ' o - /

0 0 /

�9 .,~ i - . , - o ' 0 Ir �9

~1�9 �9 / ' i / " A / ?

7 " �9 ~ '

/ / � 9

�9 / r

�9 = ; ! r

/, e l l �9

. !

,,. v 0 It m ~"

/ ~o o f A , -~

i ~- ~ i ~ �9 IJ

0 13 OnE

~F/~" o,I

/

,X o, ~ , , ' . ' ,de , U m l �9

~.. �9 . . _ C / o

�9 I:~ ~,4 ~ Silty ' i c / I : n.. = . / ,,,, "-'/o

l o / - I IV'

, . ~ , s

a o , ~ o ' ~ a D n,ag,~ c a M

M _--iJ u --~1, ~

_ n g a l ' n

Coarse- and very coal'se-griained I

Coarse- and medium-c rained

1

r Clayey

1. /m = 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36

Porosity, %

Fig. 1-12. Relationship between porosity and permeability of various types of sandstones. (After Chilingar, 1964, fig. 2, in: Chilingarian and Wolf, 1975, p. 33, fig. 1-25.) (Cores contained irreducible water saturation.)


where: k = permeability, D; q = flow rate, cm3/s; ~ = viscosity, cP; L = length of the sample, cm; A = cross-sectional area of the sample, cm2; and 6p = pressure drop across the sample, atm.

In general, the permeability of unconsolidated sands commonly ranges from 1 to 6 D, whereas that of lightly cemented consolidated samples ranges from 0.2 to 3.0 D. Indurated, well-cemented rocks have a permeability range of <0.001 to 1.0 D; the permeability of a fracture or vug can be virtually infinite.

Tsvetkova (1954), clearly showed that the presence of clays (especially those that swell when contacted by fresh water) greatly reduces the permeability of sandstones. This is especially true for montmorillonite clays where 2% of the clay in a coarse-grained sand lowers the permeability 10-fold, whereas 5% lowers the permeability 30-fold. Sandstones are practically impermeable if they contain 6-9% montmorillonite clay; on the other hand, sandstones containing as much as 15% of the non-water sensitive kaolinite clay can still remain quite permeable.

Specific surface area

Permeability and porosity measurements may be used in the Carman-Kozeny equation to determine the surface area of unconsolidated samples of particles.

Sa = 31.8,o -1 (1 -15)

where: Sa - specific surface area, m2/g; p - density, g/cm3; 4) = porosity; k = permeability, D; and x - adjustable textural factor.

An adjustable textural factor (x) equal to 5.0 for unconsolidated sands, as suggested by Carman (1937), Wyllie and Rose (1950), and Donaldson et al. (1974) after numerous tests, is required for accuracy. The textural factor is related to the tortuosity of the fluid flow path. The basic form of the equation was developed by Kozeny (1927) and critically reviewed and extended by Carman (1937) who conducted numerous experiments to verify the validity of the equation. Wyllie and Rose (1950) extended the equations to applications for the petroleum indus~ try and Donaldson et al. (1974) proved its validity for unconsolidated sands by comparing the results to measurements made by gas adsorption. In addition, they presented experimental data showing that the ratio of the specific surface areas of consolidated sandstones measured by nitrogen adsorption to that determined by the Kozeny-Carman equation ranged from 26 to 43. Thus, although the equation is accurate for unconsolidated samples, it cannot be used for consolidated porous media. The Carman-Kozeny equation provides a measure of the external surface of the solid particles contacted by the fluid moving through the porous medium. On the other hand, the gas adsorption method yields a measure of the total external areas and surface contributed by dead-end pores that hold, but do not transmit, fluid.


Surface areas of sands and san&tones

Certain relationships have been established among surface area, permeability and porosity by several authors (see Langnes et al., 1972, p. 243). Chilingar et al. (1963) developed the following formula for surface area per unit of pore volume, Sp, for sandstones in cmZ/cm3:

(2.11 x 105) 1/2 Sp = F2.i~bl.2k (1-16)

where F = formation resistivity factor (= Ro/Rw; Ro is equal to the electrical resistivity of a formation 100% saturated with formation water and Rw is equal to the formation water resistivity); q~ = fractional porosity; and k = permeability in mD.

If values of 1.25 for tortuosity, r, and 2.5 for shape factor, She, are representative for unconsolidated sands, then the following formula can be used (Chilingar et al., 1963):

( ~ 3 ) 1/2 Sb = 5650 -k- (1-17)

where Sb = surface area in cm 2 per unit of bulk volume in cm3; ~b = fractional porosity; and k = permeability in D.

Tortuosity, r, is equal to the square of the ratio of the effective length, Le (tortuous path) to the length parallel to the overall direction of flow of the pore channels, L"

r = ( L e / L ) 2 (1-18)

Shirkovskiy (1971) presented several new formulas and discussed in detail the accuracy of different formulas proposed for determination of surface areas.

It is unfortunate that in the literature various authors use different definitions for the "specific surface area", i.e., surface area per unit of grain volume, pore volume, or bulk volume. Thus, it is imperative to know the definition used by a particular author before using the data presented.

The Brunauer et al. (1938) theory of adsorption was applied to consolidated geologic samples for measurement of specific surface area by Donaldson et al. (1974). The adsorption of nitrogen is related to the concentration (or partial pressure) of nitrogen:

P 1 (C - 1)P - + ( 1 - 1 9 )

V ( Po - P ) Vm C Vm C Po

where" C = dimensionless constant related to the heat of adsorption; P = partial pressure of nitrogen, mmHg; Po = liquefaction pressure of nitrogen, mmHg; V = volume of nitrogen adsorbed at pressure P, ml; and Vm = volume of gas required to form a monolayer on the adsorbent, ml.


A plot of P / V (Po - P) vs P / Po yields a straight line having an intercept 1/Vm C and slope (C - 1)/VmC from which Vm can be determined. The total surface area of the core per gram of sample is then given by:

Vm Po N a S~ = M (1-20)

where: N = Avogadro's number; M = molecular weight of the gas; and a = area occupied by a single nitrogen molecule, 15.4 x 10 -20 m 2.

Elastic properties

The atoms and molecules of all substances above the absolute zero of temperature exhibit random motion about a mean location. Whereas these motions tend to disintegrate the molecule, they are opposed by greater atomic binding forces that hold the particles together. The resultants of these forces acting within the cohesive structure of the substance opposes deformation of the material when it is subjected to external forces. The distance between atoms, or molecules, decreases from gases, to liquids, to solids; therefore, gases exhibit a larger amount of compressibility relative to liquids and solids. The molecules of gases and liquids, however, do not have sufficient cohesive force to support an extensive force, whereas solids may be compressed or extended within the limits of their elastic properties without causing permanent deformation (Guyod and Shane, 1969; Dresser-Atlas, Inc., 1982; Ellis, 1987).

The resistance to deformation, or stiffness, of the material is its elasticity, which is expressed quantitatively by Hooke's law. Hooke's law states that the strain (deformation of the substance) is proportional to the applied stress (applied per unit area). The ratio of the applied stress (Fo/A) to the resulting strain (dL/L) is the Hookean elasticity (or modulus of elasticity of the substance). Three elastic moduli have been defined, which quantitatively describe the fractional strains of length, volume and shape within the elastic limits of substances, respectively:

Young's modulus (E) = (G/A) (dL/L)

where: E = lb/in 2 or Pa; Fo = lb or N; L = in. or m,

Bulk modulus (K) = (Fo/A) (dV/V)

where: K = lb/in 2 or Pa; V = in 3 or m 3,

Shear modulus (G) = (FolA) tan(O)

(1-21)

(1-22)

(1-23)

where: G = lb/in 2 or Pa; and | = angle of deformation. A fourth elastic property, known as Poisson's ratio, is the strain perpendicular to

the extensional force to that perpendicular to the compressional force, such that:


TABLE 1-XIII

Compressional and shear wave velocities in various materials (after Dresser-Atlas, Inc., 1982; and Ellis, 1987)

Sp. Gr. Compressive Shear velocity (ft/s) velocity (ft/s)

Nonporous solids Anhydrite Calcite Dolomite Granite Gypsum Limestone Quartz Salt Steel

Water-saturated rocks Dolomite Limestone Sandstones Sands Shales

Liquids Water, pure Water, 100 K ppm NaC1 Water, 200 K ppm NaC1 Drilling mud Crude oil

Gases Air Hydrogen Methane

2.98 20,000 11,400 2.71 20,100 - 2.88 23,000 12,700 2.65 19,700 11,200 2.35 19,000 - 2.71 21,000 11,100 2.64 18,900 12,000 2.16 15,000 8000 8.93 20,000 9500

2.88 15,000-20,000 2.71 13,000-18,500 2.65 12,000-16,500 2.65 9000-17,000 2.45 7000-17,000

4800 5200 5500 6000 4200

1100 4250 1500

8000-11,000 7000- 9000 6000- 9500

Poisson's ratio (v) = (dx/dy)

(dy/y) (1-24)

The elastic properties of subsurface geological formations (Table 1-XIII) are affected by anisotropy, diastrophism, lithology, and overburden pressure. Crystalline rocks exhibit larger values of elastic moduli than rocks having a greater degree of diastrophism, and fragmentation, or those containing colloidal materials. Poisson's ratio of sedimentary rocks ranges from 0.15 to 0.4. Poisson's ratio of some weak, unconsolidated, porous rocks, however, may approach zero.

Figure 1-13 illustrates a rectangular bar which has been extended by application of force, Fo, on two parallel faces. This causes elongation of the bar from L to L + AL which is proportional to the applied force, and contraction of the height from H to H - A H and width of the bar from w to w - A w. The stress applied to the bar (or) is equal to the force divided by the cross-sectional area and Young's


FO~.~

/4

/

/

~<--.

/ I t I

d 4- ~ - - -

I i i !

I I I H-~XH H I

/

1 , I

. . . . . . . . . . . . . L * ~ L

/ /

-7/ i e I I I I

_A 1 I I

~ F o

Fig. 1-13. Rectangular bar extended by application of force, Fo, on two faces. (After Ellis, 1987, p. 344, fig. 15-S.)

modulus (E) is the constant of proportionality between the stress and the resulting strain:

Fo/A = E ( A L / L ) (1-25)

The bulk modulus (K) is the proportionality constant that relates the applied stress to the change of volume (V) that takes place in the bar:

Fo/a = K ( A V / V ) (1-26)

The extensional force on the bar (Fig. 1-13) produces contractions of the height and width, and elongation of the bar. Poisson's ratio is the proportionality constant that relates the change of height (H) or width (w) of the bar (change perpendicular to the applied force, A H / H ) to the change of length (change parallel to the applied force, A L / L ) :

A H / H = A w / w = v ( A L / L ) (1-27)

Poisson's ratio also may be expressed in terms of the bulk and shear moduli:

1.5K - G v = (1-28)

3 K + G


Fig. 1-14. Deformation of an object subjected to a shear force. (After Ellis, 1987, p. 347, fig. 15-7.)

The deformation of an object subjected to a shear force is illustrated in Fig. 1-14. The bottom is held stationary, whereas the top is displaced by a tangential force, T. The shear modulus (S) is the proportionality constant that relates the applied tangential stress (T/A) to the maximum tangential displacement (tan |

TIA = S[tan(| (1-29)

When an elastic substance is disturbed by temporary displacement (struck with a hammer, for example), the elastic material will transmit the energy as an oscillating motion or wave. The two principal mechanisms of energy transport are the compressional and shear waves. The molecules of the substance do not travel from one end of the substance to the other, instead they oscillate about their mean position in the material, transferring energy by displacement of neighboring particles. Lon- gitudinal (compressive-extensive) waves are propagated by particle motion parallel to the direction of the displacement generating a compressional or P-wave. On the other hand, particle motions perpendicular to the direction of propagation generate transverse or shear waves (S-waves) (Fig. 1-15).

After a temporary impact, particles in the material will oscillate about an equilibrium point (Z) from B to B' (Fig. 1-15). If a single particle vibrates at a constant frequency, it will have a constant time interval t for vibration between B and B', and

B +Ao C R E S T . . . . . . . . . . . . .

/ ~'~"~ ~ " . _ D

B" - A o , T R O U G H I

' T - ~! ; I

Fig. 1-15. Analysis of an electromagnetic wave. (After Guyod and Shane, 1969, fig. 4-1.)


an amplitude Ao which is equal to the distance from A to B. The harmonic motion of the particle between B and B' may be represented as a function of time using the orthogonal projection of the oscillating point (the oscillating point between B and B' is represented by the circular motion of point P with a time period equal to T). The frequency of the harmonic motion is equal to the number of revolutions made by the point P during the time period t. The maximum amplitude Ao of the oscillating point is represented by the distance A to B, or Z to B'. The displacement D of the particle as a function of time t and frequency f , which is represented by the wave on the right-hand side of Fig. 1-15, can be mathematically expressed as follows:

D = Ao cos(27rft) (1-30)

The propagation of the wave which exhibits a decreasing displacement with respect to time is represented mathematically by including a distance term, where x is the distance from the source of the impact that initiated the wave and v is the velocity of the wave:

D = Aocos [2zrf ( t - x ) ] (1-31) v

Equation 1-31 applies only to propagation of a plane harmonic wave in a homogeneous medium and allows calculation of the particle displacement at any time t for a given distance from the source. The propagation equation for a spherical harmonic wave is:

1 [ ( x ) ] D = - A o c o s 27rf t - - (1-32)

x v

The velocity of compressional wave propagation (Vc) in elastic materials is equal to the frequency of the oscillations multiplied by the length of the transmitted wave ,~ ()~ is measured from crest to crest):

Vc-- iX (1-33)

The velocity of the compressional and shear waves, for the special case of one- dimensional propagation, also may be described in terms of the moduli of elasticity. The error introduced by the assumption of one-dimensional propagation for stiff materials such as rocks is negligible with respect to the measured quantities:

Vc = (E/P)~ = (K +O'75G) (1-34)

Vs = ( C / p ) ~ (1-35)

Compressibility

The large-scale withdrawal of subsurface fluids (water, gas, oil) is accompanied by land subsidence which may become a severe environmental hazard if the affected areas are in locations of human habitation, or industrial endeavor. The detrimental


consequences of fluid withdrawal, however, may be curtailed by examination of a sample (core) of the reservoir rock, and its fluids, followed by mathematical simulation. This preliminary examination will disclose the location and amount of compaction, and subsequent subsidence, which will take place if the fluids are withdrawn. An assessment of the environmental consequences can then be made before extraction of the subsurface fluids begins. If severe environmental damage is predicted, a program of water injection to replace the withdrawn fluids can be developed, or the project can be abandoned.

Withdrawal of subsurface fluids results in subsidence of two principal environments: (1) sinkholes associated with carbonate rocks and (2) unconsolidated sediments deposited in marine, lacustrine and alluvial environments. Sinkholes are large caverns filled with unconsolidated sediments that are buoyantly supported by the shallow groundwater. The buoyant support is removed when the water table is lowered resulting in many cases in sudden subsidence which is limited to a small area, generally less than 50 m in diameter. Abandoned mining shafts that have been filled with unconsolidated sediments, or tunnels, give rise to similar surface subsidence. This type of subsidence, however, is beyond the scope of this text.

Withdrawal of fluids from subsurface sediments results in compaction distributed over a large area with subsequent surface subsidence, which may not begin until several years after commencing fluid withdrawal and proceeds as a relentless slow process over a wide area. Compaction is the consequence of several simultaneously acting phenomena that are induced by the increases of effective stress on the matrix (caused by pore-pressure reduction due to fluid withdrawal). High compressibility of unconsolidated (or semiconsolidated) sediments, decrease in pore pressure, confinement of the reservoir, interbedded fluid saturated undercompacted shales, high porosity and low vertical permeability, all contribute to the amount and areal distribution of the final surface subsidence. Confinement of the reservoir is an integral part of the mechanism because natural replacement of the withdrawn fluids is not possible or is severely restricted. Stratigraphic confinement of the reservoir may take place after deposition of the sediments, whereas structural confinement may take place during deposition due to contemporaneous faulting, or after deposition by tectonic movements resulting in confining faults or intrusion of extraneous bodies such as salt diapirs.

The degree of compaction depends on the compressibility, c, of the sediments which is described in detail in Chapter 2.

Dusseault (1983) listed several criteria for evaluation of potential compaction, which includes the geologic history of the specific formation. Compaction of reservoirs due to fluid withdrawal is a phenomenon associated more generally with shallow reservoirs (<1000 m). Furthermore, if a shallow formation has previously been subjected to high stress by deep burial its compressibility will be reduced. If the formation is then changed to a shallow reservoir by uplift and erosion, it will retain most of its low compressibility. In a previously stressed, consolidated formation, therefore, compaction due to fluid withdrawal may be insignificant. Generally, only younger (Cenozoic) sediments less than 2000 m in depth are important with respect to significant compaction that may create a surface environmental impact.


If a confined aquifer is developed by tectonic movement during deposition of younger sediments as the depth of burial increases, a larger part of the load of the overburden will be taken by the fluids in the pores of the formation. Thus, the zones will have weak intergranular supporting stress and high pore pressure. A formation in this condition (like those of the geopressured zones of the United States Gulf Coast or the flesh-water aquifers of the San Joaquin Valley) is undercompacted in relation to its depth of burial. Withdrawal of fluids, therefore, will increase the effective stress leading to grain rearrangement and compaction. The compressibility of such an undercompacted zone is high.

Heavy oils (~ < 20) have such high viscosities that production by conventional methods is not possible unless the oil contains a considerable amount of gas in solution, which effectively reduces the viscosity and provides energy for displacement of the oil to the production well. Methods of employing heat to reduce the oil viscosity and provide energy for displacement have been developed and classified in accordance with the process used to provide the heat in the reservoir: (1) fireflood, where air is injected to maintain a burning oil zone in situ; (2) steam-soak, which is the periodic injection of steam alternated by periods of production; (3) steam-drive, where oil is displaced directly by the injected steam and condensed water from the injection well to peripheral production wells; and (4) hot-water drive, which is simply the employment of heated water.

The heavy oils frequently occur in shallow, undercompacted, unconsolidated sands; therefore, they are readily susceptible to compaction due to fluid withdrawal, which reduces the pore pressure, and begins the chain of events that lead ultimately to surface subsidence.

Compaction of the petroleum reservoir during production serves to maintain the pressure which may be a significant part of the energy available for displacement of the oil to the production wells. Thus, if the oilfield is not in an environmentally sensitive location, the subsidence may be tolerated in the interest of maximum recovery of oil. If the oilfield, however, is in a sensitive area, thorough evaluation of the impact of surface subsidence must be made and (if warranted) a water injection-pressure maintenance program must be considered to maintain the pore pressure in the reservoir and, thus, minimize compaction/subsidence. For example, after subsidence became a severe environmental problem at Long Beach, California, a water injection program for pore pressure maintenance had to be initiated to stabilize the compacting zone (Colazas and Olson, 1983).

Schenk and Puig (1983) reported an analysis of compaction/subsidence in a thermal project area, which is part of the Tia Juana oilfield in Venezuela. They studied a 30 m thick oil-saturated sand zone containing oil with an average viscosity of 2000 cP at a temperature of 45~ and initial pressure of 5.86 MPa. Production in three stages (primary by solution gas drive, stream soak, and steam drive) resulted in considerable production, which can be attributed directly to the reservoir pressure maintenance by compaction. Approximately 73% of the initial production of heavy oil was attributed to pressure maintenance by compaction of the reservoir during the initial phase of production. Compaction, however, decreased in importance ending in being responsible for only 13% of the total production. The decrease of


the importance of production attributed to compaction with respect to time, was probably due to a decrease of compressibility of the sand as compaction proceeded. Mathematical simulation is necessary for evaluation of the production-compaction relationship of a virgin field. Data for the computer simulator (compressibility, permeability-porosity relationship, etc.) must be obtained from samples of the formation and its fluids.

Detailed computer evaluation of any specific reservoir can be conducted with as much refinement as allowed by availability of reservoir and laboratory data.

N O M E N C L A T U R E

A

Ao C C

Cb

Cf

Cu

d

E

e

eo

F

Fo f G H

K

k

L

Le M

N

P

Po P

Pe

Pp q

Sa

Sb

Sp

t

U

l)

Vb Vm Up

W

= area, cm 2

= a m p l i t u d e of par t ic le d i s p l a c e m e n t

= cons t an t

= compress ibi l i ty , psi -1 (kPa -1)

= bu lk compress ib i l i ty

= fo rma t ion compress ib i l i ty

= uniaxia l compress ib i l i ty

= grain-s ize d i a m e t e r

= Young 's modu lus

= void rat io

- or ig inal void rat io (before compac t i on )

= fo rma t ion resistivity fac tor

= app l i ed force

= f requency , ( l / t )

- shea r modu lus

= f o r m a t i o n thickness , he igh t

= bulk modu lus

= pe rmeab i l i ty , m D

= length, cm

= effective length of the to r tuous pa th of pores in a rock

= mo lecu l a r we igh t

- Avogadro ' s n u m b e r

= par t ia l p r e s su re

= l iquefac t ion p re s su re

= pressure , a t m o s p h e r e s

= effective p re s su re

= p o r e p re s su re

= flow rate, cm3/s, ba r r e l s /day

- specific surface area, m a/g

= sur face a rea in cm 2 per uni t of bulk vo lume in cm 3

= surface a rea in cm a per uni t of po re vo lume in cm 3

= t ime

- se t t l ing velocity

= veloci ty (as def ined in text)

= bu lk v o l u m e

= v o l u m e of gas r equ i r ed to fo rm a m o n o l a y e r on a s ample surface

= p o r e v o l u m e

-- solids v o l u m e

= wid th


= wave length (as defined in text) K = structural parameter equal to 5.0 in the Carman-Kozeny equation 0 = angle of deformation /, = viscosity, cP v = Poisson's ratio p = density a = area occupied by a single nitrogen molecule, 15.4 x 10 -20 m 2" or applied stress (psi or

kPa), as defined in the text a ' = intergranular (grain-to-grain) stress ax, Oy, az - three principal stresses (in the x, y, and z directions) r = tortuosity ~b = porosity (fraction or percent)

= phi-size, - log 2 (d)

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Chapter 2

47

COMPACTION OF ARGILLACEOUS SEDIMENTS

G E O R G E V. C H I L I N G A R I A N , H E R M A N H. RIEKE, III and E R L E C. D O N A L D S O N

I N T R O D U C T I O N

During the past 35 years, the exploitation of oil and natural gas reserves, associated with thick sequences of very fine-grained rocks in Tertiary basins, has become increasingly important for fulfilling the world's energy needs. Argillaceous rock can be defined as the consolidated sediment mainly composed of clay- and silt-sized particles. Examples are mudstone, shale, claystone and argillite. Many reservoir development problems have arisen which demand an engineering solution based on geotechnical knowledge about these types of rocks and sediments. Successful drilling to depths greater than 20,000 ft (6096 m) in these active sedimentary basins and the amounts of hydrocarbons discovered depend upon knowledge of the fundamental physical and mechanical properties and deformation characteristics of the encountered formations and the interrelationship among various rock properties. It is important, therefore, to have a thorough understanding of how abnormal fluid pressures are created, maintained, and dissipated in these geologically young sedimentary rocks, and their relationship to compaction and subsidence.

Considerable disagreement exists among engineers and geologists as to the mechanisms responsible for the origin of abnormally high formation pressures in sedimentary basins. A number of causes for the creation and maintenance of abnormal fluid pressures in argillaceous sediments have been proposed and those with the most promise are cited here. (1) Continuous loading and incomplete gravitational compaction of the sediments. This is called in the literature "nonequilibrium compaction" (Plumley, 1980) and "disequilibrium compaction" by Magara (1975). (2) Tectonic compression. Clark (1961) coined the term "tectonic overpressure" for this mechanism. (3) Faulting (Dickey et al., 1968). (4) Phase changes in diapirism (Harkins and Baugher, 1969). (5) Phase changes in minerals during compaction and diagenesis. Gypsum-anhydrite conversion was investigated by Hanshaw and Brede- hoeft (1968) and the release of interlayer water from clay mineral (conversion of montmorillonite to illite) was proposed by Powers (1967). (6) Geothermal temperature changes creating fluid-volume expansion and/or cracking of organic compounds. Chaney (1949) proposed the fractionation and cracking of hydrocarbons, whereas the term "aquathermal pressuring" describes the mechanism by which closed volumes of sediments can be overpressured (Barker, 1972; Bradley, 1975; Sharp, 1983). (7) Osmotic and diffusion pressures (Hanshaw and Zen, 1965). Young and Low (1965) found that osmotic pressures values in core shale membranes are low (2-4 psi). This suggests that effective membranes can be absent in shales and that

48 G.V. CHILINGARIAN, H.H. RIEKE, III AND E.C. DONALDSON

osmosis may not be a major factor in overpressures. (8) Invasion of water derived from magmatic intrusions (Platt, 1962). (9) Uplift and erosion (Russell, 1972). Many geologists, however, doubt the existence of paleopressures. (10) Infiltration offluids (Tkhostov, 1963). (11) Fluid density difference arising from oil, water and gas in a reservoir (Gretener, 1969). For a detailed discussion of these mechanisms and other suggested ones see Rieke and Chilingarian (1974), Bradley (1975, 1976), Dickey (1976), and Plumley (1980).

The mechanical aspects of argillaceous sediments are sufficient to explain the fluid pressure environments in Tertiary basins. Compaction of sediments under the influence of a vertical monotonic loading has long been a well-documented geologic phenomenon (Sorby, 1908; Hedberg, 1926, 1936). No doubt that some of the previously mentioned mechanisms are active as supplementary excess-pressure generators during the depositional history of a basin. Even if several mechanisms act simultaneously, the authors stress that gravitational loading and tectonic compression exert the greatest influence on pore pressures and hydrocarbon/water migration. Knowledge of both the vertical and lateral orogenic stress patterns in a depositional basin is of utmost importance in interpreting abnormal fluid pressure environments and anticipating the location of oil and natural-gas reservoirs. The influence of tectonic forces on compaction mechanisms and fluid migration is adequately discussed by Hubbert and Rubey (1959), Berry (1969), Hergert (1973), Thompson (1973), Rieke and Chilingarian (1974), and du Rouchet (1981).

Because of the intimacy of the relations between clay-sized mineral grains and water, a reduction of pore volume in sediments under increasing loads can best be considered in terms of the removal of the pore fluids. The factors that are known to influence the water content of argillaceous sediments under applied loads include: (1) the type of clay minerals; (2) particle size; (3) adsorbed cations; (4) temperature; (5) pH; (6) Eh; and (7) type of interstitial electrolyte solutions. With the exception of particle size, the influence of these factors is deduced mainly from laboratory compaction experiments, i.e., squeezing of monomineralic clays mixed with simple electrolytes (Von Engelhardt and Gaida, 1963; Rieke, 1970; Rieke and Chilingarian, 1974; Chilingarian et al., 1994). (See Fig. 2-1.)

Overpressured, undercompacted formations in many parts of the world probably owe their origin to rapid sedimentation, which trapped water in compacting clays with practically no permeability. As mentioned previously, laterally directed stresses of tectonic origin could also give rise to overpressured formations. Dickey (1972), however, stated: "It seems improbable that the comparatively unconsolidated shales could transmit horizontal stress". Anikiev (1964), on the other hand, attributed the origin of high pressures in numerous overpressured formations to Recent and Quaternary tectonic movements. He (p. 108) stated that gravitational compaction also could not explain the origin of high pressures present in formations surrounded by halogenous deposits, in fractured limestones and tufts, and in well-consolidated Paleozoic rocks. The forced influx of additional volumes of oil and gas under high pressures into reservoirs having a definite volume could cause overpressures.

Hedberg (1974) discussed the relation of methane generation to undercompacted shales, shale diapirs, and mud volcanoes. The organic matter, which constitutes

COMPACTION OF ARGILLACEOUS SEDIMENTS 49

10 8 6 4 2 3 - ,,|

~ B

1~. "

0 0 2 .

= , 8o 3 = . - ~ , , o , ~ . ~ < - %

50 o 0 J S~tts

0 - - , , . . . . . , . . . . - : 0 ~ oa- ~ ~o i ~ ' I I0 I00 I000 EFFECTIVE O V E R B U R D E N P R E S -

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3 "-

0 2 I.- ,(

0 0 > I

0 - 1

- 7 O

Z Z W - o o a0

~o=o 3 > 5 o

. . . . . . . t i i

I00 I0,000

PRESSURE, IN KILOGRAMS PER SQUARE CENTIMETER

D

%

| . . 1

0 . 1 1

70

3 >o 5O Z

o ~

PRESSURE, IN K ILOGRAMS PER SQUARE CENTIMETER

k. z

z w 9 0 - o

w _ a .

Q . . . I

5O ~o 1 0

O

1 e~

k- Z W 0~

- 6 0 w

Lg

D .J

-50 0 >

- ~

O - 11:

O - ~

O 4 k- ty

O

2

0 . . . . . . . J I . 0 0 0.1 1 10 0.


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..... _ 1 1 . . . . 1 10


I - Z uJ

r~ w o=

80 w =E

.J O >

Z m

5 0 O

0

Fig. 2-1. Influence of different factors on the relationship between void ratio and pressure in clayey materials. (A) Relationship between void ratio and median particle diameter at overburden pressures less than 1 kg/cm 2 (after Meade, 1964, p. B6). (B) Generalized influence of particle size (modified from Skempton, 1953, p. 55). (C) Influence of clay-mineral species (modified from Chilingar and Knight, 1960, p. 104). (D) Influence of cations adsorbed by montmorillonite (modified from Samuels, 1950). (E) Influence of NaC1 concentrations in unfractionated illite, about 60% of which was coarser than 2 /zm in size (modified from Mitchell, 1960, fig. M3). (F) Influence of NaCI concentration in illite finer than 0.2 #m (modified from Bolt, 1956, p. 92). (After Meade, 1968, p. D4, fig. 1.)


a substantial part of the fleshly deposited muds, decomposes during diagenesis as a result of biochemical and thermochemical processes. The resulting methane gas could create, or accentuate, the overpressured undercompacted state of the compacting mud sediments in two ways: (1) by building up additional internal pore pressure; and (2) by further impeding the expulsion of interstitial pore water owing to the development of the second phase (gas) in the fluid (Hedberg, 1974, p. 661). The presence of gas bubbles dispersed in a liquid phase will reduce the permeability of the rock to either phase.

The origin of abnormal subsurface pressures and factors causing these pressures to persist for many millions of years in sedimentary rocks are discussed in this chapter. Mathematical descriptions of the sedimentation and the compaction of argillaceous sediments are also presented. A quantitative grasp of the compaction mechanism is based on the relationship between overburden stress, effective stress, pore fluid stress, and the physical properties of the competent and incompetent rocks. One continuum model, which represents the mechanical behavior of compacting sediments, treats the gravitational compaction process using a deformable one-dimensional porous medium (see Raghavan and Miller, 1975, for a detailed mathematical analysis).

In most sedimentary rocks, connate water is the predominant interstitial fluid. The degree of expulsion of water from the pore space by compaction provides a foundation for developing interrelationships among abnormal formation pressure, velocity of fluid expulsion, and pressure profiles through the sedimentary column. Some theories on how free and bound interstitial waters, along with hydrocarbons, are expelled and transported through the porous rocks in the form of an emulsion and/or a gaseous phase have been discussed by Chilingar and Adamson (1964), Smith et al. (1971a, b), Pandey et al. (1974), Bonham (1980), Welte and Yukler (1981), Nakayama (1987), and Korchagina et al. (1988).

COMPACTION M O D E L D E V E L O P M E N T

Dickinson (1951) performed a very thorough study on the geologic aspects related to abnormally high fluid pressures in the U.S. Gulf Coast Tertiary Basin. These high- pressure zones occur frequently in isolated Miocene and Pliocene porous sand beds surrounded by thick shale sections, which are located below the main deltaic sand series. Location of the high fluid potentials is controlled by the regional facies changes in the basin and appears to be independent of the depth or geologic age of the formation.

In sedimentary environments where sedimentation has been rapid, the thick accumulation of shales and mudstones of low permeability has retarded the expulsion of water and hydrocarbons. This excess fluid is trapped as pore fluid, which must bear a portion of the load that would normally be carried by the grain-to-grain contacts.

First basic premise in a model development is that the rate of gravitational compaction of sediments of a depositional basin is limited by the low permeability of the argillaceous members. In areas of rapid deposition, the expulsion of water from


Fig. 2-2. Diagrammat ic sketch of a pore space within a sedimentary framework and the corresponding / is the is the effective (intergranular) stress in the vertical direction; a H stress state in the system, a v

horizontal effective stress; aw is the pore water stress; and az is the total vertical stress component . The !

total horizontal stress component in the x-direction, ax, is equal to a H + aw.

fine-grained sediments has been shown to lag behind the loss of water from sands (see Rieke and Chilingarian, 1974).

One can visualize the sediments as a two-phase continuum, with sediment grains in mechanical contact with each other and fluid filling every pore space not occupied by solids and wetting everything except the areas of the interparticle contacts. A diagrammatic sketch of stresses in the pore space within a sediment is presented in Fig. 2-2. Each phase, i.e., solid and liquid, is assumed to occupy continuously a portion of the entire space, somewhat analogously to two vapors sharing a space in which they are assumed to exert their own partial pressure. The interstitial fluid is considered to be a slightly compressible homogeneous liquid and the pore pressure may vary from point to point. Pore fluids can flow through the void space under the influence of excess pore pressures. If the structure of the sediment remains rigid during the flow of fluids, a steady-state seepage will occur. On the other hand, if the grain arrangement alters to a different packing order, then an unsteady-state flow will arise. The steady-state flow, which requires a rigid stationary framework, can be easily developed from a mathematical viewpoint. Transient flow implies change in the effective stress which results in deformation of the solid matrix.


The Katz and Ibrahim compaction model

Katz and Ibrahim (1971) presented a mechanical model for explaining compaction and fluid expulsion from shales (Fig. 2-3). Their model is based on Terzaghi and Peck's simple piston and spring analogy (also see Fig. 2-4). The Katz and Ibrahim model is based on the compaction of an argillaceous layer between two permeable sand layers. As proposed by Terzaghi and Peck, the argillaceous sediment is represented by a series of springs and perforated disks. The perforated disks represent low-permeability clays, which restrict the escape of fluids, whereas the springs represent the deformable clay matrix. Sudden loading on the model correspond to a rapid sedimentation rate. Water contained in the spaces between the perforated disks represents the interstitial fluid. If a stress is applied suddenly to the system, the water between the disks initially will support the entire load. After a brief period of time, the water will be forced through the perforations in the disks either in an upward or a downward direction, depending on the relative magnitudes of pressure in the compacting systems, without lateral flow.

As the top and bottom disks move closer to the internal disks, the springs will begin to carry part of the applied load (Fig. 2-3). Consequently, the fluid pressure

Fig. 2-3. Schematic representation of clay compaction, porosity and permeability relationships, and creation of abnormally high formation fluid pressures. (After Katz and Ibrahim, 1971, fig. 12 m Courtesy of the Society of Petroleum Engineers.) k = permeability; ~b = porosity; t = time; p = pore pressure; Yw = specific weight of water; h = height to which fluid will rise in the tubes, which represents the pressure head (p/Yw); W = water; and G = gas.


Fig. 2-4. Simple schematic representation of clay compaction. (Concept after Terzaghi and Peck, 1948, p. 84; in: Hottman and Johnson, 1965, p. 718.) cr ~ = grain-to-grain bearing strength; S = axial component of total stress (overburden pressure); p = fluid pressure; and ~ = ratio of the pore stress to the total stress (e.g., 0.465 psi/ft [0.1074 kg cm -2 m -1] of depth); ~' = S - p. Stage A: overpressured system; water is not allowed to escape. Stage B: water is allowed to escape; springs carry part of the applied load. Stage C: compaction equilibrium; load is supported jointly by the springs and the water (water pressure is simply hydrostatic).

between the external disks will decrease. When the disks approach each other, it will become difficult for the pore fluid to escape from inside the system. Katz and Ibrahim (1971) mentioned that the gradual decrease of permeability from the center toward the top and bottom of the model could be represented either by a decrease in the number of openings in the disks or by an increase of the number of disks per unit length in the model. Figure 2-3 also shows the fluid pressure distribution as a function of time. Higher fluid potential is shown to exist in the central portion rather than in the upper or lower portions of the model. This means that it takes more time for the fluid in the center of the model to escape than at the outer boundaries. The permeability and porosity distribution in the model is given on the left-hand side of Fig. 2-3.

The behavior of the Katz and Ibrahim mechanical model is in general agreement with the observed performance of the overpressured formations in the U.S. Gulf Coast area. The model illustrates the reasons for the higher porosity of undercompacted shales, the extreme drop in permeability with increasing lithostatic pressure, and the entrapment of high interstitial fluid pressure in the shales.

Bonham's model

A slight modification of the Katz and Ibrahim compaction model was made by Bonham (1980). He stated that the usual view of progressive burial of sediments


and their compaction with resulting expulsion of pore fluids is not entirely correct. According to Bonham, the "implied" assumption made by previous investigators is that the fluid movement occurs in the upward direction out of the deeper zones toward the water-sediment interface, and fluid is expelled at the surface. Bonham's statement is valid only with respect to soil engineering laboratory experiments, such as those discussed by Terzaghi and Peck (1948) and to those sediments lying close to the depositional surface. The writers disagree with him that this is universally implied in the literature as evidenced by discussions of Smith (1971b) and Rieke and Chilingarian (1974, p. 17). Local, lateral, or downward movement of fluids may occur; however, the net flux of fluids is in an upward direction into porous layers. Fluid flow across the sediment-water interface only occurs in the near-surface sediment deposits undergoing initial burial and compaction (see Gibson, 1958).

Bonham (1980) developed a multilayered model (a computer application) which considered the migration of hydrocarbons in compacting basins. In the early stages of sediment compaction and basin subsidence, the flux of expelled water with reference to the depositional surface is downward. The mass movement of all buried matter is downward owing to the weight of the sediments. The flow of fluids expelled by compaction, however, is upward across stratigraphic units. The fluids move upward relative to the stratigraphic marker but they do not move to shallower positions relative to the depositional surface. Figure 2-5 illustrates Bonham's multilayer conceptual model of an open or leaky geologic system with compacting sediment layers.

In later stages, the subsiding basin contains a constant volume of water. As sedimentation, burial, compaction and basin subsidence continue, the sediments are slowly moving downward through a fixed volume of water. Bonham's depth- versus-porosity curves show that the porosity of unit 1, as well as the other units, decreases with depth (geologic time). As shown in Fig. 2-5D, the sediment column has been compacted such that the deepest layer (unit 1) is at "zero" porosity. This is Bohham's equilibrium condition. Bonham (1980, p. 550) stated that from this point on, the total volume of water in the basin sediments is a fixed amount. As compaction and subsidence continue, the sediments move downward through the fixed volume of pore water (Fig. 2-5E). No new water enters with additional sedimentation and subsidence. The pore fluids of each new layer deposited are displaced by the fluids expelled from the next deeper layer. No pore water is expelled at the surface.

Seals

A permeability seal is required in order to have a closed or leaky-proof compaction system. Abnormal formation pressures could not be maintained over geologic time without such a seal. Bradley (1975) described seals in three dimensions, that is, top, bottom and lateral containment of the fluids within the sediment body. In a multiphase fluid system of water-oil-gas, however, abnormal pressure can be sustained owing to the buoyant effect of hydrocarbons in water. The bottom of this fluid system could remain unsealed (Bradley, 1975, p. 971).


Fig. 2-5. Bonham's development model showing five sequential steps (A through E on the left side) in basin subsidence, sedimentation, and compaction. (After Bonham, 1980, p. 550, fig. 1.) The right-hand sequence illustrates the amount of pore fluids expelled during compaction. The total basin fluids can be determined by integrating the basin pore volume. D: The "equilibrium condition" where porosity becomes zero at the base of unit one. (Courtesy of American Association of Petroleum Geologists.)

Horizontal permeability seals can be faults, lateral diagenetic and lithologic changes in facies, or existence of evaporite bodies. Vertical seals arise from lithologic changes, fault displacement or diagenetic changes. Myer (1968) stated that the thickness of a seal may be variable, but it is assumed to be thin with respect to both thickness and lateral extent of an abnormal pressure zone. Pressure changes can be abrupt laterally across faults or vertically across bedding.

Bradley (1975) stated that the manner in which such a seal is maintained is an enigma. High pore pressures generated by compaction and aquathermal pressuring at great depth could fracture the argillaceous sediments. If the sediments are relatively unconsolidated, such vertically directed fracturing would be self-sealing owing to the plastic nature of the argillaceous sediments. Another healing mecha-


nism could be the precipitation of minerals resulting from the release of pressure (Bradley, 1975) and/or a decrease in temperature across this boundary, as described by Lewis and Rose (1970).

Seals in the geologic column have existed over long period of geologic time and many have survived destruction during tectonic activity. The fact that permeability seals remain intact suggests that the above-mentioned mechanisms may heal any damage to these barriers. (For further discussion, see Powley, 1990.)

CLAY MINERAL DIAGENESIS

An understanding of the role of diagenesis is important to the subsurface interpretation of what is occurring during the compaction of argillaceous sediments. Diagenesis influences the generation and expulsion of excess water during clay mineral dehydration and transformation, and the creation and/or migration of hydrocarbons during compaction.

Diagenesis

Mineral assemblages in argillaceous sediments and rocks can be classified either as being original, i.e., formed in situ (neoformation), or a modification of minerals originally present in the deposited sediments. New minerals can be formed by a combination of various geological factors such as source material, pore fluids, depositional environment, diagenesis, catagenesis, metamorphism and weathering. Changes in physical parameters, such as overburden pressure, geothermal gradient, and geological reaction time, and chemical parameters, such as pH, Eh, and ionic composition of the fluids, are indispensable for mineral neoformation and/or transformation. The following discussion is concerned only with those changes in clay minerals which could affect subsurface pressure and the expulsion and migration of hydrocarbons.

Diagenesis includes all physicochemical, biochemical, and physical processes modifying sediments between deposition and lithification, or cementation, at low temperatures and pressures characteristic of surface and near-surface environments (Aoyagi et al., 1987). Chilingar et al. (1979) pointed out that the catagenetic processes also have to be considered in clay mineral transformations. Catagenesis includes all processes at low temperature and pressure that affect sedimentary rocks after diagenesis and up to metamorphism. Berner (1980) presented a complete theoretical approach to the mechanisms involved in (early) diagenesis.

Early diagenetic changes of clay minerals in sediments

Fairbridge (1967)subdivided diagenesis into three distinct phases: syndiagenesis, anadiagenesis, and epidiagenesis. Berner (1980, p. 9) recognized two phases in early diagenesis and described the diagenetic processes quantitatively. The first phase as presented by Fairbridge consists of two stages: (1) initial stage which is regulated by


the chemistry of superjacent water; and (2) early burial stage, which is controlled by the entrapped pore water that is chemically modified by the bacteria and the bioturbation of surface organisms.

During the initial stage, clay minerals are in contact with the superjacent water resulting in a gradual change in the ionic exchange capacity of the clays. Biotur- bation disturbs the surface layers of the freshly deposited sediment and creates a relatively well-oxidized depositional environment (Aoyagi et al., 1987). The pH value may increase from seven to eight.

The early burial stage is recognized as a reducing zone. Anaerobic bacteria are dominant and the pH values rise to above nine. This results in an increase of Mg ion content and decrease of the cation exchange capacity (CEC) in the lattice structure of the smectite (montmorillonite) clays. The Mg(OH)2 becomes fixed in the smectite lattice. This fixation may affect the later transformation of smectite to mixed-layer clays and illite and/or chlorite during late diagenesis.

Rieke (1972) presented a detailed discussion on the transformation of smectite and other clay minerals with respect to field evidence and laboratory experiments, and the transformation's role in maintenance and/or origin of the abnormally high pressure zones. The kinetics of the formation of illite from smectite was presented by Eberl and Hower (1976), whereas Djevanshir (1987) discussed the influence of pore pressure on clay mineral transformations. Fertl and Rieke (1981) proposed the use of the gamma-ray spectral log to identify clay minerals in situ. The use of the gamma-ray spectral logging device was advanced as a sedimentological tool to be used in the interpretation of sedimentary sequences (Rieke and Fertl, 1981).

Clay mineral facies

The clay minerals compose special assemblages in argillaceous rocks which were called clay mineral facies by Aoyagi et al. (1975a). The clay minerals which char- acterize these facies are those originally deposited, those transformed owing to the diagenetic processes active in a burial and compaction environment, and those owing their origin to neoformation in situ. Recognition of clay mineral facies in compacting sediments and rocks helps to decipher the diagenetic history of the basin. There are five distinct types of clay mineral facies according to Aoyagi et al. (1975a).

Type I. There are three subtypes to this facies which closely resemble those clay minerals found in argillaceous sediments: Subtype Ia is composed of smectite, illite, and chlorite. Aoyagi et al. (1987) stated that it is the most common clay mineral facies found in the marine argillaceous rocks of Japan. The writers have recognized this facies in some of the Gulf Coast (U.S.A.) sediments.

Subtype Ia is composed of smectite, illite, and scarce chlorite. This facies closely resembles subtype Ia differing only in a reduced amount of chlorite. It originates in a marine environment containing pyroclastic detritus (Aoyagi et al., 1987).

Subtype Ib contains smectite, illite, scarce chlorite, and kaolinite. This facies is indicative of younger argillaceous rock deposited in shallow-sea and brackish-water environments (Aoyagi et al., 1987).


Type II. These facies are found in argillaceous rocks of older age. This facies is subdivided into two subtypes:

Subtype IIa contains smectite, illite, mixed-layer minerals and chlorite. Illite and chlorite contents are generally high, whereas smectite content is low. Marine argillites contain this clay mineral facies (Aoyagi et al., 1987).

Subtype lib is composed of smectite, illite, mixed-layer minerals, chlorite, and kaolinite. Illite and chlorite contents are usually high, whereas smectite content is low. Compacted argillites originating in brackish water and sediments of shallow seas contain this facies.

Type III. These facies are composed chiefly of illite and chlorite. Aoyagi et al. (1987) reported that the older Mesozoic and Paleozoic argillite in Japan contains this facies. This also holds true for the Devonian Shale of the Appalachian Basin (J.J. Renton, personal communication, 1988), whereas the Paleozoic shales in the Illinois Basin contain illite, chlorite and minor amounts of expandable mixed-layer clays.

Type IV. Facies which are composed mainly of sericite and chlorite. Other clay minerals are generally scarce. Compacted altered rocks in hydrothermal areas contain this clay mineral facies.

Type V. This facies is characterized by the presence of abundant smectite. Illite and chlorite are usually common. This facies is commonly found in weathered rocks, and is absent in fresh rocks (Aoyagi et al., 1987).

As a comparison to the above-described facies, recent marine sediments mainly contain smectite, mica (illite), chlorite, and kaolinite.

Clay mineral dehydration

Powers in 1967 proposed that the dehydration of smectite (montmorillonite clay) during the transformation to illite could create high pore pressure in compacting sediments. The alteration process involves the desorption of the last few layers of bound water in smectite. Inasmuch as the last few layers of bound water have a greater density than free water (Burst, 1969), this water when released increases in volume. The pore pressure increases to abnormally high levels when the water expands and is trapped in the subsiding and compacting shale. Magara (1975) used Burst's bound-water density values (1.15 g/cm 3) rather than those lower values (less than 1 g/cm 3) reported by Cebell and Chilingarian (1972) or higher values of 1.4 g/cm 3 reported by Powers (1967) to calculate shale volume expansion. The amount of released and expanding water would create a two percent expansion of the bulk shale volume. This expansion is not sufficient to create abnormally high pore pressures in the sediments even in a closed (sealed) geologic system. At the other extreme, Powers' values result in a 20% expansion which would cause rebounding in the mass of sediments. The thickness of the sediment column would drastically increase upon dehydration, approximately 0.2 ft per 1 ft of sediment (6000 ft per 30,000 ft of sediment section).


Magara (1975) deduced from the above evidence that this is an unreasonable scenario, and he concluded that smectite dehydration probably is not adequate as a single cause of overpressure generation. Plumley (1980) stated that both clay transformation and aquathermal pressuring are the sole pressure-generating mechanisms effective below the clay-transformation boundary. He claimed that field data suggest that the porosity values below some of the transition zones in the U.S. Gulf Coast are too low. These values are not consistent with the explanation that nonequilibrium compaction is the mechanism responsible for generation of the measured fluid pressures (Plumley, 1980, p. 422). According to him, there is a combination of high abnormal pressure, high shale porosity values at great depths, and subnor- mal sediment bulk density values are created initially by the disequilibrium in the compaction of argillaceous sediments. The writers point out that the intensity of the disequilibrium pressure which inhibits compaction depends upon the confinement of the sediments, that is, a closed, very "tight" cation-rich, geologic system, a leaky, somewhat cation-rich, geologic system, or an open communicating geologic system.

Djevanshir (1987) described a completely closed compaction system existing at a depth of 6.5 km in the Baku region of the former U.S.S.R. The attributes of the compacting sediment system are: (1) no systematic change in proportion of the various clay minerals with depth; (2) an average geothermal temperature gradient of 16~ (3) high pore pressures maintained near that produced by the lithostatic load; and (4) a rapid sedimentation rate of 1.3 km per million years. Apparently, these are diagenetically immature sediments where conversion of illite-to-smectite did not occur.

Plumley (1980) in his conclusions did not consider the possibility of having either a "leaky" or a late-sealed "open" compaction system. A "leaky" system would have allowed additional gravitational compaction to occur, thereby reducing the porosity values below those porosity values which would have been expected in a completely "closed" geologic system.

During the evolution of any sedimentary basin, the generated high abnormal interstitial pore pressures have a profound effect on the paths of fluid migration. The processes have to be quantitatively interpreted and correlated with field observations and laboratory experiments in order to analyze and predict these phenomena.

M A T H E M A T I C A L DESCRIPTI O N OF COMPACTION

Mathematical description of sediments undergoing compaction is extremely difficult. In addition to having elastic characteristics, the sediments may possess plastic, viscoelastic, or thixotropic properties under certain conditions. The development of a mathematical model which encompasses all of these compatibility characteristics, even as an approximation, has not been rigorously accomplished. The acceptable mathematical complexity of any sediment description is limited by the ability to solve boundary conditions. There are various phenomena related to sediment compaction, such as mineral and petroleum genesis, osmosis, reverse osmosis, variation in the


interstitial fluid chemistry, diagenesis, release of bound water from minerals, and changes in mineral stability, that are still beyond the capabilities of finite-element analysis and digital computers.

Bulk (total) volume, Vb, of the element in Fig. 2-2 is expressed as:

Vb = Vs + Vp (2-1)

where Vs is the volume of solid grains comprising the rock framework, and Vp is the volume of pores (voids) in the rock.

The porosity, ~b, of the compacting sediments is defined as:

q5 = Vp / Vb (2-2)

Another parameter frequently used in the measurement of the degree of compaction is the void ratio, e, which is defined as"

e = Vp/Vs (2-3) The void ratio can be related to porosity by using the previous relationships (Eqs. 2-1,2-2,2-3):

e = Vp/(Vb- Vp) (2-4)

Multiplying the numerator and the denominator by Vb and rearranging the terms:

e= (Vp/ Vb)[Vb/(Vb-- Vp)] (2-5)

= %/Vb + (Vb - %)/Vb (2-6)

= %/Vb + (vb/Vb - %/Vb) (2-7)

= ~/(1 - r (2-8)

Solving for the porosity, r

= e/(1 + e) (2-9)

Robertson (1967) proposed a new compaction parameter called the solid-grain proportion, G, which can be expressed in terms of void ratio, e, and porosity, q~, as follows:

G = Ybd/Ys = V s / V b = 1/(1 + e ) = 1 - r (2-10)

The solid-grain proportion, which is the ratio of dry-bulk specific weight, Pod, to grain specific weight, Fs, is a linear measure of the approach of the sediment's dry- bulk specific weight to its solid-grain specific weight at any stage of compaction. The solid-grain proportion is an index of change in mass per unit volume, whereas the void ratio is an index of volume change in the sediment. Robertson (1967) prepared a graph illustrating the relationship between G, q~, and e (Fig. 2-6). Although


[

4.0

2.0

5.0

0 1 0 o:2 ' o . ' 0.6 , o,.

SOLID GRAIN PROPORTION, G

Fig. 2-6. Relationship between void ratio, fractional porosity, and solid-grain proportion. (Adapted after Robertson, 1967, p. 124, fig. 1.)

Robertson's concept is not used at the present time, its value should be reeval- uated.

Rate of compaction

Berner (1971) presented a simplified and very elegant mathematical analysis of diagenesis and compaction. The following method of calculating compaction rate and total compaction of sediments saturated with water, is a modified Berner's approach.

Inasmuch as void ratio, e, is defined as the ratio of pore volume, Vp, to volume of solids, Vs, and the fractional moisture content, M, on a dry-weight basis is equal to the weight of water, Ww, divided by the weight of solids, Ws, the following can be

62 G.V. CHIL INGARIAN, H.H. RIEKE, III AND E.C. D O N A L D S O N

developed:

e = V p / V s - - - ( W w / y w ) Ws/?'s =M(ys/Yw) (2-11)

where Fw and ~'s are the specific weights of water and solids, respectively. The fractional moisture content, M, is usually determined by measuring the loss of weight of water-saturated sediments upon drying at 100~ (see Rieke and Chilingarian, 1974, pp. 33, 40, for the effect of drying temperature on solid-grain density determined). The volume of solids within a sediment layer per unit of horizontal cross-sectional area, Vs, can be related to the rate of deposition, Ra, in weight of sediment per unit area per year, as follows:

Vs = (Rat)/Fs (2-12)

where t is equal to time in years necessary to deposit a volume of solids, Vs. The bulk volume of a sediment per unit area, Vb, deposited annually is equal to the thickness of an annual sediment layer, ha. Combining Eqs. 2-9, 2-11, and 2-12, the following relationship can be obtained:

ha = (Rd/Ys)(1/1 -- alp) (2-13)

Fractional compaction, Cf, can be expressed as:

C f --- ( h i - h)/hi (2-14)

where h is the present thickness of the sediment layer and hi is the initial thickness of the sediment layer at the time of deposition. If the initial porosity is ~i and the present porosity is ~b, then:

h(1 - ~b) = hi(1 - ~i) (2-15)

because a volume of solids for a given layer is assumed to be constant. Thus:

hi = h[(1 - ~b)/(1 - ~bi)] (2-16)

and:

C f - - ( h i - h)/hi = (~bi - q ~ ) / ( 1 - ~b) ( 2 - 1 7 )

The rate of compaction, ddp/dt, can be calculated using a partial differential equation as follows, if porosity, q~, is a function of depth of burial, D, and time, t"

d~ = (8~/St)o dt + (6dp/gD)t dD

Dividing through by dt:

d~/dt = (8~/8t)n + (8dp/8O)t(dD/dt)

and inasmuch as dD/dt is equal to the thickness of an annual layer, ha:

d~/dt = (8~/~t )o + (Sdp/SO)tha

(2-18)

(2-19)

(2-20)


In the case of steady-state compaction, (Sck/St)D is equal to zero and, consequently:

dO/dt = (8O/SD)tha (2-21)

or combining with Eq. 2-13:

dc/)/dt = (8~/3D)t x Rd/Ys X [1/(1 -qS)] (2-22)

In the above equation, the (S~/~D)t term can be determined from depth-versus- porosity curves (e.g., see Rieke and Chilingarian, 1974).

Differential equations have been derived by several investigators (e.g., Cooper, 1966) to describe the changes in the space-time continuum for a conceptual model. The treatment is usually limited to the upward and downward movement of fluids out of one-dimensionalized, horizontal, elastic porous layers. In order to obtain a solution to the compaction process, involving the components of the overburden and tectonic stresses and particle and fluid displacements in the sediment system, one must consider the following equations and conditions: (1) continuity equations; (2) constitutive equation; (3) compatibility equations; (4) boundary conditions; and (5) equilibrium conditions.

In addition, the physicochemical factors and processes (e.g., osmosis, reverse osmosis, chemical composition of interstitial solutions, and temperature) must be evaluated. Bredehoeft and Hanshaw (1968) included thermodynamic considerations in their analysis of anomalous fluid potentials. The depositional environment, which can be visualized for the model, is a level surface of infinite extent. Water depth is constant over the entire area and may vary with time. When the upper layers of a freshly deposited, fine-grained sediment is undergoing initial compaction at the bottom of the sea, the interstitial fluid is in continuous communication with the overlying seawater and the pore pressure is essentially hydrostatic (see Fig. 2-7). Beginning at time zero, the sediment is deposited at a uniform constant rate, e.g., 0.1-0.5 m/1000 yr over the entire area. The physical characteristics of the freshly deposited sediment, such as the mineralogy, porosity, packing geometry and grain size are assumed to be constant throughout the entire area. As each sediment layer is buried under subsequently deposited mud and sand layers, a gradual compaction takes place. If the sedimentation rate is slow, the compacting sediment will gradually adjust to the additional load imposed by the overlying sediments, and as the mineral grains are pressed together, pore fluids are expelled.

Inasmuch as the argillaceous layers have high porosity and are relatively more permeable in their initial state (see Rieke and Chilingarian, 1974), the expelled fluids will flow in the direction of least resistance, usually upwards and into a porous sand layer. As long as the fluid can escape under normal loading conditions and porosity is intercommunicating, hydrostatic pressures will be encountered. If the gravitational loading rate of muds and sand layers is high, the permeability of muds decreases rapidly and, as a result, the pore fluids cannot escape from the sands through the argillaceous layers. These interstitial fluids would help to support the increasing overburden weight and further compaction of the formation is retarded or stopped. Thus, the formation becomes overpressured, because the

64 G.V. CHILINGARIAN, H.H. RIEKE, III AND E.C. D O N A L D S O N

W A T E R

" - ' ; Z : �9 :.~: .':.i." " - . > ' r ' . ' .~.-v.'.- -! �9 :v . " i,,'." ~.::~.",r -~. 4 . "

, .A .> " ~,.~.:[~: '~. ~1. '~ : .~.,, i : . . .r. . .~.:~..+ . . .~ �9 . . . . ".,~- �9 - i " "' ~ . �9

~'"~ /

C O N T I N U O U S S E D I M E N T A T I O N . - - ~ - - Z Z Z : �9 .~ : - . A . ; . w . - . v - . > . . < ' . ~ . ) . . ~ ' . r - ' . ~ . ' > . ~ . . r ~ : > : ~ : L'~" : < : .~." . ' . 7 . . . . " : I ' <..~. ~.i-." : : i ^ . - > . . . . - . . ^ . . . . ' . . . �9 . . �9 v . . ~ - < . r r :~- § .~.< , . : , ,~. ~.. ~ ,.;~-.:~.: . 4 .~ .u v ,~. " . ~ . " "~ 'n. ~ ".'~'>" ~ '~ , r . . ~ . ; . ^< .~ " ~ , " ' " , r ; ; . 4 . . . ~ . . . . . > .~ ' . / , . . n . ' ~ .~ . . . ~ .~ . . ~ . . : ~ -~ . , , . ' < . L . . , - . ~ . a ~. ~ , ' ~ .>~ : ,...~. r . n . . . < ' ~ .~

<:.~.~.x::.:-;" ." " . . : : ~ " ~;.~.'.::~.',.a

+ L'I')iI .... ~,.'. :::~,:.~;: :-:.V:'.,

, S E D I M E N T

Z

�9 ~'::.~:.,~ ~ . . . . .; , . . , . v - . ; l ' . . w - t , . , - . " . > . . - - r . ^ < , ~ . , . .J, .+. '~ r . -

r . . �9 ~ " u " A . C , r ' " '~" 4" i , , ' r ' . v " , , . ' . ' A ' . < ' . ~ . . 4 i , " - ; . ' , r . '..~...'~.~. ~.:~~.%:,.%.;.;:: :.~ ~. ~:. v '2. -'.;.,: ~ .~.~:~ ~:-;.:( �9 ~ . ' . . > ' . " 1 . . : , . . . , l ' t , " �9 . ' . . r . ^ > .< . . i . > . . ^ > ' < �9 .-'.' �9 .a, < . . ~ "

!..'.";~.'.~._-*.~.'::r:':i'~.'.~.'S'.;~'.~:: ~.~. ...~.~-..~s i~..,.~" ~ ~ :. "~" " :,.~ ':-,'~ .-' 7"

Fig. 2-7. S c h e m a t i c d i a g r a m of c o n t i n u o u s s e d i m e n t a t i o n in wa te r . ( A f t e r B r e d e h o e f t a n d H a n s h a w ,

1968, p. 1103, fig. 4 - - C o u r t e s y of t he Geological Society of America Bulletin.) l = t h i cknes s of t h e

s e d i m e n t ; t = t ime ; z = ver t i ca l c o o r d i n a t e ; a n d L = d e p t h of w a t e r ( in t e r s t i t i a l f lu id is in c o n t i n u o u s

c o m m u n i c a t i o n wi th t h e over ly ing s e a w a t e r ) .

contained fluids are subjected not only to the hydrostatic force, but also to the weight of newly deposited sediments. Bredehoeft and Hanshaw (1968) presented a hydrodynamic compaction model based on a continuous sedimentation rate, which possibly describes the creation of high pressures (see also Rieke and Chilingarian, 1974). Gibson (1958, p. 175) presented the following equation for continuous sedimentation in which the rate of sedimentation, w = 3l/3t, is constant:

h'pw _ 1 - exp - - Z 2 Ssl 2 lp' Ssl 2 ~ x 4Kt

C ~

x f 'tanh( 0

cos h exp d~' Kt 1 2 K t -4Kt

(2-23)

where h' is the excess fluid head, which is equal to pa/Pwg (Pa is the transient pore pressure in excess over the normal hydrostatic pressure, originally present); h is the head, which is equal to [h' + L(t)], where L = depth of water and t = time; z is the vertical coordinate; Ss is the specific storage and is defined as the volume of water taken into storage or discharged per unit volume per unit change in head. Ss is equal to pwg[(1/Es) + (~b/Ew)], where Pwg = weight of unit volume of water, Es = modulus of compression of the sediment matrix confined in situ (= Crz/ez, i.e., ratio of the vertical stress to the vertical strain), ~ = fractional porosity, and Ew = bulk modulus of elasticity of water; K is the hydraulic conductivity, which is equal to (kpw/lZ)g, where k = permeability, Pw = density of fluid, g = acceleration of gravity, and /z = viscosity of fluid; t is the time; p' = ,Ob - - Pw, i.e., the difference between


the bulk density, Pb, of the sediment and the density of the pore fluid, Pw; l is the thickness of the sediment; and ~'= z/ l ( t ) . Bredehoeft and Hanshaw (1968, p. 1104, fig. 5) presented a figure which enables solution (dimensionless form) of the above equation (see also Rieke and Chilingarian, 1974, p. 317, fig. 168). Gibson (1958, p. 171) stated, however, that it is unlikely that closed solutions can be obtained for arbitrary rates of sediment deposition. In addition, Gibson's equation does not take into consideration the deformable coordinates.

The development of a compaction model depends on certain fundamental concepts and several basic relationships, which must be stated at the onset so that any mathematical derivation can proceed with minimum interruption. Inasmuch as constitutive equations can define an ideal geological material, no advance can be made in the description of the sediment's properties without a prior knowledge of its behavior under an external stress. Constitutive theory is intended only to describe a limited number of physical properties decided at the outset for a given material.

It is postulated that compaction is directly related to the following parameters and is functionally represented in the following form:

C = f ( a , v , p , V, dp, k , D , t , c ) (2-24)

where C is the compaction, a is the stress on the system, v is the velocity parameter for solids and interstitial fluids in the system, p is the density, V is the volume relationships, ~b is the porosity, k is the permeability of the system, D is the burial depth, t is the time, and c is the compressibility relationship.

Figure 2-8 illustrates the spatial relationships of a compacting sediment and the coordinate system adopted by Smith (1971b). In this system, the position of the differential element of solids or pore fluid is measured as the vertical distance z

Air

I I

l I I I I I W a t e r I

~ - I I Other I - I s e d i m e n t s (?) I I h

t I I

- - Z=[ S h a l e

z-O -

Fig. 2-8. Spatial relationships and the coordinate system of a compacting sediment. (Modified after Smith, 1971b, p. 242, fig. 1.) Vw = average velocity of the water; Vr = average velocity of the matrix.


upward (positive) from the base of the argillaceous sediment. A differential element has a negative velocity if the material is moving downward and a positive velocity if it is moving upwards relative to the base of the sediment unit. The interstitial water in the unit cross-section between z and z + dz (Fig. 2-7) has an average velocity, Vw, which is a function of the time, t, distance z, and the depositional history and boundary conditions:

Vw = Vw(Z, t) (2-25)

Similarly, the average velocity of the matrix material between z and z + dz will be:

Vr = Vr(Z, t) (2-26)

Based on the law of conservation of mass, the increase in mass within the volume increment between z and z + dz, during the differential time increment dt, is equal t o :

[mass in at z] - [ mass out at (z + dz)]

= (pwVw~)zdt - (pwVw~)z+azdt = (apw~/at ) dzd t

o r

(2-27)

apw Vwqb / a z = - a p w ~ / a t (2-28)

where q~ is the porosity and Pw is the density of water. Similarly, Smith (1971b, p. 243) derived an equation for the solid matrix:

a P r V r ( 1 - - qb)/aZ = --a,Or (1 - - dp)/at ( 2 - 2 9 )

where Pr is the density of solid grains. For a detailed derivation which applies to fine-grained sediments the reader may consult Smith (1971b).

Overburden potential

Philip (1969a) viewed the overburden potential as consisting of two components: (1) the mechanical stress a on the rock column, against which work has to be done if the column deforms; and (2) the work which has to be performed at any point where liquid is added to the porous medium, inasmuch as the porous matrix is capable of being deformed and the addition of fluid results in an increase in bulk volume.

Philip (1969a), in studying swelling soils, formulated a quantity, | which is equal to the volume of liquid water per unit volume of sediment particles. This quantity, called the moisture ratio by Philip (1969a), is apparently equal to:

| = (1 + e)~b (2-30)

The volume of voids, Vp, is equal to:

Vp = Vw + Vg (2-31)

where Vw is the volume of interstitial fluid in the pores and Vg is the volume of free


gas in the pores. If the pores are assumed to be fully saturated with the interstitial liquid, then Eq. 2-30 reduces to:

| = e (2-32)

by substituting e/(1 + e) for qS. In a vertical column of argillaceous sediments with the surface unconstrained

and the mineral grains constrained from movement only at the base, the necessary upward movement of both the interstitial fluid and the solids above the point where interstitial fluid is added to the system (lateral or vertical migration from adjacent formations) requires that work be done against the gravitational field. A load on the surface of the vertical sediment column also requires that work must be done against this load. The component of the total potential which arises in this manner is termed the overburden potential. The overburden potential, fl, in swelling solids can be defined as (modified after Philip, 1969a):

z

= (de/d| + [ ydz] / I

(2-33) i , i

z0

where y is the wet specific weight of the sediment and or(z) is the total load carried by the sediment column at some convenient plane z which could be the upper surface of the column.

Philip (1969a) defined y as:

1/ = [ O + (pg/pf)]/(1 + e) (2-34)

where pg is the density of the matrix and Pe is the density of the interstitial fluid. Substituting (1 + e)4~ for | (Eq. 2-30) in Eq. 2-34, the following equation would result:

y = ~ -+- (pg/pf)[1/(1 + e)]

Utilizing Robertson's solid-grain proportion relationships in Eq. 2-10:

y = [dp -+- (pg/pf)(1 -~b)]

(2-35)

(2-36)

or:

y = [dp + (pg/pf)(G)] (2-37)

Sharp's momentum and energy balance equations

A series of coupled transient nonlinear momentum and energy balance equations, representing a one-dimensional sedimentary sequence in a thick, rapidly accumulating, compacting sedimentary basin, was derived and solved by Sharp (1974, 1976) and Sharp and Domenico (1976). Some of their work was based upon Bear's (1972, pp. 195-221) presentation on the theory of statics and dynamics of fluids in porous


media. The relationships between momentum and energy transport in abnormally pressured sediments are keys to the understanding of the geologic history of these sediments. Energy transport in compacting sediments takes mainly the form of heat conduction, convection, and dispersion. Heat conduction by radiation is negligible and is ignored. It is possible that the potential energy for petroleum migration could be provided by excess pore-fluid pressures during rapid sedimentation. The potential effects of viscous flow in the sediments on fluid and sediment temperature are greater in magnitude than the variations of temperature on fluid pressures (Sharp, 1976).

Sharp (1976) stated that the assumption of a constant geothermal gradient in thick sedimentary basins may lead to significant quantitative errors that impact sediment diagenesis and fluid flow. Sharp and Domenico (1976) stated that the reduction of the thermal gradient with depth, as indicated by studying some producing wells in the northern Gulf Coast, may be explained by: (1) varying lithologies; (2) a fluid sink near the upper sediment boundary; or (3) the relative rates of pore- fluid movement and sediment accumulation. Lewis and Rose (1970) pointed out that the temperature gradient varies with depth as a result of thermal insulators (overpressured zones).

Rainis et al. (1974) described a mathematical procedure on how to calculate this change in geothermal values for varying lithologies with depth. The method provides a realistic geothermal profile in a sedimentary sequence. Another problem with using presently measured geothermal heat flow and gradient values is that these values probably varied with geologic time during the evolution of the basin. These values, therefore, possibly do not reflect optimal thermal conditions. An attempt has been made by Lerche et al. (1984) to utilize vitrinite reflectance data from oil- and gas-well samples to determine paleotemperatures and paleoheat flow values. The accuracy of this approach is debatable.

Equation of continuity for momentum transport

Sharp's (1976) approach uses hydrogeological terms rather than those commonly used in the petroleum literature. The model for momentum transport is the classic cubic element representing a nondeforming volume of porous sediments. It is adapted to compute the net inward mass fluid flux. The cube-shaped model is then deformed in order to compute the rate of change of the fluid mass in the system. Any changes in the x- and y-directions are negligible and ignored. Changes in the vertical z-direction are measured with time. Bear et al. (1968) discussed in detail the continuity and conservation equations for a homogeneous fluid. Sharp's initial equation is:

3(AMw)/6t = 3(pwc/)Ax AyAz) /6 t

= (pwC/)6(Az)/St + pwAz6~/3t + 4)Az~pw/3t)AxAy (2-38)

where Mw is the fluid mass in an incremental volume; Pw is fluid density; ~b is porosity; and t is time.

C O M P A C T I O N O F A R G I L L A C E O U S S E D I M E N T S 69

The changes in the incremental volume are primarily a function of porosity reduction with respect to time. Use of bulk sediment compressibility, fluid compressibilities, and the change in fluid density with time results in an equation of continuity for a porous medium. This equation describes changes in the volume of its solid and fluid phases in the vertical direction:

[ St = -pwOot*Az - ~ - pwOt*(1-~b)Az ~ +pwCPflAz --~ A x A y

(2-39)

where ~ is the effective stress; or* is the bulk sediment compressibility; and/3 is the fluid compressibility.

Borrowing expression for the effective (interparticle) stress (Terzaghi and Peck, 1948), Darcy's equation expressed in terms of hydraulic conductivity, and the relationships shown in Fig. 2-7 result in the final equation of continuity for momentum transport in compacting sediments:

(K/Ss)62u/6z 2 = 3u/6t - p'3l/3t (2-40)

where K is the hydraulic conductivity; Ss is the specific storage, which is the volume of water released by fluid expansion or sediment compression under unit pressure decline; p' = Ps - Pw (Ps is bulk sediment density); 3l/6t is the rate of sediment layer growth; and u is excess head (head is pressure divided by fluid unit weight).

Sharp (1976) pointed out that inasmuch as the porous medium is deforming with time this is an "apparent" rate. An increase in the sediment amount being deposited with time is required to keep 61/6t at a constant value. The "apparent" rate of accumulation is equal to the true rate of deposition less consolidation. Analytical solutions to Eq. 2-40 do not exist for cases where there are nonconstant coefficients or fluctuating rates of sediment accumulation (Sharp, 1976, p. 310).

Equation of continuity for energy transport

Energy transport in sediments is the movement of heat by conduction, dispersion and convection. Radiation can be disregarded. Stallman (1963) derived the general equations for simultaneous transient fluid and energy flow through nondeforming porous media in hydrogeological systems. Starting with the nondeforming cubic volume element, all energy transport is in the vertical z-direction. The net rate at which heat is added to the element by conduction (1-Ic) through the lower face (1-Icl) and the upper face (1-Ic2) is expressed by:

1-I c = l " Ic 1 _ l " Ic 2 = Ks(~2T/~z2)AxAyAz (2-41)

where Xs is the thermal conductivity of the sediment and T is the temperature. Dispersivity can be defined as the effective thermal conductivity due to convection

(Dybbs and Schweitzer, 1973). If there is a moving fluid in the sediment body, then the thermal conductivity will increase proportionately to the fluid velocity. This


increase is termed the dispersivity and can be related to the thermal diffusivity (or) by an effective length (dd) (Sharp, 1976, p. 311):

= (K[ + adVw/4))p~Cs (2-42)

where Vw is the fluid velocity in which thermal dispersivity is accounted for; tCs ~ is the thermal conductivity in the absence of fluid motion; and Cs is the sediment heat capacity. The net rate at which heat is added to the volume element by interstitial fluid movement (1-Iw) through the upper and lower faces of the element is:

1-Iw = pwCw[3(vwT) /3z lAxAyAz (2-43)

If the sedimentary column is being compacted, then the sediment matrix is also moving (see Fig. 2-8). The amount of heat added by the movement of the matrix (Fir) is:

fir = IOrCr[(~ (vr T) /(~z]ax A y az (2-44)

The rate of heat accumulation in the cubic element is equal to the net heat added by conduction, convection, source terms, and the work done to the system. Source terms that may be present deal with chemical reactions, phase changes, and/or igneous activity taking place in the sedimentary body. Sharp (1976, p. 311) expressed this as a change in temperature:

p s C s ( S T / 6 t ) A x A y A z = 1-Ic + 1-Iw + Fir -t- rI -1- l-'Iwork (2-45)

where 1-I is the source term. Sharp (1976, p. 312) assumed no source terms (1-I = 0) and no major rapid

tectonic strains on the system (FIwork = 0), and by substituting Eqs. 2-41, 2-43 and 2-44 into Eq. 2-45 and solving for the continuity of energy transport obtained:

~T Xs S2T [ pwCwvw PrCrvr](~T [pwCw(~V PrCr ~Ur ] 6t = p~Cs (~z 2 ]- psCs + psCs -~z + ~- T (2-46) psCs ~z psCs ~z

Parameters and constants in Sharp's model

It is important to understand the selection of parameter values which have properties that vary with respect to time and space. The selection of proper constants and the determination of geological and thermophysical parameter values and their relationship to the state variables (u, T) is essential for a good geological interpretation of the processes operating to create abnormally high fluid pressures. Sharp (1976, p. 315, table 1) presented some typical values for various parameters treated as constants (Table 2-I). The reader is referred to the compressibility portion of this chapter and several other publications which contain a wider range of parameter values and additional references (Clark, 1966; Samuels, 1979; Edwards et al., 1982).

Sharp's (1976) empirical relationships used to determine the quantitative values of the parameters are presented in Table 2-II. The following recursive equations


TABLE 2-I

Some typical values of hydraulic and thermal parameters (after Sharp and Domenico, 1976, p. 393, table 1; Courtesy of Geol. Soc. Am.)

Property Value Reference

Hydraulic diffusivity Compression index Density of fluid Density of solids Density of sediment Fluid viscosity Gravity Hydraulic conductivity Initial porosity Rate of sediment accumu-

lation Specific storage 102 < Ss < 10 -4 m -1 Coefficient of thermal volume fit -- - 5 • 10-4~

expansion of fluid phase Geothermal gradient G = 30~ a Heat capacity of fluid phase Cw = 1.008 kcal/kg~ Heat capacity of solid phase Cr - 1195 kcal/kg~ Temperature (sediment-water TT - 20~ a

interface) Thermal conductivity of fluid

phase Thermal conductivity of solid

phase Thermal diffusivity Thermal dispersivity length

KISs = 1 m2/yr Cc = 0.3 a Pw = 1.004 x 103 kg/m 3a Pr = 2.65 x 103 kg/m 3a Ps = 2.3 x 103 kg/m 3 /z = 1.06 centipoise g = 9.8 x 1015 m/yr 2

Skempton, 1970 Lambe and Whitman, 1969, p. 323 Weast, 1968, p. F-5 Birch, 1942, sec. 2 Bredehoeft and Hanshaw, 1968 Ingelstam and Sjoberg, 1964, p. 53 Ingelstam and Sjoberg, 1964, p. 59

3 x 10 -1 < K _< 3 x 10 -4 m/yr Bredehoeft and Hanshaw, 1968 ~b = 0.50 a Hamilton, 1959 0 _< o2 _< 10 -2 m/yr Skempton, 1970

Zw = 4.75 x 103 kcal/yr m~

Ks = 1.52 • 104 kcal/yr m~

Domenico and Mifflin, 1965, p. 566 Harlow and Pracht, 1972

Lewis and Rose, 1970 Birch, 1942, sec. 16 Birch, 1942, sec. 16 Lewis and Rose, 1970; Hecht, 1973

Birch, 1942, sec. 17

Birch, 1942, sec. 17

et = 12.664 m 2/yr Cartwright, 1973 dd = 1000 m Mercer, 1973

a Estimated from reference.

were solved by numerical techniques subject to the initial and boundary conditions listed below. The one-dimensional, coupled, simultaneous, transient, nonlinear equations dealing with change in excess pore pressure with time, change in temperature with time, and apparent fluid velocity are:

(~2b/ p s ( t ~ ( U ) , / g w ( T ) ) (It + - - (2-47)

pw(T) s t

Momentum balance:

~u adZ~m(u)pw(T)g

~t (1 - ~(bl))n(T)gs(t~(tl)) ~Z 2

Energy balance:

3T

~t

kr(kw/kr) 4~(u) + ddVw/dp(u) I s2T -- (ps(q~(u), pw(T))((1 -~b(u))Cr + p(u)Cw) •z 2

pw(T)Cw - prCr ] ,~

- (ps(r - ~b(u))Cr -F t~(u)Cw) ~ZZ (pwT) (2-48)


TABLE 2-II

Equations for determining the quantitative values of the various parameters (after Sharp, 1976, pp. 312-314)

Property and equation (reference)

Hydraulic conductivity (Hubbert, 1940)

K = kpwg/ lz

where k is the intrinsic permeability; g the gravitational acceleration; pw the fluid density; a n d / z the viscosity of the fluid.

Intrinsic permeability (Magara, 1969)

k = adZdpm/(1 - dp) n

where ad z is some constant representing sediment properties. Sharp (1976, p. 312) defined ad z in terms of a hydraulic conductivity of 3.14 x 10 -2 m/yr for water at standard temperature and pressure and a porosity of 50%. Exponent values are: m = 3 or 4; n = 2.

Porosity (Poskitt, 1969)

~b0/(1 - 4~0) - Cc log ~- ~ = 1 / ( 1 - ~ b 0 ) - Cc log~

where 4~0 is the initial porosity of the unconsolidated sediments, and Cc is the compression index.

Fluid density (Sharp, 1976)

pw = Pw0 + Pwofly(T - To)

where fi t is the coefficient of thermal fluid volume expansion; and T is the temperature. Fluid density is assumed to vary linearly with temperature as a first-order Taylor's series.

Viscosity (Mercer, 1973)

/x - 5.3 + 3.8A - 0.26A3

where / z is the viscosity and has units of centipoise; and A is equal to (T - 150~176 Equation is applicable up to 300~

Thermal conductivity (Lewis and Rose, 1970)

K" = r r ( K w / K r ) ?v

where Kr and Kw denote the solid particle and fluid conductivities.

Heat capacity (Sharp, 1976)

G = (1 - ~b)Cr0[1 + ),r(T - To)] + ~Cw0[1 + Xw(T - To)]

where '~r and )~w are the thermal variation of the heat capacities for rock and water. As porosity values approach zero then the thermal diffusivity approaches that of a slate or quartzite (Sharp, 1976, p. 314).

Thermal diffusivity (Sharp, 1976)

u = [Kr (Kw/Kr ) q~ + ddVw/dp]/(dppw + (1 - ~b)pr)(~bCw + (1 - ~b)Cr)

where ot is the thermal diffusivity.

Pressure balance:

Pw -- 1)r = [ a d Z d p m ( u ) p w ( T ) g / ( 1 - ~ ( u ) ) z l z ( T ) ] 3 u / ~ z

Initial condit ions are:

(2-49)


U = 0; T = Tt + G ( z t o p - z ) ; G is the geothermal gradient; co = 6l/3t.

Upper boundary conditions at the sediment-water interface are:

U = 0; T = Tt at the sediment-water interface (constant).

Lower boundary conditions between the sediment and basement rock interface are:

~U ~T - 0 ; = G .

where U = excess pore-fluid pressure; G = geothermal gradient; T = temperature; and co = rate of sediment accumulation. Equations 2-47, 2-48, and 2-49 are the one-dimensional equations of state for an accumulating sedimentary basin, and represent a first-order approximation for evaluation of temperature, porosity and pore fluid pressure. Sharp (1974), using sensitivity analysis, showed that the viscosity variation is the major thermal variation, whereas the density terms in Eq. 2-47 can be treated as constants with little quantitative error. The numerical method is discussed in detail by Sharp (1974, pp. 113-127) and Sharp and Domenico (1976).

In conclusion, the modeling results show that the delay in gravitational compaction is the primary mechanism for generating excess pore fluid pressures in the compacting sediments of the northern Gulf Coast Basin. Sharp's derivations, however, do not take in consideration diagenetic changes, salinity, and multifluid saturation variations in those sediments. These considerations would require a minimum of one additional set of coupled mass balance equations. Equation 2-48 contains a dispersivity term for which adequate values are not presently available. Research is just beginning to address this problem. Longitudinal dispersivity values for the mixing of two miscible fluids in reservoir rocks are discussed by Menzie and Dutta (1989). In contrast to Sharp's derivations, Smith (1971a, b) disregarded the dependence of temperature variations on momentum transport.

R E S T O R A T I O N M O D E L I N G

One area in the compaction of sedimentary sequences that needs addressing is the quantitative evaluation of the changes of thickness in sedimentary layers during burial history. The loss of pore space in the sediments is central to the methodology for reconstructing original sedimentary structure and patterns of subsidence in the compacting sedimentary basin.

Quantitative evaluation of porosity in argillaceous sediments

The relationship between porosity of shales and clays and their depth of burial has been studied by numerous investigators (see Rieke and Chilingarian, 1974). Fig- ure 2-9 shows the variation in porosity values with depth from one area to another. This is due to the fact that porosity of argillaceous sediments is a complex function of numerous natural factors, often superimposed on each other (Dzevanshir et al.,


//, 5000

i !

s I--- o0 ,000

W 121

- i

15,000

zo, ooo , I 1 I 0 20 40 60

P O R O S I T Y , %

Fig. 2-9. Relationship between porosity and depth of burial for shales and argillaceous sediments. I = Proshlyakov (1960); 2 = M e a d e (1966); 3 = Athy (1930; 4 = Hosoi (1963); 5 = H e d b e r g (1936);

6 = Dick inson (1953); 7 = Magara (1968); 8 = Weller (1959); 9 = H a m (1966); and 10 = Foster and Whalen (1966).

1986). These factors include: (1) geologic age; (2) effective stress; (3) lithology; (4) mineralogy; (5) tectonic stresses; (6) speed of deposition; (7) thickness of the formations; (8) grain sorting; (9) grain orientation; (10) temperature; (11) hydrocarbon saturation; (12) amount and type of cementing material; and (13) chemistry of the interstitial solutions. The magnitude of the above variables complicates any quantitative assessment of the impact of these individual parameters on the porosity

C O M P A C T I O N OF A R G I L L A C E O U S S E D I M E N T S 75

of argillaceous sediments. Dzevanshir et al. (1986) proposed one method of solving this problem. The solution is to establish dependence of porosity of argillaceous sediments on the most important factors, such as the geologic age, lithology, and burial depth. The coefficient of irreversible compaction is related to the geologic age and the lithology. These prominent parameters either overshadow or incorporate the influence of other factors of lesser importance.

The following formulas were derived in order to quantitatively evaluate the role played by various parameters in maintaining porosity in clayey sediments. The coefficient of irreversible compaction, /3 (MPa-1), was defined by Athy (in: Buryakovskiy et al., 1986, pp. 54, 97) as follows:

~bD = ~bse -~pe (2-50)

where 4~D is the fractional porosity at burial depth, D, in m; ~bs = fractional porosity at the surface; and Pe = effective pressure in MPa.

Equation 2-50 can be expressed as follows on assuming ~bs = 0.4:

q~D = 0.4e -~176 (2-51)

Figure 2-10 shows a family of straight lines on semilogarithmic paper which represent the coefficient of irreversible compaction. Overprinted upon this family of straight lines are the actual compaction curves of argillaceous rocks. On knowing the coefficient of irreversible compaction for each one of the straight lines (Eq. 2-51), it is possible to determine graphically its average value for actual curves (Table 2-III).

POROSITY, FRACTION

0.001 0

2 0 0 0 -

4 0 0 0 -

6 0 0 0

0.01 O. l I I i w l i m I I I I I I I I I |

I 3 2

4 6 5

63 56 49 42 35 28 21 14

COEFFICIENT ,8, I / M P o , 10 . 3

Fig. 2-10. Relationship between porosity and depth of burial of clays. Coefficient of irreversible compaction /3 is also shown. 1 = Weller (1959); 2 = Aralsorskiy well SG-1; 3 = Vassoevich and Bronovitskiy (1962); 4 = Apsheron Peninsula and Archipelago, Azerbayjan; 5 = southwestern part of Apsheron and northern part of Baku Archipelago, Azerbayjan; 6 = southern part of Baku Archipelago and Along-Kurinskaya Depression; and 7 = family of curves calculated using Eq. 2-51. (After Dzevanshir et al., 1986, p. 171, fig. 2.)


TABLE 2-III

Coefficients or irreversible compaction (fl) of clays (after Dzevanshir et al., 1986, p. 172, table 1)

Curve description fl x 10 -3 (MPa -1)

Weller (1959) 58.5 Proshlyakov (1974) and Dobrynin 1970) 42.8 Vassoevich and Bronovitskiy (1962) 33.6 Apsheron Peninsula and Archipelago 42.1 Southwestern part of Apsheron Peninsula

and northern part of Baku Archipelago 27.1 Southern part of Baku Archipelago 19.3

As shown in Eq. 2-51, with the exception of depth of burial, all other variables are included in the term/3 (Dzevanshir et al., 1986). Correlation of this coefficient with geologic age and lithology becomes apparent when one compares the curves of different geologic age obtained by Weller (1959), Vassoevich and Bronovitskiy (1962), Dobrynin (1970), Durmish'yan (1973), and Proshlyakov (1974) with curves corresponding to sediments of the same geologic age in Azerbayjan, obtained from areas having different lithologies (Fig. 2-10). Scherer (1987) showed that in sedimentary basins having average geothermal gradients (<4~ m), the first-order parameters influencing porosity in compacting sandstones are age (time of burial), detrital-quartz content, maximum depth of burial, and sorting. Overpressured sandstones seem to retain about 1.9% porosity for every 1000 psi above hydrostatic pressure.

The coefficient, fl, depends on the duration of sample loading as shown by experimental data (Terzaghi, 1961; Dobrynin, 1970; Rieke and Chilingarian, 1974). It has been previously mentioned in this chapter, that in an argillaceous sedimentary sequence with an increasing thickness of shale and a decreasing number of sandstone reservoir rocks, the shales remain more porous owing to greater difficulty of pore fluid expulsion from the shaley sediments. The following Eq. 2-52 was obtained by Dzevanshir et al. (1986) from interrelationships among the coefficient of irreversible compaction, geologic age and lithology. Porosity at a burial depth, D, can be calculated by using a shale to sand ratio, expressed as a ratio of shales to the total thickness of the sequence in question.

q~D = q~0 exp[--0.014(13.3 log A - 83.25 log R + 2.79) x 10 -3 D] (2-52)

where ~b0 is the initial fractional porosity of clays; A = geologic age in millions of years; and R - ratio of thickness of clays to total thickness of the sedimentary sequence being analyzed. Dzevanshir et al. (1986) reported that the absolute error does not exceed 3% and Eq. 2-52 gives practical usable results.


Quantitative evaluation of bed thickness changes

Baldwin (1971) analyzed the effects of compaction and differential compaction on sedimentary intervals. He showed that it is possible to reconstruct original sedimentary structures and pattern of subsidence in a sedimentary basin using the concept of decompaction. This is accomplished by projecting back to an assumed earlier condition the porosities and the geometries of individual formations. The decompaction principle was employed by Conybeare (1967) to simplify correlation between wells and to reestablish the paleogeography of an area in western Canada.

Restorations of sedimentary sequences is accomplished by the application of the decompaction and the solidity approaches. The term "decompaction" was coined by Conybeare (1967). Decompaction of compacted sedimentary layers is determined by multiplying present thickness of the layer by a decompaction number, which is a function of the initial thickness and burial depth. The decompaction number, Dc, is the ratio of initial (or earlier) thickness, To, of a designated layer to its present thickness, Tz:

Dc = To/Tz (2-53)

The most suitable frame of reference for loss of pore volume is the proportion of solid grains rather than the proportion of pore space (Baldwin and Butler, 1985, p. 622). They pointed out that the conceptual and arithmetic simplicity of solid-grain proportion as proposed by Robertson (1966) (see Eq. 2-10) is that the volume of the mineral matrix does not change during compaction. Solid-grain proportion appears to be a simpler frame of reference for decompaction studies than porosity or void ratio (Baldwin, 1971, p. 293). By using a relation between solid height and porosity, Eq. 2-53 can be expressed as follows:

Dc = (1 - Cz)/(1 - r (2-54)

Dc -- Gz/ Go (2-55)

where q~z is the present porosity value; 4~0 is the initial (some earlier) porosity value; Gz is the present grain proportion; and Go is the initial (some earlier) grain proportion value.

Baldwin and Butler (1985) used the term "solidity", as recommended by Robert- son (1967), to represent the volume of solid grains as a percent of total volume of sediment. If compaction is the only process occurring, then the relation between solidity and bed thickness reduction is linear; however, solidity does not vary linearly with burial depth. The relation between porosity and bed thickness reduction is nonlinear. Shales that are normally compacted are best described by a power-law equation (Baldwin and Butler, 1985, p. 623). Figure 2-11 illustrates the Baldwin- Butler compaction curves plotted on logarithmic graph paper. The shale curves are represented by:

Z - - Zmax Sc~ ( 2 - 5 6 )

where z is the burial depth; Zmax is the maximum burial depth; S is solidity; and a is


I0 Solidity

20 30

\ \

50

!S-C

70

B-B

D "'.. i| i "'N

B Ba ldw in , 1971 (shale) " ' ~ B-B Baldwin-Butler, this repor t - ~

D Dick inson, 195:3 (shale) '.. "D" "Dickinson equation," this report ".. -.

S-C Sc lo ter -Chr is t ie , 1980 (sandstone) ".,

I00 - ~ . l m

I m

3 r

,4--

IOta o. E3

30

.I km m

.3

I km

I0 km

Fig. 2-11. A logarithmic plot of solidity compaction curves. B, D, and S-C are empirical; B-B and "D" represent equations. (After Baldwin and Butler, 1985, p. 623, fig. 3 I Courtesy of American Association of Petroleum Geologists.)

the solidity exponent. Baldwin and Butler (1985) used at = 6.35 and a Zmax -- 6.02 in Eq. 2-56, which corresponded very closely to their empirical curve throughout a range in depth from 0.5 m (20 in) to 6 km (about 20,000 ft). Undercompacted shales are expressed in Fig. 2-11 as the "Dickinson equation". The equation was plotted using values for at = 8 and Zmax = 15. Baldwin and Butler (1985, p. 625) noted that the values for Zmax and for at could be changed 2-3 % without significantly diminishing the fit to published empirical compaction curve data. The danger in using Eq. 2-56 for restoration modeling is that the user has to be able to recognize whether the sedimentary column contains undercompacted shales or not. A log-log plot does not have the appropriate mathematical sensitivity to precisely show the geological nuances in a compacting argillaceous sedimentary column.

Baldwin and Butler (1985) took their concept and applied it to the effective stress in shales. The effective stress, ~-, supported by clayey rocks at equilibrium compaction conditions and their solidity is expressed by:

~" : O'max S~ (2-57)

where O'ma x is the value of stress that will eliminate all pores. Solving for O'ma x"

O'ma x - - + 1 ) ] ( p m -- /gw)gZma x (2-58)


where p is the density; the subscripts m and w refer to mineral and water, respectively; and g is the local value of the gravitational constant. Combining Eqs. 2-56 and 2-57:

if- - - O'max (Z /Zmax) /3 (2-59)

where/3 = (or + 1)/or. This equation shows that the strength of a shale increases almost linearly with burial depth.

Modeling thickness changes in sedimentary layers

Perrier and Quiblier (1974) presented two methods for computing changes in sedimentary layers during compaction. Their approach excluded all sedimentary basins which possess a strong history of tectonic activity.

The first method is the "slice method" where porosity values from well logs are used to calculate the solid height of the sedimentary layers. The restoration expressions for a cylindrical volume of sediment for porosity under gravitational compaction are:

49 = hv/ ht (2-60)

where ht is the total height and hv is the void height.

hs = ht(1 - ~b) (2-61)

where hs is the solid height and (1 - 4)) is the grain proportion. During compaction, depth, thickness, and porosity vary continuously, but the

solid height remains constant for a given element. Mineral transformations, solution, or cementation change hs (Perrier and Quiblier, 1974). The solid height of sediment is more representative of true sedimentation, and does not depend on the degree of compaction. Any change in the total height of the sediment column can be expressed as follows for a small element:

dh~ = (1 - qS)dht (2-62)

For a vertical cylinder with the origin of heights, z, measured from its base, hs is equal to:

ht

hs = / [ 1 - 4)(z)]dz (2-63) L I

0

The first step of Perrier and Quiblier's (1974) method involves computation of solid heights. By considering only one lithology, the total solid height is obtained from:

Z2

hs - / [ 1 - ~b(z)]dz (2-64) / . I

t l

Zl

where Zl and 22 are the depths of the stage boundaries of the sedimentary layers. The


STAGE t

POROSITY 0 I

SLICE 6

SLICE 5

SLICE 4

SLICE 3

SLICE2 / _

SLICE f

ZI

0,5 0 '

t - ~ : G OEPTH Z

Fig. 2-12. Computation of the total-solid height of a stage (given by area between porosity curve and z-axis) and shale slice boundaries 1 to 6 (determined by limits enclosing equal areas). (After Perrier and Quiblier, 1974, p. 509, fig. 1 - - Courtesy of American Association of Petroleum Geologists.)

process is repeated for each lithology: sandstones, dolomites, limestones, siltstones, etc.

Perrier and Quiblier (1974, p. 508) divided each stage into slices. The division is defined by equal depositional duration of the layers (At). The values of At is chosen so that the number of slices do not exceed a few tens per stage. It was assumed by these authors that for a given lithologic layer, the sedimentation rate remains constant during the entire stage. For each distinctive lithology within a stage a different rate may be chosen.

The duration of sedimentation for each lithology can be computed, because the sedimentation rates are now fixed and the total duration of the stage is known. Perrier and Quiblier (1974) pointed out that the solid height of a slice varies within a basin (one well to another); however, its boundaries remain synchronous across the basin. Depths are then assigned to the boundaries in each well by constructing a graph of porosity versus depth of each stage (Fig. 2-12). The area in the graph between the (1 - ~b)~h curve and z-axis and the stage boundaries is divided into nsh slices of equal areas, which are equal to (Ahs)sh. The limits of these surfaces determine the depths of slice boundaries (Perrier and Quiblier, 1974, p. 509).

The initial thickness of a slice can be obtained from a porosity-depth curve for the first few meters of recently deposited sediment of identical composition and depositional environment. Compactional history of a sedimentary column, stage, or slice can be calculated by interpolating between the computed first steps of compaction of a slice and its present-day thickness (Fig. 2-13).

C O M P A C T I O N O F A R G I L L A C E O U S S E D I M E N T S

THICKNESS(m) I 0 , I .T t 7 ' 1 , ! , ! �9 T " I ~ " t " I : - !

81

5

! L ~ 4-- In i t ia l th ickness

I Calculated first St~l~

........... !n~,~t~i~

Present th ickness

- - . Present timq

i J l ' : i . ' , 1 1 1 1 ~ t ~ I 1 , |

10 5 IO s 101' I 0 II

TIME (years}

Fig. 2-13. Interpolation between the computed first steps of compaction of a slice and its present thickness. (After Perrier and Quiblier, p. 510, fig. 4 B Courtesy of American Association of Petroleum Geologists.)

Main drawback to this first approach by Perrier and Quiblier (1974) is that initial porosity values are not readily available for each lithologic type. Compressibility data for clays is presented at the end of this chapter.

Perrier and Quiblier's second method is known as the "average-porosity-curve" method. This approach employs an average-porosity curve such as those shown in Fig. 2-9. Assumption is made that a general law of compaction is valid for an area, independent of the age of the sediments. By using an average curve over the desired interval it is possible to compute the solid height of surface layer by solving Eq. 2-64 having the limits of 0 to Zmax. Then the top of the layer is set at successive burial values zl, Z2, Z3, . . . , Zmax. The integral equation is solved for each layer by keeping

~ ' which determine the layer's lower boundary and constant and setting limits Zl, z 2, z 3, its actual thickness (Fig. 2-14).

Perrier and Quiblier (1974) expressed the results as a decompaction number. Their results showed that thick shale layers are not reduced by compaction as much as the thin layers. The deformation of fossils and small sedimentary features occur in the thin layer range. Various nomographs can be constructed using Perrier and Quiblier's method and Baldwin and Butler's approach to readily provide compaction data. The reader can further evaluate these methods by reading the authors' original publications.


Fig. 2-14. Principle of decompaction calculation from an average porosity versus burial depth curve. (After Perrier and Quiblier, 1974, p. 514, fig. 9 - - Courtesy of American Association of Petroleum Geologists.)

Bonham's (1980) simulator accepts structural tops, unit thicknesses, lithologic compositions and sediment porosity values as they are present. In this model the individual units are peeled off the top, one at a time, to restore the geology suc- cessively to earlier time (Bonham, 1980). Porosity values are determined not from average porosity versus depth curves but one that considers "inhibited compaction" (Fig. 2-15). The two models of Perrier and Quiblier are forward looking, whereas Bonham's model is a retrodiction simulator.

F L O W OF FLUIDS T H R O U G H A R G I L L A C E O U S M E D I A

Bear et al. (1968) defined a porous medium as a space occupied by multiphase matter in which one or more of the phases is not solid. The solid phase is termed the solid matrix and the space within the porous medium, which is not a part of the solid matrix, is referred to as the pore space. The solid matrix has to be distributed throughout the porous medium within the domain occupied by the porous medium. The majority of the pores should be interconnected if fluid flow is to occur; however, unconnected pores can be considered as a part of the solid matrix.


5,000 k - u , l

i l v - r

I - -

w

10,000

15,000

POROSITY (%) 3 5 10 20 30 40 50

1 1 1 I . I I

- COMPACTION'" ~ ' _,'~'/

to_: GEoP.Essu.E zo~E4:.'.4__ . . . . . . .:.

. ~_" ALTER-I �9 z'~" ATION |

�9 "/." 'ZONE

::/ Fig. 2-15. Bonham's model of inhibited compaction showing porosity history and burial pathway curves for Gulf Coast U.S.A. shales. (After Bonham, 1980, p. 555, fig. 8 - - Courtesy of American Association of Petroleum Geologists.)

Henry Darcy investigated the steady flow of water in vertical homogeneous sand filters in 1856. From these investigations, Darcy concluded that the volumetric rate of flow, q, can be expressed as:

q = K a ( h l - h z ) / L (2-65)

where K is the coefficient of proportionality; A is the cross-sectional area; and hi - h2 is the difference in piezometric head across the filter of length L. Equation 2-65 has been modified into a general form that considers the viscosity, /z, of any fluid flowing in a nondeforming porous medium:

k A A p q - (2-66)

L/x

where q is in cm3/s; permeability k is in D; A is in cm2; differential pressure Ap is in atm; L is in cm; and /x is in cE Various extensions of Darcy's law have been discussed in the classical work of Bear (1972).

The potential, ~, governing the fluid flow is defined by:

P

* = g ( z - zo) + (2-67) Pf

P0

where g is the acceleration due to gravity; z is the elevation above the arbitrarily selected datum z0; z0 is the elevation of the point where �9 = 0; P0 is the pressure at the point where z = z0 (~ = 0); and pf is the density of the fluid.


The velocity of fluid flow can then be generalized as the macroscopic flow velocity, Vma (Hubbert, 1940):

Vma "-- -- ) V* (2 -68)

The macroscopic velocity, however, is not the true velocity of the liquid at any particular point. Bear (1972) pointed out that the complexity of the geometry of the porous medium precludes the use of the true velocity of the migrating fluid at any particular point. A statistically averaged microscopic velocity, Vmi, however, can be determined if the average porosity, ~b, of the formation is known:

_ Vmi = ik ~ -~ , ] V(I) (2 -69 )

The microscopic and macroscopic velocity concepts presented above are valid in a stationary coordinate system. Hubbert (1940) discussed these relationships for nondeformable media in detail and the reader is referred to his work.

Equation 2-69 does not reveal that a porous medium undergoing compaction is compressible and that there is a relative motion of the solid particles in the system. Darcy's law supposes that the fluid velocity is measured with respect to a fixed coordinate system outside the solid matrix, and that the matrix does not move or distort. Only under these conditions would Eq. 2-68 give a correct answer. Thus, this equation must be generalized, because Darcy's law applies to flow relative to the solid matrix only:

Vma,r -- ) VcI) (2-70)

where Vma,r is the macroscopic velocity relative to the motion of the solid particles. The value of the calculated permeability would be meaningless if the flow velocity is not measured relative to the solid matrix. Raghavan (1974) discussed this problem in detail.

The differential equation governing the transient three-dimensional flow of water in an elastic aquifer was derived by Jacob (1940, 1950). De Wiest (1966) questioned the validity of Jacob's derivations (see Eq. 2-75) based on the fact that on one side of the equation the net inward mass flux was calculated for a volume element without deformation, whereas on the other side of the equation, in order to compute the rate of change of the mass inside the volume element, the element itself was deformed. The solution by De Wiest (1966) did not distinguish between the rate of flow relative to the moving grains of the medium and the rate of flow across the fixed boundaries of the control volume as long as the material was being deformed:

6h S* 6h (2-71) V2h - 2pg~ 3z K 3t

where specific storage S* = pg[(1 - ~b)ot + ~bfl] and has dimensions of l/L; p is the fluid density (M/L3); fl is the compressibility of the liquid (LTZ/M); g is the gravity


field strength (L/T2); h = z 4- 1/g fpP dp/p(p) , i.e., head above common datum (L); z is the fixed spatial coordinate (L); t is the time (T); oe is the compressibility of the medium (LT2/M); and 05 is the fractional porosity of the medium (dimensionless).

Cooper (1966) pointed out that the first one of these two flows obeys Darcy's law, whereas the second one does not. Cooper (1966) derived two different forms of the flow equation for a compressible liquid in an elastic porous medium by considering mass conservation in: (1) a control volume, the boundaries of which are fixed in space (Eulerian stationary coordinates); and (2) a control volume that deforms and moves through space (Lagrangian moving coordinates) when the material deforms:

V 2 h - 2 p g ~ h p g ( ~ ~h ) 3z -- K -~- -- tog (2-72)

in the case of fixed coordinates [Wg - vertical component of velocity of grains of medium (L/T)], and"

3h 3h Pg (or + dp13)--- (2-73) V' 2h - 2p~g 3z' - K 3t

in the case of deforming coordinates, K = fluid conductivity (L/T) and z' = deforming spatial coordinate (L). Usually, the second term in Eq. 2-73 is negligible and, therefore, the equation is very closely approximated by:

Vf 2 h __= Ss 3h K 6t (2-74)

where Ss = pg(ot + 4~/3). The latter equation (Eq. 2-74) shows that Jacob's expression (Eq. 2-75), for what is referred to in the terminology on groundwater hydrology as specific storage, is essentially correct for the use in deforming coordinates. In Jacob's equation:

82h SZh ~2h Ss ~h . . . . . (2-75) (~X 2 ] ~y2 -4 (~Z2 K 3t

where h is the potential head above a common datum; K is the fluid conductivity; t is the time; and Ss is the specific storage (see Rieke and Chilingarian, 1974, p. 144). Specific storage, S~, is the volume of water which a unit volume of the formation releases from storage under a unit head of decline. It is related to Theis' storage coefficient, S, which is dimensionless, as follows:

S = bSs (2-76)

where b is the thickness of the formation. As pointed out by Cooper (1966), aside from the advantage of eliminating the grain velocity from the flow equation, several other factors point in favor of deforming coordinates in the case of nonsteady flow in elastic media, e.g., it gives a somewhat closer approximation of Darcy's law if z' is used rather than z. Statistically speaking, a vertical streamline through the deforming elemental volume A x A y A z ' would traverse the same number of pores regardless of the deformation. Streamlines through the fixed element A x A y A z traverse a greater or lesser number of pores when the sediment deforms.

86 G.V. CHILINGARIAN, H.tt . RIEKE, III AND E.C. D O N A L D S O N

The vertical component of flow per unit area relative to grains of the medium, (w' = Kgh/3z'), therefore, is more nearly proportional to the head differential across Az' than to the one across a fixed element Az (Cooper, 1966, p. 4790). Thus, K is more nearly constant when Darcy's law is approximated in terms of the deforming coordinate z'.

Tortuosity in argillaceous sediments plays an important role in compaction, more so than in the coarser-grained clastics. An important question arises here as to whether Darcy's law is generally valid for fluid flow in saturated clays and clayey sediments or not. Two main criteria must be met for Darcy's equation to be valid for clays: (1) the interstitial fluid in the pores must exhibit Newtonian behavior; and (2) the clay particles must be arranged in a rigid manner so that forces due to fluid movements do not modify the pore geometry. A deforming coordinate system violates the second premise owing to the change in tortuosity by a mobile matrix. In addition, various electrokinetic forces become operative during the flow of water through the clayey sediments, because of the presence of fixed and mobile double layers, and invalidate Darcy's equation. The occurrence of phenomena such as osmosis, reverse osmosis, and filtration through clay membranes further complicates the picture.

Water influx from overlying, overpressured shales into producing reservoirs

Dzhevanshir et al. (1987) analyzed the possibility of pore water influx from overlying, undercompacted, overpressured shales into permeable hydrocarbon zones, situated lower in the stratigraphic sequence. The authors evaluated the variation of pore pressure with time in shales overlying the producing formation and estimated the volume of the water influx from shales. Fertl and Timko (1970b) showed a change in the pulsed neutron logging index of clay caprocks as the result of porosity reduction in a south Louisiana well having high formation pressures. This observation was interpreted by them as a decrease in pore pressure owing to pore fluid expulsion to the underlying productive zones. Additional investigations by Kuz'min et al. (1975) and Yusufzade et al. (1978) in the oil fields of southwestern Turk- menistan and Baku Archipelago contributed information on an uninvaded resistivity in argillaceous zones lying above the producing zones.

Figure 2-16 illustrates the pore fluid displacement from an elementary volume of as shale during the process of producing a reservoir. The shale with the initial pore pressure of pp overlies the reservoir with an initial formation pressure of pf. The material balance equation or/-block of the elementary volume can be expressed as:

[t i wi t l O i , i - 1 - Oi+l,i "-" ~ Bwi to - Bwi t (2-77)

where Qi,i-1 = the volume of water, displaced from/-block to (i - 1)-block for the period At; Qi- l , i = the volume of water influx to the/-block from (i + 1)-block for the period At; 1,1, = the volume of/-block; At = t - to = filtration period; to, t = moments of time; ~ i " - i-block clay porosity at times to and t; Swi - - /-block water

COMPACTION OF A R G I L L A C E O U S SEDIMENTS 87

saturation in clay at time to and t; Bwi = i th block formation volume factor of water at times to and t (= ratio of volume under reservoir conditions to volume under standard conditions).

Dzhevanshir et al. (1987) used Darcy's equation (Eq. 2-66) to calculate Qi,i-1 and Qi+l,i. During filtration, water is thought to acquire the non-Newtonian fluid properties in clay rocks. R.D. Dzhevanshir (personal communication, 1987), however, questioned the justification of using Darcy's law in studying the filtration of water through clay sections, owing to the very low speed of water filtration in laboratory compaction experiments and a number of laboratory testing difficulties.

The theoretical analysis of the initial pressure gradient in the clay caprocks by Dobrynin and Serebryakov (1978) allowed Dzhevanshir et al. (1987) to propose that the pressure gradient in large pores of clay rocks under downhole conditions is considerably lower than the hydrodynamic pressure gradient typical for abnormally high formation pressure areas. The abnormal water viscosity in microcapillaries is not exhibited in the high-pressure areas having temperatures above 65-70~ Magara (1971) and Dobrynin and Serebryakov (1978) concluded that Darcy's law can be applied to water filtration in clay caprocks. The writers disagree with them based on extensive experimental work and field data (Rieke and Chilingarian, 1974; Fertl, 1976) m during compaction of argillaceous sediments, water is simply squeezed out (displaced) and Darcy's law should not be used.

Taking into account the Darcy's formula, the left part of Eq. 2-77 may be written as follows:

k i - l , i A 1 ki,i+lA 1 - - (Pi - Pi-1) - Li-l,i BwilZi Li,i+l Bw,i+l ~ ~ ( P i + I - - Pi)

gi [(ff/)iSwi) (~)iSwi) 1 A t BW) to -- Bwi t

(2-78)

where ki-l,i,ki,i+l - - permeabilities in the intervals (i - 1, i) and (i, i + 1), respectively; A --- filtration surface area; Li-a,i,Li,i+l = the length of filtration between blocks i - 1 and i, and i and i + 1; pi ,p i - l ,p i+a - pore pressures in/-block, (i - 1)- block, and (i + 1)-block, respectively; Bi,Bi+l = formation volume factors of water in/-block and (i + 1)-block, respectively; and l z i , l Z i + a - " water viscosity in/-block and (i + 1)-block, respectively.

Dzhevanshir et al. (1987) calculated the values of qS, k, and Bw depending on pressure, using the following equations:

qbi "~" qbo(1 - cpApi ) (2-79)

ki "~ ko(1 -/3k Api ) (2-80)

Bwi ~ Bwo(1- cwApi ) (2-81)

w h e r e Cp, Cw = compressibility of pores and water, respectively; and/3k = coefficient characterizing degree of permeability change.

TABLE 2-IV

Volume of water displaced from overlying shales into producing reservoir formations (after Dzhevanshir et al., 1987, p. 82, table 1; Courtesy of Energv Sources)

Depth of Initial calculation data on water influx from clays into reservoir The volume of water displaced from clays productive into reservoir, per unit of filtration surface

Reservoir Porosity Pore pressure, Formation Permeability, horizon (m) thickness, (%I in shales, pp pressure k (pm/m2)

area in lo-) m3/m2, after certain exploi-

h (m) (mPa) (mPa) tation period in years

Apsheron Peninsula and Apsheron Archipelago 2000 50 12.0 24.4 23.2 3000 40 7.5 37.5 32.4 4000 30 5.0 48.0 40.0 5000 20 3.0 55.0 49.0

Southweslern part of Apsheron Peninsula and the northern part of Baku Archipelago 2000 250 15.0 27.4 24.8 3000 235 12.0 43.8 35.7 4000 185 9.5 59.6 46.4 5000 150 8.0 74.0 58.0

Southern part of Baku Archipelago and Kura Depression 2000 900 21.0 33.4 27.0 3000 725 18.0 53.7 41.1 4000 460 16.0 74.8 56.0 5000 350 13.0 96.5 71.0


The system of equations representing the change in pore water volume in each block for period At can be obtained if the formation pressure in the reservoir at the shale-reservoir boundary is equal to pl and is lower than the initial pore pressure in the shale, clay or caprock:

kl,2A 1 k2,3A 1 (P2 -- Pl) x ~ (P3 -- P2)

L1,2 Bw2tz2 L2,3 Bw3,3

At Bw2 dt)2Sw2 ) I k2,3A 1

Bw2 t L2,3 Bw31~3 (P3 -- P2)

k3,4A ~ 1 V3 I ( q ~ 3 S w 3 ) ( q ~ 3 S w 3 ) L3,4 Bw4ll~4 (P4 - P3) = x At Bw3 to Bw3

(2-82)

Substituting for the general expression, one obtains:

Ln-l,n Bwn~n (Pn Pn-1) = - ~ Bwn to Bwn t (2-83)

The value of pl is assigned in the above system, whereas p2, p 3 , . . . , Pn are determined. As in Sharp's model, the values for the other parameters are either known, assigned or may be calculated by using Eqs. 2-79, 2-80, and 2-81. Dobrynin and Serebryakov (1978) suggested that the pore pressures in clay caprocks can be estimated with adequate accuracy by application of geophysical methods.

Dzhevanshir et al. (1987) treated the above model for three oil fields in the northwestern part of the South Caspian Depression (Table 2-IV). The authors assumed: (1) a fractional clay water saturation of 1; (2) formation volume factor of water and its viscosity in the caprock to be equal to i and i mPa s, respectively, in the first approximation. The pore water volume infiltrated to the reservoir during the period At is determined after calculating pore pressure distribution in the caprocks at time t. Permeability was assumed to decline to an end value of 20% of the initial value by the end of reservoir exploitation. Compressibility of the shale was taken as 10 -9 Pa -1, with the filtration surface area unit of 1 m 2. Productive life of each reservoir was assumed to be about 20 years, with the decline in reservoir pressure, pf, assumed to be a constant. It is possible to determine the pressure distribution in the caprock seal and the volume of displaced water into the underlying reservoir, upon production from the reservoir.

The three oil fields differ in: (1) magnitude of abnormal formation pressures; (2) the relative thickness of shales; and (3) the depth of productive horizons. The analysis in Table 2-IV shows that the maximum pore pressure decline in a clay section at the boundary with the reservoir may reach 20 MPa after 20 years. The pore pressure in the shale sequence is reduced considerably in a zone adjoining the reservoir and not exceeding 6-20% of the total shale thickness. Dzhevanshir et al. (1987) pointed out that with increasing shale thickness, lower is the relative and greater is the total thickness of the shale that takes part in the process of pore pressure decline. This confirms the information on the alteration of physical


I ~ h ~1

FILTRATION A

~' RECTION P'

I ~ " i ~ V l i ~ , ~ " 7 ~ " - - 1 ~ ~ I - " " ~ I ~ " ~ i ~ - " ~ I - " " - I T M " "

Fig. 2-16. Dzhevanshir's schematic diagram of an elementary volume of a clay bed illustrating the manner in which the pore fluid displacement was modeled. (Dzhevanshir et al., 1987, p. 80, fig. 1 - - Courtesy of Energy Sources.)

properties of clay caprock seals at the boundary zones as reported by Fertl and Timko (1970b), Kuz'min et al. (1975), and Yusufzade et al. (1978).

Table 2-IV illustrates that a considerable amount of pore water can be expelled from the caprocks into the reservoir during production. Approximately 1.9 million m 3 of interstitial water was displaced from the clay caprock with an area of 200 ha after 20 years in the oilfield located in the southern part of Baku Archipelago and Kura Depression (Dzhevanshir et al., 1987).

Dzhevanshir et al.'s (1987) model (Fig. 2-16) can be used to show the expelled water as a percentage of reservoir volume for reservoirs having different effective thickness. In the case of a small effective thickness, he, the water influx from a clay section, Vcw, can be quite high (Fig. 2-17). The Vcw/Ve ratio (Vcw = volume of water squeezed out of clays; Ve = effective oil- and gas-saturated reservoir volume) for different recovery factors may vary from 6% to 48% if he = 5 m. Dzhevanshir et al. (1987) showed that the process under examination influences the oil recovery f a c t o r , Re, especially if the reservoir is in its depletion stage. The effective gas- and oil-saturated reservoir volume is a product of effective thickness, he; porosity, 4); oil- and gas-saturation factor, Sog; and reservoir oil recovery factor, Rf. The assumed values were 4) = 0.17; Sog = 0.7; and Re = 0.3, 0.5, and 1.0.

I00 I , ,

80

6 6o

0 4 8 12 16 20 EFFECTIVE RESERVOIR THICKNESS, he

Fig. 2-17. Relation between the ratio of the volume of water displaced from clays, Vcw, after 20 years to the effective oil- and gas-saturated reservoir volume, Ve, and effective formation thickness, he, for different recovery factors, Rf. (After Dzhevanshir et al., 1987, p. 84, fig. 3 - - Courtesy of Energy Sources. )


4 0 -

d

@ > 20 ]= o

0 0

I I

R f= 0 , 3 ~

~ ] ~ ~ 1 1 . 0

8 16

TIME, YEARS

Fig. 2-18. Relation between time (years) and the ratio of the volume of water squeezed out of clays, Vcw, to the effective oil- and gas-saturated volume of the reservoir, Ve, for different recovery factors with effective thickness of reservoir, he, being equal to 5 m. (After Dzhevanshir et al., 1987, p. 85, fig. 4 - - Courtesy of Energy Sources.)

Figure 2-18 shows that the intensity of water flow from clays into reservoirs diminishes with time. This can be explained by the formation of a low-permeability zone in the caprock adjacent to the boundary with the reservoir rock.

Subsidence of producing reservoirs

Prokopovich (1978) developed a genetic classification of the subsidence phenomena. It is based on the origin of the various types of subsidence. His classification scheme contains two major subdivisions ~ endogenic and exogenic subsidence (Fig. 2-19). Exogenic subsidence is related to processes that originate near the earth's surface, including human activity, such as the withdrawal of reservoir fluids. Endo- genic subsidence is related to processes that originate essentially within the earth's crust (Prokopovich, 1983). Naturally occurring subsidence can be further divided into subsidence related to folding, faulting, volcanism, continental drift, etc.

Evans (1983) classified subsidence based on the theory of consolidation. He subdivided subsidence according to (1) the one-dimensional Terzaghi theory, (2) pseudo-three-dimensional consolidation theory based upon the diffusion equation, and (3) the three-dimensional consolidation theory based upon the Biot equations (Gambolati and Freeze, 1973).

Subsidence-prone reservoirs normally consist of young sediments in monoton- ically subsiding basins which have not experienced significant unloadings in their geologic history. These reservoirs have not experienced historical matrix stresses greater than the present stresses and are in the early stages of diagenesis (Dusseault, 1983, p. 9). Geologically young, shallow, thick, laterally extensive, argillaceous, and uncemented reservoirs lacking diagenetic fabric and having high in situ porosities (greater than 39%) are excellent candidates for being subsidence prone. Reser- voir compaction resulting from fluid withdrawal results in the deformation of the


LAND SUBSIDENCE

EXOGENIC

REMOVAL OF SUPPORT

SUPPORT

INCREASE LOADING

FOLDING

FAULTING

INCREASE OF EFFECTIVE LOADING

INCREASE OF ACTUAL LOADING

ENDOGENIC ~ VOLCANISM

ONTNENTAL DRIFT

OTHERS

Fig. 2-19. Prokopovich's genetic classification of land subsidence. (After Prokopovich, 1983, p. 37, fig. 5.)

reservoir rock and its overlying formations and can be an important oil production mechanism. If the reservoir is deep and limited in areal extent, subsidence is likely to be small and distributed over a wide area (Dusseault, 1983).

The mechanical response of the formation to fluid withdrawal was studied by Thompson and Gray (1983). They concluded that reservoir rocks can show an appreciable time-dependent deformation within the time flame associated with fluid-producing operations. They observed this creep behavior in both the volumetric and deviatoric components of strain. The decrease in total compressibility of the rocks with increasing effective stress or with increasing strain has been demonstrated by several investigators in the laboratory (Rieke et al., 1969; Chilingar et al., 1983; Thompson and Gray, 1983).

Modeling of fluid withdrawal from an anisotropic compressible porous media should incorporate the following fundamental principles (Evans, 1983):

(1) Continuity equations for the solid rock matrix (or skeleton) and for the fluid phases in the pore spaces.

(2) An equation relating the viscous drag between the pore fluids and the solid matrix.

(3) The effective stress equation. (4) Constitutive equations for the particles in the rock matrix and for the pore

fluid phases. (5) Equations relating porosity, effective stress, time, and porous media perme-

ability. (6) An energy equation that accounts for energy transfers, as heat within the

porous media, between the rock matrix and the fluid phases.


(7) Equilibrium equation which relates the stress field in the rock matrix to the flow field of the fluid in the pore spaces.

These requirements are the same ones that have been applied previously to the solution of naturally occurring sediment compaction by Smith (1971a, b, 1977) and Sharp (1974, 1976). In the future modeling, both finite element and finite difference numerical schemes should be utilized to provide more accurate predictions of subsidence.

Evans (1983, p. 94) proposed a modeling approach for making reasonable first- order approximations of land subsidence and reservoir compaction predictions consisting of the following equations.

Continuity equations: (a) Rock matrix:

& (Psq~s) + V. (ps~bs'~,) = 0 (2-84)

(b) Fluid phase:

~t (Pf~) q- V . (pfqbVs) q- V . (Pf~Vfs) i q -- 0 (2-85)

where q~ is the porosity; p is the material density; v is the velocity; and q is production or injection term. The subscripts, f, s, and fs represent the fluid phase, solid phase, and the velocity of the fluid relative to the solid, respectively (Evans, 1983).

Effective stress equation:

P - Pc - Pf (2-86)

where p is the effective pressure; Pc is the reservoir confining pressure; and pf is the pore fluid pressure.

Porosity relationship: Assuming that the confining pressure is a constant, the change in porosity with time is expressed by Evans (1983) as:

d~b = ~ ( 1 -- ~)(Cf -- Cs)--ct--P----L (2-87)

dt dt

where cf and Cs are the isothermal compressibilities for the fluids and solid matrix, respectively.

Viscous drag equation: Darcy's law is used to describe the viscous drag between the pore fluid and the rock matrix:

K Vfs . . . . (Vpf -+- pfg) (2-88)

/zf


n

m

K is the permeability tensor which takes into account hydraulic anisotropy; ttf is the fluid viscosity; and g is the gravity vector (Evans, 1983).

Equations of state: Equations of state were specified by Evans (1983, p. 94) for the fluid phase and the rock matrix. In each case, the fluid or the matrix can be treated either as incompressible, slightly compressible, or fully compressible:

(a) Incompressible:

pf = constant, Ps = constant

(b) Slightly compressible:

(2-89)

pf = pofeCf(pf-Po s)

Ps = Pos ecs(ps-p~ (2-90)

(c) Fully compressible:

pf = f (p),

Ps = f (P) (2-91)

Equilibrium equations: The rock matrix velocity Vs is related to the displacement vector ~ according to"

V. ~s = ~ / ( V . ~) (2-92)

where V. ~ = E = volume dilation; and E = Exx + Eyy 4- Ezz. Exx, Eyy and Ezz are the principal strains of the incremental strain tensor E.

Evans(1983, p. 94) stated that for a linear elastic medium the incremental strain

tensor, Eij, the stress t e n s o r f f i j and the fluid pressure pf, are related according to the following equations as defined by Verruijt (1969):

-ffi.j" V ~-- V p f (2-93) m

-ff i.j "-- Ci j E i j (2-94)

where the Cij 'S a r e the coefficients of the anisotropic elastic rock matrix.

Energy equations: Energy equations take into account non-isothermal flow within the porous media:

(a) Solid energy equation:

dTs ps(1 - O)~vs dt - V. [(1 - O)/r - pfqbto (2-95)

(b) Fluid energy equation"


dTf I ~pf ] V. Vfs + pfCW (2-96) Pf~Cvf ~ = V-[~bkVTf] - ~Tf ~ f f p f

where T is temperature; ~v is the specific heat of the material at constant volume; ~: is the thermal conductivity of the material; and w is the energy added per unit mass of fluid owing to thermal sources. It refers to the heat added to the lower- temperature fluid by a hotter matrix (Evans, 1983). Both Eqs. 2-95 and 2-96 assume that the heat flux vectors can be expressed by Fouriers law of heat conduction. Kassay (1974) demonstrated that this can only be exact if the convective energy terms are zero.

Diffusion-limited model

Evans (1983, p. 95) made the following assumptions in order to derive a diffusion equation which governs subsidence:

(1)~ Isothermal fluid flow, matrix compaction, and only vertical subsidence, i.e., Vs . - ~ . - - ,

- - U z s l z ~ b/ = Hzs/z- (2) Incompressible matrix sand grains. (3) Slightly compressible fluid. (4) Isotropic linear elastic rock matrix.

~pf (5) >> Vpf

1 (6) V. ~-~-f (Vpf + pf~) >> 2pfcfgVpf + cfKVapf

Evans' assumptions eliminated Eqs. 2-95 and 2-96; therefore, by combining the other equations and simplifying he obtained:

[_ 1 Kf V. ~ ( V p f + pf~) + q = (Cs + ~bcf) ~p--~f (2-97)

]Zf &t

Assumptions (1) and (5) imply that

V. Vs = Cs Spf (2-98) ~t

Equation 2-97 can be solved for the fluid pressure, pf, and then Eq. 2-98 can be solved for the solid velocity ~. Once ~s is known, the subsidence displacement vector ~ can be determined from Eq. 2-92 (Evans, 1983). The above equations in Evans' model can be further generalized to multiphase flow with little difficulty.

Morita et al. (1988) developed a quick method to determine subsidence, compaction, and in situ stress induced by pore pressure changes. They conducted parameter study to find parameter groups controlling the in situ stress, subsidence, and compaction. These parameter groups are used to analyze the numerical calculation results generated by a 3-D, general, nonlinear, finite-element model. The model considers not only reservoir property data, but also caprock property data. The


authors stressed that caprock property data is important owing to the fact that many hydrocarbon reservoirs are thick, shallow, or their elastic moduli are significantly different from those of the confining formations (Morita et al., 1988).

Caprock properties may significantly affect the results. If a caprock is very tight, then it can partially support the compaction and decrease its amount. An assessment of the amount of compaction is important inasmuch as any abnormal compaction of the reservoir can increase the load upon casing creating a condition for casing failure. Morita et al. (1988) pointed out that many large reservoirs are very porous and the modulus ratio between the reservoir and surrounding rock often exceeds 20. The rigidity of the surrounding rock can significantly reduce the pore volume compressibility by supporting the weak reservoir. The thickness to areal extent ratio may exceed 0.2 owing to faults. This means that such reservoirs may deplete quickly during production (one-phase oil flow) above bubble point because the surrounding rigid rock prevents pore volume reduction.

Morita et al.'s (1988) investigation showed that owing to reservoir pressure depletion some of these reservoir's top surface subsides (as expected) and the bottom surface is slightly lifted up. The subsidence is proportional to reservoir compaction and is highly affected by the ratio of reservoir depth to its radius. Any prevention of the reservoir bottom surface uplift owing to a tight bottom caprock increases subsidence when the ratio of the moduli of rigidity of the reservoir rock to the caprock are in the range of 0.2-1 (Morita et al., 1988, p. 3). The reader should consult Morita for the mathematical equations governing this model. These authors' approach is similar to the one used by Evans (1983).

CHEMISTRY OF INTERSTITIAL FLUIDS

The chemical properties of interstitial fluids, associated with abnormally and normally pressured sediments, have been considered in a very few abnormal-pressure investigations (Rieke and Chilingarian, 1974). Most investigators have ignored the pore fluids associated with less permeable shales. One reason for this was that the permeability of shales is so low that the exposed shale intervals in oil wells rarely produce fluids in measurable quantities. In addition, the produced water for the most part is not representative of the interstitial fluid because of contamination. The concentration of the in situ fluids may be due to associated salt deposits, or contamination may occur during drilling and production of the oil well. Drilling fluids may cause dilution of interstitial fluids, and mixing of fluids from several different horizons is common. Hottman and Johnson (1965) attempted to determine the salinity of interstitial fluids using electric log calculations. Analysis of water-soluble constituents, leached or squeezed from shale and clay samples, was performed by Von Engelhardt and Gaida (1963), Hedberg (1967), Chilingarian and Rieke (1968), Weaver and Beck (1969), Long et al. (1970), Manheim and Sayles (1970), Schmidt (1973), Chilingar and Rieke (1976), Smith (1977), and Aoyagi et al. (1985).

One way in which data on interstitial fluids in shales can be obtained, is by core analysis. The pore solution can be flushed or distilled out of the core, permeability


permitting, or the core can be pulverized and then leached with distilled water in order to obtain the soluble salts. The latter technique, however, will not give the true composition of the salts dissolved in the pore solution, because any soluble minerals present in the rock will also be dissolved along with the salts. Von Engelhardt and Gaida (1963) leached interstitial salts from Jurassic claystone and shale core samples. They felt that analysis for the chloride content of the leached solution alone would be sufficient, because it is very likely that it would be derived from the pore fluid only. The proportions of calcium, magnesium and sodium ions may be changed by the base exchange of the clays. They also concluded that the chloride content in shale pore waters was of the same magnitude as that in the associated permeable strata, which is questioned by other investigators, as discussed later. Possibly, the formation-logging techniques (electric, radioactive, etc.) may be improved to such an extent in the future that the chemistry of fluids in shales could be determined directly without using leaching or other procedures.

Changes in concentration of interstitial fluids during the process of compaction, as reported by different investigators, are presented in this chapter and related to field data obtained from various sources. In order to obtain reliable new data concerning the composition of interstitial water in shales, Schmidt (1973) analyzed sidewall cores from a shale section of a well in Calcasieu Parish, Louisiana. These cores were analyzed to determine (1) the concentration of various cations and anions, (2) base-exchange capacity of clays, (3) exchangeable cations of clays, and (4) clay mineralogy. Additional information was provided by (1) electric logs from selected wells, (2) subsurface temperature and pressure measurements, (3) shale density measurements, and (4) analyses of produced water.

To date, the origin of sodium chloride solutions in rocks at depth is not well understood. Problems associated with the origin of subsurface fluids are still in an area of scientific controversy. Several explanations have been proposed for the generation of subsurface salinities, which commonly are greater than that of seawater. These include (1) ion filtration, (2) evaporation of water, (3) salt diffusion from nearby evaporate deposits, and (4) gravitational segregation (Dickey et al., 1968). In the presence of salt domes or salt beds, the high-salinity brines in the surrounding strata owe their origin in large measure to solution of the available salt. Formation waters with high salinity, however, also occur in sedimentary rocks which are not associated with salt deposits. It seems probable that under certain conditions gravitational compaction acts as the main mechanism producing concentrated salt solutions.

In geosynclines, where the depositional rate is rapid, large quantities of water are continuously extracted from the hydrosphere during sedimentation. Recent muds, for example, may contain up to about 80% (and higher) water by volume (Degens and Chilingar, 1967, p. 478). The interstitial fluids occupy the pore space of most of the buried sediments. Upon compaction of the sediments, the connate waters, as the interstitial fluids are sometimes termed, are expelled into the associated sandstones. The speed with which the water is expelled from the original argillaceous sediments depends not only on the overburden pressure and the physical and chemical properties of fluids, but also on the texture, structure, and mineral composition of the sediment (see Fig. 2-1).


The composition of fluids contained in the pore space of permeable sediments at depth is known from the many analyses of formation waters obtained from drillholes and producing oilwells. In many sedimentary basins the salinity of fluids increases with increasing depth, especially in the case of those fluids that are associated with basins older than the Tertiary. These fluids differ greatly from seawater in their chemical composition. All trapped fluids in the sediments are believed to have undergone chemical alteration, which is a function of time, temperature, and pressure. In studying these fluids, the basic assumption is made that the salinity and ionic composition of seawater, especially since Mesozoic times, was the same as today. The original water, expelled by compaction, has been gradually replaced by, or mingled with, meteoric water, especially if the sediments were uplifted or exposed at the earth's surface by tectonic activity or erosional processes. The majority of analyzed fluids from these sediments are derived from permeable strata.

Composition of interstitial solutions related to seawater

Interstitial solutions can be classified as (1) syngenetic (formed at the same time as the enclosing rocks), and (2) epigenetic (owing their origin to subsequent infiltration of meteoric and other waters into already formed rocks). The main processes which alter the chemistry of buried waters are: (1) physical (compaction); (2) chemical (reactions involving rock minerals, organic matter, and interstitial solutions, etc.); (3) physicochemical (filtration through charged-net clay membranes, adsorption and base exchange, etc.); (4) electrochemical; and (5) biochemical.

Degens et al. (1964) analyzed the oxygen isotope composition of a number of connate waters ranging in age from the Cambrian to the Tertiary, and reported that the 8180 values of the highly saline oilfield brines do not deviate appreciably from the 8180 of modern seawater (also see Degens and Chilingar, 1967). Deviation from the mean value in some of the samples into the negative range of 8180 are always well correlated to a decrease in salinity. This feature can be easily explained by effects of dilution with meteoric waters during the migration of brine, or by subsequent infiltration caused by a change in the geologic setting through uplift, denudation, and faulting. The similarity between the isotope characteristics of brines and modern seawater suggests that the concentration of inorganic salts has not been accomplished by syngenetic evaporation in most cases studied. Slight deviations into the positive range of 6180 values in some samples studied may have been caused by original evaporation in a surface environment, or by isotope equilibration with the surrounding mineral matter for millions of years (Degens and Epstein, 1962).

The concentration of amino acids in the oilfield brine waters is a function of salinity (Degens et al., 1964), i.e., the content of amino acids increases with increasing salt concentration. On adjusting the salinity of brine waters to that of present-day oceans and applying the same calculation factors to the original amino acid values, the similarity between the amino acid spectra in the Recent seawater and fossil brines is pronounced (Rieke and Chilingarian, 1974, p. 222, fig. 116).

There are systematic chemical differences (both qualitative and quantitative) between the ancient and modern connate waters. Magnesium, which is abundant in


seawater, is present only in minor amounts in oilfield waters and the opposite is true of calcium. Calcium chloride waters, which are not formed in surface environment, are widespread among oilfield brines. This feature can possibly be linked to the dolomitization process.

Magnesium may also replace various cations in chlorites and clay minerals. Ad- sorption and exchange phenomena may explain variations in K/Na and Ca/Na ratios in fossil and modern interstitial solutions; the former ratio also appears to be temperature dependent (White, 1965, p. 359). It should be remembered, however, that the significance of base exchange decreases with depth and, therefore, could not account for the formation of deeply-buried calcium chloride waters. Graf et al. (1966) noted that the calcium content of the Michigan Basin brines is vei'y high, is greater than that of sodium in some fluid samples, and increases proportionately with increase in total solids content. A definite relationship appears to exist between calcium and total solids content in oilfield brines of various geological ages (Figs. 2-20 and 2-21). Graf et al. (1966) felt that the more obvious geologic processes are inadequate as explanations of the origin of concentrated calcium chloride brines, which occur in geosynclines free of major orogeny. Two simple processes were pro-

Fig. 2-20. Relationship between calcium content and total solids in various oilfield waters (data from Rail and Wright, 1953; Wright et al., 1957; Hawkins et al., 1963a, b). Name of field, sampled interval and geologic age: 1 = E1 Dorado East, 2150-3172 ft (655-967 m), Upper Cretaceous; 2 = Tinsley, 4797- 5770 ft (1462-1759 m), Upper Cretaceous; 3 = Pistol Ridge, 7423-10,964 ft (2263-3342 m), Upper Cretaceous; 4 = St. Louis, 2610-3174 ft (796-967 m), Ordovician/Pennsylvanian; 5 = Bartlesville- Dewey, 1241-2557 ft (378-779 m), Cambrian/Pennsylvanian; 6 = Hall-Gurney, 2610-3293 ft (796-1004 m), Ordovician/Pennsylvanian; 7 = Wesson, 2132-3598 ft (650-1099 m), Lower Cretaceous/Upper Cretaceous; 8 = Soso, 6498-12,045 ft (1981-3671 m), Lower Cretaceous/Upper Cretaceous.

- - ! '

Co. g l l u 0

Fig. 2-21. Relationship between calcium and total solids content in various oilfield brines, each curve representing a different formation, except curve 3 (data from Rall and Wright, 1953; Wright et al., 1957; Gullikson et a,., 1961; Hawkins et al., 1963a, b, 1964; and Graf et al., 1966). 1 = Wilcox Formation, Eocene, Gulf Coast; 2 = Ste. Genevieve Limestone, Mississippian, Illinois Basin; 3a = Arbuckle Limestone, CambrianiOrdovician; 3b = Bartlesville

0 Sandstone, Pennsylvanian, Oklahoma; 4 = Sespe Formation, Oligocene, California; 5 = Pico Formation, Pliocene, California; 6 = Nacatoch Sandstone, z Cretaceous, Texas-Louisiana; 7 = seawater; 8 = laboratory data obtained by the writers during compaction experiments.

2 M

Z K I

240

220

I 1 7 I 1 I 1 I 1

- -

t . . //-- -

/- . . 200 -

Key :

A 1 0 2 0 30 0 3b

4 0 5 x 6 e 7 r 8

0 1 1 1 I I I I I I I I 1 I t I I

C 1 2 3 1 6 7 1 9 1 0 1 1 12 1 1 - 1 5 1 6 17 Id 1 9 Z Q


posed by Graf et al. (1966) for deriving such a composition: (1) shale ultrafiltration of the dissolved solids contained in the original seawater; and (2) mixing various proportions of fresh water and seawater.

Field data from various formations showing relationships between the Na/Ca ratio and the total solids are presented in Fig. 2-22. In this figure brines from

o . = .

2 0 0

180

1 6 0

140

~ : 1 2 0

d

. J 0 I 0 0 (,n

,.J

i - - o I ' - 8 0

6 0

40

: ) 0

�9 - i 1 , , - ' 1 . . . . v . . . . l ' ' ' ' l ' . ' ' l ' r ' ' l . . . . I ' ' ' I I ' ' ' ' I ' ' ' V l V V I V I ' ' I ' I ' I , ' I , , T ~

e

A

A 6 6

A

li

A li

v v

v

Key /,, 1 c 2 + 3 �9 4 7 5 o 6 x 7 �9 8 �9 9 e 10

0

0

% o=

0 V V

o o

, , . == x r . ~ x x x x o o

x

xx o + §

§

0 §

§ 4.

. , J h t l . . . . l J = = , l . . . . l . , . . l , , , . l ~ * * J l i i * * i , , ~ I t . i , l l l , i l i c J i l i J . , l i . , . l . , , .

0 I b ZO 3 0 4 0 5 0 6 0 7 0

N o / C o

Fig. 2-22. Relation between the Na/Ca weight ratio and total solids in oilfield brines. 1 = Bartlesville Sandstone, Pennsylvanian, Oklahoma; 2 = Nacatoch Formation, Upper Cretaceous, Texas-Louisiana; 3 = Pico Formation, Pliocene, California; 4 = Sespe Formation, Oligocene, California; 5 = Wilcox Formation, Eocene, Gulf Coast; 6 = Recent marine sediments (Siever et al., 1965); 7 = Wilmington oil field, California. (Data after Wright et al., 1957; Gullikson et al., 1961; Hawkins et al., 1963a, 1964.) 8 = seawater; 9 = river water; and 10 = Great Salt Lake (Bentor, 1961).


formations older than Pliocene lie generally parallel to the y-axis (total solids), whereas brines from younger formations or marine sediments lie more or less parallel to the x-axis (Na/Ca ratio). In some cases, there is a tendency for the Na/Ca ratio to increase with increasing total solids (generally older formations), whereas in others (generally younger formations) the reverse is true. It is of interest to note that the interstitial waters of the Sespe Formation have a closer affinity with the more "stabilized" brines than the interstitial waters from the younger Pico Formation; the stratigraphic distance between the Sespe and Pico formations in Ventura County, California, is approximately 20,000 ft (6096 m).

The distribution of C1- with depth may be affected by the proximity of salt, which should promote higher salt concentrations in pre fluids. For example, Manheim and Sayles (1970) observed marked increases in interstitial water salinity in two drill holes located in the Gulf of Mexico at a water depth of more than 3500 m. They attributed the increases of diffusion of salt from buried evaporites. In one hole, however, on penetrating the oil-permeated caprock of a salt dome, they encountered fresh water, which could have originated during oxidation of petroleum hydrocarbons and decomposition of gypsum giving rise to native sulfur.

Posokhov (1966) discussed in detail many of the factors which affect the chemical composition of underground waters: (1) physicogeographic; (2) geologic; (3) hydrogeologic; (4) biologic; (5) physical; and (6) physicochemical. Under physicochemical factors Posokhov discussed: (a) oxidation-reduction conditions of underground waters; (b) solubility of salts; (c) diffusion; (d) osmosis; (e) gravitational differentiation; (f) mixing of different waters; and (g) base exchange.

Changes in the chemistry of solutions squeezed out at different overburden pressures Most of the dissolved salts present in the interstitial fluids, which are trapped

during sedimentation, are squeezed out during the initial stages of compaction. Lab- oratory results (Kryukov, 1971) showed that mineralization of expelled solutions progressively decreases with increasing overburden pressure. These experimental results led researches to conclude that the concentrations of interstitial solutions in shales should be lower than those in associated sandstones (see Chilingar et al., 1969).

A corollary of this premise suggests that solutions squeezed out at the beginning of compaction should have higher concentration than the interstitial solutions initially present in argillaceous sediments.

Rieke et al. (1964) determined the percentage increase in the resistivity of expelled solutions from a marine mud with increasing overburden pressure. The mud was obtained from the Santa Cruz Basin, off the coast of southern California. Their results indicate that the mineralization of squeezed-out solutions decreases with pressure.

In some of the experiments conducted by Rieke et al. (1964), the percentage decrease in concentrations of the principal cations and anions with increasing pressure was about the same. Their results suggested that (1) the ions being removed represent interstitial electrolyte solutions and do not include the adsorbed cations, and (2) the analysis for a single ion in the effluent (for example, C1-) might reveal as much insight into the problem as the analysis for all of the ions.


The results of Kryukov and Zhuchkova (1963) demonstrated that the last portions of water (adsorbed?) squeezed out of sediments are poor in electrolytes (Figs. 2-23a, b). According to Manheim (1966), the threshold pressure for the chloride anion in 0.86N NaC1 solution was about 1410 kg/cm 3 (also for Na-bentonite), whereas for fresher waters the influence of pressure on composition was noted at lower pressure. (Threshold pressure is the compaction pressure at which the composition of squeezed-out interstitial solutions starts to change.) Kryukov and Zhuchkova (1963) pointed out that for ordinary sediments, the pressure threshold for influence on the composition of water is shifted to higher pressures. According to Chilingarian and Rieke (1968), the chemistry of squeezed-out solutions begins to change appreciably when the remaining moisture content is about 20-25% for kaolinite and about 50-70% for montmorillonite clay.

Kazintsev (1968, p. 186) observed in laboratory experiments a gradual decrease in chloride concentration on squeezing samples of Maykop clay (eastern Pre- Caucasus) having an initial moisture content of 20 and 25% (Fig. 2-24). The final moisture contents after compaction constituted 8.83 and 10.88%, respectively. He also determined the effect of temperature (heating to 80~ on the concentration of various ions in squeezed-out solutions (Fig. 2-25). The concentration of C1- and Na + decreases with increasing pressure, and temperature does not seem to have any appreciable effect. The Mg 2+ ion concentration increases (about 1.5 times) with increasing pressure, but the absolute values are lower at high temperatures than at low temperatures. The concentration of K + decreases with pressure. Concentrations of K +, Li +, and I- are higher in solutions expelled at higher temperatures, whereas that of SO 2- is lower.

Krasintseva and Korunova (1968, p. 191) studied the variations in chemistry of solutions expelled from unlithified marine muds from the Black Sea. At room temperature, the chlorine concentration definitely decreases with increasing pressure, whereas the concentrations of some components go through a maximum at pressure of 500-1000 kg/cm 3 (Fig. 2-26). The Br- and Br 3+ contents increase with increasing compaction pressure. Krasintseva and Korunova also presented the relationship between the concentration of various ions and compaction pressure at 80~ In- creasing temperature seems to decrease the amount of Mg 2+ cation in expelled solutions (Fig. 2-27).

Some investigators, however, disagree with the above-described findings. For example, the study by Manheim (1966), who used pressures ranging from 41 to 844 kg/ cm 2, indicates that pressure does not appreciably affect the composition of extracted waters. Shishkina (1968, p. 167), on investigating interstitial solutions in marine muds from the Atlantic and the Pacific oceans and from the Black Sea, did not observe any appreciable changes in the chemistry of squeezed-out solutions up to a pressure of 1260 kg/cm 2 in some samples and up to a pressure of 3000 kg/cm 2 in others. There was some increase in Ca 2+ concentration at a pressure range of 675-1080 kg/cm 2 and then there was a decrease at higher pressure. Shishkina (1968) stated that at compaction pressures, at which 80-85% of interstitial water is squeezed out, there are no changes in concentration. Obviously, the chemistry of the remaining 20-15% interstitial fluid is also of great interest, and should be determined in most studies.

G.V

. CH

ILIN

GA

RIA

N, H

.H. R

IEK

E, 111 A

ND

E.C

. DO

NA

LD

SON

I/&

'0)

I I

0

0

8 8

3 1/0

u

'ON

* 1

.. 0

C

llku

')I


Von Engelhardt and Gaida (1963) compacted pure montmorillonite and kaolinite clay muds saturated with solutions having different concentrations of NaC1 and CaC12 at different pressures ranging from 30 to 3200 atmospheres. Their results show that for a given clay, the equilibrium porosity which is reached at a distinct overburden pressure does not depend on electrolyte concentration. For pressures between 30 and 800 atmospheres, the concentration of electrolyte in pore fluids in montmorillonite clay diminishes with increasing compaction. This was explained by Von Engelhardt and Gaida (1963) as due to the electrochemical properties of base- exchanging clays. If the pore fluids contain an electrolyte, the liquid immediately surrounding the clay particle will contain less electrolyte than fluids further away from the double layer. Base-exchanging clays suspended in electrolyte solution adsorb a certain amount of pure water which is bound in double layers around each clay particle (Von Engelhardt and Gaida, 1963, p. 929). During compression, the electrolyte-rich solution is removed and the fluid of the double layers, poor in electrolyte content, is left behind. At higher overburden pressures (from 800 to 3200 atmospheres), an increase of salt concentration within the remaining pore water may be caused by the inclusion of small droplets of fluid in the highly compressed clay, acting as a barrier to movement of ions. The passage of anions through the double layer is retarded by the fixed negative surface charges on the clay particles. Ion blocking increases ion-exchange capacity and compression of clay. Apparently, ion blocking is greater for dilute solutions than for concentrated ones.

Chilingarian et al. (1973b) experimented with a sample of montmorillonite clay that was saturated in seawater for a period of seven days (the volume of seawater was in excess of that of clay solids). The sample was shaken vigorously twice a day. Then the supernatant liquid, which was assumed to have the same composition as the free interstitial water, was removed and analyzed. The remaining saturated sample was placed in a hydrostatic compaction apparatus and the successive portions of the expelled solutions were analyzed. The final remaining moisture content was equal to 62%, which corresponded to an overburden pressure of about 35 kg/cm 2. Table 2-V shows the variation in concentration of various ions. Variation in total dissolved solids in subsequent fractions of expelled solutions indicates that the concentrations of the solutions squeezed out at the initial stage of compaction are slightly higher than that of the interstitial solution initially present in montmoril-

Fig. 2-23. (a) Changes in composition of solutions squeezed out of kaolinite clay. 1 = Na +" 2 = SO2-; 3 = C1-; 4 = Ca2+; 5 = Mg 2+. (After Kryukov and Zhuchkova, 1963, p. 97.) (b) Changes in

out of bentonite. 1 = k • 10 , specific conductivity of solution; composition of solutions squeezed 4 2 = Na +" 3 = C1-; 4 = SO~-; 5 = Mg2+; 6 = Ca 2+. (After Kryukov and Zhuchkova, 1963, p. 38.) (c) Variation of K +, Na +, and Ca 2+ concentration in expelled pore fluid from the original Fuller's earth (mainly Ca-montmorillonite) saturated in distilled water with increasing effective axial pressure at 40~ (After Rosenbaum, 1976, fig. 3 m Courtesy of Clays and Clay Minerals, Pergamon Press.) (d) Variation of Mg 2+, CI-, and SO 2- concentrations in expelled pore fluid from the original Fuller's earth saturated in distilled water with increasing pressure at 40~ (After Rosenbaum, 1976, fig. 4 m Courtesy of Clays and Clay Minerals, Pergamon Press.)


6 0 0 I 1I llI ~/" V IZl

r 500

._

=' 4 0 0 o" m i

E 30O

!

U

20O

/

0 2 4 6 8 I0 12 14 16 i8 20 22

AMOUNT OF SQUEEZED-OUT SOLUTION, g Fig. 2-24. Variation in chlorine content in subsequent fractions (I-VII) of squeezed-out interstitial solutions of Maykop clay, eastern Pre-Caucasus. (After Kazintsev, 1968, p. 186, fig. 1.) I = depth of 42 m, Divnoe area; 2 = depth of 158 m, Divnoe area, Russia.

TABLE 2-V

Variation in concentration of various components in solutions expelled from montmorillonite clay saturated with seawater (after Chilingarian et al., 1973b)

Ion Concentration (mg/1)

seawater super- expelled solutions: natant

fraction no. I II III IV V fluid

cumulative volume (cm 3) 16.5 25.5 34.5 49.5 59.0

Ca 2+ 690 560 Mg 2+ 1189 572 Na + 10,116 13,400 K + 400 210 HCO~ 520 165 SO]- 2759 4610 CI- 18,929 19,310 F - 3 20 N O ; 34 3 CaCO3 6612 3,750 Fe 2+ - 24 Mn 2+ - 5 SiO2 43 15 B 3+ 4 14 Total dis-

solved solids 34,423 38,804

460 560 580 620 560 644 557 669 657 754

13,300 13,200 13,400 13,200 12,800 226 216 206 206 160 262 165 189 165 128

5350 5840 5270 4610 5180 19,030 19,200 19,170 19,170 18,990

20 20 <20 <20 40 0 0 0.5 0 0

3800 4100 4200 4250 4500 36 56 28 28 64

<5 <5 <5 <5 <5 5 0 5 10 20

21 14 17 4 0

39,216 39,844 39,433 38,576 38,611

lonite clay saturated in seawater. Concentrations of expelled solutions, therefore, go through a maximum (peak), or at least remain constant, before starting to decrease with increasing overburden pressure.

In another experiment performed by Chilingar and Rieke (1976) a sample of clay consisting of 50% smectite (montmorillonite) and 50% illite was saturated in

Fig. 2-25. Changes in concentration of anions, cations and microcomponents with increasing compaction in subsequent fractions ( I -VII ) of extruded interstitial solutions. Maykop clay, depth of 158 m, Divnoe area, eastern Pre-Caucasus. (After Kazintsev, 1968, p. 188, fig. 2.) Solid curves = room temperatures; dashed curves = heated to 80°C. The amount of extruded solutions in grams is plotted on the abscissa.


300- 50-

E 2 5 -

5 0 - I0 -

ol

4 -

%

+,t," ,?, o,

0 0q t,,

I im'

0 (J -1- I

(..)

C I - ~

~~ \ \ \ \ \ -~2oo E25. 5- 0 " flD

so ; Mg,+ HCO~

I00 0 - O" O- " - ' - - 0 500 IO00 1500

COMPACTION P R E S S U R E ~ k g / c m 9

Fig. 2-26. Relationship between concentration of various ions in interstitial solutions squeezed out of marine mud and compaction pressure at room temperature. (After Krasintseva and Korunova, 1968, p. 195, fig. 2.)

seawater, having a salinity of 35,500 mg/1, for 10 days. The sample was shaken vigorously several times a day. The supernatant liquid was removed and analyzed (TDS = 37,900 ppm). The higher salinity of the equilibrated liquid as compared to that of the initial seawater is possibly due to the presence of soluble salts in the test clay sample. It was assumed by the authors that the supernatant liquid has the same composition as the free interstitial water. The remaining saturated sample was placed in a hydrostatic compaction unit (described in Sawabini et al., 1971), squeezed and the successive portions of the expelled solutions were chemically analyzed. Figures 2-28 and 2-29 show the concentrations of Ca 2+, Mg 2+, and e l - ions in subsequent fractions of squeezed-out solutions. Total dissolved solids versus the cumulative volume of expelled solution is presented in Fig. 2-30. Results indicate that the total concentration of expelled solutions goes through a maximum before starting to decrease with increasing overburden pressure. The concentrations of Ca 2+, and Mg 2+ ions in squeezed-out solutions, however, start to increase again during the latest stages of compaction. This can possibly be attributed to their higher concentration in the water in close vicinity to the clay platelets. The final porosity of the sample tested, at a compaction pressure of 40,000 psi, was equal to 14.8%.

Effect of compaction on the pore fluid chemistry of montmorillonite was also investigated by Rosenbaum (1976). The pore fluids were analyzed for their concentration of K +, Na +, Ca 2+, Mg 2+, SO 2+, and C1- ions which originated from


300-

ZOO- U

100-

50-

"I 0

C t " - - - - ~

B r ' ~ :

C I / B r . . . . : : : : . . . . . . . :

SOg" ~ , ,

M g + * _ _ _

o 25o 500 75o

COMPACTION PRESSURE, kg/cm =

Fig. 2-27. Variation in concentration of various ions in interstitial solutions expelled from marine mud with increasing pressure at 80~ (After Krasintseva and Korunova, 1968, p. 196, fig. 3.)

the original Fuller's earth testing material (mainly Ca-montmorillonite) saturated in distilled water. The initial concentration of all the analyzed ions decreased rapidly with increasing stress (up to 350 kg/cm 2) during the initial loading. Thereafter, the rate of decrease declined markedly (see Fig. 2-23).

Overpressured and well-compacted shale samples and associated sandstone cores also were obtained from various parts of the world and analyzed only for chlorine content (Chilingar and Rieke, 1976). Each shale sample was first divided into two almost equal parts. The volume of interstitial fluid present in the sample was determined by drying one portion of the sample at 105~ The soluble salts were determined by washing them out four times with distilled water from a finely crushed second portion of the sample. After analyzing the washed-out solution, the C1- content of interstitial water was calculated, correcting for dilution effects.

During leaching, any soluble minerals present in the rock will be dissolved along with the salts. In addition, part of the cations (e.g., Na +, Ca 2+, Mg 2+) on the clays may also go into solution. Consequently, the writers believe that analysis for chlorine alone is more significant than analysis for all other ions, because most likely it is derived mostly from the pore fluids. It should be pointed, however, that many clays and shales have a significant anion exchange (on positively charged edges)


' ' ~ ~ ~ r / ,,, w I I I '"1

600

Ca

0 I i I 1

0 20 40 60 80

0.

U 400

Z w

200 ~o

I I i _. I

CUMULATIVE VOLUME OF EXPELLED SOLUTION,ML I00

Fig. 2-28. Variation in concentrations of Mg 2+ and Ca 2+ with increasing compaction pressure in subsequent fractions of expelled solutions from illite plus montmorillonite clay mixture (50-50) saturated with seawater. (After Chilingar and Rieke, 1976, p. 675, fig. 1 -- Courtesy of Applied Publishing Corporation.)

which would give rise to analytical uncertainties (R. Torrence Martin, personal communication, 1975).

Table 2-VI presents results which indicated that water in shales is fresher than that in associated sandstones (Chilingar and Rieke, 1976, p. 676). In addition, water in well-compacted shales is fresher than in the associated, undercompacted shales (mineralogically similar and at about the same depth).

As discussed before, according to many investigators, the salinity of squeezed- out solutions progressively decreases with increasing overburden pressure. Conse- quently, the salinity of interstitial solutions in shales is possibly less than that of waters in associated sandstones, because practically all of the interstitial fluids were expelled in many of the laboratory experiments. It has been also observed that during production of crude oil from sandstones, surrounded by thick shale sequences, the salinity of produced water gradually decreases with time, possibly owing to the influx of fresher water from the associated shales.

The mineralization of solutions moving upward through a thick shale sequence as a result of compaction probably will progressively increase in salinity. It should


=E 11. O.

I m

u. 0

2o,000

Z

O .=.

E),O00 ==

t a

o u

I I i I I I I I i - -

I I I I I i 1 I J 0 2 0 4 0 6 0 8 0 I 0 0

C U M U L A T I V E VOLUME OF E X P E L L E D SOLUTION, M L .

Fig. 2-29. Variation in concentration of C1- anion with increasing compaction pressure in subsequent fractions of expelled solutions from illite plus montmorillonite mixture (50-50) saturated in seawater. (After Chilingar and Rieke, 1976, p. 676, fig. 2 - - Courtesy of Applied Publishing Corporation.)

TABLE 2-VI

Chlorinity of interstitial solutions in associated undercompacted and well-compacted shales and sandstones in the presence of overpressures (after Chilingar and Rieke, 1976, p. 676, table 1" courtesy of Applied Publ. Co.)

Number of Depth Chlorinity (mg/1)

samples (ft) Well-compacted Undercompacted Associated tested shales shales sandstones

3/3/3 2000- 3000 3000- 4000 8000-20,000 70,000- 80,000 4/2/2 3000- 4000 2000- 3000 10,000-30,000 70,000- 90,000 3/3/2 4000- 5000 1600- 3500 10,000-40,000 75,000- 90,000 2/2/3 5000- 6000 1500- 3500 9000-35,000 60,000-200,000 6/2/3 6000- 7000 3000- 6000 8000-10,000 70,000-130,000 3/3/4 7000- 8000 4000- 8000 5000- 9000 90,000-135,000 3/4 8000- 9000 10,000-20,000 - 90,000-100,000 4/3/4 10,000-11,000 2000- 3000 10,000-14,000 15,000- 70,000 5/3/2 11,000-12,000 2000- 3000 8000-14,000 13,000- 17,000 7/3/4 12,000-13,000 1500- 3000 8000-14,000 11,000- 30,000 2/2/2 13,000-14,000 2500- 4500 10,000-14,000 11,000- 50,000 2/4 14,000-15,000 10,000-14,000 - 90,000-120,000

be remembered, however, that if water from a sandstone bed moves through a shale layer into another sandstone bed, the water in the latter bed may be less mineralized because of filtration through a charged-net membrane.


5 0 , 0 0 0

4 0 , 0 0 0

0

d a 3 0 , 0 0 0 W

Q

2o, o0o

I0,000 - ! , i I I I I I , | 0 ~0 4 0 6 0 8 0 I00

CUI~JLATIVE VOLUME OF E X P E L L E D SOUJTION, ML.

Fig. 2-30. Variation in total dissolved solids content with increasing compaction pressure in subsequent fractions of extruded solutions from illite plus montmorillonite mixture (50-50) saturated in seawater. (After Chilingar and Rieke, 1976, p. 677, fig. 3 m Courtesy of Applied Publishing Corporation.)

Overton and Timko (1969) studied the chemistry of interstitial solutions in the subsurface formations (sands and shales) of the Gulf Coast area. Figures 2-31 and 2-32, which are based on their data, show on semilog paper the relationship between (1) pore water salinity in sandstones and depth; and (2) porosity of shale and depth. Overton and Timko calculated the pore water salinity from an SP log, assuming that the salinity in sandstones was in equilibrium with that in the nearby shales. Figures 2-31 and 2-32 suggest that in the normally compacted zones the shale porosity and pore water salinity are inversely related. In these examples, the normally compacted zones are the intervals above a depth of about 9000 ft (2743 m). Overton and Timko (1969) stated: "as the shale is compressed to one-half its original pore fraction, the water is pressed out, leaving salt behind to concentrate itself by a factor of two". W.H. Fertl (personal communication, 1974), however, observed that in many instances undercompacted shales contain more saline water than comparable well- compacted ones (also see Rieke and Chilingarian, 1974, p. 25).


Water sa l in i ty , ppm 2 4 G ~5105

0-~ Seawater

o Z,

~2 --f,.

14 -~,

,.,~t~.

L ~ ) I F ~ : J

j , ~ j r , i~r.1.3,~i ~'~f.- I I l

ZI "I

l i t ~ I i I t l l 0.1 0.2 0.4 07

z~ 9,g/cc

Fig. 2-31. Pore water salinity versus depth and shale porosity versus depth relationships in a Gulf Coast well. (After Overton and Timko, 1969, p. 116, fig. 2.) Ap = 2.55--Psh, where 2.55 is the matrix density in g/cm 3 and Psh is the shale density. Shale porosity ~bsh is equal to (2.55--Psh)/1.5, inasmuch as water density, Pw, can be assumed to be equal to 1. Values of 11.2, 12.3, and 13.7 lb/gal indicate specific weight of drilling fluid ("mud") used in drilling. Location: Terrebonne Parish, Ship Shoal area, Gulf Coast, U.S.A.

~- 4 0 0 o G t -

s

10

12

Water sa l i n i t y , ppm NaCI 9

JO 4 2 3 4 5 G78[105

I \ p ~

"5 oi

0)'

Clean a

14 C 0.1 0.~ 0.3 0.5 0.7

ZXg,g/cc

Fig. 2-32. Pore water salinity versus depth and shale porosity versus depth relationships in a Gulf Coast well. (After Overton and Timko, 1969, p. 116, fig. 3.) Ap = 2.55--psh, (see for explanation Fig. 2-31); C = compaction coefficient in psi -] . Location: Grand Isle area, Gulf Coast, U.S.A.

Magara (1974, p. 283) stated that the salinity distribution in shales should be a reciprocal of the porosity, due to the ion-filtration effect of the clays, and that the salinity in the shales should tend to increase towards the sand beds, because


of the higher porosity of the central zones of the clays undergoing compaction. These conclusions, however, do not seem to be substantiated by the laboratory experiments discussed above. In addition, as pointed out by Rieke and Chilingarian (1974, p. 234), a semipermeable membrane effect becomes operative only at a certain minimum void ratio, at some high overburden pressure, e.g., 11,000 psi (773 kg/cm2).

Salinity distribution in sandstones and associated shales

In 1947, De Sitter reported that the salinities of formation waters in sandstones varies from that of fresh water to ten times the salinity of seawater. The distribution of the salinities of interstitial waters present in young geosynclinal sediments along the U.S. Gulf Coast has been well documented by Timm and Maricelli (1953), Myers (1963), and Fowler (1968).

Timm and Maricelli (1953, p. 394) stated that high salinities up to 4.5 times that of normal seawater characterized the interstitial solutions in Miocene/Pliocene sediments, where the relative quantity of undercompacted shales is small. In Eocene/ Oligocene sediments, where the relative quantity of shale is large and the degree of compaction is high, interstitial solutions have salinities as low as one-half that of normal seawater. Figure 2-33 illustrates their concept that the formation waters in downdip, interfingering, marine sandstone members, which have proportionately less volume than the associated massive shales, have lower salinities than that of

Fig. 2-33. Idealized typical cross-section of some sands and shales in southwest Louisiana showing generalized salinity relationships. (Modified after Timm and Maricelli, 1953, pp. 396, 397, and 408 -- Courtesy of American Association of Petroleum Geologists.)


seawater. More massive sands updip have salinities greater than that of seawater, because of lack of influx of fresher waters from shales. Salinity was determined by using the following techniques: electrical resistivity, complete chemical analysis, and titration (see Gullikson et al., 1961). Calculations showed that all water samples, of which complete mineral analyses were made, are secondary saline according to the Palmer's system of water-analyses interpretation.

Myers (1963) stu,tied the chemical properties of formation waters, down to a depth of 12,400 ft (3780 m), in four producing oil wells in Matagorda County, Texas. Salinities of interstitial waters ranging from 5000 to 12,500 ppm were found below 10,000 ft (3048 m) in each of the four wells, as compared to salinities of about 70,000 ppm above this depth. Myers commented that in this deeper section, the proportion of massive shale is larger and the sands are near their downdip limits (become thinner). These results were in close accord with those of Timm and Maricelli (1953).

Some investigators, including Hottman and Johnson (1965), observed that the sands with abnormally high pore water pressures are associated with undercompacted shales having very high porosity. In an excellent paper, Dickey et al. (1968) observed that faults which transect oil reservoirs form pressure discontinuities and act as seals for zones of high fluid pressure for long periods of time. The high porosity of shales in such zones is reflected by the high values of conductivity. The depth marking the beginning of the abnormally high fluid pressures in the sandstones coincides with the abnormal increase in conductivity of associated undercompacted shales (Wallace, 1965; Williams et al., 1965). Yet, calculations by the writers indicate that possibly high porosity of shales alone could not account for this abnormal increase in conductivity; the salinity of interstitial waters also appears to be important.

Although the process of clay compaction is continuous until the complete (?) lithification of clays, the volume of expelled fluids into the reservoir rocks gradually decreases. Consequently, there is a gradual decrease in excessive pore water pressure in highly permeable horizons in deep parts of the basin until, finally, it becomes equal to the hydrostatic pressure. After that, theoretically the movement of waters occurs in the opposite direction, from the periphery of the basin (recharge area). The entire hydrodynamic system strives to attain equilibrium, which is controlled by the areal distribution and size of recharge and discharge areas.

The findings of Fowler (1968) for the Chocolate Bayou field, Brazoria County, Texas, seem to suggest to the writers that the salinity of water in undercompacted shales is higher than in well-compacted ones. He discovered a definite correlation between the high salinity of interstitial fluids in sandstones and abnormally high pressures. This is possibly owing to the fact that undercompacted shales did not have a chance to contribute their fresher water to the associated sandstones. In addition, he studied the variation in salinity of produced water with time. The typical pattern is one of decreasing salinity with time, and the freshest water is found in sands receiving most of this water from associated shales. This is in agreement with the experimental results of several investigators, as discussed earlier, which indicate that the salinity of waters in shales should be less than that in associated sands.


I - n UJ Q

9 9 4 0

9 9 6 0

9 9 8 0 -

I 0 , 000 -

CA)

I

I SHALE

I

z

SAND'

3600

3800

i

I

4-:

..~..~" 4 0 0 0 Q. i , i 1 :3

4200 -

4 4 0 0

(B) I I

: : .SHALE r

e - . . e . . . . , . , , . ". .e .,..

I~lam. RANGE IN ":.. S A N D i

f

I SHALE 10,020 I I I I I

I0 20 :50 40 30 50 70 90

CH LORINITY, p.p.rrq x I0 3 CHLORINITY, p.pm., x I0 3 Fig. 2-34. Chloride concentrations in shales and sands. (In: Fertl and Timko, 1970c, p. 15, fig. 4, based on data by Hedberg, 1967.)

The pore water salinities in shales and in associated sandstones are compared in Fig. 2-34. The examples include field case studies from the Middle East and Texas. Some data from offshore wells in Louisiana have been given by Fertl and Timko (1970c).

Schmidt's (1973) study showed that the compositions of interstitial water in shales and those in sandstones are different. Sidewall cores of shales, analyzed by him, were taken at intervals of every 500 ft (152 m) between depths of 3000 and 14,000 ft (914-4257 m) in a well in Calcasieu Parish, Louisiana. Abnormally high fluid pressures were encountered just below a depth of 10,000 ft (3048 m). He noted significant differences between the total dissolved solids concentrations in waters from the normally pressured sandstones (600-180,000 mg/1) and the highly pressured sandstones (16,000-26,000 mg/1). The salinity of the water in shales is lower than that in the adjacent normally pressured sandstones. The concentrations, however, were found to be more similar in the high-pressure zone. Schmidt found that in shale pore water the concentration order is generally SO ] - > HCO 3 > CI-, whereas water in normally pressured sandstones has an opposite concentration order. In all cases, the salinities of interstitial fluids in shales were found to be considerably lower than those in associated sandstones.

In summary it appears that the fluids in the center of the shale capillaries are more saline than those adjacent to the capillary walls and that the former are squeezed out first. In the case of both undercompacted and well-compacted shales, the salinities of interstitial fluids in shales should be lower than those in associated sandstones if all the other variables remain unchanged. Interstitial water in the undercompacted shales, however, should be more saline than that in well- compacted shales, because in the former case a smaller portion of the more saline fluid present in the center of capillaries is squeezed into the adjacent sandstones.


This has been confirmed by the authors. A considerable amount of research work still remains to be done in this area, however, mainly owing to inaccuracies in leaching techniques and our understanding of the role of tectonic stresses, in order to reach definite conclusions.

The reasons why several investigators report that water in the well-compacted shales is more saline than in the undercompacted shales could include the following (see Chilingar and Rieke, 1976):

(1) If conversion of montmorillonite to illite, with associated release of relatively fresh water, is in part responsible for the overpressured formations and undercompacted shales, then the latter could contain slightly fresher waters.

(2) Leaching techniques of determining salinity of interstitial waters in shales are quite inaccurate.

(3) Comparison is made between the well-compacted and undercompacted shales of diverse origins. Some investigators compared shales having different mineralogy and obtained from different depths.

(4) As compaction fluids move upwards in a thick shale sequence, they become more saline. Thus, the undercompacted shales lower in the sequence may contain fresher water.

Chilingar and Rieke (1976) stressed that the salt-filtering effect does not appear to be significant at overburden pressures below 10,500-12,000 psi. In some locations it does not appear to be operative even at higher pressures. Hanor et al. (1988) reported that at a Penrose Conference, Kraemer and Dickey attributed the chemical and isotopic compositions of water in the shales and sandstones mainly to the membrane behavior of shales, whereas Bath stressed that the difference is due to the residence time of water in the two systems. At the same conference, Gieskes presented data from the Deep Sea Drilling Project which showed that there is a large-scale migration of marine fluids along faults and permeable zones of accre- tionary prisms (Hanor et al., 1988). Such fluid migrations obviously have an effect on pore fluid chemistry within the shales and associated sandstones. The writers point out that the preliminary experimental results of McKelvey and Milne (1962, p. 250) indicate that compaction pressures around 10,000 psi would be required to attain porosities (24-41%) at which salt filtering would become significant.

F L U I D C H E M I S T R Y C O M P A C T I O N - - D I A G E N E T I C M O D E L S

Knowledge of expected salinity changes in shales and sands can be applied to the quantitative interpretation of electric logs (Chilingar et al., 1969), interpretation of the direction of hydrodynamic flow over geologic time in compacting sand-shale sequences (Magara, 1969), and determination of whether or not the more rapid water influx into producing petroleum reservoirs may have come from surrounding shales (Dzhevanshir et al., 1987). Fluid chemistry models have been proposed to explain these geologic phenomena.

During the past twelve years, several modeling approaches have been advanced for simulating the diffusion-advection-reaction phenomena in fresh sediments


(Berner, 1980), the chemistry of water expelled from the compacting clay layers in laboratory experiments (Appelo, 1977), and the thermodynamics of salinity changes owing to the compaction of clays in the laboratory (Smith, 1977). The writers explore only certain aspects of these models. Berner's (1980) approach covers the advective processes in compaction of marine sediments at "shallow" depths. Advection refers to the bulk flow of solids or pore water relative to an adopted reference frame. This concept was presented in one form or another in the earlier-discussed compaction models of Bonham, Smith, and Sharp.

According to Smith (1977), experimentalists have generally recognized that salinity changes in pore water squeezed out from hydrated clay minerals and shale samples are caused by the cation exchange capacity of the material. The Gibbs-Donnan principles of equilibrium should explain these results. Smith (1977) developed a model to explain these laboratory results and based upon the concentration of positive and negative ions in terms of the concentration of the external solution, the void ratio, and the cation exchange capacity per unit volume of the sample's matrix.

Clay minerals literature has shown that there is an association between cations and negatively charged clay particles. Complete association of monovalent and divalent cations and clay minerals would eliminate the cation exchange capacity, so that the equivalents of ions per unit fluid volume for the positive ions, N +, the negative ions, N-, and the average, N, will not change with a decreasing void ratio (Smith, 1977, p. 382). A partial association, therefore, is expected to reduce changes in these concentrations. Smith (1977, p. 382) assumed in his model that the concentration dependence in the partial Gibbs free energy equation for free exchange site is contained essentially in the term R T l n ( e N A / A ) . This is the fraction of the total exchange sites that are free or unassociated.

The conservation of exchange sites in clay minerals is expressed as"

A / e = U a + NCA (2-99)

where A is the cation exchange capacity per unit volume of matrix (meq/cm3); e is the void ratio in cm 3 pores/cm 3 matrix; N A is the equivalents of negative ions per unit fluid volume at a cation exchange site (meq/cm3); and NCA is the equivalents of ions per unit fluid volume at an associated exchange site and cation (meq/cm3).

Electroneutrality in the clay (Smith, 1977) is"

N + = N - + N a (2-100)

The Gibbs variational treatment of equilibrium for the monovalent ions and sites is:

U 2 = U + (U-) (2-101)

The corresponding term in the partial Gibbs free energy for associated exchange sites and cations is assumed to be R T l n ( e N c A / A ) (Smith, 1977, p. 382). Therefore,

NCA K = (2-102)

N + N a

where K is the equilibrium constant (cm3/meq).


Upon squeezing a differential volume of pore water from the clay sample in the laboratory:

d N - = (N - N-)d( ln e) (2-103)

Smith (1977) eliminated NCA, N A, and N + from Eqs. 2-99 through 2-102 resulting in:

K = e [ N 2 _ (N_)2] - 1 N2 (2-104)

The value and constancy of K can be determined for a given clay and salt using Eq. 2-104, just by measuring N and N - for various values of e. Smith stated that N can be eliminated explicitly from Eq. 2-103 using Eq. 2-104. This yields a differential equation in e and N- . Equations 2-94 through 2-104 provide numerical solutions for N- , N, N +, NcA, and N in terms of K, A, initial eo and initial No.

Smith's (1977) results from his laboratory compaction experiments using montmorillonite No. 25 from Upton, Wyoming, and the above model had an accuracy of 3% with better than 1% precision. Figure 2-35 shows Smith's results. The vertical scatter reflects real variations of salt concentration in successive increments of squeezed-out pore water (Smith, 1977, p. 384). The stepwise displacements of the piston by hydraulic pressure correlate with the emergence of fresher water. Smith pointed out that the piston displacements initially overcompact the clay at the filter, so that the produced water is fresher than would be expected had the entire clay

I-- 52 Z lU U E 50 0.

- 48 "e,

46

,~ 2OO

u~ 150 n.

Qo.-..r

. .1 . W 'l ~ : 3 - - - ~ n" a. 50 ~)

~, .7 ~ ,

I I I I 1 150 200 250 300 350 400 450 500

ELAPSED TIME, HOURS

Fig. 2-35. Variation of (1) salinity of squeezed-out pore water; (2) compaction pressure; and (3) calculated porosity values with time. The stepwise displacements of the piston correlate with the emergence of fresher water. (After Smith, 1977, p. 384, fig. 7 - - Courtesy of the Society of Petroleum Engineers.)


cake compacted uniformly. His explanation was that the salt is filtered from the water passing from the bulk of the clay cake through the overcompacted zone. The overall effect, according to Smith (1977), is to hold salt in the clay cake.

Appelo (1977) also treated the problem of the equilibrium during compaction of clay mineral suspensions containing a monovalent electrolyte as the interstitial fluid with each drop of squeezed-out pore water. His approach is a mathematical simplification and slightly different interpretation of Bolt's (1961a, b) colloid filtering model. Appelo (1977) retained the ratio of the product of activity coefficients in the clay mineral suspension phase to that in the external phase as an adjustable constant f2:

f 2 _ _ (}/Na}/CI) I ._. }/I.q_ NaC1 (2-105) (~,~Na}/CI)// }~It + NaC1

where }/Na and }/cl are the activity coefficients for Na + and C1-. Smith (1977) pointed out that Appelo expressed concentrations of ions in the clay as equivalents per bulk clay volume rather than per clay pore volume as he did. Rewriting Appelo's Eq. 2-105 in terms of ion concentrations per unit of pore volume gives (Smith, 1977, p. 383):

N 2 f 2 ( e ) 2 = U+U - (2-106) l + e

If the cation exchange capacity approaches zero and the pores and matrix grains are large compared with the molecular dimensions of the pore fluids, then the pore fluid and the external fluid become identical (Smith, 1977):

N + = N - -- N (2-107)

Then f = 1 and Eq. 2-105 reduces to:

= 1 (2-108) l + e

which is an adequate approximation for dilute solutions (Smith, 1977). Smith (1977, p. 383) pointed out that both his and Appelo's approach ignore

the contribution of the greater pressure of the clay phase to partial Gibbs free energies of both the positive and negative ions in the pore water. The reader is referred to Chilingarian et al. (1994) for additional experimental results and concise explanation of Bolt's (1961a), Appelo's (1977) and Smith's (1977) results.

COMPACTION EFFECTS ON THE EXPULSION OF HYDROCARBONS

During the past 50 years large amounts of geochemical and geological data have been published on the origin, expulsion, and migration of oil in sedimentary basins (Cordell, 1972; Hood et al., 1975; McAuliffe, 1979; Bonham, 1980; Korchagina et al., 1988). It is generally accepted by petroleum geologists that in elastic sequences crude oil is generated from organic matter deposited with fine-grained sediments


and very small amounts are generated in reservoir rocks (see McAuliffe, 1979). The chemical processes of oil generation are more-or-less established (Welte, 1972). Most crude oil is formed at temperatures between 60 ~ and 150~ (140-302~ corresponding to burial depths of about 4921 to 14,760 ft (1500-4500 m) in areas with normal geothermal gradients (Tissot et al., 1971). Primary oil migration from the source rock to the reservoir rock during the generation period is still poorly understood. Secondary migration of the crude oil occurs through the reservoir rocks to trap positions (McAuliffe, 1979). The migration mechanisms depend upon complex variations of temperature, salinity, pH, and ionic composition of fluids all within the sedimentary sequence of source and reservoir rocks.

Cordell (1972) pointed out that investigations on a variety of modern sediments demonstrated that there is: (1) a sparsity of liquid hydrocarbons and free hydrocarbon precursors; (2) an absence (or only traces) of many hydrocarbon and other bitumen components, which are common in ancient rocks and crude oil; (3) a dilute occurrence of dissolved organic matter and only traces of liquid hydrocarbons in interstitial waters; and (4) a major upward movement of water to the surface, representing a serious loss to proposed shallow primary migration mechanisms.

E X P E R I M E N T A L C O M P A C T I O N RESULTS

The mechanism of petroleum migration out of source rocks is still not well understood. Many geologists believe that carrier water is necessary for the primary migration of oil (Hedberg, 1964). Release of water from smectite by compaction and/or its transformation to illite during the late stage of diagenesis was considered by Chilingar (1961), Powers (1967), Burst (1969), and Perry and Hower (1972). Aoyagi and Asakawa (1977) concluded, however, that both the interlayer and interstitial water expelled during the middle stage of diagenesis were responsible for oil migration.

Based on many observations, shales composed of non-expandable clays such as kaolinite and illite did not act as source rocks owing to the absence of water necessary to push out the oil (Chilingar and Knight, 1960; Weaver, 1967). Many undercompacted, overpressured shales did not act as source rocks, because compaction mechanisms were not operative to squeeze a sufficient amount of oil into the associated reservoir rocks (Aoyagi et al., 1985).

Laboratory compaction experiments using Na-smectite (bentonite) clay mixed with crude oil and seawater was performed by Aoyagi et al. (1985) to clarify some of the problems involved in the mechanims of primary migration of crude oil from source to reservoir rocks. Factors examined in the experiment were: amount of expelled liquid; proportion of oil and water in the expelled liquid; and differences in chemical composition and physical properties both between seawater and expelled water and between initial Na-smectite clay and compacted clay samples.

The equipment used was described by Aoyagi et al. (1975b) and is of the same type used by Sawabini et al. (1971). The mixed sample was compacted at 1000 kg/cm 2 at a temperature of 60~ for 25 days. The expelled liquid was measured


and sampled three times during compaction. The physical properties and chemical composition of the compacted clay and expelled liquid were determined (Aoyagi et al., 1985, p. 386).

The results of this experiment furnishes an insight into the mechanism of primary oil migration from source rocks to porous reservoir rocks in compacting sedimentary basins. Table 2-VII shows the amount of oil and water expelled from the compacted clay sample, and the pH and the conductivity of the expelled liquid. The total amount of expelled liquid decreased geometrically as compaction progressed, whereas the proportion of oil in the expelled liquid gradually increased with compaction time (Fig. 2-36). Porosity of the bentonite decreased from about 81 to 26% (Aoyagi et al., 1985).

TABLE 2-VII

Composition and chemistry of expelled liquid from the Na-smectite clay sample at various compaction intervals (after Aoyagi et al., 1985, p. 387, table 2; courtesy of Chemical Geology)

Expelled liquid after

1 day 12 days 25 days

Oil and water contents in expelled liquid: Total amount (ml) 27.0 5.8 1.0 Oil (%) O. 1 2.5 40.0 Water (%) 99.9 97.5 60.0

Chemistry of water: pH 6.84 7.51 7.53 Conductivity (mS cm -1) 50.40 52.37 65.71

Fig. 2-36. Changes in proportions of oil and water in the expelled liquid with compaction time. (After Aoyagi et al., 1985, p. 388, fig. 2 - Courtesy of Chemical Geology.)


E Q. Q .

v

1 0 0 0 0 - -

1000 - -

100 - -

- \ \ ~ o . ~ - . .

\\\\\ x c I-

x . . . . . X~ \

" ' ' ' ~ ~ ' ' - X ~ O Na" \ \

\ \ \ \

\ \ \

o ~ . . e Ca \ 2 +

- --v~.~.~ " : : - �9 a + Mg ~ ~ 0 ~ \

., \ \ \ / o K �9 �9 , \ . .

\ . . . / \\ ~ . . ~ . . .-

\ \ \ \

\

X S04 2 -

s Sea water 1 1Z 2

Compaction Time ( d a y s )

Fig. 2-37. Changes in cation and anion contents of expelled water with time, and compared to seawater. (After Aoyagi et al., 1985, p. 388, fig. 3 - - Courtesy of Chemical Geology.)

The amount of Na +, Mg 2+, C1- and SO 2- in the expelled water decreased after a slight initial increase, whereas K + and Ca 2+ gradually increased after an initial decrease (Fig. 2-37). Aoyagi et al. (1985) reported that the pH in the squeezed-out liquid changed from a weak alkali (original seawater) to almost neutral (Table 2-VIII). Conductivity of the fluid gradually increased with compaction time. Changes in the major chemical components of the original Na-smectite clay sample are shown in Fig. 2-38.

The results of this experiment show that primary migration of oil begins during the initial compaction of the argillaceous sediments. The main carrier is the water being expelled from the pores. Percentagewise more oil is expelled during the late stage of the experiment than during the initial stage (Table 2-VIII). It is possible that the amount of water available is insufficient to push the oil out during the


TABLE 2-VIII

List of geologic events and petroleum migration mechanisms effects (after Bonham, 1980, p. 560, table 1; courtesy of American Association of Petroleum Geologists)

Geologic event Migration effect

Early basin development Mature basin Hydrocarbon generation Hydrocarbons dissolve Geothermal gradient changes Pore fluids cool Separate-phase hydrocarbons Updip migration Intermittent faulting

Net downward fluid flux Static water body; sediments move downward Source sediments move down through thermal window Pore fluids become saturated Isotherms depressed Hydrocarbons exsolve Swept to top of carrier beds Buoyancy effect Petroleum migrates to shallower traps

2 , 0 - . _ . _ t~

8 u

�9 t2- 1.0- E

u

3.0 --] Original Clay Compacted Clay

. . . . . . . . . . . . . . . . o MgO

--o Na20

) - _

............ o CaO

. . . . . . . . . . . . . . . . . . . . . o K20

0

Fig. 2-38. Changes in major chemical components of the original clay resulting from experimental compaction. (After Aoyagi et al., 1985, p. 388, fig. 4 - Courtesy of Chemical Geology.)

late compaction stage. This suggests that primary migration of oil from source to reservoir rocks during the later compaction stage will occur chiefly by the effect of continuous oil flow, or by being pushed out later by water released from the dehydration of the smectite clay (see Clay mineral dehydration section, p. 56). With these results in mind, geochemical and migration models are reviewed next.

HYDROCARBONS - - GEOCHEMICAL AND MIGRATION MODELS

Johns and Shimoyama (1972) carried out model experiments to investigate the effect of smectite as a catalyst in promoting important organic reactions in hydrocarbon generation. Smectite as a catalyst promotes the decarboxylation of fatty acids to form long-chain alkanes. It likewise promotes subsequent cracking of these alka-


nes to produce shorter chain alkanes with molecular distribution similar to those of petroleum (Bray and Evans, 1961; Welte, 1965). Johns and Shimoyama (1972) presented five important generalizations based on the comparative studies of the molecular distributions of n-fatty acids and hydrocarbons in living organisms, soils, modern and ancient sediments, and petroleum of different ages and from different localities:

(1) Concentration of n-fatty acids are higher in modern sediments than in ancient sediments and petroleum.

(2) Concentration of alkanes are lower in modern sediments than in ancient sediments and petroleum.

(3) The even/odd carbon-preference (cpi) values for fatty acids are higher in modern than in ancient sediments.

(4) The odd/even carbon-preference values for alkanes are higher in modern than in ancient sediments.

(5) Average chain lengths (molecular weights) of alkanes are smaller in ancient sediments and petroleum than in recent or young sediments (Johns and Shimoyama, 1972).

Based on the above observation, it is rational to propose that the chain of reactions starts with fatty acids and leads to petroleum-like alkanes in mature sediments. It is known that 95% of the organic matter in sediments is dispersed in shales, and that the shales contain about 250 times the amount of hydrocarbons that constitute the total estimates of primary petroleum reserves (Johns and Shimoyama, 1972, p. 2161). The widespread industrial use of smectite clays as catalysts shows that this mineral is a likely candidate for catalyzing organic reactions in natural sediments. Shimoyama and Johns (1971) investigated experimentally the catalytic effect of Ca- smectite (having 12.4 wt% H20) on the decarboxylation of docosanoic acid (C22

fatty acid). Their results showed that two major reactions occurred sequentially: (1) the catalytic decarboxylation of the fatty acid produced alkanes having fewer carbon atoms than the precursor acid; and (2) the thermal-catalytic cracking of these alkanes produced a spectrum of alkanes with shorter chains. They also discovered that the initial decarboxylation reaction could be stopped before going to completion owing to carbonaceous material deposited on the catalytic sites on the edges of the smectite.

The catalytic cracking of alkanes can be explained adequately by a carbonium ion mechanism and implies an acid catalyst, providing protons to interact with the hydrocarbons (Thomas, 1949). Johns and Shimoyama (1972) proposed that the activity of the catalyst stems from the acid character of residual interlayer water is the smectites, as shown by Fripiat et al. (1965). It is the residual water on the clay surface, not the water shown to be expelled during the smectite-illite transformation, that develops the acidic character. These authors related the alkane cracking to smectite dehydration during diagenesis.

Johns and Shimoyama (1972, p. 2162) assume that the cleavage of the carbon- carbon bonds during cracking can be represented by the first-order reaction equation and is used to determine the activation energy for their model reaction:

l n ( N / N o ) -- - k t (2-109)


where k = Ae-E/RT; N is the amount of C21 alkane after time t; No is the initial amount of C21 alkane; k is the reaction rate; A is the Arrhenius factor of 5 x 1013 s-l; E is the activation energy; R is the gas constant; and T is temperature in ~ An activation energy of 46.5 kcal/mole was obtained for the cracking of C21 alkane. Johns and Shimoyama (1972) concluded that the catalysis in the smectite-water system affects about an 18% reduction in activation energy.

As the sediments and the fatty acids undergo compaction in a subsiding sedimentary basin, they undergo progressive diagenesis at rates dependent on the geothermal conditions and subsidence rates. Residence times at various depths and temperatures are controlled by the subsidence rates. A geothermal gradient value of 1.1~ ft and a continuous subsidence rate of about 10,000 ft/40 m.y. was selected by Johns and Shimoyama (1972, p. 2162) for their model. The interrelation among time t, temperature T, and depth d is presented by the following equation:

T N

= exp(-1.15 x 1012A ] e-E/RTdT) (2-110) / . D

No 296~

Johns and Shimoyama (1972, p. 2163) differentiated Eq. 2-110 with respect to T giving Eq. 2-111, which denotes the change in degree of cracking with progressively changing temperature:

-d(N/No) I N ] e_E/RT ) d r = N00 (1.15 x 1012A (2-111)

By using Eqs. 2-110 and 2-111 and experimentally determined kinetic constants, the differential curve for alkane cracking can be modeled with respect to temperature, reaction and depth.

It is known that the subsidence in sedimentary basins can be interrupted inter- mittently during the basin's history. The authors have attempted to simulate this situation by analyzing the kinetics of the cracking reaction using an "isothermal" model (Johns and Shimoyama, 1972):

N - exp[-1.15 x 1012(A e-F'/RT)(T -- 296)] (2-112)

N0

This equation simulates a situation where a pelitic sediment is held at a temperature T for a period of time necessary for the chosen subsidence rate alone to get the sediment to the chosen depth.

Johns and Shimoyama (1972, p. 2163) differentiated Eq. 2-112 resulting in the following equation:

-d(N/No) 1 15 x 1012A e - e / R r ( r - 296) R T 2 + 1 x (N/No) (2-113) dT "

It denotes the change in degree of cracking with progressively changing temperature. Solution of Eqs. 2-112 and 2-113 leads to the differential plot presented in Fig. 2-39. The effect of interrupted subsidence is to shift the cracking peak to substantially


Fig. 2-39. Decarboxylation-cracking zonation as a function of temperature/depth. Curves a and c represent the alkane cracking and fatty acid decarboxylation for Johns and Shimoyama's dynamic model, based on Eqs. 2-109 and 2-110, whereas curves b and d are based on their isothermal model m Eqs. 2-111 and 2-112. (After Johns and Shimoyama, 1972, p. 2163, fig. 2 m Courtesy of American Association of Petroleum Geologists.)

lower temperature (lesser depth). Johns and Shimoyama (1972) concluded that in a real subsiding basin they would expect the alkane cracking curve to peak somewhere between the extremes of their two models in Fig. 2-39.

Figure 2-40 is Johns and Shimoyama's geochemical model for petroleum formation, maturation, and migration. The authors superimposed their results upon Perry and Howers' (1972) water-expulsion curve. In a sediment column of 12,000-13,000 ft, two distinct, if overlapping, zones can be defined, representing the diagenetic processes encountered during burial and diagenesis.

Bonham's (1980) model considers the mass balance of fluids in a sedimentary basin. His model differs from Johns and Shimoyama's by not considering the reaction kinetics. The approach uses the restoration of the sedimentary column, isothermal depths, volume of pore space in a shale column, and the release of hydrocarbons from solution in the expelled pore water owing to a drop in temperature as the water rises. Price (1976) presented data on solubilities of whole crude oil in water at elevated temperatures. Bonham (1980, p. 560) presented a summary of the mechanisms he considered in his conceptual petroleum migration model (Table Z-VIII).

Deep sedimentary basins tend to develop a static body of water with sediments moving downward through the water. This is a dynamic-extraction system whereby heated pore waters can become saturated with hydrocarbons as they are thermally


Fig. 2-40. A geochemical model showing the alkane production and maturation with respect to smectite-illite transformation and water expulsion during burial and diagenesis. (After Johns and Shimoyama, 1972, p. 2165, fig. 4 m Courtesy of American Association of Petroleum Geologists.)

generated in the source beds (Bonham, 1980). If exsolution of crude occurs in porous and permeable carrier beds, then the separate-phase hydrocarbons can migrate to traps in response to buoyancy. Bonham tested his migration concept in the Gulf Coast area of the U.S.A. using computer modeling. The known accumulation in the area can be explained by his model. The solution-exsolution mechanism probably is only one of several that contributed to primary petroleum migration.

Bonham (1980) considered a condition by which a volume of hot, high-pressured pore fluid could be expelled from deep shales in the basin and moved to a shallower zone. The assumed migration route is either through faults and/or fractures. Bonham (1980, p. 566) concluded that using reasonable geologic assumptions, this mechanism can account for only a small fraction of known hydrocarbon accumulations.

Welte and Yukler (1981) presented a deterministic three-dimensional model to simulate geologic, hydrodynamic, and thermodynamic development of petroleum generation, migration, and accumulation. Figure 2-41 illustrates their development scheme for this model. A generalized flow chart for the three-dimensional quan-


titative basin model is presented in Fig. 2-42. Yukler et al. (1978) derived a new equation for fluid flow in sediments with moving boundary conditions, considering sedimentation, compaction, and erosion. The pore pressure or hydraulic head in sediments can be computed in three-dimensions as a function of time (Welte and Yukler, 1981). The inflow-outflow is equal to the net accumulation owing to grain and fluid compressibility plus the net accumulation due to the change in sediment density, change in sedimentation rate, and change in water depth:

1 [ , ,h , ,h , , h i P -~xPK~x + ~ypK~y + ~zpK~z

,h [ aH] = &-~- + ot - ( L - z)--~- - (})s - ~/w)--~- - Yw--~- (2-114)

where h is the hydraulic head, L; H is the water depth, L; L is the sediment thickness, L; K is the hydraulic conductivity, L/T; Ss is the storativity, l/L; t is the time, T; x, y, z are the three orthogonal vectors; ot is the compressibility of solid rock, LT2/M; },'s is the specific weight of bulk sediment, M/L2T2; },'w is the specific weight of the fluid, M/L2T2; and p is the density of the water, M/L 3 (L is the length, M is the mass, T is the time) (Welte and Yukler, 1981, p. 1390).

The compressibility of the fluid term is neglected, inasmuch as the error is negligible. Stallman's (1963) heat flow equation for the simultaneous transfer of heat both by conduction through the fluids and rocks and by convection of water flowing in the system is:

S K (~ Tm S 6 Tm 6 (~ Tm pw Cpw [ (~ (~ 6 1 -g;x + K- y + Vz K- z Vx Vm + Vy Vm + Tz Vz Vm

conduction convection

6T + Q = pwsCws 6---7 (2-115)

source/sink net/accumulation

where E is the energy term; Cps is the specific heat of fluid, E/M ~ Cws is the specific heat of the bulk sediment, E/M ~ K is the thermal conductivity, E/L ~ Q is the sink ( - ) or source (+) term, E/L3T; T is the temperature, ~ Vx Px, Vv Py, and Vz Pz are fluid flows in the x-, y-, and z-direction, L/T; Pw is the density of fluid, M/L3; and Pws is the density of bulk sediment, M/L 3.

Figure 2-43 shows the flow chart that compares the model-generated results with selected real values determined for an unidentified basin (Welte and Yukler, 1981). One important aspect of Welte and Yukler's model is the manner in which they determined the temperature-time index, I, which is the sum of the products of effective geologic heating time (G) and temperature correction factor (T) (concept of resident time of heating the sediments):

I = T1G1 + T2G2 +. . . + TnGn (2-116)

HEAT FLOW (Paleoterrpmkre)

MIGRATION DETERMINATIONS

I

INPUT

GEOCHEMCAL ;n' AND "uT'ONs

Fig. 2-41. Development schema of three-dimensional deterministic dynamic model. (After Welte and Yukler, 1981, p. 1389, fig. 2 - Courtesy of American Association of Petroleum Geologists.)

4 Mathematical

Model +

System El-El \~q~l'~r1+pl Real System

I ,Ff&, 1 i

hnt Results

L b. Conceptual

American Association of Petroleum Geologists.)

El = Fig. 2-42. A generalized flow chart for a three-dimensional quantitative basin model. (After Welte and Yukler, 1981, p. 1390, fig. 3 - Courtesy of


Pressure ---

1

Porosity ----

SOLUTION "~ I WITH I REAL CASE

IIII II Amount of petroleum

Fig. 2-43. Schematic comparison of model-generated results with selected known basin values from an unidentified basin. (After Welte and Yukler, 1981, p. 1391, fig. 4 - Courtesy of American Association of Petroleum Geologists.)

These authors developed a correlation equation between the vitrinite reflectance, Rm % , and the temperature-time index:

Rm % - 1.301 lg I - 0.5282 (2-117)

The simultaneous solutions of Eqs. 2-114 and 2-115 give the temperature as a function of time and space. Welte and Yukler (1981) then determined the T and G values. By Using Eqs. 2-116 and 2-117, the vitrinite reflectance values are calculated as a function of space and time. These authors used Lopatin's method as a first approach (Lopatin, 1971).

Their next step was to determine the amount of hydrocarbons to be expected from possible source rocks within the three-dimensional sedimentary basin as a function of time. The calculated vitrinite reflectance values are used to give a plot of a hydrocarbon generation curve for type II and type III kerogen (Fig. 2-44). It must be realized by the reader that the hydrocarbon generation curves represent observed maximum values of hydrocarbons which are not always reached. Nevertheless, Welte and Yukler, for the time being, used them for calculations of the hydrocarbon potential within a basin.


~ 0.5

z

or-

1.0

1.5

HYDROCARBONS (mg /g Corg) 0 50 100 150 200

Fig. 2-44. Hydrocarbon generation curve for Type II and Type III kerogen. (After Welte and Yukler, 1981, p. 1393, fig. 7 - - Courtesy of American Association of Petroleum Geologists.)

Welte and Yukler (1981, p. 1395) stated that buoyancy, capillary pressure, and hydrodynamics control secondary migration of oil. The buoyancy values can be computed by subtracting the oil density from the formation water density and multiplying by the height of the petroleum column. There is an absence of reliable data for estimating the height of a petroleum column and, therefore, these values are problematic. Pore size values in the capillary pressure equation are computed using Berg's (1975) equation. The interfacial tension values are corrected for temperature as given by Schowalter (1979). Welte and Yukler used Eq. 2-114 to calculate the pore pressures. The combination of all these parameters, as a first approach, enables identification of possible secondary migration directions of petroleum and traps that most likely contain petroleum (Welte and Yukler, 1981, p. 1395).

The results obtained by their application of this model to sedimentary basins were reasonable. Sensitivity analysis of the parameters discussed in Eqs. 2-114 and 2-115 provides the necessary corrections. The allowable errors were: -t-8% in physical and thermal parameters; 2~ in temperature; +10% in maturity; and +15% of petroleum in place (WeRe and Yukler, 1981).


STRESSES IN SEDIMENTS

Hydrostatic stress

Jtirgenson (1973) recommended that the term hydrostatic stress be clarified. This is necessary in order to apply the term properly to the constitutive relationships.

The term hydrostatic stress is usually defined as the fluid pressure exerted by a liquid at rest, and at a given point it acts with equal intensity in all directions. A submerged solid is subjected to equal pressure from all sides. For all practical purposes, the hydrostatic stress caused by water does not affect the friction between mineral grains and does not contribute to the strength (shearing resistance) of the sediment body.

Hubbert and Rubey (1959, p. 129) stated that within depths of 1 to 2 km, the pressure of the water as a function of the depth, D, can be closely approximated by the equation:

Pw = pwgD (2-118)

where pw is the hydrostatic pressure of a column of water extending from the surface of the ground to a depth of D within the porous column; Pw is the density of the water; and g is the acceleration of gravity.

The specific weight of any fluid, yf, can be expressed as:

yf = pf g or pf = yf / g (2-119)

Thus, the hydrostatic pressure, pf, at a depth D is equal to:

Pf = yfD (2-120)

The specific gravity, SG, is equal to:

SG = Yf/Yw and yf = SGyw (2-121)

where Yw is the specific weight of water. On combining Eqs. 2-120 and 2-121:

pf -- SG Yw D (2-122)

If Yw is in pounds per cubic foot and D is in feet, then pf is in pounds per square foot. The pressure gradient ( p f / D ) for pure water (Yw = 62.4 lb/ft 3) is equal to 0.433 psi/ft [= (62.4 lb/ft3)/144 in2/ft2)].

Resolution of the total stress field

The stress tensor for a porous, homogeneous, isotropic sediment body can be written in the conventional way:

Crx rxy rxz

S- - ryx cry ryz (2-123)

rzx Zzr az


z ~z

l

I

/L-- ~z ~ / Txy

/ �9 , /

/ ~ Ay

a~z

Fig. 2-45. Stress notation in a cubic argillaceous rock slice. Stress notation of the normal component of stress, crz, on the plane normal to the z-axis; rzx and Tzy refer to the shear stress components in the plane normal to the z-axis and acting in the x- and y-directions, respectively. Point O is in equilibrium with respect to the forces in the x- and y-directions, cr z + (3~rz/3z)dz is the incremental change in the vertical stress through the free body.

where S signifies the symmetrical tensor of the total stress; cri and "gij represent the normal and shear forces, respectively, acting on the faces of a unit volume of sediment (Fig. 2-45). Moments can be taken about point O in Fig. 2-45. The tangential stress, rxy, multiplied by the area in which it acts, gives the force 75xy dzdy, and this times dx gives a clockwise moment about O. The stress ryx times the area gives ryx dxdz, and the latter times dy results in a counterclockwise moment ryx dxdzdy. At equilibrium, the two moments balance each other:

"Cxy dzdydx = ryx dxdzdy (2-124)

or :

72xy = "gyx (2-125)

Then it follows that:

rxz = rzx (2-126)

and:

"gyz - - 75zy (2-127)


The total stress array for a point in a cylindrical body under compaction, such as the ones studied in the laboratory by numerous investigators, can be expressed in cylindrical coordinates r, | and z:

0"r trO trz

S ~ for 0"0 15Oz (2-128)

~zr "tSzO 0"z

In order to visualize more clearly the ability of sedimentary deposits to bear an overburden load, the total stress tensor is decomposed into two distinct parts for a body in equilibrium: (1) the "hydrostatic stress" tensor, which in analogy with the pressure in water, is acting with equal intensity in all directions; and (2) the deviator stress component which is not equal in all directions. The term "hydrostatic stress" above does not mean a pressure acting in the water.

Jfirgenson (1973) pointed out that in the theory of elasticity this "hydrostatic stress", which would produce the same volume stress as the actual state of stress considered, is numerically equal to the octahedral normal stress [1 (0.1 + 0.2 + 0.3)]. In the case of a sediment, it is understood to include the pore pressure, i.e., the true hydrostatic pressure. Thus, a double perplexity exists. The "hydrostatic stress" exerts an intergranular pressure and contributes to strength, which a true hydrostatic stress cannot do. In addition, one of the components of the "hydrostatic stress" is a true hydrostatic stress. The "hydrostatic stress", therefore, is merely a mathematical quantity and does not exist physically as an all-sided pressure (Jfirgenson, 1973, p. 448).

It seems that the term hydrostatic has to be retained in its true sense of a stress acting in a liquid at rest. An entirely different term must be used for the all-sided stress producing an equivalent state of volume stress. It was suggested by Jfirgenson (1973) that the term most appropriate would be volumetric stress. The magnitude of the volumetric stress varies between the limits of 1(0.1 -1- 20"2) and �89 + 0.3). The deviator component, which represents a rather complicated concept, is defined as (0. - 0.3), where 0.3 is the spheric stress that is equal in all directions.

The above division into components is very useful in explaining the strength behavior of sediments undergoing compaction, i.e., the ability of the sediments to resist shear. The spheric component, being equal in all directions within the sediment body, causes no shearing stress. When the mineral grains are pressed against each other, the frictional resistance develops, which is equal in all directions. As pointed out by Jfirgenson (1973, p. 450), the intergranular pressure and, thus, the material's strength, is raised by the deviator pressure as well, but in unequal degrees in different planes.

Spheric stress state

The component attributable to the interstitial fluid is the hydrostatic stress (pressure), 0.,, which can be regarded as being continuous throughout the medium. The normal and shear stress components are given by:


tTw x "f w x y "Cw x z

P - rwyx awy Zwyz (2-129)

"Cw z x "Cw z y Crwz

where P is the spheric stress tensor. It can be safely assumed that under hydrostatic conditions no shearing stresses exist in the interstitial fluid. As a matter of fact and by definition, a fluid is a substance which cannot sustain tangential or shear forces when in static equilibrium. This may not hold true for the adsorbed water because of its probable quasicrystalline nature. Hubbert and Rubey (1959, p. 138) stated that if a viscous liquid occupies the pore space, there are then microscopic shear stresses which are expended locally against the fluid/solid boundaries. Thus, their only macroscopic effect is to transmit to the solid skeleton by viscous coupling whatever net impelling force may be applied to the interstitial fluid.

In any stress system with the principal stresses, ax, ay, and az, one can define the local mean value of the quantity for the spheric stress, aw as:

= �89 Owx + , wy + Owz)

Now, the spheric stress tensor, P, can be represented by:

0 0

P - a--w 0

0 ~-w

and:

(2-130)

(2-131)

P = 1(3~-w) = ~-w (2-132)

The above expression represents the hydrostatic pressure of a fluid, whether it is flowing or is stationary in the porous system of a shale. Thus awx = awy = awz = a---~

and the hydrostatic portion of the total stress system causes only volume changes in the deformed material.

Devia tor ic stress state

The second component is the stress deviator from the hydrostatic state. It is expressed as the difference between the total stress and the hydrostatic stress which resists deformation:

(ax - awx) Zxy rxz

D ~ r y x (f ir - ~ ) r y z (2-133)

rzx rzy (az - awz)

where D is the deviatoric part of the total stress tensor. The effect of the deviator stress is to produce a distortion which is elastic or plastic in nature and is introduced into the sediment body.


Total stress tensor

If the sediment body is not in equilibrium, the second component will not be a symmetric tensor for rxr r ryx. This asymmetric tensor can be subdivided into symmetric and skew-symmetric parts (Ramsay, 1967, p. 282). The hydrostatic stress component is the same as in Eq. 2-130. The second symmetrical part is the deviatoric stress component which can be expressed as:

(fix --~-w) l ( "g x y n t- "g y x ) l ( "g x z n t- 72 z x )

D ~ �89 + -Cyx) (fy - i f 'w) l (72yz + r z y ) (2-134)

�89 + Vzx) �89 + rzr) (fz -Kw)

The skew-symmetric part is termed the disequilibrium component, which causes the sediment to undergo a rotation in space and is expressed as:

! 0 2('t2xy -- "gyx) 1(72xz -- Tzx)

1 (2-135) R - �89 ('gyx -- "~xy) 0 -~ (72yz -- "gzy)

�89 ( zx - xz) �89 - o

where R is the disequilibrium component. Such a stress state would be expected if tectonic forces were acting on the sediment mass in a basin within a geosyncline. The total stress tensor for a sediment body not in equilibrium is expressed as the sum of the above-described parts:

S = P + D + R (2-136)

(total stress = spheric stress + deviatoric stress + disequilibrium component)

Each one of the three components making up the state of stress is directly related to the respective component of the strain tensor. The spheric part of the stress system causes changes in volume, the deviatoric stress components cause distortion, and the disequilibrium components cause the material to undergo rotation in space (Ramsay, 1967).

Lo (1969) showed mathematically that the pore pressure induced by shear may be expressed as a sole function of the major-principal strain. According to him, the only unambiguous and correct principle of superposition of pore pressure is to consider an isotropic stress system and a deviatoric stress system, namely:

i o " 1 0 0 AO" 3 0 0 ( A f f l - Ao'3) 0 0

0 Af2 0 - 0 Ao'3 0 + 0 ( A o 2 - Ao'3) 0

0 0 0 Af3 0 0 Af3 0 0

(2-137)

where f l is the total major stress; f2 is total intermediate stress; and f3 is total minor stress.


T A B L E 2-IX

Terminology recommended by Jfirgenson (1973, p. 450)

Term Symbol a

Hydrosta t ic stress 0-w

Spheric 0-3

Deviatoric 0- -- 0" 3

Main deviator 0"1 -- 0"3 = 2rmax

Compressive strength 0-1 - 0-3 = 2rmax

V o l u m e t r i c stress 1 (0-1%- 02 %- o3)

Mean normal stress ~ (0-1%- 0-2 %- O"3)

Normal octahedral �89 (0"1%- 0"2 %- O"3)

O c t a h e d r a l d e v i a t o r i c 0- _ 1 (0-1%- 0"2 %- 0"3)

a One should consult the state of stress in Mohr 's representat ion and the state of stress in polar coordinates.

According to Lo (1969), the physical justification for Eq. 2-137 lies in the fact that under ambient stress, the induced pore pressure corresponds almost exactly to the applied pressure, because the compressibilities of pore water and sediment grains are much lower than that of the sediment structure. In the experience of the writers, however, most of the pore pressure equations presented in the literature give almost identical results, provided they are properly used.

According to Jfirgenson (1973): "Defenders of the old terminology adopted in the theory of elasticity use as their main argument the longevity of their 'hydrostatic' and 'deviatoric' stress." Although this is perfectly true, it does not take into account that the mechanics of sediments deals with a type of material quite different from metals, which have been the main concern in the theory of elasticity. Jfirgenson (1973) continued to state that "the difference in the physics of the strength of these materials can well be compared considering that in metals the intergranular pressure is estimated to reach several hundred thousand atmospheres and the angle of internal friction is measured in decimals of a degree, while in soils the intergranular pressure and the pore pressure (which as a term is a comparative newcomer) usually do not exceed a few atmospheres, but the angle of internal friction may exceed 40 degrees."

As pointed out by Jfirgenson (1973), the insufficiency of the old terminology is caused by the peculiarities of the mechanics of sediments and soils, which require the consideration of widely different factors of strength. The pressure caused by water is included here (Table 2-IX).

T E C T O N I C O V E R C O M P A C T I O N

In some areas where overpressures in the reservoirs are caused by tectonic activity, the associated shales have been either well compacted or overcompacted. The water squeezed out of shales was in many cases more than sufficient to cause

1 4 0 G.V. CHILINGARIAN, H.H. RIEKE, III AND E.C. DONALDSON

overpressuring in associated reservoir rocks. The writers suggest that in such areas predictive indicators are (1) increased electrical resistivity; (2) increased bulk density; and (3) increased sonic speed, etc., of shales, due to overcompaction. Zavgorodniy and Pakhol'chuk (1985) presented an excellent study of abnormal formation pressures in carbonate reservoirs of the Pripyatskiy Deep in the former U.S.S.R.

The formula developed by Anikiev (1971) to determine porosity, 4~D, of shales at a particular depth, D, is as follows:

t~D -" ~bi(1 - 0 . 2 S / 3 D ) (2-138)

where (~i ---- initial shale porosity at the surface; and fl = irreversible rock compressibility. Zavgorodniy and Pakhol'chuk (1985) used values of 35% for t~i and 27 x 10 -5 MPa for ft. Thus, at a depth of 3000 m the porosity is reduced by 13% (from 35% to 22%) (see Fig. 2-46). The volume of expelled water (0.13 m 3 per m 3 of shale) was more than sufficient to overpressure associated carbonate reservoirs, with overpressures reaching 35-40% above hydrostatic pressure (see Fertl and Chilingarian, 1989,

10 20 3 0 r % 1.0 1.1 1.2 1.3 1.4 ' ' ' ' ' h ' , . , w ~ I

1000 0 ~ ~ m.m i I I :

t / ' " ' ~ ,11 1500 �9 ~ I J15 I I �9 ,'t I I :oootl" !:., ',I

U I I I 2500 ii

I i .'tun asi p

1o IP ~r.,__J2.__2~ . - l ~ooo 17too - . . . . . . . - I v - _--P'-~., - ~ - =0 / . ;~,~ ~ I I~ , .:llJa. t=~.~,,. ~n

1 2 4ooo ~ o o ~,~ , n~ , ,8 ,,,,

o i o I o i l t oO 4500 I- \ ~ 0 ~ : ~ . ~ L~'; ,9_ ! o o o r - o I i 1 7 " 6 % ~ '11 I~ i''-5 15

L i o o o '" , ooo [l I , D,m n

Fig. 2-46. Change with depth of (I) electric resistivity of the Buregskiy shales, (I/) porosity, and (III) Pres/Pah ratio for the subsalt carbonates of the nor thern structural-tectonic zone in the Pripyatskiy Deep. Prospects with the overpressure: 1 = Dneprovskaya; 2 = Vetkhinskaya; 3 = Krasnoseli 'skaya; 4 = Barsukovskaya; 5 = South Rechitskaya; 6 = Malodushinskaya; 7 = Demikhovskaya; 8 = East Pervomayskaya; 9 = Pervomayskaya; 10 = South Ostashkovichskaya; 11 = Rudninskaya; 12 = Vishans- kaya; 13 = Sudovitskaya; 14 = Malynskaya; 15 = Glusskaya; and 16 = East Drozdovskaya. Pres - -

measured reservoir pressure and Pah = assumed hydrostatic pressure.


for details). Usually, overpressures occur at depths below 3000 m, and are more pronounced where thickness of Buregskiy Shale is around 30-60 m. When shale thickness is reduced from 30-60 m to 5-10 m, overpressures do not exceed 15% and usually range from 6 to 10%.

The electrical resistivity of shales varies from 2.2 to 129 ohm-m. Down to a depth of 3000 m, resistivity varies from 2 to 10 ohm-m, with slight increase with depth. At a depth interval of 3000-3500 m, the resistivity increases at a rate of 12.0 ohm-m/1000 m, and reaches 30 ohm-m at a depth of 4100 m. At the latter depth, resistivity gradient increases with depth in excess of 100 ohm-m/1000 m.

The writers suggest that the ratio of thickness of shales to the thickness of reservoir rocks can be used as an indicator of the presence of overpressures. The thicknesses of both shales and reservoir rocks should be measured below the hydrostatic seal (e.g., caprock).

COMPRESSIBILITIES OF SAND AND CLAYEY SEDIMENTS

Compressibility, c, can be defined as the rate of change of volume, 8V, with respect to the applied stress, a, per unit of volume, V:

c = - V ~ (2-139)

There are several different usages of the term compressibility, which appear in the literature depending on the method of determination: (1) bulk compressibility; (2) pore compressibility; (3) formation compressibility; (4) rock solids compressibility; and (5) pseudo-bulk compressibility (Table 2-X).

Although many consolidation (compressibility) studies on clays and shales have been performed in soil-mechanics laboratories for more than 60 years, these tests have been limited largely to a low-pressure range [<1000 psi (70.3 kg/cm2)]. During the same period, high-pressure confining tests on consolidated sedimentary rocks have exceeded 15,000 psi (1055 kg/cm2). Most investigators used mainly well- indurated sandstones or limestones in their laboratory experiments. Knutson and Bohor (1963) tested the oil-reservoir rocks typical of the Texas-Louisiana Gulf Coast region (orthoquartzites to calcareous subgraywackes). Van der Knaap and Van der Vlis (1967) determined the compressibilities of unconsolidated clays and sands from the Bolivar Coast of Venezuela.

Carpenter and Spencer (1940) measured the "pseudo-bulk" compressibility of various consolidated sandstones in an attempt to investigate whether or not fluid withdrawal from U.S. Gulf Coast oil reservoirs and the resulting volume reduction could account for ground subsidence. They defined "pseudo-bulk" compressibility as:

/3 = Vb \-~Pt ,] (2-140)

where fl is the pseudo-bulk compressibility in psi-i; Vb is the original bulk volume in cm3; 3 Vp is the change in void volume in cm3; and ~Pt is the change in the applied


TABLE 2-X

Various compressibility formulas used in the literature

Formula

Bulk compressibility:

1 (igVb)

Cb-- e + l

or

Cb "-- --~

Pore compressibility:

1 I O V p ) C P = - - E ~ , ' -~ pp,T

01"" l ~igVp h

=-E Formation compressibility (pore compressibility of some authors):

cf = - E

Rock solids compressibility:

Cr --" - - K Ik ~Pp ] K = p p , T

1

C r -'- - "Vss k, 0-'-'~ / "ff = p p , T

Pseudo-bulk compressibility:

1 (8Vb h Cbt = --'~bb tk'~Pp J K T

!

Coefficient of compressibility:

8e av - 8p

Change in the bulk volume (3 Vb) per unit of bulk volume (Vb), per unit change in total external stress (K), while keeping the pore pressure (pp) and temperature (T) constant.

Change in the bulk volume (i9 Vb) per unit of bulk volume (Vb), per unit change in effective pressure (Pe = ~ ' - Pp), while keeping the total external stress (K) and temperature (T) constant.

Determined in the uniaxial compaction apparatus, if pore pressure pp = 0, i.e. K = Pe. Void ratio, e, is equal to the volume of voids (Vp) divided by the volume of solids (Vs): e = Vp/Vs = ~b/(1 - q~), where ~b is fractional porosity, h is a sample thickness in a uniaxial compaction apparatus, i.e. thick-walled cylinder.

Change in the pore volume 09 Vp) per unit of pore volume (Vp), per unit change of external stress (K), keeping the pore pressure (pp) and temperature (T) constant.

Change in the pore volume (O Vp) per unit of pore volume (Vp), per unit change in effective pressure (Pe), while keeping the total external stress (K) and temperature (T) constant.

Change in the pore volume (8 Vp) per unit of pore volume (Vp), per unit change of pore pressure (pp), while keeping the total external stress (K) and temperature (T) constant.

Change in the rock solids volume (8 Vs) per unit of rock solids volume (Vs), per unit of external stress (~-), at constant temperature. If a rock sample is tested without a jacket, external stress will be equal to the pore pressure (K = pp).

Change in the bulk volume (i9 Vb), per unit of bulk volume (Vb), per unit change of pore pressure (pp), at constant external stress (K) and temperature (T).

Change in void ratio (Oe) per unit change of net confining pressure (3p).

Note: In calculating bulk and pore compressibility, one can use either the initial bulk (lib) or pore (Vp) volume in all cases, or measure volumes at each particular pressure for which compressibility is being calculated. The results appear to plot better in the former case.


pressure in psi. Their experiments showed that sediments compact owing to fluid withdrawal from the pore space.

Fatt (1958a, b) studied the relationship between compressibility and rock composition. He reported that unconsolidated sediments, which are poorly sorted and contain clay, have higher compressibilities than do consolidated and well-sorted sands. Fatt (1958b) found that the bulk compressibilities of sandstones are a function of rock composition for a given grain shape and sorting. If sandstones are divided into two groups (one with well-sorted, well-rounded grains and the other with poorly sorted, angular grains), then for each group the compressibility is a linear function of the amount of intergranular material.

The procedure used in the laboratory by Fatt (1958b) was similar to that of Carpenter and Spencer (1940), but in the former case the fluid was expelled under constant external pressure with a reduction in pore pressure rather than an increase in the external stress. This is believed to closely duplicate petroleum-reservoir producing conditions. Fatt's (1958b) procedure was to apply a constant external stress to the core and decrease or increase the pore pressure. His apparatus simultaneously measured both the bulk- and pore-volume changes at room temperature. Volume changes of the core in the pressure cell were measured through the use of a linear potentiometer that could resolve a movement of 1 x 10 .3 inch (2.54 x 10 .3 cm).

Van der Knaap (1959) noted that pore compressibility increases with decreasing porosity. It has been suggested by some investigators that between certain minimum and maximum pressures, the relationship between pore compressibility and the logarithm of pressure can be approximated by a straight line. A straight-line relationship has been found to exist between the log of the bulk compressibility and the log of the "effective" pressure, which in this case was equal to the direct applied axial load, because pore pressure was atmospheric (Van der Knaap and Van der Vlis, 1967). Bulk compressibilities of unconsolidated clays and sands decreased with increasing overburden pressure (Fig. 2-47a, b). From their studies, Van der Knaap and Van der Vlis concluded that clay and sand layers compact almost to the same extent, the main difference being that the low permeability to water of the clay prevents instantaneous compaction and time effects become important.

In his classical paper on the compaction of freshwater-bearing alluvial clays, silts, and silty sands in California, Meade (1968) found that the loss in pore volume that resulted from compaction by effective overburden pressures in the range between 3 and 70 kg/cm 21 averages about 0.3 void ratio (e = Vp/Vs) units or about 15% of the bulk volume of the fine-grained sediments. Meade stated that when one allows for the lesser compaction of the interbedded coarser sands and gravels, the reduction of the total volume of the alluvial sediments amounts to about 12% in the pressure range of 10-70 kg/cm 2 on the east side of the San Joaquin Valley and about 10% in the 3-33 kg/cm 2 pressure range in the Santa Clara Valley, California. The factors that directly influence the compressibility of shallow marine and alluvial sediments are average particle size, the particle sorting, the amount of

1 1 kg/cm 2 = 14.223 psi and 1 psi -1 = 14.223 cm2/kg.


Fig. 2-47. (a) Relationship between the bulk compressibility in psi -1 and effective pressure in psi. 1 = montmorillonite (API no. 25); 2 = kaolinite (API no. 4); 3 = P-95 dry lake clay (Buckhorn Lake, California); 4 = the area encompassing compressibilities of post-Eocene sand samples from the Bolivar Coast, Venezuela (4 = after Van der Knaap and Van der Vlis, 1967). Samples 1, 2 and 3 were hydrated in distilled water. (After Rieke et al., 1969, p. 823, fig. 4.)

montmorillonite clay, the proportion of exchangeable sodium cations relative to the calcium and magnesium cations in the clay minerals, presence of diatom skeletons and, probably, the mica content.

EXPERIMENTAL VALUES

Compressibilities of unconsolidated sands and clays are of the order of 10 -3 to 10 -5 psi -1 in the 100-10,000 psi -1 pressure range. Chilingarian et al. (1973a) found that the bulk compressibilities [cb = (-1/Vb)(~Vb/3pe)Pt] of unconsolidated


Fig. 2-47 (continued). (b) Relationship between bulk compressibility in psi -1 for various clays. 1 = illite (API no. 35); 2 = halloysite (API no. 12); 3 = dickite (API no. 15); 4 = soil from weathered limestone terrain (Louisville, Kentucky); and 5 = the area where compressibilities of post-Eocene clay samples from the Bolivar Coast, Venezuela, fall (5 = after Van der Knaap and Van der Vlis, 1967). Samples 1, 2, 3 and 4 were hydrated in distilled water. (After Rieke et al., 1969, p. 824, fig. 5.)

sands range from 7.4 x 10 -4 to 3 x 10 -5 psi -1 at an effective pressure range of 0-3000 psi, whereas the pore-volume compressibilities [Cp = (-1/Vp)(3Vp/3pp)Pt] range from 1 x 10 .3 to 1 x 10 .4 in the same pressure range using a hydrostatic compaction apparatus (pressure being equal in x-, y-, and z-directions). These values are greater by about 55-500% than those obtained using uniaxial compaction equipment. Different possible loading conditions on sediments are presented in Fig. 2-48.

The bulk compressibilities obtained on compacting montmorillonite clay saturated in seawater, using the hydrostatic compaction apparatus (5 x 10 -4 to 2.9 x 10 .5 psi -1), were found to be about 300-500% higher than those obtained on using uni-


Fig. 2-48. Compaction loading classification. (After Sawabini et al., 1974, p. 133, fig. 1.) (A) Polyaxial loading (Px :/: Py ~ Pz), called triaxial loading by some investigators. (B) Hydrostatic loading (Px = Py - Pz). (C) Triaxial loading (Px - Py ~ Pz), called biaxial loading by some investigators. (D) Uniaxial loading (four sides parallel to the stress Pz are kept stationary), referred to as biaxial loading by some investigators. (E) Biaxial loading (Px = Py anc~ sides parallel to these two stresses are kept stationary).

axial loading (1.85 x 10 -4 to 5.4 x 10 -6 psi -1) in the applied pressure range of 400- 20,000 psig (pounds per square inch, gage). Compressibilities of the consolidated sandstones, shales, and carbonates are lower, and range from 10 -s to 10 -7 psi -1 in the 500-15,000 psi pressure range (see Fig. 2-49).

The compressibilities of unconsolidated sands appear to be very close to those of clays. Unconsolidated sands are as compressible as clays, or even more so. Compressibility values of sands obtained in a hydrostatic compaction apparatus are usually about twice as high as those determined using uniaxial compaction equipment. Sawabini et al. (1974) found that compressibility increases with increasing feldspar content.

Effect of rock compressibility on the estimation of petroleum reserves

The material balance equation for a finite reservoir containing undersaturated oil can be presented as follows:

Np Bo~[So~co+Swicw+Cf] N - Bo (1 - Sw) ( P i - P) (2-141)

COMPACTION OF ARGILLACEOUS SEDIMENTS 1 4 7

T~Q. Id4

7

~ io-~

15 16" - " ~ ~ i ~ 7 . . . . . . . . i I . . . . . . . .

.o' ".o" .o~ i v

Fig. 2-49. Relationship between compressibility (psi -1) and applied pressure (psi) for unconsolidated sands, illite clay, limestone, sandstones and shale. (After Sawabini et al., 1974; Chilingar et al., 1983.)

No. Investigator Rock type Type of applied pressure Compressibility

1 The writers California unconsolidated Hydrostatic Pore [-(1/Vp)(0 Vp/OPe)a] arkosic sands a California unconsolidated sands California unconsolidated arkosic sands a California unconsolidated sands Illite clay (API No. 35) (wet) b Illite clay (API No. 35) (dry) Repetto Fm. (Grubb Zone) (wet) a Lansing-Kansas City Lime- stone (wet) a Woodbine Sandstone (wet)

2 Kohlhaas and Miller Uniaxial Pore (1969)

3 The writers Hydrostatic Bulk

4 Kohlhaas and Miller Uniaxial Bulk (1969)

5 The writers Uniaxial Bulk 6 The writers Uniaxial Bulk 7 Knutson and Bohor Net confining Pore

(1963) 8 Knutson and Bohor Net confining Pore

(1963) 9 Carpenter and Spen- Net confining Pseudo

cer (1940) bulk 10 Fatt (1958b) Feldspathic graywacke Net confining d Bulk

(No. 10) (wet) c 11 Fatt (1958b) Graywacke (No. 7) (wet)c Net confining Bulk 12 Fatt (1958b) Feldspathic graywacke Net confining Bulk

(No. 11) (wet) c 13 Fatt (1958b) Lithic graywacke (No. 12) Net confining Bulk

(wet) c 14 Fatt (1958b) Feldspathic quartzite Net confining Bulk

(No. 20) (wet) c 15 Podio et al. (1968) Green River shale (dry) Net confining Bulk 16 Podio et al. (1968) Green River shale (wet) b Net confining Bulk

17 Chilingarian et al. Montmorillonite clay satura- Hydrostatic (1973b) ted in seawater

18 Chilingarian et al. Montmorillonite clay satura- Uniaxial (1973b) ted in seawater

[-(1/Vb)(O Vb/Ope)o]

[ - (1 /e + 1)(de/dpe)] [-(1/h)(dh/dpe)] [-(1/Vp)(OVp/Oa)pp]

[-(1/Vp)(3 Vp/Ocr)pp]

[-(a/ Vb)(O Vp/Op)]

[-(1/Vb)(0 Vb/Opt) Pp ]

Cb - --V-bb \ ~Pe Ja, T

1 Oh Cb -- --~ (~p)

a Saturated with formation water. b Saturated with distilled water. c Saturated with kerosene. d Net confining pressure = external hydrostatic pressure on a jacketed specimen = Pe = (a - 0.85pp), where a is the total overburden stress and pp is the pore pressure. Stresses in the triaxial apparatus of Sawabini et al. (1971) approached hydrostatic; i.e., three principal stresses in x, y and z directions are equal.


where N = initial oil-in-place in the reservoir; Np = volume of stock-tank oil produced; p = reservoir fluid pressure (Pi > P > Pb); Pi = initial reservoir fluid pressure; Pb = bubble-point pressure; Bo = formation volume factor (= volume at reservoir conditions/volume at standard conditions); Boi = initial formation volume factor; cf = pore compressibility [= (--1/Vp)(SVp/Spp)-&T, where Vp is the pore volume; pp is the reservoir fluid pressure; ~ is the average external pressure; and T is the temperature]; Co = compressibility of oil; Cw = compressibility of w a t e r ; Swi --" initial water saturation; and Soi = initial oil saturation. Thus, the significance of pore compressibility, cf in Eq. 2-141, depends on the numerical value compared with (Soico + Swicw) (Scorer and Miller, 1974). At bubble-point pressure, oil compressibility varies from 5 x 10 -6 to 25 x 10 -6 psi -1, whereas water compressibility is about 3 x 10 -6 psi -1.

The effective gas compressibility in gas reservoirs can be estimated by using the following equation:

r Sw -t- r (Cg)effective "-- r "]" (2-142) Sg

Inasmuch as r usually is much larger than r the latter can be neglected. In deep formations and, especially, unconsolidated ones, cf is of the same order of magnitude as Cg, which decreases with increasing pressure. As pointed out by Scorer and Miller (1974, p. 16), the above expression (Eq. 2-142) must be continuously evaluated as the pressure changes, and any attempt to use an average gas compressibility in flow equation is likely to lead to serious errors.

C O M P A C T I O N O F C A R B O N A T E S

The significance of compaction and its role in pore space reduction in carbonates has long been a matter of debate. An excellent discussion of this problem appears in a paper by Bathurst (1980). Originally, it was thought that the onset of cementation in carbonates is so early that compaction is either low or even as good as nonexistent (Pray, 1960; Steinen, 1978). Extensive presence of deformed fossils, compactional drapings, etc., however, demonstrates moderate to high degrees of compaction in some calcareous rocks (Carozzi, 1961; Kahle, 1966; Wolfe, 1968; Brown, 1969; Zankl, 1969; Baldwin, 1971; Rieke and Chilingarian, 1974; Kendall, 1975; Chilingarian and Wolf, 1976; Wolf and Chilingarian, 1976; Chilingarian et al., 1979; Bathurst, 1983; Meyers and Hill, 1983; Gaillard and Jautee, 1985). Also, porosity reduction data in pelagic carbonate ooze recovered by the Deep Sea and Ocean Drilling Projects (i.e., DSDP/ODP) support the occurrence of compaction (Matter, 1974; Schlanger and Douglas, 1974; Garrison, 1981). Arguments recently made by Ricken (1986) and Bathurst (1987) show that carbonate compaction seems spatially concentrated in relatively narrow zones in bedded carbonate rocks from various environments, characterized by fabrics of mechanical compaction and pressure dissolution.


Derivation of the Ricken's carbonate compaction equation

The carbonate compaction equation of Ricken (1986, 1987) is a basic and theoretically founded relationship among the following three sediment or rock parameters: carbonate content, compaction, and porosity. This relationship can be derived by considering a sediment-rock transformation of calcareous sediment containing various proportions of pore space, and carbonate and noncarbonate contents (Fig. 2-50). The noncarbonate fraction is usually composed of clay minerals, quartz, and organic matter (Wedepohl, 1970). During the sediment-rock transformation, the pore volume is reduced due to compaction or cementation and the initial carbonate content is changed because of cementation or carbonate dissolution. Only the carbonate fraction remains essentially unaffected (Fig. 2-50). The noncarbonate fraction (NCd in vol.%), however, is the only constant factor in carbonate diagenesis, when it is standardized to the primary, or uncompacted, sediment bulk volume:

(100 - K ) ( 1 0 0 - n ) ( 1 0 0 - C ) NCd -- (2-143)

10,000

where C is the volume of solid carbonates expressed as the percentage of the compacted sediment (bulk) volume; n is the porosity, percent of bulk volume; K is the degree of compaction expressed as the percentage of the original volume of the sediment; and NCa is the solid noncarbonate fraction expressed as a percentage of the original sediment volume. This N Co value is standardized to the original sediment volume and will be, therefore, referred to simply as the "standardized noncarbonate content". Equation 2-143 was termed the "carbonate compaction law" by Ricken (1986, 1987), because in most rocks with low porosity, it essentially relates the carbonate volume to the degree of compaction. As the specific grain densities for the carbonate and noncarbonate fractions are very similar, the volume percent of carbonate in Eq. 2-143 is essentially equivalent to the weight percent content of carbonate. This compaction law is valid regardless of whether the diagenetic carbonate system is closed or open.

Fig. 2-50. Principles of volume changes during sediment-to-sedimentary rock transformation for carbonates. Left: uncompacted sediment with original porosity (no) and original carbonate content (Co). Right: compacted and lithified calcareous rock volume (compaction = K) with diminished porosity (n) and altered carbonate content (C). The non-carbonate fraction (NCd) remains constant when it is expressed as percentage of the original sediment volume. (After Ricken, 1986, p. 13, fig. 5.)


Carbonate compaction equation for rocks with low porosities (Ricken, 1986, 1987)

In many lithified calcareous rocks and marls, porosities are below 15%, whereas limestones commonly have porosities below 5% (Bathurst, 1980). Thus, for these low-porosity rocks, the compaction equation (Eq. 2-143) can be simplified to the following:

(100 -- K r ) ( 1 0 0 - C ) NC~ = 100 (2-144)

where the percentage of compaction (Kr) in low-porosity calcareous rocks is equal to :

100 • NCd) Kr -- 100 - (100 - C (2-145)

Thus, compaction can be calculated for porous and partially lithified sediments, and essentially nonporous rocks with various standardized noncarbonate fraction (i.e., NCa) and carbonate contents by using Eqs. 2-143 and 2-145, respectively. As follows from Eq. 2-145, the degree of compaction in non-porous rocks is non-linearly related to the carbonate content (Fig. 2-51). For a constant value of the standardized noncarbonate fraction content (NCa), compaction is low at high carbonate contents, large at medium carbonate contents, and very large at low carbonate contents. Such nonlinear carbonate content versus degree of compaction relationship can be explained by compacting a nonporous carbonate rock through pressure dissolution as indicated in Fig. 2-51.

For most calcareous rocks, however, this curved relationship between the carbonate content and degree of compaction reflects the presence of both less compacted cemented, and more compacted dissolution-affected rock portions. For sites at low degrees of compaction and high carbonate content, the sediment was cemented early in its diagenetic history (after some mechanical compaction by the precipitation of additional cement in the original pore space, thus inhibiting further compaction. On the other hand, low carbonate contents and a high degree of compaction are usually associated with pressure dissolution of carbonate or chemical compaction. As a consequence, the degree of compaction and the carbonate content in calcareous rocks can be viewed to reflect the diagenetic history, related to mechanical compaction, cementation, and pressure dissolution.

Testing of compaction equation by compaction measurements (Ricken, 1986, 1987)

In order to test whether the theoretically derived carbonate compaction equation is documented in the rock record, compaction, carbonate content, and porosity were measured in the interbedded marl-limestone alternations mentioned above. These values were then compared with the theoretical curves for carbonate content versus degree of compaction. Among these parameters, compaction is the most difficult to determine. Many authors have addressed compaction measurement by using various methods, included grain orientation and deformation (e.g., Wolf and Chilingarian,


Fig. 2-51. Simplified illustration of the carbonate compaction equation, depicting how the initial carbonate content of 90% in a non-porous limestone sample will change by constantly increasing the degree of compaction (K, in %) and removing carbonate by dissolution. The percentage of carbonate fraction (C) is indicated by small numbers within columns, with a scale on the right-hand side. It should be noted that the same values for carbonate content and compaction will be obtained when a porous sediment with the same standardized percentage of non-carbonate fraction undergoes first mechanical compaction and then cementation. Lower diagram shows the theoretical relationship between degree of compaction (%) for samples with various NCd contents and porosities ranging from 0 to 15% (solid and dashed curves). (After Ricken, 1986, 1987.)

1976; Bathurst, 1987), deformation of primary sedimentary structures (e.g., Baldwin, 1971), deformation of vertically emplaced sedimentary dikes (e.g., Beaudoin et al., 1984), compactional draping relative to early concretions (e.g., Einsele and Mosebach, 1955; Chanda et al., 1977), density of bioturbation pattern (Galliard and


Jautee, 1985), and experimental studies (Chilingarian and Rieke, 1976; Shinn et al., 1977). Inasmuch as most of these methods can be considered relative and only semiquantitative, the deformation of originally circular bioturbation tubes (parallel to the bedding) are used, because these sedimentary structures deform with the sediment and, therefore, their degree of compaction can be reliably determined (Plessmann, 1966).

Bioturbation tubes are usually formed within the upper meter of the sediment, but below the mixed uppermost sediment layer (Ekdale et al., 1984). Bioturbation structures undergo the same amount of compaction as the surrounding sediment, except burrows with early diagenetic cementation (Fig. 2-52). Burrows suitable for direct compaction measurement must have originally circular tubes, such as Thalassinoides, Teichichnus, Chondrites, and Planolites (HfintzscheI, 1975); this can be confirmed on examining the cross-sections of vertically emplaced burrows. Such burrows are abundant in shelf and pelagic sediment (Kennedy, 1975; Ekdale and Bromley, 1984). Burrows must be parallel to the bedding and only cross-sections perpendicular to the burrow tubes must be used for measuring the burrow axes. Measurements can be performed in the field utilizing suitable rock samples with burrows. During compaction, only the length of the vertical axis (b) is reduced and, thus, the degree of compaction (K) can be expressed as a percentage of the undeformed horizontal axis (a) (Fig. 2-51).

K = ( a - b ) l o 0 = l O 0 - ( a (2-146)

Burrows with early cementation can be recognized by their significantly higher carbonate content and lower degree of compaction than the surrounding rock (Fig. 2-52). Despite this, compaction can be indirectly determined by using the carbonate content of the burrow fill and that of the surrounding rock. From the partial compaction and carbonate content of the burrow, a standardized noncarbonate fraction content (NCd) can be calculated (Eq. 2-143), which is assumed to be the same for the burrow and the carbonate content of the host rock. Compaction is obtained either by solving Eq. 2-143 for K or by using Eq. 2-145. Repeated direct and

Fig. 2-52. Compaction measurement using the deformation (D) of an originally circular burrow tube (a). Normally, burrow deformation equals the actual sediment or rock compaction (b: D = K = 60%). In early cemented burrows, compaction (K) is higher than the burrow deformation (c: D = 40%). (After Ricken, 1986, 1987.)


indirect determinations of compaction using burrow deformation show the accuracy of -+-10%. Consequently, only the means of several measurements allow a correct determination of compaction. The following example demonstrates this:

Example: One wants to know the degree of compaction in a lithified marl containing cemented burrows (75% CaCO3) with a significantly higher carbonate content than in the surrounding rock (50% CaCO3) . From the degree of shortening of the vertical burrow axes, compaction of the cemented burrow is calculated to be 60% (Eq. 2-146). Because porosities are low enough to be ignored, the NCo value can be calculated according to Eq. 2-144 using the burrow tube carbonate content and the degree of compaction, which results in a NC0 of 10%. Under the assumption that the N Cd value (i.e., the noncarbonate fraction of the original bulk sediment volume) is the same for the cemented burrows and the surrounding sediment, the actual degree of compaction can be calculated using the carbonate content of the surrounding rock (50% C a C O 3 ) and the NCd value of the burrow (Eq. 2-145). Thus the degree of rock compaction in the rock matrix is calculated to be 80%, which is substantially higher than that indicated by the degree of compaction (60%) determined in the cemented burrow. (See Ricken, 1986, 1987, for details.)

Buryakovskiy et al. (1991) discussed similarities and differences in the processes of compaction of carbonate and terrigenous rocks. They presented a generalized model of compaction and numerous curves showing a relationship between porosity and depth of carbonates, sandstones, siltstones and clays.

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(Editors), Fundamental Aspects of Petroleum Geochemistry. Elsevier, Amsterdam, pp. 37-75. Weaver, C.E. and Beck, K.C., 1969. Changes in the Clay-Water System with Depth, Temperature and

Time. OWRR Proj. No. A-008-GA, Soc. Ceram. Eng. Georgia Institute of Technology, Atlanta, Ga., WRC-0769, 95 pp.

Wedepohl, K.H., 1970. Geochemische Daten von sediment/iren Karbonaten und Karbonatgesteinen in ihrem faziellen und petrographischen Aussagewert. Verh. Geol. Bundesanst. Wien, 4: 692-705.

Weller, EA., 1959. Compaction of sediments. Bull., Am. Assoc. Pet. Geol., 43: 273-310. Welte, D.H., 1965. Biogeochemistry of organic matter, 2. Thermal reaction kinetics and transformation

products of amino compounds. Geochim. Cosmochim. Acta, 28: 157-188. Welte, D.H., 1972. Petroleum exploration and organic geochemistry. J. Geochem. Explor., 1: 117-136. Welte, D.H. and Yukler, M.A., 1981. Petroleum origin and accumulation in basin evolution - - A

quantitative model. Bull., Am. Assoc. Pet. Geol., 65: 1387-1396. White, D.E., 1965. Saline waters of sedimentary rocks. In: A. Young and J.E. Galley (Editors), Fluids in

Subsurface Environments. Am. Assoc. Pet. Geol., Mem., 4: 342-366. Williams, D.G., Brown, W.O. and Wood, J.J., 1965. Cutting drilling costs in high-pressure areas. Oil Gas

J., 63: 145-152. Wolf, K.H. and Chilingarian, G.V., 1976. Compaction diagenesis of carbonate sediments and rocks. In:

G.V. Chilingarian and K.H. Wolf (Editors), Compaction of Coarse-Grained Sediments. Developments in Sedimentology, 18B. Elsevier, Amsterdam, pp. 719-768.

Wolfe, M.J., 1968. Lithification of a carbonate mud: Senonian chalk in Northern Ireland. Sediment. Geol., 2: 263-290.

Wright, J., Pearson, C., Kurt, E.T. and Watkins, J.W., 1957. Analysis of brines from oil-productive formation in Oklahoma. U.S. Bur. Mines, Rep. Invest., No. 5326, 71 pp.

Young, A. and Low, P.E, 1965. Osmosis in argillaceous rocks. Bull., Am. Assoc. Pet. Geol., 47(7): 1004-1008.

Yukler, M.A., Corford, C. and Welte, D.H., 1978. One-dimensional model to simulate geologic hydrodynamic and thermodynamic development of a sedimentary basin. Geol. Rundsch., 67: 960- 979.

Yusufzade, Kh.B., Nabiev, G.I. and Dergunov, E.N., 1978. Expulsion of water from clays with anomalously high pore pressures into reservoirs. Geol. Nefti Gaza, 4: 18-22.

Zankl, H. 1969. Structural textural evidence of early lithification in fine-grained carbonate rocks. Sedimentology, 12: 241-256.

Zavgorodniy, A.L. and Pakhol'chuk, A.A., 1985. The distribution and nature of the overpressure in carbonate reservoirs of the Pripyatskiy Deep. Geol. Nefti Gaza, 11: 51-56.


Chapter 3

165

STRESSES IN SEDIMENTS

E R L E C. D O N A L D S O N , G E O R G E V. C H I L I N G A R I A N and H.H. R I E K E

Subsidence in or near human development results in serious environmental concerns that may not be amenable to control or abatement, such as the breaking of a dam or subsidence within a city (Hamilton and Meehan, 1971; Colazas and Olson, 1983). Land subsidence is the ultimate result of: (1) tectonic motions, (2) subsurface grain compaction caused by overburden loading, and (3) withdrawal of fluids (gas, water or oil).

A cube of subsurface sediment has nine stress components acting on it: three principal, normal stresses, cri, acting along the perpendicular axes and six tangential, shear stresses, vii, that act on each surface face of a free-body cube normal to the axes (Fig. 3-1). The stress tensor (S), or resultant, of the nine stresses is described mathematically as:

Ox rxy "Cxz

S ~ 7@ x Cry "C y z (3-1)

rzx r.zy Crz

In Fig. 3-1, a slice of the free-body that has differential thickness, width, and length is presented. As the edge dimensions of this elemental volume approach zero, the components of the resultant couple on any cube face becomes zero. When this occurs, the stress components, cr and r, approach a finite value (Rogers, 1964):

Fx = { Crx "Cx y Cxz } A y A z

Fy = { 72yxOy "Cy z } A x A Z

Fz = { rzx rzyaz } Ax Ay

(3-2)

(3-3)

(3-4)

Fx, Fy and Fz are the forces in the x-, y- and z-directions. The surface forces (stresses) have the dimensions pounds per square inch, whereas body forces are measured in units of force per unit volume. Examples of these are pressure and specific weight, respectively.

The stresses acting on subsurface accumulations of sediments are neither equal nor static. They undergo changes of magnitude as the geologic structure is impacted by exo- and endogenic processes. The conditions also are complicated by the variable geothermal and geopressure gradients and the presence of fluids in the pore spaces of the grain-to-grain skeletal matrix. Hubbert and Rubey (1960) showed that the overburden pressure, Pob, is supported jointly by the effective grain-to-grain pressure, Pe, of the skeletal matrix and by the pressure of the fluids in the pores, pf:

166 E.C. DONALDSON, G.V. CHILINGARIAN AND H.H. RIEKE

~z Z

,lgz

> Y

Fig. 3-1. Stress notation in a cubic argillaceous rock slice. Stress notation of the normal component of stress, Crz, on the plane normal to the z-axis; rzx, and Tzy refer to the shear stress components in the plane normal to the z-axis and acting in the x- and y-directions, respectively. Point O is in equilibrium with respect to the forces in the x- and y-directions, oz + (&rz/,~z)dz is the incremental change in the vertical stress through the free body. (From Rieke and Chilingarian, 1974, fig. 52, p. 93.)

Pob - - Pe q- Pf (3 -5)

The average local overburden pressure is equal to the specific weight of the water-saturated overlying sediment, Fb, multiplied by the depth (Eq. 3-6). Inasmuch as the effective skeletal stress Pc, increases continuously with decreasing porosity, q~, it is a function of either porosity or the remaining fluid content (Eqs. 3-7 and 3-8):

P oh = Yb X D (3-6)

Pe = f(~b) (3-7)

Pe = f ( S g + Sw + So = 1.0) (3-8)

During sedimentary deposition, these three stresses (Eq. 3-5) attain temporary equilibrium with different degrees of support assumed by the rock matrix skeletal structure and the fluids occupying the pores. Rapid sedimentation accompanied by tectonic movements leads to confined, undercompacted reservoirs. Decrease of the pore pressure of an undercornpacted reservoir by removal of interstitial fluids increases the grain-to-grain pressure, which results in one, or a combination of several, type(s) of compaction.

STRESSES IN SEDIMENTS 167

There are two types of recoverable and non-recoverable deformations that may take place in response to the imbalance of the three forces expressed in Eq. 3-5. Increase in the grain-to-grain stress can result in recoverable elastic and visco-elastic (time dependent) deformation of the grains, or the grains may permanently deform by structural yields (crushing under the increased load) and plastic deformation of shape (Dusseault, 1983; Lofgren, 1976).

In addition to the grain response to increased stress, the subsurface reservoir as a whole undergoes several types of change adjusting to the imbalance of forces caused by fluid withdrawal. Loosely cemented grains undergo permanent rearrangement of grains and pore spaces, resulting in the loss of porosity and permeability. This type of compaction resulting from grain mobility is only partially reversible if the fluid pressure is increased once more by water injection, for example.

C O M P A C T I O N

Cemented sand reservoirs may undergo significant compaction if the reservoir has great thickness (>50 m) and large areal extent. Shallow reservoirs will undergo viscous creep, deforming horizontally as well as vertically, if the overburden pressure is supported principally by the grain-to-grain stress over a long period of time. If the conducive conditions of great thickness and large areal extent do not exist, even a slightly cemented sand will not undergo significant compaction and the problem may consequently be ignored.

Shale and clay beds interspersed within a productive zone can contribute significantly to the overall reservoir compaction. In relatively young, shallow oil reservoirs these shale and clay beds are commonly undercompacted and exhibit high compressibility. Compaction takes place over a long period of time, because the process involves expulsion of water which is partially controlled by a diffusion mechanism (Dusseault, 1983; Geertsma, 1973).

Clay and sand layers compact almost to the same extent. The principal difference is the plastic behavior of the clay bodies, because of the extremely low effective permeability to water, which must be expelled in order for compaction to take place. Over a period of several years, however, the slow contribution of shales and clays to compaction (and subsequent subsidence) can be of major importance (Van der Knaap and Van der Vlis, 1967).

Significant compaction with subsequent subsidence, may take place in productive zones containing interbedded clay and shale even if the productive formation itself has low compressibility. Thus, in the evaluation of a zone for compaction/ subsidence, one must consider the total hydraulically connected zone. In any of the classifications of compaction/subsidence, however, the amount of potential subsidence decreases exponentially with depth. Thus, shallow sedimentary deposits, in which the entire thickness of the reservoir is preserved without uplift, erosion and reburial have the greatest potential for significant surface subsidence if fluids are withdrawn from the subsurface reservoir (Chilingarian et al., 1983; Prokopovich, 1983).


LABORATORY AND MATHEMATICAL ANALYSIS OF COMPACTION

The laboratory observations of compaction may be divided into two principal types (Rieke and Chilingarian, 1974): (1) the first consists of laboratory results of compression tests on materials at low and high pressures, and (2) the second type of data is provided by measurements on large sedimentary core samples from gas and oil wells. Unfortunately not all of the factors are known, or have been scaled properly in the laboratory experiments, to insure proper understanding and correlations to geological systems. Laboratory equipment have been developed to measure various physical properties of saturated sedimentary samples subjected to uniaxial and triaxial stresses, but these only partially simulate the conditions existing in the subsurface. Several types of free body loading conditions are illustrated in Fig. 2-48 of Chapter 2.

Figure 2-48A illustrates hydrostatic loading where the three principal stresses are equal (px = Py = Pz). Under hydrostatic conditions no shearing stresses exist in the interstitial fluid because a fluid is a substance which cannot sustain tangential, or shear forces, when it is in static equilibrium. This is not true for adsorbed water because of its quasi-crystalline nature. If a viscous fluid occupies the pore space, there may be some microscopic shear stresses, which are expended locally against the fluid-solid boundaries. Thus, the only macroscopic effect is transmission of the remaining net impelling force to the solid skeletal matrix. With the shear stress equal to zero, the hydrostatic stress tensor for a porous system, whether the fluid is flowing or stationary, is expressed as:

0 0

P ~- Nw 0 (3-9)

0 ~-w

and, the mean value of the hydrostatic stress, ~-w, is:

P = (3 x -~w)/3 (3-10)

Figure 2-48B illustrates triaxial loading where two of the three principal stresses are equal (Px = Py 5~ Pz). The equipment generally uses hydrostatic pressure exerted on samples encased in a sleeve made of rubber or lucite (Rieke and Chilingarian, 1974; Donaldson et al., 1980). The equipment is used to measure compressibility effects on porosity, permeability and skeletal strength at various temperatures. Donaldson et al. (1988) and Donaldson and Obeida (1991) used the equipment to measure the relative permeabilities and microbial enhanced oil recovery at simulated reservoir conditions of depth and temperature.

Bulk compressibility, measured under triaxial loading conditions, is defined as the change in bulk volume per unit of bulk volume, as a function of the change of vertical stress:


Inasmuch as bulk compressibility includes horizontal deformation as a function of vertical stress, it is representative of the changes occurring in the subsurface formation as the components of the stress balance change with deepening burial during sedimentation. It also applies to the changes that occur due to the reduction of the pore pressure caused by the withdrawal of fluids. The lateral motions (horizontal creep) of the subsurface reservoir during fluid withdrawal, however, are extremely slow. Uniaxial compressibility can be applied to the analysis of compaction with the assumption that the time-dependent horizontal dimension changes are insignificant with respect to the vertical change in dimension of the reservoir (compaction). Geertsma (1957) demonstrated that the bulk and pore volume compressibilities of cemented sandstones are functions of the elastic and viscous deformation of the cemented rock matrix, rock bulk material, and the porosity. On the basis of mathematical analysis, he also showed that for many oil sands, which show isotropic elastic behavior, pore volume compressibility measured in the laboratory under uniform and constant pressure is about twice the compressibility in the reservoir. Fatt (1958a, b) compacted a number of consolidated sandstone cores having relatively low porosity under triaxial (hydrostatic) compaction equipment and found them to be only slightly compressible up to 345 MPa [50,000 psi]. He classified the samples according to composition and texture and found that the compressibility of poorly sorted sands was much higher than that of well sorted ones. Handin et al. (1963) conducted a comprehensive series of experiments on the deformation of cemented sandstones under triaxial pressures as high as 345 MPa [50,000 psi]. They found that beyond the realm of elastic compressibility, some samples showed grain fracturing along small shear planes, whereas in the case of others, fractures were distributed throughout the sample. Handin et al. stated that, generally, frictional resistance was high and deformation was cataclastic (breakage across grains and cement) at high confining pressure of about 117 MPa [17,000 psi]. Due to frictional resistance to slippage, shearing and fracturing occurred across the grains, because the major mineral present (quartz) preferentially fractured rather than slipping.

Figure 2-48C shows polyaxial loading where the three principal stresses have different magnitudes (px ~ py ~ Pz). This condition can exist in the subsurface, especially when the geologic structure is in motion due to tectonic forces; however, it is difficult to duplicate in the laboratory because of the difficulties involved in containing the sample and making the measurements.

When a single compacting force is applied, while the sides perpendicular to the applied force are held stationary, the system is designated uniaxial compaction (Fig. 2-48D; Px ~ Pz; Px = P y ) .

Uniaxial compressibility is defined as the change in length per unit length, as a function of the change of vertical stress:

Cu = - - (3-12) Z

Geertsma (1973) proposed a simple method of making a quick evaluation of the magnitude of compaction based on the uniaxial compressibility. By assuming a fixed

1 7 0 E.C. DONALDSON, G.V. CHILINGARIAN AND H.H. RIEKE

value for the formation compressibility over the pressure range being considered, the change in vertical dimension of the reservoir, Az, can be estimated"

A z = (Cu x A p ) z (3-13)

Numerous authors have presented laboratory data showing relationships between porosity and permeability. Using such data, especially that obtained from samples of a specific formation, one can obtain an estimate of the magnitude of change for porosity and permeability that are anticipated:

q~l X ha - AZ 4~2 = (3-14)

h2

k = A • 108~ (3-15)

where A and B are constants; h = thickness of the formation; k = permeability; z = vertical distance; and 4~ = porosity.

This simple analysis indicates whether a more detailed computer simulation of the entire reservoir is necessary if fluids are to be withdrawn from an environmentally sensitive area.

Van der Knaap and Van der Vlis (1967) compacted (uniaxially) both sand and shale core samples from oil wells in Lake Maracaibo, Venezuela, at pressures up to 41.4 MPa (6000 psi). These authors found that the sands and shales were both compressible (Fig. 3-2) and estimated that their contribution to compaction and subsequent subsidence should be about equal. They also showed that the rates of shale compaction were very slow compared to unconsolidated sands under similar loading conditions. This difference in compaction rate is due to the low permeabilities of shales and their relatively strong internal structure.

Roberts (1969) tested (uniaxially) a large number of samples of oil sands, beach sands, and mixtures of quartz sand and other materials prepared in the laboratory. The comparisons of these tests showed that sands were either as compressible as, or more compressible than, clays in the pressure ranges of 7-70 MPa (1000-10,000 psi). Both Roberts and De Souza (1958) and Roberts (1969) concluded that in deep sedimentary deposits the compressibility of sands can be either equal or greater than that of clays. Roberts (1969) interpreted the sharp "break" present on some of his sand compression curves (plotted as void ratio versus log of pressure) as being the point at which sand grains commenced shattering (Fig. 3-3). The shattering- point pressure was considered to be related to the initial density, angularity and grain size in these unconsolidated sands. Densely compacted, well-rounded, smaller- sized grains have a high break-point pressure, whereas lesser compacted sands with angular, large grains tend to have a lower break-point pressure. According to Roberts (1969), clays undergo most of the compaction at low pressures and high void ratios, whereas at pressures above 34.5 MPa (5000 psi) unconsolidated sand may be more compressible. A similar break in the slope of the void ratio 1-versus- log pressure curve is often present in the case of clays and solids. This break is

1 Void ratio is the ratio of the voids volume (pore volume) to the solids volume: e -- Vp/Vg.


0.6

0.5

SAND ( 3 1 0 0 ' )

0

O" 0.4 I-- < IZ:

C) m

0 0.3 >

CYCLE

0.2

o.I 2oo 400 6oo IOOO 2000 4000

I - I

I INTERSECTION

~ ' ' ' " ~ " , , , , , , , , , , , , , , , , ~ POINT ........... "'. l

I I 1 I 1 1 I I I WX)

EFFECTIVE PRESSURE, psi

Fig. 3-2. Relationship between the effective pressure (difference between total pressure and pore pressure) and void ratio for adjacent clay and sand samples from a post-Eocene formation of the Bolivar Coast, Venezuela. (After Van der Knaap and Van der Vlis, 1967, p. 89, in: Chilingarian and Wolf, 1975, fig. 2.9, p. 58.)

1.0

0.9

0.8 o

o 0.7 l - et '

0 . 6

0 > 0.5

0.4

0.3

APPLIED PRESSURE, PSI , =o0 ~ooo Io000

' - - - - \ 3 ~ - - - - - _ ~ X

6

4 5

i I

k

\ �9 ~ ~ \ \ \

,;o ,o;o APPLIED PRESSURE, KG/SQ CM A 13

APPLIED PRESSURE, PSI I00 I000 I0000

6 4 - - - " " - - i

I

I l

k . - - - - . -

\

I(~0 I 0 0 0

APPLIED PRESSURE tKG/SQ CM Fig. 3-3. Relationship between void ratio and applied pressure for ground quartz, ground feldspar, ground dolomite, and various natural sands. (A) Curve 1 = 20-40 ground quartz (loose); 2 = 20-40 ground quartz (dense); 3 = 20-40 Ottawa Sand (loose); 4 = 20-40 Ottawa Sand (dense); 5 = graded Ottawa Sand; 6 = core sample of oil sand from California. (After Roberts, 1969, fig. 2, p. 370.) (B) Curve 1 = Rhode Island Sand, Sandy Point; 2 = Plum Island Sand; 3 = 20-40 ground quartz; 4 = 20-40 ground feldspar; 5 = 20-40 ground dolomite; 6 = 100-325 ground quartz. Numbers, e.g., 20-40, refer to sieve sizes, U.S. Bureau of Standards. (After Roberts, 1969, fig. 3, p. 371, in: Chilingarian and Wolf, 1975, fig. 2.8, p. 58.)

172 E.C. D O N A L D S O N , G.V. C H I L I N G A R I A N A N D H.H. R I E K E

considered to be an indication of the magnitude of previous overburden load, called the preconsolidation pressure. The portion of the compression curve at pressures above this point is termed the "virgin" range, meaning that the specimen has not been previously subjected to loads of that magnitude (Fig. 3-2). The resemblance of this change of slope on the void ratio-log pressure curves of both clay and unconsolidated sand samples may be coincidental and not related in origin if fracturing of sand grains occurs.

Allen and Mayuga (1969) compared uniaxial compaction data from oil well cores of arkosic sands and siltstones with that of shallow clays and silts. They concluded that surface subsidence was caused by compaction and that the sands constitute the major compacting material in the Wilmington oil field, California (Fig. 3-4). The shales and siltstones appeared to have already achieved an indurated state relative to the shallow-zone sands. With sufficient time, however, the shales may also have contributed about one-third of the total volumetric compaction. It is interesting to note that at comparable depths in this field, the shale and sand porosities are often similar, even though the apparent structural strength of the shales is far greater than that of the sands (Fig. 3-4).

Figure 2-48E illustrates biaxial loading where two of the principal stresses (Pz top and bottom) which are in the same plane, are equal, whereas the two faces of the cube parallel to the applied stresses are stationary (Px = P y ) . This system will occur at boundaries of a very limited number of reservoirs and has not been discussed as an experimental problem.

Deviatoric stress state. The second component in Eq. 3-16 is known as the stress deviator from the hydrostatic state (Eq. 3-9). It is expressed as the difference between the total stress and the hydrostatic stress which resists deformation:

(O'x - - tTwx) Txy "tJxz

D ~ -Cy x ( O y - Owy ) ry z (3-16) "tJZX rzy (O" z - - O'wz )

where D is the deviatoric part of the total stress tensor. The effect of the deviator stress is to produce a distortion, which is elastic or plastic in nature and is introduced into the sedimentary body.

Total stress tensor. If the sedimentary body is not in equilibrium, the second component will not be a symmetric tensor for the case where "~xy ~ "tJyx. This asymmetric tensor can be subdivided into symmetric and skew-symmetric parts (Ramsay, 1967). The hydrostatic stress component is the same as in Eq. 3-9. The second symmetrical part is the deviatoric stress component which can be expressed as:

(,,x - ~ w ) �89 + ryx) �89 + Tzx)

D ~ �89 + ryx) (O-y --~w) l(ryz + rzy) (3-17)

�89 (rxz -1- rzx) l (ryz Jr "Czy) (Oz -if-w)


APPLIED PRESSURE, PSI I0 I00 I,000 I0,000

1.50

1.40

1.30

1.20

1.10

1.00

Q

.90

O I.- '~ 8O

m

o .7o

.Go

.50

.40

.30

.20

.10

0

APPLIED PRESSURE, KG/SQ CM Fig. 3-4. Comparison of compression tests on Wilmington Oil Field sands and shales, shallow sediments from water-bearing strata, and oil-zone shale and sand from Lake Maracaibo, Venezuela. Void ratio, e, is plotted versus applied pressure. (After Allen and Mayuga, 1969, fig. 7, p. 415. In: Chilingarian and Wolf, 1975 fig. 2.10, p. 60.)


The skew-symmetric part (Eq. 3-17) is termed the disequilibrium component, which causes the sedimentary structure to undergo a rotation in space and is expressed as:

! 0 2('r2xy -- "tSyx) l ( 'Cx z -- "rSzx )

1 (3-18) R = �89 - - "Cxy) 0 "~('Cy z -- "Czy )

1 (.r2zx _ .Cxz) 1 (Tzy __ "~yz) 0

where R is the disequilibrium component. Such a stress state would be expected if tectonic forces were acting on the sedimentary body in a basin within a geosyncline. The total stress tensor (hydrostatic + deviatoric + disequilibrium component) for a sedimentary body not in equilibrium is expressed as the sum of the parts described above:

S = P + D + R (3-19)

Each one of the three components making up the state of stress is directly related to the respective component of the strain tensor. The hydrostatic part of the stress system causes changes in volume, the deviatoric stress components cause distortions, and the disequilibrium components cause the material to undergo rotation in space (Ramsay, 1967).

Overburden stress

Assuming no lateral variation in the state of stress owing to tectonic stresses, the stress should vary through a sediment body mainly in the vertical direction. The stress components acting in the z-direction at a point (x, y, x + dz) can be presented in the Cartesian coordinate system as follows:

( t x z --t-- d 'cxz)( 'Cyz + dryz)(Crz + doz) (3-20)

Inasmuch as dz is small, the changes in az, ryz and rxz may be considered as linear variations, which depend on the rates of change of stress in the sedimentary body:

dcrz = (3Crz/~Crz) dz (3-21)

drxz = (3rxz/dz) dz (3-22)

dryz = (~ryz/dz) dz (3-23)

Considering the balance of forces on the unit volume for the vertical direction:

Oz + dcrz + rxz + drxz + "Cyz "Jr- dryz + Fz = O'z + rxz + ryz + maz (3-24)

where Fz is the body force, m is the mass of the sediment body, and az is the acceleration in the z direction.

If the element is in static equilibrium, the accelerating force is zero and the body force, Fz, is equal to pg where the sediment is subjected to body forces due only to gravity. Equation 3-21 then reduces to (Rieke and Chilingarian, 1974):


Scrz /Sz --t- S T x z / S X Jr- S ' r y z / S y -Jr- Fz = 0 (3-25)

Equation 3-25 expresses both the normal and shear stresses at a point on a plane. It can be written as Eq. 3-26 which may then be integrated with respect to z between the limits of z equal to zero and Z:

~ o z = p g S z - ( 3 T x z / 3 X ) 3 Z - ( 3 r y z / 3 y ) 6 z (3-26)

Z Z Z Z

f doz=pg f dz- f (~rxz/~X)dz- f (~ryz/~y)dz o o o o

(3-27)

Z Z

= f f ( yz/ y dz 0 o

(3-28)

Equation 3-28 shows that the vertical stress, Oz., at the point of depth, Z, equals the overburden weight per unit area of the sediment less the contributions from the vertical shear components. Four probable cases are presented below with the first two cases being acceptable geological possibilities. The vertical normal component of stress at a point is equal to, or nearly identical with, the overburden weight of the sediments in three of the cases:

(1) The vertical-shear stresses are either non-existent or constant in the sediment mass (if 75xy = "gyz = constant):

S T x z / S X = S 'Cyz/Sy -- 0 (3-29)

Inasmuch as the magnitudes of Zxz and Zyz do not change with depth and the derivative of a constant is equal to zero, the net contribution of shear stresses is zero; therefore, Eq. 3-28 reduces to:

cr z = p g Z (3-30)

(2) Integrals of the vertical components of shear are approximately equal to zero"

Z Z

f (~rxz/~x)dz= f (~ryz/~y)dz,~O o o

(3-31)

Sanford (1959) noted that in some types of geologic structures some differences must have existed between the vertical normal component of stress at a point and the weight of the overburden. Namely, the integral of the gradients of the vertical components of shear were non-zero. Over geologic time, however, such stresses may disappear through creep and Eq. 3-28 becomes the same as Eq. 3-30.

(3) Integrals of the vertical components of shear are equal in value and opposite in direction on two planes perpendicular to each other:

z Z

0 0


Equation 3-28 becomes identical to Eq. 3-30, but this is geologically a restrictive case, because the possibility of its occurrence in nature is very slight.

(4) The two integrals of the vertical components of shear are equal:

Z Z

f (3rxz/~x)dz= f (~ryz/3y)dz o o and, therefore, Eq. 3-28 becomes:

z

az = p g Z - 2 f (6"rxz/6x)dz

0

(3-33)

(3-34)

Estimation o f the magnitude and direction o f stress

So far only variations in the stress pattern have been discussed with respect to the vertical overburden load. Berry (1969) pointed out that the pore-fluid pressures of thick Franciscan geosynclinal sediments of Great Valley of California reach near-lithostatic (or geostatic) values. The origin of these anomalous near-lithostatic fluid pressures is attributed to compression between the granitic Sierra-Klamath and Salinas blocks which act like the jaws of a vise closing in on the argillaceous sediments in the Great Valley. High fluid pressures are thus related to the current tectonic compaction.

It has also been argued that creep (rock flow) will occur in sediments for a non-zero differential stress acting over geologic time. Hubbert and Willis (1957) demonstrated that the hydrostatic relationship where the principal stresses are approximately equal (ax ~ ay ,~ az = pD) , cannot be the case in tectonically active regions where normal or thrust faulting is prevalent.

In tectonically relaxed sedimentary basins, such as the Gulf Coast Tertiary basin, which are characterized by normal faulting, the minimum stress direction is approximately horizontal and the stress magnitude is approximately equal to one third of the effective pressure of the overburden. On the other hand, in depositional basins under tectonic compression, such as the Great Valley of California, which are characterized by thrust faulting and folding, the minimum stress direction is nearly vertical and the stress magnitude is equal to the effective overburden pressure. The ratio of the horizontal to vertical stress in the latter case is between 2 and 3.

Another theoretical approach to estimating in situ stress is to assume that a plane strain condition exists in the horizontal plane at depth (Price, 1959). Under this assumption, the following expression relates the stresses in the x and y directions to the vertical overburden stress for rocks in compression:

I) / A A J W ~

a x = a , , = a h - - 1 - - v a z ( J - ' ~ )

where Oh is horizontal stress in general, v is Poisson's ratio, and cr z = p D. This condition requires the sediment to become isotropically elastic before being subjected


to gravity forces. Poisson's ratio values in this case are normally assumed to be equal to 0.25. If the latter value is used in Eq. 3-35, horizontal stress will be equal to one third of the vertical stress. The question arises as to whether 0.25 is a realistic Poisson's ratio value or not.

According to Birch et al. (1942), Poisson's ratio for consolidated sedimentary rocks ranges from 0.18 to 0.27, which gives rise to compressive stress between 5 and 8 kPa/m (0.22 and 0.35 psi/ft of depth). On the other hand, according to Harrison et al. (1954), the unconsolidated sands and shales found in the Gulf Coast regions of Texas and Louisiana can be considered to be in a plastic state of stress and to possess horizontal stresses in excess of 8 kPa/m (>0.35 psi/ft of depth).

Several investigators used pressure data obtained during hydraulic fracturing of oil wells to calculate the stresses (Scheidegger, 1962; Dunlap, 1963; Fairhurst, 1964; Pulpan and Scheidegger, 1965; Perkins, 1967). By determining (1) the maximum pressure required for fracture initiation, (2) the pressure necessary to extend the fracture, and (3) the formation fluid pressure, realistic values of ax and ay were obtained. In some cases, however, one of the horizontal stresses is greater than the overburden stress (ax > az > ay). This state of stress is one of potential wrench faulting. Gretener (1965) has shown that the large calculated horizontal stress values may be due to the author's assumptions rather than to the pressure data.

Pressure-depth-dens i ty relationships

The discussion above (Eq. 3-30) shows that the overburden pressure is approximately equal to the pressure exerted at any depth by the weight of the overlying sediments. By changing the density term in this equation to that of the bulk density of a fluid-saturated shale, the pressure-depth relationships in the field can be determined.

Hubbert and Rubey (1959) stated that within depths of 1 to 2 km, the pressure of the water as a function of the depth, D, can be closely approximated by the equation:

P = p w x g x D (3-36)

where p is the hydrostatic pressure of a column of water extending from the surface of the ground to a depth of D; Pw is the density of the water; and g is the gravitational acceleration. The pressure (in lb/ft 2) at any depth is equal to:

p = S G • Fw • D (3-37)

where S G = specific gravity of interstitial water; Fw = specific weight of water in lb/ft3; and D = depth in ft.

Figure 3-5 shows the concept of overburden load and the load transfer. This is very important, because upon fluid removal subsidence would not occur without a load transfer. (Effective stress Pe = [Fs(1 -~b) + gw~b - gw]D, where gs is the specific weight of solids, lb/ft 3, and q5 is the fractional porosity.) (For details, see Allen and Chilingarian, 1975.)


Fig. 3-5. Illustration of load transfer owing to water-level drop or reduction in pore-water pressure in unconfined and confined aquifers. Geostatic, hydrostatic, and intergranular pressure gradients are plotted assuming that solids and water have specific gravities of 2.7 and 1.0, respectively, and that porosity is equal to 35%. (Modified after Allen et al., 1971, fig. 4, p. 285. Courtesy of Enciclopedia della Scienza e della Tecnica, Mondadori. In: Rieke and Chilingarian, 1974, fig. 154, p. 293.)

SUBSIDENCE OF DEPOSITIONAL BASINS

Physical changes occur r ing in the sed imen t s dur ing subs idence of a depos i t i ona l bas in a re di rect ly r e l a t ed to the evo lu t ion of s tresses within the basin. I n f o r m a t i o n on the th ickness of sed iments , facies changes , fluid d i sp l acemen t p h e n o m e n a , distri-


bution of unconformities, structural geometry, stress-strain relations, and location of abnormally high fluid pressure zones is needed for a satisfactory analysis of subsidence.

The methods, which are employed in determining the stress distribution in an active, sinking sedimentary basin, can be grouped into three general categories: (1) direct measurement of stresses (hydraulic fracturing and strain relief approaches), (2) inferred stress distribution from structural geometry (study of fracture patterns, fault displacement, and settlement features), and (3) inferred stress distribution from structural processes (application of rock mechanics principles) (Currie, 1967). Whereas a measure of stress distribution in rocks during one interval of time may assist one to anticipate structural features, such as a system of fractures that contributes to productive permeability, the future history of these fractures cannot be predicted (Currie, 1967). Permeability and porosity can be changed by subsequent structural events, such as folding and faulting, or by physicochemical events, such as recrystallization, solution and cementation. Thus, the capacity of the sediments to contain and conduct fluids may be changed. The hydrodynamic conditions, which exist during subsidence, may control the physical and chemical mechanisms involved in fluid migration from shales. Present knowledge of compaction indicates that relative displacements of considerable magnitude can result from compaction of shales.

Dusseault (1983) listed several criteria for evaluation of potential subsidence, which includes the geologic history of the specific formation. Compaction of reservoirs due to fluid withdrawal is a phenomenon associated more generally with shallow reservoirs. Furthermore, Dusseault showed that if a shallow formation has previously been subjected to high stress as a result of deep burial, its compressibility will be reduced. If the formation is then changed to a shallow reservoir by uplift and erosion, it will retain most of its low compressibility. In a previously stressed formation, therefore, compaction due to fluid withdrawal may be insignificant. Generally only younger (Cenozoic) sediments less than 2000 m (6600 ft) in depth are important with respect to significant compaction that may create a surface environmental impact.

If a confined aquifer is developed during deposition of younger sediments by tectonic movement, as the depth of burial increases, a larger part of the load of the overburden will be supported by the fluids in the pores of the formation. Thus the zone will have low grain-to-grain supporting pressure and high pore pressure. A formation in this condition (like those of the geopressure/geothermal zone of the United States Gulf Coast or the fresh-water aquifers of the San Joaquin Valley) is undercompacted in relation to its depth of burial (Prokopovich, 1983). Withdrawal, therefore, will increase the effective stress leading to grain rearrangement and compaction. The compressibility of such an undercompacted zone is very high, probably at the maximum for the specific formation.

BASINS AND GEOSY N CLI N ES

According to Dallmus (1958), the size, shape, and dynamic condition of the earth automatically impose definite limits on the vertical displacements, which may take


A 3 ~ 2 ~ 10 0 10 2 ~ 3 ~ I I I I I i I

I I I o 5okra I

,o r '".SASEME.T 0 ,~0 k m

A A' C I I

ii ii

(D) "-.SASEMENT 0 5Ok,.

Contour Interval, 500m

Fig. 3-6. Cross-section of the Michigan Basin. (A) True-scale cross-section. (B) Exaggerated curvature and thickness. (C) No curvature, exaggerated thickness. (D) Diagram of basement surface. (After Dallmus, 1958, fig. 2, p. 886; simplified by Currie, 1967, fig. 4, p. 45. Courtesy of the American Association of Petroleum Geologists. In: Rieke and Chilingarian, 1974, fig. 148, p. 285.).

place in and on the crust of the earth. He stated that the shape of the earth sets the pattern for the shape of any local departures from the spherical shape caused by local disturbance in the stability of the crust. The cross-sectional shape of a depositional basin evolves from an arc of the earth's surface, and during subsidence, rocks of the basin floor must experience compression until the original surface becomes coincident with the chord of the initial arc (Fig. 3-6). Subsidence of a portion of a spherical surface means shortening, because the arc is longer than the corresponding chord. As successive layers of sediment are warped downward, they too will undergo general compression (Currie, 1967). Because of the pressure differential between the compressional central area of a dynamic basin and the tensional rim, there should be a continuous and diminishing expulsion of interstitial fluids from the central portion towards the rim until compaction ceases. As long as the basin is subsiding, the expulsion of interstitial fluids from the fine-grained clastics takes place in an up-dip direction into the coarse-grained clastic sediments, preferentially parallel to the bedding planes. If most of the sediments are argillaceous, then there is little or no continuous permeability in an up-dip direction in the basin. Consequently, hydrocarbons are trapped at random throughout such a basin (Dallmus, 1958).

Dailmus (1958) classified depositional basins as being dynamic or sedimentary. A dynamic basin is created where any portion of the earth's crust is actively sinking as


a unit with respect to the center of the earth. A primary dynamic basin, by definition, is formed by flattening of the original surface to a curvature less convex than the curvature of the earth. Its areal limits are, therefore, defined by the shape of the deformed profile upon which the sediments accumulate. A sedimentary basin is defined by Dallmus as an existing topographic depression receiving sediments; and its size and shape are controlled only by the existing topography. A sedimentary basin may comprise several dynamic basins or parts of such basins, whereas a dynamic basin may be divided into separate sedimentary basins by preexisting topography at the time of subsidence. Sediments laid down in a dynamic basin are subjected to two types of stresses: (1) tangential dynamic stresses caused by vertical movements imposed on a spherical shell, and (2) small vertical stresses imposed by the static load. These two types of stresses are independent of each other (Dallrnus, 1958; Bissell, 1970).

Secondary dynamic basins, as described by Dallmus (1958), are graben and half- graben formed by normal faulting on top of an actively rising large regional uplift. During the growth of basins, such features are in tension normal to their long axis and in compression parallel to the long axis. The size and shape of secondary dynamic basins are related in the first place to the size and shape of the uplift upon which they occur. Currie (1967) noted that observed variations in thickness and character of basinal sediments suggest that rates of subsidence and consequent departure from the initial arc are by no means uniform throughout a basin. Areas of slow departure become depositional shelves, areas of rapid departure become basin troughs, and transitional areas comprise hingebelts or flexure zones (Fig. 3-7). Throughout the course of basin development, bending of strata constitutes a common process of rock deformation. Flexing of sedimentary strata may result from processes other than basin subsidence. Bending will occur in strata overlying an area in which differential compaction of sediments is in progress (Fig. 3-7) (Currie, 1967).

j I N I T I A L ARC A _ -..-~.-'y" . . . . . / ~ _ ~ I ~ /~--~.___ ~ . I - ~ - - - ~ ~

. . . . . 7 ~ . " - - , : ~ . . . . . ~.~- . . . . . . . . . . " ~ -- 2I ~ "" _.-',.-.,e'-" " ~ - ~ . . . ~ 2 - ----I-- '--. . . , ,

HINGEBELT (FLEXURE) \PROFILE OF BASIN FLOOR

B SHELF I HINGEBELT I TROUGH

v v v BASEMENT COMPLEX

Fig. 3-7. Generalized development of shelf, hingebelt and trough area during growth of a basin structure. (A) Possible stages in basin subsidence. (B) Common form of basin structure (after Weeks, 1952). (After Currie, 1967, fig. 5, p. 45. Courtesy of World Petroleum Congress. In: Rieke and Chilingarian, 1974, fig. 149, p. 286.)


NORMAL GEOSYNCLINAL I

hw,6w J ~ WATER

rn'~m ~l hq,gq

Pl P2 LEVEL OF COMPACTION Fig. 3-8. Comparison of normal and geosynclinal upper layers of the earth, according to Scheidegger and O'Keefe's differentiation-compaction mechanism. (Modified after Scheidegger and O'Keefe, 1967, fig. 2, p. 6276. Courtesy of Journal of Geophysical Research. In: Rieke and Chilingarian, 1974, fig. 151, p. 9.88.)

The development of a depression caused by accumulation of sediments was discussed by Scheidegger and O'Keefe (1967). They used a differential compaction mechanism to illustrate that the old idea of a depression in the crust resulting from the deposition of sediments in shallow water may be valid because of the principle of isostasy. Their model consisted of compensating the sedimentary load on the crust by the migration of a low melting-point fraction in the mantle (Fig. 3-8). This fraction may have nearly the same density as the sediments. Scheidegger and O'Keefe (1967) stated that his process would most likely take place in the mantle, because the Mohorovicic discontinuity appears to be depressed beneath such depositional basins. The isostatic level of compensation of the overburden load is assumed to be at a level beneath the Mohorovicic discontinuity. They assumed that the specific weight of the compacted mantle beneath the geosyncline, yq, is greater than the normal specific weight, Ym, because of losing the lighter fraction through migration.

In order to satisfy isostatic principles, the pressure at point 1 must be equal to the pressure at point 2, thus:

Pl = hw Fw + he Fc + hm Fm = P2 = h~v Fw + hsFs + hcFc + hqFq (3-38)

where Fw, Fs, and Fc are the specific weights of water, sediment, and crust, respectively.

Also:

hw -+- he -F hm = h~w -F hs --t- he -I- hq (3-39)

If h~v is equal to zero, Eqs. 3-38 and 3-39 may be reduced to Eq. 3-40 (Rieke and Chilingarian, 1974, p. 288):


LIJ n," :::) or) U') LIJ

A' g

LEVEL OF COMPACTION

DEPTH Fig. 3-9. Total mass (pressure) in normal (solid line) and geosynclinal (dashed line) region (h' w = 0). A ~ A' are corresponding points before and after the geosyncline formation; pressure is higher at A' than at A. (After Scheidegger and O'Keefe, 1967, fig. 3, p. 6277. Courtesy of Journal of Geophysical Research. In: Rieke and Chilingarian, 1974, fig. 152, p. 289.)

hq = h s Ym - Fs _ hw Ym - - Yw ( 3 - 4 0 )

Yq--Ym Yq--Ym

The overburden pressure versus depth curve beneath a geosyncline differs from that of the normal crust due to different density distributions (Fig. 3-9). The total mass is less over the region of the compacted-differentiated mantle than in the normal mantle. Inasmuch as corresponding points are deeper in the "compacted" crust than in the normal crust, the pressure at such corresponding points is greater in the geosyncline than in the normal crust (Scheidegger and O'Keefe, 1967).

HYDROGEOLOGICAL CYCLE

Kartsev et al. (1969) described a simple hydrogeological cycle which starts with tectonic depression and transgression, followed by a period of subsequent uplift and regression, and terminates prior to the initiation of a new depression and regression (Fig. 3-10). The first stage of a hydrogeological cycle (sedimentation state) terminates when a sedimentation basin, upon ceasing to subside, is uplifted and denudation of the water-bearing horizons occurs (Fig 3-10A).

During the second stage (infiltration stage) there is infiltration of atmospheric waters (epigenetic waters), which gradually displace and replace original connate


Fig. 3-10. Hydrogeologic cycle of Kartsev. (A) First sedimentation stage. (B) Infiltration stage. (C) Second (subsequent) sedimentation stage. I = muds and clays formed during sedimentation stage A and containing syngenetic waters; 2 = coarse-grained rocks containing syngenetic waters; 3 = reservoir rocks containing epigenetic waters (infiltrated atmospheric waters); 4 = bottom of depositional basin; 5 = muds and clays formed during stage C; and 6 = direction of water movement. (From Kartsev et al., 1969, fig. 6, p. 24. In: Rieke and Chilingarian, 1974, fig. 153, p. 290.)

waters (syngenetic waters) (Fig. 3-10B). This stage ends as a result of new tectonic depression of the basin accompanied by accumulation of younger sediments. As a result, the infiltration of atmospheric waters terminates. At this time, a new hydrogeological cycle is initiated (Fig. 3-10C). During the second hydrogeological cycle, some remaining syngenetic waters of older shales and mudstones may be squeezed out into older coarse-grained rocks, thus replacing the epigenetic waters. Subse- quent infiltration of atmospheric waters into both older and younger coarse-grained rocks further complicates the situation, and obscures the effect of compaction on the chemistry of interstitial fluids in coarse-grained rocks.

During the sedimentation stage most of the water movement occurs from argillaceous sediments into sands, whereas during the infiltration stage the major movement is from sands into shales. In both cases, there is a secondary movement of fluids in the opposite direction.

SUBSIDENCE AS A RESULT OF FLUID WITHDRAWAL

Land subsidence today is usually caused by the removal of fluids (water, gas or oil). The principal lithological and structural characteristics of the subsiding areas include the following:

(1) sediments are unconsolidated and lack appreciable cementation; (2) sediment section is thick;


(3) porosity of the sands is high (20-40%); (4) sands are interbedded with clays, fine silts and/or siltstones, and shales; (5) fluid production is voluminous; (6) standing fluid levels in the wells exhibit large drops; (7) in the case of water-producing areas, aquifers cover large areas and are

shallow and flat-lying; (8) subsidence rate is cyclic, controlled by seasonal fluid-level fluctuations; (9) age of sediments is Pliocene or younger in the case of water-producing

horizons and Miocene or younger in the case of oil-producing areas; (10) producing formations are located at shallow depth, 300-1000 m (1000-

3300 ft); (11) overburden is composed of structurally weak sediments; (12) in oil-producing areas, the reservoir beds have flat or gentle dips at the

structure crest; and (13) tension-type faulting, often with a graben central block, are present. Horizontal surface movement is common to most present-day subsiding areas.

The subsiding surface area is placed in tension peripherally and in compression at the center. These stresses cause horizontal movement with all peripheral points vec- toring toward the subsiding center. The degree of horizontal movement is a function of the depths and thicknesses of the compacting horizons and the magnitude of the subsidence.

Subsidence due to fluid withdrawal occurs when (a) reservoir fluid pressures are lowered, (b) reservoir rocks are compactable (usually uncemented) and/or are unable effectively to resist deformation upon the transfer of load from the fluid phase to the grain-to-grain contacts, and (c) the overburden lacks internal self- support and can easily deform downward (Allen et al., 1971).

When the hydrostatic head is lowered, the overburden support is decreased and grain-to-grain load increases. As a result, sands and silts compact by grain rearrangement and crushing, whereas plastic flow occurs in argillaceous sediments. Water from clays and shales move into associated sands and, consequently, there is a decrease in the volume of fine-grained sediments. The relative contribution of sands and of clays to compaction varies with depth and with the geologic history. According to Allen et al. (1971), at very shallow depths clays and silts are usually the major compacting materials, whereas at greater depths (300-100 m or 1000-3300 ft) sands constitute the major compacting material.

Susceptibility of the formation to subsidence is dependent upon many factors, such as the degrees of compaction due to previous depth of burial during geologic time, types of clays and sands, shape and size of sand grains, and relative proportions of interbedded clays and sands.

Load transfer occurs as fluid level is lowered. The two concepts used in calculating the overburden load are as follows:

(1) the effective stress acts in a dynamic situation, with downward seepage of fluid through the overburden (Lofgren and Klausing, 1969); and

(2) the static load represents the effective weight of the overburden material. The latter concept is the easiest to use, because the former approach requires


knowledge of the magnitude of the volumetric rate of fluid flow and permeability of the sediments.

The concept of overburden load and load transfer is extremely important, because upon fluid removal subsidence would not occur unless there is a load transfer. The concept of a static overburden load (geostatic pressure) has been widely accepted. The maximum amount of load transfer possible at a particular depth is equal to the fluid pressure (hydrostatic pressure) at that point (Allen et al., 1971).

The manner in which the load change could occur upon production of fluids is illustrated in Fig. 3-5. Initially, the geostatic pressure gradient (20.6 kPa/m or 0.91 psi/ft) is equal to the sum of the intergranular pressure gradient (10.9 kPa/m or 0.48 psi/ft), and hydrostatic pressure gradient (9.7 kPa/m or 0.43 psi/ft). Assuming no residual fluid in the pores, the buoyant effect of the water is lost and the intergranular load is increased as the fluid level is lowered from A to B, for example. Geostatic load decreases (curve 3 shifts to curve 3b, Fig. 3-5) as water is removed. The intergranular and geostatic loads are equal if the pores are dry (curve 2b, Fig. 3-5). Compaction can occur if the intergranular load is increased.

In the case of a confined aquifer, which has a relatively impermeable cover (cap rock), as the fluid level is lowered from A to C, for example, the intergranular load gradually increases until it becomes equal to the geostatic load and curve 2 shifts to curve 2c (Fig. 3-5). If pore spaces still contain some residual water, the intergranular load and geostatic load are not equal below the level C.

Upon the reduction in pore-water pressure and consequent load transfer in the aquifers, pressure gradients are set up across the interfaces of interbedded siltstones, shales, and clays. As a result, water movement occurs from these fine-grained beds into coarse-grained aquifers. The volumetric rate of flow (q, cm3/s) depends on the permeability of clays and silts (k, mD), cross-sectional area (A, cm2), pore-water pressure drop (Ap, atm), viscosity of the water (/x, cP), and length of the drainage paths (L, cm):

kdayA Ap (3-41) q = /xL

and velocity u (cm/s) is equal to q/A. In shallow, unconsolidated sediments, consisting of interbedded clays, silts, and sands, which have void ratios of about 0.6 or greater, clays and silts are the major compactable materials upon dewatering. On the other hand, at depths of 300 m or greater and/or where the void ratios are below 0.6, sands constitute the major compacting material (Allen et al., 1971). At void ratios of 0.6, or greater, and pressures of about 3.5 MPa (500 psi), sands are as compactable as clays, or even more compactable (Fig. 3-11). The clays having high void ratios are very compactable at high pressures. Void ratio-versus-pore pressure data obtained by Roberts (1969) shows that in the 7 to 140 MPa (1000 to 20,000 psi) pressure range, certain sands may be at least as compressible as the typical clays, if not more compressible (Fig. 3-12). At a depth of 900 m (about 3000 ft), Boston Blue Clay could undergo about 6% compression; hence, for an initial stratum thickness of 30 m (100 ft), a total settlement of approximately 1.8 m (6 ft) can occur.


16o

APPLIED PRESSURE, psi.

1.40

1.20

I00

o" i,,,- o:: 8o

o O

60

40

2 0

o o~ .~ s IO ~00

APPLIED PRESSURE, kg/cm z

Fig. 3-11. Relationship between void ratio and applied pressure for sand, silt and clay cores obtained at different depths from various areas. I = Corcoran Clay (depth of 425 ft); 2 = very loose sand; 3 = Corcoran Clay (depth of 735 ft); 4 = silt (depth of 1345 ft); 5 = average Wilmington (California) sands (depth of 2000-4000 ft); 6 = average Wilmington (California) siltstones (depth of 2000-2900 ft) 7 = sand from Maracaibo, Venezuela (depth of 3100 ft); 8 = intermediate compacted sand; 9 = average Wilmington (California) siltstone (depth of 3000 ft); 10 = very compacted sand; 11 = average Wilmington (California) siltstone (depth of 3100-3500 ft); 12 = clays from Maracaibo, Venezuela (depth of 3104 ft)" 13, 14 = average Wilmington (California) siltstones (depth of 3600-6000 ft). (After Allen and Mayuga, 1969. In: Rieke and Chilingarian, 1974, fig. 155.)

Compression of the oil sand, which was disturbed and repacked into an initially loose condition could result in a settlement of 15% less than that of the Blue Clay (Roberts, 1969).

At a depth of 1500 m (5000 ft), the Blue Clay could undergo 5.5-6% compression. At this depth, various sands could undergo 1-7.5% compression (Fig. 3-12). At a depth of 2400 m (8000 ft), the Blue Clay could undergo about 5% compression,


0.7

6 I--- 0.5 n,,

0.3

0.1

0.8

o" I-- 0.6 <[ fie

O m

o

0.4

0.2 10

A C lay a n d S h a l e I I I I

5~ 4

I I i 1

3\ / \ \

\ \

T

1 I I I i I i 1 IOO iooo

1 I I 1 IO,OOO I00,000

APPLIED PRESSURE, psi. B Oil F ie ld S a n d s

I I I I I I I 1 I

5 1 1 ,

I I I I , ,

IOO I 1 I

IOOO IO,OOO IOO

A P P L I E D P R E S S U R E , psi. Fig. 3-12. Relationship between void ratio and applied pressure for clay and shale (A) and for sands (B). (A) 1 = undisturbed Boston Blue Clay; 2, 7, 8 = clay cores from Venezuela obtained from depths of 2486 to 4769 ft below ground surface; 3, 4 = Skempton's (1953) compression curves for plastic clays with liquid limits of 80% and 30%, respectively (P.I. of 50 and 12, respectively); 5 = undisturbed shale (Cl l ) ; and 6 = undisturbed shale (C5). (B) 1 = remolded (25.10); 2, 6 = remolded (M.I.T., Geol. Dept.); 3 = undisturbed (1.1); 4 = undisturbed (25.1); 5 = remolded (25.13); and 7 = undisturbed (14.1). (After Roberts, 1969, fig. 1, p. 369, and fig. 4, p. 372. In: Rieke and Chilingarian, 1974, fig. 156, p. 295.)


w h e r e a s v a r i o u s s a n d s c o u l d u n d e r g o c o m p r e s s i o n v a r y i n g f r o m a b o u t 2 t o 1 0 % . A t

t h i s d e p t h , a 1 0 - 4 0 m e s h O t t a w a s a n d is a b o u t t w i c e as c o m p r e s s i b l e as t h e B l u e

C l a y ( R o b e r t s , 1 9 6 9 ) .


A = area Cb = bulk (triaxial) compressibility, psi -1 Cu = uniaxial compressibility, psi -1 D = depth, m or ft D T = deviatoric stress tensor e = void ratio (Vp/Vs) F = body force due to gravity g = acceleration of gravity h = vertical dimension k = permeability, mD L = length p = pressure, Pa or psi Pe = grain-to-grain skeletal matrix stress, Pa or psi P = hydrostatic stress tensor Pob = overburden pressure pf = fluid pressure pp = pore pressure P T = hydrostatic stress tensor q = volumetric rate of flow, cm 3/s R T = disequilibrium component of the deviatoric stress S = stress tensor Sg = saturation of gas So = saturation of oil ST = total stress tensor Sw = saturation of water SG = specific gravity u = fluid velocity, cm/s Vb = bulk volume Vp = pore volume Vs = solids volume Z = vertical dimension

Greek symbols ~o = specific weight, lb/ft3; to convert to density in g/cm 3, divide by 62.4 Yrn = normal specific weight of the mantle yq = specific weight of compacted mantle beneath a geosyncline ys = specific weight of sediments yw = specific weight of water /z = viscosity v = Poisson's ratio a = principal stress acting on the axes of a free-body, Pa or psi r = shear stress, Pa or psi ~b = porosity


RECOMMENDED BIBLIOGRAPHY

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Carey, S.W., 1954. The Rheid concept in geotectonics. J. Geol. Soc. Aust., 1: 67-117. Magara, K., 1981. Mechanisms of natural fracturing in a sedimentary basin. Bull., Am. Assoc. Pet. Geol.,

65(1): 123-132. Morita, N. and Whitfill, D.L., 1988. A quick method to determine subsidence, reservoir compaction,

and in-situ stress induced by reservoir depletion. Society of Petroleum Engineers Proc. Form. Damage Control Syrup., Bakersfield, Calif. SPE Pap., 17150: 72-84.

Ozkaya, I., 1986. Analysis of factors influencing excess heads in shales during burial. Marine Pet. Geol., 3: 74-78.

du Rouchet, J., 1981. Stress fields, a key to oil migration. Bull., Am. Assoc. Pet. Geol., 65(1): 74-85. Stephenson, E.L., Maltman, A.J. and Knipe, R.J., 1994. Fluid flow in actively deforming sediments:

'dynamic permeability' in accretionally prisms. In: J. Parnell (Editor), Geofluids: Origin, Migration and Evolution of Fluids in Sedimentary Basins. Geological Society (England), Bath, 374 pp.

Van Balen, R. and Cloetingh, S., 1994. Tectonic control of the sedimentary record and stress-induced fluid flow; constraints from basin modelling. In: J. Parnell (Editor), Geofluids: Origin, Migration and Evolution of Fluids in Sedimentary Basins. Geological Society (England), Bath, 374 pp.

Warpinski, N.R. and Teufel, L.W., 1992. Determination of the effective stress law for permeability and deformation in low-permeability rocks. Soc. Pet. Eng. Form. Eval., 7(2): 123-131.

REFERENCES

Allen, D.R. and Chilingarian, G.V. 1975. Mechanics of sand compaction. In: G.V. Chilingarian and K.H. Wolf (Editors), Compaction of Coarse-Grained Sediments, L Developments in Sedimentology, 18A: 43-77.

Allen, D.R. and Mayuga, M.N., 1969. The mechanics of compaction and rebound, Wilmington Oilfield, Long Beach, CA, USA. In: Land Subsidence. lASH-UNESCO, Tokyo, 89(2): 410-413.

Allen, D.R., Chilingar, G.V., Mayuga, M.N. and Sawabini, C.T., 1971. Studio e previsione della subsidenza. Enciclopedia della Scienza e della Tecnica. Arnoldo Mondadori Editore, Milan, pp. 281-292.

Berry, EA., 1969. Origin and tectonic significance of high fluid pressures in the California coast ranges. J. Pet. TechnoL, 21(1): 13-14.

Birch, A.E, Schairer, J.E and Spicer, H.C., 1942. Handbook of Physical Constants. Geol. Soc. Am., Spec. Pap., 36:325 pp.

Bissell, H.J., 1970. Realms of Permian tectonism and sedimentation in western Utah and eastern Nevada. BulL, Am. Assoc. Pet. Geol., 54: 285-312.

Chilingarian, G.V. and Wolf, K.H., 1975. Compaction of Coarse-Grained Sediments, I. Elsevier, Amster- dam, 552 pp.

Chilingarian, G.V., Yen, T.E, Rieke, H.H. III and Fertl, W.H., 1983. Compressibilities of sands and clays. In: E.C. Donaldson and H. Van Domselaar (Editors), Proceedings 1982 Forum on Subsidence due to Fluid Withdrawals. NTIS, Springfield, Va., CONF-821199, pp. 25-32.

Colazas, X.C. and Olson, L.J., 1983. Subsidence monitoring methods and bench mark elevation response to water injection, Wilmington Oil Field, Long Beach, CA, USA. In: E.C. Donaldson and H. Van Domselaar (Editors), Proceedings 1982 Forum on Subsidence due to Fluid Withdrawals. NTIS, CONF-821199, pp. 121-132.

Currie, J.B., 1967. Evolution of stress in rocks of a sedimentary basin. Rock Mechanics in Oilfield Geology, Drilling and Production. Proceedings World Petroleum Congres, Mexico City. Elsevier,


Amsterdam, pp. 41-51. Dallmus, K.E, 1958. Mechanics of basin evolution and its relation to the habitat of oil in the basin. In:

L.C. Weeks (Editor), Habitat of Oil. Am. Assoc. Pet. Geol., Tulsa, Okla., pp. 883-931. Donaldson, E.C. and Obeida, T., 1991. Mechanism of microbial enhanced oil recovery at simulated

subsurface reservoir conditions. In: E.C. Donaldson (Editor), Proceedings 1990 Conference on Microbial Enhancement of Oil Recovery. Elsevier, Amsterdam, 530 pp.

Donaldson, E.C., Kendall, R.E, Pavelka, E.A. and Crocker, M.E., 1980. Equipment and Procedures for Fluid Flow and Wettability Tests of Geological Materials. US Department of Energy, DOE/BETC/ IC-79/5, NTIS, Springfield, Va., 40 pp.

Donaldson, E.C., Civan, E and Alam, M.W.U., 1988. Relative permeability at reservoir conditions. Soc. Pet. Eng., Res. Eng., Nov.: 1323-1327.

Dunlap, J.R., 1963. Factors controlling the orientation and direction of hydraulic fractures. J. Inst. Pet., 49(477): 282-294.

Dusseault, M.B., 1983. Identifying reservoirs susceptible to subsidence due to fluid withdrawal. In: E.C. Donaldson and H. Van Domselaar (Editors), Proceedings 1982 Forum on Subsidence due to Fluid Withdrawals. NTIS, CONF-821199, pp. 6-14.

Fairhurst, C., 1964. Measurement of in situ rock stresses, with particular reference to hydraulic fracturing. Rock Mech. Eng. Geol., 29(3-4): 129-147.

Fatt, I., 1958a. Pore volume compressibility of sandstone reservoir rocks. J. Pet. Technol., 10(3): 64-66. Fatt, I., 1958b. Compressibility of sandstones at low to moderate pressure. Bull., Am. Assoc. Pet. Geol.,

42: 1924-1957. Geertsma, J., 1957. The effect of fluid pressure decline on volumetric changes of porous rocks. Trans.

Am. Inst. Min. Metall. Pet. Eng., 210: 331-340. Geertsma, J., 1973. Land subsidence above compacting oil and gas reservoir. J. Pet. Technol., 25(6):

734-744. Gretener, EE., 1965. Can the state of stress be determined from hydraulic fracturing data? J. Geophys.

Res., 70(24): 6205-6212. Hamilton, D.H. and Meehan, R.L., 1971. Ground rupture in the Baldwin Hills. Science, 172(3981):

333-344. Handin, J., Hagger, R.V. Jr., Friedman, M. and Feather, J.N., 1963. Experimental deformation of

sedimentary rocks under confining pressure; pore pressure tests. Bull., Am. Assoc. Pet. Geol., 47: 717-755.

Harrison, E., Kieschnick, W.J. Jr. and McGuire, W.J., 1954. The mechanics of fracture induction and extension. Trans. Am. Inst. Min. Metall. Eng., 201: 254-255.

Howard, J.H., 1966. Vertical normal stress in the earth and the weight of the overburden. Geol. Soc. Am. Bull., 77(6): 657-660.

Hubbert, M.K. and Rubey, W.W., 1959. Role of fluid pressure in mechanics of overthrust faulting, I. Mechanics of fluid-filled porous solids and its application to overthrust faulting. Geol. Soc. Am. Bull., 70: 115-166.

Hubbert, M.K. and Rubey, W.W., 1960. Role of fluid pressure in mechanics of overthrust faulting, a reply to discussion of H.R Laubscher. Geol. Soc. Am. Bull., 71: 617-628.

Hubbert, M.K. and Willis, D.G., 1957. Mechanics of hydraulic fracturing. Trans. Am. Inst. Min. Metall. Eng., 210: 153-168.

Kartsev, A.A., Vagin, S. B. and Baskov, E.A., 1969. Paleohydrogeology. Nedra, Moscow, 150 pp. Lofgren, B.E., 1976. Land subsidence and aquifer-system compaction in the San Jacinto Valley,

C a l i f o r n i a - a progress report. J. Res., U.S. Geol. Sum., 4(1): 9-18. Lofgren, B.E. and Klausing, R.L., 1969. Land subsidence due to ground-water withdrawal, Tulare-Wasco

area, California. US. Geol. Sum., Prof. Pap., 437B: 103 pp. Perkins, T.K., 1967. Application of rock mechanics in hydraulic fracturing theories. Proc. 7th World Pet.

Congr., 3: 75-84. Price, N.J., 1959. Mechanics of jointing in rocks. Geol. Mag., 96: 149-167.


Prokopovich, N.P., 1983. Tectonic framework and detection of aquifers susceptible to subsidence. In: E.C. Donaldson and H. Van Domselaar (Editors), Proceedings 1982 Forum on Subsidence due to Fluid Withdrawals. NTIS, CONF-921199, Springfield, Va., pp. 33-44.

Pulpan, H. and Scheidegger, A.E., 1965. Calculation of tectonic stresses from hydraulic well-fracturing data. J. Inst. Pet., 51(497): 169-176.

Ramsay, J.G., 1967. Folding and Fracturing of Rocks. McGraw-Hill, New York, N.Y., 568 pp. Rieke, H.H. III and Chilingarian, G.V., 1974. Compaction of Argillaceous Sediments. Elsevier, Amster-

dam, 424 pp. Roberts, J.E., 1969. Sand compression as a factor in oil field subsidence. In: Symposium on Land

Subsidence. IASH/UNESCO, Tokyo, 89(2): 368-376. Roberts, J.E. and De Souza, J.M., 1958. The compressibility of sands. Proc. ASTM, 58: 1269-1277. Rogers, G.L., 1964. Mechanics of Solids. Wiley, New York, N.Y., 250 pp. Sanford, A.R., 1959. Analytical and experimental study of simple geologic structures. Geol. Soc. Am.

Bull., 70(1): 19-52. Scheidegger, A.E., 1962. Stresses in the earth's crust as determined from hydraulic fracturing data.

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deposition. J. Geophys. Res., 72(24): 6275-6278. Van der Knaap, W. and Van der Vlis, A.C., 1967. On the cause of subsidence in oil-producing areas.

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Assoc. Pet. Geologists, 36: 2071-2124.


Chapter 4

193

POSSIBLE IMPACT OF SUBSIDENCE ON GAS LEAKAGE TO THE SURFACE FROM SUBSURFACE OIL AND GAS RESERVOIRS

A L E X A N D E R E. G U R E V I C H and G E O R G E V. CHILINGARIAN


Fractures in rocks in producing oil and gas fields are due to: (1) previous tectonic and diagenetic history, (2) current tectonic and seismo-tectonic movements, and (3) deformations caused by compaction of reservoir rocks and subsidence of overlying formations. The new deformations, both natural and man-induced, enhance previously formed fractures and form new ones.

Fracturing modifies production, gives rise to upward gas migration, and damages surface and subsurface structures. In most cases, water or gas are injected to maintain formation fluid pressure in producing oil and gas reservoirs. This eliminates almost completely major subsidence above oil and gas producing fields, which have high permeability, simple structure, and high hydraulic connectivity of their reservoirs. However, in compartmentalized reservoirs, especially those that are divided into blocks by faults, stresses in the boundary zones of adjacent blocks can be high enough to cause fracturing.

A free gas phase exists in natural gas reservoirs, oil reservoirs with a gas cap, and in underground gas storages. In oil reservoirs, reduction of formation pressure below the bubble pressure produces gas caps. If there are paths for escape from a pool, free gas migrates to the surface, which may be a cause of explosions and fires. In areas subjected to earthquakes, the upward gas migration can be a major hazard. If the oil or gas pool is intersected by an active fault, during an earthquake there will be an upsurge of gas that can cause fires well beyond the ability of Fire Departments to control them. Then a real possibility exists, especially in the presence of winds, of major disastrous fires.

The basis to more effective solutions to this problem may be provided by a more thorough and rigorous analysis of the nature of the processes involved.

C U R R E N T T H E O R I E S OF F L U I D - S O L I D FORCE INTERACTION: A CRITICAL REVIEW

There is no consensus of opinion in the literature on whether the total formation fluid pressure or just a part of it imparts stresses in a fluid-filled rock. This diversity of opinions reflects the fact that there is no consensus in understanding of the physics of fluid-solid interactions and that neither opinion can be considered as final and complete. A short analysis of the problem is, therefore, necessary.

194 A.E. G U R E V I C H A N D G.V. C H I L I N G A R I A N

Correct understanding of the fluid-solid force interaction is a must for the analysis of deformations of fluid-saturated rocks. The outcome of such an analysis has many areas of application: earthquake mechanism, hydraulic fracturing, compaction of rocks in the course of geological history and owing to reservoir pressure decline, and deformation of rocks in subsiding formations above compacting depleted reservoirs. The same theoretical basis is used in solving deformational problems in earthquake prediction and hydraulic methods of dissipating tectonic stresses by means of small earthquakes, deformations associated with oil, gas, and water production (including sand production), and environmental consequences of this production. Although this basis is very important, it is not completely clarified. Studies of fluid-solid interaction should, therefore, be continued.

It is obvious that fluid-solid force interaction takes place only at the fluid-solid contacts on the surfaces of mineral and rock grains. The force acting against this surface is pore pressure. As Jaeger (1979) notes, "Pore pressures produce two separate effects: they compress the solid matter, thus reducing the volume of the solid matrix; and create body forces proportional to the variations of the pressure dp." The term "body force" is rather confusing in this application. It is correct physically to define the latter forces not as body forces (like gravity, acting on every particle of a body), but as resultants of nonuniform surface forces (pore pressures) acting against the surfaces of solid grains.

There are two different approaches to the role of pore pressure in deformations of the fluid-filled rocks. One is a poro-elasticity approach (Biot, 1941; Geertsma, 1957, 1973; Jaeger and Cook, 1969; Jaeger, 1979; Fjaer et al., 1992). This approach can be illustrated by the formula for a component of the stress tensor (Geertsma, 1973):

[ V eSij] - ( l - f l ) pS i j O'ij = 2 G eij -[- 1 -- 2 V

where cri.i = stress component related to the bulk stress system; eij = strain component; e = ~-,eij = dilatation or relative volume change of the bulk material; G = bulk shear or rigidity modulus; v = Poisson's bulk ratio; p = pore-fluid pressure; 13 = ratio between rock matrix and rock bulk compressibility; and ~ij ---- Kronecker's delta.

This approach is based on the rigorous and definite physical concept, but it is correct for and can be applied to purely elastic, reversible deformations only. The majority of deformations due to natural and engineering processes, however, contain irreversible components that often prevail.

The other approach, introduced by Terzaghi in 1923 (see Terzaghi, 1943; Terzaghi and Peck, 1967), is a concept of effective stress. It is assumed that the load, applied to a fluid-filled soil or rock, is supported by the sum of effective stress (grain-to-grain stress) of the solid frame and of pore fluid pressure. This concept was formulated purely phenomenologically. It has no clear and definite physical basis, which causes certain confusion. To some extent, an analysis of physical aspects of this concept was presented by Gurevich (1980).

The effective-stress concept was first formulated on the basis of laboratory experiments. It was assumed that the applied load, L, is supported by the sum of the pore

POSSIBLE IMPACT OF SUBSIDENCE ON GAS LEAKAGE 195

pressure increase Ap, caused by the load application, and the stress in a solid flame, ere. The support provided by solids, within this scheme, was called effective stress. Effective stress is just a computed value and not a measured one, and is determined as follows:

ere = L - Ap (4-1)

It is necessary to emphasize that Ap, although called the pore pressure, actually was the pressure increase, the elastic response of the pore water to deformation of a sample, caused by the applied load, and not the total pore pressure itself. The height of a laboratory specimen is, usually, about 1 inch. Thus, the hydrostatic pore pressure, before load application, is negligible in such a specimen and the excess pressure above the hydrostatic one was taken for the whole pressure value. Numerically, mathematically this was correct, but physically it was not and led to unavoidable confusion. Thus, in fact the load was supported by the excess pore pressure and additional stress in solid frame.

In this model, physical meanings of measured values are quite definite: L is a new, additional load applied to a physical body in mechanical equilibrium, Ap is elastic response of the pore fluid to the total (elastic, reversible, and plastic, irreversible) deformation of the specimen. The physical meaning of the value ere, however, is not defined clearly. It is assumed that effective stress is the stress in the solid frame under these conditions, whereas actually it is the stress in the model medium, being an average stress on a horizontal plane.

Later this concept was extended to the relation between the total load, including the weight of rock column, and the total pore fluid pressure acting through a buoyancy mechanism. Whereas in the previous model fluid pore pressure existed only dynamically, in the course of the deformation process, in this extended case pore fluid pressure exists even at equilibrium. At equilibrium, pore fluid pressure due to its gradient provides buoyancy of grains which results in the reduction of their weight. But owing to the fact that grain contacts are not point contacts, relation

O'e = L - p (4-2)

where total value of pressure acts, is doubtful for the majority of cemented rocks (Laubscher, 1960; Jaeger, 1979; Gurevich, 1980). It is easy to see that Eqs. 4-1 and 4-2 are physically different.

In dynamic situation, hydrostatic uplift and elastic response act together. Thus, physical meaning of the effective stress concept being applied to deformations of rocks in situ is rather obscure physically and often leads to confusion. This is especially so because the effective-stress concept completely ignores both the nature of deformations and mechanical properties of rocks that are deformed. It does not take into account that not just a small piece but a large mass of rocks is being deformed as a single whole. Thus, when deformation can not be reduced to a one-dimensional model, some additional problems arise. For example, generation of vertical tension and strain of rocks in the course of subsidence of formations above a compacting reservoir is not compatible with the effective-stress concept:

196 A.E. GUREVICH AND G.V. CHILINGARIAN

the overburden weight is not fully transmitted to the reservoir but, nevertheless, compaction continues.

Substantial additional problems arise from heterogeneity of the rock mechanical properties and fractures. Owing to heterogeneity, some scale effects arise and should be somehow taken into account (Enever et al., 1990: Ito et al., 1990; Li, 1990; Ratigan, 1990; Bell and Dusseault, 1991).

One more source of confusion is a tendency to believe that compaction in the laboratory tests and compaction in situ do not differ. At the same time, dependence of compressibility on loading history is a well known fact and actually measured compaction in situ is also lower than predicted from laboratory tests. For example, radioactive bullet surveys in the Groningen gas field showed that the actual compaction values were three times lower than the amount predicted (Mess, 1979).

Actually, compaction in the natural environment is accompanied by many more processes and occurs at a much slower rate (Gurevich, 1969, 1980). Compaction in nature depends both on acting overburden or tectonic load and on rock strength. The rock strength is influenced by the continual tectonic movements. However slow and weak, these movements break one grain contact here, one there and, thus, provide rearrangement of grain packing and compaction without additional load. The same impact on compaction is provided by periodic changes of temperature, by seismic waves, and other factors. These mechanisms of compaction are missing in laboratory tests.

In situ loading and compaction are sometimes more than six to eight orders of magnitude slower than in the laboratory tests. This means that molecular processes of slippage along grain crystal boundaries also play an incomparably more significant role in nature than in the laboratory.

In addition, Gurevich et al. (1987) believe that a similarity between three-dimensional laboratory tests and natural three-dimensional deformations is at least doubtful. Any piece of rock in situ compressed by vertical force cannot change its form horizontally because it is surrounded by adjacent "pieces" that tend to have the same horizontal deformation but in opposite direction. Thus a layer of rock subjected to a vertical compression deforms only vertically. If a specimen in a laboratory test, coated on its sides with elastic material (copper foil, rubber, or other), is hydraulically compressed horizontally and by a plunger vertically, vertical compression turns an initially cylindrical specimen into a barrel; this cannot happen in situ. Naturally, stress and strain distributions in a laboratory specimen and in situ are also different. This is a very serious problem, because 3-D tests of cylindrical specimens are widely used.

The effective stress concept is attractive because of its simplicity. It is believed to work well in simple cases when deformation is just a one-dimensional compression. Rieke and Chilingarian (1974) relied heavily on uniaxial compaction apparatuses because they believed that "as the overburden load becomes large enough, the pressures are probably uniaxial."

In more complex situations, when deformation is two- or three-dimensional and cannot be represented by a simple compression only, this concept may not be adequate to represent the actual phenomena. To overcome this problem, the physical basis of this concept should be analyzed in great detail.


F R A C T U R I N G D U E T O S U B S I D E N C E

Subsidence phenomena have not been studied well enough from the viewpoint of fracturing, increase in the vertical permeability of rocks, and, thus, in the upward migration of gas leaking from pools. Therefore, only indirect estimations are possible.

History and causes of subsidence

Subsidence caused by withdrawal of groundwater, oil, and gas has been observed and studied for more than a hundred years (Poland and Davis, 1969; Strehle, 1989). Some of the earliest best known examples of subsidence due to groundwater withdrawal are Osaka, Japan (first noted in 1885), London, England (first noted in 1865), and Mexico City, Mexico (first noted in 1929). One of the earliest examples of subsidence caused by withdrawal of oil is Goose Creek oil field, Texas, USA (first noted in 1918), described by Pratt and Johnson (1926). Thus, the phenomenon of subsidence is well known and thoroughly studied by many investigators up to now. It is physically obvious and fully recognized that subsidence is caused by compaction of reservoir rocks due to the increase of stress due to reduction of fluid pore pressure. Pratt and Johnson (1926) also indicated one more factor, which is important in formations with loose sands and other unconsolidated granular sediments: extraction of sand.

Rates of subsidence

Published information on total and annual rates of subsidence is relatively abundant but quite incomplete. It allows to get an idea of an approximate maximum amount of subsidence. It is impossible, however, to get some definite dependence of the subsidence rates on pressure decline rates and on thicknesses, depths, and characteristics of reservoir and overlying rocks.

The authors would also recommend the following references: Carbognin et al., 1979; Deflache, 1979; Holzer and Thatcher, 1979; Kumar, 1979; Lofgren, 1979; Scott, 1979; Meyer and Powly, 1988; Strehle, 1989; Andronopoulos et al., 1991; Balestri and Villani, 1991; Bravo et al., 1991; Esaki et al., 1991; Holdahl et al., 1991; Gambolati et al., 1991; Morales et al., 1991; Murria, 1991; Pottgens and Brouwer, 1991; Prokopovich, 1991; Rivera et al., 1991.

The total subsidence can reach as much as 10 m. The largest subsidence in the San Joaquin Valley, California, by the year 1970, reached 8.5 m (28 ft). In Wilmington oil field total subsidence was 8.8 m. Lesser values of subsidence of the order of 0.9-1.5 m (3-5 ft) are commonplace. The annual rate of subsidence depends on the rate of pore pressure decline and may be as high as 0.6 m (2 ft) per year. In the San Joaquin Valley average annual rate of subsidence was up to 2.4 m (8 ft) for 10 years (1959-1969), i.e., 24 cm (0.8 ft) per year. In the Wilmington field the annual rate was up to 70 cm (2.3 ft), the total for a period of 3 years (from 1951 to 1954) being 2.1 m (7 ft). Rates of about 0.3 m (1 ft) per year are encountered often: 25 cm (0.84 ft) per


year in Taipei basin, Taiwan; and 32 cm (1.07 ft) per year (in 1960) in Tokyo, Japan. Rates of the order of several cm per year are quite common.

Stress and strain distribution in subsiding formations

Distribution of stress and strain within the rock mass above the compacting reservoir is the most important feature of subsidence from a viewpoint of fracturing of rocks and increase in vertical permeability. Several points should be emphasized.

Horizontal tension is the highest in the zone around the central core of the subsidence bowl where horizontal compression predominates (Fig. 4-1). Horizontal displacement in the Wilmington oil field reached a maximum of about 3.66 m (Allen, 1973; Kosloff et al., 1980). This extension can be presented, for example, as four new 0.5 mm-wide fractures per each meter in the zone of tension.

Vertical tension is the highest in approximately the same zone. Figure 4-2, modified after Poland and Davis, 1969, shows measured elongations in five successive moments. This combination of horizontal shear stress with vertical tension caused several small earthquakes (Lee, 1979; Kosloff et al., 1980). As Kosloff et al. emphasize, "The hypocenters were at shallow depths between 450 and 550 rn in bedded shale formation. The fault planes were always close to horizontal (Richter, 1958; Mayuga, 1970; Kovach, 1974)." Locations of epicenters are shown in Fig. 4-3 modified after Kosloff et al. (1980). It is obvious that these deformations, that released tensile strain and caused earthquakes, also formed open fractures, both lateral and vertical.

EXTENS I ON ZONE :~ COMPRESS I ON z " . : EXTENSION ZONE ~ .

o : �9 ZONE : :

�9 ! / -

: - ~ - ~ I E

M (n

r �9

E �9 o [ u

SIDEN

Fig. 4-1. Scheme of compressive and tensile stress distribution in subsiding formations.


Fig. 4-2. Scheme of casing count surveys of a typical well in the Wilmington oil field. (Modified after Poland and Davis, 1969.)

Fig. 4-3. Locations of epicenters and slip planes of subsidence earthquakes. (Simplified after Kosloff et al., 1980.)

It is necessary to emphasize that the very fact of the existence of vertical tensile strains and elongat ions above the compact ing reservoir is a direct evidence that the weight of the overburden is not t ransmi t ted fully to the compact ing rocks due to the


Fig. 4-4. Deformation pattern of strata above longwall extraction with strong overburden (physical model). (Simplified after Whittaker and Reddish, 1989.)

bridge-effect of overlying formations. That means that the effective-stress concept and models based on it do not exactly fit this deformation. In a sense, the existence of vertical tensile strain means that the reservoir compacts faster than the overlying beds bend down. Thus, beds break apart vertically. It is worth noting that in the case of sand production, when extraction of sand forms a cavity around the borehole, this effect will be enhanced and deformation similar to those shown in Fig. 4-4, modified after Whittaker and Reddish (1989), may be possible.

The role of the strength of formations above a compacting reservoir is also indicated by a time lag in subsidence. Meyer and Powly (1988) noted that "surface subsidence commonly lags behind cumulative production". This means that for some time compaction of the reservoir is compensated not by equal subsidence but by vertical extension of the formation above the reservoir, whereas the deformation zone slowly expands upwards. Thus, first fractures should form in the caprock of a depleting reservoir. This may impair the caprock's reliability and provide some paths for the leakage of gas from the pool.

Surface fissures caused by subsidence

Tensile horizontal strain causes fissures on the Earth's surface (Guacci, 1979; Holzer, 1984; Lister and Secrest, 1985; Love et al., 1987; Pewe et al., 1987; Pampeyan et al., 1988; Beckwith et al., 1991; Contaldo and Mueller, 1991; Haneberg et al., 1991; Keaton and Shlemon, 1991). Mostly, large surface fissures are caused by withdrawal of water from shallow aquifers, as a rule, alluvial. Withdrawal of oil, with substantial formation pressure decline, also causes surface deformation, which mostly consists of horizontal displacements and fractures (Pratt and Johnson, 1926; Strehle, 1989). Cracking of surface due to oil and gas withdrawal is usually not


Fig. 4-5. Trench logs of the Pixley fissure, San Joaquin Valley, California. (Simplified after Guacci, 1979.)

investigated. Thus, fissures due to water withdrawal give useful indirect information on phenomena above oil and gas fields.

Holzer (1984) reviewed occurrences and origins of earth fissures associated with groundwater overdraft in Arizona, California, and Nevada. Mostly, these fissures are associated both in space and time with the dewatering of phreatic aquifers. The preferred mechanism of fissuring is localized differential compaction of unconsolidated aquifer material over bedrock irregularities. Jachens and Holzer (1979) believe that "The association of earth fissures with zones of variable aquifer thickness suggests that differential compaction is occurring near these fissures... This is the dominant source of horizontal tension causing earth fissures in Picacho Basin. This analysis indicates that tensile strains at fissures at times of their formation ranged from 0.1 to 0.4%." These observations of the relationship between fissures and heterogeneity of formations are very important.

The deepest fissure reported ~ more than 16.8 m (55.1 ft) was located near Pixley in the San Joaquin Valley, California (Guacci, 1979). It was 0.8 km (0.5 mi) long and 2.4 m (8 ft) wide. The fissure was open to a depth of 1.8 m (6 ft) (Fig. 4-5). Beckwith et al. (1991) report that "Cracks that were clearly attributed to hydrocompaction extended up to 4.4 rn (14.5 ft) deep and were no more than 1 cm (0.4 in) wide."


WEST EAST 0

196• DATUM

l.iJ U z ,,, 0,5

1,0

t Fig. 4-6. Subsidence profiles across the Picacho fault, Arizona. (Simplified after Holzer and Thatcher, 1979.)

One of the most extensive investigations was carried out by Contaldo and Mueller (1991) who studied 13 discrete locations in the Mimbres Basin in southwestern New Mexico. They found out that "measurable fissure depths range from less than 0.3 to 12.8 m... and the width of fissures ranges from incipient hairline to 9.7 m."

The issue of the full depth range of fissures, most important from the gas leakage viewpoint, stays unexplored. It may be suggested that actually cracks extend much deeper than measured, but the whole problem needs more extensive field exploration.

Impact of subsidence on faults

Papers on faulting related to subsidence are not numerous (Kreitler, 1977; Gabr- ish and Holzer, 1978; Holzer and Thatcher, 1979; Van Sickle and Groat, 1981). Holzer and Thatcher (1979) investigated changes of surface altitudes on both sides of the Picacho fault (Fig. 4-6). They simulated the process of differential movements of fault sides and showed that the difference in changes of altitudes of sides depends on the angle of a fault.

Physically, it is quite clear that existing faults will provide differential movements of their sides if a shear stress exists, relative to the fault plane. The most important question from the upward gas migration viewpoint is: what are the widths of old and new fractures, that such differential movements can provide? This issue is still to be explored.

MECHANISMS OF GAS SEEPAGE FROM POOLS

Gas may migrate upwards through the water-filled permeable rocks either actively, by molecular diffusion and/or by mechanical flow, and/or passively, being transported in solution by upward flow of water (Gurevich, 1969). These three mechanisms work both separately and in combination. As gas is transported by the upward water flow, there is a partial gas separation and subsequent free-phase gas flow along with water. But mostly only one mechanism prevails.


Upward diffusion of gas

Gas diffuses from a flee-gas accumulation in all directions. There is no need in sophisticated mathematical models, however, to make an approximate, especially maximized, estimate of possible upward diffusion of gas. Moreover, sophisticated estimation is meaningless due to many uncertainties in parameters of this diffusion flow. It is most reasonable to assume that this flow is strictly vertical and to evaluate its rate assuming a steady-state flow (Fig. 4-7). Then diffusion flow, I (cm3/sec), through a unit (1 cm 2) area of horizontal cross-section will be

I - D(C/z) (4-3)

where D is the diffusion coefficient, C is the concentration of gas in water just above the gas pool, and z is the depth of the top of the gas pool. It is most reasonable, for this kind of estimation, to assume a uniform value for the diffusion coefficient within the whole range of depths, z.

In the case of a steady-state diffusion and complete saturation of water with gas on the boundary with the gas pool, the value of C/z may be obtained from a solubility coefficient. Indeed, gas concentration will be proportional to pressure, and in the case of hydrostatic pressure distribution the value of C/p = C/pgz is equal to the value of the solubility coefficient. Somewhat overestimating the real values, the solubility coefficient for a natural gas may be taken as 0.3 (m3/m3)/MPa, which corresponds to C/z = 0.003 (m3/m3)/m. The diffusion coefficient value may be assumed, also with an obvious overestimation, to be 10 -6 cm2/s. Using these values, the diffusion flow rate through a unit horizontal area will be 3 x 10 -11 cm3/s.

Fig. 4-7. Schematic diagram of steady-state diffusion from the gas pool to the surface.


This diffusion flow encounters, at a shallower depth, a lateral flow of groundwater that absorbs the incoming gas. If the width (W) of a gas source and, therefore, of the assumed lateral extent of vertical diffusion flow, can be traversed by a certain particle of the lateral groundwater flow within time t, then the volume of gas (Q) absorbed by a unit column of flowing groundwater from the diffusion flow will be:

Q = I t = I W~ v (4-4)

where v is the lateral velocity of groundwater flow. Assuming typical values of W = 10 km and v = 1 m/day, Q will be equal

to 2.6x10 -2 cm 3. Taking the height of a groundwater column, i.e., thickness of a groundwater aquifer, as 10 m, which is smaller than usual, gives average gas concentration in water of 0.000026 cm3/cm 3.

Thus, even with overestimation this lucid calculation gives a concentration of gas in water very far from the saturation value (approximately 0.03 m3/m 3 or more). This means that diffusion flow cannot form free gas phase near the surface.

Mechanical mechanisms of gas migration

Gas migration mechanisms depend on whether gas displaces pore water or not, and on whether a gas globule is smaller than the conducting channels or vice versa. Thus, it is convenient to consider these cases separately.

Upward migration of separate gas globules Transport of globules through porous media. The term "porous media" is referring here to rocks with intergranular and microfracture porosity. It is assumed that every gas globule is sufficiently larger than the individual pore throat or microfracture channel and the gas moves through a water-filled rock.

Floating-up of oil and gas globules have been thoroughly investigated in petroleum geology (Aschenbrenner and Achauer, 1960; Gurevich, 1969; Berg, 1975; and many others). To begin moving upwards, such a globule should overcome capillary pressure at the upper gas-water interface where gas displaces water. Such a globule moves very slowly and, thus, for small globules pressure losses to overcome friction are often negligible. Except for some very special cases of intensive underground water flows, it is the excess pressure of gas that overcomes the capillary pressure at the advancing interface.

Whatever the globule's shape, this excess pressure, Ap, will be equal to the difference in pressure in gas and in the corresponding column of the surrounding water. It is equal to the difference between specific weights of gas and water (see Fig. 4-8):

Ap = (Yw- yg)h (4-5)

where Yw and yg are specific weights of water and gas, respectively, and h is the globule height. The value of Yw may be assumed to be 1 g/cm 3 and that of gg, 0.2 g/cm 3 at a depth of about 2000 m, i.e., at a pressure of about 200 kg/cm 2.


~aTE~-S~TURa~ED ROCKS

"i . W~T~RrSa;URaTZD ROCKS

DEPTH

Fig. 4-8. Schematic diagram of excess pressure formation.

PRESSURE

GAS --~

WATER

\

Capillary pressure, Pc, at the gas-water interface that resists the upward progress of globule depends on the values of the surface tension, contact angle, and pore radius (Fig. 4-9):

Pc = 2o cos 0 / r (4-6)

where cr is the surface tension, 0 is the contact angle, and r is the radius of a pore throat.

It is obvious that to enable a globule to move upwards, the excess pressure should exceed the capillary pressure:

Ap > Pc (4-7)

Equation 4-7 can be rewritten in the following form:

2o- cos 0 h > (4-8)

r ( y w - yg)

The surface tension value for the gas-water interface depends on temperature and pressure. It is about 40 dynes/cm at a pressure of 200 kg/cm 2 and a temperature of 60~ The angle 0 may be assumed to be 60 ~ Radii of pore throats in very coarse, medium, and very fine sands are about 0.02, 0.005, and 0.001 cm, respectively. The


W a t e r

I

I I

G a s

Fig. 4-9. Schematic diagram of the gas-water interface in a water-wet pore throat.

values of h, necessary for the gas globule to begin moving upwards, will be 2.5, 10.2, and 51.0 cm, respectively. Clays have smaller pore openings and, thus, the gas globule height necessary to overcome the capillary forces will be greater. Pore radii of 10/zm and lower are common for clays. Thus, initial heights of at least 5 m are necessary.

In gas pools or gas caps, the height of a continuous gas body almost always exceeds 5 m and often is more than 20 or 30 m. In most cases, therefore, the upward migration of gas through a caprock is possible. In recent unconsolidated clays that did not lose their colloidal properties, pore channels are blocked with bound water, partly or completely, at depths with temperatures below 50~ Gas cannot penetrate such a clay mechanically, i.e., as a free phase. After gas enters the caprock, its migration rate depends on the rate of water displacement. At low permeabilities of caprocks, it is very slow and geological times are required for gas to reach the earth's surface.

Buoyancy as such does not determine the upward movement of a gas globule through a porous medium. The excess pressure, that overcomes capillary-force resistance, depends only on the height of the globule and on the pressure losses, within the globule, in the upward flow. The value of the buoyant force acting on the globule is not important in this case.

Floating-up of gas globules in water If the gas globule size is smaller than that of a channel, a fracture for instance, the entire globule floats up. In this case buoyancy force Fb moves the globule upwards (Fig. 4-10). For a spherical globule, this force is equal to:

Fb = ~R3(yw - yg) (4-9)

where R is the radius of the globule.


Fig. 4-10. Gas bubble floating up through water in an open fracture.

The frictional resistance, according to the Stokes law, is:

Ff = 6zr lzRv (4-10)

where/z is the dynamic viscosity of water and v is the velocity of the bubble floating up or of the water flowing down. This globule will stay still in the case of downward flow of water if the forces of buoyancy and friction are equal. On equating Eqs. 4-9 and 4-10, therefore, one will obtain a formula for the critical velocity v:

V 2R2 [ 1 ] (4-11) ~Z(yw - yg)

At a temperature of 25~ and a pressure of 20 kg/cm 2, the specific weight of a hydrocarbon (methane) gas is about 0.015 g/cm 3. Water viscosity is n e a r 10 - 2 P. Then, for a bubble with the radius of 0.1 cm, critical velocity is 0.22 cm/s. Thus, a bubble of gas can float up in a rather strong, for a geological environment, downward stream of water. This conclusion is especially important in the case of a depleted reservoir with a pressure noticeably lower than the hydrostatic one. Open fractures often exist in normal fault systems.

Upward migration of the continuous gas phase The continuous gas phase can move from a gas pool to the surface or to another

pool, lying at a shallower depth, through subvertical zones with higher permeability and/or through open fractures.

Upward flow of gas through porous media. If, owing to facies variation, lithological heterogeneity, or presence of a microfractured zone there is a vertical zone or


sequence of zones of higher permeability above a gas pool, gradually continuous gas flow will be established. In such a flow there is no need to overcome the capillary forces and to displace water. Owing to lower density, pressure at the top end of a static gas column will be always higher than that at the top of the water static column through which the gas has to move (Fig. 4-8).

It is possible to make an order of magnitude estimation of the flow rate in the vertical column of gas saturating permeable rocks.

At any depth, the vertical flow rate of gas will be:

k - ( 4 - 1 2 )

Vp -- ~ ( - - O p / O z -Jr- yg)

where k is the permeability coefficient. If bottom and top pressures in the gas column are equal to water pressures, then Op/Oz are equal to the specific weight of water (1 g/cm3), i.e., 10 .3 kg cm -2 cm -1. Assuming that permeability k is 10 .2 D and gas viscosity/z is 1.5 x 10 .2 cP, v will be 7 x 10 .4 cm/s or 60 cm per day. Actual rates of the upward gas migration depend on the permeability of such subvertical zones of rocks and mostly on the lowest permeability along this path.

Upward gas migration through open fractures. It is obvious that fluid motion through open fractures is incomparably easier than through porous media, because the latter provide much more resistance to flow (friction) than the open space of a fracture. Ignoring high gas compressibility, it is possible to make an order of magnitude estimation of such gas migration using Boussinesque's formula:

U = ~ 3Z "[- yg (4-13)

where b is the fracture width. Using the same gradient and assuming b to be 1 cm, gives v equal to 5 m/day.

Leakage of gas through open fractures

Abandoned boreholes penetrating gas reservoirs become rapidly filled with gas (Fig. 4-11). Pressure distribution in the gas column in the borehole is described by a well-known formula:

0.00341Hp) PH ---= Pb exp -- ZT (4-14)

where PH and Pb are pressures at a distance H from the well bottom and at the bottom, respectively; p is the gas density relative to that of air (0.7 for methane); Z is the average gas supercompressibility (deviation from ideal gas behavior); and T is the average absolute temperature.

Assuming that the depth of a gas reservoir is 3500 ft (1068 m), formation pressure (depleted) is 200 psi (14 kg/cm2), temperature is 307~ and supercompressibility is 0.98, the wellhead pressure will be 185 psi (13 kg/cm2). If pressure distribution


Fig. 4-11. Schematic diagram of the pressure distribution in a gas-filled wellbore and in surrounding water-saturated formations. Arrows show escape of gas through holes in the casing, formed as a result of corrosion.

in water-saturated formations surrounding the well is hydrostatic, then at a depth of 426 ft (130 m) pressure in the borehole will exceed outside pressure and gas can escape into these formations and then to the surface through damaged or poor cement sheath and holes in the casing. The latter are caused by chemically aggressive corrosive waters.

SUMMARY

To summarize, the writers would like to list the areas of necessary research in this field:

(1) Theoretical analysis of the fluid-solid force interaction for the full scope of natural deformation patterns and development of a system of models for these patterns.

(2) Special analysis of actual force interaction in laboratory experiments and of adequacy of laboratory tests to phenomena in situ.

(3) Development of new, physically definite models for different patterns of fluid-filled rock deformation.

(4) A most thorough investigation of the physics and mechanics of reservoir rocks compaction and deformation of overlying subsiding rocks. Role and parameters of creep (deformation in time under constant load and effective stress) should be investigated for the compaction process. The role of discontinuous deformations should be explored for processes in subsiding formations. The precise physical mechanism of the time lag should be analyzed and included in models.

(5) Empirical correlations between subsidence rates and fracturing, on the one hand, and lithology, thicknesses, and tectonic history of deforming formations combined with rates and areas of pressure decline, on the other hand, should be developed.


(6) Rates of subsidence corresponding to an economically acceptable level of damages should be defined for different combinations of geologic environments and parameters of production.

(7) Analysis of the San Andreas fault zone complex to determine areas (faults) where oil and gas fields may produce upsurge of gas to the surface during earthquakes, with resulting fires, especially in urban environments. It is necessary to establish the most dangerous areas and develop recommendations on preventive measures.

(8) The authors propose that continuous measurements of properly placed gas detectors possibly can serve as an earthquake predictive technique.

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Chapter 5

215

SUBSIDENCE STUDIES IN ITALY

GIOVANNI BRIGHENTI , GIULIO C. BORGIA and EZIO MESINI

G E N E R A L I N T R O D U C T I O N

Because of its geology, Italy is subject at present (and has been in the past) to the phenomena of natural land subsidence, due principally to the slow compaction of the sediments and, in some cases, to volcanism and earthquakes. In the vicinity of coastal areas the effects of subsidence are aggravated by eustatic phenomena. Despite all of these problems, the natural subsidence is clearly less than the anthropogenic subsidence.

Italy, with a surface area of 301,000 km 2, of which only 23% is flat, has a population of approximately 57 million inhabitants. Thus, the Po-Veneto Plain (Fig. 5-1) - - characterized by a high population density, intense agriculture and dense industrial concentrations m is an area where intense use is made of the land and all of its available resources, with consequent rapid degradation.

As early as the Renaissance, a vast amount of reclamation work in the Ferrara region was undertaken by the Este family. This, however, was terminated after just a few years, due to land compaction consequent to the sinking of the phreatic water-bearing strata. In recent years, the intensity of human activity has become

46~ l' ' I ' I1 AWlLI~I~ '[ ' IAII [L I ~'1S I I1 ]..[....'..2"~176 " t N

' I t , �9 . ' ' : i ..... "" . . . . . . . . . . . . . ~ .... '"""" ""' . . . . . . . "i i'?'''" Ill . . . . iiiii i:: ; l

.

5* 4* 3* 2 ~ 1" 0 ~ 1" Fig. 5-1. Simplified map of the Po-Veneto Plain. The triangles indicate main hydrocarbon reservoirs.

216 G. BRIGHENTI, G.C. BORGIA AND E. MESINI

excessive, as a result of the technological progress, and clear land subsidence has occurred. This is due both to direct interventions, principally the withdrawal of fluids (water and gas) from underground, and indirect interventions, for example the embankment and change in the profiles of rivers and the excessive exploitation of river-bed aggregates. These are all factors which have modified solid transport, which no longer compensates for the natural land subsidence and erosion of coastal areas.

As already mentioned, these phenomena are particularly marked in the Po- Veneto Plain, which is the site of some of the largest industrial concentrations, the most advanced agricultural activity and the most important gas reservoirs. Over the last 30 years, serious damage has occurred due to subsidence in this area. The severity of this damage has led to an awareness of the need for a global management policy for the entire territory in order to avoid benefitting a few people at the cost of the entire community. This would lead to considerable economic disorder and a consequent reduction in the standard of living. This has resulted in growing interest in the study of land subsidence, particularly its causes, as well as the measures required to stop it and remedy the damage.

In order to define the problem, a brief geological description of the Po-Veneto Plain is presented here.

The entire Po-Veneto Plain is the site of a wide sedimentary basin, which has experienced intense and differential subsidence, particularly since the Neogene. In certain areas, the depth to the base of the Pliocene sediments exceeded 8000 m and that of the Pleistocene sediments at times measured 3000 m. The Pliocene sedimentary basin, extending beyond the confines of the current Plain, also included part of the Apennine area and the northern and eastern Pre-Alps.

The migration of the Apennine structural axes towards the Alpine chain, which had already been delineated, determined the formation of a subsidence basin where considerable volumes of terrigenous sediments were deposited. The Po-Veneto Basin did not have a smooth base but was furrowed by systems of longitudinal ridges. Consequently, the thickness of the sediments varied between the depressions and ridges, and the grain sizes found depend on the type of depositional environment and the processes of deposition. Diverse movements, often of considerable size, were superimposed on the tectonic activity which caused folding, and were large enough to accentuate the subsidence and lifting.

Synsedimentary tectonic activity continued throughout the Quaternary when the sea still occupied almost the entire Plain. During the most recent Quaternary, there was a decisive prevalence of sedimentation over subsidence, as a result of which the sea has withdrawn and continental alluvium has covered the marine sediments. In some subsidence areas the alluvium layer may reach 400-500 m in thickness.

Towards the eastern border of the Plain, variations in the sea level, particularly of the glacio-eustatic type, provided the final stage of evolution.

Continental sedimentary materials (fluvial and swampy) principally consist of fine sands and clayey silt. There are tongues and gravelly lenses in the mountain border areas associated with fluvial and alluvial fan deposits. The deeper marine formations are formed of clay and sand with a varying degree of cementation.

SUBSIDENCE STUDIES IN ITALY 217

The entire Plain has a vast and complex regional hydraulic system, nourished from its sides (Alps and Apennines) by surface waters with the formation of fluvial fans. There is also a deep and complex aquifer system, characterized by a hydrodynamism towards the east.

Knowledge of the geological evOlution of the Po River Basin has profited a great deal from the intense research activity conducted by the Italian State Oil Company (Agip) in search of oil and gas. The petroleum basin is characterized by a wide and diversified spectrum of hydrocarbon generation and migration (Mattavelli et al., 1983; Borgia and Ricchiuto, 1985c; Borgia et al., 1987a, b). The central-eastern part of the Plain is characterized by the presence of numerous biogenic gas reservoirs (which are almost always autochthonous), located particularly in the vicinity of the plicated systems (submerged Apennine area). During the Pliocene-Pleistocene there was a widespread formation of structural stratigraphic traps which has allowed gas retention in this area. The development of biogenic gas was favoured by the abundant and long-lasting sedimentation. This gas, which is very light isotopicaUy, was formed by immature sediments at a low temperature. In certain areas (for example, Ravenna) the gas formed and accumulated in large quantities after synsedimentary tectonic activity in the presence of thick sand and clay banks. This resulted in the formation of abnormally deep biogenic gas.

M E A S U R E M E N T S

The types of measurements used in Italy to monitor vertical land movements, as well as operational methods, do not differ substantially from those normally used in other countries, as evidenced by the specialized bibliography and the Proceedings of the International Congresses on the subject.

Italy, like many other countries, has tended to develop some aspects more than others, for reasons which include its geology, land features, and its artistic and architectural heritage. The problems encountered constitute a strong stimulus for the development of particular technical and scientific aspects of measurement. Some aspects of its historical evolution (for example, land reform and partition or the use of land for military needs) have also made a contribution. Thus, accurate land registration and cartographic data in the areas where most of the cases of subsidence in Italy have occurred is of the utmost importance.

In this chapter only the effects of the anthropogenic type of subsidence are considered, although a clear distinction between anthropogenic subsidence and natural subsidence is not possible, because the two types often coexist.

Over the past few decades, many towns (particularly those in the Po Plain), whether large or small, have experienced subsidence problems to a greater or lesser extent due to a considerable withdrawal of water. Loading by new constructions has also played a role. The entire Po Plain has gradually become covered by a network (locally dense) of piezometers and levelling bench marks. These are monitored by public institutions (at either national or local level) and by private organizations (reclamation societies, etc.). Unfortunately, during the altimetric monitoring, the


absence of coordination and of a unique general technical standard became evident. This was due to several reasons. First, the diversity of institutional goals caused each operator to adopt different standards. The lack of coordination was also caused by professional jealousy and/or a conflict of interests. It is desirable to overcome this unfortunate situation, because it is often difficult to use heterogeneous data for scientific purposes, or even for studies of a more general interest.

As for high-precision levelling, at present a single "guide" is available in Italy, which was devised by the Italian Geodetic Commission in 1975. Inasmuch as considerable time has elapsed since its publication, it is inadequate. Thus, it is important to establish general standards for the entire process of high-precision levelling: from planning of the network, to execution of measurements, to the processing of data. Based on updated technical regulations, it would be possible to develop specific regulations, concerning, for example, methods of surveying and the criteria for the choice of bench marks.

The experiences obtained in Italy with the monitoring of subsidence phenomena suggests that only high-precision levelling should be used. This is characterized by the assumption of a tolerance on the discrepancy between eight forward and backward measurements, from bench mark to bench mark, equal to T - 4 - 3 v ~ mm, where D is the distance in kilometres (Barbarella et al., 1990). The use of measurements of differing precision in the area of the same control network partially reduces the time required for the survey. It also has economic advantages. At times, however, it creates problems with regards to how these data, of differing weight, should be dealt with.

In areas which have active subsidence, the effect of land movement on measurement may be limited (1) during the survey if the measurement is carried out as quickly as possible (for example, using more than one team at the same time) and (2) during the data processing by means of kinematic adjustment of the network. This was done in Bologna where the rate of sinking in certain areas in the period 1970/1973-1983 exceeded 15 cm/year. At this location, the network was divided into seven lots, with a 45 day time limit established for the survey of the network. Moreover, "critical lines" were surveyed first and all within the first 30 days.

With regard to the possible need to minimize the time required for surveying, it may be observed that motorized levelling, which is certainly a valid method for areas having a favourable orographic distribution, a low level of human activity and a small amount of traffic, is of limited application here. Trigonometric levelling might be more suited to these areas (motorized is better), to be carried out by using coupled electronic theodolites and distance meters with modulated waves. Experimentation on this method is still being carried out in Italy (Gubellini and Unguendoli, 1987).

Another problem occurring in a young sedimentary basin with little compaction like the Po area, concerns the evaluation of possible influences on bench marks of variations in the level of shallow aquifers. In our case, the normal climate-related factors must be added to those related to high rates of pumping - - which also has a seasonal nature - - due to the needs of industry and agriculture, which are particularly developed in the only large Italian Plain.

SUBSIDENCE STUDIES IN ITALY 2 1 9

Variations in the level of shallow aquifers may thus influence the stability of the bench marks, subjecting them to vertical movements. These have been experimentally determined to be between 10 -4 and l0 -2 times the variation in the level of the quota of the aquifers in sandy or clayey soils. Poland (1984) suggested taking into account the seasonal course in levellings operated in those basins where the annual difference in the hydraulic head exceeds 10 m. These effects, which have already been acknowledged, were measured experimentally by Cunietti et al. (1984), using for comparison a suitable type of stem bench mark anchored to a depth of 5-6 m. This has also made it possible to obtain a first calibration for these sedimentary soils. The comparison between the behaviour of surface and stem bench marks may thus be particularly useful for distinguishing movements due to superficial factors (vibrations, mechanical or hydrostatic stress, land oxidation, etc.) from those due to deeper causes.

In this connection, anchoring at the bases of old buildings, whenever possible, has proven to be an excellent solution. This practice has been particularly adopted in the historical centres of cities and especially in the dense control networks set up for certain monuments damaged by locally differential sinking phenomena. In these cases, the joint application of high-precision levelling methods and photogrammetry has at times proven to be quite useful in revealing vertical movements in the structures and correlating them to those of the land in the immediate vicinity. Examples of these applications are reported in the case histories of Bologna and Modena.

Another viable technique is that of the in-well measurement of compaction using extensometers. In Italy, extensometric measurements were carried out in the Po Delta during the 1960s using a cable specifically designed and built for this purpose (Borgia et al., 1982a). Although based on the same principle of extensometers already in use in other locations, the instrument differed from the rest by the simplicity of its construction and because it could be moved, making it possible to use the same extensometer in different wells. The instrument worked well and played an important role in defining the causes of unbalance in the Po Delta.

A detailed analysis of its use was made by Borgia et al. (1987b), showing that the instrument is characterized by precision and economy, which make it a valuable tool. One of the aspects of a research plan financed by the Italian Ministry of Public Education foresees the construction, with the necessary devices, of a similar instrument. At present, extensometers have been installed or are in the progress of being installed in Bologna, Venice and Modena.

T H E G E O T E C H N I C A L FEATURES OF SEDIMENTS

Sampling

The first studies conducted in Italy on land subsidence due to the fluid withdrawal from the subsoil were of a typically geological nature and, as such, the researchers principally examined the geological and mineralogical features of the layers, ignoring geotechnical studies. These studies were mainly qualitative, seeking


out empirical correlations between hydraulic head lowering and soil sinking. The gradual passage towards the realization of physical models of the phenomenon and to their study by means of mathematical models required a parallel passage towards a systematic survey of the geotechnical features of the sediments. Nonetheless, in Italy progress in this direction was slow, as the result of little interest initially de- voted to the phenomenon of land subsidence, as well as the cost and the technical difficulties involved in determining the geotechnical features of loose soil located at a considerable depth and from which it was difficult to obtain samples of good quality.

Until the 1960s, the few samples available were collected without special devices, while perforating wells for the production of water or hydrocarbons. Thus, these samples were quite disturbed and the original packing arrangement was modified.

While carrying out research on the subsidence at Venice, the first deep exploratory well, Venezia 1-CNR (950 m deep), was drilled. Continuous coring was carried out using techniques from the petroleum industry (CNR, 1971): continuous coring (Christensen Rubber Sleeve Core Barrels) from 60 to 920 m, and cuttings obtained from 0 to 60 m and from 920 to 944 m; from 944 to 950 m a bottom core was obtained. Geotechnical, palaeontological and mineralogical studies were made on the samples obtained. The wells were also tested in three principal aquifers and geophysical well logs were also obtained.

Continuous coring was also carried out in the 488 m deep Ravenna 1 Subsidence well in 1983 (Comune di Ravenna, 1988). From 72 to 480 m, the Christensen Rubber Sleeve Core Barrel was used (average recovery = 93.8%), whereas from 480 to 498 m, plastic liners (average recovery = 75%) were used. The core sampling in the Ravenna area was carried out during exploration for gas-bearing sands.

Typically, geotechnical techniques were used during drilling (1987) while studying subsidence in Bologna (Idroser, 1988). The wells were approximately 300 m deep, and continuous coring was done from 50 to 300 m. Undisturbed samples were obtained approximately every 10 m by means of a thin-walled wireline sampler (85-100 mm in diameter). Further measurements were performed using static penetrometers (wireline) with a piezocone, logs were obtained and well-testing was carried out. For the first 50 m the studies were integrated by using the geotechnical standard techniques. All of the samples were radiographically examined at the site to assure their good quality.

Laboratory tests and the influence of sampling disturbance

Inasmuch as the cost of obtaining deep undisturbed samples, or at least high- quality samples, is high, so the number of samples must be limited. For this reason, it is important to determine the layers which influence subsidence the most, and on which the sampling must be concentrated, so that the maximum amount of useful information can be obtained at a minimum cost. With regard to this problem, several parametric studies have been conducted (Brighenti, 1976; Brighenti and Mesini, 1986). These studies, starting from the original research of Geertsma (1973) and Van Opstal (1974), defined the effect of a rigid basement and the unimportance


Fig. 5-2. Effect of the distance of a rigid basement from a disk-shaped reservoir; lm and lo indicate, respectively, the maximum subsidence and the maximum sinking of an isotropic and homogeneous medium. K = distance to rigid basement; C = depth; v = Poisson's ratio; R = radius of disk-shaped reservoir. (After Brighenti and Mesini, 1986.)

of the mechanical features of the layers located far from those subject to a pore pressure decrease (Figs. 5-2 and 5-3).

The properties of sediments which influence subsidence most are those characterizing their deformability and permeability.

As far as permeability is concerned, in the opinion of the authors, laboratory tests are of a limited value, mainly because the absolute values are not determined. This is caused by both the strong influence of packing disturbance of the samples, and only the local validity of the values obtained. Of some interest, instead, are tests which determine the variation in permeability of the same sample with changes of applied stresses. For example, Figs. 5-4 and 5-5 show the effects of the vertical stress variations on porosity (and porosity on permeability) measured on some samples of sandy clay layers from the Po Plain (Brighenti, 1965a, b, c, 1967, 1985b, 1994; Brighenti and Fabbri, 1982b, 1984).

As for the mechanical features, these are usually characterized by bulk compressibility and Poisson's ratio. Bulk compressibility, however, may be defined differently, and it may have different values depending on the type of stress applied to the sample (Baldini and Di Molfetta, 1975a, b, c; Chilingarian et al., 1975; Chilingarian and Rieke, 1976; Wolf et al., 1976). The following types of stresses are usually applied in the laboratory: (1) hydrostatic-uniform stresses in all directions (using a hydrostatic compaction cell); (2) triaxial differential stresses in a vertical direction and on a horizontal plane (using a triaxial cell); (3) uniaxial vertical stress with zero lateral strain (using an oedometer).

The latter type of stress may approximate the actual situation. All three types of stress, however, have specific fields of application. Simplicity of construction characterizes the first and third ones, whereas the second has greater precision (as well as the possibility of determining the Poisson's ratio).


1.4

1.2

1.0

0 I--.8 ,< r r

O

.E.6

.2

\

"-

0 1

2

3 ' '"

2

C/R RATIO Fig. 5-3. Effect of three different laws of variation of rock bulk compressibility (Cb, MPa -1) with depth (z, m) on the dimensionless ratios lm/lo and C/R. Quantities Im and lo indicate, respectively, the maximum sinking and the maximum subsidence of an isotropic and homogeneous medium, whereas C is the depth and R is the radius of a disk-shaped reservoir. 1" Cb = 3.2.10 -3 MPa -1 = constant; 2: Cb = exp(2.7501 -- 1.2038 ln z); 3: Cb = exp(9.3557- 2.1382 ln z). (After Brighenti and Mesini, 1986.)

100

>.-

( / ' )10 O r r O 13.

0 10 20 30 40 EFFECTIVE VERTICAL

STRESS, MPa Fig. 5-4. Relationship between porosity and effective vertical stress for some samples of silty clay and schists of the Po Valley. (After Brighenti, 1985b.)


ld s

d7 I.-I

>.- I-. _J m

u.I

IT" I.U a. ld ~

-11 lO

o

d

/ i / I I /

/

/ ,//

//, I

i

/

/

/

!O 20 30 40 POROSITY, %

Fig. 5-5. Relationship between permeability and porosity for various samples of silty clay and schists of the Po Valley. (After Brighenti, 1985b.)

All of these methods have been utilized in Italy. Furthermore, due to the fact that deformation of loose rock is, for the most part, inelastic and irreversible, accurate tests have been carried out (Brighenti, 1965c; Brighenti and Fabbri, 1982b, 1984) to determine the validity of the measurement techniques and, in particular, the possibility of extending certain formulas to these materials as well, deduced from the theory of elasticity. These formulas determine deformation under a specific system of stress. Deformation was determined in the laboratory by applying different systems of stress to the rock sample.

It was important to find out whether or not the following relation may be used for loose sands and clays:

( l + v ) 1 - 7 Cb ' (5-1)

Cb = C b 3(1 - v)

In isotropic elastic media, Eq. 5-1 correlates the bulk compressibility obtained by oedometer (Cb):


Cb = --~- Ex=~v; T=constant (5-2)

to the bulk compressibility obtained in a hydrostatic loading cell (c~)

Cb = ])b ~ ~ J O.x=O-y=O.z; T=constant (5-3)

where Cr is the rock solids compressibility; v is the Poisson's ratio; h and Vb are the height and the bulk volume of the sample, respectively; aez is the effective vertical stress; ~-e = (aex + aey + ae~)/3 is the average effective stress; ~x and ~v are strains in the horizontal plane; and T is the temperature.

From a series of tests, Brighenti (1965c) and Brighenti and Fabbri (1984) ob- ' utilizing Eq. 5-1 are lower by served that the values of Cb, determined from c b

20-40% or more than those obtained directly using an oedometer in the case of loose sands and clays.

The samples collected are rarely totally undisturbed. In addition, inasmuch as they experience unloading during passage to the surface conditions, in the laboratory they in effect undergo a second loading cycle (Mess, 1978). Consequently, the effect of the two factors acting in opposite directions on the value of compressibility is evident: the presence of unloading and reloading cycles would lead to a lower value, whereas disturbance gives rise to a greater value. The results of some measurements of rock bulk compressibility (Cb) by Brighenti and Fabbri (1982b) during the first and second loading cycle on samples obtained between depths of 1300 and 1600 m are presented in Figs. 5-6 and 5-7. Measurements on samples taken at shallower depth were carried out by Ricceri et al. (1974).

Values of the compressibility of unconsolidated sediments of the Po-Veneto Plain

In Italy, geotechnical studies have rarely involved sediments located at a depth exceeding 50 m. Tests on some samples taken at a greater depth (as much as 500 m) in the Po-Veneto Plain have been reported by some authors (Carbognin et al., 1976; Cancelli et al., 1982; Cancelli and Pellegrini, 1984; Cancelli, 1984; Poland, 1984). The compressibility values determined during exploratory drilling of the wells Venezia 1 CNR (Carbognin et al., 1976) and Ravenna 1 Subsidence, are presented in Figs. 5-8 and 5-9, respectively.

Brighenti (1964, 1965, 1994) and Brighenti and Fabbri (1982b, 1984) determined the compressibility of normally consolidated samples obtained from the Po-Veneto Plain at depths ranging from 500 to 4000 m at the site of natural gas reservoirs. At present, the study is in progress and sandy clay samples from the northern Adriatic Sea are under investigation.

The relationship between initial compressibility and depth for samples obtained in the Po-Veneto Plain is presented in Fig. 5-10. The location of samples is indicated by a triangle in Fig. 5-1. The compressibility of both clays and sands approach each other with increasing depth, as reported by van der Knaap and van der Vlis (1967).


-1 10

'T 13.

16 2 ._1 m

ii! rr" 13. 2~ O l d 3 0

J

rn

- 4

10

31

I 1 10 100

E F F E C T I V E V E R T I C A L S T R E S S , M P a

Fig. 5-6. Rock bulk compressibility as a function of effective vertical stress for undisturbed samples of sands (1-2) and clays (3-4) of the Po Valley. I = first loading cycle, H = second loading cycle. (After

Brighenti and Fabbri, 1982b.)

-1 lO

"T 13.

>.." -2 I--10 . . , . .

._I m .,,.,...

cO cO LU rr n

d3 0 1 0

_d

rn

1() 4

41

\ / / 1 I

21.

2

I 10

E F F E C T I V E V E R T I C A L S T R E S S , M P a

100

Fig. 5-7. Rock bulk compressibility as a function of effective vertical stress for disturbed samples of sands (1-2) and clays (3-4) of the Po Valley. I = first loading cycle, H = second loading cycle. (After

Brighenti and Fabbri, 1982b.)


Fig. 5-8. Rock bulk compressibility versus depth in samples taken from the Venezia 1 CNR test borehole. Continuous lines refer to conventional oedometric test, whereas dashed lines refer to oedometric test where the load is increased up to the "in-situ" pressure. Maximum and minimum values refer to loading and unloading cycles, respectively. (After Ricceri and Butterfield, 1974.)

Thus, compressibility depends principally on depth. For the Po Plain, the following relation may be used as a first approximation where depth exceeds 500 m:

Cb - - exp(A - B In z) (5-4)

where Cb is the bulk compressibility obtained by oedometer and z is depth.

Variations in water salinity

A considerable lowering in the hydraulic head, which has occurred over the last 30 years in many parts of Italy, has caused the intrusion of sea water in many coastal


100

2 0 0

3 0 0

4 0 0

500

Cb, MPa -1

3.5 - 5.0 x 10 -2

3.0 - 6 . 0 x 10 -2

2.0 - 3 . 0 x 10 -2

- ~ ~ 2.0 + 3.0 x 10 -2

1.5 + 2 . 0 x 10 -2

1.0 -: 2.0 x 10 -2

1.5 x 10 -2

1.0 + 1 . 8 x 10 -2

1.0 - 1 . 5 x 10 -2 1.0 + 1 . 5 x 10 -2

0.8 + 1 . 0 x 10 -2

~ - - ~ ~ 1.0 + 1.5 x 10 -2

Fig. 5-9. Rock bulk compressibility (Cb) (in a loading cycle) versus depth in samples taken in Ravenna. (After Comune di Ravenna, 1988.)

5 , 0 0 0

tz:: 1~,000

::1:.- I-.. 13_ LU 5 0 0 a

m

m

B

1 0 0 -4 10

& I I

& � 9

e- sand A - clay

i !

BULK COMPRESSIBILITY,. MPa -1 Fig. 5-10. Rock bulk compressibility versus depth of sand and clay samples taken both in the Po and Veneto plains.

I I I I I I i I t I I I I I 10 -3 10-2


0

"1" ~ .

I~1 ~ . 4

e- Z ~ . 6 u.I (.9 Z ,,~ . 8 "1" 0

1.0 10

m

m

�9 Beginning of sea water injection

I 10 2

TIME, hr 10 3

Fig. 5-11. Effect of sea water flooding on sample height. (1) ~rez = 1.5 MPa, fine fraction (<2 /zm) = 21% (mainly illite and chlorite); (2) ~rez = 0.9 MPa, fine fraction (<2 #m) = 25% (40% illite, 60% quartz and calcite); (3) ~rez = 1.2 MPa, fine fraction (<2 tzm) = 35% (mainly illite and chlorite); h = sample height. (After Brighenti and Fabbri, 1982a.)

aquifers and aquitards. Although this phenomenon has been observed in many locations, a definite correlation between the salinity variations in clay sediments and land subsidence has not been determined.

Compaction experiments have been performed under constant loading on some samples of clay soils in the Ravenna and Bologna regions by using water of different salt concentrations (Brighenti and Fabbri, 1982a; Brighenti, 1985a). In Fig. 5-11 the results of three tests on the possible effects of sea water flooding are reported. They suggest that the variation in water salinity must also be considered, particularly in the case of subsidence in the coastal areas.

M O D E L L I N G OF THE PHENOMENON

Introduction

As mentioned previously, the first studies on subsidence conducted in Italy were of a qualitative nature and for the most part involved the empirical correlations between variations in the hydraulic head and the corresponding subsidence of the ground.

McCann and Wiltis (1951), Geertsma (1957, 1966) and Sandhu and Wilson (1970) studied the subsidence using mathematical models. Not only is this a powerful tool for the interpretation of the phenomenon, but it could also be used for predicting the evolution of land subsidence with time, in terms of the management of underground fluid production. This could be of great value in a rational utilization of the territorial resources.


Although the physical laws which describe the phenomenon of ground deformation remain the same, two different approaches were used in modelling, depending on whether aquifers (including those with gas dissolved in water) or hydrocarbon reservoirs were being examined. For the latter, characterized by a greater ratio between depth and areal extent, the study of deformation must always include three-dimensional models.

A short overview of the principal studies of numerical and analytical analyses conducted in Italy, in order to measure the amount of subsidence caused by both the production of water from aquifers and the production of gas, is presented here. The results of these studies are presented in the section on case histories.

Aqui fers

The first studies on aquifers were initiated in the 1970s (Gambolati, 1970, 1972) using a simplified one-dimensional model based on Terzaghi's theory of vertical consolidation. In particular, these studies were aimed at calculating the amount of ground-sinking in the city of Venice.

An uncoupled mathematical model, also known as a "two-step" model, was used for the studies on subsidence at Venice (Gambolati and Freeze, 1973) and for those at Ravenna (Gambolati et al., 1984, 1991). The model was based on the premise that subsidence was the primary result observed, at the surface, of the compaction of underground sediment layers upon intense water drainage from an unconsolidated aquifer-aquitard system.

The study was divided into two distinct stages, represented by two models: (1) flow, or hydrological model, and (2) deformation, or subsidence model.

During the first stage, the "hydrological model" enables calculation of the piezometric declines in a vertical axial-symmetrical section with radial coordinates (r, z), solving the equation of the diffusion for a multilayered aquifer-aquitard system. This equation, which is solved using finite-element techniques for the general aquifer/aquitard of index i, is as follows:

( 0o) 0*0( 0.) 0 Kri -t Kzi (Cbi + d/)ifl) O~ ( 5 - 5 )

O---r ~ r Or O z ' --~z = F O t

where Kri, Kzi, Cbi, ~i, fl, di), F, t are, respectively, radial and vertical hydraulic conductivity, rock bulk compressibility, porosity, water compressibility, piezometric head, soil specific weight, and time.

During the second stage, the "subsidence model" uses the values of the piezometric decline (calculated using the preceding model) as entry values for a one- dimensional consolidation model, which is then solved using finite-difference numerical techniques.

The model was designed to function during the first stage of data identification of past history (history matching) at a first attempt to obtain (a) piezometric declines observed in previous years in control wells, and (b) ground-sinking values obtained by topographical measurements.


During the first stage, the data on hydraulic conductivity and compressibility of the formations were suitably calibrated until a "best fit" for both the hydrological and subsidence models was obtained. Subsequently, during a second stage, future subsidence was predicted based on various production assumptions at wells.

For Bologna, an uncoupled model is also being used (Idroser, 1988). The hydrological model for Bologna, as compared to those used for Ravenna and Venice, has been simplified and refers to the behaviour of the layer equivalent to a monostratum and to free-surface conditions. In this model the flow domain has been discretized using a network of more than 200 square elements 1 km in length. The network derives from the thickening, on a local scale in the province of Bologna, of a more wide hydrological model of the regional aquifer (Idroser, 1978). The consolidation model also uses Terzaghi's equation along the vertical direction.

From a theoretical point of view, it may be stated that the variations in the hydraulic head and the consequent deformations influence each other. The separate consideration of the phenomenon, as it occurs in uncoupled models, leads to a considerable simplification (Gambolati and Freeze, 1973) and saves calculation time. According to some researchers (Gambolati et al., 1974) more sophisticated models are not justified because of the small amount of knowledge that exists about the geometrical, physical and mechanical features of the medium.

In addition to the uncoupled model, some other researchers have proposed a "fully-coupled" one (e.g., Lewis and Schrefler, 1978a, b). In this model, developed by using the method of finite elements, a matrix equation is solved directly; it contains the equilibrium equations of the porous matrix and the equation of fluid mass balance.

According to the authors cited, compared to an uncoupled model, the fully coupled one should demonstrate better adherence to the physical reality of the phenomenon when the time delay between drawdown in the aquifer and compaction in the adjacent strata is investigated. This is due to an intrinsic feature of the fully coupled model which provides the simultaneous solution of the equation of flow and deformation.

The fully coupled model was thus used to study subsidence at Venice, using the same values of the geomechanical, hydrogeological and geometrical parameters presented by Gambolati et al. (1974). The fully coupled model was also used to interpret subsidence phenomena in the Po Delta area (Schrefler et al., 1977; Mazzalai et al., 1978).

Hydrocarbon reservoirs

The studies conducted in Italy on subsidence phenomena caused by the exploitation of hydrocarbon reservoirs (particularly gas reservoirs), are in effect theoretical studies. The only practical study was carried out in the Ravenna-Terra area (see section on case history of Ravenna).

The first study conducted on the phenomenon of the land subsidence related to variations in layer pressure is that of Evangelisti and Poggi (1970). In their study, among other findings, a mathematical model was proposed based on the theory of


poroelasticity, which considers elastic porous solids with pores saturated by pure elastic fluids. The set of stress-strain relations describing the three-dimensional deformation of a porous matrix are quite similar to those used in the field of elasticity concerned with thermal effects, which is called thermoelasticity. This analogy was first pointed out by Lubinski (1954) and Geertsma (1957). Subsequently, the term poroelasticity was coined (Geertsma, 1966) to describe macroscopic stress-strain deformation of porous solids.

In their study, Evangelisti and Poggi examined the movement of the land surface due to compaction or rebound of a porous layer located at depth by using both analytical and numerical techniques. The results obtained by applying the theory of poroelasticity are extremely general and have a wide range of applicability. In particular, this study provided the analytical relations which extended Geertsma's previous solution (Geertsma, 1966) to the case of gas reservoirs related to lateral aquifers. The aquifer pressure distribution was determined by Van Everdingen and Hurst (1949). Thus, a mathematical model, capable of calculating subsidence versus time, is presented for the aquifer system plus gas reservoir. With reference to the lateral aquifer characterized by cylindrical symmetry (Fig. 5-12), in which a step approximation of the decline in pressure is used, the analytical solution of surface sinking is as follows:

{ " [ Uz(r, O) - 37r cbh Apl I (rDw, CDw) + E Apj I (rDj .j=2

' ) ] ] (5-6) , CDj) -- I (rg.j , CD.j

where: v = Poisson's ratio; Cb = rock bulk compressibility; h = thickness of the reservoir; I (rD, CD) = function suitably tabulated and denominated the Geertsma integral; D = depth of the reservoir; Apl = decrease in reservoir pressure; Apj = decline in pressure in the aquifer at a distance r i from the axis of the reservoir; row = r/rw; cow = D/rw; roj = r/rj Coj = D/r/ roj = r/r/_ 1 and c' -

' ' ' D . j - -

D/ri-1. The study of subsidence, in the case of disk-shaped reservoirs, was extended by

numerical models to cases of anisotropic and non-homogeneous media using the finite-element method for axial-symmetrical geometries (Brighenti, 1972a, b, 1976; Gambolati et al., 1984; Brighenti and Mesini, 1986).

A parametrical analysis was made by Gambolati et al. (1984) for a circular- shaped reservoir in a transversally anisotropic stratified media, where each single layer was characterized by five elastic constants [El, 131, E2, I)2, G1, where E, v and G, respectively, denote the Young's modulus, the Poisson's ratio and bulk shear in horizontal (1) and in vertical (2) directions]. The study showed: (a) the influence of the accuracy of determining the geomechanical parameters of both depressurized and surrounding formations; (b) the influence of the Poisson ratio; and (c) the influence of a rigid basement underlying the reservoir.

An analogous parametrical analysis was conducted by Brighenti and Mesini (1986) with particular examination of the following:

(a) the influence of the rigidity of basement placed directly under the reservoir (Fig. 5-13);


Fig. 5-12. Schematic representation of a disk-shaped gas reservoir with lateral aquifer. The step approximation of decline in pressure is indicated according to Evangelisti and Poggi (1970).

(b) the effect of the distance of a rigid basement from a disk-shaped reservoir (Fig. 5-2);

(c) the influence of the variations in the mechanical properties of the ground with depth (Fig. 5-3);

(d) influence of ground anisotropies (Fig. 5-14); and (e) influence of the reservoir geometrical shape (Fig. 5-15). In a study of subsidence at Ravenna (Comune di Ravenna, 1988; Gambolati et

al., 1991), an uncoupled model was developed by using finiteelement techniques for the study of hydrocarbon reservoirs of any shape. The model was used to study the influence of the exploitation of the Ravenna-Terra gas reservoir on subsidence in the city of Ravenna.

As far as the subsidence in geothermal areas is concerned, Carradori et al. (1981) developed a mathematical model with finite elements to calculate the geothermal subsidence in horizontally stratified geological formations. Geothermal models,


Fig. 5-13. Influence on sinking ratio (lm/lo) of the rigidity of a basement with elasticity of Eb placed directly under a disk-shaped reservoir having elasticity modulus Eo. Quantities lm and lo indicate, respectively, the maximum subsidence and the maximum sinking of an isotropic and homogeneous medium, whereas dimensionless radius rq/R indicates the dimensionless radius for which sinking is reduced to one tenth of the maximum value. (After Brighenti and Mesini, 1986.)

Fig. 5-14. Influence on sinking ratio (Im/lo) of the ground anisotropies. Quantities lm and lo indicate, respectively, the maximum subsidence and the maximum sinking of an isotropic and homogeneous medium, whereas E1 and Ee indicate, respectively, elasticity modulus parallel and normal to the horizontally stratified layers. (After Brighenti and Mesini, 1986.)


Fig. 5-15. Influence of reservoir geometrical shape on ground-sinking. Solid lines refer to a one-disk- shaped reservoir of radius R and thickness h; dashed lines refer to reservoirs formed by two or three disks, close to each other, but having an area equivalent to that of the reservoir formed by one disk only. 1/Ah indicates the ratio of the maximum subsidence to the reservoir compaction. (After Brighenti and Mesini, 1986.)

proposed in particular for the monitoring of sinking in geothermal areas in Tuscany (Narasimhan and Goyal, 1984), make it possible to study the effect of variations in pressure and temperature for different reservoirs.

IMPACT OF SUBSIDENCE ON AN AREA AND REMEDIES

Damage

The most apparent damage to an area usually takes place when ground-sinking occurs near seas and lakes, particularly when the environmental equilibrium is already precarious. In Italy, this is the case for subsidence phenomena observed in the Po Delta, Venice, Ravenna and in some parts of the High Adriatic coast, where the surface of the land is at an altimetrical level, approximately equal to or lower than that of the average sea level. In these areas, even modest changes in the level of the land (in Venice, for example, of approximately 20 cm (Carbognin et al., 1984b, c) may cause flooding over wide areas, particularly when unfavourable meteorological events take place (high-tide, sea storm, wind blowing in the direction of the shore, etc.).


These situations are often aggravated by erosion of the littoral zone (Dal Cin, 1983), caused, among other things, by the changes in the supply of river solids. The latter is due to the variations in river profiles by subsidence. According to Montanari (1983), ground subsidence along the coast of Ravenna, measuring approximately 20 cm during the years 1957-1967, led to a retreat of the shoreline of approximately 60 m.

Subsidence, however, often leads to an upsetting of the area's entire hydraulic system (Mazzalai et al., 1978; Montori, 1983; Zambon, 1983; Gelmini and Pellegrini, 1983; Carbognin et al., 1984b; Gambolati et al., 1984; Gambardella and Mercusa, 1984). For example, in large areas of the Po Delta and Romagna Plain (where over vast areas the level of the land is a few metres less than that of the average sea level), the meteoric waters are evacuated by means of canals and drainage systems. In this critical case, subsidence has led to a reduction or even an inversion of the slope of the canals, with a considerable decrease in their ability to function and, in some cases, to the formation of depressed areas without any possibility of drainage. Thus, it is necessary to modify the network of drainage canals. Many water drainage plants could no longer be utilized, and in many places the aggravated technical conditions increased their operational costs.

Furthermore, it was necessary to change the network of irrigation canals and to raise and strengthen the river embankments (river levels in some areas are almost always greater than land levels). This increases, in addition to other factors, the danger of siphoning, due to the greater difference in level between the river and the land. Raising of the embankments has finally lead to the abandonment or the reconstruction of many man-made structures (bridges, navigation basins, retaining walls, etc.). Moreover, agriculture has undergone other types of damage. For example, changes in reclamation clearances have damaged farming (e.g., Zambon, 1983, reported elimination of many orchards in Romagna), resulting in poorer yields due to the worsening of water quality, etc.

As for damage to buildings, in addition to listing, severe cracks have occurred due to sudden facies changes and, therefore, sudden compressibility changes. For example, the Church of St. Giacomo in Bologna (Pieri and Russo, 1985; Capra et al., 1991) has experienced ground subsidence rates varying from 2.5 to 4.4 cm/year at distances of less than 100 m (see Figs. 5-16 and 5-17). This has produced dangerous cracks in the walls and breakage in the vault chain. Analogous cracks have been observed in Modena (Cancelli et al., 1984; Pellegrini, 1986), in the city's principal monuments located in the historical centre and, in particular, in the Ducal Palace (currently the Military Academy).

Remedies

The main cause of subsidence related to the underground withdrawal of fluid is the compaction of layers, due to the decrease in pore pressure. Therefore, to stop subsidence it is necessary to prevent any further decrease in this pressure, or better yet, to increase it.

It should be noted, however, that, at least in unconsolidated sediments, the


Fig. 5-16. Contour lines (in cm) of the average annual ground-sinking for the St. Giacomo Church of Bologna in the period 1979-1983. (After Gubellini et al., 1984.)

Fig. 5-17. Ground-sinking measured in Bologna along the Zamboni Street. (After Gubellini et al., 1984.)

c o m p a c t i o n p h e n o m e n o n is for the mos t par t i r revers ible and, thus, an inc rease in p o r e p r e s su re to the initial values is no t e n o u g h to ob ta in a sensible r e b o u n d (see the case his tory of Venice in a la ter sect ion) .

SUBSIDENCE STUDIES IN ITALY 2 3 7

As clearly defined in the section on case histories, stopping a reduction in pore pressure can be attained by (1) interrupting the fluid withdrawals from underground (gas-bearing water in the Po Delta, freshwater in Venice and Ravenna, etc.); or, more rationally, (2) re-balancing the hydrological equilibrium of the underground layer, that is, not withdrawing more than what the aquifers can provide in order to stabilize the piezometric surface. The latter approach has been attempted in the case of the thermomineral waters of Abano (Padua Province) (Schiesaro, 1983), the management of which was entrusted to an Unified Board. Obviously, stopping or reducing the freshwater withdrawal from the aquifer was made possible in most cases by its total or partial substitution with surface waters taken from rivers or new water basins by new civil or industrial aqueducts or new irrigation canals (Lanzoni and Magagnoli, 1980; Moruzzi, 1980; Zanovello, 1980).

To at least reduce the damage already done, dams were built to protect the shorelines, but this often led to a worsening of landscape, as in the Po Delta area. Moreover, there is a plan to raise the quays of the port of Ravenna and to use movable gate sluices to close off the mouths of the Venetian lagoon. An interesting attempt at raising the ground was made in a little island of the Venetian lagoon by means of pressure grouting in the underlying ground (Gallavresi and Rodio, 1984); the results seem to be quite promising.

The organization of reclamation activity is covered in a later section. As for the building impairments, Alessi (1985) and Alessi and Raffagli (1994)

pointed out how these differ in the case of an exhausted phenomenon (routine consolidation and restoration interventions in damaged buildings) and in the case of subsidence which is in progress. For the latter, repairs which tend to make buildings more rigid may prove to be damaging. It may be a good idea, instead, to adapt the structures to future ground movements, even inserting joints into the structure. Only after this is done will it be possible to perform consolidation.

Legal considerations

As indicated by Caia (1983, 1984), in Italy the Public Administration's interest in defense of the environment was created only recently. This explains why in the Italian legal system there is no general law on the subject. Explicit mention regarding the withdrawal of water or hydrocarbons from underground reservoirs and the change in the conditions of shallow and deep aquifers is found in the Ministerial Decrees dated, 21 January, 1981, and 11 March, 1988, which concern geotechnical problems. Instead, with regards to specific legislation concerning hydrocarbons (Law 11, January, 1957, Ministerial Decree 2, May, 1968, etc.), a correct use of the reservoir, which is considered to be public property, is favoured instead of the protection of the surrounding environment. It must be remembered that, in Italy, first category minerals do not belong to the owner of the land but to the State, which may grant the exploitation rights through concessions. In the case of hydrocarbons, the mining law may only be applied to some marginal gas-bearing reservoirs, which are not considered in the aforementioned legislation. Caia (1984) observed that, when the exploitation of gas-bearing water from the Po Delta was stopped, the


measure was not taken on the basis of general laws motivated by danger or damage related to subsidence. Instead, it was done: (1) by agreeing on the suspension of activity with some of the concessionaires; (2) by not renewing the concession; or (3) only in a few cases, by proceeding to the revocation of the concession due to general reasons of public interest. Laws of an exceptional nature, however, exist that refer to the withdrawal of underground water in particular areas of Italy. They specifically take into consideration the phenomenon of subsidence as follows:

(1) Law 30, December, 1970, regarding environmental protection in the provinces of Padova, Treviso, Venezia, and Vicenza.

(2) Law 10, May, 1976, regarding the town of Pisa (Leaning Tower). (3) Law 10, December, 1980, regarding environmental protection in the town

of Ravenna, but extended with some modifications to a wide area of the Emilia- Romagna region.

In the opinion of the writers, however, it would be better to unify all these laws into one comprehensive law.

CASE HISTORY OF THE PO DELTA

Introduction

The first major subsidence area studied closely in Italy was that of the Po Delta. Subsidence, which reached its peak in the early 1950s, was caused by the exploitation of gas-bearing waters (Borgia et al., 1982b), aggravated by the overlapping effects of recent land reclamation, the natural settlement of young soils, and the rise in the average sea level (about 1 mm/year over the past century with a sharp increase in the past 20 years). In addition, there was an added effect of the embankment of the drainage system, which prevented river sediments from spreading onto the surrounding area (Bondesan and Simeoni, 1983). As a result, today the middle section of the delta appears to be "spoon"-shaped, with a depression over 3 m deep in the middle. The survival of the whole basin is, therefore, dependent on the effectiveness of the man-made water control works. This is especially critical at its eastern edge bordering on the sea where there has been subsidence of the order of 2 rn in the last 40 years.

Geology

The subsidence area is bounded to the north by the lower course of the Adige River and to the south by the northern section of the Ferrara Province. Thus, it is located in the eastern part of the Po Plain (Fig. 5-18), covered by fairly thick Quaternary sediments of marine and continental origin (Fig. 5-19).

The rocks have a subhorizontal bedding; however, folds are present, basically resulting from a differential compaction of sediments. Sedimentary deposits mainly consist of medium- to fine-grained sands and clayey silts, generally occurring in alternate layers. Silts and peats, which are also present in the top layers of the continental or lagoonal environment, are unevenly arranged and sparsely distributed.


Fig. 5-18. Land subsidence in the Po Delta in the period 1951-1962 expressed in cm. The grey area indicates the area in which in 1960 the withdrawal of gas-bearing water was discontinued. (After Borgia et al., 1985a.)

Fig. 5-19. Schematic cross-section of the Po Plain sediments.

Here, in the past, there was a brisk extraction of gas-bearing waters from Oua- ternary reservoirs over a surface area of about 1000 km 2. Large quantities of gas dissolved in the brine were stored in these reservoirs.

There is a considerable accumulation of gas-bearing waters, with an estimated


several dozens of billions scum. The gas is primarily found in solution, as confirmed by the comparison between production data and the curve of gas solubility in water at varying pressures and depths (scum = standard cubic meter).

The gas-bearing interstitial brines are quite similar to sea water in their ionic composition. They are, however, characterized by a lower salinity (5-27 g/l) and can be interpreted as residual brackish water, sea water, or a mixture of freshwater and fossil waters.

Gas production and subsidence

Although the existence of gas reservoirs has been known for a long time, their systematic exploitation began only in the late 1930s, at a time of great shortage of oil in Italy. In the post-war period, production gradually increased and in the late 1950s reached 300 million scum per year. Although small by modern standards, production figures were remarkable for the time and in the context of the local economy. Based on drilling, the gas-bearing Quaternary layers reach down to a depth of about 800 m. Five horizontal, frequently not well-defined layers can be distinguished between 100 and 600 m. Below this, other layers are known to exist which have not been adequately explored.

At the height of development, about 1700 wells were in production, drawing water primarily from strata down to a depth of 600 m. It is estimated that a total of over 3700 wells were drilled, especially in the Rovigo Province. The average well depth, estimated at about 200 m in the first decade of exploitation activity, increased steadily as deeper aquifers were developed. Initially, water flowed spontaneously from the wells. With the progressive decrease in the hydraulic head, however, submersible pumps or gas lift became necessary.

The gas was separated from the brackish water, which was discharged into the surface drainage system. The gas was then moved to compression plants. Originally, it was compressed into cylinders and used as fuel for cars. Later, a gas network, extending approximately over a length of 650 km and connected to the national gas pipelines, was established in this area to convey gas to the gasworks in some nearby towns, including Padua and Venice.

Half of the production, handled by over a hundred gas stations, was fed into gas pipes, whereas the remaining part was either sold as car fuel or used by the plants themselves or by other users connected to the system. Figure 5-20 shows the main pipeline networks and the location of compression and distribution plants. It clearly exhibits the intensity and extent of exploitation.

In spite of its steady growth, gas production from the Po Delta gradually lost much of its significance at a national level, because of the discovery of new dry gas reservoirs in the middle of the Po Plain. The Po Delta gas production dropped from over 40% of national gas production in 1942 to a negligible proportion in 1952, in spite of growing production.

Due to its low GWR ratio (1-1.4 scum/m3), extraction of gas in the delta area involved massive liquid withdrawals, estimated at 3 billion scum. This, in turn, caused substantial subsidence of the hydraulic head, which originally almost reached the land


Fig. 5-20. Gas pipelines (dashed lines) and locations of the compression plants of the Po Delta (dots). (After Borgia et al., 1985a.)

surface. At the time, the relationship between pore-pressure change and sediments compaction was not undisputed, because large-scale subsidence was known to occur in the Po Delta and the surrounding area long before gas extraction was started.

During 1845-1875, considerable natural subsidence was recorded, with peaks of 70-80 cm. Elevation measurements conducted between 1884-1887 and 1950 revealed average sinking rate in the middle of the delta area of about 0.5 cm/year (Caputo et al., 1970; Borgia et al., 1985a).

In the 1950s, when the ground-sinking became worse, subsidence was regarded by many as a temporary accentuation of known phenomena. However, the progressive impairment of the area (decreased embankment clearance, reverse gradients of canals, and lowering of drainage plants) turned out to be an impending threat to a local population hit by frequent floods. It was then decided that a number of field measurements (mainly topographic and piezometric surveys) should be made by private and public institutions.


Fig. 5-21. Contour lines of equal subsidence (in cm) recorded in 1957 in the Po Delta. (After Borgia et al., 1985a.)

Just a few examples are sufficient to reveal the severity and the impact of subsidence. In the withdrawal areas, subsidence of the water-table surface down to a depth of 50 m was recorded. At the same time, subsidence proceeded at a rate of up to 25-30 cm/year in the middle area of the delta (Fig. 5-21) and reached a total of 2.5 m over 1951-1962 period (Fig. 5-18). The average land subsidence of the whole delta in the same period was estimated at 115 cm. Inasmuch as a considerable amount of the data suggested that gas-bearing water extraction was the main cause of the phenomenon, a committee appointed by the Italian Government stopped production over the 25,000 acre area where subsidence was greatest (Fig. 5-18, grey area). This step, implemented in 1960, proved highly successful in showing the close relationship between subsidence and gas production. As a result, this committee decided to enforce this policy all over the delta (1961) and, later, in the remaining areas, i.e., in the entire Rovigo Province in 1963 and Ferrara Province in 1965.

S U B S I D E N C E STUDIES IN ITALY 2 4 3

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Year Fig. 5-22. Average sinking rate (solid line) and annual gas production (dashed line) in the period 1 9 5 6 - 1 9 6 1 in the Po Delta. (After Borgia et al., 1985a.)

The average subsidence rate in the delta area and the natural gas production per year are presented as a function of time in Fig. 5-22. As can be seen, sinking decreased rapidly once production was discontinued. The discontinuance of extraction activities caused the water-table surface to rise rapidly (Fig. 5-23). The subsidence rate decreased exponentially with time. Based on recordings at a large number of bench marks (Zambon, 1967), the relationship between sinking (h, in m) and time (t, in years) can be expressed by the following equation:

h = ho exp( -k t ) (5-7)

where ho = maximum sinking, and k is a dumping constant varying from 0.24 to 0.70.

Sediment compaction

Obviously, a change in elevation with respect to a surface bench mark does not allow the thickness of layers to be established, unlike well measurements using extensometers. Figure 5-24 shows the length variations of a nearly 700 m deep well

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YEARS Fig. 5-24. Depth variation of a nearly 700 m deep well, located in the Po Delta, measured by means of a movable extensometer, h = depth (m); t = time (years). (After Borgia et al., 1982a.)


located close to Ca' Vendramin (specially drilled and located within the grey area of Fig. 5-18) obtained through measurements carried out during a period of about 3.5 years, starting from May 1960, using a specially designed movable extensometer (Borgia et al., 1982a, b). These measurements showed that ground-sinking was related to the compaction of layers up to a depth of 700 m. This was further proved by the fact that total well shortening, over the period under consideration, turned out to be very close to the subsidence values as measured through specially performed geometric levellings, deviation being less than 8%. Moreover, even the dumping constant (k = 0.39) was in agreement with the values yielded by surface measurements.

Other series of tests were carried out in three abandoned wells close to the previous one and ranging from 180 to 415 m in depth. The data obtained were in agreement with that shown by specially designed levellings and confirmed the reliability of extensometer measurements.

Present trend of the subsidence

The delta area displays unique hydraulic and environmental conditions, where sea, river and continental environments coexist in a delicate equilibrium. The understanding of the system was enhanced from the recordings at times of greatest stress and in the following stages during attainment of equilibrium.

As far as levelling is concerned, unfortunately only some of the available data can serve scientific purposes. This is because in most cases different bench marks were used and data thus obtained can hardly be conveniently standardized (Bondesan et al., 1986). The ground-sinking charts of some significant bench marks based on the most recent measurements are presented in Fig. 5-25. These confirm the gradual rebound of land, starting in the early 1960s. The temporary reversal of the subsidence trend recorded in 1 9 6 2 - revealed also by other surveys in the nearby Ferrara Province - - probably resulted from defective network adjustments, although occasional height fluctuations of uncertain nature had been noticed in other areas and at times of maximum extraction activities. Figure 5-25 suggests that subsidence has not stopped, because human activities certainly did not stop as gas extraction was discontinued. In addition, the lower course of the Po River is adversely affected by human intervention carried out even a long distance from the mouth. Thus, the above-mentioned decrease in solids in the river led to a predominance of erosion over sedimentation. In its terminal course the river tends to become deeper, thus impairing the stability of embankments (Fig. 5-26). This, in time, may turn out to be a somewhat critical factor, as here the level of the river is greater than the surface of the land.

Remedies

In the past few years, big efforts have been made to find a remedy, whenever possible, for the disruptive effects in areas where ground-sinking was highest. Mea- sures taken or about to be taken pursue a dual goal: (1) to control floods and


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restore the water balance, and (2) to prevent the sea from eroding away the land (Montori, 1983; Carbognin et al. 1984a, b; Gambardella and Mercusa, 1984). In spite of this action, some areas nevertheless had to be abandoned. The "spoon" shape of the delta and the depressions resulting from land reclamation in the northern area of the Ferrara Province (southern part of Po Delta) require that water be drained mechanically, as extensive areas are below sea level by a few metres. Ground-sinking, therefore, impaired m at times even s e r i o u s l y - the performance of drainage equipment, either by a costly increase in the discharge head required or by damaging new equipment. Before the dramatic and rapid subsidence mentioned earlier, drainage equipment was strategically located. As a result of subsidence, more marked in some areas than in others, some of these drainage plants were located at the edges of the funnel-shaped area, thus severely impairing the function of the discharge equipment.

Damage to irrigation works and the canal system was also caused by a reduced


Fig. 5-26. Examples of variation in the cross-section of the Po River which occurred near Polesella, Rovigo Province, with time. (Courtesy of M. Bondesan and A. Bizzarri.)

gradient (or even reverse gradient) of canals. Hence a major part of the water supply system had to be rebuilt.

River and sea embankments suffered functional damage as a result of a change in pattern and increase in stresses. They had to be repeatedly raised and strengthened in order to withstand filtration (blowouts) and offset the weakening of embankment structures resulting from increased loading. Further increase in loading on sea embankments was brought about by the lowering of the sea bed, which, in turn, was due to a decrease in the transport solids by rivers. This resulted in flooding of some beaches and made it necessary to build dams designed to recover at least part of the damaged land, but frequently with disfiguring effects on the landscape.

Final remarks

Recently, the question of the gas development in the Po Delta was brought up again, as this accounts for a significant proportion of Italian reserves (Borgia et al., 1983a, b; Borgia, 1984). Based on the experience with Japanese reservoirs having similar features (Marsden and Kawai, 1965; Marsden, 1980), a feasibility study was conducted on the possibility of maintaining pressure by the injection of de-gassed water back into the formation. One of the issues dealt with was the simulation of a pilot field using a numerical model (Borgia et al., 1985b). Among other things, it appeared that the effects of exploitation could be kept within reasonable limits even in the presence of extreme and exceptionally unfavourable anisotropies. Moreover, the simulation proved to be an advantageous tool in selecting the distribution of wells and their rates. Whether this solution will be successful or not can only be demonstrated by a pilot field equipped with piezometric level and ground altitude recording instruments.


VENICE CASE HISTORY

Introduction

On account of its artistic and historical uniqueness, for over 20 years Venice has attracted the world's attention due to the hazard of destruction by flooding. This is due to the process of ground-sinking that, minor as it may seem by absolute standards, has nevertheless caused great damage, especially because the area affected is altimetrically about at mean sea level.

The combined effects of natural and man-induced subsidence and eustasy (about 1.3 mm/year in this century) have caused the so-called "acque alte" (local phrase meaning "high waters") to occur more frequently. The maximum degree of severity ever recorded (nearly 2 m) was reached in November 1966 (Polli, 1967). The consequences of subsidence become even more alarming when aggravated by the action of tides, seiches and special weather conditions (for instance, differences in atmospheric pressure between the northern and southern part of the Adriatic Sea, etc.).

Ground subsidence in Venice, however, has stopped, because its triggering factor (groundwater withdrawals, particularly in the northern industrial area) has ceased to exist. Inasmuch as Venice is now about 20 cm below the ground level of the beginning of the century, the impact of this subsidence on the city and the life of its inhabitants is immense.

Geology and hydrogeology

Venice comprises a cluster of islands in the northern part of the Adriatic Sea (Fig. 5-27). The Venetian alluvial plain consists of coarse-grained sediments (gravels and sands) in the Pre-Alps area (groundwater recharge area). Finer-grained sediments

Fig. 5-27. Map of the area around Venice. (After Carbognin et al., 1976.)


Fig. 5-28. Hydrogeological section of the Venetian system of artesian aquifers. (After Mozzi et al., 1975.)

(fine sands, silts and clays) are found as one moves closer to the coast and the sediments differentiate into various water-bearing strata (Fig. 5-28).

Whereas in the mainland bordering on the lagoon the sediments are still rather coarse-grained (gravel horizons), in the city centre and in the littoral zone the sediments are particularly rich in fine-grained materials. As a whole, the series dips south-eastward (limited to the top layers down to a depth of 70 m) and exhibits a gentle reverse gradient from the urban area to the shore, probably due to recent differential subsidence (Gatto, 1972).

Deep drilling and geophysical surveys, carried out when prospecting for hydrocarbons, revealed that Quaternary alluvial sediments vary in thickness, from a few metres at the foot of the mountains (50 km north of Venice) to roughly 1500 m near the Po Delta (50 km south of Venice). In the Venetian lagoon, the mean thickness of these sediments is estimated at about 1000 m.

The passage of facies to the underlying Pliocene basement is gradual, resulting from the continued submersion of the land by the sea up to the mid-Quaternary. The alluvial sediments formed as a result of deposition taking place in various environments: from continental, river, lake and coastal in the northwestern area, to lake and deep-sea environments in the southeastern lagoon area.

The Venetian aquifer system has been reconstructed in some detail based on the results of geophysical measurements and the analysis of the well cores sampled from the deep exploratory borehole VE 1 CNR and three other wells, VE 2, Lido 1, and Marghera 1. In order to reconstruct the Venetian aquifer system, a large amount of scattered stratigraphic information provided by the artesian wells drilled in the area under consideration (Alberotanza et al., 1972) was taken into account. Figure 5-29 illustrates a hydrogeologic section of the Venetian aquifer system. It shows the six major artesian aquifers, down to a depth of 350 m, from which water was drawn in the past to supply the whole Venetian area.

History of subsidence

To trace the history of subsidence in Venice, one can start by examining the diagrams showing the piezometric depression recorded at various times.


Fig. 5-29. Schematic hydrogeological cross-section of the Venetian plain. (After Gambolati et al., 1974.)

Fig. 5-30. Average piezometric levels from 1910 to 1980 in Venice.

It can be noted that the extent of artesian water withdrawals and the resultant piezometric variations depend upon the socio-economic environment and the consequent human activities. For a better understanding of the phenomenon, therefore, the Venetian district has been divided into four main areas (Fig. 5-27): mainland, industrial area, city centre and littoral zone. Figure 5-30 shows the mean piezometric sinking sustained by artesian strata in the four above-mentioned areas, starting from the first decade of the century. Three discrete periods can be identified in the figure for each one of the areas considered.


In the first period (up to 1952), water withdrawals from artesian layers were rather infrequent and subsidence was almost entirely due to natural causes, with ground-sinking rates of the order of 0.4 mm/year (Leonardi, 1960; Fontes and Bortolami, 1972). Over this period, the piezometric level stayed positive with respect to the surface level (artesian wells) everywhere, except for the city centre where, starting from the post-war period, negative levels (of a few metres) were recorded.

In the second period (1952-1969), increasingly large amounts of water were withdrawn to meet the increased requirements for household and, above all, industrial purposes. In the industrial area, the mean lowering of piezometric level reached 0.70 m/year, so that in 1969 a maximum piezometric depression of 16 m was recorded in the fourth and fifth aquifers. In the city centre, on the other hand, a maximum piezometric depression of about 7 m was recorded in the third and fourth aquifers. In order to understand the relationship between piezometric depression in the industrial area and in the city centre more clearly (the latter being for the most part man-induced), it should be pointed out that, in 1969, water withdrawals in the industrial area (about 0.5 m3/s) were 50 times as large as those in the city centre (Carbognin et al., 1976).

Along with piezometric measurements, over the 1952-1968 period geodetic measurements were also carried out. These measurements showed a ground-sinking rate of 6.5 mm/year in the industrial area and of 5 mm/year in the city centre. Later, between 1968 and 1969, alarming increases in subsidence rates were observed: 17 mm/year in the industrial area and 14 mm/year in the city centre (Caputo et al., 1972).

An evaluation of the available data up to 1969, revealed a close relationship between artesian water withdrawal and subsidence in the Venetian area. This relationship was also confirmed on the basis of worldwide experience (Lofgren and Klausing, 1969; Poland and Davis, 1969; Poland and Mostertman, 1969).

In the third period (from 1970 onwards), and in particular in the early 1970s, theoretical studies and a large volume of experimental data resulted in a better understanding of subsidence. All this was part of the campaign aimed at awakening public opinion to the problem of subsidence and which, from its start in the late 1960s, soon spread beyond national borders. World-renowned experts were sent by UNESCO to design a scheme for the safeguard of the historical and artistic treasures of Venice.

In the same period (late 1960s) the Laboratory for the Study of Large Mass Dynamics of the National Research Council was set up in Venice, and became concerned with theoretical and experimental studies on land subsidence. These studies resulted in a better understanding of the phenomenon of subsidence. Starting in 1970, artesian wells were shut down. At the same time, water supply sources were diversified and greater volume of water was obtained from the municipal aqueduct, which in the meantime had been considerably enlarged.

In 1975, artesian water withdrawals in the industrial areas were reduced to 60% of 1969 figures. As shown in Fig. 5-30, starting from 1980 the mean piezometric levels in the industrial area and the city centre correspond, once again, to the ground surface.


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,,>, "J 0

uJ

0 4 N U.I E 6 UJ (.'3 - 8 n" W - 1 0 > ,<

12

E 0 O

0 " - 2 z

O - 4 m, uJ rr - 6 D Z - 8 < LU 0 -10 z uJ o -12 0 t ~ . .

A MA'NLAND ! 'NDUSTR'AL ZONE [ vENEz'' B

l ~ 1970

1952 ( BASE ) i . i i

%

5km "~ D -14

Fig. 5-3]. Comparison between the average piezometric level and subsidence during the negative stage of land subsidence ( ]952-]969) and in the positive stage (rebound) (1969-1975). (After Carbognin et al., ]976.)

Starting from 1970, levels were measured annually for monitoring ground movement. At the same time a network of 112 piezometers (24 of which were continuously recording) was established, in order to monitor the piezometric levels of six major aquifers. Thus, it became possible to obtain a comprehensive picture of the ground level and the trend of piezometric surfaces on annual basis. In Fig. 5-31 a comparison is made between the recovery of the average piezometric level and the ground surface rebound recorded between 1969 and 1975 (Carbognin et al., 1976). This figure reveals a close relationship between the water withdrawals and subsidence. In particular, the 1975 measurements show a rebound of about 2 cm as compared to 1969. In addition, as shown in Fig. 5-31, on account of different nature of terrains, during the rebound phase significant piezometric recoveries result in a small altimetrical rebound in the industrial area, whereas smaller piezometric recoveries in the city centre produce a greater altimetrical rebound.


As mentioned before, interesting results were obtained by studying the Venetian multi-layer aquifer system using mathematical models (Gambolati and Freeze, 1973; Gambolati et al., 1974; Lewis and Schrefler, 1978b). These studies accurately anticipated the 2 cm rebound of the ground surface, considering partial and/or total shutdown of wells since 1969. These models proved to be useful tools for the study and control of the ground movements resulting from the subsurface fluid removal.

Final remarks

Results of experimental investigations confirmed that subsidence in Venice was the consequence of heavy artesian water withdrawals in the industrial area. These, in turn, affected the system of aquifers underlying the city centre, giving rise to considerable piezometric depression. Due to the greater compactability of deposits underlying the city centre as opposed to the industrial area, a 1 m lowering of the piezometric level causes the ground to sink by just 1 cm in the industrial area and by twice as much in the city centre.

About 70% of the total subsidence occurred in the 1952-1969 period: a time of great industrial expansion when most artesian water withdrawals took place.

Measures taken after 1969, mainly providing for a gradual shutdown of wells, were responsible for the progressive cessation of man-induced subsidence and, in addition, for a slow, 2 cm rebound of the ground surface.

Only less than 20% of the total man-induced subsidence, however, can be recovered (rebound). The remaining subsidence (= 80%, corresponding to 10 cm), in addition to the 3 cm of natural subsidence and about 9 cm due to eustasy, amounts to a total sinking of 22 cm since the early 20th century. This may constitute cause for alarm, especially because "high waters" are becoming more frequent in Venice. The high tides, that at the beginning of the century would not have flooded the City of Venice, today must be regarded as high waters. One of the measures suggested as a means of controlling high waters, is the construction of movable gate sluices at the three mouths of the lagoon. This would enable cutting off tides only when the high waters exceed a given magnitude. At the same time, this solution would not adversely affect the biologic balance of the lagoon waters that would continue to be freely exchanged with sea water.

R A V E N N A C A S E H I S T O R Y

Introduction

The town of Ravenna is the home of architectural and mosaic monuments which are considered among the highest artistic expression of the late Roman Empire, the reign of the Goths, and the Byzantine period. Over the last 30 years the ground has been progressively sinking. The subsidence reached a maximum rate at the beginning of the 1970s and is still in progress, but at a decreasing rate.

The chief reason for subsidence is groundwater withdrawal (in particular, from the deepest aquifers) after development, around the 1960s, of (1) an industrial


Fig. 5-32. Gas reservoirs (stippled) in the onshore and offshore areas of Ravenna.

area next to the deep-water (ship) canal, (2) tourist settlements, and (3) irrigation farming.

Another cause is the exploitation of onshore and perhaps of offshore gas reservoirs (Fig. 5-32). This subsidence is further aggravated by natural subsidence (a few millimetres per year on the average) and a rise in the sea level (values are similar to those reported for the Po Delta and Venice). All these phenomena have resulted in ground subsidence of more than 1 metre, thus seriously impairing harbour, industrial, and urban infrastructures and upsetting the coast equilibrium. Due to its seriousness, subsidence has been closely observed and studied by the local authorities and the "Municipal Geological Office", working together with the Venice Laboratory for the Study of Large Mass Dynamics (Various Authors, 1971; Bertoni et al., 1972; Carbognin et al., 1974; Carbognin et al., 1978; Bertoni, 1980; Mozzi and Zambon, undated). After intervention of the State (see the special laws mentioned previously), a Study Commission was established for this specific purpose. This commission has organized topographic, hydrogeologic, geotechnical and mining surveys (the two latter were made possible by the cooperation of Agip) and has developed mathematical models to study the effects of gas and groundwater production.

Geology

The Ravenna plain is part of the Po subsiding sedimentary basin, formed by a succession of marine, deltaic, lagoon, marsh and alluvial deposits of the Quaternary and Upper Pliocene age, the extent and distribution of which are influenced by the deep geological structure and local geological history (see Fig. 5-33).


Fig. 5-33. Schematic cross-section of the Ravenna aquifer system. (After Carbognin et. al., 1978.)

The pre-Quaternary strata form a complex structure characterized by a large number of folds entrapping rich gas accumulations.

The Quaternary sediments are variable in thickness: they are thicker in depressions (up to 3000 m in depth) and thinner in the positive buried structures, having a minimum depth of about 1500 m. The structure of the deep Quaternary sediments is similar to the one of the substratum, whereas at shallower depths the recent alluvial deposits followed the directions of the present Apennine watercourses. Owing to the different types of deposits, the Pliocene-Quaternary complex is characterized by alternations of sands, silts and clays and their mixtures. The extent of these sediments shows that this area has been subjected to subsidence for a geologically long period of time, an occurrence which is still under way (average sinking rate: 1.5-3 mm/year) (Bertoni et al., 1972; Selli and Ciabatti, 1977; Pieri and Groppi, 1981).

Water production from underground strata and subsidence

The Ravenna area is characterized by a freshwater system of aquifers reaching 450 m in depth, limited at its base by a freshwater/salt-water interface. It is possible to distinguish:

(1) A water-bearing layer at a maximum depth of 25-35 m, fed by local infiltra- tions and by the natural and artificial hydrographic systems. Very small quantities of water are withdrawn from this layer.


Fig. 5-34. Amount of ground-water withdrawals from the aquifers of Ravenna. (Courtesy Dr. W. Bertoni.)

(2) A series of thin, confined aquifers with low potential, interlayered with clay and silt beds at a depth of 70-80 m.

(3) An artesian multi-aquifer fed by groundwater from the plain lying behind. Large quantities of water are withdrawn from it for civil, agricultural, and industrial uses. According to the first studies made by the CNR (National Research Council) and by the Municipal Geological Service, this aquifer is composed, at least locally, of nine independent, very thick artesian aquifers with high potential (Figs. 5-34 and 5-35). Subsequent studies, however, seemed to show that some of these aquifers are interconnected locally; hence, the number of the main aquifers was reduced to six.

Since the 1950s, these deep aquifers have been intensively exploited, with a progressive depressurization. A thorough study, necessary for the modelling interpretation, enabled division of water consumption according to the different uses, specifying both the areal distribution and the depth of the aquifers from which water was withdrawn. The analysis of cumulative consumptions in the municipal area of Ravenna from 1950 to 1983 (Fig. 5-35) shows that water consumption increased (due to the economic development of the town and its outskirts) up to 1975-1976. The increased water production resulted in a parallel reduction in the hydraulic head (Fig. 5-36), leading to the gradual subsidence of ground at a rate of 3-4 cm/year, on average, from 1949 to 1972. The rate progressively increased during the following years, reaching 6-7 cm/year in 1977. Until 1972 subsidence was localized around the industrial area and the area subsiding at a rate of more than 3 cm/year was only 4 km 2. In 1977, this area expanded by 80 times and covered the whole municipal area (Fig. 5-37). This alarming development persuaded the local authorities to reduce groundwater withdrawal by closing several artesian wells. This decision was aided by construction of an industrial aqueduct drawing water from the Reno


E - - 1 0

U.I Z ._1 o ILl a

0 - 2 0 re I-- i!1

O N I.!.1' 30

- 4 0

I I I i

. . . . . . . i

. \ ~ . \

!

\ \

".

,�9

0

, ! I 1 9 5 0 ' 6 0 ' 70

YEARS

V

�9 .. IV o ~ � 9 1 4 9

I ' 7 7

Fig. 5-35. Piezometric levels from 1944 to 1977 of the aquifers below the historical centre of Ravenna. I through V = aquifer number (see Fig. 5-33). (After Carbognin et al., 1978.)

River and the expansion of the aqueduct system. In addition, industrial production and, consequently, water consumption were further decreased owing to economic recession of the 1970s.

After 1976, therefore, aquifers underwent a new pressurization process, which initially was slow and then became faster (Fig. 5-38). The subsidence rate decreased and during the period 1977-1982 was equal to 1 cm/year, on average, with a maximum rate of 1.5 cm/year in the industrial area.

The latest measurements made in 1992 showed a further decrease: an average rate of 0.5 cm/year to a maximum of 1-1.5 cm/year in the coastal area.

The subsidence trend was well reproduced by the model study (Comune di Ravenna, 1988) covering the whole water system of the Ravenna plain, from the Apennines to the Adriatic coast (Fig. 5-39). Subsidence is continuously monitored by means of periodic, precision levellings. Moreover, since 1986, control has been extended to the main monuments of the town.

Gas production and subsidence

Figure 5-32 shows the location of the main gas reservoirs in the Ravenna area. Traps of industrial interest were formed during the Early Pliocene to Quaternary and are about 1500 to 4000 m deep. It is difficult to establish, however, to what extent


Fig. 5-36. Areal distribution of subsidence rates in 1949 (a) and 1972-1977 (b). (After Carbognin et al., 1978.)

Fig. 5-37. Average piezometric level variation in Ravenna. (After Mozzi and Zambon, 1982.)


v

Fig. 5-38. Discretization of the multilayer aquifer system of Ravenna. (After Comune di Ravenna, 1988.)

Fig. 5-39. Longitudinal cross-section through the Ravenna-Terra gas reservoir. (After ENI, 1969.)

their exploitation influences ground subsidence compared to the water withdrawal from the aquifers.

Interesting results, however, were obtained by the modelling study of the Raven- na-Terra reservoir (Comune di Ravenna, 1988). Although this reservoir is composed of 7 traps, 95% of the gas reserves reside in the two main ones, about 1700-2000 m deep (Fig. 5-39). Production started in 1955 and practically stopped in 1980. In this period the formation pressure decreased by about 10 MPa. The modelling study has shown that subsidence is at a maximum (i.e., about a few dozens centimetres) in the vicinity of the reservoir axis. Subsidence decreases outside the limits of the reservoir.

The magnitude of subsidence seems to be confirmed by the anomalous subsidence values along a vertical section of the reservoir, as can be seen in Fig. 5-40 (Comune di Ravenna, 1988).


20

E 0 v

,-- 40 . _

r -

t -

O

1 I I I

I I I I

1949-72 I I

~ Ah

" " ' ' ~176

RAVENNA-TERRA gas reservoir

1949-77 i,,~--- -

I

w * * , ]

1949-82

" . ,

" ' , . . . . . 80 m I I m 0 500

C' C ~ ~ I I

Fig. 5-40. Profile of land subsidence close to the Ravenna-Terra gas reservoir f rom 1949 to 1982; the ground-sinking is due to gas production. (Af ter Comune di Ravenna, 1988.)

Considering the critical susceptibility of coastal areas to subsidence, the study should be extended to the effects of production from offshore reservoirs.

Summary

Subsidence has caused, besides retreats of the coastline, serious damage to the industrial area, frequently flooded with water during sea storms, and to harbour infrastructures, some of which are now under sea level. This made it necessary to build protection walls and to raise the quays, as well as to rearrange accessory infrastructures. In addition, there is damage to the monuments; e.g., the crypt of the "Basilica di San Francesco" is constantly flooded at present. The complex of the "San Vitale" and "Galla Placidia" monuments would have been in a similar situation if pumping had not been used to lower the water table. Human-made subsidence is mostly irreversible but slows down or stops upon the discontinuance of water use and/or gas production. Natural subsidence aggravated the subsidence caused by human activities, which should be continuously kept under control. Although the exploitation of gas reservoirs may result in localized subsidence, it should be continuously controlled, particularly in the case of offshore reservoirs close to the coast.

B O L O G N A C A S E H I S T O R Y

Introduction

The city of Bologna lies in the central area of the sub-Apennine section of the Po Plain at a height of about 50 m above sea level and extends to the edge of the


hills. Since the 1950s, the urban area of Bologna and its surroundings have been experiencing a marked land subsidence of over 2 m in some areas. At times, the high sinking rates, along with differential subsidence, have been responsible for severely damaging some buildings in the town centre. The sewage system was also damaged.

The consequences of subsidence at Bologna are certainly not as sensational as those at Venice, Ravenna and the Po Delta, only because of this city's different altimetric position. The magnitude of subsidence, however, has been considerable, with rates of over 15 cm/year in the period 1970/1973-1983. Indeed, excepting Po Delta areas, Bologna exhibits the highest subsidence rate in the whole Po Plain. The entire urban area (city centre and outskirts) exhibit high subsidence rates, which reduce to nearly zero at the edge of the hills.

The chief reason for subsidence is water withdrawal: the growing demand for water supply has been met by drilling an increasingly larger number of wells. Since the 1950s, water consumption from the municipal aqueduct has shown almost a fourfold increase, reaching 70 million m3/year in the early 1980s (Lanzoni and Magagnoli, 1980). In the same period, the water level in wells, which supplied 80% of the total drinking water requirement until very recently, dropped over 45 m, approaching -7 0 m, with local depression rate peaks of - 5 m/year (Borgia et al., 1977).

Geology

Two main geological settings are found in the Bologna area: the edge of the Apennines and the alluvial plain, with substantial structural and geotectonic differences (Elmi and Bergonzoni, 1985). The former is subject to earth upheavals and erosion, whereas the latter undergoes land subsidence and accumulation of sediments. Besides this moderate subsidence on a regional scale, a local subsidence of a considerably higher magnitude, both in terms of velocity and total magnitude, occurs in the plain. For a better understanding of both local and regional subsidence, and their cumulative effects, it is necessary to understand the geology and stratigraphy of the area (Fig. 5-41) (Elmi et al., 1984). Highly folded and faulted sedimentary rocks of marine origin, ranging in age from mid-Miocene to Late Pleistocene, outcrop in the hilly area. These rocks are highly consolidated and well cemented. The strata of marine origin, which have been lowered to a great depth by an E - W oriented fault system running along the edge of the hilly area, can be found, in the plain area, covered by a thick layer of recently formed alluvial sediments (Pleistocene-Oligocene). They constitute the so-called "submerged Apennines".

Thus, virtually incompressible, well-consolidated rocks are present in the uplifted Apennine area, whereas marine sedimentary rocks, very similar in character to those found in the outer Apennines, are present in the plain. The latter are covered by a layer of unconsolidated alluvial deposit, with compressibility increasing upwards.

The recently formed alluvial overburden of the plain, severely affected by local subsidence, has been thoroughly studied. A considerable amount of data were obtained from surveys, wells, geophysical and penetrometric tests, excavations, and various field tests carried out at about 700 sites across the Bologna municipal area over the past 30 years. Although most of the data pertains to the layers 50-100 m


Fig. 5-41. Geological map of the Bologna area. 1 = Liguride nappe ("argille scagliose" and allo- chothonous units of the Emilian sequence; 2 = shales and evaporites (gessoso-solfifera fm); 3 = shales and sands (Pliocene); 4 = litoral sands (Pleistocene); 5 = alluvial deposits; 6 = top of the marine substratum. Contour lines are referred to the sea level. (After Elmi et al., 1984.)

deep, some information is also available on strata at greater depths (Pieri and Russo, 1977). Several alluvial fans are present in the upper part of the Bologna plain, the most important of which is the one formed by the Reno River extending over 10 km into the plain. This fan exhibits marginal lobes resulting from floods and major di- versions of the river course, represented by gravelly-sandy deposits. The same is true for the smaller fans. These gravel heaps represent the main aquifers supplying the city and its outskirts with water. They are supplied by meteoric and irrigation waters and by the water from rivers flowing in extremely permeable beds (Idroser, 1978).

The distribution pattern of land subsidence, however, is not related as much to the distribution of aquifers and water withdrawal sites, as to the sediment compressibility. Subsidence has been reported to be lower (Lanzoni and Magagnoli, 1980; Elmi and Bergonzoni, 1985; Borgia et al., 1988, 1990) in areas of gravelly- sandy fan deposits than in areas with finer-grained sediments. In addition, it should be pointed out that subsidence becomes more severe as one moves from the edge of the hills (where it is virtually nil) to the plain, depending on the thickness of recent alluvial deposits.


In summary, local subsidence almost solely affects the recent alluvial overburden, particularly in fine-grained, low-permeability sediments. In fact, the equal- subsidence contour lines largely overlie the area of distribution of finer-grained alluvial materials. This further demonstrates that only alluvial overburden is undergoing compaction: the deeper-lying marine sediments are unaffected.


Although land subsidence in Bologna has been known since the 1950s, it became apparent only 20 years later. The warning came from repeated levelling performed in the early 1970s in order to check the stability of the foundations of the Asinelli Tower, symbol of the city. A new component of the foundations' movement was identified, causing a rotation virtually normal to that resulting from the movements known up to then, and due to the local settlement of foundations. The Asinelli Tower (Fig. 5-42), almost completed in the 12th century, is 97.20 m high and has a 8.80 m square plan. The narrow bearing section of the foundations (Fig. 5-42) was clearly responsible for very high pressure being exerted on the ground and compacting it rather unevenly, thus causing a conspicuous inclination of the tower axis (more than 2.2 m) to the northwest. The estimated maximum load on the ground is of the order of 1 MPa, an exceptionally high figure for this type of ground where a 0.1-0.2 MPa load is generally permitted.

Since November 1972, tests have been carried out on the tower and on its surroundings by investigators from Bologna University (Borgia et al., 1977, 1978; Pieri and Russo, 1977; Capra et al., 1991) using piezometers or precision geometric levelling in order to record absolute and relative displacements of the tower foundations. Repeated levelling tests revealed relative vertical movements of bench marks that could be justified only for a subsidence in the town centre which, though known for some time, had not been quantified. Levelling tests performed in the years 1947, 1972, 1974, 1976 were analyzed and part of the findings obtained are summarized in Figs. 5-43 and 5-44. These figures provide a fairly comprehensive picture of the extent of subsidence and its increasing acceleration over the past few years. The northern area of the city was found to be particularly hit by subsidence.

Systematic piezometric surveys were also carried out. The 1978 isopiezometric lines and the location of the withdrawal sites are presented in Fig. 5-45 (Pieri and Russo, 1980).

Based on these and other data, a team of experts was entrusted by the Bologna Municipal Authorities with the task of undertaking a "Project for the study of ground-sinking in the Bologna area". Thus, the present levelling network, covering around 460 km 2 in the Bologna district, was developed (Fig. 5-46). During the planning of the levelling network, most bench marks (475 in total) were concentrated in the most densely populated areas and in areas showing the highest magnitude of subsidence. The number of bench marks is highest in the city centre because of the hydraulic and stability problems of buildings, resulting from the considerable differential movements. The levelling network trend is as parallel as possible to the zone of maximum ground subsidence. Figure 5-47 (Pieri and Russo, 1978) shows the con-


Fig. 5-42. Vertical section of the Asinelli Tower. (After Borgia et al., 1977.)

tour lines of equal subsidence in the Bologna area over the periods 1943-1950 and 1970-1972. Up to the early 1970s the maximum subsidence rate was estimated at around 5 cm/year. Subsequently, piezometric and levelling measurements in the period 1970-1973 and in 1983 showed a total maximum subsidence of nearly 2.5 m, at a rate of 15-16 cm/year in two areas, one west and the other north of the city, on both sides of the large fan of the Reno River. More recent data (Barbarella et al., 1990; Capra et al., 1991) showed a reduction in the subsidence rate (to about 8 cm/year).

As far as the city centre and the immediate outskirts are concerned, the most alarming finding is the steep gradient of ground subsidence recorded when moving from the land strip at the foothills to the plain, where values of about 10 cm/year have been recorded. Having this in mind, two more local levelling networks were developed in the city centre for special purposes. These subsidence gradients caused


- O. 324 1.3 -1.2

+ O. 0 t0

- 0 011

:0.9 - 0 . 8

-0.7

- 0.521 0.6

- - -0.5

- - - - - -0.4

- - - - - - - - - o. I

O. 0

- 0 . 3 - 0 . 2

Fig. 5-43. Contour lines of equal subsidence (in m) in the urban centre of Bologna during the 1947-1972 period. (After Borgia et al., 1977.)

N

0. 222

~-0.20 - 0 . 1 8

- 0 . t6 - 0 . 1 4 - 0 . 17. , ~ . ~ ~ l

O. 10 o. 08 ~

- 0.06 - 0.04

0.00

Fig. 5-44. Contour lines of equal subsidence (in m) in the urban centre of Bologna during the 1972 to 1976 period. (After Borgia et al., 1977.)


Fig. 5-45. Location of the withdrawal sites (dots) and 1978 piezometric surface around Bologna. Equipotential lines are given in metres above sea level. (After Pieri and Russo, 1980.)

damage to buildings and monuments in the NW section of the city centre. In particular, the architectural group of San Giacomo Church and the "G.B. Martini" Academy of Music suffered severe damage, which is rapidly increasing. The specially designed levelling network was controlled in 1983, 1987 and 1991 (Bitelli et al., 1991) with the aim of measuring the vertical movements of the architectural group and surrounding ground. At the same time, deformation in the hardest hit sections of the architectural group was assessed by photogrammetric surveys. The analysis of the combined observations showed that the movements are considerable and closely related to subsidence (Gubellini et al., 1984; Capra et al., 1991).

As similar damage is assumed to have occurred in other buildings of lesser artistic importance, the Bologna Town Council is conducting a sweeping survey in an attempt to identify further possible damage, including private homes. A further action was taken in 1985 by the Bologna Town Council in agreement with the Emilia-Romagna Regional Authorities. It involved commissioning Idroser (Balestri and Villani, 1985) to undertake a comprehensive study of subsidence, designed


Fig. 5-46. Levelling network of the Bologna area. (After Pieri and Russo, 1985.)

to establish the extent of ground subsidence on adopting different groundwater management options. The study is essentially based on the mathematical model of the subsidence and involves (Brighenti and Bucchi, 1985): (1) collection of hydrogeologic, geotechnic, topographic, and geophysical data; (2) evaluation of fluid withdrawals from aquifers; and (3) definition of geotechnic parameters of sediments over a depth of 300 m.

In addition, Idroser is determining the extent of fluid withdrawals. The findings obtained by deep drilling are integrated with the above-mentioned data.

Summary

The effects of land subsidence in the Bologna area are evidenced: (1) locally, by damage to buildings in the city centre; and (2) over a broader area, by height variations in topographic profiles; and, possibly, in the profile of the equilibrium of streams, as well as in minimal slopes in the plain, that may severely impair the outflow of surface waters.

There is clear evidence that subsidence is primarily caused by humans, a major role being played by groundwater withdrawals.

Although the measurements and assessments carried out in recent years have made it possible to delineate the affected areas, accurate predictive techniques are still lacking, owing to the increasing acceleration of subsidence. In spite of this,


Fig. 5-47. Contour lines of equal subsidence (in cm) in the Bologna area (1943-1950 and 1970-1972). (After Pieri and Russo, 1978.)

having identified the chief cause of subsidence, action is being taken to overcome it, bearing in mind that the cost involved in restoring the initial conditions grows in a non-linear relation to the induced alteration. Owing to the rapid rate at which land subsidence occurs, by the time it becomes apparent, considerable damage has already been caused and measurements to check its progress must be coordinated and extended over wider areas.

Stopping withdrawal of large amounts of water from wells is the only effective way to stop the present trend. To achieve this, surface waters, originating in the upper basin of the Reno River, are properly conveyed, adequately controlled, and used, thus partially reducing the supply role of the underground waters of the plain.

A number of far-reaching measures are being considered, ranging from recycling of effluents from water conditioning plants for farming and industrial applications to the artificial recharge of underground water-bearing strata.

In addition, flooding of the large pits left behind by sand and gravel quarrying activities in the vicinity of streams is being considered. Thus, considerable amounts of water, collected at times of heaviest rainfalls, could be drawn upon to ensure regular water supply throughout the year. As far as the storage capacity is concerned, basins with a total working capacity of over 30 million m 3 have been identified (Lanzoni and Magagnoli, 1980).


M O D E N A CASE HISTORY

Introduction

The town of Modena is situated in the sub-Apennine portion of the Po Plain at an elevation of about 35 m above sea level, 15 km from the foothills, 40 km from the Po River, and about 150 km from the Adriatic coastline. Starting from the middle of the 1970s, the town centre of Modena and its outskirts experienced serious land subsidence, with total values reaching almost 1 m. Rapid subsidence rates (5-8 cm/year max) and differential compaction have caused damage, occasionally quite serious, to the town buildings and monuments, also bringing about a decrease in the slopes of the sewers and irrigation canals, with a consequent danger of flooding. The phenomenon was quantitatively outlined at the end of the 1970s, when the Land- Office Authorities published the results of levelling tests carried out between 1974 and 1978, taking as a reference some levelling tests conducted by the IGM (Italian Military Geographic Institute) in 1949. Consequently, in 1980 the Municipality of Modena sponsored studies and research on subsidence. They envisaged: (a) the project and installation of a high-precision geometric levelling network (Russo, 1984); (b) the systematic collection of all the existing geotechnical data and the performance of geognostic investigations, in particular beneath the town centre, in order to determine the nature and the strength of the strata subjected to compaction more precisely (Cancelli et al., 1982; Cancelli, 1984).

The changes in the elevation of the water-table surface were systematically recorded in the wells of a special control network installed in 1979. The maximum depression of the piezometric surface (recorded north of the town centre and compared with the 1945 values) amounted to some 10 m.

Geology and hydrogeology

Information on sediments below Modena was provided mainly by geophysical investigation (seismic prospecting and well logging) and lithostratigraphies of wells drilled for hydrocarbons and water.

The geological and hydrogeological setting of Modena is quite similar to the one illustrated for Bologna. The only difference is that Bologna lies immediately behind the Apennines, whereas Modena is about 15 km further away. The alluvial deposit of Middle to Late Pleistocene-Holocene age is 250 m deep, 2-3 km south of the town centre, and 350 m deep north of Modena. It comprises gravels intercalated with silty sands and clays intercalated with silt (Pellegrini, 1986; Colombetti et al., 1984; Cancelli and Pellegrini, 1984). Figure 5-48 shows the structural and stratigraphic setup of the alluvial deposit formed by the Secchia River in the upper Modena plain. The alluvial formations overlie first clay sequences with scanty conglomerate lenses, belonging to a transition environment, and then clays of marine origin. Pliocene- Quaternary marine formations, composed of over-consolidated clays and weakly cemented sands, are characterized by thicknesses of 2000 and 3000 m south and north of the town, respectively. Figure 5-49 presents a deep geological cross-section of sediments in the Modena area.


Fig. 5-48. Cross-section of the alluvial deposits of the River Secchia fan. Alluvial deposits (Middle- Upper Pleistocene-Holocene): 1 = silts and clays; 2 = sands; 3 = gravels with sandy matrix; 4 = gravels and conglomerates; and 5 = Lower Pleistocene marine formations. Fan boundaries: 6 = present, 7 = recent, and 8 = ancient. 9 = Boundary between continental and marine deposits. 10 = Limit of investigated strata. (After Colombetti et al., 1984.)

Fig. 5-49. Geological formations beneath the town of Modena. uM = Upper Miocene; mM = Middle Miocene; lPl = Lower Pliocene; umP = Upper-Middle Pliocene; and Q = marine Quaternary. (After Pieri and Groppi, 1981.)

Hydrogeologically, the upper Modena plain is characterized by some alluvial fans, the most important of which is that of the Secchia River (Fig. 5-50), stretching over more than 15 km in the plain and covering an area of about 70 km 2. This fan is a hydrogeological unit of the big Po hydrogeologic system. From a morphological point of view, such an alluvial deposit constitutes, up to a depth of about 120 m, a single-layer aquifer with free-surface water-table in the area at the foothills and confined water-table immediately south of the town, owing to the presence of thick impermeable covers. Up to a depth of about 180 m, the fan gravel horizons constitute 20-40% of the total thickness. Their top is found at depths ranging from 17 m to the south of the town to 35 m to the north.

Over the past few years, the hydrogeological balance of the Secchia River fan has been negative. In fact, starting from the 1960s, the water output (losses under the river bed, infiltration of meteoric waters and infiltration from irrigation canals),


Fig. 5-50. Alluvial fan of the Secchia River: 1 = alluvial deposits; 2 = terraced alluvial deposits; 3 = impermeable marine formations of the Apenninic margin. Fan boundaries: 4 = ancient; 5 = Recent; 6 = present. (After Colombett i et al., 1984).

estimated at about 3 m3/s (total), was not sufficient to recharge the water-bearing stratum. The reason for this may be both the intense urbanization process, which has reduced by some 20% the permeable infiltration areas, and the altered morphological conditions of the river beds, due to the excavation of aggregates for the building industry.


In 1979, the results of high-precision geometric levellings indicated a considerable lowering of the urban area of Modena; subsidence at the town centre was particularly serious. The measurements recorded, compared with previous levelling tests conducted by the Municipal Authorities in 1962, by the Land-Office Authorities in 1974, and by the IGM in 1949, indicated significant subsidence rates, particularly during the 1970s.

Differential vertical compaction of sediments caused serious damage to the town buildings, particularly to the ones of high historical and artistic value, such as the "Palazzo Ducale", the "Palazzo Comunale" and the University. In order to identify the causes of subsidence, investigations were initiated. These included further levellings, geotechnical and geognostic studies, and a systematic spatial-temporal control of the hydraulic-head level through control wells. Figures 5-51 and 5-52 show the


Fig. 5-51. Groundwater piezometric level at Modena based on the water level in 55 wells. Water levels have been measured in May 1982 and are expressed in metres above sea level. (After Pellegrini, 1986.)

contour lines of equal hydraulic head and subsidence, respectively, during the 1962- 1981 period. These figures show a direct relation between hydraulic head lowering (down to 10 m) and ground subsidence. As in the case of the town of Bologna, the north part of the town is subjected to more land subsidence. The investigations carried out have shown that groundwater withdrawal (estimated at more than 40 million m3/year) is mostly responsible for subsidence. Differential compaction is due to the inhomogeneity of the sediments. In general, it is more pronounced north of the town centre where, in addition to the larger water withdrawal for industrial uses, silty-clayey sequences predominate over the sandy or gravelly ones.

Summary

The subsidence of Modena due to water withdrawal reached maximum values of 5-8 cm/year in the 1980s. In addition, there is geological or natural subsidence, which, in absolute values, is at least one order of magnitude lower than this, i.e., 3 mm/year for the last 2000 years.


Fig. 5-52. Contour lines of equal subsidence (in cm) at Modena during the 1962-1981 period. (After Pellegrini, 1986.)

Results obtained from a geotechnical model considering an oedometric compaction equal to 1.20 m (Pellegrini, 1986) and from the levellings performed in the period 1981-1985 (which have pointed out average subsidence of about 1 cm/ year) indicate that the current rate of subsidence is decreasing, providing that the hydraulic head remains constant.

Due to the damage of town monuments, buildings, and infrastructures, however, the Modena Local Authorities recommend the use, at least for industrial purposes, of surface waters taken from the upper basin of the Secchia River.

OTHER CASES OF SUBSIDENCE

The case histories described do not cover all land subsidence phenomena due to fluid use which have occurred in Italy. As already mentioned, the Po-Veneto Plain is intensively populated and exploitation of natural resources has been high everywhere. Thus, an exhaustive description of all subsidence cases due to fluid use


is impossible (also due to the fact that a systematic study of subsidence over all Italy has not been carried out so far).

The following cases of subsidence in the Po Plain have been reported: (1) Recordable subsidence in the centre of Milan, with a maximum of 25 cm in

the period 1950-1972 (Cunietti, 1989) and differential subsidence in some adjacent buildings ("Duomo, Palazzo della Regione"), due to the extensive exploitation of the phreatic aquifer, mostly at the beginning of the 1950s (Oberti, 1978; Bonaldi, 1980).

Fig. 5-53. Shoreline variations in the Ravenna area during the 1943-1954 period. The arrows show the mean annual rate of the beachline changes. (After Giorgi and Marabini, 1983.)


(2) Subsidence in Forl] (4-5 cm/year in the period 1972-1976) and Rimini (0.5 cm/year, approximately during the same period), as reported by Pellegrini (1986).

(3) Remarkable shoreline variations at several points along the Emilia-Romagna coast, extending from the Po Delta to Cattolica (Giorgi and Marabini, 1983) (see Figs. 5-53 and 5-54). It should be noted that in this case the phenomenon is rather complex, because it is due to several interactive causes including: (1) the construction of piers, breakwaters, etc.; (2) the destruction of sandy dunes;

Fig. 5-54. Shoreline variations in the Ravenna area during the 1968-1978 period. The arrows show the mean annual rate of the beachline changes. (After Giorgi and Marabini, 1983).


(3) a decrease in the quantity of solid material transported by rivers; (4) the excavation of aggregates; and (5) the construction of an intermontane basin.

It is also important to mention the Euganean Hydrothermal Basin, situated south of Padua and comprising, among the main localities, Abano Terme, Montegrotto, and Battaglia. The waters produced may reach temperatures higher than 85~ supplied by Alpine basins more than 1500 m above sea level and running for 70-80 km at depths greater than 2000-3000 m prior to water production (Piccoli et al., 1976).

The consumption of these waters has rapidly increased since the 1960s, reaching, just in the area of Abano, 13 million m3/year (Schiesaro, 1983). This progressively lowered the hydraulic head (average rate of 2.5 m/year at the beginning of the 1970s). Water withdrawal by several hotels was uncontrolled. The necessity for the unified management of the whole hydrothermal basin then became apparent. In practice, however, the Ministry responsible for all local policy decisions imposed a law entitled "Unified Management of Abano and Teolo" by Ministerial Decree of 30 April, 1962, providing for separate management from the other areas of the basin. This regulation brought about the beginning of the stabilization of the annual average piezometric level in 1974-1975.

Significant subsidence probably occurred during the period of maximum exploitation, sometimes causing local land sinking (Schiesaro, 1983). Subsidence, however, is very difficult to evaluate because any previous reference high-precision levelling is lacking. Systematic recordings, which started in the 1980s, indicate that ground is still sinking at a rate of about 2 cm/year (Di Filippo et al., 1986; Brighenti, 1991; Ballestrazzi et al., 1991).

ACKNOWLEDGEMENTS

With great pleasure the writers would like to express their appreciation to Professor George V. Chilingar for inviting them to participate in this endeavor, for his suggestions and for reviewing the manuscript.

Particular appreciation is also expressed to the Comune di Bologna, Comune di Ravenna, Gestione Unica del Bacino Idrotermale di Abano e Teolo and Idroser for releasing valuable data.

The authors are also indebted to Professors A. Bizzarri, A. Capra, C. Elmi, G. Folloni and A. Gubellini of Bologna University, to Professors G. Gambolati and G. Ricceri of Padova University, to Professors M. Bondesan, P. Russo and E. Vuillermin of Ferrara University, to Professor M. Pellegrini of Modena University, and to Dr. W. Bertoni of Comune di Ravenna.

The financial support of the Italian MURST is also gratefully acknowledged.

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PP. Leonardi, P., 1960. Cause geologiche del graduale sprofondamento di Venezia e della sua laguna. Ist.

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Evaluation Prediction Subsidence, Pensacola Beach, Fla., pp. 400-416. Lewis, R.W. and Schrefler, B., 1978b. A fully coupled consolidation model of the subsidence of Venice.

Water Resour. Res., 14(4): 223-230. Lofgren, B.E. and Klausing, R.L., 1969. Land subsidence due to ground water withdrawal, Tulare-

Wasco area, California. US. Geol. Surv., Pap.: 437-B, 101 pp. Lubinski, A., 1954. The theory of elasticity for porous bodies displaying a strong pore structure. Proc.

2nd US. Congr. Appl. Mech., pp. 247-256. Marsden, S.S., 1980. The status of dissolved gas in Japan. Pet. Eng. Int., 52(6): 23-34. Marsden, S.S. and Kawai, K., 1965. Suiyoseiten'nen gasu, a special type of Japanese gas deposit. Bull.,

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gases in Po Basin, northern Italy. Bull., Am. Assoc. Pet. GeoL, 67(12): 2239-2254.

Mazzalai, P., Ricceri, G. and Schrefler, B., 1978. Studio della subsidenza nel delta padano. Proc. Workshop "Problemi della Subsidenza nella Politica del Territorio e della Difesa del Suolo", Pisa, 15 pp.

McCann, G.D. and Wiltis, C.H., 1951. A Mathematical Analysis of the Subsidence in the Long Beach- San Pedro Area. Int. Rep. Calif. Inst. Technol., Pasadena, Calif., 119 pp.

Mess, K.W., 1978. On the interpretation of core compaction behaviour. Proc. Int. Conf. Evaluation Prediction Subsidence, Pensacola Beach, Fla., pp. 76-91.

Montanari, M., 1983. Eabbassamento del suolo nel territorio ravannate. Analisi dei fattori naturali ed antropici che lo determinano. Proc. Workshop "Subsidenza del Territorio e Problemi Emergenti", Bologna, 12 pp.


Montori, S., 1983. Effetti della subsidenza sui territori di bonifica. Proc. Workshop "Subsidenza del Territorio e Problemi Emergenti", Bologna, 11 pp.

Moruzzi, A., 1980. II rifornimento idrico alternativo nell'ipotesi di una adeguata riduzione dell'attingimento di acqua da pozzi artesiani. Proc. Workshop "La Subsidenza del Suolo nell'Attingimento di Acque Sotterranee", Ravenna, pp. 117-142.

Mozzi, G. and Zambon, G., 1982. La nuova tendenza evolutiva della subsidenza nel ravennate. Progetto Finalizzato Conservazione del Suolo, Venezia, U.O. 7, Publ., 275:27 pp.

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Mozzi, G., Benini, G., Carbognin, L., Gatto, P. and Masutti, M., 1975. Situazione Idrogeologica nel Sottosuolo di Venezia. CNR Tech. Rep. 66, Venice, 37 pp.

Narasimhan, T.N. and Goyal, K.P., 1984. Subsidence due to geothermal fluid withdrawal. In: T.L. Holzer (Editor), Man-Induced Land Subsidence, Rev. Eng. Geol., 6: 35-66.

Oberti, G., 1978. Applicazione dei modelli fisici per lo studio del comportamento statico del duomo di Milano. Publ. ISMES, Bergamo, 101:9 pp.

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Pieri, L. and Russo, P., 1977. Studio del fenomeno di abbassamento del suolo in atto nella zona di Bologna. Boll. Geod. Sci. Aft., 36: 365-388.

Pieri, L. and Russo, P., 1978. Nuovi contributi allo studio del fenomeno di abbassamento del suolo in atto nella zona di Bologna. Proc. Workshop "Problemi della Subsidenza nella Politica del Territorio e della Difesa del Suolo", Pisa, 32 pp.

Pieri, L. and Russo, P., 1980. Abbassamento del Suolo nella Zona di Bologna: Considerazioni sulle Probabili Cause e sulla Metodologia per lo Studio del Fenomeno. Pitagora Publ., Bologna, 44 pp.

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Chapter 6

285

SUBSIDENCE IN THE WILMINGTON OIL FIELD, LONG BEACH, CALIFORNIA, USA

X E N O P H O N C. COLAZAS and RICHARD W. STREHLE


The Wilmington Oil Field is located approximately twenty miles south of down- town Los Angeles, California in the Wilmington-Long Beach Harbor area. The field is one of a chain of oil fields that overlie a basement high extending for approximately 21 miles in a southeasterly direction from the Torrance Oil Field to the Huntington Beach Offshore pool (Fig. 6-1).

Fig. 6-1. Location map of Los Angeles Basin oil fields.

286 X.C. COLAZAS AND R.W. STREHLE

With respect to cumulative and ultimate oil production, the Wilmington Oil Field is the largest field in California and one of the largest in the United States.

The Wilmington Oil Field was officially discovered in 1931, but intensive development did not begin until 1936. By 1951, yearly production was more than fifty million barrels of oil, along with about 53,000 MMcf of gas. By 1965, approximately 3500 wells had produced about one billion barrels of oil from 7825 acres.

Until 1965, production was confined to the western portion of the Wilmington Oil Field. With the successful solution to the subsidence problem in this portion, development was started in the eastern portion (Long Beach Unit) which extends east of the harbor area in the City of Long Beach. From its discovery in 1931 to the end of 1990, more than 2.34 billion barrels of oil and 1.1 billion Mcf of gas have been produced from the Wilmington Oil Field. Current production is about 71,000 barrels of oil per day and 1,081,000 barrels of water per day. Remaining reserves for the field are approximately 600 million barrels. There are approximately 3100 injection and production wells.

Since the early 1940's the Wilmington Oil Field has been plagued by an unusually large amount of land subsidence. This was an especially critical problem because the field is located under the Long Beach and Los Angeles Harbor areas. The City of Long Beach, U.S. Navy, and Southern California Edison Company engaged qualified engineers, geologists and soil experts to investigate the causes and assist in finding a solution to the potential destruction of the industrial, port and naval facilities within the area of subsidence. They concluded that restoration and maintenance of subsurface pressures by water injection would prevent further subsidence. The result is one of the largest waterflooding programs in the world.

Current field injection is in excess of 1.2 million barrels per day into 700 injection wells. With this program in effect, subsidence was stopped. In the areas of maximum repressuring the surface has rebounded over one foot of the lost elevation.

G E O L O G Y

General

The Wilmington Oil Field lies along the center of the southern margin of the Los Angeles Basin. This great depositional basin is bounded on the southwest by the Palos Verdes Hills and the Pacific Ocean, on the north and northeast by the Sierra Madre and Santa Monica Mountains, on the east by the Santa Ana Mountains and on the west by the Pacific Ocean.

The entire area of the field is one of low topographic relief and provides no surface indications of underlying geological conditions. A study of the electric logs and cores of the oil wells provides a wealth of subsurface information regarding the structure and the lithologic character of the sediments.

SUBSIDENCE IN THE WILMINGTON OIL FIELD, LONG BEACH, CALIFORNIA, USA 287

Stratigraphy

The geology and stratigraphy of the field have been described extensively by Mayuga (1970), Truex (1972, 1974) Yeats (1973), Wilcox et al. (1973), Randell et al. (1983), Clarke (1987), and Henderson (1987). The following is supplied as a summary of this previous work.

The sequence of rocks encountered in the Wilmington Oil Field, including the age, thickness, and character of the sediments, are summarized in Table 6-1 and in Figs. 6-2 and 6-3. Zone names, boundaries and markers within the zones are those designated by the City of Long Beach, its contractors and other operators in the Wilmington Oil Field.

The oil-bearing formations in the Wilmington Oil Field range in thickness from 6400 to 7500 ft. The age of these formations ranges from questionable Jurassic for the Catalina Schist-Basement complex to early Pliocene, Repetto, for the Tar Zone.

Fig. 6-2. Composite electric log showing stratigraphic units and markers. (From Colazas, 1971.)

Geologic formations, oil producing zones and summary of reservoir data of the Wilmington Oil Field (from Colazas, 1971)

Age Stage Formation Formation Zone Electric Zone Sand thickness log markers thickness in zone (ft) (ft) (%)

Recent Unnamed f 1000 Gaspur f 180 Pleistocene San Pedro "200" and "400 f 220

Silverado 3~600 Pliocene Upper Pica &BOO Upper Pico =t800

Middle Pico 0- 200 Upper Pico 0- 200

Unconformity Pliocene

Gravity Average Average Lithology and remarks range porosity permeability (""w (%) (mD)

Fresh-water sands, gravels and clays

Alternating sands and siltstones Sands and siltstones

Repetto 700-1400 Tar S-F 300- 400 f 4 0 12-15 35 f 1000 Gray and green shales, silt- (old area) stones, and sands at top, gra- T-Fo 200- 400 ding to interbedded grayish (new area) brown shales and fine-grai-

ned sands toward bottom. Upper Ranger F-G 400- 500 f 4 0 12-25 35 700-1500

(old area) F,-G 600- 700 (new area)

(Inconformity Miocene Delmontian Puente f 5300 Lower Ranger G-HX

(old area) 150- 250 f 3 0 12-25 35 700-1500 Hard brown shales and sands; G-HXI sands are fine and unconsoli- (new area) dated at top, becoming firmer

and coarser grained toward bottom. Top part contains layers of laminated diatomaceous shale.

Upper Terminal HX-AA 400- 850 50-70 14-25 35 450 (old area) HXI-AA 400- 900 60-80 14-25 35 450 (new area)

Lower Terminal AA-AE 500- 800 60-80 20-31 30 450 Upper Union Pacific AE-AM 400- 900 25-30 27-32 20-25 150 Mohnian

Ford AM-BA 750-1200 25-35 28-32 25 100 "237" BA-Basement 200-2650 20-40 28-32 25 275

Unconformity Jurassic Basement Basement &lo0 Schist, fractured

Fig. 6-3. Geologic section along axis of Wilmington anticline showing approximate oil-water limits. (After Mayuga, 1970.)

290 x.c . COLAZAS AND R.W. STREHLE

Several major unconformities are present, notably between the lower 237 Zone and the schist basement, between the middle and upper Miocene, and between the lower and middle Pliocene separating the San Pedro, Upper Pico and Middle Pico formations from the Repetto and Puente formations.

The unconformity between the middle and upper Miocene probably represents the time of initiation of the ancestral Wilmington anticline. Upper Miocene and Repetto sediments are "drape folded" over the middle Miocene and basement core, with the younger zones usually displaying thinning on the axis of the structure and considerable thickness on the flanks. This is probably due both to a differential compaction, and to deposition on a rising structure (Law, 1956). Approximately 7500 ft of sediments were deposited in a deep-water environment between the Lower Mohnian and the Lower Pico.

These extensive unconformities represent intervals of time during which the surface of this region was uplifted and subjected to erosion. The end of each erosional period is marked by the resumption of deposition, brought about by sinking of the region below sea level. Such rising and sinking with consequent erosion and deposition, respectively, are equivalent to repeated loading and unloading of rock samples in the laboratory. The removal of loading is known to destroy, in part, the internal bonding of earth materials and thus increases the compactibility of the oil sand upon reduction in interstitial pressures.

Oil zones There are seven recognized productive zones in the field. In increasing depth

sequence these are the Tar, Ranger, Upper Terminal, Lower Terminal, Union Pacific, Ford and 237-Basement. Table 6-II illustrates these zones, their approximate depths at the crest of the anticline, gross thickness and net oil sand thickness.

Upper four zones The Tar, Ranger, Upper Terminal and Lower Terminal zones are of great eco-

nomic importance not only because they have produced the greatest amount of oil, but also because they have made the greatest contribution to subsidence. In addition, they have been the subject of numerous compression tests conducted by investigators.

The Tar Zone consists primarily of unconsolidated fine- to coarse-grained, fairly well sorted lenticular sands, with soft, light brown to olive green interbedded siltstones. The sands average approximately 40% of the bulk of the zone.

In the Ranger Zone, the top of the Miocene is found near the "G" electric log marker. The Ranger Zone consists of alternating layers of fine- to coarse- grained, fairly well to poorly sorted unconsolidated sands. The Pliocene siltstones are firm, sandy and have a distinctive brown to olive green color, whereas the Miocene siltstones and shales are dark brown to grey, becoming progressively darker with depth. The Miocene shales are well laminated, diatomaceous and are locally referred to as "poker chip" shales. The sands average approximately 40% of the bulk of the zone.

The Upper Terminal Zone consists primarily of soft to easily friable very fine- to medium-grained, fairly well sorted arkosic sands, interbedded with layers of


TABLE 6-II

Depth and thickness of oil zones of the Wilmington Oil Field (from Colazas, 1971)

Depth range Gross thickness Net oil sand (ft) (ft) (ft)

Tar 2050-2350 200- 400 50- 95 Ranger 2350-2850 400- 750 220-420 Upper Terminal 3350-3850 600- 750 400-500 Lower Terminal 3350-3850 700-- 800 450 Union Pacific 3850-4500 900- 950 230-285 Ford 4500-5400 950-1200 500-600 237 5400-5600 2650 75 Basement (Schist) +5600

claystone, siltstone and occasional hard sandstone calcareous members locally referred to as "shells". The lower sand members are generally coarser than the upper members. The sands average approximately 70% of the bulk of the zone.

The Lower Terminal Zone consists primarily of sands that are similar to the Upper Terminal Zone, but somewhat coarser and more massive, becoming firmer with depth. The siltstones and shales are well indurated and have a dark grey color. The sand content is estimated as being 60% to 80% of the bulk of the zone.

L o w e r three zones

The Union Pacific, Ford and 237 zones consist primarily of thin to massive sands ranging in grain size from fine to coarse and pebbly. The shales vary from siltstones, soft claystones and mudstones to true, hard, dense shales. Generally, the amount of subsidence in these zones is considered to be small.

The sands of the Union Pacific and Ford zones are thin-bedded to massive, fine- to coarse-grained, fairly well to poorly sorted and are interbedded with hard, dense, dark grey to black siltstones and shales. Hard sandstone members, previously called "shells", are more prevalent in these formations. Usually, during coring operations the core barrel has to be pulled out of the hole in order for the "shells" to be drilled with a rock bit and, thus, resume coring operations. The Union Pacific Zone is thinly bedded, with the sands becoming massive, coarse and pebbly in the lower part of the Ford Zone. The degree of induration of sediments is, in general, directly related to the depth of burial. The hard dense shales in the deeper horizons grade to siltstones, soft claystones and mudstones.

The 237 Zone consists of 2000 ft of massive, poorly sorted, locally friable to well cemented arkosic sandstones interbedded with dense black shales. The lower 650 ft consist of black, dense, locally fractured, well-bedded shale, with brown phos- phate nodules and occasional thin interbeds of hard, medium- to coarse-grained sandstone.

The fractured nodular shale and the upper 100 ft of fractured basement is oil productive in the East Wilmington portion and is known as the "D-118" sub-zone.


STRUCTURE

The Wilmington structure is a large, broad, asymmetrical anticline having a northwest-southeast axial trend (Fig. 6-4). The low angles of dip of the unconsolidated beds near the crest, the presence of tension faulting and the heavy overburden result in an unstable structure susceptible to compaction. The structure is cut by numerous major and minor faults thus dividing it into hundreds of fault blocks, down-dropped wedges and individual reservoirs.

The field is separated to the northwest from the Torrance anticline by a saddle, to the southeast from the Belmont Offshore "Surfside" Oil Field by a large fault and to the northeast from the Seal Beach Oil Field by a major syncline and several northwest-southeast trending faults believed until 1975 to be pressure and fluid barriers. This belief was changed when the two oil fields were found to be in direct pressure communication in some reservoirs. To the south, seismic data indicate a series of complex geologic structures which may or may not be fluid barriers.

In summary, the Wilmington Oil Field geologic structure and the geologic structures surrounding it are extremely complex. Flow paths and pressure conduits do exist peripheral to the field and there is no guarantee that all fluids injected into the reservoirs for subsidence control will remain within the Wilmington Oil Field structure. As a matter of fact, chances are they will not. Constant surveillance and monitoring of pressures are and will be of extreme importance for a considerable time into the future in order to prevent a renewal of Long Beach's past disastrous subsidence.

Fig. 6-4. Structural contours on top of Ranger Zone ("F" electric log marker).


DRILLING AND COMPLETION METHODS

Directional drilling

Most of the wells in the Wilmington Oil Field are directionally drilled and generally have four basic vertical profile configurations as shown on Fig. 6-5.

Coring

Coring of the oil zones has provided material for use in compaction testing. The coring method selected for a particular zone depends on a number of factors, i.e., cost, formation hardness, and core size desired. The methods, which have been used in the Wilmington Oil Field, are conventional, diamond, wireline, PVC, and rubber sleeve.

Completion methods

In order to economically and successfully produce from the unconsolidated sands of the upper four zones, most wells are completed utilizing the gravel flow pack method. This method consists of drilling to the top of the oil zone, running the necessary electric logs and running and cementing the 8-5/8-inch casing in the shale above the zone. After the 8-5/8-inch casing has been cemented, the well is drilled to total depth, the necessary electric logs are run in order to determine the exact completion interval, and the hole is enlarged to 14 inches. A 6-5/8-inch slotted liner is run and gravel flow packed with the desired size gravel. Upon completion of the gravel packing operations, the production equipment is run in the well and the well is placed on production or injection (Wade, 1966). This completion method has been followed since 1949 in most of the wells drilled and it has been found to provide positive means for sand control (Fig. 6-6).

Fig. 6-5. Directional drilling basic profile configurations. (After Lyons and Mecham, 1968.)


Fig. 6-6. Typical injection well completion.

Certain modifications have been developed and have been followed in both the western and eastern portions of the Wilmington Oil Field. In the western portion, earthquakes occurred in December, 1947; November, 1949; August, 1951; and October, 1952. These earthquakes caused casing shearing in 165 wells at the following levels: 1575 ft, 1700 ft and 2050 ft. In order to provide safety for future wells, protective methods were developed which involved the running of stronger casing strings equipped with devices permitting lengthening or shortening of the string without damage. Sufficient room for movement around casing strings to prevent transmission of earth movement stresses to the casing was provided by scraping 'bell holes' up to 30 inches in diameter from approximately 1400 ft to approximately 2100 ft depending upon the angle of the directional hole (Fig. 6-7). These "bell holes" were filled with a special packing of oil-base fluid chemically treated to increase gel strength to a high level. By the use of these installations, a high degree of protection has been obtained (Roberts, 1953). Inasmuch as the current repressurization program provides adequate protection against subsidence and thus against man-made earthquakes, the "bell hole" packing method has been discontinued.

SUBSIDENCE

History

Subsurface compaction resulting in surface subsidence has occurred in many oil-producing, fresh-water producing and mining areas of the world. Some of the presently known subsidence areas are: the Santa Clara and San Joaquin Valleys of California (Johnson et al., 1968); the Goose Creek area near Galveston Bay, Texas (Gabrysch, 1969); the Bolivar Coast of Venezuela (van der Knaap and van der Vlis,


Fig. 6-7. Bell hole protection at slippage planes.

1966); the area of La Ciudad de Mexico; the Po Valley in northern Italy; and Tokyo and Niigata, Japan (Aoki and Miuabe, 1969).

Geodetic leveling surveys established that the San Pedro-to-Seal Beach coastal areas have been naturally subsiding since the early 1900's. Since the 1930's, survey crews from the cities of Los Angeles and Long Beach, the United States Coast and Geodetic Survey, and other agencies have regularly conducted leveling surveys across the Wilmington area. Generally, during this time, the surveys indicated an average subsidence rate of between 0.02 and 0.04 ft per year.

During the summer of 1941, the U.S. Coast and Geodetic Survey conducted a first order leveling survey from the cities of Redondo Beach and San Pedro to a point east of Long Beach over the same level network they had established in 1931. This latest survey showed a subsidence of 0.2 ft at the west city boundary of Long Beach with a gradual increase to 1.3 ft at the easterly end of Terminal Island and then gradually decreasing to practically zero under the City of Long Beach. Inasmuch as the area of maximum subsidence coincided with a Navy dewatering project for the construction of a graving dock, it was thought that subsidence would stop and perhaps part of the lost elevation would be recovered when the dry dock construction was completed. In July, 1945, the U.S. Coast and Geodetic Survey confirmed leveling surveys of the Long Beach Harbor Department which indicated that the easterly end of Terminal Island had subsided 4.2 ft from 1931 to 1945. The results of these surveys and other data indicated that progressive ground movement, oil field development and production were perhaps dependent events.

Along with the problems of subsidence, there also were several minor earth movements between 1947 and 1952. These earthquakes were caused by slippage


Fig. 6-8. Total subsidence in Wilmington Oil Field area.

along several nearly horizontal planes of shale located at depths between 1500 ft and 2000 ft. Well damage alone was in the millions of dollars. A large amount of horizontal movement was also occurring on the surface. Most long structures such as railroads, pipelines, and transit sheds were being cracked, buckled, and bowed.

While various studies were being made by experts to determine what was causing subsidence, the subsiding area continued to grow, gradually assuming the shape of an elliptical bowl superimposed on top of the Wilmington Oil Field structure (Fig. 6-8). The subsidence rate increased to a maximum in 1951 when the center of the bowl was sinking at a rate of more than two ft per year and the field had attained its maximum production of oil and gas (Fig. 6-9). Cumulative subsidence reached 15 ft. By 1952, the ground elevation of the Navy Shipyard had sunk below high tide water. By 1958, the total area affected covered 20 square miles. Horizontal surface movements of more than 10 ft accompanying vertical subsidence caused extensive damage to the existing structures, oil wells, and the U.S. Navy installations.

Figures 6-9 and 6-10 indicate that cumulative subsidence between 1926 and 1967 reached 29 ft at the center of the bowl. In addition, these figures indicate that the surface subsidence has been confined almost entirely to within the outlines of the underlying producing reservoirs.


Fig. 6-9. Subsidence, oil production and effect of water injection in Wilmington Oil Field.

Fig. 6-10. Northeast-southwest cross-section showing profile of subsidence bowl on top of the Wilming- ton anticline. (After Colazas, 1971.)


Compaction theory

Many reports covering the subsidence problem in the Long Beach-Wilmington area have been written; therefore, a detailed description and history of these investigations is not warranted here. Two reports are worth mentioning, however, because they were perhaps the first comprehensive reports written regarding Wilmington Oil Field subsidence. Also, after investigating the same data, the authors arrived at similar conclusions but attributed compaction to different sediments.

Gilluly, Johnson and Grant prepared a report on subsidence in 1945. A modification of this report was later published in the Bulletin of the Geological Society of America (1949). After considering all possible causes, they showed that the progressive surface depression was most probably due to compaction of sediments in the oil zones. They examined the evidence and found that the history of the surface movement since 1937 could be explained by compaction of reservoir sands.

At about the same time, Harris (1945) made an extensive study for the U.S. Navy, reaching the same conclusion except that he attributed the subsurface compaction to the reservoir shales.

Hudson (1957) and other investigators considered all the following factors in their examination of compaction and surface subsidence in the Wilmington Field:

(1) Lowering of hydraulic head due to groundwater withdrawals. (2) Oil reservoir sand compaction owing to fluid withdrawals. (3) Compaction of shales and siltstones interbedded with the oil sands. (4) Surface loading by structures. (5) Vibrations due to land usage. (6) Regional tectonic movements. (7) Lack of rigidity of the Wilmington structure. (8) Movements along known faults in the field. (9) A lack of preconsolidation in the sediments. Most investigators who studied the problem concluded that withdrawals of fluids

from the oil zones and the consequent lowering of pressure within these zones resulted in compaction of the oil sands and the interbedded siltstones and shales. The relative amounts of compaction between the sands and shales can be inferred from both laboratory compaction and porosity tests and from oil field operational practices and measurements.

Subsequent to the early studies, some of which concluded shales were the compacting material and some that sands were, more data has been accumulated and new interpretations prepared.

In view of the newer data, Allen and Mayuga (1969) attributed Wilmington Oil Field subsidence to the following causes: (1) reservoir pressure decline due to rapid development and production; (2) the unconsolidated reservoir sands having little or no cementation; (3) the thin, interbedded shales being susceptible to drainage; (4) the relatively flat overburden supplying a constant load; (5) the lack of severity of folding causing a weak structure that is incapable of supporting the overburden; and (6) normal tension faulting which weakens the Wilmington structure, whereas compressional faulting would have strengthened it.


Fig. 6-11. Diagrammatic shale-water flow to lower pressure permeable sands.

The actual mechanics of compaction are believed to include sand grain rearrangement, plastic flow of soft minerals, some plastic deformation of sand grains, and perhaps some crushing of grains or breakage of sharp corners in exceptionally low-pressure reservoirs or pools. Limited crushing of sand grains was observed in the laboratory but the samples were dry and the pressure ranged to 2500 psi.

Due to the high permeability of the sands, a fairly rapid shift in grain-to-grain loading results when fluid pressures are lowered, creating a rapid loss of pore volume. In the case of the shales, however, their extremely low permeability results in a slow transfer of load from the pore fluids to the skeletal structure as the fluids are slowly forced from the shales into the relatively lower pressured and more permeable sand members (Fig. 6-11).

The length of time required for the Wilmington sands and shales to approach equilibrium has been investigated by Allen and Mayuga (1969), Colazas (1971), Converse Engineering Company (1957) and numerous other investigators. The general conclusion of all investigators was that the degree of compaction is a function of unit thickness, depth of burial, cementation, and permeability. Generally, the deeper the burial, the less the compaction due to the existing natural consolidation of the sediments.

According to van der Knaap and van der Vlis (1966), the time for a Venezuelan shale or clay layer to reach equilibrium increases as the square of the thickness. They determined that thin shales or clay layers reached equilibrium within a few days to a few weeks, whereas an 8-ft shale might require 16 years and a 20-ft shale might require upwards of 50 years (Fig. 6-12).

300

1.0

0.8

C O

o 0 . 6 0 Q, E 0

(9

0 c 0

- 0 . 4 u O

LI.

0.2

/

/

/

/ J

I

X.C. COLAZAS AND R.W. STREHLE

a

/ , / /

/ ,S

0 O. I 0 .5 I 5 I0 50 I00 2 0 0

Time in Years

Fig. 6-12. Fractional compaction of clay layers of various thickness following an instantaneous drop in reservoir pressure. (After van der Knaap and van der Vlis, 1966.)

Laboratory investigations

Extensive laboratory investigations in Wilmington and throughout the world have been conducted over the years in order to measure the compressibility of sediments and study their physical properties at relatively high pressures such as exist in various oil-producing reservoirs.

Terzaghi and Peck (1968) concluded that the compressibility of confined strata of sand could usually be disregarded for surface settlement calculation. This is probably true for the relatively low pressures imposed by various surface structures. Recent tests, however, have proven that sand is compressible under the load imposed when an oil sand buried under several thousand ft of sediments has its pore pressure reduced by a few hundred psi (pounds per square inch) below its original value.

Roberts (1969), using both natural samples of clay and sand and laboratory mixes, demonstrated that compressibilities of sands and clays might be very close at high loads.

Chilingar et al. (1969) presented an interesting study regarding the compressibilities of various dry clays in the laboratory and compared them with those saturated


with either flesh water or sea water. In addition, the relationships between the chemistry of interstitial solutions and the overburden pressures were examined.

Following is a list of investigators and a summary of their findings regarding the compaction of Wilmington sediments.

Harris (1945) attributed all compaction to shale intervals. All laboratory tests which Harris used in his estimates were made on shales-siltstones alone, although he compiled and compared various works by other authors.

McCord (1957) concluded that both shales and sands experience progressive pore space reduction and hence compaction over geologic time, but under heavy loading shales compact more quickly than sands. McCord attributed most subsidence to shale compaction, assuming that sands are relatively incompressible.

Hudson (1957) used laboratory tests on artificially prepared sand samples by Tickell et al. (1933), which showed little sand compressibility, and came to the conclusion that approximately 80% of the Wilmington Oil Field subsidence should be attributed to shales.

Converse Engineering Company (1957) was retained by the Long Beach Harbor Department to conduct laboratory consolidation tests. The results of these tests were to be utilized in calculating ultimate compaction of the various producing zones. These tests perhaps represent the most comprehensive work on the compressibility of Wilmington Oil Field siltstones and shales.

Converse engineers obtained 32 samples from cores ranging in depth from 2368 to 6009 ft below the surface representing the total Wilmington Oil Field stratigraphic column. Twenty-eight of these samples were siltstones and shales and the remaining were typical Wilmington Field unconsolidated sands. According to Converse engineers, "the results of the sand samples should be viewed with extreme caution because they do not seem to be consistent with the Terzaghi theory". They added that the inconsistent results were perhaps due to possible sampling and sample preparation disturbance.

Allen and Mayuga (1969) reviewed most of the previous work regarding Wilm- ington Field compression tests and effects of overburden pressure on the physical properties of rocks and summarized the data in the form of pressure versus void ratio graphs indicating the relative compressibility of sands and shales. They concluded that about one-third of the subsidence to that date had occurred in the shale intervals and was continuing at a slow rate.

Colazas (1971) selected 31 sand samples from Wilmington Field wells representing the Ranger, Upper Terminal and Lower Terminal zones and conducted triaxial compression tests (samples were loaded on three axes). The modified triaxial equipment is most commonly used in modern testing because it is easily adaptable for testing unconsolidated sands. In addition, three artificially mixed samples were tested in order to compare these results with those obtained from Wilmington sands.

Consolidation tests Nine samples of shale/siltstone were tested by Converse Engineering from cores

taken at depths between 2386 and 4474 ft below the surface. These samples represented the upper four zones.


TABLE 6-III

Summary of consolidation test results: Tar, Ranger, Upper Terminal and Lower Terminal siltstones (from Colazas, 1979)

Zone Well No. Location Depth Marker Description Spec. Dry Initial Final subs. MWD gravity density void void cont. VSS (lb/ft 3) ratio ratio (ft) (ft) ei ef

Tar J-107 R 4-5 4-2

W-219 R 4-23

Ranger W-219 R 4-23

J-107 R 4-5

U.T. W-219 R 4-23

W-219 R 4-23

J-107 R 4-5

L.T. J-107 R 4-5

J-107 R 4-5

2593 T + 45' Siltstone 2.57 105.8 0.519 0.389 2200 Sandy 2368 T + 48' Siltstone 2.57 104.5 0.535 0.410

2220 Shaly 2582 F Siltstone 2.62 107.8 0.517 0.435 2434 Soft 2826 F + 25' Siltstone 2.55 98.2 0.620 0.480 2375 Shells 3106 H X +80' Siltstone 2.59 107.7 0.501 0.431 2961 Sandy 3254 Y + 6' Siltstone 2.49 114.0 0.363 0.294 3100 Sandy 3688 Y + 7' Siltstone 2.45 116.0 0.312 0.244 3150 hard 4085 A B - 1' Siltstone 2.68 114.1 0.461 0.357 3551 Sandy 4474 AD + 79' Siltstone 2.62 109.8 0.490 0.413 3924 Sandy

The matrix specific gravity, oil and water content, unit dry weight, lithologic description, initial and final void ratio and porosity, and maximum change in compression and rebound expressed in terms of void ratio and porosity are all shown in Table 6-11. Other data calculated from the various consolidation (time versus volume change) curves as well as the location of the wells in relation to the subsidence contours within the subsidence bowl are also summarized in Table 6-111.

Triaxial tests Thirty-one samples of Wilmington sands were tested by Colazas (1971) under

triaxial compression in order to observe the mechanical and physical changes in sediments subjected to pressures equal to approximately twice the hydrostatic pressure.

Figures 6-13 and 6-14 summarize the data of these 31 test samples in terms of average value and show that the pore compressibility of the three zones, although similar, is not quite the same. The three curves representing the Ranger, Upper Terminal and Lower Terminal sands indicate that the greatest pore compressibility occurred in the Ranger sands and the least compressibility in the Lower Terminal sands. Rebound of the sands was approximately equal, whereas the average rebound of the siltstones was considerably higher than that of the sands.


Initial Final Maximum Com- Coef. of porosity porosity prec. pres. pres. compres. (%) (%) (lb/sq.in.) index (cm2/g)

~bi ~bf Pc Cc A v

Coef. of Maximum Maximum consol, compression rebound

" "'(cm2/s) Ae A~b (%) Ae A 4) (%) C

34.2 28.0 1500 0.296 8.0 x 10 -7 1.3 x 10 -4 0.130 11.5 0.047 4.5

34.8 29.1 1700 0.300 7.4 x 10 -4 1.0 • 10 -4 0.125 11.1 0.018 1.8

34.1 30.3 1680 0.192 4.0 x 10 -7 3.3 • 10 -5 0.082 7.6 0.035 3.4

38.1 32.5 1800 0.318 6.4 x 10 -7 1.2 x 10 -4 0.140 12.2 0.070 6.5

33.4 30.1 1400 0.148 3.0 x 10 -7 1.1 • 10 -4 0.070 6.6 0.032 3.1

26.6 22.7 2360 0.158 5.7 x 10 -7 1.1 x 10 -4 0.069 6.4 0.032 3.1

23.7 19.6 2200 0.142 2.1 x 10 -7 1.5 x 10 -4 0.068 6.4 0.033 3.2

31.6 26.3 2400 0.182 2.7 x 10 -7 1.6 x 10 -4 0.104 9.4 0.024 2.3

32.9 29.2 2700 0.101 1.4 x 10 -7 1.4 x 10 -4 0.077 7.2 0.027 2.6

The results suggest a possible relationship between compressibility, grain size, permeability, and depth of cores from which the samples were obtained. Coarse- grained samples and samples obtained from deeper cores generally exhibited less compressibility and rebound than the shallower, finer-grained samples. It appears that compressibility of laboratory samples is inversely proportional to the depth from which the cores were obtained, and is minimized in areas of maximum subsidence where the intergranular pressure is at a maximum due to the extraction of reservoir fluids.

The average bulk volume compressibilities as a function of pressure for the Ranger, Upper Terminal and Lower Terminal sands are shown in Fig. 6-15 and indicate that the compressibility of the sands is so similar that one curve can represent all three zones.

Three samples also were artificially mixed and tested by Colazas (1971) in order to compare the results with those obtained from Wilmington sands. These samples consisted of Ottawa sand, Ottawa sand and illite clay, and Ottawa sand mixed with illite and kaolinite clays.

In addition to the above tests, six sand samples containing air and various interstitial fluids, that is, tar, water, and water plus tar (Table 6-IV) were subjected to pressures of 1000 psig at the Schlumberger Well Service laboratory.


c

u

Q .

im

0 L 0

36

34~ ,,

33------

32

31

30

z9 ; ,r,~

LEGEND O Ranger Zone

(13 Samples) 0 Upper Terminal Zone

(8 Samples) Lower Terminal Zone

(i0 Samples)

2 7 �9 �9 �9 �9 m j

o ,ooo ,soo zooo 2 'oo 3000 Pressure, psiq

Fig. 6-13. Porosity vs. pressure curves showing average sand compression and rebound by zone. (From Colazas, 1979.)

The degree of compressibility of these sands was examined in order to determine whether compressibility is related to the type of interstitial fluids. The porosities obtained at the various incremental pressures were compared with the porosities calculated from the Formation Density and Acoustic logs.


0.55

0.50

0 . 4 5

0 . 4 0 t....

LEGEND O Ranger Zone

(l 3 Samp i es) 0 Uppe r T e r m i n a l Zone

; ~ ~ ~ = ( 8 Samples) & Lower T e r m i n a l Zone

(i0 Samples)

�9

, . , , ) ' .

1 r

i i i i

t

o . 3 5 , , , ! 1 1 I 0 0 500 I 0 0 0 4 0 0 0

Pressure , ps ig

Fig. 6-14. Void ratio vs. pressure curves showing average sand compression and rebound by zone. (From Colazas, 1979.)

Results of laboratory tests

For the purposes of simplicity and comparison of compressibility of siltstones and sands, each zone is considered individually.


Q Q.

w,

o X

13-

12

1 I'

)

0

0

LEGEND

O Ranger Zone (13 Samples)

Q Upper Terminal Zone (8 Samples)

Lower Terminal Zone (I0 Samples)

t... ~>

!

I "

,oo 500 ,ooo ,5"00 zo'oo 2500 3000 P r e s s u r e , psi g

Fig. 6-15. Bulk volume compressibility as a function of pressure by zone. (From Colazas, 1979.)

Tar Zone Siltstones. The compressibilities of two Tar Zone siltstones are shown graphically

in Fig. 6-16 and in tabular form in Table 6-II. The average compression and rebound of the Tar Zone siltstones are on the

TABLE 6-IV Z -1

Porosity and void ratio at various overburden pressures of samples containing various interstitial fluids, Ranger Zone sands (from Colazas, 1979) 2 F - r

Sample Depth Marker Description Overburden pressure (psig) 5 No. MWD z 200 300 400 500 600 800 1000 0 vss (ft) 8'

z Well J-321 0 32 2041-61 FO Sand + tar 36.7 a 35.5 34.6 33.9 33.3 32.3 31.5 r

2381-99 (air-filled) 0.579 0.550 0.529 0.513 0.499 0.477 0.460 2

Well J-542 36 4605-30 G 5

3215-39

Sand (air-filled)

Sand + tar (water filled)

Sand (water-filled)

Sand (air-filled)

37 4605-30 Gs Sand 25.0 23.7 22.8 21.9 21.2 20.1 19.4 C 3215-39 (water-filled) 0.333 0.311 0.295 0.280 0.270 0.250 0.241

a Porosity (%); Void ratio.

308

0 . 6 0

X.C. COLAZAS AND R.W. STREHLE

0 .55

LEGEND

O T+45' (J-107R)

El T+48 ' (W-219R)

0 . 5 0 ,

0 . 4 5

0 . 4 0

' ~ - r N

,~=-= . . . . . , . % -""",,,, PC= 1500

I i i i i I i

! ,

i

0 . 3 5 , , , = ~ , I 0 0 I 0 0 0 4 0 0 0

P r e s s u r e , ps i

Fig. 6-16. Consolidation tests showing compression and rebound of Tar Zone siltstones. (From Colazas, 1979.)

order of 6.0 porosity percent (Ae = 0.127) and 3.1 porosity percent (Ae = 0.032), respectively (Table 6-V).

Sands. Because of the highly unconsolidated state of the Tar sands and disturbance

i

TABLE 6-V r E - L

Summary of compaction data 2 Zone Average Types of Calculated data (ft) Core Test Data

Y 0

depth (ft) sediments r thickness compaction compression rebound Z

n 4 (%I A e dJ (%I Ae 6

Tar 2200 Siltstones 100 4 6.0 0.127 3.1 0.032 Sands 65 2 Assumed to approximate Ranger 6

Ranger 2600 Siltstones 330 13 Sands 250 9

Upper Terminal 3100 Siltstones 200 6 3.8 0.069 3.1 0.032 n Sands 460 13 6.9 0.148 1.3 0.025 $

Lower Terminal 3600 Siltstones 300 8 4.6 0.090 2.4 3 0.025 Sands 420 11 5.9 0.124 1.3 0.025 f

5 >


caused by poor field handling of the cores, triaxial compression results of sand samples are not presented in this section. The calculated compression of the Tar Zone sands, as shown in Table 6-V is an approximation utilizing the physical characteristics of the Ranger Zone sands with the corresponding Tar Zone net thickness.

Ranger Zone Siltstones. The Ranger Zone has the greatest areal extent of all the oil producing

zones in the Wilmington Oil Field. In order to adequately evaluate the physical characteristics of the sediments that are part of this zone, two siltstone and 19 sand specimens were subjected to pressures up to 3000 psi. The siltstone samples were from wells J-107R and W-219R. The results are shown in Fig. 6-17 and Table 6-111. The average compression and rebound of the Ranger Zone siltstones are on the order of 4.6 porosity percent (Ae = 0.111) and 3.4 porosity percent (Ae = 0.035), respectively.

Sands. The results from 13 Ranger Zone sand samples are summarized in Table 6-VI and are shown in graphic form in Figs. 6-13 and 6-14. Table 6-VI describes the sample and presents the various porosities, void ratios, and bulk volumes corresponding to the various overburden pressures applied by the triaxial compression apparatus.

Figure 6-13 represents pressure versus porosity curve, plotted on a cartesian paper, whereas Fig. 6-14 is a pressure versus void ratio curve plotted on a two cycle semi-log paper. Figure 6-18 has been included to assist in the porosity to void ratio (and vice versa) conversions without the tedious formula calculations.

The results obtained on six samples containing various fluids (Figs. 6-19 and 6-20) do not differ considerably from those obtained on dehydrated and dried samples discussed earlier. It appears, however, that the water-filled clean samples start out with a lower initial porosity than the other samples, but are just as compressible. Later laboratory work conducted for tertiary recovery programs, however, indicates that fluid-filled samples may have a higher compressibility.

In general, the compressibility of the sands is independent of the type of interstitial fluid. The dried, air-filled samples are perhaps the least compressible. It seems reasonable to assume that some consolidation occurred as the fluids were forced out of the sample and then dried causing a greater initial bulk density.

The average compression and rebound of the Ranger Zone sands are on the order of 7.7 porosity percent (Ae = 0.16) and 1.4 porosity percent (Ae = 0.03), respectively.

It appears, therefore, that the average compressibility of the Ranger Zone sands is greater than the compressibility of the siltstones. The average rebound for siltstones, however, is greater than that of the sands.

Upper Terminal Zone Siltstones. Results for three siltstone samples obtained from cores are presented

in Table 6-III and Fig. 6-21. The average compression and rebound of the Upper Terminal siltstones are on

the order of 3.8 porosity percent (Ae = 0.069) and 3.1 porosity percent (Ae - 0.032), respectively.

SUBSIDENCE IN THE WILMINGTON OIL FIELD, LONG BEACH, CALIFORNIA, USA

0 6 5

O F

LEGEND

(J-lO7R)

0 F+75 ' (W-219R)

311

0 . 6 0

0 . 5 5 -

0 . 5 0 �9

0 . 4 5

I

\ ,

\ i

\ (

~ i !

C-" 1 6 8 0

. ~ ,

0.40 . , . , , 1 I00 I000 4000"

P r e s s u r e , psi

Fig. 6-17. Consolidation tests showing compression and rebound of Ranger Zone siltstones. (From

Colazas, 1979.)

Sands. The physical characteristics and compressibilities of eight Upper Terminal sands obtained from cores are summarized in Table 6-VII and Figs. 6-13 and 6-14.

Generally, the compressibility and rebound of the Upper Terminal Zone sands

TABLE 6-VI

Porosity, void ratio and bulk volume at various overburden pressures, Ranger Zone sands (from Colazas, 1979)

Sample Depth Marker Specific Description Overburden pressure (psig) No. MWD gravity

VSS (ft\ 200 300 400 500 600 800 1000 1500 2000 2500 1000 500 200

Well J-542 1 11 3954

2744 Fa + 72' 2.64 Oil sand, medium-

to coarse-grained

Fa + 76' 2.65 Oil sand, medium- to coarse-grained

Fa + 95' 2.61 Oil sand, coarse- grained

F, + 108' 2.66 Oil sand, medium- to coarse-grained

Fa + 116' 2.65 Oil sand, fine- to medium-grained

Fa + 117' 2.55 Oil sand, fine- to medium-grained

Well J-321 20 2659 Fa + 82' 2.62 Oil sand, medium-

2410 to coarse-grained

Well D-512 30 3142

2623

Well J-542 I 17 4055

2821

Fo + 10' 2.66 Oil sand, fine- to medium-grained

F + 108' 2.65 Oil sand, fine- grained

F + 25' 2.62 Oil sand, medium- to coarse-grained

C + 23' 2.65 Oil sand, fine- to medium-grained

C + 20' 2.63 Oil sand, fine- grained

Cg + 27' 2.66 Wet sand, fine. grained

a Porosity (%); Void ratio; Bulk volume (cm3).


0.85

0.80

0.75

0.70

0.65

0.60

0.55

0.50 -

0.45

0.40

0.35

0.30 " - - - - - - - -

0.25 20 25

!

/ I

30 35 40 45 Porosity , per cent

Fig. 6-18. Relationship between void ratio and porosity. (From Colazas, 1979.)

are slightly lower than that of the Ranger sands indicating that the Upper Terminal Zone is more consolidated owing to its greater depth and natural induration.

Lower Terminal Zone Siltstones. The results of the two Lower Terminal siltstone consolidation tests are

summarized in Table 6-111 and Fig. 6-22. In general, the average initial void ratio and compressibility of the Lower Ter-

minal siltstones are higher than those of the Upper Terminal siltstones. It should be mentioned, however, that all of the tested Upper Terminal siltstones were well- indurated, which may have given an erroneously low compaction factor.


o= 1=

t,.

i=

in

O =.._

O el

3 8

3 6

3 4

3 2

3 O

F O

(J -3e /

s', ( j - s 4 e

LEGEND Q Clean eand (airfilled)

) I~ l 0 Sand + tar (airfilled) ~ ~ i A Sand + tar (waterfil-led) ~ ~%k'~ " ~ I X Clean sand (airfilled)

"lJ;k~k~[ I e Clean sand (waterfilled) k k ~ ~_ [ 7 Clean sand (waterfilled)

(J-32_./) ,~ . ~ '

28 . . . . . . . . .

, P

2 6 . . . . .~, , �9 '

(J" 5 4 2 " 1 ) ~r

i

1 2 2 ' , , ~ - ; '

N , ,....

2 0 ~ L . . . . . . .

o 200 4oo eoo Boo ,ooo ,2"oo Pressure , psiq

Fig. 6-19. Relationship between porosity and pressure for the "Fo" and "Gs" sands containing various interstitial fluids. (From Colazas, 1979.)

The average compression and rebound of the Lower Terminal siltstones are on the order of 4.6 porosity percent (Ae = 0.090) and 2.4 porosity percent (Ae = 0.025), respectively.

316 x.c. COLAZAS AND R.W. STREHLE

0.60

0.55

0.50

0.45

0.40

0.:55

0.30

0.25

F'o (J-J21) ~ Fo (J-321) , l Fo (J-321) i

Gs (J-542-1) ( ~

LEGENq) O Clean sand (alrfilled) 0 Sand + tar (alrfilled) & Sand + tar (waterfilled) • Clean sand (airfil~ed.) �9 Clean sand (waterfilled) V Clean sand (waterfilled)

�9 I �9 ~ - ~ ~ ~ ~ ; i

\ , X

F'o (J- 321) ,~.,._ ~

, . .

aa (J- 542-1) ~,~ ~ r

-,q I00 500 I000

Pressure, psi9 Fig. 6-20. Relationship between void ratio and pressure for "Fo" and "Gs" sands containing various interstitial fluids. (From Colazas, 1979.)

Sands . Test results from 10 Lower Terminal sand samples are summarized in Table 6-VIII and Figs. 6-14 and 6-15. These samples represent the AA, AB, and AC sands which constitute the upper portion of the zone. The greatest compressibility of the samples was observed between pressures of 200 and 800 psig.


0.50

0.45

" ~ \ \ P c = 1400

0 . 4 0

LEGEND

O HX+80 ' (W-219R) 0 Y+6 ' (W-219R) & Y+7' (J-107R)

0 .35 [ I - . .~

"o~

t ~

0 . 3 o . ,

i

i

0 . 2 5 . . . . . I 0 0 I0"00 4 0 0 0

PressurQ , ps=

Fig. 6-21. Consolidation tests showing compression and rebound of Upper Terminal Zone siltstones. (From Colazas, 1979.)

The AA samples demonstrated the greatest compressibility with the AC samples being the least compressible. This again may be a function of burial depth and age.

TABLE 6-VII

Porosity, void ratio and bulk volume at various overburden pressures, Upper Terminal Zone sands (from Colazas, 1979)

Sample Depth Marker Specific Description No MWD gravity

VSS (ft)

Overburden pressure (psig)

200 300 400 500 600 800 1000 1500 2000 2500 1000 500 200 - -

Well J-327 22 3939 H X l + 56' 2.64 011 sand, fine-

2910 gra~ned

23 4013 H X + 60' 2.68 Oil sand, fine- 2970 to medium-grained

24 4070 HS + 117' 2.65 Wet sand, fine- 3020 grained

25 4118 H X b + 28' 2.62 Wet sand, fine- 3060 grained

26 4209 J + 32' 2.67 Oil sand, fine- 3137 grained

27 4477 2 + 41' 2.65 Oil sand, coarse- 3837 grained

28 4550 W + 47' 2.65 Oil sand, medium- 3422 to coarse-grained

29 4590 A + 33' 2.71 Oil sand, medium- 3455 to coarse-grained



0.55

4

0.50 !

0.45

0.40

0.35

0.30

LEGEND

o As+]. (,7-I07R)

O AD (J-107R)

L

i

I00 I 0 0 0 4 0 0 0 Pressure , psi

Fig. 6-22. Consolidation tests showing compression and rebound of Lower Terminal Zone siltstones. (From Colazas, 1979.)

The average compression and rebound of the Lower Terminal Zone sands are on the order of 5.9 porosity percent (Ae - 0.124) and 1.3 porosity percent (Ae - 0.025), respectively.

TABLE 6-VIII

W Porosity, void ratio and bulk volume at various overburden pressures, Lower Terminal Zone sands (from Colazas, 1979) t3

0 Sample Depth Marker Specific Description Overburden pressure (psig) No. MWD gravity

VSS (ft) 200 300 400 500 600 800 1000 1500 2000 2500 1000 500 200

Well 0-1 14 1 4988 AA+601 2.65 Oilsand,fine- 35Aa 35.6 35.2 34.6 34.3 33.8 33.2 31.9 31.1 30.2 30.5 31.2 31.8

3597 grained 0 . 5 5 8 ~ 0.553 0.543 0.529 0.522 0.511 0.497 0.468 0.452 0.433 0.438 0.454 0.466 15.33C 15.18 15.07 14.94 14.89 14.75 14.62 14.36 14.17 14.01 14.11 14.21 14.34

2 5010 AA + 84' 2.67 Oil sand, fine- 35.6 35.4 35.2 34.7 33.9 33.2 32.6 31.4 30.6 29.8 30.3 30.5 31.7 3617 grained 0.553 0.547 0.543 0.531 0.513 0.497 0.484 0.458 0.441 0.424 0.434 0.439 0.464

14.66 14.52 14.45 14.38 14.22 14.06 13.96 13.68 13.55 13.38 13.49 13.52 13.77

3 5020 AA +94' 2.66 Oil sand, fine- 37.7 37.4 37.2 36.9 36.4 35.5 34.4 33.9 32.8 31.7 32.4 32.8 34.2 3627 grained 0.605 0.597 0.593 0.585 0.572 0.550 0.524 0.513 0.488 0.464 0.479 0.488 0.520

14.02 13.95 13.90 13.85 13.74 13.52 13.30 13.22 12.99 12.80 12.94 13.01 13.23

4 5031 AA + 105' 2.66 Oil sand, fine- 37.2 36.5 36.0 35.6 34.6 34.2 33.6 32.6 31.5 30.5 31.0 31.4 32.0 3637 grained 0.593 0.575 0.563 0.553 0.529 0.520 0.506 0.484 0.460 0.438 0.450 0.458 0.470

14.59 14.45 14.35 14.24 14.05 13.94 13.83 13.62 13.41 13.22 13.32 13.38 13.49

5 5060 AA+134 '2 .65 Oilsand,fine- 34.6 34.2 33.7 33.1 32.8 32.3 31.7 30.3 29.1 28.4 28.4 29.1 29.6 3666 tomedium-grained 0.529 0.520 0.508 0.495 0.488 0.477 0.464 0.434 0.410 0.397 0.402 0.410 0.420

14.10 14.01 13.92 13.81 13.74 13.63 13.51 13.24 13.02 12.90 12.95 13.03 13.12

6 5080 AA+154' 2.66 Oilsand,fine- 32.4 31.7 31.4 31.2 30.9 30.0 29.4 28.0 27.0 26.1 26.4 26.9 27.4 3685 tomedium-grained 0.479 0.464 0.458 0.454 0.448 0.428 0.416 0.389 0.370 0.353 0.359 0.368 0.378

15.56 15.40 15.34 15.27 15.22 15.04 14.90 14.61 14.41 14.24 14.29 14.39 14.51

7 5107 AA+1811 2.65 Wetsand,medium- 27.6 27.2 26.7 26.3 26.0 25.7 25.2 24.0 23.0 22.0 22.7 22.8 23.2 x 0

3712 tocoarse-grained 0.381 0.374 0.364 0.357 0.352 0.346 0.337 0.316 0.299 0.282 0.294 0.295 0.302 0 55.29 15.22 15.13 15.04 14.97 14.92 14.82 14.58 14.39 14.20 14.33 14.36 14.43

8 5123 AB + 1' 2.65 Wet sand, medium- 34.8 34.2 33.7 33.6 33.1 32.3 31.5 30.3 29.1 28.2 29.1 29.2 29.5 3725

E tocoarse-grained 0.534 0.520 0.509 0.506 0.495 0.477 0.460 0.434 0.410 0.393 0.410 0.413 0.418 $

12.53 12.42 12.32 12.31 12.21 12.07 11.93 11.73 11.52 11.38 11.52 11.54 11.59 % 9 5252 AC + 19' 2.65 Oil sand, fine- 31.3 30.8 30.4 30.0 29.8 29.0 28.7 27.7 26.6 26.0 26.4 26.6 27.6 u

3850 tomedium-grained 0.456 0.445 0.436 0.128 0.424 0.408 0.402 0.383 0.363 0.352 0.359 0.363 0.381 ' 15.22 15.11 15.02 14.93 14.89 14.72 14.65 14.46 14.23 14.12 14.20 14.24 14.44 s

Y 10 5263 AC + 30' 2.65 Oil sand, fine- 32.4 31.6 31.0 30.6 30.4 29.8 29.4 28.8 27.8 27.3 27.5 28.0 28.8 W

3861 m

grained 0.479 0.462 0.450 0.441 0.436 0.424 0.416 0.404 0.386 0.376 0.380 0.389 0.404 F 15.97 15.97 15.67 15.58 15.54 15.40 15.31 15.20 14.97 14.87 14.92 15.03 15.17 m



Artificially mixed samples The test results of the three artificially mixed sand and clay samples were as

expected. The pure Ottawa sand was the least compressible of all the samples tested in the laboratory, whereas the samples containing Ottawa sand, powdered illite and kaolinite demonstrated the greatest compressibility.

Application of laboratory results in estimating compaction

The relationship between the change in thickness and change in void ratio of a layer of sediments was used to calculate the compression of siltstones and sands. Thickness of the zones was determined from the sand counting records (Wells J-141, J-21, J-327, J-332, D-114, D-605). The calculated porosity changes due to compression are summarized in Table 6-IX. Table 6-V summarizes calculated and laboratory data and shows the average compaction and rebound of the sands and siltstones by zone in terms of porosity percent (bulk volume) decrease. These data were utilized as guides to make the compaction calculations which are also shown in Table 6-VII. The compressibility data used to derive the potential compaction values were taken from the pressure/void ratio graphs at the estimated load change in the reservoirs. Table 6-V indicates that test specimens of sand and siltstone are approximately equally compressible. The average compaction of the sands under laboratory conditions is in the order of 6.8 porosity percent and that of the siltstones about 4.3 porosity percent. The total compaction that might have occurred, under oil field operating conditions and using maximum reservoir pressure drops, is estimated to be in the order of 35 ft for the sands and 31 ft for the siltstones, for a total of 66 ft. This total compaction, as indicated by laboratory tests, has to be reduced for several reasons: (1) the change in load imposed by pressure depletion may be about 1/2 that placed on the laboratory samples; (2) the load imposed by the overburden is not completely transferred to the grain to grain contacts; (3) lateral support exists in the formations due to structural support; and (4) all sands and siltstones are not de-pressured due to stratigraphic discontinuities and the time necessary to complete drainage.

In terms of rebound, the simulated overburden pressure exerted on the samples in the laboratory was adequate to cause permanent deformation in all specimens, both sands and siltstones. The siltstones "rebounded" more than the sands upon a release of pressure. It appears that the sands undergo more permanent deformation due to sand grain rearrangement, crushing and plastic flow of soft materials such as clay and mica.

The siltstones are more indurated and/or cemented and show less permanent deformation during the short period of the laboratory tests. Under long-term field conditions, however, slow adjustment to stress would probably occur. Laboratory tests indicate about 18% of the porosity loss can be regained in the sands and perhaps 31% in the siltstones under ideal conditions. Applying these percentages to the 35 ft of possible sand compaction and 31 ft of possible siltstone compaction, a rebound of 6 ft for the sands and 9 ft for the siltstones can be calculated, totaling 15 ft. Inasmuch as a maximum of 1.3 ft of rebound has been measured (Fig. 6-23), these numbers obviously can only be used to indicate that rebound could be greater than that ob-

TABLE 6-IX

Average porosity, void ratio and bulk volume at various overburden pressures, Ranger, Upper Terminal and Lower Terminal Zone sands (after Colazas, 1979)

Thick- Mean Maximum Specific Overburden pressure (psig) ness depth precons. gravity (ft) VSS (ft) press. (psi) 200 300 400 500 600 800 1000 1500 2000 2500 1000 500 200

Ranger Zone 180 2990 1450 2.64 35.4a 34.8 34.1 33.6 33.3 32.5 31.6 30.3 28.8 27.7 28.2 28.6 29.1

0.547' 0.534 0.518 0.506 0.499 0.481 0.462 0.434 0.404 0.383 0.393 0.401 0.411 13.92' 13.75 13.65 13.55 13.44 13.28 13.14 12.89 12.59 12.40 12.48 12.55 12.68

Upper Terminal Zone 410 3190 1547 2.65 35.3 34.7 34.0 33.5 33.2 32.4 31.7 30.5 29.1 28.4 28.9 29.2 29.7

0.545 0.531 0.515 0.503 0.497 0.479 0.464 0.438 0.410 0.397 0.406 0.413 0.422 14.49 14.33 14.22 14.10 14.00 13.83 13.70 13.44 13.21 13.07 13.16 13.22 13.31

Lower Terminal Zone 330 3690 1790 2.66 33.9 33.5 33.0 32.7 32.2 31.2 30.9 29.9 28.7 28.0 28.5 28.8 29.3 x

0.513 0.503 0.493 0.486 0.475 0.454 0.447 0.426 0.402 0.389 0.399 0.404 0.414 0 14.73 14.60 14.52 14.44 14.35 14.20 14.08 13.87 13.67 13.51 13.60 13.67 13.81 0

0 a Porosity (%); ' Void ratio; Bulk volume (cm3). X

% % u ?J ?? 2 ;a rn 6 rn

atacn MARK no. l i r z 0- ntncn MARK no. 0 2 7

Fig. 6-23. Total rebound, in feet, during 1973, 1978, and 1979. (From Colazas, 1979.)


served. The rebounds calculated represent zero load on the test specimen, whereas in the reservoirs the weight of the overburden applies a constant downward load. Only a portion of this load is relieved by waterflooding due to the same set of parameters (previously given) that lessen the maximum possible compaction. The overburden weight acts in a direction that increases subsidence and decreases rebound.

FIELD M E A S U R E M E N T OF COMPACTION AND SUBSIDENCE

Introduction

The following is a discussion of the many techniques which were and are being used to monitor subsidence. By controlling injection and production and monitoring surface elevation changes, subsidence is being effectively controlled.

First-order level surveys

The most important method of subsidence surveillance is the leveling survey conducted semiannually by the City of Long Beach. The elevation of approximately 900 bench marks located within and adjacent to the oil development area are measured.

These data are utilized in the preparation of semiannual reports of surface elevation changes. Elevation data are then correlated with water injection data to explain any losses or gains of elevation.

Precision casing collar surveys

To date, the most successful method for measuring in-situ compaction of the Wilmington Oil Field reservoirs is "casing collar counting", which was first developed in 1950 and later modified (Law, 1950; Allen, 1981b). This method operates under the theory that the portion of the well casing opposite the producing zone will shorten or lengthen as the producing zone compacts or expands due to production or water injection operations.

The City of Long Beach has conducted numerous collar count surveys in key wells during the past thirty years and has been able to locate the zones which contribute most to compaction. These data were correlated with the numerous laboratory compaction tests (Colazas, 1979).

The high precision collar-logging tool consists of two magnetic collar locators mounted approximately 40 ft apart on a wireline logging sonde (Fig. 6-24). Inasmuch as the casing collars and collar-locators on the tool are approximately equally spaced (40 ft), both collar locators "kick" at about the same time. By knowing the exact distance between collar locators on the tool and by determining the exact distance the tool traveled between "kicks", the precise distance between collars can be determined. A composite of all collar data is then used to indicate areas under tension or compression (Fig. 6-25).


Fig. 6-24. Measuring system for casing joint length and radioactive bullet distance. (From Allen, 1981b.)

Radioactive bullet surveys

Another method to determine in-situ compaction is to measure individual zone compaction directly by the movement of radioactive bullets placed in wells.

In this technique a perforating gun, loaded with radioactive bullets, is lowered


L V

U

L__i L_J

--4-T ~ m

v m

l__J L._I # m

-1- ~m m r-

DISTANCE "C"

~ I i '

I L__I- ~ ! ! L A I. _1 F;, , -1 F �9 -I

I _1

-]1 I I

NO FOOTAGE SCALE-- DIRECTION OF TOOL MOVEMENT

Fig. 6-25. Paper and pen recorder system diagram. (From Allen, 1981b.)

into the wellbore and the bullets are shot at predetermined intervals prior to landing casing. Once the bullets are in place and the casing has been run, a gamma ray detector is lowered into the well in order to confirm the distances between the bullets and establish necessary calibration points. Thereafter, periodic surveys are made to detect any distance difference between the bullets. This technique, however, has not proved to be reliable in the Wilmington Oil Field.

Shallow-compaction recorders

Instruments to record shallow compaction have been installed in the Wilmington Oil Field in order to detect any shallow subsidence that might be caused from the shallow water-producing zones.

Tidal-gauge recorders

Self-registering tide gauges are maintained on the offshore drilling islands in order to observe and record the rise and fall of tides and to determined the relative elevation of drilling island bench marks to mean high tide.


Seismic surveys

Since May, 1972, the Geophysical Laboratory of the University of Southern California has been under contract with the City of Long Beach to conduct detailed seismic monitoring of the Wilmington Oil Field. A seismic monitoring network was established which consists of five seismometers located at various points near the Wilmington Oil Field and Long Beach areas.

The major objectives of the seismic network are: (1) to monitor the local microearthquake activity in the Long Beach area and detect possible fault movements that might be caused by production and pressuring operations, and (2) to locate precisely and identify all earthquake events that occur naturally along the nearby active faults and prevent them from being improperly attributed to oil field operations in the Wilmington Oil Field (Teng and Henyey, 1978).

From 1940 to 1960, several shallow earthquakes did occur due to subsidence and caused damage to over 160 oil wells. Earth slippage and earthquakes resulted when earth stresses were relieved by sudden horizontal movements along three shallow, thin shale beds acting as slippage planes (Kovack and Archambeau, 1974).

Reservoirpressure surveys

Maintaining a record of the bottomhole pressure on key wells located in each oil reservoir provides essential information for monitoring subsidence, because subsidence is caused by a reduction of reservoir pressure. The monitoring of reservoir pressure at Wilmington Field, however, has proved difficult due to the dynamics of the waterflooding operations.

Horizontal-strain surveys

Measured distances across Wilmington Field will lengthen due to rebound or shorten due to subsidence over a period of time, depending on whether tensional or compressional forces are acting on the ground surface. Measurements of horizontal strain lines of from 2600 to 18,000 ft in length are made biannually using electro- optical, line-of-sight instruments. Strain lines less than 5000 ft in length have proven to be better indicators of subsidence and rebound than longer lines (Allen, 1981a).

Production-injection balance

To prevent subsidence, it is essential that gross production be offset by an equal or larger volume of water injection. To achieve this, accurate records must be maintained of daily injection and gross production, including oil, gas and water. The volume of gas produced at Wilmington Field is now a minor component of the total production. An injection to production ratio of approximately 1.05 to 1 is maintained at Wilmington Oil Field.


R E P R E S S U R I Z A T I O N AND R E B O U N D

Whereas early investigators generally agreed on the causes of subsidence, there was little speculation as to how to stop or prevent subsidence (except for shutting in the wells). Water injection or flooding, which had been used successfully in the Mid-Continent and Eastern oil fields since about 1921, was slow to develop in California.

The first Wilmington waterflood was a pilot project where the City of Long Beach (with Long Beach Oil Development Company as contractor) began injection in June 1953 with two wells into the upper 50 ft of the Upper Terminal Zone.

Operators were reluctant to admit liability for subsidence or to enter into agreements for cooperative injection of water into their oil pools. Years of litigation and deliberation, during which the subsidence rate was highest, finally resulted in legisla- tive action and the unitization of the various operations into the Fault Block Units.

The Subsidence Act of 1958 resulted in unit and cooperative agreements covering virtually every oil operator.

A lawsuit was settled in 1963 by a stipulation for judgement between the United States and the City of Long Beach and State of California. The stipulation gave a broad responsibility to the City as to arresting and preventing subsidence under the Long Beach Naval Station and Shipyard.

By 1961, the cooperative units had begun injection into the upper four oil zones in all Fault Blocks. Over half of all water being injected in California was injected in the Wilmington Oil Field. Response to this injection was rapid. Bench mark elevation declines slowed and stopped within two years from the start of injection (Fig. 6-26).

Types and treatment of injection water

The present injection rate in the Wilmington Oil Field is approximately 1.3 million barrels of water per day. The total water injected in 1986 was 437,806,000 bbl. There are 828 active injection wells in the Wilmington Oil Field. The injection water comes from three sources: (1) source well water, (2) produced water, and (3) fresh water.

Source well water used for injection in the Wilmington Oil Field averages approximately 78,000 bbl per day. This represents about 6.0% of the injection water requirement for the field. Fresh water sources supply about 1.4% or approximately 18,000 bbl per day of the injection water for the field. Produced water makes up the remaining 92.6% (1,204,000 bbl/day) of the injection water used in the field.

Source well water Source well water was used extensively in the early days of the waterflood due

to the unsuitability of sea water. Source well water is pumped from the Gaspur Zone, "200-ft sand", and "400-ft gravel" zones. The wells are 200 to 400 ft deep. The water passes through a desander where solid materials are removed. The water is then sent to injection pumps and injected into the oil formation. Corrosion

Fig. 6-26. Bench mark elevation and associated net injection for central Long Beach Harbor area, Wilmington Oil Field, 1956 to 1988.


inhibitors and biocides are added for treatment purposes. Source well water now comprises only a small amount of the total injection water. The high sulfate content (1000 to 4000 ppm) limits its use because it enhances conditions for growth of sulfate-reducing bacteria. These bacteria, while reducing inorganic sulfate to sulfide, produce hydrogen sulfide (H2S) gas. Hydrogen sulfide gas is very toxic, causes corrosion problems, reacts with casing, tubing and pipes, and also must be removed before processing and sale of produced gas.

Produced water

The Wilmington Oil Field produces almost 1.2 million barrels of water per day. In order to handle such large volumes of water, adequate water processing facilities had to be constructed. All the produced water is cleaned to meet high standards before being injected into the oil formation. Typically, operators attempt to clean up produced water to meet specifications as follows:

Oil content Suspended solids Sulfides Slope rating Dissolved oxygen SRB (sulfate reducing bacteria) ATP (total bacteria) Corrosion rate

1 mg/1 or less 2 mg/1 or less 0.2 mg/1 or less 800 or higher 10 ppb or less 1-10 colonies/ml or less 75,000 organisms/ml or less 2 mpy or less

Fresh water Small amounts of fresh water are added to make up needed volumes of injection

water. The fresh water has a high oxygen content which must be removed with the use of special facilities. The fresh water passes through a counter-current stripper tower where natural gas, which has an affinity for oxygen, strips the oxygen from the water. The water is then treated with an oxygen scavenger to reduce oxygen content further. Efforts are being made to eliminate the use of fresh water as an injection fluid in the Wilmington Oil Field.

Other water sources

Sea water was considered for injection during the early days of the waterflood. Studies showed that extensive treatment would be required to remove oxygen, biomass, and particulate matter prior to injection.

Reclaimed sewage water has been studied in the laboratory, but has exhibited poor injectivity. Based on these studies, reclaimed sewage water is considered undesirable as injection water for the waterflood.

EFFECTS OF WATER INJECTION

As mentioned earlier, the pilot waterflood demonstrated increased reservoir pressures, cessation of compaction in the injected interval, and additional oil recov-

".v I,,., w.t , - . rW 1." w , . * l , r r ~ m * -"I.,. *.Ir..".nr".L.,

Fig. 6-27. Bench mark elevation and associated net injection for western Long Beach Harbor area, Wilmington Oil Field, 1957 to 1988.

- t

t C 18 c

f.. 4,

II

Fig. 6-28. Bench mark elevation and associated net injection for eastern Long Beach Harbor area, Wilmington Oil Field, 1956 to 1988.


ery. Figure 6-9 shows an approximate history of the early years of the field and the relationships between oil production and water injection and subsidence rate.

Figures 6-26, 6-27 and 6-28 show bench mark and associated net injection for three areas of Wilmington Oil Field. The bench mark curves clearly show the arresting of subsidence in the late 1960's and the close correlation of injection and surface elevation. Noticeable are the changes in elevation after subsidence was stopped. The bench marks fluctuate 0.1 ft to 0.2 ft due to the dynamics of a large waterflood program.

Figure 6-29 demonstrates the subsurface vertical casing lengthening on wells FR-405 and FA-133 as determined by collar count surveys. This lengthening is

Fig. 6-29. Casing joint length differences in wells FRA-405 (left) and FA-133 indicating tension opposite zones of water injection. (From Colazas, 1971.)


interpreted to be a direct result of zone expansion covering the total vertical injection interval. Injection well profiles obtained by various downhole instruments indicate that the fluid entering these zones has excellent vertical distribution. This supports the fact that the total zone is expanding rather than the overburden being lifted by water entry into fracture planes, as is observed in fields where more competent sediments exist.

In general, rebound coincides with expansion of injection programs and creation of high-pressure areas. Due to the rapid response of the various bench marks with injectivity, it is logical to assume that the sands are contributing the greatest amount of expansion rather than the siltstones. It is difficult to conceive of water entering the low-permeability siltstones while pore space in the sands is available.

Laboratory calculations indicate that rebound is not expected to exceed 2 ft, unless some other mechanism besides the elastic component of the reservoir sands is contributing to this rebound. Any problems created by rebound, therefore, will be relatively minor.

REFERENCES AND BIBLIOGRAPHY

Allen, D.R., 1981a. Analysis of horizontal strain measurements 1971-1980, Wilmington oil field. Assoc. Eng. Geol., Bull., 18(3): 333-339.

Allen, D.R., 1981b. Developments in precision casing joint and radioactive bullet measurements for compaction monitoring. Soc. Pet. Eng. of AIME Pap., SPE 9933, pp. 527-530.

Allen, D.R. and Mayuga, M.N., 1969. The mechanics of compaction and rebound, Wilmington oil field, Long Beach, California, U.S.A. Land Subsidence Symposium, Tokyo, IASH-UNESCO-WMO, 2(89): 410-422.

Aoki, S. and Miyabe, N., 1969. Studies on partial compaction of soil layer in reference to land subsidence in Tokyo. Land Subsidence Symposium, Tokyo, IASH-UNESCO-WMO, 2(89): 354-360.

Chilingar, G.V., Rieke, H.H. III and Sawabini, C.T., 1969. Compressibilities of clays and some means of predicting and preventing subsidence. Land Subsidence Symposium, Tokyo, LASH-UNESCO-WMO, 2(89): 337-393.

Clarke, D.D., 1987. The structure of the Wilmington oil field. In: D.D. Clarke and C.P. Henderson (Editors), Guidebook to the Oil Producing Areas in Long Beach. Pacific Section, Am. Assoc. Pet. Geol., pp. 43-55.

Colazas, X.C., 1971. Subsidence, Compaction of Sediments and Effects of Water Injection, Wilmington and Long Beach Offshore Fields. M.S. Thesis, University of Southern California, 203 pp.

Colazas, X.C., 1979. Long-Term Forecast of Compaction, Subsidence and Necessary Subsidence Control Operations, Wilmington Oil Field. Report to the Department of Oil Properties, City of Long Beach, 74 pp.

Converse Foundation Engineering Co., 1957. Report of Tests on Oil Well Cores, Wilmington Oil Field. Report to the Board of Harbor Commissioners, City of Long Beach, 15 pp.

Gabrysch, R.K., 1969. Land surface subsidence in the Houston-Galveston Region, Texas. Land Subsidence Symposium, Tokyo, LASH-UNESCO-WMO, 1(88): 43-54.

Gilluly, J. and Grant, U.S. IV, 1949. Subsidence in the Long Beach area, California. Geol. Soc. Am. BulL, 60: 461-529.

Gilluly, J., Johnson, H.R. and Grant, U.S. IV, 1945. Subsidence of the Long Beach Harbor Area, California. Report to the Board of Harbor Commissioners, City of Long Beach, 152 pp.

Harris, ER., 1945. Report of Subsidence of the Terminal Island-Long Beach Area, California. Report to the Commander of the Long Beach Naval Shipyard, 137 pp.


Henderson, C.P, 1987. Stratigraphy of the Wilmington oil field. In: D.D. Clarke and C.P Henderson (Editors), Guidebook to the Oil Producing Areas in Long Beach. Pacific Section, Am. Assoc. Pet. Geol., pp. 57-68.

Hudson, ES., 1957. Subsidence of Long Beach Harbor Area. Report to the City of Long Beach, 66 pp. Johnson, A.I., Moston, R.O. and Morris, D.A., 1968. Physical and hydrologic properties of water-

bearing deposits in subsiding areas in central California. U.S. Geol. Surv., Prof. Pap., 497-A: 71

PP. Kovak, R.L. and Archambeau, C.B., 1974. Source mechanisms for Wilmington oil field, California,

subsidence earthquakes. Seismol. Soc. Am. Bull., 64, 12 pp. Law, 3., 1950. Interrelations Between Earth Movements. Report to the Board of Harbor Commissioners,

City of Long Beach, 94 pp. Law, J., 1956. Land Subsidence. Report to the Board of Harbor Commissioners, City of Long Beach, 26

PP. Lyons, E.P. and Mecham, O.E., 1968. Design and implementation of directional driUingprograms, THUMS

offshore islands development wells, East Wilmington field. Paper presented to the American Petroleum Institute, Bakersfield, Calif., 801-44M, 28 pp.

Mayuga, M.N., 1970. Geology and development of California's giant N the Wilmington oil field. Bull., Am. Assoc. Pet. GeoL, 64(1): 158-184.

McCord, D.R. and Associates, 1957. Subsidence Control, an Example of the Application of Compaction Mechanics to the Wilmington-Long Beach Area. Report to Richfield Oil Corporation, 87 pp.

Randell, D.H., Reardon, J.B., Hileman, J.A., Matuschlea, T., Liang, G., Khan, A. and Laviolette, J., 1983. The geology of the city of Long Beach, California. Assoc. Eng. Geol. Bull., 20(1): 9-94.

Roberts, D.L., 1953. Shear prevention in the Wilmington field. Paper presented to the American Petroleum Institute, Los Angeles, Calif., 801-29G, 8 pp.

Roberts, J.E., 1969. Land compression as a factor in oil field subsidence. Land Subsidence Symposium, Tokyo, IASH-NESCO-WMO, 2(88).

Teng, T. and Henyey, T.L., 1978. Microearthquake Monitoring in the City of Long Beach Area for the Year 1977. Report to the Department of Oil Properties, City of Long Beach, Calif., 78 pp.

Terzaghi, K. and Peck, R.B., 1968. Soil Mechanics in Engineering Practice. John Wiley and Sons, New York, N.Y., 729 pp.

Tickell, EG., Mechem, O.E. and McMurdy, R.C., 1933. Some studies on the porosity and permeability of rocks. Am. Inst. Min. Metall. Pet. Eng., 103: 250-260.

Truex, J.N., 1972. Fractured shale and basement reservoir, Long Beach Unit, California. Bull., Am. Assoc. Pet. Geol., 56(10): 1931-1938.

van der Knaap, E. and van der Vlis, A.C., 1966. On the Course of Subsidence in Oil-producing Areas. Panel discussion No. 7, Koninklijke/Shell Exploratie en Productie Laboratorium, Rijswijk, 15 pp.

van Wingen, N., 1965. Land Surface Elevation Changes in Salt Lake Field, Los Angeles County, California. Report to Jade Oil and Gas Co., 12 pp.

Wade, J.E., 1966. Techniques for completion, treatment and profile improvement of water injection wells in the Wilmington field. Paper presented to Am. Inst. Min. Metall. Pet. Eng., Dallas, Texas, SPE 1543, 11 pp.

Wilcox, R.E., Harding, T.E and Seeley, D.R., 1973. Basic wrench tectonics. BulL, Am. Assoc. Pet. Geol., 57(1): 74-96.

Yeats, R.S., 1973, Newport-Inglewood fault zone, Los Angeles basin, California. Bull., Am. Assoc. Pet. Geol., 57: 117-135.


Chapter 7

337

SUBSIDENCE IN VENEZUELA

ALBERTO S. F INOL and Z.A. SANCEVIC


Venezuelan oil industry

Venezuela is an important hydrocarbon producer located on the northern coast of South America (Fig. 7-1). From this geographical location on the Caribbean Sea, it has easy access to the northern and southern continents of the Western Hemisphere as well as to the European continent, through the Atlantic Ocean, and also to the Pacific rim countries, through the Panama Canal.

Since its nationalization on January 1st, 1976, the Venezuelan oil industry has been coordinated by Petroleos de Venezuela, S.A. (PDVSA), a holding company wholly owned by the State, that has overall responsibility, through its vertically integrated affiliates, for oil, gas, petrochemical and coal activities. Its three oil- producing affiliates, Corpoven S.A., Lagoven S.A. and Maraven S.A. have important reserves of all types of hydrocarbons in different areas of the country.

Even though Venezuela has significant volumes of light and medium crudes, the bulk of its reserves consist of heavy oil (~ < 20 but > 10) and extra heavy oil

Fig. 7-1. Location of Venezuelan heavy crude oil and bitumen deposits.

338 A. FINOL AND Z.A. SANCEVIC

(~ < 10, viscosity < 10,000 cP) and natural bitumens (~ < 10, viscosity > 10,000 cP). It is in relation to these types of crudes and reservoirs that subsidence in Veffezuela occurs, due to fluid withdrawals. In fact, compaction in heavy, extra heavy and bitumen (H, XH, B) reservoirs is an important oil expulsion mechanism for these types of reservoirs, in addition to other well known driving mechanisms (gas in solution and water drive) and thermal enhanced oil recovery (EOR) processes, principally cyclic steam injection (steam soaking, "huff-and-puff") and continuous steam injection (steam drive, or flooding). Inasmuch as H, XH and B fluids in Venezuela are essentially located in relatively shallow (500-5000 ft) unconsolidated sand reservoirs that undergo compaction, surface subsidence has been observed since the late twenties. To be able to appreciate the importance and magnitude of compaction/subsidence in Venezuela, it is necessary to have some knowledge of H, XH and B reserves and production rates, their geographical distribution, and relative importance when related to other types of crudes (Borregales and Salazar, 1987).

The main H, XH and B hydrocarbon accumulations in Venezuela are indicated on the map shown in Fig. 7-1. The Lake Maracaibo Basin accumulations contain all types of crudes; from the condensates and light oils of Cretaceous and Eocene age to the H and XH oils of Miocene age. In this basin, H and XH crudes are concentrated in two areas: along the eastern shore of Lake Maracaibo, known as the Bolivar Coastal Fields (BCF), and west of Lake Maracaibo, in a huge accumulation known as the Boscan Field. Inasmuch as the Boscan Field is a deep (7000-9000 ft) consolidated sand reservoir, reservoir compaction and subsidence have not been observed there to date. In the Bolivar Coastal Fields (Tfa Juana, Lagunillas and Bachaquero fields), subsidence has been observed, as already mentioned, since the early twenties. It is in these fields that most of the experience and knowledge of compaction/subsidence in Venezuela were acquired and, consequently, most of this chapter on Venezuela will be concentrated on the BCE Maraven and Lagoven are the PDVSA affiliates responsible for the exploitation and administration of the fields bordering the lake shore, which have been the most affected by compaction/ subsidence and, therefore, have had to cope with most of the related problems.

The Eastern Venezuela Basin accumulations also contain the entire gamut of crudes, from light to extra heavy and bitumen. Along the southern edge of the Eastern Venezuela Basin and north of the Orinoco River, lies the huge accumulation known as the Orinoco Belt, which contains H and XH crudes and bitumens quite similar to those found in BCF and other fields of the Eastern Venezuela Basin. The Orinoco Belt also contains some very significant volumes of B crude oil with gravities as low as 4 ~ API. Some of the areas in the northern edge of the Orinoco Belt are being exploited at present, but most of them are as yet undeveloped (Borregales and Salazar, 1987).

Venezuelan heavy, extra heavy and bitumen reserves and production

Venezuela's total remaining reserves of H, XH and B which are producible by primary and cyclic steam technology are 156.1 x 10 9 bbl, which can be increased by

SUBSIDENCE IN VENEZUELA 339

an additional 136.1 x 109 bbl from steam drive, thus resulting in a total of 292.2 billion barrels (292.2 x 109 bbl). An important portion of these reserves, mainly of H and XH crude oils, has been exploited for many years in BCF and Boscan Field using well established technologies and at competitive costs. Of these two areas, BCF, as already mentioned, is the most affected by reservoir compaction and subsidence. In these two areas original reserves of H and XH oils amounted to 33.8 x 109 bbl, of which 19.0 x 109 bbl remain. These reserves include only those producible by primary means (mainly compaction), cyclic steam injection and the steam drive are not currently being operated. These reserves will be increased by further application of steam drive, which has proven to be very successful in the C-3/C-4 and M-6 projects in the Bolivar Coastal Fields at Tfa Juana and the Jobo project in eastern Venezuela, where recoveries in some cases as high as 40% of STOIIP are expected. Inasmuch as most of the H and XH Bolivar Coastal Fields are suitable for this process, the future additional recoveries by steam drive are estimated to be 11.0 x 109 bbl (Borregales and Salazar, 1987).

The huge H and XH crude oil and B accumulations in the Orinoco Belt contain some 1.18 x 1012 bbl of oil. Approximately 10.1% of the Orinoco Belt's STOIIP is producible by already demonstrated primary and cyclic steam technology, yielding recoverable reserves of 135.4 x 109 bbl. Application of already existing steam drive technology to the H and XH oils and B in place in the Orinoco Belt will yield an additional future recovery of 136.1 x 109 bbl (Finol and Farouq Ali, 1974). All of the Orinoco Belt reserves are found in unconsolidated sands and are consequently predisposed for future reservoir compaction and subsidence.

With respect to production, Venezuela has always been an important producer of heavy oil, owing to the BCF, which have also been affected by reservoir compaction and subsidence. The first commercial development took place in 1917 in the H oil Mene Grande field in the Lake Maracaibo Basin, 14 km to the southeast of the Bachaquero Field, the southernmost of the BCE At present, the total productive capacity of the country is 2.6 x 106 BOPD of which 40% (or 1.0 x 106 BOPD) is H and XH oil. Throughout its history, the Venezuelan oil industry has produced some 14.8 x 109 bbl of H and XH oil, mostly by compaction/subsidence, which affected the BCF. Over the past 10 years, the H and XH production rate has averaged about 600,000 BOPD, of which about 250,000 BOPD (or 42%) is contributed by thermal recovery.

Cyclic steam injection at depths of up to about 4000 ft (1220 m) has been practised in Venezuela for over 22 years and has resulted in an accumulated production of over 1.0 x 106 bbl. Two large-scale steamflood projects, the M-6 project in Tia Juana (BCF), which has been in operation since 1977, and the Jobo project in eastern Venezuela, which has been in operation since 1981, jointly contributed 25,000 BOPD to the production of H and XH crudes. As will be seen later, cyclic steam injection as well as steamflood projects cause further compaction and subsidence.

All of the above-mentioned H, XH and B production is lifted, dehydrated, desalted and partially transported by means of heating and/or dilution with lighter hydrocarbons. The technology and equipment developed through experience allow


the thermal recovery processes, as applied to H and XH crudes, to be routine and highly efficient.

Even though the H and XH oils are produced at very competitive costs, research and development are expected to reduce costs even further. Very important ex- pertise has been developed through pilot and commercial productions in the Lake Maracaibo Basin (Bolivar Coastal and Boscan Fields) and in the Orinoco Belt, which have improved efficiency and reduced operating costs. Some of these are: steam injection with additives and injection in deep reservoirs, improvements in dehydration, core and annular flow pipeline transportation and the development of inverted emulsion technology for exploitation of B, H and XH.

All of the above have been mentioned in order to be able to draw attention to the role of H, XH crudes and B in Venezuelan reserves and production potential, and to the importance of reservoir compaction and subsidence, which is intimately related to these types of crudes.

BOLIVAR COASTAL FIELDS (TIA JUANA, LAGUNILLAS, BACHAQUERO)

Geological setting and development h&tory

The first oil field in the area (Mene Grande field) was discovered in 1914. The first really prolific well in what was to become the Bolivar Coastal Fields (BCF) was drilled near a surface seep and completed in 1917, but is was not until five years later when the Shell R-4 well blew out (at an estimated 100,000 BOPD) that the real stimulus was provided for development.

The BCF are located on the eastern margin of Lake Maracaibo and comprise the Tfa Juana, Lagunillas and Bachaquero fields (Fig. 7-2). When the BCF are considered jointly, they form one of the largest oil fields outside of the Middle East and contain H and XH oil with a gravity lower than 20 ~ API. Morphologically, Lake Maracaibo is presently found in an intermontane basin enclosed on three sides by the Andes Mountains or their ramified chains. The area has a complex paleohistory and tectonic movements are still continuing. During Cretaceous the area was part of a platform in a large geosyncline, but by the Eocene it was near a coast where a series of large sandy deltas were deposited, with continental sediments to the south and thick marine shales to the north. At that time, conditions for oil generation in the shales and migrations to the sands were established, but the subsequent Oligocene faulting, uplift, and erosion may have allowed meteoric water to penetrate into reservoirs. During the Miocene and Pliocene, the basin was tilted first west and then south, and filled with continental sediments from the rising Andes. Tilting is still continuing and oil is moving up along the Oligocene unconformity, forming surface seeps. Most oil fields are located in sands above the unconformity or in fault blocks immediately below it.

The BCF are located within the limits of Bolivar District in the State of Zulia, and the name is derived from the district. They extend 55 km, from the northern tip of Tfa Juana to the southern limit of Bachaquero, and are widest in Bachaquero (25


Fig. 7-2. Bolivar Coastal Fields (BCF).

km). Some authors also include in the BCF the Cabimas/La Rosa field and its some 30 km southern extension into the lake (Fig. 7-2) and, therefore, their size definition of BCF is considerably larger than that of the present authors (70 km and 50 km in the widest section; 120,000 ha or 300,000 acres). From the point of view of structural geology and accumulation type, Cabimas/La Rosa could be included in the BCF. On the basis of reservoir typology, exploitation history, production practices, and particularly the occurrence of reservoir compaction and subsidence, however, the Cabimas/La Rosa field is excluded, thus leaving only Tfa Juana, Lagunillas and Bachaquero fields.

Active oil seeps indicated the probable existence of commercial accumulations of oil, and led to drilling that was initiated by the Venezuelan Oil Concessions, Ltd (VOC) of the Royal Dutch-Shell group of companies, with well Sta. Barbara No. 1 (now called R-I) in 1913. The following well, Sta. Barbara No. 2 (now R-2), located to the south of the La Rosa village, found the first commercial production in the area. Although the drilling of this well started in 1913, it was completed in 1917 as a producer from the Oligocene-Miocene sands of Sta. Barbara. Five years later (1922), during the drilling by VOC of the fourth well in the area, Barroso-2 (B-2),


the famous blow-out that produced an estimated 100,000 BOPD of H oil occurred, and this provided the impulse to the large-scale development effort of BDE After the discovery of La Rosa in 1917, additional exploratory drilling discovered the BCF: Lagunillas in 1926, Tia Juana in 1928, and Bachaquero in 1930.

During the initial development phases, drilling was carried out at widely spaced locations, thereby leading to the belief that a series of fields were discovered, resulting in the assignment of different names, such as Ambrosio, La Rosa, Punta Benitez, Cabimas, Tfa Juana, Lagunillas, Pueblo Viejo and Bachaquero. Lately, with sustained development drilling, these have coalesced into the three (excluding Cabimas/La Rosa) forming the BCF: Tfa Juana, Lagunillas and Bachaquero.

The BCF formations of Cretaceous, Paleocene, Eocene, Oligocene and Miocene ages are found above the basement. The Eocene, Oligocene, and Miocene rocks are productive. Eocene rocks are consolidated, low permeability, with minor and spo- radic accumulations, whereas Oligocene-Miocene (post-Eocene) unconsolidated sands are the main source of H and XH production and reserves (Figs. 7-3 and 7-4).

The Guasare Paleocene formation, which conformably overlies the Mito Juan Formation, is a relatively thin unit in BCF (265-480 ft, 81-146 m), and is composed predominantly of gray shales. It is common to find thin sandstone and limestone layers in this formation which, at least in several wells, have been able to produce small quantities of oil.

The Eocene rocks, which comprise the Trujillo, Misoa and E1 Mene formations, are separated from the overlying sediments by an unconformity. This section, whose thickness varies from 8900 to 16500 ft (2713-5039 m) consists of dark shales interstratified with very hard, fine- to coarse-grained sandstones. The thickness of the Eocene sandstones varies from less than 1 m to many hundreds of meters (Fig. 7-3).

The Miocene-Oligocene, post-Eocene section (0-4410 ft or 0-1548 m) is subdivided upwards into the following formations: Icotea, La Rosa, Lagunillas and Isnotfi (La Puerta). The Icotea Formation consists essentially of white sandstones, silts and clays, that can be locally mottled. The La Rosa Formation consists of fossilif- erous, greenish marine shales, intercalated with friable sandstones. The Lagunillas and Isnotfi (La Puerta) formations are composed of mottled clays, alternating with light gray shales and fine- and medium-grained, poorly consolidated or loose and unconsolidated sands.

�9 The Eocene and older formations have been intensely folded and faulted and, over the entire area, were eroded to peneplain before the deposition of Miocene sediments, except in the Pueblo Viejo structure between Lagunillas and Bachaquero, which was active even during Miocene deposition. Structural levels on the top of Eocene rocks are consequently a general representation of the structure of the Miocene sediments, as presently observed. This general structure is a monocline dipping to southwest with local folding in the northeastern and southeastern parts of the BCE

The major faults are to be found in Eocene and older rocks, although some of the faults extend upward and cut the Miocene-Oligocene sediments. An excellent example of this is the large eastern flank fault of the Pueblo Viejo anticline.


Fig. 7-3. BCF geological section.

There are several types of traps in the BCF: (1) asphalt seals in the oil seepage areas; (2) fault and fold traps; (3) lithological variations that form permeability barriers in the producing members; and (4) stratigraphical unconformity traps, caused by erosion of Eocene sandstones and sealing by overlying Oligocene-Miocene shales. Although many trap units have been recognized in the BCF, a southwest- northeast cross-section of the BCF (Fig. 7-4) shows that the Oligocene-Miocene monocline seal, close to the surface or on the surface, is the most important trap of H and XH crudes.

Energy-wise, the main primary driving mechanisms in the BCF are gas in solution, reservoir compaction and water. The gravity of the oil varies between 8 ~ and 22 ~ API

VLA-16 VLA-I LL-637 TJ-265 TJ-49 ROD-517-E LS-610

*onlIO.t41

0 1). 0 0 L " - Fig. 7-4. A northeast-southwest cross-section through the BCF.


for H and XH oil production, and is in the 22-43 ~ API range for minor quantities of medium and light oil (Bockmeulen et al., 1983).

On land, portions of the BCF reservoirs have crude gravities in the range of 8-18 ~ API, at moderate depths of 100-4000 ft, net oil sand (NOS) thicknesses of 50-600 ft, a high porosity of 30-40%, permeability of 1-8 D, initial oil saturation of 80%, and high in situ oil viscosity of 100-10,000 cP. In these portions of the reservoir the wells have been drilled using a 231-m triangular spacing (10 acres/well).

Development of land portions of the Lagunillas field started in 1926, and the first signs of subsidence were observed in this field's land operations in 1929. Development of the onshore Tfa Juana and Bachaquero fields, and the Mene Grande Oil Co. and Creole concessions on the lake started in the mid-thirties and even later, and there subsidence was also observed. However, it was only before and after World War II that considerable surface subsidence above the three BCF reservoirs occurred, as a result of sharp increases in production. It was at that time that it became evident that the three producers: Shell (onshore), Mene Grande (narrow strip along the shore in shallow water), and Creole (on the lake, in deeper water) were developing different production policies as dictated by the different surface conditions. The areas most affected by subsidence were on land (Shell) and on the lake, close to the shoreline (Mene Grande) operations. Creole's operations were in deeper water, less affected by subsidence, and the policy was to maintain the installations (platforms, etc.) above the water level in case more serious subsidence developed in future. Apart from this, oil properties change from the northeast to the southwest, with more viscous, lower-API gravity oils in onshore portions of the reservoirs and less viscous, somewhat lighter, higher-API gravity oils in the deeper lake portions of the reservoirs.

Owing to the fact that the BCF reservoirs were found at relatively moderate depths (1000-4000 ft) and contained H and XH crudes, the low pressures found in the reservoirs require artificial lift (sucker-rod pumping equipment). Unconsoli- dated sands, on the other hand, require the installation of slotted or wire-wrapped liners as completion techniques aimed at preventing sand entry into the wells. Sub- sequently, these techniques were replaced by gravel packing (with liner), which was more effective in controlling sand entry and decreasing the number of liner failures, wells sanding up, and, consequently, reducing the number of workovers and well-repair jobs.

The large area of the BCF and uniform spacing culminated in their division into production blocks containing 36 wells with one gathering station per block. The oil stored in the gathering stations (containing gas-oil separation facilities, with some storage and pumping facilities) was pumped to each field's processing (water separation), storage and shipping terminal. Water separation was achieved originally by wash tanks, chemical and electrical treatment, which was later replaced by chemical treatment and improved wash tanks, such as partitioned concentric wash tank facilities. Construction of a 30-inch heated pipeline along the Bolivar Coast, which transported onshore oil to the Puerto Miranda Terminal located north of Maracaibo, reduced the ship-loading port facilities to only one.


Subsidence

Geomorphologically, before the start of oil operations in the BCF in 1926, the eastern coasts of Lake Maracaibo were typical of lacustrine environments: fiat and swampy (Lagunillas in Spanish means small lagoons or marshes) barely above lake level and composed mostly of sandy-silty soils. These swamps were separated from the lake by a comparatively narrow strip of land slightly higher than the lake water level, so that these strips were flooded during high tides, storms and strong onshore winds. The coastal plains are characterized by savannas with gentle slopes (0-8 m/km), extending from the western foothills of the Ziruma Mountain Range to the coast. The area includes the deltas of the Tamare, Pueble Viejo, Machango and Misoa rivers. Shallow gutters connecting the swamps and the lake afforded drainage of flood waters during the rainy season from the shore to the lake and, during the dry season, from the lake into the swamps.

The area is characterized by a rainy season lasting from May to November. Annual precipitation ranges between 750 mm and 1000 mm. Rainstorms tend to be short (less than 6 hours) and very intense: 75% of the rain falls in the first hour (100 mm/h is typical for a rain with a 10-year return period).

The drainage in the area was achieved primarily through the Ule, Tamare, Pueblo Viejo and Machango rivers, which provided the natural discharge channels into the lake.

Venezuelan Oil Concessions (VOC), Ltd., a subsidiary of Royal Dutch Shell, was the concessionaire of the onshore area. This company was renamed Compafifa Shell de Venezuela in 1953 and in 1976 became Maraven S.A., as a result of the nationalization of the oil industry.

VOC established their base of operations near Lagunillas, a small fishing village built in the lake on stilts, very close to the coast. Because of the region's topography, a small earthen dike, a few meters wide, less than 1 meter high and several hundred meters long was built by hand to protect the installations and dwellings from lake waves, which, given the lake's physiographic and hydrographic characteristics, seldom attain heights greater than 1.5 m.

For a number of years oil field operations were concentrated on the onshore coastal strip of land of the Tia Juana, Lagunillas and Bachaquero fields (BCF), so that additional small earthen dikes were built by hand labor along the shore, often using foreshore vegetation as breakwaters. During this early period, subsidence was not yet apparent, but in 1929 the Lagunillas dike was breached and the resulting flooding of the camp area drew attention to this phenomena. For the first time, this led to the suspicion of the occurrence of ground subsidence because the foreshore became permanently submerged and the vegetation started to disappear, leaving the earthen dike exposed to wave action. Once observed, it was hoped that the subsidence phenomenon would not persist and an attempt was made to protect the earthen dike against wave erosion by use of various improvised materials to resist waterbreaks, such as junk (old tank plates, corrugated iron sheets, etc.), building palisades, clay facing, grooved wooden sheet piling with pine boards, facing with gravel and bitumen, etc. All of these types of protection, obviously, failed and it


was soon realized that the improvised structures had to be replaced by a more permanent structure, particularly over those parts of the shore where most of the subsidence occurred. Consequently, a concrete protection of the dike and a drainage system was built to protect the area from flooding.

Almost from the start of the subsidence, it also became necessary to construct inner dikes and a drainage system to dispose of the run-off by pumping it into the lake. A system of bench marks was installed in 1939 and precise levels were taken at periodic intervals to check further ground subsidence (Fig. 7-9).

As new oil was discovered, both north and south of Lagunillas, the oil companies extended their operations and established new oilfields. Tia Juana to the north and Bachaquero to the south also had to be protected by means of the construction of polders similar to the one in Lagunillas. The Mene Grande Oil Company, exploiting their concessions in the lake on a narrow strip along the coast and the Standard Oil (Creole), with their activities in deeper lake waters, had their bases of operation on the Bolivar Coast, either in Lagunillas or in T/a Juana. Both companies also began to protect their installations from the lake waters by means of small hand-built earth dams.

Given the experience of the Dutch in coastal engineering and land reclamation, the VOC was asked in 1937 by Mene Grande and the Standard to undertake the design and carry out the construction of properly engineered earth dikes.

Initially, these dikes were built along the coast as "simple" elevated roads behind a sheetpiled construction. The continued subsidence made it necessary to uplift and widen the dikes continually. With time, the initial simple elevated roads became fully developed earth dams. Figure 7-5 shows the development of a typical dike cross-section.

On the basis of present subsidence predictions (Figs. 7-6 and 7-9), it is expected that the Tia Juana and Bachaquero dikes will have to be raised only an additional 1.0-1.5 m, whereas the Lagunillas dike may have to be raised as much as 4.0 m, because additional subsidence is expected, due to the exploitation of two superposed reservoirs, Laguna and Lower Lagunillas (Figs. 7-7 and 7-10).

As construction proceeded, the coastal protection system gradually took shape and proper "polders" were produced in the T/a Juana, Lagunillas and Bachaquero/ Pueblo Viejo consisting of: (1) a coastal dike to protect the subsided area from lake water flooding; (2) inner diversion dikes to prevent run-off from the area outside moving into the subsided polder area; (3) drainage channels to convey the water to the pumping stations constructed along the coast; and (4) pumping stations to dispose of the water over the dike and into the lake.

Table 7-I gives the characteristics of the Costa Oriental polders in 1989.

Compaction mechanism

Once subsidence was observed in the BCF, there was no doubt that oil production was the cause of it. It was not clear, however, how it occurred. Initially it was ascribed to the compaction of soft clay layers in and adjoining the producing sand layers. Analyses in the late fifties showed that this concept led to discrepancies between


Fig. 7-5. Progressive raising of the dike.

the calculated and observed subsidence. Four wells were then continuously cored to obtain precise information on the distribution of sand and clay in the producing intervals and to carry out compression experiments on representative sand samples, in order to establish the contribution of the two lithologies to compaction (Nfifiez and Escojido, 1976).

Laboratory research work was conducted for Compafiia Shell de Venezuela CSV by Koninklijke/Shell Exploratie en Produktie Laboratorium (KSEPL) in Rijswijk, The Netherlands, during the sixties and seventies in order to explain compaction mechanisms. The first series of compression experiments on clays and sands recovered with rubber sleeve coring equipments were carried out and the results published by van der Knaap and van der Vlis in 1967. These results revealed that


Fig. 7-6. Subsidence history and prediction along the Bachaquero dike.

Fig. 7-7. Subsidence history along the Lagunillas dike.

under the conditions prevailing in the BCF reservoirs, the final compressibility of the two materials is of the same order of magnitude. "This means that the total reduction in thickness of an interval from which fluids have been produced is insensitive to the ratio in which sand and clay layers occur. This is only partially correct, because upon fluid withdrawal, the pressure in the permeable sand drops more rapidly than that in the almost impermeable clay. This results in a delayed compaction of the clay

3 5 0 A. FINOL AND Z.A. SANCEVIC

Fig. 7-8. Main levelling network and subsidence contours, 1986.


-1

. . - 2

lad O

Z - - 3 I.d

m

0") -.-

-5

19 20 19 40 19 60 19 80 YEAR

Fig. 7-9. Cumulative subsidence of bench mark (BM) AB (see Fig. 7-8).

TABLE 7-I

The characteristics of the Costa Oriental polders as of 1989

Oilfield Polder Coastal Inner Main drainage Pumping stations area dikes dikes channels

Stations Pumps Rate (m3/h) (km 2) (km) (km) (km)

Lagunillas 93.5 20.0 27.9 125.7 18 53 163,970 T~a Juana 26.3 8.5 18.5 14.9 6 22 97,920 Bachaquero 64.3 14.1 30.6 102.8 3 9 40,500 Pueblo Viejo 9.2 5.7 8.3 14.0 2 5 18,450

Totals 193.3 48.3 85.3 257.4 29 89 320,840

layers. The effect is naturally more marked when the clay layers are thick." (van der Knaap and van der Vlis, 1967).

"With the compaction of the clay layers, water is pressed into the oil-bearing sands, thus creating a weak water drive. An estimate of the water production to be expected in compacting oil reservoirs should, therefore, include a subsurface study of the total clay thickness and its distribution. The cores obtained from the wells were also examined for clay-mineral and granular composition. Differences in clay composition were found to be small. The clay is mostly of the illite/kaolinite type. The sands are angular and fine to medium fine. Despite the large distance separating the cored wells, no significant differences in clay mineral composition or angularity and size of the sand grains were observed. This implies that a uniform compaction behavior over the area may be expected." (van der Knaap and van der Vlis, 1967).

0

-1

taJ o_

A. FINOL AND Z.A. SANCEVIC 352

1920 1940 1960 1980 YEAR

Fig. 7-10. Cumulative subsidence of BM 215 B (see Fig. 7-8).

Compaction of porous, unconsolidated reservoir sands and clays is produced by an increase in the effective pressure, as a result of the net load on the rock matrix, and is defined as the overburden pressure minus the fluid pressure in the pores. Reservoir loading and compaction occurs as a consequence of a decrease in the reservoir pressure while the overburden remains constant. "Reservoir fluid pressure has to drop in some cases below a definite value or threshold value before compaction and hence subsidence occurs" (Nfifiez and Escojido, 1976). In a paper published by Merle et al. in 1975, the above explanation was obtained for the Bachaquero field, the southernmost of the BCF. The compaction characteristics of Bachaquero, evident from plots of compaction (as a percentage of the initial gross reservoir thickness) against pressure drops derived from field data, are shown in Fig. 7-11 for four Bachaquero blocks (delimited at the surface) at different depths. From this figure it is evident that negligible compaction occurs until a certain effective pressure has been exceeded, and that the value of this threshold pressure increases with reservoir depth, and that formation compressibility, as shown by the slope of the compaction curves in the figure, decreases at greater depths (Nfifiez and Escojido, 1976).

Observation of loading/unloading/reloading experiments on BCF sand samples showed that compaction behavior of the Bachaquero reservoir is probably related to the reservoir's subjection to higher effective pressures (larger load) during its geological history than the one that existed at the start of production. The compaction history interpreted for a particular part of the reservoir since its deposition is shown in Fig. 7-12. After deposition, the additional burial loaded the reservoir with sediments until a maximum depth had been reached. This was followed by the reservoirs' unloading, due to uplift and the erosion of overlying sediments,


d 6

o sbo ~doo

soo io'oo

c(%) H

M6

| 0

P6

500 1000

R 6

3

1 5 0 0

3

1 5 0 0

3

1500

2400'

3010'

3860'

500 10'00 15

AP (PSI)

2

4360' 1

Fig. 7-11. Compaction behavior of four reservoir blocks at different depths.

or owing to overpressuring of the reservoir fluid, or to both. During the aforementioned unloading, minimum expansion of the formation occurred because loose sand compaction is almost irreversible. When a decrease in the reservoir fluid pressure occurs, as a consequence of oil withdrawal, it results in reloading of the reservoir. Initially, compaction is relatively small, until the previous maximum load (threshold) is surpassed by at least a few hundred psi, and then the original compaction curve is followed again (Fig. 7-12).

Despite all the problems caused by compaction/subsidence, particularly on the surface: dike building, drainage of polders etc., it is necessary to bear in mind that compaction is a very effective reservoir oil recovery mechanism in the BCE In the


COMPACTION

COMPACTION DUE TO PRODUCT~

pRSTuA~TI 0

~NLOADING/'q''' Pth = THRESHOLD

L

~ DEPOSITION EFFECTIVE PRESSURE

Fig. 7-12. Compaction history of a reservoir block (schematic).

Merle et al. (1975) paper on the Bachaquero reservoir, the relative contribution of driving mechanisms is shown historically up to 1975 (Fig. 7-13) for the land and lake portions of the reservoirs. It is particularly evident that the contribution of compaction to oil expulsion and oil recovery is very high, in fact crucial, in the land portion of Bachaquero, when compared with two other sources of driving mechanisms: gas in solution and water drive. On the other hand, the predominant driving mechanism in the lake portion of the reservoir is gas in solution, with only minor contribution from compaction. In Fig. 7-14 the relative contributions of the driving mechanisms are indicated aerially. The importance of the compaction drive mechanism is again seen to be predominant in the greater portion of the field.

It is obvious from this that companies on land and on the lake portion of the Bachaquero reservoir applied different production techniques, as already mentioned. Standard's Creole and its successor, Lagoven, was promoting and estab- lishing water and gas injection in order to counteract the compaction mechanism, thereby keeping their wells and other installations' platforms above water level, and supplementing weak natural drive with water injection (started in 1967). In contrast, the successor of Shell on the greater, on-land portion of the reservoir was taking full advantage of the predominant compaction mechanism and, with the advent of enhanced thermal oil recovery (cyclic steam injection), has extensively introduced it in Bachaquero, as it had previously in the Tfa Juana and Lagunillas fields. Later, a large, successful continuous steam injection project (M-6) was also initiated in the East Tfa Juana field.


Fig. 7-13. Reservoir volumes of free gas, compaction, and invaded water (percent of initial pore volume).

The cyclic steam injection process (steam soaking and huff-and-puff) was, in fact, developed in the late fifties in the Mene Grande field to the south of Bachaquero. Steam injection was responsible for the rejuvenation of the onshore BCF and for substantial increases of their recoveries. However, steam injection, on the one hand, is taking advantage of decreased pressures in the compacted area and, at the same time, is contributing to additional compaction and subsidence. It has been estimated that primary recoveries in the onshore portion of the BCF reservoirs, due to compaction/ gas in solution, could reach 25% of STOIIP and, with cyclic steam injection and steam flooding recoveries, are expected to reach figures as high as 40% of STOIIP.


Fig. 7-14. Relative contribution of drive mechanisms by block (March, 1970).

Water injection, however, has to be limited to the less viscous portions of the reservoirs where mobility ratios (M) of displacing and displaced fluid are not extremely adverse. High viscosity, low gravity H and XH crude recoveries (as on the land portions of the BCF) are negatively affected by water injection and, obviously, even more so by injection of high mobility gas, contributing in fact to the losses of the reserves. "In studies of the overall field performance of the Bolivar Coast land portions of the reservoirs it has been found that during the more recent production history incremental subsurface volumes of produced oil, gas, and water approximately equals incremental surface subsidence volumes. From these observations it may be concluded that, following the initial production period when there was an active solution gas drive [see our Fig. 7-13], formation compaction becomes the main production mechanism. By the end of 1975, compaction drive accounted for some 60% to 80% of total oil produced." (Nfifiez and Escojido, 1976). With the introduction of steam injection, compaction drive tends to be higher, i.e., 80% contribution. "Summarizing, it has been found that for strongly subsiding oil fields, a straight-line relationship exists between subsidence and reservoir withdrawal after an initial period of low subsidence when the principal producing mechanism was solution gas drive". (Nfifiez and Escojido, 1976) (Fig. 7-15)

S U B S I D E N C E IN V E N E Z U E L A 357

o I--

0

Z

U.I

Z

t21

if) r

U.I >

I--- _.1

.

p. .

o ~ 0

00

S O L U T I O N C O M P A C T I O N G A S .,~-- ..--~ D R I V E I ' - A '

D R I V E

~ " t t

z( j -

I I

/ ._.el , / f

r,... u3 to to o') o~ o'1 o'}

I i i i i t i t i I

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4.0 8.0 12.0 160 20.0 24.0 28.0 32.0

CUM. O I L -I- W A T E R - S T E A M IN 0 / 0 S T O I I P Fig. 7-15. The relationship between subsidence and reservoir withdrawals.

Subsidence records and monitoring

As previously mentioned, commercial exploitation began in the Lagunillas field in 1926, and in 1927 a swamp survey was conducted for preliminary drainage studies in the area by the Topographical Department of VOC (Trutmann, 1949). Later on, in 1929 the observation of permanent flooding in the production areas raised the suspicion of subsidence in the field, which according to Trutmann (1949) was confirmed by a check on the swamp level survey of 1927, showing subsidence values of the order of 42 cm. This led to the immediate implementation of a preliminary monitoring scheme. The original network consisted basically of a levelling line parallel to the lake shore and connected at both ends to supposedly stable land, located well outside of the production areas. Levelling surveys were then conducted at three-monthly intervals to determine the rate and extension of the subsidence quickly. In 1931, the monitoring network was extended and a tide gauge observation was installed.

By 1934, a yearly rate of about 20 cm was determined and the interval between the surveys was increased to 1 year, complemented by spot checks on the nearshore bench marks by means of tide gauge observations at two-monthly intervals (Trutmann, 1949). The configuration of the monitoring networks in 1934 closely


followed the existing road infrastructure. Subsidence studies were also conducted in this area in combination with a drainage study between 1927 and 1928. Further observations in 1930 showed a rather insignificant subsidence rate of 5 cm over two years, which, for practical purposes, postponed subsidence investigations in Mene Grande.

The Cabimas field, where early exploitation also took place, was also included in the subsidence investigations. Between 1932 and 1933, a few benchmarks were established on land as well as offshore using well platforms. These studies indicated the presence of subsidence in this field.

As exploitation continued to expand into neighbouring areas, expansion of the surveys became necessary both on land and offshore. Monitoring began in the Tia Juana and Bachaquero fields in the years 1937 and 1938, respectively.

Between 1934 and 1942 monitoring was generally carried out annually. After 1942, the surveys were made at two-yearly intervals. Offshore subsidence monitoring probably started in the mid-thirties and was originally performed by the Creole Company.

In 1942, the entire monitoring scheme was redefined, because according to Trutmann (1949), the VOC Company took over the Creole and responsibility for the offshore subsidence monitoring surveys. Figure 7-16 shows the whole monitoring network in the major subsidence fields of Tfa Juana, Lagunillas and Bachaquero as of 1942. The drawing also includes the offshore wells used in the subsidence studies in the lake.

Fig. 7-16. The main levelling network in 1942.


Offshore subsidence has always been monitored by means of water level transfers of elevations to well platforms, using temporarily installed tide gauges (Leal, 1987). As time elapsed, and with the development of the subsidence deflections above the areas of major exploitation in Tia Juana, Lagunillas, and Bachaquero fields, the requirements of reservoir and construction engineers led to further expansion and denser monitoring network. In 1962, the connections to stable areas (i.e., baselines) in the Lagunillas field were extended and included the construction of deep bench marks to a depth of 300 m. This aimed at minimizing the influence of local movements on the reference, stable bench marks. Extensions were added to the baselines of Tfa Juana and Bachaquero fields in 1966, including the monumenting of deep bench marks.

Further densification has also taken place since then. At present, a main monitoring network, covering the Tia Juana, Lagunillas and Bachaquero fields, and two smaller subnetworks, connected to the main network and located in the Cabimas and Mene Grande fields, exist.

The main levelling network, together with the cumulative subsidence up to 1986 in the main subsidence fields, is shown in Fig. 7-8. It covers a geographical area of about 1296 km 2 and consists of 618.9 km of U.S. first-order class II levelling lines, of which 167.3 km are used for connection to the assumed stable area. Within the network itself, there exists an array of U.S. second-order class II levelling lines for densification purposes. The total length of the second-order levelling lines is 553.7 km. The two subnetworks in Cabimas and Mene Grande fields also consist of first- and second-order lines: in total, 160 km of first-order lines, 68.9 km of which connect both subnetworks to the main network. In summary, the whole scheme consists of 1469 km of levelling line and 1624 bench marks, two types of which should be distinguished: the aforementioned deep bench marks are located mainly along the connections to the stable areas, and shallow bench marks used for densification purposes and connections to the subnetworks. The shallow bench marks are cast in concrete, inside steel pipes, to a depth of approximately 1.7 m. The average spacing between the bench marks in the network is approximately 400 m.

At present, the offshore subsidence is monitored through an array of 306 well platforms distributed around the main subsidence fields. The subsidence monitoring surveys are still conducted at two-year intervals. The elevation for each bench mark has been originally referred to the Mean Lake Water Level (MLWL), estimated through a least squares static adjustment. The subsidence values are computed by direct subtraction from the elevations of the previous survey. This historic record, kept since the very beginning, consist basically of the bench mark elevation, relative subsidence between the two most recent surveys, and the cumulative subsidence since the beginning of the exploitation of each field. This information has been represented graphically in the form of isoline maps showing the cumulative and the biannual subsidence. The terrain topography is also represented graphically in the form of contour maps, using the estimated bench mark elevations after each survey. All of this was originally drawn manually, but has been replaced by computer-generated maps.

The maximum subsidence rate still remains about 20 cm per year in the area of


Fig. 7-17. The redesigned monitoring network levelling, including global positioning satellite (GPS) points.

E1 Polvorin, Lagunillas, near bench mark 215B (Fig. 7-8). The maximum cumulative subsidence up to March, 1988, had reached 5.013 m and the lowest elevation below the MLWL as of the same date was -6.455 m. In the Tia Juana and Bachaquero areas the subsidence had reached maximum values of -4.462 m and -4.470 m, with maximum rates of the order of 8 and 7 cm/year, respectively. The Cabimas and Mene Grande fields remain practically stable, with rates below 5 cm/year.

A subsidence history of sixty years is available for the Costa Bolivar, which is a significant treasure from a scientific point of view and is probably one of the few cases in the world. Since 1984, consultants from the University of New Brunswick, Canada, have been involved in the subsidence study to modernize and economize the present monitoring scheme. Major improvements have been sought by a re- design of the present network in an effort to combine traditional levelling with a


differential satellite system being implemented by the U.S. Department of Defense (DOD). Several tests have already been conducted, but the results indicate basically that the present geometry of the prototype satellites which are in orbit does not allow for a baseline accuracy compatible with the accuracy attained by the levelling methods. It is expected, however, that as the final satellite constellation becomes available, the expected accuracies will be achieved, and the combination of GPS and levelling will be feasible. The redesigned network is shown in Fig. 7-17. As one can see, the main levelling network will be practically replaced by the GPS baselines. The rest of the levelling lines will be treated as densification lines throughout the whole network. The computational scheme includes a model that allows the combination of GPS with levelling in a geodynamic adjustment. The first survey of this network was scheduled for March, 1990. For more details on the computational methodology the reader is referred to Leal (1989).

Precision measurements

Highly accurate surveys are being performed on selected sections of the coastal dikes to monitor expected strain accumulation due to subsidence. A pilot project in the Tia Juana coastal dike was initiated in 1984, together with the University of New Brunswick, using modern instrumentation and conventional surveying methods. Relative design accuracies of 2.1 ppm have proved sufficient to measure strain rates smaller than the 1.2 • 10-5/year expected from subsidence. The measured strains compare favorably with the results of an analytical study carried out for Maraven by a consultant. Dike sections in Bachaquero and Lagunillas fields have been monumented and are being monitored using the same methodology. No additional results were available at the time this chapter was written.

Design and construction of coastal dikes

The gradual nature of subsidence, together with the possibility of predicting future subsidence, has allowed for staged construction of the coastal dikes, as shown in Fig. 7-5.

The characteristics of the coastal dikes have been influenced not only by subsidence but also by geotechnical, hydrographic, seismicity and seismic geology aspects, as well as by the appearance of surface cracking in areas located several hundred meters away from the coastal dikes.

Geotechnical aspects The Delft Soil Mechanics Laboratory has studied the stability of the dikes based

on soil investigations. The results showed that, for a dike with a height of 8-10 m on a subsoil of silty sand, an outer (lake) slope is required not steeper than 1:2.5, and an inner (land) slope not steeper than 1:3. For lower dikes on the same subsoil, a somewhat steeper inner slope could be accepted. The outer slope of low dikes, however, should not be increased. For the stability of the outer slope, a shallow sliding plane is critical, whereas for the stability of the inner slope a


deep one is detrimental. On a subsoil of sandy silt, the inner slope of a dike with a height of 8-10 m requires an even gentler slope; however, for lower dikes in general a slope of 1:3 is still acceptable. The gradients of 1:2.5 and 1 : 3 mentioned above are only permissible if the material of the dike body has a shear strength at least corresponding to an angle of internal friction of 25 ~ and a cohesion of 2.2 kg/cm 2, with good drainage near the inner toe. Three types of soils are used in the construction of the dikes. The permeability of these soils is increased from the outer slope toward the inner slope.

Hydrographic aspects The height of the dike is determined by the water level and wave run-up, all in

accordance with the expected subsidence. It is known that waves generated by wind are irregular in height and length. During wave attack, some waves reach the crest and some do not; as a criterion for the height of the dike it has been assumed that no more than 2% of the waves during a storm should reach the crest. The Delft Hydraulic Laboratory and Universidad del Zulia, Maracaibo, carried out studies and model tests in 1965 and 1967, respectively, with water depths of 2.8 m or more and a dike with a smooth slope and a gradient of 1:3. The conclusion was that a dike height of at least 3.75 m above the measured low lake level (MLLL) was necessary. This height could be reduced to 1.8 m by the construction of a layer of rip-rap 1.25 m thick. For water depths of less than 2.8 m, the waves are lower and, consequently, the wave run-up is reduced so a lower dike would suffice: nevertheless a minimum dike height of 1.8 m above the MLLL is generally required.

In 1982, it was decided to raise the 1.8 m minimum freeboard to 2.30 m to account for tidal variations (• cm) and the possibility of lake body oscillations (+20 cm) in the east-west direction.

The revetment of the outer slope generally consists of a layer of stones, each weighing between 10 and 120 kg, the lowest 20 cm of the layer should be penetrated with asphalt mastic. To apply the asphalt mastic, as well as to prevent a viscous flow after application, the slope should not be steeper than 1:3. On this revetment, a layer of rip-rap is dumped with a thickness of 1.25 m on the slope and of 1.0 m on the berm, when it exists. The weight of the stones forming the rip-rap on the slope of 1:2.5 to 1:3 should be between 300 and 800 kg, with an average of 500 kg. The inner slope is protected with a grass lining (corocillo).

Seismicity and seismic geology aspects The fields under consideration are located in a seismic area of low to moderate

intensity, corresponding to zone 2 of the 5 zones into which Venezuela is divided for seismic design purposes.

Seismic geology and seismicity studies were carried out from 1985 to 1988 by INTEVEE the research and development company of Petroleos de Venezuela, together with FUNVISIS, the Venezuelan foundation for seismic research, and Woodward Clyde Consultants, retained by MARAVEN.

These studies indicated a moderate seismic risk, mainly due to the possibility of liquefaction of a fairly loose, saturated, silty sand layer in the foundation soils.


Fig. 7-18. Mitigative measures, coastal dikes.

Mitigative measures, consisting basically of downstream berms, with or without soil improvement, and, in some sections, an upstream artificial beach, will be implemented in about 25 km of the 47 km of coastal dikes (Fig. 7-18).

Work on the three polders was started in 1988 and it is estimated that it will be completed by 1995. The implementation of the mitigative measures will bring the return period of the design earthquake to about 3000 years, a period typically used worldwide for the design of earth dams in seismic areas.

Surface cracking Under the influence of compaction of the oil reservoirs, deformations of the

ground surface occur. This is certainly the case at the edges of the oil fields, where the curvature of the surface is greatest. In the Tia Juana area cracking of the dry soil crust at the surface has been occurring since 1970. In Figs. 7-7 and 7-9, the location of major ground surface deformations can be inferred.

From very rough calculations, the horizontal strain in the strongly deformed zones appears to be approximately 0.15-0.20 m over a distance of 100 m, which agrees well with the observed crack pattern. It is not unlikely that the cracking phenomenon will also occur in areas where accelerated oil production is introduced. The subsidence will increase locally, resulting in relatively large strain in the soil at the edge of such a block. A study of the conditions under which tensile strains in the soil can develop into cracks was made. Approximate calculations have shown that the occurrence of soil cracking is not likely if the capillary zone is less than 3 m thick.


If the surcharge on the ground surface exceeds a value of 5 kN/m 2, soil cracking is counteracted by a collapse of the soil structure under the prevailing stress conditions, i.e., high vertical stresses, and low horizontal stresses. In general, these conditions are fulfilled in and under the dike's body. It is very likely, therefore, that soil cracking of the nature found in the higher ground around the Tia Juana oil field will occur in the dike and its foundation. Nevertheless, all the effects of large differential settlement in and close to the dike in the deep parts of the polders cannot be estimated with sufficient certainly.

Seismicity, seismic geology aspects, surface cracking and well controls in the neighbourhood of dikes require extensive studies of mitigative measures, contin- gency planning and a sustained level of future activities in line with production forecasts and compaction/subsidence predictions.

Drainage system

For the drainage of the polders in the BCF, small pumps with a capacity of 1350 m3/h each were installed in 1939, with sufficient capacity to handle the run-off water of a 3-inch rainfall in 24 hours.

At present, the drainage system in BCF polders consists of 22 drainage stations with a total of 55 pumps. The drainage capacity is 104,445 m3/h and the total length of the ditches is 345 km. All the drainage stations are located near the coast and the water is pumped to the lake through steel piping.

During primary depletion of the BCF, the subsidence advance has been relatively uniformly distributed over the area affected, so that the drainage/ditches system in the polders was relatively easy to maintain. Subsequent to the application of cyclic steam injection, however, some impairment of the uniformity of surface subsidence was observed, as a consequence of a major or lesser unequal areal distribution of the steam injection and crude oil production. As a consequence of such nonuniform subsidence in certain areas, drainage system slopes have been negatively affected, requiring readaptation of the channels and ditches. This, in turn, also required major attention to the prediction of subsidence and the simulation of compacting reservoirs.

Drainage Master Plan

In recognition of the drainage problem affecting the area and of its dynamic character as a result of the subsidence, the petroleum industry in Venezuela, through its affiliate Maraven, in 1986 prepared a Drainage Master Plan for a 50-year planning scenario, with the intermediate scenario of 25 years. The work was carried out by Maraven with Venezuelan and Dutch consultants.

For the preparation of this Drainage Master Plan it was necessary to establish design conditions based not only on the considerations intrinsic to the drainage plant, but also on the existence of that special characteristic subsidence. The conditions established for the influence of subsidence in a drainage play, in summary, were the following:


(1) Adaptation of the drainage system to the present and future conditions of relief (up to the year 2005), thereby achieving a better integration with its changing nature. In addition, the viability of the plan was revised for the situation expected in 2030, as far as topography was concerned.

(2) Maximum independence of the drainage of the areas under study, the size of the drainage area, the progress of the subsidence over time, and the uncertainty implicit in its predictions. The year 2005 was selected as the design horizon (medium term) and the year 2030 as the revision horizon (long term).

The main purpose of the study was to establish a drainage system that can be adapted to the changes in relief expected to occur up to the year 2005 and which, in accordance with the progress of the subsidence, could continue operating up to the year 2030. The long-term functionality of the drainage system was evaluated with regard to the inherent variation of the oil production scenarios for the period and, consequently, their effect on the resulting subsidence. It is important to adapt the solutions to the real evolution of the subsidence after 2005, taking into account not only the experience obtained up to then, but also the more precise subsidence predictions made on the basis of improved simulation models, which will make it possible to define the future relief more accurately.

The drainage solution for the Costa Oriental (BCF) includes, in its first stage, the Drainage Master Plan. The purpose of this is to provide a tool for the development of drainage projects in the area. These projects will be carried out in accordance with general guidelines which take into account all the factors affecting the situation of the area. The Drainage Master Plan was divided into two phases: phase 1 is a diagnostic study to evaluate the existing drainage problems in general terms, with special emphasis on its effect in oil installations; phase 2 consists of the proposed solutions for the drainage problems in specific areas. The Master Plan is based on the planning scenarios indicated above and on the hydrological and land use conditions prevailing in each area. It also includes a preliminary cost estimate and a series of recommendations for the management and monitoring of the drainage system.

To date, several specific projects are being developed in the oil fields of Tfa Juana, Lagunillas and Bachaquero.

Prediction of subsidence and compacting reservoir simulation

Since World War II, material balance runs for the BCF reservoirs have indicated, as already mentioned, that formation compaction contributes significantly to oil production. The material balance equations have also been used to predict the recovery from a compacting field for a pressure drop and the ultimate compaction at abandonment pressure. Results of such calculations show that for complete natural depletion, compaction ranges of 7-13% of NOS may be expected, leading to natural depletion recoveries of 15-25% of STOIIE In order to check the contribution made by compaction to oil recovery, the use of radioactive bullets in conjunction with ground level measurements and material balance analysis have been investigated. Over the 1956-1964 period, nine wells in the BCF were shot with radioactive


bullets. The purpose was to provide markers for the observation of changes in subsurface thickness resulting from compaction. Bullets in the overburden were spaced approximately 100 ft apart and bullets over the productive interval at 10 ft intervals. Subsequent measurements of the bullet depth yielded information on changes in reservoir and overburden thickness. On each measurement the following was recorded: a gamma ray curve, a casing collar log, the cable magnetic marks, time marks every 4 seconds and cable tension increments. In general, results show compaction over the productive sand intervals, whereas the clays appear to have expanded. This apparent lengthening may be attributed to the presence of a systematic error, possibly in the cable marking process. The value obtained for the compaction of the reservoir after recovering the assumed systematic error is close to surface subsidence measured by the movement of the wellhead. The accuracy of the radioactive bullet surveys, however, did not prove to be completely satisfactory (Nfifiez and Escojido, 1976).

The prediction of future subsidence has been achieved through extrapolation of the volumetric subsidence/cumulative gross production trends for individual production blocks, in conjunction with production forecasts in line with Maraven's long-term estimates of future activities.

The migration pattern existing between production blocks can be studied by comparing the field trend with the individual production block trends. If no migration occurs, both trends are the same; efflux (migration >0) from the block causes the block trend to be higher, whereas trends for blocks with a cumulative influx (migration >0) will be lower than the field trend.

Results of the subsidence prediction at the bench marks along the dike in the Lagunillas field for 1976 were compared with measured values. The difference did not exceed 1.3 cm (Table 7-11) (Ntlfiez and Escojido, 1976). Very little had been accomplished by that time, however, in relating the compaction of the underground reservoir with the subsidence occurring at the surface. Among the few

TABLE 7-II

Estimated and measured subsidence (1976) of bench marks along the dike of the Lagunillas Field

Bench Estimated Measured Difference mark (cm) (cm) (cm)

AA 393.6 394.9 -1 .3 D 376.0 377.2 -1 .2 T 36.5 35.3 1.2 U 32.6 31.4 1.2

10 246.0 246.6 0.0 12 216.0 216.6 -0 .6 18 88.2 88.1 0.1 81 366.8 367.2 -0 .4 87 320.0 320.6 -0 .6

126 39.0 38.7 0.3


studies conducted on this problem, the most realistic are those that consider subsidence above a disk-shaped reservoir, in which a uniform pressure reduction has occurred (Geertsma, 1973). These studies do not simulate the fluid production behavior of the compacting reservoir as such. This is considered to be known and is used to determine the compaction of the reservoir and the accompanying subsidence.

Starting in 1971, doctorate candidates from Venezuela started introducing compaction/subsidence aspects into the simulation of H and XH oil reservoirs, having in mind the BCF. Finol and Farouq Ali presented the first results of this effort in 1974.

A two-phase, two-dimensional black oil simulator was developed for simulating reservoir production behavior with simultaneously occurring reservoir formation compaction and ground subsidence at the surface.

The flow equations were solved by both alternating direction implicit procedure and strongly implicit procedure. Reservoir compaction was described on the basis of the experimental data reported. The magnitude of areal subsidence at the surface was calculated using reservoir compaction, and the theory of poroelasticity.

Computer runs were used to generate a variety of data, such as reservoir pressure variation with oil production, for different reservoir compaction coefficients. It was found that the average reservoir pressure increased with the compaction coefficient for a given cumulative oil production.

The model was used for generating the reservoir formation profiles, as well as the ground subsidence bowls for a variety of conditions. It was found that the subsidence behavior strongly depends on the depth of burial. For example, with an increase in depth, the base of the reservoir may actually rise, whereas the top surface subsides.

The model was also used for studying the effect of subsidence on pressure buildup behavior. The calculated reservoir pressure was higher in a compacting than in a noncompacting reservoir, taking into account the variation of permeability with compaction.

Another phase studied was the effect of rebound on reservoir performance when gas is injected into the formation. Even though rebound is small in practice (of the order of 10% of subsidence), the effect was clearly evident in the reservoir pressure-production behavior. When there was no rebound, however, gas injection simply inhibited compaction.

Finally, the model was used for simulating the reported oil production and subsidence history of one of the BCF in western Venezuela. Fair agreement between the observed and the predicted behavior was obtained (Finol and Farouq Ali, 1974).

In the late sixties and seventies all-out application of steam injection (first cyclic and later continuous) by Maraven in land portions of the BCF was introduced and the effect of formation compaction on steam injection was studied. Rattia and Farouq Ali (1981) found that formation compaction, if present, can have an important influence on thermal recovery methods, as observed in the BCF and elsewhere. Their paper discussed the effect of formation compaction on oil production by cyclic steam stimulation and steamflooding, using a fully implicit steam injection simulator. The simulator accounts for three-phase mass and heat transport occurring in steam injection processes, for a wide variety of operating


conditions. It employs an implicit formulation together with a Newtonian, direct solution approach, which was shown to be stable for large time steps.

It was found that oil recovery in a compacting reservoir increases with an increase in the uniaxial compaction coefficient. Whereas cyclic steam stimulation yielded a favorable response in a compacting reservoir, the opposite was true for a continuous steamflood. The study showed that a delay in implementing a steamflood in a noncompacting reservoir can lead to a considerable loss of recovery, in the range of 10- 40% of oil-in-place, depending on the value of the uniaxial compaction coefficient. This finding has far-reaching implications for steamflooding subsequent to intensive depletion by cyclic steaming or primary production.

Although formation compaction can be beneficial from the standpoint of cyclic steam stimulation response, there is a strong dependence on the compaction coefficient. Furthermore, it was found that if the oil in question exhibits non-Newtonian flow behavior (reported for some Venezuelan oils) it must be accounted for in numerical simulations; otherwise, the oil production rates may be in error by as much as 100% (Rattia and Farouq Ali, 1981). Prior to the work of Finol and Farouq Ali (1974) and Rattia and Farouq Ali (1981) (development of numerical models), changes in reservoir thickness were usually not part of the output of reservoir simulators. The influence of compaction was taken into account by them through the pore volume compressibility and they showed the contribution of rock compressibility to oil production for both primary depletion and the cyclic steam injection processes. This concept was also included in the formulation of commercial thermal models.

Inasmuch as the above formulation does not conform with the actual behavior of compressibility, which, according to laboratory experiments, depends on effective pressure gradient, a new formulation of compaction was developed by Espinoza (1983) in INTEVEP. In a thermal reservoir simulator, a more realistic compressibility behavior was introduced and the numerical reservoir model was modified to compute the reservoir thickness changes (Espinoza and Mirabal, 1988).

According to this formulation, the pore-volume (PV) change during a time step is computed by the following equation:

PV (N+I) = PV (N) 1 + C~(P) dP

PN

(7-1)

where Ck (P) is a compressibility function depending on both the pore pressure and pore pressure trend. Thus, Ck = C1 for PN+I >_ PN and C~ = C2 for PN+I < PN. and the compressibility function Ck depends on the pore pressure. Assuming uniaxial compaction and constant rock volume, the corresponding thickness (h) and porosity changes for a given block are calculated as follows:

h N+I - - h N (otdp N + 1) (7-2)

cN+I = cN (O~ -[- 1) (7-3) (ar g + 1)


where

0/ ---- p v N + 1

p g N - 1

Sensitivity analysis, reported by Espinoza (1983), as well as additional experiences showed the convenience of using this new formulation and, at present, it is implemented in the thermal and black oil simulators in use in the Venezuelan Oil Industry (Espinoza and Mirabal, 1988).

Analytical models were also adapted to the BCF to predict compaction and subsidence. Starting with van der Knaap and van der Vlis (1967), Merle et al. (1975) and Puig and Schenk (1985) used this category of models to evaluate compaction and subsidence at different times and for different areas of the BCF with very favorable results. As a consequence of these experiences, and considering the availability of a large amount of information in the BCF, Maraven has dedicated considerable effort to building, improving, and applying the various categories of tools for calculation/prediction of subsidence (HUNDCALC, SINK) and for computing oil recoveries by compaction (CROLLA, SOLGAS).

Inasmuch as compaction and subsidence are consequences of fluid production and injection, pore pressure and temperature change, changes can occur in effective stresses. The latter produce deformations in the reservoir and overburden, leading to porosity and permeability changes, which, in turn, affect fluid production, pore pressure, and thermal profiles. A "complete solution to the problem requires, therefore coupling between fluid flow analysis (traditional reservoir simulators) and deformational analysis" (Espinoza and Mirabal, 1988). Whereas the models mentioned so far emphasize fluid flow and include deformational analysis through simplified approaches, two models developed recently, SUB-3D and COMPAC, developed by INTEVEP (Venezuelan oil industry research institute) are mainly focused on deformational analysis. A very short description of the physical and mathematical basis of the enumerated tools (modified numerical reservoir models, analytical tools adapted to the BCF, and numerical models based on deformational analysis) are presented in a paper by Espinoza and Mirabal (1988) presented at the Fourth Unitar/UNDP Conference.

O R I N O C O BELT SUBSIDENCE

The existence of impressive Orinoco Belt proven, probable, and possible reserves of H and XH crude oils and bitumens, and the potential contribution of reservoir compaction to the exploitation and recoveries of these reservoirs has made the techniques and experience developed in the BCF extremely valuable. Studies of the Orinoco Belt's future development and analysis following drilling campaigns have included the possibility of having compaction and subsidence in this area, particularly due to the unconsolidated nature of its sands. Studies by Ramirez and Zubillaga (1987) and Rajani and S~inchez (1988) have shown that compaction could occur and would be very helpful as a production mechanism. The associated


phenomenon of subsidence also has to be evaluated from the point of view of industrial, social, economic and environmental impacts.

Inasmuch as the amounts of oil produced in the Orinoco Belt are insignificant in relation to reserves, the simulation/prediction "... of compaction and subsidence in Orinoco Belt is being addressed in a different manner with respect to BCF where substantial amount of information already existed and the fitting-extrapolation methods are providing very good results, even in cases where the uncertainty of the physical properties of the porous and overburden media is considerably high. The approach taken for Orinoco Belt consisted in the development of numerical models based on the physical and mechanical properties of the media (reservoir + overburden) and the laws of rock mechanics. In addition, a geomechanical characterization of several areas was undertaken by laboratory and field measurements (Ramirez and Zubillaga, 1987; Rajani and S~inchez, 1988) to provide input data for the models" (Espinoza and Mirabal, 1988).

REFERENCES

Ab~-Saab, S.J. and Murria, J., 1985. Origen y Desarrollo del Sistema de Protecci6n Costanera, Costa Oriental del Lago de Maracaibo. I Jornada de Tecnologia de Producci6n, INTEVEP, Los Teques, Venezuela.

Ab~-Saab, S.J., Roest, P.W. and Velsink, H., 1982. Polders and dikes of the Bolivar Coast, Venezuela. Int. Symp. Polders of the World, October, Netherlands, I: 134-145.

Bockmeulen, H., Barker, C. and Dickey, P.A., 1983. Geology and geochemistry of crude oils, Bolivar Coastal Fields, Venezuela. Bull., Am. Assoc. Pet. Geol,., 67(2): 242-270.

Borger, H.D. and Lenert, E.E, 1959. The geology and development of the Bolivar Coastal Field at Maracaibo, Venezuela. Proc. 5th World Pet. Con~, 1: 481-498.

Borregales, C. and Salazar, A., 1987. The Future for In-situ Recovery, Treatment, Transportation of Heavy Oil in Venezuela. Topic 17 on Recovery of Extra Heavy Oils, Natural Bitumens and Shale Oils, 12th World Petroleum Congress, Houston, Texas.

Brenneman, M.C., 1960. Estudio qufde los petr61eos crudos de la Cuenca de Maracaibo. Tercer Congreso Geol6gico Venezolano, Caracas, 3: 1025-1069.

Caribbean Petroleum Co., 1948. Oil fields of Royal Dutch-Shell Group in Western Venezuela. Bull., Am. Assoc. Pet. Geol., 32:517-628.

Chrzanowski, A., Chen Y.P., Leeman, R. and Leal, J., 1988. Integration of the global positioning system with geodetic levelling surveys in ground subsidence studies. Proc. 5th Int. (FIG) Syrup. Deformation Measurements, and 5th Can. Symp. Mining Survey and Rock Deformation Measurements, Fredericton, N.B., pp. 142-151.

Collins, J.J., 1935. New type sea-wall built for subsiding lake shore in Venezuela. Eng. News Rec., 114(3): 405-408.

Dusseault, M. and van Domselaar, H., 1982. Unconsolidated sand sampling in Canadian and Venezuelan oil sands. Rev. Tdc., INTEVEP, 2(2): 165-174.

Espinoza, C., 1983. A new formulation for numerical simulation of compaction. Sensitivity studies for steam injection. Research Simulation Symposium of Society of Petroleum Engineers, San Francisco, Calif., Proc., SPE Pap. 12246, pp. 134-144.

Espinoza, C. and Mirabal, M., 1988. Venezuelan Experience in Simulation of Compaction and Subsidence Associated to Oil Production. Pap. No. 196, 4th UNITAR/UNDP Conf. Heavy Crude and Tar Sands, Edmonton, Alta., Preprints Vol. III.


Finol, A. and Farouq Ali, S.M., 1974. Numerical simulation of oil production with simultaneous ground subsidence. SPE Pap. 4847, SPE European Spring Meeting, Amsterdam, May 29-30; Soc. Pet. Eng. J., October: 411 enrule 424; Trans. AIME, 259 (1975): 411-424.

Geertsma, J., 1973. Land subsidence above compacting oil and gas reservoirs. J. Pet. Technol., 25: 734-744.

Gonz~lez de, J.C. and Aguerrevere, S.E., 1938. Contribuci6n al estudio de la cuenca sedimentaria Zulia-Falc6n. Bol. Geol. Miner. Minist. Fomento de Venezuela, 2 (2-4)" 123-138.

Iraz~ibal, A., Abi-Saab, S.J., Murria, J. and Groot, J., 1986. Drainage problems in areas subject to subsidence due to oil production. Proc. 2nd Int. Conf. Hydraulic Design in Water Resources Engineering: Land Drainage, Southampton University, April. Springer-Verlag, Berlin, pp. 545-554.

Leal, J., 1987. Subsidence Monitoring of Offshore Structures Using Temporal Tide Gauges. Department of Surveying Engineering, SE 6910 Graduate Seminar Paper, University of New Brunswick, Fredericton, N.B.

Leal, J., 1989. Integration of GPS and Levelling in Subsidence Monitoring Studies at the Costa Bolivar Oil Fields. M.Sc. Thesis, Department of Surveying Engineering, University of New Brunswick, Fredericton, N.B.

Mencher, E., 1953. Geology of Venezuela and its oil fields. Bull., Am. Assoc. Pet. Geol., 37: 690-777. Mencher, E., Fichter, H.J., Renz, H.H., Wallis, W.E., Patterson, J.M. and Robbie, R.H., 1951. Resumen

Geol6gico Campos Costaneros de Bolivar. Convenci6n Nacional del Petr61eo, Caracas, September 9-18. Oficina T6cnica de Hidrocarburos, Ministerio de Minas e Hidrocarburos, Caracas, pp. 48-52.

Mendoza, H. and Murria, J., 1989. Ground Subsidence Modelling in Western Venezuela. Submitted for acceptance to the Organizing Committee of the International Symposium on Land Subsidence, Dhanbad, Bihar, December 12-15.

Merle, H.A., Kentie, C.J.O., van Opstal, G. and Schneider, G.M.C., 1975. The Bachaquero study a composite of the behavior of a compaction drive/solution gas drive reservoir. 5th Annual Fall

Conference, Dallas, Texas, SPE Pap. 5529, J. Pet. Technol., 1976, I: 1107-1115. Miller, J.B., et al., 1958. Habitat of oil in Maracaibo Basin, Venezuela. In: Habitat of Oil, Am. Assoc.

Pet. Geol., pp. 601-640. Miller, J.B., Edwards, K.L., Wolcott, EP., Anisgard, H.W., Martin, R. and Anderegg, H., 1963. Medio

ambiente del petr61eo en la Cuenca de Maracaibo. Primer Congreso Venezolano de Petr6leo, Caracas, 24-31 March, 1962. Sociedad Venezolana de Ingenieros de Petr61eo, Caracas, pp. 67-70.

Murria, J. and Abf-Saab, S.J., 1988. Engineering and construction in areas subjected to subsidence due to oil production. 5th Int. (FIG) Symp. Deformation Measurements, and 5th Can. Symp. Mining Surveying and Rock Deformation Measurements, Fredericton, N.B., pp. 367-373.

Nflfiez, O. and Escojido, D., 1976. Subsidence in the Bolivar Coast. Int. Assoc. Hydrol. Sci., Proc. Annaheim Symp., Dec., Publ. 121: 257-266.

PDVSA, 1986. The Story of Venezuela Oil. Publication of Petr61eos de Venezuela, Caracas.

Puig, E and Schenk, L., 1984. Analysis of the Performance of the M-6 Area of the T{a Juana Field, Venezuela, under Primary, Steam Soak, and Steam Drive Conditions. 4th Joint SPE/DOE Symposium on Enhanced Oil Recovery, Tulsa, Okla., April 15-18, SPE/DOE Pap. 12656.

Puig, E and Schenk, L., 1985. Comportamiento de Compactaci6n/Hundimiento en el/[erea del Proyecto M-6 de Inyecci6n Continua de Vapor. I Simposio Internacional sobre Recuperaci6n Mejorada de Crudo, Maracaibo, February 19-22.

Rajani, B. and S~inchez, M., 1988. Regional Characterization of Geomechanical Properties of Unconsol- idated Sands of the Heavy Oil Belt, Venezuela. 4th UNITAR/UNDP Conf. Heavy Crude and Tar Sands, Edmonton, Alta., Pap. 167.

Ramirez, M. and Zubillaga, J., 1987. Applications of Well Logging for Compaction and Subsidence Studies in the Orinoco Oil Belt, Venezuela. 62th Annual Fall Technology Conf., Dallas, Texas, SPE Pap. 16773.

Rattia, A. and Farouq Ali, S.M., 1981. Effect of Formation Compaction on Steam Injection Response. 56th Annual Fall Technology Conf., San Antonio, Texas, SPE Pap. 10323.


Roca, L. and Neda, J., 1985. Evaluaci6n del Comportamiento Elastopldstico en Arenas no Consolidads de la Faja Petrolifera del Orinoco. 6th Venezuelan Geol. Congr., Caracas, September-October.

Rubio, EE., 1960. Condiciones de las acumulaciones de petr61eo en los campos costaneros del Distrito Bolivar, Lago de Maracaibo. Tercer Congreso Geol6gico Venezolano, Caracas, 3: 1025-1069.

Schenk, L., 1982. Analysis of the Early Performance of the M-6 Steam-Drive Project, Venezuela. 3rd Joint SPE/DOE Symposium on Enhanced Oil Recovery, Tulsa, Okla., SPE/DOE Pap. 10710.

Stainforth, R.M., Gonzfilez de, Juan C. et al., 1970. L~xico Estratigrdfico de Venezuela. Paper presented at the 4th Venezuelan Geol. Congr., November 1969, Ministry of Mines and Hydrocarbons, Caracas.

Sutton, EA., 1946. Geology of Maracaibo Basin. Bull., Am. Assoc. Pet. Geol., 30: 1621-1741. Teeuw, D., 1971. Prediction of formation compaction from laboratory compressibility data. Presented at

the 45th Annual Technology Conference, Houston, SPE Pap. 2973, October 4-7. Trans. AIME, 251. Trutmann, O., 1949. Report on the Activities of the Topographical Department. Internal Report, Shell

Caribbean Petroleum Co. Maraven Report No. EPC-8845, Jan. Van der Knaap, W. and van der Vlis, A.C., 1967. On the cause of subsidence in oil producing areas.

Proc. 7th World Pet. Congr, M6xico City, pp. 85-95.


Chapter 8

373

RESERVOIR COMPACTION AND SURFACE SUBSIDENCE IN THE NORTH SEA EKOFISK FIELD

M U S H A R R A F M. ZAMAN, A B D U L A Z E E Z A B D U L R A H E E M and JEAN-CLAUDE ROEGIERS


The North Sea has presented the most consistently demanding environmental challenges encountered in offshore oil and gas resource development (White et al., 1973). Learning how the international petroleum companies and the North Sea governments have responded to this challenge should be instructive for those planning for future development of similar hydrocarbon fields.

The North Sea is located in the western portion of the northwest European Basin. The Mid North Sea-Ringkobing-Fyb strikes east-west across the North Sea from Denmark to the United Kingdom at 55 ~ to 56~ It divides the North Sea area of the Northwest European Basin into two smaller subbasins: the southern North Sea and the northern North Sea basins.

The northern North Sea Basin consists of several subbasins, platforms, plateaus, grabens, and embayments. Most of the major hydrocarbon accumulations are associated with the Central and Viking grabens. These grabens form part of the same Mesozoic rift system but they are different especially in the age of the producing reservoirs and type of structural traps containing hydrocarbons. Almost all of the fields currently producing oil are located in two grabens and one subbasin: the Viking or East Shetland Basin and Central grabens and the Moray Firth (Fig. 8-1).

The southern North Sea Basin includes a belt of natural gas fields that extends from southern England through the North Sea, The Netherlands, and northern Germany to Poland. Permian Rotliegendes Sandstone is the main reservoir in this area. It also contains natural gas accumulations in tilted fault blocks, horsts, faulted domes and anticlines (Dietzman et al., 1983). The North Sea covers several smaller sedimentary and structural basins of different geologic ages. The rocks range in age from Paleozoic to Tertiary and consist of sandstones, shales, carbonates and evaporites. The most important reservoir rocks are the Lower Permian sandstones of the Torliegendes Formation, the Upper Permian dolomites of the Zechstein For- mation, the Triassic Sandstone of the Bunter Formation, the Jurassic sandstones, the Maestrichtian-Danian chalk, and the Paleocene and Eocene sandstones. The main source rocks are Carboniferous coal measures, Mesozoic shales and carbonates, and Tertiary shales and carbonates.

The significant structural traps are folds and fault blocks associated with salt movement and basement faulting (Dunn, 1973). Other types include rotational fault blocks, compactional structures, deep-seated salt domes, structural-stratigraphic,

374 M.M. ZAMAN, A. ABDULRAHEEM AND J.-C. ROEGIERS

Fig. 8-1. Location map of the North Sea. (After The Petroleum Resources of the North Sea Energy Administration; courtesy of World Oil, August 15, 1982.)

RESERVOIR COMPACTION AND SURFACE SUBSIDENCE IN THE NORTH SEA EKOFISK FIELD 375

TABLE 8-I

Ekofisk reservoir data (after Snyder, 1971)

Total porosity (%) 30 Permeability to oil (mD) 12 Temperature (~ 268 Solution GOR (ft3/bbl) 1707 API gravity (o) 35.6 Initial BHP (psia) 4135 Bubble point pressure (psia) 5560

and other combinations. The most productive of the salt-induced domes are located in the Norwegian sector of the Central Graben where the Ekofisk and other nearby fields, commonly referred to as the Ekofisk complex, produce hydrocarbons from Upper Cretaceous and Lower Paleocene chalk (Dietzman et al., 1983).

The Ekofisk field is located in the Central Graben in the southern part of the Norwegian sector of the North Sea (Sulak and Danielson, 1989). It is the largest of six fractured chalk fields operated by Phillips Petroleum Co. Norway on behalf of the Phillips Norway Group. Water depth in the area is about 235 ft (72 m).

The presence of massive Danian limestone is the key to Ekofisk success. The porosity of the limestone is 30% in a relatively homogeneous and clean section. Primary matrix permeability can be lower than 1 mD in some sections. However, extensive natural fracturing found in all Ekofisk wells resulted in an average 12 mD permeability to oil, calculated from well test pressure analysis. Additional Ekofisk reservoir data is shown in Table 8-I (Snyder, 1971).

A cross-section of the sedimentary basin running north to south through the area is shown in Fig. 8-2. Salt domes and ridges pushing up from the basin floor create anticlinal structures in the sedimentary layers. Seismic maps of the area reveal many such structures with different sizes and shapes, which have probably increased the reservoir permeability by contributing to fracturing in the massive, brittle Danian carbonates (Snyder, 1971).

DISCOVERY AND EXPLORATION IN THE NORTH SEA

The first exploration in the North Sea was conducted in territorial waters of the U.K. between 1956 and 1961. Before 1962, the North Sea had been held open as to international status and the tidewater countries had claimed no rights beyond their territorial waters (3 to 12 miles); they also lacked authority to issue exploration licenses beyond that limit. Little exploration occurred in the North Sea until 1962, although the geology was well known in the tidewater countries and minor oil and gas fields were found near the coasts of the United Kingdom. The discovery of the giant Groningen gas field in 1959, provided the incentive for the North Sea tidewater countries to ratify the Geneva Convention of 1958. There are now seven countries, viz., The U.K., Norway, Denmark, Germany, The Netherlands, Belgium,


Fig. 8-2. Promising structures within the major sedimentary basin that runs north to south through the North Sea based on seismic data. Ekofisk production is from 700 ft of lower Tertiary limestone illustrated here in the basin cross-section on a line from Norway to England. (After Snyder, 1971, fig. 3; courtesy of World Oil, May, 1971.)

and France, that have controlling interests in the continental shelf underlying the North Sea. The first discovery of petroleum in the U.K. sector was made in 1965 when a British Petroleum (BP) borehole was drilled to the Rotliegendes Sandstone in the southern North Sea Basin.

Exploration drilling led to the discovery of the Cod gas-condensate sandstone reservoir and the Viking field in 1968 and the Ekofisk chalk field late in 1969. In the


following years, five additional chalk fields were discovered in what is now called the greater Ekofisk area.

P R O D U C T I O N

Norway's first significant oil production from the North Sea was obtained in 1971, whereas in the case of the U.K., it was 1975. Most of the oil accumulations found to date are located in either the Moray Firth, the Viking Graben, or the Central Graben. As of January 1, 1982, there were at least 242 developed and undeveloped oil fields in the North Sea that originally contained about 96 billion barrels of oil in place and had an estimated proved reserve of 19.8 billion barrels and undeveloped reserves of 5.7 billion barrels of oil remaining to be recovered. Cumulative production until then was 3.6 billion barrels, giving a total estimated ultimate oil recovery of 29.1 billion barrels and a recovery efficiency of 30.5% of the original oil-in-place.

Oil production from the North Sea has increased steadily since its inception in 1971 with the exception of a very minor reversal in 1973. Since then output reached a rate of 216 thousand barrels of oil per day in 1975, doubled in 1976, doubled again by 1980, and in 1981 oil production was estimated to be about 2.3 MM bopd (Dietzman et al., 1983).

Production at the Ekofisk started in July, 1971, and reached a peak rate of 349,000 B/D (55,500 m3/d) in 1976. The Ekofisk complex today is the processing center for all production from the Ekofisk area fields.

E K O F I S K F I E L D D E S C R I P T I O N

The Ekofisk reservoir is large and shaped like a shallow, elliptical dome about 22,000 ft (6700 m) wide and 30,800 ft (9390 m) long. The crest of the reservoir is approximately 9500 ft (2900 m) below sea level, and the pay zone is nearly 1000 ft (300 m) thick. The reservoir initially contained undersaturated volatile oil with the properties listed in Table 8-I.

The Ekofisk Formation, which is located at a depth of 9500 ft is of Danian age in the Paleocene Period, whereas the Tor Formation, which underlies Ekofisk Formation, is of Maestrichtian age in the Cretaceous Period. The Tight zone, which exists between the Ekofisk and the Tor formations, forms an impermeable barrier between the two producing formations (Fig. 8-3). The porosity of chalks ranges from 25% to 48% with permeabilities up to 100 mD. The overall pay thickness reaches 1000 ft and more (Boade et al., 1989).

The reservoir is covered with a 9300-ft thick overburden, mostly composed of clays and shales interbedded with silty streaks. The overburden is overpressured below about 4500 ft. Permeability is extremely low (10 -6 to 10 -9 D), and there is no indication of pressure communication between the reservoir layers and overlying sediments (Sulak and Danielson, 1989).


Fig. 8-3. Representative porosity log from an Ekofisk well. (After Board et al., 1989.)

Field development

The Ekofisk field was developed in phases. The conditions for its development changed with time because the exploration also was in rapid progress along with the development plans. The Ekofisk field was the first largest oil discovery in chalk and the pressure in the reservoir was abnormally high: 7135 psi at a depth of 3100 m compared to the normal value of around 4500 psi (Kvendseth, 1988; Sulak et al., 1989).

In July, 1971, Phase I was initiated to determine if the natural fractures, essential for commercial production rates, would close during depletion. In this phase, a discovery well and three appraisal wells were completed and tied to the Gulftide, a converted jackup platform. By the end of this phase in May, 1974, approximately 28 million barrels of oil had been produced (Rickards, 1974).

Based on the successful performance of the wells in Phase I, a decision was made in 1972 to develop permanent structures for the Ekofisk. Consequently a field terminal platform, three drilling platforms and living quarters were constructed in Phase II. In addition, subsea lines were laid from the production platforms to the processing facilities and from the latter to the oil loading buoys. A concrete storage tank with a capacity of one million barrel was also constructed in this phase to allow the production to continue when weather conditions on the sea prevented offshore loading.

During Phase III, six other fields were developed in the Greater Ekofisk area, namely the West Ekofisk, Edda, Tor, Eldfisk, Albuskjell, and Cod fields. A 220-mile


oil pipeline to Teesside, England and a 274-miles gas pipeline to Emden, Germany, were also laid in this period (Sulak, 1991). By 1988, there were 25 platforms in the Greater Ekofisk area.

Enhanced oil recovery projects

Recent improved and enhanced oil recovery methods have significantly increased the oil and gas production from the seven fields. The excess gas which could not be sold was injected back resulting in high gas injection rates. Waterflooding was initiated in 1987 to cover the Tor Formation in the northern two-thirds of the field (Sylte et al., 1988; Hallenbeck et al., 1989). It was expanded in 1988 to include the southern portion of the Tor field as well as to the Lower Ekofisk. Nitrogen injection into the crest of the Upper Ekofisk was also planned to start in late 1993 (Thomas et al., 1989). Production from the Ekofisk field has increased steadily. Two-thirds of that increase is due to waterflood response. The other third is due to an effective remedial work program implemented over the past few years as well as improved communications across disciplines which has reduced the well failures (Sulak, 1991).

P L A T F O R M S S I N K I N G

In the early eighties, after more than a decade of production, it was noticed that the Ekofisk platforms were sinking. A boat-landing on the east side of the Ekofisk complex was more or less under water, whereas it had previously been visible in 1970's. The same was true for a landing on the horizontal bracing on the jacket below the 2/4-C platform. Initially no one gave any attention to check if the platforms really were sinking. In fact, as many as 87 different natural conditions can contribute to the variation of sea level. Late in the fall of 1984, however, the matter was given serious attention. It started with sounding measurements on the bridges to check clearance margins for anchor-handling boats. The results were compared with the relevant data from 1974. Photographs taken in the early and mid-seventies were also compared with recent ones (Wiborg and Jewhurst, 1986; Kvendseth, 1988). In November 1984, through measurements from fixed platform references to mean sea level, it was finally concluded that the platforms indeed were sinking.

Earlier, it was thought that if reservoir compaction occurred, productivity would decline, and if productivity was not declining, reservoir compaction was not occurring. Also, the rock mechanics and structural analysis, coupled with case studies, led to the development of certain criteria for transfer of reservoir compaction into surface subsidence. According to these criteria, which involved mainly the depth and areal extent of the reservoir and the stiffness of the overburden, reservoir compaction at Ekofisk should not have led to significant subsidence. However, that was not the case. By 1984, the seafloor in the Norwegian Sea was discovered to have subsided by more than 10 ft as a result of production-induced reservoir compaction (Sulak, 1991).


The effective stress on the rock (the difference between the overburden load on the rock and the pore pressure within the rock) increases as hydrocarbons are withdrawn and reservoir pressure declines. Certain rocks, under such conditions, exhibit a sudden increase in compressibility. This sudden increase in compressibility, coupled with a large irreversible deformation, is called "pore collapse" (Smits et al., 1988). Several investigators have observed this phenomenon in the laboratory also (e.g., Blanton, 1981; Newman, 1983). The compaction resulting from the pore collapse in the reservoir rocks is transmitted through the overburden causing the sea floor to subside. Pore collapse is believed to be the main cause of reservoir compaction and the seafloor subsidence in the Ekofisk field.

The Phillips Group had discussed the subsidence of the sea floor as a possibility in their application for test production in 1970. But it could not be noticed easily in situ because the subsidence occurred millimeter by millimeter over the years and the people accustomed to sights on everyday basis could not notice it. Another point is that the measurements taken between the structures in the Ekofisk complex showed no change in elevation from one structure to another, because all structures in the area were moving down as a unit, at approximately the same rate. Also, the Phillips engineers noted that the Ekofisk reservoir is more than 10,000 ft deep, and subsidence was never reported over a 10,000 ft deep reservoir (Kvendseth, 1988).

The following sections describe the methods of measurements of the reservoir compaction and the resulting surface subsidence. Both temporary and permanent solutions to overcome the problem are discussed next. A brief description of the factors that affect the subsidence of the ground is provided first. This is followed by a discussion of various approaches adopted by research workers to investigate the characteristics and mechanics of reservoir rocks, and to model the observed behavior. Two-dimensional and three-dimensional numerical simulations of the compacting field undertaken by different investigators are also reviewed.

CAUSES OF SUBSIDENCE

The history of fluid production from porous reservoirs has identified five key parameters when evaluating the probability of significant subsidence. In the case of Ekofisk, the relevant data for these parameters is shown in Table 8-II. Reservoir

TABLE 8-II

Ekofisk key parameters

Parameter Danian Cretaceous

1 High porosity 48% 35% 2 Thick reservoir 600 ft 400 ft 3 Large pressure decline 3200 psi (1985) 3400 psi 4 Large areal extent 5 miles x 5 miles 5 miles x 5 miles 5 Reservoir depth 9800 ft 9800 ft


depth is a significant parameter at Ekofisk. Reservoirs where substantial subsidence has been reported earlier, were producing from around 1500 m or shallower (Wiborg and Jewhurst, 1986). This aspect is discussed in detail in the later sections.

M E A S U R E M E N T S OF SUBSIDENCE

Several systems of measuring were utilized to determine the rate of subsidence, including satellite measurements of several of the platforms in the Ekofisk area. From these measurements, it became clear that the seabed was sinking at a rate of between 40 and 50 cm per year. In mid-1985, sufficient data were obtained to conclude that the platforms lay 2.5 m deeper in the water than when they were installed. The area that was affected due to subsidence was approximately 6 km in diameter and bowl-shaped, the greatest subsidence being under the Ekofisk center (Kvendseth, 1988).

Measurement of reservoir compaction Log data from the same suite of logs run in the same wells with years in between

could be used to measure the amount of reservoir compaction. There are many uncertainties attached to the interpretations, however, when using these logs to estimate the reduction in thickness or compaction (Wiborg and Jewhurst, 1986).

A special logging tool, the formation subsidence monitoring (FSMT), has been developed by Shell and Schlumberger for accurate measurement of the distance between radioactive markers. Using a time-lapse technique, relogging then allows precision monitoring of compaction rates in different intervals. The tool helps in determining the amount and areal extent of formation compaction. The data obtained from time-lapse compaction surveys can then be used for verification of theoretical studies, subsidence simulation models, and laboratory research. Figure 8-4 shows the compaction measurements taken at platform 2/4-C between October 1986 and October 1987 (Menghini, 1989).

T E M P O R A R Y R E M E D I A L M E A S U R E S

The subsidence bowl at the Ekofisk covered the entire field and affected all the platforms located in the central Ekofisk complex. Wells were drilled from only one of these platforms, 2/4-C, the others providing services such as housing, fluid handling, processing, etc. The problem was approached in two ways: through reservoir management and through surface structure modification (Bleakley, 1986). Phillips conducted extensive studies in early 1985 to find effective solutions, both temporary and permanent, for subsiding platforms and the possible harmful effects of reservoir compaction.

Gas injection. The Phillips group investigated the possibility of using waterflooding as a pressure-maintenance system rather than the gas injection, because of the demand for gas. After studying different alternatives, gas injection was proposed as


Fig. 8-4. Compaction measurements in Well 2/4 C-11 between October 1986 and October 1987. (After Menghini, 1989, fig. 8; courtesy of Society of Petroleum Engineers.)

an immediate solution, though it meant a direct loss of revenue. After the permanent platforms were installed, gas was injected back into the reservoir from platform 2/4-C which was adversely affected by the subsidence. This reduced the rate of pressure drop in the reservoir. Inasmuch as the Phillips Group was committed to deliver- ies of gas to the buyer group on the continent, an agreement was reached in late 1985 to decrease the sales and increase the volume of gas for injection (Kvendseth, 1988).

Streamlining the deck beams. Inasmuch as the 2/4-C platform suffered the largest amount of subsidence and had to be protected before the winter season of 1985- 1986, to reduce the possible wave stress on this platform in the event of a major storm, it was decided to streamline the structural beams, such as I-beams, by rounding them off by welding a semicircular fairing to cover all the flat faces. Through model testing, it was determined that such a modification would decrease the stress by more than 40%. The work on rounding off the beams was begun in the summer of 1985 (Bleakley, 1986).

PERMANENT REMEDIAL MEASURES

To secure Ekofisk permanently against the subsidence effects, different alternatives were identified and reviewed (Kvendseth, 1988) to arrive at the most positive, cost-effective and timely solution. The contribution of Ekofisk to the Norwegian economy necessitated an early and a permanent solution to this problem. The solutions fell generally into two categories. The first was to reduce the height of the storm waves in the Ekofisk complex area, and the second was to modify the existing facilities


to compensate for the increasing water depth. A solution involving wave-suppressors in the form of enormous cement blocks or even sunken super tankers, that could reduce the effect of the hundred-year wave, was proposed by Norsk Hydro. After a research study conducted at the ocean laboratory in Trondheim, however, it was concluded that this solution is very expensive with uncertain results and side-effects.

Moving all the equipment from the lower 20 m deck to a higher level on the platform was another alternative. In that way the deck would become part of the jacket, and the platform would have about 10 extra meters for safety purposes. Part of this work was in the process of being done as a temporary solution to gain time. However, the problems associated with it, especially the cost, resulting decrease in space, and a long shutdown period to carry it out, prohibited the operators from enacting this solution (Kvendseth, 1988).

Bubble curtains have been used effectively to protect small harbors and marinas where relatively shallow water depths exist and the zone of exposure is limited. However, to apply this technique to Ekofisk was impractical because of the water depth and the extensive zone of protection required (Smith, 1988).

The third solution was to jack up the sinking platforms. This was finally adopted by the Phillips Group operating at the Ekofisk.

Jack-up

It was decided to raise the six steel platforms by jacking and to crane-hoist the two flares and the 2/4-G platform. The jack-up operation secured the platform against a subsidence of at least 7.5 m, and preserved flexibility and space for the future (Kvendseth, 1988).

Lifting heavy steel platforms nearly 6.5 m by means of hydraulic jacks, swinging 6 m long extension spools into place, and then lowering the platforms onto the extension spools was a huge task. The problems relating to the jacking-up seemed impossible to overcome in the beginning, because there were many unanswered questions related to this project.

The time frame in which this plan was to be executed was a big constraint. The French company Technip had done something similar, on a small scale, for an oil company in the Arabian Gulf and they felt it could be accomplished on a large scale on the six steel platforms in question at the Ekofisk complex. The installation work at Ekofisk was carried out by two companies, Oil Industry Services and Haugesund Kaldnes de Groot. Each of them was in charge of raising three platforms.

In order to bring the heavy jacking equipment into position by the platform legs, there had to be a transportation system. The cranes on the individual platforms were not capable of executing this task. Over 2000 m of monorails were prefabricated. It was quite an extensive operation, because a number of pipelines and tanks had to be moved in order to make room for the tracks (Kvendseth, 1988).

Feasibility studies were conducted to establish that the project was technically possible and detailed risk analyses were conducted to demonstrate that the structural integrity and safety levels of the platforms would be maintained during all phases of the platform modifications (Andersen et al., 1987). Results from the


stochastic fatigue analyses established that the elevated platforms would have a useful life well into the next century (Smith, 1988). Finally, a special series of analyses were commissioned to study the possibility of raising the platforms again in case the subsidence would exceed the anticipated amount. Results from this study indicated that it was entirely feasible to elevate the decks again with an appropriately designed stiffening system while maintaining the structural integrity of the platform and foundation (Halvorsen, 1987).

During the entire design phase of the Ekofisk Jacking Project, all structural de- signs from each contractor were subjected to rigorous reviews, checks, and ultimately approval by an independent third party. Special checks were conducted to verify that the hydraulic power units, jack head bearings, lower jack bearings along with the system of power and control could function efficiently under the anticipated loadings.

The project was executed successfully well within the time limits and the platforms were secured from subsidence for a couple of decades to come (Berrefjord, 1988; Hobley and Davies, 1988; Smith, 1988).

Protective barrier for the tank

To secure the Ekofisk tank, jacking up was not the solution. Two other possibilities were also reviewed. One was to build a protective wall around the tank between the 20 and 30 m levels. However, this was only a temporary solution. In addition, there were many uncertainties about the ventilation. The other alternative was to build a protective barrier around the whole tank, outside the breakwater wall. The Phillips Group chose the second alternative, which was a permanent solution to secure the hub of the entire Ekofisk system for the future. It was planned to build the wall in two sections that would be fitted together around the tank, approximately 3 m outside the breakwater wall. The concrete wall was built like a double wall, each one about 0.5 m thick. The whole structure is around 106 m high, with the tower 30 m above sea level (OGJ, 1989).

Attention is still given to a variety of potential problems which may be caused by the reservoir compaction and surface subsidence. They include casing failures and changes in the fluid-flow properties of the reservoir. Additional remedial work is still going on. Surveillance methods of several types are continually being used to monitor the progress of subsidence with the instruments like the four-detector formation subsidence monitoring tool (FSMT) and others (Mes, 1988; Rentsch and Mes, 1988; Menghini, 1989).

C H A R A C T E R I S T I C S OF TH E EKOFISK RESERVOIR ROCKS

Considerable amount of work was done by investigators in this field in trying to establish the factors that are responsible for surface subsidence, which may be a result of pore collapse or excessive irreversible compaction of the reservoir rocks. The characteristics of the Ekofisk reservoir rocks are discussed in this section. The following section addresses the mechanics of these rocks.


Mineralogy The producing horizons of the Ekofisk field are the Ekofisk and Tor formations.

Both formations are fine-grained limestones, chalks composed of skeletal debris of pelagic unicellular algae. The porosities are frequently above 40% and matrix permeabilities are often around 0.1 mD. The composition of chalks is mainly calcite, almost 95% of which is derived from shallow-water calcareous algae, called coc- colithophorids. These algae are set in a structureless matrix of very fine crystalline calcite. They produce spherical calcareous exoskeletons, called cocospheres, consisting of a number of wheel-shaped elements called cocoliths. Cocoliths break into individual units called platelets (Fig. 8-5). Diameters of cocospheres range from 10 to 30/zm, whereas the cocoliths range from 2 to 20/zm. Cocospheres seldom stay intact, whereas unbroken cocoliths are relatively common (see Larsen and Chilingar, 1983, pp. 213-288).

Porosity Porosities in chalks may be as high as 80% (Scholle, 1977). Effect of temperature

and depth of burial ~in reducing porosities are well-known (Athy 1930; Maxwell, 1964; Stephenson, 1977).

Phenomena like pressure solution (or solution transfer) ~ a combination of solution and deposition, which results in material being removed by solution at regions of higher stresses and being redeposited in regions of lower stresses - - also have a definite effect in reducing porosity (Sprunt and Nur, 1977). Amount of porosity loss was found to be a function of pore pressure and effective stress. Geologic age of the rock is also an important factor in porosity reduction. Nevertheless, porosity values on the order of 40-48% are not uncommon in chalks.

In the case of Ekofisk, matrix porosity and permeability are functions of the packing of cocolith platelets. These platelets are held together by cementation in the form of secondary calcite overgrowth and spot welding of grain contact points. In the Ekofisk Formation, local porosities reach as high as 48%. Porosity in the lower part of the formation is higher than in the upper part. The porosity of the tight zone, which varies between 330 and 500 ft (100 and 150 m) in thickness, ranges

~IP COCCOSPHERE

COCCOLITH PLATELET

Fig. 8-5. Schematic diagrams of coccosphere, coccolith, and platelet. (After Sulak and Danielsen, 1989, fig. 6; courtesy of Society of Petroleum Engineers.)


Fig. 8-6. Cross-sections of the Ekofisk reservoir for east-west and north-south directions. (After Boade et al., 1989, fig. 3; courtesy of Society of Petroleum Engineers.)

from 10% to 20%. Porosity in the upper part of the Tor Formation too is higher as compared to its lower part. The thickness of the Tor Formation varies between 250 and 500 ft (75 and 150 m). In both the Ekofisk and the Tor formations, the porosity varies significantly both laterally and vertically, and generally decreases towards the flanks.


TABLE 8-III

The distribution of porosities in the reservoir: east-west direction (after Chin and Boade, 1990)

Layer Zone 1 Zone 2 Zone 3 Zone 4 Zone 5 Zone 6 Zone 7 Zone 8

2 36 36 34 32 32 32 30 30 3 40 40 38 38 36 36 34 32 4 34 36 36 32 32 32 30 30 5 30 30 30 30 30 30 30 30 6 36 36 36 34 32 32 30 30 7 40 40 40 38 38 38 32 32 8 36 34 34 34 34 34 30 30 9 Tightzone

10 36 36 36 34 34 32 30 30

TABLE 8-IV

The distribution of porosities in the reservoir: north-south direction (after Chin and Boade, 1990)

Layer Zone 1 Zone 2 Zone 3 Zone 4 Zone 5 Zone 6 Zone 7 Zone 8

2 36 34 32 34 32 32 32 32 3 40 38 38 38 36 34 34 36 4 34 34 34 34 32 32 30 30 5 30 30 30 30 30 30 30 30 6 36 34 34 34 32 32 30 32 7 40 38 34 34 32 32 32 32 8 36 38 34 34 32 32 32 32 9 Tightzone

10 36 36 34 34 32 30 30 30

Based on the porosity distribution, the reservoir matrix is divided into 10 layers, with each layer having eight zones, as shown in Fig. 8-6. This exercise was carr ied out by Boade et al. (1989) for numerical s imulat ion purposes and it represents the approximate distr ibution of the porosity in the reservoir. The third, seventh and ten th layers have high porosities, whereas the first, fifth and ninth have low porosities. Layers 2, 4, 6 and 9 have in te rmedia te porosities. The in te rmedia te porosity layers are essentially gradat ional layers lying be tween high- and low-porosity layers. In fo rmat ion on these porosit ies of the layers and zones were obta ined f rom porosity logs of quite a number of wells (Chin and Boade, 1990). Even values of porosit ies are assigned to each zone be tween the range of 30% and 40%. Some small segments of the reservoir have porosit ies exceeding 40%; however, these are quite small

localized areas. The chalk zone starts with layer 1, whereas the base of this layer corresponds

to the point where porosit ies reach 30%. The base of layer 10 also represents the point where porosity drops to 30%. Layer 1 and the layers below layer 10 have porosi t ies less than 30%. The distribution of porosit ies in these layers and zones of

the reservoir is shown in Tables 8-III and 8-IV (Chin and Boade, 1990).


Inasmuch as the reservoir is elliptical in shape with two axes of symmetry, porosity distribution is shown in the tables for both the east-west and the north- south directions.

Permeability Regardless of porosity, chalks have low permeabilities, usually in the range of 1 to

10 mD (Sulak and Danielsen, 1989). Permeabilities of the order of 0.1 mD can also be found (Wiborg and Jewhurst, 1986). Confining pressure (Keighin and Sampath, 1982) and water chemistry (Newman, 1983), in the case of waterflooding, are known to affect the permeability in chalks. In the case of Ekofisk chalk, the effective permeability is substantially higher than the matrix permeability due to the presence of extensive natural fracturing. Fracturing is of various origins and generally can be classified as healed, tectonic and stylolite-associated. The effective permeability ranges from 1 to 100 mD, with an average of 12 mD, due to the presence of natural fractures in the Ekofisk chalk which enhance the permeability by up to a factor of 50.

MECHANICS OF THE EKOFISK RESERVOIR ROCKS

Lack of understanding of the rock behavior generally has an adverse effect on the economics of the producing fields. In the majority of the cases, the problems were recognized only after the field had been put into production. Proper appraisal of the risk associated with such problems at the start of production and operation would have avoided expensive remedial actions. For example, had the seafloor subsidence at Ekofisk been predicted at the start of production, elevation of the operating platforms could have been avoided (see Kvendseth, 1988).

The Ekofisk chalk behaves linearly elastic at low applied loads, followed by plastic response at higher loads. The plastic response of chalk is accompanied by a process called pore collapse which involves a high reduction in porosity. The stress level at which the pore collapse occurs depends on multiple factors notably the initial porosity and the quartz content.

Strength tests Blanton (1981) studied the deformation behavior of Danian chalk from the

North Sea and Austin chalk from the Gulf Coast under confining pressure and pore pressure. The pore pressure was raised by compressing the rock faster than the fluid leak off rate. The mechanical behavior of the chalk was found to be a function of the effective stress (overburden pressure minus the pore pressure). With increasing effective stress, the chalks experienced pore collapse and reduced permeabilities. The term "pore collapse", as defined earlier, is used to describe a drastic, irreversible reduction in porosity due to the increase in effective stress on the rock matrix as a consequence of withdrawal of oil and gas. It was also found that whereas the ultimate strength of the rock (maximum stress reached during the test) increased with increasing confining pressure, the yield strength (stress at which plastic strains begin to occur) first increased and then decreased


-10 03 03 UJ rr F- 03 5 G~ < W I 03 0 o

psi 0 0 0 0 0 0 0 ,..D

0 0 0 0 0 0 0 0 0 CD 0 t.O 0 tO 0 LO 0 u'~

1500

1000

500 " - - . .

~" "~" I~~ 0 5 10 15 20 25 30

NORMAL STRESS, MPa

t,o

Fig. 8-7. Mohr envelope for dry Danian chalk. (After Blanton, 1981, fig. 6; courtesy of Society of Petroleum Engineers.)

with increasing confining pressure. At very high confining pressures the chalks experienced yielding under hydrostatic stress by pore collapse. Figure 8-7 shows this behavior for Danian chalk on Mohr's envelopes. Blanton (1981) correlated this behavior of chalks with the volumetric response because it reflects the changes in pore structure. At low confining pressure, the rocks show positive dilatancy (increase in volume or expansion). Positive dilatancy would be inhibited by confining pressure. Thus, when the rock tends to be dilatant, an increase in confining pressure would increase the yield strength. It is known that the tendency to become dilatant is due to the formation of microcracks (Brace et al., 1966). As the confining pressure increased, the rocks showed a negative dilatancy (decrease in volume or compaction) and pore collapse. Thus, with increasing confining pressure, a transition took place from microcracking to pore collapse. As a result of pore collapse, the permeability also decreased. Pore collapse would be enhanced at higher confining pressures because it involves a reduction in volume. Thus, the yield strength would be lower at higher confining pressures due to collapse of pores.

Uniaxial strain tests From the available literature on experimental research related to the deformation

behavior of reservoir rocks, it is found that previous studies have emphasized the uniaxial strain tests, which are considered more representative of the actual field conditions than triaxial tests (Addis, 1987; Johnson et al., 1989; Addis and Jones, 1990). Assuming constant reservoir diameter as the hydrocarbons are produced, the approximation of the stress conditions in the field with the uniaxial strain tests are compatible with the fact that most of the reservoir compaction is in the vertical direction. Such an assumption is not valid near a wellbore or at the boundary of the reservoir where the confining loads differ; however, it is the best currently available. A schematic of the uniaxial conditions is shown in Fig. 8-8.

The uniaxial strain tests which were performed on the chalk samples obtained from the Ekofisk field, showed a large amount of compaction as the fluid was 'withdrawn (Johnson et al., 1989). The deformation pattern obtained is shown in Fig. 8-9. To study the microscopic changes taking place during the testing,


Lateral Stress (Zero Lateral Strain)

Axial Stress

, r j

~ - . . _ _ _ _ . _ _ -

Fig. 8-8. Schematic of a uniaxial strain test.

J

Lateral Stress (Zero Lateral Strain)

ELASTIC I

E

, LOADING . . . . UNLOADING

STRESS Fig. 8-9. Porosity-stress curves for chalk showing elastic and pore-collapse regions and loading and unloading paths. (After Johnson et al., 1989, fig. 2; courtesy of Society of Petroleum Engineers.)


Fig. 8-10. Ekofisk field reservoir chalk from a depth of 11,402 ft: (a) before compaction and (b) after compaction. (After Johnson et al., 1989, fig. 3; courtesy of Society of Petroleum Engineers.)

scanning electron microscope (SEM) micrographs were taken before and after the compaction tests. Figure 8-10 shows SEM micrographs of Ekofisk reservoir chalk that was compacted from 38% to 33% porosity in a uniaxial strain test, which placed the sample well into the pore collapse region. The dark areas in these


Fig. 8-11. Stress-strain curves for low-quartz content Ekofisk chalk. (After Chin and Boade, 1990, fig. 10; courtesy of Joint Chalk Research Program.)

figures represent the pore spaces. The individual spaces are very small in size, about 1 to 5/zm, despite the fact that the porosity is high. In Fig. 8-10a, unbroken cocoliths can be seen clearly. The skeletal framework appears loosely packed. In the post test micrograph (Fig. 8-10b, porosity 33%) no intact cocoliths can be seen, presumably because of disruption of the cocoliths by translation and rotation of neighboring calcite grains. The loosely packed skeletal framework has been replaced by a "texturally homogenized" groundmass with no large pore spaces. Density of calcite grains is clearly high in the "collapsed" micrograph. A similar response was observed when chalk samples from the Danian chalk field in Denmark were stressed to about 6000 psi (Simon et al., 1982).

Johnson and Rhett (1986) and Johnson et al. (1989) conducted uniaxial strain tests on six different levels of porosities on both high-quartz and low-quartz content Ekofisk chalk (Figs. 8-11 and 8-12). The pore collapse process is particularly evident for the high-porosity, low-quartz content (<3%) chalks, as shown in Fig. 8-11 by the marked change in slope that occurs as the effective axial stress is increased. The dashed curves in Figs. 8-11 and 8-12 indicate the ultimate response of the chalk, i.e., with the inclusion of creep behavior.

Potts et al. (1988) also conducted uniaxial strain tests on chalk samples obtained from the Ekofisk reservoirs. The experiments were conducted under fully drained conditions using Ekofisk crude oil as the pore fluid. The compaction behavior of


Fig. 8-12. Stress-strain curves for high-quartz content Ekofisk chalk. (After Chin and Boade, 1990, fig. 11; courtesy of Joint Chalk Research Program.)

chalks was unaltered when experimental temperatures were varied between 25~ and 120~ The results of the tests are shown in Fig. 8-13, where each curve is identified by the sample porosity, determined prior to the test.

Hydrostatic compression tests Hydrostatic compression tests have also been used to investigate the deformation

characteristics in high-porosity reservoir rocks (Johnson et al., 1989; Hamilton and Shafer, 1991). It is also observed that the response to withdrawal of fluids is a function of the rock type, its porosity, the loading (production) rate, etc. (Smits et al., 1988). The compaction characteristics of various types of rocks are different, which indicates that it is important to investigate each rock type thoroughly under simulated loading conditions.

Effect of stress on porosity The initial porosity of a rock is a major factor influencing chalk strength and

its compressibility behavior (Smits et al., 1988). The higher the initial porosity, the earlier is the onset of pore collapse. Figure 8-14 shows this character explicitly. Samples having high initial porosity compact by a larger amount during the pore collapse, for the same stress difference or deviatoric stress, than the samples with low initial porosity.

Figure 8-9 shows a typical effective stress vs. porosity variation for the Ekofisk


Fig. 8-13. Stress-strain curves for uniaxial strain experiments on samples of Ekofisk chalk. (After Potts et al., 1988, fig. 1; courtesy of Tapir Publishers.)

chalk (Johnson et al., 1989). Similar behavior may be observed for other high- porosity carbonates (Blanton, 1981; Botter, 1985). Referring to Fig. 8-9, as the effective stress increases, porosity decreases. At low values of effective stress, the decrease in porosity is small and recoverable (elastic). At higher stress levels, however, the material undergoes a drastic reduction in porosity (high compressibility), which is not recoverable. This phenomenon of very high compressibility has been regarded in literature as pore collapse. The deformations that take place during pore collapse cannot be recovered by stress reversal, and hence are permanent or plastic. These observations can be translated into a trendline concept (Smits et al., 1988). According to this concept, the porosity of a given sample will remain more or less constant with increasing stress until the trendline is reached and pore collapse occurs. This concept is very useful for predicting reservoir compaction caused by pore collapse on the basis of porosity logs.

It is also found that the type of carbonate has an influence on the porosity/ stress plot (Smits et al., 1988). Figure 8-15 shows the behavior for four different carbonate rocks. From these figures, a "trendline" concept is derived. According to this concept, the porosity of a given sample will remain more or less constant with increasing stress until the trendline is reached where pore collapse occurs. As a result, the porosity/stress trendline should be established on the basis of laboratory experiments for the relevant carbonate types of each new field.


Fig. 8-14. Compaction curves for the Upper Ekofisk Formation. (After Johnson et al., 1989, fig. 5B; courtesy of Society of Petroleum Engineers.)

Effect of stress on permeability From a study conducted on the Ekofisk chalk samples by Teufel and Warpinski

(1990), it was found that the chalks do not show a large decrease in permeability with increasing confining stress or decreasing pore pressure. The differences in permeabilities between incremental steps in confining stress or pore pressure were found to be less than the errors of the measurements for the chalks. Consequently, no effective stress law for permeability could be established for chalks except for the low porosity and permeability samples, where the relationship is found to be nonlinear.

Stress ratio A study of in-situ stresses in the Ekofisk field was carried out by Teufel et al.

(1991) using shut-in pressure data of 32 hydraulic fractures. The effective stresses in the reservoir are found to increase linearly with pore pressure drawdown, but at different rates. The ratio (K) of the change in effective minimum horizontal stress to the change in effective vertical (overburden) stress is found to be approximately 0.20 as shown in Fig. 8-16. This value is much smaller than the K value of about 0.5 measured in uniaxial strain tests of reservoir chalk. The reason for the lower K value is that the magnitudes of the deviatoric or shear stresses in the reservoir have increased more rapidly during pore pressure drawdown, leading to shear failure,


Fig. 8-15. Porosity-stress trendlines for various carbonate rock types (loading rate: 100 bar/h). (After Smits et al., 1988, fig. 5; courtesy of Society of Petroleum Engineers.)

Fig. 8-16. Diagram of effective minimum horizontal stress vs. effective overburden (vertical) stress in the Ekofisk field. Change in effective stress is caused by pore pressure drawdown. (After Teufel et al., 1991, fig. 2; courtesy of Balkema.)

than they would have for the larger K values. The cont inued good producibility of the Ekofisk field in spite of the subsidence is perhaps due to the shear failures during pr imary product ion leading to increased fracture density and reduced matrix block dimensions.


The findings also showed that the boundary condition on the reservoir is not strictly a stress boundary condition, where an incremental increase in effective overburden stress is matched by an identical increase in effective horizontal stress, i.e., K equals 1.0. Rather, it is a displacement or a combined displacement/stress boundary condition in which an incremental reduction in pore pressure produces a greater incremental increase in effective overburden stress than in effective horizontal stress.

Loading rate The influence of loading-rate on the compaction was described by a rate-type

compaction model (RTCM) of de Waal and Smits (1988) that enables quantitative prediction of field behavior on the basis of laboratory experiments. For unconsolidated sandstone reservoirs, good agreement was found between compaction predicted with the RTCM and that observed in the field. In their model, the loading-rate sensitivity of the reservoir rock was characterized by a material constant, b, determined from uniaxial compression tests with varying loading rates. In the study reported by Smits et al. (1988) such variable-loading-rate experiments were carried out on air-filled and water-saturated Danian outcrop samples and on water-saturated Danian and Maestrichtian chalk samples from a North Sea oilfield. An example of such a test is shown in Fig. 8-17. The results obtained from these and other experiments indicate that the RTCM is also applicable to carbonates, at least under laboratory conditions. Whether the extrapolation from laboratory to

E

0.0 , ~ ~

800.0 ~lX~ \~\/800 Bar/h

1600.0

2400.0

3200.0 o.o 20o .0 " 4 0 o . 0

AXIAL STRESS (BAR) Fig. 8-17. Loading-rate effects on compaction behavior of Danian outcrop samples. (After Smits et al., 1988, fig. 9; courtesy of Society of Petroleum Engineers.)

398 M.M. ZAMAN, A. A B D U L R A H E E M AND J.-C. R O E G I E R S

>. l - m

0 n- O

f i e l d

lab

I �9

I I I I I I I

ave

~Ov,

O'vfield

AXIAL EFFECTIVE STRESS Fig. 8-18. Deviation of trendline at field depletion rate from laboratory-measured trendline. (After Smits et al., 1988, fig. 10; courtesy of Society of Petroleum Engineers.)

depletional loading rates, necessary for field application of the RTCM, is valid for carbonate reservoirs, needs to be evaluated from future field studies.

According to the RTCM, the difference in loading rate will cause the trendline in the field to be shifted relative to that measured in the laboratory by an amount AO'Ve (Fig. 8-18), given by the following equation:

A O'Ve = fiVe O'1 a b - - 1 (8-1 )

where dfield and fflab a r e the field and the laboratory loading rates, respectively, aVe is the stress level, and b is a constant. Hence, according to the RTCM, pore collapse (and subsidence) will occur at lower stresses and in considerably larger amounts than expected on the basis of conventional analysis.

Effect of seawater on compaction behavior To enhance the oil recovery and to maintain the reservoir pressure, waterflooding

programs have been carried out in the Ekofisk field. To this end, a number of studies have addressed the relationship between chalk strength and water saturation. From a series of tests conducted on Ekofisk chalk samples saturated with North Sea water, Johnson et al. (1989) observed that the chalks prepared with an irreducible brine saturation showed little or no response when injected with simulated water.


60.0

46.0

, ~ 1 7 6

35.0

30.0

I NATIVE/WATER ;~ CLEANED/WATER 3 NATIVE/AIR 4 CLEANED/AIR S CLEANED/KEROSENE

,,x N,x,. ,,\ N " - . \

',X

1

�9 1 i i

2oo.o ,oo.o eoo.o

AXIAL STRESS (BAR) Fig. 8-19. Influence of cleaning and pore saturant on pore-collapse trendline. (After Smits et al., 1988, fig. 8; courtesy of Society of Petroleum Engineers.)

Seawater floods, therefore, would not weaken North Sea reservoir chalks because they already have an irreducible formation brine saturation, wetting the rocks' mineral matrix.

Pore sa turant

Influence of core cleaning procedures and pore saturant on the pore collapse behavior was investigated by Smits et al. (1988) on five batches of Danian outcrop samples that were given different treatments with respect to the type of pore fluids content and the cleaning procedures of core. Figure 8-19 shows the influence of these treatments. There is a significant difference between air-filled and water- saturated samples. The presence of water in the pores results in a compressibility before and after collapse of twice that of the air-filled samples. Moreover, the air- filled samples collapse at a considerably higher stress. From experiments on poorly dried samples, it was found that the presence of minute amounts of water causes the samples to behave as fully water-saturated samples. The very presence of water at


the grain contacts determines the compaction behavior, whereas the composition of this water and the type of fluid in the bulk of the pore space are irrelevant.

Summary of the test results on Ekofisk reservoir rocks

Experimental data generated on the North Sea chalk have led to the following observations (Addis, 1989; Johnson et al., 1989; Jones et al., 1989; Teufel et al., 1991).

(a) There are three regimes of deformation of the chalk in response to increase in effective stress, viz., elastic, yield, or pore collapse, and hardening or post-pore collapse.

(b) The initial response of the weak rock is elastic. This is evident from the uniaxial stress-strain curves reported by Chin and Boade (1990).

(c) For a particular stress path, the material yields or experiences pore collapse at a stress value that is dependent upon porosity. During the pore collapse, deformation is seen to occur at an approximately constant deviatoric stress and is assumed to be due to a gradual breakdown of the cocolith platelets and/or intergranular cementation. The rearrangement ultimately provides increased strength and reduces further deformation.

(d) Significant deformations in the reservoir rocks occur only when they exhibit non-linear deformation characteristics.

(e) Deformation mechanics include both primary compaction and creep behavior. Short-duration experiments do not account for creep and, therefore, underestimate reservoir compaction.

(f) For samples deforming under hydrostatic or uniaxial strain conditions, breakdown of the intergranular cementation of the sediment occurs under the increased compressibility.

(g) The fundamental properties of the material are determined by the pre-pore collapse and post-pore collapse.

(h) A porosity of 30% represents the lower limit for significant compaction. Chalk with less initial porosity will not be subject to pore collapse under conditions that are anticipated in the Ekofisk reservoirs.

(i) High-quartz chalk has higher strength. Consequently, the Upper Ekofisk Formation is less compactable than the Lower Ekofisk and Tor formations because of higher silica content.

The amount of compaction in the Ekofisk chalk is a function of both the inherent rock characteristics, such as geologic age, initial porosity, quartz content, carbonate type, and external factors, such as stress, stress ratio, rate of loading and the chemistry of pore fluids.

C O N S T I T U T I V E M O D E L I N G OF THE RESERVOIR ROCKS

A review of literature shows that the pore collapse phenomenon in weak, porous rocks has been modeled primarily using curve-fitting techniques as well as consti-


tutive theories (Schatz, 1976). Most of the earlier models that were employed in prediction of subsidence were based on principles of elastic continuum mechanics (McCann and Wilts, 1951; van Opstal, 1974; Kamata et al., 1976), and on elastic and viscous deformation constants (Geerstma, 1957). A one-dimensional rate type compaction model was developed by Smits et al. (1988) to explain the observed nonlinear field behavior on the basis of loading rate effects in some sandstone reservoirs. Barton et al. (1988) used a modified Cam Clay model to simulate nonlinear void ratio-log effective stress curves. To study the reservoir compaction and surface subsidence of the Valhall field in the North Sea, Ruddy et al. (1989) employed a constitutive model based on the porosity-dependent rock compressibility curves. The works of Barton et al. (1988) and Ruddy et al. (1989) were focussed on field simulation; therefore, the description and predictions of the model were not provided.

Jones et al. (1987) modeled the chalk as a nonlinear isotropic elastic material. The stress/strain curves shown in Fig. 8-13 were used as a basis to construct a series of "best fit" curves to model the behavior of the reservoir rocks. The "best fit" curves were used to obtain a piece-wise linear variation of Young's moduli to be used in the numerical simulation.

Using elastoplastic theory and isotropic hardening, Zaman et al. (1992) developed a model to describe deformation behavior of the Ekofisk chalk. The model essentially consists of a shear failure surface and a moving cap. The cap is assumed to be elliptic in shape. To represent the pre-pore collapse behavior, which is elastic, an elastic cap is defined in the J1 - ~/-J2D space. The response in this region can be described by the elastic constants, viz., Young's modulus, E, and Poisson's ratio, v. Based on the experimental evidence (Teufel et al., 1991; Zaman et al., 1992), the equation for the shear failure surface is assumed to be linear in the J1 - ~ space, as shown in Fig. 8-20. Consequently, the equation of this surface can be written as follows:

F f ( J 1 , V / J2D) = V/J2D -- M J1 - a (8-2)

where M is the slope and 6 is the intercept of the failure surface on the ~/r'g2D axis. The initial response of porous rocks is often found to be elastic (Johnson et al.,

1989; Addis and Jones, 1990). An elastic cap is defined in the J1 - ~/-Jm space, within which the response can be described by the elastic constants, viz., Young's modulus E, and Poisson's ratio, v. Figure 8-20 shows the elastic region in the J1 - space.

On successive loading, porous rocks start to experience pore collapse and post- pore collapse deformations. In principle, a separate region needs to be explicitly defined in the J1 - ~/J2D space with a specific hardening/softening rule, including instability to account for the abrupt changes in deformation (in certain cases) during pore collapse. To keep the model simple and practical, the response in this region and the post-pore collapse region is described by a moving yield surface. The cap defining the elastic region in the J1 - ~ space is allowed to expand on successive loading and assume the role of the moving yield surface, Fc. The equation of such a cap is proposed as:


$

~ a Mo Cap/Moving yield surface

C X

d 1 Axts Fig. 8-20. Elements of the proposed constitutive model. (After Abdulraheem, 1993, fig. 5-1.)

fc(J1, V/J2D, C) = J~D2D- ~ / a 2 - ( J 1 - C)/R2 (8-3)

where C = X - R a and the parameter R, called the "shape factor" by DiMaggio and Sandier (1971), is the ratio of the major to minor axes of the ellipse, X and C are the values of J1 at the intersection of a cap with the J1 axis and the failure surface, respectively, and a is the length of the minor axis of the elliptical cap, as shown in Fig. 8-20. The failure and moving yield surfaces are assumed to intersect such that the tangents to the yield surfaces at the intersection are parallel to the J1 axis.

Movement of the yielding surface, Fc is controlled by a hardening function expressed in terms of a parameter ~. In this work, hardening of the weak porous rock is attributed to the irreversible plastic deformation, an approach commonly adopted to describe the hardening of granular materials, especially soils (DiMaggio and Sandier, 1971). Consequently, the parameter ~ is expressed as:

= 1/2 (8-4)

where the symbol f denoted history. Inasmuch as X = C + R a as shown in Fig. 8-20, the expansion of the yield surface, Fc, under increasing stresses, can be effectively described by making X a hardening function of the parameter ~ as follows:

x = x0 + • (84 )

where X0, as shown in Fig. 8-20, represents the value of J1 at the intersection of the yield cap with the J1 axis, and, or,/~ and r} are material constants. For hydrostatic compression stress paths, ot = 1. Using the concept of the associative plasticity theory, the incremental plastic strain tensor, de p can be expressed as:


Fig. 8-21. Experimental data and prediction for Ekofisk chalk with low quartz content; porosity levels: 34% and 36%. (After Abdulraheem, 1993, fig. 5-7.)

d ~ = d)~ 0 Fc (8-6) ~oi.j

where Fc is the yield function for the yield surface and d~. is an unknown scalar to be determined from the consistency condition of Prager, dFc = 0 (Desai and Siriwardane, 1984). Following the standard steps of the theory of plasticity, the

ep elastoplastic constitutive relation tensor, Cijkl , c a n be written as follows:

e Ofc Ofc ci.iu O m. C%l

ep Cijkl -- Ceikl -- 0 Fc c e 0 Fc A (~, ars )

OO'pq pqrs OO.rs

(8-7)

where C~jkt is the elastic constitutive tensor and A (~, aij) is a measure of the plastic modulus involving derivatives of the yield function Fc with respect to ~ and the derivative of the yield function with respect to the stress tensor aij.

All of the parameters employed by the model can be evaluated using simple laboratory tests. The elastic constants (E and v) can be determined from the unloading paths of conventional triaxial compression tests. Parameters 3 and M are determined from the compression path tests, conducted at different confining pressures. Test data from a hydrostatic compression test can be used to determine fl and rl. The parameter ot is determined by optimization using experimental data for a given type of rock.

Although all of the model predictions are found to be in good agreement with the experimental data, only two typical predictions are presented here. Figure 8-21 shows the comparison of uniaxial stress/uniaxial strain response at two different levels of porosities (34% and 36%).


PREDICTION OF RESERVOIR COMPACTION AND SURFACE SUBSIDENCE AT THE EKOFISK

Empirical approach

Subsidence was first recognized at the Ekofisk by the operating company in late 1984. At that time, the extent and rate of subsidence was not known, but sufficient data was available to indicate that the problem could be serious. Consequently, a number of independent studies were undertaken by different research groups to study the mechanics of the reservoir and the surrounding rocks, develop proper constitutive models to describe the behavior of the rocks, and to simulate the compaction of the reservoir and the surface subsidence of the field (Wiborg and Jewhurst, 1986; Barton et al., 1988; Boade et al., 1989; Jones et al., 1989; Chin and Boade, 1990; Chin et al., 1993; Abdulraheem et al., 1994).

Subsidence, in general, refers only to vertical land surface deformation caused by an alteration of the supporting structure. Common use of the term, however, has come to include the various other land mass displacements that can accompany vertical movement; e.g., lateral motion and faulting. Oil production and other large fluid production areas appear to be susceptible to five basic types of ground movements, viz.: subsidence or rebound of land surface due to fluid pressure changes; lateral ground movement, partially due to severe induced fluid pumping pressure gradients; vertical ground movement due to thermal expansion or contraction of the rock strata; tectonic faulting or folding; and landslides and mass wasting (slow downslope movement of rock materials due to gravity).

The surface subsidence can have detrimental effects on the producing facilities in addition to damage in the surrounding area. Agricultural areas can be affected by alterations of drainage paths of surface water, increases in flooded areas, adverse effects on water wells, triggering of minor earthquakes, damage to irrigation channels, and disruption of vegetation. In populated areas, damage can occur to houses and buildings, roads, power lines, railroad tracks, sewers and drains, dams and levies, and airfields. In the case of Ekofisk, it resulted in expensive remedial works for securing the operating platforms.

Reservoir compaction, which is the main cause of surface subsidence, can have detrimental as well as beneficial effects. Excessive compaction in reservoir rocks may lead to reduction in permeability or flow of hydrocarbons. Sand production may also result as a consequence of crushed grains. On the other hand, it may also lead to shear fractures in the reservoir matrix, thereby increasing the flow of hydrocarbons. Also, compaction may increase oil recovery: "compaction drive".

The total, or effective, compressibility of any reservoir rock is a result of two separate factors, namely, expansion of the individual rock grains, as the surrounding fluid pressure decreases, and the additional formation compaction brought about because the reservoir fluids become less effective in supporting the weight of the overburden as reservoir pressure declines. Both of these factors tend to decrease porosity (Hall, 1953).

A first attempt to arrive at a mathematical analysis of subsidence caused by oil-reservoir depletion was made by McCann and Wilts (1951). The objective of


their study was a better understanding of the subsidence behavior in the Wilmington field.

For an isotropic porous medium built up of a continuous homogeneous and isotropic matrix material, relations were established by Geertsma (1957) giving the compressibility of both pore and rock bulk volume as a function of the elastic and viscous deformation constants of rock matrix and rock bulk material and the porosity. In another work, Geertsma (1973b) presented a simple method for estimating the order of magnitude of both the reservoir compaction and accompanying subsidence, especially for reservoirs which have large lateral dimensions compared to their height and with rigidity of the overburden close to that of the reservoir. The model proposed by Geertsma, as mentioned above, was extended by van Opstal (1974), who introduced a basement at some depth below the reservoir to account for the usual stiffness of the underburden ("rigid basement" model). All these models, however, were based on the assumption of an elastic continuum.

The trendline concept discussed earlier could also be used to predict the pore- collapse stress of various layers and the total amount of compaction expected at a given stage of reservoir depletion by the following procedure (Smits et al., 1988):

(1) For the various carbonate rock types in the reservoir, a trendline should be established from a series of uniaxial compaction experiments on water-saturated core samples with as large a range of initial porosities as possible.

(2) Each trendline has to be corrected for the difference between the laboratory and the field loading rate (Smits et al., 1988).

(3) The reservoir should be divided into a number of layers (grid blocks) of more or less constant (average) porosity and carbonate rock type.

(4) For each layer (grid block), the collapse stress and the amount of compaction after collapse should be established according to the procedure illustrated in Fig. 8-22, using the appropriate trendline. The compaction might be calculated at various stages of depletion (e.g., at abandonment).

(5) The total amount of compaction Ah in a given layer can be evaluated with the following equation:

A h - - h i ~ i - q~ (fiVe)

lOO - O ( a w ) (8-8)

where hi is the initial thickness of the layer, ~bi is the initial porosity, and ~b(ave) is the porosity at the stress level ave.

(6) The total amount of reservoir compaction is then obtained by adding up the contributions of the various layers. If the collapse stress is not reached during depletion, the contribution of "normal" compaction can be taken into account, for example, by using the correlation between porosity and compressibility before collapse.

Though the trendline concept for calculation of reservoir compaction was developed for chalks and applied for other producing fields, its application to the Ekofisk field is not reported in the literature.


' (Ov,)

INITIAL VERTICAL EFFECTIVE 8TRESS

i

I I N I T I A L IN ' - $1TU

. . . . . ~ CONDITION

,, '_ ' ' . , ~ m , ~ , , . |

I I I

I I I

I s I

Lo . V E R T I C A L EFFECTIVE S T R E S S (bar)

Fig. 8-22. Procedure to calculate in-situ compaction caused by pore collapse. (After Smits et al., 1988, fig. 14; courtesy of Society of Petroleum Engineers.)

Numerical simulation

The process of compaction of the Ekofisk reservoir and the resulting subsidence of the ground surface are very complex because of the nonlinear compaction behavior of chalk and the coupled physical processes. Consequently, an appropriate simulation task requires proper incorporation of a number of aspects. Some of the important aspects which have to be taken into consideration during a simulation task are outlined below.

A subsiding field encompasses a number of zones which contribute to its subsidence. The main cause of the subsidence is the reservoir compaction resulting from the increase in the effective stress due to pore pressure depletion. Also, the surrounding areas both in the lateral (the sideburden) and the vertical directions (overburden and underburden) interact with the compacting reservoir. The most desirable simulation would obviously require a three-dimensional idealization of the field. The factors that govern the selection of a suitable spatial idealization are: (1) geometry of the field/reservoir; (2) pore pressure depletion zones and depletion scenarios; (3) amount of field data available; (4) the level of sophistication desired, depending upon the simulation goals; (5) computer time; and (6) available storage facilities.

The complex process of reservoir compaction and the associated surface subsidence can suitably be handled by numerical simulation procedures such as finite element method. In this method, the following aspects are easily handled:

(1) shape of all the different structures involved, viz., the reservoir matrix, the overburden, sideburden and the underburden;

(2) the distribution of the material properties and porosities; and (3) the distribution of pore pressure as a function of time and position.


2D simulation by Potts et al. (1987) To identify the maximum subsidence that would occur as a result of reduction in

pore pressure in the reservoir, Jones et al. (1987) employed a finite element code, ICFEP, to simulate the Ekofisk field. The most important assumption in this study was that the lateral dimensions of the reservoir, or of any of its component parts remain unchanged during the deformation. The second assumption, which follows from the first, was that the zero lateral strain condition would be maintained by mobilization of the normal effective stresses in the horizontal direction. Another grossly simplifying assumption was that the fracture system in the chalk played a passive role in the deformation. With the intact rock adjacent to the fracture able to deform with ease and with large normal stresses, the influence of the fractures was assumed to be negligible to justify the last assumption.

The values of Young's modulus and the Poisson's ratio for the layers in the overburden used in this simulation task are shown in Table 8-5. The values supplied by the Phillips group were determined from seismic velocities in the overburden. The FE mesh for the whole field and the reservoir is shown in Fig. 8-23.

Inasmuch as the long-axis cross-section (north-south direction) of field was used in the FE simulation, the calculated values overestimated the field values. The overestimation was also due to the assumption that the subsidence process at Ekofisk is time-independent.

2D simulation by Barton et al. (1988) Non-linear finite element (FEM) and non-linear distinct element (DEM) analy-

ses of the compaction and large-scale subsidence were performed by Barton et al. (1988). In the FEM analysis, the chalk was viewed as a continuum. A non-linear FEM code, CONSAX (Barton et al., 1988; D'Orazio and Duncan, 1982) with a modified Cam Clay model was utilized to simulate the non-linear void ratio versus log effective stress curves, which represent the pore collapse behavior of the most porous chalks. The code was used in an axisymmetric format, and only vertical deformation was allowed along the vertical boundaries. An approximate non-linear material model was developed by the Norwegian Geotechnical Institute (NGI) to represent the stress-strain characteristics through triaxial, one-dimensional stress tests performed on Ekofisk chalk plugs. One of the material models used is shown in Fig. 8-24. The overburden was simulated as a layered elastic continuum (4 layers).

TABLE 8-V

Mechanical properties of the Ekofisk overburden (Jones et al., 1987)

Material No. Young's modulus Poisson's ratio Depth

5 41.37 • 105 kN m -z 0.40 6 28.96 • 105 kN m -z to 0.44

24.13 x 105 kN m -2 7 27.58 x 105 kN m -2 0.42

2500 m m reservoir top 1500-2500 m

0-1500 m


Fig. 8-23. The Ekofisk finite-element mesh, with an expanded scale diagram for the reservoir section. (After Potts et al, 1988, fig. 5; courtesy of Tapir Publishers.)

Details of the layers and their elastic parameters are given in the paper by Barton et al. (1988).

An example of a typical subsidence calculation is illustrated by the deformed mesh in Fig. 8-25. It was shown that a continuum model, even a layered continuum model, provided a very poor fit to the observed subsidence bowl. This observation demonstrated justification for the use of discontinuum analyses in large-scale subsidence modeling.

The philosophy behind using discontinuum modeling for chalk subsidence is that in such cases as jointed chalks, deformation generally occurs by joint opening or shear, by fault movement or bedding plane strip. Viewed from a distance, the process appears to be one of continuous, isotropic deformation. But in reality, the mechanism is probably discontinuous, and is controlled by quite different laws.

In the discontinuous modeling, the two-dimensional time-marching finite difference program, UDEC (Cundall, 1980; Barton et al., 1988) was used. The 3 km of overlying sediments were modeled as discretely layered and jointed media. Fig- ure 8-26 shows the geometry used in the UDEC modeling. Details can be found in the report by Barton et al. (1988). Figure 8-27 illustrates the corresponding displacement vectors obtained. The discrete modeling provided a good fit to the observed subsidence scenarios. It was concluded that loading both the matrix and


i n..

0

0.6

0.5

0.1,

O~

0.2.

40 % porosity

35

3O

2S

20

In p" (MPa) Fig. 8-24. Material model B (simplified) used in the CONSAX compaction model (p~ is the mean effective stress). (After Barton et al., 1988, fig. 2; courtesy of Norwegian Geotechnical Institute.)

joints (by an internal reduction in fluid pressure in one-dimensional strain) causes joint slip, relative mass bulking, near maintenance of joint apertures (and, therefore, conductivities) and a compaction magnitude potentially smaller than in the case of unjointed chalk. This unexpected mechanism may explain the continued high productivity still experienced by the Ekofisk reservoir (Barton et al., 1988).

2D simulation by Boade et al. (1989) In the work presented by Boade et al. (1989), the constitutive behavior described

earlier in Figs. 8-11 and 8-12 was used as the basis of characterizing the compaction behavior of the Ekofisk chalk; i.e., at low effective pressures, the response is elastic, followed by plastic response at pressures when the material experiences a major porosity reduction (i.e., pore collapse). If the load is removed from a specimen in the elastic regime, the specimen recovers much of the porosity loss during unloading.


Fig. 8-25. Example of horizontal and vertical displacements for subsidence model. (After Barton et al., 1988, fig. 4, courtesy of Norwegian Geotechnical Institute.)

Fig. 8-26. An example of UDEC modeling of the subsidence process, with subvertical joints and faults. (After Barton et al., 1988, fig. 6; courtesy of Norwegian Geotechnical Institute.)


Fig. 8-27. Displacement vectors from UDEC model depicted in Fig. 8-27. (After Barton et al., 1988, fig. 7; courtesy of Norwegian Geotechnical Institute.)

In the plan view, the Ekofisk reservoir was assumed to have an elliptical shape and to be symmetric about the major and minor axes of the ellipse (Fig. 8-28). The field was treated as an axisymmetric problem. Inasmuch as the shape of the field was elliptic, however, two computational runs, each with axisymmetric idealization, were made: (1) with major axis and (2) with the minor axis of the Ekofisk field. The results of the two simulation runs were then combined to represent the actual three-dimensional response of the field.

Figure 8-28 shows two solid circles with radii corresponding to reservoir dimensions assumed for the two axisymmetric calculations. East-west direction is represented by the smaller circle with a radius of 11,000 ft (3.35 km), whereas the north-south direction is represented by the larger circle with a radius of 15,400 ft (4.69 km). Inasmuch as the part of the reservoir extending towards the south is narrow in dimensions, its effect on the compaction and subsidence was expected to be minimum, and was, therefore, ignored.

The east-west and north-south cross-sections of the reservoir are shown in Fig. 8-6. Each cross-section of the reservoir was divided into layers and zones based on the distribution of porosity. The data for these porosities were obtained from the sonic logs (Boade et al., 1989).

The finite element grid used in the simulation runs consists of the reservoir matrix, overburden, sideburden and a small portion of underburden. Sideburden consists of a large area laterally exterior to the reservoir. All these extensions of grid are incorporated in the simulation to avoid any boundary and edge effects on the results.

The overburden is assumed to be a homogeneous, linear-elastic material with a specific gravity of 2.3, a Young's modulus of 5000 ksi (3.45 GPa), and a Poisson's ratio of 0.42. The data obtained from vertical seismic profiles, sonic logs and a few triaxial tests is utilized to arrive at these values. The assumption of linear elasticity of the material is justified from the fact that the stress state in the overburden does not cause any yield in the material.


Fig. 8-28. Contour map of Ekofisk reservoir with circular and elliptical shapes assumed for subsidence simulation. (After Boade et al., 1989, fig. 1; courtesy of Society of Petroleum Engineers.)

The sideburden and the underburden of the reservoir is assumed to have identical properties. A linear-elastic modulus of 2000 ksi (14 GPa), a Poisson's ratio of 0.25 and a specific gravity of 2.22 are used for these materials in the simulation run.

The first step in simulation of the field conditions is to subject the whole structure to selfweight. This step ensures that the state of stress in the field including that in the reservoir corresponds to the initial, preproduction stage. Subsequent changes in displacement and stresses are relative to this initial state. To make sure that the strains and deformations in the reservoir regions are calculated properly, should the nonlinear behavior start during this stage, the selfweight of the whole structure is activated in 10 loading steps. Each loading step carried a load corresponding to 10% of the selfweight.

Pore pressure variation data as a function of hydrocarbon withdrawal, obtained from a fully-implicit 3-D simulator (Thomas et al., 1983) is utilized in the FE simulator for loading input. The 3-D simulator is used by Phillips Norway engineers to model the performance of Ekofisk reservoir for reservoir management purposes. Two pressure-time curves are used for each column of reservoir elements; one for upper segment of the reservoir, known as the Ekofisk Formation reservoir or the


Danian reservoir, and the other for the lower segment of the reservoir, known as the Tor Formation reservoir or Cretaceous reservoir. Pressure is assumed to be uniform within each of these two segments.

2D simulation by Abdulraheem et al. (1994) The data of the Ekofisk reservoir and the surrounding area was taken from

Boade et al. (1989). Consequently, the approach adopted by them in terms of spatial idealization has been adopted by Abdulraheem et al. (1994). The constitutive model developed by Zaman et al. (1992) mentioned earlier, was employed in this simulation task.

The entire field considered in the simulation work by Abdulraheem et al. (1994) was divided into 522 elements. The reservoir mesh consisted of 144 elements. There were 18 layers of elements, nine passing through the reservoir. For better appreciation of numerical results and improved numerical simulation, the grid was kept finer in the column containing the reservoir area.

A decrease in pore pressure implies increase in the effective stress on the rock matrix. Consequently, the pore pressure variation data, in the form of digitized input, was fed into the FE simulator as an increase in effective stress on the reservoir elements. For those time intervals where the pore pressure variation does not exist, linear interpolation is used.

The geometry of the problem was considered axisymmetric. Overburden was assumed to be a homogeneous, linear-elastic material. It was found that the subsidence, subsidence rates, and subsidence bowl profiles predicted by this model were in good agreement with the measurements until the year 1986, to which the pore pressure depletion data was available.

3D numerical simulation by Phillips group Chin and Boade (1990) developed a 3D finite-element (FE) subsidence model

for simulating the reservoir compaction processes that are in progress at the Ekofisk field. The finite-element mesh, as well as other aspects of the computational model, were designed to make it possible to realistically account for the shape and porosity distribution of the reservoir along with the dependence of reservoir pressure on position and time. The finite-element geomechanics code, DYNAFLOW, which was used in previous 2D idealization models (Boade et al., 1989), was again used for the 3D model.

The FE mesh for the entire 3D model consisting of the reservoir and the surroundings contained 12,844 eight-noded, six-sided elements. Nineteen layers of elements were used, nine passing through the reservoir, eight through the overburden, and two through the underburden. Figure 8-29 shows the FE mesh used in the analysis. The lateral configurations of the modeled zone are shown in Figs. 8-30 and 8-31, the latter showing the positions of most of the wells that were drilled into the reservoir since the early seventies.

The input data for porosity and thickness of various layers was deduced from the logs of 57 wells drilled in that area. Information from the maps was used to develop the structural model for the FE mesh of the field including the reservoir, i.e., to


Fig. 8-29. Finite element mesh for the full-field 3D model. (After Chin and Boade, 1990, fig. 7; courtesy of Joint Chalk Research Program.)

Fig. 8-30. The lateral configuration of the modeled regime for the Ekofisk field. (After Chin and Boade, 1990, fig. 5; courtesy of Joint Chalk Research Program.)


Fig. 8-31. The lateral model grid for the reservoir section overlaid on well layout. (After Chin and Boade, 1990, fig. 6; courtesy of Joint Chalk Research Program.)


prepare the data for porosity and dimensions for each element of the mesh. The reservoir pressure input data for different zones in the field was obtained from a fully implicit 3D reservoir performance simulator. A total of 648 separate pressure- time curves were used in the simulation task.

General conclusions reached by Phillips Group through early evaluations of the model are that major physical processes are treated properly by this model. For cases where comparisons have been made, agreement between field measurements and calculations were reported to be good. Later it was discovered that the field values are higher than the calculated ones. Based on the new data relating to the in-situ stress measurements reported by Teufel et al. (1990), it was concluded that the chalk is experiencing large deviatoric stresses leading to shear-induced compaction. Consequently, the constitutive model employed in the 3D FE simulator was further modified to account for this phenomenon (Chin et al., 1993). This exercise represents the latest and most comprehensive of the efforts reported so far relating to the problem of Ekofisk field subsidence.

Critical envelopes were introduced by Chin et al. (1993) in the 3D effective stress space in the constitutive model to activate the shear-induced compaction. When stress conditions in an element of the mesh reaches the critical envelope, a discontinuous transition from the original pore-collapse compaction stress-strain curve for the material in the element to another stress-strain curve that is representative of a weaker material was implemented. The shift towards the weaker curve is based on the assumption that shear-induced compaction leads to the creation of localized zones of stress concentrations. Figure 8-32 shows the subsidence prediction for the point that lies at the 'center' of the simulated section, where the field measurements were recorded. The figure shows the predictions for the two runs, each with a different value of cohesion, and the field data. Comparison between the predicted and calculated subsidence rates for the same point is presented in Fig. 8-33.

Fig. 8-32. Comparison of measured and calculated subsidence. (Chin et al., 1993, fig. 1; courtesy of Geological Engineering Program, University of Wisconsin.)


80

70 L

60 E u 50

I , I

w 3 0

z w 2o a i/1 m 10

m 0

I I I I I I I II'

-10 1970 1975 19 0

, Average subsidence rate deduced _ f rom the fietd measurements

_E7_ Computed results (Runs 37 and 40 Averaged)

Bases of Calculations: ~ _ Field HistorylPremised Future

i I , 1 I I , , , I

1985 1 9 9 0 1 9 9 5 2000 2005 2010 2015 TIME (year)

Fig. 8-33. Comparison of measured and calculated subsidence rates. (Chin et al., 1993, fig. 2; courtesy of Geological Engineering Program, University of Wisconsin.)

IMPACT OF COMPACTION ON RESERVOIR P E R F O R M A N C E

The impact of reservoir compaction on the operation and maintenance of the field has been both positive and negative. The compaction has resulted in increased recovery. On the other hand, it led to the subsidence of the platforms. Casing deformations have also been encountered in the field.

Increased recovery

The Ekofisk reservoir compaction and the resulting sea floor subsidence necessitated the raising of Ekofisk complex, at a cost of around one billion dollars. Simultaneously, the compaction drive made a significant contribution to the recovery of hydrocarbons from Ekofisk. To quantify the compaction effect, the reservoir and subsidence models were coupled to accurately describe rock compressibility in the Ekofisk field as a function of porosity, rock type, reservoir pressure, as well as areal and vertical location using a three-dimensional reservoir simulator and a three-dimensional (3D) finite element (FE) model (Sulak et al., 1989). The reservoir compaction and the associated subsidence was simulated with a FE geomechanics model DYNAFLOW (Boade et al., 1988).

One of the main factors affecting the compaction drive is the formation of 'arch' in the overburden. As the reservoir depletes, some of the overburden load that was supported by the pore fluids is transferred to the reservoir rock matrix. The remainder is transferred to the sideburden, the amount of which depends upon the rigidity of the overburden. In the case of zero rigidity of the overburden, no load transfer to the sideburden takes place and the load is taken fully by the reservoir matrix; whereas the opposite is true for the case of infinitely rigid overburden. The lateral transfer of the load has been termed the 'arch effect' (Chin and Boade, 1990).


Fig. 8-34. Depletion production profiles for the Ekofisk field with and without compaction drive. (After Sulak et al., 1989, fig. 19; courtesy of Society of Petroleum Engineers.)

Pore pressure values as a function of time and space were used as an input data for the compaction-subsidence FE computations. The results from the FE simulator determine the influence of arch effect. The arch effect as a function of time and position was then accounted for in the reservoir simulator. The result of the coupled simulation is shown in Fig. 8-34. The depletion profile without the compaction is represented by the bottom curve. The top curve represents the depletion profile with reservoir compaction taken into account. Reservoir compaction has increased the recovery to 243 million barrels of oil equivalents until the year 2011 (Sulak et al., 1989).

To increase the production, enhanced oil recovery projects have been implemented at the Ekofisk to supplement the natural mechanisms of reservoir depletion. Sulak et al. (1989) quantified the effect of the recovery projects including those carried out in the past and those planned for the future (Fig. 8-35).

Porosity reduction

The permeability in the reservoir rock is generally related to porosity. Reduction in porosity may there lead to reduced permeability. Matrix permeability is controlled mainly by the size of small pores and the pore throats. Laboratory tests did not show any significant decrease in permeability due to compaction. Compaction of the predominantly large pores perhaps had resulted in the absence of variation in the permeability (Sulak and Danielsen, 1989). The stress conditions in the field also are conducive to shear failures leading to fracturing of the matrix further. Consequently, significant changes in the productivity at the Ekofisk have not been observed and are not expected in the near future, too (Sulak and Danielsen, 1989).


Fig. 8-35. Ekofisk field production profiles showing contributions of enhanced recovery projects. (After Sulak et al., 1989, fig. 20; courtesy of Society of Petroleum Engineers.)

Casing deformation

Numerous casing deformations have been reported in the Ekofisk field. Majority of these deformations occurred in the reservoir segment with a fewer number of cases in the overburden close the reservoir. The operation and production is not expected to alter because of the casing deformations in the reservoir. But in the overburden, it may lead to tubing leaks and breakage (Yudovich et al., 1989).

Overburden compaction

A pressure gradient exists from the region just above the reservoir into the reservoir, which may lead to the compaction in the overburden. But the permeability of the overburden rock is extremely small, in the microdarcy or nanodarcy range, in spite of its relatively high porosity (about 20% to 30%). Depletion from overburden would require extensive fracture system which is not present. Overburden compaction, therefore, is not probable. Field data from compaction monitoring using radioactive markers also do not indicate any significant overburden compaction (Menghini, 1989; Sulak and Danielsen, 1989).

REFERENCES

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Abdulraheem, A., Zaman, M. and Roegiers, J.-C., 1994. A FE model for Ekofisk Field subsidence. J. Pet. Sci. Eng., 10(4): 299-310.


Addis, M.A., 1987. Material metastability in weakly cemented sedimentary rocks. Mem. Geol. Soc. China, 9:495-512.

Addis, M.A., 1989. The behavior and modeling of weak rocks. In: V. Maury and D. Fourmaintraux (Editors), Rocks at Great Depths. Balkema, Rotterdam, pp. 899-905.

Addis, M.A. and Jones, M.E., 1990. Mechanical behavior and strain rate dependence of high porosity chalk. In: T. Telford (Editor), Mechanical Properties of Chalk, Paper 17. London, pp. 239-244.

Andersen, T., Berg, M. Sorum, M. and Kanani, K., 1987. Ekofisk Jacking Operation m Total Risk and Reliability Analysis. Veritec Report, Oslo, Norway, April.

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Brace, W.T., Paulding, B.W. Jr. and Scholz, C., 1966. Dilatancy in the fracture of crystalline rocks. J. Geophys. Res., 71: 3939-3954.

Chin, L.Y. and Boade, R.R., 1990. Full-field, 3D, finite-element subsidence model for Ekofisk. A Paper Presented at the Third North Sea Chalk Symposium, Copenhagen, Denmark, June 11-12, 40 pp.

Chin, L.Y., Boade, R., Prevost, J. and Landa, G., 1993. Numerical simulation of shear-induced compaction in the Ekofisk reservoir. In: B. Haimson (Editor), Proceedings, 34th US. Symposium on Rock Mechanics, pp. 367-370.

Christensen, S.O., Janbu, N. and Jones, M.E., 1989. Subsidence due to oil-gas production. Erdoel Kohle-Erdgas, May: 185-189.

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June. Hamilton, J.M. and Shafer, J.L., 1991. Measurement of Pore Compressibility Characteristics in Rock

Exhibiting 'Pore Collapse' and Volumetric Creep. Society Core Analysts Conference, Pap. 9124, Dallas, Texas, Aug., 14 pp.

Hobley, M. and Davies, R.L., 1988. Ekofisk Jacking Project, 'The Working Parts,' Jacks, Hydraulic Systems and Controls. Paper OTC 5653 presented at the 1988 Offshore Technological Conference, Houston, Texas, May 2-5, 21 pp.

Johnson, J.P and Rhett, D.W., 1986. Compaction Behavior of Ekofisk Chalk as a Function of Stress. SPE Paper, 15872, SPE European Petroleum Conference, October 20-22, London, pp. 221-231.

Johnson, J.P., Rhett, D.W. and Siemers, W.T., 1989. Rock mechanics of the Ekofisk reservoir in the evaluation of subsidence. J. Pet. Technol., 41(7): 717-722.

Jones, M.E., 1988. Determination of the Mechanical Properties of Reservoir Rocks Using the Triaxial Test: Experimental Guidelines. Norw. Pet. Dir., YA-524, Stavangar, Norway.

Jones, M.E., Leddra, M.J. and Addis, M.A., 1987. Reservoir Compaction and Sea Floor Subsidence Due to Hydrocarbon Extraction. Offshore Technology Report, OTH 87 276, HMSO, London.

Jones, M.E., Leddra, M.J., Goldsmith, A., Berget, O.P. and Tappel, I., 1989. The geotechnical characteristics of weak North Sea reservoir rocks. In: A.T. Buller, E. Berg, O. Hjelmeland, J. Kleppe, O. Torsaeter and J.O. Aasen (Editors), Proceedings, 2nd North Sea Oil and Gas Reservoirs Conference. Kluwer Academic Publishers, pp. 201-211.

Jones, M.E., Leddra, M.J. and Potts, D., 1989. Ground motions due to hydrocarbon production from the chalk. In: T. Telford (Editor), International Chalk Symposium, Preprint No. 59, London, September, pp. 341-347.

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Keighin, C.W. and Sampath, K., 1982. Evaluation of pore geometry of some low-permeability sandstones Uinta Basin. J. Pet. Technol., 34(7): 65-70.

Kvendseth, S.S., 1988. Giant Discovery: A History of Ekofisk Through the First 20 Years. Phillips Petroleum Co., Norway, 224 pp.

Larsen G. and Chilingar, G.V., 1983. Diagenesis in Sediments and Sedimentary Rocks, 2. Developments in Sedimentology 25B. Elsevier, Amsterdam, 572 pp.

Maxwell, J.C. and Verall, P., 1954. Low porosity may limit oil in deep sands. World Oil, 138(5): 106-113. Maxwell, J.C., 1964. Influence of depth, temperature and geologic age on porosity of quartzose

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Appendix A

425

SIMULATION OF COMPACTION DUE TO FLUID WITHDRAWAL 1

ERLE C. DONALDSON

INTRODUCTION

Surface subsidence due to fluid withdrawal has become a severe environmental problem in many locations around the world; therefore, the U.S. Department of Energy (DOE) and the Ministry of Energy and Mines of the Republic of Venezuela held a joint forum on subsidence in November 1982 (Donaldson and van Domselaar, 1983). The objectives of the forum were to develop a better understanding of subsurface reservoir compaction and surface subsidence due to fluid withdrawal and to develop areas of research that could lead to abatement of the problem.

Compaction of subsurface formations leading to subsidence is a process of reservoir volume reduction, which is most severe in unconsolidated sediments when the reservoir fluid pressure is allowed to decline. If pressure maintenance is practiced in oil reservoir by water injection, large-scale compaction can be avoided and stability of the reservoir can be maintained. If the oil viscosity is very high, local compaction at production wells cannot be avoided by fluid injection into adjacent wells; however, fluid injection will aid in stabilizing the reservoir.

NUMERICAL MODEL

Pressure computation

If the overburden pressure, Pob, of a compactible subsurface sand is supported by the grain-to-grain pressure, Pg, of the sand and the reservoir fluid pressure, P, the overburden pressure is equal to the total reservoir pressure plus the grain-to-grain pressure and a static condition exists at the boundary (Fig. A-l). If the reservoir fluid pressure is reduced, compaction of the sand grains will occur, accompanied by reduction of porosity and permeability in the compacting zone. Assuming that the overburden and sand grain pressures remain constant, the pressure decline in the reservoir due to fluid withdrawal may be modeled as follows:

gx lZgX + -~y \ lzgy + Qi,j = Ce~h g---i-

1 Published with permission of the Engineering Foundation, 345 E 47th St., New York. In: Proc. Eng. Found. Internat. Conf. Compressibility Phenomena in Subsidence. Henniker, New Hampshire, July 29-August 3, 1984, pp. 441-462.

426 E.C. DONALDSON

Fig. A-1. Equilibrium of pressures at the boundary between the overburden formations and the fluid-producing reservoir.

Porosity, q~, is defined as the ratio of the pore volume to the bulk volume, Vb (total rock volume): Vp/(Vs + Vp). The elemental decrease due to compaction (decrease of reservoir thickness) is represented as:

q~ n+l r j A X �9 A Y . h i , j - A S . A Y . A h i , j ~)in, j h i , j - A h i , j (A-2 )

i , j "- A X . A Y . h i , j - - h i , j

Darcy's law is incorporated in Eq. A-1 to model the horizontal viscous flow of the reservoir fluid to the well and the effect of gravity on fluid flow is neglected. Isothermal compressibility of the fluid, Cf, is assumed and is defined by:

- 1 ( d V ) (A-3)

Application of Eq. A-1 to fluid withdrawal has been discussed by numerous authors and are summarized by Raghavan and Miller (1975). The two-dimensional analysis with the formation thickness, h, entered individually at grid nodes provides the third dimension in a finite difference solution. Equation A-1 offers considerable utility for the estimation of formation compaction using readily obtainable reservoir data. When time-dependent in-situ stress and strain data are available, a more precise predictive model can be prepared.

The numerical method used to solve the partial differential equation involves replacement of the derivatives by finite differences to develop a difference equation, which is solved to obtain the pressure distribution in the reservoir. A square integration network was used as the network for the differential equations. A difference equation analog for Eq. A-1 at a typical grid intersection (i, j ) for a square mesh network (AX = AY) is:


(kh) i+l /2 , . j (P i+l , . j - e i , . j ) - ( k h ) i - 1 / 2 , j ( P i , j - P i - l , j )

%- (kh) i , . j+ l /2 (e i , . j+ l - ei, . j) - ( k h ) i , . j - 1 / 2 ( e i , j - e i , . j -1) -at- Qi , j

a a X 2 p n + l _ pn. -- Cf~lJ'hi, .J ( i , j t,.1)

(A-4)

The rate term, Qi,j, allows the location of injection (+Qi,j) or production (-Qi,.j) wells at grid intersections of the grid network. The upstream average values of the transmissibility coefficient (kh) are calculated at the mid-intervals between the i and i + 1, and j and j + 1 grid nodes.

The grid network is used to define the physical properties of the reservoir by superimposing the grid on an isopach map with isopermeability lines drawn on the map when these data are available, or can be estimated, from core and log analyses. Values of the transmissibility and the locations of wells are then assigned at appropriate grid intersections. The reservoir boundaries which are closed to the flow of fluids (faults, pinch-outs, etc.) are simulated in the network by assigning zero transmissibility at the appropriate points along the border and outside of the reservoir boundary (Fig. A-2). Water influx across any known portion of the boundary can be simulated by placing injection wells at the grid nodes that apply and assigning appropriate flow rates.

Moving the known quantities (time increment n) to the right-hand side and writ- ing Eq. A-4 for the central nodes where: (kh)i+l,j, (kh)i-l,j, (kh)i,j+l, (kh)i,j-1 and Cfc/blzhi,j(AX)Z/At are represented by IP, IM, JP, JP, JM and F, respectively,

Fig. A-2. Integration network superimposed on an isopach map with isopermeability lines. Zero transmissibility assigned to nodes with open circles.

428 E.c. DONALDSON

the generalized equation for any row and node emerges as:

[ I M . P i - l , j - A L . Pi,j -t- I P . Pi+l,j] n+l

= [ ( 1 - w ) ( I M . Pi-l,j -Jr- I F . Pi+l,j -}- A L . Pi,j) (A-5)

- w ( J M . pn+l i,j-1 + J P" Pi,j+l -k- y " Pi,j + a i , j ) ] n

where: A L = I P + I M + J P + J M + y and w = iteration acceleration parameter in the tridiagonal matrix call (1 < w < 2). When w = 1, the equation becomes a Gauss-Seidel solution of the matrix.

Referring to Fig. A-2, Pi,j = 0 for all boundary nodes; the objective of the model is to evaluate the potential function, Pi,j, for all elements within the null boundaries. With these conditions the problem is solved by successive line overrelaxation which is an implicit method by which a line of components of p.n. ~,.I are defined simultaneously in such an interrelated manner that it is necessary to solve a linear sub-system of the whole set of components at once before a single one can be determined. That is, the equation is solved implicitly for each row, sweeping down the columns in a row-by-row fashion. The equation is written for each point within the boundaries of Fig. A-2 to create the set of simultaneous algebraic equations which is solved as tridiagonal subsets by Gaussian elimination (subroutine TRIDAG). The main program (COMPAC) and subroutine are listed at the end of this appendix.

Compac t ion computat ion

Referring to Fig. A-l, when the overburden pressure becomes greater than the total rock pressure due to fluid withdrawal, the grains in the region re-position with loss of volume to adjust the total reservoir pressure to the overburden pressure. This compaction results principally in a reduction of reservoir thickness with an accompanying decrease of porosity and permeability. Thus the compaction is principally a vertical loss of reservoir thickness and in program COMPAC the assumption that there is no horizontal movement is made. The procedure proposed by Geertsma (1973) is used, where the formation compaction is a function of the vertical strain only:

h = Cm(z)" AP(z ) . dz (A-6)

The decrease of porosity of the compacting zone is the change in total reservoir volume and is calculated at each node. The empirical relationship between porosity and permeability (Fig. A-3) was obtained from compaction data (porosity and permeability change as functions of increasing pressure) presented in a final report to the Department of Energy on unconsolidated sands of the Wilmington oilfield in California (Staub, 1983). An average curve of the data represented by Eq. A-7 was used:

k = 2.0 • 10 0"07r (A-7)


I o , o o o

5,000 I

I I I I I I I I 1 1 I I I I I 1 1 I I I 1 I 0 4 8 12 16 20 24 28 52 56 40 44

POROSITY Fig. A-3. Permeability-porosity relationship of the HX sand from the Wilmington oilfield, California.

Similar porosity-permeability relationships for numerous sands are discussed by Chilingarian et al. (1975).

Computation procedure

The computation procedure can be subdivided into two major divisions: (1) implicit calculation of the distribution of reservoir pressure decline as a function of the fluid injection-production rates and fluid expansion in the reservoir, and (2) explicit calculation of the change in reservoir thickness at each node of the grid network and the resulting changes of porosity and permeability. Figure A-4 is a simplified flow diagram of the computation procedure. The amount of printing is controlled by entering a specific amount of compaction that must occur before results are printed. A second test is incorporated to stop the program run when the total amount of compaction at the wellbore of the production well reaches some desired amount (CODE).

Discussion

Development of the model is based on the following principles: (1) The porous medium is elastic. (2) The porous medium may be heterogeneous with respect to porosity, perme-

ability and reservoir thickness; these are entered as initial values at the nodes of the grid network.

(3) The fluid in the reservoir is compressible. It may be treated as an incom-

430 E.C. DONALDSON

INITIALIZE DATA FILE CO.DAT RUN PARAMETERS

INITIAL RESERVOIR CONDITIONS

J I '-], RESET ITERATION LIMITS TO ZERO

I

I RESERVOIR PRESSURE CALCULATION ( LINE SUCCESSIVE OVERRELAXATION

CALL SUBROUTINE TRIDAG )

]

E < EMAX ~

+ EXPLICIT CALCULATION OF CHANGE

IN RESERVOIR THICKNESS, POROSITY AND PERMEABILITY

]

COMPACTION BEFORE PRINTING H _> COMP . , /

J

I TEST FOR TOTAL

J ALLOWABLE COMPACTION H _> CODE

Fig. A-4. Flow diagram of the calculation procedure of computer program COMPAC.

pressible fluid by entering zero for the coefficient of fluid expansion (Cf); if the assumption of fluid incompressibility is made, the fluid produced must equal the fluid injected.

(4) The fluid flow properties obey Darcy's law. (5) Gravity forces are neglected; this means that fluid pressure gradients due to

changes in reservoir thickness and inclination are neglected. (6) Horizontal stress is negligible; hence, no change occurs in the horizontal

dimension of the reservoir.


(7) The permeability decrease is a function of the porosity decrease. (8) No-flow boundaries are represented by zero permeability at the grid nodes

that apply. (9) Water influx at boundaries is represented by injection wells; rates may be

variable if desired. (10) Compaction is due to increase of the effective grain-to-grain stress resulting

from reservoir pressure decline accompanying fluid withdrawal. (11) Compaction and rebound are assumed to be completely reversible; if re-

bound is to be studied using COMPAC the program must be modified to incorporate a coefficient of reservoir expansion where applicable.

(12) It is assumed that horizontal flow of a compressible fluid is taking place toward a well, or wells, located in a reservoir which is undergoing compaction due to fluid withdrawal.

(13) The change in thickness of the reservoir is accounted for through calculations using the compressibility of the reservoir rock.

(14) A second-order, nonlinear, partial differential equation is used for a system in which reservoir porosity and permeability are treated as functions of pressure.

Compaction of a reservoir is a very complex phenomenon which involves horizontal as well as vertical stress, the integrity of over- and underlying formations, compressibilities of these formations, etc. The simultaneous influences of most of these effects on compaction cannot be analyzed because the state-of-the-art of in- situ determination of the required parameters is still in its infancy. Compaction due to fluid withdrawal is the result of pressure decline within the reservoir, which leads to a reduction of reservoir thickness, porosity and permeability. Since the lateral dimensions of commercially important reservoirs are usually quite large, the horizontal movements can be ignored without loss of great accuracy. With this assumption, the problem is simplified and an estimate of the degree of compaction that will occur in a specific reservoir can be obtained using a program such as COMPAC, which employs only data that are readily obtained from laboratory measurements of formation and fluid samples. The uniaxial coefficient of compaction, coefficient of fluid expansion, fluid viscosity, reservoir pressure, porosity, and the relationship between porosity and permeability are readily obtained from laboratory data. Figure A-5 shows the results of analysis of the influence of viscosity for a single 500-barrel per day production well after five years of production.

Expansion of the reservoir due to fluid injection, or rebound of a compacted zone, is not a totally reversible process. The coefficient of reservoir expansion is generally smaller than the coefficient of compaction as discussed by Espinoza (1983). This difference can be incorporated in the model by using two coefficients for the change of reservoir thickness with respect to pressure in Eq. A-6; it is not incorporated in the listed program.

The program can be used to analyze the effects of fluid viscosity, reservoir thickness, rates of production and injection, the extent of compaction as a function of time, effects of compressibility, etc. Such analyses of a productive zone, especially one which is environmentally sensitive, can be used to make decisions with respect to production, pressure maintenance, and general field management.

432 Ec. DONAU~SON

z I.O ~ ____

~ .9 o c, , I , I , I , I , I

>_ 1.0 ~ . . ..=...= ...=-=- - - - - - - . . . . .

m o a:: .9 o 11. , [ , I I , I , I

1.0--

> -

3 . 9 - 133 <[ LIJ

.8 LIJ 13E Q.

.7

/ - /

/ /

I

/ / / I f l

- - F l u i d viscosity = I0 CP - - - - F l u i d viscosity =IOOCP

I , I , l , I , I 0 200 400 600 800 I000

Fig. A-5. Inf luence of fluid viscosity on compact ion , porosi ty and permeabi l i ty . Dis tance in feet f rom

the well is p lo t t ed on the abscissa.

Fluids may be injected into the reservoir or allowed to enter from the boundaries. Fluid drive results from pressure draw-down due to pumping and compaction pressure maintenance.

Using readily obtained laboratory data of porosity, permeability and compressibility; and as much specific reservoir heterogeneity as can be deduced from cores, well-logs, and geologic correlations, one can use this simple model to obtain engineering estimates of the anticipated degree and rate of compaction as well as its areal extent, all of which are directly related to the fluid input/withdrawal rates.

The analysis is extended to a 3-dimensional system by obtaining the pressure distributions in the reservoir for the two horizontal space dimensions and introducing the thickness as a pressure-dependent quantity. The pressure distribution is calculated implicitly, and the changes of porosity, permeability and thickness are calculated explicitly for each not of the grid pattern.

If data on lateral strain are available, these as well as other influences, may be incorporated by addition at appropriate entry points in the program. Thus, this model affords a practical, quantitative, picture of a compacting reservoir and a basis for refinement of accuracy.


Cf - coefficient of fluid expansion, psi -1

Cm = coefficient of uniaxial rock compress ion, psi -1

h - reservoi r thickness, ft


k = permeabil i ty , darcy n = t ime step increment P = pressure, fluid pressure, psi Pg = sand grain-to-grain pressure

Pob -- overburden pressure Q = injection or product ion well rates, barrels per day

t - time, days

V = volume, cubic feet

Vp = pore volume

Vs = volume of solids /x = viscosity, centipoises

~b = porosi ty

C O M P A C : R E S E R V O I R C O M P A C T I O N D U E T O F L U I D W I T H D R A W A L

COMPAC

RESERVOIR COMPACTION DUE TO FLUID WITHDRAWAL

SUBROUTINE TRIDAG IS USED WITH THIS PROGRAM

INPUT DATA IS PLACED IN A DATA FILE NAMED CO.DAT

M : NUMBER OF GRID BLOCKS

KMAX = NUMBER OF ITERATIONS ALLOWED ON P (I)

KWELL = NUMBER OF PRODUCTION WELLS

INJECT = NUMBER OF INJECTION WELLS

COMP : AMOUNT OF COMPACTION (FEET) AT PRODUCTION WELL WHICH IS

DESIRED BEFORE OUTPUT (PRINTING)

CODE : TOTAL AMOUNT OF COMPACTION (FEET) DESIRED BEFORE

STOPPING THE RUN

EMAX = DEGREE OF PRECISION BETWEEN ITERATION OF P(I)

W : ITERATION PARAMETER (0 < W < 2)

DX : GRID SPACING (FEET)

DT : TIME INCREMENT (DAYS)

CF : EFFECTIVE FLUID COMPRESSIBILITY (I/PSI)

CM : UNIAXIAL RESERVOIR COMPRESSIBILITY (I/PSI)

QI : INJECTION RATE (BBL/DAY)

QP : PRODUCTION RATE (BBL/DAY)

HORG : ORIGINAL FORMATION THICKNESS (FEET)

PORG : ORIGINAL RESERVOIR PRESSURE (PSI)

PHIORG = ORIGINAL RESERVOIR POROSITY

XMU : RESERVOIR FLUID VISCOSITY (CP)

INJECTION AND PRODUCTION WELL RATES AND THEIR LOCATIONS IN THE GRID

NEq]~ORK MUST BE ENTERED WHEN CALLED FOR BY THE PROGRAM; SEE

THE PROGRAM LISTING BELOW

REAL IP, IM, JP, JM

DIMENSION Q(50,50), P(50,50), PNEW(50,50), CAP(50,50)

DIMENSION PERM(50,50), PHI(50,50), H(50,50), E(50,50)

DIMENSION DELP(50,50), DELH(50,50), QI(25), QP(25), BOUT(25)

434 E.C. DONALDSON

233

234

200

C

C

201

DIMENSION A(50), B(50), C(50), D(50), TEMP(50), AP(25), BP(25)

DIMENSION PRD(50,50), HRD(50,50), PHIRD(50,50) PERMRD(50,50)

COMMON M

NX- 50

TIME : 0.

FAC = 0.

CALL ASSIGN (i, 'CO.DAT')

JET : 1

READ(I,*) M, KMAX, KWELL, INJECT

READ(I,*) COMP, CODE, EMAX, W, DX, DT, CF

READ(l,*) HORG, PORG, XMU, PHIORG, CM

IF(INJECT .EQ. 0) GO TO 233

TYPE 982

READ(5,*) (QI(IR), IR:I,INJECT)

TYPE 984

READ(S,*) (QP(IS), IS=I,KWELL)

TYPE 904


TYPE 986

JET : INJECT

TYPE 987, (QI(IR), IR=I,JET)

TYPE 904

TYPE 988

TYPE 989, (QP(IS), IS:I,KWELL)

TYPE 920, M, KMAX, KWELL, INJECT

TYPE 922, COMP, CODE, EMAX, W, DX

TYPE 924, HORG, PORG, XMU, PHIORG, CM

DO2 I= I,M

DO 2 J : I,M

Q(I,J) = 0.

PNEW(I,J) : 0.

CAP(I,J) : 0.

CONTINUE

SET IX3CATIONS OF INJECTION WELLS


JET = INJECT

DO 200 IR = 1,JET

TYPE *, 'ENTER INJECTION WELL I,J VALUES'

READ(5,*) I,J

Q(I,J) : QI(IR)

CONTINUE

SET LOCATIONS OF PRODUCTION WELLS

DO 220 IS = I,KWELL

TYPE *, ' ENTER PRODUCTION WELL I, J VALUES'

READ(5,*) I,J

Q(I,J) = -QP(IS)


220

C

ii

C

AP(IS) = FLOAT(1)

BP ( I S ) = FLOAT (J)

CONTINUE

DO4 I : I,M

DO4 J: I,M

PHI(I,J) : PHIORG

PERM(I,J) : (2.0 * 10** (7 . *PHI (I , J) ) ) /1000 .

H(I,J) : HORG

CAP(I,J) : PERM(I,J) * H(I,J)/XMU*I.127

m(m,J) = PORG

PNE~(I,J) : PORG

CONTINUE

PERMI : PERM (2,2)

ITE : 0

K: 0

TIME : TIME + DT

ITE : ITE + i

K:K+ 1

KOK : 0

KNG: 0

DO ii J = 2,M-I

DO 9 I = 2,M-I

IP = (CAP(I,J) + CAP(I+I,J))/2.

IM = (CAP(I,J) + CAP(I-I,J))/2.

JP : (CAP(I,J) + CAP(I,J+I))/2.

JM = (CAP(I,J) + CAP(I,J-I))/2.

CMM : (CF*PHI (I,J) *DX*DX)/DT

AL = -IP-IM-JP-JM-CMM

A(I) = IM

B(I) = AL

C (I) = IP

D(I) : (I.-W)*(IM*P(I-I,J)+IP*(P(I+I,J)+AL*P(I,J)) -

IW* (JM*PNEW(I, J-l) +JP*P (I, J+l) +CMM*P (I, J) +Q (I, J) )

CONTINUE

D(2) = D(2) - A(2)*P(I,J)

D(M-I) = D(M-I) - C(M-I)*P(M-I,J)

CALL TRIDAG (A, B, C, D, TE~IP, NX)

DO ii I : 2,M-I

PNE~(I,J) : TEMP(I)

E(I,J) = ABS(PNEW(I,J) - m(I,J))

CONTINUE

DO 16 I : 2,M-I

DO 16 J : 2, M-I

IF(E(I,J) .LT. EMAX) GO TO 12

KNG: 2

GO TO 14

436 E.C. DONALDSON

12

14

16

C

17

32

C

20

26

C

28

C

30

C

53

C

KOK = i

P(I,J) = PNEW(I,J)

CONTINUE

IF(KNG .LT. KOK) GO TO 20

IF(K .LT. KMAX) GO TO 8

TYPE 900, W,K

DO 17 I = 2,M-I,5

TYPE 902, (E, (I,J), J : 2,M-I,5)

TYPE 904

DO 32 I : 2,M-I,5

TYPE 906, (P(I,J), J : 2,M-I,5)

DO 26 I = 2,M-I

DO 26 J = 2,M-I

DELP(I,J) = PORG- P(I,J)

DELH(I,J) = CM*DELP(I,J)*H(I,J)

PHI(I,J) = PHI(I,J)*(H(I,J) - DELH(I,J))/H(I,J)

H(I,J) = H(I,J) - DELH(I,J)

PERM(I,J) : (2. * 10.**(7.*PHI(I,J)))/1000.

CAP(I,J) = PERM(I,J)*H(I,J)/(XMU*I.127)

CONTINUE

DO 28 IS = I,KWELL

IX : IFIX(AP(IS))

JX : IFIX(BP(IS))

FAC = FAC + DELH(IX+I,JX)

IF(FAC .GE. COMP) GO TO 30

GOTO 7

FAC = 0.

TYPE 905

TYPE 906, (P(I,JX), I : IX, M-l)

TYPE 904

TYPE 907

TYPE 906, (H(I,JX), I : IX,M-l)

TYPE 904

TYPE 911

TYPE 908, (PHI(I,JX), I : IX, M-l) ]

TYPE 904

TYPE 912

TYPE 909, (PERM(I,JX), I : IX,M-l)

TYPE 904

DO 53 IS : i, KWELL

BOUT(IS) : QP (IS) *TIME

TYPE 915, BOUT(IS)

CONTINUE

TYPE 910, PORG, HORG, PHIORG, PERMI

TYPE 913, TIME

SIMULATION OF COMPACTION DUE TO FLUIDWITHDRAWAL 437

44

C

C

C

900

902

904

905

906

907

908

909

910

911

912

913

914

915

C

920

922

924

C

930

932

TYPE 914, XMU, K, ITE

TYPE 904

DO 44 I = IX,M-I

PRD(I,JX) = P(I,JX)/BORG

HRD(I,JX) = H(I,JX)/HORG

PHIRD (I, JX) : PHI (I, JX)/PHIORG

PERMRD(I,JX) = PERM(I,JX)/PERMI

CONTINUE

TYPE 930

TYPE 908, (PRD(I,JX), I = IX, M-I)

TYPE 904

TYPE 932

TYPE 908, (HRD(I,JX), I = IX, M-I)

TYPE 904

TYPE 934

TYPE 908, (PHIRD(I,JX), I : IX,M-I)

TYPE 904

TYPE 936

TYPE 908, (PERMRD(I,JX), I : IX,M-I)

STP : HORG - H(IX, JX)

IF(STP .GT. CODE) GO TO 40

GOTO 7

FORMAT (IX, 'NO CONVERGENCE' , 3X, 'W= ' , F4.2,3X, 'K= ' , I3)

FORMAT ( 7E8.1 )

FORMAT ( / / )

FORMAT ( IX, ' PRESSURES FROM PRODUCTION WELL TO BOUNDRY', / )

FORMAT (iX, 10El0. i)

FORMAT (iX, ' FORMATION THICKNESS FROM PROD. WELL TO BOUNDRY', / )

FORMAT (iX, 10F6.3 )

FORMAT ( IX, 10FI 0.4 )

FORMAT(IX,'P ORG. : ',F5.0,3X,'H ORG. = ',F5.0,3X,'PHI

2ORG. : ',F6.3,3X,'PERM ORIG. : ' El0.4,//)

FORMAT (iX, ' POROSITY FROM PROD. WELL TO BOUNDRY', / )

FORMAT (iX, ' PERMEABILITY (DARCIES) FROM P-WELL TO BOUN. ', / )

FORMAT ( IX, ' TIME (DAYS) = ', F8.0, / / )

FORMAT (iX, ' FLUID VISCOSITY = ', F5.0,4X, ' NO. OF ITERAT

4IONS, K = ',I3,3X,'ITERATIONS ON H (ITE) = ', I3)

FORMAT (iX, ' FLUID PRODUCED (BARRELS) = ', F9.0, / / )

FORMAT(IX,'M : ',13,' KMAX : ',13,' KWELL : ',13,' INJECT : ',13,/)

FORMAT(IX,'COMP = ',F5.2,' CODE = ' F6.2,' EMAX = ',F5.2,

1 ' W = ',F4.2,' DX = ',F3.0,' DT = ',F4.0, 'CF = ',FI0.8,/)

FORMAT(IX,' HORG = ',F4.0,' BORG = ',F4.0,

2 ' XMU : ',F7.0,' PHIORG :',F5.3,'CM = ',FI0.8,//)

FORMAT (IX, ' FRACTION OF ORIGINAL PRESSURE; P-WELL TO BOUND. ' , / )

FORMAT ( IX, ' FRACTION OF ORIGINAL RESERVOIR THICKNESS -

5PROD. WELL TO BOUNDRY',/)

4 3 8 E.C. DONALDSON

934

936

C

982

984

986

987

988

989

C

40

916

FORMAT (iX, ' FRACTION OF ORIGINAL POROSITY - PW-ELL TO BOUND. ' , / )

FORMAT (IX, ' FRACTION OF ORIGINAL PERMABILITY - P-WELL TO BOUND. ' , / )

FORMAT(IX, 'ENTER INJECTION WELL RATES (BBL/DAY)) ',/)

FORMAT (iX, ' ENTER PRODUCTION WELL RATES (BBL/DAY) ', / )

FORMAT (IX, ' INJECTION WELL RATES (BBL/DAY) ', / )

FORMAT ( IX, <INJECT>F6.0 )

FORMAT (IX, ' PRODUCTION WELL RATES (BBL/DAY) ', / )

FORMAT ( IX, <KWELL>F6.0 )

TYPE 916

FORMAT ( IX, ' END OF RUN', / / )

STOP

END

SUBROUTINE TRIDAG (A, B, C, D, V, NX)

DIMENSION A(NX),B (NX),C (NX),D(NX),V(NX), BETA(101),GAMMA(101)

COMMON M

L:M-I

IF=2

BETA(IF) : B(IF)

GAMMA(IF) = D(IF)/BETA(IF)

IFPI = IF + 1

DO 1 I = IFPI,L

BETA(I) : B(I)-A(I)*C(I-I)/BETA(I-l)

GAMMA(I) : (D(I)-A(I)*GAMMA(I-1))/BETA(I)

V(L) = GAMMA(L) LAST = L - IF

DO 2 K = 1,LAST

I =L-K

V(I) : GAMMA(I)-C(I)*V(I+I)/BETA(I)

RETURN

END

REFERENCES

Chilingarian, G.V., Wolf, K.H. and Allen, D.R., 1975. Introduction. In: G.V. Chilingarian and K.H. Wolf (Editors), Compaction of Coarse-Grained Sediments, I. Elsevier, Amsterdam, pp. 32-35.

Donaldson, E.C. and van Domselaar, H. (Editors), 1983. Subsidence Due to Fluid Withdrawal. Pro- ceedings of 1982 Joint DOE-Venezuelan Forum on Subsidence. CONF-821199. National Technical Information Service, Springfield, Va., 141 pp.

Espinoza, C.E., 1983. A new formulation for numerical simulation of compaction - - sensitivity studies for steam injection. Proc. SPE 7th Symp. Reservoir Simulation, SPE Pap., 12246: 139-144.

Geertsma, J., 1973. Land subsidence above compacting oil and gas reservoirs. J. Pet. Technol., 25(6): 734-744.

Raghavan, R. and Miller, EG., 1975. Mathematical analysis of sand compaction. In: G.V. Chilingarian and K.H. Wolf (Editors), Compaction of Coarse-Grained Sediments, I. Elsevier, Amsterdam, pp. 403-524.

Staub, H.L., 1983. Residual Oil Saturation Determination, Wilmington Micellar-Polymer Project ~ Final Report. DOE/BETC/1395-6, National Technical Information Service, Springfield, Va., 72 pp.

439

Appendix B

SURVEILLANCE TECHNOLOGY TO DETECT AND MONITOR COMPACTION AND SUBSIDENCE EFFECTS

WALTER FERTL, G E O R G E V. CHILINGARIAN and ERLE C. DONALDSON

INTRODUCTION

Several surveillance techniques are available to detect and monitor compaction and subsidence effects. These techniques include analytical modeling, laboratory tests on rock samples, surface surveillance techniques to quantify subsidence, casing deformation evaluation, and subsurface, in-situ compaction monitoring based on geophysical wireline techniques.

MODELING

A method to determine subsidence, compaction, and in-situ stress induced by pore pressure change, applicable for reservoirs whose Young's modulus is less than 20% or greater than 150% of the Young's modulus of the surrounding formation has been described by Morita et al. (1988). A parameter study was conducted to find groups of parameters controlling the in-situ stress, subsidence and compaction. These parameter groups were used to analyze the numerical calculation results generated by a 3-D non-linear, finite element model. This work clearly indicated that the Geertsma's model based upon no mudulus contrast between cap and reservoir rocks needs to be corrected in order to more closely describe (i.e., simulate) realistic reservoir conditions, which generally exhibit distinct property differences between cap rocks and reservoir formations. For example, highly porous and high-pressure North Sea reservoirs and tight sand formations surrounded by soft shales frequently fall into this category.

Numerical simulation of the reservoir compaction and subsidence processes at the Ekofisk oil field in the Norwegian sector of the North Sea has provided considerable background information about the phenomena involved, not just for Ekofisk but also about other fields which underwent similar deformation. Calculated estimates for subsidence, subsidence rate, and for subsidence bowl profiles were found to be in generally good agreement with recent measurements. This agreement in the past-history match lends confidence to predictions for future subsidence behavior. For example, by the year 2011, the subsidence at the center of the subsidence bowl is expected to be about 20 ft (6.1 m) if a depletion-type reservoir management scenario is followed (Boade et al., 1988).

440 w. FERTL, G.V. CHILINGARIAN AND E.C. DONALDSON

CORE TESTS

For simulators to realistically predict the amount of compaction and surface subsidence that will occur over the life of a field, there must be a sufficient quantitative information to describe the compaction behavior of all rock types present within a reservoir for all conditions encountered. In other words, test conditions simulate the stress, temperature, and fluid saturations.

The types of laboratory compaction tests include both the uniaxial strain test and the hydrostatic test (Johnson et al., 1988). In the hydrostatic test method, the axial and radial stresses are equal, and the core samples will deform in each direction in response to the applied stress. However, the type of laboratory compaction test, which most closely simulates the compaction behavior for most reservoir rocks, is the uniaxial strain test. In this test, the axial stress on the cylindrical rock sample is increased and the radial stress is adjusted in such a way that the radius of the core sample remains constant throughout the test. In other words, the rock samples compact axially with zero radial deformation.

Smits et al. (1986) observed that the porosity-stress compaction curves of chalk samples of a given type converge to a common path in the pore collapse region even though they may have different initial porosities. For example, there are two distinct, very well-defined intervals within the Ekofisk chalk formation, located offshore Norway, one quartz-rich and one quartz-poor, that might well be expected to exhibit different compaction characteristics, as is clearly illustrated in the mechanical behavior of the chalks from the two different zones (Fig. B-l).

40

35

0 L 0

13..

3 0 -

Lower Ekofisk Formation

and Tor Formation

Upper Ekofisk Formation

I I I I I I I I I 0 2,000 4,000 6,000 8,000

Stress (psi)

Fig. B-1. Relationship between porosity and stress for Ekofisk chalk reservoirs. (Modified after Johnson et al., 1988, p. 48, OTC 5621.)

SURVEILLANCE TECHNOLOGY TO DETECT/MONITOR COMPACTION/SUBSIDENCE EFFECTS 441

S U B S I D E N C E SURVE IL L ANC E T E C H N I Q U E S

Subsidence of Ekofisk platforms, located offshore Norway, was recognized in late 1984 (Sulak and Danielsen, 1988) and several measurement programs were initiated to determine the subsidence bowl shape as well as the subsidence history, i.e., subsidence rate, at the seabed (Rentsch and Mes, 1988). Whereas total subsidence was obtained from bathymetry and pipeline surveys as well as air-gap measurements (change of platform height with respect to mean sea level). The rate of subsidence was derived from radar water level measurements and GPS (Navastar Global Positioning System) satellite survey results.

CASING D E F O R M A T I O N EVALUATION T E C H N I Q U E S

Causes of casing failure can be many, including (1) compaction of depleted but initially overpressured, undercompacted reservoirs; (2) lateral and vertical salt movements; (3) permafrost conditions (e.g., Prudhoe Bay, Alaska); and (4) earthquakes.

It is difficult to identify the actual casing failure mechanism, because a variety of mechanical failure modes exist. The latter basically fall into two categories: (1) structural instability (Euler-type axial buckling) and (2) failure modes related to the inherent strength of the casing (e.g., collapse and axial yield). Yudovich et al. (1988) investigated casing failures at Ekofisk both in the producing formation and in the overlying intervals (with the highest concentration between 400 and 900 ft above the reservoir). Casing failures in the producing interval have no appreciable effect on well productivity, whereas casing deformation in the overlying interval typically results in a casing leak, tubing leak, or both.

Yudovich et al. (1988) developed a statistical correlation based on the near-well incremental strain and well inclination angle that can predict casing failure in the Ekofisk and can estimate future probability of casing failure for individual wells as a function of time. Table B-I summarizes the mean time prior to failure for four different sizes of non-concentric production casing/liners. Experience has shown that casing failures can be minimized through a reservoir pressure maintenance program, drilling with higher angles, and using larger diameter casing.

Inasmuch as the axial rigidity of the casing is larger than the axial rigidity of the

TABLE B-I

Mean time before failure of non-concentric production casing/liners (modified after Yudovich at al., 1988, p. 69, OTC 5623)

Casing Mean time before failure (months)

Ekofisk Eldfisk

3.5 in 9.2 lb/ft 2 - 5 in 18 lb/ft 16 28 7 in 29 lb/ft 91 52 7 in 35 lb/ft 102 -

442 W. FERTL, G.V. CHILINGARIAN AND E.C. DONALDSON

TABLE B-II

Casing collar log comparison for Ekofisk Field (modified after Yudovich et al., 1988, p. 69, OTC 5623)

Well Well Time elapsed Length change Length of angle between logs (ft) reservoir interval

(months) (ft)

2/4A-2 24 26 0 420 2/4A-5 28 24 0 363 2/4A-7 7 48 0 403 2/4A-7A 7 21 0 474 2/4A-11 28 12 + 1 574 2/4A-12 42 71 +2 438 2/4B-6 34 104 - 2 650 2/4B-18 18 79 -1 529 2/4B-21 36 41 0 616 2/4B-22 17 74 -1 581 2/4B-23 21 50 -3 447 2/4C-1 40 113 -3 449

formation, the casing string will not compress the same amount as the formation under similar loading. This means that the formation will be unloaded by the casing in a zone in the vicinity of the wellbore. The load transfer will be limited by the strength of the cement-casing bond, or cement-formation bond, whichever is weaker. Thus, the shear force along the two interfaces could cause a relative movement, or frictional slippage.

Casing Collar Logs (CCL) run in several Ekofisk wells provide indirect evidence that some slippage might have occured. Table B-II presents CCL data for twelve Ekofisk wells.

In a similar fashion, subsidence and compaction monitoring have been carried out previously in the Wilmington field, Long Beach, California (Allen, 1969) and in the Permian Rotliegendes gas reservoir at Groningen, located onshore Holland, using casing collar locators (CCL). It was, however, observed by De Loos (1973) that in the later stages of compaction when the casing shortening exceeds the maximum elastic deformation of the casing, collar movements are no longer representative of formation movement.

Caliper Logs can be used to detect deformation and to help determine casing failure mechanisms. For example, the Multi-Finger Caliper (MFC) survey uses multiple sensing arms to measure the inside radius of downhole casing. The arms make independent measurements of the internal radius, with the measurements distributed around the inner circumference of the casing. Both the maximum and minimum measured radii are recorded at the surface. The survey quantitatively assesses the degree to which the casing is internally out-of-round.

The MFC includes either 40 or 60 "feeler arms", depending upon the tool's size. During operation, the caliper tool is centralized and all of the feeler arms extend outward from the tool for contact with the inside casing wall. The caliper tool is arranged to transmit two channels of information over the wireline, namely, the


smallest measured internal radius and the largest measured internal radius. Within the caliper tool, each of the feeler arms can influence either channel of information. Consequently, the feeler arm of least extent determines the response on the channel which transmits the smallest radius. Also, the feeler arm having the greatest extent determines the response on the channel which transmits the greatest radius. The smallest and greatest measured radii are recorded at the surface.

An MFC log may be presented in two formats: (1) the left-hand trace is the recorded maximum measured radius which increases from right to left, and (2) a right-hand trace with the recorded minimum radius increasing from left to right. The traces are identified by the log heading, which also shows the scales for the measured radii. Casing collars typically cause both radii to increase and appear regularly on the traces.

A second Multi-Finger Caliper log presents both the maximum and the minimum recorded radii on the same scale, which increases from left to right. Two vertical dashed lines are plotted on the presentation; the left-hand dashed line shows the inside radius of the casing, as determined by API specifications, whereas the right- hand dashed line shows the outside radius, also from API.

The solid trace is the minimum recorded radius and the dashed trace is the maximum recorded radius. If the casing is not worn, both traces are close to the left-hand dashed line. If the casing is partially worn, the traces appear intermediate of the dashed lines. If the casing is severely worn, but "in-round", both traces appear close to the right-hand dashed line. Casing collars typically cause brief rightward projections of the maximum and minimum radii, and appear regularly on the presentation. The wireline tension is given as a right-hand trace.

IN-SITU COMPACTION M O N I T O R I N G

Compaction monitoring through casing can be achieved by several methods. For example, the compaction monitoring program at Ekofisk began with a review and analysis of neutron logging surveys (Menghini, 1988). Not only were distinctive formation characteristics from two logging runs in the same well compared to determine if any depth shift had occurred with time, but comparisons also were made between compensated neutron logs recorded in both initial and side-tracked wells. Furthermore, Ekofisk compaction data based on comparison of time-lapse pulsed neutron capture logs (PNC) to either base-compensated neutron log or pulsed neutron log is shown in Table B-III.

The potential for applying pulsed neutron capture (PNC) logging techniques as monitoring devices for the detection of overpressures and/or formation pressure depletion behind casing was first proposed and illustrated using field case examples by Fertl and Timko (1970). These authors clearly showed that ~-values in shales decrease in regular fashion with depth in normally compacted clastic sediments, whereas overpressures are flagged by divergence from their normal compaction trend to higher values (~ = macroscopic cross section from the absorption of thermal neutrons).


TABLE B-III

Cumulative Ekofisk compaction to January 1985 from convectional electric log data (modified after Menghini, 1988, p. 36, OTC 5620)

Well Comparison logs Time Ekofisk FM, TOR FM, Total (years) compaction (ft) compaction (ft) compaction (ft)

2/4A-8 07/741 and 12/84 3 10.5 5 1 6 2/4A-9 08/78 3 and 10/813 3.5 1 1 2/4A-10 10/813 and 01/84 3 2 1 1 2/4A-12 08/76 3 and 10/813 5 2 2 2/4A-13 12/731 and 08/83 3 9.6 6 6 2/4A-14 09/78 2 and 06/84 3 8 6 6 2/4B-1 10/77 3 and 12/84 3 7 3 1 4 2/4B-3/B-3A 08/74 2 and 12/812 7 5 8 2/4B-3A 12/812 and 12/843 3 4 2 6 2/4B-6 08/78 2 and 12/843 9.5 3 3 2/4B-10 08/78 3 and 09/22 3 4 4 4 2/4B-10 08/22 3 and 12/83 3 1 1 1 2/4C-3A 12/83 2 and 12/84 3 2 4 4 2/4C-8A 12/82 2 and 12/84 4 2 4 1.5 8.5 2/4C-3/C-3A 08/74 2 and 12/82 2 8 6 2 8 2/4C-9 12/74 2 and 12/843 10 4 4 8 2/4C-13 04/75 2 and 12/84 3 9.5 8 8 2/4C-14A 08/82 2 and 01/85 4 2 8 5 2/4C-14C-14A 03/782 and 08/822 7.5 8 8

1 BHCS = Borehole compensated sonic; 2 CNL = Compensated neutron log; 3 TDT = Thermal decay time; 4 NDL = Neutron detector log.

As previously summar ized by Fertl (1976), P N C logs accomplish several functions: (1) provide quant i ta t ive indication of fluid distr ibution and sa tura t ion changes over t ime in a cased reservoir; (2) have applications in fo rmat ion pressure evalua- t ion work, because the log can be run th rough the drill pipe or in cased boreho les to de tec t and evaluate pressure variations; and (3) assist in the investigation of special reservoir problems, e.g., communica t ion with and deple t ion of pay zones by wells in ad jacent fault blocks, and recharge of aquifers with oil and /o r their repressur ing f rom a nearby overpressured pay zone. Such observat ions are impor tan t in reservoir eng ineer ing and when drilling in partially p ressure -dep le ted areas.

F igure B-2 shows a useful applicat ion of P N C logs for quant i ta t ive fo rmat ion pressure evaluat ion (Fertl and Timko, 1970). Shale resistivity (Rsh) versus dep th for a well dril led in Louis iana in 1946 is shown in Fig. B-2A. All reservoir sands be low 8200 ft have been product ive for at least 25 years. This par t icular well was p roduc ing f rom the so-called Klump Series. Af ter a casing collapse below 8100 ft, the plan called for placing the well back on p roduc t ion af ter recomple t ing in the H o m e s e e k e r s 'Tk" sand at a dep th of 9060 ft by side-tracking above the casing rest r ic t ion and redrill ing to this target.

The m u d weight requ i red to safely drill this well initially in 1946 to the H o m e -

7000r 1- T

I m 0-0 0twatN.L SHALE MESS 1 9 4 1snoa1 NOPMALI r

rc---r PwEsEnr SHALE PaEss rma ISGMA CUWE~ E n m 4 m n z z

g OglUI rrm-m.) -*lCr OFF #)(MI

2 4 - 0

4, I r r r a . * v - - 81W - ss I- u I -roo I *** - .Do m* m x .uC . a. 0 - 0 3 1 l rd2 IDlglI 4 m I . o U* n -=! I . c -1. 5 z

4 0

/ c - o n 0 - O W l m ¶ m w - urn DY n t - o 31 19 n ltwgrl B

9 2 2 --. 2 8

u . I ) 5 ' 3 2 o . JO 4 7 x 1 n z

m ~ U A L E ~ E S I S T I V ~ ~ V D . SICMA SHALE I, FORMATION MESSURC 'a DW 8

1.8 tm .CI 2 0 ;i

Fig. B-2. PNC log used in quantitative formation pressure evaluation. (After Fertl and Timko, 1970.) (A) Shale resistivity plot in Tepetate field well, Louisiana, drilled in 1946; (B) Sigma shale plot in a cased well based on PNC log run in 1966; (C) original shale pressure (from short normal log, 1946)

+

and depleted shale pressures (from Sigma curve, 1966). %


Fig. B-3. PNC logs run several years following the completion of a high-pressured Louisiana well, show effects of pressure depletion. (After Fertl, 1976.) The increase in E-values in the pay is due to increased water saturations caused by production. The decrease in shale A apparently was caused by increased compaction and decreased porosity. A = shale adjacent to permeable sand; B = shale distant to permeable sand.

seekers ' ~ ' target zone was approximately 14.0 lb/gal, because both the sands and shales contained over-pressures equivalent to this specific weight of mud. Due to production-related pressure depletion over the years, however, most of the sands more recently exhibited pressure gradients throughout this oilfield considerably lower than hydrostatic. Thus it was known that the interval to be redrilled would not sustain or require the high mud weights used originally.

As a result, a PNC log was run in the old cased wellbore to evaluate present pressure conditions. Figure B-2B presents the E-trend versus depth to a depth of 9110 ft. The maximum mud weight determined to reach the Homeseekers ' ~ ' sands was 10.2 lb/gal. Figure B-2C clearly shows the change in shale pressure due to pressure depletion of the sands. The well was side-tracked at 8120 ft in 1968 and drilled to 9215 ft without difficulty with a mud weight of 10.4 lb/gal, whereas originally 14.3 lb/gal drilling fluid was required. In this field study, the equivalent depth method (Fertl, 1976) proved to be quite successful.

Shale water influx from undercompacted overpressured shales into permeable sandstone reservoirs has been discussed in detail in the literature from a reservoir engineering point of view. It is also of interest to investigate the possibility of detecting and/or monitoring such in-situ behavior with through-casing well logging techniques.

Mathematical model studies have suggested a varying pore pressure gradient in overpressured shale sections, with the highest excess pressure being located near the center of massive shales. Less excessive pressure is found in the vicinity of permeable zones, such as sands and sandstones. This concept is supported by field observations in newly drilled wells.


Over comparatively short periods of time, "shale water depletion" can be diag- nosed within the vicinity of the pay sand in an overpressured south Louisiana well (Fig. B-3). Two PNC logs had been run a year apart to monitor hydrocarbon saturation changes in the pay, which was being produced in several adjacent wells. Sigma-value changes in the pay sand are caused by the increase in water saturation. There are, however, changes in the adjacent shales. Zone A, the shale next to the pay, shows a marked decrease due to increased compaction and porosity decrease, which suggests shale water influx into the sand. In Zone B, the portion of the shale some distance from the permeable sand shows considerably less, if any, variations due to pressure drawdown (Fertl and Timko, 1970).

Collar and radioactive bullet logging for subsidence monitoring has been discussed in detail by several investigators (Allen, 1969; Ruedrich et al., 1974; Schoonbeek, 1976; Allen, 1981; Colazas and Olson, 1982; Menghini, 1988). Areas in which these techniques have been and are being applied include the Wilmington oil field near and within the City of Long Beach, California; the gas field at Niigata, Japan; the Prudhoe Bay oil field on the North Slope, Alaska; the Groningen gas field, The Netherlands; the oil fields in Lake Maracaibo, Venezuela; and the Ekofisk oil field area, offshore Norway.

According to Allen (1969), several hundred logging runs have been made in the Wilmington oil field, California, because method for measuring oil zone compaction by the deformation in casing joints was first successfully used in 1949. Measurement uncertainty was -4-0.04 ft (1.2 cm) per casing joint. The system, described in detail by Allen (1969), utilized 2 or 3 collar locators (and/or radioactive bullet locators for direct measurement of formation compaction) spaced about one joint length apart. Calculations were made from film recordings at a scale of 50 to 60 inch (1.27 m to 1.52 m) per 100 ft (30.48 m) of wellbore logged. A similar technique was applied by the Geological Survey of Japan in the Niigata gas field, utilizing both radioactive bullets shot into the formation and radioactive pellets attached to the casing wall (Allen, 1969).

Recent improvements of the techniques initially used in California, as described by Allen (1969) previously, have significantly improved measurement accuracy. Random casing joint lengths have been repeatedly measured and remeasured with a standard deviation of 0.0159 ft (0.4 cm). This was accomplished by the development of a downhole odometer and novel recording techniques, which can and have been routinely used to measure casing joints of random length in: (a) wells as deep as 9000 ft (2743 m); (b) old wells with rough interiors due to scale, corrosion, and/or tubing wear marks; and (c) deviated wellbores.

The major constraint to accurately measure the small amounts of reservoir compaction has always been the "bounce" of logging instrumentation, i.e., the erratic logging tool movement (speed) caused by drag and cable stretch, while the logging information is being recorded at the surface at a uniform scale. To overcome the "bounce" problem, a downhole tracking system utilizing small odometer wheels was devised and jointly developed by the City of Long Beach and Dresser Atlas (Frost et al., 1981). Accuracy of locating radioactive bullets at logging speeds of 25 ft/min (7.6 m/min) is 4-0.1 ft (3 cm) and can be further enhanced by logging at


the extremely low logging speed of 2 to 3 ft/min (6.12 to 3.1 m/min). The latter, however, requires special hydraulic gears on logging trucks.

The corresponding downhole logging instrumentation consists of two magnetic collar locators, two radioactive detectors, and two odometer wheels mounted in

Casing and Receiver Film Strip Diagram Diagram

Excentric Belly Spring

Downhole Measuring Wheel (See detail below)

Magnetic Collar Locator

o

._1

_a -5 '-

= 8 3

O = I1~

' ~ 0 . , , - ~ m

a

Casing Collar Center

3200

3210

3220

Top Measuring Wheel Showing Increments of Tool Travel

Top Collar

b =

Bottom Collar Locator

Tracking Sealed M a g ~ ~ . , Wheel Magnetic

�9 -,,-~::~ 01

!

Measuring Wheel Detail

Fig. B-4. Measurement of casing joint lengths and distances between radioactive bullets. (After Allen, 1981.)


a body about 45 ft (13.7 m) long (Fig. B-4). The radioactive bullet detectors are spaced 20 ft (6.1 m) apart. All four detectors and the odometer wheel markers record simultaneously on expanded scale fiber (50 or 6 inch equal 100 ft of borehole interval; 1.27 to 1.52 m/30.48 m). Multiple runs in five wells in the Wilmington field, California, showed that 88% of all usable repeat measurements were within +0.02 ft (6 mm) of the first logging run and the standard deviation was 0.0159 ft (4.8 mm).

Alternate logging systems utilize two pairs of collar locators (offset by 2 ft (0.61 m)), each pair being almost exactly the same distance apart as the specially constructed casing joint lengths, digital data recording, and analytical cross correlation techniques for signal processing based on five repeat-logging runs (Ruedrich et al., 1974).

The use of radioactive markers was initiated in the mid 1960's and initial compaction measurements were made with ordinary gamma ray (GR) devices (Schoonbeek, 1976). Subsequently, dual and triple detector GR tools were introduced coupled with improved techniques to allow accurate and precise measurements of cable movement (Allen, 1981). In 1982, a four-detector GR tool was introduced for compaction measurements in the Groningen gas field, The Nether- lands, with an accuracy of 0.06 inch (0.15 cm) per 34.4 ft (10.5 m) monitoring interval. Introduced as a second phase of the compaction monitoring program at Ekofisk, offshore Norway, at the year-end 1987, ten wells were equipped with radioactive markers and time-lapse monitoring data has been acquired in six wells (Menghini, 1988).

In this technique, a weak radioactive source (cesium 137-100 to 150 microcurie strength) is encapsuled in a stainless steel sphere of 0.09 inch (2.3 mm) in diameter. This sphere is fitted inside a stainless steel bullet, which is fired from a modified 5-inch core sampler taker gun. The gun carries 12 marker bullets which can be fired selectively; GR detector verifies bullet placement.

Optimum penetration for good GR signal response is about 8 inch (20 cm) into the formation in gauge borehole. Based on field data, a relationship of (1) charge size versus acoustic travel time for the overburden and (2) charge size versus

TABLE B-IV

Explosive charge sizes used in overburden and reservoir sections (modified after Menghini, 1988, p. 36, OTC 5620)

Overburden Reservoir

A T Charge size Porosity Charge size (/zsec/ft) (g) (%) (g)

<130 10 10-18 10 130-140 8 19-22 13.5 140-160 6 23-27 10 160-180 5 28-31 8

>180 5 + parachute/spacer 32-33 6 >33 5


porosity in the reservoir section was developed (Table B-IV). As noted in Table B-IV, the minimum charge size is 5 g. In very soft shales this charge size is still too large for optimum penetration. A special charge with a "parachute" increases the surface area of the bullet nose, thereby preventing the bullet from penetrating too far into the formation. A spacer can also be added to the base of the charge to reduce the velocity of the bullet while firing. The downhole logging instrument, called the Formation Subsidence Monitoring Tool (FSMT), has four gamma ray detectors located at precise spacing within a 2 inch (5 cm) OD Invar housing. Invar is used because the material has a minimum coefficient of thermal expansion. An accelerometer provides information on downhole tool movement. Logging passes during calibration and actual surveys are performed at 300 ft/hr (91 m/hr). Three logging runs are made over each marker interval. The resulting measurements (raw gamma ray response, accelerometer response, cable tension, and logging speed) are digitally recorded and then analyzed in a computer center.

Menghini (1988) summarized the field experiences with compaction monitoring in the Ekofisk field, offshore Norway, as follows: (1) optimum radioactive marker placement is essential for proper detection and analysis of gamma ray (GRT) response, (2) knowledge of formation porosity and mechanical properties is required when selecting proper charge sizes to implant the marker bullets, (3) FSMT measurement accuracy is highly dependent on smooth tool movement (the major constraint being cable drag due to friction), and (4) the highest quality compaction measurements are obtained in non-deviated wells without production tubing.

ACKNOWLEDGEMENT

The help extended by Dr. Rod E Hotz, Manager, Technical Communications, Western Atlas International, in providing tables and figures is greatly appreciated by the authors.

REFERENCES

Allen, D.R., 1981. Developments in precision casing joint and radioactive measurements for compaction monitoring, SPE 9933. SPE California Regional Meeting, Bakersfield, Calif., March 25-26.

Allen, D.R., 1969. Collar and radioactive bullet logging for subsidence monitoring, Paper G. SPWLA Trans., May 25-28.

Boade, R.R., Chin, L.Y. and Siemers, W.T., 1988. Forecasting of Ekofisk reservoir compaction and subsidence by numerical simulation, OTC 5622. SPE 20th Annual OTC, Houston, Texas, May 2-5.

Colazas, X.C. and Olson, L.J., 1982. Subsidence monitoring methods and bench mark elevation response to water injection, Wilmington oil field, Long Beach, California. In: E.C. Donaldson and H. R. van Domselaar (Editors), Proceedings of 1982 Forum on Subsidence due to Fluid Withdrawals, Checotah, OK, November 14-17: 121-132.

De Loos, J.M., 1973. In-situ compaction measurements in Groningen observation wells. Verh. K. Ned. Geol. Mijnbouwk. Genoot., 28: 79-104.

Fertl, W.H., 1976. Abnormal Formation Pressures. Elsevier, Amsterdam, 385 pp.


Fertl, W.H. and Timko, D.J., 1970. How abnormal pressure detection techniques are applied. Oil Gas J., 82(32): 81-86.

Frost, E., Fertl, W.H. and Wichmann, P.A., 1981. Prolog ~ A Computerized Wellsite Log Analysis System. SPE 9619, Proc. SPE Middle East Tech. Conf., Bahrain, Mar. 9-12: 395-409.

Johnson, J.P., Rhett, D.W. and Siemers, W.T.,, 1988. Rock mechanics of the Ekofisk reservoir in the evaluation of subsidence, OTC 5621. SPE 20th Annual OTC, Houston, Texas, May 2-5.

Menghini, M.L., 1988. Compaction monitoring in the Ekofisk area chalk fields, OTC 5620. SPE 20th Annual OTC Meet., Houston, Texas, May 2-5.

Morita, N., Whitfill, D.L., Nygaad, O. and Bale, A., 1988. A quick method to determine subsidence, reservoir compaction, and in-situ stress induced by reservoir depletion. SPE 17150. SPE Formation Damage Control Symposium, Bakersfield, Calif., Feb. 8-9, pp. 73-84.

Rentsch, H.C. and Mes, M.J., 1988. Measurement of Ekofisk subsidence, OTC 5619. SPE 20th Annual OTC, Houston, Texas, May 2-5.

Ruedrich, R.A., Perkins, T.K. and O'Brien, D.E., 1974. Precise joint depth determination using a multiple casing collar locator tool, SPE 5087. SPE 49th Annual Fall Meeting, Houston, Texas, October 6-9.

Schoonbeek, J.B., 1976. Land subsidence as a result of gas extraction in Groningen, The Netherlands. In: Internat. Assoc. Hydrol. Sci., Proceedings Symposium, Anaheim, Calif., December 11-13.

Smits, R.M.M., deWaal, J.A. and van Kooten, J.EC., 1986. Prediction of abrupt reservoir compaction and surface subsidence due to pore collapse in carbonates, SPE 15642. SPE Annual Meeting New Orleans, La., October 5-8.

Sulak, R.M. and Danielsen, J., 1988. Reservoir aspects of Ekofisk subsidence, OTC 5618. SPE 20th Annual OTC Meeting, Houston, Texas, May 2-5.

Yudovich, A., Chin, L.Y. and Morgan, D.R., 1988. Casing deformation in Ekofisk, OTC 5623. SPE 20th Annual OTC Meeting, Houston, Texas, May 2-5.

Appendix C

453

USE OF THE GLOBAL POSITIONING SYSTEM (GPS) FOR GROUND SUBSIDENCE MONITORING

BERNARD ENDRES and GEORGE V. CHILINGARIAN

INTRODUCTION

Many examples of land subsidence resulting from the production of oil and gas or the pumping of water from subsurface aquifers have been documented throughout the world. Frequently, the subsidence was discovered only after extensive surface damage was experienced, or it was too late to take corrective actions to control the subsidence.

In an oilfield, for example, the subsidence usually takes on a bowl-shaped appearance with the maximum subsidence occurring near the center of the field. The rim of the bowl will take on roughly the shape of the oilfield, but will frequently extend up to twice the area of the oilfield reservoir itself. Also, the vertical subsidence is usually accompanied by horizontal movements, especially in the region near the rim of the subsidence bowl.

Conventional surveying techniques have been used to measure the subsidence in some oilfields. However, this procedure is both expensive and time consuming, especially if done properly using a matrix of permanent bench marks that are monitored on a periodic basis. Also, this method requires direct line-of-sight to be achieved between bench marks, which restricts its application and prevents its use for most offshore production operations.

The operational deployment of the Global Positioning System (GPS) by the U.S. Department of Defense now makes it possible to perform subsidence monitoring much more efficiently and at reduced costs, compared to the conventional surveying techniques. Furthermore, the GPS approach can be integrated with a conventional bench mark system allowing substantial cost and time savings to be realized.

It is also possible, using the GPS, to perform subsidence monitoring at offshore oil platforms. This capability is not possible using conventional survey techniques because of line-of-sight restrictions.

THE GLOBAL POSITIONING SYSTEM (GPS)

The GPS consists of the constellation of orbiting satellites that continuously transmit radio navigation signals. The satellites are launched and maintained by the U.S. Department of Defense, and the radio signals are made available free of charge.

454 B. ENDRES AND G.V. CHILINGARIAN

A number of private companies have developed sophisticated receivers and soft- ware packages that are capable of performing precision navigation. Until recently, the main restriction was limited satellite visibility, which prevented full attainment of navigation accuracies. It has taken many years to launch and deploy the complement of satellites. Most importantly for navigation, is the need to simultaneously view four satellites to permit three-dimensional position determination through triangulation.

The operational GPS orbit constellation consists of 24 satellites arranged in six orbital planes. Each plane is inclined to the equator by 55 degrees. Each satellite travels in a 12-hour period, circular orbit at 10,898 miles above the earth. This configuration has been designated to permit a ground station, located anywhere on the earth, to receive radio navigation signals from four satellites simultaneously without interruption at any time of the day or night.

USE OF D I F F E R E N T I A L NAVIGATION

The navigational accuracies of absolute positioning in three-dimensional space using GPS are not sufficiently accurate for subsidence monitoring. Inasmuch as subsidence is nearly a pure form of surface deformation, however, differential navigation techniques can be used to achieve the required accuracies. In fact, attainment of accuracies comparable to using conventional survey techniques are well within the capability of the GPS system. These accuracies correspond to the following:

Vertical : 5 to 8 mm,

Horizontal : 3 to 5 mm.

These accuracies are more than adequate to detect and monitor subsidence rates that are usually measured in the magnitude range of centimeters per year.

Also, the ability to achieve a high degree of accuracy in the horizontal plane allows careful monitoring of horizontal movements; for example, in the vicinity of the rim of the subsidence bowl. One use is to permit subsidence model validation, which frequently shows a strong correlation in the horizontal movement at the rim of the subsidence bowl and the vertical movement at the center of the subsidence bowl.

It should be pointed out that the differential navigation technique that is being used to achieve the above accuracies requires the use of two ground receivers. One receiver is located at a reference bench mark, and the position of the second receiver is always being determined as a difference in the three-dimensional distances between the ground stations. This is much more accurate than the ability to measure the location of any ground station in the three-dimensional space (see Fig. C-1.)

EXAMPLES OF SUBSIDENCE M O N I T O R I N G USING GPS

Oil production along the east coast of Lake Maracaibo in Western Venezuela has produced cumulative subsidence of 5 m, with the rate of subsidence reaching 0.2 m

USE OF THE GPS FOR GROUND SUBSIDENCE MONITORING 455

Fig. C-1. Differential navigation receiver geometry.

per year. A conventional surveying system using 1600 bench marks has been in use for many years, with surveying performed every two years. Five survey crews needed three months to complete the survey at a total cost of over U.S. $200,000 (Leal, 1989).

In 1986, in search for a more economical monitoring method, the Department of Surveying Engineering at the University of New Brunswick in Canada, in conjunction with Maraven, S.A., the oilfield operator at Lake Maracaibo, initiated a project to test and implement the GPS.

It has been reported that the new monitoring system has resulted in savings of over 30%, and a substantial reduction in time to perform the survey (Chrzanowski, 1991).

The GPS is being used to monitor subsidence in the Po River Delta in northeastern Italy, In the 1960's the Delta area of the Po River, near the Adriatic Sea, suffered a great deal of subsidence. This reached 3.5 m in some areas, primarily due to withdrawal of natural gas and water. The subsidence covered an area of 800 km 2 and disrupted all of the water courses of the Delta. The GPS is being used for prediction of the corrective actions necessary to deal with the problem (Gambardella, 1991).

Another example of where GPS has been successfully used for subsidence monitoring is in the northern part of the Netherlands. Since 1964, natural gas has been produced from the Groningen and Friesland provinces. The gas extraction has caused continual subsidence since production began. The area is already below sea level, requiring careful monitoring to predict the need to raise dikes and to evaluate the hydrological impact on farming (Pottgens, 1991).

Michael Hatch, a graduate student at the University of Arizona in Tucson, and his

456 B. ENDRES AND G.V. CHILINGARIAN

advisor, Professor John Summer, used the GPS to measure subsidence of the Tucson basin from groundwater pumping. A total of 21 basin and four bedrock bench mark stations were measured between 1987 and 1991. The average rate of subsidence was between one and five centimeters per year.

Previous studies using conventional survey techniques had established a subsidence rate of three millimeters for every meter drop in the water table. The GPS measurements made by Hatch established that the subsidence rate was 24 mm for every meter drop in the water table. This was eight times the previously determined rate. This information has been used to suggest that the water storage capacity may be irretrievably damaged (Earth, 1992).

F U T U R E A P P L I C A T I O N S

Offshore drilling operations are not immune from subsidence problems. Inas- much as line-of-sight is not required between the two GPS receiver stations, one receiver can be placed on the offshore drilling platform and the other receiver placed on land. Although the measurement accuracy will degrade depending upon the distance between the two receivers, this method offers considerable promise in providing the only known way to monitor for subsidence on offshore drilling platforms.

Several examples exist where enormous sums of money were spent to relevel drilling platforms where subsidence was caused from oil and gas production. Ac- cordingly, the GPS could be used to predict and control the impact of subsidence on these costly structures.

The ability of the GPS to accurately measure horizontal movements of the earth's surface offers great potential in predicting earthquakes. For example, the measurement of relative earth movement across a seismic fault could be used to predict the level of build-up of stress.

C O N C L U S I O N S

The GPS provides a major technological advancement in performing ground surface subsidence monitoring associated with oil and gas production, or groundwater pumping from aquifers.

Accuracies of measurement are competitive with conventional survey techniques; however, significant cost and time efficiencies result. Inasmuch as the line-of-sight requirement between bench mark stations is eliminated, much more flexibility exists in implementing the system. Furthermore, it can be used for monitoring subsidence of offshore drilling platforms, which is not possible using conventional survey techniques.

Finally, the ability of the GPS to accurately measure the horizontal movements across seismic fault planes offers considerable promise in predicting earthquakes.

USE OF THE GPS FOR GROUND SUBSIDENCE MONITORING 457

REFERENCES

Chrzanowski, A. and Chen, Y.Q., 1991. Use of the global positioning system (GPS) for ground subsidence measurements in Western Venezuela oil fields. Proc. Fourth International Symp. Land Subsidence, May. IAHS Publ. No. 200: 419-431.

Earth, 1992, Satellites monitor sinking basin, July: 15. Gambardella, E and Bartolotto, S., 1991. The positioning system GPS for subsidence control of the

terminal reach of the Po River. Proc. Fourth International Symp. Land Subsidence, May. IAHS Publ. No. 200: 433-441.

Leal, J., 1989. Integration of satellite global positioning system and &veiling for the subsidence monitoring studies at the Costa Bolivar oil fields in Venezuela. Technical Report No. 114, Department of Surveying Engineering, University of New Brunswick, Canada.

Pottgens, Jan J.E., 1991. Land subsidence due to gas extraction in the northern part of the Netherlands. Proc. Fourth International Symp. Land Subsidence, May. IAHS Publ. No. 200: 99-108.

459

Appendix D

EARTHQUAKE PREDICTION AS RELATED TO SUBSIDENCE

SIMON KATZ, LEONID KHILYUK and GEORGE CHILINGARIAN

SHORT REVIEW AND CURRENT STATE OF THE PROBLEM

In recent publications, Gurevich and Chilingarian (1993) and Katz et al. (1994) discussed interdependence between subsidence and gas leakage over petroleum reservoirs caused by development of subvertical fractures over the reservoirs and discussed interrelationships among three groups of phenomena: seismic activity, gas leakage and subsidence. The latter is caused by production of fluids from the reservoir with resulting decrease in pore pressure followed by compaction of the reservoir rocks, redistribution of stresses in rocks over the reservoir, and ground subsidence (see Rieke and Chilingarian, 1974; Chilingarian and Wolf, 1975, 1976). Subsidence and resulting earthquakes can be accompanied by changes in the magnitude of gas leakage.

Large-scale subsidence was observed in many regions, for example, over Wilming- ton and Huntington Beach oilfields in Southern California (Martin and Serdengecti, 1984). Production-induced earthquakes caused by ground subsidence were observed in various parts of the world (e.g., Lee, 1978; Wetmiller, 1986; Krestnikov et al., 1980).

Generally, subsidence is considered as a gradual, continuous process of lowering of the level of the earth surface caused by compaction of producing reservoirs (Whittaker and Reddish, 1989). Ground subsidence may also be caused by seismic activity, which leads to changes in the rate of formation of vertically and subvertically oriented fractures that, in turn, causes gas leakage to the surface.

Research on earthquake prediction has been mostly based on analysis of seismicity over large territories. It relies on accumulated evidence that variations in integral characteristics of seismicity calculated over large territories may be correlated with large earthquakes. Inasmuch as microseismic activity may increase the permeability of pre-existing faults with consequent increase in gas migration, usage of near-surface methane concentration in the vicinity of the faults as an additional parameter in earthquake prediction may be promising.

There are several publications that contain field-measured data on compaction and subsequent subsidence over reservoirs (Helm, 1984; Holtzer, 1984). In these publications, methodology for prediction of subsidence was proposed. It utilizes parameters of ground and liquid as its input data and is based on the use of empirical mathematical models developed by Martin and Serdengecti (1984).

460 S. KATZ, L. KHILYUK AND G. CHILINGARIAN

JOINT STUDY OF EARTHQUAKE ACTIVITY AND ENVIRONMENTAL IMPACT RELATED TO OIL AND GAS PRODUCTION

To give a quantitative description of environmental phenomena related to oil and gas production in seismically active regions, it is necessary to study time-dependent relationships among three groups of phenomena: 1. Gas leakage and gas concentration in soils over petroleum reservoir as time

functions and functions of geographical location. 2. Surface subsidence as a function of time and geographical coordinates of the

location. 3. Seismic activity as a function of time in the form of time-dependent energy

of micro-tremors and integral parameters of spatially distributed earthquake sequences. It is especially important not only to identify correlation links among these

groups of phenomena but also to detect time delays between major variations in their quantitative characteristics. Results of this study will have several major applications: 1. Methodology for detection of increased danger of upward gas migration and

surface gas leakage due to oil and gas production and variation in time of seismic-tectonic processes.

2. Formulation of new earthquake precursors directly linked to current seismic- tectonic activity in the area of oil and gas production based not only on variations in seismic activity but also on analysis of environmental phenomena related to oil production.

3. Increase in the gas leakage and gas concentration in soils may also indicate formation of vertically and subvertically oriented fractures over oilfields which may be caused by reservoir compaction and consequent ground subsidence. Hence, monitoring of gas leakage at the Earth's surface can be used as an additional indicator of (1) possible increase in ground subsidence over oilfield, and (2) of movements along faults due to tectonic activity, which could render faults more permeable.

PHYSICAL AND GEOLOGICAL RATIONALE

In this section, the authors analyze interrelationships among three groups of time-dependent phenomena: (1) gas leakage to the surface and variations in concentration of gas in soil, (2) subsidence over petroleum reservoirs in the process of oil production, and (3) seismic activity. Inasmuch as these phenomena are mu- tually linked, their joint study may give information necessary for formulation of methodology for their prediction.

Modern concepts of gas migration to the surface (Gurevich and Chilingarian, 1993; Gurevich et al., 1993) assume that it occurs along vertically and subvertically oriented fractures, fault zones, and cavities formed around man-made boreholes. Inasmuch as geometry of the fractures and their widths depend on the rock properties and pressure, upward permeability and, consequently, gas migration may vary

EARTHQUAKE PREDICTION AS RELATED TO SUBSIDENCE 461

Pr~176 Com ac, ono, I . t orma, ono, fluids from a reservoir faults reservoir rocks and fractures

~ I I i1 !11 FOrmatiOn Of movement along faults and ~ Regional additional faults preexisting faults fractures subsidence and fractures

Subsidence of Microseismic ground surface activity

I ....... .. Formation of

--J additional T~I Increase in ~ fractures and ~1 gas migration "1 movement along

preexisting faults

Fig. D-1. Schematic diagram of system relationships among production of fluids, compaction, subsidence, and seismic activity.

with changing internal rock pressure. The pressure, in turn, depends on the current tectonic activity, which manifests itself in changing seismicity. In this context, variation in time of intensity of seismic activity and rock pressure may influence fracturing of rocks and upward permeability, which, in turn, leads to changes in the rate of upward gas migration.

Monitoring in time of gas leakage and gas concentration in soils may give implicit information on variations in rock pressure, which may serve as a triggering mechanism for earthquakes. Hence, monitoring of gas leakage and gas concentration in soils may lead to formulation of new earthquake prediction techniques directly linked to tectonic processes in an area of study.

In turn, earthquakes alter rock pressure, distribution and geometry of fractures and, therefore, the permeability along fractures and fault zones. Large-scale regional subsidence also gives rise to fractures and faults. Thus, possibility of major gas leakage may be correlated with history of seismic activity in an area of study.

Compaction of reservoir and formation of fractures and faults over petroleum reservoir precede subsidence process at the surface. In turn, increase in the number and density of vertically and subvertically oriented fractures may cause improvement in the upward gas mobility. Results of monitoring gas leakage and gas concentration in the soil, therefore, may indicate increase in the rate of subsidence.

Figure D-1 is a schematic diagram of system relationship among production of fluids, compaction, subsidence, and seismic activity.

462 s. KATZ, L. KHILYUK AND G. CHILINGARIAN

NONFUNCTIONAL RELATIONS AMONG QUANTITATIVE CHARACTERISTICS OF UPWARD GAS MOBILITY, GROUND SUBSIDENCE, AND EARTHQUAKE ACTIVITY IN SEISMICALLY ACTIVE REGIONS

The writers assume that there are no clearly defined functional relationships among the above three groups of environmental phenomena. Still, nonfunctional relationships among them may be successfully used for their analysis and prediction.

Formal definitions of nonfunctional relations among several physical phenomena, i.e., (a) variations in upward gas mobility, (b) ground subsidence, and (c) seismic processes are presented here. The writers define these relationships as a combination of predictable functional component and nonpredictable random component. The aim of the prediction methodology is to estimate future values of the functional components using already available measurements of a combination of functional and nonfunctional components and other relevant parameters. To guarantee both flexibility and stability of the prediction methodology, the measurements are to be done in a sliding time window.

The following notations are used: t - current time; T - width of the time window. G( t ) - gas leakage rate measured at the earth's surface in a moving time window

(t, t - T). It is assumed that this parameter characterizes upward gas mobility. S( t ) - average ground subsidence measured in the time window (t, t - T). D ( t ) - danger function equal to the maximum magnitude of the earthquakes

recorded in the time window (t, t - T). G i ( t ) ; G i ( t z - z i ) , S j ( t z - "ci), Cr( t z - r i ) , i = 1, 2, . . . , I - a se t o f m e a s u r a b l e

parameters that define time and spatial features of the process of gas leakage such as the rate of change in time of gas leakage process.

ri > 0 - characteristic time delays. Gi(t) may be defined as a normalized finite difference for the process G(t ) so

that

G1 (t) = [G(t) - G(t - d t] /d t ,

Gi ( t ) --~ [ a i - 1 ( t ) - a i - 1 (t - dt] /d t .

Sj( t ); j = 1, 2 , . . . , J - a set of measurable parameters that define time and spatial features of the process of ground subsidence such as absolute value of subsidence as a time function, rate of change in time of subsidence, and area of subsidence.

Cr(t); r - 1, 2 , . . . , R - a set of measurable parameters that are related to more than one of the above phenomena, such as density of fractures, rate of change of fracture density, average size of fractures measured in a sliding time window (t, t - T).

Dn(t); n = 1, 2 , . . . , N - a set of measurable parameters that define time and spatial features of the process of seismicity such as the rate of change in time of the danger function, average magnitude of the earthquakes in a sliding time window, a number of earthquakes with a magnitude larger than a given threshold, and average depth of the earthquakes' epicenters.


It is assumed that quantitative characteristics defining the above three phenomena are related to each other as functions of unspecified structure distorted by random noise:

G ( t ) = F l [ G n ( t - r i ) , S j ( t - r i ) , D j ( t - r i ) , C r ( t - r i ) ; i = 1, 2 . . . . . P ] + ~ l ( t ) ,

(D-l)

S ( t ) = F 2 [ G n ( t - z i ) , S j ( t - ri), D j ( t - ri), C r ( t -- ri);i = 1, 2 . . . . . P] + ~2(t),

(D-2)

D ( t ) = F 3 [ G n ( t - r i ) , S j ( t - r i ) , D j ( t - r i ) , C r ( t - r i ) ; i = 1, 2 . . . . , P] + ~3(t),

(D-3)

where ~m (t), m = 1, 2, 3 is a random component with zero mean. The form of the functions /71, F2 and F3 and the variance of the random

components in Eqs. D-l, D-2, and D-3 are assumed to be unknown. According to the Eqs. D-l, D-2, and D-3, quantitative characteristics defining

each one of the three phenomena (upward gas mobility, ground subsidence, and earthquake activity) are presented as functions of current and previous values of parameters defining all three phenomena combined with unpredictable random component ~m (t).

NONFUNCTIONAL RELATIONS BETWEEN QUANTITATIVE CHARACTERISTICS OF UPWARD GAS MOBILITY AND GROUND SUBSIDENCE IN SEISMICALLY PASSIVE REGIONS

In seismically passive regions where influence of seismic activity on upward gas mobility and ground subsidence is negligible, Eqs. D-l, D-2, and D-3 are reduced to

G ( t ) = F l [ G i ( t - r i ) , S j ( t - ri), C r ( t -- Zi);i = 0, 1 . . . . . P] + ~l(t), (D-4)

S ( t ) = F 2 [ G i ( t - z'i), S j ( t - ri), C r ( t -- ri);i = 0, 1 . . . . . P] + ~2(t). (D-5)

In Eqs. D-4 and D-5, both upward gas mobility and ground subsidence are defined as phenomena that are dependent on three groups of measurable parameters. The first two groups include parameters specifically related to one of the predicted phenomena, whereas the parameters from the third group are related to both phenomena.

FORMULATION OF NEURAL NETWORK METHODOLOGY FOR PREDICTION OF UPWARD GAS MOBILITY, GROUND SUBSIDENCE, AND EARTHQUAKE ACTIVITY

There are basically two approaches to the problem of prediction of physical phenomena based on measured parameters. The first approach uses physical models


and model-defined relationships between measured parameters and future values of the process of interest. This approach is accurate for comparatively simple models defined by a limited number of parameters. The second approach relies on model- independent, correlation-based prediction techniques that include various versions of regression-based prediction methodology and methodology of prediction based on the use of various pattern recognition techniques such as neural networks.

The process of subsidence and variations in the surface gas leakage are related to the large-scale nonlinear effects such as fracture development, changes at the faults' surfaces and nonlinear deformations. This makes it extremely difficult to develop a methodology of forecasting these phenomena based on numerical modeling of underlying physical processes.

Methodology for prediction of natural and man-caused environmental phenomena, discussed here, is based on the use of neural networks. They are especially efficient in working with data of complex structure. Neural nets have been so-named because they mimic, in a much simplified fashion, the structure and function of neurons in the brain. The neural net is a computer program that creates a network of nodes (analogous to neurons), and interconnections, together with rules that determine how the output of each node is determined by the values of all the inputs to this node. As in the brain, neural nets are commonly organized into several layers of nodes, with output of one layer feeding the next layer. In the brain, this architecture generally results in progressively more abstract representation of the input stimuli as the information is filtered through successive layers. Neural nets have shown great potential in identification of subtle patterns among data parameters and in prediction of phenomena that are linked to input data by nonfunctional relationships that can not be approximated by regression curves of pre-defined structure (such as polynomials with pre-defined number of terms).

Neural net is trained to transform a set of input data vectors Xm; m = 1, 2, . . . , M into a desired outputs gin. The structure of the neural net is chosen in such a way that the transformation error e

e. = ~--~[gm -- ~ ('Xm)]2 (D-6) m

is minimum. Here qJ (Xm) is the output of the neural net for the input data vector Xm. In Eq. D-6, the values of gm are known. After the neural net is synthesized, it may

be used to predict unknown values gz using as its input respective vector Xz. This may be written as follows:

(Xz) > gz. (D-7)

Here �9 (Xz) is the output of the neural net synthesized to minimize the criterion 6 (Eq. D-6).

In the case of environmental studies, such as those discussed in this paper, a volume of input data often may be of the same order as the number of parameters describing the neural net. In this case, minimization of criterion 6 may lead to unsta-


ble solutions. To avoid instability in the results of neural network-based prediction, the criterion 6 should be modified to (Katz et al., 1993)"

8 = ~ [ g m -- t I / (Xm)] 2 -q-~211~112, ( D - 8 ) m

where ~ is a vector of parameters defining the structure of the neural net, I1~11 is the norm of the vector ~, a2 is the regularization parameter.

PREDICTION OF GROUND SUBSIDENCE BASED ON MEASUREMENT OF SUBSIDENCE AND GAS LEAKAGE PARAMETERS

In the context of prediction of ground subsidence based on the use of measurements of subsidence and gas leakage, indexes m and z in Eqs. D-6 and D-7 are time-related, so the input data-vector used for prediction is of the form Xz -- X(tz). The value gm = g ( t m ) is a measured value of subsidence at a time tm = t - A t m ;

coordinates of the vector Xm are the values of parameters G i ( t m - "ci), S i ( t m - v i )

and Cr (tin -- ~i). After the neural net is synthesized, it may be utilized to predict a value of gz:

gz = g ( t z = t + 3 t ) m

using input data-vector Xz, with coordinates equal to the values of parameters G i (tz - v i ) , Si (tz - v i ) and Cr (tz -- r i ) .

MONITORING OF GAS LEAKAGE AND GAS CONCENTRATION IN SOILS

Monitoring of a surface gas leakage and time related variations of gas concentration in soils is important due to environmental problems associated with this phenomenon and because of its possible links with subsidence and earthquake activity. The following are locations important for monitoring of gas leakage and gas concentration in soil: (a) vicinity of abandoned wells, (b) basements of buildings, and (c) vicinity of faults.

Monitoring at fault zones and abandoned wells may be of special importance in the context of the usage of gas leakage characteristics for earthquake prediction. Figures D-2 and D-3 illustrate correlation links between subsidence and seismic activity. In the context of possible applications of gas leakage measurements to earthquake prediction, it is important to find similar relationships between these two phenomena.

It is known that increase in radon concentration measured in shallow wells may be used in some cases as one of the precursors for earthquake prediction. Analysis of variations in the mobility of methane with variations in the properties of fracture systems and faults may shed additional light on this subject.


Fig. D-2. Distribution of major earthquakes over the territory of US. (After Bolt, 1988, courtesy of W.H. Freeman and Company.). Small circles - earthquakes; large circles - volcanoes.

Fig. D-3. Locations of major subsidence events in the Western US. (After Holzer, 1984, courtesy of Geol. Soc. Am. Inc.).

MONITORING OF SEISMIC ACTIVITY

M o n i t o r i n g of seismic activity includes two components" (a) integral charac ter -

istics descr ibing fea tures and behavior of seismic processes over large geographica l


7.5

-.io .t::

.E 6...=

~o E r

_.= 5.5

g E E := 4.5 E

o ~ ;o ~'5 2'o ~'~ 3'0 3'5 ~o M O N T H S

Fig. D-4. Maximum magnitude (Richter scale) of earthquakes as a function of time for southern California region.

regions, and (b) localized parameters related to the ground behavior at the location of monitoring.

Monitoring of integral characteristics includes processing data from seismicity catalog, calculation of integral parameters of the four-dimensional time-space earthquake distribution, and preparation of sequence of maps of integral characteristics in a sliding time-window.

Among the integral parameters of seismicity, the following may be of major interest: (a) maximum magnitude in the sliding time window, (b) average magnitude in the sliding time window, (c) average depth of epicenters in the sliding time window, (d) number of earthquakes in a fixed range of magnitudes, (e) clustering of epicenters as time function, and (f) fractal characteristics of 4-dimensional time-space distribution of earthquakes.

Monitoring of the localized parameters of the ground behavior includes: (a) monitoring of intensity of local seismic activity and recording intensity of seismic

micro-tremors; and (b) monitoring of local deformations in ground, which includes separate measure-

ments of two types: (1) small-scale, high-frequency, elastic deformations, and (2) large-scale, nonelastic, low frequency deformations that result in ground subsidence.

Figures D-4 and D-5 show examples of two integral characteristics calculated for Southern California region using data starting from January 1990 to April 1993. They illustrate the type of data and the time-scale that are relevant to the problem of analysis and prediction of three environmental phenomena discussed in this paper. Integral characteristics describing the processes of gas leakage and ground


o,,,it o= I

.E_ o~

.c_ > o E m 8

._c w o 7 m o " r -

o

" o o ~4 o

3O

| |

1'0 l'S ~ ~ ~ MONTHS

40

Fig. D-5. Average depths (km) of earthquakes in the southern California region as a time function.

subsidence, calculated in the same time scale, can be used jointly with integral seismicity characteristics for prediction of these three phenomena.

JOINT MONITORING OF SUBSIDENCE AND SEISMIC ACTIVITY

Joint monitoring of subsidence and seismic activity may be of special interest because of physical links between these two phenomena. Seismic activity causes changes in features of a system of vertically and subvertically oriented fractures, which, in turn, may !ead to changes in the subsidence process. Correlational links between these two phenomena are illustrated by two maps, Figs. D-2 and D-3, which show that majority of large-scale subsidence events took place in the regions of intense seismic activity.

Inasmuch as ground subsidence is basically low-frequency slow and strongly nonlinear process, monitoring of small-amplitude, high-frequency sublinear subsidence component more closely related to seismic activity is of special interest. Similar to the methodology of prediction of strong earthquakes based on the usage of cata- logs for small and intermediate magnitude earthquake, measurements of small-scale sublinear deformation at a site of possible subsidence may be used for prediction of large-scale subsidence phenomena.

PRODUCTION-INDUCED SEISMIC PHENOMENA IN THE VICINITY OF PETROLEUM PRODUCING FIELDS

Katz et al. (1994) showed that there is a correlational link between the scale of ground subsidence over producing petroleum reservoirs and seismic activity. In the areas with intense seismic activity, the amplitude of subsidence is generally


higher compared to the seismically quiet territories. This means that seismic activity, combined with technological processes related to hydrocarbon production, causes stronger redistribution of stress and leads to intense development of additional vertical and sub-vertical fractures, which facilitates subsidence.

Fracture development and stress redistribution related to fluid withdrawal in the process of oil and gas production, in turn, causes redistribution of stress and may induce not only ground subsidence but also mid-size earthquakes both in the zone of petroleum production and in its vicinity. Analysis of production-related earthquakes shows that there are two types of earthquakes in hydrocarbon-producing areas:

1. Production-related earthquakes (in seismically quiet areas). These are the earthquakes with the magnitude around M3.0-3.5, with epicenters located in hydrocarbon-producing formations. They are related to redistribution of stress- strain fields in the immediate vicinity of the hydrocarbon reservoir. They are caused by hydrocarbon production and secondary and tertiary recovery (e. g., waterflooding). The earthquakes of this type are not related to natural seismic activity and can take place in the seismically quiet territories.

2. Production-induced earthquakes (in seismically active areas). These are the earthquakes triggered by hydrocarbon production. In this case, the epicenters may be located not only within of the hydrocarbon reservoir but also above and under or at sizable distances from the reservoirs.

There is a number of documented production-induced earthquakes in USA, Canada, France, Russia, and other countries. The following is a short list of examples of events of this type in USA, Russia, Ukraine, Uzbekistan, and Turkmenistan (Kouznetsov et al., in press), which are mostly unfamiliar to the petroleum and environmental engineers and geologists.

(1) Wilmington Field in the Long Beach and Los Angeles Harbor areas (California, USA). Several very shallow earthquakes were induced as a result of vertical ground settlement, which was caused by oil and gas removal. Maximum subsidence rate reached 71 cm/year in 1951. The peak of subsidence rate coincided with six earthquakes having the magnitude of M2.4-M3.3 at the epicenter depths of 470-640 m .

(2) Starogroznenskoe Oilfield (Russia). Earthquake was induced by intensive oil production from massive Upper Carboniferous deposits. The production was started in 1963, from a depth of 4000 m. The magnitude of main shock was M4.7 on March 26, 1971. The depth of the epicenter was 2.5 km and the main shock was followed by a large number of aftershocks. The majority of aftershocks occurred at the depth equal or smaller than the depth of the oilfield. This indicates production-induced origin of the main shock and of the following aftershocks caused by changes of stress-strain distribution above the producing oilfield.

(3) Romashkinskoe Oilfield (Tatarstan, Russia). This earthquake was caused by the continuous oil extraction with intensive pumping of water into oil-producing formation (waterflooding). The depth of the oilfield is 2-3 km. During the period of


1986-1989, 168 local events were recorded, with epicenters located at a depth of 3 to 5 km.

(4) Gasli Gasfield (Uzbekistan). In 1984 and 1986 two earthquakes were recorded in the vicinity of the Gasli gasfield at a distance of 15 and 27 km from the gasfield, respectively. The magnitudes of the earthquakes were M7.2 and M7.3.

(5) Barsa-Gelmes-Vishka Oilfield (Turkmenistan). In 1984, an earthquake having a magnitude of M6.0 was recorded in the vicinity of the oilfield. The cause of this earthquake was intensive oil production combined with waterflooding.

E X A M P L E OF E A R T H Q U A K E P R E D I C T I O N BASED ON T H E USE OF I N T E G R A L SEISMICITY PARAMETERS

The problem of earthquake prediction is an example of forecasting a phenomenon which is ill-defined, strongly nonlinear, and nonfunctionally related to the measured parameters used as input to the forecasting algorithm. In this respect, the problem of earthquake prediction is very similar to the prediction of both petroleum production induced ground subsidence and gas leakage. It includes transformation of the temporal-spatial distribution of epicenters and magnitudes of earthquakes into a set of 15 time-dependent integral attributes calculated in a moving time- window. These attributes, together with known magnitudes of large earthquakes, were used both for training of the neural net according to the criterion 8 (Eq. D-8). The neural net was trained to predict a maximum value of the magnitude of incoming earthquake one month in advance from the time when the integral seismicity attributes were recorded. Then, the synthesized neural net was used to predict the value of the maximum magnitude for the time period for which this parameter was not yet available.

Example of earthquake prediction presented in the Fig. D-6 was obtained using methodology of prediction of physical phenomena based on the use of adaptive neural nets (Katz and Aki, 1993). In this case, strong artificial precursor was generated by the neural net for Landers earthquake one month prior the earthquake. The continuous line in the Fig. D-6 is actual maximum magnitude of earthquakes in a moving time-window. The dashed line is the output of the neural net. Aster- isk (*) marks a predicted value of the maximum magnitude. Symbol A marks the corresponding value of the actual maximum magnitude.

C O N C L U S I O N S

The writers discussed three groups of problems: (1) environmental implications of oil and gas production in seismically active regions, (2) production-induced earthquakes in the areas of intense oil and gas production, and (3) earthquake and gas leakage prediction methodology in seismically active areas based on the use of adaptive neural nets.


m 6

i - s

<

4

, , , , , , , , , ~

' ' A

\ / ,20 l~ ~0 ~35 ,40

M O N T H S

Fig. D-6. Neural network based earthquake prediction. A set of integral characteristics of seismicity that included average depths and maximum magnitude, were used as input parameters.

Quantitative characteristics of ground subsidence both regional and local owing to the fluid withdrawal, seismic activity, and methane gas migration along fault zones and zones of improved upward gas mobility are linked to each other by nonfunctional relations, which may be approximated and predicted by pattern-driven algorithms such as neural networks. The input data for the predictive neural net are to be integral characteristics of all three processes calculated in the unified time-scale and similar to those used for earthquake prediction and based on seismicity analysis.

Upward gas mobility depends on distribution and geometry of vertically and subvertically oriented fractures and permeability along faults and fractured zones, that depend on rock pressure and history of seismic-tectonic processes in the region of study. On the other hand, probability of earthquakes is also linked to the rock pressure and conditions at the surface of the faults.

Ground subsidence to some degree may be caused by formation of vertically and subvertically oriented fractures in geologic section above oilfields due to seismic activity. Formation of fractures and increase in their density is commonly caused by compaction (with subsequent subsidence) due to liquid withdrawal in the process of oil production. In turn, increase in density of vertically and subvertically oriented fractures will lead to increase in upward permeability and subsequent gas mobility.

Links between large-scale subsidence and seismicity are illustrated by correlation between geographical locations of major subsidence events and zones of increased seismic activity.

Joint monitoring of seismic activity, compaction of reservoir rock due to fluid withdrawal, surface manifestations of upward gas mobility, and subsidence of geologic section in time may lead to new methods for control of possible upsurge in surface gas leakage, possible subsidence, and development of new criteria indicating increased earthquake possibility.


There have been promising demonstrations of efficiency of neural net based earthquake prediction that relies on the use of a number of time-dependent seismic characteristics calculated in a moving time-window. Expansion of this methodology to prediction of subsidence and gas leakage and integration of information on variations of gas leakage into earthquake prediction scheme may lead to new insights into the problem of prediction of all these three phenomena.

REFERENCES

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Bolt, B., 1980, Earthquakes. Freeman, New York, NY, 282 pp. Chilingarian, G.V. and Wolf, K.H., 1975. Compaction of Coarse-Grained Sediments, I. Elsevier, Amster-

dam, 552 pp. Chilingarian, G.V. and Wolf, K.H., 1976. Compaction of Coarse-Grained Sediments, II. Elsevier,

Amsterdam, 808 pp. Cristensen, S.O., Zaubi, M., and Jones M.E., 1989. Subsidence due to oil-gas production. Erdoel Kohle,

Erdgas, Petrochem., 42(5): 185-189. Erickson, R.C., 1977. Subsidence control and urban oil production -a case history, Beverly Hills (East)

oilfield, California. Proc. of the Internat. Symp. Land Subsidence, Anaheim, CA, Internat. Assoc. Hydrological Sciences Publ., 121: 285-297.

Finol, A. and Farouq Ali, S.M., 1975. Numerical simulation of oil production with simultaneous ground subsidence. Trans. SPE, 259: 411-424.

Gurevich, A.E. and Chilingarian, G.V., 1993. Subsidence over producing oil and gas fields, and gas leakage to the surface. J. Petrol. Sci. and Eng., 9: 239-250.

Gurevich, A.E., Endres, B.L., Robertson, J.O. Jr. and Chilingarian, G.V., 1993. Gas migration from oil and gas fields and associated hazards. J. Petrol Sci. and Eng., 9: 223-238.

Helm, C.D., 1984. Field-based computational techniques for predicting subsidence. In: T. L. Holzer (Editor), Man-induced Land Subsidence. Rev. Eng. Geology VI, Geol. Soc. Am., pp. 1-23.

Holzer, T.L., 1984. Ground failure induced by ground water withdrawal from unconsolidated sediments. In: T. L., Holzer (Editor), Man-induced Land Subsidence. Rev. Eng. Geology, VI, Geol. Soc. of Am., pp. 67-105.

Katz, A.S., Katz, S.A., Wickham, E. and Quijanol, R., 1993. Prediction of valve related complications using Adaptive Neural Networks. J. Heart Valve Disease, 2(5): 504-508.

Katz, S. and Aki, K., 1992. Experiments with a neural net based earthquake prediction. Am. Geophys. Union Trans., 73: 366.

Katz, S., Khilyuk, L. and Chilingarian, G.V., 1994. Interrelationships among subsidence owing to fluid withdrawal, gas migration to the surface and seismic activity. Environmental aspects of oil production in seismically active areas. J. Petrol Sci. and Eng., 11: 103-112.

Kouznetsov, O., Sidorov, V., Katz, S. and Chilingarian, G.V., 1994. Environmental impact of short-term tectonic activity release of seismic energy on the oil-gas field and effect of production on seismic activity. J. Petrol Sci. and Eng., in press.

Krestnikov, V.N., Belousov, T.P., and Shtange, D.V., 1980. Seismo-tectonic conditions for triggering Gasli earthquakes. Physics of the Earth, 9:12-28 (in Russian).

Lee, K.L., 1979. Subsidence earthquakes at a California oil field. In: S. K. Saxena (Editor) Evaluation and Prediction of Subsidence, ASCE Publ. New York, NY, pp. 549-564.

Lippman, R.E., 1987. An introduction to computing with neural nets. IEEE ASSP Magazine, 4: 4-22. Martin, J.C. and Serdengecti, S.C., 1984. Subsidence over oil and gas fields. In: T. L. Holzer (Editor),

Man-induced Land Subsidence. Rev. Eng. Geology VI, Geol. Soc. Am., pp. 23-24.


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Whittaker, B.N. and Reddish, D.J., 1989. Subsidence: Occurrence, Prediction and Control, Elsevier, Amsterdam, 528 pp.

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475

AUTHOR INDEX

Abdulraheem, A., 402-404, 413, 419, 423 Abe, H., 211 Abf-Saab, S.J., 370, 371 Achauer, C.W., 204, 210 Adamson, L.G., 50, 155 Addis, M.A., 389, 400, 401, 420, 421 Aguerrevere, S.E., 371 Akent'ev, E.P., 159 Aki, K., 470, 472 Alam, M.W.U., 191 Alberotanza, L., 249, 276 Aleksandrov, B.L., 153 Alessi, R., 237, 277 Aliyarov, P.Yu., 154 All6gre, C., 1, 8, 43 Allen, D.R., 43, 162, 172, 173, 177, 178, 185-187, 190,

198, 210, 279, 298, 299, 301, 324-327, 334, 438, 442, 447-449, 450, 472

Anderegg, H., 371 Andersen, M.A., 422 Andersen, T., 383, 420 Andre, T., 157 Andrews, P.B., 44 Andronopoulos, B., 197, 210 Anikiev, K.A., 48, 140, 153 Anisgard, H.W., 371 Aoki, K., 210 Aoki, S., 295, 334 Aoyagi, K., 56-58, 96, 121-124, 153 Appelo, C.A.J., 118, 120, 153 Archambeau, C.B., 327, 335 Asakawa, T., 121,153 Aschenbrenner, B.C., 204, 210 Athy, L.E, 74, 75, 153, 385, 420 Azeemuddin, M., 423

Baker, B.A., 44 Bakhtin, V.V., 154 Baldi, P., 282 Baldini, G., 221, 277 Baldwin, B., 77, 78, 148, 151, 154 Bale, A., 160, 451 Balestri, M., 197, 210, 266, 277 Ballestrazzi, P., 276, 277

Bandis, S.C., 420 Barbarella, M., 218, 264, 277 Barker, C., 47, 154, 370 Bartolotto, S., 457 Barton, N., 401,404, 407-411,420 Baskov, E.A., 191 Bathurst, R.G.C., 148, 150, 151, 154 Batten, R.L., 3, 8, 44 Batygina, N.B., 211 Baugher, J.W. III, 47, 158 Bear, J., 67, 68, 82-84, 154 Beaudoin, B., 151,154 Beck, K.C., 96, 163, 164 Beckwith, G.H., 200, 201,210 Bell, J.S., 196, 210 Bellati, R., 282 Belousov, T.E, 472 Benini, G., 282 Bentor, Y.K., 101, 154 Berg, M., 420 Berg, R.R., 133, 154, 204, 210 Berget, O.P., 421 Bergonzoni, A., 261, 262, 277, 280 Berner, R.A., 10, 43, 56, 61, 118, 154, 163 Berrefjord, P.M., 384, 420 Berry, EA., 176, 190 Berry, EA.E, 48, 154 Bertoni, W., 211,254-256, 277, 280 Bhattacharyya, A., 155 Binotti, C., 282 Biot, M.A., 194, 210 Birch, A.E, 177, 190 Birch, E, 71, 154 Biscayne, RE., 25, 43 Bishlawi, M., 422 Bissell, H.J., 155, 181, 190 Bitelli, G., 266, 277 Bizzarri, 247 Blanton, T.L. III, 380, 388, 389, 394, 420 Bleakley, W.B., 381, 382, 420 Boade, R., 387, 392, 393, 400, 404, 413-415, 417, 420 Boade, R.R., 377, 378, 386, 387, 404, 409, 411-413, 417,

420, 422, 439, 450 Bobrow, D.J., 212

476 AUTHOR INDEX

Bockmeulen, H., 345, 370 Boggs, S., Jr., 11, 43 Bogomolov, G.V., 154 Bohor, B.E, 141, 147, 159 Bolt, B., 466, 472 Bolt, G.H., 49, 120, 154 Bonaldi, P., 247, 274, 277 Bondesan, M., 238, 245-247, 277 Bonham, L.C., 50, 53-55, 82, 83, 120, 124, 127, 128, 154 Borger, H.D., 370 Borgia, G.C., 217, 219, 238, 239, 241-245, 247, 261-265,

277, 278 Borregales, C., 338, 339, 370 Bortolami, G., 251, 280 Botter, B.J., 394, 420 Brace, W.T., 389, 420 Bradley, J., 47, 48, 54-56, 154 Branagan, D.F., 283 Bravo, R., 197, 210 Bray, E.E., 125, 154 Bredehoeft, J.D., 47, 63-65, 71, 154, 158 Brenneman, M.C., 370 Brighenti, G., 211,220-225, 228, 231, 233, 234, 267, 276,

277-280 Bromley, R.G., 152, 157 Bronovitskiy, A.V., 75, 76, 163 Brouwer, F.J.J., 197, 212 Brown, P.R., 148, 154 Brown, W.O., 164 Brunauer, S., 34, 43 Bruno, M.S., 190 Bryant, W.R., 154 Bucchi, A., 267, 278 Bulgarelli, G., 282 Burst, J.F., 58, 121, 154 Buryakovskiy, L.A., 75, 153, 154-156 Butler, C.O., 77, 78, 154 Butterfield, R., 226, 282

Caia, G., 237, 279 Califet-Debyser, Y., 163 Cancelli, A., 224, 235, 269, 279 Capra, A., 235, 263, 264, 266, 277, 279 Caputo, M., 241,251,279 Caraway, W.H., 157 Carbognin, L., 197, 210, 224, 234, 235, 246, 248, 251,

252, 254, 255, 257, 258, 279, 282 Carey, S.W., 190 Caribbean Petroleum Co., 370 Carman, P.C., 33, 43 Carozzi, A.V., 148, 155 Carpenter, C.B., 141, 143, 147, 155 Carradori, G., 232, 279 Cartwright, K., 71, 155

Carver, R.E., 14, 43 Cataldi, R., 282 Cebell, W.A., 58, 155 Chanda, S.K., 151, 155 Chaney, P.E., 155 Chartock, M.A., 422 Chen Y.P., 370 Chen, Y.Q., 457 Cheng, J.T., 155 Chilingar, G.V., 32, 34, 43, 44, 49, 50, 56, 96-98, 102,

106, 109-112, 117, 121, 147, 155, 156, 162, 190, 300, 334, 385, 421

Chilingarian, G.V., 12, 13, 18-22, 27, 28, 30, 32, 43, 48, 51, 54, 58, 62-65, 73, 76, 85, 87, 92, 96, 98, 103, 105, 106, 112, 114, 120, 140, 144, 147, 148, 150, 152, 153, 155-157, 159, 162, 164, 166-168, 171, 173, 174, 177, 178, 180-184, 187, 188, 190, 192, 196, 212, 221, 279, 283, 429, 438, 459, 460, 472, 473

Chin, L.Y., 387, 392, 393, 400, 404, 413-417, 420, 423, 450, 451

Christensen, S.O., 210, 420 Christianson, M., 420 Christie, P.A.E, 162 Chryssanthaskis, P., 420 Chrzanowski, A., 370, 455, 457 Ciabatti, M., 255,283 Ciancabilla, E, 277 Civan, E, 191 Clark, S.P., Jr., 47, 70, 155, 156 Clarke, D.D., 287, 334 Clarke, M.M., 212 Cleveland, T.G., 210 Cloetingh, S., 190 CNR, 220, 279 Colazas, X.C., 41, 43, 165, 190, 287, 288, 291, 297, 299,

301-308, 311, 312, 314-320, 322-324, 333, 334, 447, 450

Collins, J.J., 370 Colombetti, A., 269-271, 279 Comune di Ravenna, 220, 227, 232, 257, 259, 260, 280 Contaldo, G.J., 200, 202, 210 Converse Foundation Engineering Co., 299, 301, 334 Conybeare, C.E.B.,o77, 156 Cook, N.G.W., 194, 211 Cooper, H.H., Jr., 63, 85, 86, 156 Cordell, R.J., 120, 121, 156 Corford, C., 164 Coulter, G.R., 422 Cristensen, S.O., 472 Crocker, M.E., 14, 23, 24, 26, 43, 191 Cundall, P.A., 408, 420 Cunietti, M., 219, 274, 280 Currie, J.B., 179-181, 181, 190

AUTHORINDEX 477

D'Orazio, T.B., 407, 420 Dainese, A., 277 Dal Cin, R., 235, 280 Dal Pr~, A., 282 Dallmus, K.E, 179, 180, 180, 181, 191 Danielsen, J., 375, 377, 385, 388, 418, 419, 422, 441, 451 Davies, R.L., 384, 421 Davis, G.H., 197-199, 212, 251, 282, 473 Davis, R.A., Jr., 11, 43 de Marsily, G., 212 de Waal, J.A., 397, 420, 422, 451 De Loos, J.M., 442, 450 De Sitter, L.U., 114, 156 De Souza, J.M., 170, 192 De Vecchi, Gp., 282 De Wiest, R.J.M., 84, 156 Debout, D.G., 45 Decker, B., 1, 3, 8, 43 Deflache, A.P., 197, 210 Degens, E.T., 97, 98, 156 Dekcer, R., 1, 3, 8, 43 Dergunov, E.N., 164 Desai, C.S., 403, 420 Devine, M.D., 422 Di Filippo, M., 276, 280 Di Lallo, E., 282 Di Molfetta, A., 221, 277 Dickey, P.A., 47, 48, 97, 115, 156, 370 Dickinson, G., 50, 74, 156 Dietzman, W.D., 158, 373, 375, 377, 420 DiMaggio, EL., 402, 420 Dixon, T.N., 422 Djevanshir, R.D., 57, 59, 155, 156 Dobrynin, V.M., 76, 87, 89, 156 Domenico, EA., 67, 68, 71, 73, 156, 163 Dominici, D., 277 Donaldson, E.C., 33, 34, 44, 168, 191,425,438 Dott, R.H., Jr., 2, 3, 8, 44 Douglas, R.G., 148, 162 Dresser-Atlas, Inc., 35, 36, 44 Droo, G., 163 du Rouchet, J., 48, 156, 190 Duncan, J.M., 407, 420 Dunlap, J.R., 177, 191 Dunn, W.W., 373, 420 Durmish'yan, A.G., 76, 156 Dusseault, M.B., 40, 44, 91, 92, 156, 167, 179, 191, 196,

210, 370 Dutta, S., 48, 73, 160 Dybbs, A., 69, 156 Dzevanshir, R.D., 73, 75, 76, 154, 156 Dzhevanshir, R.D., 86-91, 117, 156

Earth, 457 Ebbs, D.J., 421 Eberl, D., 57, 156 Edwards, K.L., 371 Edwards, L.M., 70, 156 Einsele, G., 151, 157 Ekdale, A.A., 152, 157 Ellis, D.V., 35-38, 44 Elmi, C., 261, 262, 277, 278, 280 Emmett, P.H., 43 Endres, B.L., 472 Enever, J.R., 196, 210 ENI, 259, 280 Epstein, S., 98, 156 Erdman, J.G., 163 Erickson, R.C., 472 Ershaghi, I., 155 Esaki, T., 197, 210 Escojido, D., 348, 352, 356, 366, 371 Espinoza, C., 368, 369, 370 Espinoza, C.E., 431, 438 Evangelisti, G., 230, 232, 280 Evans, E.D., 125, 154 Evans, R.D., 91-96, 157 Evenson, N.M., 44

Fabbri, S., 221, 223-225, 228, 278 Facchinelli, E, 280 Fahhad, S., 162 Fairbridge, R.W., 56, 157 Fairhurst, C., 177, 191 Farouq Ali, S.M., 338, 339, 367, 368, 371,372, 472 Farrell, H.E., 422 Fatt, I., 143, 147, 157, 169, 191 Favero, V., 276 Feather, J.N., 191 Ferrara, G.C., 282 Fertl, W.H., 43, 57, 86, 87, 112, 116, 140, 155-157, 162,

190, 443-447, 450, 451 Fichter, H.J., 371 Finol, A., 338, 339, 367, 368, 371,472 Fj~er, E., 194, 210 Foged, N, 422 Folk, R.L., 16, 19, 22, 24, 27, 28, 44 Folloni, G., 277, 279 Fontes, J.C., 251,280 Foster, J.B., 74, 157 Fowler, W.A., Jr., 114, 115, 157 Freeze, R.A., 91, 157, 229, 230, 253, 280 Friedman, M., 191 Friedman, T., 157 Fries, G., 154 Fripiat, T.T., 125, 157 Frost, E., 447, 451

478 AUTHOR INDEX

Gabrish, R.K., 202, 211 Gabrysch, R.K., 294, 334 Gaida, K.H., 48, 96, 97, 105, 164 Gaillard, C., 148, 151, 157 Gallavresi, E, 237, 280 Gambardella, E, 235, 246, 280, 455, 456, 457 Gambolati, G., 91,157, 197, 210, 211,229-232, 235,250,

253, 279, 280 Garrison, R.E., 148, 157 Gates, G.L., 157 Gatto, G.O., 282 Gatto, P., 210, 249, 276, 279, 280, 282 Geertsma, J., 167, 169, 191, 194, 211,220, 228, 231,280,

367, 371,401, 405, 420, 421,428, 438 Gelmini, R., 235, 279, 281 Geological Society of America, 298 Geron, G.E, 281 Ghezzi, G., 282 Ghose, S., 162 Gibson, R.E., 54, 64, 65, 157 Gilluly, J., 334 Ginsburg, R.N., 45 Giorgi, G., 274, 275, 281 Gobbetto, W., 281 Goldberg, E.D., 26, 44 Goldsmith, A., 421 Gonzfilez de, J.C., 371,372 Gottardi, G., 278 Govoni, E., 279 Goyal, K.P., 234, 282 Graf, D.L., 99-101,157 Grant, U.S. IV, 334 Gray, K.E., 92, 161,163 Gregnsnin, A., 282 Gregory, A.R., 161 Gretener, P.E., 48, 157, 177, 191 Griffin, J.J., 26, 44 Griffiths, J.C., 20, 44 Grignani, D., 281 Groat, C.G., 202, 213 Groot, J., 371 Groppi, G., 255, 270, 282 Grosvenor, G.M., 2, 44 Grout, EE, 22, 44 Guacci, G., 200, 201, 211 Guadagnini, R., 279 Gubbins, D., 1, 3, 4, 8, 44 Gubellini, A., 218, 236, 266, 277-279, 281 Gullikson, D.M., 100, 101, 115, 157 Gurevich, A.E., 194-196, 202, 204, 211,459, 460, 472 Gutjahr, C.C.M., 158 Guyod, H., 35, 38, 44

Hadzinakos, I., 210 Hagger, R.V., Jr., 191 Haimson, B.C., 212 Hall, H.N., 44, 404, 421 Hallenbeck, L.D., 379, 421,422 Halley, R.B., 163 Halvorsen, R., 384, 421 Ham, H.H., 74, 158 Hamilton, D.H., 165, 191 Hamilton, E.L., 71, 158 Hamilton, J.M., 393, 421 Hamilton, P.J., 44 Handin, J., 169, 191 Haneberg, W.C., 200, 211 Hanor, J.S., 117, 158 Hanshaw, B.B., 47, 63-65, 71, 154, 158 H~intzschel, W., 152, 158 Harada, K., 421 Harding, T.P., 335 Harkins, K.L., 47, 158 Harlow, EH., 71, 158 Harris, ER., 298, 301,334 Harrison, E., 177, 191 Harvik, L., 420 Hawkins, M.E., 99-101, 158 Hawley, J.W., 212 Hayashi, K., 211 Heacock, R.L., 158 Heath, L.J., 13, 44 Hecht, A.D., 158 Hedberg, H.D., 48, 50, 74, 121, 158 Hedberg, W.H., 96, 116, 158 Helm, C.D., 459, 472 Henderson, C.P., 287, 335 Henyey, T.L., 327, 335 Hergert, E, 48, 158 Hermansen, H., 422 Hernandez-Rubio, A., 212 Hileman, J.A., 335 Hill, B.E., 148, 160 Hobley, M., 384, 421 Holdahl, S.R., 197, 211 Holman, G., 422 Holt, R.M., 210 Holzer, T.L., 197, 200-202, 211,212, 459, 466, 472 Holzschuh, J.C., 211 Hood, A., 120, 158 Horsrud, P., 210 Hoshino, K., 158 Hosoi, H., 74, 158 Hottman, C.E., 53, 96, 115, 158 Howard, J.H., 191 Hower, J., 57, 121, 127, 156, 161

AUTHOR INDEX 479

Hubbert, M.K., 48, 72, 84, 134, 137, 158, 165, 176, 177, 191

Hudson, ES., 298, 301, 335 Hudson, J.H., 163 Huff, R.V., 44 Hunt, J.M., 156 Hurst, W., 231, 283

Ibrahim, M.A., 52, 53, 159 Idroser, 220, 230, 262, 267, 280 Iliceto, V., 282 Inami, K., 158 Ingelstam, E., 71, 158 INTEVEE 371 Iraz~ibal, A., 371 Irmay, S., 154 Ito, T., 196, 211 Ivanov, M.K., 159 Iwamura, S., 158

Jachens, R.C., 201,211 Jacob, C.E., 84, 158, 159 Jaeger, J.C., 194, 195, 211 James, N.P., 11, 44 Janbu, N., 210, 420 Jautee, E., 148, 152, 157 Jewhurst, J., 379, 381,388, 404, 423 Johnpeer, G.D., 212 Johns, W.D., 124-128, 159, 163 Johnson, A.I., 294, 335 Johnson, D.W., 197, 200, 212 Johnson, H.R., 334 Johnson, J.P., 389-395, 398, 400, 401,421,440, 451 Johnson, R.K., 53, 96, 115, 158 Jones, C.W., 158 Jones, M.E., 210, 400, 401, 404, 407, 420, 421,472 Jones, R.A., 44 Jumikis, A.R., 211 Jtirgenson, L., 134, 136, 139, 159

Kahle, C.E, 148, 159 Kalinko, M.K., 159 Kamata, A., 401, 421 Kanani, K., 420 Kapchenko, L.N., 211 Karpova, G.V., 159 Kartsev, A.A., 183, 184, 191 Kash, D.E., 422 Kassay, D.R., 95, 159 Katz, A.S., 465, 472 Katz, D.L., 52, 53, 159, 161 Katz, S., 459, 468, 470, 472 Katz, S.A., 472

Kawai, K., 247, 281 Kazama, T., 153 Kazi, A., 155 Kazintsev, E.E., 103, 106, 107, 159 Keaton, J.R., 200, 211 Keighin, C.W., 388, 421 Kendall, A.C., 148, 159 Kendall, C.G.St.C., 159 Kendall, R.E, 44, 191 Kennedy, W.J., 152, 159 Kentie, C.J.O., 371 Khan, A., 335 Kharaka, Y.K., 158 Khilyuk, L., 472 Kieschnick, W.J., Jr., 191 Kimura, T., 210 King, G., 422 Klausing, R.L., 185, 191,251,281 Knight, L., 49, 121,155 Knipe, R.J., 190 Knutson, C.E, 141, 147, 159 Kobayashi, N., 153 Kohlhaas, C.A., 147, 159 Koide, H., 158 Korchagina, Yu.I., 50, 120, 159 Korunova, V.V., 103, 108, 109, 159 Kosloff, D., 198, 199, 211 Kouznetsov, O., 472 Kovach, R.L., 198, 211 Kovak, R.L., 327, 335 Kozel'skiy, L.T., 159 Kozeny, J., 33, 44 Kraichik, M.S., 211 Krasintseva, V.V., 103, 108, 109, 159 Kreitler, C.W., 202, 211 Krestnikov, V.N., 459, 472 Kruglikov, N.M., 211 Krumbein, W.C., 12, 20, 21, 44 Kryukov, EA., 102, 103, 105, 159 Kumar, M., 197, 211 Kurt, E.T., 164 Kuz'min, A.A., 86, 90, 159 Kvendseth, S.S., 378-383, 388, 421

Lambe, T.W., 71,159 Land, L.S., 10, 44, 158 Landa, G., 420 Lane, E.W., 13, 44 Langnes, G.L., 34, 44 Lanzoni, G., 237, 261,262, 268, 281 Larsen G., 385, 421 Laubscher, H.P., 195, 211 Laviolette, J., 335

480

Law, J., 290, 324, 335 Leal, J., 359, 361, 370, 371,455,457 Lecis, I., 281 Leddra, M.J., 421 Ledoux, E., 212 Lee, K.L., 459, 472 Lee, L.L., 198, 212 Leeman, R., 370 Lenert, E.E, 370 Leonard, R.L., 422 Leonardi, P., 251, 281 Lerche, I., 68, 159 Lewis, C.R., 56, 68, 72, 159 Lewis, D.W., 44 Lewis, R.W., 230, 253, 281,283 Li, E, 196, 212 Liang, G., 335 Liao, J.S., 212 Lidz, B.H., 163 Link, EK., 1, 2, 4, 8, 44 Lippman, R.E., 472 Lister, L.A., 200, 212 Lo, K.Y., 138, 139, 160 Lofgren, B.E., 167, 185, 191, 197, 212, 251,281 Lombardini, G., 281 Long, G., 96, 160 Lopatin, N.V., 132, 160 Love, D.W., 200, 212 Low, P.E, 47, 164 Lubinski, A., 231,281 Lundegard, ED., 26, 44 Lyons, E.P., 293, 335

Magagnoli, M., 237, 261, 262, 268, 281 Magara, K., 47, 58, 59, 72, 74, 87, 113, 117, 160, 190 Main, R., 43 Makurat, A., 420 Maltman, A.J., 190 Manheim, ET., 96, 102, 160 Manning, ES., 44 Marabini, E, 274, 275, 279, 281 Marabini, M., 279 March, 356 Marchetti, M., 282 Marchin, L.M., 43 Maricelli, J.J., 114, 115, 163 Marsden, S.S., 247, 281 Martelli, G., 278 Martin, J.C., 459, 472 Martin, R., 371 Martin, T.R., 110 Martinis, B., 281 Martirosova, A.O., 154

AUTHOR INDEX

Marzetti, N., 281 Massa, T., 280 Massari, E, 282 Masutti, M., 276, 282 Mattavelli, L., 217, 281 Matter, A., 148, 160 Matuschlea, T., 335 Matveev, A.K., 159 Maxwell, J.C., 385, 421 Maynard, J.B., 44 Mayuga, M.N., 172, 173, 187, 190, 198, 212, 287, 289,

298, 299, 301,334, 335 Mazzalai, P., 230, 235, 281 McAuliffe, C.D., 120, 121, 160 McBride, E.E, 26, 27, 44 McCann, G.D., 228, 281,401, 404, 421 McCord, D.R., 301, 335 McGuire, W.J., 191 McKelvey, J.G., 117, 160 McMurdy, R.C., 335 Meade, R.H., 49, 74, 143, 160 Mecham, O.E., 293, 335 Mechem, O.E., 335 Medizza, E, 282 Meehan, R.L., 165, 191 Meents, W.E, 157 Mencher, E., 371 Mendoza, H., 371 Menghini, M.L., 381, 382, 384, 419, 421, 443, 444, 447,

449, 450, 451 Menzie, D.E., 73, 160 Mercer, J.W., Jr., 71, 72, 160 Mercusa, G., 235, 246, 280 Merle, H.A., 352, 354, 369, 371 Mes, M.J., 384, 421,422, 441, 451 Mesini, E., 220-222, 231, 233, 234, 278, 279 Mess, K.W., 196, 224, 281 Meyer, R.E, 197, 200, 212 Meyers, W.J., 148, 160 Mifflin, M.D., 71, 156 Miller, EG., 50, 147, 148, 159, 161,162, 426, 438 Miller, J.B., 371 Milne, I.H., 117, 160 Minarelli, A., 246, 277 Mirabal, M., 368, 369, 370 Mitchell, J.K., 49, 160 Mitsui, S., 158 Miyabe, N., 295, 334 Montalenti, V., 280 Montanari, M., 235, 281 Montori, S., 235, 246, 282 Moore, C.H., 45 Morales Y.M., R., 197, 212

AUTHOR INDEX 481

Morgan, D.R., 423, 451 Morita, N., 95, 96, 160, 190, 439, 451 Morris, D.A., 163, 335 Moruzzi, A., 237, 282 Mosebach, R., 151,157 Mostertman, L.J., 251,282 Moston, R.O., 335 Mozzi, G., 210, 249, 254, 258, 276, 279, 280, 282 Mueller, J.E., 200, 202, 210 Muillo-Fernandez, R., 212 Muller, L.N., 157 Murria, J., 197, 212, 370, 371 Myer, J.D., 55, 160 Myers, L.L., 114, 115, 160

Nabiev, G.I., 164 Nakayama, K., 50, 160 Narasimhan, T.N., 234, 282 Neda, J., 372 Neglia, S., 160 Neumann, A.C., 10, 44 Newman, G.H., 380, 388, 421 Nicolas, A., 212 Nirei, H., 421 Norinelli, A., 282 Norris, V.A., 283 Novak, M.T., 157 Ntifiez, O., 348, 352, 356, 366, 371 Nur, A., 385, 422 Nygaad, O., 160, 451

O'Brien, D.E., 451 O'Keefe, J.A., 182, 183, 192 O'Nions, R.R., 6, 44 Obeida, T., 168, 191 Oberti, G., 274, 282 OGJ (Oil Gas Journal), 384, 421 Olson, L.J., 41, 43, 165, 190, 447, 450 Oudin, J.L., 163 Overton, H.L., 112, 113, 161 Ozkaya, I., 190

Paine, W.R., 156 Pakhoi'chuk, A.A., 140, 164 Paltrinieri, N., 279 Pampeyan, E.H., 200, 212 Pan, K.L., 212 Pandey, G.N., 50, 161 Panichi, C., 282 Patterson, J.M., 371 Pattillo, P.D., 422 Paulding, B.W., Jr., 420 Pavelka, E.A., 191

PDVSA, 371 Peano, G.A., 279 Pearson, C., 164 Pearson, C.A., 158 Peck, R.B., 52-54, 69, 163, 194, 213, 300, 335 Pellegrini, M., 224, 235, 269, 272, 273, 275, 279, 281,282 Perkins, T.K., 177, 191, 451 Perrier, R., 79-82, 161 Perry, E.A., Jr., 121, 127, 161 Pettijohn, EJ., 12, 13, 20, 44 Pewe, T.L., 200, 212 Philip, J.R., 66, 67, 161 Pianetti, E, 276 Piccirillo, E.M., 282 Piccoli, G., 276, 282 Pieri, L., 235, 262, 263, 266-268, 277, 279, 282 Pieri, M., 255, 270, 282 Pierson, R.G., 422 Pinoteau, B., 154 Platt, L.B., 48, 161 Plessmann, W., 152, 161 Plumley, W.J., 47, 48, 59, 161 Podio, A.L., 147, 161 Poggi, B., 230, 232, 280 Poland, J.E, 197-199, 212, 219, 224, 251, 282, 473 Polli, S., 248, 282 Poncelet, G., 157 Poskitt, T.J., 72, 161 Posokhov, E.V., 102, 161 Potter, EE., 26, 44 Pottgens, J.J.E., 197, 212, 455, 457 Potts, D.M., 392, 394, 407, 408, 421 Powers, M.C., 20, 44, 47, 58, 121, 161 Powley, D.E., 56, 161, 197, 200, 212 Pracht, W.E., 71,158 Pratt, W.E., 197, 200, 212 Pray, L.C., 148, 161 Prevost, J., 420 Price, L.C., 127, 161 Price, N.J., 176, 191 Prokopovich, N.P., 91, 92, 161, 167, 179, 191, 197, 212,

473 Proshlyakov, B.K., 74, 76, 161 Pryor, W.A., 44 Puig, E, 41, 45, 369, 371 Pulpan, H., 177, 192

Quiblier, J., 79-82, 161 Quijanol, R., 472

Raaen, A.M., 210 Radicioni, E, 277 Raffagli, A., 237, 277

482 AUTHOR INDEX

Rafidi, N.R., 420 Raghavan, R., 50, 84, 161,426, 438 Rainis, A.E., 68, 161 Rajani, B., 370, 371 Rall, C.G., 99, 100, 161 Ramirez, M., 369, 371 Ramsay, J.G., 138, 161, 172, 174, 192 Randell, D.H., 287, 335 Ratigan, J.L., 196, 212 Rattia, A., 367, 368, 372 Raymond, R.H., 212 Reardon, J.B., 335 Reddish, D.J., 200, 213, 459, 473 Reed, W.E., 156 Reimers, R.E, 212 Renton, J.J., 58 Rentsch, H.C., 384, 422, 441,451 Renz, H.H., 371 Reuter, J.H., 156 Reynolds, C.B., 211 Reynolds, I.B., 211 Rhett, D.W., 421,422, 451 Ricceri, G., 211,224, 226, 279-282 Ricchiuto, T., 217, 278, 281 Richter, C.E, 198, 212 Rickards, L.M., 378, 422 Ricken, W., 148-153, 161 Rieke, H.H. III, 43, 48, 51, 54, 57, 62-65, 73, 76, 85,

87, 92, 96, 98, 102, 103, 106, 109-112, 114, 117, 144, 145, 148, 152, 155-157, 161, 162, 166, 168, 174, 178, 180-184, 187, 188, 190, 192, 196, 212, 221, 279, 334, 459, 473

Risnes, R., 210 Rittenhouse, G., 21, 44 Rivera, A., 197, 212 Robbie, R.H., 371 Roberts, D.L., 294, 335 Roberts, J.E., 170, 171, 186-189, 192, 300, 335 Robertson, E.C., 60, 61, 77, 162 Robertson, J.O., Jr., 44, 155, 162, 472 Roca, L., 372 Rodio, G., 237, 280 Roegiers, J.-C., 419, 423 Roest, P.W., 370 Rogers, G.L., 165, 192 Rogers, J.R., 210 Romaro, G., 281 Rose, C.S., 56, 68, 72, 159 Rose, W.D., 33, 45 Rosenbaum, M.S., 105, 108, 162 Ross, T.A., 420 Rossi, G., 281 Rozos, D., 210

Rubey, W.W., 48, 134, 137, 158, 165, 177, 191 Rubino, E., 160 Rubio, EE., 372 Ruddy, I., 401,422 Ruedrich, R.A., 447, 449, 451 Rukhin, L.B., 28, 44 Russell, W.L., 48, 162 Russo, P., 235, 246, 262, 263, 266-269, 277-279, 281,282

Salazar, A., 338, 339, 370 Salsilli, F., 281 Sampath, K., 388, 421 Samuels, G., 70, 162 Samuels, N.D., 26, 44 Samuels, S.G., 49, 162 S~inchez, M., 370, 371 Sandhu, R.S., 228, 282 Sandier, I.S., 402, 420 Sanford, A.R., 175, 192 Sarkar, S., 155 Sasaki, S., 153 Sawa, T., 153 Sawabini, C.T., 108, 121, 146, 147, 155, 162, 190, 334 Sayles, EL., 96, 102, 160 Sbettega, G., 282 Schairer, J.E, 190 Schatz, J.E, 401, 422 Scheidegger, A.E., 177, 182, 183, 192 Schenk, L., 41, 45, 369, 371,372 Scherer, M., 76, 162 Schiesaro, G., 237, 276, 277, 282, 283 Schlanger, S.O., 148, 162 Schmidt, G.W., 96, 97, 116, 162 Schneider, G.M.C., 371 Schoell, M., 281 Scholle, P.A., 45, 385, 422 Scholz, C., 420 Schoonbeek, J.B., 447, 449, 451 Schowalter, T.T., 133, 162 Schrefler, B., 230, 253, 281,283 Schumann, H.H., 212 Schweitzer, S., 69, 156 Sclater, J.G., 162 Scorer, J.D.T., 148, 162 Scott, R.E, 197, 211,212 Scranton, J., 211 Secrest, C.D., 200, 212 Sedea, R., 282 Seeley, D.R., 335 Sekiguchi, K., 153 Selli, R., 255,283 Serandrei-Barbero, R., 276 Serdengecti, S.C., 459, 472

AUTHORINDEX 483

Serebryakov, V.A., 87, 89, 156 Seward, J.M., 158 Shafer, J.L., 393, 421 Shane, L.E., 35, 38, 44 Sharp, J.M., Jr., 47, 67-73, 93, 162, 163 Shikata, K., 210 Shimoyama, A., 124-128, 159, 163 Shimp, N.E, 157 Shinn, E.A., 45, 152, 163 Shirkovskiy, A.I., 34, 45 Shishkina, O.V., 103, 163 Shlemon, R.J., 200, 211 Shriram, C.R., 156 Shtange, D.V., 472 Sidorov, V., 472 Siemers, W.T., 420, 421,450, 451 Siever, R., 44, 163 Simeoni, U., 238, 277 Simon, D.E., 392, 422 Sinnokrot, A., 43 Siriwardane, A.J., 403, 420 Sjoberg, S., 71,158 Skempton, A.W., 49, 71,163, 188 Skidmore, D.R., 161 Slemmons, D.B., 210 Smith, D.J., 383, 384, 422 Smith, J.E., 50, 54, 65, 66, 73, 93, 96, 118-120, 163 Smits, R.M.M., 380, 393, 394, 396-399, 401, 405, 406,

420, 422, 440, 451 Snyder, R.E., 375, 376, 423 Soranzo, M., 280 Sorby, H.C., 48, 163 Sorum, M., 420 Spencer, G.B., 141, 143, 147, 155 Spicer, H.C., 190 Sprunt, E.S., 385, 422 Squarzanti, S., 277 Stainforth, R.M., 372 Stallman, R.W., 69, 129, 163 Staub, H.L., 428, 438 Steinen, R.P., 148, 163 Stephenson, E.L., 190 Stephenson, L.P., 385, 422 Stockman, K.W., 10, 45 Strehle, R.W., 197, 197, 200, 213 Sulak, R.M., 375, 377-379, 385, 388, 417-419, 422, 441,

451 Sutton, EA., 372 Sylte, J.E., 379, 421,422

Tappel, I., 421 Teeuw, D., 372 Tek, M.R., 161

Teller, E., 43 Telli, A.N., 157 Teng, T., 327, 335 Terzaghi, K., 52-54, 69, 76, 163, 194, 213, 300, 335 Teufel, L.W., 190, 395, 396, 400, 401,416, 422 Thatcher, W., 197, 202, 211 Thomas, C.L., 125, 163 Thomas, L.K., 379, 412, 421,422 Thompson, T.L., 48, 163 Thompson, T.W., 92, 163 Tickell, EG., 301,335 Timko, D.J., 86, 90, 112, 113, 116, 157, 161, 443-445,

447, 451 Timm, B.C., 114, 115, 163 Tissot, B., 121,163 Tkhostov, B.A., 48, 163 Tongiorni, E., 282 Truex, J.N., 287, 335 Trutmann, O., 357, 358, 372 Tsvetkova, M.A., 33, 45

Unguendoli, M., 218, 279, 281 Uriman, V.I., 159

Vagin, S. B., 191 Van Balen, R., 190 Van der Knaap, E., 294, 299, 300, 335 Van der Knaap, W., 143-145, 163, 167, 170, 171, 192,

224, 283, 348, 351, 369, 372 Van der Vlis, A.C., 141, 143-145, 163, 167, 170, 171,

192, 224, 283, 294, 299, 300, 335, 348, 351,369, 372 Van Domselaar, H., 370, 425, 438 Van Everdingen, A.E, 231,283 Van Kooten, J.EC., 422, 451 Van Opstal, G., 371,401, 405,422 Van Opstal, G.H.C., 220, 283 Van Sickle, V.R., 202, 213 Van Wingen, N., 335 Vassoevich, N.B., 75, 76, 163 Velsink, H., 370 Verall, P., 421 Verruijt, A., 164 Vik, G., 420 Villani, B., 197, 210, 266, 277 Villermin, E., 211 Visher, G.S., 29, 30, 45 Vitali, D., 277, 278 Vitelli, E., 280 Vittuari, L., 277 Von Engelhardt, W., 48, 96, 97, 105, 164 Voss, C.I., 279 Vuillermin, E., 280

484 AUTHOR INDEX

Wade, J.E., 293, 335 Wadell, H., 21, 45 Wallace, W.E., 115, 164 Wallis, W.E., 371 Walsh, D., 8, 45 Walton, R.J., 210 Warner, D.L., 25, 45 Warpinski, N.R., 190, 395, 422 Watkins, J.W., 164 Weast, R.C., 71, 164 Weaver, C.E., 96, 121, 164 Wedepohl, K.H., 149, 164 Weeks, L.G., 181 Weeks, R.E., 210 Weller, EA., 74-76, 164 Weller, J.M., 27, 28, 45 Welte, D.H., 50, 121, 125, 128-133, 164 Wentworth, C.K., 13, 45 Wetmiller, R.J., 459, 473 Whalen, H.E., 74, 157 White, D.E., 99, 164 White, I.L., 373, 422 Whitfill, D.L., 160, 190, 451 Whitman, R.V., 71, 159 Whittaker, B.N., 200, 213, 459, 473 Wiborg, R., 379, 381, 388, 404, 423 Wichmann, P.A., 451 Wickham, E., 472 Wilcox, R.E., 287, 335 Williams, D.G., 115, 164 Willis, D.G., 176, 181,191 Wilson, E.L., 228, 282 Wiltis, C.H., 228, 281 Winterstein, 190

Witts, C.H., 401, 404, 421 Wolcott, EP., 371 Wold, M.B., 210 Wolf, K.H., 13, 18-22, 27, 28, 30, 32, 43, 148, 150, 155,

164, 171, 173, 190, 221, 279, 283, 438, 459, 472 Wolfe, M.J., 148, 164 Wood, J.J., 164 Wright, J., 99-101, 161,164 Wyllie, M.R.J., 33, 45 Wyllie, P.J., 3, 45

Yarzab, R.E, 159 Yeats, R.S., 287, 335 Yen, T.E, 8, 43, 45, 153, 155, 156, 159, 190 Yoh-Han Pao, 473 Young, A., 47, 164 Yudovich, A., 419, 423, 441, 442, 451 Yukler, M.A., 50, 128-133, 164 Yusufzade, Kh.B., 86, 90, 164

Zaman, M., 401, 413, 419, 423 Zambon, G., 254, 258, 282 Zambon, M., 235, 243, 283 Zankl, H., 148, 164 Zanovello, A., 237, 283 Zaslavsky, D., 154 Zaubi, M., 472 Zavatti, A., 279 Zavgorodniy, A.L., 140, 164 Zen, E-an, 47, 158 Zhuchkova, A.A., 103, 105, 159 Zilkoski, D.B., 211 Zubillaga, J., 370, 371

485

S U B J E C T I N D E X *

Absolute zero, 35 Abyssal plain, 7, 8 Accretion of islands, 8 Accretion terrains, 6, 8 Acque alte, 248 Adriatic, 257, 269 Advection, 118 Africa, 8, 26 Ahermatypic hexacorals, 11 Alaska, 8 Albuskjell field, 378 Algae, 10 Alkalinity of ocean water, 10 Alkanes, 124, 125, 128 Alluvial environment, 40 Alps, 8, 217 American continental plate, 8 Amino acids, 98 Anadiagenesis, 56 Angle of internal friction, 139 Anisotropy, 36 Antarctica, 7 Apennines, 216, 217, 257, 261,269 Apenninic margin, 271 Appalachian Basin, 58 Apsheron Archipelago, Azerbaijan, 88 Apsheron Peninsula, Azerbaijan, 75, 76, 88 Aquathermal pressuring, 47 Aquifer, 186, 200, 201,228-232, 255 - , coarse-grained, 186 - , fine-grained, 186 - , lateral, 232 - , modeling, 229, 230 - , phreatic, 201 - pressure distribution, 231 Aquitards, 228, 229 Aragonite, 10, 11 Aralsorskiy well SG-1, 75 Arc, 180 Arenite, 27

* Prepared by Dawood Momeni, Dr. George V. Chilin- garian, Dr. Erle C. Donaldson and Dr. Teh Fu Yen.

Arizona, 201 Arkoses, 24 Asian continental plate, 8 Asinelli Tower, 264 Asthenosphere, 3, 4, 6 Atlantic Ocean, 1, 26, 103 Average-porosity-curve, 81 Avogadro's number, 35 Azerbayjan, 75, 76, 88

Bachaquero field, 338, 340-342, 345, 346, 349, 350, 352, 354, 358-361

Baku Archipelago, 75, 76, 86, 88, 90 Baldwin-Butler compaction curves, 77 Bandera Sandstone, 23 Barrier-type reef, 11 Barsa-Gelmes-Vishka Oilfield (Turkmenistan), 470 Basaltic crust, 7 Basaltic material, 4, 7 Base exchange, 97 Basins, 6, 176-181 - , depositional, 176, 178, 180 -, dynamic, 180, 181 - , sedimentary, 176, 180, 181 - , sinking sedimentary, 179 Bassano, 249 Bed thickness changes, 77 Bell hole protection, 295 Bench mark elevations, Wilmington field, 329, 331, 332 Bentonite, 103, 121 Biaxial loading, 146 Bicarbonate, 10 Biot Equation, 91 Bioturbation structures, 152 Bitumen, 337, 338 Black Sea, 103 Body force, 194 Body waves, seismic, 5 Bolivar Coast, 141, 144, 145 Bolivar Coastal Fields (BCF), 338-340, 343-345, 347,

349, 350, 352, 353, 355-357, 364, 365, 367, 369 - , analytical modeling, 369 - , compaction, 339, 353 - , compaction mechanism, 347

486 SUBJECT INDEX

- , cross-section, 344 - , drainage system, 364, 365 - , geological section, 343 - , geological setting, 340 - , heavy and extra heavy oil, 338 - , oil recovery, 353, 355, 356 - , reservoir simulation, 365, 367 - , reservoirs, 345, 349, 355, 365 - , sand sample experiments, 352 - , steam injection, 355 - , subsidence, 339, 351, 352 - , subsidence contours, 350 - , subsidence monitoring, 357 - , subsidence,prediction, 365 - , traps, 343 Bologna, 218, 219, 228, 230, 236, 260, 261-269, 272 Bonham, 53-55 - compaction model, 53, 54 - depth-versus-porosity curves, 54 - development model, 55 Boscan field, 338 Boulders, 11 Boussinesque's formula, 208 Brachiopods, 10 Brazoria County, 115 Bridging, 19 Brines, 97, 99 - , calcium chloride, 99 - , generation, 97 - , high salinity, 97 Bulk compressibilities, 142-145, 194, 221-227, 229, 231,

306 Bulk modulus, 35, 37, 64 Bulk shear, 194 Bulk volume, 31, 34 Bullet, 447, 450 - , radioactive, 447 - , marker, 450 Bunter Formation, 373 Buoyancy, 206 Buregskiy Shale, 140, 141 Burrow tube deformation, 152 Burrows, 152, 153

Ca/Na ratio, 99 Ca-montmorillonite, 109 Ca-smectite, 125 Cabimas field, 358-360 CaCI2, 105 Calcasieu Parish, 97, 116 Calcite, 11,392 Calcium carbonate, 10, 11 Calcium chloride waters, 99

Calculation, 60, 62, 64, 66, 70-72, 76, 77, 79, 89, 118, 126, 134, 138, 146, 148-150, 152

- , compaction curves, 77 - , decarboxylation-thermal cracking, 126 - , decompaction number, 77 - , degree of compaction, 152 - , deviatoric stress tensor, 137 - , energy balance, 71 - , equilibrium constant, 118 - , fluid movement, 66 - , gas compressibility equation, 148 - , heat, convection, 70 - , hydraulic compaction, 64 - , material balance equation, 146 - , moisture ratio, 66 - , momentum balance, 71 - , momentum transport, 70 - , pore water pressure at depth, 134 - , porosity at a burial depth, 76 - , pressure balance, 72 - , rate of compaction, 62 - , rate of temperature change, 70 - , Ricken's carbonate compaction equation, 149 - , solid-grain proportion, 60 - , Ricken's equation for carbonate rocks with low

porosities, 150 - , spheric stress tensor, 137 - , thermal diffusivity, 70 - , thickness changes in sedimentary layers, 79 - , total stress tensor, 138 - , water influx into producing reservoirs, 89 California, 100, 102, 143 Cambrian, 98 Cambrian/Ordivician, 100 Cambrian/Pennsylvanian, 99 Canada, 77 Capillary forces, 205, 206 Caprocks, 89, 91, 95, 96, 102, 141, 206 Carbonate compaction law, 149 Carbonate ions, 10 Carbonate reservoir, 140 - - , overpressure, 140 Carbonates, 9, 10, 22, 24, 40, 153, 373, 396, 397, 405 Carbonic acid, 10 Carboniferous, 373 Carman-Kozeny equation, 33 Casing collar surveys, 324, 325, 442, 443 Casing failure, 441 Castelfranco, 249 Catagenetic, 9 Catalytic cracking, 125 Cation exchange, 118 Ca'Vendramin, 245

SUBJECT INDEX 487

Cementation, 150, 179 Central Atlantic, 7 Central Pacific, 7 Chert, 24 Chloride concentration, 116 Chlorinity, 111, 116 Chlorite, 9, 25, 57, 58 Chocolate Bayou field, TX, 115 Classification of sands, 11 Clastic rocks, 9 Clastic sedimentary particles, 11 Clays, 9, 11, 14, 18, 22, 24, 26, 153, 172, 185, 186 - , beds, 167 - , interbedded, 167, 186 - minerals, 9 - , undercompacted, 167 Claystones, 26 Coal, 373 Cobbles, 11 Cod field, 376 Coefficient of compaction, uniaxial, 431 Coefficient of compressibility, 142 Coefficient of irreversible compaction, 75, 76 Collar, casing, 442, 443 Collar locator, magnetic, 448 Colliding margins, 8 Colloid filtering, 120 Compaction, 47, 50, 53, 55, 59, 61, 82, 87, 120, 121, 123,

146, 148, 167, 169, 172, 176, 215, 398, 400, 404-406, 418, 419, 425, 426, 428

- , analytical models, 59 - b e h a v i o r , 398, 400 - , carbonates, 148 - , clay, 53 - , closed system, 59 - , computation, 428 - curves, 75 - , disequilibrium, 47 - drive, 404 - fluid flow models, 82 - grain, 165 - gravitational, 50, 73 - hydrocarbon expulsion, 120 - in situ, 196, 406 - inhibited, 82 - ionic changes in expelled water with time, 123 - laboratory hydrocarbon expulsion results, 121 - loading coefficient, 146 - leaky system, 59 - model, 50 - , nonequilibrium, 47 - , open system, 59 - , overburden, 419

- , rate, 61 - , reservoir, 91, 425 - , sediment, 59 - , subsurface, 425 - , tectonic, 176 - , testing, 300 - - , Wilmington oilfield, 300 - , triaxial, 169 - , uniaxial, 169, 172 - , volumetric, 172 - , water influx, 87 Compactional history, 80 Completion methods, Wilmington oilfield, 293, 294 Compressibility, 35, 42, 87, 89, 93, 129, 139, 141-144,

146, 147 - bulk, 168, 169 - carbonates, 146 - clayey sediments, 141 - consolidated sandstones, 146 - experimental values, 144 - fluid, 93, 129 - formation, 170 - formulas, 142 - isothermal, 426 - low, 179 - oil, 146 - pore volume, 169 - pore water, 139 - pores, 87 - , "pseudo-bulk", 141 - , sand, 141 - , sediment grains, 139 - , shales, 146 - , solid matrix, 93 - , unconsolidated sands, 146 - , unconsolidated sediments, 143 - , uniaxial, 169 - , water, 87 Compression, 176, 180, 198 - , horizontal, 198 - , tectonic, 176 Compressional waves, 38 Conductivity, 122, 123 Confined aquifer, 41 Connate water, 50 Consolidated sands, 14 Consolidated sediments, 13 Consolidation tests, 308 Continental, 4, 5, 7, 8 - c r u s t , 4, 5, 7 - m a r g i n s , 4, 7, 8 - masses, 8 - rifts, 7

488 SUBJECT INDEX

Continuity equations, 93 - - , fluid phase, 93 - - , rock matrix, 93 Continuous frequency curve, 15 Convolutions, 8 Coral reefs, 11 Coulter counter, 14 Creep, 167, 169, 175, 176, 209 - , horizontal, 169 - , viscous, 167 Cretaceous, 99-101, 338, 340, 342, 377 Crinoids, 11 Crude oil, 121, 127 - - , solubility, 127 Crust, 180, 182, 183 Crustal plates, 8 Cumulative frequency curve, 15, 16, 24 Currents, convective, 2 Cycle, hydrogeologic, 183, 184

Danian, 397 Danian chalk field, 392 Danian Limestone, 375 Darcy's law, 83-85, 87, 430 Decarboxylation, 124, 125 - of docosanoic acid, 125 Decarboxylation-cracking zonation, 127 Decompaction, 77, 81, 82 - number, 77, 81 Deep Sea and Ocean Drilling, 148 Deep Sea Drilling Project, 117 Deformability, 221 Deformation, 167, 169, 193-195, 200, 223, 230, 380, 400,

401, 404, 405 - , analysis, 194 - , cataclastic, 169 - , causes, 193, 195 - , elastic, 194 - , non-recoverable, 167 - , pattern, 200 - , plastic, 167, 169 - , recoverable, 167 - , reversible, 194 - , visco-elastic, 167 - , viscous, 169 Dendritic granite washes, 9 Density, 14, 24, 33 Deposition, sedimentary, 166 Depression, 181, 183, 184 - , tectonic, 183, 184 - , topographic, 181 Depth of burial, 74 Depth-versus-porosity curve, 63

Detectors, radioactive, 448 Detrital rocks, 29 Deviator stress, 136, 139 Deviatoric stress state, 137 Devonian shale, 58 Diagenesis, 22, 56, 60, 61, 91, 121, 149 - , carbonate, 149 - , clay mineral, 56 Diagenetic stage, 9 Diapirs, shale, 48 Diapirism, phase changes, 47 Diastrophism, lithology, 36 Dickite, 145 Differential navigation, 454, 455 - - , receiver geometry, 455 Diffusion flow, 204 - , vertical, 204 Dilatation, 194 Disequilibrium components, 174 Dispersivity, 69, 73 Displacement, fault, 179 Dissolution, carbonate, 149 Divergent margins, 8 Divnoe area, 106, 107 Dolomites, 373 Dolomitization, 99 Dry lake clay, 144 Ducal Palace, 235

Earthquakes, 2, 4, 5, 8, 467, 459, 470, 471 - , maximum magnitude, 467 - , prediction, 459, 470, 471 - - , neural network based, 471 - , Southern California, 467 - , waves, 2 Earth's surface, 180 East Africa, 7 East Shetland Basin, 373 Edda field, 377 Effective intergranular stress, 51 Effective stress equation, 93 Eh, 56 Ekofisk field, 373, 375, 376-389, 391, 392, 396, 398, 404,

406-408, 411-414, 417-419, 439, 440-442, 447, 449 - , bubble curtains, 383 - , chalk formation, 440 - , compaction measurements, 381, 382 - , compaction monitoring, 449 - , compaction tests, 391 - , contour map, 412 - , depletion profiles, 418, 419 - description, 377 - , discovery, 376

SUBJECT INDEX

- , elliptical shape, 411 - , enhanced oil recovery projects, 379, 418 - , field development, 377 - , finite-element, 408 - , jack-up, 383, 384 - , key parameters, 380 - , location, 375 - , mineralogy, 385 - , numerical simulation, 406, 439 - , oil production, 377 - , permeability, 388 - , platforms, 441 - , platform sinking, 379, 383 - , porosity, 385, 386 - , porosity distribution, 387 - , protective barrier, 384 - , remedial measures, 381 - , reservoir characteristics, 384 - , reservoir compaction, 373, 404, 417 - , reservoir data, 375 - , reservoir mechanics, 388 - , salt domes, 375 - , slippage, 442 - , stress changes, 396 - , subsidence, 373, 380, 404, 417 - , subsidence measurements, 381 - , 2D simulation, 407 - , 3D simulation, 413, 414 - , uniaxial strain tests, 389-391 - , waterflooding programs, 398 Ekofisk Formation, 377, 386, 400, 403 - , porosity log, 377 - , porosity variations, 387 Elastic, 36, 84, 85, 176, 403

- aquifer, 84 - constants, 403 - , isotropically, 176 - media, 85 - moduli, 36 -proper ty , 35, 36 Elastoplastic theory, 401 Electric logs, 97 Electrical resistivity, 141 Electrokinetic forces, 86 Endogenic, 92 Energy balance, 67, 71 Energy transport, 68, 69

- - , continuity equation, 69 Eocene, 100, 101, 114, 144, 145, 338, 340, 342 Epidiagenesis, 56 Epigenesis, 22 Epigenetic, 9

Equations, 72, 78, 94 - , Dickinson, 78 - , energy, 94 - , equilibrium, 93 - , fluid density, 72 - , heat capacity, 72 - , hydraulic conductivity, 72 - , intrinsic permeability, 72 - , porosity, 72 - , thermal conductivity, 72 - , thermal diffusivity, 72 - , viscosity, 72 Equations of state, 94 - , fully incompressible, 94 - , incompressible, 94 - , slightly incompressible, 94 Equilibrium, static, 174 Erosion, 48 Estimation of petroleum reserves, 146 - - - , effect of rock compressibility, 146 Euganean Hydrothermal Basin, 276 Europe, 8 Eurasia, 8 Evaporites, 102 Exogenic, 92 Extensometers, 243-245

Facies, 57, 58 - , clay mineral, 57 - , type I, 57 - , type II, 58 - , type III, 58 - , type IV, 58 - , type V, 58 Fatty acids, 124, 125 Fatt's pressure cell, 144 Fault planes, 198 Faulting, 47, 176, 179, 185,404 - , tension-type, 185 - , thrust, 176 Faults, 202 Feldspar degradation, 9 Feldspars, 9, 21, 22, 24, 27 Ferrara Province, 215, 245, 246 Ferro-magnesium minerals, 24, 27 Fields, 99, 115 - , Bartlesville-Dewey, 99 - , Chocolate Bayou, 115 - , E1 Dorado East, 99 - , Hall-Gurney, 99 - , Pistol Ridge, 99 - , Soso, 99 - , St. Louise, 99

489

490

- , Tinsley, 99 - , Wesson, 99 Fireflood, 41 Fissure, 200, 201 - , earth, 201 - , Pixley, 201 - , surface, 200 Fluid, 5, 54, 86, 87, 165, 429, 431 - , compressibility, 69 - , expansion, 431 - , flow, 82, 87 - - , argillaceous sediments, 82 - - , overpressured shale, 87 - , injection-production, 429 - , Newtonian, 86, 87 - , non-Newtonian, 87 - , withdrawal, 165 Fluvial, 29 Folding, 176, 179 Foraminifera, 10, 11 Forces, 165, 168, 174 - , accelerating, 174 - , body, 165, 174 - , shear, 168 - , surface, 165 - , tectonic, 174 Formation compressibility, 142 Formations, 100-102, 179, 342 - , Arbuckle Limestone, 100 - , Bartlesville Sandstone, 100, 101 - , El Mene, 342 - , Guasare Paleocene,342 - , Icotea, 342 - , Isnotu, 342 - , La Rosa, 342 - , Lagunillas, 342 - , Misoa, 342 - , Mito Juan, 342 - , Nacatoch Sandstone, 100, 101 - , Pico, 100-102 - , Sespe, 100-102 - , shallow, 179 - , Ste. Genevieve Limestone, 100 - , Trujillo, 342 - , Wilcox, 100, 101 Fourier law, 95 - - , heat conduction, 95 Fractional porosity, 34 Fractures, 193, 197, 198 - , subsidence, 197 Fracturing, hydraulic, 177, 179 Frequency probability curve, 15 Fresh water, 101, 115

SUBJECT INDEX

Friction, 5 Fuller's earth, 105, 109 Functional porosity, 31

Gamma-ray spectral logging, 57 Gas cap, 193 Gas compressibility, 148 Gas diffusion, 203 Gas drive, 41 Gas-filled wellbore, pressure distribution, 209 Gas globule, 204 Gas leakage, 461, 465 - - , monitoring, 465 Gas migration, 204, 206, 207, 460 Gas seepage, 202 Gas storage, 193 Gas supercompressibility, 208 Gasli Gasfield (Uzbekistan), 470 Gastropods, 10 Gaussian elimination, 428 Geologic system, 54, 58 - - , closed, 58 - - , leaky, 54 - - , open, 54 Geology, 286 - , Wilmington oilfield, 286 Geopressured zones, 41 Geosyncline, 174, 179, 182, 183 Geothermal gradient, 68, 73, 75 121, 126 Geothermal, temperature changes, 47 Gibbs' free energy, 118, 119 - - - , equation, 118 Gibbs-Donnan, equation, 118 Gibbsite, 25 Gibson's equation, 65 Global Positioning System (GPS), 453-456 Gondwanaland, 1 Goose Creek oilfield, 197 Graben, 181, 185, 373, 377 - , Central, 373 - , Viking, 373, 377 Gradient, 56, 165, 177, 186 - , geopressure, 165 - , geostatic pressure, 186 - , geothermal, 56, 165 - , hydrostatic pressure, 177, 186 Grain sizes, 12, 14 Grain volume, 34 Grain-size distribution, 17, 18, 27, 32 Grain-size histogram, 15, 16 Grand Isle, 113 Granitic continents, 7 Granitic rocks, 9

SUBJECT INDEX

Granular material, 11 Granules, 11 Gravel, 11 Gravitational highs, 7 Gravity anomalies, 7 Graywacke, 24 Geertsma's integral, 231 Groningen gasfield, 196, 375, 447 Ground subsidence, 453, 465

, monitoring, 453 , prediction, 465

Groundwater, withdrawal, 197 Gulf Coast, 50, 68, 73, 100, 101, 127, 141 Gulf of Mexico, 102 Gypsum-anhydrite conversion, 47

Halloysite, 145 Heat, 69 - accumulation, 70 - - , rate of, 70 - capacity, 70 - dispersion, 69 - of adsorption, 34 - transfer, 129 - - , conduction, 129 - - , convection, 69 Heavy oils, 41 Heterogeneity, lithological, 196, 207 High Adriatic, 234 Himalaya Mountains, 8 Hingebelts, 181 Histograms, 24 Hook's law, 35 Horizontal-strain surveys, 327 Hornblendes, 22 Hot spot, 6 Hot-water drive, 41 Hydraulic conductivity, 64, 129, 230 Hydraulic connectivity, 193 Hydrazine, 13 Hydrocarbon potential, 132 Hydrocarbon reservoirs, 215,229-231 Hydrogen ions, 10 Hydrostatic compaction apparatus, 108, 145 Hydrostatic compression tests, 393, 403, 440 Hydrostatic loading, 146 Hydrostatic pore pressure, 195 Hydrostatic stress, 134, 136, 137

, tensor, 136

Igneous, 22 Illinois Basin, 100 Illite, 9, 25, 57-59, 106, 110-112, 117, 121,145, 147 - , formation of, 57

India, 8 Indian continent, 8 Indian Ocean, 7, 25, 26 Indurated rocks, 33 Infiltration of fluids, 48 Influx, shale water, 427 Injection water, types, Wilmington field, 328 Inorganic calcium carbonate, 9 Interconnections, 32 Interstitial fluid, 51, 96 - - , chemistry, 96 Interstitial water, 98 - - , classification, 98 - - , isotopes, 98 - - , oilfield brines, 98 Invertebrates, 11 Ion-exchange, 24 Ion-filtration, 113 Island arcs, 4 Isostasy, 182 Isotropic hardening, 401 Italian Geodetic Commission, 218 Italy, 215-283 - Bologna case history, 260-268 - Euganean Hydrothermal Basin, 276 - Forli's subsidence, 238-273 - geotechnical features, 219 - geothermal areas, 232, 234 - legal considerations, 237, 238 - modeling, 228-232 - Modena case history, 269-273 - Po Delta case history, 238-273 - Po-Veneto Plain, 215,216 - Ravenna case history, 253-260 - subsidence damage, 234, 235 - subsidence measurements, 217-219 - subsidence remedies, 235-237 - Venice case history, 248-253

Japan, 57, 58 Jocob's expression, 85 Jurassic, 97, 373

K/Na ratio, 99 Kaolinite, 9, 25, 33, 57, 58, 105, 121, 144, 351 Kentucky, 145 Kerogen, 132, 133 - , type II, 132, 133 - , type III, 132, 133 Kronecker's delta, 194 Kura Depression, 88, 90 Kurinskaya Depression, 75 Kurtosis, 17

491

492 SUBJECT INDEX

Lacustrine environment, 40 Lagunillas field, Venezuela, 338, 340-342, 345-347, 349,

350, 354, 357-360, 366 Lake Maracaibo Basin, 338, 340, 346, 360, 447, 454 Leaching, 97, 109, 117 Leakage, gas, 208 Lime mud, 10 Limestone, 11, 147, 375 Liquefaction pressure of nitrogen, 34 Litharenite, 26 Lithic arenite, 24 Lithic subarkose, 26 Lithification, 9 Lithosphere, 3, 5, 6 Load, 181, 185, 186 - , grain-to-grain, 185 - , stresses, 181 Loading, 168, 169 - history, 196 - , hydrostatic, 168 - , polyaxial, 169 - rate, 397 Logs, 442, 443, 447 - , caliper, 442 - , casing collar, 442 - , compensated neutron, 443 - , multi-finger caliper, 443 - , radioactive bullets, 447 - , time-lapse pulsed neutron capture, 443 London, England, 197 Long Beach, California, 41, 285-287, 447 Longitudinal waves, 38 Lopatin's method, 132 Louisiana, 86, 97, 101, 114-116, 141 Louisville, KY, 145 Love waves, 2 Lower Paleocene, 375 Lower Permian, 373 Lower Terminal Zone, 290, 291, 314, 320, 322

Maestrichtian, 377, 397 Magma, 7 Magnesium calcite, 11 Magnesium ions, 10 Major earthquakes, 466 - - , distribution, 465 Major subsidence, 465 - - , locations of, 465 Mantle, 7, 182, 183 Marine basins, 11 Marine environment, 40 Marine muds, 103, 108, 109

, interstitial solutions, 108, 109

Markers, 449, 450 - , radioactive, 449, 450 Marls, 150 Matagorda County, 115 Material balance equation, 146 Matrix, 165, 166, 168 - , skeletal, 165, 166, 168 Maykop clay, 106, 107 Mean, 17 Mean size, 15 Membrane, 47 - , shale, 47 Mene Grande field, 339-341, 345, 346, 355, 358, 360 Mesozoic,58, 98, 373 Mestre, 249 Metamorphic, 22 Metamorphism, 9 Methane gas, 50 Methane generation, 48 Mexico City, 197 Mica, 58, 144 Michigan Basin, 99 Micrite, 10 Microcapillaries, 87 Mid-Atlantic Ridge, 26 Middle East, 116 Midocean ridges, 7 Mudstones, 22 Migration, mechanism, gas, 124, 207 Minerals, phase changes, 47 Miocene, 50, 114, 185, 261, 270, 340-343 Mississippian, 100 Mixed-layer minerals, 58 Mode, 18 Models, 52-55, 58, 61, 64-67, 70, 73, 79, 83, 87, 89, 93,

95, 116-119, 124, 126-127, 130, 229, 230, 232, 399, 402, 405, 407, 408, 411, 416

- , Appello's colloid filtering, 119 - , Berner's diagenetic-compaction, 61 - , Bonham's compaction, 53-55, 83, 118 - , Cam Clay, 407 - , compaction, 65, 117 - , constitutive, 399, 402, 413, 416 - , diagenetic, 117 - , diffusion-limited, 95 - , discontinuum, 408 - , Dzhevanshir's water influx, 87 - , fluid chemistry, 117 - , fluid flow, 82 - , geothermal, 232 - , hydrological, 229, 230 - , isothermal, 126

SUBJECT INDEX 4 9 3

- , Johns and Shimoyama's isothermal, 127 - , Johns and Shimoyama's geochemical hydrocarbon

formation, 124, 128 - , Katz and Ibrahim's mechanical compaction, 52, 53 - , migration, 124 - , Morita's subsidence, 95 - , Perrier and Quiblier's compaction, 79 - , Philip's moisture ratio, 66 - , Powers' dehydration, 58 - , restoration, 73 - , "rigid basement", 405 - , sedimentation, 64 - , shale capillary, 116 - , Sharp's energy balance compaction, 67, 70, 89, 118 - , Smith's, 65 - , Smith's Gibbs-Donnan, 118 - , subsidence of producing reservoirs, 93 - , UDEC, 408, 411 - , Welte and Yukler's petroleum generation, 128 Modena, 219, 269, 270, 2723, 273 Moduli of rigidity, 96 Modulus of compression, 64 Modulus of elasticity, 35 Mohorovicic discontinuity, 3, 5, 182 Moisture ratio, 66 Molten magma, 6 Mollusks, 11 Momentum equation, 67, 68, 71 - transport, 68 - balance, 71 Monolayer adsorption, 34 Montmorillonite, 9, 25, 33, 49, 58, I05, 106, 108, 111,

112, 117, 144, 147 - , pore fluid chemistry, 108 Montmorillonite No. 25, 119 Moray Firth, 373, 377 Motions, tectonic, 165 Movement, tectonic, 179 Mud, 11 Mud volcanoes, 48 Mudstones, 26, 184 Multiphase flow, 95

Na/Ca ratio, 101, 102 Na-smectite, 121, 122 NaC1, 105 NaC1 concentrations in illite, influence on compaction,

49 Neoformation, mineral, 56 Neogene, 216 Neural network methodology, 463 Nevada, 201 Niigata, Japan, 447

Nonfunctional relations, 462, 463 North Atlantic, 25 North Sea, 373-377, 397-401, 439 - - Basin, 373

, Central graben, 373 - - , discovery, 375 - - Ekofisk field, 373 - - exploration, 375 - - location, 373, 374 - - oil and gas development, 373 - - oil production, 377 - - reservoir chalks, 398-400 - - reservoir compaction, 401 - - reservoirs, 439

rock ages,373 - - seismic data, 376 - - subbasins, 373 - - surface subsidence, 401 - - Viking graben, 373 North Slope, 447 Numerical analysis, 15 Numerical mean, 16 Nummulitic limestone, 10

Ocean crust, 4, 5,7 Ocean floor, 7 Ocean regressions, 7 Ocean rifts, 5 Ocean transgressions, 7 Ocean trenches, 7 Oedometer, 221-224, 226 Oil, 90, 120, 133 - , migration, 120 - recovery factor, 90 - , secondary migration, 133 Oil/gas production, 460 - - - , earthquake activity, 460 - - - , environmental impact, 460 Oilfield brine waters, 98 Oklahoma, 100, 101 Oligocene, 100, 114, 340-343 Oolites, 10 Ordovician/Pennsylvanian, 99 Orhtoquartzites, 25 Orinoco Belt, 338, 369, 370 Osaka, Japan,197 Osmosis, 59, 63 Overburden, 36, 66, 67, 176, 177, 179, 185, 186, 196,

199, 200 - load , 176, 179 - p o t e n t i a l , 66, 67 - pressure, 36 Overcompaction, 140

494 SUBJECT INDEX

Overpressure, prospects, 140 , Barsukovskaya, 140 , Demikhovskaya, 140

- - , Dneprovskaya, 140 , East Drozdovskaya, 140

- - , East Pervomayskaya, 140 , Glusskaya, 140 , Krasnosel'skaya, 140

- - , Malodushinskaya, 140 , Malynskaya, 140 , Pervomayskaya, 140 , Rudninskaya, 140 , South Ostashkovichskaya, 140 , South Rechitskaya, 140 , Sudovitskaya, 140 , Vetkhinskaya, 140

- - , Vishanskaya, 140 Overpressured formations, 47, 48, 50 Overpressured sandstones, 75 Oxygen isotopes, 98

P-wave, 38 Pacific Ocean, 103 Pacific plate, 8 Paleocene, 342, 377 Paleotemperatures, 68 Paleozoic, 1, 58, 373 Precambrian, 1 Panama Canal, 337 Pangaea,1 Parameters, 71 - , hydraulic, 71 - , thermal, 71 Particle size, 12, 14 - - , classification, 12 Patterns, fracture, 179 Padua, 240 Pebbles, 11 Penetrometric tests, 261 Pennsylvanian, 100, 101 Penrose Conference, 117 Percentile values, 16 Permeability, 24, 32-34, 42, 52, 89, 167, 168, 170, 179,

180, 193, 207, 208, 425, 428, 431, 432 - , effective, 167 - , relation with porosity, 223 - , vertical, 198 Permian Rotliegendes Sandstone, 373 Petroleos de Venezuela, S.A. (PDVSA), 337, 362 Petroleum genesis, 59 Petroleum migration, 68 pH, 56, 57, 121-123 Phi-scale, 12-14

Philippine ocean plate, 8 PhiUipsite, 25 Photohydrometer, 14 Phyllites, 24 Picacho Basin, 201, 202 - - , subsidence profiles, 202 Piezometer, 217 Piezometric, 237, 249, 251, 252, 258, 266, 269 - , depression, 249 - , head, 229 - , measurements, 251 - , surface, 252, 266, 269 Pisolites, 10 Pixley fissure, 201 Plate spreading, 7 Plate tectonics,4, 6, 7 Plates, 6 Platform, 11 Pleistocene, 261, 262, 270 Pleistocene-Holocene, 270 Pleistocene-Oligocene, 261 Pliocene, 50, 100, 102, 114, 185, 249, 254, 262, 340 Plutonic rocks, 22, 32 Po Delta, 230, 234, 235, 237, 240-242, 244, 246, 254,

261, 275 Po Plain, 269 Po River, 245, 247 Po River Basin, 217 Po-Veneto Plain, 215, 216, 226, 273, 274 Poisson's ratio, 35, 37, 176, 194, 221, 224, 231, 401, 407,

412 Polyaxial loading, 146 Pore collapse, 380, 388-394, 398-400, 405 Pore compressibility, 142, 143 Pore fluid, flow, 51 - - , pressure, 73 Pore pressure, 52, 58, 89 - - , abnormally high, 58 Pore saturant, 399 Pore size, 24 Pore-size distribution, 32 Pore volume, 34, 48 - - , reduction of, 48 Poroelasticity, 194, 367 Porosity, 19, 29, 31, 33, 42, 73, 74, 166-170, 185, 204,

222, 223 - , in diffusion equation, 229 - , intergranular, 204 - , microfracture, 204 - , relation with effective vertical stress, 222 - , relation with permeability, 223 Porosity vesus burial depth curve, 80, 82 Porosity versus pressure curves, 304

SUBJECT INDEX 495

Porous media, 204, 405 , isotropic, 405

Pre-Alps, 216, 248 Pre-Caucasus, 106, 107 Pressure, 47, 53, 143, 144, 147, 165, 166, 168, 169, 172,

176, 177, 179, 183, 186, 425, 428, 431 - , applied,147 - , aquathermal, 55 - , diffusion, 47 - , effective, 143, 144, 165 - , formation fluid, 193 - , geostatic, 186 - , grain-to-grain, 165, 166, 179 - , hydrostatic, 168 - , lithostatic, 176, 177 - , osmotic, 47 - , overburden, 53, 55, 166, 176, 177, 183, 425, 428 - , pore, 166, 169, 179 - , pore-fluid, 176 - , preconsolidation, 172 - , reservoir, 431 - , reservoir fluid, 425 - , rock, 428 - , uniaxial, 196 Pressure dissolution, 148, 150 Pressure gradient, 5 Primary waves, 2 - - , velocity, 2-4 Pripyatskiy Deep, 140 Produced water, Wilmington oilfield, composition, 330 Production-induced seismic phenomena, 468 Production-injection balance, Wilmington oilfield, 327,

328 Prokopovich's classification, 92 Prudhoe Bay, 447 Pseudo-bulk compressibility, 141, 142 Pseudopodia, 10 Pumice stone, 32 Pyroxenes, 21, 22

Quartz, 9, 22 Quaternary, 254, 255

Radioactive bullet surveys, 325, 326 Radioactivity, 7 Ranger Zone, Wilmington oilfield, 290-292, 310, 312 Rate-Type Compaction Model (RTCM), 397, 398 Ratios, 102, 99 - , Ca/Na, 99 - , K/Na, 99 - , Na/Ca, 102 Ravenna, 228, 230, 231,234, 237 253, 254, 256, 257, 261,

274, 275

Ravenna-Terra, 230, 231,259 Rayleigh waves, 2 Rebound, Wilmington oilfield, 308, 321,323, 328 Recent, 98 Red beds, 8 Regression, 183 Reno River, 264 Resistance, frictional, 169 Reverse osmosis, 59, 63 Rhizopods, 10 Ricken's carbonate compaction equation, 149 Rifts, 1 Rigidity modulus, 194 Rim, tensional, 180 River Secchia, 270, 271 Rock solids compressibility, 142 Romagna Plain, 235 Romashkinskoe oilfield, 469 Rotlliegendes gas reservoir, 442 Roundness, 19-21 Rovigo Province, 240

Salinity, water, 110, 112-116, 226 - , distribution, 113, 114 - , field results, 115, 116 - , fresh versus saline, 110, 115, 116 - , high-pressure zone, 115, 116 - , overpressured shales, 110 - , pore water, 112 - , sandstones, 112, 114 - , shales, 113, 114 - , well-compacted shales, 110 Salinity versus depth curves, water, 113 Salt deposits, 97 Salt domes, 102 Salt-filtering, 117 Saltation, 29 San Andreas fault, 8 San Joaquin Valley, 41, 143, 197, 201 Sands, 170, 172, 177, 184, 185 - , arkosic, 172 - , interbedded, 186 - , unconsolidated, 170, 177 Sandstones, 147, 153, 373, 376 Santa Clara Valley, 143 Santa Cruz Basin, 102 Satellites, 7, 455 Scale effects, 196 Schist, 24 Seals, 54, 55, 90, 115, 141 - , hydrostatic, 141 - , horizontal permeability, 55

496 SUBJECT INDEX

Seawater, 98, 100, 101, 105, 106, 108, 110, 111, 114, 121-123, 398

Sediment, 63, 65, 69 - , compressibility, 69 - , deposition rates, 63 - , spatial relationship, 65 Sedimentary, 8-10, 77, 216 - basin, 216 - margins, 8 - ores, 10 - particles, 8 - rocks, 9 - sequences, 77 Sedimentation, 64, 80, 169 - , duration, 80 - , rate, 64 Sediments, 9, 22, 48, 73, 74, 134, 150, 176, 179, 184-186,

219, 243, 254, 255, 425 - , argillaceous, 48, 73, 74, 176, 184, 185 - , Cenozoic, 179 - , compaction, 48, 243 - , geotecnical features, 219 - , partially lithified, 150 - , Quaternary, 254, 255 - , unconsolidated, 186, 425 Seismic surveys, Wilmington oilfield, 327 Seismic, waves, 1, 5 Seismic tomograms, 6 Seismic velocity, 5 Seismic waves, 7 Sericite, 58 Sespe Formation, 102 Settling velocity, 14 Shales, 26, 40, 74, 97, 109, 111, 147, 167, 170, 177, 184-

186, 373, 446, 447 - , interbedded, 167 - , interstial water, 97 - , overpressured, 109, 446 - , unconsolidated, 177 - , undercompacted, 111, 167 - , water influx, 446 - , well-compacted, 109 Shale-to-sand ratio, 76 Shale ultrafiltration, 101 Shape factor, 34 Shear, 138 - , pore pressure, 138 Shear force, 38 Shear moduli, 35, 37, 38 Shear stress, 5 Shear vibration, 4 Shear waves, 2, 36, 38 - - , velocity, 2, 3, 5

Ship Shoal, 113 Siderite, 23 Sieve, analysis, 12 Silicon-aluminum compounds (SIAL), 4 Silicon-magnesium-iron material (SIMA), 4 Silts, 14, 18, 24, 26, 185, 186 - , interbedded, 186 Siltstones, 26, 153, 172, 185, 186 - , arkosic, 172 Sinkholes, 40 Sinking rate, 243 Sinking ratio, 233 Size distributions, 12, 14 Skeletal materials, 10 Skewness, 17 Slate, 24 Slice method, 79 Smectites, 9, 25, 57-59, 106, 121, 124-126 - dehydration, 59 Smectite-illite transformation, 125 Soil, limestone, 145 Solidity, 77 Solidity-compaction curves, 78 Solubility coefficient, gas, 203 Sorting, 16 South America, 26 South Atlantic, 25 South Caspian Depression, 89 South Pacific, 25 Specific gravity, 177 Specific storage, 85 Specific surface area, 33, 34 Specific weight, 177 Spheric stress state, 136 Sphericity, 21 Sponges, 11 Squeezed-out solutions, 102, 103, 106, 108, 109, 123

, chemical changes with time, 123 , chemistry of, 102, 103 , Chilingarian and Rieke's experiments, 106 , experimental, 102 , Kazintsev's experiments, 103, 106 , Krasintseva's and Korunova's experiments, 103,

108, 109 , Manheim's results, 103 , marine mud, 108 , overburden pressure, 102 , Von Engelhardt and Gaida's experiments, 103

- - - , resistivity of expelled solutions, 102 - - - , Rosenbaum's experiments, 108 Standard deviation, 16 Starogroznenskoe oilfield, 469 Steam drive, 41

SUBJECT INDEX 4 9 7

Steam soak, 41 Storativity, 129 Strain, 195, 198, 200, 426, 440 - , distribution, 198 - , rocks, 195 - , tensile horizontal, 200 - , uniaxial, 440 - , vertical tensile, 200 Stratigraphic layers, 8 Streamlining, deck beams, 382 Strength tests, 388 Stress, 48, 50, 51, 53, 63, 66, 69, 78, 134, 136, 137, 139,

165-169, 172, 174-177, 181, 194-196, 198, 221-224, 380, 382, 389, 392-397, 400, 407, 426, 431, 439

- , applied, 221 - , axial, 168 - , body, 165 - boundary condition, 397 - components, 165 - , compressive, 177 - , deviatoric, 139, 172, 174, 393 - , distribution, 198 - , effective, 50, 69, 78, 194, 196, 224, 380, 393, 395, 400,

407 - , effective axial, 392 - , effective horizontal, 397 - , effective overburden, 397 - , effective vertical, 225 - , grain-to-grain, 167, 194, 195, 431 - , horizontal, 48, 51, 177, 431 - , hydrostatic, 134, 136, 137, 168, 172, 174, 389 - , in situ, 176, 426, 439 - , mechanical, 66 - , normal, 165, 175 - , overburden, 50, 63, 174 - , plastic, 177 - , pore fluid, 50 - ratio, 395 - , shear, 137, 168, 175, 198 - , skeletal, 166 - - strain curves, 392, 393, 394 - , surface, 165 - , tangential, 165 - , tangential dynamic, 181 - , tectonic, 63, 198 - , tensor, 165, 172, 174, 194 - , three principal, 168 - , total, 53, 172, 174 - , triaxial, 168 - , uniaxial vertical, 221, 222 - , vertical, 51, 169, 175, 177, 181,396, 431 - , vertical-shear, 175 - , volumetric, 136

- , wave, 382 Subduction, zones, 4-7 Sublitharenite, 27 Subsidence, 91, 92, 95, 178, 193, 195, 197, 199, 200, 202,

215-217, 220, 228, 229, 294 - , anthropogenic, 217 - , causes, 197 - , classification, 92 - , earthquakes, 199 - , endogenic, 91 - , faults, 202 - , formations, 193, 195 - , history, 197 - , land, 92, 93, 215, 216 - , modelling, 228, 229 - , natural, 217 - , producing reservoirs, 91 - , profiles, 202 - , rates, 126, 197 - , reservoirs, 91 - , surface, 200 - , Venice, 220 - , Wilmington oilfield, 294 Surface area, 24, 34 Surface force, 194 Surface waves, 2 Swelling, 67 Syndiagenesis, 56 Synsedimentary, tectonic activity, 216, 217

Tangential force, 38 Tar Zone, 306, 308-310, 290, 291 Tectonic, - compression, 47 - load, 196 -movements , 193, 196 - overcompaction, 139 - overpressure, 47 Temperature gradient, 5 Temperature-time index, 129 Tension, 195, 198, 201 - , horizontal, 198, 201 - , vertical, 195, 198 Terrebonne Parish, 113 Terrigenous rocks, 9, 10, 22 Terrigenous sediments, 9, 11, 22, 25 Tertiary, 47, 98, 373 Terzaghi's theory, 91 Texas, 101, 107, 115, 116, 141, 197 Theis' storage coefficient, 85 Thermal-catalytic, cracking, 125 Thermal conductivity, 69, 95, 129 Thermal diffusivity, 70

498 SUBJECT INDEX

Thermoelasticity, 230 Tia Juana field, 41, 338-342, 345-347, 350, 354, 358-

360, 363 Tidal-gauge recorders, 326 Tor field, 377 Tor Formation, 377, 386, 400, 413 Torliegendes Formation, 373, 379 Tortuosity, 32, 34, 86 Total stress field, 134 Total stress tensor, 138 Transform faults, 8 Transformation, smectite to illite, 57, 117, 121 Transgression, 183 - , tectonic, 183 Transient flow, 51 Transmissivity, 427 Trenches, 6, 7 Triassic sandstone, 373 Triaxial compression test, 403 Triaxial loading, 146 True mean, 15 Turkmenistan, 86 Tuscany, 234

U.S. Coast and Geodetic Survey, 295 U.S. Department of Defense, 453 U.S. Gulf Coast, 41, 53, 57, 59 U.S.S.R., 140 Unconformities, 179 Unconsolidated sands, 33, 34, 146, 147 Unconsolidated sediments, 9, 40, 184 Undercompacted formation, 48, 179 Uniaxial loading, 146 Uniaxial strain test, 389, 390 Union Pacific Zone, 291 Uplift, 48, 183 Upper Cretaceous, 375 Upper mantle, 5 Upper Permian, 373 Upper Terminal Zone, 290, 291, 310, 317, 318 Upwelling magma, 4

Venetian lagoon, 237 Venetian plain, 250 Venezuela, 141, 144, 145, 337, 338, 341, 346, 347, 357,

362, 364, 367 - , bitumen deposits, 337, 338 - , compaction, 338 - , Drainage Master Plan, 364 - , foundation for seismic research (FUNVISIS), 362 - , heavy oil, 337, 338 - , hydrocarbon accumulation, 338 - , hydrocarbon producer, 337

- , modeling, 367 - , Oil Concessions (VOC), 341,346, 347, 357 - , reserves, 337 - , reservoir simulation, 367 - , steam injection, 338 - , subsidence, 337, 338 - , thermal model formulation, 368 Venice, 219, 229, 230, 234, 236, 237, 240, 250, 261 - , ground-sinking, 229 - , subsidence, 229 Ventura County, 102 Viking field, 376 Viscosity, oil, 425 Viscous coupling, 137 Vitrinite reflectance, 68, 132 Void ratio, 31, 49, 60, 61, 114, 118, 143, 170, 407 Volcanic islands, 7 Volcanic rocks, 22 Volume, - , bulk, 168 - , pore, 168

Water, - , connate, 183 - derived from magma, 48 - , epigenetic, 183, 184 - influx, 86 - , syngenetic, 184 - viscosity, 87 Water injection, Wilmington oilfield, 297 Weight, overburden, 175 Well-cemented rocks, 33 Wells, injection, 427 West Ekofisk field, 377 Wheels, odometer, 447, 448 Wilmington oilfield, California, 197, 199, 285-335, 442,

447, 449, 469 - - - , compaction testing, 300 - - - , drilling and completion, 293 - - - , geology, 286 - - - , location, 285 - - - , repressurization, 328 - - - , structure, 292 - - - , subsidence behavior, 405 - - - , subsidence history, 294 - - - , subsidence measurement, 324 Wyoming, Upton, 119

Yield surface, Ekofisk chalk, 401, 402 Young's modulus, 35, 36, 231, 401, 407, 411, 439

Zechstein Formation, 373

D E V E L O P M E N T S I N P E T R O L E U M S C I E N C E

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W.H. F E R T L - Abnormal Formation Pressures T.F. YEN and G.V. CHILINGARIAN (Editors)- Oil Shale D . W . P E A C E M A N - Fundamentals of Numerical Reservoir Simulation L.P. D A K E - Fundamentals of Reservoir Engineering K. M A G A R A - Compaction and Fluid Migration M.T. SILVIA and E.A. ROBINSON- Deconvolution of Geophysical Time Series in the Exploration for Oil and Natural Gas G.V. CHILINGARIAN and P. VORABUTR- Drilling and Drilling Fluids T.D. VAN GOLF-RACHT - Fundamentals of Fractured Reservoir Engeneering G. MOZES (Editor) - Paraffin Products O. SERRA - Fundamentals of Well-log Interpretation, 1. The acquisition of logging data O. SERRA - Fundamentals of Well-log Interpretation, 1. The interpretation of logging data R.E. CHAPMAN- Petroleum Geology E.C. DONALDSON, G.V. CHILINGARIAN and T.F. YEN (Editors) - Enhanced Oil Recovery, I. Fundamentals and analyses E.C. DONALDSON, G.V. CHILINGARIAN and T.F. YEN (Editors) - Enhanced Oil Recovery, II. Processes and operations A.P. S Z I L A S - Production and Transport of Oil and Gas, A. Flow mechanics and production (second completely revised edition) A.P. SZILAS - Production and Transport of Oil and Gas, B. Gathering and Transport (second completely revised edition) G.V. CHILINGARIAN, J.O. ROBERTSON Jr. and S. K U M A R - Surface Operations in Petroleum Production, I G.V. CHILINGARIAN, J.O. ROBERTSON Jr. and S. K U M A R - Surface Operations in Petroleum Production, II A.J. DIKKERS -Geology in Petroleum Production F. RAMIREZ- Application of Optimal Control Theory to Enhanced Oil Recovery E.C. DONALDSON, G.V. CHILINGARIAN and T.F. Y E N - Microbial Enhanced Oil Recovery J. HAGOORT- Fundamentals of Gas Reservoir Engineering W. LITTMANN- Polymer Flooding N.K. BAIBAKOV and A.R. GARUSHEV- Thermal Methods of Petroleum Production D. M A D E R - Hydraulic Proppant Farcturing and Gravel Packing G. DA PRAT - Well Test Analysis for Naturally Fractured Reservoirs E.B. NELSON (Editor)- Well Cementing R . W . Z I M M E R M A N - Compressibility of Sandstones G.V. CHILINGARIAN, S.J. MAZZULLO and H.H. R I E K E - Carbonate Reservoir Characterization: A Geologic-Engineering Analysis, Part I E.C. DONALDSON (Editor) - Microbial Enhancement of Oil Recovery - Recent Advances E. B O B O K - Fluid Mechanics for Petroleum Engineers E. FJ/ER, R.M. HOLT, P. HORSRUD, A.M. RAAEN and R. RISNES - Petroleum Related Rock Mechanics M.J. E C O N O M I D E S - A Practical Companion to Reservoir Stimulation J.M. V E R W E I J - Hydrocarbon Migration Systems Analysis L. D A K E - The Practice of Reservoir Engineering W . H . S O M E R T O N - Thermal Properties and Temperature related Behavior of Rock/fluid Systems

38. W.H. FERTL, R.E. C H A P M A N and R.F. HOTZ (Editors) - Studies in Abnormal Pressures 39. E. PREMUZIC and A. W O O D H E A D (Editors) - Microbial Enhancement of Oil Recovery -

Recent Advances - Proceedings of the 1992 International Conference on Microbial Enhanced Oil Recovery

40A. T .F . YEN and G.V. CHILINGARIAN (Editors) - Asphaltenes and Asphalts, 1

41 subsidence due to fluid withdrawal

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