s3. · pdf fileiv acknowledgements i would like to thank my supervising professors dr. gary a...

Copyright

by

Gholamreza Garmeh

2005

Simulation of Interwell Gas Tracer Test

in Naturally Fractured Reservoirs

by

Gholamreza Garmeh, B.S

Thesis

Presented to the faculty of the Graduate School of

The University of Texas at Austin

in Partial Fulfillment

of the Requirements

for the Degree of

Master of Science in Engineering

The University of Texas at Austin

August 2005



Approved by:

Supervising Committee:

Kamy Sepehrnoori

Gary A. Pope

iv

Acknowledgements

I would like to thank my supervising professors Dr. Gary A Pope and Dr. Kamy

Sepehrnoori for their supervision and guidance throughout the course of the work.

They shared with me their knowledge, experience and insight, which encouraged and

enlightened me to pursue the art and science of research.

I would like to thank Dr. Mojdeh Delshad for her valuable advice. Thanks to Joanna

for helping me with all the software and hardware problems and thanks to Esther for

all her help. I would like to thank Kaz and Elif for their help in getting started on my

research. My special thanks go to Vicencio, Farhad and Yousef for their helpful guide

in reservoir simulations. I would like to acknowledge NIOC for financial support of

this course of study.

It has been a highly rewarding experience to pursue graduate studies at The

University of Texas at Austin, and I am thankful to the people who have helped and

guided me during the course of my study.

I need to thank CMG company for all their software support.

Finally, thanks go to my family and friends for their encouragement throughout my

stay at the University of Texas at Austin.

v

Abstract



by

Gholamreza Garmeh, M.S.E

The University of Texas at Austin, 2005

SUPERVISORS: Gary A. Pope and Kamy Sepehrnoori

The main objective of this research was to investigate the gas tracer test in naturally

fractured reservoirs and compare the dual porosity and discrete fracture models for

the gas tracer test. The method of moments was used to estimate the average oil

saturation and swept pore volume in naturally fractured reservoir gas tracer tests. It

was used to estimate mobile oil saturation for a case of uniform residual oil saturation

in the matrix and fracture, and for a case of different residual oil saturation in the

matrix and fracture from total concentration of the produced tracer. Results verify that

the method of moments is a fast, simple, and accurate method of estimating the oil

saturation in fractured reservoirs. The gas tracer test in naturally fractured reservoirs

was simulated for the dual porosity and discrete fracture models and results were

vi

compared. Results of the ECLIPSE simulator were compared with the IMEX

simulator for the dual porosity and discrete fracture models. The comparison

demonstrates that the discrete facture model has properties of the dual porosity model

and the reality of a fractured reservoir. In addition, the effect of dimensionless groups

in the dual porosity and discrete fracture models were studied. The effect of

dimensionless parameters in the fracture tracer transport was analyzed and the

equilibrium condition of the gas tracer’s transport between the matrix and fracture

was obtained.

vii

Table of Contents

Acknowledgements.....................................................................................................iv

Abstract.........................................................................................................................v

Table of Contents.......................................................................................................vii

List of Tables...............................................................................................................xi

List of Figures...........................................................................................................xiii

CHAPTER 1:

Introduction..................................................................................................................1

CHAPTER 2: Literature Review...............................................................................4

2.1 Tracer tests in oil fields............................................................................................4

2.1.1 Application of tracer test in oil fields.............................................................4

2.1.2 Tracer tests in fractured reservoirs..................................................................5

2.1.3 Development of oil field tracer technology....................................................7

2.1.4 Tracer interpretation methods.........................................................................8

2.1.4.1 Method of moments..........................................................................10

2.1.4.2 Inverse modeling...............................................................................15

2.2 Application of gas tracers for reservoir characterization…...................................18

2.3 Fractured reservoirs...............................................................................................20

2.3.1 Dual porosity model.....................................................................................21

2.3.2 Discrete fracture model................................................................................22

2.4 Review of the Cantarell oil field............................................................................24

viii

CHAPTER 3: Use of gas tracers for reservoir characterization. .........................30

3.1 Partition coefficient for gas tracers........................................................................30

3.2 Estimation of gas tracer partitioning coefficient…..............................................32

3.3 Simulation of tracer flow in slimtube…................................................................33

3.4 Simulation of gas tracers in fractured reservoir.....................................................36

3.4.1 Reservoir Parameters and geology data for base case simulation...........36

3.4.2 Base case simulation with dual porosity model......................................38

3.4.3 Results.....................................................................................................39

3.5 Estimation of oil saturation and swept pore volume using method of moments.39

3.5.1 Method of moments for dual porosity Model. ..........................................40

3.5.2 Estimation of mobile oil saturation in dual porosity model. .....................42

3.5.3 Estimation of oil saturation in dual porosity model with different residual

oil saturation in the matrix and fracture. ...................................................43

3.6 Conclusion..........................................................................................................44

CHAPTER 4: Comparison of discrete fracture and dual porosity models for

gas tracer injection.............................................................................57

4.1 Driving forces in fractured reservoirs....................................................................57

4.2 Shape Factor study.................................................................................................59

4.3 Base case simulation for dual porosity and discrete fracture models. ..................61

4.4 Dual porosity model...............................................................................................62

4.4.1 Simulation of fractures by dual porosity model. ....................................62

4.4.1.1 Relative permeability tables in fractured reservoirs................62

4.4.1.2 Capillary pressure in naturally fractured reservoirs.................63

4.4.2 Simulation of fractures by dual porosity model in ECLIPSE and

IMEX........................................................................................65

4.4.3 Subgridding. ...............................................................................66

ix

4.5 Simulation of gas tracers by tracing a component in GEM...................................67

4.5.1 Simulation in dual porosity media. ........................................................67

4.5.2 Comparison of tracer test between ECLIPSE and GEM........................68

4.6 Simulation of fractures by modeling the fractures as discrete fracture network...68

4.6.1 Problem to model fractures as discrete fracture......................................69

4.6.2 Discrete fracture model...........................................................................69

4.6.3 Grid refinement.................................... ..................................................70

4.7 Simulation of fractures by modeling the fractures as Equivalent single porosity.71

4.8 Conclusion.............................................................................................................71

CHAPTER 5: Application of dimensionless groups to naturally fractured

reservoirs..........................................................................................94

5.1 Gravity Number Ng...............................................................................................94

5.1.1 Effect of Ng on oil recovery in dual porosity model……….......................95

5.1.2 Effect of Ng on oil recovery in discrete fracture model…………..............95

5.2 Effective length to thickness ratio. ........................................................................96

5.2.1 Effect of LR on oil recovery in the dual porosity model. ...........................96

5.2.2 Effect of LR on oil recovery in the discrete fracture model. .....................97

5.3 Dimensionless groups for fractures tracer transport..............................................97

5.3.1 Mean residence time in fractured reservoirs................................................98

5.3.2 Sensitivity analysis for dimensionless parameters of tracer transport.........99

5.3.2.1 Matrix number..............................................................................100

5.3.2.2 Fracture porosity. ........................................................................101

5.3.2.3 Matrix to fracture porosity...........................................................102

5.4 Conclusion...........................................................................................................104

x

CHAPTER 6: Summary, Conclusions and Recommendations for Future Work

6.1 Use of gas tracers for reservoir characterization..................................................118

6.2 Naturally fractured reservoirs model...................................................................119

6.3 Dimensionless groups study................................................................................120

6.4 Dimensionless groups in fractured reservoir tracer transport…..........................120

6.5 Recommendations for future work......................................................................121

Appendix A: Sample input files

A.1 ECLIPSE Input File for 3 phases flow of tracer test.....................................123

A.2 ECLIPSE Input File for dual porosity model.................................................132

A.3 ECLIPSE Input File for discrete fracture model.............................................140

A.4 CMG-IMEX Input File for dual porosity model.............................................158

A.5 CMG-IMEX Input File for discrete fracture model........................................164

A.6 CMG-GEM Input File for component tracking as tracer in dual porosity media.

........................................................................................................................181

Nomenclature...........................................................................................................189

References ................................................................................................................195

VITA.........................................................................................................................209

xi

List of Tables

Table 2.1: Cantarell formation test 1 Data (Lopez and Gonzalez 2001………...…....28

Table 2.2: Cantarell formation test 2 Data (Lopez and Gonzalez 2001)………...…..28

Table 3.1: Property of selected tracers (Maroongroge 1994)………………………..46

Table 3.2: Fluid composition for estimating tracer partitioning coefficient………....46

Table 3.3: Equilibrium ratio and partitioning coefficient of the selected tracers at

reservoir condition……..……………………….......................................46

Table 3.4: Partitioning coefficient and relative Retention volume for slimtube

displacement…………………………………………………………........47

Table 3.5: Data for simulation of slimtube displacement (Maroongoge 1994).……..47

Table 4.1: Reservoir data for dual Porosity model simulation………………...….…73

Table 4.2: Relative permeability and capillary pressure date for case 1……..……...73

Table 4.3: Relative permeability and capillary pressure data for case 2……...…..…75

Table 4.4: Relative permeability and capillary pressure data for case 3……...…..…75

Table 4.5: Reservoir data for discrete fracture model simulation……………...…….75

Table 5.1: primary parameters value for Scaling group analysis……………...……106

Table 5.2: Summarized data for Ng in dual porosity model…………………..……106

Table 5.3: Summarized data for effect of Ng in discrete fracture model……..……106

Table 5.4: Summarized data for effect of LR in dual porosity model………...……107

xii

Table 5.5: Summarized data for effect of LR in discrete fracture model……..……107

Table 5.6: Base Case Data for simulation of dimensionless parameter in fractured

reservoir………..………………………………………………………..107

Table 5.7: Summarized parameters values for different MaN …………..…………108

Table 5.8: summarized parameter values for case of different fφ ……..………….108

Table 5.9: summarized parameter values for case of different Sgf

mφφ …..…………109

xiii

List of Figures

Fig. 2.1: Location of Cantarell oil field (Limon-Hernandez et al. 2005)……...……29

Fig 3.1: Comparison between produced tracer concentration history of Slimtube

Experiment with ECLIPSE simulation results…..…………………….……48

Fig 3.2 Normalized tracer concentration for dual porosity simulation case…………48

Fig 3.3 Oil production rate for dual porosity simulation case………………….……49

Fig 3.4 Oil Recovery for dual porosity model simulation……………………...……49

Fig 3.5: Tracer concentration at the producer for dual porosity model (Semi-Log

scale)…………………..……………………………………………....……50

Fig. 3.6: Tracer Concentration at the producer for dual porosity model……….……50

Fig. 3.7: Tracers recovery for different partition coefficient in dual porosity media..51

Fig. 3.8: Oil saturation estimation from Method of moments in dual porosity media

with mobile oil……….……………………………………………….……51

Fig. 3.9: Sweep efficiency estimation from Method of moments in dual porosity

media with mobile oil……….………………………………………..……52

Fig. 3.10: Tracer production concentration at the producer for different residual oil

saturation in matrix and fracture (Semi-Log scale)……..…...……..……52

Fig. 3.11: Tracer production concentration at the producer for different residual oil

saturation in matrix and fracture…...……………………………..………53

Fig. 3.12: Conservative tracer concentration profile in layer 3 after 50 days of tracer

xiv

injection……………………………………………………………………..……….53

Fig 3.13: Conservative tracer profile in layer 3 after 250 days……………...………54

Fig. 3.14: Conservative tracer profile in layer 8 after 250 days……………..………54

Fig. 3.15: Conservative tracer profile in layer 9 after 250 days……………..………55

Fig. 3.16: Oil saturation estimation from Method of moments in dual porosity media

for different residual oil saturation in matrix and fracture………….……55

Fig. 3.17: Sweep efficiency estimation from Method of moments in dual porosity

media for different residual oil saturation in matrix and fracture…..……56

Fig 3.18: Tracers recovery for different partition coefficients in dual porosity media

for different residual oil saturation in matrix and fracture….…...………56

Fig. 4.1 Typical fractured reservoir model…………………………………..………75

Fig. 4.2: Relative permeability curve for matrix system contain gas and oil..………75

Fig. 4.3: Relative permeability curve for fracture system contain gas-oil…...…..…76

Fig. 4.4: Matrix oil saturation profile before gas injection in simulation case...…….76

Fig. 4.5: Matrix oil saturation after 2000 days of gas injection for case1……...……77

Fig. 4.6: Oil production rate and oil recovery for case 1……………………….……77

Fig. 4.7: Matrix capillary pressure for gas-oil system in case 2……………..……78

Fig.4.8: Oil production rate and Oil recovery efficiency for case 2…………...….…78

Fig 4.9: Matrix oil saturation after 2000 days gas injection for case 2………...…….79

Fig. 4.10: Matrix capillary pressure for gas-oil system in case 3……………...……79

xv

Fig. 4.11: Oil production rate and oil recovery efficiency for case 3…………..……80

Fig. 4.12: Matrix oil saturation after 2000 days of gas injection for case 3…...…….80

Fig. 4.13: Oil production rate in ECLIPSE and IMEX for dual porosity model.……81

Fig. 4.14: Horizontal nested subgrided matrix block in ECLIPSE (Eclipse Manual

2004)…………….………………………………………………………..81

Fig. 4.15: Schematic view of concentric subgrided matrix blocks in ECLIPSE (Sinha,

2004)…………………………..…………………………………...…….82

Fig. 4.16: Oil production rate for subgrided model and dual porosity model in

ECLIPSE……….,.…………………………………………………...…...82

Fig. 4.17: Oil Recovery Efficiency for subgrided model and dual porosity model in

ECLIPSE…………………………..………………………………..……83

Fig. 4.18: Oil production rate for subgrided model and dual porosity model in

IMEX…………..…………………………………………………….…..83

Fig. 4.19: Oil Recovery Efficiency for subgrided model and dual porosity model in

ECLIPSE………………...……………………………………………..…84

Fig. 4.20: Oil production rate comparison between ECLIPSE and GEM………...…84

Fig. 4.21: Comparison of tracer test in ECLIPSE and component tracing in GEM…85

Fig. 4.22: Mole fraction (N2B) in fracture after 50 days………………………….…85

Fig. 4.23: Mole fraction (N2B) in matrix after 50 days……………………………...86

Fig. 4.24: Mole fraction of (N2B) in fracture after 200 days…………………….….86

Fig. 4.25: Mole fraction of (N2B) in matrix after 200 days………………………....87

xvi

Fig. 4.26: Tracer concentration profile in fracture after 50 days in ECLIPSE………87

Fig. 4.27: Tracer concentration profile in matrix after 50 days in ECLIPSE………..88

Fig. 4.28: Tracer concentration profile in fracture after 200 days in ECLIPSE……..88

Fig. 4.29: Tracer concentration profile in matrix after 200 days in ECLIPSE………89

Fig. 4.30: Oil Production rate in dual porosity model and discrete fracture model…89

Fig. 4.31: Oil Recovery Efficiency in dual porosity model and discrete fracture

model……………………………………………………………………..90

Fig. 4.32: Conservative tracer response in dual porosity model and discrete fracture

model…………..……………………………………………………..…..90

Fig. 4.33: Partitioning tracer response in dual porosity model and discrete fracture

model………………………………………………………………….….91

Fig. 4.34: Oil production rate for discrete fracture model in ECLIPSE and IMEX…91

Fig. 4.35: Local Grid Refinement for discrete fracture model…………………...….92

Fig. 4.36: Oil production rate for discrete fracture model and LGR……………...…92

Fig. 4.37: Oil production rate comparison in dual porosity, discrete fracture and

equivalent single porosity models………………….…………………….93

Fig. 4.38: Cumulative oil production rate in dual porosity model and equivalent single

porosity model…………………………..………………………..…...…93

Fig. 5.1: Effect of Ng on oil Recovery efficiency at LR =20 for dual porosity model…109

Fig. 5.2: Effect of Ng on oil recovery efficiency at LR =10 for discrete fracture

model............................................................................................................109

xvii

Fig. 5.3: Effect of LR on oil recovery at constant Ng=0.02949 for dual porosity

model............................................................................................................110

Fig. 5.4: Effect of LR on oil recovery efficiency at Ng=0.02949 and for discrete

fracture model……….……………………………………………………110

Fig. 5.5: Effect of MaN on Mean residence time of tracer

response…………………………………………………………………..111

Fig. 5.6: Effect of MaN on conservative tracer response…………………………...111

Fig. 5.7: Effect of MaN on conservative tracer response in Semi-Log scale...……..112

Fig. 5.8: Effect of fφ on output tracer response at MaN =0.02……………………112

Fig. 5.9: Effect of fφ on output tracer response at MaN =0.02 (Semi-Log scale)....113

Fig. 5.10: Effect of fφ on output tracer response at MaN =20.0…………………..113

Fig. 5.11: Effect of fφ on output tracer response at MaN =20.0 (Semi-Log scale)...114

Fig. 5.12: Effect of Sgf

mφφ on Mean Residence Time at MaN =0.02……………….114


mφφ on Tracer response curve at MaN =0.02………………..115


mφφ on Tracer response curve at MaN =0.02 (Semi-Log

scale).........................................................................................................115


mφφ on Mean Residence Time at MaN =20.0……………….116

xviii


mφφ on Tracer response curve at MaN =20.0……………….116


mφφ on Tracer response curve at MaN =20.0 (Semi-Log

scale)........................................................................................................117

1

CHAPTER 1: Introduction

Fluid flow in naturally fractured reservoirs has gained more attention because

of its complex process. In fractured reservoir, flow is primarily through the high

permeability fractures, and matrix blocks contain the majority of the reservoir pore

volume and act as a source or sink to the fractures. A lot of work has been done to

model fluid flow through fractured reservoirs. The dual porosity model can handle

naturally fractured reservoir performance. In this model, two sets of properties are

specified: matrix porosity and permeability, and fracture porosity and permeability. In

the dual porosity model fluid flows only in fractures.

The discrete fracture model has many of advantages of dual porosity model plus

reality of the fractured reservoir complex. In the discrete fracture model, fractures can

be modeled based on well log, seismic data, coring, and well test data.

The partitioning interwell tracer test is a powerful tool to characterize reservoir

properties such as estimation of oil saturation, evaluation of sweep efficiency,

detection of flow barrier, flow channeling and flow pattern, identifying reservoir

heterogeneity and reservoir layering.

The study in this research focuses on simulation of gas tracer tests in fractured

reservoirs to estimate average oil saturation, swept pore volume, and to compare the

dual porosity model and discrete fracture model for gas tracer test.

2

Chapter 2 presents the review of previous work done in application of tracer

test in oil fields. It reviews application of gas tracers in oil fields and presents the

various methods that have been used to estimate reservoir oil saturation and evaluate

sweep efficiency. It also reviews the work done to model fractured reservoirs as a

dual porosity and discrete fracture models. Furthermore, it presents geology and

reservoir property of the Cantarell oil field which is a naturally fractured reservoir. Its

reservoir properties have been used in our simulation studies.

Chapter 3 presents a gas tracer test for reservoir characterization. It starts with

the definition of the partition coefficient in gas tracers. Partitioning coefficient has

been estimated by equation of state for perfluorocarbons gas tracer. The accuracy of

the simulator was tested to simulate gas tracer test by introducing an experimental

tracer test to compare the results. In this chapter we also apply the method of

moments to estimate mobile oil saturation in a naturally fractured reservoir using a

dual porosity model.

Chapter 4 compares simulation of the gas tracer test in naturally fractured

reservoirs using the dual porosity and discrete fracture models. The properties and

advantages of each model have been discussed and their results for production rate,

recovery efficiency and tracer transports have been presented. A compositional

simulator such as GEM was used to model gas tracer test by tracing a component of

injection gas as slug tracer. The results of simulations by ECLIPSE have been

compared by GEM to check the accuracy of the results.

3

Chapter 5 discusses the effect of dimensionless group on oil recovery in

fractured reservoirs. It compares results of dimensionless groups study for the dual

porosity model and discrete fracture model and subsequently analyzes sensitivity of

dimensionless parameters for fracture tracer transport.

Chapter 7 present summaries, conclusions and recommendations for future

work.

4

CHAPTER 2: Literature Review

This chapter reviews previous research that has been performed in the area of

partitioning interwell tracer tests to characterize oil field reservoirs. It reviews gas

tracers and their application in oil fields. Finally, it reviews the properties of naturally

fractured reservoirs and tracer tests in fractured reservoirs.

2.1 Tracer tests in oil fields

Tracers are used for many reasons and in a variety of circumstances. Tracers

are used to describe the reservoirs, investigate unexpected anomalies in flow, or to

verify suspected geological barriers (Zemel, 1995).

2.1.1 Application of tracer test in oil fields

Mercado and Perez (2003) used the tracer in a gas flooding project to

determine existence of flow channeling, to find flow barrier and flow pattern

direction, to evaluate sweep efficiency and magnitude of the injector and producer

communication, and to identify heterogeneity. Saad et al. (1988) applied the tracer to

study cross flow phenomena and reservoir layering. Allison (1991) used the tracer to

estimate residual oil saturation and sweep efficiency. Dugstad et al. (1999) applied

the tracer test to determine layering, channeling and evaluate WAG sweep efficiency.

Wagner (1977) found that following information could be obtained from every tracer

5

test: volumetric sweep efficiency, identification of the offending injector, directional

flow trend, delineation of flow barriers, and relative velocity of injected fluids.

A lot of work has been done to estimate residual oil saturation from tracer tests.

Wood et al. (1990) estimated residual oil saturation from tracer tests. Tang (1995)

introduced chromatographic transformation technique to estimate residual oil

saturation from partitioning interwell tracer tests (PITT). Tracers can also be used in

the test section of the field before expanding the flood (Zemel, 1995).

2.1.2 Tracer tests in fractured reservoirs

Tracer tests in fractured reservoirs have been recognized for its shortcomings

when applied to heterogeneous carbonate reservoirs. It shows the performance of

moderate dispersion, early arrival, long production tails and extreme dilution of tracer

profiles (Tang & Zhang 2001).

Tang and Zhang (2001) determined residual oil saturation in fractured reservoirs.

They used two different models: the dual porosity model, where the tracer could

distribute between the flowing and non-flowing pores through mass transfer, and a

single porosity model. The residual oil saturation was determined by simple analytical

models, including mass balance method, peak method and mean retention volume

method. The dual porosity model consisted of two parts of mass balance: tracer

transfer in flowing pores and tracer diffusion in dead-end pores.

6

Their model could handle the long tracer production tail caused by slow diffusion of

the tracer into and out of the dead-end pores.

Ramirez et al. (1993) analytically modeled the tracer flow in naturally fractured

reservoirs. The reservoir was treated as being composed of two regions: mobile

(fractures), where dispersion and convection take place, and stagnant (matrix), where

only diffusion and adsorption was allowed. Radioactive decay was considered on

both regions. The solutions were presented for linear flow of vertical fractures and

radial flow of horizontal fractures and cubic block matrix-fracture geometry. These

solutions accounted for all important mechanisms that affect tracer flow: diffusion,

convection, adsorption, and radioactive decay.

Shinta and Kazemi (1993) introduced an analytical and dynamic transfer function,

which was capable to reduce dual porosity model (DPM) into single porosity model

(SPM). They used their formulation in combination with tracer transport, to

characterize the reservoir fracture properties.

Grigorievich and Archer (1993) introduced a method for identification of residual oil

from the data of two tracers with different solubility in oil for the fractured porous

media. Their result of theoretical prediction of the tracer wave propagation was in

good agreement with the laboratory experiment’s data.

7

2.1.3 Development of oil field tracer technology

An ideal tracer test must accurately follow the path and velocity of the

carrying fluid and it must be easy to identify and measure quantitatively (Zemel,

1995).

Partitioning interwell tracers have been used to estimate None Aqueous Phase Liquid

(NAPL) saturation from the 1990’s. Pope et al. (1994) were the first to use and report

a PITT. According to the progress of tracers, Bingyu et al. (2002) divided tracers into

four generations. Chemical tracers were the first generation technology, applied in the

1950’s. It contains all kinds of inorganic saltines, stain and alcohol. Moreover, the

precision was about 10-4 ~ 10-6 (ppm) only.

Radioactive isotope tracers were the second generation technology, applied in the

1970’s. It includes tritiated water, tritiated alkane and tritiated alcohol. The purpose

of measurement was liquid phase scintillation counter, and the precision was up to

10-9 (ppm) level. The third generation of tracers was applied at the end of the 1980’s.

The significant characteristic was some stable isotope, which could be activated.

Microelement tracers were the fourth generation technology that has been applied

since the 1990’s; the basic principle was to take the matter that very little in the

formation water and reservoir fluid was applied as the tracer. The measurement

precision of this kind could reach up to the level of 10-15 (ppm).

8

2.1.4 Tracer interpretation methods

With development of computer technology, the application of tracer tests in

oil fields have been programmed by some interpretative software to interpret tracer

tests in oil fields. Interpretations include numerical methods, analytical methods, and

semi-analytical methods. Meanwhile the range of reservoir parameters interpreted

became wider with better precision. The interpretation methods are progressing to be

perfect. Recently, the methods, which interpret the produced tracer profile, combine

with the geological model (Bingyu et al. 2002).

Brigham and Smith (1965) for the first time developed some equations to predict the

time of tracer breakthrough, the peak concentration of tracer and the degree of

stratification in the five-spot pattern.

Cooke (1971) used the chromatographic method to determine residual oil saturation.

Deans and Majoros (1980) used the method of moments to estimate residual oil

saturation for a single well tracer test. Allison et al. (1991) introduced a method for

the interwell tracer test to estimate residual oil saturation, the mobile oil saturation

and sweep efficiency in the multi-well, multi-tracer project. Tang and Harker (1991)

used the landmark comparison to estimate residual oil saturation from a gas injection

in carbonate reservoir.

Maroongroge et al. (1995) developed the method of moments for estimation of

residual oil saturation and swept volume for water tracer test and the vertical tracer

profiling to stochastically model reservoirs. Zemel (1995) presents a comprehensive

9

study of oil field tracers to design and interpret tracer tests in oil fields. Dwarakanath

and Pope (1998) identified the various sources of error in both the measured PITT

and errors from data analysis of the method of moments that was used to estimate oil

saturation from PITTs.

Deeds et al. (1999) developed the method of moments for three phases and included

dispersion and diffusion, and variable saturations and porosity to it. He applied the

method of moments to analyze gas tracers in contaminated aquifers with non-aqueous

phase liquids. Tang and Zhang (2001) used the single well tracer test to determine

residual oil saturation by simple analytical models including mass balance method,

peak method, and mean retention volume method for single-porosity and double-

porosity models.

Jayanti (2003) analyzed the effect of the heterogeneity and detection limit on

partitioning interwell tracer tests.

Asakawa (2005) developed the method of moments for the three-dimensional

heterogeneous porous medium. He extended the derivation to include the calculation

of oil saturation in naturally fractured reservoirs and calculation of the oil saturations

for reservoirs with mobile oil from the total concentration of tracers in water and oil

phase.

Sinha et al. (2004) used natural tracers as a cost effective partitioning tracer to

calculate residual oil saturation. He used the method of moments for interpretation of

PITTs in heterogeneous reservoirs with spatially variable residual oil saturation.

10

Altinay (2005) combined method of moments (MOM) with inverse modeling to

obtain accurate and realistic oil saturation estimation from Partitioning interwell

tracer tests (PITT). She used method of moments in a complimentary way by using

oil saturation estimation from method of moments as an initial guess of inverse

modeling calculation.

More attention has been given to method of moments and inverse modeling to

estimate residual saturation from tracer tests in recent years.

2.1.4.1 Method of moments

Asakawa (2005) estimated the oil saturation and swept pore volume from the

zero and first temporal moment of produced tracer concentration.

His assumptions in the derivation for the case of tracer slug injected into a reservoir

are as follows:

• The partition coefficient of each tracer is constant during the test,

• Diffusion at the well boundaries is negligible,

• There is no mass transfer of tracers across the boundaries of the swept volume

of interest,

• Tracers are chemically stable during the test,

• There is no destruction or generation during tracer test,

The following equations are for slug gas tracer injection. Equations are analogous

with water tracers, except the tracer is partitioned into oil and gas instead of oil and

11

water. The mass conservation equation for thi tracer flowing in the reservoir is given

by

0NtC

ii =⋅∇+

∂φ∂ r

, (2.1)

where the total tracer concentration is

ij

n

1jji CSC

p

∑=

= , (2.2)

and for tracer flow through porous media:

∑=

∇⋅φ−=

pn

1jijijjjiji CKSuCN

rrrr (2.3)

For a tracer slug injection:

≥=

≤≤=

sluginjectorit

slugiJinjectorit

tt,0C

tt0,CC (2.4)

Multiplying Equation (2.1) by time and integrating over time gives:

0dtNtm0

ii0 =⋅∇+φ− ∫∞ r

, (2.5)

where

dtCm0

ii0 ∫∞

= (2.6)

Integrating Equation (2.5) over the reservoir volume of interest

12

0dVdtNtdVm0

ii0 =

⋅∇+φ− ∫∫∫ ∫∫∫∫

∞ r (2.7)

Applying divergence theorem to Eq. (2.7)

0dAndtNtdVm0

ii0 =⋅

+φ− ∫∫ ∫∫∫∫

∞rr

(2.8)

Since mass transfer occurs only at the wells, then

( ) 0qmdVm wellsi1i0 =+φ− ∫∫∫ , (2.9)

where

dtCftm0

n

1jijji1

p

∫ ∑∞

=

= (2.10)

This equation is the first moment and could be applied to a variety of water, oil and

gas combinations. For the specific case of oil and gas with no partitioning of tracers

into water, it can be written as follows:

( )

( )

( )( ) dVmSKS

dVdtCSKS

dVdtCSKS

dVdtCSCS

dVm

ig0oig

0igoig

ig0

oig

0iooigg

i0

∫∫∫ +φ=

∫∫∫ ∫+φ=

∫∫∫ ∫ +φ=

∫∫∫ ∫ +φ=

∫∫∫φ

∞

∞

∞

(2.11)

13

where the partition coefficient of tracer i is defined as

ig

ioi C

CK = (2.12)

and

dtC

dtCSS

0ig

0igj

j

∫

∫=

∞

∞

(2.13)

Equation (2.9) can be used to show that

( ) 0VmdVmSKS iproducerig0ig0oig =+∫∫∫ +φ− , (2.14)

where the mean residence volume of tracer i is given as

2V

dtC

dttqCV slug

0ig

0it

i −

∫

∫=

∞

∞

(2.15-1)

or mean residence time of tracer i :

2T

dtC

dttCT slug

0ig

0it

i −

∫

∫=

∞

∞

(2.15-2)

Assuming jS is not different between tracers and that ig0m is not a function of space,

it follows from Equation (2.14) that

( ) 0VdVSKS ioig =+∫∫∫ +φ− (2.16)

14

Equation (2.16) can be used to show that the average oil saturation in 3-Phase flow is:

)1()1(*)1(ˆ

2112

21−−−

−−=

KVKVVVSS wo (2.17)

And the swept pore volume is given by

21

2112 )1()1(*))1(

1(KK

KVKVS

Vw

s −−−−

−= , (2.18)

where the tracer is not partitioning into water phase.

The average oil saturation oS is at the mean residence time of the conservative

tracer 1t , therefore the average oil saturation at the end of the PITT is given by

subtracting the volume of oil produced after the mean residence time:

s

toos

o V

dtqSV

S 1∫∞

−

= (2.19)

After the mean residence volumes obtained, the swept pore volume between wells

and the average oil saturation in each swept pore volume can be calculated (Asakawa

2004). The retardation factor for partitioning tracer i is defined as follow:

or

orifi S1

SK1R

−+= (2.20)

15

2.1.4.2 Inverse Modeling

Recently, the streamline approach has received a lot of attention for

computing the sensitivity of parameters. With the streamline method, sensitivities can

be computed analytically using a single flow simulation (Cheng et al. 2004).

The streamline-based inversion approach is an analytical sensitivity computation

method that yields sensitivities of the partitioning tracer response to the porosity,

permeability and NAPL saturation in a single streamline simulation, and it uses

efficient techniques from the geophysical inversion to match the field tracer response

and estimate subsurface parameters. In this approach, the NAPL saturation estimation

is a two-step procedure: First, the conservative tracer response is matched to provide

permeability distribution then the partitioning tracer response is matched by varying

the NAPL saturation distribution in the subsurface (Yoon et al. 1999).

A streamline-based inverse model named TAMU was developed at Texas A&M

University (Vasco et al., 1999, Yoon et al., 1999, Datta Gupta et al, 2002).

Lliasov et al. (2001) used the TAMU inverse model to estimate the residual oil

saturation distribution in the Ranger field from the PITT data. Oyerinde (2004)

extended Lliasov’s derivations to estimate mobile oil saturation distributions using

the TAMU inverse model coupled with ECLIPSE to the multi-well PITT data from

the Ranger field.

16

Yoon et al. (1999) developed an approach, which decouples the flow and transport by

a coordinate transformation from the physical space to one following flow directions

versus the tracer time of flight along streamlines.

The time of flight is defined as:

∫=τ ψ dr)x(S (2.21)

Where ‘slowness’ is defined as follows:

)x(v1)x(S = (2.22)

The tracer transport along streamlines in terms of time of flight coordinates is given

by

0CtC

=τ∂

∂+

∂∂

(2.23)

The tracer concentration at the producer obtained by integrating the contributions of

individual streamlines (Datta-Gupta & King 1995).

∫ ψτ−= ψall 0 d)t(C)t(C (2.27)

0C is the tracer concentration at the injection well. For partitioning tracers, the travel

time along streamlines is increased in the presence of NAPL saturation. This can be

expressed in terms of an increased slowness as follows:

)SKS()x(v

1)x(S oow += (2.24)

17

oK is the partitioning coefficient of the tracer defined as the ratio of tracer

concentration in oil phase to that in water phase.

Finally, Darcy’s law for velocity is introduced into the equation:

)SKS()x(p)x(k

)x()x(S oow +∇

µφ= (2.25)

The next step is the sensitivity computation of the tracer response with respect to the

model parameters such as permeability, porosity and NAPL saturation. The

streamline-based method has been selected to compute sensitivities (Yoon et al. 1999).

Consider a small perturbation in subsurface property around an initial model:

)x(S)x(S)x(S 0 δ+= (2.26)

)t,x(C)t,x(C)t,x(C 0 δ+= (2.27)

Assume that streamlines do not shift as a result of a small perturbation. Then the

tracer time of flight and concentration has the following relation to the slowness:

∫ δ=δτ ψ dr)x(S)x( (2.28)

∫ δτ−−=δψ

dr)x(S)t(C)t,x(C '0 (2.29)

Slowness variation will be given by

δs(x) = +δ∂

∂ )x(kk

)x(S

φ∂∂ )x(S δ φ (x) + Sw

Sw)x(S

δ∂∂ , (2.30)

where the partial derivatives are

18

)KoSoSw(p)x(k)x(

k)x(S

2 +∇

µφ−=

∂∂

(2.31)

)koSoSw(p)x(k

)x(S+

∇µ

=φ∂

∂ (2.32)

)Ko1(p)x(k)x(

Sw)x(S

−∇

µφ=

∂∂

(2.33)

Note that in the above expressions, the pressure changes have been ignored because

of small variations in the permeability. For the unit partitioning coefficient, the tracer

response will be insensitive to saturation changes. The tracer travel time and

concentration sensitivities with respect to the permeability, porosity, and water

saturation can be obtained by integrating Equation (2.28) and Equation (2.29) over all

streamlines contributing to a producer (Yoon et al. 1999).

The NAPL saturation estimation based on the partitioning tracer response is a two-

step procedure: First, the conservative tracer response is inverted to estimate spatial

distribution of the permeability, and then this permeability distribution is applied to

invert the partitioning tracer response to estimate oil saturation distribution.

2.2 Application of gas tracers for reservoir characterization

The major difference between gas and water tracer tests is the phase in which

tracers reflect as mobile fluid. For this case, we assume that retention is only by the oil

phase. The retardation factor is defined as (Brusseau et al. 2003):

19

)SS1(KS

1Rwo

ogo

−−+= , (2.34)

where Kog is the oil–gas partition coefficient and Sw is water saturation. Tang and

Harker (1991) were the first to introduce gas-phase partitioning tracer tests to

determine residual oil saturation. Many gas tracer tests have been conducted for

reservoir characterization. In 1969, gas injection with radioactive gas tracers on East

Coalinga field, California, was carried out to determine the reservoir continuity. Gas

tracer surveys were carried out successfully and at the end of the injection period,

tracer response was detected from 11 producing wells. The test showed generally

better continuity than that inferred from the outcrop study for reservoir

characterization (Tinker 1973).

In 1998, a gas injection with a gas tracer program was planned to be carried out in EI

Furrial field. The main goal of this tracer injection was to establish the path of gas

movement through the reservoir, and according to the gas tracer test, the geological

model was revised and the main direction of the fault was changed, because the fluid

movement in the reservoir had a dramatically different tendency compared with the

previous model (Vilela et al. 1999).

Radke and Gillis (1990) developed the analytical model to determine the trapped gas

saturation during steady state foam flow by the dual gas tracer injection. Effluent

concentration of tracers was influenced by solubility of each tracer on the liquid

20

phase. The measured tracer histories were fit to a simple mass transfer model that

describes any partitioning between mobile and trapped foam.

For direct calculation of the residual oil saturation from tracer data Tang (2002) has

proposed three different forms of chromatographic transformation, namely landmark

comparison, equal recovery, and equal normalized recovery. Tang and Harker (1991)

used a landmark comparison relationship (Equation 2.35) to estimate the residual oil

saturation from a gas flood at the Golden Spike carbonate reservoir:

max,p

p

max,n

nC

)(CC

)t(C τ= , (2.35)

)1(t β+=τ , (2.36)

g

org

HSS

=β (2.37)

Equation (2.35) shows that, the partitioning to a non-partitioning tracer is equal to the

delay factor (1+ β ). Therefore, by comparing the corresponding landmarks on the

non-partitioning and partitioning tracer curves, a residual oil saturation value can be

generated for every single point on the production curve.

2.3 Fractured reservoir

Fluid flow in naturally fractured reservoirs is primarily through the high

permeability, low effective porosity fractures surrounding each matrix block. The

matrix blocks contain the majority of the reservoir pore volume and act as source or

21

sink to the fractures. The rate of recovery of oil and gas from a fractured reservoir is

function of size and properties of the matrix blocks, pressure and saturation history of

the fracture and the matrix system, and wettability (Thomas et al. 1983).

2.3.1 Dual porosity model

The dual porosity model can be used to handle naturally fractured reservoir

performance. In the dual porosity model, two sets of properties are specified: matrix

porosity and permeability, and fracture porosity and permeability. The main

difference between the dual permeability and the dual porosity model is that the fluid

can flow between matrix-matrix and fracture-fracture in dual permeability model,

while in the dual porosity model, flow does not occur between matrix-matrix.

The basic model of fluid flow in fractured media has been proposed by Barenblatt et

al. (1960) by applying the continuum approach. In this approach, a pair of average

properties is assigned to the fracture and matrix properties.

Warren and Root (1962) modeled a fractured reservoir with two parameters to

characterize a naturally fractured reservoir, with parameter (ω) relating fluid

capacitance of the secondary porosity and parameter (λ) relating the scale of

heterogeneity in the system. The model also assumes that interporosity flow occurs

under pseudo-steady state conditions.

Gilman and Kazemi (1982) developed a much more realistic model in which, variable

matrix block size was considered. Their dual porosity model was for two-phase flow,

22

in which gravity forces in the matrix/fracture transfer coefficients were included.

Their shape factor was calculated as

++=σ 2

z2y

2x L

1L1

L14 ,

where zyx L,L,L are the matrix block dimensions.

Thomas et al. (1981) developed a three dimensional, three-phase model for simulating

flow in naturally fractured reservoirs based on the matrix/fracture transfer function of

Warren and Root and accounts for gravity, capillary pressure, and viscous forces.

Both the fracture flow equations and matrix/fracture flow was solved implicitly for

pressure, water salutation, gas saturation, and saturation pressure.

2.3.2 Discrete fracture model

Natural fractures are known for their special subsurface flow and transport of

fluids. Discrete fracture network (DFN) techniques recently have gained increasing

attention in the oil industry (Dershowitz et al. 2000). The DFN is designed on

construction of fracture planes in 3D space using statistical properties of fracture

swarms, fractures geometry, and flow characteristics. The advantage of the discrete

fracture model over the dual porosity model is its ability to design complex fracture

patterns based on field data, such as cores, well logs, borehole images, seismic data,

and geomechanics. To reproduce the flow behavior in a fractured reservoir, the DFN

model can be conditioned by dynamic data such as well test, tracer and production

23

data. Such conditioning is important in fractured reservoirs because only a small

fraction of fractures in the DFN model might carry bulk of the fluid flow (Al-Harbi et

al. 2004).

Several investigators have published numerical models incorporating explicit discrete

fractures. Dershowitz et al. (2000) developed techniques to integrate the DFN and

dual porosity approach. These techniques allow analysts to maintain many of the

advantages of the dual porosity simulator approach without losing the realism of the

complex fracture system geometry and connectivity, as captured by the DFN model.

Sarda et al. (2002) developed a new DFN approach by using all transmissivity terms,

fracture/fracture, matrix/fracture, matrix/matrix, matrix/well and fracture/well in their

model. In this approach, matrix blocks of different volumes and shapes are associated

with each fracture cell depending on the local geometry of the surrounding fractures.

Basquet et al. (2004) developed a software to validate discrete fracture network. Their

DFN simulation approach was based on an optimized explicit representation for both

matrix and fracture media and a specific treatment for matrix/fracture and

matrix/matrix exchanges.

Quenes (2000) developed a new approach that combines the use of the continuum and

the discrete fracture modeling method. He introduced conditioned discrete fracture,

which was used to build a realistic and detailed model of flow in discrete fractures. In

addition, his new approach determines the number of fractures in each grid block,

based on the value of fracture intensity provided by continuum model.

24

2.4 Review of Cantarell Oil Field

The Cantarell field, which is the largest oil field in Mexico and sixth largest

oil field in the world, is located about 80 kilometers (km) offshore of the Yucatan

Peninsula in the Bay of Compeche, Mexico as shown in Fig. 2.1.

The Cantarell surface area is about 162 square kilometers (km2). It is composed of

four major fields: Akal, Nohoch, Chac and Kutz. The Akal field is the largest of the

complex with 91% of the original oil volume. The average depth for the Akal field is

estimated at 2300 meters (m) below sea level, and a pay zone thickness of about 1200

(m). It is a highly fractured carbonate reservoir with large volumes of vugs from

Jurassic, Cretaceous, and lower Paleocene geological ages (Rodriguez et. al 2001).

Two type of sedimentary accumulation have been documented near or at Cretaceous-

Tertiary boundary stratigraphy across the Golf of Mexico (Murillo et al. 2002).

The Cretaceous-Tertiary boundary stratigraphy was affected by diagenetic and

deformation history at the Cenozoic time which is more susceptible to dissolution,

dolomitization and fracturing processes that resulting in an extremely complicated,

naturally fractured and vuggy carbonate reservoirs. Pore types are very diverse and

include inherited porosity as well as vuggy, intercrystalline, and fracture porosity

(Murillo et al. 2002).

Hydrocarbon production from the field comes from two intervals of carbonate rocks.

The deepest is in the lower Cretaceous, represented by dolomitized and fractured

limestone. The upper is in the Paleocene-upper Cretaceous and is made of

25

dolomitized sedimentary breccia composed of subangular to subrounded mudstone

exoclasts and wackestone bioclasts deposited in a slope environment. The size of the

vugs varies from 1 to 15 millimeters (mm). In some areas, fracturing is intense and in

general, two fracturing systems are most important: horizontal fractures and vertical

fractures to stratification (Lopez and Gonzalez 2001).

There are three production zones within the Tithonian- Cretaceous Petroleum system:

Kimmeridgian, Cretaceous, and Eocene. The Cretaceous period formations have the

highest production rate in the Bay of Campeche. These source rocks range in

thickness from 35 to 310 meters and their source potential index (SPI) is up to 16

metric tons of hydrocarbons in immature source rocks in the northeastern part, and up

to 27 metric tons in the mature part of the system, in the south-central area. Data from

two field formation tests are shown in Table 2.1 and Table 2.2 (Lopez and Gonzalez

2001).

Typical total porosity in the reservoir is 7% and up to 25% of it may correspond to

secondary porosity (fractures, microfractures and vugs). Typical permeability in the

matrix and fracture media is 0.3 and 5000 md, respectively (Rodriguez et al. 2001).

Akal has produced under full gravity segregation condition and subject to natural

thermal convection. The gas-oil contact has been steadily moving through the years to

its current thickness of 730 (m). Water encroachment from an aquifer has also taken

place, and water-oil contact has moved 480 m from its original position of 3200 m

below sea level (Rodriguez et al. 2001).

26

There is a possibility that convection phenomena may be occurring in the Cantarell

oil field because convection is a complex phenomenon that occurs in thick and highly

fractured reservoirs and it results from a combination of thermal gradients, gas

liberation at gas-oil contact and gravity segregation, and it is made possible by high

vertical permeability. This statement has been confirmed by sampling oil at three

different zones of the reservoir. It observed that the deeper oil is lighter (Manceau et

al. 2000).

Natural depletion of the Akal reservoir has caused a pressure decline from its original

average value of 270 kg/cm2 to its current value of 105 kg/cm2. This has led to a

decreasing production rate (Rodriguez et al. 2001).

Initially, Cantarell produced from Akal field at an average rate of about 29,000

STB/D per well, but in 1995 its average production rate was about 7,000 STB/D per

well. When the Cantarell project was conceived, it required 150 gas-lift assisted wells.

Reservoir simulation studies indicated that pressure maintenance was required to

optimize hydrocarbon recovery in the Cantarell complex. Among the gas injection

technologies, nitrogen was selected by considering availability, cost, safety, handing

infrastructure, environmental and reservoir issues (Rodriguez et al. 2001).

Laboratory results and numerical studies demonstrated that a greater recovery of oil is

achieved in the gas cap than in the zone encroached by water. This is due to the

favorable structural reservoir conditions with a great vertical transmissibility, which

27

resulting a very efficient gravitational segregation in the gas cap, thereby giving up to

a 20 percent higher recovery than a water flood (Limon-Hernandez et al. 2001).

28

Table 1

Cantarell-3068 Formation Test I

Upper Cretaceous Breccia

Temperature at depth 3432-3600 m 124.9 C

Permeability 3,730 md

Static pressure at 3,432 md 311.3 kg/cm2

Flowing pressure at depth 3432-3600 m 298.2 kg/cm2

Pressure fall 13.1 kg/cm2

Damage factor +118

Qoil: tubing 4½” and f 2” (with damage) 8,582 bpd

Qgas: tubing 4½” and f 2” (with damage) 1.972 mmscf/d

Gas/oil relationship 41 m3/m3

Table 2.1: Cantarell formation test 1 Data (Lopez and Gonzalez 2001)

Table 2

Cantarell-3068 Formation Test II

Upper Jurassic

Temperature at 4,038 m 139 C

Permeability 3,730 md

Static pressure at 4,038 md 438.23 kg/cm2

Flowing pressure at 4,038 md 407 kg/cm2

Pressure fall 31.23 kg/cm2

Damage factor

Qoil: tubing 4½” and f ¾” (with damage) 8,182 bpd

Qgas: tubing 4½” and f ¾” (with damage) 4.1 mmscf/d

Gas/oil relationship 89.23 m3/m3

Table 2.2: Cantarell formation test 2 Data (Lopez and Gonzalez 2001)

29

Fig. 2.1: Location of Cantarell oil field (Limon-Hernandez et al. 2005)

30

CHAPTER 3: Use of Gas Tracers for Reservoir Characterization

The major difference between gas and aqueous-phase tracer tests is the selection of

the tracers to reflect the gas phase as displacing fluid.

3.1 Partitioning coefficient for gas tracers

The amount of tracer in each phase depends on its partition coefficient to each

phase. This requires that we first calculate the saturation of each phase and then

impose tracer concentration calculation for the phase.

Partitioning coefficient of tracer i, can be defined from a mass balance between the

gas and oil phase (Maroongroge 1994):

)Sρω+Sρω(φV=n ooo,iggg,iBi , (3.1)

where

in = total mass of tracer i,

=ω g,i mass fraction of tracer i in the gas phase,

=ω o,i mass fraction of tracer i in the oil phase.

Defining partition coefficient as

31

g,i

o,iTi ω

ω=K (3.2)

And substituting TiK in the above equation and solving for g,iω and o,iω yields

)SρωK+Sρω(φV=n oog,iTiggg,iBi (3.3)

)SρK+Sρ(φVn

=ωooTiggB

ig,i (3.4)

g,iTio,i ωK=ω (3.5)

We can use tracer concentration on mass per volume basis:

gg,ig,i ρω=C (3.6)

oo,io,i ρω=C (3.7)

g,i

o,iTi C

C=K (3.8)

where

=C g,i mass of tracer i per volume in the gas phase

=C o,i mass of tracer i per volume in the oil phase.

Note that TiK values from Equation (3.2) and Equation (3.3) are numerically

different by a factor equal to the oil-gas density ratio.

The partition coefficient for a gas tracer can be constant in the reservoir or as a

function of pressure.

32

3.2 Estimation of partition coefficient for gas tracers

The accuracy of the oil saturation estimation depends on the accuracy of the

estimation of tracer partitioning coefficients, at reservoir conditions.

Perfluorocarbon gas tracers (PFT’s) have been selected for this study. PFT’s are a

family of perfluorinated alkyl cycloalkanes. Table 3.1 shows the formulation and

properties of selected gas tracers. The detection limit of PFT’s is 1510− liter of PFT’s

per liter of reservoir gas (Senum et al., 1992).

Tracer partition coefficients can be accurately estimated based on vapor-liquid

equilibrium of tracers in reservoir fluid. The composition of the reservoir fluid used in

this study was obtained from PVT collected frm a typical oil field and it shown in

Table 3.2. The vapor-liquid equilibriums i

ii x

yK = , which obtained for reservoir

fluids components and tracers by flash calculation in PVT-SIM simulator at reservoir

conditions (reservoir temperature and pressure). The equilibrium ratio is then

converted to the partition coefficient (Maroongroge 1994).

Vi

L

Ti ξKξK = (3.9)

where

=TiK Partitioning coefficient

=ξL Liquid phase molar density (lb mole/ft3)

=ξV Vapor phase molar density (lb mole/ft3)

33

The equilibrium ratio and tracer partition coefficient are given in Table 3.3.

3.3 Simulation of tracer flow in slimtube

Dugstad et al. (1992) used a slimtube displacement experiment to test

conventional radioactive gas tracers and perflurocarbon gas tracers.

The objectives of simulating the slimtube displacement were to check the ECLIPSE

gas tracer option and comparing results with UTCOMP results that had been done in

good accuracy by Maroongroge (1994).

The slimetube experiment has been described in detail by Dugstad et al. (1992) and

Maroongroge (1994) and will be described briefly here. A thin and long tube of 5 mm

in diameter and 12 m in length was filled with oil wet Ottawa sand. The porosity of

the packed tube was 35%. The tube was saturated with liquid decane and displaced

with methane gas until residual oil saturation was reached.

The oil and gas saturation were calculated from the weight measured and the

estimated densities of both phases. Tracers were injected with injecting gas (methane)

at one end of the tube and produced from the other end. Produced tracers were

measured by liquid scintillation method for the radioactive tracers and gas

chromatography for the chemical tracers. The detection limit for the chemical tracer

was 1510− liter/liter. All tracers were injected in the same experiment so that the

partition coefficient of each tracer could be compared.

34

Gravity was considered negligible since the diameter of the tube was much smaller

than the length of the tube.

The retardation in the produced tracer concentration resulted from the different

partition coefficient of each tracer, so partition coefficients were calculated from the

retardation of each tracer. Oil was at residual saturation and gas was the only mobile

phase:

S

MRTi V

VVK −= (3.10)

where

=VM Volume of mobile gas

=VR Retention volume,

=VS Volume of stationary oil

Injection rate was assumed to be constant during the experiment, therefore the tracer

retention volume were calculated by multiplying the injection rate by the tracer

retention time.

RinjR TqV = (3.11)

The Tracer retention time was obtained from the peak arrival time of produced tracer

concentration. The volume of the residual oil and mobile gas were calculated from a

material balance. Retardation factor and partition coefficient have the following

relation:

35

or

ortiT S1

SK1R

−+= (2.23)

Location of each tracer peak concentration in the plot of tracer concentration versus

injected mobile phase volume ( MV ) determines the retardation factor of each tracer.

Maroongroge (1994) simulated the experiment with UTCOMP and obtained an

excellent match with the experiment. We tried to model the experiment using data

that Maroongroge used in his simulation, but faced problems with ECLIPSE.

Definition of partition coefficient in ECLIPSE is based on reservoir conditions that is

difficult to keep constant during the simulation since pressure and formation volume

factor are not constant in the reservoir at all times, and all places. Its units are also not

consistent since a partition coefficient value in ECLIPSE has to be multiplied by gas

formation volume factor and divided by oil formation volume factor:

gig

oioETi BC

BCK = (3.12)

ig

ioUTTi C

CK = (3.13)

o

g)ECLIPSE(T)UTCOMP(T B

BKK = (3.14)

gB = gas formation volume factor, MSCF

rb

oB =oil formation volume factor,STB

rb

36

The ECLIPSE manual does not clearly define the partition coefficient. Numerical

dispersion was another problem in ECLIPSE for this simple experiment We modeled

the slimtube by 3000x1x1 grid blocks and more than 2000 time steps for a 3-day

tracer injection to overcome the problem.

Table 3.4 shows retardation factor of each tracer and corresponding partitioning

coefficient from Equation (3.8). The input data for the simulation are given in Table

(3.5).

The result of ECLIPSE simulation and experimental results by Dugstad et al. (1992)

is shown in the Figure 3.1. It can be observed that numerical dispersion is still a

problem for obtaining a good match of the tracer concentration peaks. However, the

retention times in HCPV are close and this is most important since the oil saturation

can be calculated from retention time.

3.4 Simulation of gas tracers in fractured reservoir

The simulation study was initiated with a three-dimensional reservoir. Tracers

were injected with nitrogen into a gas cap and tracer concentrations were measured at

the producer. Oil saturations were calculated using the method of moments and the

comparison between the known model values and the estimated values were plotted.

The reservoir was considered a fractured reservoir, so first the dual porosity model

was used, and then later the discrete fracture model was used.

37

3.4.1 Reservoir parameters and geology data for base case simulation

Our simulations are based on the Cantarell oil field reservoir, which is the

largest oil field in Mexico. Data has been prepared from several Offshore Technology

Conference papers. The Cantarell oil field is located about 80 kilometers (km)

offshore of the Yucatan Peninsula in the Bay of Compeche.

The Cantarell surface area is about 162 square kilometers (km2). The average depth of

the Akal field is estimated at 2300 meters (m) below sea level, with a pay zone

thickness of about 1200 (m). It is a highly fractured carbonate reservoir with large

volumes of vugs from Jurassic, Cretaceous, and lower Paleocene geological ages

(Rodriguez et al. 2001).

Hydrocarbon production from the field comes from two intervals of carbonate rocks.

The deepest is in the lower Cretaceous, represented by dolomitized and fractured

limestone. The upper is in the Paleocene-upper Cretaceous and is made of

dolomitized sedimentary breccia composed of subangular to subrounded mudstone

exoclasts and wackestone bioclasts deposited in a slope environment. The size of

vugs varies from one to 15 millimeters (mm). In some intervals fracturing is intense

and in general two fracturing systems are most important, horizontal and vertical

fractures (Lopez et al. 2001).

Typical total porosity in the reservoir is 7% and up to 25% of it may correspond to

secondary porosity (fractures, microfractures and vugs). Typical absolute

38

permabilities in the primary and secondary media are 0.3 and 5000 md, respectively

(Rodriguez et al. 2001).

3.4.2 Base case Simulation with dual porosity model

The simulation domain is a quarter of a five-spot well pattern with dimensions

of 1000 ft long by 1000 ft wide by 1000 ft thick. Reservoir is divided in two regions:

a gas cap zone where the only mobile phase is gas and an oil zone where oil is the

mobile phase and water-oil contact is out of simulation domain, so in the initial case

there is no mobile water. The fracture and matrix permeabilities are 5000 and 0.2 md,

respectively. Residual oil saturation distribution has an exponential relation with

permeability distribution. So the residual saturations of oil and gas in rock matrix are

0.4 and 0.3, and in the fractures are 0.2 and 0.15, respectively. The matrix and

fracture porosity are 0.07 and 0.02, respectively. The shape factor is 0.36 assuming a

fracture spacing of 5 ft in the horizontal direction and 10 ft in the vertical direction.

Nitrogen injection was considered for pressure maintenance and a tracer slug with

one conservative tracer (K=0) and two partitioning tracers in a nitrogen injection with

partition coefficients of 1.5 and 2.5 based on UTCOMP definition was injected for

0.25 PV with nitrogen into the gas cap zone.

There is a rate constraint injector, which injects at constant rate of 5000 MSCF/D and

a pressure constraint producer, which produces under bottom hole pressure (BHP) of

950.0 psi. Capillary pressure is the only driving forces to produce oil from the matrix.

39

3.4.3 Results

Figure 3.2 shows the produced tracer concentration for three tracers with

different partition coefficients. The early arrival time of tracers and long production

tail in fractured reservoir can be observed. The early arrival time is for the

breakthrough of flowing traces in the fracture, and the long production tail is for the

diffusion of tracers into and out of the matrix since diffusion is a slow process.

Figure 3.3 shows oil production rate in dual porosity model; the first part with high

production rate indicates production from fracture and the low and long production

rate shows oil production from matrix. After about 2000 days of production, it can be

observed oil production rate is less than 10 STB/D. Figure 3.4 shows oil recovery in

dual porosity model. Most of the oil recovery comes from fractures because in this

case the fracture porosity and permeability are both large with respect to the matrix

porosity and permeability.

Oil saturation can be determined from two tracers of different partition coefficients

using method of moments as shown below.

3.5 Estimation of oil saturation and swept pore volume using method of

moments

Estimation of swept pore volume is very important in reservoir

characterization. It can be used to evaluate fluid flow pattern and maximize oil

40

recovery by infill drilling and designing an enhanced oil recovery process. The

reservoir swept pore volume between wells can be determined from first temporal

moment of concentration tracer production data of an interwell tracer test. Oil

saturation also can be estimated from first temporal moment of a partitioning

interwell tracer test (PITT).

3.5.1 Method of moments for dual porosity model

Method of moments theory for single porosity model was presented in Chapter

2. The derivation of method of moments has been presented in detail by Asakawa

(2005). Here we present a brief summary of his derivation for dual porosity model.

All of the assumptions and descriptions in Chapter 2 are valid for dual porosity model.

The mass conservation equation in dual porosity model is as follow:

For fracture:

0N.t

Cfmfi

fif =τ+∇+

∂∂

φr

(3.15)

where

∑==

pn

1jfijjfi CSC (3.16)

And for matrix:

0t

Cfm

mim =τ−

∂∂

φ (3.17)

where

41

∑==

pn

1jmijjmi CSC (3.18)

Adding matrix and fracture mass conservation equation:

0t

CN.

tC mi

mfifi

f =∂

∂φ+∇+

∂∂

φr

(3.19)

And total porosity is

mft φ+φ=φ (3.20)

Total tracer concentration is

t

mimfifti

CCC

φφ+φ

= (3.21)

Then mass conservation equation will be

0N.t

Cfi

tit =∇+

∂∂

φr

(3.22)

As it can be seen, Equation (3.22) is the same as Equation (2.1), so the first temporal

moment can be used in dual porosity model to calculate swept pore volume and oil

saturation in the reservoir.

The swept pore volume for three phases is

21

2112 )1()1(*))1(

1(KK

KVKVS

Vw

s −−−−

−= (2.18)

And the average oil saturation in swept pore volume is

)1()1(*)1(ˆ

2112

21−−−

−−=

KVKVVVSS wo , (2.17)

42

where mean residence volume is

2V

dtC

dttqCV slug

0ig

0it

i −

∫

∫=

∞

∞

(2.15)

3.5.2 Estimation of average oil saturation and swept pore volume in dual

porosity media

ECLIPSE was used to simulate tracer test in a quarter of a five-spot well

pattern with dimension of 1000 ft long by 1000 ft wide by 500 ft thick. The fracture

and matrix permeabilities are 5000 and 0.2 md, respectively. The shape factor of the

reservoir is 0.36. The uniform residual saturation of oil, gas and water into the system

are 0.3, 0.2 and 0.2, respectively. Water is at residual saturation in the reservoir and

tracers do not partition into the water. Reservoir was divided in two zones: gas cap

zone, where the gas is the only mobile phase, and oil zone, where oil is the mobile

phase.

Tracer transport between the fracture and matrix is by diffusion and capillary

imbibition process.

Gas is injected into gas cap and 3 gas tracers of partitioning coefficients of 0.0, 1.5

and 2.5 based on UTCOMP definition were selected to be injected for 0.25 PV.

Figures 3.5 and 3.6 show the concentrations of the tracers at the producer. Figure 3.7

shows the tracers recovery for 2000 days. It can be observed that about 95.0 % of the

43

conservative tracer and 60.0% of the partitioning tracer (K=1.5) has been recovered at

one pore volume injection. It verifies flow of the tracers to the matrix. Diffusion

phenomena, mobile oil into the matrix, and capillary pressure help tracer transport to

the matrix.

The amount of tracer that diffuses into the matrix takes a long time to be produced

because diffusion is a very slow process. The long tail tracer production shows this

phenomenon. Oil saturation can be estimated from method of moments and by using

total tracer concentration.

ooggit CfCfC += (3.23)

Average oil saturation from method of moments and reservoir simulation has been

compared in Fig. 3.8 and swept pore volume from method of moments is shown in

Fig. 3.9. The volume of oil saturation calculated from the tracer data converge to the

simulated value after about 1600 days.

3.5.3 Estimation of average oil saturation and swept pore volume in dual

porosity media for different residual oil saturation in matrix and fracture

Residual saturation distribution is a function of permeability, so in a fractured

reservoir in which the matrix and fracture have different permeabilities, residual

saturations are different. In this case, we have simulated the same case as Section

3.4.2 with different residual oil, gas and water saturations in the matrix and fracture.

44

For a fracture, residual oil, water and gas saturations are 0.15, 0.15 and 0.10,

respectively. For matrix, residual oil, water and gas saturations are 0.30, 0.30 and 0.2,

respectively. The other properties are the same as Section 3.5.2.

Figures 3.10 and 3.11 show the concentration of tracers at the producer. Conservative

tracer profiles for layer 3 after 50 days and 250 days is given in Figures 3.12 and

3.13, respectively. Figures 3.14 and 3.15 show conservative tracer profiles for layers

8 and 9 after 250 days, respectively. Note that tracer slug injection was for 150 days.

The average oil saturation from the method of moments and simulation are compared

in Figure 3.16 and swept pore volume from method of moments is shown in Figure

3.17. From Figure 3.16, it can be observed that method of moments can estimate oil

saturation with mobile oil and even for different saturations in matrix and fracture in

dual porosity media when using total tracer concentration. Figure 3.18 shows the

tracers recovery for 2000 days of tracer production.

3.6 Conclusion

Simulation of slimtube flow displacement by ECLIPSE shows lots of

numerical dispersion even for 3000 grid blocks. However, its peak concentration

arrival time is in fair agreement with Dugstad et al. (1992) experiment.

Tracer tests in fractured reservoirs show early arrival time, long production

tails and extreme dilution of the tracer, so the separation of tracer peaks can not be

45

used to calculate an accurate oil saturation. However, the method of moments can

accurately estimate the oil saturation since it takes to account the tracer tail.

A constant partition coefficient is one of the assumptions used in method of

moment, but in ECLIPSE, iK depends on oil and gas formation volume factors,

oB and Bg , which depend on pressure. However, in this study we made the oil and

gas formation volume factors constant in the simulation.

The method of moments gave accurate values of oil saturation in the fractured

reservoirs for both the residual oil saturation and mobile oil saturation (using total

concentration of tracers) where simulated with ECLIPSE in this way.

46

Tracer Tfp Tb Pc Tc Wt ω ρ L

°C °C psia °R molem lb/lb g/cc PMCP -45 48 330.8 811.9 300 0.458 1.72 PMCH -39 76 310.2 870 350 0.482 1.80

Table 3.1: Property of selected tracers (Maroongroge 1994)

Component Mole

fraction Pc Tc Vc ω MW psia R ft3/lb mole lb-mol/lbm

N2 0.2 492 227 1.44 0.04 28 C1 0.2987 667.4 343.1 1.5698 0.008 16.04

C2-C3 0.1675 669.18 598.92 2.5845 0.121 36.03 C4-C5 0.0929 519.38 795.12 4.7452 0.213 64.72 C6P1 0.1169 431 913 10.5654 0.296 86.18 C7P2 0.122 220 1420 32.3 0.59 323.08 PMCP 0.001 330.8 811.9 0.458 300 PMCH 0.001 310.2 870 0.482 350

Table 3.2: Fluid composition for estimating tracer partitioning coefficient

Symbol Name Chemical formula Equilibration ξ gas ξ liquid TiK

K Value lb mole/ft3 lb mole/ft3 PMCP methylcyclopentane C6F12 1.137 0.172 0.33 1.47

PMCH methycyclohexane C7F12 0.98 0.172 0.33 1.92 Table 3.3: Equilibrium ratio and partition coefficient of the selected tracers at reservoir condition

47

Tracer name Retention Volume Partitioning Coefficient TCH3 1.30 0.64

3314 CHCH − 1.91 1.93

PMCP 2.53 3.25 PMCH 3.69 5.72

Table 3.4: Partitioning coefficient and relative Retention volume for slimtube displacement

Dimensions (ft) Length Width Thickness

39.37

0.01453 0.01453

Porosity (fraction) 0.35 Rock compressibility (psi 1− ) Water compressibility (psi 1− ) Initial water saturation Tracer slug size (total pore volume) Initial oil saturation Initial gas saturation Reservoir temperature Initial reservoir pressure Injection rate of c1(methane) Number of Grid Blocks

0 0 0

0.006 0.32 0.68

122 °F (50 °C) 1450 psia

0.7 SCF/D

3000 x 1 x 1

Table 3.5: Data for simulation of slimtube displacement (Maroongoge 1994)

48

0.001

0.041

0.081

0.121

0.161

0.201

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Hydrocarbon Pore Volume injected

Nor

mal

ized

Tra

cer C

once

ntra

tion

simulated CH3T

Simulated 14CH3-CH3

Simulated PMCP

Simulated PMCH

Experiment CH3T

Experiment 14CH3-CH3

Experiment PMCP

Experiment PMCH

Fig 3.1: Comparison between produced tracer concentration history of Slimtube

Experiment with ECLIPSE simulation results.

0.0001

0.001

0.01

0.1

1

0 400 800 1200 1600 2000

Time, Days

Nor

mal

ized

trac

er c

once

ntra

tion

K=0.0

K=1.5

K=2.5

Fig 3.2 Normalized tracer concentration for dual porosity simulation case

49

0

2000

4000

6000

8000

10000

0 400 800 1200 1600 2000

Time, Days

Oil

Prod

uctio

n R

ate

STB

/D

Oil Rate STB/D

Fig 3.3 Oil production rate for dual porosity simulation case

0

0.1

0.2

0.3

0.4

0.5

0 400 800 1200 1600 2000

Time, Days

Oil

Rec

over

y E

ffici

ency

Oil Recovery %

Fig 3.4 Oil Recovery for dual porosity model simulation

50

0.001

0.01

0.1

1

0 400 800 1200 1600 2000Time, days

Nor

mal

ized

trac

er c

once

ntra

tion

K=0

K=1.5

Fig 3.5: Tracer concentration at the producer for dual porosity model (Semi-Log scale)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 400 800 1200 1600 2000Time, days

Nor

mal

ized

trac

er c

once

ntra

tion

K=0

K=1.5

Fig. 3.6: Tracer Concentration at the producer for dual porosity model

51

0

0.2

0.4

0.6

0.8

1

0 400 800 1200 1600 2000

time, Days

Trac

er re

cove

ry

K=0.0

K=1.5

K=2.5

Fig. 3.7: Tracers recovery for different partition coefficient in dual porosity media

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 400 800 1200 1600 2000

Time, days

Oil

Sat

urat

ion

Estimated Oil Saturation

Reservoir simulation oil saturation

Fig. 3.8: Oil saturation estimation from method of moments in dual porosity media with mobile oil

52

0

0.2

0.4

0.6

0.8

1

0 400 800 1200 1600 2000

Time, days

swep

t efic

ienc

y

Sweep Efficiency %

Fig. 3.9: Sweep efficiency estimation from method of moments in dual porosity media with mobile oil

0.001

0.01

0.1

1

0 400 800 1200 1600 2000Time, days

Nor

mal

ized

trac

er c

once

ntra

tion

K=0

K=1.5

Fig. 3.10: Tracer production concentration at the producer for different residual oil saturation in matrix and fracture (Semi-Log scale)

53

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 400 800 1200 1600 2000Time, days

Nor

mal

ized

trac

er c

once

ntra

tion

K=0

K=1.5

Fig. 3.11: Tracer production concentration at the producer for different residual oil saturation in matrix and fracture

Fig. 3.12: Conservative tracer concentration profile in layer 3 after 50 days of tracer injection.

54

Fig 3.13: Conservative tracer profile in layer 3 after 250 days

Fig. 3.14: Conservative tracer profile in layer 8 after 250 days

55

Fig. 3.15: Conservative tracer profile in layer 9 after 250 days

0

0.1

0.2

0.3

0.4

0.5

0.6

0 400 800 1200 1600 2000

Time, days

Oil

Sat

urat

ion

Estimated Oil Saturation

Reservoir simulation oil saturation

Fig. 3.16: Oil saturation estimation from method of moments in dual porosity media for different residual oil saturation in matrix and fracture

56

0

0.2

0.4

0.6

0.8

1

0 400 800 1200 1600 2000

Time, Days

swep

t efic

ienc

y

Sweep efficiency %

Fig. 3.17: Sweep efficiency estimation from method of moments in dual porosity media for different residual oil saturation in matrix and fracture

0

0.2

0.4

0.6

0.8

1

0 400 800 1200 1600 2000

Time, Days

Trac

er re

cove

ry

K=0.0K=1.5K=2.5

Fig 3.18: Tracers recovery for different partition coefficients in dual porosity media for different residual oil saturation in matrix and fracture

57

CHAPTER 4: Comparison of Discrete Fracture Model and Dual

Porosity Model for Gas Tracers

4.1 Driving forces in fractured reservoir

In fractured reservoirs, especially in the dual porosity model, the majority of

the oil is contained in the matrix, but the production of the oil to the wells is through

the high permeability fractures. Oil production from the matrix blocks needs at least

one driving force, otherwise the injected fluid can not sweep out the oil from the

matrix blocks.

Oil Expansion

As the pressure drops in the fracture system, oil will flow from the matrix to

equilibrate the matrix pressure with the surrounding fracture pressure. This oil

production is due to the oil expansion within the matrix, either above the bubble point

or by solution gas drive below the bubble point.

Capillary Imbibition

For a typical water wet system, matrix block has positive water-oil capillary

pressure and if water is injected into fractures, the water will flow under capillary

force to the matrix and oil will flow out.

58

Gravity Drainage/Imbibition

For a matrix block and surrounding fracture, the height difference between

two phases and density difference cause a pressure difference between the matrix and

fracture that allows oil flow to the fracture.

Viscous force

Viscous displacement of a fluid is simply the movement of that fluid when

pressure difference is applied. In fractured reservoirs, there is a pressure gradient in

the fracture system, which moves fluid through the fracture, toward production wells.

In most cases, this pressure gradient is small because fracture has high permeability in

which case it is reasonable to ignore the viscous displacement of the fluid from the

matrix by the fracture pressure gradient. However, if fracture permeability is

moderate, flow into and out of the matrix by the fracture pressure gradient would be a

significant driving force on production.

Diffusion

Oil may be produced by molecular diffusion between the matrix and fracture

during gravity drainage, in which the effect of diffusion mechanism on overall

recovery can be neglected on most systems. However for small matrix blocks,

diffusion can be a key mechanism in oil recovery.

59

4.2 Shape Factor study

Fracture/matrix fluid exchange process depends on shape factor and matrix

block size. The rate of fluid flow between matrix and fracture in dual porosity model

is significant and it depends on matrix-fracture transfer function which incorporates

with shape factor.

Fluid transfer between the matrix and fracture is defined as

)PP(k

tP

C mfmm

m −µ

σ=

∂∂

φ (4.1)

Where σ is the shape factor and is based on the size and shape of the matrix blocks.

The shape factor is defined as

mV)L

A(=σ , (4.2)

where A is the area of the matrix block contacted by fracture, L is the matrix block

size and Vm is the bulk volume of the matrix block.

Various shape factors reported in the literature:

Warren and Root obtained:

2L)2+N(N4

=σ (4.3)

For a cubic matrix block of dimension L and pseudo-steady state condition, N is the

number of the normal sets of fractures.

Kazemi et al. (1974) proposed:

60

]Lz

1Ly

1Lx

1[*4 222 ++=σ (4.4)

For fluid flow in three dimensions, the ECLIPSE simulator uses the above model for

shape factor definition.

Gilman and Kazemi extended the Kazemi (1974) shape factor to a more general form

for anisotropic, rectangular matrix blocks:

++=σ 2

z

z2y

y2x

xm

Lk

L

k

Lk4k (4.5)

IMEX simulator uses this model for shape factor definition.

Later Chang (1993) and Lim and Aziz (1995) recognized the time dependence of

shape factor. Edgar et al. (2003) developed time dependent shape factoras follows:

m

*D

D*s

tt

−

σ=σ For tD< *

Dt (4.6-1)

and

*s σ=σ For tD> *

Dt , (4.6-2)

where characteristic dimensionless time is approximately *Dt =0.1 and m is a function

of the flow rate and fracture aperture.

In general, shape factor is used as history matching parameter because it is impossible

to find fracture spacing for the entire reservoir.

61

4.3 Base case simulation for dual porosity and discrete fracture models

The purpose of this chapter is to compares dual porosity model and discrete

fracture model and discuss their advantages and disadvantages.

The base case simulation is a quarter of a five-spot pattern fractured reservoir. A

uniform residual oil saturation of 0.4 for matrix and 0.15 for fractures and a uniform

residual gas saturation of 0.3 for matrix and 0.10 for fractures was considered. The

reservoir has a porosity of 0.07 for matrix and a fracture porosity of 0.02. The

simulation field consists of a gas cap zone where gas is only mobile phase and oil

zone. Water-oil contact is not considered in the simulation domain and its residual

was neglected because it did not have any effect on gas tracer simulation. The

simulation field has dimensions of 100 ft in the X, Y and Z directions.

Complementary data for the simulation are given in Table 4.1.

Nitrogen injection has been chosen for pressure maintenance and a rate constraint

injector was considered to inject a conservative tracer and two partitioning tracers

with partitioning coefficients of 1.5 and 2.5 for 2.5% pore volume into the reservoir

and a pressure constraint producer was considered to produce oil, gas and tracers.

The simulation field modeled with the dual porosity, discrete fracture, and equivalent

single porosity.

62

4.4 Dual porosity Model

In a dual porosity model, the reservoir is divided in two systems; the rock

matrix, which usually provides the bulk of the reservoir fluid and the highly

permeable rock fractures, which usually provides fluid flow.

In the dual porosity model, matrix blocks are linked only through the fracture system,

and fluid flow through the reservoir takes place only in the fracture network with the

matrix blocks acting as sources.

Figure 4.1 shows an actual fracture reservoir and a modeled fractured reservoir with a

regular matrix and fracture, like dual porosity model.

4.4.1 Simulation of fractures by dual porosity model

To simulate a fractured reservoir by the dual porosity model, fracture porosity,

fracture permeability, and shape factor are essential reservoir parameters to define the

fracture properties.

Relative permeability and capillary pressure also play a significant role in fractured

reservoirs.

4.4.1.1 Relative permeability table in naturally fractured reservoir

In a fractured reservoir of gas-oil system, gas is the none-wetting phase and

oil is the wetting phase consequently moving a wetting phase from the matrix by the

none-wetting phase has small recovery efficiency.

63

A Corey-type model was used to model the relative permeability in this simulation.

Wettability has a significant effect on the end point relative permeability and relative

permeability exponent which are key factors in this model. The relative permeability

equation is

jenjrjrj )S(kk ο= (4.7)

For this study, there are only the gas and oil phases, so

g,oj,SS1

SSS

orgr

jrjnj =

−−

−= (4.8)

Two sets of relative permeability are considered for matrix and fracture based on their

residual saturation and end point relative permeability. Figure 4.2 and Fig. 4.3 show

relative permeability curves for the matrix and for the fracture, respectively.

4.4.1.2 Capillary pressure in naturally fractured reservoirs

Capillary pressure in fractured reservoirs is a significant factor for producing

oil from the matrix. Note that wettability has considerable effect on capillary pressure

phenomena and capillary pressure type.

The Corey-type capillary pressure model for gas-oil system is

pcjnnj

5.0pcjc )S()k/(CP φ= , (4.9)

where

64

oj,SS,)SS()SS(

S *o

or*

o*

nj =<−

−= (4.10)

gj,SS,)SS1(

)SS(S *

o*gr

*o

nj =>−−

−= (4.11)

Equation (4.10) is for the positive part of the capillary pressure and Equation

(4.11) is for the negative part of capillary pressure.

Based on Equation (4.9), capillary pressure depends on permeability, porosity, phase

saturation, and capillary exponent, therefore matrix and fracture should have different

capillary pressures.

In fractured reservoir simulations usually two sets of capillary pressure and relative

permeability tables are used for the fracture and the matrix.

The effect of capillary pressure has been studied for three cases: No capillary pressure

in the matrix and fracture, capillary pressure only in the matrix, and capillary pressure

in the matrix and fracture. Summarized data for Case 1 is given in Table 4.2. Figure

4.4 shows the oil saturation profile in the matrix for all three cases before gas

injection. Figure 4.5 shows the matrix oil saturation profile for Case 1 (no capillary

pressure) after 2000 days. It can be observed that oil production from the matrix is

less than 2%. Oil production rate and oil recovery of Case 1 is shown in Fig 4.6.

Summarized data for Case 2 (capillary pressure only in matrix) is given in Table 4.3

and Fig. 4.7 shows the capillary pressure curve for the first case. The system is oil-

wet and the capillary pressure is given with respect to the wetting phase. Figure 4.8

65

shows the oil recovery for this Case and Fig. 4.9 shows the oil saturation profile after

2000 days of gas injection, in which less than 3% oil production from the matrix can

be seen even for a large value of capillary pressure. This can be described by

wettability, because fractures are full of gas and the matrix contains oil and rock type

is oil-wet, so the oil does not like to be replaced by gas; in fact matrix capillary

pressure in this case help oil to remain in matrix.

In Case 3, there is capillary pressure in the fracture system. Summarized data is given

in Table 4.4 and relative permeability is same as before. Figure 4.10 shows the

capillary pressure curve for the matrix and fracture system. Figure 4.11 shows oil

recovery for this case and Fig. 4.12 shows the oil saturation profile after 2000 days of

gas injection, which illustrates considerable oil production from the matrix. It can be

described by fracture capillary pressure because fractures are full of gas and the rock

is oil-wet so fractures imbibe oil from the matrix. In the previous case, fracture did

not have capillary force to imbibe oil from the matrix.

4.4.2 Comparison of dual porosity model in IMEX and ECLIPSE

To analyze the behavior of the dual porosity model in ECLIPSE, we used

IMEX as a second simulator to compare results. The oil production rate for the dual

porosity model in IMEX and ECLIPSE are given in Fig. 4.13. There are significant

differences between ECLIPSE and IMEX. Oil recovery from the matrix in IMEX is

more than ECLIPSE. There are some differences in the recovery mechanism and the

66

shape factor definitions for ECLIPSE and IMEX. In this case, permeability

distribution is isotropic so both shape factors are the same. In ECLIPSE, driving

forces that mentioned in Section 4.1 has to be defined specifically in the simulation if

any of them is applied but in IMEX they are considered in the simulation

automatically.

4.4.3 Subgridding

In the dual porosity model, grid blocks can be divided into smaller grid blocks

to better characterize flow inside the matrix block and to model transient behavior of

the system. In ECLIPSE, matrix blocks can be divided as nested blocks in two

dimensions or as concentric blocks in three dimensions and it did not consider Z

direction subgridding, because in three dimension subgridding, all sub-divided grid

blocks have an identical center. Figures 4.14 and 4.15 show schematic view of

subgridding in ECLIPSE.

In IMEX there are two options for subgridding, horizontal subgrid which is as nested

grid block in the X-Y plane, and vertical subgrid which is as stack grid block in the Z

direction. Note that IMEX does not allow users to use both subgrid simultaneously.

The effect of subgridding on fluid flow and oil recovery for the dual porosity model

in ECLIPSE and IMEX is given in Fig. 4.16 through Fig. 4.19. For this simulation

case, changes are negligible but for some cases, subgridding affects oil recovery up to

50% .

67

4.5 Simulation of gas tracers by tracing an injection component in GEM

The GEM simulator does not have a tracer option for a tracer test. Tracers can

be modeled in this simulator by tracing a component of injection composition as a

tracer through the reservoir in a compositional simulator.

For this purpose, nitrogen is injected in two different ways, Nitrogen (A) as a

continuous injection for the purpose of pressure maintenance and Nitrogen (B) as slug

injection for the purpose of component tracing. Note that in both ways Nitrogen has

the same property and the only difference is the name. Nitrogen (B) is injected in 5%

of injection composition for 0.15 PV.

4.5.1 Simulation in dual porosity media

The simulation field is a quarter of five-spot well patterns in a fractured

reservoir. Uniform residual oil saturation for matrix is 0.4 and for fractures is 0.15.

the reservoir has a porosity of 0.07 for matrix and a fracture porosity of 0.02 and a

permeability of 5000 md and 0.2 md for fracture and matrix, respectively. The

simulation field consists of gas cap zone and oil zone. The fracture spacing is 5 ft in

the horizontal direction and 10 ft in the vertical direction. The simulation field is 1000

ft long, 1000 ft wide and 500 ft thick. In addition, gas cap thickness is 200 ft.

68

4.5.2 Comparison of the tracer test between ECLIPSE and CMG-GEM

The modeled tracer test in the compositional simulator GEM was compared

with black oil simulator ECLIPSE. Figure 4.20 shows the oil production rate for both

simulators and Fig. 4.21 shows the tracer response. It can be observed that the peak

arrival time for the two tracer tests approximately are in the same time. In addition, it

should be noted that fluid flow in the two simulators are different.

The purpose of this simulation was to compare the results of a gas tracer test in

ECLIPSE with another simulator to compare the tracer test for tracer transport in the

fracture and the matrix.

Tracer concentration profiles during gas injection for GEM is for the fracture and

matrix in Fig. 4.22 through Fig. 4.25 and for the ECLIPSE, it is given in Fig. 4.26 to

Fig. 4.29. It can be observed that the mole fraction profile of (N2B) in the matrix and

fracture are different by an order of about 30 times and the same thing is true for the

tracer profile in the matrix and fracture in the ECLIPSE simulator. Note that there is

no capillary pressure in both cases and the only mechanism for tracer transport is

diffusion, which is a slow process.

4.6 Simulation of fractures by modeling the fractures as discrete Fracture

network

The advantage of the discrete fracture model over the dual porosity model is

its ability to design complex fracture patterns based on field data, such as cores, well

69

logs, seismic data, and geomechanics. Discrete fracture is more realistic than dual

porosity, because in the dual porosity model, fractures are distributed uniformly

around the matrix while in the discrete fracture model it can be a heterogeneous

fracture distribution with heterogeneous permeability, porosity, and fracture spacing.

4.6.1 Problem to model fractures as discrete fracture

In the discrete fracture model, each fracture aperture has its own grid block, so

to calculate transmissibility between the matrix and fracture in the discrete fracture

model, large permeability contrast and large grid block size contrast between the

matrix and fracture pose problems.

To solve these problems, we increase fracture aperture size and reduce its porosity to

keep the fracture pore volume constant in the discrete fracture model.

4.6.2 Discrete fracture model

In this study, we use the discrete fracture model with the property of dual

porosity model to compare its performance with dual porosity. Each matrix block is

surrounded by fracture grid blocks. The fracture spacing is 10 ft in each direction,

which is the same as the dual porosity model. Fracture aperture in the discrete

fracture model is 1 ft. Total fracture porosity is 0.02, the same as the dual porosity

model and fracture porosity for each fracture grid block is calculated from total

fracture porosity and for this case, it is 0.08. Its permeability is 5000, the same as the

70

dual porosity model. Capillary pressure and relative permeability tables are the same

as the dual porosity model. Figure 4.30 through Fig. 4.33 show oil production rate,

recovery efficiency and tracer concentration comparisons between the dual porosity

and discrete fracture models. Figure 4.34 compares the oil production rate in

ECLIPSE and IMEX by discrete fracture model. The data for discrete fracture

simulation is given in Table 4.5

4.6.3 Grid refinement

Local grid refinement allows seeing what happens inside the grid blocks; it

allows users to refine a grid block in each direction to better characterize a grid block.

Grid refinement usually is used to refine grids near the well to better capture fluid

flow pattern near the wells. In discrete fracture model, matrix blocks can be refined to

better characterize fluid flow between matrix and fractures. Figure 4.35 shows a

schematic view of the grid refinement in discrete fracture model. A 2x2x2 refinement

was used for each matrix grid block to refine simulated discrete fracture model.

Figure 4.36 compares refinement and no-refinement models oil production rate. It can

be observed that there is no significant difference between original and grid

refinement case.

71

4.7 Simulation of fractures by modeling the fractures as equivalent single

porosity

When there is a big contrast between matrix and fracture permeability and

fractures occupy a large volume of the porous media, the reservoir could be modeled

as equivalent single porosity.

In this model the total porosity and permeability is fracture porosity and permeability.

It is assumed that production from matrix is small and negligible compare to fracture

production. Figures 4.37 and 4.38 show oil production rate and oil recovery

comparison between equivalent single porosity models, dual porosity model and

discrete fracture model. As expected most of oil production is from the fracture. The

difference between Equivalent single porosity model and the other models shows oil

recovery from the matrix.

4.8 Conclusion:

The rate of fluid flow between the matrix and fracture in the dual porosity

model is significant and it depends on matrix-fracture transfer function, which is

defined by the shape factor.

Capillary pressure depends on the permeability, porosity and wettability. End

point relative permeability strongly depends on wetting phase. For fracture system of

72

non-wetting phase displacing wetting phase the capillary pressure on the fracture

system is important to display wetting phase from the matrix.

The comparison between ECLIPSE and IMEX results for the dual porosity

model shows the difference in oil recovery from the matrix in simulators, which

results from the recovery mechanism definition in two simulators.

The discrete fracture model easily can handle all properties of the dual

porosity model and cover the certain assumptions, which make the dual porosity

model inaccurate for fluid flow in the matrix and fracture.

Transmissibity calculation is one of the problems in the discrete fracture

model and it is resulted from the big contrast between two neighbor grid blocks,

(matrix and fracture) size and permeability.

73

Dimensions (ft) Length 100 ft

Width 100 ft

Thickness 100 ft

No. of Grid Blocks 10 x 10 x 10 Grid Dimensions NX 10 NY 10 NZ 10 Matrix permeability 0.2 md Fracture permeability 5000 md Matrix porosity 0.07 Fracture porosity 0.02 Gas injection rate 10 MSCF/D Shape Factor 0.12 Fracture Spacing Length 10 ft Width 10 ft Thickness 10 ft Oil viscosity 2.5 cp Gas viscosity 0.0175cp Oil density 56.0 lb/ft3 Gas density 0.0615 lb/ft3 Sor in matrix 0.4 Sor in fracture 0.15

Table 4.1: Reservoir data for dual porosity model simulation Case Sgr Sor Kgr

o Koro Ng No Cpc Npc φ k

Matrix 0.3 0.4 1 0.2 2 2 0 0 0.002 0.07

Fracture 0.1 0.15 1 1 2 2 0 0 5 1

Table 4.2: Relative permeability and capillary pressure data for Case 1

74

Case Sgr Sor Kgro Kor

o Ng No Cpc Npc φ k Matrix 0.3 0.4 1 0.2 2 2 1 2 0.002 0.07 Fracture 0.1 0.15 1 1 2 2 0 0 5 1


Case Sgr Sor Kgro Kor

o Ng No Cpc Npc φ k Matrix 0.3 0.4 1 0.2 2 2 1 2 0.002 0.07 Fracture 0.1 0.15 1 1 2 2 1 2 5 1


Dimensions (ft) Length 109 ft

Width 109 ft

Thickness 109 ft

No. Grid Blocks 19 x 19 x 19 Grid Dimensions NX 10 NY 10 NZ 10 Matrix permeability 0.2 md Fracture permeability 5000 md Matrix porosity 0.07 Fracture porosity 0.02 Gas injection rate 10 MSCF/D Shape Factor 0.12 Fracture aperture 1 ft Fracture Spacing Length 10 ft Width 10 ft Thickness 10 ft Oil viscosity 2.5 cp Gas viscosity 0.0175cp Oil density 56.0 lb/ft3 Gas density 0.0615 lb/ft3 Sor in matrix 0.4 Sor in fracture 0.15

Table 4.5: Reservoir data for discrete fracture model simulation

75

Fig. 4.1 Typical fractured reservoir model.

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Gas saturation

Rel

ativ

e pe

rmea

bilit

y

KrgKro

Fig. 4.2: Relative permeability curve for matrix system contain gas and oil

76

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Gas saturation

Rel

ativ

e pe

rmea

bilit

y

KrgfKrof

Fig. 4.3: Relative permeability curve for fracture system contain gas-oil

Fig. 4.4: Matrix oil saturation profile before gas injection in simulation case

77

Fig. 4.5: Matrix oil saturation after 2000 days of gas injection for Case1

0

4

8

12

16

0 200 400 600 800 1000 1200

Time, Days

Oil

Rat

e ST

B/D

0

0.1

0.2

0.3

0.4O

il re

cove

ry e

ffic

ienc

y

Oil Rate

Recovery

Fig. 4.6: Oil production rate and oil recovery for case 1

78

0

4

8

12

16

20

0.3 0.4 0.5 0.6 0.7 0.8

Wetting phase saturation , So

Cap

illar

y pr

essu

re in

mat

rix

Pc-matrix

Fig. 4.7: Matrix capillary pressure for gas-oil system in case 2

0

4

8

12

16

0 200 400 600 800 1000 1200

Time, Days

Oil

Rat

e ST

B/D

0

0.1

0.2

0.3

0.4

Oil

reco

very

eff

icie

ncy

Oil Rate

Recovery

Fig.4.8: Oil production rate and Oil recovery efficiency for case 2

79

Fig 4.9: Matrix oil saturation after 2000 days gas injection for Case 2

0

5

10

15

20

0 0.2 0.4 0.6 0.8 1

Wetting phase saturation , So

Pc-m

atrix

0

0.125

0.25

0.375

0.5

Pc-F

ract

ure

Pc-matrixPc-fracture

Fig. 4.10: Matrix capillary pressure for gas-oil system in Case 3

80

0

4

8

12

16

0 200 400 600 800 1000 1200

Days

Oil

Rat

e S

TB/D

0

0.125

0.25

0.375

0.5

Oil

Rec

over

y ef

ficie

ncy

Oil Rate

Recovery

Fig. 4.11: Oil production rate and oil recovery efficiency for Case 3

Fig. 4.12: Matrix oil saturation after 2000 days of gas injection for Case 3

81

0

4

8

12

16

0 200 400 600 800

Time, Days

Oil

Rat

e S

TB/D

Eclipse

CMG-Imex

Fig. 4.13: Oil production rate in ECLIPSE and IMEX for dual porosity model

Fig. 4.14: Horizontal nested subgrided matrix block in ECLIPSE (ECLIPSE Manual

2004)

82

Fig. 4.15: Schematic view of concentric subgrided matrix blocks in ECLIPSE (Sinha

2004)

0

4

8

12

16

0 100 200 300 400 500

Time, Days

Oil

Rat

e ST

B/D

Dual porosity

SubgriddedModel

Fig. 4.16: Oil production rate for subgrided model and dual porosity model in ECLIPSE

83

0

0.125

0.25

0.375

0.5

0 100 200 300 400 500

Time, Days

Oil

Rec

over

y ef

ficie

ncy

Dual porosity model

Subgridded model

Fig. 4.17: Oil Recovery Efficiency for subgrided model and dual porosity model in ECLIPSE

0

4

8

12

16

0 100 200 300 400 500

Time, Dyas

oil R

ate

STB

/D

dual porosityModel

subgriddedModel

Fig. 4.18: Oil production rate for subgrided model and dual porosity model in IMEX

84

0

500

1000

1500

2000

2500

0 100 200 300 400 500

Time, Days

Oil

Rec

over

y Ef

ficie

ncy

Dual porosityModelSubgriddedModel

Fig. 4.19: Oil recovery efficiency for subgrided model and dual porosity model in ECLIPSE

0

1000

2000

3000

4000

5000

6000

0 100 200 300 400 500 600 700 800

Time, Days

Oil

prod

uctio

n ra

te,

STB

/D

Eclipse-Oil RateGem-Oil Rate

Fig. 4.20: Oil production rate comparison between ECLIPSE and GEM

85

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 100 200 300 400 500 600 700 800

Time, Days

Nor

mal

ized

trac

er C

once

ntra

tion

0

1.5

3

4.5

6

7.5

9

10.5

12

Mas

s (N

2B) R

ate,

LB

/Day

Conservative tracer

Mass (N2B) rate

Fig. 4.21: Comparison of tracer test in ECLIPSE and component tracing in GEM

Fig. 4.22: Mole fraction (N2B) in fracture after 50 days

86

Fig. 4.23: Mole fraction (N2B) in matrix after 50 days

Fig. 4.24: Mole fraction of (N2B) in fracture after 200 days

87

Fig. 4.25: Mole fraction of (N2B) in matrix after 200 days

Fig. 4.26: Tracer concentration profile in fracture after 50 days in ECLIPSE

88

Fig. 4.27: Tracer concentration profile in matrix after 50 days in ECLIPSE

Fig. 4.28: Tracer concentration profile in fracture after 200 days in ECLIPSE

89

Fig. 4.29: Tracer concentration profile in matrix after 200 days in ECLIPSE

0

4

8

12

16

0 200 400 600 800

Time, Days

Oil

Rat

e S

TB/D

Dual porosity Model

Discrete Fracture Model

Fig. 4.30: Oil Production rate in dual porosity model and discrete fracture model

90

0

0.125

0.25

0.375

0.5

0 100 200 300 400 500

Time, Days

Oil

Rec

over

y ef

ficie

ncy

Dual porosity model

Discrete fracture Model

Fig. 4.31: Oil recovery efficiency in dual porosity model and discrete fracture model

0

0.2

0.4

0.6

0.8

1

0 300 600 900 1200 1500

Time, Days

Nor

mal

ized

Tra

cer C

once

ntra

tion

Dual porosity model


Fig. 4.32: Conservative tracer response in dual porosity model and discrete fracture model.

91

0

0.2

0.4

0.6

0.8

1

0 300 600 900 1200 1500

Time, Days

Nor

mal

ized

Tra

cer C

once

ntra

tion

Dual porosity model


Fig. 4.33: Partitioning tracer response in dual porosity model and discrete fracture model.

0

4

8

12

16

0 200 400 600 800

Time, Days

Oil

Rat

e ST

B/D

Eclipse

CMG

Fig. 4.34: Oil production rate for discrete fracture model in ECLIPSE and IMEX

92

Fig. 4.35: Grid Refinement for discrete fracture model

0

4

8

12

16

0 200 400 600 800

Time, Days

Oil

Rat

e S

TB/D

Discrete Fracture Model

Discrete fracture modelrefinement

Fig. 4.36: Oil production rate for discrete fracture model and LGR

93

0

4

8

12

16

0 200 400 600 800 1000

Time, Days

Oil

Rat

e S

TB/D

Dual porosity modelDiscrete fracture modelEquivalent single porosity model

Fig. 4.37: Oil production rate comparison in dual porosity, discrete fracture and equivalent single porosity models

0

500

1000

1500

2000

0 200 400 600 800 1000

Time, Days

Oil

Rat

e S

TB/D

Dual porosity modelEquivalent single porosity modelDiscrete fracture model

Fig. 4.38: cumulative oil production rate in dual porosity model and equivalent single porosity model

94

CHAPTER 5: Application of Dimensionless Groups in Naturally

Fractured Reservoirs

5.1 Gravity Number Ng

Gravity number is the ratio of gravity force to viscous force, and it can vary

with injection rate, density difference, permeability, viscosity, length and thickness of

the reservoir. Ng is significant in determining the tendency of gravity override.

Lh

µugkρk

=N2

o2rx

g (5.1)

In fractured reservoir, by increasing gravity number, more fluid goes into the matrix

yielding more oil recovery. As shown by (Baker and Moore 1996) when Ng<0.1, the

flow regime is dominated by the viscous force, and when Ng> 10, the flow regime is

dominated by the gravity force. Therefore, there is a transition from viscous-

dominated flow to gravity-dominated flow when 0.1 <Ng<10. When a reservoir is

produced at low rate and there is a large density difference between displacing and

displaced fluids, gravity forces dominate over viscous forces; as the rate increase,

viscous force becomes stronger and cause the fluids to flow preferentially through

high permeability layers, then flow dominated by viscous force, this creates a vertical

non equilibrium situation. The gravity number gives an indication of the efficiency of

gravity forces in a displacement process.

95

Mobility ratio is another factor that the degree of gravity segregation depends on. In

fact, the effect of mobility ratio on gravity induces cross flow. At high mobility ratios,

the injected fluid has a greater tendency to by pass the oil and form a gravity tongue.

At a constant gravity number, mobility ratio provides gravity segregation of fluids

(Baker & Moore 1996).

5.1.1 Effect of Ng on oil recovery in dual porosity model:

Table 5.1 gives primary values of the parameters for the gravity number and

effective length to thickness ratio calculation in the following simulation with the

dual porosity model and the discrete fracture model. Figure 5.1 shows the effect of

gravity number on oil recovery efficiency and the summarized data for the figure is

given in Table 5.2.

As expected, with increasing gravity number, oil recovery efficiency increases. In

Case 1 viscous force dominated fluid flow through the reservoir because Ng<0.1, and

for Ng>1.0 at constant LR greater than 10.0 flow is dominated by gravity forces.

Note that Case 2 and Case 3 have large differences with respect to Case 1 that viscous

force drive fluid through reservoir.

5.1.2 Effect of gravity number (Ng) on oil recovery in discrete fracture model

The effect of gravity number on oil recovery in discrete fracture model is

shown in Fig. 5.2 and Table 5.3 gives the summarized data for Fig. 5.2.

96

In discrete fracture model with increasing gravity number, oil recovery will increase

and there is significant difference between Case 1 and Case 2 since flow is dominated

by gravity forces for Ng>1.0 and can be seen for case 2 and case 3 with increasing

gravity number oil recovery does not change significantly.

5.2 Effective length to thickness ratio:

LR is important to determine tendency of gravity override and cross flow

phenomena, because it controls the displacement to vertical equilibrium.

x

zL k

kHL

=R (5.2)

VE is a condition where the sum of all the driving forces in the direction

perpendicular to direction of bulk flow is zero and this condition happens by flow in

reservoir having large aspect ratio (Lake, 1989).

Based on numerical solution (Zapata, 1981) and analytical solution (Zapata and Lake,

1987) vertical equilibrium phenomena would happen for LR >10.

Actually, VE is a condition that causes maximum cross flow. LR depends on

reservoir length, reservoir thickness, horizontal and vertical permeability.

5.2.1 Effect of LR on oil recovery in dual porosity model

Effect of LR on oil recovery for dual porosity model is shown in Fig. 5.3 and

summarized data are given in Table 5.4.

97

The oil recovery efficiency will increase by increasing LR until it reaches vertical

equilibrium. As shown in Fig. 5.3 for dual porosity model vertical equilibrium occurs

at LR =40 because after that by increasing LR value to LR =80 the oil recovery

efficiency remains constant. Reservoir dimension has a significant effect on LR and

for large values of LR the reservoir behaves like a 1D reservoir. Real reservoirs have

a large length with respect to thickness.

5.2.2 Effect of LR on oil recovery in discrete fracture model

Figure 5.4 shows the effect of LR values on oil recovery in discrete fracture

model. As expected, recovery efficiency would increase by increasing effective

length to thickness ratio. Table 5.5 gives summarized data for Fig. 5.4.

Oil recovery efficiency will increase by increasing LR until it reaches vertical

equilibrium and for the discrete fracture model in gas-oil system, it happened at

LR =20 since for LR >20 oil recovery efficiency remain constant.

5.3 Dimensionless parameters for fractured reservoir tracer transport

In porous media, local equilibrium achieved for the tracer between solution

phase and carrying phases in most cases simply by controlling the flow rate of the

mobile carrying phase. In fracture media, however, low flow rate will increase matrix

diffusion effect (Deed 1999).

98

5.3.1 Mean residence time in fractured reservoir

The mean residence time is the ratio of first moment over zero moments.

Mean residence time for fractured reservoir is the sum of mean residence time of

tracer in fracture and matrix (Deeds 1999).

Mean residence time of conservative or partitioning tracer in fractured reservoir

calculated simply from theoretical mean residence time (Deeds 1999).

fRrateflowVolumetric

volumeFlowablet = (5.3)

fL

fg

Lgf R

ux

RubS2

xbS2t == (5.4)

fg

Lmm R

ubS2x)b2L(

tφ−

= , (5.5)

where retardation factor is

g

nnf S

SK1R += (5.6)

For the matrix, it is assumed there is no oil saturation in the matrix and for

conservative tracer fR =1 therefore the equation for the matrix mean residence time

can be written as

−

φφ

=

−

φ= 11

Sux1

b2L

Suxt

fg

mL

g

mLm (5.7)

The above equations can be expressed as dimensionless form by dividing tou

x L :

99

fDf Rt = (5.8)

−

φφ

= 11S

tfg

mDm (5.9)

−

φφ

+=+= 11S

Rtttfg

mfDmDfD (5.10)

5.3.2 Sensitivity analysis in dimensionless parameters of tracer transport

Retardation factor fR , Peclet number peN , Damkohler number DaN , matrix

number MaN , fracture porosity fφ andgf

mSφ

φ, are dimensionless parameters, which

may affect tracer transport. They are stated below:

g

nnf S

SK1R += (5.6)

L

Lpe D

uxN = (5.11)

u

xSK

KN L

NfN

awDa φ

= (5.12)

u

xLD4

N L2m

Ma = (5.13)

fφ

gf

mSφ

φ, (5.14)

100

where

L= fracture spacing

=mD Diffusion coefficient for the tracer in the matrix

=LD Dispersion coefficient

=φm Matrix porosity

fφ = Fracture porosity

=Lx Location of the effluent sampling point

u= Velocity

Matrix number MaN , fracture porosity fφ andgf

mSφ

φ, are special parameters for

fracture tracer transport (Deeds 1999).

5.3.2.1 Matrix number: MaN

MaN is the ratio of two characteristic time: the fracture mean residence time,

ux L , and the diffusion to the center of matrix characteristic time ,

m

2

D4L .

The parameter MaN accounts for the effect of matrix diffusion on the overall

transport. Table 5.6 shows the base case simulation data and Table 5.7 is the

summarized dimensionless parameter values for different MaN values. Figure 5.5

shows the effect of MaN on calculated mean residence time, for output tracer

101

response. Note that calculated mean residence time is given for conservative tracer,

fR =1 to eliminate effect of partitioning. When MaN =0.02 there is a very little

interaction between the tracer and matrix, therefore its mean residence time compared

to Equation (5.10) is actually fracture mean residence time.

For MaN =20.0 tracer reaches to equilibrium with the surrounding matrix, and its

mean residence time compare to Equation (5.10), which verifies our claim. For

MaN =0.8 there is some interaction between tracer and surrounding matrix but they

have not reached to equilibrium. Its mean residence time is between fracture mean

residence time and total mean residence time.

Figures 5.6 and 5.7 show tracer response curves in linear and semi-log scale. Note

that long tail of MaN =0.8 corresponds to its non-equilibrium condition.

5.4.2.2 Fracture porosity: fφ

The effect of fracture porosity on tracer response has been determined by

varying fracture porosity while keeping Sgf

mφφ constant. Table 5.8 shows

summarized parameter values for different fφ , Parameters have been calculated for

two sets of MaN values. Figures 5.8 and 5.9 show tracer response curves for

different fφ at constant MaN =0.02 and Figs. 5.10 and 5.11 shows tracer response

curves at MaN =20.0.

102

Different values of fφ have very little effect on tracer response curve while keeping

Sgf

mφφ constant since fφ is controlled by mφ in this condition.

5.4.2.3 Sensitivity analysis ofSgf

mφφ

This parameter consists of two characteristic parameters in fracture tracer

transport: First, the relative volume of matrix to fracture mφ / fφ , fφ specifies the

fraction of bulk volume occupied by fracture and mφ specifies fraction of the matrix

volume occupied by pore matrix volume, and 1/ gS parameter describe effect of

mobile fluid saturation on the tracer response.

Sensitivity of Sgf

mφφ can be analyzed in two sets of Matrix number:

Low Matrix number: MaN

At low matrix number MaN , equilibrium between matrix and fracture does not

occur. As we studied in the above section for very low matrix number like MaN =0.02,

there is very little interaction between tracer and matrix so its mean residence time

always will be around one fracture pore volume, regardless of the other parameter

values. Figure 5.12 shows an increase in Sgf

mφφ for MaN =0.02 has very little effect on

103

mean residence time even for large value ofSgf

mφφ . However, its trend describes that

an increase in Sgf

mφφ will result in an increase in mean residence time for the case that

there is a little interaction between the tracer and the matrix. Figures 5.13 and 5.14

show the tracer response for different Sgf

mφφ for MaN =0.02. The first three rows of

Table 5.9 summarize parameter values for this case.

High Matrix number: MaN

At high matrix number MaN =20.0, the flowing tracer into fracture is in

equilibrium with matrix, therefore decrease in fracture porosity increases the relative

volume of matrix to fracture so mean residence time (in terms of fracture volume)

would increase. This behavior satisfies Equation (5.10); based on Equation (5.10) an

increase in matrix volume or decrease in gas saturation increases the mean residence

time. Consequently, at high matrix number MaN , an increase in the parameter group

Sgf

mφφ will increase the mean residence time of the corresponding tracer. Figure 5.15

shows an increase in the mean residence time of the tracer for MaN =20.0 with

increasingSgf

mφφ . Figures 5.16 and 5.17 show tracer response curves for different

104

Sgf

mφφ for MaN =20. The linear decline at the end of each tracer response indicates

equilibrium for the tracer between fracture and matrix. The last three rows of Table

5.9 summarize the data parameters for this case.

5.5 Conclusion

In the discrete fracture model, vertical equilibrium for fractured reservoirs

occurred at RL>20 and in the dual porosity model this phenomena occurred at RL>40.

Ng is the ratio of the gravity force to the viscous force and in the discrete

fracture model and dual porosity model for Ng>1.0, flow through porous media is

dominated by gravity forces. The density difference is a significant factor in the

gravity override.

The matrix number strongly controls tracer transport in fractured reservoirs

between the matrix and the fracture. In addition, it is the ratio of the theoretical

fracture mean residence time to the diffusion time into the center of the matrix block.

For gas tracer tests, tracer transport between the matrix and the fracture reach to the

equilibrium condition at MaN =20.

High fracture porosity, low matrix porosity and low matrix number yield the

overall mean residence time approaches to the fracture mean residence time.

105

The accuracy of the oil saturation estimation in fractured reservoirs improves

if the overall mean residence time of the reservoir reaches to the sum of the matrix

and fracture mean residence times.

106

Kx= 0.2 md Kz= 0.2 md µ1 0.017 cp µ2 2.5 cp Ρo 56.65 lb/ft3 Ρg 0.0615 lb/ft3 g 9.8 m/s2

Krg 1 Kro 0.2 U 1.59E-07 ft/s Q 10000 SCF/D A 10000 ft2 H 100 ft L 100 ft

1 MSCF = 2.45 RB at 1500 psi Table 5.1: Primary parameters value for scaling group analysis

Table 5.2: Summarized data for Ng in dual porosity model

Case Lx h Ly Kz Kx u µ2 Kr2 RL Ng

Q MSCF/D

1 500 100 500 3.2 0.2 1.592E-07 0.5 0.2 20 0.02949 50 2 100 500 100 2000 0.2 1.592E-07 0.5 0.4 20 1.4747 50 3 100 100 100 8000 0.8 1.592E-07 0.5 1.0 20 14.747 50

Table 5.3: Summarized data for effect of Ng in discrete fracture model

Case Lx h Ly Kz Kx u µ2 Kr2 RL Ng

Q MSCF/D

1 500 100 500 3.2 0.2 1.596E-07 0.5 0.2 20 0.02949 50 2 100 500 100 2000 0.2 9.55E-08 0.5 0.5 20 3.07949 30 3 100 400 100 7000 1 1.99E-07 0.5 1.0 20 11.7949 50

107

Table 5.4: Summarized data for effect of LR in dual porosity model

Case Lx h Ly Kz Kx u µ2 Kr2 RL Ng Q MSF/D

1 500 100 500 0.008 0.2 1.592E-07 0.5 0.2 1 0.02949 50 2 500 100 500 0.2 0.2 1.592E-07 0.5 0.2 5 0.02949 50 3 500 100 500 0.8 0.2 1.592E-07 0.5 0.2 10 0.02949 50 4 500 100 500 3.2 0.2 1.592E-07 0.5 0.2 20 0.02949 50 5 500 100 500 12.8 0.2 1.592E-07 0.5 0.2 40 0.02949 50 6 500 100 500 51.2 0.2 1.592E-07 0.5 0.2 80 0.02949 50

Table 5.5: Summarized data for effect of LR in discrete fracture model

Table 5.6: Base case data for simulation of dimensionless parameter in fractured reservoir

Case Lx h Ly Kz Kx u µ2 Kr2 RL N

Q MSCF/D

1 500 100 500 0.008 0.2 1.596E-07 0.5 0.2 1 0.02949 50 2 500 100 500 0.2 0.2 1.596E-07 0.5 0.2 5 0.02949 50 3 500 100 500 0.8 0.2 1.596E-07 0.5 0.2 10 0.02949 50 4 500 100 500 3.2 0.2 1.596E-07 0.5 0.2 20 0.02949 50 5 500 100 500 12.8 0.2 3.186E-07 0.5 0.4 40 0.02949 100 6 500 100 500 51.2 0.2 3.186E-07 0.5 0.4 80 0.02949 100

Injection Rate 10 MSCF/D Reservoir Length 100 ft Reservoir Thickness 100 ft Reservoir Width 100 ft Velocity 0.013757 ft/s Diffusion Coefficient 0.000076 ft2/D Dispersion Coefficient 0.00005 ft2/D Fracture Spacing, L 10 ft

mφ 0.07

fφ 0.02 K1 0.0 K2 1.5 K3 2.5 Location of the effluent sampling point Lx 90 ft

108

MaN fφ Sgf

mφφ peN fR

0.02 0.02 5.83 41270 1.0 0.8 0.02 5.83 41270 1.0 20.0 0.02 5.83 41270 1.0

Table 5.7: Summarized parameters values for different MaN

MaN fφ Sgf

mφφ peN fR

0.02 0.002 5.83 41270 1.0 0.02 0.02 5.83 41270 1.0 0.02 0.2 5.83 41270 1.0 20.0 0.002 5.83 41270 1.0 20.0 0.02 5.83 41270 1.0 20.0 0.2 5.83 41270 1.0

Table 5.8: Summarized parameter values for case of different fφ

MaN fφ Sgf

mφφ peN fR

0.02 0.02 5.83 41270 1.0 0.02 0.02 29 41270 1.0 0.02 0.02 58.33 41270 1.0 20.0 0.02 5.83 41270 1.0 20.0 0.02 11 41270 1.0 20.0 0.02 29 41270 1.0

Table 5.9: Summarized parameter values for case of different Sgf

mφφ

109

0

0.1

0.2

0.3

0.4

0.5

0.6

0 500 1000 1500 2000

time, Dyas

Rec

over

y ef

ficie

ncy

Ng=0.02949

Ng=3.0

Ng=11.80

Fig. 5.1: Effect of Ng on oil Recovery efficiency at LR =20 for dual porosity model

0

0.2

0.4

0.6

0.8

0 400 800 1200 1600 2000

Time, Dyas

Oil

Rec

over

y

Ng=0.02949

Ng=1.4747

Ng=14.747

Fig. 5.2: Effect of Ng on oil recovery efficiency at LR =10 for discrete fracture model

110

0

0.1

0.2

0.3

0.4

0 400 800 1200 1600 2000

Time, Dyas

Oil

Rec

over

y

R=1

Rl=5

Rl=10

RL=20

RL=40

R=80

Fig. 5.3: Effect of LR on oil recovery at constant Ng=0.02949 for dual porosity model

0

0.1

0.2

0.3

0.4

0.5

0.6

0 400 800 1200 1600 2000

Time, Days

Oil

Rec

over

y

RL=1

Rl=5

RL=10

RL=20

Rl=40

Rl=80

Fig. 5.4: Effect of LR on oil recovery efficiency at Ng=0.02949 and for discrete fracture model

111

0

1

2

3

4

5

6

7

0 5 10 15 20 25

Fracture pore volume (tDf )

Mea

n re

side

nce

time

(tDf ) Nma=0.002

Nma=0.8

Nma=20

Fig. 5.5: Effect of MaN on Mean residence time of tracer response

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25


Nor

mal

ized

trac

er c

once

ntra

tion

Nma=0.002

Nma=0.8

Nma=20

Fig. 5.6: Effect of MaN on conservative tracer response

112

0.001

0.01

0.1

1

0 5 10 15 20 25


Nor

mal

ized

trac

er c

once

ntra

tion

Nma=0.002

Nma=0.8

Nma=20

Fig. 5.7: Effect of MaN on conservative tracer response in Semi-Logscale

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25

Fracture pore volume ( tDf )

Nor

mal

ized

trac

er c

once

ntra

tion

Fracture poro 0.002

fracture poro 0.02

fracture poro 0.2

Fig. 5.8: Effect of fφ on output tracer response at MaN =0.02

113

0.001

0.01

0.1

1

0 5 10 15 20 25


Nor

mal

ized

trac

er c

once

ntra

tion

Fracture poro 0.002

fracture poro 0.02

fracture poro 0.2

Fig. 5.9: Effect of fφ on output tracer response at MaN =0.02 (Semi-Log scale)

0

0.1

0.2

0.3

0.4

0 5 10 15 20 25

Fracture pore volume tDf

Nor

mal

ized

trac

er c

once

ntra

tion

Fracture porosity 0.002

fracture porosity 0.02


Fig. 5.10: Effect of fφ on output tracer response at MaN =20.0

114

0.001

0.01

0.1

1

0 5 10 15 20 25

Fracture pore volume tDf

Nor

mal

ized

trac

er c

once

ntra

tion Fracture porosity 0.002



Fig. 5.11: Effect of fφ on output tracer response for MaN =20.0 (Semi-Log scale)

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25


Mea

n R

ersi

denc

e Ti

me

( tD

f )

5.83

29

58.33

83.5S gf

m =φφ

33.58S gf

m =φφ

29S gf

m =φφ


mφφ on mean residence time for MaN =0.02

115

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25


Nor

mal

ized

trac

er c

once

ntra

tion

5.83

29

58.33

29S gf

m =φφ

83.5S gf

m =φφ

33.58S gf

m =φφ


mφφ on tracer response curve for MaN =0.02

0.001

0.01

0.1

1

0 5 10 15 20 25


Nor

mal

ized

trac

er c

once

ntra

tion

5.83

29

58.33

29S gf

m =φφ

83.5S gf

m =φφ

33.58S gf

m =φφ


mφφ on tracer response curve for MaN =0.02 (Semi-Log scale)

116

0

4

8

12

16

0 5 10 15 20 25

Fracture pore volume inj

Nor

mal

ized

trac

er c

once

ntra

tion

5.83

11.0

29.0

11S gf

m =φ

φ

29S gf

m =φφ

83.5S gf

m =φφ


mφφ on mean residence time for MaN =20.0

0

0.04

0.08

0.12

0.16

0.2

0 5 10 15 20 25


Nor

mal

ized

trac

er c

once

ntra

tion 5.83

11.0

29.0

29S gf

m =φφ

11S gf

m =φ

φ

83.5S gf

m =φφ


mφφ on tracer response curve at MaN =20.0

117

0.001

0.01

0.1

1

0 5 10 15 20 25


Nor

mal

ized

trac

er c

once

ntra

tion

5.83

11.0

29.0

29S gf

m =φφ

11S gf

m =φ

φ

83.5S gf

m =φφ


mφφ on tracer response curve at MaN =20.0 (Semi-Log scale)

118

CHAPTER 6: Summary, Conclusions and Recommendations for

Future Work

The main objective of this research was to investigate gas tracer tests in naturally

fractured reservoirs and compare the dual porosity model and discrete fracture model

for gas tracer tests. The dual porosity model and discrete fracture model was

compared and the advantage of each model was studied.

The effect of dimensionless groups like gravity number and effective length to

thickness ratio in the dual porosity model and discrete fracture model was

investigated.

The method of moments was used to estimate average oil saturation in fractured

reservoirs for gas tracer tests. The results clearly demonstrate that the method of

moments is a simple, fast, and accurate way to estimate average oil saturation.

Sensitivity of dimensionless parameters for fracture tracer transports in the dual

porosity model was analyzed and the effect of fracture parameters in tracer transport

between the matrix and fracture was studied.

6.1 Use of gas tracers for reservoir characterization

The accuracy of oil saturation depends on the accuracy of partitioning

coefficient estimation. For gas tracers, partitioning coefficient was estimated by

119

equation of state. A gas tracer experiment was used to calibrate and test the accuracy

of gas tracer test in the ECLIPSE simulator. The same study had been performed

using the UTCOMP simulator, and the result was in good agreement with the

experiment. Results of the ECLIPSE compare to the UTCOMP had some deficiency

to simulate the same experiment.

The gas tracer test in fractured reservoirs was modeled with the dual porosity model

and the method of moments was used to estimate average oil saturation in dual

porosity media. The total tracer concentration was used to estimate average oil

saturation in mobile oil case. The results confirm that method of moments is a fast,

simple, and accurate way to estimate oil saturation; moreover, it does not need lots of

data from the reservoir under study.

6.2 Gas tracer test in naturally fractured reservoir model

The gas tracer test in naturally fracture reservoirs was modeled with the dual

porosity model and discrete fracture model. Fractured reservoirs are more

complicated to be modeled by the dual porosity model since dual porosity model has

some inaccurate assumption. The discrete fracture model has the characteristic of dual

porosity model and realistic properties of fractured reservoirs. A fractured reservoir

was simulated by the discrete fracture model with the property of dual porosity model

and the results was compared for two models. Several problems encountered while

modeling a fractured reservoir by the discrete fracture model. Large permeability

120

contrast, and large grid block size contrast, in two neighbor grid blocks pose

problems, in which affect transmissibility for fluid flow between the matrix and

fracture. Problems were eliminated by assuming large fracture aperture with low

porosity and high permeability.

Wettability in gas-oil system for fractured reservoirs affects the capillary pressure,

and the relative permeability. Property of capillary pressure in fractured reservoirs

and the effect of capillary pressure in oil recovery from the matrix in fractured

reservoirs were studied.

6.3 Dimensionless group study

Dimensionless groups are parameters, in which can give a sense of reservoir

properties for various reservoirs.

The effect of dimensionless groups in fractured reservoirs was studied by the dual

porosity and discrete fracture models. Gravity number and effective length to

thickness ratio was studied in the dual porosity model and the effect of each

parameter and their sensitivities were analyzed. The assumption of fluid flow through

porous media in the dual porosity model had some deficiency to manifests the effect

of LR perfectly since it is not sensitive to vertical/horizontal permeability ratio,

instead, the discrete fracture model can easily manifests the effect of various LR and

Ng.

121

6.4 Dimensionless group in fractured reservoir tracer transport

Tracer transport in fractured reservoirs was studied by using dimensionless

parameters. The tracer transport in fractured reservoirs is sensitive to some fracture

properties like, fracture porosity, matrix porosity, fracture spacing and some transport

properties like, diffusion coefficient, dispersion coefficient and velocity.

Properties were analyzed using some dimensionless parameters and sensitivity to

each parameter was analyzed. In gas tracer transport for Matrix number MaN > 20, the

fracture and matrix are in equilibrium condition.

6.5 Recommendations for future work

The discrete fracture model in this study was limited to a regular and a simple

fracture distribution around the matrix. It would be useful to study the complicated

fracture distributions and heterogeneous permeability, porosity, and fracture spacing

distributions in the discrete fracture model based on field data. In addition, discrete

fracture model can be modified to the assumption of the dual permeability model.

Simulations in this study were limited to a quarter of a five-spot well patterns. It

should be extended to indicate irregular well pattern.

The method of moments is a robust method for estimation of the average oil

saturation. It is recommended to use the inverse modeling to find the permeability and

the saturation distributions in naturally fractured reservoirs for gas tracer tests and

compare the results of both methods.

122

In the actual field tracer tests, tracers may have adsorption, decay ratio, dispersion

diffusion which we neglect some of their properties, in our simulations, for simplicity.

Further study should be carried out to investigate inclusion of the above, mentioned

factors in simulation studies.

123

Appendix A: Sample input files

A.1 ECLIPSE Input File for 3 phases flow of tracer test

=========================================================================== RUNSPEC =========Gas Injection in Fractured Reservoirs===================== =========================================================================== TITLE Gas Injection. DUAL POROSITY BLACKOIL 3D MODEL --------------------------------------------------------------------------- --DIMENSION: -- NX NY NZ DIMENS 10 10 20/ --The first half of the grid layers are matrix cells, the rest are fratures -- DUALPORO -- NSTACK 300 / --Phases OIL WATER GAS --Units FIELD DISPDIMS 2 4 4 / FMTOUT UNIFIN UNIFOUT -- --Dimension of the Equilibration Tables EQLDIMS 2 300 / --Full Implicit Solution FULLIMP -- TABDIMS 2 1 50 50 1 50 50 / --First #,The number of saturation tables entered using SGFN,etc.in PROPS --Second #,The number of PVT tables using PVTG,PVTO,etc in PROPS section. --Third #,The number of saturation nodes in any saturation table.

124

-- WELLDIMS -- max #well -- max # of connections per well -- 1 group, # wells in groups 100 100 1 100/ -- REGDIMS 3 3 / -- START 01 'jan' 2000 / -- --gravity drainage activated --GRAVDR --GRAVDRM --YES / --Request information required by GRAF for the run-time monitoring option MONITOR -- TRACERS -- oil water gas environ diffusion 0 0 3 0 'NODIFF' / PARTTRAC -- #.partition tracer #.K(p) #.pressure point 2 2 2/ =========================================================================== GRID =========================================================================== --- THE GEOMETRY OF THE SIMULATION GRID AND THE --- ROCK PERMEABILITIES AND POROSITIES ARE DEFINED. ---------------------------------------------------- -- THE CELL TOP DEPTHS -- ( TOPS ) ARE NEEDED ONLY IN THE TOP LAYER ( THOUGH THEY COULD BE. -- SET THROUGHOUT THE GRID -- Fracture Permeabilities are NOT multiplied by fracture porosity to yield -- a net fracture permeability. NODPPM DPGRID EQUALS 'DX ' 100 1 10 1 10 1 10/ MATRIX CELLS 'DY ' 100 1 10 1 10 1 10/ 'DZ ' 50 1 10 1 10 1 10/ 'PORO ' 0.07 1 10 1 10 1 10/ 'PERMX' 0.20 1 10 1 10 1 10/ 'PERMY' 0.20 1 10 1 10 1 10/ 'PERMZ' 0.20 1 10 1 10 1 10/ 'TOPS' 4000 1 10 1 10 1 1 / -- -------------------- FRACTURE PROPERTIES (PORE VOLUME) --Secondary Porosity=25% of Total Porosity (7%)=0.0175 --Includes Fractures, Microfractures and Vugs 'PORO ' 0.02 1 10 1 10 11 20 / FRACTURE CELLS 'PERMX' 5000.0 1 10 1 10 11 20 /

125

'PERMY' 5000.0 1 10 1 10 11 20 / 'PERMZ' 5000.0 1 10 1 10 11 20 / 'TOPS' 4000 1 10 1 10 11 11 / ---------------------------------------------- -- / SIGMA 0.36 / DZMTRX 10.00 / -- Create a initialization file w/ grid,props & region values INIT -- ============================================================================ PROPS ============================================================================ -- DEFINES THE REL. PERMEABILITIES, CAPILLARY -- PRESSURES, AND THE PVT PROPERTIES OF THE RESERVOIR FLUIDS ------------------------------------------------------------ -- KRW AND CAPILLARY PRESSURE ARE TABULATED AS -- A FUNCTION OF WATER SATURATION. STONE -- --Swat Krw Pcow SWFN 0.3000 0.0000 0.00 0.5000 0.00001 0.00 / -- For Fracture 0.15 0.0000 0.00 0.75 0.00001 0.00 / --Sgas Krg PCo-g SGFN -----------FOR MATRIX 0.20 0.0 0.0 0.225 0.025 0.03 0.250 0.06 0.46 0.275 0.11 1.25 0.30 0.18 2.35 0.35 0.35 3.47 0.40 0.56 5.45 0.450 0.78 8.40 0.500 0.95 16.63 / -- For Fracture 0.100 0.00 0.00 0.25 0.08 0.01 0.30 0.15 0.03 0.35 0.22 0.05 0.40 0.31 0.10

126

0.45 0.40 0.21 0.50 0.52 0.30 0.55 0.64 0.46 0.60 0.75 0.61 0.65 0.88 0.76 0.70 0.95 0.90 / --Soil Krow Krog SOF3 -----------FOR MATRIX 0.3000 0.000 0.000 0.3250 0.002 0.002 0.3500 0.014 0.014 0.3750 0.056 0.056 0.4000 0.080 0.080 0.4250 0.140 0.140 0.4500 0.190 0.190 0.4750 0.250 0.250 0.5000 0.300 0.300 / -- for fracture 0.1500 0.0000 0.0000 0.4000 0.3000 0.3000 0.7500 1.0000 1.0000 / -- PVT PROPERTIES OF WATER -- REF.PRESS Bw Compress. Visc Viscosidad PVTW 1500.0 1.029 3.13D-6 0.31 0 / -- --ROCK COMPRESSIBILITY ROCK 1532 4.5E-6 / MATRIX SYSTEM 1532 3.4E-5 / FRACTURE SYSTEM -- SURFACE DENSITIES OF RESERVOIR FLUIDS -- OIL WATER GAS DENSITY 56.65 62.4 0.06150 / TRACER 'TR1' 'GAS' '' / 'TR2' 'GAS' '' 'OIL' 1 / 'TR3' 'GAS' '' 'OIL' 1 / / TRACERKP 0.0001 0.7 10000 0.7 / 0.0001 1.15 10000 1.15 /

127

-- requests , flux limitting scheme to reduce numerical dispersion. TRACTVD / TRDIFTR1 7.7E-4/ TRDIFTR2 7.7E-4/ TRDIFTR3 7.7E-4/ DISPERSE 0 0.0 0.0000503 1.0 0.0000502 / 900 0.0 0.0000501 1.0 0.0000500 / / / -- PVT PROPERTIES OF DRY GAS (NO VAPOURISED OIL) -- PGAS FVFG VISCO PVDG 200.0 3.0947 0.0122 400.0 2.7715 0.0127 600.0 2.4591 0.0133 800.0 2.4589 0.0139 1000.0 2.4588 0.0145 1200.0 2.4587 0.0151 1400.0 2.4586 0.0156 1600.0 2.4585 0.0162 1800.0 2.4584 0.0168 2000.0 2.4583 0.0174 2145.0 2.3454 0.0178 2500.0 2.2476 0.0188 3000.0 2.19498 0.0203 3500.0 1.8093 0.0217 4000.0 0.7045 0.0232 5000.0 0.5589 0.0260 / -- POIL FVFO VISO Data for Undersaturated Oil PVDO 200.0 1.143 5.23 400.0 1.141 4.49 600.0 1.139 3.97 800.0 1.1372 3.58 1000.0 1.1371 3.32 1200.0 1.137 3.08 1400.0 1.1369 2.87 1600.0 1.1368 2.68 1800.0 1.1367 2.55 2000.0 1.1366 2.40 2145.0 1.1349 2.32 2500.0 1.1316 2.40 3000.0 1.1312 2.53 3500.0 1.108 2.64 4000.0 1.103 2.77

128

5000.0 1.093 3.00 / PMAX 5000 5000 / RPTPROPS DENSITY SWFN SGFN SOF3 TRACER / ============================================================================ REGIONS ============================================================================ FIPOWG SATNUM -- SPECIFY THE SATURATION FUNCTION REGION TO WHICH IT BELONGS 1000*1 1000*2 / -- EQLNUM -- This keyword defines the Equilibration Region that belongs -- to every grid block. -- 2 fracture Region -- 1 matrix Region 1000*1 1000*2 / --Define tracer partitioning region. to use each K(p) for each tracer. TRKPFTR2 2000*1/ TRKPFTR3 2000*2/ =========================================================================== SOLUTION =========================================================================== --- DEFINES THE INITIAL STATE OF THE SOLUTION --- VARIABLES (PHASE PRESSURES, SATURATIONS AND GAS-OIL RATIOS) --------------------------------------------------------- -- -- DATUM DATUM OWC OWC GOC GOC RSVD RVVD SOLN -- DEPTH PRESS DEPTH PCOW DEPTH PCOG TABLE TABLE METH EQUIL -- -------FOR MATRIX 4000 1080 30000 0 4100 0 0 0 0 / -- -------FOR FRACTURE 4000 1080 30000 0 4100 0 0 0 0 / -- Ininitalaize tracer concentration for each grid block TBLKFTR1 2000*0.00 / TBLKFTR2

129

2000*0.00 / TBLKFTR3 2000*0.00 / -- OUTPUT CONTROLS (SWITCH ON OUTPUT OF INITIAL GRID BLOCK PRESSURES) RPTSOL POIL SGAS SOIL TBLK / RPTRST 'BASIC=3' -- keep all restarts, output every FREQth reporting period / ============================================================================ SUMMARY ============================================================================ RUNSUM EXCEL -- Requests that the run summary output, generated by the RUNSUM -- should be written in the FORMAT LOTUS 123. LOTUS FOPR FGPR ftpcTR1 ftpcTR2 FOPT FGOR FOSAT FOEWG ftpcTR3 ftptTR1 ftptTR2 ftptTR3 ftitTR2 FPR WBHP / FODEN FGDEN ============================================================================ SCHEDULE ============================================================================ -- The follow keyword with a series of mnemonics corresponds --to a solution or property vector to be written out to a file --which is readable by GRAF. RPTRST 'BASIC=1' 'TBLK' 'SGAS' 'TRACER' / RPTSCHED 'CPU' 'FIP' 'POIL' 'SOIL' 'SGAS' 'WELLS' SUMMARY=2' WELSPECS' 'TRACER' /

130

-- gas Re-Solution Rate DRSDT 0 / WELSPECS -- i j refdepth P1 G1 10 10 4100 'OIL' / I1 G1 1 1 4042 'GAS' / / COMPDAT --WELLS MUST BE COMPLETED IN THE FRACTURES -- i j k k Flag sat.tab ConnFactor Skin P1 10 10 20 20 OPEN 0 1* 0.5 / I1 1 1 12 12 OPEN 0 1* 0.5 / / -- Units (STB/day) WCONPROD P1 'OPEN' 'BHP' 8000 1* 4900 2* 950.01/ / -- Units (Mscf/day) WCONINJE I1 GAS OPEN RATE 5000 / / TUNING 0.001 5 0.05 0.15 3 0.3 0.1 1.25 0.75 / 0.1 0.001 1E-7 0.0001 10 0.01 1E-6 0.001 0.001 / 50 1 500 1 25 12 4*1E6 / TUNINGDP / NEXTSTEP / WTRACER -- Well Tracer Conc 'I1' 'TR1' 1.0 / 'I1' 'TR2' 1.0 / 'I1' 'TR3' 1.0 / / TSTEP 3*50 / WTRACER -- Well Tracer Conc 'I1' 'TR1' 0.0 / 'I1' 'TR2' 0.0 / 'I1' 'TR3' 0.0 / /

131

TSTEP 37*50 / END

132

A.2 ECLIPSE Input File for dual porosity model

======================================================================= RUNSPEC =========Gas Injection in Fractured Reservoirs================= ======================================================================= TITLE Gas Injection. DOUBLE POROSITY BLACKOIL 3D MODEL ----------------------------------------------------------------------- --DIMENSION: -- NX NY NZ DIMENS 10 10 20/ --The first half of the grid layers are matrix cells, the rest are fratures -- DUALPORO -- -- -- NSTACK 300 / --Phases OIL GAS --Units FIELD FMTOUT UNIFIN UNIFOUT -- --Dimension of the Equilibration Tables EQLDIMS 2 300 / --Full Implicit Solution FULLIMP -- TABDIMS 2 1 50 50 1 50 50 / --First #,The number of saturation tables entered using SGFN,etc.in PROPS --Second #,The number of PVT tables using PVTG,PVTO,etc in PROPS section. --Third #,The number of saturation nodes in any saturation table. -- WELLDIMS -- max #well -- max # of connections per well -- group, # wells in groups 100 100 1 100/ --

133

REGDIMS 3 3 / -- START 01 'jan' 2000 / -- --gravity drainage activated --GRAVDR --GRAVDRM --YES / --Request information required by GRAF for the run-time monitoring option MONITOR -- TRACERS -- oil water gas environ diffusion 0 0 3 0 'DIFF' / PARTTRAC -- #.partition tracer #.K(p) #.pressure point 3 3 3/ ========================================================================= GRID ========================================================================= --- THE GEOMETRY OF THE SIMULATION GRID AND THE --- ROCK PERMEABILITIES AND POROSITIES ARE DEFINED. ---------------------------------------------------- -- THE CELL TOP DEPTHS -- ( TOPS ) ARE NEEDED ONLY IN THE TOP LAYER ( THOUGH THEY COULD BE. -- SET THROUGHOUT THE GRID -- Fracture Permeabilities are NOT multiplied by fracture porosity to yield -- a net fracture permeability. NODPPM DPGRID EQUALS 'DX ' 10 1 10 1 10 1 10/ MATRIX CELLS 'DY ' 10 1 10 1 10 1 10/ 'DZ ' 10 1 10 1 10 1 10/ 'PORO ' 0.07 1 10 1 10 1 10/ 'PERMX' 0.20 1 10 1 10 1 10/ 'PERMY' 0.20 1 10 1 10 1 10/ 'PERMZ' 0.20 1 10 1 10 1 10/ 'TOPS' 4000 1 10 1 10 1 1 / -- -------------------- FRACTURE PROPERTIES (PORE VOLUME) --Secondary Porosity=25% of Total Porosity (7%)=0.0175 --Includes Fractures, Microfractures and Vugs 'PORO ' 0.02 1 10 1 10 11 20 / FRACTURE CELLS 'PERMX' 5000.0 1 10 1 10 11 20 / 'PERMY' 5000.0 1 10 1 10 11 20 / 'PERMZ' 5000.0 1 10 1 10 11 20 / 'TOPS' 4000 1 10 1 10 11 11 / ----------------------------------------------

134

-- / SIGMA 0.12 / DZMTRX 10.00 / -- -- Create a initialization file w/ grid,props & region values INIT -- ======================================================================= PROPS ======================================================================= -- DEFINES THE REL. PERMEABILITIES, CAPILLARY -- PRESSURES, AND THE PVT PROPERTIES OF THE RESERVOIR FLUIDS ------------------------------------------------------------ -- KRW AND CAPILLARY PRESSURE ARE TABULATED AS -- A FUNCTION OF WATER SATURATION. --STONE -- --Sgas Krg Krog PCo-g SGOF -----------FOR MATRIX 0.30 0.00 0.20 0.00 0.35 0.03 0.14 0.52 0.40 0.11 0.09 2.08 0.45 0.25 0.05 4.68 0.50 0.44 0.02 8.31 0.55 0.69 0.01 12.99 0.60 1.00 0.00 18.71/ --Sgas Krg Krog PCo-g -----------FOR Fracture 0.10 0.00 1.00 0.00 0.15 0.00 0.87 0.00 0.20 0.02 0.75 0.02 0.25 0.04 0.64 0.04 0.30 0.07 0.54 0.06 0.35 0.11 0.44 0.10 0.40 0.16 0.36 0.14 0.45 0.22 0.28 0.19 0.50 0.28 0.22 0.25 0.55 0.36 0.16 0.32 0.60 0.44 0.11 0.40 0.65 0.54 0.07 0.48 0.70 0.64 0.04 0.57 0.75 0.75 0.02 0.67 0.80 0.87 0.00 0.78 0.85 1.00 0.00 0.89/ /

135

-- PVT PROPERTIES OF WATER -- REF.PRESS Bw Compress. Visc Viscosidad --PVTW -- 1500.0 1.029 3.13D-6 0.31 0 / -- --ROCK COMPRESSIBILITY ROCK 1532 4.5E-6 / MATRIX SYSTEM 1532 3.4E-5 / FRACTURE SYSTEM -- SURFACE DENSITIES OF RESERVOIR FLUIDS -- OIL WATER GAS DENSITY 56.65 62.4 0.06150 / -- Pgas Bgas VISgas TRACER 'TR1' 'GAS' '' 'OIL' 1 / 'TR2' 'GAS' '' 'OIL' 1 / 'TR3' 'GAS' '' 'OIL' 1 / / TRACERKP 0.0001 0 10000 0/ 0.0001 0.7 10000 0.7 / 0.0001 1.15 10000 1.15 / -- requests , flux limitting scheme to reduce numerical dispersion. TRACTVD / -- PVT PROPERTIES OF DRY GAS (NO VAPOURISED OIL) -- PGAS FVFG VISCO PVDG 200.0 3.0947 0.0122 400.0 2.7715 0.0127 600.0 2.4591 0.0133 800.0 2.4589 0.0139 1000.0 2.4588 0.0145 1200.0 2.4587 0.0151 1400.0 2.4586 0.0156 1600.0 2.4585 0.0162 1800.0 2.4584 0.0168 2000.0 2.4583 0.0174 2145.0 2.3454 0.0178 2500.0 2.2476 0.0188 3000.0 2.19498 0.0203 3500.0 2.1093 0.0217 4000.0 1.97045 0.0232 5000.0 1.5589 0.0260 /

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-- -- POIL FVFO VISO /Data for Undersaturated Oil PVDO 200 1.143 1.046 400 1.141 0.898 600 1.139 0.794 800 1.1372 0.716 1000 1.1371 0.664 1200 1.137 0.616 1400 1.1369 0.574 1600 1.1368 0.536 1800 1.1367 0.51 2000 1.1366 0.48 2145 1.1349 0.464 2500 1.1316 0.48 3000 1.1312 0.506 3500 1.108 0.528 4000 1.103 0.554 5000 1.093 0.6 / / PMAX 5000 5000 / -- ACTIVATED FOR SOF3, SWFN, SGFN, PVTW, PVDG, DENSITY AND ROCK KEYWORDS RPTPROPS DENSITY SWFN SGFN SOF3 TRACER / -- =========================================================================== REGIONS =========================================================================== -- In order to quantify the oil in place in the Oil Zone FIPOWG SATNUM -- SPECIFY THE SATURATION FUNCTION REGION TO WHICH IT BELONGS 1000*1 1000*2 / EQLNUM -- This keyword defines the Equilibration Region that belongs -- to every grid block. -- 2 fracture Region -- 1 matrix Region 1000*1 1000*2 / --Define tracer partitioning region. to use each K(p) for each tracer. TRKPFTR1 2000*1/ TRKPFTR2

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2000*2/ TRKPFTR3 2000*3/ ========================================================================= SOLUTION ========================================================================= --- DEFINES THE INITIAL STATE OF THE SOLUTION --- VARIABLES (PHASE PRESSURES, SATURATIONS AND GAS-OIL RATIOS) --------------------------------------------------------- -- -- DATUM DATUM OWC OWC GOC GOC RSVD RVVD SOLN -- DEPTH PRESS DEPTH PCOW DEPTH PCOG TABLE TABLE METH EQUIL -- -------FOR MATRIX 4000 1080 30000 0 4040 0 0 0 0 / -- -------FOR FRACTURE 4000 1080 30000 0 4040 0 0 0 0 / -- Ininitalaize tracer concentration for each grid block TBLKFTR1 2000*0.00 / TBLKFTR2 2000*0.00 / TBLKFTR3 2000*0.00 / -- OUTPUT CONTROLS (SWITCH ON OUTPUT OF INITIAL GRID BLOCK PRESSURES) RPTSOL POIL SGAS SOIL TBLK / RPTRST 'BASIC=3' -- keep all restarts, output every FREQth reporting period / ======================================================================== SUMMARY ======================================================================== RUNSUM EXCEL -- Requests that the run summary output, generated by the RUNSUM LOTUS FOPR FGPR ftpcTR1 ftpcTR2 FOPT FGOR

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FOEIG FOEWG ftpcTR3 ftptTR1 ftptTR2 ftptTR3 ftitTR2 / FPR WBHP / WOPR / WGPR / WTCTR1 / WTPCTR1 / WTPCTR2 / WTPTTR2 / WTPCTR3 / FODEN FGDEN --BFLLOO --BFLOG --BTCNFTR1 --BTCNFTR2 --BTCNSTR2 ======================================================================== SCHEDULE ======================================================================== RPTRST 'BASIC=1' 'TBLK' 'SGAS' 'TRACER' / -- RPTSCHED 'CPU' 'FIP' 'POIL' 'SOIL' 'SGAS' 'WELLS' SUMMARY=2' WELSPECS' 'TRACER' / -- -- gas Re-Solution Rate DRSDT 0 / WELSPECS -- i j refdepth P1 G1 10 10 4100 'OIL' / I1 G1 1 1 4042 'GAS' / / -- COMPDAT

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--WELLS MUST BE COMPLETED IN THE FRACTURES -- i j k k Flag sat.tab ConnFactor Skin P1 10 10 20 20 OPEN 0 1* 0.5 / I1 1 1 13 14 OPEN 0 1* 0.5 / / -- Units (STB/day) WCONPROD P1 'OPEN' 'BHP' 15 1* 9.90 2* 950.01/ / -- Units (Mscf/day) WCONINJE I1 GAS OPEN RATE 10 / / TUNING 0.001 5 0.05 0.15 3 0.3 0.1 1.25 0.75 / 0.1 0.001 1E-7 0.0001 10 0.01 1E-6 0.001 0.001 / 50 1 500 1 25 12 4*1E6 / TUNINGDP / NEXTSTEP / WTRACER -- Well Tracer Conc 'I1' 'TR1' 1.0 / 'I1' 'TR2' 1.0 / 'I1' 'TR3' 1.0 / / TSTEP 3*50 / WTRACER -- Well Tracer Conc 'I1' 'TR1' 0.0 / 'I1' 'TR2' 0.0 / 'I1' 'TR3' 0.0 / / TSTEP 37*50 / END

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A.3 ECLIPSE Input File for Discrete fracture model

================================================================= RUNSPEC =========Gas Injection in Fractured Reservoirs=========== ================================================================= TITLE Gas Injection. DOUBLE POROSITY BLACKOIL 3D MODEL -------------------------------------------------------------- -------------------------------------------------------------- --DIMENSION: -- NX NY NZ DIMENS 19 19 19/ NSTACK 250 / --Phases OIL GAS --Units FIELD FMTIN FMTOUT UNIFIN UNIFOUT --Dimension of the Equilibration Tables EQLDIMS --#Reg,#nodes in any press table 2 300 / --Full Implicit Solution FULLIMP TABDIMS 2 1 50 50 1 50 50 / --First#,The number of saturation tables entered using SGFN,etc.in PROPS --Second#,The number of PVT tables using PVTG,PVTO,etc in PROPS section. --Third#,The number of saturation nodes in any saturation table. -- WELLDIMS -- max #well -- max # of connections per well -- group, # wells in groups 100 100 1 100/ -- REGDIMS 3 3 / /

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START 01 'JAN' 2000 / --Request information required by GRAF for the run-time monitoring option MONITOR MEMORY / TRACERS -- oil water gas environ diffusion 0 0 3 0 'DIFF' / PARTTRAC -- #.partition tracer #.K(p) #.pressure point 3 3 3/ =================================================================== GRID =================================================================== -- Fracture Permeabilities are NOT multiplied by fracture porosity to yield -- a net fracture permeability. NODPPM / OLDTRAN / DX 6859*10 / DY 6859*10 / DZ 6859*10 / TOPS 361*4000/ PORO 6859*0.07/ permx 6859*0.2/ COPY PERMX PERMY / PERMX PERMZ / / EQUALS DY 1 1 19 2 2 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / DY 1 1 19 4 4 1 19 / permx 5000 /

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permy 5000 / permz 5000 / poro 0.08 / DY 1 1 19 6 6 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / DY 1 1 19 8 8 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / DY 1 1 19 10 10 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / DY 1 1 19 12 12 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / DY 1 1 19 14 14 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / DY 1 1 19 16 16 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / DY 1 1 19 18 18 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dz 1 1 19 1 19 2 2 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dz 1 1 19 1 19 4 4 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dz 1 1 19 1 19 6 6 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 /

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dz 1 1 19 1 19 8 8 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dz 1 1 19 1 19 10 10 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dz 1 1 19 1 19 12 12 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dz 1 1 19 1 19 14 14 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dz 1 1 19 1 19 16 16 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dz 1 1 19 1 19 18 18 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dx 1 2 2 1 19 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dx 1 4 4 1 19 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dx 1 6 6 1 19 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dx 1 8 8 1 19 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dx 1 10 10 1 19 1 19 / permx 5000 / permy 5000 /

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permz 5000 / poro 0.08 / dx 1 12 12 1 19 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dx 1 14 14 1 19 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dx 1 16 16 1 19 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dx 1 18 18 1 19 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / / -- Create a initialization file w/ grid,props & region values INIT -- =================================================================== PROPS =================================================================== -- DEFINES THE REL. PERMEABILITIES, CAPILLARY -- PRESSURES, AND THE PVT PROPERTIES OF THE RESERVOIR FLUIDS SGOF -----------FOR MATRIX 0.30 0.00 0.20 0.00 0.35 0.03 0.14 0.52 0.40 0.11 0.09 2.08 0.45 0.25 0.05 4.68 0.50 0.44 0.02 8.31 0.55 0.69 0.01 12.99 0.60 1.00 0.00 18.71/ --Sgas Krg Krog PCo-g -----------FOR Fracture 0.10 0.00 1.00 0.00 0.15 0.00 0.87 0.00 0.20 0.02 0.75 0.02 0.25 0.04 0.64 0.04 0.30 0.07 0.54 0.06 0.35 0.11 0.44 0.10 0.40 0.16 0.36 0.14 0.45 0.22 0.28 0.19 0.50 0.28 0.22 0.25 0.55 0.36 0.16 0.32 0.60 0.44 0.11 0.40

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0.65 0.54 0.07 0.48 0.70 0.64 0.04 0.57 0.75 0.75 0.02 0.67 0.80 0.87 0.00 0.78 0.85 1.00 0.00 0.89/ / FILLEPS / / -- PVT PROPERTIES OF WATER -- REF.PRESS Bw Compress. Visc Viscosidad --PVTW -- 1500.0 1.029 3.13D-6 0.31 0 / --ROCK COMPRESSIBILITY ROCK 1532 4.5E-6 / MATRIX SYSTEM 1532 3.4E-5 / FRACTURE SYSTEM -- SURFACE DENSITIES OF RESERVOIR FLUIDS -- OIL WATER GAS DENSITY 56.65 62.4 0.06150 / -- Pgas Bgas VISgas TRACER 'TR1' 'GAS' '' 'OIL' 1 / 'TR2' 'GAS' '' 'OIL' 1 / 'TR3' 'GAS' '' 'OIL' 1 / / TRACERKP 0.0001 0 10000 0/ 0.0001 0.7 10000 0.7 / 0.0001 1.15 10000 1.15 / -- requests , flux limitting scheme to reduce numerical dispersion. TRACTVD / -- PVT PROPERTIES OF DRY GAS (NO VAPOURISED OIL) -- PGAS FVFG VISCO PVDG 200.0 3.0947 0.0122 400.0 2.7715 0.0127 600.0 2.4591 0.0133 800.0 2.4589 0.0139 1000.0 2.4588 0.0145 1200.0 2.4587 0.0151

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1400.0 2.4586 0.0156 1600.0 2.4585 0.0162 1800.0 2.4584 0.0168 2000.0 2.4583 0.0174 2145.0 2.454 0.0178 2500.0 2.4476 0.0188 3000.0 1.9498 0.0203 3500.0 1.8093 0.0217 4000.0 1.7045 0.0232 5000.0 1.5589 0.0260 / -- -- POIL FVFO VISO /Data for Undersaturated Oil PVDO 200 1.143 1.046 400 1.141 0.898 600 1.139 0.794 800 1.1372 0.716 1000 1.1371 0.664 1200 1.137 0.616 1400 1.1369 0.574 1600 1.1368 0.536 1800 1.1367 0.51 2000 1.1366 0.48 2145 1.1349 0.464 2500 1.1316 0.48 3000 1.1312 0.506 3500 1.108 0.528 4000 1.103 0.554 5000 1.093 0.6 / / PMAX 5000 5000 / -- ACTIVATED FOR SOF3, SWFN, SGFN, PVTW, PVDG, DENSITY AND ROCK KEYWORDS RPTPROPS DENSITY SWFN SGFN SOF3 TRACER / ==================================================================== REGIONS ==================================================================== -- In order to quantify the oil in place in the Oil Zone FIPOWG SATNUM -- SPECIFY THE SATURATION FUNCTION REGION TO WHICH IT BELONGS 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1

147

19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2

148

1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2

149

1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1

150

19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 / EQLNUM -- SPECIFY THE SATURATION FUNCTION REGION TO WHICH IT BELONGS 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2

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1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1

152

19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2

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1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2

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1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 / --Define tracer partitioning region. to use each K(p) for each tracer. TRKPFTR1 6859*1/ TRKPFTR2 6859*2/ TRKPFTR3 6859*3/ =================================================================== SOLUTION =================================================================== --- DEFINES THE INITIAL STATE OF THE SOLUTION --- VARIABLES (PHASE PRESSURES, SATURATIONS AND GAS-OIL RATIOS) --------------------------------------------------------- -- DATUM DATUM OWC OWC GOC GOC RSVD RVVD SOLN -- DEPTH PRESS DEPTH PCOW DEPTH PCOG TABLE TABLE METH EQUIL -- -------FOR MATRIX 4000 1080 30000 0 4043 0 0 0 0 / -------FOR FRACTURE 4000 1080 30000 0 4043 0 0 0 0 / -- Ininitalaize tracer concentration for each grid block TBLKFTR1 6859*0.00 /

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TBLKFTR2 6859*0.00 / TBLKFTR3 6859*0.00 / -- OUTPUT CONTROLS (SWITCH ON OUTPUT OF INITIAL GRID BLOCK PRESSURES) RPTSOL POIL SGAS SOIL DENO TBLK / RPTRST 'BASIC=1' -- keep all restarts, output every FREQth reporting period -- 'FREQ=20' / -- =================================================================== SUMMARY =================================================================== RUNSUM EXCEL -- Requests that the run summary output, generated by the RUNSUM LOTUS FOPR FGPR ftpcTR1 ftpcTR2 FOPT FGOR FOEIG FOEWG ftpcTR3 ftptTR1 ftptTR2 ftptTR3 ftitTR2 FPR WBHP / WOPR / WGPR / WTCTR1 / WTPCTR1 / WTPCTR2 / WTPTTR2 / WTPCTR3 / FODEN FGDEN

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=================================================================== SCHEDULE =================================================================== RPTRST 'BASIC=1' 'TBLK' 'SGAS' 'TRACER' / -- RPTSCHED 'CPU=1' 'FIP' 'POIL' 'SOIL' 'SGAS' 'WELLS' SUMMARY=2' WELSPECS' 'TRACER' / -- -- gas Re-Solution Rate DRSDT 0 / / WELSPECS P1 G1 19 19 4100 GAS / I1 G1 1 1 4044 OIL / / -- COMPDAT P1 19 19 18 19 OPEN 0 1* 0.5/ I1 1 1 6 7 OPEN 0 1* 0.5 / / -- Units (STB/day) WCONPROD P1 'OPEN' 'BHP' 15 1* 9.70 2* 950.01/ / -- Units (Mscf/day) WCONINJE I1 GAS OPEN RATE 10 / / TUNING 0.05 5 0.1 0.15 3 0.3 0.1 1.25 0.75 / 0.1 0.001 1E-7 0.0001 10 0.01 1E-6 0.001 0.001 / 35 1 250 1 25 12 4*1E6 / TUNINGDP / NEXTSTEP / WTRACER -- Well Tracer Conc 'I1' 'TR1' 1.0 / 'I1' 'TR2' 1.0 / 'I1' 'TR3' 1.0 /

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/ TSTEP 3*50 / WTRACER -- Well Tracer Conc 'I1' 'TR1' 0.0 / 'I1' 'TR2' 0.0 / 'I1' 'TR3' 0.0 / / TSTEP 37*50/ END

158

A.4 CMG-IMEX Input File for dual porosity model

**--------------------------------------------------------------------** ** GMcan001.DAT: Dual Porosity Model ** **--------------------------------------------------------------------** **--------------------------------------------------------------------** ** ** ** FILE: GMcant001.DAT ** ** ** ** MODEL: Fracture Gas Tracer Test ** ** DUAL POROSITY ** ** FIELD UNITS 3 COMPONENT FLUID ** ** ** **--------------------------------------------------------------------** ** ** ** ** **--------------------------------------------------------------------** ** CONTACT CMG at (403)531-1300 or [email protected] ** **--------------------------------------------------------------------** ************************************************************************ ** I/O Control Section ************************************************************************ *RESULTS *SIMULATOR *IMEX *TITLE1 ' GMcant001.DAT ' *TITLE2 ' Dual porosity ' *TITLE3 ' FRACTURED RESERVOIR' *INUNIT *FIELD *WPRN *WELL 1 **write well result everey 10 time changes *WPRN *GRID 1 *WRST *TIME **write restart file **DIM *MDIMPL 100 **DIM *MDICLU 200000 *OUTPRN *WELL *ALL *OUTPRN *RES *ALL **OUTPRN *TABLES *NONE *OUTPRN *GRID *SO SG PRES *WSRF *WELL *TIME **how frequency written to simulation result *WSRF *GRID *TIME **DIARY *CHANGES **IDENTIFY WHAT INFORMATION IS WRITTEN TO THE RESULT FILE *OUTSRF *WELL *OUTSRF *GRID *SG SO PRES

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*OUTSRF *RES *ALL ********************************************************************* ** Reservoir Description Section ********************************************************************* *GRID *cart 10 10 10 *KDIR *DOWN *DI *CON 10.0 *DJ *CON 10.0 *DK *CON 10.0 *DUALPOR **SUBDOMAIN **MINC 4 *SHAPE *GK *TRANSFER 3 **type of matrix-fracture model treat to phsaes *DIFRAC *CON 10 *DJFRAC *CON 10 *DKFRAC *CON 10 *DEPTH 1 1 1 4000.00 ** Depth to center of first block, in bottom layer. *POR *FRACTURE *CON 0.02 *POR *MATRIX *CON 0.070 *CPOR *FRACTURE 3.4E-5 *PRPOR *FRACTURE 1532 *CPOR *MATRIX 4.5E-6 *PRPOR *MATRIX 1532 *PERMI *FRACTURE *CON 5000 *PERMJ *FRACTURE *CON 5000 *PERMK *FRACTURE *CON 5000 *PERMI *MATRIX *CON 0.2 *PERMJ *MATRIX *CON 0.2 *PERMK *MATRIX *CON 0.2 ************************************************************************ ** FLUID PROPERTIES ************************************************************************ *MODEL *BLACKOIL *PVT *BG ** p rs bo Bg viso visg 500 100.000 1.137 0.002458 3.30 0.0145

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2500 300.01 1.338 0.00145 2.40 0.0188 8000.0 1000.1 1.400 0.00043 2.00 0.0400 *DENSITY *OIL 52.6 *DENSITY *GAS 0.0615 *DENSITY *WATER 62.4 *CO 0.000E *CVO 0.0 *BWI 1.029 *CW 3.31E-6 *REFPW 1500 *VWI 0.5 *CVW 0.0 ******************************************************************** ** ROCK/FLUID PROPERTIES ******************************************************************** *ROCKFLUID **SORG *MATRIX *CON 0.4 **SORG *FRACTURE *CON 0.15 *RPT 1 *SWT **SNORM KRW NKRWO NPCWOD 0.00 0.000 1.0000 0.01 1.00 0.0010 0.0000 0.0 *SGT **SL KRG KROG PCGOD 0.30 0.00 0.20 0.00 0.35 0.03 0.14 0.52 0.40 0.11 0.09 2.08 0.45 0.25 0.05 4.68 0.50 0.44 0.02 8.31 0.55 0.69 0.01 12.99 0.60 1.00 0.00 18.71 *RPT 2 *SWT **SNORM KRW NKRWO NPCWOD 0.00 0.000 1.000 0.01 1.00 0.001 0.00 0.0 *SGT **SNORM KRG KROG PCGOD 0.10 0.00 1.00 0.00 0.15 0.00 0.87 0.00 0.20 0.02 0.75 0.02 0.25 0.04 0.64 0.04 0.30 0.07 0.54 0.06 0.35 0.11 0.44 0.10 0.40 0.16 0.36 0.14 0.45 0.22 0.28 0.19 0.50 0.28 0.22 0.25

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0.55 0.36 0.16 0.32 0.60 0.44 0.11 0.40 0.65 0.54 0.07 0.48 0.70 0.64 0.04 0.57 0.75 0.75 0.02 0.67 0.80 0.87 0.00 0.78 0.85 1.00 0.00 0.89 *RTYPE *MATRIX *CON 1 *RTYPE *FRACTURE *CON 2 ******************************************************************* ** INITIAL CONDITIONS ******************************************************************* *INITIAL *VERTICAL *BLOCK_CENTER *WATER_OIL_GAS **VERTICAL *OFF **PRES *MATRIX *CON 4000. **PRES *FRACTURE *CON 4000.0 **SO *MATRIX *CON .75 **SO *FRACTURE *CON 1.0 *PB *MATRIX *CON 300 *PB *FRACTURE *CON 300 *REFDEPTH 4000 *REFPRES 1080 *DWOC 30000. ** WOC out of system *DGOC 4035. ** GOC at the middle **CDEPTH 6500.0 ** In initialization all single phase blocks ** will be identified as oil-filled ********************************************************************* ** NUMERICAL CONTROL ********************************************************************* *NUMERICAL ** Simulator uses default timestep size control based ** on number of Newtonian iterations *DTMAX 5.0 *DTMIN 0.00001 *ITERMAX 100 *NORM *SATUR 0.05

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**SOLVER *PARASOL **PPATTERN 2 ******************************************************************** ** WELL DATA ******************************************************************** *RUN *DATE 2000 1 1 *DTWELL 0.00001 ** the firs time step *AIMSET *FRACTURE *CON 1 *AIMSET *MATRIX *CON 1 **WELLINIT *ITER *WELL 1 'INJ' *INJECTOR 1 *INCOMP *GAS *OPERATE *MAX *STG 10000.0 *CONT *GEOMETRY *K 0.5 0.25 1.0 0.0 *PERF *GEO 1 ** if jf kf wi 1 1 4:4 1.0 *OPEN *WELL 2 'PRO1' *PRODUCER 2 ** Define the type of well 1. *OPERATE *MAX *STO 15.0 *CONT *OPERATE *MIN *BHP 950.0 *CONT *GEOMETRY *K 0.5 0.25 1.0 0.0 *PERF *GEO 2 ** if jf kf wi 10 10 10:10 1.0 *OPEN *TIME 0.01 *TIME 0.1 *TIME 1 *TIME 10 *TIME 20 *TIME 30 *TIME 40 *TIME 50 *TIME 60 *TIME 70 *TIME 80 *TIME 90 *TIME 100 *TIME 120

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*TIME 130 *TIME 140 *TIME 150 *TIME 160 *TIME 170 *TIME 180 *TIME 190 *TIME 200 *TIME 210 *TIME 220 *TIME 230 *TIME 240 *TIME 250 *TIME 300 *TIME 350 *TIME 400 *TIME 450 *TIME 500 *TIME 550 *TIME 600 *TIME 650 *TIME 700 *TIME 750 *TIME 800 *TIME 850 *TIME 900 *TIME 950 *TIME 1000 *TIME 1050 *TIME 1100 *TIME 1150 *TIME 1200 *TIME 1250 *TIME 1300 *TIME 1350 *TIME 1400 *TIME 1450 *TIME 1500 *TIME 1550 *TIME 1600 *TIME 1650 *TIME 1700 *TIME 1750 *TIME 1800 *TIME 1850 *TIME 1900 *TIME 1950 *TIME 2000 *STOP

164

A.5 CMG-IMEX Input File for Discrete fracture model

**--------------------------------------------------------------------** ** GMcan001.DAT: Dual Porosity Model ** **--------------------------------------------------------------------** **--------------------------------------------------------------------** ** ** ** FILE: GMcant001.DAT ** ** ** ** MODEL: Fracture Gas Tracer Test ** ** DUAL POROSITY ** ** FIELD UNITS 3 COMPONENT FLUID ** ** ** **--------------------------------------------------------------------** ** ** ** ** **--------------------------------------------------------------------** ** CONTACT CMG at (403)531-1300 or [email protected] ** **--------------------------------------------------------------------** ************************************************************************ ** I/O Control Section ************************************************************************ *RESULTS *SIMULATOR *IMEX *TITLE1 ' GMcant002.DAT ' *TITLE2 ' Discrete fracture ' *TITLE3 ' FRACTURED RESERVOIR' *INUNIT *FIELD *WPRN *WELL 1 **write well result everey 10 time changes *WPRN *GRID 1 *WRST *TIME **write restart file **DIM *MDIMPL 100 *DIM *MDICLU 1200000 *OUTPRN *WELL *ALL *OUTPRN *RES *ALL **OUTPRN *TABLES *NONE *OUTPRN *GRID *SO SG PRES *WSRF *WELL *TIME **how frequency written to simulation result *WSRF *GRID *TIME **DIARY *CHANGES **IDENTIFY WHAT INFORMATION IS WRITTEN TO THE RESULT FILE *OUTSRF *WELL *OUTSRF *GRID *SG SO PRES

165

*OUTSRF *RES *ALL ******************************************************************************** ** Reservoir Description Section ******************************************************************************** *GRID *cart 19 19 19 *KDIR *DOWN *DI *IVAR 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 *DJ *JVAR 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 *DK *KVAR 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 **DUALPOR **SUBDOMAIN **MINC 4 **SHAPE *GK *TRANSFER 3 **type of matrix-fracture model treat to phsaes *DEPTH 1 1 1 4000.00 ** Depth to center of first block, in bottom layer. *POR 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 361*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07

166

19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 361*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 361*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 361*0.08

167

0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 361*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 361*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07

168

19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 361*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 361*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 361*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08

169

0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 *CPOR 4.5E-6 *PRPOR 1532 *PERMI 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 361*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2

170

361*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 361*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 361*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000

171

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******************************************************************************** ** FLUID PROPERTIES ******************************************************************************** *MODEL *BLACKOIL *PVT *BG ** p rs bo Eg viso visg 500 100.000 1.137 0.002458 3.30 0.0145 2500 300.01 1.338 0.00145 2.40 0.0188 8000.0 1000.1 1.400 0.00043 2.00 0.0400 *DENSITY *OIL 52.6 *DENSITY *GAS 0.0615 *DENSITY *WATER 62.4 *CO 0.000E *CVO 0.0 *BWI 1.029 *CW 3.31E-6 *REFPW 1500 *VWI 0.5 *CVW 0.0 ******************************************************************************** ** ROCK/FLUID PROPERTIES ******************************************************************************** *ROCKFLUID **SORG *MATRIX *CON 0.4 **SORG *FRACTURE *CON 0.15 *RPT 1 **NTENA 0.178 NTENN 0.30 (1-2) *SWT **SNORM KRW NKRWO NPCWOD 0.00 0.000 1.0000 0.01 1.00 0.0010 0.0000 0.0 *SGT **SL KRG KROG PCGOD 0.30 0.00 0.20 0.00 0.35 0.03 0.14 0.52 0.40 0.11 0.09 2.08 0.45 0.25 0.05 4.68 0.50 0.44 0.02 8.31 0.55 0.69 0.01 12.99 0.60 1.00 0.00 18.71 *RPT 2 *SWT **SNORM KRW NKRWO NPCWOD 0.00 0.000 1.000 0.01 1.00 0.001 0.00 0.0

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*SGT **SNORM KRG KROG PCGOD 0.10 0.00 1.00 0.00 0.15 0.00 0.87 0.00 0.20 0.02 0.75 0.02 0.25 0.04 0.64 0.04 0.30 0.07 0.54 0.06 0.35 0.11 0.44 0.10 0.40 0.16 0.36 0.14 0.45 0.22 0.28 0.19 0.50 0.28 0.22 0.25 0.55 0.36 0.16 0.32 0.60 0.44 0.11 0.40 0.65 0.54 0.07 0.48 0.70 0.64 0.04 0.57 0.75 0.75 0.02 0.67 0.80 0.87 0.00 0.78 0.85 1.00 0.00 0.89 *RTYPE *ALL 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1

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19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2

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1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1

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19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1

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******************************************************************************** ** INITIAL CONDITIONS ******************************************************************************** *INITIAL *VERTICAL *BLOCK_CENTER *WATER_OIL_GAS *PB *MATRIX *CON 300 *PB *FRACTURE *CON 300 *REFDEPTH 4000 *REFPRES 1080 *DWOC 30000. ** WOC out of system *DGOC 4038. ** GOC at the middle **CDEPTH 6500.0 ** In initialization all single phase blocks ** will be identified as oil-filled ******************************************************************************** ** NUMERICAL CONTROL ******************************************************************************** *NUMERICAL ** Simulator uses default timestep size control based ** on number of Newtonian iterations *DTMAX 0.1 *DTMIN 0.0000001 *ITERMAX 100 *NORM *SATUR 0.05 **SOLVER *PARASOL **PPATTERN 2 ******************************************************************************** ** WELL DATA ******************************************************************************** *RUN *DATE 2000 1 1 *DTWELL 0.000001 ** the firs time step *AIMSET *FRACTURE *CON 1 *AIMSET *MATRIX *CON 1

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**WELLINIT *ITER *WELL 1 'INJ' *INJECTOR 1 *INCOMP *GAS *OPERATE *MAX *STG 10000.0 *CONT *GEOMETRY *K 0.5 0.25 1.0 0.0 *PERF *GEO 1 ** if jf kf wi 1 1 6:7 1.0 *OPEN *WELL 2 'PRO1' *PRODUCER 2 ** Define the type of well 1. *OPERATE *MAX *STO 15.0 *CONT *OPERATE *MAX *STG 9900.0 *CONT *OPERATE *MIN *BHP 950.0 *CONT *GEOMETRY *K 0.5 0.25 1.0 0.0 *PERFRG *GEO 2 ** if jf kf wi 19 19 18:19 1.0 *OPEN *TIME 0.01 *TIME 0.1 *TIME 1 *TIME 10 *TIME 20 *TIME 30 *TIME 40 *TIME 50 *TIME 60 *TIME 70 *TIME 80 *TIME 90 *TIME 100 *TIME 120 *TIME 130 *TIME 140 *TIME 150 *TIME 160 *TIME 170 *TIME 180 *TIME 190 *TIME 200 *TIME 210 *TIME 220 *TIME 230 *TIME 240 *TIME 250 *TIME 300 *TIME 350 *TIME 400 *TIME 450 *TIME 500

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*TIME 550 *TIME 600 *TIME 650 *TIME 700 *TIME 750 *TIME 800 *TIME 850 *TIME 900 *TIME 950 *TIME 1000 *TIME 1050 *TIME 1100 *TIME 1150 *TIME 1200 *TIME 1250 *TIME 1300 *TIME 1350 *TIME 1400 *TIME 1450 *TIME 1500 *TIME 1550 *TIME 1600 *TIME 1650 *TIME 1700 *TIME 1750 *TIME 1800 *TIME 1850 *TIME 1900 *TIME 1950 *TIME 2000 *STOP

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A.6 CMG-GEM Input File for component tracking as tracer in Dual porosity

media

**--------------------------------------------------------------------** ** GMcan003.DAT: Compositional Dual Porosity Model ** **--------------------------------------------------------------------** **--------------------------------------------------------------------** ** ** ** FILE: GMcant003.DAT ** ** ** ** MODEL: Cantarell GAs tracer Test ** ** DUAL POROSITY ** ** FIELD UNITS 3 COMPONENT FLUID ** ** ** **--------------------------------------------------------------------** ** ** ** ** **--------------------------------------------------------------------** ** CONTACT CMG at (403)531-1300 or [email protected] ** **--------------------------------------------------------------------** ************************************************************************ ** I/O Control Section ************************************************************************ *RESULTS *SIMULATOR *GEM *TITLE1 ' GMcant003.DAT ' *TITLE2 ' Dual porosity ' *TITLE3 ' FRACTURED RESERVOIR' *INUNIT *FIELD *WPRN *WELL 1 **write well result everey 10 time changes *WPRN *GRID 1 *WRST *TIME **write restart file DIM *MDIMPL 100 DIM *MDICLU 200000 *OUTPRN *WELL *ALL *OUTPRN *RES *ALL **OUTPRN *TABLES *NONE *OUTPRN *GRID *SO SG Z 'N2A' Z 'N2B' X 'N2A' X 'N2B' Y 'N2A' Y 'N2B' *WSRF *WELL *TIME **how frequency written to simulation result *WSRF *GRID *TIME *DIARY *CHANGES **IDENTIFY WHAT INFORMATION IS WRITTEN TO THE RESULT FILE *OUTSRF *WELL *ZWEL 'N2A' 'PRO1' *ZWEL 'N2B' 'PRO1' *XWEL 'N2A' 'PRO1'

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*XWEL 'N2B' 'PRO1' *YWEL 'N2A' 'PRO1' *YWEL 'N2B' 'PRO1' *OUTSRF *GRID *SG SO PRES Z 'N2A' Z 'N2B' X 'N2A' X 'N2B' X 'N2B' Y 'N2A' Y 'N2B' *OUTSRF *RES *ALL *SUMMARY ************************************************************************** ** Reservoir Description Section ************************************************************************** *GRID *cart 10 10 10 *KDIR *DOWN *DUALPOR *DI *CON 100.0 *DJ *CON 100.0 *DK *CON 50.0 **SUBDOMAIN 3 **MINC 4 *SHAPE *GK *TRANSFER 3 **type of matrix-fracture model treat to phsaes *DIFRAC *CON 5 *DJFRAC *CON 5 *DKFRAC *CON 10 *DEPTH 1 1 1 4000.00 ** Depth to center of first block, in bottom layer. *POR *FRACTURE *CON 0.02 *POR *MATRIX *CON 0.070 *CPOR *FRACTURE 0.0E-6 *PRPOR *FRACTURE 4000.0 *DCPOR *FRACTURE 0.0 *CPOR *MATRIX 0.0E-6 *PRPOR *MATRIX 4000.0 *DCPOR *MATRIX 0.0 *PERMI *FRACTURE *CON 5000 *PERMJ *FRACTURE *CON 5000 *PERMK *FRACTURE *CON 5000 *PERMI *MATRIX *CON 0.2

183

*PERMJ *MATRIX *CON 0.2 *PERMK *MATRIX *CON 0.2 **************************************************************************** ** FLUID PROPERTIES **************************************************************************** *MODEL *PR *NC 7 7 *COMPNAME 'N2A' 'N2B' 'C1H2' 'C2C3' 'C4C5' 'C6P1' 'C7P2' *PCRIT 33.470 33.470 45.4 45.5 35.33 29.32 15 *TCRIT 126.11 126.11 190 331 441 507 788.5 *MW 28.010 28.01 16 36 64.7 86.18 323.8 *PCHOR 41.000 41.00 77 120.4 221.2 421.4 1196.75 *AC 0.0400 0.04 0.08 0.12 0.213 0.296 0.59 *ZCRIT 0.30 0.30 0.30 0.3 0.3 0.3 0.31 *HCFLAG 0 0 0 0 0 0 0 *OMEGA 0.45723 0.45723 0.45723 0.45723 0.457236 0.457236 0.457236 *OMEGB 0.077796 0.077796 0.077796 0.077796 0.077796 0.077796 0.077796 **BIN 0.1 ** 0.1877040 0.0027222 **OMEGAS 0.67000002 0.58495221 0.64649426 ** 0.45723552 0.45723552 **OMEGBS 0.03600000 0.11000001 0.08132145 ** 0.07779610 0.07779610 **BINS 0.0027123 ** 0.2907547 0.0027222 *PHASEID *DEN *TRES 121.0 *PSAT 300. *CW 3.0E-6 ** /PSI *DENW 63.648 ** LB/CU-FT *VISW 0.22 ***************************************************************************** ** ROCK/FLUID PROPERTIES ***************************************************************************** *ROCKFLUID *SIGMA *SORG *MATRIX *CON 0.4 *SORG *FRACTURE *CON 0.15 *RPT 1 **NTENA 0.178 NTENN 0.30 (1-2) *SWT **SNORM KRW NKRWO NPCWOD 0.00 0.000 0.2000 0 1.00 0.0010 0.0000 0.0

184

*SGT **SL KRG KROG PCGOD 0.00 0.00 0.20 0.00 0.05 0.01 0.17 0.0 0.10 0.03 0.14 0.00 0.15 0.06 0.11 0.0 0.20 0.11 0.09 0.0 0.25 0.17 0.07 0.0 0.30 0.25 0.05 0.0 0.35 0.34 0.03 0.0 0.40 0.44 0.02 0.0 0.45 0.56 0.01 0.0 0.50 0.69 0.01 0.0 0.55 0.84 0.001 0.0 0.60 1.00 0.00 0.0 *RPT 2 *SWT **SNORM KRW NKRWO NPCWOD 0.00 0.000 1.000 0.0 1.00 0.001 0.00 0.0 *SGT **SNORM KRG KROG PCGOD 0.00 0.00 1.00 0.00 0.05 0.00 0.89 0.00 0.10 0.01 0.78 0.00 0.15 0.03 0.68 0.00 0.20 0.06 0.58 0.00 0.25 0.09 0.50 0.00 0.30 0.12 0.42 0.00 0.35 0.17 0.35 0.00 0.40 0.22 0.28 0.00 0.45 0.28 0.22 0.0 0.50 0.35 0.17 0.0 0.55 0.42 0.12 0.0 0.60 0.50 0.09 0.00 0.65 0.58 0.06 0.0 0.70 0.68 0.03 0.00 0.75 0.78 0.01 0.00 0.80 0.89 0.001 0.00 0.85 1.00 0.00 0.00 *RTYPE *MATRIX *CON 1 *RTYPE *FRACTURE *CON 2 ****************************************************************************** ** INITIAL CONDITIONS ******************************************************************************

185

*INITIAL *VERTICAL *BLOCK_CENTER *WATER_OIL_GAS *REFDEPTH 4000 *REFPRES 1080 *DWOC 30000. ** WOC out of system *DGOC 4175. ** GOC at the middle *ZOIL 0.000 0.00 0.1747 0.1415 0.0970 0.037 0.5498 *ZGAS 0.0 0.000 0.90 0.1 0 0 0 **CDEPTH 6500.0 ** In initialization all single phase blocks ** will be identified as oil-filled ******************************************************************************* ** NUMERICAL CONTROL ******************************************************************************* *NUMERICAL ** Simulator uses default timestep size control based ** on number of Newtonian iterations *DTMAX 1.00 *DTMIN 0.0001 *ITERMAX 50 *NEWTONCYC 25 **PRECC 0.0005 **NORM *SATUR 0.05 *MAXCHANGE *GMOLAR 0.80 **SOLVER *PARASOL **PPATTERN 2 ******************************************************************************* ** WELL DATA ******************************************************************************* *RUN *DATE 2000 1 1 *DTWELL 0.001 ** the firs time step *AIMSET *FRACTURE *CON 1

186

*AIMSET *MATRIX *CON 1 **WELLINIT *ITER *WELL 1 'INJ' *INJECTOR 1 *INCOMP *SOLVENT 0.95 0.050 0.0 0 0 0 0 *OPERATE *MAX *STG 3000000.0 *CONT *GEOMETRY *K 0.5 0.64 1.0 0.0 *PERF *GEO 1 ** if jf kf wi 1 1 3:4 1.0 *OPEN *WELL 2 'PRO1' *PRODUCER 2 ** Define the type of well 1. *OPERATE *MAX *STO 5000.0 *CONT *OPERATE *MAX *STG 3000000.0 *CONT *OPERATE *MIN *BHP 800.0 *CONT *GEOMETRY *K 0.5 0.64 1.0 0.0 *PERF *GEO 2 ** if jf kf wi 10 10 10:10 1.0 *OPEN *TIME 0.01 *TIME 0.1 *TIME 1 *TIME 5 *TIME 10 *TIME 15 *TIME 20 *TIME 25 *TIME 30 *TIME 35 *TIME 40 *TIME 45 *TIME 50 *TIME 55 *TIME 60 *TIME 65 *TIME 70 *TIME 75 *TIME 80 *TIME 85 *TIME 90 *TIME 95 *TIME 100 *TIME 105 *TIME 110 *TIME 115 *TIME 120 *TIME 125 *TIME 130 *TIME 135

187

*TIME 140 *TIME 145 *TIME 150 *WELL 1 'INJ' *INJECTOR 1 *INCOMP *SOLVENT 1.0 0.0 0.0 0 0 0 0 *OPERATE *MAX *STG 5000000.0 *CONT *GEOMETRY *K 0.5 0.64 1.0 0.0 *PERF *GEO 1 ** if jf kf wi 1 1 3:4 1.0 *OPEN *TIME 155 *TIME 160 *TIME 165 *TIME 170 *TIME 175 *TIME 180 *TIME 185 *TIME 190 *TIME 195 *TIME 200 *TIME 205 *TIME 210 *TIME 215 *TIME 220 *TIME 225 *TIME 230 *TIME 235 *TIME 240 *TIME 245 *TIME 250 *TIME 255 *TIME 260 *TIME 265 *TIME 270 *TIME 275 *TIME 280 *TIME 285 *TIME 290 *TIME 295 *TIME 300 *TIME 310 *TIME 320 *TIME 330 *TIME 340 *TIME 350 *TIME 360 *TIME 370 *TIME 380 *TIME 390 *TIME 400 *TIME 410

188

*TIME 420 *TIME 430 *TIME 440 *TIME 450 *TIME 460 *TIME 470 *TIME 480 *TIME 490 *TIME 500 *TIME 520 *TIME 540 *TIME 560 *TIME 580 *TIME 600 *TIME 620 *TIME 640 *TIME 660 *TIME 680 *TIME 700 *TIME 720 *TIME 740 *TIME 760 *TIME 780 *TIME 800 *TIME 820 *TIME 840 *TIME 860 *TIME 880 *TIME 900 *TIME 920 *TIME 940 *TIME 960 *TIME 980 *TIME 1000 *TIME 1050 *TIME 1100 *TIME 1150 *TIME 1200 *TIME 1250 *TIME 1300 *TIME 1350 *TIME 1400 *TIME 1450 *TIME 1500 *TIME 1550 *TIME 1600 *TIME 1650 *TIME 1700 *TIME 1750 *TIME 1800 *TIME 1850 *TIME 1900 *TIME 1950 *TIME 2000 *STOP

189

Nomenclature

b = Half thickness of fracture aperture

)t,x(C0 = Initial tracer concentration of the model

gIiC = Initial concentration of component i in gas

fiC = Concentration of tracer i in the fracture

fijC = Concentration of component i in phase j in the fracture

iC = Total concentration of tracer i

igC = Concentration of tracer i in the gas phase

ioC = Concentration of tracer i in the oil phase

iwC = Concentration of the tracer i in water phase

ijC = Concentration of the tracer i in phase j

iJC = Initial concentration of tracer i

itC = Total tracer concentrations for tracer i

miC = Concentration of tracer i in the matrix

mijC = Concentration of tracer i in phase j in the matrix

nC = Concentration of the conservative tracer

maxnC = Maximum concentration of the conservative

190

oIiC = Initial concentration of component i in oil

pC = Concentration of the partitioning tracer

pcjC = End point capillary pressure for phase j

maxpC = Maximum concentration of the partitioning

wIiC = Initial concentration of component i in water

je = relative permeability exponent of phase j

jf = Fractional flow of phase j

h = Reservoir thickness

fk = Fracture permeability

iK = Partition coefficient of tracer i

ijKrr

= Dispersion coefficient of component i in phase

mk = Matrix permeability

tiK = Partition coefficient of tracer i

rjk = Relative permeability of phase j

orjk = End point relative permeability of phase j

xk = Permeability in the x direction

yk = Permeability in the y direction

zk = Permeability in the z direction

191

L = Reservoir length

xL = Length of the matrix block in x direction

yL = Length of the matrix block in the y direction

zL = Length of the matrix block in the z direction

m = Mass of the tracer produced at a given producer

i0m = Zeroth temporal moment for tracer i

ig0m = Zeroth temporal moment for tracer i in gas phase

i1m = first temporal moment for tracer i

M = Total mass of the tracer injected

pcjn = capillary pressure exponent of phase j

fiNr

= Flux of tracer I in fracture

gN = Gravity number

iNr

= Flux of tracer i

cP = Capillary pressure

fP = Fracture Pressure

mP = Matrix Pressure

injq = Injection rate

oq = Oil flow rate

Q = Total injection rate

192

fiR = Retardation factor of tracer i

LR = Effective length to thickness ratio

)x(S0 = Initial slowness of the model

*S = Saturation value at zero capillary pressure

gS = Gas Saturation

gS = Average gas saturation

grS = Residual gas saturation

jS = Saturation of phase j

jrS = Residual saturation of phase j

njS = Normalized saturation of phase j

oS = Oil saturation

oS = Average oil saturation

orS = Average residual oil saturation

wS = Aqueous phase saturation

t = Time

Dt = Characteristic dimensionless time

*Dt = Characteristic dimensionless time for constant shape factor

Dt = dimensionless mean residence time

193

Dft = Dimensionless fracture mean residence time

Dmt = Dimensionless matrix mean residence time

ft = Fracture mean residence time

it = Mean residence time of tracer i

mt = Matrix mean residence time

slugt = Tracer slug time

u = Fluid velocity into the reservoir

jur = Flux of phase j

BV = Bulk volume of the reservoir

cV = Mean residence volume of the conservative tracer

iV = Mean residence volume of tracer i

pV = Mean Residence Volume of the partitioning tracer

sV = Swept pore volume

slugV = Volume of the tracer slug

ix = Mole fraction of tracer i in liquid phase

iy = Mole fraction of tracer i in gaseous phase

194

Greek Symbols

φ = Porosity

fφ = fracture porosity

mφ = matrix porosity

σ = Shape Factor

µ = Viscosity of the fluid

τ = Transit time for the partitioning tracer

fmτ = Transfer function

oρ = Oil density

gρ = gas density

195

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VITA

Gholamreza Garmeh was born in Bojnourd, Iran on Apirl 9, 1980, son of Mr. R.

Garmeh and Mrs. R. Garmeh. After completing his high school education at I.H.M.

pre-university, Bojnourd, Iran, in 1998, he entered the Petroleum University of

Technology, Ahwaz, Iran. He received the degree of Bachelor of Science in

Petroleum Engineering from P.U.T, Ahwaz, Iran, in May 2002. In September 2003,

he entered The Graduate School at The University of Texas at Austin.

Permanent Address: 12 Summar ave. 17 Shahrivar st.

Bojnourd, 94519

Iran

This thesis was typed by the author.

s3. · pdf fileiv acknowledgements i would like to thank my supervising professors dr. gary a...

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