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Petroleum Engineering Handbook

Editor-in-Chief

Howard B. Bradley Professional/Technical Training Consultant

Associate Editors

Fred W. Gipson Mohamed Mortada Senior Engineering Professional (retired) President

Conoco Inc. Mortada Intl. Inc.

Aziz S. Odeh Lewis L. Raymer Senior Scientist President

Mobil R&D Corp. Lewis L. Raymer Enterprises

Phillip S. Sizer Gerry L. Smith Senior Vice President/Technical Director Engineering Consultant

Otis Engineering Corp. (deceased)

Third Printing Society of Petroleum Engineers

Richardson, TX, U.S.A.

@Copyright 1987 by the Society of Petroleum Engineers. Printed in the United States of America. All rights reserved. This book, or parts thereof, cannot be reproduced in any form without written consent of the publisher.

Third printing, Feb. 1992, incorporating minor changes on Pages 22-3,30-3, 30-4, 33-2, and 51-52.

ISBN 1-55.563-010-3

ii

Preface The 1962 edition of the Petroleum Production Handbook filled a need at that time for a comprehensive compilation of practical information and data covering production equipment and reservoir engineering. This 1987 edition updates the original 48 chapters and adds 11 new ones. New technology, developed over the past 25 years, resulted in im- proved equipment, materials, and methods. They are described and discussed in the revised original chapters and in the new ones. The 11 new chapters are the following:

Chapter 7-Electric Submersible Pumps Chapter 1 &Offshore Operations Chapter 19-Crude-Oil Emulsions Chapter 4%Miscible Displacement Chapter 46-Thermal Recovery Chapter 47-Chemical Flooding Chapter 48-Reservoir Simulation Chapter 5 l-Acoustic Well Logging Chapter 52-Mud Logging Chapter 58-SI Metric System of Units and SPE Metric Standard Chapter 59-SPE Letter and Computer Symbols Standard

This 1987 edition, now called the Petroleum Engineering Handbook, provides a current and worthwhile addition to the industrys literature for students and experienced professionals working in the petroleum industry.

The handbook is again divided into three sections: Sec. 1, Mathematics (one chapter); Sec. 2, Production Engineer- ing (18 chapters); and Sec. 3, Reservoir Engineering (40 chapters). There are 57 chapters written by professionals who are recognized as authorities in their fields of expertise. Chap. 58 is a revised version of the 1982 SI Metric System of Units and SPE Metric Standard, and Chap. 59 is the 1986 revision of the 1984 Standard SPE Letter and Computer Symbols for Economics, Formation Evaluation and Well Logging, Natural Gas Engineering, and Petrole- um Reservoir Engineering.

The Mathematics section presents the basic tables and calculation procedures required by persons engaged in petro- leum production. The Production Engineering section covers basic types of materials, methods, and tools available for use in petroleum operations, including their capabilities and proper applications. The Reservoir Engineering sec- tion treats gas, oil, condensate, and formation water properties and correlations; reservoir rocks and traps; primary, secondary, and tertiary recovery data and methods; oil and gas reserves; formation evaluation, including well logging methods; and well treating methods. The what, why, how, and now-what aspects of each topic are emphasized. Also, at the end of the appropriate chapters, key equations are presented with SI metric units.

Special acknowledgment is due the SPE staff for their immeasurable help and advice, the associate editors for their avid dedication to the technical-editing task, and all the authors who contributed much time and effort to provide the timely and excellent information included within each chapter. We are much indebted to the editor-in-chief of the 1962 edition, Thomas C. Fricke. and to the original group of authors for their arduous 3-year job of developing the original edition of the Petro/eum Production Handbook. Special thanks are due Ed Mayer of THUMS and B.J. Dotson of Mobil Oil Corp. (now retired) for their advice and helpful discussions on the proper use of the 1986 SPE standard letter symbols throughout the handbook and for their editing of Chap. 59, the SPE Letter and Computer Symbols Standard.

Our hope is that by proper application of the updated information contained within the second edition of this hand- book, the petroleum-industry professional will be led to more efficient production and use of the worlds petroleum- energy resources.

Howard B. Bradley Editor-in-Chief

Acknowledgments The Society of Petroleum Engineers sincerely thank\ the following organizations and individuals for permission to use the cited material.

Chap. 2 Figs. 2.1 through 2.3 and 2.6 through 2.8, from Casino, Tubi,l~, and Drill Pipe, API Spec. 5A, 38th edition. API. Dallas

(1985). Fig. 2.9, from Line Pipe, API Spec. 5L, 35th edition. API. Dallas (1985). Figs. 2.10A, 2.10B, 2.11, 2.12, and 2.14 through 2.18, from 7hrt&inR, &g;,lg, and 7hveud hl.~fcct;or2, API Spec, SB.

1 Ith edition, API. Dallas (1985). Table 2.1, modified from Cusing, Tubing, and Drill Pipe, API Spec. 5A, 37th edition, API, Dallas (1984). Tables 2.2, 2.5 through 2.7, and 2.25 through 2.27, Casing, Tubing, and Drill Pipe, Bull., USS. Pittsburgh. PA

(1972). Tables 2.3, 2.4, and 2.24, modified from Performance Propertics of Casing, Tubing, and Drill Pipe, Apf Bu//. 5~2,

API. Dallas (1983). Tables 2.8 through 2.11 and 2.28, from USS Seamless Casing. Tubing, and Drill Pipe, Bu//, , USS. Pittsburgh, PA

(1972). Table 2.14, Bull. 664. National Supply Co.. Houston. Tables 2.31 through 2.33, 2.36, and 2.37, from Line Pipe, API Spec. 5L. 34th edition. API, Dallas (1984). Tables 2.38 through 2.43, from Formulas and Calculations for Casing, Tubing. Drill Pipe. and Lint Pipe Properties.

API Bull. 5C3, third edition with Supplement No. 1. API. Dallas (1983). Tables 2.44 through 2.54, from Thrrudit~~. Gaging, und thread Inspection. API Spec. 5B, 10th edition with Supplement

No. 4. API. Dallas (1983).

Chap. 3

Figs, 3.1 and 3.3, and Tables 3.1 through 3.33, from Specicarionsfor Wellhcad and Chrisrtnas Tree Eyuipment. API Spec. 6A. 14th and 15th editions, API. Dallas (April 1. 1986).

Fig. 3.2, courtesy McEvoy Co., General Catalog 58-59 (Jan. 1959). Fig. 3.5, from Eichenberg, R., Design Consideration for AWHEM 15,000 psi Flanges, ASME Paper 57.PET-23, Sept.

22, 1957. Figs. 3.6 through 3.17, courtesy Otis Engineering Corp.. Dallas.

Chap. 4

Figs. 4.1 through 4.11, from Patton, L.D. and Abbott, W.A.: Well Completions and Workovers: The Systems Approuth. second edition, Energy Publications, Dallas (1985) 57-67.

Tables 4.1 and 4.2, from Pucker Culculations Handbook, Baker Oil Tool Div. (1971).

Chap. 5 Fig. 5.1, from Winkler. H.W.: How to Design a Closed Rotativc Gas Lift System-Part I: Proccdurc, World Qj/ (July

1960) 116-19. Figs. 5.2, 5.5, 5.6, and 5.18, from Gus Lij?, Book 6 of API Vocational Training Series, revised edition. API. Dallas (1984)

65. Fig. 5.3, from Winkler. H.W.: Heres How to Improve Your Gas Lift Installations-Part I : Pressure at Depth

Determinations. World Oil (Aug. 1959) 63-67. Figs. 5.4 and 5.29, from Winkler. H.W. and Smith. S.S.: Cameo Gas Liji Manual, Cameo Inc.. Houston (1962) A2-001. Fig. 5.7, from King, W.R.: Time and V 0 umc Control for Gas Intermitters, I U.S. Patent No. 2.339.487 (Jan. 1944). Fig. 5.21, from Kirkpatrick. C.V.: Advances in Gas-Lift Technology, API Drill. and Prod. Pruc. (I 959) 24-60. Fig. 5.25, from Gas Lt, Book 6 of API Vocational Training Series. API. Dallas (1965) 109. Fig. 5.33, from CLlmco Cornplere Service Cuialog, Cameo Inc. (1962) 42.

Chap. 6

Figs. 6.1, 6.5, 6.7, 6.12, 6.13, 6.31, 6.40, 6.44, 6.47, 6.49, and 6.51, and Table 6.18, courtesy Trico Industries. Gardena. CA,

Figs. 6.2, 6.3, 6.6, 6.8, 6.11, 6.14, 6.15, 6.19 through 6.24, 6.26 through 6.29, 6.32 through 6.39, 6.41 through 6.45, 6.48, 6.50, 6.52, 6.53, and 6.55, and Table 6.1, from National-Oilwell. Los Nietos. CA.

Fig. 6.9, courtesy Otis Engineering Corp., Dallas. Figs. 6.17 and 6.52, and Tables 6.3, 6.12, and 6.17, courtesy Dresser Industries, Dallas. Fig. 6.18 and Table 6.4, courtesy of Highland Pump Co. Inc.. Midland. TX. Fig. 6.56, from Si;ing und Selecrion of Electric Submersible Pump Installations, API RP I IU, second edition, API. Dallas

(May 30, 1986). Table 6.2, courtesy Kobe Inc., Huntington Park, CA.

Chap. 7

Figs. 7.1 through 7.18 and 7.20 through 7.32, and Table 7.1, courtesy TRW Energy Products Group, Reda Pump Div., Bartlesville. OK.

Chap. 8 Fig. 8.1, from Subsurface Pumps and Fitrings, API Spec. 11 AX, seventh edition, API, Dallas (June 1979). Figs. 8.3, 8.5, and 8.7, courtesy Oilwell Div. of U.S. Steel Corp., Garland, TX.

V

Chap. 9

Figs. 9.2 and 9.3, and Tables 9.1 through 9.4, from Sucker Rods. API Spcc. 119, 2lst editmn. API, Dallas (May 1985). Figs. 9.5 and 9.9, and Table 9.9, from Cure und Hundling of Sucker Rod.,, API RP 1 IBR. seventh edition. API. Dallas

(May 30, 1986). Fig. 9.10 and Tables 9.10 and 9.11, from Reir@ced Plu~fic Sucker Rods, API Spec. 1 IC, first edition. API, Dallas (Jan,

I, 1986). Table 9.7, from Design Culrulurions for Sucker Rod P~inpini: Systems, API RP I 1 L. third edition, API, Dallas (Feb. 1977)

Chap. IO

Figs. 10.1, 10.3, 10.6, 10.7, 10.9 through 10.12, and 10.14 (pumping unit), courtesy Lufkin Industries Inc., Lufkin. TX. Fig. 10.8, from Design Calculations for Sucker Rod Pumping Sytems (Convenrional Units), API RP 1 IL. third edition.

API. Dallas (Feb. 1977). Figs. 10.13, 10.16 through 10.20, and 10.24 through 10.28, and Tables 10.5, 10.7, and 10.9, from Sargent Oil Well

Equipment Co., Odessa, TX. Fig. 10.14 (engine), from Arrow Specialty Co., Tulsa, OK. Fig. 10.15, from Waukesha Engine Div.. Dresser Industries Inc., Waukesha. WI. Fig. 10.21, from Mom-s and Generators, MG l-1978. Natl. Electrical Manufacturers Assn.. Washington. DC (1978). Figs. 10.29 through 10.31, from Ronk Electrical Industries Inc., Nokomis. IL. Figs. 10.32 and 10.33, from Classijcnlion of Areas for Electrical lnstullations at Drilling Rigs and Production Facilities on

Land and on Marine Fixed and Mobile Platform, API RP 5009, second edition, API, Dallas (July 1973) 8. Tables 10.2 and 10.3, from lnsrullation and Luhrimtim of Pumping Units, API RP 1 IG, second edition. API. Dallas (Feb.

1959) and Supplement (Jan. 1980). Tables 10.6 and 10.10, from Motor Application and Muintenunce Hundbook, second edition, R.W. Smeaton (ed.),

McGraw-Hill Book Co. Inc.. New York City, Table 1 on Page 3-7 and Table 3 on Page I l-3.

Chap. 11 Figs. 11.1 and 11.3, from C-E Natco, Tulsa. OK. Fig. 11.4, from Design and Fuhricution of Gulvunixd Products, American Hot Dip Galvanizer Assn. and the Zinc Inst.

(Nov. 1983). Fig. 11.7, from CBI Industries Inc. (Chicago Bridge and Iron Co.), Oak Brook, IL. Figs. 11.9 and 11.10, from Fenix & Scisson Inc., Tulsa. OK. Table 11.1, from Bolted Production Tanks, API Spec. 129, 12th edition, API Div. of Production, Dallas (Jan. 1977). Tables 11.3 and 11.4, from Venting Atmospheric cmd LowPressure Storage Tunk.7, API Std. 2000, third edition, API,

Dallas (Jan. 1982).

Chap. 12 Fig. 12.2, courtesy Jaragua S.A. Industrias Mechanicas. Sao Paula, Brazil. Figs. 12.7 and 12.8, courtesy Fisher Controls Co., Marshalltown. IA. Figs. 12.16 and 12.19, courtesy ACS Industries Inc., Woonsocket, RI. Fig. 12.18, courtesy Peerless Mfg. Co., Dallas. Fig. 12.20, courtesy Plenty Metrol. Newbury. England. Fig. 12.21, courtesy Vortec. Inc.. Woodside. CA. Fig. 12.22, courtesy Porta-Test Systems, Ltd., Edmonton, Alta., Canada. Figs. 12.24, 12.26, and 12.40, courtesy C-E Natco, Tulsa, OK. Tables 12.9 and 12.10, courtesy Cornsign Computer Program, Ellis Engineering Inc., Houston. Tables 12.11 and 12.17, from KWIC Index of Intl. Standards, Intl. Organization for Standardization. Geneva. Tables 12.12, 12.18, and 12.19, from ASME Boiler and Pressure Vessel Code, Sec. VIII, Div. 1, New York City (1984). Tables 12.13 and 12.14, from Megyesy, E.F.: Pressure Vessel Handbook, Pressure Vessel Handbook Publishing Inc.,

Tulsa, OK. Table 12.15, from Kimmell, G.O.: Stage Separation, paper 48.PET-15 presented at the ASME Annual Meeting.

Oklahoma City, Oct. 1949. Table 12.16, Separation Flash Calculations, Process Version 0882, Simulation Sciences Inc., Houston.

Chap. 13 Fig. 13.2, courtesy The Bristol Co. Fig. 13.3, from Orice Constunt Tub/es. American Gas Assn., Report No. 3, revised (1969). Also, ANSI/API 2530. Fig. 13.4 and Tables 13.2a, 13.2b, and 13.4, from GPSA Engineering Dutubook, Gas Processors Suppliers Assn., Tulsa,

OK (1972). Figs. 13.20 through 13.22, courtesy Fischer Governor Co. Table 13.1, courtesy American Meter Co.. Inc.

Chap. 14

Fig. 14.5, from GPSA Engineering Dutuhook, ninth edition. fifth revision, Gas Processors Suppliers Assn., Tulsa, OK (1981).

Fig. 14.14, from NGSMA Handbook. Figs. 14.19 through 14.21, and Tables 14.1 and 14.2 from Campbell, J.M.: J.M. Campbell Gas Conditioning and

Processing. Campbell Petroleum Series, Norman, OK (1962) 2.

vi

Chap. 15

Figs. 15.1 through 15.3, and Table 15.9, from Desl,qn and hstd/don of O&how P~C~CY;OH ~l+t~~ Pip;~ ~~~~~~~~~~~ API RP l4E, third edition, API, Dallas (1981) 22.

Figs. 15.4 through 15.6, and Tables 15.2 through 15.5, from GPSA Engineerirlg Durchx~k, @IS Processors Suppliers Assn.. Tulsa, OK (1980).

Fig. 15.8, courtesy Paragon Engineering Services Inc.. Houston. Fig. 15.11 and Table 15.10, courtesy Perry Equipment Co., Mineral Wells, TX. Fig. 15.12, courtesy C-E Natco, Tulsa. OK. Fig. 15.13, courtesy U.S. Filter. Fluid System Corp.. Whittier, CA. Figs. 15.15 and 15.19, from Oil-Water Separator Process Design. API Manual on Disposal of Refinery Wastes. Volume

on Liquid Wastes, API. Dallas (1975) Chap. 5. Fig. 15.20, Engineering Spccialtiea Inc.. Covington. LA. Tables 15.6 and 15.7, from Amr~rictr~~ ~triiov7d .bmk~rd. Pip /%mgr.s arzd F/m& FirtirrRs. ANSI B26.5. ASME, New

York City (1981).

Chap. 18

Fig. 18.32, courtesy CanOcean Resources Ltd., New Westminster, B.C., Canada. Fig. 18.36, courtesy Fluor Subsea Services. Irvine. CA. Fig. 18.38, courtesy Hamilton Bros. Oil Co., Denver. Fig. 18.40, from Lagers, G.H.C., Gusto, B.V., and Bell, C.R.: The Third Generation Lay Barge. Proc., Offshore

Technology Conference (1974) 1, 35-46. Fig. 18.41, courtesy Apache, Santa Fe Intl. Corp., Alhambra. CA. Fig. 18.43, courtesy Swan Wooster Engineering Ltd., Vancouver, B.C., Canada. Fig. 18.44, from Willits. K.L.: Well Completions in the Prudhoc Bay Field. Pet. Eng. (Feb. 1976). Fig. 18.45, courtesy Brian Watt Assocs., Houston.

Chap. 19

Figs. 19.1, 19.3, and 19.6 through 19.8, courtesy Shell Development Co., Houston. Figs. 19.4, 19.5, 19.9, and 19.10, courtesy Baker Performance Chemicals Inc., Santa Fe Springs, CA Fig. 19.12, courtesy ASTM, Philadelphia. PA. Fig. 19.17, courtesy Chemineer-Kenics. Dayton. OH. Fig. 19.18, courtesy Modular Production Equipment Inc., Houston. Figs. 19.19, 19.29, and 19.30, courtesy C-E Natco Inc.. Tulsa, OK. Figs. 19.20 and 19.32, courtesy Hydrocarbon Research Inc.. Long Beach, CA. Figs. 19.21, 19.22, and 19.28, courtesy Energy Recovery Div., Daniel Industries Inc.

Chap. 20 Figs. 20.2A and 20.3, from Katz, D.L. ef (il.: Hcr!rdhook of Nutuuu/ Gus Eng;nrcr;ng, McGraw-Hill Book Co. Inc., New

York City (1959). Figs. 20.2B and 20.2C, from Brown, G.G. ~1 nl.: Natural Gasoline and the Volatile Hydrocarbons. Natural Gas Assn.

of America. Tulsa OK (1948). Fig. 20.4, from Wichert, E. and Aziz. K.: Compressibility Factor for Sour Natural Gases, Cdn. J. C!zerrr. Gl,q. (1972)

49, 269-75. Figs. 20.8 and 20.9, from Stiel. L.I. and Thodos, G.: The Viscosity of Non-Polar Gases at Normal Pressures. AICIfE J.

(1961) 7, 61 l-20. Fig. 20.10, from Matthews, T.A.. Roland. C H.. and Katz, D.L.: High Pressure Gas Measurement. Proc~. , Natural Gas

A$sn. of America (1942) 41-51. Fig. 20.14 and Table 20.1, from Perry. R.H. and Chilton, C.H.: C/~cwicz/ 0tgin~er.s ffmdbook. fifth edition. McGraw-

Hill Book Co Inc., New York City (1975). Table 20.2, from GPSA Enyi~~wriufi Dorcrbonk, ninth edition. fifth revision. Gas Processors Suppliers Aasn.. Tulsa. OK,

Chau. 21

Fig. 21 .l, from Gq~~/oym/ic~ c$ C/ic,n~ic,tr/ T~~c~/tno/o,e~, The Interscicnce Encyclopedia Inc. ( 1953) 10, 1 17. Fig. 21.3, after N&on. W.L.: Parrnlertr?~ Rc$rrrj:v ~ri,t~irt~~~ri/t~, fourth edition, McGraw-Hill Book Co Inc., New York

City (1958) 910-37. Fig. 21.4, courtesy Hansen. D.N. and Hurd. C.O., Shell Devolopmcnt Co , Prtrd~wrn Rc$wr (Aprtl 1945). Figs. 21.7 through 21.21, from ASTM Slcrf&rcl.c 011 Pt,/ro/c~trfi P,.oc/lrc~f.s crnd Lubricants. Part 24, ASTM, Philadelphia

( 1975) 796. Fig. 21.22, from Matthews. T.A.. Roland. C.H.. and Katz. D.L: High Prcssurc Gas Measurements. Proc,., Natural Gas

Aasn. of America (1942) 41. Figs. 21.23 and 21.24. from Standing. M. B. : lr~lrr/tif,/rrc, t/rid Phcrsr Brhcr~~io~ r!f Oil Fir/t/ Hwlrr,c&~orr S\stc~rns, Reinhold

Publtshing Corp.. New York City (1952). Fig. 21.25, from Standing. M.13.: A Prcssurc-Volulnc-Tcmpcraturc Correlation for Mixtures of California Oil and Gases.

Drill. curd Prod. Pm , API ( 1937) 275. Fig. 21.26, courtesy Calitornia Rcjcarch Corp., 1947. Fable 2 I .7, from Nelson. W. L. : Pr~f-oic,lr!~r Rc:/iucy\ En,g;n~criyy, fourth edition, McGrawHill Book Co. Inc.. New York

City (11)5X) 910-37. Table 21.10, from A Guide to World Export Ct-udcs. Oil & Gtrv J. (1976). Table 21.11, courtesy Bartlcavillc Energy Technology Ccntcr. Bartlc~ville. OK.

vii

Chau. 22

Figs. 22.1 through 22.3, from Standing, M.B.: Volumetric and Phase Behavior of Oil Field Hydrocarbon Systems, Reinhold Publishing Corp., New York City (1952).

Fig. 22.4, from Katz, D.L.: Prediction of the Shrinkage of Crude Oils, Drill. and Prod. Prac., API (1942). Figs. 22.5, 22.9, and 22.13, courtesy California Research Corp. Figs. 22.19 and 22.20, from Baker, 0. and Swerdloff, W.: Finding Surface Tension of Hydrocarbon Liquids, Oil & Gas

1. (Jan. 2, 1956).

Chap. 23 Fig. 23.9 from GPSA Engineering Databook, Gas Processors Suppliers Assn., ninth edition, Tulsa, OK (1972). Figs. 23.12 and 23.13 from Reamer, H.H., Fiskin, J.M., and Sage, B.H.: Phase Equilibria in Hydrocarbon Systems,

lnd. Eng. Chem. (Dec. 1949) 41, 2871.

Chao. 24 Fig. 24.3, from Hoke, S.H. and Collins, A.G.: Mobile Wellhead Analyzerfor the Determination of Unstable Constituents in

Oil-Field Waters, ASTM STP 735 (1981) 34-48. Fig. 24.9, from Burcik: Properties of Petroleum Reservoir Fluids, John Wiley & Sons Inc., New York City (1957). Figs. 24.11 and 24.12, from PI-Petroleum Information,

Chap. 25 Figs. 25.3 and 25.4, from Kobayashi, R.: Vapor-Liquid Equilibria in Binary Hydrocarbon-Water Systems, PhD

dissertation, U. of Michigan, Ann Arbor (1951). Figs. 25.5, 25.10, 25.21, 25.23, and 25.24, and Table 25.4, from Katz, D.L. et al.: Water-Hydrocarbon Systems,

Handbook of Natural Gas Engineering, McGraw-Hill Book Co. Inc., New York City (1959) 189-221. Figs. 25.6, 25.8, and 25.33, from Kobayashi, R. and Katz, D.L.: Vapor-Liquid Equilibria for Binary Hydrocarbon-Water

Systems, Ind. Erg. Chem. (1953) 45, 440-5 1. Fig. 25.7, from Alder, S.B. and Spencer, C.F.: Case Studies of Industrial Problems, Phase Equilibria and Fluid Properties

in the Chemical Industry, Proc., Equilibrium Fluid Properties in the Chemical Industry (1980) 465-95. Fig. 25.14, from von Stackelberg, M.: Solid Gas Hydrates, Natunvissenschaften (1949) 36, 327-33, 359-62. Figs. 25.17 through 25.20, from Sloan, E.D.: Phase Equilibria of Natural Gas Hydrates, paper 67f presented at the

1983 AIChE Summer Natl. Meeting, Denver, Aug. 28-31. Fig. 25.22, from Song, K.Y. and Kobayashi, R.: Measurement and Interpretation of the Water Content of a Methane-

Propane Mixture in the Gaseous State in Equilibrium with Hydrate, Ind. Eng. Chem. Fund. (1982) 21, No. 4, 391-95. Fig. 25.25, from Deaton, W.J. and Frost, E.M.: Gas Hydrates and Their Relation to the Operation of Natural Gas Pipe

Lines, Monograph 8, USBM, Washington, DC (1946). Fig. 25.30, from Saito, S., Marshall, D.R., and Kobayashi, R.L: Hydrates at High Pressures: Part II. Application of

Statistical Mechanics to the Study of the Hydrates of Methane, Argon, and Nitrogen, AIChE J. (1964) 10, No. 5, 734-40.

Fig. 25.32, from Dodson, CR. and Standing, M.B.: Pressure-Volume-Temperature and Solubility Relations for Natural Gas-Water Mixtures, Drill. and Prod. Prac., API, Dallas (1944) 173-79.

Figs. 25.34 through 25.36, from Peng, D.-Y. and Robinson, D.B.: Two- and Three-Phase Equilibrium Calculations for Coal Gasification and Related Process, Thermodynamics of Aqueous Systems with Industrial Applications, S.A. Newman (ed.), Symposium Series 133. ACS (1980) 393-414.

Figs. 25.37 and 25.41, from Scauzillo, F.R.: Inhibiting Hydrate Formations in Hydrocarbon Gases, Chem. Eng. Progr. (1956) 52, No. 8, 324-28.

Figs. 25.38 through 25.40, from Gas Conditioning Fact Book, Dow Chemical Co., Midland, MI (1962) 69-71, Table 25.5, from Dharmawardhand, P.B.: The Measurement of the Thermodynamic Parameters of the Hydrate Structure

and Application of Them in the Prediction of Natural Gas Hydrates, PhD dissertation, Colorado School of Mines, Golden (1980).

Chap. 26

Fig. 26.1, from Fraser, H.J. and Graton, L.C.: Systematic Packing of Spheres-With Particular Relation to Porosity and Permeability, J. Geol. (Nov.-Dec. 1935) 785-909.

Figs. 26.3 and 26.30, courtesy Core Laboratories Inc., Dallas. Fig. 26.5, 26.24, and 26.25, from Stevens, A.B.: A Laboratory Manual for Petroleum Engineering 308, Texas A&M U.,

College Station (1954). Fig. 26.7, from Krumbein, W.C. and Sloss, L.L.: Stratigraphy and Sedimentation, Appleton-Century-Crofts Inc., New York

City (1951) 218. Fig. 26.27, from Klinkenberg, L.J.: The Permeability of Porous Media to Liquids and Gases, Drill. and Prod. Prac.,

API, Dallas (1941) 200-13. Fig. 26.29, from Kennedy, H.T., VanMeter, O.E., and Jones, R.G.: Saturation Determination of Rotary Cores, Pet.

Eng. (Jan. 1954) B.52-B.64.

Chap. 27 Table 27.12, courtesy Alaska Oil & Gas Conservation Commission, Anchorage. Tables 27.13 through 27.15 and 27.17, courtesy Core Laboratories Inc., Dallas. Table 27.16, from European Continental shelf Guide, Oilfield Publications Ltd., Ledbury, Herefordshire, England (1982).

Chap. 28 Figs. 28.3 and 28.4, from Rose. W.: U.S. Patent No. 4,506,542 (1985). Fig. 28.7, from Rose. W.: Permeability and Gas Slippage Phenomena. Drill. and Prod. Pruc., API. DalIah (1948)

127-35. Fig. 28.8, from Stone. H.L.: Probability Model for Estimating Three-Phase Relative Permeability. J. Ccl,z. P

Chap. 37

Fig. 37.6 and 37.7, from Tarncr, J., How Different Sire Gas Caps and Pressure Maintenance Programs Affect Amount ot Recoverable Oil. Oil Week!\~ (June 12. 1944) 32-44.

Figs. 37.16 through 37.24, and Tables 37.1 and 37.2, from Singh. D. and Guerrero. E.T.: Material Balance Equation Sensitivity, Oil & Gas .I. (Oct. 20. 1969) 95-102.

Figs. 37.29 and 37.30, from Cronquist, C.: Evaluating Producing Volatile Oil Reservoirs. Workl Oil (April 1979) 159-66 and 246.

Chao. 39

Figs. 39.1 through 39.3, and Table 39.1, after Eilerts. K.C. er ~1.: Phusr Rr/ution.s of Gas-Co,l~lenscite F1ui~l.s. American Gas Assn., New York City (1957).

Figs. 39.4 through 39.6, and Tables 39.2 through 39.10, courtesy Core Laboratories Inc., Dallas (1985). Fig. 39.7, after Marshall. D.L. and Oliver, L.R.: Some Uses and Limitations of Model Studies in Cycling. Trcrns.,

AIME (1948) 174, 67-87. Fig. 39.8, after Stelzer, R.B.: Model Study vs. Field Performance, Cycling the Paluxy Condensate Reservoir, Drill. trrrrl

Prod. Pruc., API (1956) 336-42. Fig. 39.9, data derived from Stelzer, R.B.: Model Study vs. Field Performance, Cycling the Paluxy Condensate

Reservoir. Drill. and Prod. Prac., API (1956) 336-42. Table 39.12, from Miller, M.G. and Lents. M.R.: Performance of Bodcaw Reservoir, Cotton Valley Field Cycling

Project. New Methods of Predicting Gas-Condensate Reservoir Performance Under Cycling Operations. Drill. wzd Prod. Prac., API (1946) 128849.

chap. 41

Table 41.11, courtesy Republic Bank of Dallas. Table 41.14. from Wilson. W.W. and Boyd. W.L.: Simplified Calculations Determine Loan Payout. World Oil (May

1958).

Chao. 44 Figs. 44.6 through 44.8 and Table 44.2, from Craft, B.C. and Hawkins, M.J. Jr.: Applied Pc~troleum Reservoir

Engineering, Prentice-Hall Inc., Englewood Cliffs, NJ (1959) 107, 357, 412-13. Figs. 44.58 through 44.61, from Guerrero. E.T. and Earlougher, R.C.: Analysis and Comparison of Five Methods Used

to Predict Waterflooding Reserves and Performance, Drill. and Prod. Prac., API, Dallas (I 961) 78-95. Fig. 44.62, from Higgins, R.V. and Leighton. A.J.: Computer Techniques for Predicting Three-Phase Flow in Five-Spot

Waterfloods, RI 7011. USBM (Aug. 1967).

Chap. 45

Fig. 45.4, from Brown, G.G. et al.: Natural Gasoline and the Volatile Hydrocarbons, Natural Gasoline Assn. of America (1948).

Fig. 45.5, from Hutchinson, C.A. Jr. and Braun, P.H.: Phase Relations of Miscible Displacement in Oil Recovery. AIChE J. (1961) 7, 64.

Fig. 45.7, modified from Slobod, R.L. and Koch, H.A. Jr.: High Pressure Gas Injection-Mechanism of Recovery Increase, Drill. and Prod. Prac., API, Dallas (1953) 82.

Fig. 45.8, modified from Sage B.H and Lacey, W.N.: Some Properties of the Lighter Hydrocarbons, Hydrogen Suljde, and Carbon Dioxide, Monograph Research Project 37, API, Dallas (1955).

Chap. 46 Fig. 46.1, from Farouq Ali, S.M.: Steam Injection, Secondary and Tertiary Oil Recovery Processes, Interstate Oil

Compact Commission, Oklahoma City (Sept. 1974) 148. Fig. 46.2, from McNeil, M.S. and Moss, J.T.: Oil Recovery by In-Situ Combustion, Pet. Eng. (July 1958) B-29-B-42. Fig. 46.5, from Smith, R.W. and Perkins. T.K.: Experimental and Numerical Simulation Studies of the Wet Combustion

Recovery Process, J. Cdn. Pet. Tech. (July-Sept. 1973) 44454. Fig. 46.34, from Mace. C.: Deepest Combustion Project Proceeding Successfully, Oil & Gus J. (Nov. 17, 1975) 74-81. Fig. 46.59, from Poettmann. F.H. and Mayland, B.J.: Equilibrium Constants for High Boiling Hydrocarbon Fractures of

Varying Characterization Factors, Pet. Refiner (July 1949) 101ll2. Tables 46.1 through 46.6, from Steam Dominates Enhanced Oil Recovery, Oil & Gas J. (April 5, 1982) 139-59. Table 46.31, from 1967 ASTM Steam Tables, ASME. New York City (1967).

Chap. 47 Figs. 47.1, 47.12, and 47.26, from U.S. DOE: drawing by J. Lindley, Bartlesville, OK. Fig. 47.3, from Mungan, N.: Rev. Inst. Fr. Pet., Editions Technip, Paris (1969) 24, 232. Fig. 47.4, from Tsaur, K.: A Study of PolymeriSurfactant Interactions for Micellar/Polymer Flooding Applications, MS

thesis. U. of Texas, Austin (1978). Fig. 47.5, from Martin, F.D., Donaruma, L.G., and Hatch, M.J.: Development of Improved Mobility Control Agents for

SurfactantiPolymer Flooding, second annual report, Contract No. DOEiBCiOCO013, U.S. DOE (Oct. 1980). Fig. 47.8, from Overbeck, J.Th.G.: Colloids and Surface Chemistry. A Self-Study Subject Guide. Part 2, Lyophobic

Colloids, Bull., Center for Advanced Engineering, Massachusetts Inst. of Technology, Cambridge, MA (1972). Fig. 47.9, from Khan. S.A.: The Flow of Foam Through Porous Media, MS thesis, Stanford U., Stanford, CA (1965).

Fig. 47.19, from Recd. R.L. and Healy, R.N.: Some Physico-Chemical Aspects of Microemulsion Flooding: A Review. Improved Oil Recovery by Sutjticttmt and Polwner Flooding, D.O. Shah and R.S. Schechter (eds.), Academic Press, New York City (1977) 383-438.

Fig. 47.20, from Harwell. J.H.: Surfactant Adsorption and Chromatographic Movement with Application in Enhanced Oil Recovery. PhD dissertation, U. of Texas, Austin (1983).

Fig. 47.23, from Lake, L.W. and Pope, G.A.: Status of Micellar-Polymer Field Tests, Pet. Eng. Intl. (Nov. 1979) 51, 38-60.

Fig. 47.27, from Minssieux, L.: Waterflood Improvement by Means of Alkaline Water, Enhunced Oil Recovery by Displacement wifh Saline Solutions, Kogan Page Ltd., London (1979) 75-90; courtesy BP Trading Co. Ltd.

Table 47.1, from Manning, R.K., Pope, G.A., and Lake, L.W.: A Technical Survey of Polymer Flooding Projects, Contract No. DOE/BETC/l0327-19, U.S. DOE (Sept. 1983).

Table 47.2, from Akstinat, M.H.: Surfactants for WOR Process in High-salinity Systems: Product selection and evaluation, Enhanced Oi/ Recovery, Elsevier Scientific Publishing Co., New York City (1981).

Chap. 49 Figs. 49.9, 49.10, 49.19 through 49.22, 49.25 through 49.30, and 49.34, from Log Interpretation Principles, Vol. 1,

Schlumberger Well Services, Houston. Figs. 49.42 through 49.44 and Table 49.2, from Calver, J:C.. Rau, R., and Wells, L.: Electromagnetic Propagation-A

New Dimension in Logging, Schlumberger Well Services, Houston. Figs. 49.46 and 49.47, from Best, D.L., Gardner. J.S., and Dumanoir, J.L.: A Computer-Processed Wellsite Log

Computation, paper presented at the 1978 SPWLA Annual Logging Symposium, June 13-16. Fig. 49.48, from Coates, G.R., Schulze, R.P., and Throop, W.H.: VOLAN*-An Advanced Computational Log

Analysis, paper presented at the 1982 SPWLA Annual Logging Symposium, July 6-9. Tables 49.1 and 49.3 through 49.6, from Bateman. R.M., Log Qunlir?, Control, IHRDC, Boston, 1984.

Chap. 50

Figs. 50.5 and 50.6, from Evans, R.D.: 7he Aromic Nucleus, McGraw-Hill Book Co. Inc., New York City (1967) 426-38. Figs. 50.9, 50.21, 50.30, 50.32 through 50.34, 50.40, 50.43, 50.50, and 50.51, courtesy Schlumberger Well Services.

Houston. Fig. 50.18, from Tidman, J.: Geophysical Well Logging. excerpts from Methods in Experimental Phyic.\: Physics,

Academic Press (1986) 24. Figs. 50.22 and 50.36, from Schlumberger Log Interpretation Charts, Schlumberger Well Services, Houston. 1984. Figs. 50.23, 50.24, and 50.26, from Edmundson, H. and Raymer, L.L.: Radioactive Logging Parameters for Common

Minerals. paper presented at the 1979 SPWLA Annual Logging Symposium, Tulsa, June 3-h. Fig. 50.29, from Hertzog, R.C. and Plasek, R.E.: Neutron-Excited Gamma-Ray Spectrometry for Well Logging. IEEE

Trms. NM. Sti. (Feb. 1979) NS-26, No. 1, Fig. 50.46, Arnold, D.M. and Smith, H.D. Jr.: Experimental Determination of Environmental Corrections for a Dual-

Spaced Neutron Porosity Log, paper W presented at the 1981 SPWLA Annual Logging Symposium, Mexico City, June 23-26.

Fig. 50.47, from Schlumbergcr Chart Book, Schlumberger Well Services, Houston (1977). Table 50.3, from Bcrtuzzi. W., Ellis. D.V., and Wahl. J.S.: The Physical Foundation of Formation Lithology Logging

with Gamma Rays, Geophy.siu (Oct. 1981) 46, No. 10.

Chap. 51 Fig. 51.2, from Sears, F.W. and Zemansky, M.W.: Unirwsi@ Physics, Addison-Wesley Publishing Co. Inc., Reading. MA

(1955) 1031. Figs. 51.3 and 51.4, from Krautkramer, J. and Krautkramer, H.: Ultrasonic Testing ofA4ateriais, Springer-Verlag. New

York City (1969) 521. Figs. 51.6 and 51.71, from Timur. A.: Rock Physics, The Arabian J. Sri. Eng. Special Issue (1978) 5-30. Figs. 51.7 and 51.15, from Timur. A.: Temperature Dependence of Compressional and Shear Wave Velocities in Rocks,

Groph~sics (1977) 42, 950-56. Figs. 51.8 and 51.9 and Table 51.2, from Jones, S.B., Thompson, D.D., and Timur. A.: A Unified Investigation of

Elastic Wave Propagation in Crustal Rocks, paper presented at the Rock Mechanics Conference, Vail, CO (1976). Fig. 51.10, from Johnston. D.H., Toksoz. M.N., and Timur, A.: Attenuation of Seismic Waves in Dry and Saturated

Rocks: Part II: Theoretical Models and Mechanism. Grophvsics ( 1979) 44, 69 l-7 1 I Fig. 51.11, from Wyllie, M.R.J.. Gardner, G.H.F., and Gregory, A.R.: Studies of Elastic Wave Attenuation in Porous

Media. Geophysics (1962) 27, 269. Figs. 51.12 through 51.14, from Gardner. G.H.F., Gardner, L.W.R., and Gregory, A.R.: Formation Velocity and

Density-The Diagnostic Basics for Stratigraphic Traps, Geophysics (1974) 39, 770-80. Fig. 51.16, from Timur, A.: Velocities of Compressional Waves in Porous Media at Permafrost Temperatures,

Geophysics (1968) 33, 584-96. Figs. 51.17, 51.19, and 51.21, from Toksoz, M.N., Cheng. C.H., and Timur, A.: Velocities of Seismic Waves in Porous

Rocks, Geoph?sirs ( 1976) 41, 62 l-45. Fig. 51.17, from King, M.S.: Wave Velocities in Rocks as a Function of Changes in Overburden Pressure and Pore Fluid

Saturants. Geophysics (1966) 31, 50-73. Fig. 51.18, Gregory, A.R.: Fluid Saturation Effect\ on Dynamic Elastic Properties of Sedimentary Rocks. Geophysics

(1976) 41, 895-921. Fig. 51.20, from Timur. A.. Hempkins. W.B., and Weinbrandt. R.M.: Scanning Electron Microscope Study of Pore

Systems in Rocks. J. Geophy. Res. (1971) 76, No. 20, 4932-48.

xi

Figs. 51.22, 51.37, 51.50, and 51.94, from Gcycr. R.L. and Myung, J.I.: The 3-D Velocity Log: a Tool for In-Situ Determination of the Elastic Moduli of Rocks. Dynamic Rock Mechanics, Proc., Twelfth Symposium on Rock Mechanics (1971) 71-107.

Figs. 51.23 and 51.24, from Minear, J.W. and Fletcher, C.R.: Full-Wave Acoustic Logging, Tr0n.c.) SPWLA (1983) paper EE.

Fig. 51.25, from Cheng. C.H. and Toksoz, M.N.: Elastic Wave Propagation in a Fluid-Filled Borchole and Synthetic Acoustic Logs, Geophysics (1981) 46, 1042-S3.

Fig. 51.26, from Cheng. C.H. and Toksoz. M.N.: Generation, Propagation and Analysis of Tube Waves in a Borehole, Trans., SPWLA (1982) paper P.

Figs. 51.27, 51.28, 51.31, and 51.46, from Thomas, D.H.: Seismic Applications of Sonic Logs, The Log Analwt (Jan.- Feb. 1977) 23-32.

Figs. 51.29 and 51.33, from Lynch, E.J.: Forrnutiorz Evu/uurwn, Harper and Row, New York City (1962) 422. Figs. 51.36 and 51.77, from Ausburn, J.R.: Well Log Editing in Support of Detailed Seismic Studies, Trans., SPWLA

(1977) paper F. Figs. 51.39 and 51.42, from Goetz, J.F., Dupal. L., and Bowler, J.: An Investigation into Discrepancies Between Sonic

Log and Seismic Check Shot Velocities, Part I, APEA J. (1979) 19, 131-41. Fig. 51.40, from Ransom, R.C.: Methods Based on Density and Neutron Well-Logging Responses to Distinguish

Characteristics of Shaly Sandstone Reservoir Rock, The Log Analyst (May-June 1977) 18, 47-62. Figs. 51.41, 51.43, 51.44, and 51.48, from The Long Spaciflg So&, Schlumberger technical pamphlet (1980). Fig. 51.45, from Misk, A. ef a/.: Effects of Hole Conditions on Log Measurements and Formation Evaluation, SAID,

Third Annual Logging Symposium (June 1976). Figs. 51.47 and 51.49, from The Long Spacing Sonic, Schlumberger technical pamphlet (1982). Fig. 51.56, from Parks. T.W., McClellan, J.H., and Morris. C.F.: Algorithms for Full-Waveform Sonic Logging, paper

presented at the 1983 IEEE-ASSP Workshop on Spectral Estimation. Fig. 51.58, from Wiley. R.: Borehole Televiewer-Revisited. Trans., SPWLA (1980) 21, paper HH. Fig. 51.60, from Seisviewer Logging, Birdwell, Div. of Seismograph Service Corp.. technical pamphlet (1981). Fig. 51.61, from Broding, R.A.: Volumetric Scanning Well Logging, Trans., SPWLA (1981) 22, paper B. Fig. 51.63, from Log Interpretation Charts. Schlumberger (1979). Fig. 51.65, from Evaluaci6n de Formaciones en la Argentina, Schlumberger (1973) 9455. Fig. 51.66, from Raymer, L.L.. Hunt, E.R., and Gardner, J-S.: An Improved Sonic Transit Time-To-Porosity

Transform. Trms., SPWLA (1980) paper P. Fig. 51.67, from Hartley. K.B.: Factors Affecting Sandstone Acoustic Compressional Velocities and An Examination of

Empirical Correlations Between Velocities and Porosities, Tram, SPWLA (1981) paper PP. Figs. 51.70 and 51.72, from Nations, J.F.: Lithology and Porosity from Acoustic Shear and Comprcssional Wave Transit

Time Relationships, Trms., SPWLA 18th Annual Logging Symposium (June 1974). Fig. 51.73 and 51.74, from Gardner. G.H.F. and Harris, M.H.: Velocity and Attenuation of Elastic Waves in Sands.

Trans.. SPWLA (1968) 9, paper M. Fig. 51.75, from Arditty. P.C.. Ahrens, G., and Staron, Ph.: EVA: A Long Spacing Sonic Tool for Evaluation of

Velocities and Attenuation. paper presented at the 1981 SEG Annual Meeting, Los Angeles. Fig. 51.76, from Domenico. S.N.: Effect of Brine-Gas Mixture on Velocity in an Unconsolidated Sand Reservoir. Thr

Log A~~nl~st (1977) 18, 38-46. Figs. 51.78 and 51.79, from Kithas. B.A.: Lithology, Gas Detection, and Rock Properties from Acoustic Logging

Systems, Trcrns., SPWLA (1976) 17, paper R. Figs. 51.80 and 51.81, from Laws. W.R.. Edwards. C.A.M., and Wichmann, P.A.: A Study of the Acoustic and Density

Changes Associated with High-Amplitude Events on Seismic Data. Trans., SPWLA (1974) 15, paper D. Figs. 51.83 and 51.84, from Herring, E.A.: North Sea Abnormal Pressures Determined from Logs, Per. Eng. (1973)

45, 72-84. Figs. 51.85 through 51.89, from Acoustic Cement Bond Log, Dresser Atlas technical pamphlet (I 979) 20. Figs. 51.90 and 51.92, from Cement Bond Evaluation in Cased Holes Through 3-D Velocity Logging, Birdwell technical

pamphlet (1978) 12. Fig. 51.91, from Cement Evaluation Tool, Schlumberger technical pamphlet (1983). Fig. 51.96, from Walker. T.: Acoustic Character of Unconsolidated Sand, Welcx paper (1971). Fig. 51.97, from Myung. J.I. and Baltosser. R.W.: Fracture Evaluation by the Borehole Logging Method. Stuhi& Rock

Sloprs. Thirteenth Symposium on Rock Mechanics (1972) 31-56. Figs. 51.98 and 51.99, from Taylor, T.J.: Interpretation and Application of Borehole Televicwer Surveys. Tram.,

SPWLA (1983) 24, paper QQ. Fig. 51.100, from Williams. D.M. et (II.: The Long Spacing Acoustic Logging Tool, Trans., SPWLA (1984) 25,

paper T. Table 51.1, from Timur. A.: Application of Acoustic Wave Propagation Methods to Evaluation and Production of

Hydrocarbon Rcscrvoirs, Pm-, IEEE Ultrasonic Symposium, Dallas (1984). Table 51.3, from Guyod. H. and Shane. L.E.: Geophysical Well Logging, Hubert Guyod, Houston (1969) I, 256; and

Wyllic, M.R.J.. Gregory, A.R.. and Gardner. G.H.F.: Elastic Wave Velocities in Heterogeneous and Porous Media, Geophysic~s (1956) 21, 41-70.

Chap. 52

Figs. 52.1 and 52.2, from MS-196, Exploration Logging Inc., Sacramento, CA (1979). Figs. 52.3 through 52.12 and 52.22 and Table 52.1, courtesy Exploration Logging Inc., Sacramento, CA. Figs. 52.13, 52.14, 52.16, 52.17, and 52.19 through 52.21, from MS-156, Exploration Logging Inc.. Sacramento, CA

(1981). Figs. 52.15 and 52.18, from AV-6. Exploration Logging Inc.. Sacramento. CA (1980). Fig. 52.23, from AV-13. Exploration Logging Inc.. Sacramento. CA (1982).

xii

Chap. 53

Fig. 53.3, from Measurement While Drilling, Technical Specifications. Anadrill Logging Unit, Schlumherger. Fig. 53.7 and Table 53.2, from Log Qualify Conrrol Munurri. Vizilog Inc., Houston. Figs. 53.9 through 53.11, from Dipme/er InferpretLltion~Vol. I, Fundamentals, Schlumberger, Houston (1981). Fig. 53.12 and 53.15, from Gilbreath. J.A.: Dipmeter Interpretation Rules, Schlumberger Offshore Services, New

Orleans. Figs. 53.13 and 53.14, from Open Hole Log Analysis and Formation Evaluation. Vizilog Inc.. Houston. Figs. 53.16 through 53.18, from 7k Lox Analyst (March-April 1979) 20. Fig. 53.20, from Well Evaluation Developments Schlumherger, Houston (1982). Fig. 53.23 through 53.25, from Dresser Atlas Production Senlices Catalog, Dresser Atlas. Fig. 53.26, from The &IR Analyst (March-April 1984) 25-28. Fig. 53.27 through 53.32, from Well Evaluation Developments 1982, Schlumherger. Table 53.1 and Fig. 53.5, from EXLOG Flyer GA 817-A. EXLOG (June 1983). Table 53.3 and Figs. 53.21 and 53.22, from Dia-Log flyer, The Dia-Log Co., Houston.

Chap. 54 Figs. 54.6 through 54.9, courtesy Dowell Schlumherger Technical Brochure TSL-2038, Acidizing-State-of-the-Art,

Tulsa, OK (1981).

Chap. 56

Figs. 56.1 through 56.8, courtesy Dowell Schlumberger Technical Brochure TSL45 19, Dowell Sand Control Techniques and Equipment Catalog (Sept. 1982). Tulsa. OK.

Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

Acknowledgments . . . . . . . . . . . . . . . . . . ..~......................___.____._. v

1. Mathematical Tables and Units and Systems of Weights and Measures Mathematical Tables . . Units and Systems of Weights and Measures . . .

............... 1-2

............... 1-68

2. Casing, Tubing, and Line Pipe Casing.. .............................................................................. 2-1 Tubing ................................................................................ 2-38 Line Pipe .............................................................................. 2-46 Equations for Calculating Performance Properties of Casing, Tubing, and Line Pipe ............... 2-46 API Threading Data ..................................................................... 2-64

3. Wellhead Equipment and Flow Control Devices Introduction . API Flanged or Clamped Wellhead Equipment. Flow Control Devices: Safety Shut-In Systems Other Flow-Control Devices Corrosion Special Application. Independent Screwed Wellhead.

4. Production Packers Production Packers Classification and Objectives ............... 4-l Tubing-to-Packer Connections. ............... 4-l Packer Utilization and Constraints ............... 4-l Considerations for Packer Selection ............... 4-4 Tubing/Packer System ............... 4-6 Tubing Response Characteristics. ............... 4-8 Combination Tubing/Packer Systems ............... 4-11 Tubing/Packer Forces on Intermediate Packers ............... 4-l I

5. Gas Lift Introduction................................................... Gas Fundamentals as Applied to Gas Lift . Gas Lift Valve Mechanics Continuous-Flow Gas Lift Intermittent Gas Lift . Unloading Procedures and Proper Adjustment of Injection Gas Rate

6. Hydraulic Pumping Introduction Downhole Pumps Principles of Operation-Reciprocating Pumps Jet Pumps Surface Equipment Appendix A-Fluid Properties Appendix B-Friction Relationships

7. Electric Submersible Pumps Introduction ESP System. Application5 ESP System Components. Selection Data and Methods Handling, Installation. and Operation Troubleshooting

............... 3-l

............... 3-l

............... 3-18

............... 3-34

............... 3-35

............... 3-36

............... 3-39

. 5-l S-3 5-12 5-21 5-38 5-53

6-1 6-2 6-8 6-34 6-49 6-66 6-69

7-l 7-l 7-l 7-3 7-9 7-12 7-14

xv

8. Subsurface Sucker-Rod Pumps Introduction ................... Pump Selection ................ Plungers ...................... Slippage Past Plungers. ......... Soft-Packed Plungers ........... Balls and Seats ................ Double Valves ................ Bottom-Discharge Valve ........ Three-Tube Pump. ............. Gas Anchors .................. Special Pumps. ................ Corrosion .................... Effect of Gases and Vapors. ..... Conclusions ...................

9. Sucker Rods Introduction ................... Steel Sucker Rods ............ Fiberglass Sucker Rods .........

.

.

..,................,..

10. Pumping Units and Prime Movers for Pumping Units: Part l-Pumping Units Introduction ............................................................ Pumping Units ......................................................... Component Parts ....................................................... Pumping Unit Loading ................................................... Counterbalance ......................................................... Sizing ................................................................. Installation ............................................................. Lubrication ............................................................ Changing the Oil .......................................................

8-l 8-2 8-4 8-5 8-6 8-7 8-7 8-8 8-8 8-9 8-9 8-9 8-10 8-10

9-l 9-l 9-10

IO-I IO-I IO-4 IO-5 IO-6 IO-7 IO-7 IO-12 IO-13

Pumping Units and Prime Movers for Pumping Units: Part 2-Prime Movers for Pumping Units Introduction ............................................................................ lo-14 Internal-Combustion Engines .............................................................. IO-14 Electric Motors for Oilwell Pumping ....................................................... IO-19

11. Oil Storage Types of Storage Tanks ................................ Tank Corrosion Protection ............................. Appurtenances ........................................ Venting Atmospheric and Low-Pressure Storage Tanks ...... Materials of Construction .............................. Production Equipment ................................. Vapor Losses ........................................ Vapor Control and Gravity Conservation With Storage Tanks Underground Storage ..................................

12. Oil and Gas Separators Summary.. ........................................... Introduction ........................................... Primary Functions of Oil and Gas Separators ............... Secondary Functions of Oil and Gas Separators ............. Special Problems in Oil and Gas Separation ................ Methods Used To Remove Oil From Gas in Separators ...... Mist Extractors Used in Oil and Gas Separators ............ Methods Used To Remove Gas From Oil in Separators ...... Estimated Quality of Separated Fluids ..................... Classification of Oil and Gas Separators ................... Centrifugal Oil and Gas Separators and Gas Scrubbers ....... Illustrations of Oil and Gas Separators .................... Comparison of Oil and Gas Separators .................... Estimating the Sizes and Capacities of Oil and Gas Separators.

xvi

. .

11-l 1 l-4 11-6 11-6 1 l-9 11-9 11-11 I l-12 11-13

12-l 12-l

. 12-3 12-4 12-6 12-8 12-l I 12-13 12-13 12-16 12-20 12-21 12-21 12-21

Computer Sizing of Oil and Gas Separators ............................. 12-25 Capacity Curves for Vertical and Horizontal Oil and Gas Separators ........ 12-27 Practical Considerations in Sizing Oil and Gas Separators ................. 12-32 Stage Separation of Oil and Gas. ...................................... 12-32 Selection and Application of Separators and Scrubbers .................... 12-35 Construction Codes for Oil and Gas Separators .......................... 12-38 Controls, Valves, Accessories, and Safety Features for Oil and Gas Separators 12-39 Operation and Maintenance Considerations for Oil and Gas Separators ....... 12-40

13. Gas Measurement and Regulation Introduction ............................................ Gas Measurement. ...................................... Regulation.. ...........................................

14. Lease-Operated Hydrocarbon Recovery Systems Introduction............................................... Low-Temperature Separation (LTS) Systems . . . . . . . . . Gas-Treating Systems for Removal of Water Vapor, CO,, and H,S

15. Surface Facilities for Waterflooding and Saltwater Disposal Introduction ............................................ Piping System Design ................................... Selecting Pumps and Drivers ............................. Separating Suspended Solids From Heater. .................. Treating Hydrocarbons From Water. ....................... Dissolved Gas Removal .................................. Dissolved Solids Removal ................................ Removing Hydrocarbons From Solids ...................... Process Selection and Project Management .................. Project Control .........................................

16. Automation of Lease Equipment Introduction ........................................... Automatic Production-Control Equipment .................. Production Safety Controls .............................. Automatic Quantitative Measurement ...................... Gas Measurement ...................................... Temperature Measurement .............................. Automatic Sampler. .................................... BS&W Monitor ....................................... Net-Oil Computer. ..................................... Supervisory Control and Data Acquisition (SCADA) Systems . Typical Automatic-Control Installations .................... Automatic Well Testing ................................. LACT ...............................................

17. Measuring, Sampling, and Testing Crude Oil Introduction ............................................ Procedure for Typical Measuring, Sampling, and Testing ...... Abstract of API Manual .................................

18. Offshore Operations Introduction ............................... Historical Review .......................... Offshore Drilling .......................... Field Operations ........................... Special Considerations ...................... Structures ................................ Offshore Production Operations .............. Arctic .................................... Electrica:, Instrumentation and Control Systems Control of Subsea Production Facilities ........

. .

. . . .

.

. .

13-l 13-l 13-49

14-l 14-l 14-17

5-l 5-l 5-14 5-18 5-2 I

15-28 15-29 1.5-30 15-30 1.5-32

16-1 16-2 16-4 16-5 16-6 16-7 16-7 16-7 16-7 16-8 16-10 16-12 16-12

17-l 17-l 17-3

18-I 18-l 18-3 18-17 18-20 18-22 18-27 18-38 18-43

. 18-48

19. Crude Oil Emulsions Introduction............................................. 19-I Theories of Emulsions 19-I Sampling and Analyzing Crude Oil Emulsions . 19-6 Methods Used in Treating Crude Oil Emulsions, 19-6 Emulsion-Treating Equipment and Systems . . 19-15 Description of Equipment Used in Treating Crude Oil Emulsions 19-16 Operational Considerations for Emulsion-Treating Equipment. . 19-28 Economics of Treating Crude Oil Emulsions . . 19-32

20. Gas Properties and Correlations Molecular Weight. . . . . Ideal Gas . .

21.

. .

Critical Temperature and Pressure . Specific Gravity (Relative Density) . . . Mole Fraction and Apparent Molecular Weight of Gas Mixtures Specific Gravity of Gas Mixtures . . . . Daltons Law . . . . . . . . . Amagats Law. Real Gases . . . Principle of Corresponding States. Equations of State . . . . . Van der Waals Equation. . . . Viscosity . . . . . Viscosity Correlations . . . Natural Gasoline Content of Gas . . . Formation Volume Factor . . Coefficient of Isothermal Compressibility Vapor Pressure . . . Cox Chart Calingeart and Davis Equation . Lee-Kesler ............................ Example Problems .....................

Crude Oil Properties and Condensate Properties and Correlations Introduction .................................................. BaseofCrudeOil ............................................ Physical Properties ............................................ True-Boiling-Point Crude-Oil Analyses ........................... Bubblepoint-Pressure Correlations ............................... Dewpoint-Pressure Correlations ................................. Sage and Olds Correlation ..................................... Total Formation Volume Correlations ............................

22. Oil System Correlations Introduction . . . . . . . Oil Density Determination. . . Bubblepoint-Pressure Correlations Solution GOR for Saturated Oils . Oil FVF Correlations . . . Total FVFs Oil Viscosity Correlations . Gas/Oil IFT . . . Glossary . . . . .

23. Phase Diagrams Introduction . . Single-Component Phase Diagrams Phase Rule . . . . . Types of Diagrams. . . Calculation of Phase Compositions. . .

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.

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. . . .

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. . . .

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. . . . . . . I

. . .

. . .

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20-I 20-l 20-2 20-4 20-4 20-4 20-4 20-4 20-4 20-4 20-6 20-7 20-9 20-9 20-10 20-I 1 20-11 20-11 20-12 20-13 20-13 20-13

21-I 21-l 21-3 21-8 21-9 21-10 2llll 21-15

22-l 22-2 22-5 22-9 22-10 22-13 22-13 22-16 22-20

23-l 23-l 23-2 23-2 23-10

XVIII

24. Properties of Produced Waters Introduction and History Sampling . . . . . . . Analysis Methods for Oilfield Waters . . . Chemical Properties of Oilfield Waters . . . Inorganic Constituents . . . . . Physical Properties of Oilfield Waters Interpretation of Chemical Analyses . . Occurrence, Origin, and Evolution of Oilfield Waters Recovery of Minerals From Brines . . . . . .

. .

. .

. . . .

25. Phase Behavior of Water/Hydrocarbon Systems Introduction ........................................................................... General Hydrocarbon/Water Phase Diagrams and Equilibrium Data Sources ..................... Hydrate Stability Conditions ............................................................. Determining the Water Content of Gas (or Hydrocarbon-Rich Liquid) in Equilibrium With Hydrates Definition of the Saturated Water Content of Natural Gases in Equilibrium With Aqueous Phases ... Quantitative Prediction of Water Content in Light Hydrocarbon Systems ........................ Quantitative Predictions of Solute Concentrations in the Aqueous Phase ......................... Sour Water Stripper Correlations ......................................................... Oil and Gas Reservoirs That Exist in the Gas Hydrate Region ................................. Hydrate Inhibition .....................................................................

26. Properties of Reservoir Rocks Introduction . . Porosity . . . . . . . . . . . . . . . . . . . . . Permeability . . Fluid Saturations. . Electrical Conductivity of Fluid-Saturated Rocks Empirical Correlation of Electrical Properties.

27. Typical Core Analysis of Different Formations Introduction ............................... Porosity .................................. Permeability .............................. Liquid Saturations ......................... Percussion Sidewall Core Data ............... Data From U.S. Areas ..................... Data From Non-U.S. Areas .................

28. Relative Permeability Introduction . . . . 28-l Historical Background . 28-2 Framework Ideas . . 28-2 Measurement Methodologies . 28-3 Recent Literature 28-9 Critique of Recent Work . . . . . 28-10 Ramifications Needing Attention. 28-12 Conclusions . . 28-13

29. Petroleum Reservoir Traps Introduction .............. .......... Trap Classification ................... Characteristics of Reservoir Rocks. ...... Glossary ................ ..........

30. Bottomhole Pressures Introduction BHP Instruments . . Pressure Transducer Technology Calculated BHP . Application of BHP .

. .

.

,.,,.,.....,

. .

.

. .

24-l 24-3 24-5 24-5 24-9 24-12 24-18 24-19 24-20

25-l 25-1 25-4 25-10 25-11 25-16 25-16 25-17 25-18 25-19

26-l 26-l 26-10 26-20 26-27 26-29

27-l 27-1 27-l 27-8 27-9 27-9 27-9 . . .

.

. . . . . . . . . .

29-l 29- 1 29-6 29-8

30-l 30-l

. 30-6 30-7 30-8

xix

31. Temperature in Wells Introduction ........... Thermometers ......... Thcrmometry ......... Summary .............

32. Potential Tests of Oil Wells Texas Allowable Rule .................... Productivity Index (PI) ................... Specific PI. ............................. Theoretical PI ........................... Pseudosteady-State Flow .................. Stock-Tank Measurement. ................. Portable Well Testers, .................... GOR .................................. GOR as a Criterion of Reservoir Performance

....... 31-l

....... 31-I

....... 31-2

....... 31-7

....... 32-1

....... 32-2

....... 32-4

....... 32-4

....... 32-5

....... 32-6

....... 32-7

....... 32-14

....... 32-15

.

. .

33. Open Flow of Gas Wells Introduction .. ........................ Pitot-Tube Gauging of Low-Pressure Wells Backpressure Testing ..... ........................ Gas Well Inflow Equation. Pseudosteady State ......... Multipoint Test and Example ....................... Isochronal Test and Example ....................... Comparison of Multipoint With Isochronal Test ........ Gas Measurement ... ............... ............. Calculation of Subsurface Pressures .................. Application of Backpressure Tests to Producing Problems Production Rate .................... ............. Causes of Deterioration in Performance ............. Examples of Remedial Operations ..... .............

....... 33-l

....... 33-1

....... 33-3

....... 33-5

....... 33-7

....... 33-10 33-l 1 ........

....... 33-13

....... 33-13

....... 33-20

....... 13-20 _

....... 33-20

....... 33-22

. . .

.

. .

34. Wellbore Hydraulics Introduction Theoretical Basis Producing Wells . Injection Wells Oil Wells Multiphase Flow. Flow Through Chokes Liquid Loading in Wells

....... 34- 1

....... 34- 1

....... 34-3

....... 34-28

....... 34-30

....... 34-35

....... 34-45

....... 34-46

. .

. .

. .

. .

.

35. Well Performance Equations Introduction. ............... Diffusivity Equation ......... Multiphase Flow. ........... Oil Well Performance ....... Gas Well Performance. ...... Transient Well Test Analysis

....... 35-1

....... 35-l

....... 35-2

....... 35-2

....... 35-10

....... 35-14

. . . .

.

. . .

36. Development Plan for Oil and Gas Reservoirs Introduction. Oil and Gas Differences Characterization of the Reservoir Prediction of Reservoir Performance

36-l 36-2 36-3 36-9

.

. .

37. Solution-Gas-Drive Reservoirs Introduction .................................. Definitions. .................................. Typical Performance .......................... Types of Models Used. ........................ Basic Assumptions of Tank-Type Material Balance Basic Data Required. .......................... Material-Balance Equation ......................

37-1 37-l 37-1 37-2 . 17-2 _ 37-3 . 17-5 _

XX

Material Balance as Equation of Straight Line for Determination of OIP and of Gas-Cap Size 37-6 Material-Balance Calculations Using Tracys Method .................................. 37-7 Comparison of Tarners and Tracys Methods ........................................ 37-10 Material-Balance Calculations Using Muskat and Taylors Method ....................... 37-10 Sensitivity of Material-Balance Results .............................................. . 37-13 Production Rate and Time Calculations .............................................. 37-17 Insights From Simulator Studies .................................................... 37-21 Volatile Oil Reservoir Performance Predictions ....................................... 37-22

38. Water Drive Oil Reservoirs Introduction ........................... Definitions. ........................... Mathematical Analysis ..................

.

. .

34. Gas-Condensate Reservoirs Introduction ................................................ Properties and Behavior of Gas-Condensate Fluids. ............... Gas-Condensate Well Tests and Sampling ....................... Sample Collection and Evaluation ............................. Operation by Pressure Depletion .............................. Operation by Pressure Maintenance or Cycling .................. General Operating Problems: Well Characteristics and Requirements Economics of Gas-Condensate Reservoir Operation ...............

40. Estimation of Oil and Gas Reserves Estimating Reserves ........................... Petroleum Reserves-Definitions and Nomenclature. Glossary of Terms ..................................................................... Computation of Reservoir Volume ........................................................ Computation of Oil or Gas in Place. ...................................................... Saturated Depletion-Type Oil Reservoirs-Volumetric Methods ................................ API Estimation of Oil and Gas Reserves. .................................................. Undersaturated Oil Reservoirs Without Water Drive Above the Bubblepoint-Volumetric Method ... Volatile Oil Reservoirs-Volumetric Methods ............................................... Oil Reservoirs With Gas-Cap Drive-Volumetric Unit Recovery Computed by Frontal-Drive Method Oil Reservoirs Under Gravity Drainage. ................................................... Oil Reservoirs With Water Drive-Volumetric Methods ...................................... Volumetric Recovery Estimates for Nonassociated Gas Reservoirs ............................. Production-Decline Curves ................ Other Performance Curves ................

41. Valuation of Oil and Gas Reserves Types of Oil and Gas Property Ownership Valuation . . . Forecast of Future Rate of Production Development and Operating Costs . . Federal Taxes . . . . . . . . Different Concepts of Valuation Interest Tables and Deferment Factors.

42. Injection Operations Introduction . . . . . . Important Factors in the Design of Injection Operations Analysis of a Reservoir for Injection Operations

43. Gas-Injection Pressure Maintenance in Oil Reservoirs Introduction. . . . . . . Types of Gas-In.jection Operations . Optimal Time To Initiate Gas Pressure-Maintenance Operations Efficiencies of Oil Recovery by Gas Displacement . Methods of Evaluating Unit-Displacement Efficiency. Methods of Evaluating Conformance Efficiency . . Methods of Evaluating Areal Sweep Efficiency . Calculation of Gas Pressure-Maintenance Performance

.

. 38-1

. 38-l 38-l

. 39-1 39-1 39-4

. 39-6 39-10 39-15 39-24

. 39-26

40- 1 40-2 40-3 40-4 40-5 40-8 40-12 40-12 40-13 40-13 40-14 40-15 40-2 1 40-26 40-32

41-l 41-2 41-9 41-l 1 41-12 41-16 41-25

42-l 42-2 42-3

43-1 43-2 43-3 43-3 43-3 43-6 43-7 43-8

xxi

Appendix A-Example Calculations of Future Performance . Appendix B-Selected References Containing Equations, Calculation Procedures, and Example

Calculations Related to Gas-Injection Performance Predictions . . . . . . Appendix C-Data Requirements for Engineering Analysis of Gas-Injection Operations

44. Water-Injection Pressure Maintenance and Waterflood Processes Introduction ....................................................... Important Factors in Waterflooding or Water-Injection Pressure Maintenance Determination of Residual Oil After Waterflooding ...................... Predicting Water Injection Oil Recovery and Performance Water-Injection Well Behavior ....................................... Water-Injection Case Histories ....................................... Pilot Floods ....................................................... Surface-Active Agents in Waterflooding ............................... Water Source and Requirements ...................................... Water Treating .................................................... Selection and Sizing of Waterflood Plants. .............................

45. Miscible Displacement Introduction . . . Theoretical Aspects of Miscible-Phase Displacement Factors Affecting Displacement Efficiency Engineering Study . . . . Appendix-Engineering Examples

46. Thermal Recovery Introduction. ........................ Two Forms of Steam Injection Processes Three Forms of In-Situ Combustion. .... Historical Development ............... Current Status. ...................... Theoretical Considerations. Analytical Models for Steam Injection ... Numerical Simulation. ................ Laboratory Experimentation ........... Field Projects ....................... Project Design ...................... Well Completion. .................... Field Facilities ...................... Monitoring and Coring Programs ....... Operational Problems and Remedies .... Case Histories ....................... Thermal Properties ...................

47. Chemical Flooding Introduction ......................... Mobility Control Processes ............ Low-IFT Processes. .................. High-pH Processes ................... Summary ...........................

.

48. Reservoir Simulation Introduction ........................................... A Brief History ....................................... General Description of Simulation Models ................. Purpose of Reservoir Simulation. ......................... Considerations in Practical Application of Simulation Models. . Validity of Simulation Results. ........................... Simulation Technology ..................................

49. Electrical Logging Fundamentals ....................... Spontaneous Potential (SP) Log ........ Resistivity Logging Devices ...........

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.

. .

.

.

. .

.

.

.

. . .

.

.

43-10

. . . 43-16 43-17

44-l . 44-2

. 44-5 44-7 44-32

. . 44-36 . . 44-37 . 44-39 . 44-41

. 44-43 44-45

. 45-l 45-l

. 45-6

. 45-8 . 45-10

46-l . 46-l

. . 46-l

. 46-3 46-3 46-4 46-7 46-l 1 46-12

. 46-13 46-17 46-19 46-19 46-20 46-2 1 46-22 46-3 I

47-l . 47- 1 . 41-9

47-18 47-22

48-l 48-l

. 48-2 . . 48-6

. 48-7 . 48-9

. 48-13

. 49-l 49-7 49-l I

xxii

Induction Logging ................................ Focused-Electrode Logs. ........................... Microresistivity Devices ........................... Uses and Interpretation of Well Logs ................ The Digital Age ..................................

49-14 49-1x 49-22 49-25 49-36

50. Nuclear Logging Techniques Introduction ...................................... Nuclear Physics for Logging Applications. ............ Nuclear Radiation Logging Devices .................. Interpretation of Nuclear Logs ......................

50-l 50-3 50-15 50-23

.

51. Acoustic Logging Introduction ...................................... Elasticity ........................................ Acoustic Wave Propagation in Rocks. ................ Acoustic Wave Propagation Methods ................. Methods of Recording Acoustic Data. ................ Applications ..................................... Conclusions ...................................... Appendix-Theory of Elastic Wave Propagation in Rocks

51-l 51-l 51-4 51-l I 51-14 51-28 51-47 51-49

. . . . .

.

52. Mud Logging Introduction . . . . Service Types . . . Formation Evaluation Services . . The Modern Mud Logging Unit The Mud Log . . . . . . . Petroleum Engineering Services . Drilling Engineering Services . . Selecting a Mud Logging Service. Standards for and Status of Services

52-l . 52-l

52-2 52-11 52-11 52-16 52-27 52-28 52-30

. . . . .

.

. .

53. Other Well Logs Introduction ...................................... MWD .......................................... Directional Surveys ............................... Dipmeter Logging ................................ Caliper Logs ..................................... Casing Inspection Logs ............................

53-l 53-l 53-3 53-7 53-16 53-17

. . . . .

.

54. Acidizing Introduction . General Principles . Acid Reaction Rates Acid Additives . Acidizing Techniques Laboratory Testing Acid Treatment Design Critical Wells Summary .

54-l 54-l 54-4 54-6 54-8 54-9 54-10

. 54-11 54-12

. . .

. . . .

. . . .

.

. . . .

55. Formation Fracturing Introduction . Hydraulic Fracturing Theory Formations Fractured . . Fracture Planes. . Fracture Area . . . . Reservoir-Controlled Fluids. Viscosity-Controlled Fluids Fluid-Loss-Controlled Fluids Stimulation Results. . . Fracturing Materials . . . Fracturing Techniques

55-l 55-l 55-2 55-2 55-2 55-2 55-4 55-4 55-4 55-5 55-8

. . . .

. . .

. .

. . .

. . .

.

.

.

. .

Multiple-Zone Fracturing. Fracturing Equipment. Treatment Planning and Design

56. Remedial Cleanup, Sand Control, and Other Stimulation Treatments Introduction................................................... Reperforation ___.,..,,,..._..___.,,.,..,,,._.._..,._____._.._. Abrasive Jet Cleaning . Mud Removal................................................. Water Blocks and Emulsions Scale Deposits................................................. Paraffin Removal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Large-Volume Injection Treatments Steam Injection General Comments . Sand Control ~~~~.~..~.~.~~~..~..~~~.~.~~~~....~~~..~~~...~~.~~

57. Oil and Gas Leases The Landowners Interest ......... The Oil and Gas Lease ........... Assignments by the Landowner .... Assignments by the Lessee ........ Unit Operations ................. Getting the Well Drilled .......... Lease Problems During Development Taxation ....................... Offshore Leasing ................

58. The SI Metric System of Units and SPE Metric Standard Preface .................................. Part 1: SI-The International System of Units

Introduction ................................................... SI Units and Unit Symbols ....................................... Application of the Metric System ................................. Rules for Conversion and Rounding. .............................. Special Terms and Quantities Involving Mass and Amount of Substance Mental Guides for Using Metric Units ............................. Appendix A-Terminology .............. Appendix B-S1 Units ................... Appendix C-Style Guide for Metric Usage . Appendix D-General Conversion Factors. .. Appendix E-Conversion Factors for the Vara ......................

Part 2: Discussion of Metric Unit Standards .......................... Introduction ................... Review of Selected Units ........ Unit Standards Under Discussion Notes for Table 2.2 ............ Notes for Table 2.3 ............ .

59. SPE Letter and Computer Symbols Standard Symbols in Alphabetical Order.. Quantities in Alphabetical Order. Subscript Definitions in Alphabetical Order Subscript Symbols in Alphabetical Order

Index . Author . . . . . . . . . . . . . . . . . Subject . .

. . . . . . . . . . .

. . . . . . . . . . .

55-9 55-9 55-9

56-l 56- 1 56-l 56-l 56-2 56-2 56-2 56-2 56-2 56-2 56-2

57-l 57-3 57-6 57-7 57-7 57-8 57-10 57-l I 57-l I

58-2 58-2 58-2 58-2 58-3 58-5 58-7 58-8 58-8 58-9 58-l I 58-14 58-20 58-2 I 58-2 I 58-22 58-24 58-25 5x-25

59-2 59-18 59-52 59-63

I 1 15

xxiv

Chapter 1

Mathematical Tables and Units and Systems of Weights and Measures Philip Franklin, Massachusetts Inst. of Technology*

L.E. Barbrow. U.S. Nat]. Bureau of Standards

Contents

Mathematical Tables By Philip Franklin

Numbers

Table 1 .l-Squares I-2 Table I.2-Gibes I-7 Table 1.3-Square Roots .i-ii Table 1.4-Cube Roots l-14 Table 1.5-Three-Halves Pow& : : : : : : : : : : : : : : : : l-19 Table 1.6--Reciprocals 1-21

Circles

Table 1.7-Circumferences by Hundredths l-24 Table 1.8-Areas by Hundredths .I-26 Table 1.9-Circumferences and Areas by Eighths l-28 Table 1 .lO-Areas in Square Feet I-30 Table 1 .l l-Segments, Given h/c ............... l-31 Table 1.12-Segments. Given h/D ................ 1-32

Spheres

Table 1.13-Segments ......................... 1-33 Table 1,14-Volumes by Hundredths .............. 1-34 Table 1 .I5-Regular Polygons .................. l-36 Table 1.16--Binomial Coefficients ............... 1-37 Table 1,17-Common Logarithms (1 .OO to 2.00) 1-38 Table I .18-Common Loqarithms I-40 Table 1.19-Degrees and-Minutes in Radians ....... l-42 Table 1.20--Radians in Degrees ...... ......... 1-43 Table 1.21-Natural Sines and Cosines l-44 Table 1.22-Natural Tangents and Cotangents l-46 Table 1.23-Natural Secants and Cosecants l-48 Table 1.24-Trigonometric Functions ........... I-50 Table 1.25-Exponentials ........... ........... 1-55 Table 1.26-Natural Logarithms I-56 Table 1.27-Hyperbolic Sines

Cosines : : : : : : : : : : : : : 1-58

Table 1.28-Hyperbolic 1-59 Table 1.29-Hyperbolic Tangents I-60 Table 1.30-Multiples of 0.4343 l-60 Table 1.31-Multiples of 2.3026 Table 1.32-Standard Distribution of Residuals :

I-60 I-61

Table 1.33-Factors for Computing Probable Error 1-61

This chapter I the 1962 edMn was written by Ph,l,p Franklm and Laws Judson (both deceased)

Compound Interest

Table 1.34-Amount of a Given Principal Table 1.35-Amount of an Annuity Table 1.36-Principal Amounting to a Given Sum

Annuities

Table 1.37-Amountino to a Given Sum (Sinking Fund) y.,

Table 1.38-Present Worth Table 1.39-Provided for by a Given Capital Table 1.40-Decimal Equivalents

Units and Systems of Weights and Measures by L.E. Barbrow

Conversion Tables

Table 1.41-Length Equivalents Table 1.42-Conversion of Lengths : : : : : : Table 1.43-Common Fractions of an Inch to Millimeters

Table 1.44-Decimals of an Inch to Millimeters Table 1.4%Millimeters to Decimals of an Inch Table 1.46-Area Equivalents Table 1.47-Volume and Capacity Equivalents Table1.48-Areas Table 1.49-Volumes or Cubic Meters Table 1.50-Volumes or Capacities : : : Table 1.51-Mass Equivalents Table 1.52-Masses .,, . . Table 1.53-Velocity Equivalents Table 1.54-Linear and Angular Velocities : : : Table 1.55--Pressures Table 1.56-Pressure Eauivalents .. Table 1.57-Energy or Work Equivalents Table 1.58-Energy, Work, Heat Table 1.59-Pow& Equivalents Table 1.60-Power . . , Table 1.61--Density Equivalents Table 1.62-Thermal Conductivity Table 1.63-Thermal Conductance : : Table 1.64-Heat Flow Table 1.65-Relative Densities Correspondtng to

OAPI and Weights per U.S. Gallon

I-62 l-63 l-64

l-65 l-66 1-66 l-67

1-71 I-71

I-72 l-72 I-72 l-73 I-73 I-74 l-74 I-74 l-75 I-75 l-76 I-76 l-76 l-77 l-77 I-78 I-78 l-78 l-79 l-79 I-79 I-79

l-80

l-2 PETROLEUM ENGINEERING HANDBOOK

TABLE 1 .I -SQUARES OF NUMBERS

1 2 3 4 5 6 7 8 9 Average Difference

1.000 1.002 1.004 1.020 1.022 1.024 1.040 1.042 1.044 1.081 1.083 1.065 1.082 1.084 1.086

1.006 1.026 I.047

1.012 1.014 1.018 1.018 2

1.05 1.08 1.07 1.08 1.09

1.102 1.124 1.145 1.166 1.188

1.210 1.232 1.254 1.277 1.300

1.105 1.128 1.147 1.189 1.190

1.107

1.087 1.088

1.109

1.008 1.028 1.049 1.089 1.090

1.010 1.030 1.051 1.071 1.092

1.032 1.034 1.036 1.053 1.055 1.057 1.073 1.094

1.111 1.128 1.130 1.132 1.149 1.151 1.153

1.113 1.134 1.156 1.177 1.199

1.221 1.243 1.266 1.288 1.311

1.334 1.357 1.381 1.404 1.428

1.452 1.476 1.501 1.525 1.550

1.575 1.6OC 1.626 1.651 1.677

1.703 1.729 1.756

1.115 1.138 1.158 1.179 1.201

1.223 1.245 1.268 1.290 1.313

1.075 1.096

1.117

1.077 1.098

1.119 1.141 1.162 1.184 1.206

1.228 1.250 1.272 1.295 1.318

1.038 1.059 1.080 1.100

1.121

1.10 1.11 1.12 1.13 1.14

1.212 1.234 1.257 1.279 1.302

1.171 1.192

1.214 1.237 1.259 1.281 1.304

1.175 1.197

1.219 1.241 1.263 1.286 1.309

1.138 1.160 1.182 1.203

1.225 1.248 1.270 1.293 1.316

1.143 1.184 1.186 1.208

1.230 1.252 1.275 1.297 1.320

1.15 1.16 1.17 1.18 1.19

1.322 1.325 1.327 1.346 1.348 1.350 1.369 1.371 1.374 1.392 1.395 1.397 1.416 1.418 1.421

1.336 1.339 1.360 1.362 1.383 1.385 1.407 1.409 1.430 1.433

1.341 1.343 1.364 1.387 1.388 1.390 1.411 1.414 1.435 1.438

1.20 1.440 1.442 1.445 1.21 1.484 1.467 1.469 1.22 1.488 1.491 1.493 1.23 1.513 1.515 1.518 1.24 1.538 1.540 1.543

1.25 1.26 1.27 1.28 1.29

1.173 1.195

1.217 1.239 1.281 1.284 1.306

1.329 1.353 1.376 1.399 1.423

1.447 1.471 1.496 1.520 1.545

1.570 1.595

1.30 1.31 1.32 1.33 1.34

1.582 1.585 1.568 1.588 1.590 1.593 1.813 1.815 1.618 1.638 1.641 1.644 1.684 1.667 1.669

1.690 1.893 1.695 1.716 1.719 1.721 1.742 1.745 1.748 1.769 1.772 1.774 1.796 1.798 1.801

1.821 1.648 1.672

1.898 1.724 1.750 1.777 1.804

1.332 1.355 1.378 1.402 1.426

1.450 1.474 1.498 1.523 1.548

1.573 1.596 1.823 1.849 1.874

1.700 1.727 1.753

1.454 1.457 1.459 1.462 1.479 1.481 1.484 1.486 1.503 1.506 1.508 1.510 1.528 1.530 1.533 1.535 1.553 1.555 1.558 1.560

1.583 1.585 3 1.606 1.610 1.833 1.838 1.659 1.862 1.685 1.887

1.780 1.782 1.806 1.809

1.578 1.580 1.803 1.805 1.628 1.831 1.654 1.658 1.680 1.682

1.708 1.708 1.732 1.734 1.758 1.761 1.785 1.788 1.812 1.814

1.711 1.713 1.737 1.74c 1.764 1.766 1.790 1.793 1.617 1.820

1.35 1.822 1.825 1.828 1.831 1.38 1.850 1.852 1.855 1.858 1.37 1.877 1.880 1.882 1.885 1.38 1.904 1.907 1.910 1.913 1.39 1.932 1.935 1.938 1.940

1.839 1.841 1.844 1.847 1.886 1.889 1.871 1.874 1.893 1.896 1.899 1.902 1.921 1.924 1.927 1.929 1.949 1.952 1.954 1.957

1.40 1.960 1.963 1.966 1.968 1.41 1.988 1.991 1.994 1.997 1.42 2.016 2.019 2.022 2.025 1.43 2.045 2.048 2.051 2.053 1.44 2.074 2.076 2.079 2.082

1.977 1.980 1.982 1.985 2.005 2.008 2.011 2.014 2.033 2.036 2.039 2.042 2.062 2.065 2.068 2.071 2.091 2.094 2.097 2.100

1.45 2.102 2.105 2.108 2.111 1.48 2.132 2.135 2.137 2.140 1.47 2.181 2.164 2.187 2.170 1.48 2.190 2.193 2.198 2.199 1.49 2.220 2.223 2.226 2.229

2.120 2.123 2.126 2.129 2.149 2.152 2.15" 2.158 2.179 2.182 2.184 2.187 2.208 2.211 2.214 2.217 2.238 2.241 2.244 2.247

1.50 1.51 1.52 1.53 1.54

2.250 2.253 2.258 2.259 2.280 2.283 2.286 2.289 2.310 2.313 2.316 2.320

1.833 1.880 1.888 1.915 1.943

1.971 1.999 2.028 2.056 2.085

2.114 2.143 2.173 2.202 2.232

2.282 2.292 2.323

1.836 1.863 1.891 1.918 1.946

1.974 2.002 2.031 2.059 2.088

2.117 2.146 2.176 2.205 2.235

2.285 2.295 2.326

2.268 2.271 2.298 2.301 2.329 2.332 2.359 2.362 2.390 2.393

2.274 2.277 2.304 2.307 2.335 2.338

2.341 2.344 2.347 2.350 2.353 2.356 2.372 2.375 2.378 2.381 2.384 2.387

2.385 2.389 2.396 2.399

1.55 2.402 2.406 2.409 2.412 2.415 2.418 2.421 2.424 2.427 2.430 1.56 2.434 2.437 2.440 2.443 2.448 2.449 2.452 2.455 2.459 2.462 1.57 2.465 2.488 2.471 2.474 2.477 2.481 2.484 2.487 2.490 2.493 1.58 2.496 2.500 2.503 2.506 2.509 2.512 2.515 2.519 2.522 2.525 1.59 2.528 2.531 2.534 2.538 2.541 2.544 2.547 2.550 2.554 2.557

Exolanation of Table of Souares

This table givesthe value of N2 for values of N from 1 to 10, correct to four figures. (Interpolated values may be in error by 1 in the fourth figure.) To find the square of a number N outside the range from 1 to 10, note that moving the decimal point one place in

Column N is equivalent to moving it two places in the body of the table. For example, (3.217)'=10.35, (0.03217)'=0.001035, and (3,217)' =10,035,000. This table also can be used inversely to give square roots.

MATHEMATICAL TABLES & UNITS & SYSTEMS OF WEIGHTS & MEASURES 1-3

TABLE l.l-SQUARES OF NUMBERS(continued)

7 8

2.582 2.586 2.815 2.818 2.647 2.650 2.680 2.883 2.713 2.716

Average 9 Difference

2.589 3 2.621 2.654 2.688 2.719

2.748 2.749 2.752 2.779 2.782 2.788 2.812 2.816 2.819 2.848 2.849 2.853 2.880 2.883 2.887

2.914 2.948

2.962 2.965 2.989 2.972 2.978 2.979 2.983 2.996 3.000 3.003 3.007 3.010 3.014 3.017

3.045 3.049 3.052

3.080 3.084 3.087 3.115 3.119 3.122 3.151 3.154 3.158

2.917 2.921 2.952 2.955 2.986 2.989 3.021 3.024 3.058 3.059

N 0 1 2 3

2.570

4 5

1.60 1.61 1.62 1.83 1.84

2.560 2.592 2.824 2.657 2.690

2.583 2.595 2.828 2.680 2.693

2.566 2.599 2.602 2.631 2.634 2.683 2.667 2.696 2.899

2.729 2.732 2.762 2.768 2.796 2.799 2.829 2.832 2.863 2.866

2.897 2.900 2.931 2.934

2.573 2.805 2.637 2.670 2.703

2.576

6

2.579 2.608 2.811 2.641 2.644

1.65 2.722 2.726 1.88 2.758 2.759 1.87 2.789 2.792 1.88 2.822 2.828 1.89 2.856 2.859

2.738 2.789 2.802 2.836 2.870

1.70 2.890 1.71 2.924 1.72 2.958 1.73 2.993 1.74 3.028

2.893 2.928

2.904 2.938

2.673 2.676 2.706 2.709

2.739 2.742 2.772 2.776 2.806 2.809 2.839 2.843 2.873 2.876

2.907 2.910 2.941 2.945

1.75 3.082 1.78 3.098 1.77 3.133 1.78 3.188 1.79 3.204

3.031

3.066 3.101 3.138 3.172 3.208

3.035

3.070 3.105 3.140 3.176 3.211

3.247

3.038

3.073 3.108 3.144 3.179 3.215

3.042

3.077 3.112 3.147 3.183 3.218

3.254

3.091 3.126 3.161

3.186 3.190 3.193 3.197 3.222 3.226 3.229 3.233

1.80 1.81 1.82 1.83 1.84

3.240 3.244 3.251 3.258 3.262 3.285 3.289 3.276 3.280 3.283 3.287 3.291 3.294 3.298 3.301 3.305 3.312 3.316 3.320 3.323 3.327 3.331 3.334 3.338 3.342 3.349 3.353 3.356 3.360 3.364 3.367 3.371 3.375 3.378 3.386 3.389 3.393 3.397 3.400 3.404 3.408 3.411 3.415

1.85 3.422 3.426 3.430 3.434 3.437 3.441 3.445 3.448 3.452 1.88 3.480 3.463 3.467 3.471 3.474 3.478 3.482 3.486 3.489 1.87 3.497 3.501 3.504 3.508 3.512 3.516 3.519 3.523 3.527 1.88 3.534 3.538 3.542 3.546 3.549 3.553 3.557 3.561 3.565 1.89 3.572 3.578 3.580 3.583 3.587 3.591 3.595 3.599 3.602

1.90 1.91 1.92 1.93 1.94

3.610 3.614 3.618 3.821 3.825 3.829 3.833 3.837 3.648 3.652 3.656 3.680 3.663 3.667 3.671 3.675 3.888 3.725 3.784

3.713 3.752 3.791

3.640 3.679 3.717 3.758 3.795

1.95 3.802 1.98 3.842 1.97 3.881 1.98 3.920 1.99 3.960

3.890 3.694 3.698 3.702 3.706 3.709 3.729 3.733 3.738 3.740 3.744 3.748 3.787 3.771 3.775 3.779 3.783 3.787

3.806 3.810 3.814 3.818 3.822 3.826 3.846 3.849 3.853 3.857 3.861 3.865 3.885 3.889 3.893 3.897 3.901 3.905 3.924 3.928 3.932 3.964 3.968 3.972

3.944 3.984

4.024 4.064 4.105 4.145 4.188

3.830 3.834 3.869 3.873 3.909 3.912 3.948 3.952 3.988 3.992

2.00 4.000 4.004 4.008 4.012 2.01 4.040 4.044 4.048 4.052 2.02 4.080 4.084 4.088 4.093 2.03 4.121 4.125 4.129 4.133 2.04 4.162 4.186 4.170 4.174

3.936 3.976

4.016 4.056

3.940 3.960

4.097 4.137 4.178

4.020 4.060 4.101 4.141 4.182

4.028 4.032 4.036 4.068 4.072 4.076 4.109 4.113 4.117 4.149 4.153 4.158 4.190 4.194 4.198

2.05 4.202 2.08 4.244 2.07 4.285 2.08 4.328 2.09 4.388

4.207 4.211 4.215 4.219 4.223 4.227 4.231 4.235 4.248 4.252 4.258 4.280 4.284 4.268 4.272 4.277 4.289 4.293 4.297 4.301 4.331 4.335 4.339 4.343 4.372 4.378 4.381 4.385

4.314 4.318 4.358 4.360 4.397 4.402

2.10 4.410 4.414 2.11 4.452 4.458 2.12 4.494 4.499 2.13 4.537 4.541 2.14 4.580 4.584

4.418 4.423 4.427 4.461 4.465 4.469 4.503 4.507 4.511

4.306 4.310 4.347 4.351 4.389 4.393

4.431 4.435 4.473 4.477 4.516 4.520

4.545 4.550 4.554 4.558 4.562 4.588 4.592 4.597 4.801 4.605

4.439 4.444 4.448 4.482 4.486 4.490 4.524 4.528 4.533 4.587 4.571 4.575 4.610 4.814 4.618

2.15 4.622 4.627 4.831 4.635 4.640 4.844 4.648 4.653 4.857 2.18 4.886 4.670 4.674 4.679 4.683 4.887 4.692 4.696 4.700 2.17 4.709 4.713 4.716 4.722 4.728 4.731 4.735 4.739 4.744 2.18 4.752 4.757 4.761 4.765 4.770 4.774 4.779 4.783 4.787 2.19 4.796 4.800 4.805 4.809 4.814 4.818 4.822 4.827 4.831

3.094 4 3.129 3.165 3.201 3.236

3.272 3.309 3.345 3.382 3.419

3.458 3.493 3.531 3.566 3.606

3.844 3.683 3.721 3.760 3.799

3.838 3.877 3.916 3.956 3.996

4.239 4.281 4.322 4.364 4.406

4.661 4.705 4.748 4.792 4.836

r =9.66960; l/r2 2

=0.101321, e2 =7.38906. x2 =9.669w; (T/z)* =2.46740; l/n2 =0.101321.

(continued on next page)

I-4 PETROLEUM ENGINEERING HANDBOOK

TABLEl.l-SQUARES OF NUMBERS(continued)

4 Average

9 Difference N 0 1 2 - - ~ 5 8 7

4.840 4.844 4.849 4.884 4.928 4.973 5.018

4.889 4.893 4.933 4.937 4.977 4.982 5.022 5.027

3

4.853 4.897 4.942 4.986 5.031

4.858 4.882 4.888 4.871 4.902 4.906 4.911 4.915 4.948 4.951 4.955 4.960 4.991 4.995 5.000 5.004 5.036 5.040 5.045 5.049

5.062 5.067 5.072 5.076 5.081 5.085 5.090 5.094 5.108 5.112 5.117 5.121 5.128 5.130 5.135 5.139 5.153 5.157 5.162 5.167 5.171 5.176 5.180 5.185 5.198 5.203 5.208 5.212 5.217 5.221 5.226 5.230 5.244 5.249 5.253 5.258 5.262 5.267 5.272 5.276

5.290 5.295 5.338 5.341 5.382 5.387

5.299 5.304 5.308 5.313 5.318 5.355 5.359 5.364 5.401 5.408 5.410 5.448 5.452 5.457 5.494 5.499 5.504

5.322 5.327 5.388 5.373 5.415 5.420

8

4.875 2.20 2.21 2.22 2.23 2.24

2.25 2.26 2.27 2.28 2.29

2.30 2.31 2.32 2.33 2.34

2.35 2.38 2.37 2.38 2.39

2.40 2.41 2.42 2.43 2.44

5.429 5.434 5.478 5.480

5.345 5.350 5.392 5.396

5.522 5.527 5.570 5.574 5.871 5.822 5.884 5.889 5.712 5.717

5.438 5.443 5.485 5.490

5.532 5.537 5.579 5.584 5.626 5.631 5.674 5.879 5.722 5.726

5.482 5.488 5.508 5.513

5.541 5.548 5.551 5.555 5.580 5.565 5.588 5.593 5.598 5.603 5.807 5.612 5.636 5.641 5.645 5.650 5.855 5.660 5.883 5.688 5.693 5.698 5.703 5.707 5.731 5.738 5.741 5.746 5.750 5.755

5.780 5.808 5.856 5.905 5.954

5.785 5.770 5.774 5.779 5.784 5.813 5.818 5.823 5.827 5.832 5.861 5.866 5.871 5.876 5.881 5.910 5.915 5.919 5.924 5.929 5.958 5.963 5.988 5.973 5.978

5.794 5.842 5.890 5.939 5.988

2.45 2.48 2.47 2.48 2.49

8.002 6.007 6.012 6.017 6.022 6.027 8.502 6.057 6.061 6.088 8.071 6.078 8.101 6.108 6.111 6.116 6.121 6.126

5.789 5.837 5.885 5.934 5.983

6.032 8.081 6.131

6.037 6.086 6.136

6.150 6.155 6.180 6.185 8.170 8.175 6.180 6.185 6.200 6.205 6.210 6.215 6.220 6.225 6.230 6.235

2.50 8.250 6.255 6.260 8.265 6.270 6.275 6.280 6.285 2.51 8.300 6.305 6.310 8.315 6.320 6.325 6.330 6.335 2.52 6.350 6.355 6.380 8.366 8.371 6.378 8.381 6.388 2.53 6.401 6.406 6.411 8.416 8.421 6.428 8.431 8.438 2.54 6.452 6.457 6.462 8.467 6.472 6.477 8.482 6.487

2.55 8.502 6.508 6.513 8.518 8.523 6.528 8.533 8.538 2.56 6.554 8.559 6.564 6.569 8.574 6.579 8.584 6.589 2.57 6.605 8.810 6.815 8.620 8.625 6.831 6.636 8.641 2.58 6.656 6.862 6.667 8.672 8.677 6.882 6.687 8.693 2.59 6.708 8.713 6.718 6.724 8.729 6.734 6.739 8.744

2.60 2.61 2.62 2.63 2.64

6.780 8.765 6.812 8.817 6.884 8.870 6.917 6.922 6.970 8.975

6.770 6.323 6.375

8.776 8.781 8.833 8.885 6.938 8.991

6.788 6.791 8.798 6.849 6.901 6.954 7.007

2.65 7.022 7.028 2.68 7.076 7.081 2.87 7.129 7.134 2.68 7.182 7.188 2.89 7.238 7.241

2.70 7.290 7.295 2.71 7.344 7.350 2.72 7.398 7.404 2.73 7.453 7.458 2.74 7.508 7.513

6.927 f5.980

7.033

8.828 8.880 6.933 8.985

6.838 6.843 6.891 6.896 6.943 6.948 6.996 7.001

7.086 i.140

7.038 7.044 7.049 7.092 7.097 7.102 7.145 7.150 7.158 7.198 7.204 7.209 7.252 7.258 7.263

7.306 7.312 7.317 7.360 7.366 7.371 7.415 7.420 7.426 7.469 7.475 7.480 7.524 7.530 7.535

2.75 2.76 2.77 2.78 2.79

7.562 7.618 7.673 7.728 7.784

7.588 7.623 7.678 7.734 7.790

7.193 7.247

7.301 7.355 7409 7.484 7.519

7.574 7.629 7.884 7.740 7.795

7.579 7.585 7.590 7.634 7.840 7.645 7.690 7.895 7.701 7.745 7.751