Carbonate Reservoir Characterization: A Geologic-Engineering Analysis, Part II (Developments in Petroleum Science)

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Developments in Petroleum Science, 44

carbonate reservoir characterization: a geologic - engineering analysis, part II

DEVELOPMENTS

IN PETROLEUM

SCIENCE

Volumes 1-5, 7, 10, 11, 13-17A, 18A-B, 21, 24-26 are out of print ,

8. 9. 12. 17B.

D.W. PEACEMAN-

Fundamentals of Numerical Reservoir Simulation

L.P. D A K E - Fundamentals of Reservoir Engineering

K. M A G A R A Compaction and Fluid Migration T.D. VAN G O L F - R A C H T - Fundamentals of Fractured Reservoir Engineering E.C. DONALDSON, G.V. CHILINGARIAN and T.F. YEN (Editors) - Enhanced Oil Recovery, II. Processes and operations 19A. G.V. CHILINGARIAN, J.O. ROBERTSON Jr. and S. K U M A R - Surface Operations in Petroleum Production, I 19B. G.V. CHILINGARIAN, J.O. ROBERTSON Jr. and S. K U M A R - Surface Operations in Petroleum Production, II A.J. DIKKERS - G e o l o g y in Petroleum Production 20. E.C. DONALDSON, G.V. CHILINGARIAN and T.F. Y E N - Microbial Enhanced Oil Recovery 22. J. H A G O O R T - Fundamentals of Gas Reservoir Engineering 23. G. DA P R A T - Well Test Analysis for Naturally Fractured Reservoirs 27. E.B. NELSON (Editor) - Well Cementing 28. R . W . Z I M M E R M A N - Compressibility of Sandstones 29. G.V. CHILINGARIAN, S.J. MAZZULLO and H.H. R I E K E - Carbonate Reservoir 30. Characterization: A Geologic-Engineering Analysis, Part I E.C. DONALDSON (Editor) - Microbial Enhancement of Oil R e c o v e r y - Recent Advances 31. E. B O B O K - Fluid Mechanics for Petroleum Engineers 32. E. FJ./ER, R.M. HOLT, P. HORSRUD, A.M. RAAEN and R. RISNES - Petroleum Related 33. Rock Mechanics M.J. E C O N O M I D E S - A Practical Companion to Reservoir Stimulation 34. J.M. V E R W E I J - Hydrocarbon Migration Systems Analysis 35. L. D A K E - The Practice of Reservoir Engineering 36. W.H. SOMERTON - Thermal Properties and Temperature related Behavior of Rock/fluid Sys37. tems W.H. FERTL, R.E. CHAPMAN and R.F. HOTZ (Editors) - Studies in Abnormal Pressures 38. E. PREMUZIC and A. WOODHEAD (Editors) - Microbial Enhancement of Oil R e c o v e r y 39. Recent Advances - Proceedings of the 1992 International Conference on Microbial Enhanced Oil Recovery 40A. T. F. YEN and G.V. CHILINGARIAN (Editors) - Asphaltenes and Asphalts, 1 E.C. DONALDSON, G. CHILINGARIAN and T.F. YEN (Editors) - Subsidence due to Fluid 41. Withdrawal S.S. RAHMAN and G.V. CHILINGARIAN - Casing Design - Theory and Practice 42. B. Z E M E L - Tracers in the Oil Field 43. G.V. CHILINGARIAN, S.J. MAZULLO and H.H. R I E K E - Carbonate Reservoir Charateriza44. tion: A Geologic - Engineering Analysis, Part II

Developments in Petroleum Science, 44

carbonate reservoir characterization: a geologic, engineering analysis, part II G.V. CHILINGARIAN

School of Engineering, University of Southern California, Los Angeles, CA, U.S.A. S.J. MAZZULLO

Geology Department, Wichita State University, Wichita, KA, U.S.A. H.H. RIEKE

DGMR, P.O. Box 345, Jeddah, Saudi Arabia* Associate editors: G.C. DOMINGUEZ and E SAMANIEGO V. With contributions from: H. Cinco Ley G.M. Friedman W.E. Full S. Jalal Torabzadeh C.G.St.C. Kendall G.L. Langnes

D.E Murphy J.O. Robertson Jr. E Samaniego T.D. Van Golf-Racht N.C. Wardlaw G.L. Whittle

*presently: Petroleum Engineering Department, University of Southwestern Louisiana, Lafayette, LA, U.S.A.

ELSEVIER A m s t e r d a m - Lausanne - N e w Y o r k - Oxford - Shannon - Tokyo

1996

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

ISBN: 0-444-82103-1

9 1996 Elsevier Science B.V. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Science B.V., Copyright & Permissions Department, P.O. Box 521, 1000 AM Amsterdam, The Netherlands. Special regulations for readers in the USA - This publication has been registered with the Copyright Clearance Center Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the USA. All other copyright questions, including photocopying outside of the USA, should be referred to the copyright owner, Elsevier Science B.V. unless otherwise specified. No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. This book is printed on acid-free paper. Printed in The Netherlands

Dedication

This book is dedicated to

HIS MAJESTY THE S U L T A N A N D YANG D I - P E R T U A N OF BRUNEI D A R U S S A L A M ON THE O C C A S I O N OF HIS 50TH BIRTHDAY. HIS M A J E S T Y IS A S T A U N C H A D V O C A T E A N D S U P P O R T E R OF R E S E A R C H A N D E D U C A T I O N IN THE FIELD OF G E O S C I E N C E S

To the following outstanding geologists and petroleum engineers Geologists."

Petroleum engineers."

R. G. C. Bathurst J.D. Bredehoeft R. W. Fairbridge J. W. Harbaugh PM. Harris K. Magara J.F. Read A.M. Reid G. Rittenhouse P. O. Roehl J.F. Sarg P.A. Scholle R.F. Walters

S.M. Farouq Ali K. Aziz W.E. Brigham J. C. Calhoun Jr. J.M. Campbell Sr. J.M. Coleman R. C. Earlougher L. W. Lake Ph.E. Lamoreaux K.K. Millheim N.R. Morrow M.Muskat F. Poetmann

and to our inspirer

DR. PROE N.M. STRAKHOV

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vii

PREFACE

This second volume on carbonate reservoirs completes the two-volume treatise on this important topic to petroleum engineers and geologists. The two volumes form a complete, modem, reference to the properties and production behavior of carbonate petroleum reservoirs. This volume contains valuable glossaries to geologic and petroleum engineering terms providing exact definitions for writers and speakers. Professors will find a useful appendix devoted to questions and problems that can be used for teaching assignments as well as a guide for lecture development; in addition, there is a chapter devoted to core analysis of carbonate rocks which is ideal for laboratory instruction. Managers and Production Engineers will find a review of the latest laboratory technology for carbonate formation evaluation in the chapter on core analysis. The modem classification of carbonate rocks is presented with petroleum production performance and overall characterization using seismic and well test analyses. Separate chapters are devoted to the important naturally fractured and chalk reservoirs. Throughout the book, the emphasis is on formation evaluation and performance. The importance of carbonate reservoirs lies in the fact that they contain as much as 50% of the total petroleum reserves of the world. This is sometimes masked by the uniquely different properties and production performance characteristics of carbonate reservoirs because of their heterogeneity and the immense diversity that exists among them. This two-volume treatise brings together the wide variety of approaches to the study of carbonate reservoirs and, therefore, will fit the needs of Managers, Engineers, Geologists and Teachers. ERLE C. DONALDSON Professor Emeritus The University of Oklahoma Norman, Oklahoma

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ix

LIST OF CONTRIBUTORS

G.V. CHILINGARIAN

School of Engineering, University of Southern California, Los Angeles, CA 90089-1211, USA

H. CINCO LEY

Division de Estudios de Posgrado, Facultad de Ingenieria, UNAM, 0451 O, Mexico D.F., Mexico

G. M. F R I E D M A N

Brooklyn College & Graduate School of the City University of New York, c/o Northeastern Science Foundation, PO Box 746, Troy, NY 12171-0746, USA

W.E. FULL

Wichita State University, Dept. of Geology, 1845 Fairmount, Wichita, KS 67260, USA

S. JALAL TORABZADEH

Mechanical Engineering Department, California State University, Long Beach, CA 90840, USA

C.G.ST.C. KENDALL

Department of Geology, University of South Carolina, Columbia, South Carolina 29208, USA

G.L. LANGNES

Kemang Indah H-5, Jakarta, Selatan, Indonesia

D. R MURPHY

Petrophysical Engineering Instructor, Head Office E&P Technical Training, Shell Oil Company, P.O. Box 576, Houston, TX 770010576, U.S.A.; Formation Evaluation Lecturer, Petroleum Engineering Graduate Program, University of Houston, Houston, TX 77204-4792, USA

S.J. M A Z Z U L L O

Wichita State University, Dept. of Geology, 1845 Fairmount, Wichita, KS 67260, USA

H.H. RIEKE, III

University of Southwestern Louisiana, Petroleum Engineering Dept., USL Box 44690, Lafayette, LA 70504-4690, USA

J.O. R O B E R T S O N JR.

Earth Engineering Inc., 4244 Live Oak Street, Cudahy, CA 90201, USA

F. S A M A N I E G O V.

UNAM, Division de Estudios de Posgrado, Facultad de Ingenieria, Apdo. Postale 70-256, Mexico 20, 04510 D.F., Mexico

T.D. VAN G O L F - R A C H T

42 Rue de Ranelagh, Paris 75016, France

N.C. WARDLAW

University of Calgary, Dept. of Geology and Geophysics, 2500 University Drive, Calgary, Alta T2N 1N4, Canada

G.L. WHITTLE

Department of Geology, University of South Carolina, Columbia, South Carolina 29208, USA

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xi

CONTENTS

Preface List o f Contributors C H A P T E R 1. I N T R O D U C T I O N ..................................................................................................... G.V. Chilingarian, H.H. Rieke and S.J. Mazzullo ........................................................................ O v e r v i e w .......................................................................................................................................... Fluid flow relationships .................................................................................................................... I m p o r t a n c e o f fractures .............................................................................................................. S a m p l e p r o b l e m s ......................................................................................................................... H y d r o c a r b o n recovery ................................................................................................................ Reservoirs in karsted carbonates ...................................................................................................... Reservoirs in chalks .......................................................................................................................... Seismic identification o f carbonates ................................................................................................. References ........................................................................................................................................ C H A P T E R 2. S E I S M I C E X P R E S S I O N OF C A R B O N A T E R E S E R V O I R S Y S T E M S .................... C.G.St.C. Kendall, W.E. Full and G.L. Whittle Introduction ...................................................................................................................................... Seismic and synthetic s e i s m o g r a m s ................................................................................................. Seismic data ................................................................................................................................ Seismic events ............................................................................................................................ L i m i t a t i o n s o f seismic m e t h o d .................................................................................................... Synthetic seismic traces ............................................................................................................. Use o f synthetic seismic for m o d e l i n g ....................................................................................... L i m i t a t i o n s o f synthetics ............................................................................................................. Carbonate play types ......................................................................................................................... C a r b o n a t e sheet reservoirs .......................................................................................................... Carbonate organic buildups ......................................................................................................... Carbonate c l i n o f o r m plays .......................................................................................................... A n o m a l o u s carbonate reservoirs ................................................................................................. R e c o g n i t i o n o f carbonate reservoirs ................................................................................................. Seismic character o f carbonate systems .......................................................................................... B a s i n and slope ............................................................................................................................ P l a t f o r m m a r g i n .......................................................................................................................... Sand shoals ................................................................................................................................. P l a t f o r m interior .......................................................................................................................... Terrestrial .................................................................................................................................... Lakes and f a n g l o m e r a t e s ............................................................................................................. S u m m a r y and c o n c l u s i o n s ............................................................................................................... R e f e r e n c e s . ....................................................................................................................................... C H A P T E R 3. C O R E A N A L Y S I S A N D I T S A P P L I C A T I O N IN R E S E R V O I R C H A R A C T E R I Z A T I O N .................................................................................................................... D . E Murphy, G.V. C h i l i n g a r i a n and S.J. Torabzadeh Introduction ...................................................................................................................................... R e s e r v o i r characterization ................................................................................................................ R e p r e s e n t a t i v e n e s s o f core data .................................................................................................

1

1 1 2 3 7 17 47 49 50 51 59 59 59 60 62 67 68 71 72 72 72 74 79 80 81 86 86 91 95 95 97 97 98 98

105 105 106 106

xii Depth alignment o f data .............................................................................................................. Coring ............................................................................................................................................... Introduction ................................................................................................................................. Conventional whole coring ......................................................................................................... Oriented whole coring ................................................................................................................ Wireline retrievable whole coring ................................................................................................ Containerized whole coring ......................................................................................................... Pressure whole coring ................................................................................................................ Sponge whole coring .................................................................................................................. Wireline sidewall coring .............................................................................................................. Core handling .................................................................................................................................... W h o l e cores ................................................................................................................................ Sidewall cores ............................................................................................................................. Core analysis ..................................................................................................................................... Introduction ................................................................................................................................. Sampling ...................................................................................................................................... Conventional (routine) core analysis ........................................................................................... Petrographic core analysis .......................................................................................................... Special considerations for core analysis o f carbonate reservoirs .................................................... Heterogeneities ............................................................................................................................ Multimineral composition ............................................................................................................ L o w porosity and low permeability ............................................................................................ Wettability .................................................................................................................................... A c c u r a c y and reproducibility ...................................................................................................... R o c k catalogs ................................................................................................................................... Introduction ................................................................................................................................. General rock properties catalogs ................................................................................................ Specific formation rock properties catalogs ............................................................................... S u m m a r y .......................................................................................................................................... A c k n o w l e d g m e n t s ............................................................................................................................ References ........................................................................................................................................ C H A P T E R 4. F O R M A T I O N EVALUATION ................................................................................... D.P. M u r p h y Introduction ...................................................................................................................................... Formation evaluation philosophy ...................................................................................................... First and foremost: understand petrophysics ............................................................................. F o r m a t i o n properties o f interest ....................................................................................................... P r i m a r y formation properties o f interest .................................................................................... Other formation properties o f interest ........................................................................................ Formation evaluation tools ................................................................................................................ Formation evaluation situations ........................................................................................................ Formation evaluation o f drilling wells ......................................................................................... F o r m a t i o n evaluation for flood process pilots ............................................................................ Production surveillance formation evaluation ............................................................................. Petrophysical models ........................................................................................................................ Determination o f formation properties o f interest ............................................................................ O v e r v i e w ..................................................................................................................................... Simultaneous determination o f porosity, pore fluid saturations, lithology c o m p o n e n t fractions, and pore fluid properties ............................................................................................. Lithology determination .................................................................................................................... L i t h o l o g y from examination and/or analyses o f rock ................................................................. L i t h o l o g y from well logs ............................................................................................................. Porosity determination ...................................................................................................................... Porosity from examination and/or analyses o f rock ................................................................... Porosity from well logs ..............................................................................................................

107 107

107 108 110 111 111 112 113 114 115 115 116 116

116 117

118 139 144 144 145 145 145 146 146 146 147 147 148 149 149 155

155 155 155 156 156 157 157 159 159 159

160 162 164 164 165 167 167 168 178 178 179

xiii Pore fluid saturation determination ................................................................................................... Saturations from examination and/or analyses of rock .............................................................. Saturations from well logs .......................................................................................................... Pore fluid property determination ..................................................................................................... Introduction ................................................................................................................................. Formation water properties ......................................................................................................... Hydrocarbon properties .............................................................................................................. Permeability determination ................................................................................................................. Permeability from examination and/or analyses of rock ............................................................ Permeability from testing ............................................................................................................ Permeability from well logs ........................................................................................................ Fracture and vug detection ......................................................................................................... Net formation thickness determination ............................................................................................ Structural and stratigraphic determination ....................................................................................... Propagation of error considerations ................................................................................................. Summary .......................................................................................................................................... Acknowledgments ............................................................................................................................ References ........................................................................................................................................

182 182 184 196 196 196 198 201 201 203 203 205 210 212 216 220 220 221

CHAPTER 5. P E R F O R M A N C E A N D CLASSIFICATION OF CARBONATE RESERVOIRS ...... H.H. Rieke III, G.V. Chilingarian and S.J. Mazzullo Introduction ...................................................................................................................................... Technical overview ........................................................................................................................... Reservoir classification schemes ...................................................................................................... Classification of reservoirs based on fluid composition ............................................................. Classification of oil reservoirs based on drive mechanism ......................................................... Classification of carbonate reservoirs based on type of pore system ........................................ Classification based on the geological nature of the carbonate reservoirs ................................. Incremental recovery technology ..................................................................................................... Implementation and control ........................................................................................................ Infill development ........................................................................................................................ Infill drilling activity .................................................................................................................... Background and field examples .................................................................................................. Slant-horizontal-drainhole wells .................................................................................................. Advanced fracturing treatments ................................................................................................. Carbonate reservoir characterization ................................................................................................ Reservoir heterogeneity models .................................................................................................. Microscopic heterogeneity: p e r m e a b i l i t y - c o n d u c t i v i t y - p o r o s i t y relationships ..................... Laboratory and field characterization of carbonate reservoirs ........................................................ Laboratory/outcrop characterization of heterogeneity ................................................................ Determination of heterogeneity in carbonate pore systems from laboratory gas-drive tests .... Some theoretical and practical aspects of carbonate reservoir performance ............................ Summary of reservoir characteristics and primary performance data, and references for selected carbonate reservoirs categorized on pore type and drive mechanism (Table) ........................... References ........................................................................................................................................

231

C H A P T E R 6. W E L L TEST ANALYSIS IN CARBONATE RESERVOIRS ..................................... F. Samaniego V. and H. Cinco Ley Introduction ...................................................................................................................................... Pressure transient behavior of reservoirs ......................................................................................... Linear flow behavior ......................................................................................................................... Radial cylindrical flow ...................................................................................................................... Spherical flow behavior .................................................................................................................... Bilinear flow behavior ....................................................................................................................... Flow diagnosis ................................................................................................................................... Pressure drawdown analysis ............................................................................................................

231 232 234 234 243 254 274 295 297 298 300 302 310 333 358 358 389 435 435 471 480 518 534 549 549 552 554 557 557 559 563 584

xiv Skin factor ........................................................................................................................................ Pressure transient analysis for gas wells .......................................................................................... Example 6-1. Pressure buildup test in naturally-fractured gas well A-1 .................................... Example 6-2. Pressure analysis for exploratory well A-1 .......................................................... Agarwal's (1980) method to account for producing-time effects in the analysis o f buildup test .. Pressure transient analysis for high-permeability reservoirs ...................................................... Example 6-3. Pressure and flow test in oil well A- 1 .................................................................. Example 6-4. Pressure drawdown and buildup test in oil well B-1 ............................................ Example 6-5. Pressure drawdown and buildup tests in oil well B-2 .......................................... Analysis o f well interference tests .................................................................................................... Example 6-6. Transmissivity and diffusivity mapping from interference test data ................................................................................................................... Determination o f the pressure-dependent characteristics o f a reservoir ......................................... Analysis of variable flow rate using superposition, convolution and deconvolution (desuperposition) .. The superposition time graph ...................................................................................................... Drawdown type curve matching ................................................................................................ A general approach to well test analysis .......................................................................................... Additional well test examples ........................................................................................................... Example 6-7. Pulse test in well pair A4-A8 ................................................................................ Example 6-8. Pressure buildup test in well South Dome IS-2 ................................................... Example 6-9. Pressure buildup test in a partially penetrating oil well ........................................ Concluding remarks .......................................................................................................................... Nomenclature .................................................................................................................................... References ........................................................................................................................................

586 591 596 598 611 615 615 621 623 631

CHAPTER 7. NATURALLY-FRACTURED CARBONATE RESERVOIRS ...................................... T.D. Van Golf-Racht Introduction ...................................................................................................................................... Specific features o f the fractured carbonate reservoir .............................................................. Fracturing vs. geological history ...................................................................................................... Geological condition of fracturing .............................................................................................. Folding vs. fracturing ................................................................................................................. Role o f stylolites and joints ......................................................................................................... Fracture evaluation ...................................................................................................................... Basic characterization of "single fracture" and o f a "group of fractures". ............................... Simplified correlation and procedures ........................................................................................ Qualitative fracture evaluation through FINT ............................................................................. Data processing of fractures ...................................................................................................... Physical properties of fractures and matrix ..................................................................................... Porosity and permeability in fractured carbonate reservoirs ...................................................... Rock compressibility in fractured limestone reservoirs ............................................................. Relative permeability and capillary pressure curves in fractured carbonate reservoirs ............. Fractured carbonate reservoir evaluation through well production data ......................................... Single porosity case (impervious matrix) ................................................................................... Basic equations describing flow in fractures .............................................................................. Coning in fractured reservoirs .................................................................................................... Fractured limestone reservoir evaluation through transient flow well data ..................................... Basic discussion o f Warren-Root method .................................................................................. Warren-Root procedure for the evaluation o f a fractured limestone reservoir .......................... Evluation o f matrix-fractures imbibition fluid exchange .................................................................. Single-block imbibition process .................................................................................................. Simplified behavior evaluation ofimbibition process .................................................................. Evaluation o f gravity drainage matrix-fracture fluid exchange .................................................. Single-block gravity-drainage process ........................................................................................ Concluding remarks .......................................................................................................................... References ........................................................................................................................................

683

634 638 641 648 649 653 659 659 660 664 673 673 676

683 684 687 689 692 696 698 698 704 708 709 710 711 719 720 727 728 732 738 740 741 747 750 752 753 762 763 769 769

XV C H A P T E R 8. C H A L K R E S E R V O I R S ............................................................................................... G.M. F r i e d m a n G e n e r a l statement ............................................................................................................................. R e s e r v o i r s in chalks .......................................................................................................................... N o r t h Sea reservoirs ................................................................................................................... N o r t h A m e r i c a n reservoirs ......................................................................................................... Epilogue ............................................................................................................................................ R e f e r e n c e s ........................................................................................................................................ C H A P T E R 9. H Y D R O C A R B O N R E S E R V O I R S IN K A R S T E D C A R B O N A T E R O C K S ................. S.J. M a z z u l l o and G.V. Chilingarian Introduction ...................................................................................................................................... Karsts and their relationship to u n c o n f o r m i t i e s ................................................................................ Karst origins ................................................................................................................................ Karsts and causative m e c h a n i s m s o f subaerial exposure .......................... ................................. Relationships to u n c o n f o r m i t i e s .... .............................................................................................. C l a s s i f i c a t i o n o f karst reservoirs ...................................................................................................... Previous classifications ............................................................................................................... P r o p o s e d classification and e x a m p l e s ......................................................................................... H y d r o c a r b o n s p r o d u c e d from karsted carbonate reservoirs ........................................................... G e o l o g i c and p e t r o p h y s i c a l characteristics o f karsted reservoirs ................................................... R e s e r v o i r systems ....................................................................................................................... R e s e r v o i r continuity .................................................................................................................... P o r o s i t y - p e r m e a b i l i t y and r e c o v e r y efficiency in karst reservoirs ............................................. Subsurface r e c o g n i t i o n o f karsted carbonates ................................................................................. Seismic and subsurface g e o l o g i c m a p p i n g prior to drilling ........................................................ Karst r e c o g n i t i o n from drilling characteristics and well data ..................................................... Conclusions ...................................................................................................................................... R e f e r e n c e s ........................................................................................................................................ Chapter 10. F A C T O R S A F F E C T I N G OIL R E C O V E R Y F R O M C A R B O N A T E R E S E R V O I R S A N D P R E D I C T I O N OF R E C O V E R Y .............................................................................................. N.C. W a r d l a w Introduction ...................................................................................................................................... P r i m a r y r e c o v e r y .............................................................................................................................. Waterflooding and residual oil .......................................................................................................... D i s p l a c e m e n t efficiency ................................................................................................................... Effects o f fluid properties and wettability on trapping ............................................................... Effects o f r o c k - p o r e properties on trapping ..................................... .......................................... Effects o f w e t t a b i l i t y on r e c o v e r y from fractured carbonates .................................................. Volumetric sweep efficiency ............................................................................................................. C o n t i n u i t y o f beds, wells spacing and position .......................................................................... Vertical sweep ............................................................................................................................. Areal sweep ................................................................................................................................. Shales and other p e r m e a b i l i t y barriers ........................................................................................ R e s e r v o i r m o d e l s for s i m u l a t i o n o f p r o d u c t i o n ................................................................................ Biases o f core m e a s u r e m e n t s ...................................................................................................... A v e r a g i n g core data to represent flow at the g r i d - b l o c k scale .................................................... The variogram, kriging and conditional simulation ..................................................................... C o m p a r i s o n o f p e r m e a b i l i t y - d e r i v e d from core and from pressure well tests .......................... Tertiary oil r e c o v e r y in C a n a d a ........................................................................................................ Miscible solvent flooding ............................................................................................................ I m m i s c i b l e gas flooding ........................................... '................................................................... Conclusions ...................................................................................................................................... R e f e r e n c e s ........................................................................................................................................

773 773 775 775 784 792 793 797 797 798 798 800 801 806 806 807 828 833 833 841 845 847 847 851 856 856

867 867 868 870 872 874 876 880 882 882 884 884 884 886 887 888 890 894 895 895 896 898 899

xvi A P P E N D I X A . G L O S S A R Y OF S E L E C T E D G E O L O G I C T E R M S ............................................... S.J. Mazzullo and G.V. Chilingarian

905

A P P E N D I X B. P E T R O L E U M E N G I N E E R I N G G L O S S A R Y .......................................................... J.O. Robertson Jr., G.V. Chilingarian and S.J. Mazzullo R e c o m m e n d e d references ................................................................................................................

921

A P P E N D I X C. F U N D A M E N T A L S OF S U R F A C E A N D C A P I L L A R Y F O R C E S ........................... G.V. Chilingarian, J.O. Robertson Jr., G.L. Langnes and S.J. M a zz ullo Introduction ...................................................................................................................................... Interfacial tension and contact angle ................................................................................................ Effect o f contact angle and interfacial tension on m o v e m e n t o f oil ................................................ Water block ....................................................................................................................................... References ........................................................................................................................................

939

A P P E N D I X D. S A M P L E Q U E S T I O N S A N D P R O B L E M S ............................................................ G.V. Chilingarian, J.O. Robertson Jr. and S.J. Mazzullo General geology ................................................................................................................................ Source rocks ..................................................................................................................................... Capillary pressure ............................................................................................................................. Permeability and porosity ................................................................................................................. Production ........................................................................................................................................ E n h a n c e d recovery ........................................................................................................................... Logging ............................................................................................................................................. Acidizing ........................................................................................................................................... Fracturing .........................................................................................................................................

951 951 951 952 952 954 955 955 956 957

A U T H O R I N D E X .............................................................................................................................

959

S U B J E C T I N D E X ............................................................................................................................

979

937

939 939 944 949 949

Chapter 1

INTRODUCTION G.V. CHILINGARIAN, H.H. RIEKE, and S.J. MAZZULLO

OVERVIEW

The approach in Part 2 of this book builds on the various geoscience and engineering methodologies and technologies presented in the first volume. Part 1 presented fundamentals of geologic and engineering concepts for characterizing and evaluating carbonate reservoirs using a wide range of scales. Carbonate rocks are not homogeneous or isotropic in their properties. Hence, porosity, fluid saturation, bed thickness, and carbonate rock types show very little uniformity throughout reservoirs. Permeability, in most cases, also is strongly anisotropic in carbonate reservoirs. Detailed reviews of the classification, depositional models, and diagenesis of carbonate rocks in Part 1 exposed the reader to a wide range of viewpoints on these subjects. Correlations among permeability, porosity, irreducible fluid saturation, specific surface area, and capillary pressure were established, and used to characterize the static nature of fluid in carbonate reservoirs. Fluid flow dynamics in oil and gas reservoirs were reviewed. Presentation of the volumetric, material balance, and performance decline methods for oil and gas reserve estimation focused on the business side of analyzing production from carbonate reservoirs. The application of computer modeling was shown to be effective in characterizing carbonate reservoirs. Practical application of acid stimulation techniques used to increase the productivity of wells in carbonate reservoirs was discussed in the final chapter of Part 1. Part 2 concentrates on state-of-the-art technologies and practices used to obtain basic information on carbonate reservoirs. There are many challenges in properly characterizing a carbonate reservoir, such as reservoir classification schemes, incremental recovery strategies, and carbonate reservoir heterogeneity. These issues are discussed in Chapter 5. Figure 1-1 is an interactive flow diagram that presents a scheme of contemporary reservoir evaluation. Worthington (1991) pointed out that the integration of the data obtained by using downhole measurements and core analysis into a physically equivalent, unified reservoir model is a process of reservoir characterization. Such technical efforts in reservoir analysis can have only beneficial results in defining the influence of heterogeneities on fluid flow in carbonate reservoirs. Closely-spaced drilling, extensive and specialized coring, advanced well logging tools, tracer tests, digital production, and pressure monitoring provide detailed information needed to perform such analyses. Weber (1986) suggested that another reason for the improved capacity to decipher the influence ofheterogeneities on reservoirs is our ability to simulate fluid flow using advanced reservoir models with the aid of supercomputers. Both static and dynamic reservoir models are linked through reservoir characterization. In order for the link to be effective, a proper understanding of fluid flow constraints in the carbonate reservoir rocks is necessary for predicting and evaluating primary, secondary, and tertiary recovery operations. Enhancement of reservoir productivity is the goal, but it has its price.

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Fig. 1-1. Reservoir-evaluation scheme emphasizing the role of downhole measurements; conforms to the progressive calibration of data at scales larger than mesoscopic of heterogeneity by higher-resolution measurements at smaller scales: VSP = vertical seismic profiles; MWD = measurement while drilling; FMS = formation microscanner. (After Worthington, 1991, Fig. 3; reprinted with permission of Academic Press, Inc.)

Information costs money and there are many independent operators and small companies that do not have large budgets with which to acquire sophisticated data using advanced technologies. The writers realize this problem and try to show, where it is appropriate, how minimum data can sometimes be "milked" for additional value. Operating on a small budget is not a reason not to use the latest reservoir management procedures and controls, because such an approach can give a company's operation a chance for maximizing recoverable reserves.

FLUID FLOW RELATIONSHIPS

Elkins (1969) pointed out the importance of a thorough geologic description of cores in establishing reservoir performance and analysis of the low-permeable, fractured (jointed) Hunton Limestone in the West Edmond Field, Oklahoma, U.S.A. Littlefield et al. (1948) successfully forecasted the oil-in-place volume in the West Edmond Field largely on the basis of oil-stained fracture porosity in cores. Oil was confined mainly to the fractures and dissolution channels, which made up about 10% (?) of the total reservoir void space. Littlefield et al. (1948) predicted that this system of fractures would result in severe channeling of naturally encroaching water or injected fluids with little or no benefit to the ultimate recovery of oil. This analysis was proved to be correct. Other engineers disagreed with Littlefield et al.'s (1948) inter-

pretations regarding fluid distribution, fracture continuity, and effect of fractures on reservoir performance. It was erroneously assumed by these engineers that the extensive production of oil at solution GOR meant that the entire reservoir was necessarily oil saturated. Subsequent deepening and coring a down-structure well indicated that a substantial part of the tight matrix did in fact contain free gas. It was discovered later that initial pressure buildup tests (see Chapter 6 in this book) were of insufficient duration, thus resulting in erroneous conclusions based on data first obtained. Overemphasis of any one method failed to account for the many complexities introduced by the internal anatomy of the Hunton reservoir rock (Felsenthal and Ferrell, 1972).

Importance offractures The writers have placed strong emphasis on the importance of fractures in carbonate reservoirs in these two volumes on reservoir characterization. It has been shown in the geological and engineering literature that fractures can constitute the most important heterogeneity affecting production. Craze (1950) cited carbonate reservoirs in Texas, U.S.A., which have low matrix permeabilities, that produce moveable oil from fractures and vugs. Also, Daniel (1954) discussed the influence of fractures on oil production from carbonate reservoirs of low matrix permeability in the Middle East. Reservoirs are not mechanically continuous owing to the presence of fractures. In this sense, the reservoir rock is a discontinuum rather than a continuum. The nature and spatial relationship of discontinuities, such as fractures, dissolution channels, and conductive stylolites that affect fluid flow in carbonate rocks are best evaluated using large-core analysis (see Chapter 3 in this book). Chapter 7 (in this book) discusses fractured carbonate reservoirs in detail. Geological conditions which create fractures and control fracture spacing in rocks include: (1) variations in lithology; (2) physical and mechanical properties of the rocks and fluids in the pores; (3) thickness of beds; (4) depth of burial; (5) orientation of the earth's stress field; (6) amount of differential stress (tectonic forces); (7) temperature at depth; (8) existing mechanical discontinuities; (9) rate of overburden loading or unloading; (10) gravitational compaction (rock or sediment volume reduction as a result of water loss during compaction); (11) anisotropy; and (12) continuum state at depth (competent versus incompetent character of the rocks).

Permeability of a fracture-matrix system One is interested in the total permeability of the fracture-matrix system rather than the permeability contributions of its various parts. The studies of Huitt (1956) and Parsons (1966) provided the following two equations for determining permeability values in a horizontal direction (kH) through an idealized fracture-matrix system (using English units): kH= k + 5.446 • 101~

(1-1)

where k is the matrix permeability (mD); w is the fracture width (in.); L is the distance between fractures; and ct is the angle of deviation of the fracture from the horizontal plane in degrees. If w and L are expressed in mm, then Eq. 1-1 becomes"

k. = km+ 8.44 x

107w3cos2(a/L).

(1-2)

Various mathematical models have been proposed to describe the velocity of a fluid in a fracture, to estimate tank oil-in-place in fractured reservoirs, to determine the fracture porosity, and to calculate average "height" of fractures (Chilingarian et al., 1992).

Fluid flow in deformable rockfractures Witherspoon et al. (1980) proposed a model analyzing fluid flow in deformable rock fractures. This study has ramifications with respect to the migration and production of subsurface fluids. The withdrawal of fluids from carbonate rocks can cause a fracture to close due to induced compaction of the reservoir. The above proposed model consists of a single-phase fluid flowing between smooth parallel plates. The pressure drop is proportional to the cube of the distance between plates (w = width or aperture of a fracture). For laminar flow (Witherspoon et al., 1980): q = 5.11 • 106 [w3Apa/lp],

(1-3)

where q is the volumetric rate of flow (bbl/D); w is the width (or aperture) of a fracture (in.); Ap is the pressure drop (psi); a is the width of the fracture face (ft); l is the length of the fracture (ft); and p is the viscosity of the fluid (cP). But natural fractures are rarely smooth and, therefore, head loss owing to friction, hLf, and is equal to:

hLf=

fI

d lV: 2g

]

(1-4)

where f is the friction factor, which is a function of the Reynolds Number, NRe, and relative roughness that is equal to the absolute roughness, e, divided by the width (height or aperture) of the fracture, w (or b) (Fig. 1-2). The Reynolds Number is equal to VdeP/p, where V is the velocity of flowing fluid (ft/sec); d is the equivalent diameter (ft); p is the mass per unit volume, i.e., specific weight, y, in lb/ft 3divided by the gravitational acceleration, g, in ft/sec/sec (= 32.2). Effective diameter, d , is equal to hydraulic radius, R h, times four (R h= area of flow/wetted perimeter). Lomiz6 (1951) and Louis (1969) studied the effect of absolute and relative roughness on flow through induced fractures, sawed surfaces and fabricated surfaces (e.g., by gluing quartz sand onto smooth plates). They found that results deviate from the classical cubic law at small fracture widths. Jones et al. (1988) studied single-phase flow through open-rough natural fractures. They found that NR~c (critical Reynolds Number where laminar flow ends) decreases with decreasing fracture width (b or w) for such fractures. Jones et al. (1988) suggested the following equations for open, rough fractures with single-phase flow: q = 5.06 x 104a[Apw3/flp] ~

(1-5)

|

--A

tL..

~ bmin

~

~

T bmax

i' e

Fig. 1-2. Simple fracture-fluid-flow model showing the length of the fracture, L; width, a; thickness, b; and the absolute roughness, e.

and k = 5.3 9 x 1051.t[wl/fA pp]O.5,

(1-6)

where k is the permeability in darcys; p is the density of the fluid (lb/ft3); and f is the friction factor, which is dimensionless. Based on experimental data, Lomiz6 (1951) developed many equations relating friction factor (f) and Reynolds Number (NRe) for both laminar and turbulent flows. He also prepared elaborate graphs relating friction factor, Reynolds Number, and relative roughness of fractures (e/b or e/w) (Fig. 1-3). Lomiz6 (1951) found that at the relative roughness (e/b) of less than 0.065, fractures behave as smooth ones (e/b = 0) and friction factor (f) is equal to: f = 6/NRe.

(1-7)

In the turbulent zone, with e/b varying from 0.04 to 0.24 and NRe < 4000-5000, friction factor is equal to" f = B/(NRe )n.

(1-8)

Coefficient B is equal to 0.056 and n can be found from Fig. 1-4 or by using the following equation: n = 0 . 1 6 3 - [0.684(e/b)] + [2.71/e765(e/b)].

(1-9)

The following example illustrates how to use the discussed equations and graphs, and the significance of the results.

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e,cm

e/b

3 4 9

0.055 0.055 0.175

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RELA TIVE ROUGHNESS, e/d Fig. 1-4. Graph showing the relation between the coefficient, n, and the relative roughness, e/b (b = d), where the coefficient B = 0.056. (Modified after Lomiz6, 1951.)

Sample problems Problem" Effect o f fractures on total permeability If w - 0.005 in., L - 1 in., a = 0 ~ and k = 1 roD, then using Eq. 1-1 kH= 6,800 mD. This example shows the overwhelming contribution which relatively small fracture can exert on total permeability.

Problem: Pressure drop in a vertical fracture Determine the pressure drop in psi in a vertical fracture (flow is in upward direction) given the following information: absolute roughness, e = 0.065 mm; fracture width (w) or height (b) = 0.68 mm; width of fracture face, a = 5 m m (a > b); length of fracture, l= 5 cm; volumetric rate of flow, q = 1 cm3/sec; specific gravity of flowing oil (sp. gr.) = 0.8; and Reynolds Number (NR= 4000) (see Fig. 1-2). Using B e m o u l i ' s Equation for flow from point 1 to point 2: p l / ) ," + V]/2g + z 1= p2/?' + V2/2g + z 2 + hlf

and

pl/)/--p2/); = Ap/y = (z 2 - Z1) "~"hlf= l + hlf, where Pl and P2 a r e pressures at points 1 and 2, respectively, in l b / f t 2 absolute; V = velocity of flowing fluid in ft/sec; z~ and z 2 = potential heads at points 1 and 2 in ft; g = gravitational acceleration, ft/sec/sec (=32.2); h~f= head loss due to friction in ft. All terms in the above equation are in ft-lb per lb of fluid flowing or in ft. q = 1 cm3/sec = 1 ( c m 3 / s e c ) x 3.531 x 10-5 (ft3/cm 3) = 3.531 x 10.5 ft3/sec A (cross-sectional area of flow) = a x b = 5 x 0.68 m m x (1.07639 • 10 -5 ft2/I/ln] 2 • 3.6597 x 10 -5 ft 2

V= q/A = 3.531 x 10-5/3.6597 x l0 -5- 0.965 ft/sec Hydraulic radius R = (flow area)/(wetted perimeter) = (a x b)/(2a + 2b) = 9.814 x 10-4 ft Equivalent diameter = d = 4R = 2ab/(a + b) - 3.9277 x 10-3 ft Inasmuch as NReiS 4000 and relative roughness, e/b = 0.065/0.68 = 0.095, one can use Eq. 1-8 (and Fig. 1-4 to determine n):

f = B/(NRe )n-- 0.056/(4000) 0.'2= 0.0207 Thus: hlf-f(l/d)(VZ/2g)

= 0.0207(0.164/3.93 x 10 -3) [(0.965)2/(2 x 32.2)] = 0.0197 ft

and

Ap = 9/(l + h~f) = [(0.8 •

62.4)(0.164 + 0.0197)]'144 = 0.062 psi

(Note the relative contribution of potential head and

hlfto Ap.)

Fracture orientation Permeabilities in carbonate rock reservoirs can be highly directional; permeabilities are often drastically different in one direction from those in another direction. This anisotropy commonly is a result of the geologic stresses imposed upon the reservoir rocks (Blanchet, 1957; Harris et al., 1960; Martin 1967; Alpay 1969; Overbey and Rough, 1971; Aguilera, 1980; Weber and Bakker, 1981; Magara, 1986; Corbett et al., 1987: Heifer and Bevan, 1990). Knowledge of this anisotropy is important in the optimum location of wells for recovery (see Chapters 5 and 10, this volume). Lineament analysis of Landsat data, airborne radar imagery, and aerial photographs have shown that lineaments observed on the surface commonly bear a striking resemblance to the orientation of major fracture directions in reservoirs in that area (Pasini and Overbey, 1969; Sabins, 1969; Partain, 1989). Fertl and Rieke (1979) used gamma ray spectral evaluation techniques to identify fractured reservoirs.

Pressureinterferencetests. Information about a specific reservoir's anisotropy can be gained during initial development of the field, if the reservoir oil is undersaturated (Felsenthal and Ferrell, 1972). Elkins and Skov (1960) investigated a reservoir's fracture orientation in the Spraberry-Driver producing area in west Texas. Although this is a sandstone reservoir production, it is a good example of the application of pressure interference test technique. They measured initial reservoir pressures in 71 wells using pressure interference tests (See Chapter 6, this volume) immediately after completion. Initial assumptions were that the reservoir is isotropic and that production resuited in circular drawdown isopotentials in the area surrounding each well. The isopotentials, however, had elliptical shapes, with the ratio of the major axis to the minor axis (a/b)proportional to the maximum/minimum permeability ratio (kax/kin). The relation between the axis and permeability ratios is: a/b = 4kax/kin.

( l-l 0)

Elkins and Skov (1960) assumed values of kax/kin and the azimuth of kax. These values were evaluated by a trial and error procedure using a computer. Seventy sets of iterations were performed to establish the "best fit" of assumed values and observed pressures using:

= Pi--P

-qluB~

E.-

4.16 fk k h

~

xy

I [(X-x~176

(1-11)

25.28(t/~oC~)

where p~ is the initial pressure in psi; p is the pressure at x,y at time t in psi; q is production rate in B/D;/.t ois oil viscosity in cP; B ~is the oil formation volume factor

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-u Fig. 1-5. Isopotential lines for k a x / k m i n - " 8. (AfterArnold et al., 1962, Fig. 2; reprintedwith permission of the Society of Petroleum Engineers.) in reservoir, bbl/STB; h is the thickness of the producing zone in ft; t is the time in days; c is total compressibility of oil, water, and rock in psi-l; ~bis fractional porosity; k is the effective permeability in the x 9 direction in darcys; ky is the effective perme. ability in the y direction in darcys; x - x ~ ~s the d~stance from producing well to pressure point in x direction in ft; andy-yo is the distance from producing well to pressure point in y direction in ft. Coordinates were rotated in each test run so that k = k and k k

. .

max

x

mln

Amold et al. (1962) presented a method for estimating reservoir anisotropy from production data using pressure buildup tests. Figure 1-5 presents a typical plot of isopotential lines for a k / k i n = 8/1 from Arnold et al.'s (1960) theoretical analysis. The center well was the producing well, and reservoir pressures in the outlying shutin wells were measured until approximate steady-state flow was established. The assumption made was that the producing wells in the reservoir were far enough from each other so that there was essentially no interference between them. Interference will distort the elliptical isopotential lines. Multiple interference can be solved by making effects additive (principle of superposit!on" Felsenthal and Ferrell, 1972). F r a c t u r e s p a c i n g 9 The distance between fractures is required input into many reservoir simulation studies and, therefore, needs to be characterized. Aguilera (1980) stated that, in some instances, the spacing is impossible to obtain from well-test analysis. Also there is a problem of measuring surface joint patterns and projecting the pattern without risk into the subsurface. Models, such as Narr and Lerche's (1984) probabilistic

10 model and Aguilera's (1988) binomial theorem approach, have been developed to calculate vertical parallel fracture spacing from cores. However, these studies do not address the lateral continuity of the pattern(s) within the reservoir. Cores from several wells would have to be analyzed in order to establish a pattern or lack of pattern with some degree of certainty. LaPoint and Hudson (1985) pointed out that joint (fracture) patterns can be divided roughly into those that are homogeneous or those that are inhomogeneous. A homogeneous pattern has characteristics, such as spacing, that are constant and independent of location. The characteristics in an inhomogeneous pattern vary, and may depend on location. Aguilera's approach is valid only for determining the spacing between vertical parallel fractures, and is lithologically sensitive due to the differences in mechanical properties. Vertical parallel fractures can play an important role in the displacement of injected gases in a carbonate reservoir during enhanced recovery operations. A good example of the influence of vertical fractures in a carbonate reservoir was revealed by the injection of CO2/N 2(a field test) in the Coulommes-Vaucourtois Field

T _ '~1 L

T

T2

_t_ -.

.

.

-fT3

$3

T BOREHOLE

Fig. 1-6. Block diagram showing a wellbore through fractured beds of two different thicknesses. Cores cut in the upper and lower beds (T~and/'4) intersect fractures. S is the spacing between fractures and T is the bed thickness. (After Narr and Lerche, 1984, Fig. 3; reprinted with permission of the American Association of Petroleum Geologists.)

11 located in the Paris Basin, France. Denoyelle et al. (1988) attempted to match the test results with the geologic description of the field. Fractures are vertical and parallel to a north-northeast to south-southeast direction, widely spaced, and exhibit no apparent slippage. This orientation corresponds to the direction of the most important tectonic feature in the basin, the Pays de Bray Fault. The production history of the field showed that the reservoir exhibits a single-porosity behavior. A secondary and weaker set of fractures may exist perpendicular to this main direction as shown by the displacement of the CO 2 toward the center of the structure. Gas analyses showed that the areal extent of the gas bubble was 15-20 times larger than the injection pattern area (Denoyelle et al., 1988). This field test shows that extreme caution has to be used when planning injection operations. If different lithologies are present, then the following analysis has to be repeated for each lithology (Aguilera, 1988). It is, however, a relatively simple technique. It is assumed that a core intercepts only some of the vertical fractures present in the reservoir (Fig. 1-6). This situation implies that some fractures are limited to a particular bed, and the probability of a core intercepting a vertical fracture in a bed using the binomial theorem is: (Q + p ) N : QN + N Q N - , p + N ( N - 1 ) lx2 N ( N - 1) ( N - 2 ) . . .

( N - r + 2)

(QN-Z)p2 + . . . . .

(QN--r+l)p,-~ + pN,

(1-12)

1 x 2 x...x(r-1) where Q is the probability of the core not intercepting a vertical fracture (Q = 1 - P ) ; P is the probability of the core intercepting a vertical fracture; r is the successive number of beds; and N is the total number of intercepted beds and is a positive integer (Aguilera, 1988). It was assumed that all beds contain vertical fractures and these may or may not be intercepted by the core as shown in Fig. 1-6. Aguilera (1988) defined the probability (P) of intercepting a vertical fracture in a bed as: P = D/S=

DI

,

(1-13)

Ta v e where D is the core diameter; S is the distance between fractures; Tav e is the average thickness of the bed (summation of individual thickness of each bed divided by the total number of intercepted beds); and I is a fracture index defined as" I-

T

',

(1-14)

S.1 where the subscript i refers to properties of the i th bed. Aguilera's (1988) approach differs from that of Narr and Lerche (1984) by using an average bed thickness rather

12 than an elaborate probabilistic model. Equation 1-14 leads to calculated fracture indices, which are close to the average measured indices (Aguilera, 1988). An application of Aguilera's (1988) procedure consists of the following steps described below. This approach also appears to be readily adaptable to obtaining fracture spacing from well logs: 1. Use Eq. 1-12 to perform a probability evaluation. The probability of intercepting a fracture in a bed is calculated using Eq. 1-13 (remember that P + Q = 1). 2. Determine the median number of fractured beds from a plot of the number of fractured beds versus the probability of intercepting at least the number of fractured beds indicated in the study (probability of success). If the probability of occurrence of a given combination of fractured and unfractured beds in the core's intercepted sequence is PC, and PS is the probability of intercepting at least the number of fractured beds indicated in a given combination, then the probability of a core intercepting unfractured beds is calculated from PC = (DI/Tave)TM,and PS is 1.0 - P C (except in the case where N is zero). 3. Plot the fracture index of 1.0 versus the expected number of fractured beds on coordinate paper. Construct a straight line through the plotted median data point and the origin. Determine the fracture index by entering the measured average number of fractured beds intercepted by an actual core or measured at the outcrop, and reading the corresponding I from the abscissa. Aguilera (1988) states that this line is an approximation that appears to give reasonable results for most practical situations. 4. The vertical fracture spacing is calculated using Eq. 1-14. 5. Using well logs [Aguilera (1988) suggested that the fractured beds be identified on the logs], calculate/, and on the basis of bed thickness obtained from the logs compute the fracture spacing. The following is a sample problem. The original data are from Narr and Lerche (1984), and were reworked by Aguilera (1988).

Problem: Calculate the vertical fracture spacing for horizontal fine-grained limestone beds of the Ordovician Axemann Formation along State Truck Route 45 near Water Street, Pennsylvania, U.S.A. Core diameter, D, is 10 cm. Average thickness of five beds being considered [(46.5 + 14 + 7.5 + 18.5 + 30.5)/5] is 23.4 cm. The probability of intercepting a fractured bed using Eq. 1-13 is [10(I/23.4)] = 0.4274(/). For an I = 1, the P is 0.4274 and Q is 0.5726. Table 1-I gives the probability evaluation for the case o f / = 1, and was compiled using Eq. 1-12 in the following manner. Five unfractured beds: PC = (0.5726) 5 - 0.0616 Four unfractured beds plus one fractured bed combination:

PC = 5(0.4274)(0.5726) 5-1= 0.2297 PS = 1.0 - 0.0616 = 0.9384

13 Three unfractured

beds plus two fractured beds combination"

5 ( 5 - 1 ) ( 0 . 5 7 2 6 ) 5-2 • ( 0 . 4 2 7 4 ) 2

PC =

= 0.3429 lx2

PS - 1.0 - 0 . 2 2 9 7 - 0 . 0 6 1 6 = 0 . 7 0 8 7 Two unfractured beds plus three fractured beds combination: 5(5-

1) • ( 5 -

PC=

2)(0.5726) 5-3x (0.4274) 3 = lx2x3

0.2560

PS = 1.0 - 0 . 3 4 2 9 - 0 . 2 2 9 7 - 0 . 0 6 1 6 = 0 . 3 6 5 8 One unfractured bed plus four fractured beds combination: 5(5-

1) x ( 5 -

2) x ( 5 -

3)(0.5726)5-4 x (0.4274) 4

PC =

= 0.O955 lx2•215

PS = 1.0 - 0 . 2 5 6 0 - 0 . 3 4 2 9 - 0 . 2 2 9 7 - 0 . 0 6 1 6 = 0 . 1 0 9 8 Five fractured beds:

PC = ( 0 . 4 2 7 4 ) 5 = 0 . 0 1 4 3 PS = 1.0 - 0 . 0 9 5 5 - 0 . 2 5 6 0 - 0 . 3 4 2 9 - 0 . 2 2 9 7 - 0 . 0 6 1 6 PS = 0 . 0 1 4 3 TABLE 1-I Probability of intercepting a fracture in a bed at fracture index I = 1, outcrop 1, case 1" (After Aguilera, 1988, Table 3" reprinted with permission of the American Association of Petroleum Geologists.) Combination of events

Probability of combination

Probability of success**

Unfractured

Fractured

(%)

(%)

5 4 3 2 1 0

0 1 2 3 4 5

6.16 22.97 34.29 25.60 9.55 1.43

93.84 70.87 36.58 10.98 1.43

* Probability of not intercepting a fracture in a bed = 0.5726, probability of intercepting a fracture in a bed = 0.4274, total number of intercepted beds = 5. Location from Narr and Lerche (1984). *" Probability of success means probability of intercepting at least the number of fractured beds indicated under combination of events column.

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SUCCESS

(%}

Fig. 1-7. Probability distribution showing the number of fractured beds and the probability in the success of intercepting a certain number of fractured beds at a fracture index of 1. The number of fractured beds intercepted at 50% is 2.6. (After Aguilera, 1988, Fig. 4; reprinted with permission of the American Association of Petroleum Geologists.) Figure 1-7 is a plot of the data from Table 1-I. The number of fractured beds at 50% probability is 2.6. Figure 1-8 is constructed by plotting the expected number of fractured beds versus a fracture index of 1.0. A straight line is drawn between this point (1,2.6) and the origin. The value of Narr and Lerche's (1984) fractured beds intercepted by the core is 2.45. This value is entered on Fig. 1-8, and a fracture index of 0.94 is read from the graph. Aguilera's (1988) determined value of 0.94 compares with 0.98 measured at the outcrop and 0.83 as calculated by the probabilistic method of Narr and Lerche (1984). Narr and Lerche (1984) and Aguilera (1988) considered the effect of a bed with an angle between the core axis and bedding, 0, and an angle between the core axis and fractures,/3, on calculating a vertical fracture spacing under such conditions (Fig 19). A true fracture index (/) can be calculated using the angles 0 and ,/3: /sin0cos/3 I=

,

(1-15)

sinO +/sin/3cos/3 where I e is the apparent fracture index. Table 1-II presents Aguilera's (1988) results using Narr and Lerche's (1984) data from the above example problem: 0 = 60 ~ and fl = 30 ~ and / = 1. The calculation

15 I ,.,

(E)

I

1

!

1

5 //

~J

/

/

/

/

// .,'"

~ 11 jt

I--

/

/

I.i. mid

/

D = ao cm

O = 9o~

/ L ,"l

,=00o

-'~ /

...... iI "..... 1 :"/.. I

1 /i:/

TA

= 46 5 cm

TB

=

TC

=

TO

=

J// 9i ) / ///i!i // /'i:

TE

/i I

Norr

//

ii

14.0cm

7Scm I

"

cm

= 30.5cm and

L erche(1984)

i!

I

2 FRACTURE

3

4

5

INDEX

Fig. 1-8. Expected number of fractured beds versus fracture index (and its uncertainty) for the five beds. Mean number of fractured beds intersected by a hypothetical core plotted at 2.45. Observed fracture index measured at the outcrop is shown by an arrow at I = 0.98. The stippled bar at the lower left comer indicates one standard deviation. (After Aguilera, 1988, Fig. 5; reprinted with permission of the American Association of Petroleum Geologists.)

procedure is like in the above example with the following modification to be taken into consideration: the dip of the beds. The core penetrates an apparent thickness, T (Fig. 1-9). The average apparent thickness Taveofthe 5 beds [(53.7 + 16.2 + 8.7 + 21.4 + 35.2)/5] is 27.04 cm. The probability of intercepting a fractured bed is [ 10(//27.04)] = 0.3698(/). Equation 1-15 is used to calculate the true fracture index (I = 0.577) w h e n / = 1. The number of fractured beds at 50% probability is 2.31 and was obtained from a cartesian plot of the number of fractured beds versus probability of success (Aquilera, 1988, Fig. 7). The expected number of fractured beds intercepted by the core is 3.70 (Narr and Lerche, 1984). A fracture index of 0.79 was obtained from a cartesian plot of the expected number of fractured beds intercepted versus the fracture index (Aguilera, 1988, Fig. 8). This compares with Narr and Lerche's (1984) measured value of 0.98 and their calculated value of 0.81. As far as the drill bit is concerned, it cuts a core having an effective fracture spacing, S, for inclined beds (Fig. 1-9). Equation 1-14 was modified to reflect the true perpendicular fracture spacing, S: e

S = S(cosfl)- T(sinflcosfl), or

s S= cos/ + T(sinfl).

(1-16)

16 TABLE 1-II Probability of intercepting a fracture in a bed at an apparent fracture index I = 1, outcrop 1, case 2" (After Aquilera, 1988, Table 5; reprinted with permission o f the AmericanAssociation of Petroleum Geologists.) Combination of events

Probability of combination

Probability of success**

Unfractured

Fractured

(%)

(%)

5 4 3 2 1 0

0 1 2 3 4 5

9.94 29.16 34.23 20.08 5.89 0.69

90.06 60.90 26.67 6.58 0.69

* Probability of not intercepting a fracture in a bed = 0.6302, probability of intercepting a fracture in a bed = 0.3698, total number of intercepted beds = 5. Location from Narr and Lerche (1984). ** Probability of success means probability of intercepting at least the number of fractured beds indicated under combination of events column.

CORE

/ / / FRACTURE PITCH ANGLE

\

/

\

....

\

BEDDING

/

I

\

\

\

\

I Ii / / /

~..J

/ tl

\ \ \

/

FRACTURE PLANES

Fig. 1-9. A schematic of a fractured bed and core sample. The bedding plane is perpendicular to the core axis; Tsin0 = T, so that T = T when 0 = 90 ~ is the angle between core axis and fracture, 0 is the angle between core axis and bedding, S is the spacing of the fractures, S e is the effective fracture spacing relative to the borehole incidence, T is the bed thickness, T is the effective bed thickness parallel to the core axis. (After Narr and Lerche, 1984, Fig. 5; reprinted with permission of the American Association of Petroleum Geologists.)

17 The term S(cosfl) corrects for the apparent spacing of fractures that strike parallel to the bedding strike (fracture pitch = 0~ and T(sinflcosfl) accounts for a non-zero pitch angle. A value for S can be obtained from Eq. 1-14 (T= Tsin0). Hydrocarbon recovery

The amount of hydrocarbons recovered from carbonate reservoirs is largely controlled by variations in reservoir rock permeability arising from heterogeneities. Establishment of recovery estimates requires in some instances the use of complex computer models involving successive scaling-up of permeability. This complexity is due to the many scales of permeability variation present in a carbonate reservoir. It is imperative that petroleum engineers and geologists have a "feel" for permeability input values which go into such models. In Part 1 of this book (Chapter 8), Honarpour et al. (1992) discussed generalized permeability and relative permeability relationships for carbonate rocks. The following information focuses on the relation of k / k field-derived data and liquid saturation values for carbonate reservoirs. Some comparisons of laboratory k / k data for sandstones also are presented as reference points for the reader. The intent here is to provide data that supplement data given in Chapter 5 of this volume, which discusses the performance and classification of carbonate reservoirs. Calculation of field-derived k / k curves for solution gas-drive reservoirs can be a strong diagnostic tool for comparing solution gas-drive reservoir performance in a play. 9

g

o

.

Primary recovery

Primary recovery of oil, gas, or oil and gas can be defined as any method (natural flow or artificial lift) that may be used to produce them through a single wellbore. The fluid enters the wellbore by action of the reservoir's native energy (Langnes et al., 1972). In order to predict the primary recovery from a solution gas-drive carbonate reservoir, the relation between the ratio of gas to oil permeability ( k / k ) and the liquid saturation (SL) must be known. The k/ko values are derived from measured field data of solution gas-drive reservoirs and t~rom laboratory measurements on core samples believed to be representative of the reservoir. Starting with the gas/oil ratio in the reservoir, which is simply the ratio of gas flow to oil flow, using Darcy's law for radial flow, and correcting reservoir flow data to surface conditions results in the following equation: (1-17)

R = ( k / k ) (~oBo/~gBg) + R s,

where R is the surface gas/oil ratio (SCF/STB), Rsis the solution gas/oil ratio (SCF/ STB), k is the effective gas permeability (mD), k is the effective oil permeability (mD), ~ is the oil viscosity at reservoir conditions (cP), /.t is the gas viscosity at reservoir conditions (cP), Bo is the oil formation volume factor (reservoir barrels/STB), and B is the gas formation volume factor (reservoir barrels/SCF), If B gis reported in CF/S~F, then this value must be divided by 5.614, which is the number of cubic feet in a U.S. barrel, to convert to reservoir barrels/SCF. g

o

.

.

g

18 The reservoir oil saturations corresponding to the field-derived k/k ratio are evalu.g ated by the following equations from standard reservoir engineering ~ (e.g., 9

Dake, 1978, p. 45; Craft and Hawkins, 1959, p. 116)" S = (1 - S ) (1 - N/N)

(ao/aoi),

(1-18)

and

SL= S+ S,

(1-19)

where S is the fractional oil saturation, S is the fractional water saturation, N is the oil produced (STB), N is the oil-in-place at bubble point pressure (STB), Boi is ~he oil volume factor at bubble point pressure (reservoir barrels/STB), and S Lis the fractional I0

I

I

1

I

I

'1

I'

'1 ....

I

1

1

I,U I-"

3= I I,g ..J m ,==, U r Ill Q=: n," m

"

o

0.1 =.=,,,.,.

hi 0 Z ILl Or)

Ill

IE Q. Z

-

O.Ol

,/ 7"

0.001

I00

90 LIOUID

80 70 SATURATION,

%

60 PORE

50 SPACE

40

Fig. 1-10. Field-derived k / k data for dolomites. 1 - Fullerton-Clear Fork, Texas; 2 - Skaggs-Grayburg, New Mexico; 3 - South ~owden-Foster (Grayburg), Texas; 4 - North Cowden (Grayburg), Texas; 5 Goldsmith, North Dome (Grayburg-San Andres), Texas; 6 - Goldsmith, South Dome (Grayburg-San Andres), Texas; 7 - Wasson (San Andres), Texas; 8 - Harper (San Andres), Texas; 9 - Penwell (San Andres), Texas; 1 0 - Slaughter (San Andres), Texas. Producing formation(s) in parentheses. (Data from Arps and Roberts, 1955; after Felsenthal and Ferrell, 1972, Fig. 18; courtesy of Elsevier Publ. Co.)

19 IO

I

'!

I

I

I'

1

I

1

I

i

I......

__

RANGE FOR

OF DATA

TEN F I E L D S

u

-J m

CONSOL IDA TED S A N D (BOTSET)

0 ::) W G: (Z:

0

o.I

IJJ 0 Z

UNCONSOLIDATED

I~J (/) I~J n. a.

(LEVERETT

8

SAND

LEWIS)

z

o.ol

0.001 I00

I 90 LIQUID

80 70 60 50 SATURATION, % PORE SPACE

40

Fig. 1-11. Field-derivedk/k data for dolomites from Fig. 1-10are compared with selected laboratory k / k data for sandstones. Sandstoneg o curvesare from Botset (1940) and Leverett and Lewis (1941). (After Felsenthal and Ferrell, 1972, Fig. 19; courtesy of Elsevier Publ. Co.) liquid saturation. These equations were used to construct the field-derived k / k curves shown in Figs. 1-10 to 1-15 (Felsenthal and Ferrell, 1972). g o Figure 1-10 gives field-derivedk/k curves for Permian dolomite reservoirs in Texas and New Mexico, U.S.A. The k / k gda~a shown in Fig. 1-11 are laboratory derived for a consolidated sandstone ( k i r - ~ 0 ~ ) mD, ~b= 22%) (Botset, 1940) and unconsolidated sand (kir- 10,000 mD, ~b = 42%) (Leverett and Lewis, 1941). These data are compared to the range of 10 dolomite reservoirs presented in Fig. 1-10. Felsenthal and Ferrell (1972) stated that the k / k curves for dolomite show a remarkable and unexpectedly good agreement withgtl~e range of the literature data for consolidated and unconsolidated sand above a k g/ k o = 0.01 and corresponding to liquid saturations lower than 91.5%. The discrepancy 5etween the k g/ k o data in Fig. 1-11 could be attributed to the difficulty in measuring extremely low gas rates with sufficient accuracy in the laboratory. Felsenthal and Conley (1955) performed laboratory tests, which indicated that the k g/ k o curves in the low k g/ k o region probably match the field-derived data much . more closely than shown m Fig. 1-11.

20 I0

1

!

I

i

/ "

!

I

I

I

I

!

W I"

RANGE OF DATA FOR NINE FIELDS

W

I U

-

/

v

-_

--

W n,"

/

I i/

t

-

/

_

/

/

/I

/

t /

-----"-

/

-

I

--

--

CONSOLIDATED SAND (BOTSET)

-

0 1.1 L; Z I11 U~ ill Q: a.

0.1

/

/I

-I ~ v

--

,

Z

~

_

i I

0.01

I

-

..

I

'o

UNCONSOLIDA TED SAND (LEVERETT 8 LEWIS)

-]

I I I ! I i I ! I I

0.001 I00

90 LIQUID

80 70 SATURATION,%

60 PORE

50 SPACE

44:)

Fig. 1-12. Field-derived k / k data for sandstones compared with selected laboratory data. Data from Arps and Roberts (1955), Botsegt(~ Leverett and Lewis (1941), and Kaveler (1944). (After Felsenthal and Ferrell, 1972, Fig. 20; courtesy of Elsevier Publ. Co.)

Generally speaking, a steep k / k curve from a k/k-liquid saturation plot indicates a low solution gas-drive efficier]c37 (Felsenthal anal Ferrell, 1972). A fiat curve indicates a favorable drive efficiency. Figures 1-11 and 1-12 show a comparison between field-derived data for dolomite and sandstone reservoirs. The fields shown are all solution gas-drive reservoirs and cover a wide range of geologic ages (Ordovician to Miocene) and various geographic locations in the U.S.A. (Arkansas, California, Louisiana, Oklahoma, Texas, and Wyoming). These plots indicate that primary solution gas-drive efficiency may actually be as good as or better on a percentage pore volume basis in dolomite reservoirs than in sandstone reservoirs. Felsenthal and Ferrell (1972) suggested that the heterogeneous features of dolomites may help rather than hinder oil recovery of internal solution gas drive. Field-derived k/k data for limestones appear to span a wider range of values than was evident for dolomites (Figs. 1-13 to 1-15). Some of the limestone reservoirs contain appreciable amounts of chert. The laboratory data shown in Fig. 1-14 were obtained on full-diameter core samples, which probably possessed pore geometries representative of the reservoir. The steepest (least favorable) k / k curve is for a fractured chert and

21 I0'

I'

I

I

I

I

i

1

I

I

I

t

I

-

m

ix) Q

0.1

z

m

z

0.01 w

~~

~

v

0.001 I00

90

LIQUID

80

70

SATURATION, %

6O

50

40

PORE SPACE

Fig. 1-13. Field-derived k / k data for limestones. 1 -Haynesville (Pettit), Louisiana; 2 - West Edmond (Bois d'Arc-Hunton), Oklahoma; 3 - Wheeler (Devonian chert and limestone), Texas. (Modified after Arps and Roberts, 1955, Fig. 2; reprinted with permission of AIME.)

limestone (Stewart et al., 1953). Microscopic examination indicated that the reservoir rock in Field F is made up of a large number of small, irregularly shaped pieces of fractured chert cemented by calcite with intergranular porosity. The permeability of the test sample was 2.4 mD, associated with an unusually high (for limestone) porosity of 30.3%. High porosity may have been one reason for the steepness of the curve (Felsenthal and Ferrell, 1972). A trend of increasing steepness ofk/k curves with increasing poros. g o lty values had been observed previously for sandstones (Felsenthal, 1959). Felsenthal and Ferrell (1972) emphasized that the calculations based on Eqs. 1-17 to 1-19 are applicable only to reservoirs with gravity drainage, strong gas-cap, or water influx drives. 9

Hydrostatic and hydrodynamic pressures Many carbonate reservoirs are surrounded by very large aquifers that will offset a production-produced pressure drop by providing an influx of water into the reservoir. Water influx into the reservoir is governed by hydrostatic and hydrodynamic pressures in the aquifer. Hydrostatic pressure is defined as the static weight of a column of

22 I0

i

I

I

I

n.. t.l FIELD ..... --

I

-

o w

-

n,,

-

DATA

/

-

...,..

DATA

LABORATORY

I t

/

/

I

z

I

-

I

/

1

/

I

I i

t

///I

l

/ 0.1 - - -

I

s

I

a/I

/ /i I I

/

/,,, ,'///

- ' /I1; //,y i

'

II II.i

_z

oJ:

0.01 ~,/

v

!

0.001

9 I00

f

I 90 LIQUID

I

I

i

I

80 70 SATURATION,

I

i

f

60 PORE

SPACE

I 50 %

I 40

Fig. 1-14. Laboratory and field-derivedk/k data for limestones and chert. 1-Fractured chert and limestone, Field F; 2 - limestone with intergranula~ porosity, FieldA; 3 - with intergranular porosity, Field B. (Data from Stewart et al., 1953; After Felsenthal and Ferrell, 1972, Fig. 22; courtesy of Elsevier Publ. Co.)

water, increasing vertically downward from the ground surface to the point of production in the reservoir. Hydrodynamic pressure is the difference between a higher and a lower elevation of the piezometric surface in the aquifer. Figure 1-16 illustrates various hydrostatic pressure gradients observed in carbonate reservoirs in the U.S.A. The hydrostatic gradient for the Viola Limestone, for example, is less than that of normal sea water gradient of 0.65 psi/ft. Both the Smackover Limestone (Gulf Coast, U.S.A.) and the Ellenburger Dolomite (Texas, U.S.A.) have gradients greater than 0.465 psi/ ft. Deviation from the seawater trend line is common, and depends on the variation in the fluid density, the amount of solution gas, and the imposed hydrodynamic pressure gradient. An imposed hydrodynamic pressure gradient occurs when aquifers rise to the surface (e.g., to the edge of the structural basins, which lies considerably above the reservoir) so as to provide artesian flow. In highly permeable and extensive aquifers, which are in full communication with the reservoir, pressure gradients developed during production can extend a considerable distance outward from the reservoir. Moore and Truby (1952) made an analog study

23 I0~

I

[

!

!

I

!

!

I

I

1

I.r

..I El

J

2

......

z) o Iz; n? Iz. O I~1 r Z I~1 r ILl n? n

0.1--

m

m

Z 0.01

O.OOI I00

m

~

1

1

90 LIQUID

1 80

1

1

1

70

SATURATION~

1

1

60 96

PORE

1 50

40

SPACE

Fig. 1-15. Laboratory kolk data for reefs. 1 - Pennsylvanian reef A; 2 - Pennsylvanian reef B; 3 - Strawn Reef; 4 - Palo Pinto Re~ef.~ (Modified after Arps and Roberts, 1955, Fig. 2; reprinted with permission o f AIME.)

of five fields completed in the Ellenburger Dolomite of west Texas, U.S.A. Eighty percent of the pressure drop was due to production from the surrounding fields. Pressure interference has also been noticed in the fractured reservoirs of the Asmari Limestone of Iran and in the oolitic Smackover Limestone in southem Arkansas, U.S.A. Pressures in sealed carbonate reservoirs, such as bioherms and biostromes, could be caused by the weight of the overburden. For highly permeable and continuous oolite reservoirs, it may be necessary to consider the effects of pressure interference from surrounding reservoirs in order to make reliable material balance calculations.

Secondary recovery Definitions of several hydrocarbon recovery terms are in order. Enhanced hydrocarbon recovery is similar to that of primary except that more than one wellbore may be involved, and the reservoir's intemal energy is augmented by the injection of fluids with or without heat (Lagnes et al., 1972). There is a generally accepted, but somewhat restricted definition of secondary recovery (i.e., waterflooding). This term is used

24 0~\

I

I

I

I

1

I

I

I

I

I\\

~.Lz \ ~

9 \%

v,o,.. * V \ ~

\

L,-ESrO.E \ ~ .

\".%

~..

\

\

I-IX. t~f

\,

\

\

e II

8

SMACKOVER LIMESTONE FIELOS

m

~

I~)[LLENBURGER ~

\

\*i3 DOLOHITE $*~.' FIELOS ~ 27~94

\

',ko \

9 -

m

\,,

\

I0--

\ II

0

1

I

200o

1

I

4000

~

, 1

1

6o0o

I

8ooo

, iO

boo

INITIAL RESERVOIR PRESSURE, psi Fig. 1-16. Relation between initial reservoir pressure and depth for various carbonate reservoirs in the U.S.A. Data from the following fields were used: Viola Limestone (Kansas): (1) Wilmington, (2) Wichita, (3) Strahm, (4) Newbury, (5) Mild Creek, (6) John Creek, (7) Comiskey, and (8) Ashbum. Smackover Limestone (Arkansas): (1) Midway, (2) Buckner, (3) Village, (4) Texarkana, (5) Magnolia, (6) Schuler, (7) Big Creek, (8) Atlanta, (9) Macedonia Dorcheat, and (10) McKamie. Ellenburger Dolomite (Texas): (1) Martin, (2) Yarbrough and Allen, (3) Sweetie Peck, (4) Shafter Lake, (5) South Fullerton, (6) Block 31, (7) Bedford, (8) Embar, (9) University-Waddell, (10) Jordan, ( 11) Keystone, (12) TXL, (13) Wheeler, (14) Wilshire, (15) Monahans, (16) Todd, and (17) Elkhorn. (After Chilingar et al., 1972, Fig. 14; courtesy of Elsevier Publ. Co.)

only when water injection is started late in the production life of the reservoir, i.e., when the primary energy is nearly exhausted. The term pressure maintenance is used when the injection is initiated early in the life of the field and includes injection fluids other than water.

25 Weber (1986) pointed out that reservoir heterogeneity is one of the major reasons why enhanced oil recovery is so difficult. Waterflooding and enhanced recovery, as well as primary recovery projects that are undertaken without proper planning and/or a detailed reservoir evaluation often end in failure. These failures can be related to flow barriers (often expressed as microscopic boundaries, such as shale baffles or macroscopic compartmentalization, such as compartments formed by sealing faults in a reservoir), permeability heterogeneities, or wrong estimates on the distribution of reservoir fluids. It is difficult to generalize the impact of a given heterogeneity owing to the large variety of heterogeneity classes. Table 1-III is a generalized guide to the influence ofheterogeneities which affect major oil recovery parameters (Weber, 1986). Fault morphology and boundaries of genetic carbonate units have strong influence on the continuity of the carbonate reservoir and on the volumetric sweep efficiency during waterflooding or enhanced recovery. Permeability zonation and baffles within and between genetic units have a major impact on vertical sweep efficiencies (Weber, 1986). A non-uniform residual oil saturation distribution (ROS) arising from water flooding creates problems for EOR. Small-scale heterogeneities, such as sedimentary structures, interlamination of different rock types, pore types, and non-carbonate minerals are thought to be of great importance. Chapter 10 in this book discusses enhanced oil recovery (EOR), whereas Chapter 5 presents carbonate reservoir heterogeneity effects on primary recovery.

Geochemical logging. The elemental composition of carbonate rocks (major, minor, and trace elements) can be used for correlation purposes in carbonate rocks (Chilingar and Bissell, 1957; Wolfet al., 1967; Mattavelli et al., 1969). Elemental ratios, such as Ca/Mg and Sr/Ca, and isotope ratios, such as ~80/~60, hold much promise. The Ca/Mg ratio has been used successfully for correlation by Chilingar and Bissell (1957) and by Mattavelli et al. (1969) (Fig. 1-17). TABLE 1-III Significance of reservoir heterogeneity types for oil recovery. (After Weber, 1986, Table 1" reprinted with permission of Academic Press, Inc.) Sweep efficiency Reservior heterogeneity type

Reservoir continuity

1. Sealing fault Semi-sealing fault Non-sealing fault 2. Boundaries genetic units 3. Permeability zonation within units 4. Baffles within genetic units 5. Lamination, cross-bedding 6. Microscopic heterogeneity, Textural types, Mineralogy 7. Fracturing- Tight - Open

X

(x) (x) X

Horizontal Vertical X X X X

X X X

(x) (x) (x)

x (x) (x)

X = strong effect; (X) = moderate effect; ROS = remaining oil saturation.

ROS in swept Rock/Fluid zones interaction

(x) X X

(x) X X

26 WELL GELA

~)'~, x

"

32

Ca/2Mg

Ix

FINEAND VERYFINE DOLOMITE

,.. ].L,. .~r

i

i

J-

MEDIUMGRAINEDDOLOMITE

n-i~

x

i x

~

CALCITEIN GENERAL

x!

BRECCIAFRAGMENTS ~

X)LITE RELICS

-?:..-.or

INTRACLASTS x

~ar

x/

H

z/

,,

J"

STROMATOLITES ~']

ONCOLITES MACROFOSSILAND MACROFOSSIL RELICS

I

ANHYDRITE x

,,

IRREGULARPORESPACES INSIDE DOLOMITECRYSTALS

x

x ROMBIC PORESPACE INSIDE DOLOMITECRYSTALS

x

x: x: x

,.

=

7

/

o /

/

o

.L

/

/

,."~

~]

SCATTEREDCRYSTALSAND PATCHES OF CALCITEREPLACINGDOLOMITE VUGSANO FRACTURES FILLED BY CALCITE

A

x "

QUARTZ

t x GEOPETALFABRICS _t. =/

I/

. /

-l_,~!

.

x

x VUGSANOCAVITIESOFTEN WITHVADOSETEXTURE

x x

~x x. x x x z/-

//

,/-

/

-

.r

I x

o

_

o

o

1

x

x

~xx x

i

N

x

CORERECOVERY

x

.

i x

x x

x

x

x

x

-.~*.'.*."~*.~ /

o /

.

/

:~ /

* .I/el

:x

,

L

x

I '-'

~

FIELD

~" RAGUSA:

x,

! l.,c

x;

.!

I

I

'x PAL[ RMO

.i i :i x -!

,I ".2..._

"~

Fig. 1-17. Petrographic-petrologic log and Ca/Mg ratio line of the Taormina Formation, Gela Oil Field, Sicily, Italy; well Gela 32. (After Mattavelli et al., 1969, Fig. 1" courtesy of Elsevier Publ. Co.)

27 A geophysical-based geochemical logging tool (Hertzog et al., 1989) has been developed by Schlumberger to eventually be a cost-effective alternative to expensive and time-consuming, extensive chemical analysis of well cores. The tool known as the Geochemical Logging Tool (GLT TM) measures elemental concentrations of aluminum, silicon, calcium, iron, sulfur, gadolinium, titanium, thorium, uranium, potassium, and magnesium. The tool is used in conjunction with resistivity and nuclear logs. Application of this technology was made to a single well in a Middle East reservoir that exhibited a high degree of heterogeneity in terms of dolomitization, shale/ clay content, secondary porosity, and porosity distribution (Herron et al., 1992). Zone correlation from well-to-well was a problem. In conjunction with computer analysis programs and element concentration validation using core chemical and mineralogical data, it was possible to describe the formation with an accuracy that was not previously obtainable without full core analyses throughout the test well. Herron et al. (1992) stated that the logs clearly delineate zones of dolomitization, and quantitatively interpret the concentrations of non-carbonate minerals. This test was not able to demonstrate the usefulness of geochemical logs for well-to-well zone correlation.

Waterflooding. Fractures help to drain solution gas-drive reservoirs during primary production owing to the gas coming out of solution and expelling the oil from the pore space into the wellbore. During conventional waterflooding operations, however, these fractures become potential avenues for the injected water to bypass large volumes of oil contained in the matrix of the reservoir. Two dynamic situations arise when water is displacing oil in a water-wet reservoir. One is imbibition, in which the wetting phase (water) saturation is increasing, and the other is drainage, in which the wetting phase saturation is decreasing (Dake, 1978). Felsenthal and Ferrell (1972) described two situations where the imbibition process was not effective owing to fractures (Fig. 1-18). An operator should be cautious about early water injection (before primary production is at an end) in fractured carbonate reservoirs on the theory that one is more certain about primary production recovery. Early waterflooding under these conditions may be speculative (Tarr and Heuer, 1962). Felsenthal and Ferrell (1972) suggested that a pilot waterflood in fractured reservoirs must be used to evaluate the effect of fractures so that directional permeability trends and fracture orientation can be used to plan infill well locations and assign optimum spacing between the wells. A poorly designed well pattem can result in early water breakthrough and a poor sweep efficiency. A moderate degree of induced fracturing in order to stimulate wells is usually needed in low-permeability carbonate reservoirs so as to complete a waterflood in a reasonable time period. The degree of fracture stimulation should be kept under control. Planning and implementation of quality control procedures should be and are a responsibility of the producer, rather than the service company, in order to ensure a proper stimulation job. The degree of fracturing can be analyzed with the aid of pressure falloff analyses (Clark, 1968; Chapter 6 in this volume). Felsenthal and Ferrell (1972) noted that if fluid injection pressures exceed the parting pressure of the formation and injection is allowed to proceed without restraint and control, then excessively long fractures may form. Such fractures can lead to an early water breakthrough, leaving by-passed oil in the pore space. Fracturing of the reservoir cap rock

28

JL

l

SECONDARY

Fig. 1-18.Effect of fractures on primaryand secondaryrecoverywhere imbibition is not effective. (After Felsenthal and Ferrell, 1972, Fig. 27; courtesyof Elsevier Publ. Co.) could also result in a loss of oil and injection fluid. Chapter 13 in Part I (Hendrickson et al., 1992) of this book discusses fracturing and acidizing technology presently used by industry to stimulate carbonate reservoirs. Induced fractures in tectonically relaxed areas, characterized by normal faulting, generally have a preferred orientation. It is extremely important to recognize this directionality and to make the flood pattern take advantage of it. Cames (1966) and Lane (1969) described specially designed pilot waterflood tests to ascertain fracture and permeability directionality. Other evaluation procedures include: (1) gas injection tests discussed by Armstrong et al. (1961), Crawford (1962), and Alpay (1969); (2) interference tests performed by Elkins and Skov (1960) and Kunkel and Bagley (1965); (3) tracer flow tests by Baldwin (1966); (4) impression packer tests by Fraser and Pettitt (1962) and Anderson and Stahl (1967); (5) borehole televiewer logging to improve well completions by identifying fractures and injection thief zones by Clerke and Van Akkeron (1988); (6) seismic imaging to identify fractures and mini-caverns (Hurley, 1990; Zimmerman and Chen, 1992); and (7) downhole acoustical measurements discussed by Zemanek et al. (1969). McKinley et al. (1968) used pulse testing to successfully determine interwell properties in a highly permeable (kir-- 1,200 mD) dolomitic limestone reservoir. Campa and Romero (1969) used statistical methods for analyzing porosity trends in a carbonate reservoir. Some carbonate reservoirs that contain large gas caps underlain by comparatively thin oil zones, or which have good gravity drainage or strong natural water drives, may

29 1.0 .5 z 0 p. o (t w.

>. v-

m

OIL

.t

.o5

~E

w uJ >,

I--.
.01

WATER .005

.001 20

30 WATER

40

50

SATURATION,

60

70

%

Fig. 1-19. Average oil and water relative permeabilities for the Permian Brown and White Dolomite, Panhandle Field, Texas, U.S.A. (After Abemathy, 1964, Fig. 4; reprinted with permission of AIME.) be not conducive to waterflooding. Felsenthal and Ferrell (1972) pointed out that there may be exceptions, but one should proceed cautiously under such circumstances. A basic evaluation of residual oil saturation behind the water front is needed so that the flood could be modified to lower this saturation. Buckley and Leverett's (1942) classical paper and Pirson's (1958) pioneering book presented the basic equations for such analyses:

fw

1 1 +(kro/aw/~/ao ) '

(1-20)

1 1 + (/Co )---~w---/~o/Cw

(1-21)

or fw

30 where fw is the fractional flow of water at the producing end of the system. Equations 1-20 and 1-21 are identical as long as the relative permeabilities koand kware referred to the same base permeability. An example would be that kir and k in the presence of the irreducible water saturation. Abernathy (1964) provided some typical laboratorybased koand krwversus saturation curves for dolomites in Figs. 1-19 to 1-21. There are a wide range of"end point" krwvalues, ranging from 0.04 (Fig. 1-19) to 0.52 (Fig. 121). It is these "end point" values that govern injectivities into the matrix of the rock (Felsenthal and Ferrell, 1972). Abernathy (1964) noted that the curve for absolute permeabilities greater than 1.8 mD has higher k values than the curve for absolute permeabilities less than 1.8 mD, at the same water saturation (Fig. 1-20). There was no corresponding change in the k curve. Figure 1-22 is a typical k / k ratio curve based on laboratory measurements. Hendrickson (1961) suggested that, if complete relative permeability curves are not available, then one should let the k / k ratio equal 1,000 at the connate water saturation and 0.01 at the residual oil saturation. By connecting the two points with a straight o

w

1.0

OIL

.5

'•

K <'1.8 md

WATER

z 0 m

K > 1.8 md

uI..e~

\

.05

\

>., I-..I (13

\\ .01

w 3E

I=: I,&J a,.

~

I

.005

I,=.1 I-_1

.001

o=:

090 0 5

.0001 I0

20

30 40 50 60 70 W A T E R SATURATION, %

80

Fig. 1-20. Average oil and water relative permeabilities, Permian Grayburg-Brown Dolomite, Foster Field, Texas, U.S.A. (AfterAbemathy, 1964, Fig. 8; reprinted with permission of AIME.)

31 1.0 .5 O/L WATER

.I z

o I-. m

o

.05

Q:

I-.J m

.~

.01

n,,

tu

.005

I.,I i.d n,,

.OOl .0005

''

.OOOIt 20

I

1

1

I

30

40

50

60

WATER

70

SATURATION,%

Fig. 1-21. Average oil and water relative permeabilities, Permian San Andres Dolomite, Welch Field, Texas, U.S.A. (After Abernathy, 1964, Fig. 12; reprinted with permission of AIME.)

line (Fig. 1-22; dashed line), the resulting data can be used in Eq. 1-20. Very useful information can be gained from laboratory measurements of the "end points" of oilwater relative permeability curves, such as values for (1) the critical oil saturation at which oil will first begin to flow, (2) initial (residual or irreducible) water saturation in a water-wet rock, (3) oil permeability at residual water saturation, and (4) a means by which relative permeability values can be estimated between the end points. It is a common experience that the performance of individual wells varies widely in a carbonate reservoir. Complex situations require a synergistic approach between engineers and geologists. Excellent examples of such cooperation have been reported

32 I000

I00

I0

ko/kw

.01 I0

20

:50 40 50 60 WATER SATURATION, %

70

80

Fig. 1-22. Typical k / k ratios. Solid curve: based on laboratory measurements (Tarr and Heuer, 1962). Dashed line: based on approximation (Hendrickson, 1961). (After Felsenthal and Ferrell, 1972, Fig. 31" courtesy of Elsevier Publ. CO.)

in the petroleum engineering literature. Willingham and McCaleb (1967), for example, reviewed engineering and geologic data from the Permian Phosphoria reservoir of the Cottonwood Creek Field, Wyoming. Their analysis defined geologic heterogeneities consisting of extensive lithofacies changes and variations in fracture frequency. As a result, there was a revision of operating practices that led to beneficial changes in secondary recovery operations, causing an increase in production from 2,100 to 3,600 B/D of oil during the first year. A recent detailed study was conducted by integrating geologic, engineering, and economic evaluations of three Texas reservoirs (Dune, Robertson Clear Fork and West Ranch fields) along with data from other reservoirs in order to delineate the resource and production potential of unrecovered mobile oil (ICF and BEG, 1990a,b,c,d,e).

33

~srsc ~s~rm

IE Fig. 1-23. A three-dimensional diagram showing the depositional facies relationship of the San Andres Dolomite in the Means Field, Texas, U.S.A. (After George and Stiles, 1977, Fig. 2; reprinted with permission of the Society of Petroleum Engineers.) Many of these fields are old (some have been producing before World War II), and have been subjected to secondary or enhanced recovery. A majority of these reservoirs are found in the dolomitized strata of the Lower Clear Fork, Upper Clear Fork, and Glorieta formations and some in the Grayburg and San Andres formations. The West Ranch Field produces from the non-carbonate clastic Oligocene Frio Formation and will not be discussed (ICF and BEG, 1990c). The Dune Field and Robertson Clear Fork Unit produce from carbonates that were formed on the semi-restricted Central Basin Platform (west Texas and southeastern New Mexico, U.S.A.) in shallow, moderate-to high-energy depositional environments. Most of the producing fields on the Central Basin Platform exhibit a complex interfingering of various carbonate facies types. Numerous transgressions and regressions of the sea during deposition caused rapid vertical and lateral lithologic changes, which created very stratified reservoirs (Ward et al., 1986). The Means Field, Texas, U.S.A., is an example of this complex facies relationship (Fig. 1-23). The schematic block diagram shows an intertidal-lagoon-bank depositional sequence (George and Stiles, 1977). The best porosity generally occurs in the oolitic facies, whereas the skeletal facies deposited in front of the oolite bank has good secondary porosity formed by leaching. Although Fig. 1-23 is generalized, it does help explain some of the problems in waterflooding from this type of reservoir. Table 1-IV compares the average reservoir properties of the Means Field with those of the Fullerton and Robertson fields. The low primary recoveries were the basis for initiating waterfloods in these three fields. In highly heterogeneous carbonate sequences, as shown in Fig. 1-23, there may be more than 50 individual pay stringers. George and Stiles (1977) pointed out that only rarely will all of these pay zones be completed in a specific well. This practice presents problems in establishing reliable reserves by not accounting for mobile oil behind pipe. Volumetric reserve calculations will be incorrect owing to inexact data on the individual pay stringers. Material balance reserve calculations require that only the oil-in-place, which is contacted by the producing wells, should be considered, and those zones that have not been completed will not

34 TABLE 1-IV Average reservoir properties of three Permian carbonate reservoirs, in west Texas, U.S.A., undergoing waterflooding. (Data from George and Stiles, 1977; courtesy of the Society of Petroleum Engineers) Reservoir parameters

Fullerton

Means

Robertson

Area, ac Depth, ft Formation Gross thickness, ft. Depositional environment Heterogeneity Porosity, % Permeability, mD Connate water, % Primary drive mechanism

17,300 7,000 Clear Fork 600 Shallow shelfward Numerous 9.9 3 22 Solution gas

15,723 4,400 San Andres 300 Carbonate margin Porosity 9.0 20 29 Combination solution gas and water

4,800 6,500 Clear Fork 1,400 Shelf-margin stringers Stringers 6.3 0.65 30 Solution gas

Primary recovery factor (OOIP), %

18

15

8

Fluid parameters Stock tank gravity, ~ Oil viscosity, cP Formation volume factor Saturation pressure, psi

42 0.75 1.62 2,370

29 6 1.04 310

32 1.2 1.25 1,700

influence such calculations. A discussion on various heterogeneous and homogeneous carbonate reservoir models was presented by Mazzullo and Chilingarian (1992) in Chapter 3, Part 1. A full exploitation of the unrecovered mobile oil resource in these carbonate rocks hinges upon the ability to characterize carbonate reservoir heterogeneity, such as pay continuity of stratified horizons and permeability discontinuities. In addition, ineffective well completions complicate the calculations. Results of the individual reservoir assessments can then be extrapolated to groups of reservoirs with common carbonate depositional histories, collectively known as "plays" (ICF and BEG, 1990a). Methodologies developed in the ICF and BEG study and additional case histories are presented in Chapter 5 of this book. Waterflood recovery predictions. Felsenthal and Ferrell (1972) discussed instances where waterflood performance in carbonate reservoirs matched prediction. The prediction methods used were modifications of the methods of Stiles (1949) and Dykstra and Parsons (1950). Hendrickson (1961) described a close agreement between prediction and performance in a five-spot pilot waterflood in the Permian San Andres Dolomite, Welch Field, Texas, U.S.A. Figure 1-24 illustrates the results. The band concept was employed by Hendrickson to predict the flood performance. The band concept combines the layer cake principle of Stiles with the fractional flow Eq. 1-19. Permeability values were arranged in descending order. The resulting array was then subdivided into 10 bands of equal pore volume. Each band's performance was calculated separately, and then the individual values were added to obtain the total predicted reservoir performance.

35 500

i

I

I

1

I

i

I

CA LCUI..A rED

r.u m

_

400

ooooo A C T U , 4 L o

_7

300

o r ILl I--

ZOO

~s~

u r

o,=,= I--

3

t

--I m

o I

2

0 I 0 sS _~OsS

....

.

i'"--

~o

s

0

.

=: uJ

SS S

oo.O

,--.

I00

0

4

sS

oOO

-"

..d

=E r

ssS

o~" d O

=

I00

,.,"o'o" " 200

300

WATER

400

500

600

700

INJECTED~ M BBL

Fig. 1-24. Calculated versus actual performance, Permian San Andres Dolomite, Welch Field pilot waterflood, Texas, U.S.A. (After Hendrickson, 1961, Fig. 1" reprinted with permission of AIME.)

Abernathy (1964) performed an additional evaluation of the Welch Field and two other pilot floods in carbonate reservoirs (Table l-V). He used three prediction methods: (1) Stiles (1949), (2) Craig et al. (1955), and (3) a combination of the two methods known as the Craig-Stiles method. The results shown in Figs. 1-25 to 1-27 indicate that the Craig-Stiles method gave the best predictions for the three fields (Felsenthal and Ferrell, 1972).

I00

I

~'

~

'u

I

~

i

2 z"

o_a_

80

I.:~ u. a o..J

60

a . I - -o

40

~

zo

INJECTION STARTED

~I-.U.l

/ / I

I

0 0

5

I0

1

I

1

I

I

15

ZO

2.5

:50

:5,5

40

PERCENT OF ORIGINAL O I L - I N - P L A C E RECOVERED

Fig. 1-25. Comparison of actual performance with two prediction calculations, Permian San Andres Dolomite, Welch Field pilot waterflood, Texas, U.S.A. Legend: 1 -actual; 2-calculated by Craig-Stiles method; and 3 -calculated by the band method. (AfterAbernathy, 1064, Fig. 13; reprinted with permission of the Society of Petroleum Engineers.)

36 TABLE 1-V Comparison o fwaterflood predictions and performances in selected Permian carbonate reservoirs, Texas, U.S.A. (After Abemathy, 1964; reprinted with permission of AIME) Field Welch

Panhandle

Foster

Formation

San Andres Dolomite

Brown and White Dolomite

Grayburg-Brown Dolomite

Average depth, ft Net pay, ft Average prosity, % Average permeability (cores), mD Connate water saturation, % B 0, res. bbl/STB /.t0, cP Pw, cP ~ gravity BHP at start of flood, psi N p/ N at start of flood Current actual recovery, % oil-in-place Calculated ultimate recovery under flood, % oil-in-place

4,950 75 10 6.3 23 1.008 at 325 psi 2.32 at 325 psi 0.82 34.4 325 0.03

3,000 65 11.7 7.2 39 1.044 2.33 0.83 40

4,200 129 8.6 2.6 23 1.061 at 244 psi 2.91 at 244 psi 0.80 35 244 0.12

0.256 ~

21.7

34.2

21

38

35

38

* Includes gas injection.

The Craig-Stiles method provides for growth of the swept zone after initial water breakthrough, reduction of the residual oil in the swept zone after water breakthrough, and liquid resaturation of initial gas space before flooding in each layer. Oil recovery in stock tank barrels, N from a given layer is equal to: N--

W E(Swr-Swi)gs-S

i

]1

Bo '

(1-22)

where V is the pore volume (reservoir barrels), S i s the final average fractional water saturatio~n in the swept area, Swiis the initial fractional water saturation at the start of the flood, S i is the initial fractional gas saturation at the start of the flood, Eas is the fractional areal sweep efficiency, and B ~is the oil formation volume factor (reservoir barrels/STB). After resaturation of the reservoir was complete (fillup had occurred), water injection was set equal to total liquid production. Felsenthal and Ferrell (1972) pointed out that when using the Craig-Stiles method, special care should be taken to subdivide the reservoirs into only a few layers so that the combined performance of the layers was representative of the performance of the entire reservoir. The layering technique of Miller and Lents (1946), which requires sufficient core analysis data, was used. The Welch Field was subdivided into 12 layers, whereas the Foster and Panhandle fields were subdivided into 3 layers. Core analysis data provided the permeability values and associated reservoir properties for

37 o .J
po ~,

INJECTION STARTED

IOO

r

8o

7 . ~

/

/

~= ~o o

/

-

40-

a. e:

20

I-. '~

0

~ t 3r

\

I

i

,.

26

l

i

28 %

i

l

i

30 ORIGINAL

l

I

J

32

34

OIL-IN-PLACE

I

/ t J

36

38

RECOVERED

Fig. 1-26. Calculated versus actual performance, Permian Brown and White Dolomite, Panhandle Field pilot waterflood, Texas, U.S.A. Legend: 1 -actual; 2-calculated by Craig-Stiles method; and 3-calculated by Craig et al. method (1955). (After Abernathy, 1964, Fig. 5" reprinted with permission of AIME.)

I

i. . . .

~

I

i

I

I

IOO

t o

80

_~

60

i

/

0 t.J :~

"I,4

START OF" INJECTION

'

//

/

, ....." -'

40

0n," a. a:

20-

M,I 3r

0

5

I0 %

ORIGINAL

15

20 OIL-IN-PLACE

25

30

35

40

RECOVERED

Fig. 1-27. Calculated versus actual performance. Permian Grayburg-Brown Dolomite, Foster Field pilot waterflood, Texas, U.S.A. Legend: 1 -actual; 2 - calculated by Craig-Stiles method; 3 - calculated by Craig et al. method (1955); and 4 - calculated by Stiles method. (After Abernathy, 1964, Fig. 9; reprinted with permission of AIME.)

each layer from the wells at the same relative position in the reservoir. No cross flow was assumed to occur between layers. As pointed out earlier, natural water drives are generally less effective in carbonate reservoirs than in sandstone reservoirs. The difference stems from the greater heterogeneity of the carbonates. Results of a 1967 API study of natural water drives in 72 sand and sandstone reservoirs and 39 limestone, dolomite, and other rock types are

38 TABLE 1-VI Range of parameters of reservoirs with water drive as the predominant recovery mechanism. (After Arps et al., 1967; reprinted with permission of the American Petroleum Institute) Sand and Sandstone

Ultimate recovery Residual oil, % pore space bbl/acre- ft Rock perameter k,mD ~, % bulk volume S i, % pore space

Limestone, dolomite, and other

Worst

Median

Best

Worst

Median

Best

63.5 155

32.7 571

11.4 1,641

90.8 6

42.1 172

24.7 1,422

11 11.1 47

568 25.6 25

4,000 35.0 5.2

10 2.2 50

127 15.4 18

1,600 30.0 3.3

*Values shown for each separate parameter; values do not necessarily belong to same case history.

summarized in Table 1-VI. Carbonate reservoirs contain higher percentages of residual oil than do sand and sandstone reservoirs. Improvements in overcoming reservoir heterogeneities, thereby increasing the additional production of the unrecovered mobile oil, are discussed in Chapter 5, Part 2 (Rieke et al.).

Injection rate predictions. Injection calculations require knowledge of either k h or k h permeability capacity terms. This information can, in many cases, be derived from koh data obtained from pressure buildup tests, when the reservoir was undersaturated, and from appropriate relative permeability test data (Felsenthal and Ferrell, 1972). For water injection predictions the k h can be evaluated using: kh

= kh

• (k'rw/k'ro),

(1-23)

where k'rwiS the relative permeability to water at residual oil saturation, and k'ro is the relative permeability to oil at irreducible water saturation. Typical k'rwand k'rodata are represented by the end points of the oil-water relative permeability curves shown in Figs. 1-19 to 1-22. Gas well tests yield k h data, but these tests are often affected by turbulence in the wellbore region. A factogr of turbulence can be evaluated either from well tests (Energy Resources Conservation Board, 1975) or from laboratory tests. Gewers and Nichols (1969) measured turbulence factors on cores from microvugular carbonate gas reservoirs in the Turner Valley Member of the Rundle Formation (Mississippian) of western Canada. Values were obtained that were as much as one order of magnitude higher than previously reported for non-vuggy rocks. Felsenthal and Ferrell (1972) stated that the best approach for obtaining k h data is to use the results of injectivity tests and/or subsequent pressure falloff tests. Care must be taken during the injectivity tests that the formation is not being fracture parted, which results in an erroneously high permeability capacity value. Creation of new fractures can be evaluated with the aid of step-rate injectivity tests (Yuster and Calhoun, 1945). In these tests, injection rates are increased stepwise and plotted against (Pw-Po), where

39 Pw is the bottomhole injection pressure and p~ is the shut-in formation pressure. It is assumed that no new fractures are being opened as long as the curve is a straight line and goes through the origin of a Cartesian plot. One of the limitations of this method for determining kh values is that it does not take into consideration the spatial distribution of flow capacity values within the reservoir. P6rez-Rosales (1979) presented a statistical method for obtaining the continuous areal distribution of the flow capacity in heterogeneous reservoirs. The mathematical technique used is normal distribution analysis, which allows the representation of random distributions as a linear combination of normal density functions. It was postulated by P6rez-Rosales (1979) that natural random spatial distributions can be considered as the supposition of elementary distributions, known as basic accumulations. The mathematical model of basic accumulations is the normal distribution. A limestone reservoir (Cretaceous), Sitio Grande Field located in southeast Mexico, was chosen by P6rez-Rosales to illustrate the method. Flow capacity values corresponding to each of the 18 wells were determined by using pressure buildup tests described by P6rez-Rosales (1978). Two three-dimensional spatial distributions of the kh variability in the Sitio Grande Field are presented in Fig. 1-28. Fracturing or pressure parting pressures can also be predicted and evaluated by means of the fracture gradient presented by Hubbert and Willis (1957) and Eaton (1969): PDf =

Po_ -D

_

1-v

+ -D- '

(1-24)

where pfis the bottomhole pressure that causes fracture propagation, p is the reservoir pressure, Po is the overburden pressure, D is the depth, and v is the Poisson's ratio. A plot indicating observed fracture gradients and Poisson's ratios for a Mississippian limestone reef and a Permian dolomite reservoir is shown in Fig. 1-29. Analysis of pressure falloff tests is described in detail by Matthews and Russell (1967, pp. 72-83). A method developed by Hazebroek et al. (1958) appears to apply well to carbonate reservoirs (Felsenthal and Ferrell, 1972). His method yields a k h value and also a dimensionless skin factor, s, which is defined as: s + In

rJrw=O.O0708(Pw-p)(kh/il~w),

(1-25)

where r is the external boundary radius, ft; rwiS the wellbore radius, ft; i is the stabilized injection rate, bbl/D, before pressure falloff testing; and/~wiS the viscosity of the water, cP. If the skin factor is negative, one may assume that r is in effect larger than the originally assumed value based on hole size. The effective wellbore radius, rw~, which later must be substituted into all injectivity prediction equations, can then be evaluated by setting s = 0. This results in:

rwe= re -a, where a = O.O0708(Pw-Pr

(1-26)

40 A

B.

Fig. 1-28. Flow capacity (kh) distributions in the Sitio Grande Field (Cretaceous), Mexico. A - South to north view; B - north to south view. Numbers refer to well numbers. (After Perez-Rosales, 1979, Figs. 7 and 8; reprinted with permission of the Society of Petroleum Engineers.)

41 1.0 POISSON RATIO

-I w

I--

Z~

P

-II-. o. I,i j Q

~. z m

I--z t,d ,,,.. c~ <~

0.5

(..)
o/t

1

1

1

1

o s. I . "

l 0.5

FORM. DEPTH

l

~

i

l

I.O

PRESS., ~

psi f- T

"

Fig. 1-29. Observed fracture pressure gradients and Poisson' s ratios as a function of the shut-in formation pressure/depth ratios, o - Mississippian limestone reef at 6,500-ft depth; A Permain dolomite reservoir at 3,900-ft depth. (After Felsenthal and Ferrell, 1972, Fig. 36; courtesy of Continental Oil Co. and Elsevier Publ. Co.)

Clark (1968) devised a practical method for evaluating the true matrix permeability of a formation. This method has been found to be useful for evaluating the properties of carbonate rocks surrounding water injection wells. Millheim and Chichowicz (1968) described a similar method for low-permeability fractured gas wells. Both methods first evaluate the effect of possible induced fractures and then separate this effect from the contribution of the rock matrix. Adams et al. (1968) described transient pressure tests in a complex gas reservoir, indicating a tight dolomite matrix near the wellbore and a higher matrix permeability at some distance from the well.

Infill drilling strategy. Infill drilling as a recovery strategy was briefly mentioned in the Introduction Chapter of Volume 1 of this book. Here in Volume 2, the application of this incremental recovery strategy to carbonate reservoirs in west Texas is discussed in Chapter 5. Van Everdingen and Kriss (1980) noted that in the past the relationship between primary ultimate recovery and well spacing was not well established because of the lack of consideration of reservoir heterogeneity. Infill drilling, which decreases the spacing between wells, can increase the ultimate recovery of mobile oil during waterflooding. The optimum location of infill wells is in certain

42 situations an important cost-reducing production strategy for heterogeneous carbonate reservoirs. Waterflood programs utilizing knowledge about in-situ stress in a number of carbonate reservoirs located in the Permian Basin have shown improvement in reservoir pressures and production rates (Nolen-Hoeksema et al., 1992). The improvement is due to the strategic placement of injector and infill wells with respect to the major insitu stress. Measured in-situ stress magnitude and orientation values by using microfracturing techniques and borehole televiewer revealed that directional waterflood effects in the oil reservoirs coincided with hydraulic-fracture propagation directions. The new well patterns and spacing minimized floodwater channeling (Nolen-Hoeksema et al., 1992). Wu et al. (1989) presented results of a decline curve analysis coupled with an economic evaluation of waterflood infill drilling projects in 14 Clear Fork and 11 San Andres Permian carbonate reservoirs in west Texas (Table 1-VII). Results indicated that there was a statistical medium value increase of 7.78% in recovery of the original-oil-in-place using infill drilling waterflooding over conventional waterflood for the Clear Fork units. There was a statistical medium value increase in oil recovery of 11.38% of the original-oil-in-place using infill drilling waterflooding over conventional waterflooding for the San Andres units. From an economic viewpoint, Wu et al. (1989) showed that in general the San Andres units had a higher rate of return for infill drilling waterflood projects owing to a shallower reservoir depth and a higher infill drilling recovery efficiency.

Enhanced recovery Enhanced oil recovery processes are usually divided into three main categories: miscible flooding, chemical flooding, and thermal recovery. These methods have not been widely used by independent operators owing to constraints such as scarce financial resources, lack of technical knowledge and expertise, absence of detailed reservoir data, inherent high economic risk, and unstable sale price. Designing an EOR project in a carbonate reservoir requires a "best effort" reservoir characterization, which can be used in a model to predict the performance of the project. The more realistic the reservoir description is, the more reliable the EOR performance predictions will be (Dowling, 1970). Application of carbonate depositional environmental concepts will lead to better definition of field limits, quality and continuity of each zone, including delineation of potential productive zones that were either cased off or not penetrated as a result of early evaluation techniques. In order to meet the requirement of optimal design, process screening and initial computer model studies are performed before the EOR process is pilot tested in the field. Miscible flooding. Miscible flooding is a technique where a solvent bank rich in LPG (ethane through butane) is generally injected at the existing gas-oil contact and then driven downward by dry gas. A miscible fluid displacement of the oil results from a reduced capillary force. There is no phase boundary or interface existing between the oil and displacing fluids. Recoveries as high as 96% of the initial oil-inplace are claimed for these processes, which include processes such as high-pressure dry gas (Lee and Reitzel, 1981; DesBrisay et al., 1981), enriched gas (Davis et al.,

TABLE 1-VII Reservoir properties, recovery efficiencies, and well spacing data for waterflood infill drilling in the Permian Clear Fork and San Andres carbonate reservoirs, west Texas, U.S.A. (After Wu et al., 1989, Tables 1 and 2; reprinted with permission of the Society of Petroleum Engineers) Field/Unit

N

Primary

Initial waterflood Infill drilling

(Acres)

Depth Thick- Poro- Permea- B 0 Gravity S i ness sity bility (RBL/ (ft) (ft) (%) (mD) STB) (~ (%)

320 720 4,850 29,542 4,693 2,133 3,120 6,828 2,000 8,510 4,400 3,760 4,320 4,720

3,170 3,170 6,380 6,700 5,800 6,525 6,700 6,700 6,450 7,350 5,675 6,600 6,400 6,400

34 32 30 72 218 78 102 105 100 101 85 150 82 180

7.0 7.0 12.7 10.0 6.3 5.0 7.0 5.6 6.2 5.2 6.4 6.4 5.1 6.4

8.0 3.0 6.0 3.0 0.7 1.2 7.7 3.0 3.0 1.0 1.0 1.0 0.1 1.0

1.18 1.18 1.23 1.62 1.27 1.15 1.15 1.15 1.15 1.28 1.25 1.25 1.30 1.25

30.5 30.5 32.2 42.0 34.6 27.0 29.0 28.0 28.0 34.7 35.0 30.0 30.0 35.0

40.0 38.0 27.0 23.6 30.0 30.0 35.0 42.3 38.6 24.0 27.0 32.0 35.0 27.0

3.0 6.5 84.9 738.0 275.0 39.5 80.5 162.0 51.3 206.0 110.0 152.0 68.9 247.0

8.65 7.88 12.66 13.56 15.37 9.33 20.80 20.57 14.20 22.31 17.31 9.12 14.53 16.76

105 116 55 40 70 50 45 45 40 53 50 45 53 36

16.00 9.54 16.85 21.33 17.75 17.08 30.79 29.56 32.19 23.60 21.55 10.90 15.71 22.61

45 54 49 36 40 50 35 40 30 38 50 40 53 30

25.10 13.09 28.51 37.04 21.40 25.53 39.12 52.56 50.49 29.75 27.70 14.25 20.29 24.54

25 25 44 29 18 40 22 27 20 30 40 35 40 25

San Andres Units Adair 5,338 Fuhrman-Mascho/Blk 9 3,948 Johnson/J.L. "AB" 840 Johnson/Grayburg 3,720 Means 14,328 Ownby 2,960 Shafter Lake 11,080 Triple-N/Grayburg 2,192 Wasson/Denver 25,505 Wasson/Willard 13,360 W Seminole 3,720

4,900 4,450 4,100 4,150 4,300 5,200 4,300 4,325 4,800 5,100 5,112

50 80 60 50 200 32 49 20 200 111 118

14.1 7.0 8.0 6.7 9.0 14.1 6.5 12.1 10.0 8.5 9.9

3.7 4.0 1.8 5.3 29.0 4.5 5.0 6.6 5.0 1.5 20.7

1.12 1.12 1.20 1.20 1.04 1.35 1.24 1.23 1.31 1.31 1.38

33.5 29.0 38.8 32.5 29.3 32.0 32.0 31.9 33.0 32.0 32.4

35.0 30.0 30.0 21.8 28.8 38.0 25.0 40.0 15.0 20.0 18.0

168.0 79.0 19.6 45.7 382.0 52.0 165.0 20.0 2108.0 624.0 174.0

15.02 8.41 7.36 21.41 23.88 11.17 12.30 14.30 7.27 11.86 8.13

49 51 56 45 52 60 45 80 66 60 62

25.31 10.68 12.12 31.23 39.03 20.59 19.09 25.60 23.50 19.35 16.52

41 29 36 34 35 50 35 60 43 44 41

41.64 13.25 34.29 36.06 45.44 29.11 21.03 37.10 46.15 29.32 24.49

23 23 10 27 33 41 31 40 18 35 31

Clear Fork Units: Diamond M/Jack Diamond M/McLaughlin Flanagan/U. Clear Fork Fullerton/U. Clear Fork N. Roberston Ownby Prentice/Central Prentice/NE Prentice/SW Russel Wasson/Gaines Wasson/Gibson Wasson/North Wasson/South

Area

Recovery Spacing RecoverySpacing Recovery Spacing (MMSTB) (%N) (Acres/W) ( % N ) (Acres/W) ( % N ) (Acres/W)

4~

44 1976; Young and Martin, 1980), and carbon dioxide or nitrogen injection (Watts et al., 1980; Holm, 1987; Stein et al., 1989). The general rule of thumb is that naturally-fractured carbonate reservoirs are poor candidates for miscible CO 2flooding. Beliveau et al. (1993) reported on a pilot miscible CO 2 flood in the Midale Field (Mississippian) located in southeastern Saskatchewan, Canada. The results of the pilot test showed that a substantial tertiary recovery is obtainable using CO 2in a fractured reservoir owing to favorable gravity effects and open vertical fracture system. The pilot injection wells were aligned in pairs along the fracture system, providing two linedrive injection rows (Beliveau et al., 1993), and the flood was non-cyclical. The test was designed to displace oil in the off-trend direction (perpendicular to the strike of the predominant vertical fracture system). A scale-up of the CO 2pilot results, using a dual-porosity simulator, showed that a tertiary recovery of 20% OOIP can be expected from a field-scale CO 2flood (Beliveau et al., 1993). Also, there are unique opportunities for very efficient vertical miscible displacement drives in the Devonian pinnacle reef reservoirs in western Canada (Willmon, 1966; Young and Martin, 1980; Mazzocchi et al., 1988).

Cyclicflooding. The principle behind cyclic flooding is to move oil out of the rock matrix by forcing an injection fluid, either water or gas and water, into the rock, thereby raising reservoir pressure. A depressuring phase follows forcing oil from the matrix. Cycles can be repeated several times. During the depressuring phase of the cycle, water is retained by capillary attraction, and oil is released into the natural fractures or high-permeability zones (Felsenthal and Ferrell, 1972). This process is used in reservoirs that are difficult to waterflood by conventional methods. This process is closely related to the imbibition process described by Graham and Richardson (1959) and Mattax and Kyte (1962). Bokserman and Shalimov (1967), Tatashev (1968), and Felsenthal and Ferrell (1969) presented laboratory data and theoretical analysis supporting the concept of cyclic flooding. One of the best examples of an application of cyclic flooding is from the Permian Spraberry trend in the Midland Basin, west Texas, U.S.A. Although the Spraberry reservoir is composed mainly of a massive siltstone, there are shale and shaly limestone interbeds present (Marshall, 1952). The major void space in the reservoir is in nearly vertical fractures. What was learned early on from cyclic flooding in the Spraberry was conveniently applied to fractured carbonate reservoirs. Field data on the use of cyclic flooding in the Spraberry Field, Texas, U.S.A. were presented by Elkins and Skov (1963). Here, injection wells had been lined up carefully with the fracture trend. The spacing of the fractures ranged from a few inches to a few feet. Matrix permeability was less than 1 mD, and porosity was in the 8-15% range. High injection rates were used to repressure the reservoir to above the bubble point pressure. The injection was stopped upon reaching this pressure. Within a few days, oil production rose substantially and then gradually declined. The pressuring phase lasted 1 month, whereas the depressuring phase lasted about 7 months. This process was repeated three times, causing substantial oil rate increases, but each cycle produced less oil than the preceding one. Only one pressure cycle was successful in the extremely low-permeable Cretaceous Austin Chalk and the Buda Limestone, Salt Flat Field, Texas, U.S.A. These

45 formations are characterized by a tight matrix (k~ = 0.1 mD; ~b = 12%). The low permeability shown by cores was confirmed by well performance. Hester et al. (1965) described a fairly successful test in one well that yielded 10,000 bbl of oil after water was injected into it at pressures just below the fracturing pressure. Only one third of the injection water was produced back. A second cycle essentially failed to produce any oil, probably because of low permeability and the lack of intemal energy to push the oil into the wellbore during the depressuring phase of the cycle. Today, the standard recovery strategy for the Austin Chalk is to drill horizontal wells to intersect the major vertical fracture systems. Horizontal wells also have been used to improve miscible flood performance in carbonate reservoirs (Patel and Broomhall, 1992; Trocan et al., 1992). Willingham and McCalef (1967) and Elkins (1969) reported somewhat more successful applications of the injection-production scheme described above. The first project occurred in a highly-fractured portion of the Permian Phosphoria Formation at Cottonwood Creek, Wyoming, U.S.A. Twelve former water injection wells (cumulative injection of 25.4 million bbl of water) were put on production. After 2-3 weeks they started to produce oil. At the end of 1 year the wells were producing 1,850 B/D of oil with a 67% water cut. In the second case, a former injection well after receiving 1 million bbl of water produced 131,500 bbl of "cyclic" oil from the heterogeneous Devonian Bois d'Arc Limestone, West Edmond Field, Oklahoma, U.S.A. In both instances, conventional waterfloods were unsuccessful in the areas surrounding these wells. Successful cyclic flooding in a highly-permeable fractured carbonate reservoir was described by Vasilechko et al. (1969). The injection-production scheme in this project was similar to the one reported for the Spraberry Field in Texas, U.S.A. During the water injection phase, which lasted 1.5-2 months, formation pressure was increased. Injection was stopped for 1-1.5 months to allow depressuring of the reservoir. Contrary to the Spraberry, the reservoir of the A 4 Formation in the Pokrovsk Field, Russia, had a high permeability and porosity (k = 1,065 mD; ~b= 23%). Cyclic flooding was started after conventional waterflooding produced oil at a 75% water cut. During 8 cycles, about 1.5 million extra bbl of oil were recovered. As expected, production declined with each successive cycle. Vasilechko et al. (1969) concluded that cyclic waterflooding should be effective in other carbonate reservoirs as well. Thermal recovery. Thermal recovery methods consist of cyclic steam stimulation, steamflooding, in-situ combustion and their variations. The latter method does not hold much promise in carbonate reservoirs, inasmuch as field tests have not be encouraging. Results of unsuccessful tests are important in pointing out the failures that often are not discussed in the literature. Marchant and Menzie (1966) reported on the California Company's experimental field test in the Irvine-Fumace Field located in eastem Kentucky, U.S.A. This reservoir is the coarsely crystalline Silurian Lockport Dolomite (Comiferous p a y - a driller's term) and the test was not successful. Marchant and Menzie (1966) studied the changes in limestone under in-situ combustion temperatures in the laboratory. Limestone supplies its own fuel at high temperatures in the form of free carbon, carbon monoxide and oxygen. A temperature of 1300~ is required for the following reaction to occur at atmospheric pressure for

46 limestone: 3 C a C O 3 + heat -~ 3CaO + C O 2 -1- 0 2 ) , whereas dolomite will break down at about 1000~ and lower if sulfur is an impurity (Marchant and Menzie, 1966). It should be noted that in the manufacturing of lime, temperatures are much higher, usually between 2000 and 2500~ (Boynton and Gutschick, 1960), giving the following reactions: (1) for limestone: C a C O 3 + heat ~ 3CaO + CO2, and (2) for dolomite: CaCOa/MgCO 3 + heat ~ CaO/MgO + 2 C O 2. With high calcium limestone, 44% of the weight of the limestone is lost and with dolomite the loss is 48%. Limestone does not begin to evolve C O 2 freely until a temperature of approximately 1800~ is reached under normal kiln conditions, as reported by Boynton and Gutschick (1960). They also noted that both reactions are chemically reversible by the absorption of CO 2. A more stable form is a hydrated lime that is formed under the conditions of adding water to the lime: CaO + HzO ~ C a ( O H ) z + heat. The tests by Marchant and Menzie (1966) showed that the samples underwent complete bleaching, sustained appreciable loss in weight, had a large increase in effective porosity, exhibited increase in air permeability, and became a weak incompetent "chalk-like" material. It is apparent that carbonates mechanically breakdown under high in-situ combustion temperatures, thereby reducing the pore space and providing flow channels. Sahuquet and Ferrier (1980), however, noted that the decomposition of limestones during steamflooding occurs without unfavorable effects. Briggs et al. (1988) estimated that the amount of heavy oil contained in carbonate reservoirs is 1.6 x 1012 bbl of oil-in-place worldwide. Very little attention has been paid to this resource owing to the conceptually difficult task of recovering viscous oil from naturally-fractured carbonate rocks. Nolan et al. (1980) discussed thermal expansion as a mechanism (which would move oil into fractures) operative during steamflooding of carbonate reservoirs. Previously, Elf Aquitaine initiated a steam-drive pilot test in 1977 in the Lacq Superieur Field (reservoir is a lower Senonian limestone of Upper Cretaceous age) (Sahuquet and Ferrier, 1980). This is an anticlinal field that is located in the southwestern part of France. Primary production began in 1950 and by 1975 only 17% of the original oilin-place was recovered from this heterogeneous and fractured reservoir. The reservoir is surrounded by a large aquifer, which maintains a constant, but low, reservoir pressure. The producing limestone beds in the anticline exhibit two facies: (1) central portion of the anticline contains very fractured, occasionally karstic dolomites (porosity values range from 10-15%) and a matrix having permeability of about 1 mD. The fractured nature of this zone gives rise to a high productivity: (2) the north-west and south-east parts of the field contain limestones with an average porosity of 20% and permeability ranging from 1-10 mD. This facies contains only few microfractures and its productivity is low (Sahuquet and Ferrier, 1980). The 21.5 ~ API crude has a viscosity of 17.5 x 10-3 Pa.s. Sahuquet and Ferrier (1980) stated that steam-drive was chosen because the matrix blocks could be efficiently heated by heat conduction. The oil trapped in the blocks would be also heated and the oil's viscosity reduced. Thermal expansion would move the oil towards the fractures. The test was successful in increasing production. Sahuquet and Ferrier (1980) believe that the oil expelled from the matrix blocks moves quickly through the fracture network towards the producers. They also noted that these carbonates are dissociated by the steam under the pressure and temperature conditions

47 without unfavorable effects. Carbon dioxide, which is a result of this dissociation, perhaps improved the efficiency of the operations. It was suggested by Briggs et al. (1989) that a pressure cycling steam recovery process could possibly be used to recover heavy oil from the carbonate reservoirs. The concept tested in the British Petroleum laboratory involved a two-stage process of combining pressure cycling steam with imbibition and internal-gas drive and/or steam flashing. It was assumed that the fracture system would allow efficient heating of the reservoir rock matrix by thermal conduction. This could result in displacement of oil into the fractures by thermal expansion, accelerated imbibition, gravity drainage, and expansion by solution-gas drive of oil from the matrix during the blowdown phase. The mobilized oil can then be produced via the inter-connected fracture network (Briggs et al., 1989). In the Komi Republic of the former Soviet Union, a 4,330- to 4,900-ft deep, highly complicated, heterogeneous 1,150-ft- thick carbonate formation containing 18 ~ API, 700 cP heavy oil and having a reservoir temperature of 68~ was successfully steamflooded in the Usa Field. Primary and secondary recovery from this carbonate formation did not exceed 7-10% of the original oil-in-place (Bokserman et al., 1991). Average porosity of the formation was 20% with a permeability of 3 D. Beginning in 1982, superheated-water, with temperatures of 485-560~ was injected into the carbonate formation. Bokserman et al. (1991) stated that the recoverable oil reserves increased by 800 to 1,000 million bbl. They estimated that the ultimate oil recovery will reach 27% of OOIP.

RESERVOIRS IN KARSTED CARBONATES

Reservoirs in karsted carbonate rocks are discussed in Chapter 9 of this book (Mazzullo and Chilingarian). Such reservoirs are, with few exceptions, notoriously heterogeneous in terms of effective porosity and permeability in both the lateral and vertical directions. Such heterogeneity results from the irregular distribution of porous zones and the complex nature of pore systems in karsted strata, and poses special problems in reservoir development, petrophysical modeling, management, and hydrocarbon producibility. The most common type of gross porosity-permeability system represented in karsted reservoirs is sediment-filled and unfilled paleocaves and caverns. On the megascale, extreme vertical reservoir compartmentalization in fields occurs because of the presence of successive levels of cave or cavern systems separated by impermeable host strata, and by impermeable strata within individual cave or cavern level, in the productive section (e.g., Kerans, 1988; Bliefnick, 1992). Compounding this inherent heterogeneity is the fact that productive zones commonly are multiporosity systems which clearly have extreme variations in the effective porosity and permeability and, hence, in fluid flow, internal pressure gradients, and reservoir performance. The polygenetic origin of many such pore systems (i.e., where karst-related dissolution has overprinted a pre-existing porosity system) further complicates reservoir petrophysical characterizations. Pore types commonly found in karsted reservoirs include interparticle pores in cave-filling breccias, matrix porosity in host carbonates (e.g., micropores, interparticle and moldic pores, vugs, and intercrystalline

48 pores, the latter common in dolomites), dissolution-enlarged fractures and joints, and large, tortuous cavernous pores. Impermeable strata that serve as barriers to lateral fluid flow also occur irregularly throughout such sections. Many hydrocarbon reservoirs in karsted carbonate rocks have values of porosity and permeability that far exceed those for typical, average-porosity (i.e., 15% or less) carbonate reservoirs. Furthermore, they characteristically have some of the highest flow rates and recovery efficiencies of all reservoirs. Recovery efficiencies of many karsted reservoirs range from 21% (Amthor and Friedman, 1989) to as high as 80% (Brady et al., 1980). Horizontal drilling recently has proven to be an excellent method of enhancing production from compartmentalized, karsted carbonate reservoirs (Dussert et al., 1988). The few examples, wherein karstification has resulted in the formation of nearly homogeneous reservoirs with well-connected rather than compartmentalized porosity-permeability and fluid transmission systems, include Yates Field (Permian) in the Permian Basin of Texas, U.S.A. (Craig, 1988), Amposta Marino Field (Cretaceous) in Spain (Wigley et al., 1988), and Renqiu Field (Precambrian to Ordovician) in China (Guangming and Quanheng, 1982; Qi and Xie-Pei, 1984). Despite their typically heterogeneous characters, karsted carbonate reservoirs constitute one of the most economically significant category of reservoir types because of typically huge reserves. Volumes of oil and gas already produced from karsted limestones and dolomites of Precambrian to Tertiary age around the world amount to minima of 8.45 billion barrels and 911 trillion cubic feet, respectively. Total ultimate producible oil reserves (at current technology) from such reservoirs are at least 111 billion barrels, a figure that amounts to no less than 11% of total global oil reserves from Phanerozoic carbonate and siliciclastic reservoirs. Hydrocarbon production from karsted carbonate reservoirs accounts for a minimum of 18% of the hydrocarbon reserves stored in all types of traps in carbonate rocks. Traps associated with karsted carbonate reservoirs are classified into seven types based on reservoir occurrence and geometry of enclosing strata (described in Chapter 9 of this volume), all of which fall under the general category of subunconformity traps (Martin, 1966; Halbouty, 1972; Rittenhouse, 1972). The most common occurrence of karsted carbonate reservoirs is as buried hill traps, that is, residual hills on a karsted geomorphic terrane wherein intense subaerial meteoric dissolution (either monogenetic or polygenetic, and either monocyclic or polycyclic) typically has created porosity or has significantly enhanced pre-existing porosity. Buried hill traps may: (1) occur on horizontal to gently-dipping strata (Type I); (2) represent erosionally modified reefs (Type II); (3) be residual hills that, by virtue of their paleotopographic expression, isolate strata with pre-existing porosity (Type III); (4) occur in strata that have been tectonically structured (Type IV); and (5) be hybrids of these types. Many of the world's giant hydrocarbon reservoirs occur in these types of traps, including: (1) the Golden Lane and Campeche-Reforma trends (Cretaceous) in Mexico; (2) the Horseshoe Atoll Trend (Pennsylvanian) in the Permian Basin of west Texas; (3) Bu Hasa, Fahud, Fateh, and Natih fields (Cretaceous) in the Middle East; and

49 (4) Renqiu Field (Precambrian to Ordovician) in China. Other types of traps include: (1) karsted zones in structured strata (Type V: e.g., Oklahoma City Field, Ordovician, in the Anadarko Basin of Oklahoma); (2) reservoirs associated with linear fracture or fault trends (Type VI: e.g., the Albion-Scipio-Pulaski Trend in the Michigan Basin); and (3) the extremely subtle traps in karsted, gently-dipping strata (Type VII: e.g., various fields in the Ordovician dolomites of Permian Basin of Texas and New Mexico, U.S.A.). Exploration for karsted reservoirs traditionally has employed seismic surveys (conventional and 3-D; and offset-dependent seismic reflector amplitude analysis of conventional seismic), and in mature basins with ample well control, subsurface geologic mapping as well. The existence of karsted, potential reservoir zones commonly is indicated during drilling by dipmeter data, sudden drill bit drops, rapid increases in drilling rates, lost circulation, and very high initial flowing potentials.

RESERVOIRS IN C H A L K S

Chalks are fine-grained (micritic) limestones composed dominantly of the skeletons ofnannofossil coccoliths (brown algae). Although these pelagic organisms have wide environmental and latitudinal distributions (McIntyre and Be, 1967), their rates of production are slow. Hence, coccolith chalks accumulate into thick beds only in settings that have low rates of sediment input from other sources. In modem seas, chalks are accumulating mainly in the deep sea (100--4000 m depths). In contrast, the thick chalk deposits of the Cretaceous and Paleocene around the world, such as those in northwestern Europe and in the Gulf Coast and western interior seaway of the United States, likely were deposited in shallow epicontinental seas (depths of 100500 m), when high eustatic sea level stands during these times limited the amount of siliciclastic sediment input (Scholle, 1974, 1977). Newly-deposited chalks have initial interparticle porosity as high as 80%, which is rapidly reduced during early compaction and dewatering and later diagenesis to values approaching 10% (Schlanger and Douglas, 1974; Scholle, 1974, 1977). Permeability values of most chalks, exclusive of fractures, are very low, generally being less than 10 mD (Scholle, 1977). Accordingly, hydrocarbon production from chalks was, prior to the 1960s, considered to be unlikely. In fact, many major oil companies at that time simply were not interested in exploring for chalk reservoirs (see Chapter 6, this volume). As stated by Scholle (1977), significant production from chalks was once considered to be "miraculous". The discovery shortly thereafter of commercially significant hydrocarbon accumulations in chalks in the Ekofisk Complex in the North Sea, in the Gulf Coast and western interior seaway, and elsewhere in the world clearly changed that perception. Reservoirs in the North Sea, for example, have producible reserves on the order of several billion barrels of oil and trillions of cubic feet of associated gas. Although many chalk reservoirs, particularly those in the North Sea, average about 30% porosity, according to Scholle (1977) all primary interparticle porosity in chalks theoretically should be eliminated when the rocks are buried to depths of about 3000 m. The real

50 miracle is why such high porosities, which account for huge hydrocarbon storage volumes in inherently low-permeability chalks, are preserved in ancient chalk reservoirs. Several workers (Harper and Shaw, 1974; Rickards, 1974; Scholle, 1974, 1977; Byrd, 1975; Mapstone, 1975) have shown that most of this porosity is primary interparticle porosity that has been preserved because porosity reduction by mechanical and chemical compaction and cementation were retarded largely by reservoir overpressuring. In the Ekofisk area, for example, abnormally high pore pressures of 7100 psi at depths of 3050 m were reported by Harper and Shaw (1974), depths at which normal pore pressures and lithostatic loads should be only about 4300 psi and 9000 psi, respectively. As discussed in Chapter 8 of this volume (Friedman), other factors that may have contributed to porosity preservation in chalks include early entry of hydrocarbons into the reservoir, limited thickness of overburden, and the presence of pore fluids enriched in magnesium, which retards dissolution and subsequent cement reprecipitation. Fractures are ubiquitous in highly-productive chalks, and exploration for potential reservoirs always is concerned with fracture prediction and occurrence. Fractures create permeabilities of up to 200 mD in some typically low-permeability chalk reservoirs. The newest approach to enhancing production from low-permeability chalks began in the 1980's with the advent of horizontal drilling. According to Friedman (Chapter 8, this volume), a horizontally-drilled well may recover as much as five times the amount of oil as a comparable vertical well if the borehole encounters multiple sets of fractures.

SEISMIC IDENTIFICATION OF CARBONATES

Exploration for carbonate reservoirs has, as is the case for other reservoirs, been heavily dependent in the past on seismic reflection profiles. Of course, reservoirs in structured strata are relatively easy to identify on seismic sections, as are reefs. Accordingly, many hydrocarbon reservoirs have been discovered "on structures" and, particularly, in reef facies. More subtle traps in carbonate strata, for example, those developed along depositional facies pinchouts in shallow and deep-water strata, are inherently more difficult to discern using seismic exploration because of constraints due to stratal thickness and, commonly, limited impedance contrasts between potential reservoirs and enclosing strata. The various responses of carbonate strata on conventional seismic sections are discussed and illustrated in Chapter 2 of this volume (Kendall et al.). The use of seismic sequence stratigraphy in the 1970's (Mitchum et al., 1977; Vail and Mitchum, 1977) led to dramatic new advances in the exploration for potential reservoir facies in carbonate strata. Models of carbonate deposition based on seismic response, described by Bubb and Hatlelid (1977), and especially, Sarg (1988), now allow for enhanced predictive capabilities in terms of the recognition of potential reservoir facies. These models relate carbonate deposition, subsidence, and sea level changes to predicted spatial mosaics of depositional facies and potential reservoirs through time. Computer forward-modeling of carbonate rock stratigraphies has been a fundamental goal of many explorationists over the last decade as a tie-in to understanding the development

51

of sequence stratigraphies as identified on seismic sections. Chapter 2 also discusses this aspect of seismic analysis as it applies to the generation of detailed reservoir petrophysical models that allow geologists and reservoir engineers to fully exploit hydrocarbon reservoirs.

REFERENCES

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56 Sabins, KS., 1969. Thermal infrared imagery and its application to structural mapping in southern Califomia. Bull. Geol. Soc. Am., 80(3): 397-404. Sahuquet, B.C. and Ferrier, J.J., 1980. Steam Drive Pilot in a Fractured Carbonate Reservoir Lacq Superieur Field. SPE 9453, Soc. Petrol. Engrs. 55th Ann. Fall Techn. Conf. and Exhib., Dallas, TX, 12 pp. Sarg, J.E, 1988. Carbonate sequence stratigraphy. In: C.K. Wilgus, B.S. Hastings, C.G.St.C. Kendall, H.W. Posamentier, C.A. Ross and J.C. Van Wagoner (Editors), Sea-Level Changes: An Integrated Approach. Soc. Econ. Paleont. Min., Spec. Publ. No. 42, pp. 1 5 5 - 181. Schlanger, S.O. and Douglas, R.G., 1974. Pelagic ooze-chalk-limestone transition and its implications for marine stratigraphy. In: K.J. Hsu and H.C. Jenkyns (Editors), Pelagic Sediments on Land and Under the Sea. Intl. Assoc. Sedimentologists, Spec. Publ. No. 1, pp. 117 - 148. Scholle, P.A., 1974. Diagenesis of Upper Cretaceous chalks from England, Northern Ireland and the North Sea. In: K.J. Hsu and H.C. Jenkyns (Editors), Pelagic Sediments on Land and Under the Sea. Intl. Assoc. Sedimentologists, Spec. Publ. No. 1, pp. 177- 210. Scholle, P.A., 1977. Chalk diagenesis and its relation to petroleum exploration: oil from chalks, a modem miracle?. Bull. Am. Assoc. Petrol. Geologists, 61 (7): 9 8 2 - 1009. Stein, M.H., Frey, D.D., Walker, R.D. and Pariana, G.J., 1989. The Slaughter Estate Unit C02Flood: A Comparison Between Pilot and Field-Scale Performance. SPE 19375, Soc. Petrol. Engrs. Production Techn. Symp., Lubbock, TX, pp. 1 - 12. Stewart, C.R., Craig, F.F., Jr. and Morse, R.A., 1953. Determination of limestone performance characteristics by model flow tests. Trans. AIME, 198:93 - 102. Stiles, W.E., 1949. Use of permeability distribution in waterflood calculations. Trans. AIME, 186:9- 13. Tarr, C.M. and Heuer, G.J., 1962. Factors Influencing the Optimum Time to Start Water Injection. SPE 340, Soc. Petrol. Engrs. 5th Biennial Secondary Recovery Symp., Wichita Falls, TX, 10 pp. Tatashev, K.K., 1968. Effect of the change in layer pressure on the oil displacement from blocks of fissured-porous oil reservoirs by water imbibition. Geol. Nefti i Gaza, 1: 5 5 - 59. (In Russian.) Trocan, V.N., Frydl, P.M. and Robertshaw, E.S., 1992. Horizontal wells improve mature miscible flood performance- Rainbow Lake Field, Alberta, Canada. SPE 24125, Soc. Petrol. Engrs./U.S. Dept. of Energy 8th EOR Syrup., Tulsa, OK. Vail, P.R. and Mitchum, R.M., 1977. Seismic stratigraphy and global changes of sea level, part I: overview. In: C.E. Payton (Editor), Seismic Stratigraphy- Applications to Hydrocarbon Exploration. Am. Assoc. Petrol. Geologists, Mem No. 26, 516 pp., pp. 51 - 52. Van Everdingen, A.F. and Kriss, H.S., 1980. New approach to improved recovery efficiency. J. Petrol. Techn., 32(6): 1164 - 1168. Vasilechko, V.P., Gnatyuk, R.A. and Petrash, I.N., 1969. Effectiveness of cyclic water flooding in oil formations of Pre-Carpathian fields. Nauch.-Tekh. Sb. Ser. Nefiepromyslovoe Delo, 1" 1 0 - 12. Ward, R.E, Kendall, C.G.St.C. and Harris, P.M., 1986. Upper Permian (Guadalupian) facies and their association with hydrocarbons - Permain Basin, west Texas and New Mexico. Bull. Am. Assoc. Petrol. Geologists, 70(3): 239-262. Watts, R.J., Gehr, J.A., Wasson, J.A., Evans, D.M. and Locke, C.D., 1980. A Single CO 2Injection Well Minitest in a L o w - Permeability Eastern Carbonate Reservoir- A Preliminary Report. SPE 9430, Soc. Petrol. Engrs. 55th Ann. Fall Techn. Conf. and Exhib., Dallas, TX, 10 pp. Weber, K.J., 1986. How heterogeneity affects oil recovery. In: L.W. Lake and H.B. Carroll, Jr. (Editors), Reservoir Characterization. Academic Press, Inc., New York, 659 pp., pp. 487-544. Weber, K.J. and Bakker, M., 1981. Fracture and Vuggy Porosity. SPE 10332, Soc. Petrol. Engrs. 56th Ann. Fall Tech. Conf., San Antonio, TX, 11 pp. Wigley, EL., Bouvier, J.D. and Dawans, J.M., 1988. Karst and mixing-zone porosity in the Amposta Marino Field, offshore Spain. Bull. Am. Assoc. Petrol. Geologists, 72(8): 1031. Willingham, R.W. and McCaleb, J.A., 1967. The Influence of Geologic Heterogeneities on Secondary Recovery from the Permian Phosphoria Reservoir, Cottonwood Creek, Wyoming. SPE 1770, Soc. Petrol. Engrs. Rocky Mountain Reg. Meet., Casper, WY, 12 pp. Willmon, G.J., 1966. Vertical miscible flood to hike recovery by 70 million barrels. Worm Oil, 162(1): 75 -78. Witherspoon, P.A., Wang, J.S.Y., Iwai, K. and Gale, J.E., 1980. Validity of the cubic law for fluid flow in a deformable rock fracture. Water Resources Res., 16(6): 1016 - 1024. Wolf, K.H., Chilingar, G.V. and Beales, EW., 1967. Elemental composition of carbonate skeletons, min-

57 erals, and sediments. In: G.V. Chilingar, H.J. Bissell and R.W. Fairbridge (Editors), Carbonate Rocks, 9B. Elsevier Publ. Co., Amsterdam, 413 pp., pp. 2 3 - 149. Worthington, P.F., 1991. Reservoir characterization at the mesoscopic scale. In: L.W. Lake, H.B. Carroll, Jr. and T.C. Wesson (Editors), Reservoir Characterization II. Academic Press, Inc., New York, 726 pp., pp. 1 2 3 - 165. Wu, C.H., Flores, D.P., Briens, F.J., Brimhall, R.M. and Poston, S.W., 1989.An evaluation of water flood infill drilling in west Texas Clearfork and San Andres carbonate reservoirs. SPE 19783, Soc. Petrol. Engrs. Ann. Techn. Conf. and Exhib., Reser. Eng. vol., pp. 121 - 136. Young, M.N. and Martin, W.E., 1980. The Wizard Lake D-3A pool miscible flood. J. Can. Petrol. Techn., 19(2): 65 - 75. Yuster, S.T. and Calhoun, J.C., Jr., 1945. Pressure Parting. Producers Monthly, 9(4): 16 - 26. Zemanek, J., Caldwell, R.L., Glenn, E.E., Holcomb, S.V., Norton, L.J. and Straus, A.J.D., 1969. The borehole televiewer- A new logging concept for fracture location and other types ofborehole inspection. J. Petrol. Techn., 21 (6): 7 6 2 - 774. Zimmerman, L.J. and Chen, S.T., 1992. Geophysical Methods for Reservoir Characterization. SPE 23953, Proc. Soc. Petrol Engrs. Permian Basin Oil and Gas Rec. Conf., Midland, TX, pp 241 - 250.

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59

Chapter 2 SEISMIC EXPRESSION OF CARBONATE RESERVOIR SYSTEMS CHRISTOPHER G.ST.C. KENDALL, WILLIAM E. FULL, and GREGORY L. WHITTLE

INTRODUCTION

This chapter addresses the use of seismic data, particularly where they are correlated with well information, to identify and interpret the carbonate depositional systems associated with three major types of carbonate play. Commonly, these plays can be ranked in order of decreasing size as: (1) carbonate sheets, (2) carbonate buildups, and (3) clinoform carbonate shelf margins. Sheet plays are found in carbonate shelf sediments associated with the shallow water behind the basin margin; buildup plays occur down-slope from the margin and on the shallow shelf immediately adjacent to the margin; clinoform plays are associated with the margin crest (Fig. 2-1). The depositional porosity and geometry of these plays may be modified by subsequent fracturing and diagenesis (see volume 1, Chapter 4). With the exception of chalks, most of these carbonate plays are related to highstand system tracts: the aggradational sheet play geometry is formed as shoaling-upward cycles during sea-level highstands when carbonate accumulation matches sea-level rise (keep-up); the buildup lens-like carbonate geometry is formed on drowned shelves during and following rapid sea-level rises (keep-up and give-up); and the progradational clinoform geometry of the platform margin is formed during stillstands by carbonate accumulation that not only keeps-up with the sea-level rise, but advances in a seaward direction (Kendall et al., 1991). Seismic interpretations of these plays can be tested with computer simulations which model the fill of sedimentary basins. The input parameters to such simulations are assumptions about the processes of sedimentation, sea level history and tectonic evolution of the study area and are based on currently accepted sedimentological, tectonic and eustatic models (Scaturo et al., 1989; Kendall et al., 1990; Lawrence et al., 1990). Before discussing these carbonate plays and their seismic response, it is important to provide the reader with some background on seismic and synthetic seismograms.

SEISMIC AND SYNTHETIC SEISMOGRAMS

The purpose of this discussion is to try to bring an understanding of the inherem limitations and strengths of seismic and synthetic seismogram data as they relate to the subsurface recognition of carbonate systems. Without some understanding of the principles underlying seismic analysis, the carbonate modeler is more prone to potential misinterpretation. If the reader is interested in a more complete discussion of these subjects, many points raised here are discussed in a number of works which describe: ( 1) the theory and application of seismic data and their tie to well data: Widess (1973), Dobrin (1976), Sheriff (1976, 1977, 1978), Telford et al. (1976), Coffeen (1978),

60 CARBONATE

PLAYS

IIa. Reef on Shelf ~ / x _ r - x

IIb. Reef Downslope

~ / x J ' x . _ / x

KEY

~

Limestone -~

iShale ~

Evaporite]

Fig. 2-1. Common carbonate plays include: I. Plays with sheet-like geometry formed during sea-level stillstands and rises whose aggradation matches the rise in sea level (keep-up). II. Shelf and downslope reef plays with lens-like geometry formed during and following sea-level rises (catch-up, IIa) and stillstands on shelves drowned by the rapid rise (give-up, lib). III. Clinoform plays with progradational platform margin geometry formed during sea-level stillstands, both at sea-level highs and sometimes at lows; the latter when associated with shallow basins.

McQuillin, Bacon, and Barclay (1979), Robinson, and Coruh (1980), Sengbush (1983), Kearey and Brooks (1984), Sharma (1986), and Waters (1987); and (2) synthetic seismic seismograms: Neidell (1980), Bally (1983, 1984, 1987, 1989), Schlee (1984), Berg and Woolverton (1985), and Gries and Dyer (1985). Sek~mic data

From a simplistic viewpoint, reflection seismic data are recordings of acoustic waves that have traveled through the earth starting at a known position and were reflected

61 from surfaces, be they carbonate or some other lithology, marking changes in acoustic impedence (acoustic impedance is the product of the density and seismic velocity in media). These recordings are processed to produce an image of the layered character of the earth. These layers are represented by events delineated as deflections on a seismic trace (a "wiggle" trace). Each deflection is the summed result of spatial changes in the elastic moduli (bulk modulus, rigidity, Poisson's ratio, or Young's modulus) and/or density of the rocks which result when the energy of the acoustic wave is reflected at successive layer boundaries (acoustic impedance boundaries) in the earth. The collection of variables describing the magnitude of all the seismic reflections versus time or depth is called "earth information" (eT). In an ideal earth, a source of energy, such as an explosion, produces an impulse whose overall shape is not altered except in amplitude, as it interacts with changes in earth properties along the wavefront. Mathematically, the impulse at any location in the earth could then be represented by the following function: Impulse = k (del) T

(2.1)

where: k is a constant describing the amount of energy recorded in an individual event (the amplitude squared), and (del)x represents the impulse function at time T. In this ideal situation, the seismic trace can be considered the end result of the interaction of the acoustic impulse with the earth properties. This interaction is called "convolution" and represents a filtering operation. The seismic trace (ST) can then be described by the following: S v = k (deI)T (convolve)e T

(2.2)

where: the symbol (convolve) represents the convolution (filtering) function. The convolution function represents the formula or process detailing the "how to" of the interaction of the impulse with the earth properties. Just as the earth is not physically ideal, neither is the seismic response. Deflections on seismic traces need not be a function solely of earth layering. In reality, they are the product of the convolution of non-ideal seismic impulses with less than perfect earth properties. The net outcome is that additional energy from other sources, such as multiple reflections, background noise (microquakes), occasional noise (trains, buses, cars), and coherent noises are included within the seismic traces. Additionally, the near-surface weathering zone interferes with and slows the velocity of the acoustic signal, a factor that can result in what is known as a "statics problem" where "events" appear to be displaced vertically and/or less coherent. Other influences include potential inefficiencies in the instruments, non-optimal geophone array patterns, and incomplete field recording of the seismic signals themselves. Relative to a seismic wave propagation, rock anisotropy relative to seismic wave propagation can also affect a clear definition of the earth properties. In only a few situations does the initial seismic record clearly depict the earth properties one desires to define. The seismic records are usually computer-processed so as to remove some of the undesired effects discussed above. The processing may entail trace editing, static corrections, amplitude adjustments (muting, gaining, and

62 amplitude recovery), normal move out (NMO) corrections, stacking and averaging traces, filtering (velocity and frequency varieties), deconvolutions (undoing a convolution or filtering process), and migration (the process of locating the proper position in two- and three-dimensions of a particular event). Usually, the processing is performed by specialists guided by the interpreter's specific needs. The result is that most seismic sections (collection of related individual seismic traces) are processed with specific models in mind. No standard method of seismic processing exists which enhances all the key information that can be extracted in all the portions of the seismic section. That is, the seismic processing performed for enhancing thin lithologic units in shallow subsurface sections differs appreciably from the processing required for thick units at greater depth. The more the seismic interpreter understands what processing the seismic signal has undergone, the more effective the interpretation. Without such a background, earth properties can be either missed or misinterpreted. Seismic events

A seismic event, as defined here, is simply a coherent or recognizable deflection on seismic traces that appears to be similar on two or more seismic traces. An event can be considered as two or more seismic deflections that can be correlated in some fashion, or as complicated as one wants them to be. The correlation of deflections can be based on: (1) matching relatively large amplitude trace deflections across two or more signals, or (2) matching various other waveform characteristics, such as gradually changing deflection shapes, common phases, frequencies and polarities, or any other property one wishes to define. Interval seismic velocity (average velocity within an interval of time) can also be used to correlate events. It should be noted that not every seismic event necessarily implies earth layering insofar as noise can sometimes be correlatable. Additionally, not all earth layers produce distinctive seismic shapes. The "cleanest" events on a seismic section are those defined by relatively large amplitude deflections. Events that span an increasing number of seismic traces, however, are less likely to be noiserelated. The actual amplitude of an observed event is a function of: (1) source-receiver distance; (2) properties of the media through which the wavelet (collection of acoustic frequencies comprising the initial seismic disturbance) has traveled; (3) geometric character of the traversed media; (4) noise processing of the earth; and (5) the character and spectra of energy associated with the source of the elastic disturbance. The total energy of the acoustic disturbance travels away from a source in spherical waves, and decreases as a function of the square of the distance from the source. Insofar as the square root of the energy associated with an individual disturbance is proportional to the amplitude of the disturbance, it follows that the amplitude should vary as a simple function of distance from the source. That is, if A ~ is the original

63 amplitude, then in a homogeneous media, geometric spreading (GS) can be expressed as:

(2.3)

GS = Ao/D

where: D is the distance from the source (Dobrin, 1976). The properties of the media normally affect the amplitude of the impulse wavelet in two ways: (1) as frictional dissipation; and (2) as an interaction with a surface marking a change in acoustic impedance. Frictional dissipation of the elastic energy into heat (or deformation of the grains within media, such as by compaction) causes a loss of wavelet amplitude. This loss is called "absorption" and is governed by the following equation: A - Ao e-alphaD

(2.4)

where: A is the original amplitude, A is the amplitude at distance D from the source, and alpha is the absorption coefficient which depends on the media being traversed. The absorption coefficient can vary greatly for different media, and generally reflects a high loss of energy for pulses traveling through media like anhydrite, halite, and some shales. For media such as dense carbonates, quartzite, and igneous rocks, the percent loss of energy is comparatively low. What makes the calculation and subsequent application of absorption coefficients difficult is the fact that this coefficient is dependent on (1) the frequencies present in the seismic pulse; and (2) the confining pressure (depth) of the rock, both of which must be precisely known. Figure 2-2 displays the effect of increasing depth relative to an arbitrary input wavelet. The second property of the media which affects the amplitude of the impulse wavelet is the change in acoustic impedance (which occurs where there are heterogeneities in the lithology, diagenetic fabric, or other rock properties) that form boundaries to the seismic wavefront. Acoustic impedance (p V) is the product of the bulk density of the media (p) and the velocity of the compressional wave as it passes through the media (V). An acoustic boundary occurs where there is a difference between the acoustic impedances along the path of the wavefront. It is along these boundaries that reflections, refractions, diffractions, and the creation of additional seismic disturbances are created. The amount of energy that an incoming (incident) wave disperses as reflections, refractions, and additional seismic energy, is a function of the angle of incidence and the contrast in acoustic impedance at the boundary. For normal (90 ~) incident waves, only reflected and refracted waves are generated. The proportion of incoming energy in the reflected wave can be calculated by: o

Energy = R 2 = [(p2 V2- Pl

VI)/(Pl V1 "[- P2V2 )]2

(2.5)

where: R is the reflection coefficient, Pi is the bulk density of medium i (the wave is traveling from medium i to medium i+ 1), and Vi is the P wave velocity in medium i. In this normal incidence case, the energy not reflected will be transmitted into the second medium. Angles other than 90 ~ mean less energy is reflected and new forms of seismic disturbance are created at the boundary (they can consist of reflected

64 Surface ,,

Lithology

-IO00m (350Oft)

I

I-

Seismic Response

Large positive reflection coefficient 50 hertz

1

wavelet.

ACoustic impedance of shale increases with depth. Limestone's i n c r e a s e s only sltqhtly.

Acoustic imped<;nce of shale increcs,ng with cam pact <.'~

Acoustic impedance

contro.",t dec.reo,',,::.

Decrease in wavelet frequency and strenqth with depth.

with depth.

- 3000 m ( 9900 f t )

5000m (16,500ft)

--1

S,

Smaller positive reflection coeff~cient 25 hertz wavelet.

-

Weak positive reflection coefficient and weak 12hertz wavelet.

De :~th

Fig. 2-2. Sketch showing the effect of increasing depth, through changes in acoustic impedance and seismic-wavelet frequency, on the seismic response from an acoustic-impedance contrast between clay and limestone. The Earth attenuates the seismic signal, preferentially removing the higher frequency components. The combined effect of decreasing frequency and acoustic-impedance contrasts produces a change from shallow, strong and sharp reflections to weak and long reflections at depth. (From Badley, 1985, Fig. 2.22.)

and refracted shear waves in addition to reflected and refracted P-waves). For the most part, one observes the clearest reflections when the angle of incidence is 90 ~. If there is no change in acoustic impedance, there will be no reflection observed. The greater the change in acoustic impedance, the greater is the amount of reflected energy.

65 Reflection tmcn top limestone Maximum interfenmce Decreasing amplitude No i n ~ e

\

Soparole refleclions from top ond base lim~s'l~

Ref lectic~ from bose lime.slone

Below I/,.o ,,,,ovelength ~,~ no reflectbon

Shale 3000 m/s wavelonqth (5Ore) Tuninq thickness

_

= No interference

Limestone 5CXX) m/s

Shole 3000 m/s ( ~ ~ i

50

hertz wavelet

Amplitude

Wavelength

Frequency - Number wavelengths per second 1 wavelength per second ,, 1hertz

Time

Waveform attributes

Fig. 2-3. Interference effects associated with a high acoustic-impedance wedge encased in lower acousticimpedance shale. The limestone must be thicker than half the seismic wavelength for no interference between reflections from its top and base. Maximum interference and amplitude of the resulting reflection occur at a limestone thickness equivalent to one-quarter of the seismic wavelength. For limestone thickness below one-quarter wavelength, the reflection remains the same but decreases in amplitude. Once the limestone is about one-thirtieth wavelength or less, reflections from the top and base effectively cancel, and there is no detectable seismic response. (From Badley, 1985, Fig. 2.14.)

The geometry of the reflecting boundaries can also affect amplitude. If the boundaries are convex, seismic waves can be focused. If concave, energy can be spread out resulting in loss of amplitude. There are cases where all or portions of boundaries are not observed because the waves were deflected by the geometry of the overlying boundaries. This latter point is important in areas of less-than-flat interfaces, where one might not presume to observe all the features that were expected on the seismic section. Furthermore, seismic reflections are additive and can produce constructive and destructive interference effects, especially when two or more events are closely spaced (Fig. 2-3) or when there are phase changes at closely spaced boundaries (Fig.

2-4). Extra events may be observed in a seismic section that are not directly below the geophones. These events may represent impedence boundaries outside the planes of the defined seismic section, which is a three-dimensional effect that must be considered whenever two-dimensional (or even one-dimensional) seismic data are analyzed. Moreover, boundaries that reflect acoustic disturbances in an ideal manner must be of

66 Reflection coefficients

Individual responses

Composite response

Constructive

interference I L

Destructive interference

Fig. 2-4. Constructive and destructive interferences affecting a minimum-phase normal-polarity wavelet. (From Badley, 1985, Fig. 2.10.)

a minimum area (the "Fresnel Zone"). Interaction of the acoustic wavefront with boundaries of less than minimum Fresnel sizes will result in the creation of reflection of smaller, sometimes distorted, shapes. The same holds true if there are "holes" in the reflecting boundary. To complicate matters further, the size of the Fresnel Zone is a function of the frequencies present at the wavefront. For example, the Fresnel Zone is larger at greater depths and smaller at shallower depths simply due to the fact that higher frequency acoustic signals display greater attenuation in the earth than do longer wavelength signals. The implication of this observation is that the prediction of the effect of reduced regions of acoustic boundary interaction is difficult to ascertain without computer modeling. Noise in all forms can also affect the amplitude of the signal reflected by an individual event. This noise can be random, coherent, or even induced by the recording instruments. Similarly, data processing can alter both the amplitude and character of the seismic pulse. This alteration can be caused by gain and mute procedures, or more complicatedly by Wiener filtering and other computerized signal enhancements. The net result is that distinct events can be created, enhanced, remain the same, or may even be lost by the data processing. As stated previously, the more we know about this critical step, the better we can predict where on the seismic section individual events have been affected and, more importantly, how they have or have not been altered. Finally, the amplitude of an individual event is a function of the amount of acoustic energy and, as briefly mentioned above, how this energy is distributed among the seismic spectrum of the initial acoustic impulse created by the source. For example, an initial wavelet dominated by high frequency energy would probably not help

67 PAR AIR GUN 300 c u - l n w a v e s h a p e d ( W S K - 1805- IH)

......i

AIR PAR

24

A/"x

I0 ,n

o

0 I

o

depth

H-cut

o:~

o 15 see

0

v IV'-

125Hz

0:2

6-80

o 3 sec

1 KJ

13 m d e p t h

o:1

0:2

sec

~, 0-~ sec

I

~,

0~2

U

_25o. lore

O: 2 sec

0

0-1

depth

"

0-2 sec

SPARKER

AA./L -

300 Hz

depth

SODERA MICA WATER GUN

Hz

0:1

FLEXOTIR 1 GUN

5-

O~l

FLEXlCHOC F 123- 20

15m d e p t h o:1

_ _

,

o:os

RCHOC

~]

r~/~ ~

I0 m

0.3 sec

2

GGUNS u n s in array

,,

V''"" 6m

o:os

depth

o:o~

o-o~s sec

Fig. 2-5. Signatures of a range of seismic sources used in marine seismic. (From McQuillin et al., 1979, Fig. 2/19.)

define a relatively deep structure or depositional feature. Conversely, low frequency energy commonly cannot define shallow information. The characteristics of the input signal are critical in understanding which information can be gleaned from a seismic signal. Figure 2-5 displays several initial sources used commonly in marine seismic gathering. In conclusion, the interpretation of seismic data requires a multi-disciplined approach which may not provide one with the unique solution one would expect. Limitations of seismic method In addition to the general limitations of seismic as discussed above, the application of seismic to carbonate systems seems to have shortcomings that are unattractive to many carbonate modelers. As pointed out by Rafavich et al. (1984), primary lithology and secondary mineralogy have only a relatively small influence on acoustic impedance and seismic velocities. Porosity was found to be the major factor influencing these variables, whereas other variables, including pore-fluid type and petrographic

68 fabric, seem to have little, if any, significant influence on seismic velocities. Rafavich et al. (1984) found that, in addition to porosity, an increase in bulk density also increases seismic velocity. Furthermore, increases in quartz content decrease velocity but have less influence on velocity than does porosity. Changes in calcite, dolomite, anhydrite, and clay content of the rocks can also produce complex relationships with seismic velocity, and depend greatly on burial history. In many regions, such as Little Knife field in the Williston Basin, the pressure effect on seismic velocity was found to be essentially independent of lithology, a fact that further complicated lithologic interpretations. Whereas some statistical approaches, such as examining p-wave to swave velocity ratios, can be used to discriminate between some limestones and dolomites, it appears that seismic alone cannot produce solutions. Additional information, such as well log interpretation and laboratory descriptions of rock samples, are critical to impedance models and, ultimately, to the correct formulation of the carbonate model. Despite all the limitations discussed above, often one can still recognize gross geometries, and thereby, predict presumed changes in lithofacies via the study of carbonate stratigraphy and creation of synthetic models. Synthetic models represent an essential tool for the carbonate modeler, especially where there are complex lithologic, petrophysical and tectonic relationships present. Synthetic seismic traces

Synthetic seismic cross-sections involve the use of well logs, geologic models and acoustic wave theory. Synthetic seismic records are used to predict major geologic features on a seismic section. The greater the understanding the modeler has of the Inteqrated Sonic log

V Io~

Lith. log

1_-1

p log

pV Io~

rI

rl

Itva-rq II

I

II

so,t VELOCITY

RClog RCloq

Composite seismic trace

-t .

[

Fig. 2-6. Diagram showing the hypothetical seismic response to lithologic changes along with pertinent geophysical logs. (From Badley, 1985, Fig. 2.9, after Anstey, 1980.) The symbol V is velocity, t9 is density, and RC are reflection coefficients.

69

I~

Pulse from above (wave length is 200 tt at 10,000 ft/$)

20 ms ~

Velocity, ft]$

10,000

coefficient

--0.0110 0 11,500 IS~

~

",,

13.500

11.500

-,

I

,

,-

,,,q,,,

/

I

\,

S

9.000

12,500

Reflection signal

/ above

~

/

~~#j/

Fig. 2-7. Composition of reflection from series of five interfaces with separations small in comparison to wavelength. Note change in waveform caused by reflection process. Waveforms indicated by dashed lines represent reflections with phase reversal. (From Dobrin and Savit, 1988, Fig. 8-4.)

rocks, theoretically the closer the match between the synthetic seismic sections and the seismic lines. Synthetic seismograms are constructed by determining the acoustic impedances in a rock section, and using these to determine the reflection coefficients at layer boundaries. Normally, density and velocity from which the impedance is derived are measured from sonic logs (Fig. 2-6). Insofar as the resolution of well logs is much greater than that of seismic, these logs are smoothed to minimize noise and reduce the complexity of subsequent steps in the procedure. Smoothing of the sonic log is more pronounced with greater depth. Where density is not directly measured

70 from core samples, it must be determined indirectly from velocity, lithology and depth (Dobrin, 1976). If sonic log velocity is not measured from a well, then empirical relationships can be used to derive it from resistivity and other wireline log variables. Where wells are not available, velocity and density information are estimated directly from the seismic. Velocity can be calculated from observed or modeled normal moveout (NMO) relationships, or by the analysis of the coherence of seismic amplitudes for which a range of velocities have been assumed (Dobrin 1976; Dobrin and Savit, 1988). Estimates of density are usually accomplished either by the modeling of the presumed lithology, or by using empirical relationships which tie density to derived velocity. One such formula used to estimate the density of non-evaporitic sedimentary rock density is: p = 0.23 V ~

,,',~

_

~._ '~,,,,,.',~ ~Di,",

____~, ~

9 0.1

9

l,,,if,,IP,If,'If, '.p ,.btD.D - - ~ t

*-.--

l

~r..

-

'lIIt

1.0

t~ ij~

' ~"

-

0.5

"-

--~I~I!

I ~

~,~;~,~, _:'ff'~,.

1.o

' "~ -'i~,_)1.?!: FtELD SEtSMIC DATA

SYNTHETIC SEISMIC DATA

RE.FLECTIVITY TIME SERtES

VELOCITY LOG

FtELD SEtSMIC DATA

Fig. 2-8. Visual relationship between field seismic data, synthetic seismic data, the reflectivity time series calculated from the velocity log (RC log), and the velocity log itself. (From Dobrin and Savit, 1988, Fig. 8.5, modified from Wood, 1982.)

71 where: p is bulk density, and V is the velocity of P waves through the media. These estimates are generally not as accurate as one would like, but when no other data are available they do represent a usable approximation. Given estimates for velocity and density, acoustic impedance can be calculated for each rock interval. The reflection coefficient is then calculated for each major change in acoustic impedance from this collection of data. This information is usually plotted against two-way travel time (Fig. 2-6) and results in a RC log, informally called a "reflection coefficient tree." These "trees" are as detailed as the modeler cares to make them and represent the raw input needed for synthetic seismic work. The second step in the creation of synthetic seismograms is determination of the characteristics of the seismic wavelet for the energy source that will be used to model the seismic section. For example, if the seismic section was processed with a zero-phase wavelet, then the synthetic must also be processed with a wavelet with similar properties. The reason that similar wavelets are used for both the seismic section and the synthetic is that more accurate correlations can be made between them. Given the proper wavelet reflection coefficient tree, a synthetic trace consisting of the sum of the individual reflections plotted against two-way travel time can be produced. The phase and amplitude of each reflection are determined by the sign of the reflection coefficient and its magnitude. Although there is an amplitude loss in the transmission of a seismic wave through an interface, it is usually assumed that there is none in this procedure (Sheriff, 1977). Consequently, amplitudes of individual events can be related to relative differences between the acoustic impedances of adjacent layers rather than to their absolute magnitude for that depth. The sum of all of these reflections against two-way travel time represents the synthesized seismogram for that well or station (Figs. 2-7 and 2-8). Corrections to the synthetic can then be made by comparing it to the migrated seismic section at that location, and adjusting the assumed model parameters, and then repeating the process. Several adjacent seismic traces can be plotted to form simple synthetic seismic sections in two or more dimensions.

Use of synthetic seismic for modeling The synthetic seismogram is based on an assumed geologic model which is tested by comparison with the recorded seismic. Iterative changes are made to the geologic model untii the best match is made with the seismic. The more well data, the greater confidence one has in identifying a particular depositional facies. Similarly, the greater the amount of seismic, especially on a regional scale, the more confident one is of the geologic model. Geologic models derived from one or only a relatively few seismic traces tend to be suspect. Increased seismic resolution, and advances in seismic signal processing and wavetheory, tied to the use of higher capacity computers, have opened the door to more realistic two-dimensional and three-dimensional synthetic modeling. In these models, factors such as refraction, multiples, and diffractions can be incorporated into the synthetic traces. These more complicated synthetic seismograms are referred to commonly as "wave-theory models." Whereas wave-theory models are usually more

72 computational-intensive, they often provide insight into the geologic information contained within the seismic section. Finally, because of the large number of variables that can affect an individual seismic event, unique interpretations of any one seismic section, whether based on synthetic correlations or well data, are unobtainable. Reasonable interpretations are usually the best one can hope for.

Limitations of synthetics Synthetics have not only the same limitations as seismic, but additional shortcomings as well. For instance, well logs have high vertical resolution and weaker lateral continuity, whereas seismic has generally poorer vertical resolution, but good lateral continuity. To maintain the vertical resolution of a synthetic seismic trace, the best match is achieved by using a heavily filtered sonic or density log (Sheriff, 1977, 1980). Another shortcoming is that correlations are difficult where seismic amplitudes decrease with depth and are distorted by layers of rock thinner than the wavelength of the signal. Additional deficiencies are produced by: (1) filter delays in recording and/or processing of the seismic; (2) the use of different reference data in the CDP stack; (3) phase shifts due to arbitrary choices of initial wavelet waveforms; (4) small systematic errors that accumulate in the creation of the synthetic; and (5) failure to take migration effects into account. A second series of limitations involve the modeling of lithology with synthetics. A seismic reflection is recorded only when there is a change in acoustic impedance from one interval to the next. However, even though there may be no difference in acoustic impedance at a particular lithologic surface, it is sometimes assumed that a reflection is from such a boundary. Despite these limitations, visual interpretation of reflection configurations, when used in conjunction with seismic parameters such as amplitude, frequency, continuity, and interval velocity, can lead to reasonable seismic correlation with well data, and to more accurate recognition of vertical and horizontal sequences on the seismic sections.

CARBONATE PLAY TYPES

Carbonate sheet reservoirs Carbonate sheets are the most common and can be the most widespread and largest of carbonate plays. They are commonly composed of shallow-water shelf grainstones and wackestones, often dolomitized, and are usually associated with shale and evaporite seals. Most of the giant oil fields of the Middle East (Jurassic and Cretaceous), the Williston Basin (Paleozoic and Mesozoic), and the Permian Basin of west Texas and New Mexico (Paleozoic) are developed in sheet carbonate plays and are sealed by evaporites (Fig. 2-9). There are two kinds of sheet shelf carbonate reservoir plays: (1) one which retains depositional porosity, and (2) one which has secondary porosity. These are extreme end-members, and commonly both depositional and diagenetic porosity occur together

73

SHELF SHEET C A R B O N A T E PLAY (hnlP

~haat

Marls &/or IV ~hales

~abkha Evaporites Ir Tidal Flat V Carbonates

High 9

m

oJ

Low

~

_

,

"Grainstones V

HIGHSTAND

Wackestones IV .

.

.

.

.

.

_

-o

-I-I-I.- - _~-_w~§

w~o~

l/larls &/or IV

I.

Im

SIN FAN

.........

Shales IV

I KEY ~~

Limestone ~

----

Shale

~

Evaporit

4

Fig. 2-9. Shelf sheet carbonates include: (1) Grainstone keep-up sheets that aggraded during highstands in sea-level just landward from breaks in slope, marginal to basins that lie below wave-base. (2) Dolomitized leached wackestone keep-up sheets which accumulated in epeiric seas of the continental interior when sea-level was particularly high and formed widespread interior seas.

within the same reservoir. Usually sheet carbonates are associated with shallow-water shelves of the platform interior. The best reservoirs in sheet carbonates are represented by sands that have accumulated behind the shelf-slope break. Sediment types include oolitic grainstones, or more commonly grapestones, and pellet sands with varying quantities of lime mud representing shoaling-upward cycles of tidal flat and

74 lagoonal sedimems. The shoaling-upward cycles often have a shaley, marley, or micritic transgressive unit at the base of the cycle which grades up into grain carbonates, reflecting the higher energy, low subtidal to tidal fiat settings normally associated with the central and upper part of the cycle. The cycles present within a field may be numerous or may be a single event, representing a complete geological stage. The transgressive micritic layers of the next cycle may act as seals, particularly where these are stylolitized (e.g., as in the Bu Hasa Formation of the Bu Hasa Field: Alsharan and Kendall, 1986), and overlie carbonate grainstones. Shales, which occur in an overlying cycle, may be seals to underlying cycles. Alternatively, the cycles may be terminated by prograding upper intertidal to supratidal carbonate muds with or without evaporites. This latter association with evaporites is found in many of the sheet carbonates fields and is important because it may be a seal, particularly as an updip pinchout. Commonly, the depositional porosity may be only slightly modified by some early isopachous cements which surround the carbonate grainstones and local echinoderm overgrowths. Locally, dolomitization of carbonates may occur, and porosity can result from either the leaching of the remaining carbonates or the retention of porosity present before dolomitization. Some carbonates may be completely dolomitized and porosity is developed between individual clear dolomite rhombs. In contrast, dolomite may float in the matrix of sediment and cement of carbonate sediments. These may include some porosity, but probably are not important to reservoir character. The seismic character of sheet carbonate plays is highlighted by the striking continuity of reflectors (Fig. 2-10). Local evaporite pinchouts and porosity changes will show up as changes in the amplitude of the reflectors, some of which thicken and others which disappear. Normally, a higher resolution seismic source and specialized processing must be used to see many of the individual features present in these systems.

Carbonate organic buildups Carbonate organic buildups, i.e., reefs, are the next most common carbonate play and occur on either drowned carbonate shelves (Fig. 2-11) and/or on ramps downslope from platform margins (Fig. 2-12; see also volume 1, Chapter 3). They are commonly sealed by basinal shales, micrites and/or evaporites. Examples of organic buildup reservoirs include reefs in the Upper Devonian of western Canada (sealed by shales and or evaporites); Silurian pinnacle reefs of the Michigan Basin (sealed by evaporites); Pennsylvanian algal-plate buildups of Kansas and Oklahoma (overlain by shale and non-porous carbonates); Paleocene reefs of the Sirte Basin in Libya (enveloped in shale, and in some cases, extremely low-permeability micritic rocks); and Miocene reefs in the South China Sea. Although the petroleum fields associated with carbonate organic buildups are not normally as large as those associated with sheet carbonates, once their seismic character has been established these plays are easy to identify and to drill. Even though encompassing less areal extent than sheet carbonate plays (a few square miles vs. tens of square miles), the organic buildup reservoirs can typically contain enormous quantities of oil.

s.,;

LINE

W-2

~IE

A

I i

.

.

.

.

.

.

.

.

.

.

.

.

L

a

.,

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, . . ~

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.

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.

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.

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.

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;P"l,~r.I k'.,:,Ei(FE

"OP .JF;a.5.~E ~$~'R.E:

kil"-"Ri.J,SS~"

~C Fig. 2-10. Example of sheet shelf carbonate reservoir system in southwest-northeast seismic of Oxfordian carbonates of eastern Saudi Arabia. Synthetic tie-in for wells W-1 and W-2 shown in Fig. 2-15. Note striking continuity of reflectors throughout the section. (From Langdon and Malecek, 1987, Fig. 4.)

76 Shelf Reef

ao

High

Low

III

~V 9

HIGHSTAND WEDGE

BO

III. . II.

"~W STAND t_

WEDGE

SL-}P F_A_N.... FAN

C0

II

[ KEY ]:':':':I Limestone

i Shale I

Fig. 2-11. Give-up and catch-up slope buildups on shallow water back from the platform margin. (a) Shallow water carbonate stillstand wedge, possibly formed during low sea-level stand; (b) Buildups form on irregularities on the shelf at the stillstand following a rapid sea-level rise; (c) Bioherms initially keep pace with the rise in sea-level, and are terminated when the depth of water inhibits the growth of the reefs. Bioherms are later covered by shale deposited as the sea-level rise continues.

Overall, carbonate organic buildups are ideally suited for exploration techniques that use stratigraphic interpretation combined with seismic data geologic modeling. The reason for this is that their bed geometry shows pronounced pinches and swells, and lithofacies usually have strong acoustic contrasts with enveloping strata (Bubb and Hatlelid, 1977). Other potential carbonate reservoirs can be predicted on seismic as well, but often with less success. Carbonate organic buildups form in shallow normal-salinity marine waters, commonly at a break in slope on the sea floor, although some are also found seaward downslope, and others are found landward of this break-in-slope within slightly deeper water of platform interiors and epeiric settings. Buildups have two major forms: (1) either as continuous, elongate bodies parallel to depositional strike of the shelf edge (e.g., barrier reefs); or (2) as a series of isolated buildups which may occur on either side of the shelf break (e.g., mud-skeletal banks, mounds, pinnacles, atolls, and patch reefs) (see volume 1, Chapter 3).

77

Downslope Reef High

Low

ao ......... .

HSTAND .

.

.

.

-~T-_R'ANS-GRESS _H_I,_..

bo II

I VE

......

IN FAN

CQ

Open Lowstand C. Shale Basin

Confined Lowstand Evaporitic Basin

III

] KEY ~

Limestone ~

s

Evaporite]

Fig. 2-12. Give-upand catch-upbuildups downslope from platform margins. (a) Shallow water carbonate stillstand wedge, possibly formed during low sea-level stand. (b) Buildups form on irregularities at the base of the basin margin on small bathymetric highs (possibly downslope fans) during stillstands following rapid sea-level rise. (c) Bioherms initially keep pace with the rise in sea-level, and are terminated when the depth of water inhibits the growth of the reefs. Bioherms are later covered by either: (1) evaporites when small drops in sea-level isolate the basin; or (2) shales as the sea-level rise continues.

Although carbonate organic buildups have several general origins, (e.g., initiated over irregularities on the sea floor either on a shelf or on a ramp downslope from a shelf break), they usually begin local growth following a rapid sea level rise that, prior to the rise, had limited carbonate production. The cause of the sea level rise may be either rapid tectonic subsidence (relative rise) or eustatic. As a further complication, the organisms composing the buildup may also have been stressed by rapid sea level rise or by an increase in nutrients (Hallock and Schlager, 1986; Hallock et al., 1988) so that carbonate production was reduced. However, once a stillstand in sea level was reached, carbonate production was usually able to increase (i.e., catch-up)

78

W.

2 - 31 - I 0 9 - 8 w . 6

7- 32- I09'- 8w6

+

W. I0-27-109-9

+

*

7-32-109-8 2-31-109-6 12-33-,09-8 9

+

9

E. 2-28-109-0

9-24-109-8

+

+

SILTY LIMESTONEUNIT

~

--

--

-

0

- " ~" PRE.CAMBRIAN ..........

--~,~o~~:Ec,:--s

9 KEG

RIVER

2

I

r.--.

3

M,LES

o

i

2

3

4

0

"

,'

5.,

6

KILOMETERS

Fig. 2-13. A. Rainbow field CDP seismic section (east-west) across Devonian Rainbow field, western lauada (from Hriskevich, 1970). B. Geological cross-section across Rainbow field (after Hriskevich, 1970). (McQuillin et al., 1979, Fig. 10/7.) as the growth rates of the organisms responded to the shallower water, and a local shoaling-upward sequence commonly resulted. Organic buildups may have two end-members: (1) composed of foraminiferal-algal assemblages tied to deposition in temperate environments, vs. (2) tropical reefs wherein corals or other colonial organisms like stromatoporids or rudists grew (Simone

79 and Carannante, 1988). Some buildups are resistant to waves, while others are not, forming at or possibly below wave base. In cases where the bases of buildups occur on a downslope ramp, their number decreases seaward of the ramp margin. Buildups in isolated basins like the Michigan Basin (Silurian) sometimes seem to have grown through several phases of carbonate production, interrupted by the deposition of evaporites. The origin of these evaporites is related to lowstands of sea level which caused the isolation of the basin and resulted in hypersalinity. However, basins apparently may freshen as a consequence of periodic influx of normal marine waters several times in their history, and consequently, buildups are subsequently able to re-establish themselves as sites of carbonate accumulation after periods of evaporite deposition. Many times, the evaporites act as seals for potential and discovered reservoirs in such situations. In other cases, carbonate production ceases and instead, shales accumulate which act as sources for, and seals to, encased buildups. The seismic character of organic buildups varies according to their size and enclosing lithologies. In some cases, they are easy to locate and show up as "pimples" that disrupt the railway-like continuity of the seismic response of the adjacent shelf and basinal sediments. In other cases, they are difficult to see and are represented by subtle discontinuities in the adjacent seismic (Fig. 2-13). Buildups can be detected on seismic through the use of CDP (common depth point) flattened to specific geologic horizons. Irregularities in surface sediments and geology interfere with the seismic, but when reflectors are flattened and correlated as widespread horizons, buildups often become more obvious. The Devonian Rainbow field of Alberta, Canada, is an example of using this procedure to highlight the seismic expression of buildups (Fig. 2-13). Thus, through CDP stacking and event flattening in acoustic geophysical data, it is possible to enhance the recognition of buildups.

Carbonate clinoform plays Plays in clinoform carbonate shelf margins (both in the crest and extending to turbidite fans in the clinoform toe) are somewhat rarer than the play types described above and are usually the least productive. Limited production is due to the fact that traps are uncommon along carbonate platform margins, and any hydrocarbons that migrate into them pass through into the updip shelf, thus leaving marginal deposits water-prone (Ward et al., 1986). Fields in this play type may occur along the shelf margin (Fig. 2-14) where: (1) the carbonate margin builds up above the adjacent shelf and basin, forming a topographic high; (2) shelf evaporites extend to the shelf edge and act as seals to trap hydrocarbons in the underlying strata (this situation is not common insofar as evaporites tend to occur farther back from shelf margins); or (3) tectonism elevates the margin above the shelf and basin prior to oil migration. In contrast, hydrocarbon production from the turbidite fans in the clinoform toe is even less common because the porosity of the sediment is usually occluded by a fine matrix of carbonate mud.

80

Clinoformed Margin

KEY iT'~'I'~ Limestone ]

V

HIGHSTAND WEDGE

IV~ANSGRESSIVE

ili-- LO_'STND 'WEDGE .

.

.

.

.

Fig. 2-14. Keep-up progradational clinoform margin plays form during sea-level stillstands (usually highstands but sometimes lowstands). The marginal sediments prograde basinward, and are uncommon during rapid sea-level rises.

Examples of hydrocarbon production in reservoirs deposited in shelf margin slope settings (see volume 1, Chapter 3) are commonly sealed by evaporites, shales or dense micrites. Examples include the Lower Cretaceous clinoform buildups in the Shuaiba Formation of Saudi Arabia and the United Arab Emirates (Bu Hasa Field). The Middle Cretaceous Mishrif Formation of the United Arab Emirates also contains marginal clinoforms with the Fateh Field of Dubai being a premier example. Each of these fields has a shale seal. Other clinoform production occurs in the Midland Basin of West Texas, where Permian San Andres Formation dolomites are productive where they pass updip into evaporites. Margins also produce in the Gulf of Mexico in, for example, the Cretaceous Poza Rica trend in Mexico. Anomalous carbonate reservoirs

Other carbonate reservoirs exist which may be considered by some geologists not to fall within the above classification (see volume 1, Chapter 3). The sheet plays formed by Cretaceous chalks in the North Sea for example, are pelagic limestones wherein primary interparticle porosity and permeability were preserved by

81 overpressuring and a lack of cementation, and were further enhanced by later salt movement which fractured the reservoir rocks (see Chapter 8, this volume). The coincidence of overpressuring of chalk and the movement of salt appears unique to the North Sea. The Cretaceous chalks o f the Atlantic margin o f North A m e r i c a have not

proved productive despite early exploration attempts, and the Austin Chalk in the U.S. Gulf Coast has proved to be almost equally disappointing. Apparently, the preservation of primary porosity and creation of additional permeability have not occurred insofar as the combination of salt movement and overpressuring is missing (Scholle,

1977). RECOGNITION OF CARBONATE RESERVOIRS

The first step in the interpretation of seismic data is to establish the geologic framework of the basin under exploration, and to find any description of existing hydrocarbon fields, lithostratigraphy, and structure from a literature search. This knowledge is combined with available well information and logs, details of relative and eustatic sea level, and any gravity, magnetic or resistivity data available to the modeler. Wells =E ,<: r r

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Fig. 2-15. Correlation of the 1-D synthetic seismograms to the seismic sections at well sites W- 1 and W2. This figure correlates with Fig. 2-3. (From Langdon and Malecek, 1987, Fig. 7.)

82 are then tied to the seismic lines, and sequence boundaries are identified and related to relative sea level position (Haq et al., 1987; Vail et al., 1977; Vail 1988). A structural interpretation is then made at this time. Individual reflectors and the character of these reflectors within the defined sequences are determined (Fig. 2-15). Depositional models are established from which to infer facies characteristics and to predict carbonate sheet, organic buildup, and/or clinoform margin plays and their hydrocarbon potential. These inferences are based on analogy with producing fields in the basin and at other locations. If more than one seismic line is available, isopachs are made of the various seismic facies in order to interpret depositional setting and expand on models from which to predict potential reservoirs. For the most part, the three major carbonate reservoir systems described earlier occur at different positions within the basin: (1) sheet carbonates occur usually landward of the shelf margin or less commonly on the basin floor; (2) carbonate organic buildups generally occur along the shelf margin itself, although they may occur behind the shelf edge, on the platform, and less commonly, downslope of the margin (Fig. 2-1; see also volume 1, Chapter 3); and (3) basin margin clinoforms occur between the shelf edge and the basin margin. Sea level fluctuations, climate, age, and basin architecture affect the location of the individual carbonate settings, and ultimately, the presence or absence of potential hydrocarbon reservoirs (Kendall et al., 1991). Not only can one use seismic and well data to determine the carbonate stratigraphy of a basin and the occurrence of oil but it is also possible to relate this stratigraphy to the Haq et al. (1987) sea-level charts (Kendall et al., 1991, and Sarg, 1988), aiding the ability to predict the distribution of potential reservoirs and identify prospective areas to be drilled. This is because eustasy, the composition and rates of sedimentation, and local crustal movements control the character of stratigraphic sequences and the facies and diagenetic patterns formed by marine carbonates. Carbonate reservoirs can thus be further classified in terms of sea-level behavior at the time of their deposition. Kendall et al. (1991) classify major carbonate reservoirs as highstand keep-up sheet reservoirs, rapid rise and highstand catch-up and give-up build-up reservoirs, and highstand prograded clinoform margin reservoirs. They associate source rocks with transgressive sediments of rapid rise systems tracts. Data from seismic surveys will usually be the major sources of information on carbonate plays at a drill site. For this reason, the initial interpretation is often speculative and based more on models than on hard data. The test of the interpretation is sometimes a costly program of drilling. Computer simulation of the drill site's sedimentary history is potentially a much cheaper initial test of the interpreted basin evolution. A successful simulation computer program can account for all the relevant parameters that are responsible for the observed stratal geometry. The input parameters to the computer program are the assumptions about sedimentation processes and tectonic evolution of the study area. These assumptions should be based on currently accepted sedimentological, tectonic and eustatic models (Scaturo et al., 1989; Kendall et al., 1990; Lawrence et al., 1990) and not blind creations of the users. The user weighs these parameters according to their interpretation. If the simulated geometries match with the geometries on the seismic lines, then the interpretation is a possible solution. The simulation does not confirm the absolute truth of the interpretation, but constrains its boundary conditions.

83 There are many forward models which simulate sedimentary processes and lend themselves to testing the effects of variations in sea level and tectonic behavior. Some are two-dimensional mixed clastic and carbonate basin fill models (Aigner et al., 1987; Lawrence et al., 1987; Strobel et al., 1987; Lawrence, 1988; Helland-Hansen et al., 1989; Kendall et al., 1989a, b, c; Nakayama and Kendall, 1989; Scaturo et al., 1989; Strobel et al., 1989a, b; Tang et al., 1989; Lawrence, 1990; and French and Watney, 1990). Others are two-dimensional carbonate shelf models which respond to sea-level changes and erosion, allowing redeposition of sediment with user-defined production functions (Dromgoole et al., 1986; Lerche et al., 1987; Bice, 1988; Demicco and Spencer, 1988; Graus et al., 1988; Koerschner and Read, 1989; Spencer and Demicco, 1989; and Bosence and Waltham, 1990a, b). Both of the latter kinds of models respond to sea-level changes and erosion, allowing redeposition of sediment with user-defined production functions. Other two-dimensional simulations handle clastics alone and are used to: (1) create synthetic seismograms for sediment packages by modeling subsidence, sea level, sediment supply and erosion (Turcotte and Willemann, 1983; Turcotte and Bernthal, 1984); (2) use sediment compaction and tectonic movement to provide sedimentation rates for clastic fluvial systems (Bridge, 1975, 1979; Bridge and Leeder, 1979);

Sedpak

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100

Left

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Right

i

L

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Fig. 2-16. Computer simulation output matching the geometries seen in the seismic line from the west margin of Bimini Bank in the Bahamas in Fig. 2-17.

84 (3) simulate transport, deposition, erosion and compaction of clastic sediments emphasizing fluid velocity (Paola, 1989; Pinter, 1990; Bitzer and Harbaugh, 1987). Other simulations are one-dimensional and: (1) use defined third-order sea-level curves to infer the origin of peritidal cyclic carbonates (Read et al., 1986; Grotzinger, 1986; Read and Goldhammer, 1988); (2) model the interdependence of sea level, depth-dependent carbonate accumulation and the flexural response of the earth's crust (Cisne et al., 1984; Cisne 1985); (3) handle diagenesis of carbonate as coupled to the eustatic record (Matthews and Frohlich, 1987; Humphrey and Quinn, 1989; Quinn, 1989). Other simulations which might be considered are those of Angevine (1981), Jordan and Flemmings (1989), Flemmings and Jordan (1990) and Slingerland and Furlong (1990), which model foreland basin settings in terms of sediment erosion and fill responding to depositional slope and relief, the rheology of the crust, plate tectonics and thermal subsidence. Finally, there are three-dimensional process models (Tetzlaff, 1986; Tetzlaff and Harbaugh, 1989; Takao et al., 1990). All these various simulations can be used to test responses to sea level variation, tectonic mechanisms that cause regional sea level variations, and whether changes in the regional .stress field are sufficient to produce "apparent" eustatic sea level variations akin to those described by Cloetingh et al. (1985), Cloetingh and Wortel (1986), and Cloetingh (1986). In particular, the mixed two-dimensional clastic/ carbonate simulations can be used to test the occurrence of eustatic sea level events and their effects, for instance, confirming or denying that there may be errors in Exxon's Om -

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Fig. 2-17. Top: A West-Southwest-East-Northeast seismic section from the west margin of Bimini Bank in the Bahamas (after Eberli and Ginsburg, 1989). Sedimentary sequences are interpreted as a function of sea level (see computer simulation output in Fig. 2-16). Bottom: Cross section showing changing slope angles and tracing progradation of margin.

85 coastal onlap charts, particularly the chronology of fluctuating sea levels since the Triassic as described by Gradstein et al. (1987). Figure 2-16 illustrates an example of simulation of a seismic line from the Westem Bahamas (Eberli et al., 1990). The authors proposed that variations in eustatic sea level exerted an important control on the sedimentary sequences, and they related pulses of progradation to these sea level events. They used a sequence stratigraphic approach to seismic interpretation and used a defined sea level chart (Haq et al., 1987) to date the seismic reflectors (Fig. 2-17) (Eberli and Ginsburg, 1989). In the simulation of the seismic lines they took the sea-level curve of Haq et al. (1987) as given, and varied such parameters as rates of carbonate accumulation and tectonic movement. These parameters are known to influence carbonate platform evolution; however, not all of them are quantitatively determined. The interactions of these parameters and the assumptions can be evaluated in the simulation. Because Eberli et al. (1990) chose to use the Haq et al. (1987) curve as an input parameter for the sea level curve, the simulation of the GBB seismic lines not only tested their interpretation but also tested the sequence stratigraphy concept. They were able to test their model which proposed that third-order sea-level fluctuations were responsible for the pulses of carbonate progradation. Carbonate deposition was simulated over 60 ma. to reproduce sequence geometries seen on the seismic section. TABLE 2-1 Controls on carbonate productivity, deposition, and reservoir development System

Basin and slope

Major processes

Major facies

Plays

(Gravity and current dominated)

A. Pelagic and benthonic sediments B. Carbonate turbidites C. Carbonate debris flows

Chalks Clinoform toe Clinoform toe

D. Downslope buildups Buildups (Wave dominated) Platform margin

(Current dominated) Platform interior

Terrestrial

A. Framework reef bodies and other organic buildups B. Carbonate sand: a. Bioclastic b. Nonskeletal C. Carbonate mud and silt A. Patch reefs and mounds B. Subtidal epeiric sea, lagoon and/or bay sediments C Tidal fiat sediments A. Soils B. Dunes C. L a k e s - fresh and saline sediments D. Fanglomerates E. Cave deposits

Clinoform crests Clinoform crests

Buildups

Sheets

86 SEISMIC CHARACTER OF CARBONATE SYSTEMS

Carbonate facies and their geometries are predominantly the product of processes acting in the depositional setting (Table 2-1), and it is therefore possible to group these facies on the basis of depositional settings (Table 2-1 and Fig. 2-1). These settings occur in the basin, on the shelf margin, and the shallow shelf, commonly in association with terrigenous systems. It is because the basic basin configuration can be identified from seismic, and that within that basin configuration the geometry of carbonate bodies can be identified, that we can predict the potential occurrence of carbonate plays.

Basin and slope With the exception of chalk, carbonate plays are not common in basin settings, whereas on the slope they are found as downslope mounds and in the toe of clinoforms. The facies of the basin and slope are primarily a product of: (1) pelagic sediments in the water column which settle out to produce laterally extensive units with great continuity of bedding; and (2) turbidites and debris flow deposits from the basin margin which have less continuity. Carbonate plays which are the commonest in this setting are toes of clinoforms and downslope organic buildups. The geometry of the different sedimentary facies, and the associated plays, can be recognized in the seismic.

Pelagic sediments Pelagic calcareous sediments commonly accumulate below depths affected by NNW SP 0 ,

lP?

SE 500 ,

--.....

I000 ,

1500 i

0

25

2000 ,

f.

2500 i -0

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fK? V.E.~5x

M~E VE.--'3X

Fig. 2-18. Sequence of reflectors in a north-northwest--southeast seismic section showing Cretaceous and Paleogene basinal deposits which thicken in a southeast direction toward the anticline. TP = top of Paleogene; TK = top of Cretaceous; TLK = top of lower Cretaceous; MKE = inferred mid-Cretaceous event. Note changes in vertical exaggeration with depth. (From Ball et al., 1985, Fig. 5.)

87 wave action. They often collect along margins of shelves and platforms, and extend basinward into areas below the photic zone. Bedding is uniform and usually thin (510 mm, rarely much thicker than 1 m). Bed character is the product of gravitational settling, the dominant mechanism of deposition for this group of sediments. Bedding surfaces are planar to nodular, and sets of beds commonly are continuous over wide areas. As one moves toward a basin margin, the autochthonous sediment derives some of its character from the nature of the sediments upslope on the margin, and sometimes from the shelf itself (e.g., allochthonous components). Beds generally thicken toward this margin. The seismic response of basinal sediments reflects the character of the bedding and is commonly a series of quite continuous reflectors which thin toward the basin and thicken toward the basin slope (Fig. 2-18). Due to the higher density of these sediments, the reflections are generally well-defined when first encountered in the subsurface. Because pelagic deposits are often quite extensive, they can act as carbonate sheet reservoirs. The planar to nodular bedding can preserve porosity and constrain lateral migration of any hydrocarbons. Near the basin margin, the allochthonous material supplied from up-slope is deposited in graded beds, which may also preserve porosity and create a good reservoir character. However, this is unusual and is a high risk play in the toe of the clinoforms.

Turbidites and debris flow Basinal sediments shed from shelf margins include turbidites and debris flows. Close to platform margins, carbonate turbidites form irregular ribbons of channel-fill that are commonly deposited normal to depositional strike. Farther from margins, the turbidites form fan-shaped wedges (e.g., submarine fans) composed of evenlybedded sheets. Bedding in turbidites varies from thin to almost massive, and is irregular and discontinuous. This character reflects channel-fill and levee deposition on submarine fans. Bases of beds are contour-fills over the scoured upper surfaces of previously deposited beds. Sediment composition and grain size are extremely variable, and may include a wide range of shallow to deep water (e.g., allochthonous and autochthonous) material. Distal turbidites are characterized by regular and planar bedding, and these carbonates are commonly interbedded with marls and shales. The seismic character of these sediments is expressed by discontinuous and quite heterogeneous reflectors which are mounded and channeled, particularly close to basin margins and slopes (Fig. 2-19). Carbonate debris flow deposits are characterized by wide varieties of carbonate lithologic types and sizes of angular fragments with anomalously oriented stratification. Debris flows include megabreccias composed of blocks, which may be larger than 25 x 30 m in cross-section, floating in an enclosing matrix of lime or terrigenous muds and sands. Debris flows vary from lens-like or ribbon channel-fills, to irregular beds that are adjacent locally to carbonate basin margins. Some megabreccias are associated with high relief, active tectonism, or steep slopes, whereas others are the result of pervasive bioerosion, submarine dissolution of fore-reef carbonates by fleshwater springs, or oversteepening of platform margins. Debris flows have often been misinterpreted as shallow water conglomerates, in-situ bioherms, organic mounds,

88 LINE

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Fig. 2-19. Top: Interpreted southwest-northeast seismic section (Line H79-10) showing reflectors from distal turbidite-submarine fan deposits from the northeast. Note mounding and channeling in the vicinity of the well. (Vertical scale in seconds). Bottom: Uninterpreted seismic section from above. (Vertical scale in seconds). (From Middleton, 1987, Fig. 10; Upper Devonian of Canning Basin, Western Australia.)

and reef talus, and are probably much more widespread than previously thought. See volume 1, Chapter 3, for details of reservoirs in pelagic deposits, turbidites, and debris flows. The seismic character of debris flows is such that the continuity of the reflectors varies tremendously, and, in some cases, the pinching and swelling of reflectors is so great that some of the geometries resemble downslope bioherms and organic buildups

89

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Fig. 2-20. Top: Illustration of the seismic character of a detrital facies. Bottom: Series of debris flows expressed as high-amplitude, concave-upward reflectors on the slope of a southwest-northeast bypass margin in the Tertiary Terumbu Carbonate, South China Sea, Indonesia. Pinching and swelling of geometries resembles downslope buildups. (From May and Eyles, 1985, Fig. 21.)

(Fig. 2-20). Often, no internal reflections are discernible in such deposits. The graded bedding associated with both turbidite and debris flow deposits can have the kind of primary porosity necessary for a reservoir in carbonate sheet plays, but this is not common because lime mud is usually the matrix of these sediments. Various diagenetic effects can enhance this porosity (e.g., dissolution) or destroy it (e.g., cementation). The pinch and swell geometries can confine the lateral migration of any hydrocarbons.

Downslope buiMups These sometimes occur at the base of basin margin slopes (Fig. 2-12), as in the

90

Fig. 2-21. A northwest-southeast seismic section through porous Jurassic Smackover reef on the U. S. Gulf Coast. The reef, indicated by amplitude anomaly (loss of seismic character) is located on the upthrown block of a down-to-basin fault. (From Baria et al., 1982, Fig. 29.)

Shuaiba Formation of the United Arab Emirates. The buildups (i.e., reefs) form on small bathymetric highs during highstands. Buildups usually begin with a pioneer community associated with a mud mound seaward of the platform margin (Hassan et al., 1975; Alsharhan, 1985a and b). As this community becomes established, the rate of sedimentation accelerates as organisms trap and precipitate more carbonate. Eventually, the buildups reach sea-level and often a diverse wave-resistant fauna and flora develops with resistance to erosion (Hassan et al., 1975; Alsharhan, 1985). The seismic character of downslope buildups show reflectors tend to lose continuity and, in many cases, the carbonate margin is reflectionless, probably a product of the lack of acoustic contrast in these features (Fig. 2-21). Geometrically, the reflec-

91

A

A'

0-1- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .___ . . . . . . . . . . _. .

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Fig. 2-22. An east-west seismic line from offshore west Africa. Note the Jurassic margin shown by sequence J3.1. The margin (on the west) loses reflection character but has relief above the lagoon and back reef.

tors that enclose the carbonate margin may bow up, tracing a tendency in the margin carbonate to thicken and have higher relief than the adjacent back reef or lagoon (Fig. 2-22). Unfortunately, velocity anomalies associated with the dense, bank-edge carbonates often cause the same effect. Anomalous thickening is also sometimes a response to early marine cementation of the basin margin which inhibits local compaction; whereas the back reef, lacking cement, is reduced in thickness by the loading of the overlying sediment (Playford, 1966). The vertical relief of downslope reefs commonly matches the depth of water on the slope and, because these reefs are common to restricted basins where small falls of sea-level can isolate a basin and initiate evaporite sedimentation, reef growth is frequently interrupted by the basin drying-up. For this reason, evaporites often act as seals to these plays. The best quality plays usually occur in the uppermost fringe of the reefs, where waves have winnowed lime mud from the carbonates that accumulated there. However, diagenesis can be quite severe because the crest is subject to subaerial exposure. Dolomitization, leaching and evaporative replacement are common. Thus both reservoir enhancement and destruction can be found in these buildups as a result of diagenesis.

Platform margin The reefs, mud-skeletal banks, and atolls of the platform margin comprise the organic buildup or clinoform plays described above. Some carbonate sheet plays occur

92 close to the margin and are represented by the sand shoal facies.

Barrier reefs and mud-skeletal banks Reefs that form a barrier on the shelf margin tend to be massively bedded but may contain associated discontinuous thin beds of coarser-grained sediment. Reef geometry is expressed as thick sheets or ribbons which parallel depositional strike. Reefs through geologic time have been built by a variety of calcareous organisms including corals, stromatoporoids, calcareous sponges, algae, and rudists (James and Ginsburg, 1979), but there have been times when lime mud banks and mud-skeletal banks have been the dominant break-in-slope buildups (e.g., during the Pennsylvanian). These mud-skeletal banks are elongate massive bodies that formed both parallel and normal to the seaward edge of the platform margin. They range from knoll-like mounds of a few square meters to massive linear belts trending for hundreds of kilometers along depositional strike. The thickness of the banks varies from 1-100 m or more. Beds may be thick to massive and range from horizontal to clinoform (see volume 1, Chapter 3). Reef and mud-skeletal banks are best developed where open marine waters shoal against the platform margin. The slope of the sea floor on which the buildups grew may have been controlled by antecedent topography, by faulting, or by the juxtaposition of active shallow-water accumulation and deeper water basin starvation. The major sub-environments for barrier reefs and mud-skeletal banks are the reef frame (the reef crest and reef wall), reef apron (fore-reef), back reef, and leeward barrier islands (sand cays). Reefs act as a sediment source to areas both landward and seaward of them. Reefs and barrier margins usually occur at a break-in-slope along platform margins, where waves once broke. They usually are discontinuous but, in some cases, are locally continuous bodies that parallel depositional strike and are sometimes part of a thick sheet of carbonate that may be overprinted by clinoforms that prograded upsection. Sediments that form at a break-in-slope may be reefal and formed by colonial organisms, or they may be dominated by lime mud or silt (e.g., mud-skeletal banks). The geometries and seismic character of both reefs and mud-skeletal banks are similar. Both beds and reflectors thicken toward the break-in-slope and, in many cases, lose character and disappear. Beyond the break-in-slope, bedding and reflectors pick up again, thin gradually, and then have a uniform thickness across the shelf. Many reefs and mud-skeletal banks accumulate at breaks-in-slope (both in outcrop and on seismic sections) and thicken locally to take on lens-like geometries seaward. In contrast, others show a clinoform geometry. Internal reflection geometry is usually absent to chaotic. However, whereas these features are extremely easy to identify on seismic it is difficult to identify dip seals seismically. It is also extremely difficult to locate prospects along shelf margins, particularly because most margins are waterprone. See volume 1, Chapter 3 for details of reservoirs in these facies types. Reef aprons are composed of debris derived from platform-margin facies (generally reef frame and in-situ fore-reef). In general, most pre-Holocene reef aprons slope between 10-30 ~ into the basin. Beds upslope become irregular and massive, whereas downslope they thin to between 5-10 cm and eventually become more constant in thickness. A general rule of thumb is that the steeper the reef apron slope, the greater

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Fig. 2-23. East-west seismic section showing seismic mounded facies from carbonate buildups on the Banyak shelf of the South China Sea. Note discontinuity of reflectors as they approach the buildup labeled 2a. Numbers denote base of sequences. (From Beaudry and Moore, 1985, Fig. 11.)

94 ~.-2 .iooooo,,.Noooo:ou,o. o...o ,v.l.,,.:,~...~:.,,.o,.o~.~,.'.~..~~ ......'.,...~mv;,,.::gv~..;.~ .; ............. .... ,,l:;";' .............. ::: ..... :': ":r'"".'l~'~.oo....OlOO._O,jt..~,di.jj~q,a~o~~U~~le~.t.j~~l.;~~o._o ............... b: j ""' ........ oj ,,,,.-.i j. 9.ol.......ap " o.~. "~2|:,l~ ;l~.,.. ~lJ~176176 io~,..oo.:l,,,,o../,,op N .

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Fig. 2-24. Two patch reefs in the Etosha Basin of Southwest Africa. "C" denotes the carbonate portion of the section. "B" is the base of the reefs. Note the mounded character of the continuous reflectors. The arrows below the section indicate the lateral extent of the reefs. (From Sheriff, 1980, Fig. 5.15.)

the chance that it was syndepositionally marine-cemented, and is composed partly of slumped cemented and brecciated debris derived from the upper slope and reef crest. The most precipitous Quaternary and Holocene fore-reef slopes owe most of their major topography to pre-Holocene antecedent topography. Similar fore-reef cliffs occur in the Upper Devonian of the Canning Basin in Australia (Playford, 1966), portions of the Mesozoic margin of the U.S. East Coast (Morgan and Dowdale, 1983), and Paleozoic margins in Greenland (Hurst, 1980). The seismic character of the fore-reef apron is of a series of quite continuous reflectors that converge away from the reef crest into the basin and diverge into the reef, where they lose their continuity (Fig. 2-23). The amplitudes of the reflections can be quite variable. Back reef patch reefs tend to be massive and lens-like, while the adjacent back reef sediments are widespread and sheet-like. Beds have heterogeneous lithologies and vary in thickness but are quite continuous. This shows up in the seismic, so that the result is seismic lines which exhibit more continuous reflectors with varying amplitudes (Fig. 2-24). Pinnacles and atolls Pinnacles and atolls are formed in response to relatively rapid sea level rises, and/ or relatively rapid subsidence, at times when only local carbonate production manages to keep pace with the sea level rise. These features differ from shelf-edge reefs in that they have more symmetrical geometries and have relatively less orientation with

95 respect to wave and wind directions (see volume 1, Chapter 3). Pinnacle reefs and atolls are usually localized on the floors of shallow, more isolated epeiric basins, seaward of the crest of the basin margin on downslope ramps, or landward of the margin on back reef shelves. The pinnacles and atolls, wherever they occur, are usually localized on highs, formed either by: (1) previous karst topography or some other local irregularity that caused waves to shoal and break, or (2) focused swift tidal currents and encouraged biological opportunism. Core facies of these bodies are generally massive to thick bedded, whereas flank beds are thin and irregular. Changes in texture tend to radiate outward from the core of such buildups. The seismic character of these buildups show: (1) a local thickening of reflectors; or (2) interruptions in the continuity of the seismic (Fig. 2-23) where the buildups are thin and are at the edges of seismic resolution. The internal character of these features can vary greatly.

Sand shoals Carbonate sand accumulations (see volume 1, Chapter 3) can commonly extend from near the seaward edge of banks, platforms, and shelves to back onto the shelf as carbonate sheet plays which have potential reservoir sizes of enormous proportions. Individual beds have continuity that may extend over several miles along strike and normal to it. The beds vary in thickness and lithofacies content. The consequent seismic character for these sediments is shown by continuous reflectors which have quite good continuity, especially those interbedded with evaporites or dense shales (Fig. 2-25). In some cases, the reflectors stretch across the seismic sections like railway lines. Where relatively thin beds occur with increasing depth, only a few internal random reflections are observed. It is because these sheet plays fall between the shelf interior and the platform margin that we consider them here under "Platform Margin." They could equally be called "Platform Interior" facies.

Platform interior The platform interior facies are a primary site for carbonate sheetplays, though organic buildup plays can occur here too.

Epeiric sea, lagoon or bay These depositional settings, protected by wide shallow seas, reefs, or mobile carbonate sand barriers, are characterized by continuous wide sheets of carbonate sediment. These sediments either formed in situ or were locally transported from a seaward barrier by the action of waves and currents. They are well-bedded, have a wide lateral distribution, and contain variable lithofacies, though they are more homogeneous than the immediate backreef sediments. The seismic character of these rocks is very similar to that of the backreef sands discussed above. Where these sediments are dolomitized they can form extensive carbonate sheet plays as do the tidal fiat settings discussed below. An example of this kind of play is the Lower Cretaceous Lekhwair Formation which is an important exploration objective in eastern Abu Dhabi, and contains oil and gas in one or several of its porous members. The porous grain

96 0..~0

0.1 b

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 Fig. 2-25. East-west section from the Mississippian "Chat", Mid-Continent U.S.A., showing local disappearance of generally continuous reflectors where tidal flat deposits include large lenses of evaporite minerals, chert or porous dolomite. K.C. = Kansas City; B/K.C. = base of Kansas City; Miss. = upper Mississippian boundary. (From Thomasson et al., 1989, Fig. 9.)

carbonates of the Lekhwair Formation appear as low velocity events on sonic logs and increase in thickness upwards.

7 da/flats Tidal flat sediments include those forming in the intertidal and the supratidal zones (Fig. 2-25). Sediments range from carbonate sands to muds, often dolomitized, and commonly contain algal stromatolites as well as other carbonate producers. Tidal fiat sediments occur as local wedge-shaped sheets, often widespread, that are usually dissected by channels (see volume 1, Chapter 3). Bedding is thin and even, and contacts are even and sharp. Locally, evaporitic minerals and beds are present and are represented by irregular bedding which may be nodular. Collapse breccias formed after evaporite dissolution tend to parallel depositional strike and are local in extent. The occurrence of much of the oil in the Jurassic rocks of western Abu Dhabi, Qatar and Saudi Arabia is related to this kind of tidal fiat carbonate sheet deposit and the presence of the Hith Anhydrite, which traps the hydrocarbons in these rocks (Alsharhan and Kendall 1986). Similar plays occur in the backreef shelf of the Permian Reef in New Mexico and West Texas (Ward et al., 1986).

97 The seismic character of these rocks can show quite continuous reflectors (Fig. 225), but locally these may lose intensity and disappear in response to the occurrence of the evaporite beds.

Terrestrial Terrestrial sediments include dunes, soils, lake sediments, and fanglomerates. Normally (except in a few rare instances), these types of deposits generally are not targets of hydrocarbon exploration. Dunes and soils are not commonly seen on seismic sections (for an exception, see Steeples and Miller, 1988), but lakes and fanglomerates can be recognized, and can contain carbonate sheet plays from terrestrial settings. These latter types are not common.

Lakes and fanglomerates Lakes may be present in fault-block intermontane basins or on delta plains. Carbonates may accumulate in the lakes if terrigenous influx is low and climatic conditions are favorable. The deposits vary from localized thin sheets of individual lake origin to widespread and complex sequences of beds related to stacked lakes, especially common in some rift valleys. The seismic character of lake sediments is variable, but in larger ancient lakes, seismic reflectors have considerable continuity. Local thickening and thinning of reflectors is common, particularly towards lake margins (Fig. 2-26). Fanglomerates are usually found on the down-thrown sides of faults in arid regions. The deposits are fan-shaped wedges formed of braided stream and sheet-flow deposits. The seismic character of fanglomerates is such that seismic continuity of reflectors is variable, thickening away from lake and valley centers. The continuity of internal reflectors is poor but, depending on circumstances, boundary reflections can be quite sharp. LINE

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Fig. 2-26. East-west seismic section (Line 78) from Lake Tanganyika showing its relationship to rill geometry. Note continuity of reflectors in lake and splayed sediments influxing from the margin to the west. INAZ (interference accommodation zone) refers to the linkage of half-grabens, appearing as a topographic high (see Scott and Rosendahl, 1989, for discussion). (After Scott and Rosendahl, 1989, Fig. 8.)

98 SUMMARY AND CONCLUSIONS

Seismic interpretation of carbonates involves the use of well data tied to the seismic sections being interpreted. Three major carbonate play types can be recognized on seismic sections. These are sheets, buildups, and clinoform margins. These can be identified as part of a continuum of sedimentary facies and geometries that can be traced from basin to shelf. The basin margin is marked by continuous reflectors that thicken toward the slope. The slope is marked by reflectors that dip basinward and thicken updip to a reflectorless area at the basin margin crest. The shelf is marked by continuous railway-like reflectors which locally thin and thicken at facies changes. The seismic character of sheet plays matches that of the character of the seismic of shelf sediments; the buildup plays' seismic character are the pinch-and-swell features; the seismic of the clinoform play shows en echelon seismic wedges that reflect the progradation of basin margins. In addition to seismic and well data, the carbonate stratigraphy of a basin can be related to the Haq et al. (1987) sea-level curve. This is because eustasy, the composition and rates of sedimentation, and local crustal movements all control the character of marine carbonate sequences and their facies and diagenetic patterns. Major carbonate reservoirs can be classified in terms of sea-level behavior at the time of their deposition as: (1) highstand keep-up sheet reservoirs, (2) rapid rise and highstand catch-up and give-up buildup reservoirs, and (3) highstand progradational clinoform margin reservoirs. Associated source rocks match sediments of transgressive, rapidrise systems tracts. Computer simulation of carbonate accumulation can test seismic interpretations of these plays. The input parameters to such a simulation are assumptions about carbonate rates of accumulation, sea level history and tectonic evolution of the study area, and are based on currently accepted sedimentological, tectonic and eustatic models.

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100 Goldhammer, R.K., Dunn, EA. and L.A. Hardie, 1987. High frequency glacio-eustatic sea level oscillations with Milankovitch characteristics recorded in Middle Triassic platform carbonates in Northern Italy. Am. J. Sci., 287: 8 5 3 - 892. Goldhammer, R.K., 1988. Superimposed platform carbonate cycles: eustatic response of an aggradational carbonate buildup, Middle Triassic of the Dolomites. Bull. Am. Assoc. Petrol. Geologists, 72: 190. Gradstein, F.M.,Agtergerg, F.P.,Aubry, M.P., Berggren, W.A., Flynn, J.J., Hewitt, R., Kent, D.V., Klitgord, K.D., Miller, K.G., Obradovich, J., Ogg, J.G., Prothero, D.R. and Westermann, G.E.G., 1988. Chronology of fluctuating sea levels since the Triassic: A critique. Science, 241: 5 9 9 - 601. Graus, R.R., Macintyre, I.G. and Herchenroder, B.E., 1988. Computer simulation of the Holocene facies history of a Caribbean fringing reef: Galeta Point, Panama. Proc. Fifth Internat. Congr. Coral Reefs, Tahiti, pp. 25 - 53. Gries, R.R. and Dyer, R.C., 1985. Seismic exploration of the Rocky Mountain region. Rocky Mountain Assoc. Geologists and Denver Geophys. Soc., 299 pp. Grotzinger, J.P., 1986. Cyclicity and paleoenvironmental dynamics, Rocknest platform, northwest Canada. Geol. Soc. Am. Bull., 97: 1208- 1231. Hallock, P. and Schlager, W., 1986. Nutrient excess and the demise of coral reefs and carbonate platforms. Palaios, 1: 3 8 9 - 398. Hallock, P., Hine, A.C., Vargo, G.A., Elrod, J.A. and Jaap, W.C., 1988. Platforms of the Nicaraguan Rise: examples of the sensitivity of carbonate sedimentation to excess trophic resources. Geology, 16:1104 - 1107. Haq, B., Hardenbol, J. and Vail, P.R., 1987. Chronology of fluctuating sea levels since the Triassic (250 million years to present). Science, 235: 1156- 1167. Hassan, T.H., Mudd, G.C. and Twombley, B.N., 1975. The stratigraphy and sedimentation of the Thamama Group (Lower Cretaceous) of Abu Dhabi. Ninth Arab Petroleum Congress, Paper No. 107 (B-3), Dubai, pp. 1 - 11. Helland-Hansen, W., Kendall, C., Lerche, I. and Nakayama, K., 1988. A simulation of continental basin margin sedimentation in response to crustal movements, eustatic sea level change and sediment accumulation rates. J. Math. Geology, 20:777 - 802. Helland-Hansen, W., Steel, R., Nakayama, K. and Kendall, C.G.St.C., 1989. Review and computer modelling of the Brent Group stratigraphy In: M.K.G. Whately and K.T. Pickering (Editors), Deltas: Sites and Traps for Fossil Fuels. Geol. Soc. London, Spec. Publ. 41:237 - 252. Hriskevich, M.E., 1970. Middle Devonian reef production, Rainbow area, Alberta, Canada. Bull. Am. Assoc. Petrol. Geologists, 54: 2260-2281. Humphrey, J.D. and Quinn, T.M., 1989. Coastal mixing zone dolomite, forward modeling, massive dolomitization of platform-margin carbonates. J. Sediment. Petrol., 59: 4 3 8 - 454. Hurst, J.M., 1980. Paleogeographic and stratigraphic differentiation of Silurian carbonate buildups and biostromes of North Greenland. Bull. Am. Assoc. Petrol. Geologists, 64: 5 2 7 - 548. James, N.P. and Ginsburg, R.N., 1979. The seaward marginal Belize Barrier and atoll reefs. Spec. Publ. 3, lnt. Assoc. Sediment., 191 pp. Jordan, T.E. and Flemmings, P.B., 1989. From geodynamic models to basin fill - A stratigraphic perspective: In: T.A. Cross (Editor), Quantative Dynamic Stratigraphy, Prentice-Hall, NJ, pp. 1 4 9 - 164. Kearey, P. and Brooks, M., 1984.An Introduction to Geophysical Exploration. Blackwell Scientific Publ., Oxford, England: 326 pp. Kendall, C.G.St.C., Bowen, B., Alsharhan, A., Cheong, D.K. and Stoudt, D., 1991. Eustatic controls on carbonate facies in reservoirs, and seals associated with Mesozoic hydrocarbon fields of the Arabian Gulf and the Gulf of Mexico. Marine Geology, 52:215 - 238. Kendall, C.G.St.C., Strobel, J., Jie, T., Moore, P., Cannon, R., Bezdek, J. and Biswas, G., 1989a. Simulation of the west Texas, New Mexican Permian Guadalupian basin margin- a response to eustatic change, an example of SEDPAK. In: P.M. Harris and G.A. Grover (Editors), Subsurface and Outcrop Examination of the Capitan Shelf Margin, Northern Delaware Basin. SEPM Core Workshop No. 13: 423 -426. Kendall, C.G.St.C., Moore, P., Strobel, J., Cannon, R., Bezdek, J. and Biswas, G. 1989c. Simulation of sedimentary fill of basins. Proc. Kansas Geol. Surv. Centennial (1889-1989), Conf. on Sedimentary Modeling: Computer Simulation of Depositional Sequences. Subsurface Geology Series 12, Kansas Geol. Surv., Lawrence, Kansas: 1 - 4 . Koerschner III, W.F. and Read, J.F., 1989. Field and modeling studies of cambrian carbonate cycles,

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102 P. Crevello, J.F. Sarg and J.F. Read (Editors), Controls on Carbonate Platform and Basin Development. SEPM Spec. Publ. 44: 6 4 - 7 6 . Schlee, J.S. (Editor), 1984. Interregional unconformities and hydrocarbon accumulations. AAPG Mem. 36:184 pp. Scholle, P.A., 1977. Chalk diagenesis and its relation to petroleum exploration- oil from chalks a modem miracle? Bull. Am. Assoc. Petrol. Geologists, 61: 982 - 1009. Scott, D.L. and Rosendahl, B.R., 1989. North Viking graben: an East African perspective. Bull. Am. Assoc. Petrol. Geologists, 73: 155-165. Sengbush, R.L., 1983. Seismic Exploration Methods. Internat. Human Resources Development Corp., Boston, MA, 296 pp. Sharma, P., 1986. Geophysical Methods in Geology. Elsevier, Amsterdam, 428 pp. Sheriff, R.E., 1976. Inferring stratigraphy from seismic data. Bull. Am. Assoc. Petrol. Geologists, 60(4): 528-542. Sheriff, R.E., 1977. Limitations on resolution of seismic reflections and geologic detail derivable from them. In: C.E. Payton (Editor), Seismic Stratigraphy-Applications to Hydrocarbon Exploration. Am. Assoc. Petrol. Geologists Mem. No. 26, pp. 3 - 14. Sheriff, R.E., 1978. A First Course on Geophysical Exploration and Interpretation. IHRDC Press, Boston, MA, 313 pp. Sheriff, R.E., 1980. Seismic Stratigraphy. Intemat. Human Resources Development Corp., Boston, MA, 227 pp. Simone, L. and Carannante, G., 1988. The fate of Foramol ("temperate-type") carbonate platforms. Sedimentary Geology, 60:333 - 346 Slingerland, R.L. and Furlong, K.P., 1990. Shoreline position in clastic wedges of marine foreland basins: a modeling study. Bull. Am. Assoc. Petrol. Geologists, 74: 765. Spencer, R.J. and Demicco, R.V., 1989. Computer models of carbonate platform cycles driven by subsidence and eustasy. Geology, 17:165 - 168. Steeples, D.W. and Miller, R.D., 1990. Seismic-reflection methods applied to engineering, environmental, and ground-water problems. In: S. Ward (Editor), Volume on Environmental Geophysics, Review and Tutorial, Soc. Expl. Geophys.: 1 -30. Strobel, J., Kendall, C.G.St.C., Biswas, G., Bezdek, J.C. and Cannon, R., 1987. Preliminary description of the program SEDFIL with carbonate module added. In D.C. Peters and S.A. Krajewski (Editors), Proc. Denver Geo Tech Computer-Aided Methods and Modeling in Geology and Engineering, pp. 341 -349. Strobel, J., Cannon, R., Kendall, C.G.St.C., Biswas, G. and Bezdek, J., 1989. Interactive (SEDPAK) simulation of clastic and carbonate sediments. In: Shelf to Basin Settings. Computers and Geoscience 15: 1279- 1290. Strobel, J., Soewito, F., Kendall, C.G.St.C., Biswas, G., Bezdek, J. and Cannon, R., 1989. Interactive simulation (SED-pak) of clastic and carbonate sediments In: T.A. Cross (Editor), Shelf to Basin Settings. Quantative Dynamic Stratigraphy, Prentice-Hall, NJ, pp. 433-444. Syvitski, J.P.M., 1990. Numerical prediction of the sediment characteristics, including carbon content, of basin fill. Bull. Am. Assoc. Petrol. Geologists, 74: 7 7 4 - 775. Takao, I., Yamamura, T., Suinouchi, H. and Miyata, Y., 1990. Three-dimensional computer simulation system of deltaic sedimentary sequences. Bull. Am. Assoc. Petrol. Geologists, 74: 6 8 2 - 683. Tang, Jie, Kendall, C.G.St.C., Strobel, J., Cannon, R., Moore, P., Bezdek, J. and Biswas, G., 1989. Simulation of the sedimentary fill of the Sichuan Basin by Upper Permian coals and carbonate sequencesan example of the use of SEDPAK. Bull. Am. Assoc. Petrol. Geologists, 73(3): 418. Telford, W.M., Geldart, L.P., Sheriff, R.E. and Keys, D.A., 1976. Applied Geophysics. Cambridge University Press, New York, NY, 860 pp. Tetzlaff, D.M., 1986. Computer simulation model of clastic sedimentary processes. Bull. Am. Assoc. Petrol. Geologists, 70: 655. Tetzlaff, D.M. and Harbaugh, J.W., 1989. Simulating Clastic Sedimentation. Van Nostrand Reinhold, New York, NY, 202 pp. Thomasson, M.R., Kettle, R.W., Lloyd, R.M., McCormack, R.K. and Lindsay, J.P., 1989. Seismic detection and interpretation of porosity in Carboniferous age rocks of Kansas and Oklahoma. Geophysics, 54: 1371- 1383. Turcotte, D.L. and Bemthal, M.J., 1984. Synthetic coral-reef terraces and variations ofQuartemary sealevel.

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Earth and Planetary Science Letts., 70:121 - 128. Turcotte, D.L. and Willemann, R.J., 1983. Synthetic cyclic stratigraphy. Earth and Planetary Science Letts., 63: 8 9 - 96. Vail, E, 1988. Seismic stratigraphy interpretation using sequence stratigraphy, Pt. 1: Seismic stratigraphy interpretation procedure. In: A.W. Bally (Editor), Atlas of Seismic Stratigraphy, AAPG Studies in Geology No. 27, 1:1 - 10. Vail, ER., Mitchum, R.M., Jr. and Thompson, S., 1977. Part three: Relative changes of sea level from coastal onlap. In: C.E. Payton (Editor), Seismic Stratigraphy- Applications to Hydrocarbon Exploration. Am. Assoc. Petrol. Geologists Mem. 26:63 - 82. Walker, K.R., Shanmugan, G.S. and Ruppel, S.C., 1983. A model for carbonate to terrigenous clastic sequences. Geol. Soc. Am. Bull., 94: 7 0 0 - 712. Ward, R.F., Kendall, C.G.St.C. and Harris, P.M., 1986. Hydrocarbon occurrence in Guadalupian sediments, the Permian Basin, West Texas and New Mexico. Bull. Am. Assoc. Petrol. Geologists, 70: 2 3 9 - 262. Waters, K.H., 1987. Reflection Seismology-A Toolfor Energy Exploration (3rd Ed.). John Wiley and Sons, New York, 538 pp. Widess, M.B., 1973. How thin is a thin bed? Geophysics, 8: 1176- 1180. Wood, L., 1982. Imaging the subsurface. In: K.C. Jain and R.J.P. de Figueiredo (Editors), Concepts and Techniques in Oil and Gas Exploration. Soc. Explor. Geophys., Tulsa, OK, pp. 4 5 - 90.

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105

Chapter 3 C O R E ANALYSIS AND ITS A P P L I C A T I O N IN R E S E R V O I R CHARACTERIZATION DAVID PATRICK MURPHY, GEORGE V. CHILINGARIAN, AND S. JALAL TORABZADEH

INTRODUCTION

Core analysis involves recovery, preservation, examination, and testing of samples of sedimentary rocks (cores) to obtain information on the characteristic properties of the potentially hydrocarbon-beating reservoir rocks. The information obtained by core analysis in conjunction with other reservoir, field, basin, and analog data is used to construct the most accurate picture possible of the reservoir, its reserves and productive potential, to maximize the economic payback from the production of hydrocarbons from the reservoir. Understanding the rock properties of a reservoir from direct measurement on representative rock samples is paramount in reservoir characterization. Whole coring, which involves drilling into the formation with a hollow-section drill pipe (a core barrel and bit) to cut and retrieve the rock samples, provides us with long continuous rock samples that provide not only analytical information (porosity, permeability, etc.), but geological information as well. Sidewall cores are small rock samples individually selected and taken from the side of the borehole wall, usually with wireline tools. Core analysis has advanced over the years from a simple visual examination of lithological properties to complex procedures involving computerized tomography, magnetic resonance imaging, scanning electron microscopy, and automation of data acquisition and analyses. Core analysis provides insight into rock properties which can be incorporated into the interpretation of other formation evaluation measurement techniques such as wireline, measurement while drilling and mud logs, and drillstem and wireline tests, to develop a complete picture of the reservoir and its reserves and productivity. Core analysis data are needed in all phases of oil and gas field exploration, development, and production, which include: (1) Exploratory wells to study the structure, physical properties of the formation, and its production capacity. Core data are essential for calibration of well logs and seismic data in exploration. (2) Optimization of completion procedure for selection of best completion technique, selection of subsequent testing intervals, interpretation of drillstem test data, and evaluation of completion effectiveness. (3) Field development, including drilling, facility sizing and optimization, artificial lift, workovers and recompletions. (4) Production design, including reserve estimation, and evaluation of primary, secondary, and enhanced oil recovery processes. Core analysis can be done on either a qualitative or quantitative basis. It can provide

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Fig. 3-1. A pictorial view of typical information that can be obtained from core analysis. This is only a partial list. (From Archer and Wall, 1986.)

direct measurements of rock porosity, permeability, fluid saturations and their distribution, grain density, lithology, capillary pressure, wettability, electrical and acoustical properties, cation exchange capacity, multiphase flow properties such as relative permeability, petrographic properties, and pore fluid properties. Core analysis can contribute to improved reservoir characterization if measurements of rock properties are made at reservoir conditions, i.e., under in-situ stress. A pictorial view of typical information that can be obtained from core analysis is shown in Fig. 3-1.

R ES ER V O I R C H A R A C T E R I Z A T I O N

If core analyses are to provide information for reservoir characterization, the resulting data must represent the full range of reservoir properties and values or the reservoir characterization will not be comprehensive.

Representativeness of core data

Inasmuch as representative rock samples covering the full range of rock property values are needed to fully characterize the reservoir, the rock samples should not be biased towards the better quality reservoir rock, for example. One approach to determining the representativeness of core data to the reservoir (Thomeer, personal communication, 1987) is to compare histograms of rock properties from the core data to corresponding well log data. Well log data are generally the most complete data set

107 available in a well, and, therefore, should be most representative of the range of reservoir property values. A histogram of core porosity compared to a histogram of well log density-neutron crossplot porosity, and a histogram of core permeability compared to a histogram of nuclear magnetism log permeability would show if conventional core analysis porosity and permeability coverage is sufficient for characterizing the reservoir over the range of these properties. Well log density-neutron crossplot point cluster analysis or spectral density photoelectric data over the entire reservoir can be compared to core mineralogy descriptions to assure that all of the different mineralogy types have been analyzed. Well log density-neutron crossplot grain densities can be compared to core grain densities to also assure representative mineralogies for reservoir characterization.

Depth alignment of data Depth alignment of core data with other formation evaluation data is critical for accurate application of core data to reservoir characterization. Typically one of the primary well logs, e.g., a resistivity or porosity log, is selected as the well's depth reference. All other wellbore data are shifted to be on depth with the well's depth reference log. Depth alignment of core data can be done using core porosity versus well log porosity, core CT bulk density versus well log bulk density, core gamma scan data versus well log gamma ray data, core mineralogy description versus well log density-neutron point cluster analysis, core permeability versus nuclear magnetism log pore size distribution, etc. When one tries to correlate core to log data, best results are obtained when the data are regularly sampled (no bias). As heterogeneities approach sample size, denser sampling or whole core analysis will be needed to match logs. Figure 3-2 provides some insight into potential problems with core sampling.

CORING

Introduction Planning prior to coring is critical. Formation evaluation objectives dictate which (if any) core types are taken and which analyses are performed. Taking the wrong type/size core or using an inappropriate drilling fluid can prevent or invalidate core analyses that are needed to meet evaluation objectives. Cores are cut from the formation for testing by different tools using different methods and appropriate coring fluids depending on the types of data required. Whole coring encompasses a wide range of core barrels and cutting heads including conventional, oriented, wireline retrievable, containerized (rubber sleeve, PVC, fiberglass, and aluminum liners), pressure, and sponge insert core barrels. Wireline sidewall coring can obtain rock samples from the side of the borehole after the zone of interest has been drilled and logged. Wireline sidewall coring encompasses three types of coring tools including percussion, rotary drilled (the most-used wireline sidewall tool for carbonates), and gas press.

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Fig. 3-2. Representative core sampling for analysis is not trivial. In this example, the core contains thin (plug width plus a little) tight streaks. The density log, which averages over about a couple of feet, is shown responding to the tight streaks, but not resolving them. Three different sampling picks are shown. The high graded sampling excludes the tight streaks. The 14 sampling on 14 points only hits one tight streak, and the slightly shifted 14 sampling hits two tight streaks. These three sampling approaches create different visions of the core density. A core this heterogeneous should not be analyzed using plugs. Whole core analysis is more appropriate. (Graphic from E.C. Thomas, personal communication, 1987.)

Coring fluids are generally designed to have a very low fluid loss and high solids content to minimize spurt loss of mud filtrate into the core. The type of data that is needed from core analysis will dictate the type of coring fluid to be used. Various coring techniques, coring fluids, core handling, and preservation procedures have been discussed in detail by many investigators including Keelan (1972), Anderson (1975), Monicard (1980), IHRDC (1985), Whittaker (1985), W o r m Oil Coring Series (1985-1986), and Archer and Wall (1986). C o n v e n t i o n a l w h o l e coring

Conventional whole coring is designed for structurally competent rocks which need no special fluid containment. Conventional whole coring is the simplest of the whole coring methods (see Fig. 3-3). The conventional whole core barrel consists of an outer barrel and an inner barrel. The function of the outer barrel is to transmit rotation to the core bit, which does the cutting. As the core is cut, it slides into the inner core barrel for storage. A bearing system keeps the inner barrel stationary, even while the outer barrel rotates, so that the core (still attached to the formation at the core bit face) is not damaged by rotation.

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A check valve at the top of the inner barrel diverts mud flow to between the inner and outer barrels during coring. The check valve also allows mud to exit the inner barrel as the core enters. A core catcher at the bottom of the coring assembly retains the core in the inner barrel as the core is pulled out of the hole when core cutting is complete. Core barrel lengths are usually small multiples of 30 ft (9 m), with typical barrel lengths being 30, 60, or 90 ft (9, 18, or 27 m). One of the most probable times for a core to jam in the core barrel while coring is during a drill pipe connection at the surface. Minimizing connections by using only a 30 ft (9 m) barrel (which adds cost

110 due to more drill pipe trips to recover core) or using a top drive rig (where the rotating mechanism can move 60-90 ft (18-27 m) in the derrick without a drill pipe connection) reduces the chance of jamming the core in the barrel.

Oriented whole coring Whole core can provide much structural and stratigraphic insight if the in-situ orientation of the core is known. Davison and Haszeldine (1984) provided a review of four simple techniques, listed in Table 3-I, that are used to orient conventional cores back to their in-situ position. One of these methods is oriented whole coring. Oriented core barrels use a scribing shoe located below the core catcher (Worm Oil Coring Series, 1985-1986, Part 2). Three notches are made on the core as it enters the inner barrel. One is the identifying notch and the other two are rotated 135 ~ around the core from the identifying notch. Three notches are used because one notch cannot TABLE 3-I Methods for orienting conventional cores back to their in-situ position (Davison and Haszeldine, 1984) Method

Comments

Oriented core barrels Dipmeter a Highly deviated wells b

Can be used on any rock type sequence Must be recognizable structural plane Directional survey must be used in conjunction with regional dip knowledge Origin and age of remanent magnetism component must be identified

Paleomagnetic

Imaging logs could be used today, and would provide better accuracy than a dipmeter because of their increased circumferential coverage. There are three different types of imaging logs: electrical array, pulsed acoustic, and video camera, which are described in Table 4-I in Chapter 4 of this book. The Society of Professional Well Log Analysts Reprint Volume on Borehole Imaging (1990) provided a comprehensive reference set for these imaging logs. bSkopec et al. (1992) discussed procedures for the successful recovery of oriented horizontal core from highly fractured carbonate rocks. The authors' specific objectives for this coring included formation evaluation and drilling reasons: efficient recovery of core sections, high core recovery rates, quality core material, accurate orientation data, comprehensive core analysis, and maintenance of borehole angle while coring. To accomplish these objectives in a horizontal situation, they had to develop or adapt equipment or procedures. The problem of frequent core jamming in the coring assembly was largely overcome by the use of flexible fiberglass inner barrels and multiple core-catcher assemblies. They achieved a recovery rate of almost 100% by using shorter core sections and improved inner- and outer-barrel stabilization. For orientation purposes, a slip scribe was used in conjunction with an electronic multishot instrument that uses an array ofaccelerometers for determination of inclination. This orientation instrument alleviated many of the problems that had been associated with camera surveys. To operate the electronic multishot instrument in a horizontal configuration, it was necessary to develop specialized equipment. Skopec et al. state that their newly designed rotatable non-magnetic blade centralizer, enhanced running gear, and a high frequency shock absorber were needed to be used to obtain accurate core orientation data. To ensure positive alignment of the orientation instruments and the coring assembly, a laser alignment system was invented and used successfully. Specialized horizontal core handling procedures were developed to ensure accurate core orientation data. It is obvious that these authors needed to go beyond using off-the-shelf equipment to meet their coring objectives. Their efforts were successful because of their planning for and development and adaptation of procedures and equipment that would let them accomplish their objectives. a

111 be cut satisfactorily without causing undue core jamming. Two notches spaced equally apart could be used; however, a mistake might be made in determining which one is the identifying notch. Three notches, unequally spaced around the circumference of the core, leave no doubt about which is the identifying notch and still allow satisfactory coring. A multishot directional survey tool in a monel collar is attached to the inner barrel by a connecting rod (which, in turn, is connected to the scribing shoe). This system allows determination of the direction (based on the multishot compass) in which the identifying notch was scribed. The system is operated by a timer, and depending on the timing cycle, as with conventional surveying practices, the rotary is stopped prior to firing the multishot to allow the compass to stabilize. This gives an accurate indication of core orientation, and the process is repeated throughout the coring operation.

Wireline retrievable whole coring Wireline retrievable whole coring is used when it is more cost effective to retrieve the core to the surface by pulling the inner barrel out through the inside of the drill string using wireline rather than tripping the entire drilling string out of the hole. An empty inner barrel can then be inserted back down the inside of the drill string into the core barrel assembly by wireline for continued coring. Wireline core barrels are made in a variety of sizes and usually cut 15 or 30 ft (4.5 or 9 m) of core (Worm Oil Coring Series, 1985-1986, Part 2). One negative aspect of a wireline core barrel is that the removable inner barrel must be small enough to be retrieved through the drill pipe. Of course the core diameter would be even smaller.

Containerized whole coring Containerized whole coring is used when the core would fall apart when not kept inside of a container. It is also used for fractured formations that would jam inside of a conventional inner barrel. Types of containers include rubber sleeves, PVC liners, fiberglass liners, and aluminum liners. These containers provide physical stability, but not a pressure seal for the core. The core is typically kept inside of the container from the time it is removed from the core barrel until it arrives in the core analysis laboratory and stabilized by freezing. Rubber sleeve containerized core assembly is a complex mechanism which ratchets a thick rubber sleeve around the core as it enters the inner barrel. Barrel length is about 20 ft (6 m). When coring has been completed, the core (still surrounded by the rubber sleeve) is removed from the core barrel. Typically, rubber sleeve core barrels are the least desirable of the containerized coring devices. They are the most mechanically complex and, therefore, most subject to failure during coring. The rubber sleeve is the most easily torn container, so it is the most likely to fail as a container, and the rubber sleeve is the most flexible container, so it is the most likely to allow flexure (and subsequent damage) of the core during removal from the core barrel and during transport to the core analyses laboratory.

112 PVC liners are the least expensive of the remaining containers. However, coarse manufacturing internal diameter tolerances can lead to j a m m i n g of hard rocks in smaller-diameter portions of the liner. In addition, a PVC liner is the container least tolerant of high temperatures. Fiberglass and aluminum liners are typically the most desirable of the containers. They have the best manufacturing internal diameter tolerances and the best high temperature tolerance. They are also the least flexible of the containers.

Pressure whole coring The pressure coring apparatus retains pressure on the core in the inner barrel to prevent pressure blowdown from altering the fluid saturations of the core as it is brought to the surface (Hyland, 1983). Invasion still occurs as the core is cut, so the in-situ fluid saturations (coring with a water-based mud) are not representative of insitu conditions unless the rock is at residual oil saturation to waterflood (see Fig. 313). The p r i m a r y use of pressure coring is to provide residual oil saturation

Latch Spring

Gas reservoir

Upper seal ring

Regulator

Inner barrel

Ball valve

Core catcher Bit

Fig. 3-4. Pressure coring is a method of maintaining a core's formation fluid integrity (after invasion, but before pressure blowdown) by sealing the core chamber at downhole pressure. The pressure core barrel illustrated here has a lower ball valve that closes by ratchet action after the core barrel is picked up off bottom and the outer barrel drops downward. A nitrogen gas system then maintains pressure within the core chamber against leaks. (From WorldOil Coring Series, 1985-1986, Part 2.)

113 information from reservoirs after waterflood to assess a tertiary flood target. Pressure coring with oil-based mud and subsequent analyses can provide irreducible water saturation information. In general, pressure coring is the ultimate in coring and analysis expense. After being cut, the sealed core is brought to surface under downhole pressure, then frozen and preserved in dry ice. While still frozen, the inner barrel is removed and the core cut in sections and sent to the lab for testing. The pressure core must be kept frozen in dry ice at all times until it is analyzed.

Sponge whole coring Like pressure coring, the primary use of sponge coring is to provide residual oil saturation information from reservoirs after waterflood to assess a tertiary flood target. Sponge coring is much less expensive than pressure coring, but more expensive than conventional, oriented, or containerized coring. The inner-facing portion of the sponge coring liner is covered with an oil-wet polyurethane sponge material. As the core is brought to the surface, it will blow down. The sponge captures and retains the blow-down oil. The sponge offsetting a particular portion of the core is analyzed for oil content. The resulting oil volume is added back into the oil saturation determination for the core offsetting that particular portion of sponge. This accounts for pressure blowdown and provides accurate residual oil saturation information. Prior to running in the hole with the sponge core barrel, six 5-ft sections of the sponge liner are placed within the inner barrel and sealed. To eliminate the possibility of producing a filter cake between the core and sponge liner, the sponge is first evacuated and then pressurized with water up to 1,600 psi (11,000 KPa). This pressure is maintained as the core barrel goes into the well. Once the sponge core barrel has been run in the hole, coring procedures are the same as with conventional coring. Several features of the sponge core make it unique (Worm Oil Coring Series, 19851986, Part 2). Where CO 2 floods are in widespread operation, it is desirable to determine where CO 2 is penetrating the pay formation, and sponge coring can be modified to analyze a core for CO 2 and/or HzS. Whereas standard practice in sponge coring uses water to pressurize the inner barrel, substituting a 15% monoethylene amine solution will allow capture and analysis of up to 25 liters (6 gal) of CO 2 per ft. This is an ample amount to quantitatively examine formations as far as determining how and where CO 2 has penetrated. Water saturation of cores is another application of sponge coring. Oil mud is used for the process because, if filtrate invasion occurs, there will be less chance of water loss from the core. Some modifications are required to run water saturation with the sponge core. First, the sponge is wet and pressurized with mineral oil (with a viscosity close to that of a 30-weight motor oil) instead of water. Once coring is complete, the barrel is brought to the surface slowly after the bubble point of the oil within the core is reached. This allows gas to trickle out of the core with minimum transport of oil and water from the core. The sponge is then analyzed for water content.

114 Wireline sidewall coring Once an interval has been drilled, sidewall coring can be used to take rock core plugs from the side of the borehole. Sidewall cores yield information regarding formation lithology, and interstitial fluids. Coring points may be selected after downhole logs have identified zones of interest. Also, accurate positioning can be accomplished with standard logging depth correlation devices, e.g., a gamma ray log. However, small samples cannot provide continuous information regarding vertical section properties. Two types of sidewall coring tools are available today: rotary and percussion. Sidewall rotary coring tools (Fig. 3-5) are used the most for carbonates and other hard rock formations. After the coring tool is positioned at the desired depth, a decentralizing arm pushes it against the formation while a motorized core drill cuts a rock

TOOL POSITIONING SHOE

HYDRAULIC DRILL MOTOR ~ . . DRILL ACTUATOR PLATE DRILL BIT " FLEXIBLE HYDRAULIC LINE CORE STORAGE TUBE ---

CORE PUNCH

RECOVERED CORE

CORE RECOVERY INDICATOR

Fig. 3-5. Wireline rotary coring tool for taking sidewall samples in hard rocks. The left schematic portrays the tool drilling a sidewall core. Selection of coring locations can be made from wireline or measurement while drilling logs. The coring tool is positioned at the desired depth using a gamma ray log at the top of the coting tool. The tight schematic portrays the tool storing the core sample in the storage tube. Most wireline rotary sidewall coting tools place a marker (ball bearing or disk) between core samples to indicate missing samples (two or more markers found together in the storage tube). After sidewall cores have been taken, the wellbore can be logged with a wireline imaging log to more accurately ascertain the coring locations with respect to formation layers. (Courtesy of Halliburton Energy Services.)

115 sample from the side of the borehole wall. Then the core drill containing the core is rotated back into the tool and the rock sample is pressed into a receiving tube. The percussion sidewall coring tool is used in soft to medium-hard rocks. It is the least expensive sidewall coring device. It is positioned and the sample barrel is fired into the formation by an explosive charge. In carbonates, the sample barrel will typically bounce off the borehole wall or break without obtaining a rock sample. However, this device would be useful for obtaining sidewall cores in softer source rocks.

CORE H A N D L I N G

Core retrieval, preservation, and handling should be done by following careful and special procedures, because they dictate whether or not subsequent core analyses data would be representative of actual reservoir behavior. Whole cores

Core retrieval typically is done by one or more geotechnicians or geoscientists. About one hour before the core barrel is due at the surface, they should begin preparing the area of the rig floor that has been designated as the core retrieval area (IHRDC, 1985). Materials that should be available include a labeled set of core boxes for temporary holding of the core, geological hammer, soft metal hammer, broom, work gloves, supply of clean gloves, pencils, and note pad on clipboard. The temporary-holding core boxes are used to keep the core in correct order while it is being retrieved from the core barrel on the rig floor and after it has been removed to the work area. The work area is generally adjacent to the mud logging unit, preferably at bench height, with sufficient space for two or more people to work around it. On arrival in the work area, the core must be transferred to clean boxes, fitted together where possible and measured (IHRDC, 1985). As each piece of core is taken from the temporary box, it should be wiped clean of drilling mud using dry rags only. Obvious features (such as fractures, bedding planes, oil or gas bleeding) should be noted on a worksheet. The core piece should then be transferred to its place in the new, clean core box. Loose rubble should be put in a clean sample sack and labeled with well and core identification information and an estimation of the number of feet of core it represents. When a box is about full, the core is fitted together as well as possible and properly labeled with waterproof marker pens. A tally sheet should be kept with the core length and estimate rubble content of each box. When the total length of core is known, the length measurements are converted to depths. Missing core is always assumed to have been lost from the bottom of the barrel. Following the brief examination made while boxing the core, a more thorough description should be made of all features of the core (IHRDC, 1985). The geoscientist should also be taking small chips of core that will be used for microscopic examination. (1) Core description should include (IHRDC, 1985) the following: (2) Lithology and thickness of major formation units. (3) Dip and strike of geologic structures.

116 (4) Nature of lithological boundaries. (5) Nature of bedding planes, and of sedimentary and diagenetic structures. (6) Gradational features such as grain size. (7) Spacing and surface texture of fractures and joints. In special cases where a core sample needs to be carefully preserved, such as native-state cores for enhanced oil recovery tests or special wettability-sensitive analysis, the core, after being wrapped in plastic and aluminum foil, is dipped into a plastic-like sealing or coating material for long-term preservation. The core may be frozen and stored in dry ice for shipment to the core analyses laboratory. Detailed procedures for whole core handling can be found in IHRDC (1985). Sidewall cores

After sidewall cores have been removed from the coring tool, they can be damaged by improper handling. Wellsite personnel should be aware of the amount of sample that is required for a particular analysis, so that sufficient core can be preserved. Samples should be packaged in individual, sealed containers and protected from excessive jarring that may occur as they are transported. The container and its lid should be properly and completely labeled (Worm Oil Coring Series, 1985-1986, Part 6). The cores may be frozen and stored in dry ice for shipment to the core analysis laboratory.

CORE ANALYSIS

Introduction

Core analysis can be carried out in different ways with different degree of complexity depending upon the type of information required, the type and size of samples, and the type of analysis facilities available. In general, core analysis can be divided into the following categories: conventional (routine), special, petrographic, and geochemical core analyses. Conventional (routine) core analysis usually includes measurement of porosity, air permeability, fluid saturations, grain density, and determination of lithology and texture. Core photographs may also be taken. Special core analysis usually includes measurement of porosity and (brine and gas) permeability at reservoir stress conditions, capillary pressure, relative permeability, close-density permeability measurements, core gamma scans, electrical resistivity properties such as resistivity index and formation factor, nuclear magnetic resonance (NMR), X-ray computerized tomography (CT), acoustical properties, mechanical properties, residual saturations, preferential wettability, coreflood tests, slimhole continuous core analysis, and cation exchange capacity. Petrographic studies include such methodologies as thin section analysis, scanning electron microscopy, image analysis, X-ray diffraction, Fourier transform infrared spectroscopy, calcimetry, dating and fracture analyses. Geochemical analysis provides data concerning the hydrocarbons in the core

117 samples. Thermal extraction chromatography and pyrolysis chromatography are two "heat and sniff' methods that provide chromatographic fingerprints that can be used for hydrocarbon identification and typing. Source rock can be analyzed for richness.

Sampling Muscat (1949) pointed out that no matter how complete the coring, one is still limited to an examination and study of rock samples which can constitute, at the most, a fraction of the total reservoir volume only of the order of 0.0001%. One should keep this in mind as one compares core-derived rock properties to those derived from, for example, well testing which can have a large volume of investigation. Sampling strategy for core analysis should be influenced by this also. The reliability of core analysis data, particularly special core analysis, is strongly dependent on how the core sample is selected, preserved, and prepared for analysis. Core analysis can be performed on whole pieces (6 in. to 12 in. long: 15 to 30 cm) of core or on plugs taken from the core as shown in Fig. 3-6. Whole core analysis is more expensive and takes a longer time to complete than plug analysis. One should

Fig. 3-6. Full-diameter whole core compared to plug-size sample (round hole to the left) for fractured rocks. (After Bergosh et al., 1985.) Plug size is 2.5 cm (1 in.) diameter.

118 consider whole core analysis when the rock is so heterogeneous that a plug is not representative of the rock surrounding it. Plugs can be taken parallel or perpendicular to the core axis. The orientation should be selected based on the need for directional information, such as vertical versus horizontal permeability. Plugs should be taken in a non-biased fashion. If one selects only the best quality rocks for analysis, one will end up with a small cluster of rock property values that are not representative of the range of rock properties of the formation (making for a poor regression). One non-biased selection process would be to take a plug exactly every foot (30 cm), only moving slightly up or down or to the side if the core is physically damaged at the foot mark. Another non-biased selection process is to scan the core with a CT or NMR scanner to locate and classify different rock types; then sample each rock type a statistically significant number of times. Figure 32 shows that representative sampling is not trivial. Answers to the following questions (E.C. Thomas, personal communication, 1987) might help one pick sample points effectively: (1) What use will be made of the data? (2) How are the results going to be "averaged" to accurately characterize the full range of formation properties? When doing core sampling and analysis for reservoir characterization, one must consider the following: (1) Results needed. (2) Accuracy needed. (3) Tumaround time needed. (4) Cost. Note that (2) and (3) are mutually exclusive and (2) and (4) are strongly correlated (E.C. Thomas, personal communication, 1987). Core data, like any other formation evaluation or reservoir characterization data, should be acquired in a cost effective manner.

Conventional (routine) core analysis Conventional (routine) core analysis usually includes measurement of porosity, air permeability, fluid saturations, grain density, and determination of lithology and texture. Core photographs may also be taken. Figure 3-7 shows a typical conventional core analysis data graph based on data obtained on plug-sized samples taken every foot (30 cm). Saturation changes pinpoint gas/oil and oil/water contacts. Average data for various zones are also illustrated.

Porosity There are several core analysis methods for porosity determination (American Petroleum Institute, 1960). Typically core analysis porosity determination methods measure the bulk volume and the pore volume or grain volume of the rock sample. Most methods require that the core be cleaned of formation and filtrate fluids before or as part of the analysis process. The lower the permeability of the rock sample, the longer it takes to perform the cleaning and/or porosity analysis. Heterogeneous rocks,

119

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like vuggy carbonates, require whole core analysis rather than plug analysis to produce representative results. However, the larger the rock sample, the longer it takes to perform the cleaning and/or porosity analysis. Routine porosity determination methods include summation of fluids, Boyle's law, hydrostatic weighing, and mercury injection. Summation of fluids begins with determination of the gas volume in the core sample. Mercury is injected into the core sample at high pressure (1,000 psi or 7,000 KPa) using a porosimeter like that shown in Fig. 3-8. The gas is effectively compressed to a negligible volume by the mercury and the volume of mercury injected is representative of the gas volume. The core sample is then put into a saturation still retort (Fig. 314) to heat out and measure the oil and water volumes. The sum of theses volumes (gas plus water plus oil) is the pore volume. Pore volume divided by bulk volume, measured separately or at the beginning of this analysis using the porosimeter (Figs. 3-8 and 3-9a), yields the porosity of the core sample. Summation of fluids is the fastest of the conventional porosity determination methods because the core does not have to be cleaned first. However, solid kerogens will be cracked at high temperature and be counted in the oil volume. Hydrostatic weighing uses Archimedes principle to obtain porosity on a cleaned

120 core plug. Pore volume is determined from the weight of empty rock plug and the weight of the rock plug containing a wetting fluid, usually toluene, knowing the density of the toluene. Grain volume is determined hydrostatically weighing the core plug in a toluene bath, knowing the weight of the empty rock and the toluene density. Bulk volume is the sum of pore volume plus grain volume. Porosity is pore volume divided by bulk volume. Hydrostatic weighing is the most accurate method for porosity determination (it uses an analytical balance for weighing) if the wetting fluid stays in the pores during analysis. Therefore, it will not work well for vuggy rock where the toluene drains out of the vugs during weighing for pore volume determination. Boyle's law method (Fig. 3-9b) uses pressures and volumes on clean rock samples to determine grain volume. Pore volume is divided by the bulk volume (measured separately) to yield the porosity of the core sample. Boyle's law method is especially useful for vuggy rock. Mercury injection uses a porosimeter (Fig. 3-8 and Fig. 3-9a/c) on a clean rock sample to obtain bulk volume by surrounding the core sample with mercury, and pore volume by injecting mercury to fill the pore volume. Pore volume divided by bulk volume is porosity.

SCALESTOP

PYCNOMETERLID ~=~"- PRESSURE

Fig. 3-8. Ruska porosimeter for routine porosity measurement on a core plug. A core plug is surrounded by mercury to obtain the bulk volume of the sample. Mercury is pumped into the pores of the core plug to obtain void space volume. This apparatus can be used on core plugs which have been cleaned to obtain total interconnected porosity. Or it can be used on core plugs still containing oil and water to obtain gas volume as part of the summation of fluids methodology.(Schematic from Whittaker, 1985.)

121

(8)

Bulk volume pycnometer

(b) Grain volume ( Boyle's law)

Solid reference] J ~ J or sample I "1--" X XSample Reference chamber volume Solid volume

- Gas supply

P2 v s = v I - P--~2

9 v2

(Calibration curve vs against P2 / Pl-P2 can be established using steel blanks ) (C) Bulk and pore volume porosimete r

Reference mark Isolation valve

Dead weight tester

tu

Micrometer mercury pump

[~i\ ~'

'

"

l

Fig. 3-9. Measurement of core sample porosity: (a) bulk volume pycnometer, (b) grain volume (Boyle's law), and (c) bulk and pore volume porosimeter. (After Archer and Wall, 1986.)

Permeability The gas permeability of a sample is measured by placing the dry sample in a Hassler-type core holder subjected to a certain confining pressure and flowing a dry gas, usually nitrogen or air, through the sample. The pressure drop across the core and the flow rate are measured and Darcy's law is used to calculate the permeability. The gas permeability is usually measured at three or more mean pressures (average of the upstream and downstream pressures). The Klinkenberg-corrected permeability, which is equivalent to the specific or absolute liquid permeability, is obtained by plotting the gas permeability as a function of the inverse of the mean pressure and extrapolating to infinite mean pressure. A permeameter schematic is

122 WMETERS PRESSURE GAUGE

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.:

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Fig. 3-10. Ruska permeameter for measuring gas permeability on a plug sample. A detailed cut-away schematic of the core sample holder is shown in Fig. 3-11. (After Whittaker, 1985.) shown in Fig. 3-10, whereas a close-up schematic of the core sample holder is shown in Fig. 3-11. If plugs are taken, their orientation should be selected based on the need for directional information, e.g., vertical versus horizontal permeability. Directional permeability tests can be conducted on core plugs drilled around the core periphery or on full-diameter cores. These data are most helpful when generated on spatially oriented cores and include permeability at 30--45 ~ increments around the circumference of the rock. For heterogeneous carbonates, whole core measurements of permeability would probably be the most representative technique, unless fractures are present which may form during the pi'ocess of core recovery. Whole core permeability measurements done perpendicular to the borehole axis typically provide two measurements (see Fig. 3-12). The larger of the two measurements is termed kax. The other, taken 90 ~ to the maximum value, is termed kgo.

Fluid saturations Usually pore fluid saturations cannot be determined directly from examination or analysis of rock. Saturations of a rock brought to the surface differ from its in-situ saturations because of two factors: invasion and blowdown (Fig. 3-13). Invasion of the drilling mud filtrate will change the saturations and pore fluids of the permeable rocks. As the rock is brought from formation depth to the surface, the pressure on the rock decreases. Fluids will expand as the rock moves upward toward the surface. If the bubble point pressure of the oil is reached, gas will evolve. Expansion of gas with

123

!RMOMETER

OVERLAP

SLEEVE

TEST SAMPLE

O-RINGS

BASE

Fig. 3-11. Permeameter core holder. Gas flow is directed through the core parallel to the long axis of the core plug. (After Whittaker, 1985.)

reduced pressure (Boyles law) is much more dramatic than that of liquids. As the pore fluids expand they push pore fluids from the core, i.e., blowdown occurs. Other factors can have influence on core saturations. These include mud overbalance pressure, mud fluid/spurt loss, core diameter (large diameter is better), horizontal and vertical permeability, interphase tension between mud filtrate and reservoir oil, viscosity contrast between reservoir and invading fluids, rate of bit penetration, rate of mud circulation, coring fluid and additives (surfactants can substantially reduce core oil saturation), relative permeability, core handling and preservation, gas/ oil ratio, and core bit mud discharge direction (Core Laboratories, 1989). With water-based muds there are three situations in which invasion and blowdown might not change the pore fluid saturations: (1) Zones that are already at 100% water saturation. (2) Zones that are already at waterflood residual oil saturation, with the effects of blowdown on the oil saturation being accounted for or eliminated by the use of a sponge core liner pre-saturated with water or by the use of a pressure core barrel (Worm Oil Coring Series, 1985-1986, Part 2). (3) Zones containing very viscous (near-solid) tar or heavy oil. In these situations, the hydrocarbons (if present) are immobile to mud filtrate invasion with possibly little or no effect on the resulting lab-measured oil saturation. Blowdown either is not a factor or is accounted for.

124 F l o w g a s t h r o u g h c o r e in this d i r e c t i o n

I I I I I I I I I

o

~ - - -lliiiiiii!i!iii~i~i~i~'~'!,~!r--'-"

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Whole core

Fig. 3-12. Schematic diagram showing the basis for a whole-core gas permeability apparatus. Screens and core are inserted in a Hassler-type sleeve. Gas is passed through the screens across the core and permeability is determined. Then the core is rotated 90~around the borehole axis and the permeability for that direction of gas flow is determined. Both measurements are recorded. The larger one is termed k the other is kgo. max ~

With oil-based muds there is one situation in which invasion and blowdown might not change the pore fluid saturations: (1) Zones that are at in-situ irreducible water saturation. Invasion of oil-based mud filtrate might have little or no effect on the water saturation of zones which are at irreducible water saturation. In this case, the effects of blowdown on the water saturation can be accounted for or eliminated by the use of a sponge core liner pre-saturated with mineral oil or by the use of a pressure core barrel (Worm Oil Coring Series, 1985-1986, Part 2). After the sample is selected, it undergoes the conventional procedure of fluid extraction and saturation measurement by one of the following methods: (1) high vacuum distillation of oil; (2) high-temperature (1200~ 650~ retorting at atmospheric pressure (Fig. 314); (3) distillation of water and solvent extraction of oil (Dean-Stark extraction) at low temperature (240~ 115~ (Fig. 3-15); and (4) combination techniques. High-temperature retorting is an extension of the previously discussed summation of fluids porosity determination methodology. Inasmuch as pore volume is determined by summing the gas, oil, and water volumes, fluid saturations can be determined by dividing each fluid volume by the pore volume. This is the fastest method for saturation determination. However, solid kerogens will be cracked at the high temperature and be counted in the oil saturation.

125

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CONDITIONS

20% RESIDUAL OIL (OR LESS]" 40% WATER [MAINLY DRILLING FILTRATE) 40% GAS SPACE (DUE TO EXPANDING GAS FROM

ATMOSPHERIC TEMPERATURE & PRESSURE

OIL) , MUD FILLED BORE HOLE

BLOWDOWN OFTEN INCREASES AS PERMEABILITY DECREASES

MUD FILLED DRILL PIPE

22 % OIL 60% WATER 18% GAS

SHALE

PRESSURE & TEMPERATURE REDUCTION

(INSIDE CORE BARREL] GAS ~/ATEI OIL i POSS. MUDCAKE

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(OVERBURDEN REMOVED]

::i]ilil]i!i!i]ii!..O.!..L, 20% WATER (IRREDUCIBLE) 80% OIL WITH DISSOLVED GAS

ORIGINAL CONDITION

Fig. 3-13. Analyzed pore fluid saturations are typically altered from in-situ conditions by water-based mud filtrate invasion and pressure blowdown. The example saturations shown in this schematic will not be representative of all formations, but the general trends will be valid. In certain situations, e.g., heavy oil or tar as the hydrocarbon phase, invasion and blowdown will not occur. Invasion may not change the oil saturation if the formation is already at residual oil saturation to waterflood. Blowdown can be prevented or accounted for by using pressure or sponge core barrels. The original in-situ stress condition surrounding the rock is removed after the core is cut. (From E.C. Thomas, personal communication, 1987.)

126 1GHT FITTING SCREW CAP

HEATING ELEMENT

SAMPLE STAINLESS STEEL SAMPLE CHAMBER (BOMB)

AIR COOLER FINS

INSULATION

;CREEN

VAPOR TIGHT SEAL

WATER OUTLET WATER INLET

%

CONDENSING TUBE

WATER BATH

RECEIVING

Fig. 3-14. Saturation still retort: fluid extraction and saturation measurement device. In addition to determinationof fluid saturations,this device and the datait supplies can be used for porosity determination by the summation of fluids method. (After Whittaker, 1985.) Dean-Stark extraction begins with an uncleaned core sample. The weight of the rock containing oil and water is measured. Then extract the core sample with a solvent, typically toluene or xylene, using the Dean-Stark apparatus (Fig. 3-15) to boil the solvent up through the core sample and then drip back down through the core sample after it has been cooled by the condenser. The solvent will remove oil from the rock with the oil staying in the solvent. The boiling temperature of the solvent is slightly above that of

127 UNIFORM I.D:" THROUGHOUT LENGTH

WATER OUT

REFLUX CONDENSER

Ale

WATER IN

GROUND

GROUND JOINT WATER T R A P ~ 5 ml CAPACITY WITH l l l O t h ml GRADUATIONS ( 1 3 0 turn • 5 ram)

EXTRACTOR

=OUR INDENTATIONS SPACED UNIFORMLY TO HOLD THE SAMPLE THIMBLE PYREX GLASS FLA~r VOLUME - 2 5 0 ml

Fig. 3-15. Dean-Stark distillation fluid extraction and saturation measurement device.A heater underneath the flask refluxes solvent through the core sample to remove water and oil from the rock pores. Water volume is obtained directly from reading the water trap. Oil volume is obtained from the weights of the rock sample before and after extraction, accounting for the weight of the water removed and knowing the oil density. (From Whittaker, 1985.)

water, so the water is removed from the core and collects in the water trap. The volume of the distilled water in the trap is converted to water weight by multiplying by the density of distilled water at the trap temperature. The solvent may not get all of the oil out of the rock sample, so further extraction may be needed. In any case, it is prudent to continue extraction until all solvent(s) come out clear, indicating that all oil has been removed from the rock sample. Next, salts left behind in the pores from the water (mostly drilling mud filtrate) need to be removed. The weight of the cleaned core sample is then measured. The weight of the oil taken from the core sample is derived from the original weight of the uncleaned core sample minus the weight of the water minus the weight of

128

the cleaned rock. Additionally, nuclear magnetic resonance measurements may be made on the solvent(s) to provide a second measure of oil volume. The water saturation is obtained by dividing the water volume by the pore volume (determined elsewhere). The oil saturation is obtained by dividing the oil weight by the oil density (determined elsewhere) and then dividing by the pore volume. The low temperature of this procedure (so that kerogens are not cracked) and the accuracy obtained by using an analytical balance, make it a very accurate saturation determination methodology.

Grain density Analyses of core for grain density to provide insight into mineralogy can be done a number of ways (American Petroleum Institute, 1960). Core analysis grain density results can be related to known grain densities for particular rock types. For example, the grain density of dolomite is in the 2.85-2.87 g/cm 3 range according to the references of Edmunson and Raymer (1979), Wells et al. (1979), Ellis et al. (1988), and Carmichael (1989). These four references provide a comprehensive listing of physical properties of rocks, including the grain or matrix properties and the responses of nuclear and acoustic logs. Grain density can also be used to calibrate density logs for porosity determination (also see Chapter 4, Vol. I, p. 247). In complex lithologies, such as carbonates with intermixed limestone, dolomite, and other minerals, grain density may vary considerably vertically within the reservoir and horizontally from well to well as shown in Fig. 3-16.

Determination of lithology and texture Examination of the core for lithology and texture determination can be done at the wellsite or in the laboratory. Containerized core barrels can hamper wellsite core examination inasmuch as the core is covered by the container. Swanson (1985) described methods for determination of lithology and texture and for documentation of results.

]/! "~40 E

~:

-.~ 30 -

~li

i

i i [_J' i '

'

ll "1 i J 1 J j i I

9

100 ,n 80

E

0

"N E ~

I~'mtW " ]

"- 20 ,-, 10 0 2.411

2.50 2.60 2.10 2.80 2.90 3.1111 3.10 Grain Density: Em/cc

Fig. 3-16. Grain density variation between wells A andB in a formationwith complex geology. (After Keelan, 1982.)

129

Core photographs Core photos allow one to "see" the core without actually having to go to where the rock is stored or transporting the core. Core photos come in many formats. Usually an overview format will cover 18 ft (5.5 m) of core per 8 • 10 in. (20 • 25 cm) photo. A detailed format will cover 18 in. (45 cm) of core per 8 • 10 in. (20 • 25 cm) photo. Core photography with both natural and ultraviolet lights reveals bedding planes, orientation and other structural features, which indicate observed difference in permeability, porosity, saturations, and depositional environment (Fig. 3-17). Ultraviolet photography reveals oil fluorescence and, hence, location of liquid hydrocarbons in the core. Special core analysis Special core analysis usually includes measurement of porosity and (brine and gas) permeability at reservoir stress conditions, capillary pressure, relative permeability, close-density permeability measurements, core gamma scans, electrical resistivity properties such as resistivity index and formation factor, nuclear magnetic resonance (NMR), X-ray computerized tomography (CT), acoustical properties, mechanical properties, residual saturations, preferential wettability, coreflood tests, slimhole continuous core analysis, and cation exchange capacity. Usually special core analysis is done on a small percentage of the core. Higher cost and longer analysis time are reasons for this. However, it is important to cover the range of pertinent rock types with special analysis (see Representativeness of core data earlier in this chapter). Stressed analyses The effective confining pressure, or mean effective stress, S ' is required to properly specify laboratory conditions for stressed core analysis so that the analysis is done under the equivalent of in-situ stress conditions. It is defined as" m

s '=

'

+ s.

+

~

(4-1)

-

It is the average of the three principle stresses minus some fraction n of the fluid pressure p, reflecting that the internal pore fluid pressure is able to carry a portion of the total material load acting on a given volume. Subscripts h, H, and V represent the three principal stresses: the least horizontal stress, the greatest horizontal stress and the vertical stress, respectively. The fraction n is defined as follows" n = 1 -13 < 1 for deformation prior to failure, and n = 1 at point of failure. The quantity f5 = K / K , where K is the elastic bulk modulus of the dry or drained porous rock frame (the matrix) and K is the bulk modulus of the individual solid grains. The matrix K can be calculate~d from the drained Young's modulus E m and Poisson's ratio v measured in conventional triaxial tests: m

g

m

m

E K

~.. m

m

.....................................

3(1 --2Vm)

(4-2)

130

Fig. 3-17. Core photographs from various depositional environments. (After Keelan, 1982.)

The grain modulus K g can be estimated from the K gt. of the individual mineral constituents i using Wood's formula, which provides the inverse or harmonic average:

131

K ..........i_..................

(4-3)

g /~ / KiVt 9) where Vi is the volume fraction of each mineral. For highly compressible rocks such as unconsolidated sands, high-porosity chalks, or diatomite, K < < K and the quantity 1 -13 is approximately 1. For "hard" rocks, however, 1 -13 may be ~s small as 0.6. Values of K may range anywhere from 1 x 104 to 2 x 106 psi (7 x 104 to 14 x 106 KPa), whereas values of K commonly range from 5 x 106 psi (35 x 106 KPa) for quartz to 12 x 106psi (84 x 106 ~d~a) for dolomite (K.S. Hansen, personal communication, 1992).

m

Capillary pressure Core analysis data in the form of drainage capillary pressure curve saturation distributions can be representative of the original hydrocarbon saturation distributions in a reservoir (Leverett, 1941; Rose and Bruce, 1949; Jodry, 1992), provided that the rock from which the data are acquired is representative of the formation. Mercury-air capillary pressure points (Purcell, 1949) can be related to reservoir height above the free water level (see the definition in Table 4-XVII, Chapter 4) of the formation by Eq. 4-3, Chapter 4, provided that the in-situ formation hydrocarbon and water specific gravities, interphase tensions, and contact angles are known. For the mercury-air capillary data, mercury is the non-wetting phase. For Eq. 4-3, Chapter 4, to be representative of the reservoir height relationship for the original saturation distribution in the reservoir, the hydrocarbons are assumed to be the non-wetting phase during the original oil migration and subsequent saturation distribution equilibrium. Thomeer (1960) provided a methodology that can uniquely describe a capillary pressure curve and quantify the saturation distribution using three parameters. These socalled Thomeer parameters that describe the capillary pressure curve can be used to calculate the original saturation at any height above the free water level in the reservoir. A correlation between the capillary pressure curve's height above free water level and the reservoir depth must be found. Smith (1990) showed examples of capillary pressure to reservoir depth correlation using well log data. Figure 4-6 in Chapter 4 shows an example of capillary pressure to reservoir depth correlation using wireline test data. Permeability can be estimated from capillary pressure core data (Purcell, 1949, for historical perspective on early work; Swanson, 1981, for use on cuttings or samples with large closure corrections; Thomeer, 1983, for general use). The Thomeer and Swanson methodologies provide permeability estimates within a factor of two, for a one standard deviation confidence level, based on their calibration data sets. For rocks with more than one pore type, Thomeer (1960) pointed out that the relatively larger pores of a rock contribute the most to the permeability and, therefore, any capillary curve permeability estimate should be based on the lower-pressure capillary curve portion of multiple-curve capillary pressure data. The Micromeritics* Autopore capillary pressure apparatus can attain mercury-air *Company names mentioned in this chapter are for reference only and are not meant as an endorsement of any particular company or product.

132 capillary pressures up to 55,000 psi (380,000 KPa). This is a magnitude higher than can be attained by conventional mercury-air capillary pressure devices. High capillary pressures provide detailed information about microporosity distribution. The Autopore acquires capillary pressure data in two steps. The first step covers capillary pressures up to 25 psi (172 KPa), the second covers beyond 25 psi (172 KPa). Potential low accuracy of information in the immediate vicinity of 25 psi (172 KPa) is a weakness of this tool if a particular pore type has a mercury-air capillary entry pressure of 25 psi (172 KPa). Yuan (1991 a) described a quantitative method of determining pore scale heterogeneity from the apparatus for pore examination (APEX), a rate-controlled capillary pressure measurement apparatus, which can lead to a quantitative assessment on the efficiency of enhanced oil recovery processes. APEX data can be used to resolve individual pore bodies and throats. Yuan (1991 b) also described APEX models used for the determination of Archie's lithologic exponent, m, and permeability, and the models' agreement with experimental measurements on a set of samples for which the lithologic exponent, absolute permeability, and additional APEX data have been measured. A centrifuge may also be used to obtain capillary pressure data. Cores are saturated with water (or oil) and spun within air or oil at increasing speeds. Average liquid content at each speed is calculated from observations of liquid spun out. The liquid volume out is read with a stroboscope while the centrifuge is in motion. The average saturation data are used to establish a water saturation versus pressure curve (Core Laboratories, 1982).

Relative permeability A rock's relative permeability is generally defined as the effective permeability of one fluid in a multi-fluid situation divided by the specific permeability of a single fluid when only that fluid occupies the pores. Relative and effective permeabilities are specified for a particular fluid saturation situation. A relative permeability curve is made up of multiple measurements at different fluid saturations. Relative permeability is used in conjunction with the fluids' viscosities to determine the fraction flow (production percentage) of each fluid from the rock. Effective and relative permeability of carbonate reservoirs are discussed in detail in Chapter 8, Part I of this book. Matching the core wettability condition to the reservoir wettability condition is the key to obtaining relative permeability information that is truly representative of a particular reservoir. Native-state coring (taking a core without changing the rock wettability) can be difficult, if not impossible. Restored-state core analysis (aging the core containing reservoir fluids at reservoir temperature for at least a month) can be time consuming and expensive. Common methods for measuring relative permeability include steady state and unsteady state (Core Laboratories, 1982). Hawkins (1988) provided a comparison of relative permeabilities on restored-state core using the following methods: unsteady state at ambient conditions, steady state at ambient conditions, and unsteady state at reservoir conditions. Although the residual oil saturations varied, the shape of the relative permeability curves from the three methods were similar.

133

Mini-permeameters So-called mini-permeameters are pressure-decay devices that flow gas from the end of a tube-like probe that is sealed against a rock sample to estimate local permeability. Georgi and Jones (1992) discussed the evolution of mini-permeametry and the application of this technique to reservoir description. Inasmuch as the device can provide estimates of permeability with resolution down to about five mm (0.2 in.), geologists can quantify the impact of both depositional and diagenetic features on permeability. Lab-based mini-permeameters can be used on small-diameter core plugs or full-diameter core samples. Portable mini-permeameters, like the University of Texas mechanical field permeameter (Chandler et al., 1989), can be used to characterize the outcrop permeability distribution. Work done at the New Mexico Institute of Mining and Technology (Chen et al., 1993) expanded use of these tools to include porosity determination. Core gamma scans Scanning a continuous whole core with a gamma scanner is analogous to logging a well with a gamma ray log. A record is made of the rock's natural radiation versus the depth of the core. This information can be used to correlate the core recovery to reference log depths. Some core analysis labs have spectral gamma scanning devices which record the contributions of potassium, thorium, and uranium to the natural radiation of the rock, analogous to a spectral natural gamma ray logging tool. The additional information provided by a spectral gamma scan can help Out in tough correlation conditions, such as the alternating layers of radioactive and non-radioactive dolomites found in some West Texas fields. Resistivity properties Determination of the Archie formation factor, F (to obtain the lithologic exponent, m) and the resistivity index, I (to obtain the saturation exponent, n) can be done using core analysis (Archie, 1942). Detailed definitions of F, m,/, and n can be found in Chapter 4 of this book. Matching the core wettability condition to the reservoir wettability condition, is the key to obtaining resistivity property information that is truly representative of a particular reservoir. Native-state coring (taking a core without changing the rock wettability) can be difficult, if not impossible. Restored-state core analysis (aging the core containing reservoir fluids at reservoir temperature for at least a month) can be time consuming and expensive. Several laboratory techniques for measuring resistivity index curves and a study of their accuracies have been documented by de Waal et al. (1989). Mahmood et al. (1988) performed an experimental study to investigate the influence of variation in test conditions and laboratory procedures on the electrical properties of rocks. The results of resistivity measurements on a synthetic porous medium, Berea sandstone, Shannon sandstone outcrop, Shannon subsurface, and carbonate reservoir cores are presented. This study provides some insight into the complication involved in rock electrical resistivity laboratory measurements under simulated reservoir conditions. It also contributes to understanding the combined effects of temperature and pressure on resistivity properties.

134

Nuclear magnetic resonance (NMR) Nuclear magnetic resonance (NMR) scans and spectroscopy provide non-destructive three-dimensional analysis of particular nuclei in the pore liquids. NMR can be used to locate and quantify hydrogen (in water and oil), carbon (in oil), sodium (in water), and fluorine (in tracers) (Edelstein et al., 1988). Liquid-filled porosity, pore liquid saturations, pore size distribution, pore liquid viscosity and rock permeability information are obtainable. NMR responds to the liquids in the pore space. Gas in the pore space is not measured directly, but can be inferred by the difference between the NMR liquid (%BV) and the total porosity (%B V). If the pore space contains gas, the rock must be resaturated with liquid for accurate total porosity determination. Because the NMR apparatus responds to liquids, the pore liquids cannot be frozen. NMR scanning and spectroscopy can be done on whole cores, core plugs, and fluid samples. NMR scanning and spectroscopy cannot be done on rock through ferro-magnetic or other NMR-opaque containers. The use of proton NMR in tight, gypsum-bearing carbonates has been shown to be valuable for saturation determination where extraction core analysis methods proved inaccurate due to gypsum dewatering and extremely low permeability of the rock (Vinegar et al., 1991 b). Whole core analysis by 13C NMR for oil saturation determination has been demonstrated in cases where 1H NMR might not work well, like in shaly rock (Vinegar et al., 1991 a). NMR has also been demonstrated to be a useful tool in quantifying oil volume in extracts from other saturation determination procedures; such as extracts from polyurethane sponge core liners using freon-ll, Dean-Stark extracts using xylene, and miscible flooding extracts using chloroform/methanol (Tutunjian and Vinegar, 1990). Determination of formation water salinity by the use of nuclear magnetic resonance imaging of 23Na in cores has been demonstrated (Tutunjian et al., 1991), for those cut in oil-based muds. This method will work for formation water salinity determination as long as sodium is the predominant cation in the formation water. The core must be handled and protected so that pore water evaporation does not occur. Pore water evaporation would increase the apparent salinity of the water. Proton NMR measurements on tight, gypsum-bearing carbonates have also provided quantitative oil viscosity information where extraction methods proved costly due to extremely low permeability of the rock (Vinegar et al., 1991b). Whole core analysis by ~3C NMR for oil viscosity has also been demonstrated (Vinegar et al., 1991 a) without extracting the oil from the core. NMR oil viscosity determination has also been done on oil present in core analysis extracts from polyurethane sponge core liners using freon-11, from Dean-Stark extracts using xylene, and from miscible flooding extracts using chloroform/methanol (Tutunjian and Vinegar, 1990). Whole core analysis for hydrocarbon chemistry by 13C NMR has been used to determine aliphatic/aromatic ratio (Vinegar et al., 199 l a) without extracting the oil from the core. Proton NMR measurements have been shown to estimate permeability from sandstone core samples (Seevers, 1966, for first work; Howard et al., 1990, for recent work). Howard et al. related the time constant for NMR longitudinal relaxation, T/, to pore body size, for intergranular/intercrystalline rock. Kenyon et al. (1988) reasoned

135 that the permeability from NMR is, therefore, a function of the relation between the size of the pore throats to the size of the pore bodies, with NMR providing the pore body information. NMR permeability estimation for vuggy rocks will be less accurate than that for intercrystalline rocks because of the poorer relationship between pore throat size and pore body size for vugs (H.J. Vinegar, personal communication, 1992). NMR spin-lattice (T~) and spin-spin (T2) relaxation times are typically used for porosity and permeability determination because they are related to surface-to-volume ratio of pore systems by surface relaxivity which in turn is influenced by mineralogy, wettability, and concentration of paramagnetic and ferromagnetic impurities on grain surfaces. Paramagnetic ions in drilling mud filtrate may also have influence on measurements. Restrictive diffusion, another NMR measurement, is also proportional to surfaceto-volume ratio but is not dependent on surface relaxivity. Restrictive diffusion measurements also offer the possibility of estimating in-situ crude oil viscosity (Tutunjian et al., 1993). NMR scans can be made during reservoir flood tests on cores. Liquids can be tagged with tracer elements which can be seen by the scanner. The container encasing the core must be made of a NMR-transparent material such as glass.

X-ray computerized tomography (CT) X-ray computerized tomography (CT) scanning of rocks was introduced to the petroleum industry in the mid-1980s. CT scans provide quantitative, non-destructive, three-dimensional density and atomic composition core analyses. CT density scans yield porosity and fluid saturation information. CT atomic composition scans yield lithology information. Although most CT usage is for visual quality and descriptive assessment of core material, quantitative analysis can be done if the machine is properly calibrated (Coles et al., 1992). It consists of a rotating X-ray source and detector, which circles the core and takes images of different cross sections. The core setup is such that it can advance incrementally a desired distance in a certain direction and three-dimensional images can be obtained. The X-ray digital data are acquired by a computer and are converted to images that are displayed on a computer screen or printed to show various materials and heterogeneities in the core. CT scans provide spatial information with resolution as fine as a few millimeters. Cores can even remain frozen during the scan. Scans can be made through core containers, unless they are made of lead or thick stainless steel. CT scanning (Wellington and Vinegar, 1987) can be used for saturation determination. Invasion and blowdown most likely have altered the saturations from in-situ values. If two fluid phases are present, a single energy scan is sufficient to measure the two saturations. When three fluid phases are present, two different energy scans are needed to determine the three saturations. Wellington and Vinegar discussed the use of CT scanning saturation determination for flow studies, and showed results from several different types of coreflood experiments. CT scanning can be used for quality assessment of the core, with millimeter resolution, so that further analysis can be made on non-altered core samples. Several core quality problems can be seen without opening up the core container(s): whole mud invasion, fractures, and disturbed core. Use of the CT scan should be strongly

136 considered before any other core work is begun. It can save money and time by optimizing the use of good quality core for analysis and can provide useful analytical information, too (Wang et al., 1984a, 1984b; Vinegar, 1986; Wellington and Vinegar, 1987; Hove et al., 1987; Hunt et al., 1988; Withjack, 1988; Hicks et al., 1992).

Acoustic properties Acoustic properties, such as velocity (compressional and shear) and anisotropy can be measured on cores (Core Laboratories, 1989). These data can be useful in seismic calibration. Matching the core stress condition to the reservoir stress condition is a key to obtaining acoustic information that is truly representative of a particular reservoir. Effective confining pressure determination has been discussed earlier in this chapter. Mechanical properties Rock mechanical properties such as Young's modulus, Poisson's ratio, unconfined compressive strength, tensile strength, and compressibility can be determined from core measurements (Monicard, 1980). These data can be useful in quantifying the compressibility effects of formation pressure reduction on reservoir pore volume, selecting drilling parameters and equipment, predicting hydraulic fracture shape, and predicting surface subsidence. Skopec (1991) used vertical pilot-hole oriented coring and rock characterization along with open hole small-volume-hydraulic fracturing to provide valuable insight into the design of a horizontal wellbore in a naturally fractured reservoir. Results such as rock mechanical properties, fracture strike and principal in-situ stress magnitudes and directions were used to reduce risk in the drilling of horizontal wellbore and optimize its placement with respect to in-situ stresses and fracture orientation. Residual oil saturation determination The determination of residual oil saturation after waterflood provides the information concerning the target for a subsequent tertiary flood (CO 2, caustic, chemical, etc.). Direct determination methods include sponge and pressure core analysis. Both sponge and pressure core account for blowdown such that the resulting oil saturation determination is representative of the residual oil saturation after mud filtrate invasion. Other determination methods include corefloods and imbibition capillary pressure and relative permeability analyses. Wettability Reservoir wettability is not a simply defined property (Morrow, 1990). Morrow stated that classification of reservoirs as water-wet or oil-wet is a gross oversimplification. Wettability has significant effect on all multiphase flow situations of a reservoir, from source rock oil migration to tertiary flood. Two methods of quantifying wettability based on rock~rine/oil displacement behavior, the modified Amott test (Amott, 1959) and the USBM test (Donaldson et al., 1969), are in common use. Detailed fundamental information concerning wettability and its effect on reservoir performance can be found in Hirasaki (1991) and Morrow (1990).

137 Cleaning the fluids out of a core (as is done during routine core analysis) can make the core behave more water-wet. Aging the core containing reservoir fluids at reservoir temperature for at least a month can be time consuming and expensive, but is required to restore wettability at or near in-situ conditions. Hirasaki et al. (1990) evaluated wettability changes during stages of restored-state core analysis for a North Sea reservoir. Their goal was to determine the proper core analysis technique for estimating the remaining oil saturation after waterflooding. Amongst their conclusions were: (1) USBM and Amott indices measured by automated centrifuge were a good measure of wettability. (2) Core cleaning methods affect the restored state capillary pressures, relative permeabilities, and residual saturations. Traditional Dean-Stark extraction with toluene followed by chloroform-methanol did not adequately clean the cores and made the rock appear more oil-wet than more thoroughly cleaned cores. Wunderlich (1991) discussed the three situations (coring, storing, and preparation) in which core wettability can be altered. His comprehensive discussion of recommendations for obtaining samples with preserved wettability includes: Introduction. Coring. Wettability alteration due to interactions with drilling fluids. Pressure and temperature. Storing. Laboratory preparation. "No solvents" procedures. "Clean and restore" procedures. "No hysteresis" procedures. Recommendations for cleaning procedures. Experimental conditions. Concluding remarks and references. Wunderlich's recommendations provide detailed procedures for obtaining reservoir rock in a wettability state representative of in-situ wettability (also see Introduction Chapter, Vol. I, pp. 30-31).

Corefloods Reservoir performance information for characterization of the reservoir response to specific production mechanisms can be obtained from corefloods. These include waterflood tests and enhanced oil recovery (EOR) coreflood tests, such as hot water flood, steamflood, steam soak, fire flood, miscible flood, chemical flood, and CO 2 flood. Monitoring saturation changes during a coreflood can be done by CT scanning (Wang et al., 1984a, 1984b; Hove et al., 1987; Withjack, 1988) or by NMR scanning (H.J. Vinegar, personal communication, 1992). For CT, fluid densities or atomic compositions can be used to differentiate fluids. CT can see through any container except thick stainless steel or lead. For NMR, liquids can be tagged with tracer elements which can be seen by the scanner. The container encasing the core must be made of a NMR-transparent material such as glass.

138 There is always a question of how well in-situ conditions are duplicated in the laboratory even during the most careful laboratory analysis. Variances in any of the following conditions could cause discrepancies between laboratory-measured and insitu values (Wyman, 1976): (a) Fluid type (e.g., does Soltrol, a synthetic oil, represent in-situ crude?). (b) Fluid distribution (including the per cent saturation of oil initially in place). (c) Wettability (what exactly is it? how should it be measured in actual pores?). (d) Flow rate of flooding water. (e) Total quantity of flow (e.g., number of pore volumes, or time that water flows past a given point. (f) Oil/water interphase tension. (g) Pressure. (h) Temperature. (i) Fluid viscosities. (j) Length of time fluids being measured are exposed to the rock (which may affect the wettability). (k) Hysteresis effects of core restored to in-situ conditions. (1) Influence of third phase (gas). Slimhole continuous core analysis Slimhole continuous core analysis is wellsite usage of available core analysis technology on continuous small-diameter cores for cost-effective formation evaluation of exploratory wells. This approach has the potential for providing the ultimate in geological data and insight, and is also used to calibrate seismic and well log data. Spain et al. (1992) have used an on-site automated instrumentation system to extract much information from the core, developing high-speed slimhole coring into an integrated exploration tool. "Inverse logging" (logging the core instead of the borehole) is the primary goal of on-site geological evaluation. Up-hole measurements on cores included gamma scan, magnetic susceptibility, infrared mineralogy, ultraviolet fluorescence, nuclear magnetic resonance porosity, and pyrolysis (source rock) data; macroscopic and microscopic video images for analysis and archiving; and sedimentological/ lithological description. Jantzen et al. (1993) described a wellsite slimhole core logging facility which included natural gamma ray, density and caliper, porosity, permeability, total organic carbon and pyrolysis, together with high-resolution, white and UV light digital images. Drilling, mud-gas, geological, core and wireline log data provided a fully integrated formation evaluation data set. Cation exchange capacity Cation exchange capacity (CEC) is a measure of the ability of clay minerals to exchange ions between clay mineral surfaces and surrounding water. Its magnitude is a function of the rock's clay mineral type and amount (Keelan, 1982). CEC can be determined by wet chemistry techniques with an ammonium or barium exchange, through use of a correlation between CEC and adsorbed water content of test samples (Bush and Jenkins, 1977), or from membrane potential (Yuan and Diederix, 1989). Data on CEC are very important in calculation of water saturation in clay mineral-

139 bearing formations, especially if the formation water is fresh. It has also been related to stripping of ions from injection fluids, trace element accumulation, and formation overpressure. CEC effects typically are more pronounced in siliciclastics than in carbonates because carbonates tend to contain a lower percentage of clay minerals than do siliciclastics.

Petrographic core analysis Petrographic studies include such methodologies as optical mineralogy, thin-section analysis, scanning electron microscopy, image analysis, X-ray diffraction, Fourier transform infrared spectroscopy, calcimetry, dating and fracture analyses. Detailed optical mineralogy theory and techniques for mineral identification were described by Ehlers (1987). Carver (1971) provided several chapters dealing with petrographic mineral analysis, including preparation of thin sections, point counting, heavy mineral analysis, staining, and X-ray diffraction. Scholle (1978) provided a comprehensive color illustrated guide to carbonate rock constituents, texture, cements, porosities, and techniques for identification and classification.

Thin sections Thin sections are thin slides made of rock, commonly, after the pores have been impregnated with an epoxy that solidifies. They furnish samples for visual study of textural properties, for mineral identification and abundance, and the processes that have affected the rock, e.g., depositional and diagenetic activity. Petrographic microscopes utilizing optical techniques are used in this work (Core Laboratories, 1982). Carver (1971) provided details concerning procedures in sedimentary petrology. The relatively low vertical resolution (direction coincident with the objective lens axis) of petrographic microscopes makes it somewhat difficult to resolve grain boundaries, especially at higher magnifications needed to detect microporosity and small fractures. Impregnating the sample with epoxy and an admixed fluorescent dye allows the use of a confocal microscope, a specialized form of epifluorescence microscopy, which can image a very thin focal plane, or very thin layer, of the thin section (Owen et al., 1992). A series of focal plane images can be acquired and then reassembled or stacked to generate a full three-dimensional image of the thin section. Scanning electron microscopy In a scanning electron microscope (SEM), a rock sample that has been previously coated with a thin film of conductive material is bombarded with electrons in a high vacuum, resulting in a secondary electron emission picture for sample study (the SEM) and a characteristic set of X-rays (EDX spectrum). The SEM allows mineral identification and a high-magnification visual examination of microporosity, a single pore or a small group of pores and the surrounding grains or crystals of the rock. The most reliable way to identify minerals through the SEM is to compare their morphologies, i.e., shapes, to morphologies of known minerals with elemental compositions determined by the EDX system (Welton, 1984). Welton (1984) provided a SEM and EDX atlas of known minerals for comparison with unknown SEM samples.

140

Image analysis Core images come in several sizes: scanning electron microscope (very small), thin section (small), and core photographs (regular). Core images can be used for visual analysis of the rock, or can be used to acquire quantitative data for characterization of petrophysical and geological rock properties. Pore-size scale image analysis of thin sections and scanning electron micrographs provides rapid, quantitative porosity data. Image analysis also provides quantitative data concerning the size and geometric complexity of reservoir pore systems (Ehrlich and Davies, 1989). An understanding of the nature and distribution of pore types becomes increasingly important with decreasing porosity values. Reservoirs which have undergone diagenetic modification, such as carbonates, are frequently characterized by the co-existence of several disparate types of porosity. In such rocks, reservoir behavior is much less dependent on total porosity than on the pore type assemblage that makes up that porosity (Davies, 1990; Chapters 4 and 6 in Part I of this book). Examples of permeability determination from image analysis have been published for sandstones (Davies, 1990), but not for carbonates. However, a similar approach aimed at the different pore systems found in carbonates should be valid. Some recent image analysis efforts incorporate the confocal microscope (Owen et al., 1992) for quantifying petrophysical properties on layers within a thin section. Digital core photograph (or video) image analysis can be used to distinguish formation layering on a millimeter-by-millimeter basis by color differentiation (Georgi et al., 1992). Core images presented on the same scale as log data can be used to calibrate and supplement wireline logs. Bed boundary locations derived from core image analysis can be used with forward modeling to evaluate thin-bed well log response. In addition, high-resolution mini-permeametry data can be used to distinguish permeable from non-permeable layers to calibrate the image analysis and well logs. Georgi et al. (1992) reported image analysis and mini-permeameter applications for sand-shale cores. The methodologies will work for carbonates as long as there is color and permeability contrast between different geological layers.

X-ray diffraction Every crystalline material has a unique X-ray diffraction pattem, comparable to a fingerprint. Analysis of sediments of unknown composition with X-ray diffraction (XRD) can provide rapid mineralogy identification and abundance information (Core Laboratories, 1982). Smallsamples (less than 10 g) can be used.

Fourier transform infrared spectroscopy Mineral analysis by Fourier Transform Infrared (FTIR) Spectroscopy, like Core Laboratories' MINERALOG (Harville and Freeman, 1988), can provide rapid quantitative mineralogical information.* Typical samples such as drill cuttings, trimmed ends of core plugs, and sidewall core samples are suitable. FTIR may be used in combination with X-ray diffraction (XRD) to supply complementary mineralogical information on complex formations. These two techniques have * C o m p a n y names mentioned in this chapter are for reference only and are not meant as an endorsement o f any particular company or product.

141 comparable accuracies in analyzing bulk mineralogy (Ruessink and Harville, 1992). Ruessink and Harville concluded that one of these two techniques may be preferred over the other on the basis of its applicability to certain mineral classes: FTIR can analyze poorly crystalline material; XRD can deal with halides, and it offers the possibility of a detailed analysis of the clay-sized fraction of minerals. In other cases, the two techniques might be applied simultaneously to obtain complementary bulk mineral analysis information.

Calcimetry Calcimetry determines the percentage of limestone, dolomite, and insoluble residues in the rock. It is helpful in determining mineralogy, classifying rocks, and correlating various rock properties.

Dating Paleontology is the study of plant and animal fossils in order to determine the age of the rock in question. Micropaleontology is the study of fossils not identifiable without magnification using a petrographic or scanning electron microscope. Palynology is the study and classification of acid-insoluble plant fossils such as spores and pollen. The results of these studies, when related to sedimentary structures, texture, and lithologic characteristics, can also aid in the classification of depositional environments (Keelan, 1982).

Fracture analyses Detection of fractures and vugs from core can be done qualitatively by examination. A more quantitative analysis can provide detailed geological information. The study of a fractured reservoir (van Golf-Racht, 1982) must follow a special pattern, beginning with the examination of local basic characteristics of a single fracture and only afterwards continuing with the examination of a multifracture system. In establishing the relationship among the various groups of fractures, the local relationships are examined at reservoir scale by comparison, trends and extrapolation of parameters. Basic parameters obtained from an evaluation of fractures and the relationships between those parameters are shown in Fig. 3-18. Some core analysis techniques used for naturally-fractured reservoirs are listed in Table 3-II. Fracture orientation measured by a goniometer in conjunction with core orientation data obtained by coring with a special orientation tool, a goniometer (Rowley et al., 1967) defines dip and strike of observed fractures, which can be presented as shown in Fig. 3-20. Computerized goniometer and a fracture description program or fracture classification inventory list (Bergosh et al., 1985) improves the description of different fracture types and their quantification. To better present the complex nature of heterogeneous rocks, construction of a three-dimensional diagrams similar to the one shown on Fig. 3-19 (Bergosh et al. 1985) can be very helpful. These data, combined with core fracture logs (Snyder and Craft, 1977), can be used to estimate fracture depth, length, frequency, density per foot, lithology, rock hardness and fracture dip on a foot-by-foot basis. Additionally, core porosity and matrix oil saturation can be presented. This is particularly important in thick carbonates with wide variations in rock properties and sporadic zones of oil saturation that appear and disappear with depth (Keelan, 1982).

142 Single Fracture

Group of Fractures

1

/ ~

9Width

9Size

9Orientation

9Distribution -,,- Matrix Block Shapes

9Density

-Intensity-

9Nature Environment

i

I

l

(lithology) (morphology) Fig. 3-18. The basic parameters of fractures and their relationships are shown here. (After van GolfRacht, 1982.)

Table 3-II Core analysis methods for naturally-fractured reservoirs (After Bergosh et al., 1985; Bergosh and Lord, 1987) Method

Comments

CT scanner

Sees through core containers Sees interior of core Can be done under stress

Computerized goniometer

Can determine orientation of each fracture Can segregate different fracture types Must differentiate natural from induced fractures

Full-diameter core analysis

More representative than analysis on core plugs Porosity and saturation measurements Multidimensional permeability measurements Can be done under stress

Fluorescent epoxy impregnation

Slabs viewed under UV light Fracture porosity determined Can be done under stress

Many carbonate reservoir rocks are naturally fractured and require full-diameter core measurements to evaluate fracture effects. Plug analysis of dense-matrix rocks can indicate a non-productive formation, whereas the whole core analysis reflecting fracture permeabilities and porosities would indicate hydrocarbon production. In cases where actual well productivity greatly exceeds productivity calculated from permeabilities determined by core analysis, reservoir fractures not observed in the core are suspected. In some cases, fractures are observed in cores and question arises as to whether they were induced during coring of whether they occurred naturally. A study of the fracture faces, minerals contained therein, and truncation of the fractures may lead to understanding of their occurrence (Keelan, 1982).

143 S A M P L E ~# 7 6 DEPTH : 1 1 9 5 9 ' K v = 1 . 1 mD

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W.2~

Fig. 3-20. Fracture strike distribution from core fracture orientation. (After Keelan, 1982.)

144 Fracture analysis provides directional permeability information that can aid in well spacing and pattern design, evaluation of directional drilling and enhanced oil recovery projects. Knowledge of the fracture trend and current stress forces on the reservoir also aids fracture stimulation projections (Core Laboratories, 1989).

Geochemical core analysis Geochemical analysis provides data concerning the hydrocarbons in the core samples. Source rock evaluation, hydrocarbon-source rock correlation studies, regional or basin evaluation studies, and formation hydrocarbon versus contaminant identification are amongst the uses of geochemical data (Bond, 1988). A detailed introduction to geochemistry, analytical techniques, sample collection and preparation, and the evaluation and applications of geochemical data can be found in Bond (1986 and 1988).

SPECIAL CONSIDERATIONS FOR CORE ANALYSIS OF CARBONATE RESERVOIRS

Several factors typically unique to carbonates cause special considerations for core analysis of carbonate reservoir rocks. These include their heterogeneous nature, multimineral composition, low porosity and low permeability, wettability, and analyses accuracy and reproducibility.

Heterogeneities Pore space in carbonate rocks is highly variable and porosity can exist as microporosity, intergranular porosity, vuggy porosity, fracture porosity, or a combination of all four. These characteristics impose unique procedures when acquiring and analyzing carbonate reservoir cores. Core retrieval from carbonate reservoirs requires special considerations. Experience has shown that core barrels which use inner liners like fiberglass or aluminum containers are most effective in maximizing core recovery and minimizing damage to the recovered fractured core by providing a smooth, constant-diameter cylinder for the core to slide into, reducing the chance of jamming. During oriented coring (for fracture analysis), the communication and cooperation among the geologist or engineer requesting the core, the drilling, coring and surveying companies, personnel laying down and boxing the core, and the core services laboratory are the key to obtaining representative, analyzable core. The heterogeneous nature of carbonates often requires whole core rather than plug analysis. Whole core analysis is typically more costly and requires more time. The CT scan can help in early quantification ofheterogeneities, even while the core might still be in a container. In vuggy and fractured formations, it is still very helpful to drill and test plugs from the matrix part to define its properties, such as capillarity. These properties are important because they control initial water content and, hence, matrix hydrocarbon saturation. Carbonates containing multiple pore systems present challenges to obtaining representative capillary pressure data. Physically-larger pore systems, e.g., fractures and vugs, do not appear on capillary pressure measurement results or appear as apparent

145 closure effects at low capillary pressures. Physically-smaller pore systems, e.g., microporosity, require very high capillary pressure measurements to characterize.

Multimineral composition Carbonate reservoirs can contain complex mineral composition. It is not unusual to have evaporites, e.g., halite (salt), anhydrite, or gypsum (if shallow), layered with or in the pores of the carbonate rocks. Limestone and dolomite mixtures are possible. Dolomites can contain uranium salts, left in the rock during dolomitization, which make the traditionally low gamma ray rock radioactive. Inasmuch as carbonate rock composition can be multimineral, any petrophysical model (see Chapter 4) used to evaluate the rock in a drilling well, for example, needs to have as many measurements available (well logs, fluid analyses, rock analyses) as there are mineral types. Core can add a substantial amount of information to bring an evaluation to fruition. Gypsum presents a difficulty in obtaining accurate core analysis. Gypsum de-waters at temperatures just above 100~ (38~ The presence and de-watering of gypsum can be recognized by examination of core analysis saturation results. The sum of water saturation and oil saturation will total more than 100%, a physical impossibility. Core analysis of gypsum-bearing rock needs to be done below de-watering temperature. Halite (salt) can add complexity to core analysis. Pore-filling salt can dissolve during coring if the drilling mud is not kept at saturated salinity (at the downhole temperature). In this case, porosity that is not present in situ could be created by the salt dissolving out of the pores. Pore-filling or nodule salt can be a problem during Dean-Stark saturation analysis. The salt originally in solution in the mud filtrate, but left in the pores during extraction, needs to be removed for accurate oil saturation determination. Any method used to remove the mud filtrate salt can not differentiate it from salt which is part of the rock and will tend to remove all salt indiscriminately. If one knows the salinity and extracted volume of the mud filtrate, one can sort out which salt is which.

Low porosity and low permeability Rock that has low porosity and low permeability can take longer to clean and analyze if accuracy is a concern. If a drilling well disposition decision is to be based on core analyses results, one might consider doing a quick analysis to obtain results with enough accuracy needed to make the decision. Then additional slower analysis must be made to obtain results with the accuracy needed for reservoir characterization. The Klinkenberg correction to reduce gas permeability to an equivalent liquid value varies with permeability. Low-permeability formations require large corrections (Core Laboratories, 1989). Typical values are shown in Table 3-III.

Wettability Wunderlich (1991) discussed the three situations (coring, storing, and preparation) in which core wettability can be altered and, therefore, core analyses results may not be representative of in-situ conditions. Wettability changes can be due to interactions

146 Table 3-III Typical Klinkenberg permeability corrections (after Core Laboratories, 1989) Air Permeability k (mD)

Klinkenberg Permeability k, (mD)

Ratio of kl/k a

.18 1.00 10.0 100.0 1000.0

.12 .68 7.80 88.0 950.0

.66 .68 .78 .88 .95

with drilling fluids, pressure and temperature changes causing pore fluid phase changes, and exposure to air and other fluids during the core retrieval, storing, and analysis preparation processes. Wunderlich's recommendations provide detailed procedures for obtaining reservoir rock in a wettability state representative of in-situ wettability.

Accuracy and reproducibility The accuracy required of core analysis depends on how the data will be used. This is a general consideration and obviously not limited to carbonates. Thomas and Pugh (1989) discussed Amoco's* preparation of core sample sets that have been tested repetitively in-house and by commercial laboratories around the world. They discussed the data accumulated and showed the expected accuracy for measurements in a single laboratory by multiple operators over a long period of time. Results were compared to data on the same samples measured by other laboratories. Acceptable ranges of variation within a laboratory and between laboratories were defined and compared to those limits developed by experience.

ROCK CATALOGS

Introduction The use of a rock catalog to estimate missing formation property information can be beneficial. The suggestions for users from one rock catalog (Thomas and Sneider, 1971, plus updates) describe the information that can be obtained from a rock catalog as follows: (1) When one has some general concept of the reservoir type for which values of rock parameters are needed, one can search in the catalog for rocks matching this concept. By comparing properties of interest one may develop a feel for the spread in values and include this knowledge in whatever analysis is required for reservoir characterization. (2) When one has some specific petrophysical and/or geological information, the * Company names mentioned in this chapter are for reference only and are not meant as an endorsement of any particular company or product.

147 process described in (1) is facilitated and the range of reservoir properties can be narrowed. (3) When one has substantial but incomplete information on the reservoir, one can estimate (by comparison of the data in hand with those of the catalog) the likely values of the missing data. (4) Finally, when looking at data available from one or more comprehensive rock catalogs, interrelations among rock properties can be derived. Items (1) through (3) can help solve specific formation evaluation or reservoir characterization problems. Item (4) has more general applications, e.g., pore combination modeling for the determination ofArchie' s m value from examination of a rock's pore types (see Chapter 4) was derived from rock property interrelations found in the Shell Development Company* Catalog of Petrophysical and Geological Properties of Typical Reservoir Rocks (Thomas and Sneider, 1971, plus updates), according to M.T. Myers (personal communication, 1982). Rock catalog data can be found in notebook form or on computer storage media such as floppy disks or CD-ROM. Figure 3-21 is an example of a core photograph taken directly from a CD-ROM rock catalog and shows the typical number of core plugs taken to provide the wide spectrum of data found in a rock catalog.

General rock properties catalogs General rock properties catalogs provide access to information from a wide variety of rock types. One can use general catalogs on rocks anywhere in the world. Reservoirs, Inc. and Robert M. Sneider Exploration, Inc.* have put together a World Wide Rock Catalog on a CD-ROM disk (Reservoirs, Inc. and Robert M. Sneider Exploration, Inc., 1987, plus updates). The disk can be accessed from a PC or a MAC. Comprehensive geological and engineering data are available for both sandstone and carbonate rocks. Core images include scanning electron microscope images, thin sections, and core photos. Analog rock data can be found by using information known about the rock of interest. PoroTechnologies* provide the Shell Development Company Catalog of Petrophysical and Geological Properties of Typical Reservoir Rocks (Thomas and Sneider, 1971, plus updates). All photographic, numeric, and text data have been digitized and placed on CD-ROM disks for rapid access using PC, MAC or UNIX systems. PetroTech added to the catalog data base new rock sample and thin section photomicrographs, petrophysical data tables, and "simulated cuttings" sample comparators.

Specific formation rock properties catalogs Specific formation rock properties catalogs provide access to information from the complete range of rock types of a single formation, usually from a single field. One can use specific catalogs for the field and formation from which it was created. * Company names mentionedin this chapter are for reference only and are not meant as an endorsement of any particular company or product.

148

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Fig. 3-21. Rock catalog sampling technique which provides sufficient plug samples for the wide range of core analysis measurements found in a rock catalog. The range in porosity, permeability, and grain density values gives an idea of the heterogeneity of the rock. This core photo and data for the Shell Granger #3 are from the World Wide Rock Catalog, CD-ROM version. (From Reservoirs, Inc. and Robert M. Sneider Exploration, Inc., 1987, plus updates.)

Reservoirs Inc. has compiled formation- and region-specific rock catalogs to address petrophysical and geological properties contributing to reservoir performance. These catalogs use rock classification systems developed specifically for rock types encountered in subject formations. Petrophysical testing for each rock type concentrates on particular local formation evaluation problems. Catalogs include: Wilcox Drilling and Completion Procedures, Vicksburg Formation, Prairie du Chien Formation, Texas and Louisiana Offshore Miocene, and a Yemen Rock Catalog (W.K. Hudson, personal communication, 1993). SUMMARY

Coring and analyses for accurate reservoir characterization requires cost-effective, acceptable-quality (meeting the accuracy needs of the particular characterization) core data over full range of rock properties of that reservoir. Of course the core data are not the only data available (or needed) and should be integrated with other formation evaluation and reservoir characterization data, either taken directly from that reservoir

149 or analogous reservoirs. To recognize problems that can be solved by core analyses (in a cost-effective manner), one might consider answering the following questions: (1) What kind of formation evaluation or reservoir characterization problems need solving? (2) Which ones of these problems can be solved by core analyses? (3) Are there other formation evaluation or reservoir characterization tools that can be used to solve these problems? (4) What is the accuracy needed in the problem solution? (5) Which evaluation tools provide the solution to these problems with the required accuracy, at the lowest cost? (6) If core analyses provides the solution, what kind and how much should be done? Which lab(s) should do it? (7) How should the problems be solved if sufficient core can not be obtained? (8) Is there other information or other problem solutions that need to be obtained from any of these tools? (9) Does this alter the decision on the cost-effective approach to obtain the formation evaluation or reservoir characterization solutions?

ACKNOWLEDGMENTS

Mr. Murphy wishes to thank Shell Oil Company for permission to contribute this chapter. Thanks also go to the Shell Development Company Information Services Library at the Bellaire Research Center, in particular to Kathy Harris, for providing references in a very timely manner.

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150 Carmichael, R.S. (Editor), 1989. CRC Practical Handbook of Physical Properties of Rocks and Minerals. CRC Press, Inc., Boca Raton, FL, 741 pp. Carver, R.E. (Editor), 1971. Procedures in Sedimentary Petrology. Wiley-Interscience, New York, 633 pp. Chandler, M.A., Goggin, D.J. and Lake, L.W., 1989. A mechanical field permeameter for making rapid, non-destructive, permeability measurements. J. Sed. Pet., 59(4): 613 -615. Chen, Z., McLemore, J. and Heller, J.P., 1993. The miniporopermeameter for simultaneous measurement of permeability and porosity. SPE paper 26508, SPE 68th Ann. Tech. Conf. and Exh., Formation Evaluation and Reservoir Geology Proc., Houston, TX, Oct. 3--6: 897-905. Coles, M.E., Muegge, E.L. and Marek, B.F., 1992. Use of attenuation standards for CAT scanning applications within oil and gas production research. SCA paper 9223, The Soc. of Core Analysts Preprints, Oklahoma City, OK, 28 pp. Core Laboratories, 1982. A Course in Special Core Analysis. Dallas, TX. Core Laboratories, 1989. A Course in the Fundamentals of Core Analysis. Houston, TX, Ver. 3.1. Davies, D.K., 1990. Image analysis of reservoir pore systems: state of the art in solving problems related to reservoir quality. SPE paper 19407, SPE Formation Damage Control Symp. Proc., Lafayette, LA, Feb. 22-23: 73-82. Davison, I. and Haszeldine, R.S., 1984. Orienting conventional cores for geological purposes: a review of methods. J. Petrol. Geol., Bucks, England, 7(4): 461-466. de Waal, J.A., Smits, R.M.M., de Graaf, J.D. and Schipper, B.A., 1989. Measurement and evaluation of resistivity index curves. Paper II, SPWLA 30th Ann. Logging Symp., Denver, CO, July 11-14:10 pp. plus figs. Donaldson, E.C., Thomas, R.D. and Lorenz, P.B., 1969. Wettability determination and its effect on recovery efficiency. Soc. Pet. Eng. J., 9(1): 13-20. Edelstein, W.A., Vinegar, H.J., Tutunjian, P.N., Roemer, P.B. and Mueller, O.M., 1988. NMR imaging for core analysis. SPE paper 18272, SPE 63th Ann. Tech. Conf. and Exh., Formation Evaluation and Reservoir Geology Proc., Houston, TX, Oct. 2-5:101 - 112. Edmunson, H. and Raymer, L.L., 1979. Radioactive logging parameters for common minerals. The Log Analyst, 20(5): 38-47. Erratum The Log Analyst, 21(2). Ehlers, E.G., 1987. Optical Mineralogy, 1Iol. 1-Theory and Technique, Vol. 2-Mineral Descriptions. Blackwell Scientific Publications, Palo Alto, CA. Vol. 1,158 pp.; Vol. 2, 286 pp. Ehrlich, R. and Davies, D.K., 1989. Image analysis of pore geometry: relationship to reservoir engineering and modeling. SPE paper 19054, SPE Gas Tech. Symp. Proc., Dallas, TX, June 7-9:15-30. Ellis, D., Howard, J., Flaum, C., McKeon, D., Scott, H., Serra, O. and Simmons, G., 1988. Mineral logging parameters: nuclear and acoustic. The Technical Review, 36(1): 38-52. Georgi, D.T. and Jones, S.C., 1992. Application of pressure-decay profile permeametry to reservoir description. Presented at the 16th Ann. SPE (Nigerian Council) Internat. Conf. and Exh., Lagos, Nigeria, Aug. 26-27:12 pp. Georgi, D.T., Phillips, C. and Hardman, R., 1992. Applications of digital core image analysis to thin-bed evaluation. Presented at the 16th Ann. SPE (Nigerian Council) Internat. Conf. and Exh., Lagos, Nigeria, Aug. 26-27:12 pp. Golf-Racht, T.D. van, 1982. Fundamentals of Fractured Reservoir Engineering. Elsevier Sci. Publ. Co., New York, 710 pp. Harville, D.G. and Freeman, D.L., 1988. The benefits and application of rapid mineral analysis provided by Fourier transform infrared spectroscopy. SPE Paper 18120, SPE 63th Ann. Tech. Conf. and Exh., Formation Evaluation and Reservoir Geology Proc., Houston, TX, Oct. 2-5:141 - 150. Hawkins, 1988. Comparison of three methods of relative permeability measurement. SCA paper 8804, The Soc. of Core Analysts Preprints, 16 pp. Hicks Jr., P.J., Deans, H.A. and Narayanan, K.R., 1992. Distribution of residual oil in heterogeneous carbonate cores using X-ray CT. Soc. Pet.. Eng. Form. Eval., Sept. 7(3): 235-340. Hirasaki, G.J., 1991. Wettability: Fundamentals and surface forces. SPE Formation Evaluation, 6(3): 217-226. Hirasaki, G.J., Rohan, J.A., Dubey, S.T. and Niko, H., 1990. Wettability evaluation during restored-state core analysis. SPE paper 20506, SPE 65th Ann. Tech. Conf. and Exh., Formation Evaluation and Reservoir Geology Proc., New Orleans, LA, Sept. 23-26:361-375. Hove, A., Ringen, J.K. and Read, P.A., 1987. Visualization of laboratory corefloods with the aid of computerized tomography of X-rays. Trans. AIME, 283:148-154.

151 Howard, J.J., Kenyon, W.E. and Straley, C., 1990. Proton magnetic resonance and pore-size variations in reservoir sandstones. SPE paper 20600, SPE 65th Ann. Tech. Conf. and Exh., Formation Evaluation and Reservoir Geology Proc., New Orleans, LA, Sept. 23-26: pp. 733-742. Hunt, P.K., Engler, P. and Bajsarowicz, C., 1988. Computerized tomography as a core analysis tool: applications, instrument evaluation, and image improvement techniques. J. Petrol. Tech., 40(9): 1203-1210. Hyland, G.R., 1983. Pressure coring-an oilfield tool. SPE paper 12093, SPE 58th Ann. Tech. Conf. and Exh., San Francisco, CA, Oct. 5--8:8 pp. IHRDC, 1985. Sample and Core Handling and Analysis. GL303, International Human Resources Development Corporation, Boston, MA, 114 pp. plus video. Jantzen, R.E., Syrstad, S.O., Taylor, M.R., Spicer, P.J., Stockden, I., Dodson, T. and Saunders, M.R., 1993. Answering geological questions from slimhole coring exploration. Paper T, SPg"LA 34th Ann. Logging Symp. Trans., Calgary, AL, June 13-16, 18 pp. Jodry, R.L., 1992. Pore geometry of carbonate rocks. Carbonate Reservoir Characterization: A Geologic-Engineering Analysis, Elsevier Publ. Co., Amsterdam, Part I, Chapter 6 of this book, pp. 331377. Updated from: 1972, Oil and Gas Production from Carbonate Rocks, American Elsevier Publ. Co., Inc., New York, NY, pp. 35-82. Keelan, D.K., 1972. A critical review of core analysis techniques. J. Cdn. Petrol. Tech., 11 (2; Apr.June): 42-55. Keelan, D.K., 1982. Core analysis for aid in reservoir description. J. Petrol. Tech., 34(11): 2483-2490. Kenyon, W.E., Day, P.I., Straley, C. and Willemsen, J.F., 1988. A three-part study of NMR longitudinal relaxation studies of water-saturated sandstones. SPE Formation Evaluation, 3(3): 622-636. Leverett, M.C., 1941. Capillary behavior in porous solids. Trans. AIME, 142:152-168. Mahmood, S.M., Maerefat, N.L. and Chang, M-M., 1988. Laboratory measurements of electrical resistivity at reservoir conditions. SPE paper 18179, SPE 64th Ann. Tech. Conf. and Exh., Formation Evaluation and Reservoir Geology Proc., Houston, TX, Oct. 2-5: 705- 719. Monicard, R.P., 1980. Properties of Reservoir Rocks: Core Analysis. GulfPubl. Co., Houston, TX: 168 pp. Morrow, N.R., 1990. Wettability and its effect on oil recovery. J. Petrol. Tech., 42(12): 1476-1483. Muscat, M., 1949. Physical Principles of Oil Production. McGraw-Hill, New York: 922 pp. (p. 142). Owen, L.B., Greaves, K.H., Lord, G., Bereskin, S.R. and King, E., 1992. Improved pore visualization by confocal microscopy. SCA paper 9226, The Soc. of Core Analysts Preprints, Oklahoma City, OK: 16 PP. Purcell, W.R., 1949. Capillary pressures-their measurement using mercury and the calculation of permeability therefrom. Trans. AIME, 186: 39-48. Reservoirs, Inc. and Robert M. Sneider Exploration, Inc., 1987, plus updates. A Catalog of Geological and Engineering Properties for Sandstones and Carbonates. Reservoirs, Inc., Houston, TX, July. Eight volume notebook version and CD-ROM version. Rose, W.D. and Bruce, W.A., 1949. Evaluation of capillary character in petroleum reservoir rocks. Trans. AIME, 186: 127-142. Rowly, D.S., Burk, C.A. and Manual, T., 1967. Oriented Cores. Christensen Diamond Products Co., Salt Lake City, UT. Ruessink, B.H. and Harville, D.G., 1992. Quantitative analysis of bulk mineralogy: the applicability and performance of XRD and FTIR. SPE paper 23828, SPE Internat. Symp. on Formation Damage Control Proc., Lafayette, LA, Feb. 26-27: 533-546. Scholle, P.A., 1978. A Color Illustrated Guide to Carbonate Rock Constituents, Textures, Cements, and Porosities. Memoir 27, AAPG, Tulsa, OK, 241 pp. Seevers, D.O., 1966. A nuclear magnetic method for determining the permeability of sandstones. Paper L, SPWLA 7th Ann. Logging Symp. Trans., Tulsa, OK, May 8-11:14 pp. Skopec, R.A., 1991. In-situ stress evaluation in core analysis. SCA paper 9103, The Soc. of Core Analysts Preprints, San Antonio, TX, Aug. 21-22:14 pp. Skopec, R.A., Mann, M.M., Jeffers, D. and Grier, S.P., 1992. Horizontal core acquisition and orientation for formation evaluation. SPE Drilling Engineering, 7(1): 47-54. Smith, D.G., 1990. Predicting a down dip water level using capillary pressure relationships. Paper Z, SPWLA 31st Ann. Logging Symp. Trans., Lafayette, LA, June 24-27:11 pp. Snyder, R.H. and Craft, M., 1977. Evaluation of Austin and Buda formations from core and fracture analysis. Trans. Gulf Coast Assn. Geol. Socs., 27: 376-385.

152 Soc. of Professional Well Log Analysts, 1990. Borehole Imaging Reprint Volume. Houston, TX: 472 pp. Spain, D.R., Morris, S.A. and Penn, J.T., 1992. Automated geological evaluation of continuous slimhole cores. J. Petrol. Tech., 44(6): 662-668. Swanson, B.E, 1981. A simple correlation between permeabilities and mercury capillary pressures, jr. Petrol. Tech., 33(12): 2498-2504. Swanson, R.G., 1985. Sample Examination Manual. Am. Assoc. Petrol. Geologists, Third Printing, May. Thomas, D.C. and Pugh, V.J., 1989.A statistical analysis of the accuracy and reproducibility of standard core analysis. The Log Analyst., 30(2): 71-77. Thomas, E.C. and Sneider, R.M., 1971, plus updates. A Catalog of Petrophysical and Geological Properties of Typical Reservoir Rocks. Shell Development Co., TPR-EPR-31-7 l-P, July, 3 vol. Thomeer, J.H.M., 1960. Introduction of a pore geometrical factor defined by the capillary pressure curve. Trans. AIME, 219: 354-358. Thomeer, J.H., 1983. Air permeability as a function of three pore-network parameters. J. Petrol. Tech., 35(4): 809-814. Tutunjian, P.N. and Vinegar, H.J., 1990. Petrophysical applications of automated proton high resolution NMR spectroscopy. SCA paper 9020, The Soc. of Core Analysts Preprints, Dallas, TX, Aug. 14-16: 23 pp. Tutunjian, P.N., Vinegar, H.J. and Ferris, J.A., 1991. Nuclear magnetic resonance imaging of sodium23 in cores. SCA paper 9111, The Soc. of Core Analysts Preprints, San Antonio, TX, Aug. 21-22:18 PP. Tutunjian, P.N., Vinegar, H.J. and Ferris, J.A., 1993. Characterization of pore microgeometry by NMR diffusion measurements. Paper II, SPWLA 34th Ann. Logging Symp. Trans., Calgary, AL, June 13-16:13 PP. Vinegar, H.J., 1986. X-ray CT and NMR image of rocks. J. Petrol. Tech., 38(3): 257-259. Vinegar, H.J. and Wellington, S.L., 1987. Tomographic imaging of three-phase flow experiments. Rev. Sci. Instruments, 58(1): 96-107. Vinegar, H.J., Tutunjian, P.N., Edelstein, W.A. and Roemer, P.B., 1991a. Whole-core analysis by ~3C NMR. SPE Formation Evaluation, 6(2): 183-189. Vinegar, H.J., Tutunjian, P.N., Crabtree, P.T., Raffaldi, F.J., DiFoggio, R. and Edelstein, W.A., 1991b. NMR spectroscopy of tight, gypsum-bearing carbonates. The Log Analyst, 32(5): 527-535. Wang, S.Y., Ayral, S., Castellana, F.S. and Gryte, C.C., 1984a. Reconstruction of oil saturation distribution histories during immiscible liquid-liquid displacement by computer assisted tomography. Am. Inst. Chem. Eng. jr., 30(4): 642-646. Wang, S.Y., Ayral, S. and Gryte, C.C., 1984b. Computer assisted tomography for the characterization of oil displacement in porous media. Soc. Pet. Eng. J., 24(1): 53-55. Wellington, S.L. and Vinegar, H.J., 1987 X-ray computerized tomography. J. Petrol. Tech., 39(8): 885989. Wells, L.E., Sanyal, S.K. and Mathews, M.A., 1979. Matrix and response characteristics for sonic, density and neutron. Paper Z, SPWLA 20th Ann. Logging Symp. Trans., Tulsa, OK, June 3-6:25 pp. Welton, J.E., 1984. SEM Petrology Atlas. AAPG, Tulsa, OK, 237 pp. Whittaker, A. (Editor), 1985. Coring Operations-Procedures for Sampling and Analysis of Bottomhole and Sidewall Cores. EXLOG, Boston, MA, 174 pp. Withjack, E.M., 1988. Computed tomography for rock-property determination and fluid-flow visualization. SPE Form. Eval., 3(4): 696-704. World Oil Coring Series, 1985-1986. Composed of the following articles: Part 1 - W h y it's done. Dare Keelan, March 1985: 83-90. Part 2 - C o r e barrel types and uses. Art Park, April 1985: 83-90. Part 3 -Planning the job. Art Park, May 1985: 79-86. Part 4 - B i t considerations. Art Park, June 1985: 149-154. Part 5 -Avoiding potential problems. Art Park, July 1985: 92-98. Part 6-Sidewall operations. James B. Toney and J. Lee Speights, Aug. 1985: 29-36. Part 7-Analytical aspects of sidewall coring. M. Craft and D. Keelan, Sept. 1985: 77-90. Part 8 - P l u g and full diameter analysis. Dare Keelan, November 1985: 103-112. Part 9-Geological aspects. David G. Kersey, January 1986: 103-108. Wunderlich, R.W., 1991. Obtaining samples with preserved wettability. In: N. R. Morrow (Editor), Interfacial Phenomena in Oil Recovery. Marcel Dekker, Inc. NY, NY, Chapter 8, pp. 289-318.

153 Wyman, R.E., 1976. How should we measure residual oil saturation. Joint Convention on Enhanced Recovery, Petroleum Society of CIM-Canadian Society of Petroleum Geologists, Calgary, AL, June 711:37 pp. Yuan, H.H., 1991a. Pore scale heterogeneity from mercury porosimetry data. SPE Form. Eval., 6(3): 233 -242. Yuan, H.H., 1991 b. Advances inAPEX technology: determination of cementation exponent and absolute permeability. The Log Analyst, 43(5): 557-570. Yuan, H.H. and Diederix, K.M., 1989. The role of membrane potential measurements in shaly sand evaluation. The Log Analyst, 30(6): 415-423.

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155

Chapter 4 FORMATION EVALUATION DAVID PATRICK MURPHY

INTRODUCTION

This chapter was written to provide a fairly detailed overview of carbonate formation evaluation. Emphasis was put on several carbonate evaluation subjects and concepts to increase reader awareness concerning the following: Philosophy of formation evaluation. Understanding petrophysics. Formation evaluation properties of interest. Formation evaluation tools. Different approaches for different evaluation situations. The definition and uses of petrophysical models. Determination of formation evaluation properties of interest. Magnitude of error in and reliability of determined results. References that provide even more detail on carbonate formation evaluation. The focus of this chapter is on formation evaluation of carbonate reservoirs. However, many of the tools and techniques discussed in this chapter can be applied to the evaluation of other rock types if a proper petrophysical model is used.

FORMATION EVALUATION PHILOSOPHY

First and foremost: understand petrophysics To accurately perform an evaluation of a formation of interest, the evaluator must understand the physics and chemistry of the rock in that formation. Petrophysics is a term used to express the physical and chemical properties of rocks which are related to the pore and fluid distributions, particularly as they pertain to the detection and evaluation of hydrocarbon-beating layers in contrast to non-hydrocarbon-bearing layers. This definition closely follows the one coined by G.E. Archie and J.H.M.A. Thomeer, and published by Archie in 1950 (J.H.M. Thomeer, personal communication, 1990; Archie, 1950). They intended that petrophysics refer to the physics of particular rock types, whereas geophysics is associated with the physics of the larger rock systems composing the earth. Contained within this definition of petrophysics are four words which should be defined very carefully in order that there will be no misunderstanding of the manner in which they are used in this chapter. These words are rock, hydrocarbons, detection, and evaluation. Rock is defined as mineral matter and its associated fluids (if fluids are present) occurring naturally in large quantities; also, a particular mass of it. This definition of rock is somewhat different from the one given in dictionaries, primarily because of

156 the inclusion of the contained fluids as part of the rock itself. Fluids contained within the rock are of particular importance, inasmuch as it is these fluids which are produced. Hydrocarbons are any of a number of compounds of hydrogen and carbon in the liquid or gaseous states. Within the producing arm of the petroleum industry these hydrocarbons usually are referred to as oil and gas, both of which are produced in great quantities. In addition, one might be interested in evaluating CO 2 reservoirs as a source of flood injectant fluid in tertiary recovery processes. In this chapter, a fluid will be designated as a gas if it is in the gaseous state. A fluid will be designated as a liquid if it is in the liquid state. A fluid will be designated as a fluid if its state is unknown or irrelevant to the situation. Detection is defined as the recognition of the presence of hydrocarbons in rock. The presence of hydrocarbons in rock does not necessarily mean they are present in either commercial, or even producible, quantities. Too often hydrocarbons are detected but are found to be nonproducible. Such might be the case when the structural configuration of the subsurface has been altered through tectonic movement of rock. Subsequent water flow through a subsurface stratum can then effectively water flood an existing accumulation. Not all of the hydrocarbons will be removed during this water flooding process. Hydrocarbons which are detected are those which have been left behind. Evaluation is defined as the determination of the volume of hydrocarbons in place in the area, e.g., one acre, surrounding the wellbore; and estimation, if possible, of the initial rate at which they can be produced. This word, evaluation, is quite definitive. In a nutshell it defines the job of the formation evaluation specialist. Evaluation entails the use of all data available including mud log and measurement while drilling information; production, drill stem, and wireline tests; cores and core analyses; and wireline log data. All of these data must fit into a consistent petrophysical and geological model that describes the physical situation. If the formation evaluation specialist understands petrophysics, he or she can understand the response of various evaluation tools, and can then best predict pertinent rock and fluid properties and the performance of the formation.

FORMATION PROPERTIES OF INTEREST

Primary formation properties of interest The job of the formation evaluation specialist is to evaluate hydrocarbon reservoirs to provide information needed for the economic optimization of that reservoir. The economics of a hydrocarbon reservoir are directly related to the volume of hydrocarbons in place, the production rate, and the optimization of spending to produce the hydrocarbon reservoir. For a person concerned about obtaining this kind of information from formation evaluation, six formation properties typically fall out as being of primary interest: (1) net formation thickness; (2) porosity; (3) pore fluid saturations; (4) permeability;

157 (5) lithology, structure, and stratigraphy; and (6) pore fluid properties. The volume of hydrocarbons in place is proportional to the product of net formation thickness, porosity, and hydrocarbon saturation. This volume is the ultimate target for the economic development of a field. Volume I, Chapter 11 of this book gives details on oil and gas reserve estimation methods. The recoverable reserves depend upon the production mechanism. Accuracies required in formation evaluation results depend on the cost of implementing that producing mechanism. Accuracies need to be tighter for pre-waterflood evaluation than for primary production evaluation because of the cost of implementing the waterflood. Formation evaluation results need to be even more accurate for pre-CO 2 flood evaluation than for waterflood evaluation because of the much higher cost of implementing a CO 2 flood. The production rate of a well is related to the combination of the net formation thickness, the permeability, and pore fluid properties, e.g., fluid viscosities. Production rate has significant impact on a well's economic performance because of the present value of future revenues and production-related expenditures. Determining the correct interpretation of the geological situation, i.e., the correct geologic model, for a hydrocarbon reservoir, allows optimal selection of well locations, prediction of well performance, and optimal management of the producing asset. Determination of the correct geologic model requires, as a minimum, knowledge of lithology, structure, stratigraphy, and net formation thickness throughout the reservoir.

Other formation properties of interest Other formation properties can provide additional insight into the hydrocarbon volume, production rate, and optimization of spending to produce the reservoir. A partial list of other formation properties of interest includes: (1) formation pressure; (2) wettability; (3) seal capacity; (4) source rock richness; (5) fractional fluid flow properties; (6) depositional environment; (7) diagenesis; (8) rock mechanical properties; and (9) acoustic velocity and anisotropy. The formation evaluation results provide the information that is needed for the economic optimization of the reservoir. The particular formation properties of interest that need to be determined depend on the specific evaluation situation.

FORMATION EVALUATION TOOLS

The principal categories of tools that are to used in the evaluation of formations are listed below. These tools are readily available and are routinely used in the acquisition of formation evaluation data. The reference(s) listed with each tool category can

158 provide the reader with an introductory overview of those tools and their application to formation evaluation: (1) wireline logging (Dewan, 1983"); (2) mud logging (Jorden and Campbell, 1984, Chapter 4); (3) measurement while drilling logging (Allen et al., 1989); (4) coring and core analyses (Worm Oil Coring Series, 1985-1986t); (5) drill stem testing (Donohue, 1984); (6) wireline testing (Atlas Wireline Services, 1989a; Schlumberger, 1981); and (7) production testing (Donohue and Ertekin, 1982; Donohue, 1986; LeBlanc, 1988). Wireline logging and measurement while drilling logging will be collectively termed well logging in this chapter. Other categories of tools that are available for use in the evaluation of formations are listed below. In carbonates, these tools seem to be used substantially less than the aforementioned principal categories of tools because they provide very specialized results that are not needed in most evaluations. The reference(s) listed with each tool category can provide the reader with an introductory overview of those tools and their application to formation evaluation: (1) single- and multi-well tracer tests (Deans, 1978); (2) geotomography (Worthington, 1984, for acoustic tomography; Dines and Lytle, 1979, for electromagnetic tomography; Kretzschmar and Witterholt, 1984, for historical background and EOR surveillance in pilots); and (3) seismic (Ausburn et al., 1977, for general seismic applications to formation evaluation; Ausburn, 1979, for well log editing to improve seismic calibration; Brown, 1986, for 3-D seismic applications). In general, the use of seismic in carbonates is limited to structural and stratigraphic determination. Fluid content detection from seismic, that works well in unconsolidated, high-porosity siliciclastic sediments (Domenico, 1977), does not generally work in consolidated, low-porosity rocks (Domenico, 1974), which would be common for carbonate reservoirs. In the design of formation evaluation programs, the choice of evaluation tools to use depends upon the formation evaluation questions that need to be answered. It is not economically prudent to run particular tools to gather information just to satisfy one's general sense of curiosity. The correct evaluation tool or tools that should be used are the ones that answer the questions that need to be answered, with acceptable accuracy, at the lowest cost. * Dewan provides a good introduction to wireline logging for readers who have little or no background in formation evaluation. Two additional references can provide much more technical detail on well logs. Tittman (1986) addresses the physics of logging measurements. The techniques universally used in formation evaluation (electrical, nuclear, and sonic) are described in some detail, whereas only short descriptions are given of less widely exploited methods such as electromagnetic propagation and nuclear magnetic resonance. Ellis (1987) emphasizes the importance of physics in well logging and includes discussions and problems which explain the mechanics of obtaining the usual petrophysical parameters from well log data. t The WorldOil (1985-1986) articles provide a good introduction to coring and core analysis for readers who have little or no background in formation evaluation. Spain et al. (1992) describe the automated geological evaluation of continuous slim-hole cores. "Inverse logging" (logging the core instead of the borehole) is the primarygoal of on-site geologicalevaluation.This approachhas the potential for providing the ultimate in geological data and insight, and is also used to calibrate seismic and well log data.

159 FORMATION EVALUATION SITUATIONS

Different formation evaluation situations require different questions that need to be answered in order to characterize a reservoir. Therefore, they require somewhat different approaches and use different combinations of the principal categories of evaluation tools to obtain formation evaluation answers. Three common formation evaluation situations are drilling wells, flood process pilots, and production surveillance.

Formation evaluation of drilling wells Formation evaluation of drilling wells provides for evaluating formations exposed by the drill bit during drilling or deepening of a well. The evaluation must provide answers to the questions concerning how to economically explore, drill, and produce the formation/well/field. A partial list of questions that might need to be answered by evaluation of a drilling well are listed in Table 4-1. Evaluation activity can be focused not only on the planned primary objectives, but also on uphole objectives that may or may not have been anticipated beforehand. Data are usually acquired in the open hole, although cased hole data can be preferable due to lower cost or can be required because of poor openhole conditions. The specific types of tools used to acquire formation evaluation data depend on the type of well, its objectives, and the questions that need to be answered. A well drilled to test a seismic play needs a plan to acquire data to calibrate the seismic. A well drilled to prove a geological model needs to acquire geological data. An infill well drilled close to the offset wells may only need to determine the location of the productive zone: all other formation properties can usually be correlated from surrounding wells. Some of the openhole data (e.g., data from mud logs, measurement-while-drilling logs, core examination) become available in near-realtime, usually within minutes or hours after the formation is penetrated. Other openhole data (e.g., wireline logs, formation tests, core analyses) become available a day or more after the formation has been penetrated by the bit. Cased hole data become available at a much later time, after casing has been set. Time involved in formation data acquisition and evaluation of drilling wells is usually costly due to the daily drilling rig cost for the data acquisition and evaluation. If casing has to be set to evaluate the well, additional expense is involved.

Formation evaluation for flood process pilots Formation evaluation for flood process pilots provides for evaluating the production of additional hydrocarbons from a formation using that process. Acquiring data to characterize the response of the formation to enhanced recovery processes is the main objective of a pilot. This usually involves the measurement of remaining oil saturation and its distribution before and after the flood process, and monitoring of the flood progress and results on a zone-by-zone basis. Methodologies for this type of evaluation are detailed by Thomas et al. (1987). A partial list of questions that might

160 TABLE 4-1 Partial list of questions that might need to be answered by the evaluation of a drilling well Specialist*

Questions

All

Which exploration, drilling, and completion approach will result in the optimum economic results?

Geologists

Does the actual geological situation fit my geological model? Is there source rock in the geological column? What is the richness of the source rock? What is the seal capacity of the seal?

Geophysicists

What are the acoustic velocities or impedances? What is the acoustic anisotropy? What are the acoustic impedance trends in this area?

Petrophysicists

What is the appropriate petrophysical model? What are the log-core relationships? Can overpressures be predicted? What is pay?

Drilling Engrs.

What What What What

pressures will be encountered? are the fracture gradients? is the rock integrity during drilling? are compatible drilling muds?

Reservoir Engrs.

What What What What

are the fluid properties? are the fractional flow characteristics of the rock? is the formation pressure? are the directional permeabilities?

Production Engrs.

How is the pay distributed vertically? Is stimulation needed? What are compatible fluids?

Facilities Engrs.

Is the production going to be oil, gas, and/or water? What are the production rates going to be? What are the produced fluid properties?

* A person involved in evaluating a well may or may not be a specialist focused on only one aspect of technology. In some cases, a single person would have the responsibilities of several or even all of the specialist jobs listed here. This table shows that there can be many different perspectives in an evaluation effort.

need to be answered by evaluation of a flood process pilot is given in Table 4-11. Examples of typical CO 2 flood process pilots are discussed by Charlson et al. (1978), and Tanner et al. (1992). These pilots involved a brine pre-flood, a CO 2 or alternating CO2/brine main flood, and a brine post-flood. Pilots can take several years to complete and they may cost several, maybe tens of millions of dollars. The evaluation procedures can involve many, if not all, of the formation evaluation tools.

Production surveillance formation evaluation Production surveillance formation evaluation provides for evaluating methodologies that optimize the profit and recovery of an already producing formation as part of the reservoir management plan for that formation. A partial list of questions that might

161 TABLE 4-11 Partial list of questions that might need to be answered by the evaluation of a flood process pilot Specialist

Questions

All

Which flood process approach will result in the optimum economic results?

Petrophysicists

What is the change in residual oil saturation and distribution caused by the process flood injectant? How do the saturations change over time? What are the errors in the saturation results?

Production Engrs.

Can adequate CO 2 injection and follow-up water injection rates be attained?

Geologists

Is the geology of the pilot area representative of the geology of the whole field? What is the importance of structure and stratification in the flood process?

Reservoir Engrs.

Is there any other process, e.g., gravity segregation, that will affect the flood response? What is the injection profile? What are the volumetric production results from the flood process pilot? What are the errors in the volumetric production results? Can a flood simulator history match be made with the flood process pilot response? Can the flood simulator be scaled up to the field level?

need to be answered by surveillance formation evaluation is given in Table 4-Ill. One example of surveillance evaluation is the monitoring of a CO 2 flood using wireline-derived petrophysical data (Kittridge, 1992). According to Kittridge, results TABLE 4-11I Partial list of questions that might need to be answered by surveillance evaluation Specialist

Questions

All

Which production approach will result in the optimum economic results?

Production Engrs.

Are there productive zones that are not perforated or completed properly? Are there thief zones that need to be closed off?. Do the completion intervals have zonal isolation integrity? What is the mechanical integrity of each wellbore? How long will each wellbore be usable?

Petrophysicists

What are the original and current fluid saturations in each zone in each well?

Reservoir Engrs.

Can a flood simulator history match be made with the field production history? What should be the fractional fluid production of each zone in each well?

Geophysicists

Will 3-D seismic or geotomography help in monitoring fluid contacts or flood fronts? Are there deeper potential hydrocarbon zones?

Several

Which zones are producing the oil, gas, and/or water? Are the fluid contacts moving in the reservoir? Is the pay moving because of water or gas encroachment? Into which zones is the injectant (e.g., water, natural gas, or carbon dioxide) being injected? At what rates should each zone in a well be producing? How does the production rate of each zone compare to that zone's potential? Why is a zone not producing up to its potential? Are there portions of the field that need additional wells?

162 obtained with surveillance monitoring of this type are useful for quantifying CO 2 saturation, monitoring flood progress and vertical sweep, identifying potential outof-zone injectant losses, and detection of non-responding layers. Another example of surveillance evaluation is flood monitoring with induction logs run in wells that are completed with fiberglass casing specifically for the purpose of induction log monitoring. Induction tool monitor logg!ng during a chemical flood, a polymer flood, and a CO 2 flood pilot is detailed by Richardson (1979). Production surveillance data acquisition need to be scheduled so as not to adversely impact the revenue from producing operations. Existing wells can be used during workovers, or in many cases, even while the well is producing. Wells drilled to or through the formation of interest during the time of surveillance can also be used to acquire formation evaluation data to assist in the surveillance effort. Or as detailed by Richardson (1979), wells can be drilled and completed solely for the purpose of surveillance data acquisition.

PETROPHYSICAL

MODELS

A petrophysical model is a description of the physics of a rock and the fluids it contains. This description is in the form of an equation or equations. The result of the equation is the formation property of interest. One example of a petrophysical model is the determination of porosity from the formation bulk density. The description of the physical situation is: the bulk density of the formation is related to its porosity and rock by a linear, volumetric mixing law. The formation bulk density is, therefore, equal to the rock matrix density weighted by its fractional volume plus the pore fluid density weighted by its fractional volume. The equation for this physical situation is:

Pb= d~Pi§(1-dP)Pr~

(4-1)

where: Pb = bulk density (g/cm3); Pl = pore fluid density (g/cm3); Pma- - rock matrix density (g/cm3); and d~ = porosity (fractional). Bulk density, Pb' is usually measured by a wireline or measurement while drilling log, whereas Pl and Pma are determined from other logs or core samples correlated to the Pb measurement. Porosity, ~, is the desired property of the formation needed for reserve definition. Equation 4-1 rearranged to solve for the desired property of interest, porosity, yields: ~b =

Pma-- Pb

Pmo--Pl

(4-2)

Petrophysical models have two general requirements. First is that the number of unknowns must be less than or equal to the number of equations. Unknowns are the

163

100% Sw line

50% Sw line

25% Sw line

Sw-n _ Rt Ro

10.0

Hydrocarbon bearing zones

Water-bearing zones form Ro (Rzero)line. Slope of line is-m.

1.0

True Resistivity, Rt, (ohm-m)

0.1

Intercept of Ro line at 100% ~ is the formation water resistivity, Rw, at the formation temperature.

0.01 1%

10%

100%

Porosity, ~, (%) Fig. 4-1. This Pickett plot (Pickett, 1966) example is a plot of porosity (from a porosity log or logs) vs. true resistivity (from a resistivity log suite) for several zones from a particular formation. This plot is a graphical representation of Archie's equation (Archie, 1942) for the determination of the formation's water saturation.

164 answers that are required (porosity, water saturation, percentage of a particular lithology type, etc.). The knowns are the available pieces of data and information (logs, core analyses, test results, geologic insight, estimates, etc.). The second requirement is that the parameters used in the equations must be readily available. One could have the best petrophysical model in the world, but if there is no way to obtain the parameters for that model, then it is not very practical. These two general requirements sometimes lead to the use of petrophysical models which are approximations of the actual physical situation. The petrophysical model used to evaluate a particular formation needs to adequately describe the physical characteristics and properties of that formation. The assumptions inherent in the petrophysical model need to be appropriate for that formation, also. For example,Archie's equation for water saturation determination (Archie, 1942) assumes that the water phase of the pore fluid is the only electrically conductive medium in the formation. An incorrect water saturation from Archie's equation will be obtained if it is applied to a rock containing pyrite inclusions, which causes the rock matrix to exhibit electrical conductivity (Clavier et al., 1976). As can be seen, one must understand the petrophysics of the rock that is being evaluated to be able to apply the appropriate petrophysical model. Petrophysical models can be presented graphically for clarity and ease of interpretation. An example is the Pickett plot (Pickett, 1966). A Pickett plot, shown in Fig. 41, is simply a graphical representation of Archie's equation (Archie, 1942), Eq. 4-13, for water saturation determination.

DETERMINATION OF FORMATION PROPERTIES OF INTEREST

Overview

The use of data available from formation evaluation tools to determine formation properties of interest utilizing a petrophysical model is detailed in the next several pages. All available data should be used in an evaluation. But many times, all required data are not available. The use of a rock catalog to estimate missing formation property information can be beneficial. The introduction to one rock catalog (Reservoirs, Inc. and Robert M. Sneider Exploration, Inc., 1987, plus updates) describes that catalog's general objectives and associated applications as follows. A. Provide a reference manual containing "analog" sandstone and carbonate rock types for a more accurate estimate of formation "zone of interest" parameters when evaluating a given well. The Rock Catalog will contain a large amount of standardized geological/petrophysical/engineering data over a broad spectrum of reservoir rock types. Geologists and engineers routinely make assumptions concerning reservoir properties during, for example, log analysis (e.g., grain density, logging parameters). The Rock Catalog provides a reference manual of "analog" rock types. That is, a limited amount of information on a particular formation "zone of interest" can lead to a Rock Catalog analog sample which, in turn, provides other geological/engineering properties and parameters which can be applied to the "unknown" interval of interest.

165

B. Provide a comprehensive geological/engineering data base over the spectrum of reservoir-quality sandstone and carbonate rock types for the acquisition of new knowledge and insight into correlations and relationships among geological and logging/fluidflow/engineeringparameters. Rock Catalog data can be used to quantify relationships among geological and petrophysical properties and to establish rock-type correlations. Such information could, for example, improve log S w calculations, which would be especially valuable where the calculated S value serves as the primary criteria for completion recommendations. The Rock Catalog will contain data correlating the various rock properties of those reservoir rock samples. The Catalog sample entry numerical classification scheme was chosen for ease of data storage and processing by computer. Such data correlation should aid the user in identifying the more relevant aspects of formation evaluation, and also to compare non-Catalog reservoir samples to an established base line. C. Estimate reservoir rock properties from visual observation of core, sidewall and/ or cuttings rock material. The Rock Catalog, in combination with simulated cuttings "comparators," will g i v e . . , a valuable tool for developing expertise in calibrating rock/pore type observations from core or cuttings to reservoir rock parameters related to formation productivity (e.g., porosity, permeability). The geologist or engineer at the well site, with Rock Catalog and comparators in hand, can evaluate core or cuttings samples to provide rapid estimates of porosity, permeability, and reservoir potential of a particular zone of interest. With time, considerable expertise can be developed in relating that macroscopic properties of rock samples with known, geological, petrophysical, and/or engineering properties (i.e., Rock Catalog samples) to estimates of drill stern/production tests across intervals of interest. Rock catalog data can be found in notebook form or on computer storage media such as floppy disks or CD-ROM (Reservoirs, Inc. and Robert M. Sneider Exploration, Inc., 1987, plus updates). Simultaneous determination of porosity, pore fluid saturations, lithology component fractions, and pore fluid properties The determination of porosity, pore fluid saturations, and lithology component fractions can be accomplished by using a multi-mineral, multi-fluid petrophysical model for simultaneous solution of each evaluation tool's response equation to each formation property. These models are usually in the form of computer programs. The number of unknowns in the formation cannot exceed the number of equations handled by the computer program. These models fall into two general classes: deterministic models and error minimization models. Deterministic models directly solve the tool response equations to provide the lithology component fractions, porosity, and pore fluid saturations.A deterministic model example is the DAK (Dolomite,Anhydrite, Potassium) model used for lithology evaluation of some West Texas Clearfork carbonate reservoirs (Clerke et al., in progress). The model uses the natural gamma ray spectroscopy potassium log response to determine the percentage of silt in the zone. The bulk density and the photoelectric cross section log responses are used to determine the percentages of dolomite and anhydrite. Log response equations for each lithology component are solved directly.

166 TABLE 4-IV General outline of error minimization petrophysical models Item

Details

Results from model

Porosity Fluid saturations Mineralogy component fractions Some number of tools (depends on model) - well logs, mud logs, core analyses, test data, etc.- but, the model must not be underdetermined. Some number of mineralogies (depends on model) Some number of fluids (depends on model) Physical properties of each fluid and mineral component Upper and lower result boundaries Logging tool accuracies Calculated from logging tool response equations Function of porosity Function of fluid properties and volume fractions Function of mineral properties and component fractions Material balance (usually built in) Upper and lower result boundaries supplied by user Model finds best fit between theoretical and actual logs. Iterative solution can begin with equal volume fractions. Solutions incorporate all logs, other data, and known constraints simultaneously. Flags indicate quality of fit (residuals, incoherence)

Input to model

Theoretical log reading

Constraints Volume fraction solution

Error m i n i m i z a t i o n m o d e l s inversely solve the log response equations to provide the lithology c o m p o n e n t fractions, porosity, and pore fluid saturations. These m o d e l s construct theoretical log readings from the logging response equations, and obtain results by finding the best fit b e t w e e n the actual and theoretical logs. A general outline o f these types o f m o d e l s is s h o w n in Table 4-IV. E x a m p l e s o f error m i n i m i z a t i o n m o d e l s (programs) are listed in Table 4-V. Multi-mineral, multi-fluid petrophysical models, either deterministic or error minimization, require that the user supply the log response parameters for each fluid and lithology c o m p o n e n t . Errors in these p a r a m e t e r s - for example, p a r a m e t e r selection is a " b o o k " value w h i c h does not exactly m a t c h that o f the f o r m a t i o n - will cause TABLE 4-V Examples of error minimization petrophysical models (programs) Model

Associated company*

References

ELAN FLAME GLOBAL OPTIMA ULTRA

Schlumberger SIPM Schlumberger Atlas Halliburton

Quirein et al., 1986 Peeters and Visser, 1991 Mayer and Sibbit, 1980 Mezzatesta et al., 1988; Rodriguez et al., 1988 Alberty and Hashmy, 1984; Gysen et al., 1987

* Company names mentioned in this chapter are for reference only and are not meant as an endorsement of any particular company or product.

167 inaccuracy in the results. Accurate evaluation results require that the formation evaluation specialist understands the petrophysics of the rock and the fluids it contains. The use of knowledge-based or expert systems can potentially supplement the technical expertise of the formation evaluation specialist. However, knowledge-based system use in formation evaluation has rarely been reported. One knowledge-based system, LOGIX (Hoffman et al., 1988), has been used in the petrophysical interpretation of vuggy (oomoldic) carbonate reservoirs in the Middle East. The authors reported that the system's interpretation in these types of rocks encountered in five wells were checked with core data, geological descriptions, and well test data, and the agreement was excellent. Formation properties can also be determined with simpler petrophysical models. These models focus on one formation property at a time. The next sections of this chapter discuss the determination of each of the six primary formation properties of interest using simpler models. Simple petrophysical models that use well logs can usually be done by hand, using a calculator, crossplots, and/or nomographs. These models should not be used in isolation. So, also covered in the next sections of this chapter is the determination of each of these formation properties from the examination and/or analyses of rock (cores, sidewall samples, and cuttings), mud log information (cuttings analysis and hydrocarbon shows), and tests (wireline, drill stem, and production tests).

LITHOLOGY DETERMINATION

Lithology from examination and~or analyses of rock Rock samples can be from drill cuttings, whole cores, sidewall cores, and/or outcrops. Many methods exist for the determination and classification of lithology by petrographic rock examination. Carver (1971) provided several chapters dealing with petrographic mineral analysis, including preparation of thin sections, point counting, heavy mineral analysis, staining, and X-ray diffraction (XRD). A Fourier transform infrared (FTIR) spectroscopy method for petrographic mineral analysis is also available (Harville and Freeman, 1988). Ruessink and Harville (1992) compared FTIR and XRD for bulk mineral analysis. They concluded that one of these two techniques may be preferred over the other on the basis of its applicability to certain mineral classes: FTIR can analyze poorly crystalline material; XRD can deal with halides, and it offers the possibility of a detailed analysis of the clay-sized fraction of minerals. In other cases, the two techniques might be applied simultaneously to obtain complementary bulk mineral analysis information. The AAPG Sample Examination Manual (Swanson, 1985) provided practical methods and procedures for rock examination and lithologic logging, primarily of drill cuttings, but also of core and surface samples. Chapter 2 of Volume 1 of this book provides details concerning several lithologic classification methods used for carbonate rocks. Analyses of core and cuttings for grain density to provide insight into mineralogy can be done a number of ways (American Petroleum Institute, 1960). Grain density

168 results can be related to known grain densities for particular rock types. For example, the grain density of dolomite is in the 2.85-2.87 g/cm 3 range according to the references of Edmunson and Raymer (1979), Wells et al. (1979), Ellis et al. (1988), and Carmichael (1989). These four references provide a comprehensive listing of physical properties of rocks, including the grain or matrix properties and the responses of nuclear and acoustic logs. A C T scan on rock (Wellington and Vinegar, 1987) can be used for mineralogy determination. A calibrated (Coles et al., 1992) high energy CT scan for density in non-porous zones will provide grain density information. A calibrated dual energy CT scan will provide atomic composition information for the rock. CT scans provide spatial information with resolution as fine as a few millimeters. Cores can even remain frozen during the scan. Scans are totally non-destructive and can be made through core containers, unless they are made of lead or thick stainless steel.

Lithology from well logs Lithology, particularly the mineralogy aspect, can be determined or inferred from well log data, both wireline and measurement while drilling. The methods discussed in this chapter are from resistivity and spontaneous potential logs, from the use of conventional porosity/lithology log crossplots, from natural gamma ray and natural gamma ray spectroscopy logs, and from induced gamma ray spectroscopy logs. Also discussed are the reliability of determining lithology from logs, complications with determining lithology from logs, and some other considerations.

Resistivity and spontaneous potential Resistivity and spontaneous potential (SP) logs are not primarily lithology logs. In certain circumstances, however, they can indicate the lithology of a zone by one or two methods: (1) log values match trend or marker bed log values; and/or (2) log response indicates permeable vs. non-permeable zones. Resistivity logs, e.g., laterologs and induction logs, respond to changes in porosity, rock texture, pore fluid properties, and pore fluid saturations. For more details, see the section in this chapter concerning saturation determination fromArchie's equations. A zone with consistent rock types containing consistent fluids should have consistent resistivities within a region, i.e., the zone is a marker bed, and can be used to identify that particular zone and its lithology from well to well. Permeable zones are interpreted from multi-depth-of-investigation resistivity logging tools or from time-lapse logging with resistivity logging tools. These logs would show different resistivity values at different depths of investigation or at different times due to mud filtrate invasion, provided the mud filtrate and formation fluids have different resistivities. Spontaneous potential logs (Doll, 1949) require mud filtrate invasion to show response. Therefore, permeable vs. non-permeable zones can be differentiated, provided there is a contrast between the mud filtrate and formation water salinities. In low-porosity carbonates there can be problems with spontaneous potential log response due to the high formation resistivities, and the SP log may not be usable.

169

Conventional porosity/lithology log crossplots Conventional porosity/lithology logs are those which are commonly run in wells. These include: (1) (2) (3) (4) (5)

Density logs. Spectral density logs. Thermal neutron logs. Epithermal neutron logs. Acoustic logs.

Conventional porosity/lithology log crossplots are crossplots involving the aforementioned conventional porosity/lithology logs. These crossplots are two-dimensional visual representations of the log response equations to the various mineralogies. Rocks containing more than two mineralogies can be evaluated using multiple crossplots. Several of the conventional porosity/lithology crossplots are: (1) Density-neutron crossplots (see Fig. 4-2) use bulk density (or density log porosity) vs. neutron porosity for determination of mineralogy and porosity*; (2) Density-acoustic crossplots use bulk density (or density log porosity) vs. acoustic travel time for determination of mineralogy and porosity*; (3) Neutron-acoustic crossplots use neutron log porosity vs. acoustic travel time for determination of mineralogy and porosity*; (4) Density-photoelectric factor crossplots use bulk density (or density log porosity) vs. photoelectric factor for determination of mineralogy and porosity (Gardner and Dumanoir, 1980); (5) Hingle plots are plots of RJ/m vs. another log value that is proportional to porosity (e.g., bulk density, neutron porosity, or acoustic travel time) on special "Hingle" graph paper for determination of mineralogy and water saturation (Hingle, 1959); (6) M-N plots are plots of acoustic-density crossplot slope (M) vs. neutron-density crossplot slope (N) for mineral identification (Burke et al., 1969); (7) PmaaVS. Atmaamatrix identification plot compares apparent matrix density (fgmaa) to apparent matrix acoustic travel time (Atmaa) for determination of mineralogy (Clavier and Rust, 1976); (8) PmaaVS. Umaa matrix identification plot compares apparent matrix density (p~tmaa) to apparent matrix volumetric photoelectric factor (Uaa) for determination of mineralogy (Gardner and Dumanoir, 1980), see Fig. 4-3; and (9) Shear vs. compressional travel time plot for mineralogy determination (Pickett, 1963). Two concerns arise from using conventional porosity/lithology crossplots to determine lithology in complex (multiple component) rocks. First, there must be as many equations (logs) as there are unknowns (rock types). Mineralogy components found in carbonate reservoirs might be dolomite, limestone, anhydrite, gypsum, salt, chert, * These crossplots are found in each well logging service company chart book (e.g., Atlas Wireline Services, 1989b; Halliburton Logging Services, Inc., 1991; SchlumbergerEducational Services, 199la). Raymer and Biggs (1963), and Savre (1963) provide two of the early references on the subject of using crossplots and/or simultaneous log response equation solutions to determine mineralogy/porosity.

170

Porosity

Bulk

(Log)

-

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versus

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171

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6 7 8 9 10 11 12 13 14 Urea, Apparent Matrix Volumetric Photoelectric Factor vs.

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Logging

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Services,

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172 time: compressional, shear, etc. The acoustic petrophysical model which best fits the rock should be used: e.g., Wyllie time average (Wyllie et al., 1956), Raymer-HuntGardner (Raymer et al., 1980), acoustic formation factor (Raiga-Clemenceau et al., 1986), Krief-Garat-Stellingwerff-Ventre (Krief et al., 1990), or a local empirical correlation with core data. Neutron log response varies with logging service company, type of logging tool, vintage of logging tool, and log acquisition software. The Atlas Wireline Services Compensated Neutron tool response to dolomite (Atlas Wireline Services, 1989b, Chart 5-35), for example, is different from the Halliburton Logging Services Compensated Neutron tool response to dolomite (Halliburton Logging Services, Inc., 1991, Chart POR-10). An example of logging tool response variation with vintage of logging tool and log acquisition software is found in the Foreword of Historical Charts (Schlumberger Educational Services, 1990): Neutron porosity equivalence curves and environmental correction charts for the Compensated Neutron Log (CNL*) tool were first presented in the 1972 charts book. These charts were modified in the 1978 charts book to represent function former changes for logs run after 1976. The openhole environmental corrections were changed slightly in the 1984 charts book based on additional lab measurements. New CNL charts presented in the 1988 and 1989 charts books are based on improved environmental corrections. Natural gamma ray and natural gamma ray spectroscopy Natural gamma ray logs measure the natural radioactivity of the formation near the borehole. If different lithologies in a particular formation have different known levels of natural radioactivity, then the natural gamma ray log can help differentiate and determine lithologies. However, some knowledge of the expected lithologies is usually needed. In some cases, e.g., differentiating limestone and chert (see Table 4-VI), the natural gamma ray log is not at all useful. Unlike the conventional gamma ray log, which measures only the total radioactivity, the spectral natural gamma ray log looks at the energy spectrum of the measured gamma radiation to provide information relating to the amounts of potassium, uranium, and thorium in the formation. The three separate element concentration curves do not lend themselves to ease of interpretation. A more useful presentation uses only two curves, a total gamma ray curve and a combination of the thorium and potassium. The difference between the two curves is the uranium contribution to the total radiation. The additional information provided by the spectral natural gamma ray log over the conventional gamma ray log can be used for the following carbonate formation evaluation purposes (see Fig. 4-4). Distinguishing shales and radioactive dolomites. Shales are typically high in potassium. The spectral natural gamma ray response in shales should show the potassium plus thorium curve to be nearly the value of the total gamma ray curve. Radioactive dolomites are radioactive due to water-soluble uranium salts that were deposited in the rock during dolomitization. The spectral natural gamma ray response in radioactive dolomites should show the potassium plus thorium curve to be a small fraction of the value of the total gamma ray curve. The uranium salts would be the major * Mark of Schlumberger.

173 TABLE 4-VI Typical relative natural gamma ray log values for various lithologies Lithology

Relative natural gamma ray value*

Anhydrite Chert Dolomite Dolomite (radioactive) Granite wash Gypsum Halite Limestone Sand (little clay or feldspar) Sand (some clay and feldspar) Shale Source rock or organic shale

Low Low Low High High Low Low Low Low to moderate Moderate High Very high

* Actual gamma ray log readings for a particular lithology will vary with tool position in the borehole, borehole diameter, mud type and density, and formation density.

contributor to the total natural radiation. Source rock delineation. Source rocks have high uranium content in the organic material. This is because a uranium molecule is large and the organic material provides a structure into which it can fit. The uranium stays behind when the kerogen converts to oil. In source rocks the uranium is typically the major contributor to the total natural radiation. General evaluation uses. Natural gamma ray spectroscopy provides three more pieces of information about any zone of interest. If the lithology, or its deposition or diagenesis, or the pore fluid(s) can be delineated by evaluating the potassium, uranium, and/or thorium content, then this tool can yield up to three more equations to help solve for the unknowns. Induced gamma ray spectroscopy

Induced gamma ray spectroscopy tools (see Table 4-VII for tool list) analyze the inelastic and capture spectra of gamma rays resulting from neutron interactions with the different elements in the formation. The gamma ray spectra analyses are used to estimate the relative yield of elements in the formation. TABLE 4-VII Induced gamma ray spectroscopy tools Service Co.*

Tool name (mnemonic)

Reference

Atlas Atlas Halliburton Schlumberger Schlumberger

Carbon/Oxygen Log (C/O) Multiparameter Spectroscopy Instrument Pulsed Spectral Gamma-Ray Tool (PSG) Induced Gamma Spectroscopy Tool (GST) Reservoir Saturation Tool (RST)

Dresser Atlas, 1981 Chace et al., 1985 Jacobson et al., 1991 Hertzog, 1978 Scott et al., 1991

* Service company names mentioned in this chapter are for reference only and are not meant as an endorsement of any particular company or tool.

174

Spectral Natural Gamma Ray Log Response Examples

0 Total GR (API Units) 0 --.-,----- K+Th (API Units) - - - - , -

100 100 4000 rn Shale resoonse. K+Th reading (88 API Units)is nearly the value of the total gamma ray curve (94 API Units).

Radioactive dolomite response. K+Th reading (17 API Units) is a small fraction of the value of the total gamma ray curve (94 API Units).

Source rock response. K+Th reading (89 API Units) is that of a shale. The total gamma ray value (284 API Units)is high because of the large amount of uranium in source rocks. The total gamma ray can be even larger, up to 1000+ API Units, in some cases. 4100 m GR backup scale 100-200 API Units GR backup scale 200-300 API Units

Fig. 4-4. A useful presentation of the spectral natural gamma ray log is shown here. The dashed curve is the contribution of the potassium plus the thorium to the total radiation. The other curve is the total gamma ray (GR) log response. The difference between the two curves is the uranium contribution to the total radiation. The gamma ray log values for these lithologies will not be the exact readings shown here. The relationship between the K+Th and the total curve will be similar to these responses for these lithologies. The actual gamma ray log readings for a particular lithology will vary with tool position in the borehole, borehole diameter, mud type and density, and formation density.

175 TABLE 4-VIII Elemental yields and other information from induced gamma ray spectroscopy tools Mode of measurement

Yield or information determined

Inelastic mode

Carbon Oxygen Silicon Calcium Sulfur Iron

Capture mode

Hydrogen Silicon Calcium Chlorine Iron Sulfur Titanium

Ratio of inelastic to elastic or capture counts

oc

Formation capture cross section

E

Induced gamma ray spectroscopy tools can be run in open or cased holes and provide elemental yields for the elements listed in Table 4-VIII. Ratios can be computed from the yields to aid in lithology, porosity, and saturation determination. Useful yield ratios are listed in Table 4-IX. TABLE 4-IX Useful induced gamma ray spectroscopy yield ratios Yield ratio

Common name

Uses in formation evaluation

Si/(Si + Ca) Ca/Si [inelastic] Si/Ca [capture] Fe/(Si + Ca) CI/H H/(Si + Ca) C/O

Lithology indicator Calcium/Silicon ratio Silicon/Calcium ratio Iron indicator Salinity indicator Porosity indicator Carbon/Oxygen ratio

Siliciclastics vs. carbonates Siliciclastics vs. carbonates Siliciclastics vs. carbonates and salinity Clays and pyrite Chloride salts Liquid-filled porosity and clays Hydrocarbon saturation

Results from induced gamma ray spectroscopy tools can be combined with other information to provide additional formation evaluation information. Indirect combinations of the induced gamma ray spectroscopy tool information can be done with any other formation evaluation tool by using a computer program that describes the appropriate petrophysical model for that particular tool combination and rock properties.

Geochemical logging tools Direct combination examples using induced gamma ray spectroscopy with other formation evaluation tools are the geochemical logging tools (Hertzog et al., 1989 and Schlumberger Educational Services, 1992). These tools are a combination of a capture mode induced gamma ray spectroscopy tool to analyze silicon, calcium, iron,

176 sulfur, gadolinium, and titanium; a natural gamma ray spectroscopy tool to analyze thorium, potassium, and uranium; neutron and possibly density logs for porosity and additional mineralogy information; and a second natural gamma ray spectroscopy tool adjacent to a neutron source to determine the aluminum yield. Herron et al. (1991 ) described the application of geochemical logging of a Middle East carbonate reservoir. The geochemical log provides elemental weight percentages for the formation. Mineral abundances are determined using an element-to-mineral transform that must match the mineral components of the reservoir rock.

Reliability of determining lithologyfrom logs The reliability of determining lithology from logs is directly related to: (1) How much insight and knowledge are available concerning the rocks. This is usually a function of how much work has been done in the area. (2) How well the lithology needs to be known. This is usually a function of the amount of money that will be spent on the project and what the risks are. Figure 4-5 shows a qualitative view of the reliability of lithology determination from logs under different situations. Determining lithology from logs only is much less reliable than incorporating other information. Having cuttings or core samples to examine and to calibrate log response increases the reliability of the lithology determination and provides insight into rock texture which is not readily available from well logs.

Complications There are several factors which can complicate lithology determination from logs: (1) Bad or failed logs may need to be edited or recalibrated to correct erroneous data. If a field-wide or regional study is involved, log data will probably need to be normalized to provide for a consistent interpretation. (2) Gas in the pores of the rock affects density, neutron, and acoustic log responses. An additional log or other knowledge is required to account for gas effects. (3) Pad tools, such as density and sidewall neutron logs, are especially affected by poor hole conditions. Washouts and/or rugose hole can render log response invalid. (4) Underdetermined situation (complex geology or not enough logs) requires acquiring additional log data, making some assumptions, and/or estimating properties from analogous rock types using a rock catalog. (5) The acoustic log does not "see" non-touching vuggy porosity until it becomes the dominant pore type. This causes the calculated apparent matrix travel time and subsequent lithology determination to be in error. (6) If the evaluation is applying the wrong petrophysical model, e.g., using a timeaverage model for the acoustic-porosity-lithology relationship when the rock fits an acoustic formation factor model, then the lithology interpretation will be in error. The presence of these factors increases the uncertainty in lithology determination from logs.

Other considerations The various methods oflithology determination from well logs usually only provide information concerning mineralogy, i.e., the rock's fractional mineral composition. The textural nature of the rock is not addressed nor determined at all. It is the texture

177 Reliability of Lithology D e t e r m i n a t i o n from Wireline and M W D Logs

Wildcat Well (Log-Core Work)

" xx

Confirmation Well (Much Log-Core Work) Routine Development Well

l;I

Field Step-Out Well 0.0

I

I

I

I

0.2

0.4

0.6

0.8

1.0

Reliability (Arbitrary Units) 1.0 = Very Reliable 0.0 = Not Reliable

Lithology from Logs Alone Logs + Sample Examination Logs + Sample Examination + Core Analyses + Tests + Geological Insight

-0,,-- - - , 0 , - - - v

9

v

Fig. 4-5.A qualitative view of the reliability oflithology determination from logs under different situations. (Adapted from E.C. Thomas, pers. comm., 1987.)

of the rocks which governs porosity and permeability (Archie, 1952; Enos and Sawatsky, 1981; Lucia, 1983; Jodry, 1992), and fluid saturation distribution (Leverett, 194 l; Rose and Bruce, 1949; Jodry, 1992) in the reservoir. One must look at the rock to gain insight into the rock texture.

178 POROSITY DETERMINATION

Porosity from examination and~or analyses of rock Rock samples for porosity determination can be from drill cuttings, whole cores, and/or sidewall cores. Outcrop porosities are not usually representative of reservoir porosities due to surface weathering, dissolution, and dedolomitization. For heterogeneous carbonates, larger samples tend to be more representative of the formation. Porosity estimation from rock examination is possible using, e.g., the Archie classification (Archie, 1952) or Lucia classification (Lucia, 1983). The AAPG Sample Examination Manual (Swanson, 1985) provides practical methods and procedures for rock examination and lithologic logging for porosity estimation, primarily of drill cuttings, but also of core and surface samples. Chapter 2 in Part I of this book provides details concerning several porosity classification methods used for carbonate rocks. Porosity can be determined from thin section point counting. Carver (1971) provided details concerning procedures in sedimentary petrology. The relatively low vertical resolution (direction coincident with the objective lens axis) of petrographic microscopes makes it somewhat difficult to resolve grain boundaries, especially at higher magnifications needed to detect microporosity and small fractures. Impregnating the sample with epoxy and an admixed fluorescent dye allows the use of a confocal microscope, a specialized form of epifluorescence microscopy, which can image a very thin focal plane, or very thin layer, of the thin section (Owen et al., 1992). A series of focal plane images can be acquired and then reassembled or stacked to generate a full three-dimensional image of the thin section. Image analysis of thin sections and scanning electron micrographs, provides rapid, quantitative porosity data. Image analysis also provides quantitative data conceming the size and geometric complexity of reservoir pore systems (Ehrlich and Davies, 1989). An understanding of the nature and distribution of pore types becomes increasingly important with decreasing porosity values. Reservoirs which have undergone diagenetic modification, such as carbonates, are frequently characterized by the co-existence of several disparate types of porosity. In such rocks, reservoir behavior is much less dependent on total porosity than on the pore type assemblage that makes up that porosity (Davies, 1990; Chapters 4 and 6 in Volume I of this book). There are several core analyses methods for porosity determination (American Petroleum Institute, 1960). Typically core analysis porosity determination methods measure the bulk.volume and the pore volume or grain volume of the rock sample. Most methods require that the core be cleaned of formation and filtrate fluids before or as part of the analysis process. The lower the permeability of the rock sample, the longer it takes to perform the cleaning and/or porosity analysis. Heterogeneous rocks, like vuggy carbonates, require whole core analysis rather than plug analysis to produce representative results. However, the larger the rock sample, the longer it takes to perform the cleaning and/or porosity analysis. CT scanning (Wellington and Vinegar, 1987) of core material is a non-destructive

179 method for obtaining porosity data. A calibrated (Coles et al., 1992) high energy CT scan can provide bulk density data in porous and non-porous zones. The petrophysical model associated with Eq. 4-2 can be used to determine porosity from such data. CT scans provide spatial information with resolution as fine as a few millimeters. Cores can even remain frozen during the scan. Scans can be made through core containers, unless they are made of lead or thick stainless steel. Nuclear magnetic resonance (NMR) spectroscopy and scanning (Edelstein et al., 1988) are other non-destructive methods for obtaining porosity data from core material. NMR responds to the liquids in the pore space. Therefore, if the pore space contains gas, the rock must be resaturated with liquid for accurate porosity determination. The pore liquids cannot be frozen either. The use of NMR for porosity determination in tight, gypsum-bearing carbonates has been shown to be valuable where extraction core analysis methods proved inaccurate due to gypsum dewatering and extremely low permeability of the rock (Vinegar et al., 1991 b).

Porosity from well logs Density, acoustic, and neutron logs Porosity can be obtained from well logs, both wireline and measurement while drilling. The so-called conventional porosity logs include density, spectral density, acoustic, thermal neutron and epithermal neutron logs. Earlier sections of this chapter covered the determination of lithology from multiple porosity logs. Many of those methods provide porosity as an auxiliary result. Porosity can also be obtained from using a single porosity log. However, tool response to the formation of interest, the appropriate petrophysical model, and the lithology of the formation must be known. The lithology must usually be translated into a matrix log response value for use by the petrophysical model. Matrix log response values for numerous lithologies can be found in the references by Edmunson and Raymer (1979), Wells et al. (1979), Ellis et al. (1988), and Carmichael (1989). To determine porosity from density and spectral density logs, use the petrophysical model associated with Eq. 4-2. The lithology needs to be known to obtain a matrix density value. If lithology is not available from an independent source, the spectral density photoelectric factor, Pc, curve can provide insight into lithology. Crossplots are available (Gardner and Dumanoir, 1980) for a graphical solution of using the Pe to obtain lithology, and, therefore, a matrix density, to use in the determination of porosity. The fluid density value also must be known. The formation fluid density can be obtained from fluid samples or from wireline test pressure gradients. However, the depth of investigation of nuclear logs is fairly close to the borehole wall, usually within 15 cm (6 in.) (Tittman, 1986, p. 15). Therefore, when invasion has occurred, the fluid density is dependent upon the densities and relative percentages of mud filtrate and formation fluids within the investigation volume of the density tool. When invasion has occurred, it is difficult to determine the exact fluid density within the volume of investigation of the density log. As a first order approximation, use the fluid density values from Table 4-X. If one of the formation fluids is gas, these fluid density values are too high and the calculated porosity will be too high. Density logs are usually run in open, not cased, boreholes.

180 TABLE 4-X Estimation of fluid density values for determination of porosity from a density log* Drilling mud type

Range of fluid densities (g/cm 3)

Commonly used fluid density (g/cm 3)

Supersaturated brine Brine Fresh-water Oil-based

1.15-1.2 1.05-1.15 1.00-1.05 0.75-1.0

1.2 1.1 1.0 1.0

* Assumes invasion of drilling mud filtrate. If invasion has not occurred, use fluid density of formation fluid(s). For water densities: Dewan (1983), p. 105, suggests using pf= 1.0 + 0.73 N, where N is NaC1 concentration in ppm x 10-6;Atlas Wireline Services (1989b), Chart 1-6, shows the variation of brine density with temperature, pressure, and salinity. To determine porosity from acoustic logs, use the acoustic petrophysical model which best fits the rock. Examples of acoustic petrophysical models include Wyllie time average (Wyllie et al., 1956); Raymer-Hunt-Gardner (Raymer et al., 1980); acoustic formation factor (Raiga-Clemenceau et al., 1986); Krief-Garat-Stellingwerff-Ventre (Krief et al., 1990); or a local empirical correlation with core data. Typically a local empirical correlation will be the most accurate of these models when it is based on representative formation rock. Most acoustic log porosity determination models, including the first three aforementioned models, use compressional acoustic information only. Using shear velocity information to augment compressional data can be beneficial when compressional wave amplitudes are small (Pickett, 1963) or when complex formations are encountered (Krief et al., 1990). Acoustic logs are usually run in open boreholes. If full waveform data are acquired, acoustic logs can be used to determine compressional and shear velocities and transit times in cased boreholes (see Table 4-XV for partial listing of tools and references for acoustic waveform logs). Determination of porosity from a thermal or epithermal neutron log requires knowledge of the logging service company, type of logging tool, vintage of logging tool, and log acquisition software used to obtain the log data. The lithology must also be known. Knowledge of the rock matrix and near-borehole fluid thermal neutron capture cross sections can lend more accuracy to the porosity results from a thermal neutron log (e.g., see Halliburton Logging Services, Inc., 1991, Chart POR-9; Schlumberger Educational Services, 1991 a, Charts Por- 16, - 17, and - 18). If one of the formation fluids is gas, the neutron log will determine a porosity that is too low. Neutron logs can be run in open and cased boreholes. Service company charts are available for porosity determination from each of their conventional porosity logs. Environmental corrections may need to be made to correct for the influence of the borehole and near-borehole region on the log response. Service company environmental correction charts are also available for each of their conventional porosity logs.

Pulsed neutron capture logs The pulsed neutron capture (PNC) log can be used to determine porosity. The near to far count rate ratio is used with lithology (Halliburton Logging Services, Inc., 1991,

181 Chart TMD-1 b) or sigma (Schlumberger Educational Services, 1991 a, Charts Tcor-3, -4, and -5). The logging service company may provide the PNC porosity directly on the log. Usually assumptions are made concerning the borehole environment and there is a practical upper limit on the validity of porosity determination at about ~ = 40% (Schlumberger Educational Services, 1989b, p. 3-25). If one of the formation fluids is gas, the PNC log will determine a porosity that is too low. Gas in borehole degrades the accuracy of the PNC porosity and may even make results invalid. Porosity determined from pulsed neutron capture logs is less accurate than porosity determined from conventional porosity logs. Pulsed neutron capture logs are almost always run in cased boreholes.

Induced gamma ray spectroscopy logs Induced gamma ray spectroscopy logs, their elemental yields, and their useful yield ratios are listed in Table 4-VII, Table 4-VIII, and Table 4-IX, respectively. Table 4-XI lists approaches used to determine porosity from these logs. Salinity and lithology variations cause inaccuracies in the resulting porosity. If one of the formation fluids is gas, the determined porosity will be too low. Induced gamma ray spectroscopy logs can be run in open or cased boreholes for porosity determination. TABLE 4-XI Determination of porosity from induced gamma ray spectroscopy log data Approach

Reference

Ratio of capture to inelastic counts Ratio of inelastic to capture counts H/(Si + Ca) porosity indicator ratio

Atlas Wireline Services, 1989b, Chart 7-13 Jacobson et al., 1991, p. 6 Hertzog, 1978, pp. 8-9

Geochemical logging tools The matrix density (sometimes called grain density) of the formation rock can be determined on a continuous basis from the geochemical log mineral abundance resuits (Herron et al., 1991). This matrix density can then be used with bulk density data measured from a density log run across the same formation to provide porosity (see Eq. 4-2).

Nuclear magnetism logs Brown and Gamson (1960) described the original type of nuclear magnetism log (NML) tool. This tool design was the basis for commercial NML logging tools until the 1990s. The log provided a measurement of the total hydrogen, i.e., liquid-filled porosity, called the free fluid index (FFI). The FFI represents the liquids, as a percentage of the bulk volume, that are not influenced by nearby rock materials (such as in extremely small pores) nor by local magnetic materials. Timur (1972) found the FFI to be an excellent predictor of porosity in carbonate rocks, regardless of variations in the ratio of limestone to dolomite in the matrix. The original type of commercial tool was useful at providing liquid-filled porosity, but was somewhat cumbersome to use because of the need to eliminate the borehole signal by doping the borehole with

182 magnetic material, because of the large tool diameter of about 15 cm (6 in.), and because of the hole diameter limitations of only between 18-28 cm (7-11 in.) (Schlumberger Educational Services, 1991b, p. 108). The results from the original type of commercial NML t o o l s - some of them are still available- are somewhat unsophisticated by today's standards. New nuclear magnetic resonance well logging tools (Coates et al., 1991, and Morris et al., 1993) are more in line with the technology used in the NMR core analysis tools. Many of the same measurements done by the NMR core analysis tools can be done by the new well logging tools. Porosity determination from the new tools is more accurate than that from the original type of NML tools. In addition, the borehole does not have to be doped to eliminate the effect of its signal with the new tools.

Considerations with determining porosity from logs Knowledge of the petrophysics of the rock leads to the most accurate determination of porosity from well logs. The proper petrophysical model must be used, and the logging tool response to the rock and its fluids needs to be understood. Approaching the determination of porosity with an understanding of the rock can minimize its uncertainty.

PORE FLUID SATURATION DETERMINATION

Saturations from examination and~or analyses of rock Usually pore fluid saturations cannot be determined directly from examination and/ or analysis of rock. Saturations of a rock brought to the surface differ from its in-situ saturations because of two factors: invasion and blowdown. Invasion of the drilling mud filtrate will change the saturations and pore fluids of the permeable rocks. As the rock is brought from formation depth to the surface, the pressure on the rock decreases. Fluids will expand as the rock moves upward toward the surface. If the bubble point pressure of the oil is reached, gas will evolve. Expansion of gas with reduced pressure (Boyles law) is much more dramatic than that of liquids. As the pore fluids expand they push pore fluids from the core, i.e., blowdown occurs. With water-based muds there are two situations where invasion and blowdown do not change the pore fluid saturations: (1) Zones that are already at 100% water saturation. (2) Zones containing very viscous (near-solid) tar and heavy oil. Invasion of water-based mud filtrate can have little or no effect on the resulting lab-measured oil saturation of zones which are already at residual oil saturation. In this case, the effects of blowdown on the oil saturation can be accounted for or eliminated by the use of a sponge core liner pre-saturated with water or by the use of a pressure core barrel (Worm Oil Coring Series, 1985-1986, Part 2). With oil-based muds there is one situation where invasion and blowdown do not change the pore fluid saturations: zones that are at irreducible water saturation and contain very viscous (near-solid) tar and heavy oil. Invasion of oil-based mud filtrate

183 can have little or no effect on the water saturation of zones which are at irreducible water saturation. In this case, the effects of blowdown on the water saturation can be accounted for or eliminated by the use of a sponge core liner pre-saturated with mineral oil or by the use of a pressure core barrel (Worm Oil Coring Series, 1985-1986, Part 2). Core analysis data in the form of drainage capillary pressure curve saturation distributions can be representative of the original hydrocarbon saturation distributions in a reservoir (Leverett, 1941; Rose and Bruce, 1949; Jodry, 1992), provided that the rock from which the data are acquired is representative of the formation. Mercury-air capillary pressure points can be related to reservoir height above the free water level (see the definition in Table 4-XVII) in the formation by the following equation, provided that the in-situ formation hydrocarbon and water specific gravities, interphase tensions, and contact angles are known: h=

PcHg-Air OH- ~VCOSVH_W 0.433(SG W- SG u) CrHg_AircOSOHg_Ai r

where: h

(4-3)

= height above free water level (ft);

P~m-Air = mercury-air capillary pressure (psia); SGw = specific gravity of formation water (dimensionless); SGH = specific gravity of formation hydrocarbons (dimensionless); cyH_W

~l-Ig-Air OH_W

Oug-Air

= interphase tension of formation hydrocarbon-water system (dynes/cm); interphase tension of laboratory mercury-air system (dynes/cm); = contact angle of formation hydrocarbon-water-rock system; and = contact angle of laboratory mercury-air-rock system. =

Mercury-air interphase tension and contact angle are usually taken to be 480 dynes/ cm and 140 ~ respectively. Formation values should be measured using representative, unaltered formation fluid samples at in-situ conditions. Interphase tension values often quoted in the literature, 72 dynes/cm for gas-water and 35 dynes/cm for oil-water, are for laboratory fluids (air, water, and soltrol) at ambient laboratory conditions (J.H.M. Thomeer, pers. comm., 1989), and would only match the in-situ reservoir values by coincidence. For the mercury-air capillary data, mercury is the non-wetting phase. For Eq. 4-3 to be representative of the reservoir height relationship for the original saturation distribution in the reservoir, the hydrocarbons are assumed to be the non-wetting phase during the original oil migration and subsequent saturation distribution equilibrium. Thomeer (1960) provides a methodology that can uniquely describe a capillary pressure curve and quantify the saturation distribution using three parameters. These so-called Thomeer parameters that describe the capillary pressure curve can be used to calculate the original saturation at any height above the free water level in the reservoir when combined with Eq. 4-3. A correlation between the capillary pressure curve's height above free water level and the reservoir depth must be found. Smith (1990) shows examples of capillary pressure to reservoir depth correlation using well log data. Figure 4-6 shows an example of capillary pressure to reservoir depth correlation using wireline test data.

184 Examination of the rock can provide insight into the original hydrocarbon saturation of the reservoir. Various classification methods (Archie, 1952; Lucia, 1983) have presented capillary pressure type-curves for rocks fitting specific classification criteria. Examination of rock can also provide descriptive parameters that can be used as input to a rock catalog (Reservoirs, Inc. and Robert M. Sneider Exploration, Inc., 1987, plus updates) to find a capillary pressure curve from an analogous rock. Image analysis of thin sections and scanning electron microscope photographs can be used to characterize the pore systems of a rock (Davies, 1990). The quantitative description of each pore system can be related to a particular capillary pressure curve, e.g., by pore throat diameter relationships (Washburn, 1921), for determining original fluid saturations. CT scanning (Wellington and Vinegar, 1987) can be used for saturation determination. Invasion and blowdown most likely have altered the saturations from in-situ values. If two fluid phases are present, a single energy scan is sufficient to measure the two saturations. When three fluid phases are present, two different energy scans are needed to determine the three saturations. Wellington and Vinegar (1987) discussed the use of CT scanning saturation determination for flow studies, and showed results from several different types of coreflood experiments. Proton nuclear magnetic resonance (~H NMR) spectroscopy and scanning (Edelstein et al., 1988) can be used to obtain liquid saturations from core material. Gas in the pore space is not measured directly, but can be inferred by the difference between the NMR liquid (%BV) and the total porosity (%BV). Because the NMR apparatus responds to liquids, the pore liquids cannot be frozen. The use of proton NMR in tight, gypsum-bearing carbonates has been shown to be valuable for saturation determination where extraction core analysis methods proved inaccurate due to gypsum dewatering and extremely low permeability of the rock (Vinegar et al., 1991 b). Whole core analysis by ~3C NMR for oil saturation determination has been demonstrated in cases where ~H NMR might not work well, like in shaly rock (Vinegar et al., 1991 a). NMR has also been demonstrated to be a useful tool in quantifying oil volume in extracts from other saturation determination procedures; such as extracts from polyurethane sponge core liners using freon-11, Dean-Stark extracts using xylene, and miscible flooding extracts using chloroform/methanol (Tutunjian and Vinegar, 1990).

Saturations from well logs The following section of this chapter will cover saturation determination using Archie's equations with porosity and resistivity logs, using dielectric logs, pulsed neutron capture logs, induced gamma ray spectroscopy logs, and nuclear magnetism logs.

Saturation determination from Archie's equations using porosity and resistivity logs Archie's equations (Archie, 1942) are the most-used equations for determining water saturation from well logs. The use of Archie's equations makes one critical assumption concerning the rock: the water phase in the pores of the rock is the only

185

Example of Capillary Pressure Curve Correlation to True Vertical Depth

Pc Hg/A] (psla)t

TVD (ft) 9780 -

:arDon Grad, = 0.346 psi/ft c Gravity = 0.80

400 t

300 t

200 t

9900

I

I

I

I

I

I

I

I

l

100%

SHg (% PV)

0%

0%

Sw (% PV)

100%

Free Water Level

10140 -

Other P~rtin~nt Parameters OH-W = 20 dynes/cm OH_w = 0 degrees

Formation Water Press. Grad. = 0.450 psi/ft SpecificGravity = 1.04 10260 4900

I

I

I

!

!

Wireline Test Pressure (psig)

I

I

I

5150

Fig. 4-6. The graph on the left is a mercury capillary pressure curve. It shows the distribution of nonwetting phase, in this case mercury (Hg), vs. capillary pressure. If the reservoir non-wetting phase is oil, the mercury saturation distribution is equivalent to the oil saturation distribution. The graph on the right is a plot of wireline test pressures vs. depth. The intersection of the water gradient line with the oil gradient line is the free water level (see Table 4-XVII for water level definitions). The free water level is equivalent to the zero capillary pressure value on the left graph. Conversion of capillary pressure to height above free water level is done with Eq. 4-3. The 100% water level is the equivalent depth of the extrapolated displacement pressure, Pd, of the capillary pressure curve. The capillary pressure curve provides the water saturation (Sw) at the reservoir depths shown on the wireline test data plot.

186 electrically conductive medium, i.e., the rocks contain no conductive clays or iron minerals. Of course the hydrocarbons (if present) are non-conductive also. This assumption usually works well with carbonates. Archie's (1942) equation f o r 100% water-saturated rock Begin by considering the manner in which rock resistivity varies as a function of porosity for rocks that are 100% saturated with water. The resistivity of a rock with zero porosity would be infinitely high, whereas the resistivity of a 100% porosity rock would be equal to the resistivity of the water. The resistivity of the rock at any other porosity is proportional to the resistivity of the water in the pores. Archie (1942) found that the equation given below fits his data.

(4-4)

Ro=FR w

where: R o (Rzero) F Rw

resistivity of rock containing 100% water, i.e., 0% hydrocarbons (ohm-m); = formation factor (dimensionless); and = resistivity of water in pores (ohm-m).

=

Therefore: R0

~--= F

(4-5)

w

Archie (1942) found that F was a constant for rock with a particular pore structure. He found the formation factor to be" F ~ ~--m

(4-6)

where: F = formation factor (dimensionless); = porosity (fractional); and m = lithologic exponent (dimensionless). Thus:

Ro = ~)-mRw

(4-7)

The value of m, the lithologic exponent, is a function of the rock type, in particular the rock's pore type or combination of pore types. For a large number of carbonate rocks, it falls between 1.9 and 2.2. Data from Traugott (1970) and Lucia (1983) show that vuggy carbonates can have values of m larger than 3.0. Detailed insight as to the effect of different pore types on the lithologic exponent is covered in the pore combination modeling section of this chapter. A graphical representation of Archie's equation for an example of a 100% water-saturated rock is shown in Fig. 4-7. One practical use of applying Archie's first equation in a 100% water-bearing zone is the determination of the formation water resistivity value. Rearranging Eq. 4-7:

187

Rw-- ~mRo

(4-8)

When this equation is applied in zones that are not known to be 100% water-bearing, the water resistivity, R w, is designated as the apparent water resistivity, Rw.

Archie's (1942) equation for hydrocarbon-bearing rock Archie (1942) analyzed others' data and found that the resistivity of a rock that is hydrocarbon-bearing is proportional to the resistivity of the rock as if it was 100% water saturated. The following relation fit his analysis: R = I R0

(4-9)

where" resistivity of rock containing hydrocarbons and water in pores (ohm-m); I = resistivity index (dimensionless); and R 0 (Rzero) resistivity of rock containing 100% water, i.e., 0% hydrocarbons (ohmm).

R t

=

=

Therefore"

R' I--=

(4-10)

Ro I is constant for rock with a particular pore structure and wettability. The resistivity index is defined as"

I = S -w"

(4-11)

100" 10" R o c k Resistivity

Ro (ohm-m)

~Slope

=-m

1.0 "

0.1 0.01 0.01

|

0.1 (fractional)

1.0

Fig. 4-7. This is a graphical representation o f A r c h i e ' s (1942) equation (R 0 = 100% water-saturated rock, on a log-log scale.

d~-"Rw)for an example of a

188 where" I = resistivity index (dimensionless); S = water saturation (fractional); and n = saturation exponent (dimensionless). So:

Rt =S--"Ro=S-" w w q~-mRw

(4-12)

Archie (1942) found that n, the saturation exponent, approximately equaled 2.0 for a large number of rocks. The value of n is a function of the rock pore structure and the rock's wettability. As the rock becomes less water-wet, the saturation exponent will increase. Values ofn in the 8.0-12.0 range have been found in carbonates that exhibit strong non-water wet behavior (Sweeney and Jennings, 1960). A graphical representation of Archie's (1942) equation for an example of a hydrocarbon-bearing rock is shown in Fig. 4-8. Notice the symmetry between the 100% water saturation case (Eqs. 4-4 through 47, and Fig. 4-7) and the hydrocarbon-bearing case (Eqs. 4-9 through 4-12, and Fig. 48). The symmetry suggests that the effect of electrical conductivity being taken away is similar in each case even though the physical situation is somewhat different; nonconductive rock takes away conductivity in the 100% water saturation case and nonconductive hydrocarbon takes away conductivity in the hydrocarbon-bearing case. The m value describes how fast conductivity (or resistivity) changes as porosity changes. The n value describes how fast conductivity (or resistivity) changes as water saturation changes. A form of Archie's (1942) equation which solves for water saturation is: !

S'-

(4-13)

~met

For the case where m = n = 2, the equation is simplified to:

1JRw L-"---~-

Rt

(4-14)

The only reason that the formation evaluation specialist should use m = n = 2 is if the rock in the zone of interest actually has those m and n values.

Resistivity of the flushed zone From Archie's (1942) equations, one realizes that the electrical resistivity of the flushed zone near the wellbore can be significantly different from that of the undisturbed zone, even in 100% water-saturated intervals. This is because the mud filtrate resistivity can be very different from the formation water resistivity. As complex as the invasion profile is, one can take advantage of the fact that in the flushed zone the water resistivity is known. The zone has been completely flushed

189

1000 100 Rock Resistivity Rt (ohm-m)

10 1.0

R.o. 0.1" l

0.()1

0.1

1.0

Sw (fractional) Fig. 4-8. A graphical representation of Archie's (1942) equation hydrocarbon-bearing rock, on a log-log scale.

(R t -

Sw-"Ro) for an example of a

with mud filtrate so the water phase resistivity is RmS.Rmsis normally measured at the surface and its value and the measurement temperature are recorded on the well log heading. Using a temperature vs. R vs. NaC1 concentration chart (Atlas Wireline Services, 1989b, Chart 1-5; Halliburton Logging Services, Inc., 1991, Chart GEN-5; Schlumberger Educational Services, 1991a, Chart Gen-9) or Arps equation (Arps, 1953), R ~can be calculated for any depth (temperature) in the wellbore. Archie's (1942) equation mJ still applies, so for water-bearing zones" w

Rxo

~=F=~

Rms

where" Rxo = Rms = = F = = m

-m

(4-15)

(in this case) resistivity of rock containing 100% mud filtrate (ohm-m); resistivity of mud filtrate in pores (ohm-m); formation factor (dimensionless); porosity (fractional); and lithology exponent (dimensionless).

The Archie (1942) equation for hydrocarbon-bearing zones in a form which solves for the flushed zone mud filtrate saturation, S O(fractional), is:

SxO=(RmZ) l (~m ex 0

(4-16)

The calculated difference between S and Sx0is a measure of movable hydrocarbons. Movable hydrocarbons are usually taken as a positive indication of producibility.

190 Archie 's parameters The Archie (1942) approach to water saturation determination requires knowledge or acquisition of the Archie's (1942) equation input data and parameters:

formation water resistivity, R w (ohm-m); porosity, ~ (fractional); true formation resistivity, R t (ohm-m); lithologic exponent, m (dimensionless); and saturation exponent, n (dimensionless). And for the determination of the mud filtrate saturation, Sx0, in the flushed zone: mud filtrate resistivity, Rml (ohm-m); and flushed zone resistivity, Rx0 (ohm-m). These data and parameters must be known at in-situ conditions. Determination of formation water resistivity is discussed later in this chapter. Determination of the mud filtrate resistivity is typically done by the well logging service company. A sample of representative drilling mud is filtered to obtain a sample of mud filtrate. The resistivity is measured and the temperature of the filtrate is recorded. Determination of porosity has been discussed earlier in this chapter. Determination of the true formation resistivity requires the use of a resistivity or conductivity logging tool, and is not a trivial task. Logs that have been used in the past include normal, lateral, and limestone devices (Guyod, 1944). Logs that are used today include focused resistivity logs, e.g., laterolog, guard, toroid, etc.; induction conductivity logs; and 1- to 2-MHz electromagnetic propagation tools (Maute, 1992, for a state-of-the-art review). Complications such as tool resolution vs. zone thickness, influence of the borehole resistivity, mud filtrate invasion, and limitations of logging tool performance due to tool design and calibration, typically dictate that the raw resistivity log readings, even for a deep investigating tool, do not represent the true formation resistivity. Environmental correction charts are available from the service company chart books to correct for resolution, borehole, and invasion effects. If R~ accuracy is critical, modeling and deconvolution programs specific to particular resistivity tools are available (e.g., Tumer et al., 1991, for the Halliburton Logging Services, Inc. dual laterolog). Flushed zone resistivity determination is from focused microresistivity logs. Mudcake thickness and mud resistivity affect microresistivity log response. Environmental corrections may be required to correct for these effects to obtain an accurate value of Rxo. Determination of m and n can be done using core analysis (Archie, 1942). Values for m and n can be obtained using a rock catalog (Reservoirs, Inc. and Robert M. Sneider Exploration, Inc., 1987, plus updates) from analogous rock types. Some authors have found relationships for m based on vuggy porosity vs. total porosity (Traugott, 1970, from log responses calibrated with local core control; Lucia, 1983, from examination of rock). A more holistic approach can be used for the determination of the lithologic exponent by considering all pore types as is done by pore combination modeling.

191 TABLE 4-XII Fitted lithologic exponents (k) for individual carbonate pore types (from Myers, 199lb) Carbonate pore type

Definition

Lithologic exponent (X)

Vugs Intergranular Microporosity

Pores larger than the grain size Intergranular or intercrystalline Not visible on 10x thin section

1.11 1.91 1.56

Pore combination modeling Determination of the lithologic exponent, m, can be accomplished using pore combination modeling (Myers, 1991 b) if the rock's pore types and their proportion of the total porosity can be defined. Petrographic analysis, including thin sections, and capillary pressure curves can provide pore type characterization. Table 4-XII shows Myers' (199 l b) lithologic exponent fits for each of the major carbonate pore types. An example of the application of pore combination modeling to determine m is as follows. Suppose there is a carbonate rock with 17% B V total porosity, composed of intergranular porosity (10% B V of the total) and vuggy porosity (7% B V of the total). The intergranular porosity is the dominant connected pore system and the vugs comprise the second pore system. A graphical representation of the application of pore combination modeling to obtain the composite Archie lithologic exponent, m, is shown in Fig. 4-9. The procedure starts with the dominant connected pore system. A line can be drawn from the origin (F = 1, ff = 100%) at a slope corresponding to the negative lithologic exponent for intergranular porosity (-Z,i) of -1.91. A second line is drawn starting from the intercept of the intergranular porosity line at the intergranular porosity value, 10%. The slope of this second line corresponds to the negative lithologic exponent of the vuggy porosity (-Lv),-1.11. The intercept of the vuggy porosity line at the total porosity, 17%, defines one point 100 -

Formation Factor, F (dimensionless)

10 -

=-

.

ugs)

T.Z'! = - ! " 9 1 , ,~', Slope = - m of rock in question. ~nterg

1 1

10

100

Porosity, (% BV)

Fig. 4-9. Graphical representation of determination of composite Archie lithologic exponent, m, from a carbonate with vuggy and intergranularporosity types, using pore combination modeling.

192 used in the determination of the composite Archie lithologic exponent, m. The other point is the origin (F = 1, ~) = 100%). The slope of the line between these two points defines the negative composite Archie lithologic exponent,-m. The use of pore combination modeling can be extended to describe the saturation dependence of a rock's resistivity behavior (Myers, 1991 b). The shape of curves plotted from resistivity index vs. water saturation measured data can give insight into a rock's pore system(s) and wettability. For a particular rock, pore combination modeling could be used to estimate n if the pore types are known and the wettability effect can be characterized. Myers (1991 b) pointed out that pore combination modeling provides a means for petrophysical properties to be calculated directly from a knowledge of a rock's pore structure. This allows the petrophysicist to incorporate geologic data in his/her petrophysical models. Not only does this make more accurate models possible, but such models may be changed to incorporate changing geology.

Saturation determination using dielectric logs Poley et al. (1978) found that a dielectric constant measurement of a formation can be used to determine water saturation without any knowledge of the formation water properties, provided that the measurement is done at a very high frequency (at or above 1 GHZ). Very high frequency dielectric logging tools (Calvert et al., 1977; Rau et al., 1991) and interpretation techniques (Wharton et al., 1980) are available. These tools have a shallow depth of investigation, 2-15 cm (1-6 in.) depending on the conductivity (Wharton et al., 1980). Because these tools normally respond to the flushed zone in the near-borehole region, most dielectric log saturation determination applications have been in formations containing heavy oil or tar. Viscous heavy oil or tar is not affected by invasion, so that the oil saturation in the near-borehole region is representative of the oil saturation in the rest of the formation. Dielectric log depth of investigation can be extended by using a lower frequency tool. However, the measurement is then dependent on the formation water salinity and the frequency of the measurement. Myers (1993) has characterized this dependence for carbonates, finding that dielectric dispersion in carbonates is dominated by two terms: a term proportional to the interparticle porosity and a term proportional to the vuggy porosity. The parameters in this model were found to be consistent with earlier published models for the dielectric constant in clastics (Myers, 199 l a). The dielectric log's ability to separate vuggy from interparticle porosity allows accurate determination of oil saturations through improved estimates of the Archie lithologic exponent, m (see the pore combination modeling portion of this chapter). Saturation determination using pulsed neutron capture logs Pulsed neutron capture (PNC) logs are designed to determine water saturation in a cased well (Youmans et al., 1964), after the drilling mud filtrate invasion has dissipated. PNC tool diameters are typically less than 5 cm (2 in.); thus they can be run through tubing. The log measures the thermal neutron capture cross section, E, of the formation which is related to the fractional volumes of oil, water, and rock matrix by a linear volumetric mixing law, as shown in Eq. 4-17:

193

~-~formation= ~hydrocar6on(l -- Sw)~ + ~waterL~ q" ~matrix(| -- ~)

(4-17)

where: E = thermal neutron capture cross section (capture units or cu); Sw - water saturation (fractional); and = porosity (fractional). However, the log does not actually measure the intrinsic ~formation. A diffusion correction is needed (Youmans et al., 1964). The diffusion correction is tool and environment dependent, and is part of the service company's characterization of the tool's response. Thus, the equation for the log response to the formation is: ~log-" ~hydrocarbon(1 --Sw)~ -~" ~-~wateraw~+ ~matrix(|- ~) -I- A

(4-18)

where" A = diffusion correction (capture units or cu). Thus, solving for water saturation yields: g - (1 -

S

w=

~)~matrix- Zhydrocarbon~-- A (Zwater_

hydrocarbon)

(4-19)

The logging service company will provide the necessary diffusion correction. One can obtain the values for Swa,e " and Y"hydro~arbo,, from, for example, measurement on samples or from tables in service company chart books, if the fluids' compositions are known (see the discussion of pore fluid property determination later in this chapter for details). One can obtain the value of ~ from, for example, a porosity log or logs (see the discussion of porosity determination earlier in this chapter for details). One can get a value for ~matrix from the references by Edmunson and Raymer (1979), Wells et al. (1979), Ellis et al. (1988), and Carmichael (1989), if the rock composition is known. ~matrix c a n also be obtained from a 100% S wzone as follows (in this case, the hydrocarbon terms drop out)"

~-~formation= ~matrix( l -- ~) "~- ~water ~

(4-20)

So, solving for Zmatrix yields" S motr~ =

~formation- ~Zwater 1 -- Ck

(4-21)

If the porosity of the formation is moderate to high and the salinity of the formation water is moderate to high, then the PNC logs can provide water saturation results with reasonable accuracy. However, there are some borehole and near-borehole conditions, e.g., logging just below a packer with liquid in the tubing and gas in the tubing-casing annulus, which can be problematic to obtaining an accurate ,~formaiont'

194 even after full data processing at the logging companies' computer centers (Bonnie, 1991). In carbonates with saturated saline formation water, the use of pulsed neutron capture logs for water saturation applications is usually limited to porosities above about 15% (see the discussion of error propagation later in this chapter for details). As formation water salinity gets fresher, the lower porosity limit for determining water saturation with this tool goes up. Another use of pulsed neutron capture logs is to determine residual oil saturation, S using the log-inject-log process (Richardson et al. 1973) This process involves twice logging a zone that is already at residual oil saturation. One needs to know the Later of the formation water. One then must be able to inject water of a different, but known, Later into the zone between the logging passes. It does not matter if the zone is cased with perforations or is openhole, as long as injection across the entire zone of interest occurs. Invasion should not be a concern because the zone's saturation is at S r. However, careful planning is needed to ensure that the residual oil saturation is not reduced by the evaluation method (Kidwell and Guillory, 1980). When the pulsed neutron capture log is run the first time, the resulting capture cross section as seen by the log, Z~, depends on the rock contribution, the formation water contribution, and the hydrocarbon contribution:

z~,1 = Z~matrix(1--~) "k",~water_lawO-I- ,~hydrocarbon(1--L ) O -I" A

(4-22)

Then water of a different, but known, capture cross section is injected into the formation at a slow rate so that the saturation is not changed by viscous stripping. When the pulsed neutron capture log is run the second time, the resulting capture cross section as seen by the log, 22, depends on the rock contribution (which has not changed), the injected water contribution (which has changed because of the change of its E), and the hydrocarbon contribution (which has not changed): z~2 = Z~matrix(l -- ~ )

+ Later_2L~ -st-~hyarocarbo.(1-S)qb + A

(4-23)

Combining the two equations yields:

Z~l- Z~2-~ (~water-1- ~water-2) L ~

(4-24)

Rearranging this equation yields:

~ l - 2;2 S~=Later_l-~water_ 2

(4-25)

and

27,- S 2 S=~(~water_l-~water_2) Therefore"

(4-26)

195 (1 - So,)q~ =

27, - 2; 2 Z ~ w a ter _ l - -

(4-27)

Z ~ w a ter _ 2

and S = 1or

271- S 2

(Swater_

)

(4-28)

It is common practice to leave the equation in the form of Eqs. 4-25 and 4-27 so that the results automatically incorporate the porosity-saturation product into the volumetric residual oil determination. This minimizes the error propagated to the volumetric result because of the reduction in the number of input parameters for the equation: the E values from the two log runs and for the two waters are needed, not the Z values for the hydrocarbons nor the matrix. One other saturation application of pulsed neutron capture logs has been to determine CO 2 saturation in carbonate reservoir surveillance evaluation of a tertiary flood (Kittridge, 1992). This process involved empirical correlation of PNC log response to CO 2 saturations at in-situ conditions for a specific PNC logging tool (not just a specific type of tool, but a specific physical tool, neutron source, detectors, etc.).

Saturation determination using induced gamma ray spectroscopy logs Interpretation models are published for saturation determination using induced gamma ray spectroscopy logs (Hertzog, 1978, and Jacobson et al., 1991, for interpretation models; Westaway et al., 1980, and Wyatt et al., 1992, for examples) making use of the carbon and oxygen yields. The models are affected by changes in mineralogy. Carbonates (i.e., rocks containing carbon) have significant effect on results. Saturation accuracies get worse as porosity decreases (Hertzog, 1978). But accuracies improve as logging speed is slowed or as stationary measurement time is increased (Wyatt et al., 1992). Saturation determination using nuclear magnetism logs Brown and Gamson (1960) described the original type of nuclear magnetism log (NML) tool which was the basis for commercial NML logging tools until the 1990s. The log provided a measurement of the total hydrogen, i.e., liquid-filled porosity, called the free fluid index (FFI). The original type of NML tools can determine formation fluid saturations in certain situations without knowledge of formation water salinity. Those situations include: (1) The hydrocarbon in the formation is heavy oil or tar. The tar acts as a solid, so the NML sees only the formation water saturation. (2) The formation is at residual oil saturation. The formation water signal can be eliminated by injecting a paramagnetic ion into the formation so the NML only responds to the residual oil saturation. With the original type of NML there is still a requirement to eliminate the borehole signal by doping the borehole with magnetic material. New nuclear magnetic resonance well logging tools (Coates et al., 1991, and Morris et al., 1993) are more in line with the technology used in the NMR core analysis

196 tools. Many of the same measurements done by the NMR core analysis tools can be done by the new well logging tools. Saturation determination from the new tools is more accurate than that from the original type of NML tools. In addition, the borehole and formation fluids do not have to be doped to eliminate the effect of its signal with the new tools.

PORE FLUID PROPERTY DETERMINATION

Introduction

Pore fluid property information is needed in formation evaluation and reservoir performance characterization, usually as a parameter for a particular model, e.g., the formation water resistivity parameter in Archie's (1942) equation for water saturation determination (Eq. 4-13). Pore fluid property information is also needed in the optimization of well completions and design of surface facilities for producing fields. Pore fluid property information, e.g., gas vs. oil, is needed for economic analysis. Pore fluid property information can be obtained from measurement or analysis of representative formation fluid samples. The representativeness of formation fluid samples is usually better from larger samples, e.g., from long-term production tests. Fluid samples from wireline formation tests and even drill stem tests can be contaminated with mud filtrate. Drill stem test fluid samples can also be contaminated by the mud initially trapped across the test interval below the packers and/or by a fluid cushion which is sometimes placed inside the drill string to limit the pressure differential across the packers. The drill stem test fluid sample that should be most representative of the formation fluids is the last sample caught in the test tool sample chamber, usually a volume of about two to two-and-a-half liters (about a half gallon). Earlougher (1977), Appendix D, provides a comprehensive set of correlations useful for estimating fluid properties needed when analyzing transient-test pressure data. Included are pressure-volume-temperature (PVT) properties; oil, water, and gas compressibilities; and gas, oil, and water viscosities. Although representative samples of formation fluids are the best source of data, many times representative samples are not available, so other methods (in addition to the aforementioned Earlougher correlations) are used to aid in the determination of formation water and hydrocarbon properties. Formation fluid properties discussed in this chapter are some of those that are most needed in formation evaluation and reservoir performance characterization. Formation water properties

Knowledge of formation water salinity or resistivity is needed for water saturation determination using resistivity and porosity logs. Formation water density information is needed for density log porosity determination of uninvaded wet zones and for interpretation of invasion profiles in highly permeable zones. Knowledge of formation water thermal neutron capture cross section is needed for water saturation determination using pulsed neutron capture and porosity logs.

197 Formation water density

Wireline tester pressure gradient results in 100% water-bearing zones provide formation water density information. Gunter and Moore (1987) provide procedures for wireline testing quality control that can reduce the errors in wireline test results and the subsequent determination of formation water density. Dewan (1983, p. 105), relates water density to salinity by: pj= 1.0 + 0.73N

(4-29)

where" /~= the water density (g/cm3); and = the NaC1 concentration (ppm x 10-6). Chart 1-6 of Atlas Wireline Services (1989b) shows the variation of water density with temperature, pressure, and salinity. Formation water salinity and~or resistivity

Formation water salinity can be obtained from formation water resistivity information, and visa versa, using a temperature vs. R w vs. NaCI concentration chart (Atlas Wireline Services, 1989b, Chart 1-5; Halliburton Logging Services, Inc., 1991, Chart GEN-5; Schlumberger Educational Services, 1991 a, Chart Gen-9). If ions other than Na and C1 are present, equivalent NaC1 concentrations can be determined using conversion charts (Atlas Wireline Services, 1989b, Chart 1-4; Halliburton Logging Services, Inc., 1991, Chart GEN-4; Schlumberger Educational Services, 1991 a, Chart Gen-8). Jorden and Campbell (in progress), Chapter 14, provide details conceming water composition evaluation of carbonate rocks. A single measurement log method, the use of the spontaneous potential (SP) log to determine water resistivity is not generally applied in carbonates due to the adverse effects of highly resistive zones on the SP log response. Multi-measurement log methods, all based on Archie's (1942) equations, include: (1) Pickett plots, see Fig. 4-1 (Pickett, 1966); (2) Hingle plots (Hingle, 1959); (3) apparent water resistivity, Rwa, curves, see Eq. 4-8 (Tixier et al., 1960); (4) crossplots of R vs. SP (Schlumberger Educational Services, 1989a, p. 4-4); (5) formation factor, F, overlays (Schlumberger Educational Services, 1989a, p. 8-5); and (6) the ratio technique (Schlumberger Educational Services, 1989a, p. 8-6). wa

Jorden and Campbell (in progress) point out that methods based on resistivity and porosity log combinations work better in carbonate evaluation compared to siliciclastic evaluation because the large variations in carbonate porosity allow more certainty in curve fitting and curve extrapolation. Determination of formation water salinity by the use of nuclear magnetic resonance imaging of 23Na in cores has been demonstrated (Tutunjian et al., 1991), for those cut in oil-based muds. This method will work for formation water salinity deter-

198 mination as long as sodium is the predominant cation in the formation water. The core must be handled and protected so that pore water evaporation does not occur. Pore water evaporation would increase the apparent salinity of the water. Water salinity and/or resistivity information can also be found in catalogs. Water catalogs have been published by service companies, govemment agencies, industry groups, and technical societies (e.g., Permian Basin Chapter of the AIME, 1954). Formation water thermal neutron capture cross section Formation water thennal neutron capture cross section can be obtained from pulsed neutron capture log readings in a 100% water-bearing formation. Rearranging Eq. 420 to solve for the water parameter, Z , ~ r, yields: _ "~'formation - ( 1

-- ~)~matrix

(4-30)

This equation can be presented graphically as a porosity vs. sigma crossplot (Clavier et al., 1971) to solve for the formation water thermal neutron capture cross section. Water sigma values can also be obtained from charts (Atlas Wireline Services, 1989b, Charts 7-1 and 7-2; Halliburton Logging Services, Inc., 1991, Chart TMD-2; Schlumberger Educational Services, 1991 a, Charts Tcor-2a and Tcor-2b). Knowledge of water salinity is required; although reservoir pressure, gas-oil ratio, boron compounds, and reservoir temperature effects are characterized by some of the charts. Hydrocarbon properties Determination of some hydrocarbon properties pertinent to formation evaluation are discussed below. In general, a representative formation hydrocarbon sample can be used to provide almost any hydrocarbon property desired. Hydrocarbon fluid type Hydrocarbon fluid type, gas vs. oil, can be determined from well log response (wireline and measurement while drilling), wireline tester pressure gradient results in the hydrocarbon-bearing zones, mud log show types and/or chromatographic gas detector ratios, core and cuttings analysis and examination, and mud filtrate nuclear magnetic resonance. Gas effects on density and neutron logs appear as an apparent lower bulk density and an apparent lower neutron porosity on a density-neutron crossplot. In gas-bearing zones, the resulting apparent matrix density will appear lower than the actual matrix density of the rock. Knowledge of the actual matrix density can be obtained from core analysis or other unaffected logs (e.g., photo-electric effect readings are not significantly affected by gas). Pulsed neutron capture (PNC) logs also provide indications of gas vs. oil. The thermal neutron capture cross section of gas (in the range 0-18 capture units) is typically less than that of oil (in the range 18-22 capture units. Condensate runs in the

199 range of 15-18 capture units (Schlumberger Educational Services, 1991a, Chart Tcor-1). Therefore, a gas zone may show a shift to a lower formation sigma value vs. an oil zone, all other properties being equal. In gas zones the near to far count ratio curve may go to a lower value compared to that in oil zones. PNC inelastic ratio response has proven to be an extremely diagnostic gas indicator in turbidite sands (Scheibal et al., 1992). The inelastic ratio response has provided gas indication in sands with porosities down to 9%. As long as there is a change in the formation's hydrogen content (e.g., gas vs. liquid) for similar porosity zones, the inelastic ratio response should provide gas indication in lower porosity sands and in carbonates also (J.M. Worrell, personal communication, 1992). As another indication of hydrocarbon type, the PNC-derived porosity will appear lower than the actual porosity in a gas zone. Wireline tester pressure gradients in the hydrocarbon-bearing zones provide hydrocarbon density information. This density information can be used with reservoir temperature and pressure data, also available from the wireline tester, to help differential gas from liquid hydrocarbons. Gunter and Moore (1987) provide procedures for wireline testing quality control that can reduce the errors in wireline test results and the subsequent determination of hydrocarbon density. Mud log show types are indicative of gas-bearing vs. oil-bearing formations. As a simple evaluation, if there are hydrocarbons indicated from the well log analysis and there is no oil staining in the rock show descriptions, most likely the hydrocarbon type is gas. A method which is used to quantify mud log fluorescence shows that occur outside the visible range is Quantitative Fluorescence Technique (QFT) (Delaune, 1992). This methodology works only for water-based muds. Condensate, which usually has no visible fluorescence, is easily identified with QFT. Threedimensional crossplots of show intensity vs. emission wavelength vs. excitation wavelength have been used to distinguish heavy oil from light oil from condensate. Delaune documents that if an oil sample is available to calibrate the QFT equipment, show intensity can predict oil saturation. However, the surface oil saturation in cuttings, cores, etc., have been altered from in-situ saturations because of mud filtrate invasion and pressure blowdown. Another mud log technique that is used to determine hydrocarbon type is chromatographic mud gas show ratios, the light to heavy component ratio. Application of these ratios typically requires local calibration. Core and sidewall sample examination and analysis will indicate oil staining or quantify oil content. Again, if there are hydrocarbons indicated from the well log analysis, and there is no oil found in the rock, most likely the hydrocarbon type is gas. Analysis of mud filtrate samples by nuclear magnetic resonance can identify the presence of gas, oil, or water in the formation (Youngblood, 1971). A mud filtrate sample can be obtained by the use of a wireline test tool. The mud filtrate sample is subjected to magnetic polarizations which are at right angles to the earth's magnetic field. These polarizations are of various time durations in order to indicate the thermal relaxation time, T~, of the mud filtrate sample. The relaxation time (see Table 4XIII) identifies the nature of the virgin formation fluid before contamination by the flushing action of the mud filtrate.

200 TABLE 4-XIII Nature of virgin formation fluid from T~ analysis of mud filtrate (fromYoungblood, 1971) Thermal relaxation time, T~, range 0 . 1 - 0.6 seconds 0.6- 1.2 seconds 1 . 2 - 2.5 seconds

Fluid Gas Oil Water

Hydrocarbon density Wireline tester pressure gradients in the hydrocarbon-bearing zones provide hydrocarbon density information. Gunter and Moore (1987) provide procedures for wireline testing quality control that can reduce the errors in wireline test results and the subsequent determination of hydrocarbon density. Oil viscosity Proton NMR measurements on tight, gypsum-bearing carbonates has provided quantitative oil viscosity information where extraction methods proved costly due to extremely low permeability of the rock (Vinegar et al., 199 l b). Whole core analysis by ~3C NMR for oil viscosity has also been demonstrated (Vinegar et al., 1991 a) without extracting the oil from the core. NMR oil viscosity determination has also been done on oil that is in core analysis extracts from polyurethane sponge core liners using freon-11, from Dean-Stark extracts using xylene, and from miscible flooding extracts using chloroform/methanol (Tutunjian and Vinegar, 1990). Oil chemistry Oil chemistry affects the wettability behavior of a crude oil/brine/solid system (Buckley and Morrow, 1990). They noted that subtle changes in pH can cause a drastic change in oil adhesion behavior. Dubey and Doe (1991) found that acid to base content of the oil can be useful indicators of the wetting properties of the oil in crude oil/brine/silica systems, but they indicated that it will be necessary to extend this work to other mineralogies before predictions can be made for carbonate reservoirs. In the process of doing this work, Dubey and Doe developed a new potentiometric titration method to properly quantify the base content of crude oils. Geochemical analyses can be done on small samples or even cuttings using thermal extraction chromatography (Price, 1985) or pyrolysis analyses (Horsfield et al., 1983). These techniques have been used to fingerprint hydrocarbons for evaluation of shows to determine hydrocarbon origin, oil gravity determination, and contaminant recognition. The two techniques are also used to evaluate source rock richness, to quantitatively and qualitatively identify kerogen type, and to classify bitumens and coals. Whole core analysis for hydrocarbon chemistry by ~3C NMR has been used to determine aliphatic/aromatic ratio (Vinegar et al., 1991a) without extracting the oil from the core. Hydrocarbon thermal neutron capture cross section Hydrocarbon thermal neutron capture cross section values can be obtained from charts (Atlas Wireline Services, 1989b, Charts 7-3, 7-4, 7-5 and 7-6; Halliburton

201 Logging Services, Inc., 1991, Charts TMD-3, -4, -5, and -6; Schlumberger Educational Services, 199 l a, Chart Tcor-1). Knowledge of gas/oil ratio for oil, and reservoir temperature and pressure for gas are required; although effects of condensate content and gravity of the gas are characterized by some of the charts.

P E R M E A B I L I T Y DETERMINATION

Permeability from examination and~or analyses of rock Muscat (1949) pointed out that no matter how complete the coring and precise the data, one is still limited to an examination and study of rock samples which can constitute at the most, a fraction of the total reservoir volume only of the order of 0.0001%. One should keep this in mind as one compares core-derived permeability to permeability derived from, for example, well testing which can have a large volume of investigation. Permeability measurement by direct core analyses is documented in the American Petroleum Institute (1960) reference. Absolute permeability can be measured using gas or brine. Klinkenberg-corrected gas permeability is an extrapolation of gas permeability to an apparent infinite gas pressure to approximate a liquid permeability. Effective and relative permeability of carbonate reservoirs are discussed in Volume I, Chapter 8 of this book. If plugs are taken, their orientation should be selected based on the need for directional information, e.g., vertical vs. horizontal permeability. For heterogeneous carbonates, whole core measurements of permeability would probably be the most representative core analysis technique. Whole core permeability measurements done perpendicular to the borehole axis typically provide two measurements (see Fig. 410). The larger of the two measurements is termed k o . The other, taken 90 ~ to the maximum value, is termed k90. So-called mini-permeameters are devices that flow gas from the end of a tube-like probe that is sealed against a rock sample to estimate local permeability. Georgi and Jones (1992) discussed the evolution of mini-permeametry and the application of this technique to reservoir description. Inasmuch as the device can provide estimates of permeability with resolution down to about 5 mm (0.2 in.), geologists can quantify the impact of both depositional and diagenetic features on permeability. Lab-based mini-permeameters can be used on small-diameter core plugs or full-diameter core samples. Portable mini-permeameters can be used on outcrops. Permeability can be estimated from capillary pressure core data (Purcell, 1949, for historical perspective on early work; Swanson, 1981, for use on cuttings or samples with large closure corrections; Thomeer, 1983, for general use). The Thomeer and Swanson methodologies provide permeability estimates within a factor of two, for a one standard deviation confidence level, based on their calibration data sets. For rocks with more than one pore type, Thomeer (1960) pointed out that the relatively larger pores of a rock contribute the most to the permeability and, therefore, any capillary curve permeability estimate should be based on the lower-pressure capillary curve portion of multiple-curve capillary pressure data.

202 Lucia (1983) provided a field classification of carbonate pore space and a methodology for estimating permeability from a visual description of carbonate rocks. Average particle size and interparticle porosity are used to provide permeability estimation within an order of magnitude for 70% of the rocks in Lucia's calibration data set. His methodology is meant to be applied to carbonates with interparticle porosity. The effect of adding separate vugs to a non-vuggy rock is to increase the porosity with little or no increase in permeability. As Lucia pointed out, this allows his methodology to still be used to estimate permeability in vuggy rock as long as the vugs are not touching. The intergranular porosity is used for the permeability estimation. If vugs are touching, it is the size of the connecting opening between the vugs that affects the permeability the most, and in a field description there is no effective method for making this observation. Petrographic examination can provide pore throat diameter information used for the construction of synthetic capillary pressure curves. Carver (1971) provided detailed procedures in sedimentary petrology. Estimating permeability from capillary pressure curves was discussed above. The petrographic rock description could also be used to select an analogous rock type from a rock catalog (Reservoirs, Inc. and Robert M. Sneider Exploration, Inc., 1987, plus updates) for permeability estimation. Image analysis of thin sections and scanning electron microscope photographs can be used to characterize the pore systems of a rock. It is the pore type assemblage that can be related to permeability. Examples of permeability determination from image analysis has been published for sandstones (Davies, 1990), but not for carbonates. However, a similar approach aimed at the different pore systems found in carbonates should be valid. Flow gas through core in this direction

j

Screens

Whole core Fig. 4-10. This schematic shows the basis for a whole core gas permeability apparatus. Screens and core are inserted in a Hassler-type sleeve. Gas is flowed through the screens across the core and permeability is determined. Then the core is rotated 90~around the borehole axis and the permeabilityfor that direction of gas flow is determined. Both measurements are recorded. The larger one is termed k , the other is k90.

203 Proton NMR measurement has been shown to estimate permeability from sandstone core samples (Seevers, 1966, for first work; Howard et al., 1990, for recent work). Howard et al. related the time constant for NMR longitudinal relaxation,/'1, to pore body size, for intergranular/intercrystalline rock. Kenyon et al. (1988) reasoned that the permeability from NMR is, therefore, a function of the relation between the size of the pore throats to the size of the pore bodies, with NMR providing the pore body information. NMR permeability estimation for vuggy rocks will be less accurate than that for intercrystalline rocks because of the poorer relationship between pore throat size and pore body size for vugs (H.J. Vinegar, personal communication, 1992). In any NMR work, tool response is only to liquids, so the core must be 100% liquid saturated and the pore liquids must not be frozen.

Permeability from testing Permeability can be obtained from pressure transient analyses. The classic references on the subject are the following. Matthews and Russell (1967) presented the first comprehensive documentation of well testing and analysis. Earlougher (1977) provided a stand-alone, comprehensive update to the Matthews and Russell reference. Several references have provided newer insight into pressure transient analysis. Cinco-Ley and Samaniego-V. (1981) discussed the analysis of fractured formations. Bourdet et al. (1983) introduced a new set of type curves partially derived from the derivatives of the dimensionless pressure and time functions normally used in most type curves. Gringarten (1984) summarized analysis of reservoirs with double-porosity behavior, including both naturally fissured reservoirs and multilayered reservoirs with high permeability contrast between layers. The special cases of fractured and doubleporosity reservoirs would be applicable for heterogeneous carbonate reservoirs.

Permeability from well logs No well log can quantify permeability unilaterally; thus, well logs provide detection, not evaluation, of the permeability of a particular zone. Some well logs (e.g., resistivity logs, micrologs, calipers, and spontaneous potentials) can indicate which zones are permeable by showing mud filtrate invasion. Some well logs and their results (e.g., porosity logs, porosity-saturation combinations, and geochemical logs) can be used to estimate permeability by empirical correlation of log response to core permeability data. One possible exception to the lack of a direct permeability evaluation well logging tool may be found in recent versions of nuclear magnetic resonance logs (Coates et al., 1991). The tool response combined with T~ data (Seevers, 1966) or restrictive diffusion data (Vinegar and Rothwell, 1988) may provide permeability information (Coates et al., 1991).

Detection of permeability from mud filtrate invasion Several well logs detect permeable zones by indicating water-based mud filtrate invasion. Invasion is usually only an indication of permeability and not related to the quantitative permeability. Recent experiments (Allen et al., 1991) found that on all

204 but the tightest formations- rocks with more than 10-millidarcy permeability- filtrate is lost at rates that depend on interactions at the mud/mudcake interface at the borehole wall, not on formation properties such as permeability. The exception is when formation permeability and differential pressure (borehole vs. formation) are so low that the mud filtrate loss rate even without a mudcake is less than the equilibrium invasion loss rate during dynamic circulating conditions. In this case of formations with low permeabilities, no external mudcake forms under dynamic conditions and filtrate loss rate is controlled primarily by formation permeability. Higher differential pressures lower the permeability threshold at which this relationship exists. Wettability effects on the invasion rate are not considered. Otherwise, at higher formation permeabilities, the filtrate loss is likely to be the same into every permeable zone. The diameter of i n v a s i o n - a parameter extracted from resistivity l o g s - should, therefore, vary inversely with porosity. The microlog responds to mudcake build up on the borehole wall by the invasion process (Doll, 1950). The Doll reference provided detailed interpretation rules, and even exceptions to the rules, for detection of permeable intervals. His introduction mentioned that the microlog found its first field of application in limestone areas. When designing a formation evaluation program, do not forget about the m i c r o l o g it is old technology and does not have a prefix like array, spectral, or digital to make it more attractive. But it does an acceptable job of indicating permeable zones, and it can resolve very thin zones. Mudcake may also be seen on caliper logs. If the borehole remains at the bit diameter, i.e., in gauge, decreased hole diameter can be indicative of mudcake. If the borehole erodes somewhat, it can be difficult, if not impossible, to use a caliper log as a mudcake indicator to detect permeable zones. The effects of invasion can also be seen on resistivity log profiles if the resistivity of the invading fluids are different from that of the formation fluids. Invasion will appear as different resistivities on different depth-of-investigation logs. Or invasion will appear as different resistivities on similar depth-of-investigation logs run at different times. Resistivity logs used in this manner should have equal resolutions and be corrected for borehole effects. Otherwise, resolution differences might be interpreted as invasion. Spontaneous potential log response requires invasion into a permeable zone and a contrast between the mud filtrate resistivity and the formation water resistivity. Doll (1949) detailed the complexities of SP response in the case of limestone formations and more generally of permeable beds in highly resistive formations, e.g., permeable zones within evaporite zones or within low-porosity carbonates.

Estimation of permeability from empirical correlation One of the most generally-used empirical correlations to estimate permeability is porosity-permeability relationship. This correlation works best if there is only one pore type in the rock. For rock with only one pore type, the porosity-permeability crossplot will show a clear-cut relationship with little scatter. Additional pore types will enlarge the scatter and, therefore, enlarge the error bars of the resulting permeability estimate. The literature contains several references for estimation of permeability for hydrocarbon-bearing intergranular rocks at irreducible water saturation from log-derived

205 porosity and water saturation values (Wyllie and Rose, 1950; Morris and Biggs, 1967; Timur, 1968; Coates and Dumanoir, 1973). Non-intergranular rocks are not considered. Well logging service company chart books (e.g.,Atlas Wireline Services, 1989b; Halliburton Logging Services, Inc., 1991; Schlumberger Educational Services, 1991 a) contain graphical versions of these estimation methods (also see Chapter 7 in Vol. I of this book). Herron et al. (1991) described the application of geochemical logging mineralogy results to permeability estimation for a Middle East carbonate reservoir. The procedure incorporates porosity and a knowledge of whether a particular mineral will increase or decrease permeability (Herron, 1987). There is an inherent assumption here that the relationship between the rock's mineralogy and its texture is consistent and predictable. Fracture and vug detection

Fractured and extremely vuggy zones provide high-permeability pathways that can contribute to high well production rates. But, fractured and extremely vuggy zones are usually not beneficial for secondary or tertiary floods. They become thief zones taking expensive injectant fluids. Fracture porosity volume generally will be insignificant with respect to the total reservoir storage volume. A fracture system will generally contribute less than 1% bulk volume to the rock porosity (Hensel, 1989; Chapter 1, Part II of this book). A value of 1% bulk volume is typically within the accuracy of conventional porosity log measurements. Vuggy porosity can be significant with respect to the total reservoir storage volume. Fracture and vug detection from cores and sample examination Detection of fractures and vugs from core can be done qualitatively by examination. Or a more quantitative analysis can provide detailed geological information. The study of a fractured reservoir (Golf-Racht, 1982) must follow a special pattern, beginning with the examination of local basic characteristics of single fracture, only afterwards continuing with the examination of a multifracture system. In establishing the relationship among the various group of fractures, the local relationships are examined at reservoir scale by comparison, trends and extrapolation of parameters. Basic parameters obtained from an evaluation of fractures and the relationships between those parameters are shown in Fig. 4-11. Some core analysis techniques used for naturally-fractured reservoirs are listed in Table 4-XIV. Skopec et al. (1992) discussed procedures for the successful recovery of oriented horizontal core from highly-fractured carbonate rocks. The authors' specific objectives for this coring included formation evaluation and drilling reasons: efficient recovery of core sections, high core recovery rates, quality core material, accurate orientation data, comprehensive core analysis, and maintenance of borehole angle while coring. To accomplish these objectives in a horizontal situation, they had to develop or adapt equipment or procedures. The problem of frequent core jamming in the coring assembly was largely overcome by the use of flexible fiberglass inner barrels and multiple core-catcher assemblies. They achieved a recovery rate of almost 100% by using shorter core sections and improved inner- and outer-barrel stabilization. For

206

Single Fracture

Group of Fractures

--~

,, Distribution --~ Matrix Block Shapes

f

9Width ,, Size 9Nature

,, Orientation

, Density

-Intensity-

t.Nl Environment

I

I

l

(lithology) (morphology) Fig. 4-11. The basic parameters of fractures and their relationships are shown here. (After van GolfRacht, 1982).

orientation purposes, a slip scribe was used in conjunction with an electronic multishot instrument that uses an array of accelerometers for determination of inclination. This orientation instrument alleviated many of the problems that had been associated with camera surveys. To operate the electronic multishot instrument in a horizontal configuration, it was necessary to develop specialized equipment. Skopec et al. state that their newly designed rotatable non-magnetic blade centralizer, enhanced running gear, and a high frequency shock absorber were needed to be used to obtain accurate core orientation data. To ensure positive alignment of the orientation instruments and the TABLE 4-XIV Core analysis methods for naturally-fractured reservoirs (after Bergosh et al., 1985; Bergosh and Lord, 1987) Method

Comments

CT scanner

Sees through core containers Sees interior of core Can be done under stress

Computerized goniometer

Can determine orientation of each fracture Can segregate different fracture types Must differentiate natural from induced fractures

Full-diameter core analysis

More representative than analysis on core plugs Porosity and saturation measurements Multidimensional permeability measurements Can be done under stress

Fluorescent epoxy impregnation

Slabs viewed under UV light Fracture porosity determined Can be done under stress

207 coring assembly, a laser alignment system was invented and used successfully. Specialized horizontal core handling procedures were developed to ensure accurate core orientation data. It is obvious that these authors needed to go beyond using off-theshelf equipment to meet their coring objectives. Their efforts were successful because of their planning for and development and adaptation of procedures and equipment that would let them accomplish their objectives.

From well logs Well logs that most commonly provide fracture and vug detection and pertinent references are listed in Table 4-XV. These wireline logging tools fall into the general TABLE 4-XV Logs that can detect fractures and vugs Log type

Name of tool (reference)

Company*

Acoustic waveform

Array Sonic (Morris et al., 1984) Digital Array Acoustilog (Atlas Wireline Services, 1990) EVA Full Wave Tool (Fortin et al., 1991) Full Wave Sonic (Welex, 1986)

Schlumberger

Diplog/dipmeter

Electrical array

Pulsed acoustic

Video camera

Fracture Identification Log (Brown, 1978) High Resolution 4- or 6-Arm Diplog (Atlas Wireline Services, 1988) Six Arm Dipmeter (Goetz et al., 1986) Stratigraphic High Resolution Dipmeter (Chauvel et al., 1984) Formation Microlmager (Safinya et al., 1991) Formation MicroScanner (Ekstrom et al., 1986)

Atlas Elf Aq., CGG Halliburton Schlumberger Atlas Halliburton Schlumberger Schlumberger Schlumberger

Borehole Televiewer (Zemanek et al., 1969) Borehole Televiewer Tool (Schlumberger Educational Services, 1991b, p. 48) Circumferential Acoustic Scanning Tool (Torres et al., 1990) Circumferential Borehole Imaging Log (Faraguna et al., 1989)

generic

Video Camera (Briggs, 1964) Time Delay Video System (Offshore, 1992, p. 37)

generic

Schlumberger Halliburton Atlas

Hitwell

* Company names mentioned in this chapter are for reference only and are not meant as an endorsement of any particular company or tool.

208 categories of acoustic waveform logs, diplogs/dipmeters, and imaging logs. Imaging logs are of three different types: electrical array, pulsed acoustic, and video camera. The Society of Professional Well Log Analysts Reprint Volume on Borehole Imaging (1990) provides a comprehensive reference set for these imaging logs. Acoustic waveform logs digitally acquire full acoustic wave data, the amplitude vs. time information from each acoustic receiver on the tool. The waveforms can provide velocity and attenuation information on compressional, shear, mud, and tube waves. Fracture and vug detection from attenuation of compressional wave amplitudes (Tixier et al., 1959) and from attenuation of shear wave amplitudes (Pickett, 1963) was noted early in the life of the acoustic log. Other references (Anderson and Walker, 1961; Morris et al., 1964) looked at the physics behind this log response. Many other acoustic waveform fracture detection techniques are discussed by Crary et al. (1987), including compressional amplitude spike analysis, X-Z waveform crisscross analysis, Stoneley wave attenuation, Stoneley reflected-to-incident energy ratio, and slowness differences of compressional, shear, and Stoneley velocities between two equally-spaced but offset transmitter-receiver pairs. Qualitative and quantitative interpretation of fracture permeability, derived from empirical correlation of acoustic waveform log tube wave data to measured fracture permeability, is discussed by Paillet (1991). Use of the diplog/dipmeter for fracture detection has been documented for West Texas Ellenburger dolomites, the South Texas Austin Chalk formation, and North Louisiana and Mississippi Cretaceous limestones (Brown, 1978). Fractures filled with water-based drilling mud show up as conductive response on any diplog/dipmeter pad that traverses the fracture. Conductive response on one or more of the pads can be interpreted as a fracture. A special curve presentation of the dipmeter log which permitted easier identification of fractured zones was named the Fracture Identification Log. The Formation MicroScanner was originated as a multi-electrode electrical array on one pad of a dipmeter, providing a resistivity image of approximately 10% circumferential coverage (depending on hole size) of the borehole. The tool was later upgraded to place electrical arrays on two and then four pads, ending up with about 40% circumferential coverage of the borehole. The Formation Microlmager was introduced as a replacement to the original resistivity imaging tool. Each of its four fixed array pads has a flip-out array pad extending to the side, which increases the coverage to about 80% of the borehole circumference. Serra (1989) provided a detailed interpretation reference for these resistivity imaging tools. A Formation Microlmager produces an image related to electrical resistivity measurements. A core or core photo produces an image of reflected light. Formations and borehole features may reflect light in a manner that is not representative of their electrical resistivities. One must be thinking in terms of electrical resistivity when looking at a Formation Microlmager image, or else an erroneous interpretation may result. The borehole televiewer tool is a pulsed acoustic logging device. The acoustic wave originates at the tool's acoustic transducer, progresses to the borehole wall, reflects off the borehole wall, and is received back at the transducer. The acoustic transducer is continuously rotated to provide complete circumferential, i.e., helical, borehole coverage as the tool is pulled up the borehole by the wireline. Two images are derived from the acoustic wave received back at the transducer: one from the first

209 arrival waveform amplitude and one from the waveform two-way time of flight. The amplitude image mainly represents the acoustic impedance (product of density and acoustic velocity) of the formation-however, the tool decentralization and the acoustic attenuation of the mud column can have significant effect. The time of flight image mainly represents subtle borehole irregularities such as vugs, fractures, and washouts -however, again the lack of tool centralization can have significant effect. If a geological feature is small, like the width of a fracture might be, it is possible that it might be plugged with drilling mud solids and might not have enough acoustic impedance contrast to be visible on a borehole televiewer log. The idea of volumetric scanning well logging from an pulsed acoustic tool (Broding, 1982) allows insight into not only features at the borehole wall, but features away from the borehole wall as long as that feature has an acoustic impedance contrast with the rock nearer the borehole wall. Rambow (1984) showed many geologically interesting examples of borehole televiewer logs. The use of a borehole televiewer for vug detection to optimize completions in a carbonate waterflood has been documented (Clerke and Van Akkeren, 1986). Massively vuggy zones acted as thief zones in a waterflood and degraded the waterflood performance if they were open to the borehole by perforations. A borehole televiewer produces an image related to acoustic impedance measurements. A core or core photo produces an image of reflected light. Formations and borehole features may reflect light in a manner that is not representative of their acoustic impedances. One must be thinking in terms of acoustic impedance when looking at a borehole televiewer image, or else an erroneous interpretation may result. Video camera logging technology is usually limited by the opaque borehole fluid. Openhole formation evaluation applications have got around this limitation by putting a clear fluid bubble in front of the camera lens (Mullins, 1966). Cased hole video camera logging can be done in a borehole containing clear fluid, but cased hole applications are usually for determining the mechanical configuration of the casing and other tubulars, not for formation evaluation. One cased hole formation evaluation application is the monitoring of the perforations for type of fluid production, e.g., oil vs. water. Crary et al. (1987) pointed out that all of these well logging fracture detection methods can, at times, mistake other geological features (such as thin soft beds and bed boundaries) and drilling features (such as washouts, induced fractures, and drill string damage) for natural fractures. They also discussed other much less useful and more ambiguous well logging fracture detection methods including resistivity log apparent invasion profiles, spectral density log response if the tool pad crosses a fracture, spectral natural gamma ray detection of uranium salts deposited on fracture faces, and spontaneous potential electrokinetic (sometimes called streaming) potential. Non-touching vug detection is possible using a comparison of acoustic log porosity with porosity derived from a density and/or neutron log. The acoustic log tends not to see the vuggy porosity until it becomes the dominant pore type, whereas the density and neutron logs see the total porosity. Traugott (1970) showed an example of detection of non-touching vugs using an acoustic log comparison to neutron log porosity. Traugott used increased vug porosity to determine the Archie' s (1942) lithologic exponent for his water saturation calculation.

210

From well testing Indications of vugs and fractures can be obtained from pressure transient analyses. Matthews and Russell (1967) and Cinco-Ley and Samaniego-V. (1981) discussed the analysis of fractured formations. Gringarten (1984) summarized analysis of reservoirs with double-porosity behavior, including both naturally-fissured reservoirs and multilayered reservoirs with high permeability contrast between layers, e.g., vuggy vs. intercrystalline porosity layers. From drilling procedures Flow from fractured zones can be detected during underbalanced drilling or while using gas as a drilling fluid. The Austin Chalk trend in Texas requires wellbores to intersect fractures to produce oil at commercial rates. Many times, a well will begin flowing when a fracture is encountered and the well may need to be put on choke to control the well while drilling proceeds. The Ellenburger Group, also in Texas, produces gas from brecciated layers within a very thick, predominantly low-porosity and low-permeability dolomite. Some of the Ellenburger wells in the J.M. Field have been drilled using produced gas from nearby wells as the drilling fluid. The drilling gas is flowed through the rig circulation system at rates up to six million cubic feet per day. The return drilling gas is flared at a safe location away from the rig. When a permeable (brecciated) gas-productive zone is encountered, the flare size increases. Drilling gas flow is then ceased and the formation gas production rate is measured. NET FORMATION THICKNESS DETERMINATION

The following definitions of depth and thickness are adapted from the Society of Professional Well Log Analysts (1984):

Measured depth (MD): Depth measured along the drilled hole. It is reported in drilling records, measured by wireline-logging cables, and shown on well logs. This depth has not been corrected for hole deviation. True vertical depth (TVD): The vertical distance between a specific location in a borehole and a horizontal plane passing through the depth datum. It is determined from directional surveys. True bed thickness (sometimes called true stratigraphic thickness): The thickness of the stratigraphic unit measured along a line normal to the direction of extension of the unit. True thickness can be derived from information determined by the dipmeter. Apparent bed thickness (sometimes called measured thickness)" Corresponds to the distance the borehole remains in the bed. The borehole may not have penetrated the bed normal to its upper or lower boundary surface because of hole deviation and formation dip. True vertical thickness: The thickness of the stratigraphic unit measured along a vertical line. True vertical thickness can be derived from information determined by the dipmeter. These thickness definitions relate to the gross formation thickness, i.e., the total thickness of the formation between its upper and lower boundary. Net formation

211 TABLE 4-XVI Methods for determination of net apparent formation thickness Tool

Concerns

Wireline logs MWD logs Mud log penetration rate Mud log cuttings Core

Usually most accurate method, except in thin beds Need accurate data acquisition time to drilling depth correlation Penetration rate can be related to net formation properties Cuttings location smears during circulation to surface Most accurate method in thin beds; missing core not considered

thickness is the thickness of the permeable rock layers in that formation which can contribute to production. Hydrocarbon productive net formation thickness, sometimes called pay thickness, is a subset of net formation thickness. Methods for determination of net apparent formation thickness are listed in Table 4-XVI. Bed boundary determination and zoning can be done from well logs. A simple approach would be to manually select bed boundaries at inflection points on log curves. A more sophisticated approach would be to use a forward modeling or deconvolution program. This approach has the potential to provide a more accurate bed thickness determination and has the added result of providing a log value for the zone. Serra (1986, Volume II, Chapter 5) related the facies as seen by a well log to the rock facies. He defined the term electrofacies as the set of log responses which characterizes a bed and permits it to be distinguished from the others. Electrofacies are observed to have certain well log shapes. A ramp-shaped log response is termed an electrosequence. An electrosequence is indicative of a geologic change. Serra noted that the ramp may reflect: (1) a progressive change in mineralogical composition with depth; (2) the evolution of a textural parameter; (3) a simultaneous variation in mineralogical composition and in texture; or (4) a saturation transition between water and hydrocarbons. Bed boundary determination should consider all of the geological and petrophysical changes in the rock and fluid sequence. As discussed in earlier sections of this chapter, well logs respond predictably to changes in lithology, porosity, pore fluid saturations, and pore fluid properties. Thus, zoning can be made directly dependent upon changes in these properties. However, well logs do not respond proportionally to permeability magnitude, unless there is a relationship between permeability and one of the other properties. Thus, well log bed boundary determination based on changes in permeability needs to be calibrated, preferably to core data. There are resolution considerations in the determination of net formation thickness. Whereas wireline logs usually provide the most accurate zone thickness values, they do have a finite resolution. If the net productive layers in the formation are thinner than the resolution of the logging tool, then the log cannot provide adequate thickness determination. Cores can show the layering with the finest resolution, if sufficient core recovery is obtained. Geological inspection provides detailed bed boundary information. Digital core image analysis can be used to distinguish layering on a millimeter-by-millimeter basis by color differentiation (Georgi et al., 1992). Core images presented on the same scale as log data can be used to calibrate and supplement

212 wireline logs. Bed boundary locations derived from core image analysis can be used with forward modeling to evaluate thin-bed well log response. In addition, highresolution mini-permeametry data can be used to distinguish permeable from nonpermeable layers to calibrate the image analysis and well logs. Georgi et al. (1992) reported image analysis and mini-permeameter applications for sand-shale cores. The methodologies will work for carbonates as long as there is color and permeability contrast between different geological layers. In cases where the well encounters hydrocarbons, but does not penetrate the hydrocarbon-water contact (sometimes called the water level), it is beneficial to determine the true vertical depth of the water level to be able to make representative reserve calculations and subsequent drilling well location selection. The term water level can have one of three different meanings depending on the context. Table 4XVII lists these definitions. The distance between these water levels is less than a meter for very good quality rocks, i.e., darcy magnitude permeability, but can be several tens of meters or more for moderate to low quality rocks. Determination of the reservoir free water level from one well penetration, which does not encounter the free water level, is possible (Roach, 1963, using pressure gradients; Smith, 1990, using capillary pressure properties), but rock and fluid properties of the reservoir must first be known. TABLE 4-XVII Reservoir water level definitions Water level

Definition

Producing water level

Shallowest of the three water levels; level above which a near water-free completion can be made; determined from production tests or from fractional water flow calculations.

100% water level

Level with 100% water saturation just below and positive hydrocarbon saturation just above; determined from core fluid saturation data, from log water saturation calculations, or from the equivalent depth of the capillary pressure extrapolated displacement pressure.

Free water level

Deepest of the three water levels; level at which competition between capillary and buoyancy forces begins in the reservoir; determined from intersection of water and hydrocarbon fluid pressure gradients from multiple wireline pressure tests, or from the equivalent depth of zero capillary pressure.

STRUCTURAL AND STRATIGRAPHIC DETERMINATION

Serra (1986) defined structure, a megascopic feature of a rock mass or rock unit, as the general disposition, attitude, arrangement, or relative positions of the rock masses of a region or area. Serra (1986) defined stratigraphy as the arrangement of rock strata, concerned with all characters and attributes of rocks (succession, age, form, distribution, composition, fossil content, geophysical and geochemical properties). Keep in mind that evaluation tools that limit data acquisition to the borehole or near~ borehole region (logging tools, cores, etc.) are seeing a limited volume and may not be representative perspective of the formation structure and stratigraphy. Evaluation

213 tools that acquire data well beyond the borehole (seismic, geotomography, etc.) will see a more megascopic picture, but will probably miss the more subtle structural and stratigraphic features. Structural and stratigraphic information is obviously available from examination of rock. Whole core can provide much insight if the in-situ orientation of the core is known. Davison and Haszeldine (1984) provided a review of four simple techniques, listed in Table 4-XVIII, that are used to orient conventional cores back to their in-situ position. Carver (1971) discussed details of the measurement of stratification orientation and the mathematical treatment of orientation data. Information can also be obtained from cuttings and sidewall cores. Cuttings and sidewall cores are of limited size and cannot provide as continuous information as whole core can. In addition, the use of cuttings suffers from problems with exact depth correlation. TABLE 4-XVIII Methods for orienting conventional cores back to their in-situ position (Davison and Haszeldine, 1984) Method

Comments

Oriented core barrels Dipmeter* Highly deviated wellst Paleomagnetic

Can be used on any rock type sequence Must be recognizable structural plane Use directional survey in conjunction with regional dip knowledge Origin and age of remanent magnetism component must be identified

* Imaging logs could be used today, and would provide better accuracy than a dipmeter because of their increased circumferential coverage. t Skopec et al. (1992) discussed the successful recovery and orientation of core from highly-fractured carbonates in horizontal wells, using an oriented core barrel.

Serra (1986, Volume II) provided comprehensive insight into the use of all types of well log data for structural (Chapter 4) and stratigraphic (Chapter 13) determination, and also for other geological uses. Serra detailed the use of well logs run in multiple boreholes providing geographical distribution. A list of well logs that provide structural and stratigraphic information from only a single borehole and the pertinent references is found in Table 4-XIX. Of all the tool types on this list, the diplog/dipmeter tools have the most history behind them (Schlumberger et al., 1933), although several somewhat different tool designs have been used over time. Digitally recorded magnetic tape data allowed for automatic computation of dipmeter logs (Moran et al., 1962). Early dipmeter interpretation techniques (Gilreath and Maricelli, 1964) utilized what was then high-density computations to define depositional and structural features. Machine computations of dipmeter surveys, with dips computed as frequently as three per meter (one per foot), were very crude by today's standards. Inasmuch as these tools are microresistivity logs, diplog/dipmeter tools can be easily run in water-based drilling mud. Special modifications have been made for these tools to be run in non-conductive oil-based mud or air-filled boreholes (e.g., Fons, 1966). Today, processing of diplog/dipmeter data can be done manually from paper log copies (consultants still advertize this service) or by computer processing using magnetic tape data (by a service company or by using commercially available software). Processing parameters and criteria depend on which geological features are important to the interpretation. Serra (1985),

214 TABLE 4-XIX Logs that can provide structural and stratigraphic information from a single borehole Log type

Name of tool (reference)

Service company*

Diplog/dipmeter

HighResolution 4- or 6-Arm Diplog (Atlas Wireline Services, 1988) Six-Arm Dipmeter (Goetz et al., 1986) Stratigraphic High Resolution Dipmeter (Chauvel et al, 1984) FormationMicrolmager (Safinya et al., 1991) Formation MicroScanner (Ekstrom et al., 1986) Azimuthal Resistivity Imager (Davies et al., 1992) Vertical Seismic Profile (Johnston and Markowitz, 1992) Array Sonic (Morris et al., 1984) Digital Array Acoustilog (Atlas Wireline Services, 1990) EVA Full Wave Tool (Fortin et al., 1991) Full Wave Sonic (Welex, 1986) Borehole Televiewer (Zemanek et al., 1969) Circumferential Acoustic Scanning Tool (Torres et al., 1990) Circumferential Borehole Imaging Log (Faraguna et al., 1989) Borehole Televiewer Tool (Schlumberger Educational Services, 199 l b, p. 48) Video Camera (Briggs, 1964) Time Delay Video System (Offshore, 1992, p. 37)

Atlas

Electrical array

Acoustic

Pulsed acoustic

Video

Halliburton Schlumberger Schlumberger Schlumberger Schlumberger generic Schlumberger Atlas Elf Aq., CGG Halliburton generic Halliburton Atlas Schlumberger generic Hitwell

* Service company names mentioned in this chapter are for reference only and are not meant as an endorsement of any particular company or tool. Schlumberger Limited (1986), and Atlas Wireline Services (1988) provide much insight into the interpretation of data from these tools. The diplog/dipmeter multiple independent pad (four or six) configuration also provides for a detailed caliper log of the borehole. Formation Microlmager and Formation MicroScanner tools have been discussed earlier in this chapter. Formation MicroScanner and Formation Microlmager image features can be segregated into geologically significant categories, e.g., fractures, bed boundaries, faults, unconformities, and cross bedding, using interactive workstations (Boyeldieu and Jeffreys, 1988) to aid in structural and stratigraphic interpretation.

215 Inasmuch as these tools are essentially sophisticated versions of the diplog/dipmeter tools, it is probable that resistivity imaging tools eventually will completely replace the diplog/dipmeter tools. Azimuthal Resistivity Imaging tools can provide structural and stratigraphic information, but at a resolution larger than that of the Formation MicroImager tools (Davies et al., 1992). An array of twelve azimuthal electrodes is incorporated into a dual laterolog array so as to provide twelve deep, oriented resistivity measurements while retaining the standard deep and shallow laterolog measurements. Though the fullcoverage azimuthal resistivity image has much lower spatial resolution than borehole microelectrical images, it complements these because of its lower sensitivity to shallow features such as borehole rugosity and washouts. Borehole televiewer tools have been discussed earlier in this chapter. The acoustic picture of the borehole wall provided by these pulsed acoustic tools can show the layering, fractures, vugs, etc., of the formation to provide structural and stratigraphic information, provided there is acoustic impedance contrast between these geological features and the background. Full-wave acoustic logs have been used to provide acoustic reflective imaging around a wellbore. Fortin et al. (1991) documented the imaging range to reach about 7 m (23 ft) away from the borehole. Hornby (1989) extended the imaging range to about 18 m (60 ft) away from the borehole. Vertical seismic profile (VSP) surveys have been used to provide high resolution imaging of features away from the borehole (Johnston and Markowitz, 1992). For acoustic reflective and VSP methods to be effective, the structural and/or stratigraphic features of interest must have acoustic impedance contrast with their adjacent features. Structural and stratigraphic information from these types of intermediate depth-of-investigation tools can provide a tie between information limited to or near to the borehole, e.g., from Formation MicroImager or diplog/dipmeter, and information from far away from the borehole, e.g., from seismic or geotomography. Seismic can provide information concerning structural and stratigraphic changes without the need of a borehole. Some pertinent references include Ausburn et al. (1977) for general seismic applications to formation evaluation, Ausburn (1979) for well log editing to improve seismic calibration, and Brown (1986) for 3-D seismic applications. In general, the use of seismic in carbonates is limited to structural and stratigraphic determination (see Chapter 2, Vol.II). Geotomography, i.e., cross-well tomography as shown in Fig. 4-12, can provide information concerning structural and stratigraphic changes between wellbores. A contrast, electromagnetic or acoustic impedance, between the layers of interest is needed. Resolution is no better than the minimum of the spacing between the transmitters within one wellbore or the spacing between the receivers within the other wellbore (Dines and Lytle, 1979, for electromagnetic tomography; Worthington, 1984, for acoustic tomography; Kretzschmar and Witterholt, 1984, for historical background and EOR surveillance in pilots). Distance between wellbores is limited to about 3060 m (100-200 fl) for electromagnetic tomography, and about 300--600 m (10002000 ft) for acoustic tomography. An integrated formation evaluation approach to the determination of stratigraphy can contribute significant insight into a reservoir model (Kern and Schepel, 1991).

216 Kern and Schepel described a multi-specialty team effort that interpreted 720 km (450 miles) of seismic, examined 1800 m (6000 ft) of core, correlated over 50 wells with modem openhole logs, and used petrographic analysis to develop a sequence stratigraphic-based reservoir model of a carbonate formation. The seismic data were interpreted to determine the sequence boundaries (relative sea level drops) and then tied to regional well log cross sections using synthetic seismograms. Core description emphasized recognition of depositional facies, shallowing upward depositional cycles, and depositional cycle stacking patterns. Epifluorescence petrographic examination techniques were used to determine facies and pore types of altered dolomites, and isotopic data and thin section descriptions were used to determine the diagenetic history of the dolomite. For the reservoir studied, porosity was primary and was clearly linked to facies types which were controlled by water depth. Sequence stratigraphic analysis allowed prediction of paleo water depth. Thus, for CO 2 flood optimization, completions based on sequence stratigraphic correlation will improve flood conformity by ensuring that wells are completed considering paleo water depth (or porosity) continuity. The authors felt that the results of the study will facilitate continued infill drilling, fieldwide projects to add pay and deepen wells, and subsurface mapping of reservoir flow units. The results will also aid in flood prediction, surveillance, and overall reservoir management.

PROPAGATION OF ERROR CONSIDERATIONS

In any calculation or determination, errors in the input parameters propagate through to the result. In formation evaluation situations potentially involving the spending of a large amount of money, it is prudent to know the magnitude of the error in the evaluation results and their effect on the economic results. Two methods are generally used to determine errors: partial differential error equations and Monte Carlo iterative method. The confidence level of the input error values, e.g., one standard deviation, becomes the confidence level of the propagated error. The partial differential equation technique uses the standard error equation. For the function X = f(A, B, C, D, E, F), the error equation is of the form:

(4-31) where: X AX A

.,. ,,,

= = = =

dependent variable being solved for as the result; most probable error in the result; independent variables, i.e., input parameters to the function; and errors in the independent variables or input parameters to the function.

One advantage of use of the error equation is that it provides information about the magnitude of individual parameter contributions to the error in the result. However, there are three main assumptions that must be met for valid use of the error equation:

217

Ground level One borehole contains transmitters, the other contains receivers.

I1 Wellbore 1

11 1

receiver spacing

Wellbore 2

Fig. 4-12. Geotomography (electromagnetic or acoustic) ray paths between transmitters in one wellbore and receivers in another wellbore. Layering that has contrast (electromagnetic or acoustic) can be differentiated. (1) input variables must be independent; (2) errors must be small; and (3) errors must be normally distributed. The Monte Carlo iterative technique requires a computer program to do hundreds or thousands of iterations. The technique uses probability distribution functions for each input variable. Randomly selected input values from each input distribution function are used to calculate results. The iterations provide an output probability distribution function for the result. Some economic risk analysis programs, e.g., @RISK (Palisade Corporation*, 1991), can easily be adapted to error analysis of technical computations. Programs of this type allow specified dependences between input variables. Examples of the propagation of error through to formation evaluation results are shown in Figs. 4-13 and 4-14, for a version of the previously discussedArchie's (1942) water saturation calculation equation: ! S w "- ( B R w / R t ~ m ) n (4-32) One graph, Fig. 4-13, shows the effect of small input errors. These small errors are about the best-case scenario. The other, Fig. 4-14, shows the effect of moderate input errors. These moderate errors are about the normal-case scenario. The graphs have plotted the most probable error in water saturation (% P V) as a function of the water *Company names mentioned in this chapter are for reference only and are not meant as an endorsement of any particular company or product.

218

Propagation of Small Error in Archie's Equation 0

.

.

.

.

.

15

Input Parameter Errors

10 . . . . . . . . . . . . . . . . . . . . . . . . . . .

a

Saturation Error (% PV) i

= 1.O_+O.O1

Rw = 0.1 _+0.002 ~'2-m 0

1

.

.

_

~

/

/

/

~

.

-15

-20 0

R!t = varies 5%% BV 20.0 4"-+ 1.0 = 2.0 -!- 0.05

j =2.0_+005

, , , , , , , , , 10 20 30 4 0 50 6 0 70 80 9 0 100 Water Saturation (% PV)

Fig. 4-13. The effect of small input errors (tabulated above) onArchie's (1942) water saturation calculations. The error increases as water saturation increases.

Propagation of Moderate Error in Archie's Equation

0

15 10 . Saturation Error (% PV)

-

-

InDut Parameter Errors

.

.

. .

20~ 0

.

.

. .

.

.

.

.

.

B Rw Rt (~ m n

= 1.0_+0.05 = 0.1 _+ 0.005 ~-2-m varies _+ 5% = 20.0 _+ 2.0 % B V = 2.0+0.1 = 2.0-+0.5

, , . , . , , , , 10 2 0 3 0 4 0 50 6 0 70 80 90 100 Water Saturation (% PV)

Fig. 4-14. The effect of moderate input errors (tabulated above) on Archie's (1942) water saturation calculations. The error increases as water saturation increases.

saturation (% P V) itself. The water saturation is changed by changing the true resistivity value. The error varies with the water saturation determined, and the error is largest for high water saturations (low hydrocarbon saturations). At 95% calculated water saturation, the results are 95% +7% for the small error case and 95% • 12% for the moderate error case. In either case, from log calculations only it is not possible to tell if a 95% calculated water saturation is really 95% water saturation (5% hydrocarbon saturation) or if it is really 100% water saturation (no hydrocarbons) and within

219 error bars. To come to an unambiguous conclusion, one would have to augment the log calculation with other data, e.g., hydrocarbon show information from a mud log. Of course, the error propagated through to the result can be reduced by decreasing the number of input parameters in the petrophysical model. Input parameter reduction can be attained by using a different (but still appropriate) petrophysical model or by determining several parameter values in a simultaneous dependent method. For example, the Pickett plot (Pickett, 1966) allows simultaneous determination o f R w and m (and B if included in the model) from the position of the R0 line through the water points (see Fig. 4-1). Changes in R w simultaneously change m. In this case, the interdependence of these parameters will substantially reduce the error propagated through to the resulting water saturation calculation because Archie's (1942) equation reduces to:

( R~ Sw=\Rt)

(4-33)

The resulting error in S using a Pickett plot for R wand m can be much smaller than if the variables were truly independent as in the case when R wis from a produced water sample and m is from core analysis (R.J. Conser, personal communication, 1992). Additional examples of the propagation of error through to formation evaluation results are shown in Fig. 4-15 and Fig. 4-16, for the previously discussed pulsed neutron capture log water saturation calculation:

S

--

"~---~lo--g (1 -

q~)Z~matrix

r

-

--

"~hydrocarbon r

Z~

(4-19)

"~hydrocarbon)

The errors are calculated for a resulting water saturation of 50%. One graph, Fig. 415, shows the effect of small input errors. These small errors are about the best-case

Propagation of Small Error in PNC Sw Equation Inout Parameter Errors ~oil = ~water = ~-~natrix = X;Iog t~ A = Sw =

Saturation 1 Error

(% PV) _ l

-40 ~ 0

!

|

|

|

10

20

30

40

22 + 0.25 cu 125 4- 1 cu 7 4- 0.25 cu varies 4- 0.25 cu varies + 1 % BV 0 4- 0.25 cu 50 % PV

50

Porosity (% BV) Fig. 4-15. The effect of small input errors (tabulated above) on pulsed neutron capture log water saturation calculations. The resulting water saturation is fifty percent of the pore volume. The error increases as porosity decreases. In this case, formation water is saturated (salinity). Fresher formation waters would add more error to the resulting water saturation calculation.

220

Propagation of Moderate Error in PNC Sw Equation 40 30 20

Inout Parameter Errors

................

~oil ~--,water ~matrix ~log t~ A Sw

Saturation Error (% PV) m

~30 -40

. 0

I0

20

.

. 30

.

. , 40

= 22 __ 0.5 cu = 125 + 2 cu = 7 -t- 0.5 cu varies + 1.0 cu varies __+2 % BV = 0 + 0.5 cu = 50 % PV

50

Porosity (% BV) Fig. 4-16. The effect of moderate input errors (tabulated above) on pulsed neutron capture log water saturation calculations. The resulting water saturation is fifty percent of the pore volume. The error increases as porosity decreases. In this case, formation water is saturated (salinity). Fresher formation waters would add more error to the resulting water saturation calculation.

scenario. The other, Fig. 4-16, shows the effect of moderate input errors. These moderate errors are about the normal-case scenario. The graphs have plotted the most probable error in water saturation (% PV) as a function of the porosity (% B ~ . The error is largest for low porosities. Also, inasmuch as in this case the formation water is saturated (salinity), fresher formation waters would add more error to the resulting water saturation calculation.

SUMMARY

This chapter was written to provide a fairly detailed overview of carbonate formation evaluation. The best approach to formation evaluation of carbonates, or any other rock type, is to first and foremost understand the petrophysics of the rock. If the formation evaluator understands the petrophysics of the rock, he or she can understand the response of the various evaluation tools to that rock, and can then best predict pertinent rock and fluid properties and the performance of the formation. Starting with the evaluation tool response without considering the rock can lead to ambiguous results.

ACKNOWLEDGMENTS

The author wishes to thank Shell Oil Company for permission to contribute this chapter. Two skilled Shell Oil Company petrophysical engineering instructors, E.C. Thomas and the late Charles L. Rabe, provided the definitions associated with the term petrophysics. Justin Freeman of Shell Development provided the error equations

221

for the pulsed neutron capture error graphs. The author appreciates the guidance and insight provided by other exploration and production instructors at Shell Oil Company's Head Office Training, concerning the application of their technical specialty areas to formation evaluation. James R. Jorden, Shell Oil Company Manager of Continuous Performance Improvement Training and also a skilled petrophysical engineer, has been and still is a valued discussion partner on many aspects ofpetrophysics and formation evaluation. Thanks go to the staff members of the library at Shell Development Company's Bellaire Research Center: Carmen Miller, Jeff Pharis, Mary Estrada, Sean Williams, Shirley Purcell, and Carla Rhone, who were able to find references in a very timely manner. The author also wishes to thank Lavelle Zander of Shell Oil Company's Head Office Production Training for her assistance in copying additional references. Finally, the author appreciates the review of this chapter by E.C. Thomas and James R. Jorden. Acknowledgment is made to the following publishers, service companies and professional societies for permission to reproduce material from their publications: Elsevier Scientific Publishing Company; Halliburton Logging Services, Inc.; Reservoirs, Inc.; Schlumberger Educational Services; and the Society of Professional Well Log Analysts.

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231

Chapter 5 PERFORMANCE AND CLASSIFICATION OF CARBONATE RESERVOIRS HERMAN H. RIEKE, III, GEORGE V. CHILINGARIAN, AND S.J. MAZZULLO

INTRODUCTION

A chapter on hydrocarbon recovery should bring together the technical insights presented in two volumes of this book to serve as a guide for operators. The objective of presenting a potpourri of technology provides a knowledge base for characterizing the reservoir's anisotropic and/or heterogenetic nature with respect to its producing capabilities. This knowledge is implemented by employing an effective field development strategy. Recoveries from reservoirs using conventional technology range from about 10-50% of the original mobile oil in place for most carbonate reservoirs as compared to 5-80% for clastic reservoirs. Over 100 billion barrels of light oil (>20 ~ API) exist in United States carbonate reservoirs as a potentially recoverable resource (Nuckols, 1992). The shallow-shelf class of carbonate reservoirs contains about 68 billion barrels of this original oil-in-place (Fig. 5-1). The remaining 22 billion barrels of original oil-in-place are in reefs, peritidal, slope-basin, and shelf-margin reservoir classes. Table 5-I shows the magnitude of the original light oil-in-place resource in the United States for shallow-shelf carbonate reservoirs. Far greater reserves

Proved Reserves 3.7 Billion Bbl

(s.s%)

Original Oil-In-Place = 68.0 Billion Bbl Fig. 5-1. Status of the original oil-in-place (>20 ~ API) for selected shallow-shelf carbonate reservoirs located in the United States. (After Nuckols, 1992; courtesy of the U.S. Department of Energy.)

232 TABLE 5-1 Magnitude of the resource base of the original oil-in-place in United States carbonate reservoirs 9 Over 100 billion barrels, nearly 1/3 of the U.S. light (>20 ~API) OOIE are from the 6 DOE carbonate reservoir classes (peritidal, shallow-shelf/restricted, shallow-shelf/open, shelf margin, reefs and slopebasin). 9 The combined shallow-shelf carbonate classes (total of 382 carbonate reservoirs) contained about 68 billion barrels (over two-thirds) of the carbonate OOIE - Shallow-shelf/open - 43 billion barrels - Shallow-shelf/restricted = 25 billion barrels 9 The remaining 32 billion barrels of carbonate OOIP resides in the remaining classes. Source: Information is from the Tertiary Oil Recovery Information System (TORIS) database, maintained by the U.S. Department of Energy, Bartlesville Project Office, Bartlesville, Oklahoma, U.S.A. The database contains data on 67% of the U.S. original oil-in-place resource (modified after Nuckols, 1992).

lie to be tapped in the Middle East in similar geological settings. Shallow-shelf carbonate reservoirs are the reserve targets that the writers will focus on in this chapter owing to their great production potential. The operational and development goals of a producer are to recover a maximum of reserves with a minimum number of wells. Such goals demand that there be a reservoir management plan in place. It is not a goal of Chapter 5 to show how to develop such a detailed plan, but rather to encourage thinking about the consequences of technical actions that affect reservoir management. A reservoir management plan needs to address the following practical questions: (1) Are the geology and engineering properties of the reservoir accurately defined? (2) What is the optimum number of wells to be drilled? (3) Are infill or enhanced recovery wells necessary? (4) Where should the wells be located? (5) What types of wells should be drilled: vertical, directional, or horizontal? (6) How should the wells be completed? (7) How will recoveries be optimized? (8) Will pressure maintenance be needed, and when? (9) When will enhanced recovery be needed? (10) How much will this all cost? The ensuing technical discussion and presented strategies are necessary in helping to formulate possible answers to some of the above-mentioned questions.

TECHNICAL OVERVIEW

Large and small oil and gas companies alike are conducting ongoing, interdisciplinary studies of reservoir characterization and analysis of production performance. Application of petrophysics, fluid flow behavior, formation evaluation, well-testing, and reserve estimation disciplines to carbonate reservoirs were presented in the other chapters of this two-volume book. That what remains is to apply this knowledge to carbonate reservoir classification schemes and production practices so that more

233 accurate and reliable predictions can be made of the reservoir's productive potential and performance. Production strategies can be formulated to recover additional uncontacted and bypassed mobile oil and gas from these reservoirs. An early attempt was made by Craze (1962) to relate well spacing, withdrawal rates, and general field development plans to ultimate performance and recovery in carbonate reservoirs. Rieke et al. (1972) also addressed the problems that arise in the development and production of carbonate reservoirs owing to their unique characteristics. Chilingar et al. (1967) noted that the complex carbonate depositional environments and post-depositional diagenetic alterations of the rock fabric, such as dolomitization, make it difficult for independent operators to acquire geologic information applicable to reservoir characterization. Data concerning many reservoirs that are already depleted or nearing depletion, which could be used as valuable case histories, represent lost knowledge. Many of these reservoirs were in their prime before the 1930s when pressure measurements and rock and fluid sampling techniques were not routinely used by the producers. Early on, Bulnes and Fitting (1945) discussed the problems associated with reservoir performance in limestones. Accurate gas/oil ratios and water/oil ratios were not available from producers because the operator only could estimate, at best, gas and water production. This lack of knowledge and paucity of data, concerning the heterogeneous nature of the geological and engineering properties of these reservoirs, needs rectifying. Worldwide economic conditions affecting oil and gas operations have changed drastically since 1982, and, therefore, require a focused attention to present-day production practices and economics. The rationale for characterizing reservoir heterogeneities is economics in that optimization of ultimate recovery occurs at a minimum cost for both major and independent producers. To increase the recoverable reserves on a reservoir, or on a well-by-well, basis is probably the least expensive way of building a reserve base. This development strategy is important in managing the production of oil and gas from carbonate reservoirs. The recognition of fluid flow barriers and their avoidance are the keys to optimizing both primary and enhanced production. Not all the problems associated with predicting carbonate reservoir performance are due to meager knowledge of the subject or economic conditions. For example, one problem is the use of the concept of reservoir analogy, which is used to predict reserves, reservoir characteristics, and future recoveries by comparison with other reservoirs. Although it can be a powerful tool in the hands of the experienced estimator for sandstone reservoirs, it carries a high risk when applied to carbonate reservoirs, because of unpredictable microscopic and megascopic variations in reservoir properties from one reservoir to another. The analog approach assumes that reservoirs with similar geological and fluid characteristics will have similar performances. The application to carbonates has been made by grouping reservoirs into larger families called plays (Galloway et al., 1983). Geologists contend that plays often exhibit similar production characteristics and production problems because they have a common geologic history that gives rise to similar heterogeneities (White, 1980). Petroleum engineers know that this is not always the case, because performance depends on many factors, such as how the reservoir is developed and produced. One geological constraint is that this genetic grouping of reservoirs should be confined to a small geographic area. Another constraint is the extent to which one can use the volumetric method to estimate accurately the reserves. Material balance analysis is the only sure

234 way of predicting a carbonate reservoir's production history. Ulmishek and Harrison (1984) discussed the criteria for analog comparisons. There are many such constraints with respect to carbonate reservoirs, because oil in carbonate reservoirs is more unevenly distributed than oil in clastic reservoirs. A central theme of this chapter is to discuss the impact of geologic parameters on the recovery of oil and gas from carbonate rocks. Every reservoir is unique in some respects and must be treated as such. It is necessary, therefore, to review additional technologies, such as sequence stratigraphy, laboratory characterization approaches, new drilling technology, and infill drilling strategies. The presentation of five selected fields at the end of this chapter, based on a variety of reservoir configurations and field performances, give examples of integrated geological engineering approaches for optimum reservoir development. Statistical data and summary of reservoir characteristics are supplied for additional selected carbonate reservoirs. RESERVOIR CLASSIFICATION SCHEMES Four carbonate reservoir classification schemes will be discussed based on" (1) fluid composition in the reservoir; (2) type of available reservoir energy (drive mechanism); (3) type of pore system; and (4) geological nature of the reservoir.

Classification of reservoirs based on fluid composition Craft and Hawkins (1958) classified hydrocarbon accumulations by fluid types regardless of the reservoir rock type, using the familiar pressure-temperature phase envelope for a hydrocarbon mixture. Possible reservoir types are dissolved-gas reservoirs (saturated or undersaturated), gas-condensate reservoirs at or above the dew point, and dry-gas reservoirs. It is sometimes helpful to expand this classification. Eremenko (1968) proposed such an expanded version based on the relative quantities by weight percent of oil, gas, and condensate present in the reservoir (Fig. 5-2). TYPE 100 IT

I

~r

n

II

"~

OF

DEPOSIT

IE

lZ

,,

~

GAS

W

z w Iz

0 ~j i

Fig. 5-2. Eremenko's (1968) classification of hydrocarbon accumulationson the basis of their oil, gas, and condensate contents. (Reprinted with the permission of Dr. N.A. Eremenko.)

235

Type 1: Highly undersaturated oil reservoir Saturation pressure is lower, by an order of magnitude or more, than formation pressure with a correspondingly low solution-gas/oil ratio. Formation pressure is the pressure acting upon the fluids contained in the pore space of the reservoir (for a complete discussion see Fertl et al., 1993). Pools are normally shallow with low-gravity oil. In extreme cases, saturation pressure may approach atmospheric, with well depths of only a few hundred feet and oil gravities as low as 8-10 ~ API. Type IIa: Moderately undersaturated oil reservoir with no free gas cap. Saturation pressure is somewhat lower than formation pressure. Type lib: Moderately undersaturated oil reservoir with initial free gas cap. Saturation pressure is lower than formation pressure. Paradoxically an initial gas cap exists in spite of the undersaturated oil zone. Reservoirs in the Asmari, Bangestan, and Khami limestones in Iran are good examples (Andresen et al., 1963). Possible explanations for this condition include changes in the depth of burial and thermal diffusion effects. Standing (1969) suggested that circulating formation waters possibly removed some gas from the oil after accumulation, owing to the differential solubility of the various hydrocarbons in water. The lighter hydrocarbons have a higher solubility in water than the heavier constituents. The importance of this subclass is that gas-cap energy is available from the inception of production. Type III: Saturated oil reservoir with no free gas cap. Reservoir pressure is initially at the bubble point pressure of the oil. Pressure depletion may result in early formation of the secondary gas cap. Type IV." Saturated oil reservoir with initialfree gas cap. Initial reservoir pressure equals saturation pressure. No retrograde condensation occurs in the gas cap with decrease in pressure. Minor amounts of liquid production may consist of natural gas liquids. Type V: Gas-condensate reservoir with black oil band. Depending on the structural position in the reservoir, liquid production from individual wells may consist entirely of condensate, a mixture of condensate and black oil, or entirely of black oil. Type VI: Gas-condensate reservoir with no black oil band. Initial producing gas/oil ratio is always greater than 3,000 standard cubic feet per barrel and normally exceeds 6,000 scf/bbl. The gas/oil ratio is a function of reservoir temperature, pressure, and gas composition. Condensate gravity is in the range of 40-50 ~ API. There does not appear to be any correlation between condensate gravity and initial producing gas/oil ratio. Type VII: Dry-gas reservoir. Reservoirs contain only "dry" gas, and no condensate forms as the pressure decreases. Application Reservoir pressure and temperature and the hydrocarbon composition determine the reservoir type (I to VII). Changes in the depth of burial of a reservoir, after entrapment of the oil and gas, may result in a change in reservoir type. A type III reservoir, for example, may revert to a type II when subjected to deeper burial caused by gravitational compaction, tectonic subsidence, or downwarping. Erosional processes can produce shallower burial depths that may cause a free gas cap to form (type III

236 reservoir becomes a type IV). As formation pressure decreases, the gas cap will expand, owing to the removal of the overburden, and force oil out of the trap at the bottom. In extreme cases, all the oil may be expelled from the trap to form a gas or gas-condensate reservoir (type VI or VII). The mechanism of gas expansion in traps caused by a decrease in pressure due to uplift or erosion is discussed by Gussow (1954) and Levorsen (1967). Observations made by these authors provide possible explanations for the difference in oil and gas content of adjacent or nearby traps. Gussow's (1954) study suggested that the nature of the hydrocarbons trapped in the reservoirs depends on the proximity of these reservoirs to source beds. As oil migrates and encounters a series of traps, the process of "differential entrapment" becomes operative. A trap filled with oil and gas may eventually lose the oil to another trap updip as oil and gas continue to migrate into the area. Figure 5-3 illustrates the differential entrapment concept.

TRAP A

TRAP B

o,,

I. /

TRAP C

.,._./

TRAP D

Woter wot.r

oil

f

Oia

Woter

Oil

2. /

Gos

Oil

3. /

Gas

Fig. 5.3. Theory of differential entrapment: different stages in the migration and accumulation of oil and gas in the interconnected traps. (Modified after Gussow, 1968, fig. 3; courtesy of the Society of Petroleum Engineers.)

237 Trap A is an oil reservoir with a free gas cap (type IV). Stage 1 (Fig. 5-3) shows that when trap A is filled additional oil cannot enter the trap unless oil spills updip into trap B, which contains only oil (type III). The migrating gas, however, will continue to be trapped in trap A during stage 1. Traps C and D contain only water. In stage 2, trap A is completely filled with gas (type VI or VII) and all the oil has been displaced to trap B, which is completely filled with oil (type III). Additional influx of oil to the system forces oil to spill out to trap C (type III). Trap D still contains only water. In stage 3, trap A remains a gas reservoir, and both oil and gas are bypassing it. Trap B now has a gas cap (type IV) and oil is bypassing it; oil is also expelled as the gas cap expands. Trap C now filled with oil still does not have a gas cap. Water fills Trap D. Gussow (1968) cited the oil and gas accumulations in the Leduc reefs on the Acheson--Homeglen-Rimbey trend, Alberta, Canada, as a general illustration of this process (Fig. 5-4). Homeglen-Rimbey is an oil reservoir with a very large gas cap. Westerose South, immediately updip, is all gas. Farther up the trend, Westerose, Bonnie Glen D-38, and Bonnie Glen D-3A are oil reservoirs with free gas caps. The presence of gas caps in the last three reservoirs, positioned updip from the two reservoirs not having gas caps, can be explained by the large difference in depth of burial between the two areas, which approximates 1,000 ft (305 m). The lower pressure in the shallower reservoirs allowed some gas to come out of solution and form a gas cap. Table 5-11 lists the reservoir parameters for the Acheson-Homeglen-Rimbey D-3 trend. The Swan Hills oil and gas fields in northern Alberta, Canada, shown in Fig. 5-5, DEPTH SUBSEA

ST. ALBERT BIG LAKE

-

ACHESON

-

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SP,K(_

A

It II

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HOME

- 5,000' 0il

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w,,,,

~

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Fig. 5.4. Cross-sectionalprofile of the Acheson--Homeglen-Rimbey-Leducreef trend. (After Horsefield, 1962 and Hnatiuk and Martinelli, 1967; reprinted with the permission of the Petroleum Society of the Canadian Institute of Mining, Metallurgy and Petroleum.)

to oo

TABLE 5-I1 Comparison of reservoir parameters for Acheson-Homeglen-Rimbey D-3 Reef Trend Pool Acheson Leduc-Woodbend Glen Park Wizard Lake Bonnie Glen Westerose Westerose South Homeglen-Rimbey

Depth (ft) 5,076 5,344 6,304 6,458 6,995 7,233 7,740 7,934

Porosity (%) Oil zone Gas cap

Connate water (%)

Permeability (md) Horizontal Vertical

Area (acres)

9.1 8.0 9.6 9.4 9.4 9.34 ... 7.6

10 15 7.6 7 6 7 10 10

3.100 1.000 1,604 700 350 1,934 1,200 250

3.640 21,600 433 3,250 8,800 1,757 10,720 14,053

7.5 7.4 ... ... 8.3 7.95 8.6 7.8

1.500 5-100 105 n.a. n.a. 195 60 72

Maximum total pay (ft)

Oil-in-place (million bbl)

Gas-in-place

234 232 421 646 711 589 673 110

149 308 28 380 625 158 0 110

10 420

Source: After Hnatiuk and Martinelli, 1967; reprinted with the permission of the Petroleum Society of the Canadian Institute of Mining.

(BcO

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, ~

430 117 1,915 1,285

239

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.

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:":~'!?-!:""C A R S O N

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Judy Creek South 420

B

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Fig. 5.5. Differential entrapment along the Swan Hills reef trend, northern Alberta, Canada, showing oil and gas accumulations in the carbonate reefs and shoals of the Upper Devonian Beaverhill Lake Subgroup. Spill points and migration paths are shown. (Courtesy ofW.C. Gussow, 1972.)

240 are another example of differential entrapment in carbonate reservoirs (Gussow, 1968). An estimated 4.7 billion bbl oil-in-place occurs in the carbonate rocks in this succession of traps. The presence of nonassociated wet gas downdip at the Carson Field can be explained by the theory of differential entrapment. Oil originally trapped here has been flushed updip, as has some of the oil at Carson Creek North, which has a free gas cap. All the traps farther updip (Judy Creek South, Judy Creek, South Swan Hills, Swan Hills, and the C Pool of Swan Hills North) are filled with oil and have no free gas caps. The Virginia Hill Field contains only oil and may have been isolated from the other reservoirs at the time of fluid migration. Gussow (1968) discussed the effects of differential entrapment on the distribution of oil of varying gravities in the oil pools of the Swan Hills area. The mechanism is simple: where gravity effects predominate in the individual pools, the higher API gravity oil is at the top and the lower API gravity oil at the bottom. As the oil is displaced from a trap by migrating gas, the lower API gravity oil at the bottom is displaced initially updip, thereby accumulating in updip traps. Accordingly, there may be a decrease in API gravity along the migration path toward the updip edge of a basin. In fact, the oil in the Swan Hills trend ranges from 43 ~ API at Carson Creek North to 39 ~ API at Swan Hills North. Rieke et al. (1972) showed that the API gravity of Illinois Basin crudes can be characterized by simple individual frequency distribution plots. The gravity data were from producing Illinois oil fields (Bell et al., 1959). Histograms constructed for the crudes are from three formations: Cypress Formation (Mississippian, Chesterian), Aux Vases Sandstone (Mississippian, Chesterian), and the members of the Ste. Genevieve Formation (Mississippian, Valmeyeran), consisting of the Ohara Limestone, Rosiclare Limestone, and the McClosky Limestone, as presented in Fig. 5-6. The API gravity frequency distributions from each pay zone are generally similar in that they are all unimodal, with the mode lying between 36 ~ and 39 ~ API. With respect to texture, the McClosky Limestone is highly oolitic and very much like a homogeneous, clean sandstone. The API gravity histogram of the McClosky pay is nearly symmetrical (Fig. 5-6E), possibly indicating regional migration and mixing of the crude oils. Histograms of the other pay zones are irregular, but not lognormal (Fig. 56A, B and C). The McClosky Limestone is permeable over great distances. In contrast to the Illinois Basin crudes, the gravity histograms characterizing the Viking Sandstone (Cretaceous), and Frobisher Limestone (Mississippian) tend to be Gaussian (Fig. 5-6A and B). The Devonian D-1, D-2, and D-3 zones in western Canada show a possible bimodal distribution (Fig. 5-7C). These distributions show a much wider API gravity range than the crudes in Illinois (Fig. 5-6). The spread of gravity values in the Devonian carbonates illustrate the frequency distribution of differential entrapment (Fig. 5-7). Similar histograms can be useful in the correlation and prediction of other reservoir properties, and help in determining the source of the crude. The differential entrapment mechanism proposed by Gussow (1968) is a distinct possibility in instances such as those cited above. In the case of aquifers having good porosity and permeability properties over a wide area, so that regional migration of fluids is possible, the theory is plausible. It is difficult, however, to envision, as noted by Dickey (1968), "Differential entrapment as a valid explanation for oil accumulations in the common instance of oil fields with lenticular sands and limited aquifers."

241

)u

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Fig. 5.6. Histograms of API gravity of selected crudes in the Illinois basin. (A) Cypress Sandstone; (B) Aux Vases Sandstone; (C) Ohara Limestone; (D) Rosiclare Limestone; (E) McClosky Limestone. (From Rieke et al., 1972, fig. 5" courtesy of Elsevier Publ. Co.)

Coogan (1991) provided such an example. Differential entrapment is seen in the Silurian age gas and oil traps in northeastern area of Ohio, U.S.A. The reservoirs are lenticular shoestring sandstones showing the entrapment of oil updip to the west and gas downdip to the east. The general trend of the lenticular sandstones are towards the

242 25

,>,rO

2O

Z

I,iJ 15 :) Ct I,iJ (l:: I0 tl,.

o~ 5 i

6

28

30

32

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~ 25

>. o z

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z

::) n-~

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: .: ....

:~:::

0 26

28

30

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38

40

42

OAPI

Fig. 5-7. Histograms of API gravity of selected crudes in western Canada. (A) Viking Sandstone; (B) Frobisher Limestone; (C) Devonian D-1 and D-3 limestone pays. (From Rieke et al., 1972, fig. 6; courtesy of Elsevier Publ. Co.)

northwest, away from the Appalachian Basin, ending as river mouth bars at the western delta edge (Coogan, 1991). The classification ofoil reservoirs based on fluid content is useful for several reasons. First, a reservoir is readily identifiable in its initial state on this basis. Also some interesting theories, based on the fluid content, can be advanced regarding the events leading up to its generation and migration into a trap. In addition, information on the original reservoir fluids-in-place helps one to formulate ideas on how the reservoir may behave initially and how it should be exploited. For example, if an oil reservoir is highly undersaturated, the initial production period about the bubble point pressure is predictable. Under conditions of oil expansion, oil production rates will exhibit a

243 sharp decline with a possible moderate increase in the producing gas/oil ratios. In addition, the wells can be produced at capacity during the initial period without danger of harming the reservoir. If the reservoir has an initial free gas cap, the individual well rates, especially in the wells near the gas-oil interface, should be controlled to prevent gas coning. Immediate steps should be taken to conserve gas energy and to provide for gas cap expansion, if possible, and guard against gas-cap shrinkage. In the case of a gas reservoir it is important to know whether or not it is a gas-condensate reservoir, because it directly influences production economics: special separators to recover the oil from the gas; the manner in which the reservoir is produced; and difficulty in establishing reserves. Classification of oil reservoirs based on drive mechanism Although the above reservoir categorization by fluid content is helpful, an energy drive classification is imperative for a careful study of the technology of oil and gas recovery. In many cases, performance of a reservoir throughout its productive life cannot be explained by a clearly defined drive mechanism. A combination of two or more of these mechanisms is usually operative. Classification of producing mechanisms, however, permits a stepwise examination of the predominant factors that influence reservoir behavior, either individually or in combination. The potential energy sources available to move oil and gas to the wellbore include: (1) gravitational energy of the oil acting over the vertical distance of the productive column; (2) energy of compression of the free gas in the gas cap or within the oil-producing section; (3) energy of compression of the solution-gas dissolved in the oil or the water; (4) energy of compression of oil and water in the producing section of the reservoir; (5) energy of compression of the waters peripheral to the production zone; (6) energy of capillary pressure effects; and (7) energy of the compression of the rock itself. These forces are active during the productive life of a reservoir. The predominant producing mechanism operating to produce the oil and gas reflects the relative influence each energy source has on reservoir behavior. The major drive mechanisms are: (1) solution-gas; (2) gas-cap expansion; (3) water encroachment; and (4) gravity drainage. Each drive mechanism, when effective in a pool, will give rise to a certain characteristic form of reservoir behavior, although in practice most reservoirs behave in a manner that represents a combination ("mix") of two or more drive mechanisms. For simplicity, each mechanism is described here in the context of a single-drive reservoir. The common characteristics of each drive mechanism are discussed for carbonate reservoirs having only intergranular porosity before being related to other types of porosity. Interest is centered on the record of performance: variation of oil, gas, and water production rates, gas/oil and water/oil ratios, and reservoir pressure with time. Movement of the water-oil contact and creation of a free gas cap are also of great importance. In addition, individual well performance is of concern.

244

Solution--gas drive In solutiorv-gas drive the source of reservoir energy comes from the evolution of dissolved gas in the oil reservoir as pressure declines during production. Solution-gas drive is known also as depletion drive, dissolved gas drive, or internal--gas drive. No initial free gas cap exists, and the free gas phase formed remains within the oilproducing section. The reservoir is sealed off to a large extent from communication with contiguous water zones by faults or permeability pinchouts. As a result, the water influx into the reservoir is minor as pressure declines. Figures 5-8 and 5-9 illustrate a typical solution-gas drive performance. Initially, there is no free gas phase and the instantaneous producing gas/oil ratio is equal to the original solutiorv-gas/oil ratio. Except in cases of undersaturated reservoirs, a finite gas saturation quickly develops and continues to increase as depletion proceeds. When the gas saturation reaches the equilibrium value of 5-10%, the gas phase has sufficient mobility and free gas is flowing to the wellbore with the oil. The gas/oil ratio continues to rise with increased gas saturation, reflecting the rapid increase in gas flow rate and the attendant decrease in oil production rate. At a gas saturation of 2030%, the flow of oil becomes negligible, and the gas/oil ratio will peak and then decline as the reservoir reaches the latter stages of depletion. In understanding reservoirs, where the initial reservoir pressure is substantially above the saturation pressure, as mentioned above, the production mechanism is oil expansion. Under these conditions, the producing gas/oil ratio will remain at a low level during the time that the reservoir pressure is above bubble point pressure. The GOR will approximate the solutiorr-gas/oil ratio, and ideally, should actually decrease slightly as the pressure falls, even though this is rarely observed in the field. The peak I

I

PROOUCEO GAS-OIL RATIO

~

~.~

iI

N

\ \

RESERVOR I ~~~ESSURE PRODUCTO IN

f

'

0

20

PER CENT

40

OF

~ ;

60

ULTIMATE

,%

\

80

I00

PRODUCTION

Fig. 5-8. Generalized performance of a solution-gas-drive reservoir. (After Torrey, 1961; reprinted with the permission of Prentice-Hall, Inc.)

245 "~

,,oo

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isoo

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Vl u~ I~J

1300

Q"

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~

S

S

U

R

s

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ul w

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~

in

,

d

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aooo

6

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o

n ~

~

i

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Q. ~

0

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a940

1945

19S0

19S5

o960

0

Fig. 5-9. Performance of the Slaughter SanAndres Dolomite reservoir, west Texas, under predominantly solution--gas-drive. (After Sessions, 1963; reprinted with the permission of the Society of Petroleum Engineers.)

gas/oil ratio before starting to decline, reflecting ultimate reservoir depletion, will normally be 5-10 times as great as the solution-gas/oil ratio. In purely solution--gas-drive carbonate reservoirs with intergranular porosity, reservoir pressure depends primarily on cumulative oil recovery. Neither reservoir pressure nor ultimate oil recovery is sensitive to oil production rate unless the production rate affects the producing gas/oil ratio. A rapidly increasing gas/oil ratio, after equilibrium gas saturation is reached, is in general a characteristic of solution--gas-drive reservoirs. Reducing the production rate, however, will not serve to increase the ultimate oil recovery appreciably. An exception to this rule is when excessive drawdowns of individual wells lead to extensive transient effects on the reservoir. Time is not normally a factor with solution-gas-drive reservoirs because neither water influx nor gravity segregation occurs (Craft and Hawkins, 1959). Any tendency for the reservoir to exhibit significant gravity drainage or water influx, or to form a secondary gas-cap, may make ultimate recovery sensitive to production rate. Solution--gas-drive performance is closely related to a number of physical parameters. The ratio of reservoir oil viscosity to reservoir gas viscosity (/~//~o), solution0 gas/oil ratio, formation volume factor, interstitial water saturation, and oil and gas permeability relationships largely control performance. A change in any one factor results in a change in one or more of the other factors showing the close interrelationship among these parameters. Some general and meaningful observations can be made regarding the effect of altering the value of a single factor. As oil viscosity increases, for example, there is a corresponding rise in the instantaneous producing gas/oil ratio because of greater gas bypassing. The increase in GOR results in lower solutiorv-gasdrive efficiency and lower oil recovery. As the amount of gas available in solution decreases, the oil recovery also will decline. Muskat (1949), however, found that

246 doubling the solution--gas/oil ratio resulted in only a 10% increase in ultimate recovery. The greater oil shrinkage, at higher solution-gas/oil ratios, serves to somewhat dampen the effect of increased oil solubility on oil recovery. The shrinkage effect, however, is of only minor importance. An increase in crude oil gravity (~ as an overall characteristic of the fluid system likewise results in an increase in ultimate recovery. Again, the effect is dampened at the higher gravity ranges owing to greater oil shrinkage, and the ultimate recovery will actually decrease with an increase in oil gravity in the 40-50 ~ API range.

Gas-cap drive Oil pools with initial free gas caps are subject to a gas drive, which is extemal to the oil zones and separate from the solution--gas-drive mechanism. The oil expulsion mechanism is typically a combination of solution--gas-drive within the oil column plus the added benefit of gas permeating and diffusing into the oil zone from the gas cap. The idealized performance of a gas-cap-drive reservoir is presented in Fig. 5-10. The decline in production rate and reservoir pressure are not as rapid as in solutiongas-drive reservoirs. The gas/oil ratio performance is more favorable. Gas-cap-drive reservoirs are more sensitive to production rate than are solution--gas-drive pools, because the recovery equation contains a throughput velocity term and is, therefore, rate sensitive (Craft and Hawkins, 1959, p. 368). Wells producing from intervals close to the gas cap must be produced at low rates to prevent gas coning, or recompleted to exclude the upper intervals. The overall gas/ oil ratio performance largely reflects such procedures. The performance of the Goldsmith San Andres Dolomite pool in west Texas (Fig. 5-11) early in its history, for example, typifies gas-drive performance with a gradual increase in gas/oil ratio. The oil production is curtailed, and no decline is evident. v

~ ~

~ .

T

.

_ ,

_

I

RESERVOIR __~SSURE PRODUCTION

/ '

/

/

/

I

i

PRODUCED GAS-OIL

,

.0 I o

20 PER CENT

40 OF

60 ULTIMATE

ir" 80

' ioo

PRODUCTION

Fig. 5-10. Idealized performance of a gas-cap-drive reservoir. (After Torrey, 1961; reprinted with the permission of Prentice-Hall, Inc.)

247 r a.

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Fig. 5-11. Typical gas-cap-driveperformance, Goldsmith San Andres Dolomite reservoir in west Texas. (After Craze, 1950, fig. 5; reprinted with the permission of the Society of Petroleum Engineers.) Some gravity segregation of oil and gas takes place in almost every gas-cap-drive reservoir. More pronounced fluid segregation will promote the expansion of the gas cap and downdip movement of the oil, with resultant higher oil recoveries. The size of the gas cap also will affect oil recovery. Normally, increased ultimate recoveries are associated with a thicker gas cap. Notable exceptions are the carbonate pools in the Acheson-Homeglen-Rimbey reef trend, Alberta, Canada, which have large gas caps underlain by thin oil bands. The estimated ultimate oil recoveries under primary production are often very low (5-10%) owing to excessive gas and water coning problems. A comparison of the performance of these reservoirs indicates that those with thicker oil bands and correspondingly thinner gas caps have higher oil recoveries. Water drive

A reservoir having high permeability (such as a fractured or cavernous limestone) in contact with an extensive aquifer will normally have an active water drive. The degree to which the reservoir withdrawals are replaced by water determines the efficiency of the water-drive mechanism. In complete water-drive systems, which are not common, substantially all the fluid withdrawals are replaced by intruding water. Some excellent examples of complete water-drive reservoirs in carbonate rocks are Arbuckle Dolomite fields in Arkansas and Kansas. If the reservoir is initially undersaturated, natural pressure maintenance by water influx may result in oil production above the bubble point pressure for an extended period. As a result of this production, a small portion of the reservoir pore space is replaced by expanding oil. Later in the life of the reservoir a free gas phase may form, which will provide part of the energy for the oil expulsion. The existence of the free gas will depend largely on the rate of withdrawal of fluids.

248 In all water-drive reservoirs, an initial pressure decline results in the necessary pressure differential at the reservoir boundary to induce water movement into the reservoir. Figure 5-12 illustrates this initial rapid production decline preceding water influx. The Schuler (Reynolds), Magnolia, Buckner, and Midway fields are Smackover limestone reservoirs, and the Hobbs and Yates reservoirs produce from a Permian dolomite. The remaining fields shown in Fig. 5-12 are sandstone reservoirs. All these reservoirs, except the solutiotr-gas-drive Schuler Jones Sand pool (which is included for comparison purposes) are subject to at least substantial, if not complete, water drive (Elliott, 1946). To summarize water-drive performance, the producing zone is in contact with a broad aquifer, normally of high permeability. A decrease in production capacity is minor until water begins to be produced. The produced gas/oil ratio is substantially constant. Figures 5-13 and 5-14 illustrate this type of performance. Recovery factor depends on reservoir rock characteristics such as pore size and fracture distribution,

~ 30OO L ~

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CUMULATIVE OIL PRODUCTION (PER CENT OF ULTIMATE RECOVERY) Fig. 5-12. Pressure-production performance of some water-drive reservoirs. (After Elliott, 1946, fig. 1" reprinted with the permission of the Society of Petroleum Engineers.)

249 I

I

I

t

1

RESERVOIR PRESSURE

OIL PRODUCTIONRATE

f

i

-

GAS-OIL RATIO

0

,

1

O

2O

PER CENT

~'40 OF

PROOUCTJONRaTE 60 80

ULTIMATE

, I00

PRODUCTION

Fig. 5-13. Idealized water-drive performance. (After Torrey, 1961" reprinted with the permission of PrenticeHall, Inc.)

values for mobility ratio (kPolkPw) and reservoir geometry. The rate at which the reservoir is produced also may affect recovery, particularly if the reservoir is subject to only partial water drive. Reservoir withdrawal rates greatly in excess of the rate of water influx can lead to performance similar to that of solution--gas-drive reservoirs. Free gas saturations in the reservoir can develop in the more permeable sections to the extent that incoming water will bypass tighter sections. The water will move preferentially into areas of high gas saturation, with a resulting loss in recovery.

Gravity drainage In oil reservoirs subject to gravity drainage, the gravity segregation of fluids during the primary production process is evident in the production history. Oil migrates downdip to maintain down-structure oil saturation at a high level, and free gas accumulates high in the structure. If a primary gas cap exists, then it will expand as a result of the segregation process. A reservoir without a primary gas cap will soon form a secondary gas cap. Early in the life of the reservoir, the gas/oil ratios of the structurally high wells will increase rapidly. A program of shutting-in wells with high gas/oil ratios and controlling individual well rates will maximize gravitational fluid movement. Figure 5-15 shows the two generalized performance cases of a gravity-drainage reservoir with and without such control. The oil gravity, permeability of the zone, and formation dip dictate the magnitude of the gravity drainage. The combination of low viscosity and low specific gravity values (high API gravity), high zone permeability, and steeply dipping beds accentuate the down-structure oil movement. Typically, in gravity-drainage reservoirs the water influx is minor and the down-dip wells produce at the lowest gas/oil ratios and have the highest oil recovery. In cases of strict gravity drainage, a major portion of the recovery occurs after complete pressure depletion. Gravity is the primary dynamic force moving the oil to the wellbore.

250

I (.f)

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Fig. 5-14. Performance of a water-drive pool, Excelsior D-2 reef pool, Excelsior Field, Alberta, Canada. (Data from the Alberta Oil and Gas Conservation Commission.)

Hamon (1988) pointed out that in oil-wet fractured reservoirs, the ultimate recovery depends on the balance between the capillary and gravity forces. The water--oil capillary pressure is negative when water displaces oil from an oil-wet rock. Gravity forces must overcome the capillary resistance to the entrance of water into the fractures. If the fractures act as capillary discontinuities, then the capillary and gravity forces control the static and dynamic equilibrium of each individual matrix block (Hamon, 1988). This means that reliable field performance predictions for highly fractured reservoirs depend on representative and accurate measurements of the capillary pressure curve in the very low-pressure range (0 to-0.5 psi). Jodry (Volume I, Chapter 6) provides examples of capillary-pressure curves for such carbonate rocks. Combination-drive reservoirs

Some reservoirs may produce under the influence of one or more of the drives discussed above. A sequence of drive mechanisms in reservoirs, such as solution-gas drive, gravity drainage, water drive, may develop during primary production. Also

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Fig. 5-15. Generalized performance of a gravity-drainage pool. (A) produced without control; (B) produced under control by shutting in high gas/oil ratio wells. (Courtesy of E.C. Babson.)

252

two different drives may compete simultaneously (e.g., water-drive reservoir with a primary gas cap). Combination-drive reservoirs may be further classified as open or closed, as proposed by Babson (1965).

Open combination-drive reservoirs. The performance of open combination-drive reservoirs is affected by the method of operation and by individual well and reservoir rates. This type of reservoir is in open communication with the aquifer. Sources of energy include water drive, gravity drainage, and gas expansion. In uncontrolled operations, a gas-expansion stage may occur first, accompanied by a rising gas/oil ratio and declining pressure. A gravity-drainage stage may come next at a reduced reservoir pressure. The effects of a moderate water influx will frequently be evident in the latter stages of the life of the reservoir. Curtailing production rates will cause buildups in reservoir pressure as water influx exceeds fluid withdrawals. The performance of the D-3 Pool, Redwater Field in Alberta, Canada, which is a typical open combination-drive reservoir, demonstrates this effect (Fig. 5-16). To facilitate gravity drainage, the rate of water influx into the reservoir can be reduced by maintaining high water-withdrawal rates from the high-water/oil-ratio wells close to the water table, and controlling the rates of the wells situated higher on the structure. In order to take full advantage of the water influx, wells producing at high

1 n,"

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oo0

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1961

Fig. 5-16. Performance of an open combination-drive pool, Redwater D-3 reef pool, Redwater Field, Alberta, Canada. (Data from the Alberta Oil and Gas Conservation Commission.)

253 water cuts should be shut-in, and rates on other wells carefully regulated to reduce problems of nonuniform water influx and coning. The combined effect of water drive and an expanding gas cap can serve as a very effective oil displacement mechanism. The Leduc D-3 Pool is currently under both water and gas-cap injection, and flushing efficiencies in the gas cap and water zone appear to be about 80%. Oil movement into the primary gas cap must be prevented when a reservoir with an initial free gas cap is subject to an active water drive. Oil encroaching into the gas cap, even if subsequently displaced, will leave a residual oil saturation, causing a substantial loss in ultimate recovery. Bruce (1944) cited the case of the Mount Holly Pool in Arkansas, producing from the Smackover oolite limestone. Due to oil lost in the shrinking primary gas cap, only 30-40% is recoverable from this reservoir. The recovery of the other Smackover reservoirs in the area is 60% or higher. Closed combination-drive reservoirs. There is no significant water encroachment in closed combination-drive reservoirs owing to the faulting and/or facies changes that are so common in carbonate rocks. A gas-expansion stage usually is followed by gravity drainage. Reservoir pressure is low, gas/oil ratios are falling, and updip wells produce very little fluid of any kind during the secondary stage. The influence of

TIME

Fig. 5-17. Generalized performance of a closed combination-drive reservoir produced without control. (Courtesy of E.C. Babson.)

254 gravity drainage depends on the net effect of the dip and permeability and the oil gravity, in addition to the individual well rates. The control of production rates to allow for effective gravity drainage is normally more critical than in the case of strict gravity-drainage reservoirs. This is due to a reduced tendency for downward oil migration. Figure 5-17 presents a generalized performance example of a closed combination-drive reservoir produced without control. A good example of this type of reservoir is the Golden Spike Field in Alberta, Canada.

Classification of carbonate reservoirs based on type of pore system Classifications, based on fluid type or drive mechanism, apply to both carbonate and sandstone oil reservoirs. A classification system for carbonate reservoirs based on the configuration of the void space is, by its very nature, unique to carbonate rocks. The fundamental difference, between the performance of sandstone and carbonate reservoirs, is due to the unique variations in limestone and dolomite porosity and their influence on fluid properties. Discussion here centers on the role of porosity and the interconnectiveness of the pore space to form permeable facies in carbonate reservoirs. Also presented is an introduction and overview on the applicability of fractal measurements to describe carbonate pore space.

Synopsis of carbonate porosity A number of porosity classifications have been proposed during the past thirty years. Most of these classifications are generic and they do not account for pore system features that may affect fluid movement and withdrawal. Such features are important factors in the production of hydrocarbons from these rocks (Kent, 1987). Both Reeckmann and Friedman (1982) and Mazzullo et al. (1992) presented a comprehensive review on pore classification schemes used to relate porosity and texture in carbonate rocks. The most notable of these classifications is that of Choquette and Pray (1970). Their scheme interprets porosity to be either related or not related to the fabric of the rock. These classifications delineate the pore geometry, pore interconnections, and relationships between lithology and porosity. All are operative on the microscopic to macroscopic scale (Chilingarian et al., 1992a). The value of this approach lies more in their applicability to exploration and carbonate reservoir description than with reservoir performance. At present there is no classification system, whether it is comprehensive, simple or complex, which is entirely satisfactory to exploration and development geologists, and reservoir engineers. Different porosity classification schemes exist for different situations. Discussion here shows the more practical application of relating porosity and permeability classification schemes to production problems in the field.

Diagenetic effects. Porosity can be considered as either primary or secondary. Primary porosity is pore space that forms in the depositional environment. Diagenetic alteration is the rule rather than the exception in carbonates. Pores that form during diagenesis are known as secondary porosity. As an example, when limestones are dolomitized, the porosity becomes vuggy or intercrystalline (Fig. 5-18). Diagenetic processes frequently modify or obscure (overprint) the primary depositional porosity

5EnlNG ,,,

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to t~

256 characteristics. Another type of overprint is structural styles, which are discussed in the carbonate reservoir characterization section. Jardine and Wilshart (1987) stated that porosity and permeability heterogeneities in carbonate rocks are due to the variety of carbonate depositional environments and any subsequent diagenetic alteration. Geophysical well log signatures and reservoir quality directly relate to facies and diagenesis. Existence or lack of permeability influences recovery efficiency. Permeability relates the depositional facies through textures of carbonate facies to reservoir performance. Figure 5-18 summarizes the important characteristics of these depositional settings, which form the basis of various carbonate reservoir classes, with porosity types. This classification is derived from the approach by Dunham (1962), who tied depositional texture of carbonates with reservoir rock properties. (Refer to Mazzullo et al., 1992, p. 80 for a discussion on Dunham's classification). Other applications, which appear in the petroleum engineering literature, are by Dowling (1970), Jardine et al. (1977), Reitzel and Callow (1977), and Jardine and Wilshart (1982). Diagenetic effects were defined by the Reservoir Task Force (ICF, 1992, p. II-28) in terms of the diagenetic processes that have directly influenced the flow characteristics of the reservoir. This classification focused on: (1) the pore types present in the reservoir; (2) the diagenetic process(es) most responsible for producing the pore types; and (3) the relationship of the pore types to reservoir flow characteristics. ICF (1992) provided statistics from the TORIS' data base on shallow-shelf carbonate reservoirs in the United States. Table 5-111 presents a ranking of 382 shallow-shelf carbonate rock reservoirs based on the predominant diagenetic process altering the pore space. TABLE 5-Ili Ranking of diagenetic processes for shallow-shelfcarbonate reservoirs in the U.S.A. Diagenetic process

Number of reservoirs

Percent of reservoirs

Dolomitization Compaction/Cementation Massive dissolution Grain enhancement* Dolomization with evaporites Silicification Intergranular dissolution Authigenic clay precipitation

233 57 47 29 12 4 0 0

61 15 12 8 3 1 0 0

Total

382

100

Source: Data from the Tertiary Oil Recovery Information System (TORIS) database maintained by the

U.S. Departmentof Energy,Bartlesville Project Office, Bartlesville, Oklahoma(modifiedafter ICF, 1992, table 1I-3, p. II-29).* See Chapter 4, Vol.I. Relevance. Among the early investigators studying reservoir performance of carbonate formations were Bulnes and Fitting (1945). They recognized three distinct classes of porosity in carbonates and termed them intergranular, intermediate, and

257 foramenular. Performance of carbonate rocks with an intergranular type of porosity approaches that of sandstones. Such carbonate rocks are composed of calcareous fragments (shells or oolites). The size, shape, and packing of the solid fragments determine the pore space geometry. Intermediate porosity displays, in addition to the intergranular openings, fissures, dissolution caverns, and other openings induced by dissolution and fracturing. In the case of dissolution processes, the pore space has sizes and shapes independent of the geometrical properties of the constituent fragments, grains, and crystals. The volume of fissures, fractures, vugs, and other diagenetic voids is frequently much greater than the initial intergranular pore space. Consequently, the intermediate type of porosity system is much more complex than the intergranular system. The foramenular porosity class consists of void spaces in an otherwise nonporous continuous solid, such as a fractured reservoir with essentially no matrix porosity. There are slight differences in performance between sandstone and carbonate reservoirs having intergranular porosity. For example, in carbonates permeability parallel and perpendicular to the bedding are commonly equal, whereas in sandstones permeability parallel to the bedding is much greater than that perpendicular to the bedding. Carbonate reservoirs with intermediate porosity, however, deviate in performance over a wide range from sandstone reservoirs with comparable fluid content and drive mechanism. To demonstrate this difference, it is helpful to make general comments on recent investigations of fluid flow in porous media. Originally, it was widely believed that porosity and effective permeability were sufficient to characterize reservoir rock performance. Barfield et al. (1959) and Mortada and Nabor (1961) have shown that directional permeability is also a pertinent characterization factor. Fatt (1959), Klute (1959) and Goodknight et al. (1960) proposed a fourth parameter: storage porosity, which is the pore space that contributes significantly to the pore volume of the reservoir but little to the flow capacity. In sandstones with intergranular porosity, on a microscopic scale, these regions consist of"dead-end" or "storage" pores. The variation of sandstone reservoir performance falls normally within a narrower range as compared to carbonate reservoirs of intermediate porosity. This is due to differences in the directional permeability and storage porosity. Carbonate reservoirs with intermediate porosity show a wider variation in reservoir performance. Vugular or reef carbonates illustrate the importance of directional permeability. They usually exhibit fair to good vertical permeabilities and their performance may be controlled more by movements in the vertical direction than in the horizontal. The Golden Spike Field in the western Canada Basin illustrates thin internal permeability barriers to vertical flow within a bioherm reef. Such barriers can interfere (break-up and disperse) enhanced recovery processes such as a gravity-controlled, gas-driven miscible flood. A pressure maintenance operation was established to offset rapidly declining reservoir pressure during primary production. The dead-end or storage pores in sandstones correspond to the large volumes of low-permeability matrix porosity in naturally-fractured carbonate reservoirs. Although the fracture system generally constitutes a very small percentage (<1%) of the total porosity, it serves as a path for oil movement to the wells. The matrix, which contains most of the oil, normally has low permeability and yields oil and gas to the fractures reluctantly. In carbonates, the directional permeability and the double-porosity effects

258 are more exaggerated than in sandstones. Accordingly, carbonate reservoirs will vary in performance to a much greater extent than sandstone reservoirs. Warren and Root (1963) developed an idealized model to study the characteristic behavior of reservoirs with intermediate porosity. Their unsteady-state reservoir flow model defined two additional parameters that are sufficient to distinguish the flow behavior in an intermediate-porosity rock from fluid flow in homogeneous media. One parameter relates to the degree of heterogeneity of the system, and the other is a measure of the fluid capacitance of the secondary porosity. These parameters can be evaluated from pressure buildup tests, which take the form of parallel segments. Stratified reservoirs, however, yield a similar type of buildup curve and, therefore, unambiguous interpretations are difficult. Foramenular porosity in carbonate rocks is somewhat rare (Bulnes and Fitting, 1945). This term applies to fracture porosity in a nonporous matrix. An example is the Dean-Wolfcamp pay in west Texas and the San Andres Formation in the Chaveroo and Cato fields in southwestern New Mexico (Groves and Abernathy, 1968). In the Mississippi-Solid Formation, which is a dense, massive, and cherty limestone in the S.W. Lacey Field, Kingfisher County, Oklahoma, production comes from fracture porosity (Morris and Tracy, 1965).

Porosity classification scheme It appears that a classification of carbonate reservoirs is needed based on type of pore systems and having at least a generalized correlation with reservoir performance. Kent (1987) pointed out that in reservoir studies it is more significant to determine the manner in which the nature of pore systems influences fluid flow. No one geologically-based pore structure classification can be completely satisfactory in describing the reservoir's pore structure with respect to the recovery of fluids. Rieke et al. (1972) presented the following classification, which is simple in that it has three porosity categories: (1) intergranular-intercrystalline porosity, (2) vugular-solution porosity, and (3) fracture-matrix porosity. This porosity classification can be easily connected with mercury injection analyses (Jodry, 1992) and is more appropriate than a scheme based on a relation to rock textures. Kent (1987) proposed a similar threecategory classification scheme consisting of intercrystal, cavity, and mixed (combined intercrystal and cavity) porosities.

Intergranular-intercrystalline porosity. As stated previously, carbonate reservoirs having intergranular porosity are comparable to unfractured sandstone reservoirs in behavior. The spatial distribution and the general configuration of the pores are more orderly than in systems assigned to the above categories (2) and (3). Commonly, the basic building blocks (allochemical constituents) of the system are predominantly oolites, skeletal fragments, well-rounded and equant intraclasts or pellets, or other similar transported calcareous constituents (Folk, 1959). Organic components of reefs normally would not form an intergranular pore system. In category (1), the size and the shape of the allochems have a direct bearing on the nature of the void space. Dolomitization also may create inter-rhombohedral porosity. Intergranularintercrystalline porosity is common in dolomites, micrites, and in cemented grainstones and packstones. There is also a microintercrystalline porosity.

259

Vugular-solution porosity. Vugular-solution porosity (e.g., karstic) systems are inherently more complex than either intergranular-intercrystalline or fracture-matrix porosity systems. The original pore structure has usually been altered by the formation of dissolution cavities and channels. Pore structures in many reefs usually belong in this category. Reefs formed by organic buildups, subjected to only slight disruption during burial, are prime candidates for the development of vuggy and moldic porosity. Such porosity consists of macro-to micro-size vugs. Directional permeability may be very pronounced. Although fractures may exist, they do not dominate the mechanics of fluid flow. The performance of carbonate reservoirs with vugular-solution porosity may closely resemble sandstone pool performance, but commonly differs considerably owing to a wide distribution of pore throat sizes. Fracture-matrix porosity. A double-porosity system may be well developed in reservoirs having fracture-matrix porosity. Strong directional permeability also may exist. The matrix is usually of low permeability and contains most of the hydrocarbons. The fractures contribute only a minor amount of the total hydrocarbon pore space, but allow the reservoir to produce at economic rates. Reservoir performance is markedly different from that of sandstone reservoirs. The size of the matrix "blocks" varies from a few inches to several feet. An overprint of diagenetic alterations has to be considered when using a porosity classification. Figure 5-19 presents a summary of the diagenetic processes and secondary porosity. It should be noticed that dolomitization, fractures, recrystallization, and cementation can have unfavorable effects on the porosity and permeability and, ,

PROCESS

,,

LEACHING

,,,,

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FAVORABLE EFFECTS ,

EFFECTS ,

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Fig. 5-19. Favorable and unfavorable effects of diagenetic alteration in carbonate rocks. (After Jardine and Wilshart, 1987, fig. 5; reprinted with the permissionof the SEPM (Societyfor SedimentaryGeology).) Note: Based on extensive experience of the authors of this chapter, dolomitization usually increases porosity (~b)and permeability (k).

260 therefore, alter the flow capacity of the reservoir. Production practices used in the development and depletion of carbonate reservoirs must be in tune with the nonisotropic and heterogeneous nature of the rock fabric. Attention should be given to the spatial distribution of the composition of the reservoir rock, nature and type of the pore system, and capillary pressure conditions. These factors influence the behavior of the fluids during production. Oil recovery owing to water invasion in fractured reservoirs Oil displacement in a fractured reservoir exhibiting water influx into the fractures is controlled by the following mechanisms: (1) the flow of water under naturally imposed pressure gradients (viscous forces), and (2) imbibition, which is the spontaneous movement of water into the matrix under capillary forces. The environmental conditions of fractured carbonate reservoirs are conducive to the predominance of capillary forces over viscous forces. Water has the tendency to channel through the more permeable zones, but is offset by its imbibition into the tight matrix displacing the oil into fractures. Numerous investigators examined imbibition behavior using mathematical models and in the laboratory (e.g. see Aronofsky et al., 1958; Graham and Richardson, 1959; Handy, 1960; Mattax and Kyle, 1962; Blair, 1964; Parsons and Chancy, 1966). Graham and Richardson (1959) for example, investigated in the laboratory the role of water imbibition in the recovery of oil from a fracture-matrix porous system. Their results are particularly interesting as they pertain to fractured carbonate reservoirs. This mechanism entails water imbibing from the fracture system into the matrix with simultaneous counter-current movement of the oil from the matrix into the fractures. The rate of imbibition is directly proportional to the interfacial tension and the square root of the permeability. It is dependent on the wettability, the fluid viscosities, and the rock characteristics. Production at high gas~oil ratios from carbonates having fracture-matrix type porosity Low-permeability matrix blocks in carbonates having fracture-matrix porosity types often do not easily yield oil to fractures, through which most of the flow occurs. This results in very low matrix-block oil recoveries. In order to correct this problem, JonesParra and Reytor (1959) proposed that in some cases in order to remove the maximum amount of oil it is necessary to produce at high gas/oil ratios, with resulting lower pressure in the fractures. Low-permeability matrix thus will release the oil to fractures more readily. Jones-Parra and Reytor (1959) used the following derivations to prove their point: VFG : [NB~/Sit ] [ H(1 - f ) + S f ] ,

(5-1)

where VFG is the volume of free gas;f is the fraction of total pore volume of the lowpermeability zone (matrix) where gravity drainage is minimal; (1 -J) is the fraction of the total pore volume where gravity drainage takes place; H is the fraction of (1 -fl) occupied by gas; St is the saturation based on the total pore volume (o = oil; i - initial); S is the saturation of gas based on matrix pore volume; and N is the initial stock-tank oil-m-place, bbl. .

261 The volume of free gas also can be obtained from the following equation. VFG = B g [NR sl. - nR p - ( N - n)R s ], Imtial Produced Remaining in solution

(5-2)

where Bg is the volume in bbl occupied in the reservoir by a standard cu ft of gas, R s is gas in solution, cu ft/bbl, Rp is the cumulative produced gas/oil ratio, cu ft/bbl, and n is stock-tank oil produced, bbl. Combining Eqs. 5-1 and 5-2: n / N = {Bo~[H(1 - f )

+ Sf]/[SitBg

(R s- Rp)]} - (Rsi- Rs)I(R s Rp),

(5-3)

where B is the initial oil formation volume factor, bbl/bbl. The n / N ratio can be also obtained from the following equation. Ol

n / N = [(So./Bo, ) - (Sot/Bo) ] " (So,t/Bo,)

(5-4)

Inasmuch as the Jones-Parra and Reytor's (1959) model (Fig. 5-20) indicates that S t = (1 - H ) ( 1 - f ) + f S o ,

(5-5)

and the n / N ratio is equal to: n / N = 1 - [ ( f SoBoi)/(SoitBoi)] - [(1 - H) (1 - f )Boi/SoitBoi ]

(5-6)

Combining Eqs. 5-3 and 5-6, and solving for H: H = [(Rp/Rsi) A - B ] " [(Rp/Rsi ) C + D ] ,

(5-7)

where: A = RsiBg[1 - f + f S o - ( B o S o , / B o 3 ] , B = BgRs (1 - f + fSo) + fSgBo- (BoBgiRs~So~t/Boa), C = RsiBg (1 - f ) , and

D = (1 - f ) (Bo- BgRs). Using Eq. 5-6 and H from Eq. 5-7, the n / N ratio is equal to: n/N = E - (1- H) F ,

(5-8)

where: E = 1-[(JSoBo) / (S~tBo)], and F = [(1 -f)Boi ] " ( S i A o ) . If all the production occurs though the fractures and vugs, then the decline in productivity index ( D P I or D J) is equal to:

262 (5-9)

D J = [(1 - I4) / (,UoBo)] 9[1/(,UoBoi)] ,

where ~toiS the viscosity of the oil and (1 - H ) has been substituted for the permeability ko. By assuming that the pressure drawdown is a constant fraction of the static pressure, then

Qo/Qoi=

(5-10)

[(1 - H)(~toBo)iP ] 9(~toBoPi) ,

where Qo is the production at any pressure p, STB/D; Qoi is the production capacity at the initial conditions; and Pi is initial pressure, psi. On assuming f = 0.95 and S =0.20, Jones-Parra and Reytor (1959) found that the production declines less when producing at higher gas/oil ratios in spite of the fact that at any given stage of depletion the pressures are lower. In the opinion of the writers, the reasoning is very simple; by keeping the pressure in the fractures and vugs low, more oil will move out of the tight matrix and the oil recovery will be greater. Obviously, experts working with sandstones will object to producing at high gas/ oil ratios and will find many shortcomings in the above derivations of Jones-Parra and Reytor. These results also appear to contradict the inferences reached by Elkins (1946) on observations of a limited number of carbonate reservoirs. Elkins (1946) believed that the faster production rate in the Harper-SanAndres Pool in Texas, U.S.A., probably caused a lower recovery than did the slower production rate in the PenwellSan Andres Field in Texas. But then recovery is so low in many reservoirs with double-porosity systems that one should try unconventional methods. One of the writers (GVC) started to implement these ideas in a carbonate reservoir in the Middle East, with promising results.

f-

/-f

H

GAS

So /-H

-f

Sg

S.

01L

Fig. 5-20. Model of a carbonate reservoir, where f = fraction of total pore volume when gravity segregation does not take place; H = fraction of coarse porosity occupied by gas. (After Jones-Para and Reytor, 1959; reprinted with the permission of the Society of Petroleum Engineers.)

263 Fractal dimension analysis o f pore space

It has been shown above that the geological framework of a carbonate reservoir influences the flow of fluids during production. Production plans for carbonate reservoirs, especially ones scheduled for enhanced recovery, require detailed, integrated geological engineering studies. In order to explain and assess how production is influenced by microscale phenomena, one needs an appropriate geological description of the reservoir at that scale. The effective integration of geological properties into reservoir simulation models would significantly improve production performance. Unfortunately, most reservoir engineering models rely on Euclidean geometry for spatial descriptions. This approach is inadequate in quantifying naturally-occurring objects that appear to be purely random. Euclidean geometry provides a concise and exact description of homogeneous man-made objects, but it is not appropriate for natural shapes. These structures are too unpredictable and chaotic to be measured accurately using classical geometry. Mandelbrot (1975) inventedfractals to describe chaotic phenomena in nature. The word is derived from the Latin word 'fractus', which means to break up into fragments. Fractal geometry is a statistical approach to the spatial characterization of an object or group of objects. Fractals, therefore, provide an excellent description of many geological objects, such as the size distribution of oil and gas fields, faults, fractures, porosity, and pore microstructures, within a geometric mathematical flamework. Several statistical tests can verify the existence of self-similarity in an object. These distributions are identified as power-law phenomena, inasmuch as they do not have a characteristic length scale. Fractal shapes, therefore, are self-similar and independent of scale or scaling (resolution): that is, they are scale invariant. Although rocks are not exactly self-similar, they exhibit this characteristic in a statistical sense over a limited range of length scales. Carbonate rocks can be regarded as stochastic fractals and can be characterized by fractal dimensions. It will be shown later in this chapter that the concept of fractal statistics is being used as a powerful predictive tool in the characterization of carbonate reservoirs and for defining their heterogeneous nature. The self-similar scaling relationship of objects is introduced by the power-law: N = Cr -D ,

(5-11)

where N is the number of identical parts with a characteristic linear dimension r, C is a constant defined by the straight line intersection with the x-axis, and D is thefractal dimension. The direction of the slope of the straight line (D) is negative. In Euclidean geometry D = 0 represents a point, D = 1 represents a line, and D = 3 represents a three-dimensional object. A fractal dimension need not be an integer. The physical meaning of Eq. 5-11 is that a D-dimensional self-similar object can be subdivided into N smaller copies of itself. Each copy is scaled down by a factor r. A general rule is to scale down each iteration by halves or thirds. N is normally determined by using one of several different algorithms, such as the divider, box-counting, power spectral, or scanline. Klinkenberg (1994) reviewed such methods. The method's use depends on the object, function, or process being measured. It should be remembered, that natural fractals have limits beyond which the objects do not show a log-normal distribution.

264 One of the most favored methods of analysis is the simple square-grid counting (box algorithm). Its use in geology and geophysics is widespread. The fractal (similarity) dimension, D, is calculated by: log (N) D = log (1 / r)"

(5-12)

Arab et al. (1994) provided an example of the use of Eq. 5-12 by employing the boxcounting algorithm to characterize the spatial geometry of fault traces. This approach can be expanded and used to determine the fractal values of fractures occurring in oil and/or gas reservoirs. The writers refer the reader to Mandelbrot (1982) and Turcotte (1992) for a complete explanation of fractal principles and their general applications. The following provides an introduction to some fractals applications, which can be used to dissect carbonate rock pore systems. These discussions will provide new insights into the micro-scale nature of porosity and permeability, as well as what their fractal nature means to reservoir productivity. Heterogeneity aspects are discussed in the carbonate reservoir characterization section of this chapter. Pore microstructure. The complexity of sedimentary rocks has made geometrical measurements of pore space difficult. The reason for this is that unlike most geometrical measurements of grain size or shape, pore interfaces can contain dissolution structures, and pore fillings such as authigenic minerals. Fractal analysis of the spatial geometry and distribution of pore space is another way of describing primary, secondary, and fracture porosity. Diagenesis results in the creation of fine structures such as fractured surfaces and diagenetic minerals on the surfaces of the grains forming the walls of the pores. These microstructures can have a large effect on permeability, surface wetting, electrical resistivity, and capillary effects in carbonate reservoirs. Fractal measurements of fine structure are important in understanding fluid flow within these rocks. Krohn (1988a and b) studied the fractal nature of various rock types, including carbonates. Fractal dimensions of carbonate pores were obtained using two methods: (1) the fracture surface technique; and (2) the thin-section technique. Both techniques measured a one-dimensional section of the pore-rock interface. The fracture surface technique is an automatic method, which statistically measures structural features using scanning electron microscope images of rock surfaces (Ruzyla, 1984; Krohn, 1988a). These structural features represent protrusions of the pore surface into the pore space and consist of grains and clay particles along with bumps and pits on the mineral grain surfaces. Drawing lines across the rock surface images gives a one-dimensional look at the surface features. The statistical fluctuations are very high and, therefore, one needs to make many measurements to achieve statistical confidence. Such features are tallied for a hundred horizontal scanlines imposed upon a digitized image of a fracture surface. The count is repeated for a number of magnifications and locations. This technique does not depend on the delineation of the grain or pore space. The counting of features indicates the presence or absence of features of each size. Counting the features creates a histogram, which shows if the results follow the power-law distribution.

265 The thin-section technique requires delineating pore space from grain space and measuring the pore volume distributions for rocks (Krohn, 1988a). It is not as accurate as the fracture surface method, but it can be used to measure the amount of pore volume that does not fit power-law behavior. The above concept is similar to the Rosiwal intercept method as used in petrography (Chayes, 1956). The volume percentage of an object in a thin-section is the same as the length of the chords crossing the object divided by the total length of the randomly-placed scan lines. Random lines decrease the bias in the measured data. Both methods are based upon the premise that any image of rock surface features represents an infinitely-thin section of those features. Krohn (1988b) stated that the porosities associated with power-law behavior measured in thin-sections agree with those calculated from the following equation. ~=(L,/L2)3-D,

(5-13)

where ~bis porosity, and L~and L 2 a r e the lower and upper limits for power-law behavior. For the pore-rock interface, D should be greater than 2 and less than 3 (Krohn, 1988a). The rock-pore interface could extend from the order of 10 ,~, the size of crystal nuclei, to 100 ~m, the size of grains. Table 5-IV presents some measured fractal dimension values (surface fracture technique) from Krohn's (1988b) study. Five carbonate formations are compared with sandstones and shales. Fractal behavior exists for all carbonates, sandstones, and shales TABLE 5-IV Summary of fractal values, determined by the automatic fracture surface technique, for carbonates, sandstones and shales. A is a proportionality constant Formation

Fractal dimension

A

10-3

L2* lam

2.27 2.35 2.59 2.65 2.75

4.27 5.90 5.83 4.44 7.34

8 3 6 36 26

2.49 2.61 2.71 2.85 2.89

4.29 3.50 5.89 7.65 8.62

4 18 4 >32 40

2.54 2.74 2.75

7.19 7.11 7.33

15 > 10 33

Carbonates Arab D Bedford Limstone Austin Chalk Smackover Dolomite Smackover Limestone

Sandstones Navajo (red, fine-grained) St. Peter Navajo (red, coarse-grained) Berea Blackhawk (well s a m p l e - 188 m)

Shales Niobrara (well s a m p l e - 2 5 2 6 m) Maim (well sample - 2308 m) Mowry (well s a m p l e - 2780 m)

Source: Modified after Krohn, 1988b, table 2; courtesy of the American Geophysical Union. * L 2 marked with > denotes the lower limit for L 2 where the end of the fractal regime was not observed by Krohn.

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with fractal dimensions ranging from 2.27 to 2.89. Although Krohn stated that only one fractal regime was found for each sample, many of the plots exhibited a bifractal (a dual fractal regime) nature. Figure 5-21 presents a bifractal example of the Bedford Limestone from Indiana, U.S.A. showing that the fractal nature of the features have limited ranges. The lowest measured D values, 2.27 and 2.35, are for the Arab D Formation and the Bedford Limestone, respectively. The highest values given in Table 5-IV, 2.85 and 2.89, were measured for the Berea Sandstone and the Blackhawk Sandstone, respectively. What interpretation can be placed on these values? There are two potential sources of fractal behavior in Krohn's study. One is the original deposition of mineral grains or carbonate particles of various sizes and roughness, and the other is diagenetic alteration by the precipitation and dissolution of minerals. Diagenesis will lead to inhomogeneous structures as smaller pores are preferentially altered owing to the reduced flow of fluids within the pores. Such alteration involves two competing processes of mineral growth and nucleation on the pore surface. Results in Table 5-IV show that higher fractal dimensions correspond to the rock pore interface filling three-dimensional space more than those associated with lower D values. The Blackhawk Sandstone has been extensively diagenetically altered, whereas the Arab D sample showed very little alteration. Both the carbonates and shales appear to be more homogeneous than sandstones with respect to their surface texture. Krohn (1988b) stated that if the rock contains some Euclidean porosity, which is not associated with the fractal pore rock interface, then the calculated porosity using Eq. 5-13 should be less than measured core porosities obtained using a Boyle's law porosimeter. Carbonate rocks can have Euclidean porosity exhibited by moldic porosity and vugs. Any match between the calculated and measured (core) porosities verifies that the pore surface and volume are fractals with the same fractal dimension.

267 Studying the diagenetic alteration of pores in sandstones, Katz and Thompson (1985) reached the following three conclusions: (1) the pore-grain interface is a fractal; (2) the pore volume is fractal; and (3) the pore interface and volume have the same fractal dimension D over the scale range from approximately 1 nm (L~) to 100 gm (L2). This latter point is important, because the pore space can be fractal or nonfractal depending on the extent of diagenetic alteration. Physically, it means that surface conditions of pores range from smooth, nonfractal walls in an unaltered rock to where the diagenetic materials fill the pore space. Another consequence of their study was that self-similarity in rock pore spaces leads naturally to an explanation of Archie's law, which depends on the geometry of the pore space. Katz and Thompson (1985) stressed that there is presently no detailed understanding of this relation. They could not draw conclusions about the transport properties of one rock from those of another with different pore geometries. The fractal structure of pore space suggests that dynamics within the pore space should scale with the length parameter L (see Eq. 5-13). Katz and Thompson (1985) presented the following equation to describe this relation with respect to conductivity, a, of a rock sample as: a - aw~ (L,/L2)Z(D-D0/Df =

O'w~ n ,

(5-14)

where the second equality is from Eq. 5-13; n = (Dr+ D ( 2 - D r ) ) / (3 - D ) Dr; a wis the ionic conductivity of the fluid filling the pore space; and Dfis the spectral dimension that must be determined on a rock-by-rock basis. Equation 5-14 is consistent with the form of Archie's law (Katz and Thompson, 1985). Roberts (1986) pointed out that the above discussion does not rule out the possibility that the pore interface and volume are both fractals, but have different fractal dimensions. This is explored next for carbonates.

Fractalpores. In order to characterize porosity with fractals one must first develop models that mimic the actual shape of pores for carbonate rocks. The same fractal concepts described in Eqs. 5-11 and 5-12 apply to a square and a cube. In fractal geometry, these two constructions are the Sierpinski carpet and the Menger sponge. A cross-section through the rock-pore system is modeled on the Sierpinski carpet and is equivalent to the face of the Menger sponge (Garrison et al., 1992). Figure 5-22 illustrates some Sierpinski carpet patterns. As one focuses down (increasing magnification) the pore space pattern does not change in distribution or shape, but only gets more minute. Shapes of different fractal dimensions can be fabricated by employing different construction algorithms. Three stages or orders are shown for each shape. Each stage is a repetition of the initial view scaled down. Conceptually speaking, such geometric constructions can be carried out ad infinitum. One then has a system, which is invisible, because it has zero surface area. The construction contains an infinite number of holes, bounded by an infinite number of threads of infinite length, in which none of the holes (pores) are interconnected. These stylized pore shapes in Fig. 5-22 compare favorably in an ideal sense with

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Fig. 5-22. Sierpinski carpet patterns mimicking two-dimensional pore space. (A) a square-shaped pore having a fractal dimension of 1.87. (B) the pore is now H-shaped owing to the deposition of cement on its surface. Two squares represent the filling giving this shape a fractal dimension of 1.92. (C) growth of the pore filling reduces the pore space to an I-shape having a fractal dimension of 1.97. As the pore is filled, its surface fractal dimension approaches the Euclidean dimension of 2. Fractal dimensions were calculated using Eq. 5-12. Garrison et al. (1992) used the following four Sierpinski carpet models in their study of increasing order of pore complexity. (D) Sierpinski carpet generated with Euclidean square holes (D S = 1.8917). (E) Sierpinski carpet generated with Euclidean circular holes (D s = 1.9202). (F) Sierpinski carpet generated with Triadic Koch Island holes [prefractal (m = 3). Koch curve generator was used to give a complex perimeter reflecting boundary roughness] (D s = 1.9459). (G) Sierpinski carpet generated with Quadric Koch Island holes [prefractal (m = 3) Koch curve generator was used to change the perimeter roughness] (D s = 1.9665). m is the number of iterations of carpet generation. (After Garrison et al. (1992), figs. 4, 5, 6 and 7; reprinted with the permission of Marcel Dekker, Inc.)

those cross-sectional pore views of carbonate rocks by Teodorovich (1958) and Choquette and Pray (1970). Increased complexity in the pores due to cementation goes from left to right in Figs. 5-22 A-C. Increasing fractal values, using Eq. 5-12 to calculate these values, illustrate the complexity of the stylized pore system. Although highly stylized, the individual pore shapes can be topologically expressed as other "cementation" configurations as illustrated in Fig. 5-23. The fractal geometry of the example pore shape variations (Fig. 5-23) will be the same for a given configuration series. It should be noted that the surface area and permeability values will not always be the same for all possible configurations of a given pore. This is the basis why Teodorovich's method for estimating porosity and permeability values from thinsections works on a microscale level: that is for small rock samples (see Mazzullo and Chilingarian, 1992a). Under these conditions, the only assumption is that pore spaces are interconnected to provide permeability. On a microscopic scale, the fluid flow within a carbonate reservoir depends not only on the pore shape but also on the

269

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10 Fig. 5-23. Examples of variations in pore space configurations "H" and 'T' within the original square pore shown in Figs. 5-22B and 5-22C. Dark areas represent the void space. All configurations for a given shape have the same fractal dimension. Relative surface area values* are the sums of the sides of the pore space in contact with the pore filling and rock surface. A change in the distribution of the void space can create an increase in surface area and in roughness, along with narrowing of the flow channels. All these parameters have an impact on the wettability, fluid saturations, and effective permeability values. *Below each example.

distribution of the cement ('roughness') within the pore space. Roughness increases the surface area and flow path lengths within a pore and flow network. It influences the surface tension between fluids and the rock (mineral) pore surface. Mandelbrot (1963) presented "Swiss cheese" examples of an ideal Sierpinski carpet containing circular holes mimicking pores (Fig. 5-24A). Garrison et al. (1992) used a sophisticated image analysis approach to analyze various Sierpinski carpet models in their study on pore roughness and the processes responsible for the formation of pore space in rocks. Numerous equations were developed for determining the effective fractal dimensions of a rock-pore system from measurements of hole properties and hole distributions, such as hole diameter, perimeter, and randomness. The digitized Sierpinski carpet models varied in complexity. Although Garrison et al.' s (1992) approach to analyze Sierpinski carpets was somewhat different from our approach, their calculated D s values (see Eq. 5-12) also increased (approaching the Euclidean topological dimension of 2) as the pore-shape area became more complex. The spatially ordered Sierpinski carpet models used by Garrison et al. (1992) in the order of complexity are" (1) a modified square pattern (N - 21 and 1/r - 5) having an apparent D s - 1.8917; (2) a circle (Mandelbrot's Swiss cheese), which is inscribed in the square so its diameter equals the side of the square, having an apparent D s - 1.9202; (3) a triadic Koch hole having an apparent D s - 1.9459; and (4) a quadratic Koch hole having an apparent D s - 1.9665 (Figs. 5-22D-G).

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Fig. 5-24. (A) example of Mandelbrot's Swiss cheese, which is an ideal Sierpinski carpet with round holes. (After Mandelbrot, 1983; reprinted with permission from W.H. Freeman and Co.) (B) an example of Katz and Thompson' s (1986) Euclidean pore-space. Each one of the largest squares is of linear size L 2. The hatched areas are grains, the white squares are pores, and the dotted area is a Euclidean pore. (After Katz and Thompson, 1986, fig. 1; reprinted with the permission of the American Physical Society.) (C) Sierpinski carpet generators that produce six different looking carpets satisfying the relationship D s = N~ k with N = 65, k = 9, and D s = 1.8998; N is the number of measuring units of size 1/r n (r n is the size of measuring unit) and k is the similarity ratio, a fundamental integer equal to 1/r. The generator C is more lacunar (holes are larger and the spatial distribution is more sparse) than the carpet produced by generator A (visualize that the large hole is formed from the coalescence of 16 holes in generator A). (After Garrison et al., 1992, fig. 8; reprinted with the permission of Marcel Dekker, Inc.)

In addition, the measurement results from their image study showed that measured D s values were similar to the calculated D s values. Any discrepancies between the calculated dimensions and the actual measured surface fractal dimensions are artifacts of digitization of the hole area in the carpet (Garrison et al., 1992). Katz and Thompson (1986) commented on the problem of large, erratic pore sizes occurring in rocks. Large pores can be viewed as infrequently and randomly-occurring Euclidean fluctuations as shown in Fig. 5-24B. In this model, different probability

271 values were assigned to grain size, Euclidean pores, and open pores to create a statistically self-similar version of a Sierpinski carpet. Randomization permits overlapping of holes to create larger voids. The Euclidean (large) pores yield large variations in local porosity. Equation 5-13 can approximate the macroscopic porosity over a suitable range defined by the choices of L~ and L 2 (Katz and Thompson, 1986). A new measure, D ' which is the apparent surface fractal dimension of a Sierpinski carpet derived from the hole diameter distribution, was developed by Garrison et al. (1992). D ' values are calculated from image analyses of the pore diameter distributions of simulated carpets. This measure is necessary in order to evaluate the textural aspect of fractal carpets known as lacunarity (Garrison et al., 1992). Lacunarity is visualized as a gauge of the size of holes in the carpet and/or the tendency for holes to cluster together (Fig. 5-24C). Each of the six generated Sierpinski carpet examples have been spatially ordered and of constant lacunarity. These carpets are too simplistic to be used as rock-pore system models. More realistic carpet models can be generated if the lacunarity is allowed to vary randomly, thereby creating carpets having varying hole distributions and size clustering. To evaluate lacunarity in pore system development, the true surface fractal dimension of an equivalent square hole Sierpinski carpet (D") is calculated for a rock by using the maximum Feret diameter method as described by Garrison et al. (1993a, p. 46). If D ' is not equal to D " then lacunarity exits. The difference between the surface fractal dimension, D s, and the apparent surface fractal dimension, Ds', is known as the lacunarity symmetry index, q. If q has a negative value, then the hole population is dominated by a lacunar distribution of large holes, which appears as an apparent over-abundance of small holes (Garrison et al., 1992). A positive q indicates that the hole population is dominated by a lacunar distribution of small holes. This distribution appears as an apparent over-abundance of large holes. Garrison et al. (1993a) extended their equations and relationships from the Sierpinski carpet model study to actual rock-pore systems by applying data acquired from image analysis of sandstone and carbonate rock thin-sections. Two types of multiple fractal rock-pore systems were identified by Garrison et al. (1993a). The first system consists of singular fractals of rock-pore systems with two or more natural fractal processes with different surface fractal dimensions, each scaling over a discrete range of lengths. Garrison et al.'s (1993a) second system consists of rock-pore systems with two or more natural fractal processes, each with the same fractal dimension and each scaling over a discrete range of lengths with different integral abundances. Garrison et al. (1993a) devised a classification of natural multiple fractal objects based on curve shapes observed in size-frequency distributions plots (Fig. 5-21). Two fundamental fractal classes were identified" (1) singular fractals, and (2) multifractals. The singular fractals can be subdivided into two groups: (1) simple, and (2) disjunct. The simple fractals exhibit only one size-frequency distribution representing a single fractal population. The simple type is illustrated by the dashedstraight line shown in Fig. 5-21. The dashed-line assumes a single fractal nature of the measured surface features. The disjunct group of curve shape consists of separated parallel fractal trends representing multiple populations with same fractal dimensions. s ~

S

S

272 The multifractals also are subdivided into two groups, dextral and sinistral, based on two separated and distinct curve shapes. The dextral curve shape is illustrated by the two solid lines in Fig. 5-21, which shows the bifractal nature of the measured surface features. The upper solid line has a D s' value less than the D's value of the lower solid line (Dsu' < Ds~'). The sinistral curve shape dog-legs to the right in the opposite direction of the upper solid line in Fig. 5-21 and D s u ' > D sl ' " The fractal dimensions of two carbonate reservoir rocks were measured from thinsections using SEM-based pore image analysis by Garrison et al. (1993a). Two samples of the San Andres Dolomite from west Texas, U.S.A. have calculated surface fractal dimensions (Ds) of 1.992 and 1.984, and composite D s' values of 1.733 and 1.967, respectively. D s' results from the interpretations of the pore diameter-number (size-frequency) distributions showed that in the first sample there were four pore processes present: three well-defined and one poorly defined. In the second San Andres Dolomite sample only two well-defined processes were delineated by the D s' determinations. Both San Andres samples showed parallel apparent surface fractal distributions (disjunct relationship) occurring over different length ranges with some overlap. Two thin-sections from the Arun Limestone (Indonesia) were analyzed in the same manner. The calculated Dsvalues are 1.952 and 1.978, and have composite D s ' values of 2.394 and 2.977, respectively. The logarithmic pore diameter-number distribution results for the first Arun Limestone sample shows that three natural fractal processes with similar apparent surface dimensions of D s l ' = 2.198, D s 2 ' = 2.189, and D s 3 ' = 2.209 essentially occur over the same length ranges. The second sample has two well defined processes with dimensions Ds~i m- 2.800 and Ds2!.._ 2.865 . Both Arun Limestone samples showed parallel apparent surface fractal distributions (disjunct relationship) occurring over different length ranges with some overlap. The pore-rock systems in the San Andres Dolomite and Arun Limestone were shown that they could not be represented statistically as a single fractal process. The value of the lacunarity symmetry index provides valuable insight into the nature of the poreforming processes and to the progressive development of the pore system over geological time. Comparing the value of q and the petrographic character of the pore system can help in deciphering the pore system development in carbonate rocks. Garrison et al. (1993a) pointed out that some pore-forming and pore-altering processes, such as dissolution, progressive crystallization, recrystallization, and dolomitization, may change the pore system without dramatically changing the total pore cross-sectional area and hence the dimensions D and D ". Other processes such as compaction, cementation, and solution enhancement could alter the pore system pore diameter-number distribution, as well as the total pore cross-sectional area and hence the dimensions D s and Ds" (Garrison et al., 1993a). It was suggested by Garrison et al. (1993a) that the only ways in which these processes can be shown to be operative are by: (1) logarithmic pore-size distributions having a D s' value that is either abnormally high or low; or (2) a suite of carbonate rocks that exhibit a progressive change in D s' and Dswith progressive diagenetic alteration. At present, it is difficult to decipher the diagenetic history of carbonate rock pore space using fractals. Pore altering processes can be distinguished using logarithmic pore-size frequency plots, but can not be identified using single fractal values.

273

Fig. 5-25. An example of a Menger sponge having a fractal dimension of 2.727. This construction is a three-dimensional analog of the Sierpinski carpet pattern shown in Fig. 5-22A. (Modified after Mandelbrot, 1982; courtesy of W.H. Freeman and Co.) As stated previously, an ideal Menger sponge is a three-dimensional extension of an ideal two-dimensional Sierpinski carpet (Fig. 5-25). By using the same concepts of fractal geometry as discussed above for the Sierpinski carpet, pores o f a Menger sponge can be randomized to produce statistically self-similar systems. The Menger sponge has an infinite surface area and zero volume. The sponge can be used as a model for flow in rocks having a log-normal distribution of porosity. Turcotte (1992) presented the following equation, where porosity, ~, for a fractal medium can be related to its fractal dimensions: dp = 1 - ( r o / r n )

3-D ,

(5-15)

where r 0is the initial linear dimension of the sample (in this case a solid cube), r is the linear dimension of the Menger sponge of order n (r~ = 3r 0 (first order cube); r 2 = 9r0; r n = 3~r0), and D is the fractal dimension. For a first order cube D = ln20/ln3. Another realistic and general rock-pore model is one proposed by Kaye (1989) and McCauley (1992). Different thin rock slices (e.g., thin-sections) are stacked together to simulate a rock. This construction provides for a variation in both porosity and the number of pores from one thin slice to another. This will be discussed in more detail later in the section on a multifractal rock model. This foregoing discussion on the use of porosity classification systems brackets the scope of porosity's role in carbonate reservoirs. At present, the evaluation of a reservoir or well performance, based on present-day knowledge of porosity and

274 permeability, is effectively limited to a simple classification. In order to move to a higher level of understanding it will be necessary to overcome the inherent problems associated with scaling laws relating permeability to porosity and conductivity to porosity. Distributions of porosity and permeability, as used presently in computer models, need adjustments obtained by history matching. Wrong assumptions made about permeability and porosity distributions are corrected in this manner after a reasonable period of production. Heterogeneity creates "noise" in the system and the question is how to handle it in order to increase the production performance of a carbonate reservoir. These aspects will be discussed in the section on carbonate reservoir characterization. Classification based on the geological nature of the carbonate reservoirs At this point it should be clear that reservoir characterization and classification require a synergistic approach. This demands the use of geology, reservoir engineering, geophysics, petrophysics, and geostatistics to describe quantitatively the reservoir at various scales. Figure 5-26 gives an overview of scales used in the description of hetRELATIVE

S CA LE

. ~;IZE

MICROSCOPIC

_-~ ,U m

MESOSCOPIC

mm

RESIERVOIR PROPERTy

PICTORIAL D E S C R I P T I O N

PORE SPACE

PORE NETWORK Ol ST RIBUTION

GEOLOGIC E N T I T Y

FRAMEWORK

~~,~. LAMINATIONS

f SYSTEM

BEDDING

STRA TI GRAPHIC MEGASCOPIC

m to km

LI THOHYORAULIC UN I T

A NO STRUCTURAL TRAPS

GIGASCOPIC

~> km

REGIONAL FLOW / MIGRATION PAT TE RNS

OE PO S ITI ONA L AND DIEFORMATIONAL SYSTEMS

Fig. 5-26. Heterogeneity scaling description of pore space with respect to a reservoir and surrounding geology (From Chilingarian et al., 1992a, fig. I-2; reprinted with the permission of Elsevier Science Publishers B.V.)

275 erogeneity in reservoirs (Chilingarian et al., 1992a). The necessity for proper reservoir characterization is driven by: the maturity of oil reservoirs worldwide; war damage to reservoirs in Kuwait; improper exploitation of Russia's reservoirs; and the United States' eroding light oil (>20 ~ API) reserve base. More crude has to be recovered from the existing reservoirs. In this section, quantitative and qualitative geological information at the interwell scale will be used to formulate a geological carbonate reservoir classification scheme. A practical application of this scheme will be made in evaluating the incremental recovery of unrecovered mobile oil in carbonate reservoirs.

Background Fisher and Galloway (1983) pointed out that physical, chemical, and biologic processes active in specific depositional environments determine many reservoir attributes. These attributes directly or indirectly relate to hydrocarbon generation, migration, entrapment, and reservoir productivity. The application of sequence stratigraphic rules is important to the development of a classification of carbonate reservoirs based on their geological nature. What is desired is to be able to distinguish not only the internal facies, but also to define facies as part of the reservoir anatomy (geometry). The following four simple rules capture the essence of carbonate reservoir rocks and form a basis that leads to a semiqualitative characterization and prediction of their properties. The four rules are" (1) carbonate rocks are largely of organic origin; (2) the organic systems can build wave-resistant structures; (3) the sediments undergo extensive diagenetic alteration before and after lithification owing to the metastable nature of the carbonate minerals; and (4) these rocks sustain structural modifications. The implications of these rules in the establishment of a carbonate reservoir classification are pervasive. Depositional processes control the primary attributes of a reservoir. This concept came about in order to tie the intemal reservoir's architecture, which is a product of sedimentation style, to the additional recovery of mobile oil and recovery of residual oil from existing reservoirs. Mobile oil is the oil that can be expelled from the pore space into the well during primary or secondary recovery. Mobile oil remains in the pores of carbonate reservoirs after primary recovery for a variety of reasons. The main reason is that lithological complexity resulting from variations of reservoir properties can result in pockets of trapped oil. Residual or immobile oil is crude locked in the pore space by capillary and surface forces acting at the microscopic scale. Immobile oil can be recovered by using enhanced oil recovery (EOR) methods, such as steam injection, in-situ combustion, polymer flooding, alkaline flooding, miscible fluid displacement, carbon-dioxide flooding, and micellar-polymer flooding. Unrecovered mobile oil can be classified as either (1) areally uncontacted or bypassed oil, or (2) vertically bypassed oil. Both the areally unrecovered oil and vertically bypassed oil are present in all carbonate reservoirs. The efficiency of recovering oil is based on certain factors, which contribute to a wide range of primary, waterflooding, and EOR methodologies. These factors are tied to the physical character of the reservoir, variations in fluid properties, and drive (energy) mechanisms. A fundamental difference exists between carbonate reservoir classification schemes with respect to exploration criteria and reservoir characterization criteria.

276 Exploration criteria are sometimes confused with criteria needed to define a reservoir. Exploration identification criteria deal with the external geometry of length and width, burial depth, thermal history, and structural style of the exploration target. Reservoir characterization is defined by internal boundaries and barriers (heterogeneity), which can be related to the geometry of individual depositional components. These control fluid saturations, fluid distribution, and flow properties-the producibility of the reservoir. Galloway et al. (1983) showed that carbonate and sandstone reservoirs in west Texas can be grouped into geologically related families called plays. This analog approach defines plays as a group of geologically related reservoirs exhibiting source, trap, and reservoir characteristics. A delineation of a play depends upon the original depositional setting of the reservoir rocks. This concept contributed to the U.S. Department of Energy's supported research effort into maximizing the producibility of the United States' domestic oil resource. Reservoir classification Tyler et al. (1984) presented a reservoir classification scheme (Fig. 5-27) which compares the recovery efficiency cross-plotted against reservoir genesis and lists the drive mechanism for both clastic and carbonate oil reservoirs located in the State of Texas, U.S.A. Figure 5-27 shows that there is a well-defined trend of decreasing oil recovery from these reservoirs. Reservoirs composed of deep water sediments appear to be excellent candidates for additional oil recovery. This is due to the high percentage of nonproduced moveable oil remaining in these reservoirs at abandonment. Carbonate plays do not exhibit as broad a range of recovery efficiencies as do the clastic reservoirs. Reservoir classes. The U.S. Department of Energy is presently classifying light oil carbonate reservoirs based on seven major depositional categories (Table 5-V). The development of this classification system involved the use of the TORIS database located at the U.S. Department of Energy, Bartlesville Project Office, Bartlesville, Oklahoma, U.S.A. Trial groupings of distinct, internally consistent, carbonate reservoir classes were compiled for statistical analysis using Analysis of Variance (IOCC, 1990). The statistical analysis helps to establish a number of manageable reservoir classes that are: (1) collectively exhaustive; (2) mutually exclusive; (3) internally consistent; and (4) different from each other with regard to heterogeneity (IOCC, 1990). The reservoir groupings, although geologically defensible, are based on the premise that reservoirs from the same reservoir class will have similar heterogeneities. Depositional systems are the dominant geologic factor influencing the development of reservoir heterogeneity. The categories are differentiated on the position of their depositional environment as a function of relative water depth and diagenetic overprint. Several criticisms need to be considered when evaluating the universality of this classification system: (1) only 450 carbonate reservoirs from the United States were available from the TORIS database; (2) omission of well known reservoirs; (3) improper interpretation of the depositional setting assigned to a reservoir; (4) evaporite associations, such as structural effects of evaporite dissolution or salt

277 TABLE 5-V Classification of carbonate depositional systems and their subcategories based on the position of their depositional environment as a function of the relative water depth and basin morphology (see Fig. 528)

Peritidal Supratidal Intertidal Subtidal

Reef (sup) (int) (sub)

Pinnacle Bioherm Atoll

Shallow shelf

(p) (b) (a)

Slope/basin

Open shelf Restricted shelf

(os) (xs)

Debris fan Turbidite deposits Mounds

(df) (td) (m)

Shelf margin Rimmed shelf Ramp

Basin Drowned shelf Deep basin

(rs) (r)

(ds) (db)

Source: Modified after DOE, 199 l, table 1.

o

0

o

E

.~

v

2

"E~: ";

..~

"s

";

"~

m

o

a. 80

9

o

o

o

~.

g a.

o~

:~

\ \ \ o\

\

\ % \

60

ON

\ %

\

c

%

\

8

40-

\

", \

\

\

9

\ \

\

i

l" 1 9

\

40 ~ o

x x

"

9

\

Q

%

IT

\

20

I

\

"~ tight clostic

lJ modified by suboerlal leoching

reservoir O'&

0 Reservoir genesis 0nd drive mechanism

Fig. 5-27. Plot of the average recovery efficiency versus reservoir genesis for important clastic and carbonate oil reservoirs in Texas, U.S.A. Drive mechanisms appear next to the depositional environments: C - combination (some combination of GCE, SG, and W); G C E - gas-cap expansion; G D - gravity drainage; S G solution gas; M - mixed; and W - water. (Modified aiter Tyler et al., 1984; courtesy of the Bureau of Economic Geology.)

278 piercement structures, were not integrated into the groupings; and (5) structural compartmentalization, which is difficult to quantify, was lumped under "other" factors. The investigation scale of heterogeneity in this classification approach is at the macroscopic (interwell) level. The principle is that the internal architecture and heterogeneity of reservoirs are dominantly controlled by processes operating at the depositional level. Modifications after deposition are important in determining reservoir recovery efficiency on the macro- and mega-scale levels. Figure 5-28, a three-dimensional representation of geological data, considers the effects of the diagenetic overprint and structural compartmentalization on reservoir productivity. Figure 5-29 is a simplified version of Fig. 5-28. Reservoir class descriptions provide

FAULTED/FOLDED FOLDED

FAULTED

NATURAL FR POROSITY

, /

UNSTRUCTURED

DEPOSITIONAL SYSTEMS

Leve~and / LACUSTRINE

COMPACTION CEMENTATION GRAIN OISSOLUTIOi~

GHAIN ENHANCEMENT

PERITIIDAL |

! I ~ I

SHAL LOW SHELF

,

7 k REEF/ISLOPE/BASIN~

Snyder SHELF EDGE

Mo•dak Fairway

Glennbur~L-". . . . . . . . . . // ,

I

BASIN

/ ,

I~_~ I I I

~

t

'

\,,

Austin Chalk

i

I DOLOMITIZATION

(Evoporites)

DOLOMITIZATIO

N

MASSIVE DISSOLUTION

SIL ICl FICATION

Fig. 5-28. A three-dimensional classification scheme of carbonate reservoirs with examples of reservoirs from the U.S.A. Reservoirs can appear in more than one box. Abbreviations are defined in Table 5-V, except for ss (strike-slip fault), rf (reversed fault), and nf (normal fault). (Modified after DOE, 1991, fig. 2; courtesy of the U.S. Department of Energy.)

GEOLOGICAL RESERVOIR CLASSIFICATION SYSTEM

I

.

I CARBONATE

I

:

Deposltlonal _ System

I Dlagenetlc Overprint

,,

9 Lacustrine

9 CompactionCementation

9 Peritidal Sur~etJd~ 9 . bleftJdal . Sublidal

SILICICLASTIC

I Structural Comp, artmentallzatlon

!

Shelf Open 9 Shell

9 Natural Fracture Porosity

9 Aulhigenic

9 Faulted

9 Natural Fracture Porosity

9 Lacustrine Basin Margin

9 Dolomitization

9 Faulted

9 Alluvial F a n

Canter

- Humid (Sveam-Dominaled) A 9 n d / S e m i Arid 9Fan Deltas

9 Folded

"Ramp

Clay

9 Folded 9 Chertificalion 9 Faulted/ Folded

9 Fluvial

9 Faulted/ Folded

.

Braided Sueams 9

Meande,i~

Sueams

Delta

9

Reefs *

9 Unstructured

9 Grain Dissolution

9 Grain Enhancement

9 Massive Dissolution

Structural Compartmentalization

9 CompactionCementation

9 Dolomitization

9 Shelf M a r g i n mnmed 9 Sh~

- Ptnnade Reels . Biohecml

Overprint

I

9 Eolian - E,Os Coasud Dunes

(Evaporites)

. ResVicled Shell

I Dlagenetlc

System

9 Unslructured

RESERVOIRS

......

Deposltlonal

B 9 un

9 Shallow

9

I RESERVOIRS

- Wave-Domimlled

Silicification

F 9luvial.Dominamd - T~le- D o r n i n a t e d

-A ~

9 Strandp~ain 9l~norC.,cN'es . B~der Shorofaces Bad~ Baniers TKIal 9 Channels - W u h o ~ FmVTidal Deltas

9 Slope/Basin Delxis 9 Fans Tu, 9 l~lite Fans . Mounds

9

9 Basin D 9 r o w n e d Shell . Deep

9 Shelf (Accrelionary Processses)

Basin

Sand Waves - S a n d |10dges'Bars

9

Slol~/Basin - Tud~dde

Fans

Dol~Is F a n s 9

Basin 9Pelagic

Fig. 5-29 9 A simplified geological reservoir classification system based on depositional system, diagenetic overprint, and structural compartmentalization for carbonate and clastic reservoirs. (After Ray, 1991" courtesy of the U.S Department of Energy.) 9

t,a -..I

280 generalized geological images of carbonate reservoirs and their productivity, and a comparison is made with clastic reservoirs. This presently used classification considers in a general way whether or not the reservoir is structurally influenced.

Carbonate depositional systems and reservoir properties. The following is a generalized description of the carbonate depositional systems used in the classification with comments on reservoir drive mechanisms. For a detailed classical-geological description of depositional models refer to Volume I (Mazzullo and Chilingarian, 1992b). Recovery efficiency values can be obtained from Fig. 5-27. Lacustrine carbonate reservoirs are not common in the United States. Some fractured lacustrine carbonate reservoirs exist in the Green River Formation, Unita Basin, Utah, U.S.A. (DOE, 1991). Peritidal carbonate reservoirs are rocks deposited in intertidal to supratidal environments, including hydersaline sabkhas. Terrigenous elastics can frequently interfinger with these carbonate sediments. Where evaporation dominates evaporite deposits can be expected. One aspect that has not received much attention is carbonate tidal channel facies (Wright, 1984). The significance of carbonate tidal channels is that their migration creates a shallowing upward sequence like the prograding low-energy facies model. Reliable criteria for tidal channel recognition are lacking. Peritidal deposits are a mosaic of tidal flat, tidal channel and, where present, associated beach deposits. Sheet-like geometry of peritidal reservoirs is common, as is the typical cyclic arrangement of peritidal and subtidal deposits. Shallow shelf~restricted carbonate reservoirs include a wide variety of carbonate platform deposits originating in shallow water under arid and evaporitic climatic conditions. The term 'restricted' refers to the presence of restricted marine fossil assemblages in contrast to a system that has open marine fossil assemblages (DOE, 1991). Dolomitization of the original sediments produces extensive beds of dolomite. This results in highly stratified reservoirs having moderate to high residual oil saturations. Solution-gas-drive reservoirs predominate owing to the isolation of permeable zones. These reservoirs exhibit low to moderate recovery efficiencies. Tyler et al. (1984) revealed that this reservoir class accounts for 53% of all production from carbonate rocks in Texas, U.S.A. Shallow shelf~open carbonate reservoirs develop in a wide variety of facies deposited on a broad, shallow to moderately deep, gently sloping shelf. A carbonate ramp is a platform built from loose sediment without reef construction or lithification at the shelf break (Schlager, 1992). Recovery efficiencies can vary greatly owing to postdepositional modifications. Drive mechanisms are either solution-gas or combination types. Reefal reservoirs produce from stratigraphic reefs, such as open-shelf atolls, pinnaele reefs, and bioherms (patch). Most reefs are encased in low permeable shales, micrites, and mudstones; however, associated facies include grainstones that accumulate as flanking beds around the reefs. Dominant drive mechanism is solution-gas, sometimes augmented by a water drive. The vertical relief and lateral isolation, coupled with strongly developed layering of permeability are characteristic of these reservoirs. Irregular oil-water contacts occur owing to these facies changes. Shelf margin reservoirs are platform margin deposits, which include reefal and

281 nonreefal limestones, sometimes intercalated with sandstones, draped over the shelf margin. The reservoirs have diverse lithologies and diagenetic histories. Facies belts tend to be thin, narrow, elongated and internally complex reflecting bar, bank, and island facies deposited under low-to high-energy conditions. Permeability is highly stratified and lenticular. Most reservoirs have low recovery efficiencies. DOE (1991) recognizes two subcategories of shelf-edge reservoirs: rimmed shelves, which may contain barrier reef facies, and ramps. Slope basin reservoirs originate as carbonate submarine-fan, debris apron, and turbidity flow deposits on basin slopes around carbonate platforms. These types of reservoirs are not common and contain carbonate sands, muds and breccias. Schlager (1991) provided three rules, which govern the geometry and facies of such reservoirs: (1) The volume increase in sediment required to maintain a slope as the carbonate platform grows upward is proportional to the square of the height for conical slopes. It is proportional to the first power of height for linear slopes. (2) The slopes of most high-rising platforms are steeper than siliciclastic ones. (3) The internal angle of friction governs the angle of repose of loose sediment. At zero confining pressure the angle of repose approximates the angle of internal friction. Values for internal angles of friction for some lithified carbonates are: Wolfcamp Limestone -34.8~ Indiana limestone --42~ and Hasmark Dolomite -35.5 ~ Computer model studies by Bosscher and Southam (1992) showed that changes in composition of sediment dumped on a slope can produce unconformities (Fig. 5-30). At initial conditions, the platform grows with an empty lagoon. Sand and rubble from the reef margin are the only input into the lagoon. With time, the lagoon fills up and exports large volumes of mud burying the reef talus at a more gentle slope angle.

run tile: 2000 yrs; tizestep: I00 ?rs; platforz height: 164 ft (50 .); platf0rl width: 1312 tt (400 .); Gzargia: i0 .z/rr; Giateri0r: 4 u/rr. k: 0.66/ft (0.2/m); initial depth: 6.6 ft (2 z) iinear sea-level rise: 3u/yr; wavebase: 33 ft flO z); ziR ang]e/naxang]e: 5/35 degrees; width of section: 1083 ft [330 z). G is the gr0sth rate of the reef, and k is the lilht extinction coefficient.

unconformity caused by change in sediment composition

Fig. 5-30. An example of CARBPLAT output showing a grain-size unconformity on the slope of a continuously growing carbonate platform. The model considers a platform with an empty lagoon. Initially the lagoon and the slope receive only sand and rubble from the reef margin. After the lagoon fills up, carbonate mud is then exported to the slope covering the reef talus at a gentler slope angle, which creates a mud wedge unconformity over the reef rubble. (After Schlager, 1992, fig. 1-27a; reprinted with the permission of the American Association of Petroleum Geologists.)

282 Depositional models such as CARBPLAT help in deciphering and predicting facies when applied to the analysis of the geological nature of carbonate reservoirs and plays (Fig. 5-30). Basinal carbonate reservoirs occur in chalk deposits that accumulate from the raining down of pelagic organisms onto drowned platforms and basin floors. Friedman (see Chapter 8) recognized three categories of chalk reservoirs: (1) ones that were never deeply buried, lacking significant compaction, and having primary porosity; (2) those buried to a moderate depth and having an extensive fractured porosity; and (3) ones deeply buried, but having a high pore pressure to preserve high primary porosity.

Measurement of interwell heterogeneity- volumetric sweep. The classification systems presented in Figs. 5-28 and 5-29 have a statistical basis for their grouping. The IOCC's (1990) report suggested that the volumetric sweep efficiency (E) be used as an indicator of reservoir heterogeneity at the interwell scale. Sweep efficiency is a measure of the volume of the reservoir swept by water to the total volume subject to invasion. The aim of IOCC's methodology is to measure reservoir heterogeneity at the macroscopic scale. This approach helped IOCC to sort reservoirs into distinct classes whose members are geologically similar and which have similar heterogeneity (Table 5-V). Volumetric sweep efficiency directly reflects the gross reservoir heterogeneity along with other factors. These factors consist of well spacing, primary drive mechanism, and in secondary recovery operations, the injection rate, pressure, mobility ratio of the injection fluid relative to oil, and type of injection water. Evis broadly defined as the portion of a reservoir's hydrocarbon pore volume effectively swept by a waterflood. The volumetric sweep efficiency can be estimated from the ratio of ultimate recovery, by primary or secondary means, to the volume of displaceable mobile oil" Ultimate Recovery E = 9 v Displaceable Mobile Oil

(5-16)

As discussed in previous chapters in Volume I (Jodry, 1992; Samaniego et al., 1992), rock producibility can be determined from plots of oil and water relative permeability curves for a particular rock as a function of water saturation. Figure 5-31 is an example for a water-oil relative permeability curve for the San Andres Dolomite. The fractional displaceable mobile oil in Fig. 5-31 is the amount of oil that could be theoretically produced if the entire reservoir was reduced to its residual oil saturation. Displaceable mobile oil (Dmo), also known as just oil recovery (Craft and Hawkins, 1959), is expressed as: (1 -- Swi) - Soc Omo = (1 -

s.;,i)

,

(5-17)

where SW. l is the initial pore-water saturation, and S is the residual or critical oil saturation. This is the saturation at which oil will begin to flow as the oil saturation increases under the influence of a natural water influx or an artificial water drive. For the San

283 1.0

I

I

I

0.5 O/

0.1 Z 0 1

~" 0.05 U >.-, F.J

I

1

~9

0.01 -.---

l.iJ IX

tu 0 0 0 5

1

IX.

l.iJ > I-.

/--

_J 14.1 n,,

0.001 - -

0.0005 2O

80

30 40 50 60 WATER SATURATION,% PV

70

70

30

60

OIL

50

40

SATURATION~% PV

Fig. 5-31. Average oil and water relative permeabilities, San Andres Dolomite, Welch Field, Texas, U.S.A. For the values of S c = 0.32 and S i = 0.30 the displaceable mobile oil is 54% for the water--oil system. (Modified after Abernathy, 1964; courtesy of the Society of Petroleum Engineers.)

Andres Dolomite example in Fig. 5-31, the displaceable mobile oil is 54%. Estimation of the ultimate recovery is by decline curve analysis of historical production data. The volume of displaceable mobile oil on a reservoir condition basis can be estimated using a volumetric approach for a water drive having no gas. The equation is:

D =7758(A)(h)(~b)I (l-Si)-Sc I , mo

(1

-Si)

(5-18)

where A is the area of the reservoir, h is the net pay thickness, and ~ is fractional

284 porosity. Similar relative permeability curves are obtained for a gas-water system as for the oil-water system. For secondary recovery the volume of displaceable mobile oil for stock-tank conditions can be estimated from: = 7758 (14) (h) (~b) Dm~

S

oi

Bo i

S

orw

Boa

J

(5-19)

where Dmo is in stock tank barrels, A is in acres, h is in ft, ~ is fractional, S i -- (1 - S i - S 9gl.) and is fractional, SWl is the fractional initial water saturation, Sg! is the fractional . . . inmal gas saturation, Boi 1s the initial oil formation volume factor m reservoir bbl/ stock-tank bbl, S wis the fractional residual oil saturation in the swept zone at the end of water flooding, andB o a is the oil formation volume factor at the end ofwaterflooding (abandonment) in reservoir bbl/stock-tank bbl (IOCC, 1990). IOCC's (1990) report presented a volumetric sweep efficiency equation, which contained terms for reservoir heterogeneity, Eh,t; mobility ratio of injection fluid relative to oil, Enuid; well spacing, Ew.,; and other influences such as, primary drive mechanism and mechanical design of the waterflood, Eoth~r. The IOCC's viewpoint focuses on the additional recovery beyond primary recovery or pressure maintenance operations: E v = Ehet(Efluid)(Ewe, l)(Eother).

(5-20)

Several adjustments were made by IOCC (1990) to Eq. 5-20 for Enu~dand Ewe, by normalizing all the sweep data to a mobility ratio of 1.0 and a well spacing of 40 acres (16 ha). The residual influences (Eother) w e r e not segregated in the IOCC's analysis and remained as "noise" in the system. The adjustment for fluid behavior is a complex procedure. E vcan also be defined as the product of the areal sweep efficiency, E a, and the vertical sweep efficiency, Eh: E = E(Eh).

(5-21)

The areal sweep efficiency depends very strongly on the degree of vertical conformance (permeability variation) along the producing interval (IOCC, 1990). Fassihi (1986) described a method by which E can be determined from the empirical curves for three different water injection-well patterns: direct-line drive, staggered line drive, and five-spot. The curves are based on the measured sweep efficiency in a two-dimensional waterflood model. Fassihi's (1986) empirical equation, which fitted the curves, by using the mobility ratio, M, and fractional water cut, fw is:

1-Ea

- (alln [M + a2] + a3)fw + a41n (M + as) + a 6 .

(5-22)

Table 5-VI presents the empirical constants a, through a 6 values for the three pattern geometries. E hcan be determined by substituting the calculated value of ERfrom Eq. 5-22 into Eq. 5-21 and the value of E from Eq. 5-16. The value thus calculated is

285 TABLE 5-VI Coefficients in areal sweep efficiency correlations for three different well pattern geometries used in waterflood operations Waterflood well patterns Areal sweep coefficient

Five-spot

Direct-line drive

Staggered-line drive

aI

-0.2062 -0.0712 -0.511 0.3048 0.123 0.4394

-0.3014 -0.1568 -0.9402 0.3714 -0.0865 0.8805

-0.2077 -0.1059 -0.3526 0.2608 0.2444 0.3158

a2 a3 a4 a5

a6

Source: Modified after Fassihi, 1986; courtesy of the Society of Petroleum Engineers

consistent with data on M and Ev. A value for E , at a mobility ratio of 1.0, can be calculated using Fassihi's correction. It is now possible to adjust the volumetric sweep for the fluid effects: Eva=

EhE1. 0 ,

(5-23)

where Eva is the adjusted volumetric sweep for the fluid effects and Eal.0 is the areal sweep efficiency standardized to a mobility ratio of unity (IOCC, 1990). The effect of well spacing also can be removed by standardizing the sweep data for all reservoirs to specified well spacing. IOCC (1990) selected 40 acres (16 ha), a generalized function, which incorporates the effect of well spacing on reservoir (lateral pay) continuity. Reservoir continuity is the percentage of the total volume of reservoir rock that is in pressure communication between the injector-producer well pairs. Figure 5-32 presents a series of continuity functions based on actual field data from west Texas, U.S.A.(Gould and Sarem, 1984). This figure shows the fraction of gross pay that is continuous between the wells having different spacings. It is apparent in Fig. 5-32 that for a given reservoir a semi-log relationship exists between reservoir continuity and interwell distance. Barber et al. (1983), however, showed that such curves tend to exhibit less continuity as more data become available at smaller well spacings. The Fullerton Clear Fork and Wasson Clear Fork reservoir curves are based on relatively large spacing. Infill drilling at closer spacings could move them downward. The well spacing of a reservoir can be converted to an interwell distance by using the following geometric, power-law relationship: WD = 208.66(AC) ~ ,

(5-24)

where WD is the interwell distance in ft and A C is the well spacing in acres. The Interstate Oil Compact Commission's (1990) methodology cross plots the In(Eva) against interwell distance. A straight line is drawn between two points, one of which has the coordinates of zero interwell distance and nearly perfect sweep efficiency (0, ln[0.999]). The other point is the actual interwell distance and sweep efficiency for the reservoir or pay (WD, Eva ).

286 IO0

-~.

90

-

80

-

"

70

-

60

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ao ",. ~~ l~ "'~,~ ,'~"._,u.. ,t i ~ "'-:~

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Between

II

I

I

2,000 Welle

2,500

~ ~

I .

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3,000

3,500

(Feet)

Fig. 5-32. Pay-continuity diagram showing the fraction of gross pay that is continuous between wells at various spacings. (Modified after Gould and Sarem, 1989, fig. 5" courtesy of the Society of Petroleum Engineers.)

By interpolating or extrapolating the straight line, EvawaS obtained by IOCC at an interwell distance of 1,320 ft (40-acre well spacing). Eaat the 40-acre (402 m; 16 ha) well spacing is defined as Ehet. The semi-log function specific to each reservoir or pay zone is f(Ea, WD). f(Ea, WD) = d , , w o

+ b) ,

(5-25)

where m is the slope of the semi-log plot (ln[Ea] - ln[0.999])/WD, b is the intercept of the straight line with the y axis (ln[0.999]), and WD is the interwell distance in ft. By entering the standardized well distance (1,320 ft for 40-acre spacing) into Eq. 5-25, IOCC (1990, p. 17) adjusted the value of Eva for well spacing to yield the 40acre (16-ha) well spacing Eh~t: Ehet = f(Eva, 1320) 9

(5-26)

Table 5-VII presents the adjusted volumetric sweep efficiency values for some 450 categorized carbonate reservoirs. The IOCC analysis is a statistical resolution of carbonate reservoir data in the TORIS database. Figure 5-33 shows the data spread for the average volumetric sweep plotted against the heterogeneity indicator (Eh~t) for the

287 TABLE 5-VII Adjusted volumetric sweep efficiency values for nine carbonate reservoir subcategories defined by deposition and diagenesis. Carbonate shelf class includes shallow-shelf and shelf-margin reservoirs. Total number of reservoirs analyzed is 450. Adjusted volumetric sweep efficiency Reservoir class Peritidal Non-dolomitized Dolomitized Shelf Non-dolomitized Dolomitized Dolomitized + evaporites

Number of reservoirs analyzed

Mean

Variance

51 57

0.703 0.706

0.038 0.030

48 79 109

0.633 0.676 0.582

0.066 0.054 0.063

Reef Atoll: Non-dolomitized Others: Non-dolomitized Dolomitized

35

0.698

0.036

25 28

0.576 0.715

0.042 0.039

Slope-basin All

18

0.667

0.033

Source: Modified after IOCC, 1990, table 5

same carbonate reservoir data set. A comparison to clastic reservoirs is also illustrated in Fig. 5-33 (IOCC, 1990). This plot shows that carbonate reservoirs appear to be slightly less heterogeneous than clastic reservoirs based on volumetric sweep efficiency data from the TORIS database. Unrecoverable mobile oil ICF and BEG (1988) reported that over 80% of reserve additions in Texas, U.S.A., since 1979 can be attributed to intensive development of older reservoirs. Various primary recovery, waterflooding, and EOR techniques were used to increase recovery. The application of these methods, which produce significant amounts of additional remaining mobile and immobile oil, has proved to be highly cost effective. It is necessary to evaluate the unrecoverable mobile oil in carbonate reservoirs in order to assess various incremental recovery techniques. As mentioned previously, the efficient recovery of either mobile or immobile oil depends on the ability to map and predict the intemal architecture of carbonate reservoirs. The intemal architecture is profoundly influenced by the depositional conditions, which control the distribution of the various facies. Uncontacted mobile oil in reservoirs is attributed to many reasons such as fault compartments, flow heterogeneities, well spacing, facies changes, and physical properties of the crude. The writers concentrate in the discussion below on those methods that increase the recovery of the uncontacted and bypassed mobile oil. Uncontacted oil refers to oil trapped in isolated compartments within the reservoir, which is uncontacted by wells at current well spacing (ICF and BEG, 1988). The term

Plus One Slandard

................... c

C)

[

...................

Deviation

cJ

Mean Minus O n Slandard

Deviation

........................................................................................

CARBONATES

......................

CLAST1CS

Fig. 5-33. The heterogeneity parameter, Ehe1, range in values, and mean are presented for 25 different carbonate and clastic reservoir classes developed in the IOCC (1990) study. Carbonate reservoirs appear to have higher E,,, values than clastic reservoirs. A high Ehelvalue is indicative of a low level of heterogeneity. (After IOCC, 1990, fig. 6; courtesy of the US.Department of Energy.)

289 bypassed oil refers to oil unswept by injected fluids during secondary or enhanced oil recovery. Bypassed oil owes its origin to a high degree of vertical and areal heterogeneity or to an unfavorable mobility of the injected fluids. The determination of the amount of uncontacted oil requires knowledge about the macroscopic heterogeneity, facies information, and lateral pay continuity within the reservoir. ICF and BEG (1988) used a volumetric reservoir evaluation approach in solving this problem. A major drawback to their approach is that the solution is based on reservoir conditions after waterflooding. It does not apply to carbonate reservoirs undergoing primary production. The first step is to classify the unrecovered oil into two components: (1) areally unrecovered oil that includes both uncontacted and areally bypassed oil, and (2) vertically bypassed oil. Both areally unrecovered oil and vertically bypassed oil exist in all carbonate reservoirs. Their relative volumes depend upon the reservoir's architecture and the diagenetic effects in the producing zone(s). Determination of the gross unrecovered mobile oil volume requires data on the reservoir's ultimate production potential, fluid saturations, and the crude formation volume factor at initial, present, or abandonment conditions. By subtracting the estimated ultimate recovery (for decline curve analyses techniques refer to Mannon, 1972) from the original oil-in-place gives an estimate of the remaining oil-in-place. The volume of mobile oil remaining in the reservoir can be calculated as follows: UMOIP

= ROIP

OOIP(S~176

,

(5-27)

(Soi/Boi) where U M O I P is the unrecovered mobile oil (STB); R O I P is the remaining oil-inplace (STB), O O I P is the original oil-in-place (STB), Sra is the final fractional residual oil saturation, Boa is the oil formation volume factor at abandonment of the waterflood (bbl/STB), S i is the fraction of the initial oil saturation, and Boiis the initial oil formation volume factor (bbl/STB). The immobile oil-in-place ( I M O I P ) is defined as"

IMOIP = ROIP-

UMOIP =

OOIP(Sora/Boa) (Soi/Boi)

(5-28)

where Sor a is the final residual oil fraction in the waterflooded reservoir or zone. The distribution of unrecovered mobile oil can be determined from: U M O I P = A UO + V B P O ,

(5-29)

where A U O is the gross unrecovered mobile oil volume, and V B P O is the vertically bypassed mobile oil volume. Vertical s w e e p efficiency (Eh). To calculate the volume of vertically bypassed oil, the vertical sweep efficiency component (Eh) needs to be quantified. Fassihi (1986)

290 provided an empirical correlation for vertical sweep as a function of the mobility ratio and the fractional amount of produced water (water cut). This correlation defines vertical sweep efficiency as a function of the vertical permeability variation (DykstraParsons coefficient). Dykstra and Parsons (1950) introduced a method for describing the distribution of the absolute permeability of reservoir rocks determined from core data. It is difficult to describe heterogeneities deterministically, especially within carbonate reservoirs. Statistically, the permeability distribution defined by the cores is usually log normal. By assuming permeability to be a random function, with a known mean, variance and spatial correlation, the permeability can be characterized by a log-normal frequency distribution (Fig. 5-34). This widely used method is critical in predicting the effect of reservoir heterogeneity on waterflood performance. The method estimates the fractional waterflood coverage only for a vertically stratified reservoir with no lateral discontinuities. The Dykstra-Parsons coefficient, VDpiSequal to:

VDp=

ks0- k~ k5~ ,

(5-30)

where ks0 and ka are the 50th and the 84.1th percentile values from a log-cumulative permeability distribution. Core permeability values are arranged in a descending order of magnitude. The "greater than" permeability cumulative frequency is calculated and plotted. Figure 5-34 gives four examples of the spread of permeability values as quantified by Vop. The Vopvalues were calculated from core data for two "C" zone members of the Ordovician Red River Formation (a limestone and an interbedded dolomite and limestone) and the "D" zone member (burrowed dolomitized carbonate mudstones and wackestones) in the Williston Basin, U.S.A. This plot illustrates the degree of permeability contrast between different adjoining layers within the carbonate sequence. The Dykstra-Parsons permeability coefficient can provide a means of estimating the absolute permeability of individual layers when an average permeability value is available for the reservoir (ICF and BEG, 1988). Vop is estimated using cores from representative wells in the reservoir. The coefficient is then applied to the average permeability values to determine the vertical conformance profile throughout the reservoir. This information is used in determining the sweep efficiency of waterfloods. The Dystra-Parson coefficient also is a good indicator of the reservoir's potential during primary recovery. Honarpour et al. (1990) showed that a good statistical correlation (R = 0.9) exists between VDpvalues and initial production in a clastic reservoir. Low Vopvalues are associated with high initial oil production rates, whereas high Vop values are indicative of lower initial production rates. ICF and BEG (1988) developed a statistical correlation relating the permeability variation to the vertical heterogeneity component (H) (Fig. 5-35). This correlation helps in estimating the permeability variation coefficient for reservoirs where there is no detailed injection and production information. The correlation gives the average, minimum, and maximum values of VDpfor a known reservoir H v component and is based on an analysis of 156 reservoirs under waterflood in the states of Texas and New Mexico, U.S.A. The adopted scale ranges from H = 1 for very homogeneous

291 99.99 tO0

~.'

99.999.8 99 ' '""'1 '1 ' ''V''l~'"

~e , ,

915 '~"

90 i i i~0 70 60 ,,,'~, ,',,I,,l,l=,,

1501 40 23[0Z 0 | , ,,lW,, I,=l,,,,',-

!/I Z

5

2 ; 0.5 (~.2 0.1 0.05 i,=,,i.,,i = = w p.=l,i

II I I =

0.01 ,.,

9 -

E >:

.

_

-

-

_

I..err

t.l.I

lO

-

:E n, tJd

.....

i~

"

-

i

"

2

|

,,,

'~ ' ~ " ~

.

-

0.ol,,,I .... I , I , , I , , , , I , ~ , , I 0.01 0.0,5 0.1 0.2 0.,5 I

2

, , i,,,,L ......... li,,,l,,lll,l,, 5 I0 20 30 40 CUMULATIVE

i,lil,,,illllil,,, 50 (GO 70

FREQUENCY

X ~

80

i,,,lllt 90

ilst

I

hillhltill 98 99

I

I, 5.11,,a~ 99.8 99,9 99.99

K

Fig. 5-34. Examples showing the calculation of Dykstra-Parson coefficients using a log-normal plot of the cumulative distribution of core permeability values on log-probability paper. Core data from the "C" zone (subtidal depositional environment) of the Red River Formation, well Melby No. 4-1, Bush Lake Field, Sheridan County, Montana, U.S.A. No. 6: VDp = 0.74; 35.5 ft (11 m) of limestone composed of mudstone and wackestone containing some 12 different Archie classes (Oave = 3.9). No. 7: VDp = 0.50; 95 ft (30 m) of interbedded dolomite and limestone comprising a single Archie class (Oave = 1.8). (Core data and lithologic descriptions from Ikwuakor, 1992; courtesy of the U.S. Department of Energy.) The VDp results are very similar to values obtained from core data from the Red River Formation "D" zone (equal to the "C" Burrowed Member) in two wells (No. 1-25 Alexander and the No. 2-31 Hilton), South Horse Creek Field, Bowman County, North Dakota, U.S.A. The Dykstra-Parsons coefficients are 0.75 (well No. 1-25) and 0.53 (well No. 2-31). Higher values of VDp indicate less efficient water drive and/or waterflood systems when water displaces oil. (Modified after Longman et al., 1992, fig. 8; courtesy of the American Association of Petroleum Geologists.)

carbonate reservoirs to H v = 10 for very heterogeneous carbonate reservoirs. The following equations developed by Fassihi (1986) can be used to estimate the vertical sweep efficiency once the Dykstra-Parsons coefficient correlations are k n o w n either from direct measurements or using Fig. 5-35" x=-0.6891

+ 0.9735VDp+ 1.6453VZDp ,

(5-31)

292 i

A > v C

I

I

'

I

'

t

'a

I

i

0.9

.g

15

)

0.8

-

.............. ~ ~ o

.

.,2., .o o

~~-J"

.

,

~

0.7 n

no

0.6t

-------"-+i

~ " ~

". o.., o'~176176176 ~176176 "~176

~

......

~

~

_

13

== 0-5

~ -

.,..-.--

Data not avoiloblefor ~ s range ~*-- Of:ranShelf, Rofform--~

E3

0

Unhoclurod Chalk~ .,,O~).SIXIIf I

I

2

:3

Homogeneous

. . . .

4

Rotform

I,,,

I

I

I

i

5

6

7

8

9

Vertical Heterogeneity Descripta" (Hv)

,

I0 Heterogeneous

Fig. 5-35. Variation in the Dykstra-Parsons coefficient values cross-plotted against the vertical heterogeneity component for selected carbonate depositional systems. (Modified after ICF and BEG, 1988, fig. A-7; courtesy of the U.S. Department of Energy.)

y =

(WOR + 0.4) (18.948 - 2.499(VDp))

(M + 1 . 1 3 7 - 0.8094(Vop))10 x

(5-32)

and y = a,(Eha2 ) (1 -- Eh)a3 ,

(5-33)

where WOR is the water oil ratio; M is the mobility ratio, VDpis the Dykstra-Parsons permeability coefficient, E h is the vertical sweep efficiency, and Table 5-VIII gives values for the empirical constants a~, a2, and a 3. Equation 5-33 is solved for the vertical TABLE 5-VIII Coefficients used in Fassihi's vertical sweep correlation Coefficient

Value

aI a2 a3

3.33409 0.77373 -1.22586

Source: Data from Fassihi, 1986.

293 sweep efficiency (Eh) by iterative techniques. The volume of the vertically bypassed oil can be determined from standard engineering calculations for oil-in-place. The vertical sweep efficiency can be estimated based on areal and volumetric sweep efficiencies obtained from an analysis ofwaterflood performance. ICF and BEG (1988) presented a simplified one-step volumetric solution for E that is an expansion of Eq. 5-16"

E =

Nu

v

7758 (A) (~b) (Soi/Boi - Sor/Boa )

,

(5-34)

where N is the ultimate recovery in STB obtained from performance decline curves. Equation 5-34 can be used only with reservoirs where the entire primary drainage area is under a secondary recovery injection program. In ongoing waterflood projects, where there are no basic core data to determine VDpVDpcoefficient can be grossly estimated based on flood performance history (ICF and BEG, 1988). The methodology involves the following steps: (1) Use Eq. 5-34 to determine the volumetric sweep efficiency of the reservoir. (2) Use Eq. 5-22 to provide an estimation of the areal sweep efficiency of the reservoir. (3) Use Eq. 5-21 to determine E h. (4) By using Eqs. 5-31, 5-32 and 5-33, a value for VDpcan be determined. u

Areal sweep efficiency (H). Fassihi's correlation (Table 5-VI) excludes the effect of lateral reservoir heterogeneity. ICF and BEG (1988) pointed out that lateral reservoir heterogeneity is defined by the variability of geologic parameters at the intrawell scale. Key geological parameters include matrix porosity, effective permeability, and pay discontinuity. A reduction in well spacing reduces the effect of lateral heterogeneity in the carbonate reservoir by allowing more volume contact by the injection fluid. This increases the areal sweep and recovery efficiency. ICF and BEG (1988) prepared a family of curves that correlate the areal sweep efficiency to total well spacing for three different ranges of lateral heterogeneity components ( H ) (Fig. 5-36). A total of 484 reservoirs in the states of New Mexico, Oklahoma and Texas, U.S.A., were analyzed using the TORIS database. Low areal sweep efficiencies have values ranging from 1 - 4 , medium efficiencies range from 5 - 7, and high values range from 8 - 10. At large well spacings greater than 100 ac/2087 ft (40 ha; 636 m) per well, the sweep efficiency is low regardless of the H value (Fig. 536). Lateral heterogeneity at well spacings of less than 80 ac (32 ha) per well substantially influences areal sweep. Figure 5-36 illustrates that mean sweep efficiencies in reservoirs having low lateral heterogeneity components increase from about 60% to over 75% as well spacing decreases from 80 ac (32 ha) to 20 ac (8 ha) per well. Mean sweep efficiencies, however, in reservoirs having high H values increase from around 50% to only 65% in this well-spacing range. Constraints The discussion above is an illustration ofjust one approach that has been developed in order to evaluate a carbonate reservoir's potential using a geological classification

294 I

i, =I

l

I

I

I

I

I

i

I

i

i

I

I

I

I

I

0.9 : 0.8

c

0.7-

- Low H I ( I_
"'c

r. o <,,., u

0.6-

k_

LL 0.

0.5-

I1)

or)

0.4-

0.30.20.10

I 0

i

20

i

I

40

I

I

60

I

i

I

80

I

I00

I

I

120

I

I

140

I

160

Well Spacing (acres) Fig. 5-36. Effect of well spacing on the mean areal sweep values for three lateral heterogeneity classes. (Modified after ICF and BEG, 1988, fig. A-8; courtesy of the U.S. Department of Energy).

of reservoirs at the "macroscopic" scale. One drawback to any approach is the requirement for detailed knowledge of the reservoir's properties. This presents a problem: how to properly utilize measurements of reservoir properties taken at different scales? Worthington (1991) discussed the practical aspects of this problem of tying in downhole measurements to scale. Figure 5-37 presents the scale resolution in meters of downhole measurement technology used to obtain reservoir data. It is apparent from Fig. 5-37 that the downhole-measured data are at the mesoscopic scale. This is the scale of bed boundaries, stratification, and small-scale geological features usually obtained from well-log measurements. An integration of core data (microscopic/ mesoscopic scales) and well log data (mesoscopic scale) is necessary to provide a calibration of a particular well log response. Worthington (1991) pointed out that acquired high-resolution data under appropriate conditions can be used for the calibration of related data at larger scales. This problem of scale is very important in reservoir model studies. As an example, Wattenbarger et al. (1991) discussed how to obtain the optimal geologic representation scale (maximum grid size blocks) for representing permeability heterogeneity in reservoir models. Two numerical models were considered with respect to transport phenomena, such as tracer flows, in reservoirs. The first model explored the effects of changes in the scale at which permeability variations are explicitly represented (representation scale). They found that reservoir response may continue to change as the representation scale is decreased. This suggests that

295 DOWNHOLE MEASUREMENTS

I

r "" " -- "" "' -" "' " "-1

CTSCAN

I

TOOLS

. . . . .

I"" __--t

i

I

MEASUREMENTS

I

t. . . . . . .

"1

-

I I

MERCURY POROSIMETRY .........

'

|

I

I I

i

WELL LOGS

I

SEISMIC PROFILES

I

L ....

"l

L------'I I

I

[- . . . . . . . .

I I

I

IMAGE ANALYSIS

I

FORMATION TESTS

ASIN SIUDIES

I

L L . . . . . . . . . . . . . . . . . . . . .

I

l

10 -:~

10*

i

ANALYSIS CORE

_ I

I

i

J

i

SURFACE GEOPHYSICS

1

1

i

I

10 3

1

I

I 1

i

,1.

10 6

i

i

1

METRES I~

.-

-

MICROSCOPIC

--

~14~

MESOSCOPIC

r 14---- MAC ROSCOPIC -----'--~14'-------~ MEGASCOPIC

-=14-- GIGASCOPIC-.l,

Fig. 5-37. Scales of geologic property measurements expressed in terms of resolution. Downhole well measurements are emphasized. (Modified after Worthington, 1991, fig. 2; courtesy of the Academic Press, Inc.)

mixing induced by non-represented permeabilities can be represented implicitly using mixing parameters, such as dispersivity. The correlation length of the non-represented permeabilities was reduced by decreasing the representation scale. A second study demonstrated that the effects of small- and large-scale heterogeneities can be represented by a combination of explicit representation through varying gridblock permeabilities and implicit representation through effective mixing parameters. The robustness of the effective mixing parameters were best improved by reducing the representation scale while holding the averaging scale of the effective mixing parameters constant. In computer modeling, the costs associated with explicit representation demand that a geologic representation scale be as coarse as possible, while retaining model accuracy and robustness. Wattenbarger et al.' s (1991 ) work defined the optimal representation scale as the largest scale at which the effective mixing parameters are robust. Scaling problems, which influence reservoir concepts, and their impact on porosity and permeability are discussed in the section on carbonate reservoir characterization. INCREMENTAL RECOVERY TECHNOLOGY

Incremental recovery strategy addresses the problem of handling macroscopic heterogeneity in practice. The approach is to apply new drilling technology, and the application of secondary recovery techniques to primary development of reservoirs. There are three proven incremental recovery options available to assist operators in reducing well spacing, and to recover more of the potential unrecoverable mobile oil and gas in complex carbonate reservoirs during primary production. The three techniques discussed are: infill drilling, slant-horizontal-drainhole drilling, and advanced

296 fracturing. Other strategies applicable to waterflooding and EOR, such as polymer flooding, pressure maintenance programs, selective completion of new wells and existing wells, and profile modification, will not be discussed in this chapter. Infill drilling is a conventional method used to accelerate production from proven reserves and until recently was not thought of as a method by which an operator could increase amounts of recoverable reserves. There are four conditions affecting intrareservoir reserve growth: (1) new technology; (2) socio-economic factors; (3) leadership and improved decision-making by management; and (4) reservoir re-exploration. Holtz etal. (1992) pointed out that in Leonardian restricted-platform carbonate reservoirs in the Permian Basin, U.S.A., an average of only 18% of the original-oil-inplace is recovered from matured reservoirs. By using infill drilling strategy, however, the recovery efficiency in these Leonardian carbonate reservoirs tripled as reservoir development increased from 80-acre primary recovery to 10-acre secondary recovery (Holtz et al., 1992). Growth-rate potential of the remaining mobile oil is estimated to be 27%. Application of slant-horizontal-drainhole drilling in carbonates provides for development of naturally-fractured, low-permeability (tight) and heterogeneous carbonate reservoirs, and solves water-gas-coning problems. Advance fracturing, such as massive hydraulic fracturing, is used mainly to stimulate thick, low-permeability formations. Horizontal, lateral, or drainhole well technology is not a new concept. Lateral well drilling tool patents were filed in the early 1920s. Lateral holes with 20--40 ft (6-12 m) of penetration were used extensively in the 1930s, 1940s, and early 1950s to overcome wellbore damage and stimulating low-permeablility formations. This technology disappeared from general use with the development of hydraulic fracturing. A horizontal well can be thought of as being a controlled vertical fracture (Joshi, 1988a,b). Horizontal well technology for the purpose of improving oil and gas recovery had its beginning in the 1950s through independent research programs in Russia and United States. Advancements in directional drilling technology brought on by extended-reach requirements furthered horizontal drilling technology. Original applications of this technology addressed specific problems with vertical well completions, such as the coning down of gas or the pulling up of water from the base of oil zones. Horizontal wells can dramatically increase pay zone penetration, as compared to vertical wells, resulting in hundreds or even thousands of feet (meters) of exposure to the oil column. This capability was made possible by the development of reliable bit-guidance (directional) technology in the late 1970s, and the establishment of a viable service industry to support it in the field, during the 1980s. Today, the application of modified petroleum technology to horizontal wells in carbonate reservoirs is helping to overcome recovery problems related to flow heterogeneities. The induction of fractures with nitroglycerin, so as to stimulate wells, started around 1890. "Shooting a well" increased initial flows and ultimate recoveries of oil and gas by creating fractures and/or increasing the wellbore's diameter (rubble zone) in the target formation. The idea of using a fluid to create fractures in the subsurface is based on study of pressure parting in formations during squeeze cementing of wells, acid stimulation of carbonate reservoirs, and water injection during waterflood operations (Grebe and Stosser, 1935; Torrey, 1940; Yuster and Calhoun, 1945a,b). In 1947, a mixture of a gasoline-based napalm gel fracturing fluid was pumped into the Klepper

297 No. 1 well, Hugoton gas field, located in western Kansas (Howard and Fast, 1970). This well had been completed originally with an acid treatment of four Lower Permian limestone pay zones. The goals of the test were to increase the well's low deliverability, and to compare the effectiveness of the two stimulation treatments. Flow test results showed that the well's deliverability was not changed appreciably, and it was concluded that this process could not compete economically with acidizing in this particular limestone reservoir (Howard and Fast, 1970). Clark (1949) proposed the treatment which is known today as hydraulic fracturing. Advances in fracturing technology have made this process applicable in effectively stimulating heterogeneous carbonate reservoirs. The viability of each technique discussed above is considered more fully below.

Implementation and control The success of implementing incremental recovery techniques in the field relies on the following factors: (1) quality and amount of available reservoir and well data; (2) quality control procedures exercised in obtaining new information, and in executing the incremental recovery technique (Rieke and Perry, 1983); and (3) costs. Quality control is an important part of improved reservoir management decision making. The producer's commitment to obtain necessary reservoir information and testing of wells is expressed in the established test objectives (Barnum andVela, 1984). As an example, more common well test objectives include: (1) to identify, collect, and review all available reservoir and well data; (2) to establish and execute testing, data acquisition, and cost control procedures; (3) to obtain suitable fluid and rock samples for laboratory analysis; (4) to log the well(s), and analyze and interpret the logs; (5) to determine the nature of formation fluids and petrophysical properties; (6) to measure well productivity; (7) to measure reservoir pressure and temperature; (8) to analyze and model data for reservoir characterization; (9) to estimate well completion efficiency; (10) to conduct a post-mortem review of the effectiveness of the tests and to verify that test objectives were met; and (11) to prepare recommendations for planning the next test and reducing risk based on what was learned. Each of the above operational objectives must be specific, measurable, acceptable, realistic, and timely. Any objective failing one of the above criteria must be restated in order to provide an opportunity of minimizing risk and maximizing cost control (Rieke and Perry, 1983). Quality control involves not only establishment of the appropriate test and data acquisition procedures, but should also include sequencing of the required activities. This is normally documented by creating a flow chart showing a network of activities and management approvals. Rieke and Perry (1985) proposed that a microcomputer-based consultant system is a productive means by which such quality control procedures could be initiated and used in oil and gas field development and production activities.

298

Infill development ICF and BEG (1990b) stated that development drilling (infill and extension) accounted for 82% of reserve additions in the United States from 1979 through 1986. Step-out (extension) wells are used to define and hopefully to extend reservoir boundaries. The new rationale for step-out drilling strategy is to increase recoverable reserves and this has not been explored thoroughly for heterogeneous carbonate reservoirs. Application of advance exploration and reservoir engineering technology to stepout wells in mature reservoirs has lagged behind that of infill well technology. The accepted methodology used to define initial field boundaries is drilling and testing exploratory well(s), estimating the pay continuity from the data, and then validating the geologic model through performance and pressure-transient testing of selected development wells. The more information acquired, the better the estimation of the reservoir's boundaries, but costs are higher. This approach is part of the concept of reservoir re-exploration, which stimulates reserve growth through extension drilling, and the deepening and recompletion of bypassed zones in existing wells (Holtz et al., 1992). It should be noted that fluid, stratigraphic, or structural constraints existing in reservoirs create "fuzzy" boundaries and/or compartmentalization of the reservoirs. Some operators have pursued a strategy of extending the field boundaries in carbonate reservoirs, especially in reefs, by acquiring leases on surrounding properties that are thought to contain extensions of the production trend (E.B. Nuckols, 1993, personal communication).

Reserve-growth potential ICF and BEG (1990a,b,c,d,e) used the Tertiary Oil Recovery Information System (TORIS) to model and evaluate the unrecovered movable oil recovery (UMO) potential in selected carbonate and sandstone reservoirs. Regional economic assessments based on blanket and target infill drilling, polymer flooding, and profile modification treatments were conducted on a reservoir-by-reservoir basis to determine the current status of oil recovery in each zone and to describe producing zone characteristics affecting recovery. Target (strategic) infill drilling is a type of infill well development strategy. Other types are blanket infill development, and irregular placement of infill wells. Both approaches were technically and economically analyzed by ICF and BEG (1990d,e). The blanket approach assumes that internal reservoir heterogeneities trapping hydrocarbons are distributed randomly across reservoirs. Each well will intersect, on average, similar volumes of previously uncontacted mobile oil and associated gas (ICF and BEG, 1990d). Blanket pattern drilling will then progress at closer interwell distances over the extent of the reservoirs. In reality, carbonate reservoir geology is such that there are localized concentrations of unrecovered mobile oil (UMO) owing to variances in hydrocarbon accumulation and intra-reservoir traps created by heterogeneities. Target infill drilling requires a delineation of reservoir heterogeneities that control the hydrocarbon distribution so that wells can be strategically located. ICF and BEG (1990d) noted that for maximum productivity and economic success, targets with high UMO saturations must be drilled

299 at a much closer well spacing than what is acceptable in blanket drilling. Some generalized statistical results are presented based on economic comparison of two general cases: base case (blanket pattern infill drilling) and a d v a n c e case (target pattern infill drilling). Both cases are also compared by combining blanket and target infill drilling with two other recovery processes: polymer flooding and profile modification (ICF and BEG, 1990b). Both polymer injection and profile modification are used in secondary recovery operations to increase waterflood sweep efficiency in carbonate reservoirs. Profile modification reduces the volume of injected water that flows through previously-swept layers of the reservoir which possess good continuity and high permeability between wells. With respect to primary recovery operations, profile modification is used to seal water producing zones; cross-linked polymers are used to plug highly permeable zones. These two methods are effective both in previously produced reservoir compartments, and in compartments contacted by infill drilling. The presented statistical results are derived from the generated recoverable UMO reserve addition data contained in tables 3, 4, 8, and 9 of the ICF and BEG (1990b) report. A total of 484 reservoirs in Texas, Oklahoma, and New Mexico, U.S.A., were evaluated using TORIS. This analysis is presented as a prelude to studies of reserve-growth potential by infill drilling in specific carbonate reservoirs with a specific economic evaluation of the Dune Field, west Texas, U.S.A.. The term "reserve additions" used in the following two cases is interchangeable with "recovery potential". B a s e case scenario summary. This scenario gives predicted UMO recovery potentials by process and shows that for an oil price of $16 per barrel, polymer flooding contributed 11.6%, profile modification contributed 14.9%, and blanket infill drilling 73.6% to recoverable reserve additions (recovery potentials). At $20 per barrel, polymer flooding contributed 9.8%, profile modification 11.5%, and blanket infill drilling 78.7% to reserve additions. At $36 per barrel, polymer flooding contributed only 6.8%, profile modification 8.1%, and blanket infill drilling 85.1%. The economic viability of the blanket infill drilling's technological strength with respect to polymer flooding and profile modification is clearly shown by these statistics (ICF and BEG, 1990b; table 3). The next step in the analysis was to combine predicted reserve additions from blanket infill drilling, blanket infill drilling coupled with polymer flooding, and profile modification. The base case scenario showed that at an oil price of $16 per barrel, three combined processes account for 75.9%, whereas polymer flooding and profile modification contributed only 24.1% of predicted reserve additions. At a $20 per barrel oil price, three combined infill drilling processes accounted for 83.6% of the reserve additions, and at a $36 per barrel price the three combined processes contributed 87.6% (ICF and BEG, 1990b; table 4). Above $16 per barrel, blanket infill drilling projects (individual and combined) as a percentage of total projects would increase from 40--60%. These projects, however, would account for a greater percentage of the predicted reserve additions (ICF and BEG, 1990b; fig. 9). A d v a n c e case scenario summary. ICF and BEG's (1990b) advance case reserve potential study revealed that predicted UMO reserve additions by process for an oil price

300 of $16 per barrel to be: polymer flooding contributed 6.8%, profile modification contributed 4.4%, and target infill drilling contributed 89.1%. At $20 per barrel, polymer flooding contributed 3.8%, profile modification contributed 3.7%, and infill drilling contributed 92.5% to reserve additions. At $36, polymer flooding contributed 2.9%, profile modification contributed 3.1%, and target infill drilling contributed 94% (ICF and BEG, 1990b; table 8). Technological superiority of target infill drilling over blanket infill drilling (even when combined with other processes) is apparent at a $16 per barrel oil price. At $16 blanket infill drilling contributed 73.6% and blanket infill drilling combined with the two other processes contributed 83.6%, versus target infill drilling contribution of 89.1% to reserve additions. The disparity between target infill drilling and blanket infill drilling becomes even larger when the results of target infill drilling are combined with the other two processes: target infill drilling with polymer flooding, and target infill drilling and profile modification. This advance-case scenario shows that at a $16 oil price the three combined processes accounted for 90.6% of predicted reserve additions, whereas polymer flooding and profile modification contributed only 9.4% of reserve additions. At $20 per barrel, the three combined target infill drilling processes accounted for 93.4% of reserve additions, and at $36 per barrel, the three combined processes contributed 95% (ICF and BEG, 1990b; table 9). The current barrier to achieving high estimated recovery potentials in practice is knowledge of how and where to apply this technology to maximize per well recovery resulting from reduced well spacing.

Infill drilling activity Recently in the United States, most infill drilling attention focused on the unswept mobile oil resource in carbonate reservoirs of the Permian Basin in west Texas and southeastern New Mexico, U.S.A. (Fig. 5-38). ICF (1992) reported that 46% of all shallow-shelf carbonate reservoirs in the U.S.A. are located in this area of about 80,000 square miles (207,110 km2). Sizes of Leonardian restricted-platform carbonate reservoirs range from 160-35,000 acres (65-14,164 ha) on the Central Basin Platform of Texas and New Mexico, U.S.A. Holtz et al. (1992) stated that 84% of the 84 reservoirs studied in this play are less than 8,000 acres (3,237 ha) in size. The reservoirs have low recovery efficiencies, and occur in cyclic, interbedded carbonate and clastic sediments deposited in low-energy, semi-restricted platform environments. The depositional environments created diverse reservoir facies reflecting the mixed clastic and carbonate deposition. The facies consist of peritidal deposits of dolomites, lenticular bodies of high-energy oolite and pellet bars that accumulated on the shallow shelf, and thin zones (0.5-2-ft; 0.15-0.6-m thick) of high-energy packstones and grainstones encased in lower-permeability wackestones (see Fig. 1-23). Vertical facies changes result from variations in facies-stacking patterns caused by three orders of cyclicity, and horizontal facies changes are due to paleotopographical variations during deposition (Holtz et al., 1992). Complex postdepositional diagenetic changes are imprinted upon these sediments. It is no wonder that the resulting small-scale changes in vertical and horizontal facies patterns produce high reservoir heterogeneity and poor interwell continuity of the pay zones. Holtz et al. (1992) reported that 75% of the reservoirs are developed currently on a 40-acre (16-ha) well spacing. Well spacing

Northern Montana

W M e t o nBasin /

Mloh~an Mt

Basin Central Kansas

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Permian Basin East Texo# South Texas Cretaceous

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Fig. 5-38. Location of shallow-shelf, light-oil carbonate reservoirs in the U.S.A. Map generated from data in the TORIS database. (Modified after ICF, 1992, fig.l 1-5" courtesy of the U.S. Department of Energy.)

t~

302 averages 33 acres (13 ha) and ranges from 10--80 acres (4-32 ha); 53 reservoirs are under primary production, 31 are under waterflooding, and 1 has been abandoned (Holtz et al., 1992). The following references adequately describe the geology and infill drilling effort in the Permian Basin: Barber et al., 1983; Barbe and Schnoebelen, 1987; Laughlin et al., 1987; ICF and BEG, 1988; Wu et al., 1989; ICF and BEG, 1990 a,b,c,d,e; ICF, 1992. Another area, containing about 4% of the oil-producing, shallow-shelf carbonate reservoirs in the U.S.A., is underlain by the Ordovician/Silurian Hunton Group and the Pennsylvanian Lansing and Kansas City Groups in Kansas and Oklahoma, U.S.A. The largest natural-gas field in the contiguous 48 states (U.S.A.) is the Hugoton Field, which is located in southwestern Kansas and in portions of the "panhandles" of Oklahoma and Texas. Production is from Lower Permian Council Grove and Chase Groups containing shallow-marine carbonate rocks. Infill drilling projects in these reservoirs are described by Sorenson et al. (1987); Cottrell et al. (1988), Fetkovich et al. (1990a,b), McCoy et al. (1990), and Siemens and Ahr (1990).

Background and field examples The concept of OlStimal well spacing for oil recovery has been a controversial subject. Before 1960, ultimate recovery by primary means was considered to be independent of well spacing (Schilthius, 1936; Elkins, 1953). Muskat (1949) discussed in detail this accepted view indicating that decreasing the distance between wells would not increase physical ultimate recovery or reserves in certain types of reservoirs. Physical ultimate recovery of a reservoir denotes the maximum possible recovery for a given production mechanism, regardless of the time required or production cost. This concept is in contrast to the idea of economic ultimate recovery, which refers to the oil and/or gas that can be recovered at a profit to the time of abandonment. The latter term does not consider "noncommercial" pay zones. Muskat (1949) stated that there is actually no significant evidence that physical ultimate recoveries do vary with well spacing. This is obviously true for very "homogeneous" reservoirs. The lack of an established relationship between primary ultimate recovery and well spacing was due possibly to a deficiency in knowledge about reservoir heterogeneities. The issue of the maximum well spacing that will effectively drain oil and gas reserves needs resolution. An analytical challenge to this issue was advanced by Davis and Shepler (1969), Driscoll (1974), Ghauri et al. (1974), Stiles (1976) and Ghauri (1980). Their investigations indicated that a blanket infill drilling pattern will increase reservoir continuity and improve waterflood pattern conformance in heterogeneous carbonate reservoirs in west Texas. Davis and Shelper (1969) reported that primary oil recovery from the Sacatosa Field in Texas was increased by about 14% when well spacing was reduced from 40 acres (16 ha) to 20 acres (8 ha). Barber et al.'s (1983) analysis of production data of infill drilling in 9 fields in Texas, Oklahoma, and Illinois proved additional oil reserves, and showed that additional oil recovery was realized by improving reservoir pay continuity with increased well density. The fields studied included dolomite, limestone, and sandstone reservoirs with porosities

303

A

_

W E L L

.

_

, B.

_

Fig. 5-39. Type cross-section in the Fullerton Clear Fork reservoir, west Texas, U.S.A. The section shows the number of pay zones identified on well logs, which are continuous between the original wells A and B, and those pay zones that exist only between the infill well and wells A and B. (After Barber et al., 1983, fig. 1; reprinted with the permission of the Society of Petroleum Engineers.)

varying from 4-21%, and with average permeabilities varying from 0.65 to about 184 mD (0.00064--0.182 ~tm2) (Barber et al., 1983). Figure 5-39 is a type cross-section illustrating the concept of limited pay continuity in a Fullerton Clear Fork reservoir of west Texas, U.S.A. Pay continuity is the percentage of pay that is continuous between wells. Two important conclusions, which were brought out by Barber et al.'s (1983) study, are: (1) increased oil recovery from the 870 infill wells in the 9 fields ranged from 56-100% of their wellbore production; and (2) additional reserves totaled 60.8 million bbl (9.7 x 106 m 3) of oil based on prevailing economic conditions in the early 1980s. The application of increasing pay continuity by infill drilling in secondary recovery operations was previously discussed in this chapter. In 1983, two of the nine fields (Dorward Field and Sand Hills area in west Texas) were still on primary production. The two examples are discussed below in order to illustrate the impact of

304 infill drilling programs on increasing additional oil recovery from reservoirs near their economic limits. Dorward Field. Dorward Field is located in Scurry and Garza Counties, Texas, U.S.A. and has commingled production from the Permian San Angelo (dolomite interbedded with shale and sandstone) and the San Andres (dolomite, anhydrite and shale) formations. The average porosities are 15% and 13.5%, respectively. Average permeability is about 3 mD (0.00296 ~tm2) in both reservoirs (Barber et al., 1983). The field was discovered in 1950, and infill drilling began in 1971 when production (average of 4.8 B/D (0.8 m3/D) per well) was nearing the economic limit. One hundred and fortynine wells on 40-acre (16-ha) spacing initially were drilled to blanket the lease; an additional 123 infill wells were drilled on a 20-acre (8-ha) spacing between 1971 and 1980. Seventeen additional wells were drilled on a 10-acre (4-ha) spacing pattern by the end of 1980 (Barber et al., 1983). All the production from the infill wells is considered as increased recovery inasmuch as the initial wells were reaching their economic limit. The infill wells would provide additional recovery of 4.6 x 106 bbl (0.73 x 106 m 3) ofoil (33,000 bbl; 5,244 m 3) per well (Fig. 5-40A). The original wells on the 40-acre spacing averaged 49,400 bbl (7,850 m 3) per well. Sand Hills Field. Infill drilling in the Sand Hills area of Crane County, Texas has been concentrated in the Tubb and McKnight reservoirs. The Tubb reservoir (Permian, Lower Clear Fork Formation) at a depth of 4,250 ft (1,295 m) was developed on a 40acre (16-ha) spacing during the period between 1936 and 1941. Development of the McKnight reservoir did not begin until 1955 and it was erratic, depending largely on recompletions from the depleting dolomites in the Tubb reservoir, coupled with additional drilling and workovers (Barber et al., 1983). The McKnight reservoir produces from the Permian, lower San Andres Formation at a depth of 3,200 ft (975 m). A 40acre (16-ha) well program was initiated from 1955 to 1965. Both of these reservoirs have poor continuity owing to the lenticular nature of the producing formations. In 1979, a 20-acre (8-ha) infill drilling program was begun and 56 wells (most dualcompleted) were drilled by 1981. These 56 wells contributed 45% of total production. The strategy was to intersect the dolomitic pay stringers that were partially depleted or had not been penetrated by the initial wells. Figure 5-40B shows the performance of both the 20-acre (8-ha) infill and 40-acre (16-ha) offset wells. A substantial amount of total production was flush production from the recently-drilled wells, because 40-acre (16-ha) development continued up to the time when the 20-acre (8-ha) infill program began. Barber et al. (1983) reported that the economic ultimate recovery of 28,400 bbl (4,513 m 3) additional oil per well compares favorably with the estimated remaining 9,000 bbl (1,430 m 3) per well from the older 40-acre (16-ha) spacing. Kansas Hugoton Field Not all infill drilling scenarios have produced positive results for carbonate reservoirs. A comprehensive assessment of infill drilling in the Hugoton gas field of Kansas and Oklahoma has failed to prove that additional gas reserves are added by drilling an additional well on the allowable acreage of 640 acres (259 ha) (Fetkovich et al., 1990a,b; McCoy et al., 1990; McCoy et al., 1994). This three-phased Phillips Petro-

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Fig. 5-40. Production graphs showing oil production from (A) The Douthit Unit, Howard-Glasscock Field, Texas, U.S.A." and (B) Sand Hills Field, McKnight reservoir, Texas, U.S.A. (Modified after Barber et al., 1983, figs. 13 and 14; courtesy of the Society of Petroleum Engineers.) leum Company study investigated the performance of about 2,177 infill-replacement wells and their companion original wells drilled in the field. The study consisted of: (1) statistical analysis of pressure and well deliverability data from the Hugoton wells in Hamilton, Kearny, Finney, Stanton, Grant, Haskell, Morton, Stevens, and Seward counties, Kansas, U.S.A. (McCoy et al., 1994);

306 (2) a review of engineering and geological data of Mesa Petroleum Co.'s 1977 five replacement well program in Kansas (Fetkovich et al. 1990b; (3) engineering performance comparison between infill wells and companion original wells using well deliverability tests and production history (McCoy, 1990); and (4) results from a reservoir model exercise using well log and core information, historical deliverability test data, and well-production history data from wells located in Texas County, Oklahoma, U.S.A. (Fetkovich et al., 1990a). The Hugoton Embayment, which cuts across southwestern Kansas and the Texas and Oklahoma Panhandles, contains two carbonate gas-producing Lower Permian carbonates: the Council Grove Group, and the major gas reservoirs in the Chase Group. Siemens and Ahr (1990) stated that the Lower Permian section reflects cyclic sedimentation here. The rocks are composed of successive cycles of laterally continuous and mappable (based on well-log signatures), shallow marine carbonates and interlayered shaly units. The Chase Group is subdivided into interbedded limestones and shales, with dolomitic limestones and shales at the top. The shales act as barriers to vertical flow between the carbonate reservoirs as indicated by flowmeter data from the five replacement wells (McCoy et al., 1990). Dolomitization produced an intercrystalline pore system that created good areal continuity of reservoir porosity and permeability within each of the dolomitized carbonate intervals (Fetkovich et al., 1990a). Clausing (1985) illustrated the lateral continuity of the reservoir layers and shaly barrier units across the Kansas Hugoton Field using north--south and east-west geological cross-sections based on characteristic and recognizable well-log signatures. Additional evidence of good lateral communications between wells is demonstrated by similar well pressures in the newly-drilled infill wells and in the original wells (Siemens and Ahr, 1990). A multiwell, no gas-crossflow, three-dimensional gas reservoir model was developed by Fetkovich et al. (1990a) to evaluate the layered carbonate reservoirs through history-matching and forecasting reservoir performance. The model simulated surface shut-in and flowing pressures from actual tests to history-match 40 years of official annual shut-in and deliverability test data. The shut-in wellhead pressure reflects the pressure of the lowest pressure zone open to the wellbore. Fetkovich et al. (1988) demonstrated that commingled shut-in pressures in a twolayer, no-crossflow system followed the pressure in the more permeable layer assuming equal skins on each layer. The cumulative production from the well reflects production from all layers, although, each layer is being depleted at a different rate. Forecast results from the model showed that no additional reserves are added with an additional well on 640 acres (259 ha). McCoy et al.'s (1990) engineering and statistical analysis of the infill and replacement well performance data confirmed that there is no evidence of additional gas-in-place. Good lateral continuity in the reservoir was evidenced by 72-hr wellhead shut-in pressures. The average shut-in pressure for the Hugoton infill wells is 148.8 psia (1.02 MPa) with a most probable value of 143.1 psia (1.00 MPa). McCoy et al.'s (1994) results showed that the average difference between initial infill and original well shut-in pressures was 17.4 psi (0.12 MPa), with an expected value of 13.0 psi (0.09 MPa). Almost 25% of the infill wells had lower initial wellhead shut-in pressure than the wellhead shut-in pressure for the original well (McCoy et al., 1990).

307 These infill wells were tapping into the existing drainage area of the original well. Only 7.1% of the infill wells had pressures 50 psi or higher than those in the companion wells. Higher deliverabilities exhibited by the majority of infill wells did not reliably indicate new gas. McCoy et al. (1994) attributed the higher deliverabilities to a combination of two factors: (1) average higher initial pressures give infill wells having equal completion efficiencies a temporarily higher deliverability; and (2) a better well completion efficiency can have a higher official deliverability. In summary, the higher pressures and deliverabilities were attributed by McCoy et al. (1994) to differences in completion efficiencies between the infill and companion wells and by the pressure gradient in the most permeable layers. Based on this study, it is apparent that there were no microscopic to megascopic reservoir heterogeneities in the Hugoton Field, which resulted in uncontacted reservoir gas.

Economic evaluation of infill drilling scenarios- Dune Field The ICF and BEG (1990b) report gave a detailed analysis of infill drilling scenarios for Section 15 of the Dune Field (Upper Permian, Grayburg Formation) in Crane County, west Texas, U.S.A. Table 5-IX and Fig. 5-41 present the predicted results of an economic analyses for several types of blanket and target infill pattern development programs before and during waterflooding in this part of the field. The methodology used to make the predictions involved modeling of incremental primary production at progressively closer well spacings using decline curves, and secondary oil recovery using a simple waterflood model. Several ICF economic models were used in this study. The engineering-based cost and field development model simulated the development of a typical pattern by linking oil recovery and well drilling with costs and timing of the infill development. This TABLE 5-IX Economic comparison between blanket and targeted infill drilling scenarios for Section 15, Dune Field located in west Texas, U.S.A. Blanket

Targeted*

Crude oil price

Minimum econ. spacing

Econ. recov. oil

Minimum econ. spacing

($/bbl)

(acres/well) (MMB)

(acres/well)

(MMB)

Grainstone

Nongrainstone

Grainstone

$10 $20 $30

40 20 20

40 20 20

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$10 $20 $30

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80 40 20

0 0.8 1.6

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80 40* 40

0 1.5 2.1

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Fig. 5-41. Results of an economic evaluation of Section 15 in the Dune Field, west Texas, U.S.A. using four different development scenarios. (After ICF and BEG, 1990b, fig. 31; courtesy of the U.S. Department of Energy.) model examined the economics of changes in oil recovery as a function of when infill drilling is undertaken. Three approaches were analyzed: (1) undertaking infill drilling while waterflooding; (2) undertaking infill drilling at the start of a waterflood; and (3) undertaking infill drilling in a depleted field. An ICF industry-standard financial analysis model linked oil production, investment and operating costs, and oil prices. The target infill drilling approach assumed that a detailed description of the geologic facies of the Grayburg reservoir is clearly defined.

Field geology. The Permian (Guadalupian) Grayburg Dolomite is part of a progradational cycle composed of subtidal facies in the lower part, and tidal flat deposits in the upper part (Bebout et al., 1987). Dune field is divided into five laterally

309 extensive carbonate zones bounded by siltstones. Hydrocarbons are mainly produced from porous, dolomitized crinoidal grainstones originally deposited as bars on a shallow shelf (ICF and BEG, 1990b). The grainstone facies is bounded vertically and in an updip direction by nonporous, anhydrite-cemented pisolite and mudstone facies (supratidal). As the paleoshoreline moved basinward, the latter two facies were stacked over the bars, whose trend is oriented northwest to southeast and subparallel to depositional strike, creating lenticular bands having contrasting productivity and reservoir quality. The reservoir trap results from updip and downdip porosity pinchouts owing to facies changes along the flanks of an anticlinal structure (Bebout et al., 1987).

Economic analysis. For blanket infill pattern development in an ongoing waterflood (Section 15), an economic recovery of 1 million bbl (0.16 million m3), at an oil price of $10 per barrel, is achievable by reducing well spacing from 80 to 40 acres (32 to 16 ha) (Table 5-IX). It is economically feasible to produce a total of 2 million bbl (0.32 million m 3) of oil, at $20 per barrel, by having the 40-acre spacing reduced to 20 acres per well (16 to 8 ha). ICF and BEG (1990b) report that further blanket infill drilling below a well spacing of 20 acres per well is not economically feasible at $30 per barrel. Under the target infill drilling scenario, it was assumed by ICF and BEG (1990b) that blanket infill development would take place from 80 to 40 acres (32 to 16 ha) per producer. This single reduction in well spacing has to occur before sufficiently detailed geologic delineations become available and used in target infill drilling operations. Figure 5-41 and Table 5-IX show that more UMO recovery is obtained from target infill development than from blanket development. The results conform to the results of the TORIS study discussed previously. The minimum well spacing patterns in each facies, which are economically productive under target and blanket infill drilling program, are compared in Table 5-IX. ICF and BEG (1990b) results show that at $10 per barrel, economic infill development in an ongoing waterflood in the grainstonedominant facies is feasible up to a well spacing of 20 acres (8 ha) per producer. A geologically targeted infill development program focuses on the more heterogeneous grainstone-dominant facies, allowing closer development in this facies. Table 5-IX compared this scenario to a 40 acre (16 ha) per well spacing in the non-grainstone facies assuming blanket infill drilling at 40 acres (16 ha) per well producer. An infill drilling program starting at the end of the waterflood operation is also presented in Fig. 5-41. This scenario shows that delaying infill development lowers the economic potential at all oil prices and drilling strategies considered. It is important to implement the infill drilling program early in order to increase recoverable reserves and accelerate oil recovery. In the selective reservoir-wide case (limited knowledge), where blanket infill drilling occurs at the minimum economic spacing, the differences in UMO recovery between the blanket and target drilling narrowed as the oil price increased to $30 per barrel (Fig. 5-IX). ICF and BEG (1990b) attributed this to a larger fraction of the UMO becoming economic to develop by blanket infill drilling, resulting in a smaller share of the UMO available for strategic development. Also under blanket development, as prices rise the return from the grainstone-dominant production in the Dune Field is high enough to economically support wells in the less-homogeneous non-grainstone facies, resulting in economically recovering the

310 much less-productive, non-grainstone oil resource under the blanket infill program. The non-grainstone facies would not be economic at the prices considered in Table 5IX if evaluated separately (ICF and BEG, 1990b). Consequently, the economics of the infill wells in the grainstone-dominant facies improved considerably when these wells no longer support the non-grainstone wells. ICF and BEG's (1990b) study predicted that infill wells in the grainstone-dominant facies can produce at a considerably lower cost per barrel than an average well, allowing target development at a closer spacing than possible under blanket infill drilling. Other economic model studies by Laughlin et al. (1987) and Wu et al. (1988, 1989) on the use of blanket infill drilling in connection with waterflood recovery from west Texas carbonate reservoirs showed similar results. Some additional conclusions were reached. Laughlin et al. (1987) noted that about 68% of the infill drilling incremental payout was less than two years, with an incremental discounted cash flow rate of return greater than 20%. Also, as well spacing decreased the infill drilling incremental payout decreased and the incremental cash flow rate of return increased. According to Wu et al. (1988), as well spacing decreases, waterflood recovery increases. Decreasing spacing from 40 acres (16 ha) to 20 acres (8 ha) generally gave a 14% incremental recovery of the original oil-inplace. Wu et al. (1989) showed that San Andres waterflood units, located in the Central Basin Platform and northern Delaware Basin of west Texas had a high rate of return for infill drilling projects owing to a shallower reservoir depth, and a high infill drilling recovery efficiency.

Slant-horizontal-drainhole wells At present, horizontal drilling has developed into five separate technology categories. Each is generally defined by the radius of the well's curvature required to turn the well from a vertical borehole to a horizontal one. Each of the drilling technologies has a special set of tools, techniques, and constraints. The main well categories are: (1) Long-radius well (slant [high-angle] directional) of 600 to 2000 ft (183 to 610 m) radius of curvature. Well lengths range from about 1000 ft to over 3000 ft (305 to 914 m). (2) Medium-radius well (horizontal) having radius of 200 - 500 ft (61 - 152 m). Well lengths range from 500 to about 2000 ft ( 1 5 2 - 610 m). (3) Short-radius well (drainhole) of 20 - 40 ft ( 6 - 12 m). Drainhole length ranges from 50 to over 700 ft ( 1 5 - 213 m). (4) Ultra-short radius well (drainhole) having radius of 1 - 2 ft (0.3 - 0.6 m). Drainhole length can reach 200 ft (61 m). (5) Hybrid well: combinations of the above well categories. Choice of drilling technology is based on technical considerations, economics, legal aspects, geology, location, and the nature and depth of the target reservoir. Longradius wells are normally drilled at an angle from 7 0 - 80 ~ ( 1 . 2 - 1.4 radians) rather than horizontal to reach designated targets. Medium radius drilling is the most widely used method to drill horizontal wells on land. Short-radius wells (multiple drainholes) can be drilled from a preexisting vertical well. The ultra-short radius well method is best suited to soft or unconsolidated formations with relatively low formation pressure,

311 and are drilled using proprietary water jets. A hybrid well combines the drilling technologies of different radii, such as multiple drainholes branching off a horizontal well (or at different elevations within the vertical wellbore), resulting in many configurations. Joshi (1988b) estimated the cost of drilling a horizontal well to be 1 . 2 - 2 times that of a vertical well. The drainhole costs in 1988 ranged from $130,000 to $500,000 depending upon well depth and location.

Productivity comparison of different well configurations Joshi (1988b) stated that a horizontal well can be mathematically considered as a controlled infinite-conductivity vertical fracture of limited height. A horizontal well drains an ellipsoid, whereas a conventional vertical well drains a right circular cylindrical volume resulting in different drainage volumes for the same reservoir height (Joshi, 1988a). An in-depth comparison of productivity indices (ratio of stimulated to unstimulated PI) was made by Joshi between both a horizontal well and a fractured vertical well, and a horizontal well and a slant well. Each of these technologies compete with each other. The criteria for his initial study were restricted to reservoirs having thicknesses up to 164 ft (50 m) with steady-state, single-phase flow, local fracturing experience, and costs of stimulation treatments and horizontal drilling. Joshi (1988b) used production forecasting models to describe horizontal wells in naturallyfractured and bottom-water-drive reservoirs. Well productivity measures. The following equation was used by Joshi (1988b) to evaluate steady state oil production from a horizontal well: 5.35 x 10-4 (khh p/(PBo) qh = In

Ea+a2Lj221 L/2

(5-35)

InEhJ2 2 '21 (hrw/2)

L

forL > flh, where qh is the flow rate in ma/day, fl = ~[kh/kv , k his the horizontal permeability in mD, kvis the vertical permeability in mD, h is the reservoir thickness in m, p is oil viscosity in cP, p is the pressure drop in kPa, B o is the formation volume factor in R m a / S T m 3, L is the horizontal well or fracture length in m, r w is the wellbore radius in m, and l~ is the vertical distance between the reservoir mid-height and the horizontal well location. The term a is defined as"

I

a = (L/2) 0.5 + ~/0.25 +

(2re,h/L)

4

I 0.5

,

(5-36)

where re.h is the effective wellbore radius for a horizontal well in m. In reservoirs where the vertical permeability is lower than the horizontal permeability, a decrease in kvresults in an increase in the vertical-flow resistance in horizontal wells. This, in tum, decreases the oil production rates (Joshi, 1988a). The term~lkh/k v was used by Muskat (1949) to account for reservoir anisotropy by modifying the vertical axis as z' = h'~kh/k ~ and the average permeability as ~/kh kv . The modification of the z axis

312 makes the wellbore elliptic; therefore, Eq. 5-35 accounts for reservoir anisotropy (Joshi, 1988a). Joshi (1988a) showed that for steady-state conditions an equivalent vertical wellbore diameter of a horizontal well, r e, can be formulated, assuming equal drainage volume, re,h re,v, and equal productivity indices, (q/P)h (q/P)v: =

=

re.h (L/2) rw~=

.

(5-37)

a [1 + ~1 - ( L / 2 a ) 2 l th/2r]~ 2L The following equations can be used to compare the productivity indices of horizontal and vertical wells under steady-state conditions (Joshi, 1988b):

Jh/Jv = [In (re,v/rw)]/[ln (re,h/rwe)] ,

(5-38)

for L > flh and L < 1.8re,h , where Jh is the productivity index for the horizontal well and Jv is the productivity index for the vertical well. Units for J are m3/day/kPa (or bbl/day/psi). Joshi (1988b) showed that a similar productivity index ratio expression for the pseudo-steady state, derived from Dake's (1978, p. 145) radial inflow equations for stabilized flow conditions, is based upon the pressure drop between the drainage boundary and the wellbore (p = Pe; r = re):

Jh/Jv =

In (re,v/rw) - 0.5 In (re,h/rwe) -- 0.5

9

(5-39)

Another equation can be devised from Dake's (1978) equation, where the productivity index is derived from the pressure difference between the average reservoir pressure and the wellbore pressure"

Jh/Jv =

In (re,v/rw) - 0.75 In (re,h/rwe) -- 0.75

.

(5-40)

where Eqs. 5-39 and 5-40 are also valid for L > flh and L < 1.8re,h (Joshi, 1988b). Chang and Pautz (1992) pointed out that when the viscous force of reservoir fluid is not significantly greater than the gravity force, a gravity correction factor must be included in Joshi's productivity Eq. 5-35 and other productivity index equations given in Table 5-X. To account for the gravity effect, a correction factor (Cg), must be used to correct productivity index (J) from the equations given in Table 5-X. The Chang and Pautz (1992) equation is: Jg = Cg • J ,

(5-41)

313 where Cg is defined as, C = AP/(AP-APg),

(5-42)

or

C = , g (1 + 0.433(~,) (AH)(J)/q)

(5-43)

where AP is the average reservoir pressure minus the wellbore pressure in psi, APg is defined on page 314, psi, 9/is the specific gravity of the fluid, AH is defined on page 314, ft, and q is the flow rate, bbl/D. H o r i z o n t a l versus vertical wells. A comparison of the productivity indices ratios of unstimulated horizontal and vertical wells is presented in Table 5-XI, which is based on Eq. 5-38. The data show that for steady-state flow, productivity improvements result from an increase in the length of the horizontal well and in thin reservoirs (thickness ranging from 32 to 164 ft: 1 0 - 50 m). In reservoirs having high vertical permeability, horizontal wells are more effective producers than vertical wells under the same conditions (Joshi, 1988b). Lithology and heterogeneity of the reservoirs were not considered. A horizontal well has several advantages over a fractured stimulated well. It offers an almost permanent infinite-conductive flow path, whereas a fracture-stimulated well has the problem of fracture closure with time. Mathematically, a horizontal well can be envisioned as a fracture having a height equal to the wellbore diameter with a known direction. In contrast, hydraulic fracture heights and orientations are highly variable and their magnitudes from a practical viewpoint are for the most part unknown, although they can be estimated mathematically. These hydraulic fracturing factors introduce risks into the project that are difficult to ascertain, whereas in horizontal wells these factors are measurable. Joshi (1988b) estimated that the costs of stimulating a vertical well and of horizontal drilling could be comparable. His comparison of horizontal wells and fractured vertical wells was restricted to a horizontal length of 480 ft (146 m), and all fractures were assumed to be fully penetrating. It should be noted that most common fracture lengths range from around 66 to 131 ft ( 2 0 - 40 m), and that massive hydraulic fracturing could result in fracture half-lengths of about 787 ft (240 m). Comparisons of productivity ratios between a horizontal and vertical wells were made for an 80-acre (32-ha) drainage area by Joshi (1988b) assuming the following conditions: (1) reservoir permeability values were 0.1, 1.5, and 10 mD (0.000099, 0.00148 and 0.00987 ~tm2); (2) fracture and horizontal well lengths ranged from 66 to 1574 ft ( 2 0 - 480 m); (3) reservoir thickness ranged from 33 to 164 ft ( 1 0 - 50 m); (4) k / k h values ranged from 0.1 to 1; and (5) fracture types considered were infinite-conductivity and finite-conductivity with kfbfbeing equal to 36 (acid fracture), 70 (sand proppant), 300 (precured resin coated sand), and 1040 mD-m (Mullite- an intermediate strength manufactured proppant), where kfis the fracture conductivity in mD and bfis the fracture width in m.

314 TABLE 5-X Horizontal well productivity index equations, and nomenclature Borisov:

2rckh/laoBo

J In 4

+

(1)

In

Giger:

2 ~kL/(jaoBo)

(2)

!

L h [

(L/2re)2 L/2r

2~r.

Joshi: 0.007078khh/(iXoBo

J

in[a +ca 2-(L/2)2LI2

+

In

)

(3)

(h/2)2+ hr /2

tbr L >- h, 6 -<. h/2, and L < !.8 re.

Key: A

= = = Bo = b = CH D = F = AH = h = = J = J = k = L, L w =

Reservoir area, sq ft Half the major axis of a drainage ellipse, ft Formation volume factor of oil Reservoir width, ft Shape factor Non-darcy flow constant Kuchuk's function (table 1 of Kuchuk et al., 1988) (Depth of well b o r e ) - (Depth in the middle of pay), ft pay thickness, ft Productivity Index Gravity-corrected J value Horizontal permeability, mD Vertical permeability, mD Half the well bore length, ft Lx, Ly = Half the reservoir length and width, ft AP = (Average reservoir pressure) - (Well bore pressure), psi APg = (Hydraulic pressure at depth of well b o r e ) - (Hydraulic pressure in the middle of pay), psi a

v

315 T A B L E 5-X Continued. Babu and Odeh:

0 . 0 0 7 0 8 b k ~ ~ h k~ g

(4)

__

HV[-A/rw - 3

Bola o[in(C

Kuchuk et al.:

g

khh/70.6p o

._

F

(

L x) i ,hs

(5)

I

Yw L v Ly L

~,

L

+

L

k

~

Mutalik et al.: O.O0708kh/~toB o J

_.

In

(6)

- A +s c a +s+Dq

Mutalik et al. (modified)" O.O0708kh/laoB o J =

In

q re rw s Sca sR sz Xw, Yw 6 7

= = = = = = = = = =

-,4 +sc a +s +Dq + 1.386

Flow rate, b/d Reservoir radius, ft Well bore radius, ft Skin factor Pseudosteady-state skin factor Skin due to partial penetration Skin-related function Well bore coordinates in x and y directions, ft Vertical distance between the pay center and horizontal well location, ft Specific gravity of fluid

Source: After Chang and Pautz, 1992; reprinted with the permission of Penn Well Publ. Co.

(7)

316 TABLE 5-XI Comparison of ratios of productivity indices of unstimulated horizontal and vertical wells for an 80 acre (32 ha) well spacing, and assuming that L/2 < 0.9 (reh),rw = 0.328 ft (0.1 m), and L > h d k x Jh'Jv

L (m)

(k,/k,,) = 0.1

(kJkh)= 0.5

(k&)

h = 10 m (32.1 A) 20 50 100 120 200 300 400 480

1.37 1.98 2.18 2.83 3.55 4.22 4.76

1.15 1.76 2.35 2.54 3.19 3.91 4.61 5.17

1.29 1.88 2.46 2.65 3.29 4.01

50

-

100

120 200 300 400 480

1.43 1.61 2.22 2.88 3.50 4.00

1.35 1.95 2.15 2.80 3.51 4.19 4.73

1.53 2.14 2.33 2.99 3.71 4.39 4.94

h = 30 m (98.4 ft) 50 100 120 200 300 400 480

1.10 1.25 1.80 2.39 2.95 3.39

1.07 1.65 1.83 2.47 3.16 3.81 4.32

1.27 1.87 2.06 2.72 3.42 4.09 4.62

h=40m(131.2ft) 50

-

120 200 300 400 480

1.01 1S O 2.03 2.53

1.41 1.59 2.20 2.86 3.47 3.96

1.07

100

1.84 2.48 3.16 3.81 4.33

1.23 1.40 1.97 2.60 3.18 3.65

1.47 1.65 2.27 2.93 3.56 4.05

= 1.0

4.71

5.28

h = 20 m (65.6 ft)

h = 50 m (164.0 A) 100 120 200 300 400 480

-

2.93 -

1.27 1.75 2.20 2.56

I .65

Source: After Joshi, 1988b, table 11; reprinted with the permission of the Society of Petroleum Engineers.

317 i !

2 I

3 I

4 I

5

, 3 I

6709 I I I

;

2 i

81"/09 I II1

3 I

4 I

511789 l t t l

2

3

4

t

t

1

8

6789

i

iii

,,,

/

~.;

/v

i0 -I

8

: 10"2 I0-1

I0 0

I0 I

I0 2

I0 3

FCD Fig. 5-42. Variation in the effective wellbore radius and fracture half-length having a dimensionless fracture conductivity. (After Cinco-Ley and Samaniego, 1981, fig. 14; reprinted with the permission of the Society of Petroleum Engineers.)

Dimensionless fracture conductivities were calculated using the following equation: FCD = kfbf/(kfmXf) '

(5-44)

where kfm is formation conductivity in mD, andXf is fracture half length in m (Xf = L/2). Figure 5-42 was used to calculate the effective wellbore radius, rwe, of a fracture treatment for Fco values greater than 0.1. For FCD values less than 0.1, Joshi (1988b) used the following equation:

rwe= 0.2807

I kfbf 1 kfm ,

(5-45)

For a given formation with a given stimulation treatment, FCDdecreases as fracture length increases, implying that the incremental gain in fracture productivity declines as the fracture gets longer. Figure 5-43 is an example of Joshi's (1988b) results showing one comparison between the productivity ratios of both an unstimulated horizontal well to a stimulated vertical well, and a stimulated vertical well with respect to an unstimulated vertical well. Also included in the graph is an infinite-conductivity fracture line, which represents an idealized upper productivity improvement limit, for induced fractures. Some generalized conclusions were reached by Joshi (1988b) on the basis of his calculations. For a formation permeability of 0.1 mD (0.00001 ktm2) as shown in Fig. 5-43, the performance of horizontal wells for kv/k h > 0.5, is about 25% lower than that for a fracture having a kfbf> 700 mD-m. All fractures were assumed in his calculations

318 I

I

1

a

a

i

I

1

Formationn Permeability = O. l lmdl 4-1F~176 Thickness = 20 m J

/

lq

//

/~'_.~<~'~''~"_~..~.~.~'~~" ~/'~/

....

'

o,

f

o

L,/

~Horizontal

I t '

I

so

1

/..~-/~-~ "'" /

~ . :

>

2

I

= 300 md-m

I

,

>

,!

Fracture, k f b f = 1040 m d - m - - - ~

Infinite - Conductivity ~ Fracture

t

>

.... ~ I

=

70 m d - m

=

36

md-m

Well

I I '

go

I

I

200

2so

I

I

I

3so

,oo

I

450

500

H o r i z o n t a l Well o r Fracture L e n g t h , m

Fig. 5-43. A comparisonof productivities betweenhorizontal and stimulatedvertical wells in the 0.1-mD case. (Modified after Joshi, 1988b, fig. 6; courtesyof the Society of Petroleum Engineers.) to be fully penetrating; therefore, fracture productivities are independent of reservoir height. Horizontal well productivity depends strongly on reservoir height and the permeability ratio, kv/kh. Joshi (1988b) pointed out that if fracture lengths are about 164 ft (50 m), then all fracture treatments used will give the same productivity results for a stimulated vertical well with respect to an unstimulated vertical well. Improvement would be about 2.2 times the productivity of an unstimulated vertical well (Fig. 5-43). Further, his results revealed that for a horizontal well productivity improvement of about 3 times that ofunstimulated vertical well, horizontal well length of 656 ft (200 m) would be required in reservoirs with kv/k h values that ranged from 0.1 to 1. With respect to reservoir height, Joshi (1988b) found that horizontal wells are more effective in 33 ft (10 m) thick reservoirs than in 164 ft (50 m) thick reservoirs as was shown earlier by the data presented in Table 5-X. Figure 5-44 is an example plot showing the 5 mD (0.00493 ~tm2) case. His plots also showed that it is important to consider length limitations of fracturing and horizontal drilling in low-permeability reservoirs having formation permeabilities of less than 1 mD (0.000987 ~tm2), and in thick reservoirs. Using conventional fracturing techniques, it might be difficult to create long fracture lengths in a thick reservoir; however, using horizontal drilling it may be easy to drill long horizontal wells. Inasmuch as conventional fracture length range from 66 to 131 ft ( 2 0 - 40 m), if the maximum fracture length would be limited to 164 ft (50 m), any stimulation improvement would have to come from horizontal drilling.

319 6 1

1

I

I

._

I

I

I

1 ..

I

1

I

Formation Permeability = 5 md . . . . . . . . . k v / k h = 1.0 , Jlnfinite - ConductivltyJ , [ fracture l--q_ ~ [Horizontal W e l l ~

I

J "

2-

~_:-"Wl"

i'i~/_.-- ~ ' ~ i ' f

.- ~

=

1040

=

.................................

/"

I "~

~

.. ~ ~ . . ~ "

!

>

_,=

I

- "

=

m d - m

300

- - J

md-m

70 m d - m

-

-.-...-..--.--.-.i-

~'/~~'J

Fracture, k f b f =

36 r o d - m - - - - /

I i 0

--

o

so

,. . . .

loo

|'

''

i. . . . . .

,

-

i

. . . . .

l

lso 200 2so 500 ~so Horizontal Well or Fracture Length, m

i

(oo

"

.

4so

500

Fig. 5-44. A comparison of productivities between horizontal and stimulated vertical wells in the 5-mD case. A comparison between Figs. 5-43 and 5-44 shows that in order to reach a productivity ratio of 3, a 656 ft- (200 m)-long horizontal well with akv/kh= 1.0, or a thin 33 ft- (10 m)-pay zone with k = 5 mD and having a horizontal well length of 525 ft (160 m). (Modified after Joshi, 1988b, fig. 12; courtesy of the Society of Petroleum Engineers.)

This limit is marked in Figs. 5-43 and 5-44. It shows that in practice, longer horizontal wells may be the operational altemative to conventional stimulated wells. Costs, oil price, and local fracturing and drilling experience will determine this decision. Clearly, Joshi's (1988b) results showed that horizontal wells with a length above 656 ft (200 m) would give better productivity than conventional stimulation treatments having Xf values ranging from 66 to 164 ft (25 - 50 m), formation permeability values greater than 1 mD, and a kv/k h _>0.1. It is apparent from this study that horizontal wells are competitive with conventional stimulation treatments, especially for reservoirs having formation permeabilities greater than 1 mD (0.000987 lt.tm2). Joshi (1988b) also reported generalized results from evaluation of production forecasts for vertical and horizontal wells. Cumulative oil recovery from a horizontal well under single-phase flow conditions can be larger than from a vertical well. This is due to the larger drainage area of a horizontal well. A vertical well has a much smaller drainage area. With respect to a fractured reservoir, horizontal wells would accelerate initial production rates and improve the economics (Joshi, 1988b). In solutiorv-gas-drive reservoirs, higher recovery efficiencies associated with horizontal wells could be due to the fact that horizontal wells help gravity segregation of the produced gas.

320 704 /

. . . . . .

J 60 t

-

t. o

/ 40

.,ol o

|o

!

I~_L..._L..__I__LJ,...1.

~

9. . . .

L ....

L . J _ J

J

I

LL._

. . . .

9. . . . . .

L.__L_.L_L_LJ_.L

.._.....- ~ , "

152.4 m (500 ft) Horizontal well

t

121.9 m (400 ft

E 201

~ , -

./..

I0

JLI

Well spacing = 16.19E04 m 2 (40 acres) Initial all column thickness = 45.7 m (150 ft) Oil recovery without water coning /.~.

Vertical well

~

-

o

"""

-

0

--r

1

10

100

t

v

f

0

9

1000

Months Fig. 5-45. A comparison of cumulative oil recoveries for a conventional vertical well and two horizontal wells. (After Joshi, 1988b, fig. 18; courtesy of the Society of Petroleum Engineers.)

Segregation helps maintain reservoir pressure and this may result in a high recovery factor. Horizontal wells have a distinct advantage over vertical wells in bottom-waterdrive reservoirs by reducing water coning. Vertical wells have less reservoir contact area than horizontal wells; therefore, at the same production rates, there is a lower pressure drawdown for horizontal wells than for vertical wells. Horizontal wells are able to produce at high initial production rates, above the critical rates, without premature water coning. J0shi's (1988b) calculations showed that the reservoir oil column thickness for a horizontal well declines more rapidly than that of a vertical well, resulting in a rapid decrease in horizontal well rates when compared to those of vertical wells. Based on the premise that money is time and time is money, the higher initial oil production rates given by horizontal wells result in a higher initial recovery factor and better returns (Fig. 5-45). A word of caution: after water breakthrough in the case of a horizontal well, the water-cut will rise at a slightly faster rate than in a vertical well (Joshi, 1988b). Slant versus horizontal and vertical wells. Joshi's (1988a) study of productivity of slant (directional) vs. horizontal and vertical wells was based on the productivity equations [slant angle < 75 ~ (<1.3 rad)] ofCinco-Ley et al. (1975) and Van Der Vlis et al. (1979). A horizontal well is a special case of a directional well [slant angle is 90 ~

321 7.0

I

I 9R e s e r v o i r

I height

9 Drainage area

6.0

I

I

9IOOfl. ( 3 0 . 4 8 m

I

I

I

I

I

I eoo

I soo

I ~ooo

I ~oo

I

93 0 acres ( 1 2 . 1 4 E O 4 m t I

Horizontal - -

5.0

.--

Slant

---

4.0

3.0

.O.f~ 2.0

:0. I

Lo i - ~ - ~ ' r - ~oo 2o0

I 3o0

~

I

I

I

400

500

6o0

700

t 30.4e I

( 152.40 )

( 304.8

)

~zoo ( 365.76

)

Well length, ft. ( m } ~

30

,

4B

i

60

I

70

I

75 Well slant angle, deg.

Fig. 5-46. A comparison of slant- and horizontal-well performance in a reservoir 100 ft (30 m) thick. (After Joshi, 1988a, fig. 11" reprinted with the permission of the Society of Petroleum Engineers.)

(1.6 rad)]. The difference between these two methods is that the Van Der Vlis equation is based on effective wellbore radius of a directional well, whereas Cinco-Ley's equation considers the skin factor of a directional well. Both equations, however, show excellent agreement (Joshi, 1988a). Joshi (1988a) calculated well-productivity enhancements for reservoirs having the following conditions: (1) horizontal well lengths of 100 - 2000 ft (30 - 610 m ); (2) reservoir thickness ranging from 25 to 400 ft ( 8 - 122 m); (3) k / k h values at 0.1, 0.5, and 1; and (4) vertical-well drainage areas of 10, 20, 30, 40 and 80 acres (4, 8, 12, 16 and 32 ha). Other assumptions were that all three well scenarios have an equal drainage area, and that there is an equal reservoir contact area for slant and horizontal wells. Figures 5-46 and 5-47 show productivity comparisons of slant, horizontal, and vertical wells for 100 and 400 ft (30 and 122 m)-thick reservoirs. Joshi's results show that in a 100-ft (30-m)-thick reservoir, horizontal-well productivities are 2 - 5 times greater than those of unstimulated vertical-or slant-wells, depending on reservoir anisotropy. It was shown that a slant well, with a 6 0 - 70 ~ (1 - 1.2 radians) angle to a vertical through a pay zone, will produce oil at a rate of 2 - 3 times faster than a vertical well under similar pressure-drawdown conditions. It was stated by Joshi (1988a) that a minimum slant of 35 ~ (0.6 radians) was required to increase oil production by at least

322

4,0

m

1

9R e s e r v o i r height: = 4 0 0 ft (121.9 m I

3.5

area, . ., . . . , = -... 30 acres t =~:.~r.u,,m2 J

/

"Drainage

/

/ 3.0

_

---------

-.j

/

/

/ V o ca

/

f

Horizontal Slant

' ~ . .~, , ~ K - . - - = 1.0

~

2.5

...)

2,0

.,

I 300

f

~

... ~ ' ~

.,"J'.-.-I--'--~ 500

~

I

700

I

0.5

I

I

900

( 152.4 )

( 304.8

I

WOO

I 1300

)

I

I

I

1500 ( 457.2 )

I 1700

I 1900 ( 579.12 )

Well length, ft Ira)

30

45

60

70

75

Well slant angle, deg.

Fig. 5-47. A comparison of slant- and horizontal-well performance in a reservoir 400 ft (122 m)-thick. (After Joshi, 1988a, fig. 12; reprintedwith the permission of the Society of Petroleum Engineers.) 1.2 times that of a vertical well. In a 400 ft (122 m)-thick reservoir, however, slant wells perform better than horizontal wells if the vertical permeability is less than horizontal permeability. Chang et al. (1989) developed a well model, which was incorporated into a black oil simulator (BOAST) to make production rate predictions for vertical, horizontal, and slanted wells on a 40-acre (16-ha) well spacing. BOAST is a three-dimensional, three-phase model based on continuity equations and Darcy's expression as a momentum balance for each phase (oil, gas and water) (Fanchi et al., 1987). BOAST assumes that fluid and rock properties are single-valued functions of pressure only, and that there is no mass transfer between different phases. The model was checked against the analytical formulas of transient wellbore pressure in an infinite slab reservoir. There was good agreement between the simulation results and published pressure transient tests for both horizontal and slanted wells (Chang et al., 1989; Chang and Pautz, 1992). This is the first reported mathematical model that was validated for a slanted well simulation. Chang et al.'s (1989) results support the findings of Joshi (1988a,b) in that slanted and horizontal wells showed an advantage over vertical wells at lower formation permeability (1 mD) than at higher permeabilities greater or equal to 100 mD (0.0987 ~tm2) (Fig. 5-48). A decrease of vertical permeability reduced the production from slanted or horizontal wells simulated under the conditions given in Table 5-XII.

323

H V

-.Q .Q ql"

9Horizontal :Vertical

Well

K

Well

/

9 IOOmD H IOOrnD V

I00

!00

75

75

50

50

0

K

0

IOmD H IOmD V

25

lind

ImdV

0

500

I000 PRODUCTION

1500

25

H .=.=.....

2000

T I M E (Days)

Fig. 5-48. Cumulative oil production from vertical and horizontal wells at formation permeabilities of 1, 10 and 100 mD. (After Chang et al., 1989, fig. 16; reprinted with the permission of the Society of Petroleum Engineers.)

TABLE 5-XII Reservoir and well properties used in Chang et al.'s (1989) model for production simulation of directional wells (slanted/ horizontal/vertical) Porosity, % Permeability, mD

kx, ky k~ Formation thickness, ft Formation width/length, ft Oil formation volume factor, RB/STB Oil viscosity, cP Rock compressibility, psi -~ Formation pressure, psig Wellbore pressure, psig Well radius, ft Production time, days Well length vertical wells, ft horizontal wells, ft slanted wells, ft Slant angles, slanted wells, degrees

22 1-100

0 . 1 - ]00 50 1350 1.01 1.0 6 x 10-5 5000 4000 0.25 1830 50 5 0 - 1350 54 - 1351 2 2 - 88

Source: After Chang et al., 1989, table 6; reprinted with the permission of the Society of Petroleum Engineers)

324 Vertical permeability has a more pronounced effect on horizontal wells than on slanted wells. A slanted well having a higher slant angle (more deviation from the vertical) has a longer wellbore, and showed a higher cumulative production and earlier reduction in well production rate than a well with a smaller slant angle. Chang et al. (1989) studied the effect of eccentricity (well's position in the formation) in the model by varying the location of the horizontal well at different distances from the top and side of the reservoir. The effect of eccentricity on five years of cumulative oil production from horizontal wells having a 350 ft (93 m)-long wellbore showed that a horizontal well positioned in the middle of the reservoir produced at the highest recovery rate. A well located immediately below the middle of the formation was the next fastest producer owing to the effect of gravity. The next most productive well was situated immediately above formation's center, whereas the horizontal wellbore near the reservoir boundary produced the least (Chang et al., 1989). Horizontal versus infill wells. Giger (1983a,b) devised a replacement ratio, F R, which accounts for the different drainage areas of horizontal and vertical wells. The value o f f Rindicates the number of vertical wells required to produce at the same rate as that of a single horizontal well. The ratio assumes an equal drawdown for the horizontal and vertical wells. Giger's methods provide means by which horizontal wells can be compared to infill wells. Joshi (1988a) evaluated the influence of well spacing, reservoir thickness, and reservoir anisotropy on FR. His calculations assumed that r h = L.

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Fig. 5-49. Influence of well spacing on the vertical well replacement ratio, F R. (Modified after Joshi, 1988a, fig. 7" courtesy of the Society of Petroleum Engineers.)

325 Figure 5-49 is a plot depicting F Rvalues for a 100 ft (30 m)-thick reservoir having vertical permeability equal to the horizontal permeability. A 1000 ft (305 m)-long horizontal well would replace 4.2 and 3.1 conventional vertical wells drilled on a 10 and 80 acres (4 and 32 ha) well spacing, respectively (Joshi, 1988a). The thicker the reservoir, the fewer conventional vertical wells are replaced by a horizontal well. Joshi's (1988a; fig. 8) results show that a 1000 ft (305 m)-long horizontal well would only be equivalent to 1.8 vertical wells in a 400 ft (122 m)-thick reservoir compared to 4.2 vertical wells in a 25 ft (7.6 m)-thick reservoir. With respect to reservoir anisotropy, those reservoirs having lower k / k h values show that fewer conventional vertical wells are replaced by a horizontal well. As an example from Joshi (1988a; fig. 9), a 1000 ft (305 m)-long horizontal well would only replace 2.1 vertical wells for a k / k h = 0.25; 3.1 wells for a k / k h - 0.5; and 3.3 wells for a k v / k h 1.0. The information provided in this discussion, and shown in Figs. 5-43 through 549, should help one maximize oil production by selecting between conventional vertical, stimulated vertical, slant, and horizontal wells. Horizontal wells appear to be suitable for reservoirs that are thin, show high vertical permeability, or exhibit gasand water-coning problems. Many carbonate reservoirs fit this description. There are other geologic constraints, such as multilayered reservoirs where pay zones are separated by impermeable beds, which could exclude the drilling or could require fracture stimulation of a slant/horizontal well. Slant-

horizontal-

drainhole

drilling

The application of horizontal drilling is steadily increasing worldwide. Operators are slowly applying this technology to carbonate reservoirs in several countries. Each drilled horizontal well is being tested and evaluated for its effectiveness. In the United States operators are carving out niches in horizontal plays by carefully selecting prospects, methodically planning well-site procedures, and establishing characterization of the reservoirs. A rule-of-thumb is that about 2 - 3 horizontal wells are needed to be drilled in a new area to solve localized technical and recovery problems. The focal point of the horizontal well drilling activity in the United States is the Upper Cretaceous Austin Chalk play in south Texas. There are other areas, however, that have on-going activity. The second most active play area in 1992, for example, was the Cretaceous Buda Limestone in Texas (Koen, 1992). The Buda Limestone is micritic, about 100 ft (30 m) thick, and generally with reserves that are not quite as high as from the Austin Chalk. Some other drilled carbonate targets in North America include: (1) the Cretaceous Saratoga Chalk in the Fort Jessup Field, Sabine Parish, northwestern part of Louisiana, flowing 104 bbl/day (17 m3/D) of 41.4 ~ API gravity oil and 15 Mcfd (0.42 Mm3/D) gas (Petzet, 1990); (2) the Permian Brown Dolomite in Carson County, Texas; hydraulically fractured slanted well was drilled into the bottom water zone with unsuccessful results (Petzet, 1990); (3) a horizontal well was drilled in 1990 in the Jurassic Smackover Formation, Huxford Field, Escambia County, Alabama, U.S.A. Production averaged 215 bbl/day (34 m3/D) of oil for 114 days (Petzet, 1990). The Smackover depositional environment

326 closely approximates present-day carbonate sedimentary environments in the Persian Gulf (Mancini and Benson, 1981); (4) some 200 horizontal wells were drilled in the Mississippian Madison Group (mainly carbonates) just north of the border between Saskatchewan, Canada, and North Dakota, U.S.A., producing up to 700 bbl/D (111 m3/D) oil (Lyle, 1993). These wells show dramatic improvements of as much as 13 times the production of vertical wells in the area. Lyle (1993) pointed out that as in many horizontal reservoirs that involve natural fracture systems, the wells show rapid decline after several months. Canadian operators report that their analyses indicated that more oil was being recovered in addition to the higher production rates; and (5) directional drilling into Lower Ordovician carbonates has been successful by greatly increasing the recovery of oil over vertical wells in Clinton County, south central Kentucky, U.S.A. These wells intersect fracture trends. The following is a more detailed discussion on the production results of horizontal well technology. Examples of selected carbonate reservoirs from Texas, U.S.A., Argentina, and the Middle East serve as illustrations of the application of this technology. Austin Chalk Formation. Wells in the Austin Chalk Formation present a problem owing to the extreme heterogeneity of the producing system. Upon drilling horizontal wells based on seismic data, however, producers are recovering large amounts of oil from fractured reservoirs in south Texas, U.S.A. (Kuich, 1990). The Austin Chalk produces along a trend 1 0 - 25 miles ( 1 6 - 40 km) wide and 250 miles (402 km) long from northeastem Mexico's Burro-Picachos Platform to Brazos Country, east Texas, U.S.A. The Austin Chalk in northeastem Mexico is the upper part of the Boquillas Formation, and is designated as being a source rock in this area. Zwanziger (1978) reported gas production from fractured Eagle Ford beds (lower part of the Boquillas Formation) northwest of Neuvo Laredo on the Burro-Picachos Platform. In the eastem part of Texas there is some scattered production from the Austin Chalk. The lowermost portion of the Austin Chalk supplies the majority of the oil and gas production within the entire Austin Chalk section (Poston et al., 1991). The largest producing area is the Giddings Field located in Burleson, Lee, Fayette, and Washington Counties, south Texas, U.S.A. (Fig. 5-50). The field covers about 1,200 square miles (3,107 sq km). Areally, it is one of the largest fields in the Texas Gulf Coast province. The Austin Chalk is a vertically-fractured, massive and brittle limestone containing interspersed ductile marls, and ranges in thickness from 200 to 800 ft (61 - 244 m). The rhythmically bedded chalk-marl sequences generally range from 1 to 5 ft (0.3 1.5 m) and are separated by marls ranging from 1 to 6 in. (up to 0.15 m) in thickness (Stapp, 1977). Reservoir development in the Austin Chalk is almost wholly the result of fracturing. Stapp (1977) and Poston et al. (1991) commented that the permeability of the matrix is on the order of 0.01 to 0.0001 mD (0.000001 - 0 ~m2), whereas fracture permeabilities usually range from 10 to 100 times greater. The average porosity is about 6% at the productive depths of 7,500- 9,500 ft (2286 - 2896 m) and on outcrops ranges from 30% near Dallas to 9% near Langtry, Texas, U.S.A. Vertical or near-vertical fractures in the Chalk, which trend northeast-southwest, generally parallel regional structural strike (Mexia andTalco fault zones) and have a variable density

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of occurrence. Typically, the natural fractures occur in swarms, where fracture spacing can be less than 1 ft (0.3 m) (Lichtenberger, 1990). Locally-occurring conjugate sets of fractures may develop in the Austin Chalk and have an effect on the ultimate recovery of oil in horizontal wells. Fractures in the Austin Chalk may or may not be fully penetrating, depending on the thickness of the marls. The determination of the

328 effective net thickness of the Austin Chalk contributing to hydrocarbon production depends on establishing the vertical extent of the fractures. If unknown, then effective net thickness for a horizontal well will have to be inferred from pressure transient tests (Lichtenberger, 1990). The development and reservoir aspects of the Giddings and Pearsall fields in south Texas (Fig. 5-50) are presented below as examples of how conjugate and single fracture systems affect flow dynamics. Horizontal wells in the two fields have different ultimate primary oil recovery responses owing to the types of fracture system creating the reservoir. Solution--gas drive is the prevailing drive mechanism.

Giddings field productivity. Kuich (1990) presented a geologic model that illustrates the developmental geology concepts of the Austin Chalk in the Giddings Field (Fig. 5-51). Based on the interpretation of seismic data and fault penetrations, most of the structural movement here apparently occurred during the Eocene. Tectonic extension of the area toward the Gulf Coast resulted in normal faulting with horsts and grabens. Seismic data indicate that near-vertical fractures are concentrated on the downthrown sides of normal faults and within the grabens. Interpretation of seismic data indicates that there are abundant, minor faults contained in only the Austin Chalk, with displacements as little as 3 0 - 100 ft ( 9 . 8 - 328 m). The larger faults cut both the upper and lower parts of the Austin Chalk (Kuich, 1990). Initial development of the Giddings Field was in the later 1970s and early 1980s

Fracture trend NE-SW ,

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Fig. 5-51. A geologic model of fracture systems in the Austin Chalk, showing vertical wells with good and poor production, and a horizontal well intersecting a major fracture system. Conjugate micro-fractures are not shown, but are orthogonal to the NE-SW trend of the major fractures. (After Kuich, 1990, fig. 3; reprinted with the permission of the Gulf Publ. Co.)

329 using vertical wells to intersect vertical fractures. Various well-logging techniques and computer-generated interpretations involving caliper, dipmeter (multi-caliper), gamma ray, televiewer, and acoustical logs were used to detect fractures intersected by vertical wells with varying degree of success. Interpretation of electric logs did not provide an accurate evaluation of the Austin Chalk's productivity in the field (Kuich, 1990). Calcite-filled and hydrocarbon-bearing fractures could not always be adequately distinguished on the logs. Careful examination of sample cuttings could help in picking up rock chips showing fracture faces lined with calcite crystals and/or oil stains, the latter being indicative of open fractures. Owing to the spacing of major fractures, initial performance of vertical wells ranged from being highly prolific to exceptionally poor (Sheikholeslami, 1991). The prolific wells possibly were linked to only one vertical fracture system, whereas the poor wells were draining the tight matrix and not tapping unpenetrated fractures (Fig. 551). The occurrence of gas downdip of oil production, and highly variable GORs in the wells show that there is an overall lack of permeability communication within the Giddings Field (Horstmann, 1977). Major lease operators in the middle 1980s preferred to drill horizontal wells, instead of infill wells, to effectively drain the reservoir. The operational goal to be achieved by drilling horizontal wells was to intersect and produce from multiple vertical fractures. Poston et al. (1991) reported that the productivity of an individual Austin Chalk well will depend not only on the number of intersected macro- and micro-fracture systems, but also on their extent and the permeability of matrix. Sheikholeslami et al. (1991) demonstrated that there is a strong correlation between the length of a horizontal well and the producing rate ratio defined as q h / q v . Under equal pressure conditions, 500 - 2,200 ft (152 - 671 m) horizontal completions produce at rates 2.5 - 7 times higher than vertical completions (Sheikholeslami et al., 1991). Kuich (1990) and Poston et al. (1991) stated that future production and ultimate recoveries can be calculated effectively by decline curve analysis of average initial production rates. Claycomb (1983) interpreted pressure transient data from Austin Chalk vertical wells in the Giddings area. His results indicated that radial flow or linear flow due to fractures was followed by pseudoradial flow suggesting the existence of dual porosity. Lichtenberger (1990) reviewed Claycomb' s results and horizontal production data from the Giddings and Pearsall areas. The performance of the horizontal wells in the Giddings area was not always what it should have been because of pressure depletion by vertical wells. Lichtenberger's analyses suggested that there is a higher incidence of conjugate fracturing in the Giddings Field, which would improve vertical well performance through a more isotropic permeability in the horizontal plane. Claycomb's (1983) pressure transient tests supported this idea. His analysis of vertical wells showed radial or pseudoradial flow in addition to fracture signatures. Apparently, the conjugate fracture system is composed ofmicrofractures oriented normal to macro-fractures. Microfractures connect the larger fractures to each other, and act as conduits for production from matrix blocks (Poston et al. 1991). Studies of both Austin Chalk cores and outcrops show the conjugate fracture pattern; however, microfractures are not always present in cores. Flow patterns near producing Giddings Chalk wells will be governed more by the fracture geometry of the fractures intersecting the wellbore than by wellbore effects

330 (Poston et al., 1991). The flow pattern out in the reservoir is controlled by the connectivity and distribution of the natural fracture system in the rock matrix blocks and the permeability ratios of the flow regimes. Pearsall Field productivity. Lichtenberger (1990) presented pressure transient field data from horizontal wells in Pearsall Field (Fig. 5-50) together with an interpretation of the data in terms of a dual porosity model. Pressure transient well responses were different from those encountered in the Giddings Field, indicating that the fracture systems are different in the two fields. Horizontal cores taken from unfractured sections in Pearsall field indicated that the Austin Chalk matrix has negligible permeability. In the Pearsall Field area the Austin Chalk appears to contain many more smaller fractures than in the Giddings Field (Shirley, 1990). Micro-fractures appear to be important components in the producing mechanism of the chalk (Lichtenberger, 1990). Analyses of multiple buildup tests on individual wells show the same signature of wellbore storage followed by a short period of radial flow, and a good linear flow signature (Lichtenberger, 1990). Radial flow data from type curve matches and using Larsen and Hovdan's (1987) method indicated fracture permeabilities of 0 . 5 - 10 mD (0.00049- 0.00987 ~tm2). The net thicknesses drained by the horizontal wells ranged from about 100 to 350 ft ( 3 0 - 107 m) based on Lichtenberger's radial flow permeability estimates. The dual porosity model is considered to consist of a rock matrix divided into fracture-defined blocks. Fractures account for only a small fraction of total porosity, but have high permeability values. Most of the pore space is present in matrix blocks, which have low permeability. The matrix recharges the fracture system. Dual porosity is characterized by two parameters: (1) the storativity ratio, 03; and (2) the interporosity flow coefficient, ~. The equation for defining co is: ~fCf CO = ~fCf q- I~mCm '

(5-46)

where ~bfis fracture porosity, Cf is fracture wellbore storage coefficient in bbl/psi (m3/ kPa), ~bm is matrix porosity, and c m is matrix wellbore storage coefficient in bbl/psi (m3/kPa). The equation for 9~is:

)~ =

4n (n + 1)kmrw2 H2 kf

(5-47)

where n is the fracture dimensionality, k is the matrix permeability in mD (m2), r w is horizontal wellbore radius in ft (m), H is the total effective net pay thickness in ft (m), and kf is the fracture permeability in mD (m 2) (Lichtenberger, 1990). The initial production behavior of a well, using the dual porosity model concept, shows that fluid production comes out first from the fracture system. Figure 5-52 is an example from a horizontal well in Pearsall Field. As the pressure gradient between the matrix and fractures increases, recharging of the fractures will occur and a transition

331

PRESSURE p 9

Z~p

LOG or LOG

I~

I DERIVATIVE p,'

1-

LOG WELL BORE STORAGE

RADIAL FLOW

EARLY LINEAR F L O W

DOUBLE POROSITY TRANSITION

~t

LATE LNEAR FLOW

Fig. 5-52. Schematic log-log plot of the Austin Chalk pressure responses vs. closed-in time observed in horizontal wells, Pearsall Field, Texas, U.S.A. The distinct valley in the derivative curve indicates that the dual porosity recharge systems appear to be present. (After Lichtenberger, 1990, fig. 5; reprinted with the permission of the Society of Petroleum Engineers.)

period is observed where the measured pressure decline rate slows down. As the well is produced, the pressure decline rate will again increase owing to the simultaneous depletion of the fractures and the matrix. This creates a flattening in the pressure vs. time curve (Fig. 5-52). The associated valley in the derivative of the pressure data is considered to be a diagnostic feature of dual porosity behavior. Radial flow is distinguished by a shallower valley on the log-log plot of the pressure derivative versus t, whereas linear flow shows no valley at all. For Pearsall Field the dual porosity storativity ratio (co) was found by Lichtenberger to range from 0.1 to 0.01, whereas the interporosity flow coefficient (k) values ranged from 5 x 10 - 6 to 1 x 10 -8.

Argentina. Pocovi et al. (1991) reported that, in the late 1980s, 26 horizontal and drainhole wells were drilled at various locations in Argentina. Thirteen drainholes were drilled by Yacimientos Petroliferos Fiscales (YPF), the Argentine state oil company. Four of these wells were drilled in the Neuqu6n Basin carbonate reservoirs of Chihuido de la Sierra Negra and Loma de la Lata fields located in the west-central part of Argentina. The Neugu6n Basin is the second most prolific basin in the country, and major oil and gas deposits occur in Jurassic and Cretaceous formations and occasionally on top of volcanic rocks (Pucci, 1987). Major structures in the basin consist of tightly folded anticlines associated with reverse faults trending north along the Andean front. Pucci (1987) reported that, in addition to structural traps, oil has been found in stratigraphic and combination structural and stratigraphic traps. Two drainholes (YPF Nq. LLL-46q Po Hor and YPF Nq. LLL-86q Po Hor) were drilled in microfissured limestones of the Loma de la Lata Field, to test the field's

332 main oil producing horizon, the Q interval of the Lower Cretaceous Quintuco Formation. Thickness of the Q interval in well LLL-46q is 108 ft (33 m), average porosity is 6% and the formation permeability is not greater than 1 mD (0.000987 ~tm2) . The thickness of the Q interval in LLL-86q is 98 ft (30 m) (Pocovi et al., 1991). The vertical wells, from which these drainholes were drilled, showed that the Q interval was barren. Both wells proved to be unsuccessful due to either the lack of hydrocarbons or the zone being impervious. It was hoped that these drainholes would intersect hydrocarbon-bearing fractures. Such failures emphasize that future horizontal drilling in the carbonates of the area has to be carefully planned. Previously, two drainholes were drilled and are producing successfully from the low-permeable, Cretaceous Avile Sandstone (Chihuido de la Sierra Negra Field) and the tight sandstones of the Upper Jurassic Sierra Blancas Formation (Loma de la Lata Field). Middle East. In Saudi Arabia, Oman, and Abu Dhabi, horizontal wells have produced oil at rates 2 - 10 times that of offset vertical wells. The application of horizontal drilling is one method by which Saudi Aramco can increase its daily production above 8 million bbl/D. At the end of 1992, a total of 13 horizontal wells had been drilled, both onshore and offshore, into carbonates in SaudiArabia.Aalund and Rappold (1993) reported that productivity improvements in the Saudi reservoirs are due to: (1) controlling water coning and edge water influx into carbonate reservoirs having thin remaining oil columns (Ghawar F i e l d - Upper Jurassic Arab D); (2) improvement of waterflood sweep efficiency in carbonate reservoirs by having horizontal injectors and producers (Berri F i e l d - Upper Jurassic Hanifa and Hadriya reservoirs; Abqaiq F i e l d - Arab D and Hanifa reservoirs; Ghawar F i e l d - Arab D reservoir); and (3) improvement of production in thin and low-permeable sandstone and carbonate reservoirs. Horizontal drilling in Oman is extensive. Aalund and Rappold (1993) reported that some 70 horizontal wells were drilled and completed in fields of the Petroleum Development Oman (PDO) concession areas. This allowed PDO to increase its overall oil production rate without any significant increase in the number of operating rigs. The Saih Rawl Field in the central Oman, which contains undersaturated light oil in a thin oil column less than 82 ft (25 m) thick, is underlain by water that cones into the vertical wells (A1-Zarafi, 1993). The producing formation is the low-permeable, Lower to Middle Cretaceous Shuaiba (Thamama) Limestone, where oil is trapped in a flat but slightly undulating structure. In 1991, a horizontal well was drilled into the limestone resulting in an initial rate of 4,237 B/D (674 m3/D), which is about three times higher than the productivity of a vertical well. It appears that the well's performance was dictated by the oil column height, reservoir quality, and well spacing of 50 acre (20 ha). It should be noted that the well was drilled within 6 ft (2 m) of the top of reservoir (see previous discussion on the effect of horizontal well eccentricity). The Safah Field in northern Oman produces from Lower Cretaceous Shuaiba carbonates. Beydoun (1988) stated that the discovery well tested 1,650 B/D (262 m3/D) of 39 ~ API oil. The field is compartmentalized by faults and contains about 650 million bbl of oil-in-place and 54 bcf(1.53 bm 3) gas in the gas cap. Chen (1993) reported that seven horizontal wells were completed in the field, which will improve ultimate

333 recovery. The first horizontal wells came on line at 1,500- 1,800 bbl/D ( 2 3 8 - 286 m3/D) oil, which is around 5 times the rate of the vertical wells (Aalund and Rappold, 1993). Drilling cost ranged from 2.5 to 3.5 times the cost of the vertical wells (Chen, 1993). An interesting observation is that there is no direct correlation between initial well productivity index and the length of the horizontal section (Aalund and Rappold, 1993). Future horizontal wells will be placed closer to the oil-water contact owing to the presence of weak aquifer and large gas cap. A1-Muhairy and Farid (1993) reported that some 48 horizontal wells (19 onshore, 29 offshore) had been drilled in Abu Dhabi, U.A.E. The 19 onshore horizontal wells were drilled in five different fields using short, medium, and long-radius technology. Well lengths ranged from 175 ft to 2,393 ft (53 - 729 m). The discovery field (1954) of Abu Dhabi is the Bab Field. Oil and gas come from several porous limestone zones of the Lower Cretaceous Thamama Group, segregated from each other by lowpermeable lime mudstones. Bab Field was brought on line in 1964, producing 40.6 ~ API oil with 0.8% sulfur content from the B zone (Beydoun, 1988). Horizontal wells are designed in the field to recover gas from the large gas cap that occurs in the Thamama A and B zones.

Advanced fracturing treatments For a well to produce additional hydrocarbons as a result of fracturing, it must first have the oil and/or gas to produce. In addition, there must be sufficient reservoir pressure to move the oil to the induced fracture and then into the wellbore. Massive hydraulic fracturing and refracturing of wells are two advanced approaches used to recover additional oil and gas in carbonate reservoirs. These fluid-based technologies result in greater benefits than those attributed to standard formation fracturing techniques. The initial use of hydraulic fracturing was to overcome permeability heterogeneities around and near the wellbore that affected production. Hydraulic fracturing can bring various benefits to the well's ability to produce, such as: (1) increasing its productivity by creating high-flow capacity conduit(s), thereby, increasing the flow rates and flowing bottomhole pressure; (2) enlarging drainage area and flow patterns by penetrating through wellbore damage and geologic barriers, e.g., zones with low permeability and porosity; (3) stimulating reservoir flow by distributing the pressure gradient along the fracture, resulting in an increase in the pressure drop along a unit length of the fracture; (4) accelerating the recovery of oil and gas by creating a number of higherpermeability channels to the wellbore; (5) increasing the ultimate recovery of oil by penetrating isolated zones and lenses; and (6) decreasing the abandonment pressure by being able to produce more oil/gas at lower pressures. Advanced techniques were developed to extend the reach of the induced fracture(s) long distances (>50 ft: >15 m) out into the formation and overcome previous stimulations that were not up to today's standards. One problem with designing hydraulic fracturing jobs is the inability to measure accurately and cheaply the fracture's

334 height, width, length, and azimuth. Mine-back studies, where the induced fracture has been exposed, have shown that hydraulic fractures can have a high degree of tortuosity, i.e., they do not always follow a "straight" line. These induced fractures can curve back to the wellbore region by comering, are often wider at the wellbore than predicted, and can have variable heights. A fracture does not always have a consistent shape. Well logs, coupled with interpretation software, have the capability to provide logderived design values for hydraulic fracture treatments. Ameri and Rieke (1981 ) compiled a source list correlating the hydraulic fracture design parameters with the type of well logs (Table 5-XIII). Formation stimulation selection process

In Part 1 of this book, Hendrickson et al. (1992) discussed stimulation of lowpermeable carbonate reservoirs using acid fracturing. The principle behind acid fracturing is that the creation of an uneven, etched-out fracture does not allow fracture closure upon release of the fracturing pressure. No proppant is used to keep the fracture open, therefore, lowering the cost of the stimulation. Not all carbonate reservoirs, however, respond to acid stimulation. Misuse of acid treatment can be nonproductive and harmful to the well's hardware and create damage to the reservoir. A three-year fracture treatment study by the Sun E & P Company showed that there was a higher percentage of non-service company problem-fracture jobs in carbonate reservoirs (83%) than in sandstone reservoirs (67%) (Dees and Coulter, 1986). This may indicate a fluid leak-off (screen-out) problem with carbonate rocks that contain natural fractures. Inasmuch as knowledge about density of the naturally-occurring fractures in carbonate reservoirs is generally limited, this can result in highrisk fracture treatments (See Introduction Chapter in this volume). Analysis by Dees and Coulter (1986) of successful and problem jobs for carbonates and sandstones in 1985 showed that problem occurrence with deep carbonates (10,000 ft: 3048 m) was 100%. A main conclusion reached by the Sun E & P Company's in-house study is that carbonate reservoirs have a 15 - 20% higher risk than sandstone reservoirs for nonservice company job problems. These problems, whether caused by fluid loss control, fracture height containment, or other downhole factors, need to be reduced to increase success in fracture treatment of carbonate reservoirs (Dees and Coulter, 1985). The risk can be reduced by increased knowledge of the reservoir, treatment planning, instituting quality control measures, and on-the-job monitoring of fracture treatments. Criteria. Two questions are frequently asked by operators producing from carbonate reservoirs: "What is the best stimulation method for carbonate formations?", and "Under what conditions is it better to acidize, acid fracture, or hydraulic fracture?". The following guide might be useful when selecting and evaluating the type of formation treatment to be used in stimulating carbonate reservoirs (Hurst, 1961; Henrickson et al., 1992): (1) Acid fracturing is advantageous in carbonate reservoirs having a high density of naturally-occurring fractures or those not are karsted (owing to proppant drop out). (2) Proppant is used in fracturing of carbonates to create deep-penetrating fractures >100 ft (>30 m).

335 (3) Malleable proppants are used in fracturing impure, dense hard carbonates having low acid solubility, such as dolomite, with confining pressures >6,000 psi (>41.4 MPa). (4) Silica sand proppant is used in fracturing impure, dense hard carbonates having low acid solubility with confining pressures <6000 psi (<41.4 MPa). (5) Acidizing is advantageous in permeable hard carbonates having heterogeneous structures and an acid solubility >30 %, such as limestone, with high confining pressures. (6) Proppant is used in fracturing sucrosic or soft carbonates with low confining pressures.

Evaluation of results of carbonate reservoir stimulations. Black and Stubbs (1975) presented results of a study that evaluated hydraulic fracturing, acidizing, and fracture-acidizing of 25 wells in 5 fields producing from the San Andres Formation in the Permian Basin, U.S.A. (Fig. 5-53). A goal of their study was to compare formation treatments in similar types of carbonate reservoirs. Each of the selected reservoirs exhibited one or more of the three basic San Andres productive carbonate facies: reef, backreef, and lagoonal. Actual and theoretical productivity index ratios were calculated for each treatment using three methods: (1) semi-steady state conditions (McGuire and Sikora, 1960); (2) steady-state conditions (Yinsley et al., 1969); and (3) transient conditions (low-permeability reservoirs; short conductive fracture lengths) (Morse and Von Gonten, 1972). Laboratory tests indicated that permeabilities ranged from 4 to 32 mD (0.003950.03158 [.tm2), porosity ranged from 10 to 18%, and hydrochloric acid solubilities averaged about 85% for the San Andres reef cores (Black and Stubbs, 1975). The backreef facies had permeabilities ranging from <0.1 to 3 mD (<0.000098- 0.00296 lam2), porosity ranged from 4 to 10%, and hydrochloric acid solubilities averaged about 75%. The lagoonal facies had permeabilities less than 0.1 mD (<0.000098 ~m2). Fluid leak-off and spurt loss values were determined for reef and backreef cores using various fluids and fluid loss control additives, such as San Andres crude, gelled 1% KC1 water, 15 and 28% HC1 acid, highly viscous water gel, and a water external emulsion. Values obtained were used in treatment design calculations. The tests showed that for the reef rock, about 25 - 50 lb of fluid loss additive per 1000 gal (3 - 6 kg/m 3) was needed to control fluid leak-off, whereas only 25 lb of fluid loss additives per 1000 gal (6.3 kg/m 3) using gelled water or crude oil was needed for the backreef facies. Fluid leak-off for acid solutions was more severe requiring up to 5 0 - 200 lb of additive per 1000 gal ( 5 . 6 7 5 - 24.75 k g / m 3) (Black and Stubbs, 1975). Fluid loss additives are not required for the tight lagoonal facies. Acid reaction tests indicated that large amounts of fines were released with all three rock types and various acid solutions, which could cause plugging of the fractures (Black and Stubbs, 1975). The fracture flow capacity required to stimulate a formation is dependent upon formation permeability. Black and Stubbs (1975) presented three plots (Figs. 5-54, 555 and 5-56), which can be used to determine the productivity index ratio. The productivity index ratio is the productivity index of the fractured rock to the productivity index of the unfractured rock (Jfs/Ji) from relative fracture flow capacity (RCF) values. Figure 5-54 gives a comparison of fracture flow capacities for San Andres backreef

336

TABLE 5-XI11

Hydraulic fracture design parameters as derived from geophysical well logs Fracture design information obtained from basic logging tool measurements Fluid and rock quantitative data

Hole conditions or applicability BoreHole

Geological and engineering qualitative data

hole

fluid

Potential Spontaneous potential Natural earth potential SP dipmeter 3 SPs 120" apart Resistivity Short normals Laterals Guard and laterolog Induction Microlog Microlaterolog Proximity Resistivity dipmeter

Shallow zone resistivities Deep zone resistivities Moderate depth resistivities Deep zone restivities Flushed zone resistivities Flushed zone resistivities Flushed zone resistivities 3-4 shallow zone resistivities

Acoustic Velocity Wave amplitude 3-D Variable density Oscilliographs Seisviewer

Acoustic velocity Amplitude of acoustic wave Full acoustic wave display Photographs of wave train Acoustic travel time

x x

x x

x x x x x x x x x

x x x x x x x

X

x x x x x

x

x x x x x

X

X

X

x x x x x x x x x x x

X

X X

x x

X

x x

x x x

x

X

X

X

X

X

X

X

X

x x

x x x x x x

x x x x X

X X

x x x x x x x x x x x x x x x x x

x x x x x x x

x x x x x x x x x x

x x x x x x

x x x x x x x

x x x x x x x

X

X

x

x x x x x x x X x x x x

x x x x x x x x x

x x

x x x x x x x x

X

X

X

X

x

x

X

X

X X

x X X

X

X

x x

X

X

x

x

x

Seiscaliper

Acoustic travel time

X

Air gun velocity

Formation velocity

X

Noise

F r e q u e n c i e s 2 0 0 , 600,

X X

1000, 2 0 0 0 H z Nuclear Gamma ray

Natural radioactivity

Neutron

Neutron capture

x

Density

Electron density

x

Pulsed neutron

Capture cross section

x

Spectral

Gamma ray energies

Nuclear magnetism

Nuclear procession

Carbon/oxygen

C, O, Si, C a s p e c t r a

Temperature

x

X

X X

X X

X

x

x

x

X X X

X X X

X X

X X X

X X

X

x

x

x

x

X X X

X X X

X X

X X X

X X

X

x

x

x

X

X X

X

x x

x

x

x

x

x

x

x

x

x

X

X

x X

x

X

X

X X X

X

X

X X

X X

x x

X

X

X

X X

X

X

X X

X

X X X

M u d or f o r m a t i o n temperature

Chemical Salinity

Mud salinity

Hydrocarbon

H y d r o c a r b o n in m u d

x x

x

x

Mechanical Drilling depth

Drilling depths

Directional

Deviation and direction

x

inclinometer Caliper

Hole diameter - geometry

x

Photographic Borehole television

Continuous oriented

x

X X

Borehole camera

Photographs

x

X X

Source: A f t e r A m e r i a n d R i e k e , 1981, t a b l e 1" r e p r i n t e d w i t h the p e r m i s s i o n o f the S o c i e t y o f P e t r o l e u m E n g i n e e r s . * F r e s h or s a l i n e f l u i d s only. N o oil m u d s .

338 ........... ! l ! l

i~;;:;;;:

!!,!lllIlllll

!

II

I

I

Ill

--

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,,

.

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Illllll

'

!:::::::~

i

I

II

-

II

I IIlll

[

OEBAGs LEY

I !

Z ..J

.

~*

i/' U~A ~i~

f

L~ I L""'~~

:.!, 9 9

,~

FLOYD MOTLEY ~i COTTJrE J-4,..__ ~ - ' - " " ~

HiAIJ[

I

"

~AO~IL UPt.F'rt DICKENS i KtHG

CHAVs .........j LEA

SGt~RY I F~NE-R EDDY N~LAI~

L J

/ ....... ~W. ~ x ~ o ....

i .JX.

.-

t

:~evzs

qOAeLO

./,.

REAGAN

I

"

COKE

i

i~ ~ TOM GREEN'-'~

/

JEFF DAVIS

kLCROCKETT ~l

PECOS AINS

/ /

',LI~" -

,/

j, ~. Pt~E$10O

L

BtEWSTEtZ

/ 1

i

1

!

i/

Vt~tt~t~

1

:i E1PWARD$

REPU.BUCOF MEXICO

i

FIELDS OF STUDY OTHER 8AN ANDRE$ FIELDS

Fig. 5-53. Location map of SanAndres fields in the Permian Basin, New Mexico and west Texas, U.S.A.: (1) Slaughter-Levelland Field on the Northern Platform (Cochran and Hockley counties, Texas); (2) Wasson Field on the Northern Platform (Yoakum and Gaines counties, Texas); (3) Vacuum Field in the Northwestern Shelf (Lea County, New Mexico); (4) Hobbs Field in the San Simon Channel (Lea County, New Mexico); and (5) Dune Field on the Central Basin Platform (Ector and Crane counties, Texas). (After Black and Stubbs, 1975, fig. 1; reprinted with the permission of the Society of Petroleum Engineers.)

339 c)

9

I,.--

I i I i

SAN A N D R E S CORES x Io(:-- W A S S O N FIELD I--ROCK TYPE: B A C K R E E F u_ I C L O S U R E PRESSURE" 2 0 0 0 "~

513

_ 71

PSi

-

E 40----O < 2o-n < O 10~ O ..j

=

LL 5~ 41

9

Iii E 3: D I-i 2~

(D<

'

i

.

.

.

.

/

E 1

10 2

10

10 3

SAND C O N C E N T R A T I O N ,

LB PER

I0 4

1 0 0 0 FT 2

OF PROPPED AREA

Fig. 5-54. Relation between the propped fracture flow capacity and sand concentration in the fracture for different sand sizes (Wasson Field, Yoakum and Gaines counties, west Texas, U.S.A.). (After Black and Stubbs, 1975, fig. 2" reprinted with the permission of the Society of Petroleum Engineers.)

cores using different sand sizes and concentrations, whereas Fig. 5-55 gives the acid etched fracture flow capacities without sand for two different acid solutions. Highlypermeable carbonate rocks, such as those of the San Andres reef facies, require a high fracture flow capacity in order to have a large contrast between the fracture flow capacity and the formation permeability. The permeability contrast is more significant than the length of the conductive fracture (Black and Stubbs, 1975). An example calculation of JfJJ~ ratio using data from Fig. 5-54 for the San Andres backreef facies is shown in Fig. 5-56. If there is no significant increase in Jfs/J i ratio owing to small differences in the fracture flow capacity values obtained from Fig. 5-54 using different sand concentrations, then a way to increase Jfs/Ji ratio would be to use a larger treatment volume to create a longer propped length and a larger L/r e value.An example considering 2 0 - 4 0 vs. 1 0 - 2 0 mesh sand at concentrations of 1000 lb per 1000 ft 2 (5 kg/m 2) having a ki = 1 mD (RCF = 5 and 15, respectively) gives a Jfs/Ji = 2 for both cases for L/r = 0.1 (Fig. 5-56). At L/r = 0.8, Jrs/J~ = 5 ( 2 0 - 40-mesh sand) and 5.8 (10 -20-mesh sand) showing a slight increase in the productivity of the fracture (Fig. 5-56). Table 5-XIV presents Black and Stubbs' (1975) results of San Andres treatment. Damage removal treatments using acid solution in Dune Field were successful in three wells (in the high-permeability reef facies), whereas in the backreef facies it was considered to be not successful (Table 5-XV). The general conclusion derived from Tables 5-XIV and 5-XV is that hydraulic fracturing with gelled water containing either 2 0 - 40 or 1 0 - 20 mesh sand is usually successful in stimulating San Andres wells e

e

340

,,,,,,,

"~

'

0

~

.

.

.

.._

.

.

.A

.

"'~'~.,I

. . . . . . . . . . . . .

_

w I

~

3

/

< r I,

2

-

J

,~--

SAN ANDRES CORES

--

"

WASSON FIELD ROCK TYPE: BACKREEF CLOSURE PRESSURE: 2 0 0 0 PSI

O

10

20

30

40

50

60

ACID INJECTION TIME , MINUTES

Fig. 5-55. Relation between etched fracture flow capacity and acid injection time. (After Black and Stubbs, 1975, fig. 3; reprinted with the permission of the Society of Petroleum Engineers.) producing from the backreef facies. In the low-permeability lagoonal facies, fracture treatments that give a long, moderately conductive fracture is desirable. Wells in the high-permeability- high-porosity reef facies should be stimulated using a controlled damage removal acid treatment containing a surfactant and, where required, an iron sequestering agent (Black and Stubbs, 1975). Short conductive acid fractures would also fit this requirement. A recent study by Hoover and Adams (1988) evaluated advances in fracturing techniques in San Andres dolomitic reservoirs of the Howard Glasscock Field located on the Eastern Shelf of the Permian Basin (Howard, Glasscock, Sterling and Mitchell counties, Texas, U.S.A.: Fig. 5-53). Increased fracture conductivity was required to properly implement a waterflood. The reservoir's drive mechanism is a combination drive consisting of solution-gas and water drives (small quantity of water) in the wells along the western edge of the field. Hoover and Adams (1988) discussed the application of geophysical well logging, perforating techniques, new programmable blending equipment, and computer software to increase the volume of proppants used during hydraulic fracturing of the San Andres Formation. A fracture simulator was used to design an optimum treatment program. Input data to the simulator was obtained from well logs and a test fracturing treatment. This "data frac" was performed on one of the wells to gather formation information and to determine the feasibility of using different fracturing fluids. The

341 EXAMPLE CALCULATION

Jfs > PR.ODUCTIVITYINDEXRATIO(~i_i VS RELATIVE

I L - - - - - - =,O.e

hf i = 1.0 6

dfs

RockType: Bockreef ki =0.1 mD Sond concentroltion in frocture = I000 Ib/lOOOft2 Type propp_ont used: 2 0 - 4 0 sond FC =SxlO~md-ft (From Fig. 5 - 5 4 ) W e l ~ f i ~ g = 2 0 acres re= rw= O.33feet LW=233 feet hf = I 0 0 feet hi = I 0 0 feet

CAPACITY

RCF =0.00159

hf hi

.//

X

-,

5

.=0.7 re

I'

!

L -'-0.5re

4

t.I-0.3

i i

L -13.1 -1

o

I

0.1

2

4

1.0

2

4

I0

2

4

I00

2 4

IGO0 2

4

I0000

RCF(-~i) WHERE:

Ji = PRODUCTIVITY.INDEX OF UNFRACTURED SYSTEM, bbl doy"1 psi'= Jfs = PRODUCTIVITY INDEX OF FRACTURED SYSTEM bbl day "I psi "l Jfs --= PRODUCTIVITY INDEX RATIO, FOLDS OF INCREASE di FC = Wkfl FRACTURE FLOW CAPACITY, roD-f! k i = FORMATION PERMEABILITY ( UNDAMAGED), mD hf = PROPPED FRACTURE HEIGHT, ft hi = FORMATION THICKNESS, ft r e = RADIUS OF DRAINAGE, ft r w = WELLBORE RADIUS, ft S = WELL SPACING, ACRES RCF = RELA'IIVE CAPACITY FACTOR AS IDENTIFIED ABOVE

RCF= 0.00,59 (~.i) In ( - ~ ) . V r ' ~ T RCF= O. 0 0 1 5 9 ( I ) I n ( .~-~-..).~/ Io__RCF = O. 00815 u.=~ zo ,c o~oo,,sxsx,o 3 " "= o., CCF= ~-~T'I RCF = 4 0 8 t. =Z_~ = 0 . 5 re FC L If RCF ( ~ . 1 : 4 0 8 ond T~.e= O. 5 ,

then Jfs = 4.3 fol d increose. Ji In the obove example if L were only 47 feet: _k. 4_1. : 0 . 1 r e 4tS then: Jfs = 2 . 0 fold increase

RCF (-~;) = RELATIVE CAPACITY L = CONDUCTIVE FRACTURE LENGTH, fl

Fig. 5-56. Productivity index ratio (Jfs/J~) values cross-plotted against the relative capacity (FC/ki) show the importance of long conductive fracture lengths in low-permeable carbonate rocks, such as those of the San Andres Formation backreef facies. (After Black and Stubbs, 1975, fig. 4; reprinted with the permission of the Society of Petroleum Engineers.)

fracture treatments were executed by using programmable blending equipment to accurately schedule and place the proppants. The equipment made it possible to schedule higher sand concentrations of larger mesh sizes in significantly smaller fluid volumes. Coupled with measured reservoir stress values, fracture heights could be effectively predicted, resulting in creation of controlled fracture heights. A perforating procedure was developed to ensure the desired friction pressure drop. Prior to fracturing, all perforations were acidized using 100 gal (0.4 m 3) of 15% HC1 (cationic corrosion inhibitor, nonionic non-emulsifying agent, and iron stabilizer) per perforation to insure that the perforations are open and able to accept fracturing fluids. The average treating breakdown pressure was 1,300 psi (9 MPa) and the

342 TABLE 5-XIV A comparison of actual vs. theoretical productivity index ratios as calculated by the McGuire and Sikora (1960), Tinsely et al. (1969), and Morse and Von Gonton (1972) methods for wells in five San Andres fields, Permian Basin, U.S.A. The wells are designated as A through X (first letter) and the five fields are designated as: C = Vacuum, D = Dune, H = Hobbs, S = Slaughter-Levelland, and W = Wasson (second letter). Assumed radius of drainage is 466 ft (142 m) and well spacing is 20 acres (8 ha) Conductive fracture length, ft

Productivity index ratio

Well rock type

Treatment Vol., Gal.

AW (75% B, 25% R) k = 2.98 mD

22,500 (GW, sand-out)

406

8.3 - 1.0 (64 days)

BW (B) k = 2.98 mD

27,500; GWV

221

CC (B) k = 2.98 mD

20,000; GW

DC (B) k = 2.98 mD

Actual*

Tinsley

Morset

9.0

2.1

9.2 (8 days)

2.8 (1 day)

6.6

3.7

6.3 (8 days)

861

2.4 - 2.2 (1 yr)

8.1

2.1

9.7 (8 days)

20,000; GW

497

3 . 6 - 1.8 (1 yr)

8.0

2.0

9.7 (8 days)

EC (B) k = 0.33 mD

20,000; GW

625

11.4 - 3.9 (3 yrs)

12.4

3.7

9.7 (64 days)

FC (B) k - 0.4 mD

5,250 (20% HC1; 10,500 PF)

38

2 . 1 - 1.4 (1 yr)

1.5

1.8

2.3 (32 days)

GD (B) k - 0.3 mD

5,000 (20% HC1, FSA; 5,000 PF)

112

3 . 0 - 1.4 (4 mo)

4.2

3.1

4.0 (64 days)

KH (B) k=3mD

2,500 (15% HCI, FSA)

30

2.0 (1 day)

1.5

1.6

2.1 (8 days)

MD (B, L) k - 0.11 mD

10,000 (20% HC1, FSA)

8

10.4- 1.0 (1 mo)

1.7

1.1

1.3 (128 days)

NW (50% B; 50% R) k = 0.33 mD

33.000; GW

798

12.7

3.2

9.7 (64 days)

OS (R) k - 11 mD

5,250 (15% HC1, 10,500 PF) 8,000 (15% HE1, FSA)$

29

3.0 - 1.3 (1.5 yrs)

2.1

1.5

2.0 (4 days)

28

2.6 - 1.7 (2.5 yrs)

1.9

1.5

2.0 (4 days)

3.7 - 6.4 (1.5 yrs. FR)

McGuire

343

Well rock type

Treatment Vol., Gal.

Conductive fracture length, ft

PW (50% B, 50% R) k = 5 . 5 mD

22,000; GW

597

QW

7,200

14

Productivity index ratio Actual*

McGuire

Tinsley

Morse# 10.0 (4 days)

8 . 7 - 5.8 (5 mo)

6.7

1.4

1.2 - 0 . 8

1.2

1.3

(4.5 mo)

1.5

(50% B, 50% R) k = 7 mD

(15% HC1, FSA, Matrix Acid)

(4 days)

RD (B, L) k = 0 . 3 mD

43,000; Emulsion

511

1 4 - 1.2 (3.6 mo)

12.6

3.9

9.7 (64 days)

SW (B) k = 0.1 mD

20,000; GW

595

2 . 9 - 5.1 (4 yrs 11 mo, FR @ 2 yrs 3 mo)

13.4

3.7

10.1 (128 days)

TC (B) k = 0 . 3 mD

20,000; GW

968

5.4 (1 day)

12.6

4.2

9.7 (64 days)

UW (B) k = 0 . 3 mD

20,000; GW

758

6 . 0 - 3.0 (5 mo)

12.6

3.1

9.7 (64 days)

VS (50% B, 50% R) k=2mD

8,000 15% HC1, FSA)

65

10.1 - 3.9 (1.5 yrs)

3.3

2.0

3.1 (8 days)

WS (50% B, 50% R) k = 2 . 1 mD

6,000 (15% HC1)

68

4.3-2.9 (1.5 yrs)

3.3

2.1

3.1 (16 days)

XC (B) k = 0.4 mD

5,250 (20% HC1; 8,250 PF) WO; IP

180

3.1 - 1.4 (2 yrs)

2.8

5.3 (32 days)

7.1

Source: Modified after Black and Stubbs, 1975, table 4; courtesy of the Society of Petroleum Engineers.

* Time to reach the final productivity index ratio shown. t Approximate time shown to reach steady-state flow conditions and productivity index ratio shown. :l: Retreatment 1.5 years after first treatment. GW: Gelled water GWV: Gelled water, viscous B: Backreef rock type R: Reef rock type L: Lagoon rock type PF: Pre-flush for acid treatment FSA: Fines suspension additive, acid FR: Flood response WO: Workover IP: Installed pump

344 TABLE 5-XV Evaluation of acid damage removal treatments in the San Andres Formation, Dune Field, Permian Basin, Texas, U.S.A. Well and treatment type

Volume, gal

Zone thickness, ft Gross Net

Production, B/D Before After

Rock type: Reef (Dune Field) HD 15% HCI acid, Fe additive*

2000

135

8

ID 15% HCI acid Fe additive* JD 15% HCI acid, Fe additive*

2000

140

20

45 (oil)

836 (oil)

1000

125

11

30 (oil)

867 (oil)

GD 20% HC1 suspension type acid (6.5 BPM)

5000

9.1 (oil) 3.9 (water)

7.2 (oil) 10.8 (water)

0

1016 (oil)

Rock type: Backreef (Dune Field) 51

Unknown

Source: Modified after Black and Stubbs, 1975, table 1; courtesy of the Society of Petroleum Engineers. * Iron sequestering agent.

average instant shut-in pressure ranged from 600 to 800 psi ( 4 - 5.5 MPa) (Hoover and Adams, 1988). A 1 2 - 20-mesh Texas brown sand was used to obtain adequate fracture permeability and have the required closure stress resistance. Sand volumes in the treated wells ranged from 59,000 to 109,100 gal ( 2 2 3 - 4 1 3 m3). The fracturing fluid composition consisted of: 2% KCl-based fresh water, 30 lb of hydroxypropyl guar gum gelling agent per thousand gallons of fluid, borate crosslinker, fluoro-surfactant, quaternary ammonium chloride bactericide, external oxidizer breaker, and an oil-soluble resin to control fluid loss. Table 5-XVI presents treatment parameters and fracture height data obtained from a three-stage data frac used to test the performance of several fracturing fluids. Gamma ray logging results using radioisotopes showed that all the treatments stayed within the predicted perforated interval of 182 ft (55 m). The pump schedule used on the test well was designed to give a fracture extension of about 140 ft (43 m). This distance is less than half of the attributed drainage radius for the well's spacing (Hoover and Adams, 1988).

Massive hydraulic fracturing One fracture treatment that shows promise of recovering gas and oil from lowpermeable carbonates is massive hydraulic fracturing (MHF). A conventional hydraulic fracturing job is considered by industry to be one that takes up to 100,000 gal (379 m 3) of fluid and up to 75,000 lb (34,020 kg) of proppant. The primary difference between a conventional hydraulic fracture and a massive hydraulic fracture treatments is the size of treatment. A massive hydraulic fracture treatment involves the use of up to 1,000,000 gal (3,785 m 3) of fluid and up to several million

345 TABLE 5-XVI Data from a San Andres Formation three-stage fracture treatment test evaluating one non-crosslinked and two crosslinked fluids, Howard Glasscock Field, Howard County, west Texas, U.S.A. Impregnated beads (1 millicurie of Iridium 192 per thousand gallons of fluid) were used to tag the stages for the gamma-ray log determination of fracture height

Pump rate, bpm Surface pressure, psi Bottomhole pressure, psi Perforated interval, ft Gross height (predicted), ft Net height, ft Logged fractured height, ft A. Temperature, log B. Gamma ray, log Polymer loading, ppt Crosslinked (Y/N)

Stage A

Stage B

Stage C

10 1370 1870 151 182 151

40 1915 2440 151 182 151

40 2044 2489 151 182 151

176 150 10 N

193 159 50 Y

154 159 80 Y

Source: After Hoover and Adams, 1988, table 2; reprinted with the permission of the Society of Petroleum Engineers).

pounds of sand proppant. MHF treatments are designed to create fractures that extend 500 - 2,000 ft (150 - 610 m) or more from the wellbore. The term "minimassive fracture treatment" refers to the collective use of several hydraulic fracturing techniques, such as gelled water, high amounts of 100-mesh sand in the pad fluid to control leak off, high proppant concentration as is operationally feasible ( 5 - 10 lb/ gal: 5 9 9 - 3356 kg/m3), and a quick bleed-back of the well as soon as possible (Crow, 1977). Mini-massive fracture treatment. The first mini-massive fracture job was completed in June, 1976, in the Mississippian Salem Limestone, Gibson County, southwestern Indiana, U.S.A. This reservoir has an average permeability of 0.42 mD (0.00041 pm 2) and an average porosity of 7.3% (Crow, 1977). Previous treatments on a well involved large acid jobs, and large water-base, oil-base, acid-base and viscous gel fracture treatments, which did not decrease the operator's ten year payout time. The formation was fractured with 20,000 gal (76 m 3) of gelled water (30 cP viscosity), 9,000 lb (4,082 kg) of 100 mesh sand, and 77,000 lb (34,927 kg) of 2 0 - 40 mesh sand. Injection rate was 15 bpm (2.4 ma/min) and sand concentrations ranged up to 8 lb/gal (959 kg/m 3) (Crow, 1977). The well paid out in 35 days. Another Salem Limestone well in Gibson County, Indiana, U.S.A., which had initially undergone acid fracture treatment with 31,000 lb (14,062 kg) of sand, and later acidized with 1,500 gal (5.7 m 3) of 15% HC1, did not respond to these treatments. A mini-massive treatment was performed using 30,000 gal (114 m 3) of gelled water, 20,000 lb (9,072 kg) of 100-mesh sand, 58,000 lb (26,309 kg) of 2 0 - 40-mesh sand, and 5,000 lb (2,268 kg) of 1 0 - 20 mesh sand. The well, which was producing at about 3 bbl/D (0.5 m3/D), responded with a production of 768 bbl/D (122 m3/D), declining to 90 bbl/D (14 m3/D) after 120 days (Crow, 1977).

346 The success of the fracture treatment in the above two examples is thought by Crow (1977) to be due to the prevention of premature screenouts in the very lowpermeable carbonates, and the ability to create the proper fracture penetration into the formation. Crow (1977) based his conclusions on the principle of dilatancy in rock failure: as the rock approaches its breaking (fracture) point, a myriad of tiny fractures form (Brace, 1972). All subsurface formations are under triaxial load conditions, which consist of the overburden stress and two additional horizontal stresses. Under these conditions, when a pressure is applied from within a rock, the rock will fracture in a plane perpendicular to the least amount of stress on the formation. The stresses control fracture directions and determine whether fracture planes are horizontal, vertical, or inclined. Before rupturing, tiny cracks will form and dilatancy will continue to occur along the leading edge of the fracture as it progresses outward into the formation. This explains the response failure of the previous treatments in the two Salem Limestone wells. Crow (1977) suggested the following sequence of steps in applying the mini-massive fracture procedure: Step 1: Pump a pad fluid containing 100-mesh sand (diameter: 0.0059 in.; 0.015 cm), which will enter into the tiny thief cracks and bridge the openings, thereby reducing fluid loss. This prevents premature screenouts that would prohibit the hydraulic fracture to penetrate a proper distance into the formation. Step 2: Use a viscous fracturing fluid, which will control the leakoff into the carbonate matrix. Step 3: Use as high a proppant concentration as is operationally feasible to fill the entire fracture height. A properly designed and controlled injection rate will keep the fracture within the desired interval so that the desired fracture length out into the formation can be achieved. Step 4: Bleed the well back and as fast as practical so that the fracture will close and trap the proppant while it is still suspended inthe fluid.

Massive hydraulic fracture program. The objective of this analysis was to evaluate a massive fracture stimulation program recovering natural gas from deep ( 11,000 ft: 3353 m), naturally-fractured, low-permeable gas-bearing carbonate rocks (Kozik et al., 1980, 1981). Under the sponsorship of the U.S. Department of Energy and the Mitchell Energy Corporation, two massive hydraulic fracturing tests in the Jurassic Haynesville Limestone (Cotton Valley Group), Limestone County, east Texas, U.S.A., were studied in detail to determine well spacing and fracture length radius necessary for optimum development of the Fallon and North Personville fields. The Haynesville Limestone is the lower member of the Cotton Valley Group, which covers more than 250,000 square miles (6.47 million km 2) in east Texas, western Louisiana, and southeast Arkansas (Kozik et al., 1980). The Haynesville Limestone ranges in thickness from 300 to 500 ft (91 - 152 m) and is massive, oolitic to pisolitic, and finely crystalline to micritic. Porosity ranges from 2 to 14% in the oolitic zones, whereas matrix permeability ranges from around 0.003 to 0.7 mD (0.000003 -0.00069 ~tmZ). The measured trend of naturally-occurring fractures from cores in the Muse-Duke No. 1 well is NW-SE (strike between 280 ~ and 320~ Effective and relative permeabilities to nitrogen gas were measured in the

347 1.0

i

'~ "\

MEC:

i

COTTON RELATIVE

O)

4) 1 1 3 0 2

i n

0,8

--

0.6

--

0.4

--

0.2

--

lll l

MUSE-DUKE

VALLEY

WELL

§

LIMESTONE

PERMEABILITY

VS.S

w

FT.

(n (.g o I->. I-.J .....

m

W CE

a. W ~ m

I-I

\ \ \ 0

_ 0

I 20

I 40

I 60

WATER SATURATION

I, 80

100

(Sw), %

Fig. 5-57. Variation in the relative permeability to gas with increasing water saturation in two Cotton Valley Limestone core samples from the Muse-Duke well No. 1; both cores show a similar trend. The relative permeability to gas is virtually unaffected by the presence of water up to 20% S . When S w is about 85%, relative permeability to gas approaches zero. (After Kozik et al., 1980, fig. 5; courtesy of the U.S. Department of Energy.)

laboratory at a reservoir temperature of 285 ~ F (141 o C) and at various water saturations (Fig. 5-57). Initial production rates, using standard 1970s stimulation technology, were moderately good (1 - 4 MMCF/D: 0 . 0 3 - 0.11 MMm3/D) in the Haynesville Limestone. Five of the first six wells completed received light acid stimulations and began to produce at about 1 MMCF/D per well and soon declined to 0 . 2 - 0.3 MMCF/D (0.006 - 0 . 0 0 8 MMm3/D). The Burleson No. 1 well received a hydraulic fracture treatment of 48,000 gal (182 m 3) of gelled water and 178,000 lb (80,741 kg) of sand. Initial production was 4.4 MMCF/D (0.125 MMm3/D), but declined to 0.5 MMCF/D (0.014 MMm3/D) in two years. The natural fracture system was not sufficient to maintain initial flow rates. The Muse No. 1 was the first well to receive the MHF treatment. As was the case in the mini-massive fracture stimulations, 100-mesh sand (48,000 lb: 21,773 kg) was

348 pumped ahead of the 2 0 - 4-mesh sand to control fluid loss. A total of 340,000 gal (1,287 m 3) of gelled water and 450,000 lb (204,120 kg) of 2 0 - 40-mesh sand was pumped (Kozik et al., 1980), resulting in an initial production rate in excess of 4 MMCF/D (0.113 MMm3/D) that declined to 1.1 MMCF/D (0.031 MMm3/D) after 28 months. A larger, or so called "super-massive hydraulic fracture stimulation treatment" was performed on the Muse-Duke No. 1 well following an acid stimulation of the well. This treatment consisted of using 95,000 gal (360 m 3) of treated-water prepad containing 10 lb/gal salt water; no 100-mesh sand was pumped. A total of 842,850 gal (3,190 m 3) of gelled water (Versagel) containing 2,800,000 lb (1,270,080 kg) of 2 0 - 40-mesh sand was displaced into the limestone. Initial production after fracturing was 6 MMCF/D (0.17 MMm3/D), which declined to 2.1 MMCF/D (0.06 MMm3/D) after 22 months. By 1980, four other wells were fractured using sand volumes ranging from 450,000 to 1,000,000 lb (204,120-453,600 kg). Kozik et al. (1980) reported that initial production rates indicate performance similar to the Muse No. 1 well. Figure 5-58 presents a comparison of the performance curves for the Muse No. 1, Muse-Duke No. 1, Burleson No. 1, and three best acidized wells (11year production history). 10,000-.. g,O00-~ e,O00|

FALLON

7,000~

AND NORTH PERSONVILLE LIMESTONE CO.. TEXAS 2-1-80

FIELDS

9. , o o

s,ooo ! 4,ooo !

_..use-ouKt., ...s,v.

F..c,

. -= ,.0o0 r =E 1=

1,000. 900 800 700

URLESON ,F, 1 IONAL FRAC)

6O0

500 400 300

AVERAGE OF 3 WELLS (NOT FRACED)

200

100

I

.1

9

I 1

CUMULATIVE

i

I 2

PRODUCTION

ii

i

i

I 3

(BILLION

CU. FT.)

Fig. 5-58. A comparisonbetweendaily flow rates and cumulativeproduction for massive fracture stimulation, conventional fracture treatment, and non-fracturedwells in the Cotton Valley Lime (Haynesville Limestone). (After Kozik et al., 1980, fig. 7; courtesy of the U.S. Departmentof Energy.)

349 Reservoir simulation studies of the Muse No. 1 and Muse-Duke No. 1 wells consisted of varying formation permeability, fracture length, and fracture conductivity to match well performance and assess the sensitivity of costs (Kozik et al., 1980). Unfortunately, a unique history match was not obtained for the Muse No. 1 well owing to insufficient pressure buildup data. Definitive fracture half-length could be not determined for this well. A fracture half-length of 1500 ft (457 m) was determined for the Muse-Duke No. 1 well. From the reservoir simulation history matching analysis of these two wells, the formation gas permeability ranges from 0.01 to 0.04 mD (0.00001 - 0 . 0 0 0 0 3 9 ~m2). A computer model FRACOP (Holditch et al., 1978) was used to determine optimum fracture length and well spacing for a well similar to the Muse No. 1 and the MuseDuke No. 1. The model uses reservoir and well parameters, and fracture length values, to generate a production function, which is used to determine net cash flow and net present value for any specified discount rate. Results are presented in Fig. 5-59, which shows ultimate gas recovery as a function of permeability, fracture length, and drainage area (well spacing). At a 160-acre (65-ha) spacing, increase in the fracture halflength from 250 ft to 1250+ ft ( 7 6 - 381 + m) does not have a significant influence on 30-year ultimate recovery (Kozik et al., 1980). The effect of higher permeability values ...

,,

I

I

I

i

I

12

.I .I W

K -- O , 0 4 m d

~1o

640a0.

u_ U m

8

E

J

K :

O.01md

640ec.

Is 8

-

0 lU

W m

~

0

K-~ 0 . 0 1 ,

:12011r

4 8r

0

K ~ 0.01

I

,,

800 PROPPED

,

160at,

I

I

1000

1800

FRACTURE

LENQTH

,

I

2000

,,

2800

(FT.)

Fig. 5-59. The effect of permeability upon 30-year ultimate gas recovery per well as a function of fracture half-length. Ultimate recovery increases as permeability, fracture length, and well spacing increase. Higher permeability values, however, have a pronounced effect as the drainage area increases. Results are based on a FRACOP model study using Haynesville Limestone reservoir parameters and economic costs from the Muse No. 1 and Muse-Duke No. 1 wells. (After Kozik et al., 1980, fig. 19; courtesy of the U.S. Department of Energy.)

350 becomes more pronounced as the drainage area increases. This suggests that the best well spacing would be 4 wells per section (one sq. mile = 640 ac = 259 ha), inasmuch as this well density results in a maximum recovery efficiency. Kozik et al. (1980) stated that to properly optimize well spacing and fracture length from an economic viewpoint, the maximum discounted present value profit for each case must be determined. Figures 5-60 and 5-61 show the 10% profit per section for permeabilities of 0.01 and 0.04 mD (0.00001 -0.00039 ~tm2), respectively. Table 5XVII lists the economic parameters and fracturing costs used in the study. The optimum well spacing for these conditions is 320 acres (129 ha), and the propped fracture half-length is 1500 ft (457 m).

Massive hydraulicfracturing-horizontal drilling comparisons. As described above, tight gas reservoirs with matrix permeability values in the microdarcy range can contain zones of natural fractures having relatively high permeability. A major risk associated with the development of such reservoirs is the possibility of having water breakthrough as a result of fractures tapping underlying water zones. Van Kruysdijk and Niko (1988) assessed this risk using a reservoir prototype model based on Shell Oil Company's black oil simulator. The first phase of the study assumed single-phase compressible flow, and utilized Green's function theory to derive transient pressure response. Results from the model study (Fig. 5-62) indicated that a horizontal well 3.0

320 Acres. 1140 A c r e s

2.,5

~W ~

2.0 160 A c r e s

m

~- a0 1.5 0 n

Z) 1.0

0

NOTE: F i g u r e s a r e on a per s e c t i o n b a s i s

. m

0

-0.5 800

1000

1500

2000

2500

PROPPED FRACTURE LENGTH (FT,)

Fig. 5-60. Results from a FRACOP model study showing a comparison of the 10% discounted presentvalue profit per section (one square mile: 2.59 square kilometers) with propped fracture length for a formation having 0.01 mD permeability. (After Kozik et al., 1980, fig. 21; courtesy of the U.S. Department of Energy.)

351

om IU m

8 820 Acres 640

c~ m

Acres

180 Acres

41 .9,0 N O T E : Figures are on a per section basis

I

I 500

.

lOOO PROPPED

I

.

18oo

FRACTURE

LENGTH

I 2000

,

2500

(FT.)

Fig. 5-61. Results from a FRACOP model study showing a comparison of the 10% discounted presentvalue profit per section (one square mile: 2.59 square kilometers) with propped fracture length for a formation having 0.04 mD permeability. (After Kozik et al., 1980, fig. 22; courtesy of the U.S. Department of Energy.)

TABLE 5-XVII Economic values and fracturing costs (1979 rates) used in the optimization of fracture length and well spacing evaluation from Mitchell Energy Corporation's Cotton Valley Lime (Haynesville Limestone) massive hydraulic fracturing test data, Fallon and North Personville fields, Limestone County, east Texas, U.S.A. Note that any economic evaluation or technical evaluation involving economic analyses is sensitive to each operator's economic parameters, such as current product price, price escalation or deflation, operating costs, initial investment, interest rates, and net working interest (data from Kozik et al., 1980) Economic parameters

Fixed investment: Product price: Operating expenses: Net revenue interest: Production Tax rate: Federal Income Tax rate:

$1,000,000 $1.52/MCF constant $8,400/yr constant 79.7% 13.0% 0%

Fracturing costs

Designed fracture-length radius, ft

Costs, $

250 500 750 1000 1250 1500 1750 2000

75,000 100,000 150,000 200,000 250,000 300,000 400,000 700,000

352

W.I E L. L B. O R. E

'I

y

!

I

Ze

//

Z

J ~

--X

L_ .

,,

RESIERVOIH ~

_1

A .

..-._.__

WELL|ORE

i I I I I

I I I I I

MASSIVE HYOA,tUUC FRACTURE

_ Z

~_7.T s

X'

~ / -

~

I

RLSE~K)In

B Fig. 5-62. Two semi-analytical models used to assess alternatives for draining tight naturally-fractured gas reservoirs: (A) Horizontal well reservoir model containing a naturally-fractured zone of finite width extending over the full height and width of the reservoir; (B) Double-fracture reservoir model showing a massive hydraulic fracture intersecting a vertical fracture plane. (Modified after Van Kruysdijk and Niko, 1988, figs. 1 and 5; courtesy of the Society of Petroleum Engineers.)

draining a natural fracture zone compares well with massive hydraulic fracture treatment, which connects the well to the fracture zones. Figure 5-63 presents typical pressure responses of both the horizontal well and a massive hydraulic fracture (MHF) intersecting a fracture zone. Inasmuch as the models used in Van Kruysdijk and Niko's (1988) assessment involve single-phase flow, additional advantages of the horizontal well with respect to water coning control were ignored. Table 5-XVIII presents the reservoir parameters used in this study.

353

L|

1(~

!~ !~ i-

'

'~ ..... ' "' ............... , ,, 9

9U - - H- -r, C , t t=0' , " ' , , ' s

..r ~Hr uHr kIHu

cfo = CI0 s CIOCIO :

...... "

"'""

..............

.......

,o-,

w

........

,

2.~ $ tO 1S

--.

y

V......-::

I0"*

o

I 0 "s

I0"

I 0 "s

I0"

10"

I 0~

Io'

1o'

OIMENSIONLESS TIME. I0

Fig. 5-63. Typical pressure responses of a horizontal well and a massive hydraulic fracture, both tapping a large natural fracture zone in a tight gas reservoir, with respect to dimensionless time. Cro is the dimensionless fracture conductivity and is equal to w(kf)/xf(k), where w is the fracture width, kf is the fracture permeability, Xf is the fracture wing length, and k is the reservoir (average) permeability. (After Van Kruysdijk and Niko, 1988, fig. 11; reprinted with the permission of the Society of Petroleum Engineers.)

TABLE 5-XVIII Basic reservoir parameters used in the model studies assessing the production performance of massive hydraulic fracturing and horizontal well scenarios in a naturally-fractured gas reservoir fractured zone width, w e reservoir thickness, z e reservoir width, ye wellbore length wellbore radius, r w fractured zone permeability, kns reservoir permeability, k fractured zone porosity, (I)f reservoir porosity, ~

9 30 ft 9 750 ft 9 1500 ft 9 1500 ft 9 0.3 ft 9 250 mD 9 20 I~D 9 0.01 9 0.07

Source." After van Kruysdijk and Niko, 1988, table 1" reprinted with the permission of the Society of Petroleum Engineers.

Van Kruysdijk and Niko (1988) pointed out that the horizontal well's early-time pressure response is considerably lower than that of a similar stimulation by the MHF (ignoring fracture linear flow), which is attributed to the horizontal well's direct entrance to the high-conductivity fracture zone. The MHF curve crosses the horizontal well response when the MHF conductivity is sufficiently high (above the

354 I.S

II

1.0

....

I

= C o ........ : ~. = 9

x..

-ll 0 o :. --0 I

o110=10 (x!=O.STe) oi tO 9100 (X! : O.S re) a l ID 910 ( x l - 0.2S 'ire) ot ID = I 0 0 (X! : 0.2S Ye) ol 10 : I0 (XI : 0.125 Ye) ol 10 = 100 (Xl = 0.12S Ye)

O.S

0.0

X

-O.S

b.

" ' ~ ' " t ~ -

-.---.._.__..__.....~.._._____.

I

"1.0

-I.~)

. 0.0

1.0

I

I

i

2.0

3.0

4.0

....

l

s.a

9

6.0

MHY r

1

7.o

I

s.a

!

~.0

1

~0.0

1

,I.0

1

12.0

i

13.0

|

14.0

i~.0

CfD

Fig. 5-64. Production improvements in a naturally-fractured tight gas reservoir. Both the horizontal well and the massive hydraulic fracture tap into the large zone of natural fractures as a function of the massive hydraulic fracture length, t D is dimensionless time and is equal to

k(t) O~tctY-----~,where k is reservoir permeability, t is the 2 time, t3 is the porosity, ~t is the gas viscosity, ct is the total compressibility, and yf is the fractured zone half-length. MHF fractured zone interaction at 0.5 Ye; Xf is the fracture wing length and Ye is the fractured zone length. (After Van Kruysdijk and Niko, 1988, fig. 12; reprinted with the permission of the Society of Petroleum Engineers.)

break-even point as shown in Fig. 5-64), so that the extra fracture surface compensates for the finite conductivity link to the fracture zone. The break-even point for the MHF intersecting a fracture zone with respect to a horizontal well is determined by the balance between extra fracture surface and pressure drop over the fracture wing (Fig. 5-62B) intersecting the fractured zone. Figure 5-64 illustrates the effect of MHF length and conductivity. Van Kruysdijk and Niko (1988) pointed out that short fractures (with respect to the fractured zone) require very high conductivities in order to be competitive with horizontal wells. Another drawback to massive hydraulic fracturing treatments is a lack of fracture direction control. The horizontal well can be considered then as having an advantage in the development of naturally-fractured carbonate reservoirs.

Refracturing About 80% of all active wells in the U.S.A. are producing at less than their potential. Results of recent advances in computer software, operational hardware, and materials have created opportunities to successfully refracture these existing wells. Abou-Sayed (1993) pointed out that most refracturing treatments have been applied to wells where original design parameters, materials, or operational procedures were

355 below current standards. Advance techniques, such as in the pumping of proppants, high overpressure perforating, and dynamic formation breakdown and fracture initiation are successful in improving the fracture-to-well connectivity and reducing fracture cornering and tortuosity in the near-wellbore region. An excellent example of applying refracturing technology to increase reserves was the acid refracturing of the Permian Ervay Member (dolomite), (Phosphoria Formation), in the Cottonwood Creek Unit, Washakie County, Wyoming, U.S.A. The reservoir covers about 60 mi2(155 km 2) in the Big Horn Basin and is not naturally fractured (Aud et al., 1992). The Cottonwood Creek Unit is developed on an 80 - 320 acre ( 3 2 - 130 ha) spacing. Early field development concentrated on the updip part of the reservoir owing to good production response from high-permeability streaks. At that time, the operator assumed that the field was producing from natural fractures. As development continued, poorer producing wells were drilled in lower-permeability zones. These wells were treated initially with a conventional acid fracture stimulation of 5 , 0 0 0 - 30,000 gal (19 - 114 m 3) of 15 - 28% HC1 pumped at 5 - 15 bbl/min (0.8 - 2.4 m3/min). The treatment evolved into one requiring 4 0 , 0 0 0 - 60,000 gal (151 - 2 2 7 m 3) of 28% HC1 with and without nitrogen gas. Large conventional acid fracture treatments used 125,000 gal (473 m 3) of 15% HC1 pumped at injection rates as high as 25 bbl/min (4 m3/min). Gelled acid with and without CO 2 was used as an economic alternative to the large acid treatments. Sand fracture treatments were unsuccessful owing to sand production problems associated with etched regions around the wellbore resulting from remedial matrix treatments (Aud et al., 1992). Typical porosity and permeability values are 8 - 10% and 1 mD (0.000987 ~tm2), respectively. Core analysis, however, revealed porosity values of 1 5 - 20% with associated permeabilities up to 800 mD (0.789 ~tm2). Reservoir modeling indicated that vertical permeability values are low (0.001 - 0.00001 mD: 0.00000001 - 0 ~tm2). The thin, high-permeability streaks constitute a low percentage of the reservoir, and have TABLE 5-XIX Average Phosphoria (Ervay Member) reservoir-fluid and formation properties in the Cottonwood Creek Unit, Washakie County, Wyoming, U.S.A. Original reservoir pressure, psi Original Pb, psia FVF at Pb' RB/STB Solution GOR at Pb' scf/STB Oil gravity, ~ Reservoir-fluid viscosity at Pb' cP Total compressibility at Pb, Psi-I Total compressibility at 800 psi, psiq Net pay, ft Connate water saturation, % Reservoir temperature, ~ Wetting characteristic Formation embedment strength, psi Acid solubility, %

:3608 : 1126 :1.14 : 313 :27 : 4.75 : 2.25 • 10-5 : 1.78 x 10-4 : 20 - 120 :10 : 125 :Oil :70,000 : 95

Source: After Aud et al., 1992, table 1" reprinted with permission of the Society of Petroleum Engineers.

356 values above 2 mD (0.00197 ktm2). Average reservoir parameters and their values are presented in Table 5-XIX. The reservoir originally contained an undersaturated crude with an average bubblepoint pressure of 1,126 psig (7.8 MPa). Reservoir pressure measurements indicated that the pressure, Pb, is slightly below the bubblepoint in most parts of the field (Aud et al., 1992). Waterflooding operations pressurized some areas of the reservoir, but this pressure is now dropping quickly because the waterflood is no longer operational. A detailed reservoir and geologic study involving a fully implicit, 3D, multiphase reservoir simulator with an acid fracture design program, indicated that many wells in the reservoir had short infinite-conductivity fracture half-lengths of 100 - 300 ft (30 91 m) (Aud et al., 1992). Reservoir simulation results suggested that an increase in the effective fracture half-length would increase the production rate and ultimate recovery. Five wells were retreated using 60,000 gal (227 m 3) of 15% HCI plus 60,000 gal (227 m 3) of 20% HC1. No significant incremental fracture half-lengths were obtained in these wells. The reason for the poor results was attributed to poor fracturingfluid efficiency caused by high fluid leakoff. Aud et al. (1992) pointed out that the free gas phase below the bubblepoint significantly increases reservoir fluid compressibility, and is an important parameter in the refracture treatment design. The fracture fluid encountered a highly compressible gas instead of a relatively incompressible liquid in the pores, therefore, resulting in a high leakoff. Refinement of the reservoir model resulted in a new treatment design. The wells were refractured using an external oil-emulsion acid system containing 70% by volume of 28% HC1 and 30% by volume of diesel oil and gelled water used in multiple alternating stages. Crowe and Miller (1974) developed the external oil-emulsion acid system for use in high-temperature limestone reservoirs. Fracture lengths of 250 ft (76 m) or longer were necessary to achieve reasonable economic results in wells having infinite-conductivity fracture half-lengths of 1 0 0 - 300 ft ( 3 0 - 91 m). Gelled acid treatments were not used owing to model predictions showing inadequate conductivity development in low-permeability regions. Table 5-XX presents results of the 1990 refracturing program, as well as data relative to treatment size and design. The program was successful. The sixteen wells, which were acid-fractured, showed an incremental production increase of 750 BOPD. Eleven wells of the 16 wells, which were refractured, contributed about 460 BOPD (73 m3/D) to the incremental production increase. The effective fracture half-lengths obtained by refracturing ranged from 300 to 800 ft (91 - 2 4 4 m). The refracturing treatments resulted in incremental reserves of about 105,000 bbl (16,694 m 3) of oil per well for these 11 wells. Aud et al. (1992) attributed the remaining difference of 290 BOPD (46 m3/D) of the production increase to five wells that had not been previously fracture-stimulated. Four of these wells were not stimulated on initial completion owing to high water production rates from high-permeability zones. Modeling for predicting post-fracture production response and reserves on these four wells was impossible (Aud et al., 1992). The wells were modeled only for fracture design purposes to ensure that proper flow capacity was accounted for in treatment design.

TABLE 5-XX Summary of the 1990 refracturing well stimulation results, Phosphoria Formation, Cottonwood Creek Unit, Washakie County, Wyoming, U.S.A. Acid volume (gal)

Gelled Gel load water (Ibm/ volume 1000 gal) (gal)

Well

Treatment date

Job type

165

22 Feb 90

RF

185

29 Mar 90

FR

180

24Apr90

RF

184

17May90

RF

183 190

5 June 90 20 June 90

RF RF

151

27June90

RF

172 173 163

11 July 90 25 July 90 8 Aug 90

RF RF FR

182

22 Aug 90

RF

201

5 Sept 90

FR

167 161 169

20 Sept 90 3 Oct 90 20 Oct 90

RF RF FR

88,000 E 40 40 75,000E 25 75,000 E 25 67,000E 40

168

31 Oct 90

FR

67,000 E 40

Interval Permeability thickness (mD) (ft)

Fracture half-length (ft) Initial Final

Pretreatment rate (BOPD/BWPD)

Post-treatment production rates (BOPD/BWPD) 30 days 60 days 90 days

20

65,000 L

0.5

52

200

500

14/0

122/50

58/4

54/3

20

74,000 L

1.9

59

0

300

9/0

80/15

40/3

34/0

20

75,000 L

0.3

50

300

650

15/0

95/15

55/3

50/0

40 40 25 40

65,000X 42,000 L 117,000 L 95,000 L

100 1 1.2 0.3

5 35 52 60

* *

19/0

106/50

60/3

55/0

150 200

300

30/0 6/0

198/29 33/5

130/7 18/10

120/5 17/0

40

99,000 L

1

40

100

70

6/0

127/2

83/9

73/9

20 20 40 40 80,000 E 25

119,000 L 122,000 L 19,000X 90,000 L 25,000 X 85,000 L 80,000 X 30,000 L 110,000 L 120,000 L 20,000 X 76,000 L 125,000 X

1 1.5 100 1 2.5

40 40 8 22 50

300 0

# 800 *

22/0 29/8 12/15

67/28 240/48 172/119

100

450

32/0

150/19

150 1 0.5 0.8

20 30 42 60

*

28/100

120/201

# 700 *

7/0 19/0 5/30

32/18 78/12 50/85

150 1

15 45

*

67/67

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Source: After Aud et al., 1992, table 6; reprinted with the permission of the Society of Petroleum Engineers. RF = refracture treatment; E = external oil-emulsion acid; L = linear gelled water; * = high-permeability streak; FR = initial fracture treatment; C =conventional acid: 15% HCI; X = crosslinked gelled water; # = not modeled yet.

-.z

358 CARBONATE RESERVOIR CHARACTERIZATION

This section will focus on the present-day use of various mathematical strategies in determining reservoir heterogeneity. The term heterogeneity, as described previously in geological terms, is a measure of the continuity of a particular reservoir property. In the previous sections, it was shown that heterogeneity in carbonate reservoirs is the critical overall productivity parameter for characterizing these reservoirs. Examples of present-day oil-field practice to overcome heterogeneity effects were presented earlier in the chapter. A discussion of the relationship between porosity and permeability, and their heterogeneity is a central premise in the development of fluid transport models for carbonate reservoirs.

Reservoir heterogeneity models Carbonate reservoir heterogeneity is a challenge, which needs to be clearly defined not only geologically, but also from a reservoir mechanics viewpoint in order to increase well and reservoir productivity. This section acquaints the reader with some of the technical aspects by briefly discussing various approaches, with a focus on micro- to macro-scale applications to reservoir performance, used in attempting to mitigate reservoir heterogeneity problems. The production of hydrocarbon fluids from heterogeneous carbonate rocks depends on variations in reservoir and fluid properties and their spatial correlations. The concept of reservoir heterogeneity was revived in the late 1970s and early 1980s owing to advances in geoscience and engineering technology, and the political necessity to produce from complex reservoirs. There have been three (as of 1993) reservoir characterization technical conferences sponsored by The National Institute for Petroleum and Energy Research (NIPER), Bartlesville, Oklahoma, held to address reservoir heterogeneity. The first one was held in Dallas, Texas, U.S.A., in 1985 (Lake and Carroll, 1986). Haldorsen and Damsleth (1993) pointed out that despite many recent advances in reservoir characterization technology, its practice and accompanying publicity by the oil industry, there appears to be no sign of a general increase in productivity. Their statement was based on the observation that (1) there has been only a slight increase in province-average recovery factors, (2) production forecasts are still notoriously in error, and (3) the mainstream, day-to-day forecast modeling of reservoir behavior by a typical oil company has not changed appreciably since 1987. The writers do not completely agree with Haldorsen and Damsleth's statement. Our outlook is that productivity increases (or decreases) should be measured on a well-by-well basis and/or on an individual reservoir basis. Rationale for this opinion is given in the previous discussions on: (1) the classification of carbonate reservoirs based on their geological nature, and (2) the incremental recovery technology. These problems were shown to be solvable, and the solutions produced favorable returns to the operator. It should be noted that other factors have a strong influence on overall productivity of the older established reservoirs, such as: (1) present economic adversity, (2) oil price stability, (3) technology affordability and its acceptance, (4) management and staff education, (5) lack of technical and field personnel owing to company

359 downsizing, (6) sloppy practice, (7) poor planning and execution, (8) competing internal company reservoir development projects with better bottom-line returns, (9) lack of quality control, (10) large, long-term projects which are underway, and (11) the focus on higher investment returns from exploration efforts in less developed countries. These factors have a strong impact on the effectiveness of reservoir characterization "applications" to cure day-to-day production problems. The bottom-line, however, is that any approach to characterization has to be cost effective. Disregarding costs, however, it is technically possible to offer methods to the operator, whereby one can obtain precise and accurate reservoir information at various scales for reservoir modeling. These information acquisition methods could involve a 3-D seismic acquisition and processing that could provide a tomographical picture of the reservoir, interwell seismic definition of geological conditions, wellbore image analysis for fracture definition and magnitude of damage, and use of algorithms to help describe the reservoir by relating the measured petrophysical properties procured by advanced well-test and well-logging techniques. Analysis of this information involves the application of statistics and geostatistics. Such mathematical tools provide the foundation to evaluate and simulate conditions in and near the wellbore (at microscopic and mesoscopic scales) and between existing wells (at mesoscopic and macroscopic scales) (see Figs. 5-26 and 5-37) for primary recovery operations. Methods for integrating seismic data with well-log data in the construction of reservoir models, and potential pitfalls, were reviewed by Araktingi et al. (1991). A non-statistical method (Eq. 5-20) for determining interwell heterogeneity involving waterflood sweep efficiency was previously presented on page 282. Values determined in this manner are used in the design of advanced recovery operations. In present-day practice, macroscopic heterogeneity is usually addressed by using the previously discussed incremental recovery technology. Unfortunately, variability in geological aspects of carbonate reservoir heterogeneity is still a descriptive process in the minds of most geologists. Reservoir examples are frequently given in the literature using the classical descriptive approach. An example of this practice is illustrated by Mancini et al.'s (1991) study of Jurassic Smackover carbonate reservoirs in the southeastern U.S.A. This approach describes reservoir geology by portraying data variability for various geological properties as a series of generalized maps. The detail expressed in these maps depends on the amount of money spent to acquire and analyze the data and the spacing of the data both vertically and horizontally within the reservoir. In practice, it is normal not to address the vertical variations within a reservoir in great detail unless they strongly influence reservoir performance. Overall, this descriptive approach is one of defining anisotropic properties rather than dissimilar properties or heterogeneity occurring within the reservoir. Elk Basin FieM case history

The following case history describes an early example of an effort to define several megascopic (field) scale heterogeneities in a large producing carbonate reservoir. Wayhan and McCaleb (1969) described reservoir heterogeneities in the lower Mississippian Madison Limestone (Elk Basin Field), Montana, U.S.A. They instituted appropriate corrections to production operations based on the obtained geological data.

360 The methodology used to handle these heterogeneities was based on classical geological and engineering analyses practiced in the 1960s. Whether or not Wayhan and McCaleb were successful in increasing the recovery of additional oil is a matter of opinion. The Elk Basin anticline is a giant oil field which contained more than a billion barrels of oil originally in place and produced at rates in excess of 70,000 bbl/D (11,129 ma/D) from seven horizons ranging in depth from 1,000 to 6,500 ft ( 3 0 5 1981 m) (Fig. 5-65). Production from the Madison Limestone began in 1946. The early conceptual model of a homogeneous reservoir (no zonation) was influenced by the operating practice of completing the wells open-hole through the entire 920 ft (280 m) Madison section. Any low-permeable streaks were thought not to be continuous. During the first 10 years of production, the reservoir exhibited a water drive with only a slight pressure decline (Wayhan and McCaleb, 1969). Wells were drilled near the crest of the anticline so that oil would be recovered as it moved updip ahead of the natural water drive. Flank wells were added as needed to accelerate production and to ensure good areal sweep of the reservoir. The operational strategy called for progressive plug-backs to minimize lift requirements as water cuts increased in the wells. In 1957, water cuts increased, affecting the overall reservoir productivity.

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361 A review of core analyses and well logs in 1957 revealed highly complex zonation in the Madison section. Four zones (A, B, C and D) were identified, all of which were still thought to be under a natural water drive. During the period 1 9 5 8 - 1961, singlezone completions were made in the Madison reservoir. The completions showed that the A zone exhibited solution-gas-drive, whereas the other three zones continued to show water-drive performance. In 1961, water was injected into the reservoir. The A and B zones, in early 1962, began to produce water. Wayhan and McCaleb (1969) stated that only minor waterflood response was observed and the producing rate continued to decline sharply. Operational modification in 1963 rerouted the available water to the reservoir's A-zone interior injection wells. Production rate began to improve immediately; however, by early 1965 water breakthrough occurred in the interior and production started to decline. Severe curtailment of production occurred owing to wellbore scaling of the interior offset production wells. A new integrated geological and engineering program was executed in 1965 to define the problem by gathering additional reservoir data using 12 new development wells. A detailed study was made to define the degree of continuity in the reservoir on a zone-by-zone basis. Interpretation of core and well-log data showed that the Madison reservoir has a fluid flow heterogeneity (low-permeability streaks) within its four Madison producing zones. The A zone, which for the most part was deposited in a high-energy environment, exhibited a very complex vertical and areal zonation. Zone A consists of three major oolitic pay sub-intervals with limited areal continuity. These sub-intervals are interspersed with layers of lime mud creating limited fluid communication between the subzones. The B, C, and D zones are blanket limestones deposited in a low-energy environment. The B zone was divided into two pay sub-intervals, the upper one of which has two sub-members. The C zone has a productive horizon only at its base. The D zone has only one-pay horizon. Varying degrees of dolomization in the zones occurred after lithification. Subsequent erosion, karst development giving rise to collapse features and dissolution breccias, and leaching of relict limestone by meteoric water greatly altered the original Madison heterogeneity and permeability of the A zone. A major permeability discontinuity discovered by additional drilling lies on the anticlinal crest of the A zone (Fig. 5-66). Collapse and remineralization was so severe at the crest that they created a barrier subdividing the A zone into east side and west side reservoirs. Natural water drive is from west to east in the B and D zones toward a permeability restriction in the crestal area and toward a fault on the east flank of the anticline (Wayhan and McCaleb, 1969). At the anticlinal axis, remineralization by anhydrite and calcite of the lower Madison zones reduced porosity and permeability, thereby destroying potential reservoirs. The original heterogeneity and flow characteristics of Madison section were greatly altered by erosion, solution, and diagenetic overprinting. A detailed integrated study resulted in production practice changes during the 1960s. Waterflooding changes consisted of returning water into only the A zone, and stopping water injection into the B zone. Wells were drilled on the east flank of the anticline to take advantage of lower water cuts of 1 0 - 50 % in the B and D zones. This is in contrast with the original production plan of drilling wells near the crest of the structure to recover the oil moving updip ahead of the natural water drive. Flank wells

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were added as needed to accelerate production and to ensure good areal sweep efficiencies. Scaling was greatly diminished by shifting water injection to the periphery of the A zone. No definitive answer could be given by Wayhan and McCaleb on the potential magnitude of the increase in recovery that could be ascribed to the change in production practices. Their only answer is that the reservoir by 1968 has produced 5.4 million bbl of extra oil and that the current rate was 8,500 BOPD above the old trend. Numerical reservoir model studies were not performed at that time, owing to the assumption that the 'reservoir' was so complex that a model would not be beneficial (Wayhan and McCaleb, 1969).

Importance of models Weber (1982) stated that the value of having a geological/petrophysical model lies in estimating well drainage areas, completion design, and as input into the appraisal of development drilling pattems. Development of accurate reservoir performance models has been difficult owing to problems in extrapolating values for petrophysical properties between wells. The simulation of reservoir performance is now limited primarily by the petroleum industry's ability to numerically model geological uncertainty. The following discussion is a brief overview ofprobabilistic modeling presently in use by the petroleum industry. Attention is focused here on how fractal and multifractal distributions can be used to describe reservoir heterogeneity in reservoir simulation models. Application to carbonate reservoirs follows the overview discussion on fractal models. In the early development stage, knowledge of reservoir anisotropy and heterogeneity

363 is scarce. Fluid flow problems are usually solved by using volume-average approaches under conditions of minimal data. Flow characteristics in reservoirs are described by Darcy's law, which prescribes a linear relation between the pressure gradient and flow. In order to predict future reservoir performance behavior for the initial development plan, one has to use reservoir simulation models with a minimum of data. The accuracy of the model's predictions depends on the available data, which reflects the amount of investment made to procure information. It should be noted that the lack of "maximum" acquired data usually precludes accurate modeling; however, data estimation algorithms and sensitivity analyses, which evaluate various reservoir parameters relating to production, can be used in a "first pass". A statistical analysis of reservoir data is necessary to estimate the range of reservoir properties. Application of fuzzy set theory may be one way to obtain a more reliable estimation of values, inasmuch as it returns values closer to sensitivity specifications than those values fitting an exact Boolean (crisp) output. An example in the use of fuzzy set theory is given by Fang and Chen (1990). Their study on the estimation of petroleum volumes in prospect appraisals presented a comparison between the classical Monte Carlo probability approach and possibility approach (Dubois and Prade, 1988). The possibility method via fuzzy arithmetic method can handle uncertainties in the estimation of values for hydrocarbons in place when some of the data are missing, subjective, or vague. Chen and Fang (1993) pointed out that the possibility method is an appropriate alternative approach, but not a substitute for conventional methods based on probability theory. One advantage of applying either approach in numerical models is that these methods provide a low-cost, rapid procedure for preparing generalized maps and measuring risk for a "first pass" scenario. Ideally, a carbonate reservoir is envisioned to be deterministic if at every point in the reservoir true properties exist which can be measured. A resulting model description of the reservoir, however, would have to be of a statistical nature. Hewett and Behrens (1990) pointed out that incompleteness of available data and their spatial disposition, coupled with the intrinsic variability in the geology of the reservoir, would preclude deterministic mapping of properties between points. It is also more than a question of the scaling of flow processes and properties, and uncertainty resulting from missing information in reservoir descriptions. Also, the simulation has to address reservoir property continuity. These problems force one to describe the reservoir in a probabilistic manner. There are three probabilistic reservoir-property modeling techniques used in a Eulerian framework: (1) Monte Carlo simulation (Warren and Price, 1961), (2) models built up from genetic flow and lithological barrier units (Haldorsen and Lake, 1984), and (3) geostatistical interpolation using kriging (Journel and Huijbregts, 1978). There are important shortcomings in the first two techniques. The Monte Carlo approach ignores the spatial correlations in reservoir properties by assigning values to locations within the reservoir without regard to the values of the neighboring points (Hewett and Behrens, 1990). The genetic flow and lithological barrier unit model honors a stratified reservoir at each location. This technique, however, does not have variability included within the units, and the dispositions and sizes of successive units are completely independent (Hewett and Behrens, 1990). A variety of techniques are available for constructing reservoir parameter contour maps, which interpolate between data points (Crichlow, 1977; Robinson, 1982; Hohn,

364 1988). Two types of interpolation are used in geostatistics: universal kriging, and stochastic interpolation (Hewett, 1986). The choice of which one to use in modeling depends on the intended application. Kriging, which gives the minimum variance of distribution at each location, is used in reserve estimations and conditional simulations of fluid flow to predict the most likely value of concentration at a given location (Journel and Huijbregts, 1978). Stochastic interpolation intercalates between measured values using a realization of a random function having a variance structure similar to the original structure. Journel and Huijbregts (1978) stated that stochastic interpolation does not provide as good an estimate of values at any given location. It is appropriate to use stochastic interpolation in modeling the dispersion characteristics of a heterogeneous formation (Hewett, 1986). Unfortunately, the computer-generated maps give only information reflecting reservoir property variations that have a scale similar to, or larger than, the sample spacing. In most cases, well spacing controls sample spacing. Reservoir property variations at scales below the field's well spacing will be smoothed out. The variations, therefore, are not useful in the interpretation of properties at the macroscopic mapping scale. All three of the above probabilistic reservoir-modeling techniques have the same weakness attributed to deterministic interpolation schemes in that property variations at scales smaller than the data sample spacing are smoothed. Most reservoir-simulation models are based on transport equations derived for the interwell scale.

Geostatistical modeling overview. Hewett and Behrens (1990) adopted the method of geostatistics for probabilistic modeling of reservoir-property distributions. Their model addressed the issue of resolution of interwell property variations on a scale where the rock-property variations are sufficiently resolved to reproduce the effect of permeability variations on fluid-displacement fronts. They employed two geostatistical strategies to achieve the desired results in their reservoir performance model. One geostatistical strategy employed a power-law variogram model (other models are spherical, exponential, and Gaussian) defining a fractal distribution of geologic properties, whereas the other geostatistical strategy used conditional simulations to determine effective flow properties at different scales. Journel and Huijbregts (1978) defined conditional simulation as a process of constructing unsmoothed realizations of the random function that honor data at the sample point, whereas unconditional simulation is one that does not necessarily honor data values at location points. Presently, experience in using conditional simulations of process performance in heterogeneous formations is limited, and is an adopted approach used by Hewett and Behrens (1986). The first strategy used by Hewett and Behrens (1990) was to generate a description of reservoir heterogeneity by creating fractal model property distributions having any desired resolution. This allowed for the scaling of reservoir properties and addressed the problem of incomplete effective flow property information. The strategy does not consider a fault, which excludes a large-scale heterogeneity. A variogram measures similarities in the values of a variable at various distances and is a type of size measure (Yuan and Strobl, 1991). Another previously-mentioned component is connectivity, which addresses property continuity within the reservoir, and it is not well captured in the variogram. The variogram of random fractals, which is based

365 on a measure of variability, is defined by Mandelbrot and Van Ness (1968), Delhomme (1978), and Hohn (1988) as: 2r(h) = E{[Z(x + h ) - Z(x)]2},

(5-48)

where r(h) measures the mean-square variation of property as a function of the spatial separation of its sample locations; Z(x) is the value of the variable at locationx; Z(x + h) is its value at a lag distance, h, away from x; and E{ } indicates the expected or mean value of a random variable, x. The greater the variogram value, 2 r(h), the less related are the two variables. When estimating values at unsampled locations, the function v(h) is regarded as the meansquare error incurred, if the value of a sample is used from one location as the estimate for the value at a distance h away. Delhomme (1978) stated that in most cases x and h are regarded as vectors; therefore, anisotropies in the distribution can be accommodated. The above variogram is based on the behavior of fractal Brownian motion, fBm, which is a good starting point for understanding anomalous diffusion and random walks on fractals (Voss, 1988). It was pointed out by Jensen et al. (1985) that it may be necessary to include other forms for a normalized cumulative probability distribution function in order to describe distributions of permeability and other reservoir properties having skewed marginal distributions. Geological properties often exhibit correlations that can be observed over a range of scales (i.e., microscopic to megascopic). Hewett and Behrens (1990) pointed out that distributions exhibiting this nested structure can be characterized by superimposing a series of transitional variograms with different ranges and sill values. A sill value is the semi-variance value where this value essentially does not change with increasing distance. On a semi-variance vs. distance plot, the resulting curve would increase until reaching a break-point value where it then becomes essentially constant. If the sill and range for each scale increase in a geometric progression, then the form of the variogram characterizing each variation scale is said to be geometrically similar to the others. The superposition of many variograms results in a power-law variogram (Delhomme, 1978). Distributions having the form of Eq. 5-48 for their increments are said to be statistically self-similar (Manelbrot and Van Ness, 1968). Fractal distributions are characterized by a power-law semivariogram ( 89of 2v(h) of Journel and Huijbregts, 1978) model having the form:

v(h) = voh2H,

(5-49)

where Vo is a characteristic variance scale at a reference-unit lag distance; and H is known as either the Lipschitz-H61der exponent or Hurst exponent and characterizes the scaling behavior. Emanuel et al. (1989) called H an intermittency exponent, which quantifies the intermittent or "spotty" nature of the geometries of fractal distributions. Here it represents the fractal co-dimension equal to the difference between the Euclidean dimension in which the distribution is described and the fractal dimension of the distribution. The reader should be aware that there is a major drawback to the use of the Hurst exponent. The Hurst exponent is only a single scaling exponent. Most geologic analyses involve bivariant statistical conditions, which are effectively

366 examined using multiscaling statistics. The equality (Eq. 5-49) must be valid only in a statistical sense; that is, the functions r(h) and roh TM, should be realizations of the same stochastic process. Equation 5-49 implies that the variance at any scale can be determined from the variance measured at any other scale (Mandelbrot and Van Ness, 1968). As the scaling parameter H increases through the range of 0 < H < 1, the functions become smoother (Korvin, 1992). Figure 5-67 shows samples of the behavior offBm traces for different values of H and D, where D is the fractal dimension (see Eq. 5-11). When H is close to 0, the traces are roughest. As H increases in value toward unity, the persistence of correlations increases and the contribution of the smallest scales of variation (highest frequencies) decreases (Hewett, 1986). A value of H = 0.5 indicates a totally random structure. H values derived from measurements of topographic features of the earth's surface (roughness) typically fall in the range of 0.7 < H < 0.9, compared with the theoretically expected value of 0 . 5 - a Gaussian distribution (Hurst, 1957; Hewett, 1986; Emanuel et al., 1987). A class of functions known as fractional

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367 Brownian motion (fBm) is defined when H is not equal to 89and r(h) is the error function, with: H=d-D,

(5-50)

where d is the Euclidean dimension (Hewett, 1986). When r(h) is the probability distribution function of a log-normal distribution then Eq. 5-50 simply becomes: H/2 = d - D.

(5-51)

When distributions satisfy Eq. 5-48 with a non-Gaussian cumulative probability distribution, they are referred to as fractional motions (Hewett, 1986). In the case where the fractal dimension D (see Eq. 5-11) is related to H for a twodimensional Euclidean dimension, the D value is simply D = 2 - H . Voss (1988, p. 45) stated that fractals, like traditional Euclidean shapes, typically reduce their dimension by one under intersection with a plane. As an example, the intersection of a solid three-dimensional sphere with a plane is a two-dimensional circular area; an intersection of the circular area with another plane is a one-dimensional segment; and the intersection of this line with another plane is a zero-dimensional point. Unconditional simulations were used by Hewett and Behrens (1990) to simulate the continuity and regularity of distributions described by the variogram. The techniques available for constructing these realizations included the turning-bands method, lower/upper-triangular decomposition of the covariance matrix, and spectral methods. Hewett and Behrens (1990) chose the Weierstrass-Mandelbrot random function, which is based on a Fourier series that involves a geometric progression (see Voss, 1988, p. 57, for details). The Weierstrass-Mandelbrot function, which is continuous but not differentiable, is widely used to describe irregular surfaces. This method provides an analytical representation of the realization that can be used to calculate property values at arbitrary locations. The second geostatistical strategy deals with scale averaging of fluid flow properties. Transport equations were derived for the macroscopic scale in a Eulerian framework where local continuum properties can be defined. In a simulation model, where the simulation scale is larger than the interwell scale (scaled-up model), the property variations within the volume block to which flow properties must be assigned will generally require the definition of scale-effective flow properties and fluid compositions. Hewett and Behrens (1990) stated that the primary flow properties of interest are: (1) absolute permeability, (2) dispersivity, and (3) relative permeability. Hewett and Behrens (1990) stated that the primary factor influencing the definition of effective flow properties is heterogeneity in the permeability distribution. In response to a uniform pressure gradient, fluid velocities within a volume will be proportional to the local permeability. Any heterogeneity in the permeability distribution results in a nonuniform flow velocity field. Such a field can distort the shape of a displacement front during secondary and EOR operations creating by-passed oil pockets. Hewett and Behrens (1990) reviewed the effect of permeability heterogeneity on absolute permeability, dispersivity, and relative permeability.

368 The influence of heterogeneity on effective absolute permeability has been studied by petroleum engineers and groundwater hydrologists. In modeling, the terms 'effective' or 'pseudo' permeability were associated originally with finite-difference (or element) techniques used to solve the pressure equation in conventional numerical simulations. Effective has a special meaning that may not be obvious to the reader and is equivalent to the old term 'pseudo' used previously. Effective permeability is an average value of permeability of a grid block used in reservoir simulation. Those who work in reservoir modeling use the term 'pseudo' in a different context. This term is derived from pseudoization procedures used to correct for enhanced numerical dispersion (King et al., 1993, p. 245). King (1989) pointed out that it is necessary to use a suitable effective reservoir property value in numerical models, which is determined from reservoir core samples or logs. The effective value is a single value for an equivalent homogeneous grid block in a model. As an example, grid blocks are on the scale of hundreds of meters, whereas reservoir property heterogeneities occur over a wide range of scales (refer to Figs. 5-37 and 5-81). In the case of absolute permeability the size of fluctuation ranges over many orders of magnitude. King (1989) stated that this makes it difficult to assign a single effective value to absolute permeability that would give the same mean flow. Many attempts have been made to address the above stated problem of assigning an effective absolute permeability value. The analytical methods used are based on effective medium theory (EMT) or perturbation expansions. The effective permeability estimates, however, are accurate only when permeability fluctuations are small (King, 1989). In carbonate reservoirs this is rarely the case. Warren and Price's (1963) method is still taken as the petroleum industry standard. They used numerical simulations to show that the geometric mean usually gives the closest estimate to the effective permeability for a random, isotropic distribution. As King (1989) pointed out, there are many distributions for which this is not a good estimate. Dagan (1979), in numerical simulation of groundwater flow, presented an approach that placed upper and lower boundaries on effective permeability. He established the lower boundary to equal the harmonic mean, which corresponds to the effective permeability of a layered formation to flow perpendicular to the layering direction. The upper boundary equals the arithmetic mean, which corresponds to the effective permeability to flow parallel to a similarly layered formation. His approach avoided the geometric mean. Hewett and Behrens (1990) advocated the use of conditional simulations of permeability fields that honor measured data and mimic permeability variability and spatial correlations in the field of interest to derive effective permeabilities from flow simulations. The standard to which the effective permeability calculation must be compared to is the fine-scale flow simulation. From the groundwater literature, the effect of permeability heterogeneity on the dispersion of solutes in single-phase flows provides analytical procedures for deriving effective values ofdispersivity (Dagan, 1984). Araya et al. (1988) noted that when the permeability field has a finite range of correlations, the effective dispersion coefficient becomes constant when the length of the flow path is large compared with the range of correlations. Hewett (1986) and Araya et al. (1988) noted that field measurements of dispersivity derived from tracer tests show a scale dependence. These

369 results indicate that there is an influence of long-range correlations on the dispersion characteristics of heterogeneous reservoirs. The solutions of the convective-dispersion equation with an effective dispersion coefficient will be unsatisfactory for predicting dispersion effects in interwell flows. This statement is based on the observed scale effect occurring over large distances compared with typical well spacings in oil fields. Hewett and Behrens (1990) stated that more accurate predictions of dispersivity can be obtained by simulating the flow through conditional simulations of the heterogeneous permeability distribution. Several theoretical approaches have been proposed for generating pseudo (effective) relative permeabilities in layered systems, and are based on the assumption that there is a high degree of vertical communication existing in the reservoir (Coats et al., 1971). One would make the assumption that stratified flow or vertical equilibrium conditions exist. Problems arise due to the use of pseudo relative permeability values based on flow simulation through models that are more finely resolved than the scale for which effective properties are desired. The effective relative permeability values required to reproduce the observed behavior in the fine-scale simulation are backcalculated. Hewett and Behrens (1990) advocated that these values have to be validated, and described a method to do so. Reason for validation is that if a streamwise dependence for the pseudo relative permeability is indicated, then flow properties can no longer be defined locally. Flow properties depend on the simulation's boundary conditions and the position of the coarse gridblock (scaled-up model) along fluidflow paths, which violates the basic assumption of the Eulerian formulation of the transport equations. In order to be able to scale-up in the Eulerian formulation, it is necessary to use streamtube methods and front-tracking simulators. Emanuel et al. (1989) showed that streamtube scale-up of flows in conditional simulations of heterogeneous geology have been successfully used to match waterflood production history in carbonate reservoirs. The authors refer the reader to Hewett and Behrens (1991) for a complete discussion on scaling behavior of solutions to the transport equations for flow in permeable media. How is lateral and vertical property continuity exhibited in the fractal models? Connectivity of properties between wells is an important consideration in carbonate reservoir characterization. A variogram does not examine whether particular lithofacies or units with distinct permeability values are connected. As a result, stochastic simulations designed to reproduce a particular variogram usually produce cross-sectional areas having high proportion that are connected, and low proportion areas that are disconnected (Yuan and Strobl, 1991). Hewett (1986) provided an example of stochastic interpolation between neutron porosity well logs taken from three wells in an unidentified west Texas carbonate reservoir. Figure 5-68 shows the resulting synthetic pattern obtained in his study. The cross-section exhibits a variability between the wells that is quite representative of the actual lithological units. It was pointed out by Hewett (1986) that in any smooth interpolation scheme, contours beginning at one well must either connect with data at a neighboring well, or die out between wells. Other stipulations are that no new features can arise between the wells, and all of the bedding exhibited in the original three well logs are preserved in the interpolated field (Hewett, 1986). If low porosity or low permeability zones were discontinuous

370

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Fig. 5-68. Iso-porosity contours of an interwell cross-section exhibiting an interpolated porosity field. Dark areas indicate porosity values less than 0.10, whereas white areas indicate porosity values generally in the range of 0 . 1 0 - 0.20; some values are higher. (Modified after Hewett, 1986, fig. 17; courtesy of the Society of Petroleum Engineers.)

within the formation, however, then the model would not reflect their actual containment. This is analogous to having a proper description of whether or not shales exist within a reservoir (as an example of a flow barrier) as: (1) distinct and continuous shale beds; (2) discontinuous shale beds (non-continuous shale stringers); (3) shale casts; (4) randomly dispersed clay particles (shaly or clayey limestone); and (5) a combination of all these conditions. Haldorsen and Lake (1984) discussed this problem of managing flow barriers (shales) in field-scale models. Two flow barrier (or a reservoir property) types are distinguished based on whether the dimensions and spatial disposition of the barriers (properties) are known. Stochastic barriers or properties cannot be correlated between wells and appear to be scattered randomly within the reservoir. Deterministic barriers or properties are continuous between the observation points. Haldorsen and Chang (1986) addressed the generation of discontinuous shales beds having a lateral extent less than the well spacing for stochastic reservoir models. The reader needs to be aware of a recent effort to develop quantitative measures of variable connectivity for stochastic reservoir simulation studies. Yuan and Strobl (1991) proposed a unique but complex approach to measure reservoir continuity, which is essential for accurate reservoir characterization. Their approach defines reservoir continuity by quantifying the connectivity of reservoir variables, and is based on mathematical morphology and image analysis. The methodology consists of two proposed measures: the connectivity number and the connectivity indicator. The connectivity number (Serra, 1982) or Euler number (Russ, 1990) is equal to the number of disconnected objects minus the number of holes in those objects. Figure 5-24A provides an example of their concept. This measure can be used on both categorical variables and continuous variables such as permeability (Yuan and Strobl, 1991). The connectivity number, however, treats all objects with the same importance regardless of their size, making it highly sensitive to small objects and noises. The connectivity indicator is equal to the total amount of rough area divided by the total sand (matrix) area, and varies between 0 and 1. Zero indicates that all object areas are disconnected, whereas 1 indicates a high degree of connectivity. It is limited to cat-

371 egorical variables and is less affected by variation associated with small objects and noise. Yuan and Strobl (1991) tested these measures on synthetic images and on an outcrop. There are several limitations to implementing the two measures: (1) the measures rely on the availability and sedimentological study of appropriate outcrop analogues; (2) the outcrops need to be matched to nearby subsurface reservoirs producing from the same formation (facies); and (3) the requirement of complete two-dimensional data from the outcrop. Well and seismic data cannot be used directly. Generally, seismic data do not have the necessary resolution for detailed reservoir continuity studies (Yuan and Strobl, 1991). In order for the petroleum industry to have better reservoir performance prediction results, models need to address four issues: (1) flow-property scale-up, (2) incomplete property information, (3) uncertainty in the reservoir's description, and (4) connectivity. Development of a performance model that indirectly considers the difference between carbonate and sandstone reservoirs by accounting for porosity and permeability heterogeneities using fractal distributions is a new approach. Fractal-based reservoir performance model Emanuel et al. (1989) presented a reservoir performance prediction method incorporating many points of Hewett's (1986) fractal geostatistical methodology and using an approach developed by Lake et al. (1981). This developed approach consists of: (1) blending detailed geological, fluid-flow and fluid-property data; (2) creating fractal distributions of reservoir property data; (3) using generated interwell data in a finite-difference simulation to obtain a crosssection representing displacement efficiency and vertical sweep; and (4) incorporating this fractional-flow information into the areal coverage of a streamtube model to obtain fluid displacement values for the section, thereby completing calculation for the areal conformance. Their goal was to have the ability to make more accurate performance predictions for large-scale waterflood and EOR projects by detailed accounting of reservoir heterogeneity with a reduced history-matching effort at a lower overall simulation cost. A generalized logic schema of this procedure is presented in Figs. 5 - 6 9 A - D . The tasks and stepwise procedures, which are similar to Emanuel et al.'s (1989) methodology, were modified in order to provide the reader with an overview picture of the connectivity of geologic quantification, data integration, simulation of geological property distributions, the scaling of effective flow properties, and the possible extension of the procedure to infill drilling. Comments about the tasks that describe the major computational operations and decisions are necessary, inasmuch as different methodologies are coupled together (Figs. 5 - 6 9 A - D). Task 1 - Collect reservoir data. As in all reservoir analyses, one has to establish first the porosity-permeability character of the reservoir in order to analyze the data for statistical structure and to develop a heterogeneous reservoir cross-sectional model between two wells (Fig. 69A). The necessary points to be considered include: (1) using conventional methods to analyze well logs and core analyses for porosity and permeability and tying the data to depth;

372 (2) establishing empirical relationships between porosity and permeability so that missing data can be generated; (3) normalizing the data to zero mean, unit variance, and a unit interval; (4) establishing the probability density of the normalized values for the data sets; (5) calculating H values using the R/S rescaled adjusted range procedure (plot of R/ S vs. time) as applied to geophysical records is described in detail by Mandelbrot and Wallis (1968; 1969a). R/S plot, variogram, and Fourier series are spectral functions used to analyze correlations defined by bivariant statistics. The procedure, which consists of analyzing random processes and time series with the help of the behavior of R(t,s)/S(t,s), is known as 'R/S analysis'. R is the sample sequential range of a stationary time series X(t) for its lag s, and S is the sequence variance, which scales as R/S -- (as) H, where a is a constant. This test evaluates the long-run behavior of statistical series and detects the presence of long-run correlations (statistical dependence) in fractal distributions (Mandelbrot and Wallis, 1969b). Dependence implies that what happened at a previous time has an after-effect in the future. Mesa and Poveda (1993) and Muller et al. (1992) provide thorough discussions on the Hurst effect and its limitations.

Task 2 - Establish fluid properties and fluid flow paths. It is necessary to have representative fluid-property and fluid-flow data from the candidate wells (Fig. 5-69B). This can be accomplished by: (1) choosing the appropriate fluid-flow path(s) for analysis based on the well pattem; (2) selecting the wells defining the flow path; (3) checking if fluid-property and fluid-flow data is available. If not, then obtain such information from corefloods from selected well cores and PVT measurements on reservoir fluids samples. Coreflood data from noncandidate wells would be suitable, if the cores are reasonably representative of the zone; (4) determining if the well pair is separated by average field spacing; and (5) establishing geological markers fi'om well logs for the wells. These markers should be correlatable not only between the well pair, but to the majority of other wells in the reservoir. If not, then either another well pair having universal correlatable markers has to be selected, or this simulation approach possibly is not applicable to the reservoir. Task 3-Perform interwell stochastic interpolation. In order to generate an interwell cross-sectional porosity-permeability map from the data sets, it is necessary to consider the following data preparations (Fig. 5-69B): (1) the property value distributions values have to exhibit a normal (Gaussian) distribution with mean zero and unit variance. If the distributions are skewed, they are transformed to normally-distributed variables before interpolation (Emanuel et al., 1989). After interpolation the distributions are transformed back to their skewed form; (2) the interpolation program starts with porosity and permeability well-log values for each of the two wells. Porosity and permeability values are selected on a foot-byfoot basis by the program for each well in the cross section and the intermediate values are generated using the fractal interpolation scheme. This process is accom-

373

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1 Fig. 5-69A. TASK 1 flow diagram presents the activities that define the steps necessary in the collection and the analysis of data for fractal statistical structure. Initial task in a fractal geostatistical-logic schema, which can be used to calculate the effect of waterflood, miscible gas injection, and infill drilling operations on reservoir performance.

plished by calculating the initial variance using the mean-square variation of values on a foot-by-foot basis between the wells. Emanuel et al. (1989) pointed out that this measures the scale of variations at the interwell distance. It is assumed that the value of H, derived from the well logs, applies to the reservoir. The interpolation equations reduce the magnitude of the variance through recursion according to a power law determined by the value of H. Emanuel et al.'s (1989) study provides an example of the interpolation equations for multiple iterations; and (3) the end results of Task 3 are porosity and permeability cross-section maps between the selected wells.

Task 4 - Develop finite-difference cross-sectional model. A vertical cross-sectional hybrid model has to be developed, which will represent interwell flow in the reservoir (Fig. 5-69C). The approach consists of: (1) Choosing the appropriate finite-difference schemes (explicit or implicit forms), creating a grid (block, lattice, or irregular pattern) having 2 0 - 100 blocks between

374

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NEASURED DATA SKEMED

PUT -COREFLOOD RUN NFCESSARY TESTS

Fig. 5-69B (continued at top of next page).

NO

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375 t ,, USE i I11' IERPOL~ T i OII PROGRI~N TO GEl" I r R A C T A L DI S l r R I B U r I OHS

1 GENERArir ! Nr ENMLLL DA rA DI S l r R l B U r I oH',

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Fig. 5-69B (continued). TASKS 2 and 3 are shown in the flow diagram. Task 2 activities define the steps necessary to establish representative fluid property and flow data. Task 3 activities scope the stochastic interpolation procedure. Second and third tasks are part of a fractal geostatistical-logic schema, which can be used to calculate the effect of waterflood, miscible gas injection, and infill drilling operations on reservoir performance. the wells and testing the stability of the solution. Crichlow (1977) provides a good discussion on developing finite-difference models. (2) Creating a simulator model that is highly detailed in the vertical direction in order to represent measured log and/or core data as closely as possible (Emanuel et al., 1989). Simulation layers should be 1 - 2 ft ( 0 . 3 - 0.6 m) thick. The intent is to model heterogeneity near the same level of detail as that of the available data. (3) Setting the transverse (y) direction of the cross-section so it represents the shape of a stream channel. Emanuel et al. (1989) noted that this geometry is intended to model the transition from radial flow near the wellbore to more linear flow midway in the pattern. Additional discussion of finite-difference models was provided in Volume I by Dominguez et al. (1992). (4) The finite-difference model is run for the projected conditions. The results will correlate as fractional flow at the producer and average interwell saturation for each phase as a function of pore volumes injected. Task 5 - Develop Streamtube Map Model. The streamtube mapping approach can take the cross-sectional data and use it to estimate field-wide performance (Fig. 569D). The two-dimensional cross-sectional results and reservoir operating conditions are used as input to a streamtube program (or conformable mapping program) to account for pattern and areal confinement effects. Streamtube models can accurately calculate the positions of fluid banks (maintaining saturation discontinuities), thereby overcoming the effects of numerical dispersion. Emanuel et al. (1989) used a single-layer

376 I

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Fig. 5-69C. TASK 4 flow diagram presents the activities that define the steps necessary in the development of an appropriate finite-difference, cross-sectional model. Fourth task in the fractal geostatisticallogic schema, which can be used to calculate the effect of waterflood, miscible gas injection, and infill drilling operations on reservoir performance.

streamtube model, because the fractional flow generated by the cross-sectional simulation accounted for permeability distribution, layering and gravity override, and the model can accommodate large patterns. Streamtube maps, which are based on streamline networks, can be constructed according to Doyle and Wurl (1971): (1) Generate a streamline network having both the sides and axes of channels connecting to well pair(s) based on a combination of Darcy's law and the continuity equation for a homogeneous incompressible fluid where the effects of gravity can be

377 RUli MODEL EliD PROJECT

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Fig. 5-69D. TASK 5 flow diagram presents the activities that show the steps necessary in the use of a streamtube map model to forecast future reservoir performance. Final task in a fractal geostatistical-logic schema, which can be used to calculate the effect of waterflood, miscible gas injection, and infill drilling operations on reservoir performance.

378 neglected. Martin and Wegner (1979) expanded the approach to two-phase flow using the Buckley-Leverett theory to calculate the fluid displacement along streamlines. For details, Hewett and Behrens (1993) discussed the one-dimensional transport equation for multicomponent, multiphase flow in a porous medium and the applicable scaling laws in such a displacement process. Flow-diagrams for a streamline program, a shape-factor program, and Higgins-Leighton's waterflood program were presented by Doyle and Wurl (1971). The model used in Emanuel et al.'s (1989) study was more or less based on the streamtube model procedure discussed by Lake et al. (1981). (2) Map the fractional-flow solution onto each tube. The total mobility in each tube was determined by line integration as described by Martin and Wegner (1979). Emanuel et al. (1989) chose a timestep increment so that the injected volume is allocated among the streamtubes in proportion to tube mobility. The incremental pore volume injected for each tube is the injected volume divided by the tube's volume. The cumulative value of the injected pore volumes determines the fractional phases, such as oil, gas, water or solvent, comprising the employed recovery method. The gross fluid volume is equal to the incremental pore volume injected (Emanuel et al., 1989). The assumption is that the project is run on the basis of voidage balance between production and injection. (3) Check the model against known reservoir performance by adjusting the gross fluid voidage to the history value. (4) Repeat the calculation for each tube. Summation of all the contributions from the tubes results in the flow of each phase for each well at a given timestep (Emanuel et al., 1989). (5) Impose a planned injection rate to forecast future performance. Emanuel et al.'s (1989) above-described scale-up model is generally limited to: (1) waterflood or miscible gas injection, (2) injection/production voidage balance, and (3) Negligible pressure depletion. Hewett and Behrens (1991) pointed out that streamtube methods are not suitable for modeling primary depletion, because they are based on incompressible flow. A suggested addition of infill drilling to the overall schema (Figs. 5-69A- D) was made to show how fractal-generated interwell distributions can be used in forecasting incremental recovery of by-passed oil during primary production operations. Hewett and Behrens (1993) reviewed some of the inherent limitations to Emanuel et al.'s (1989) model. They discussed the effects of length dependency of the dispersion coefficients derived from simulations of miscible displacements. Such a length dependence precludes the definition of an effective dispersion coefficient or the use of numerical dispersion to represent the effects of permeability heterogeneity on miscible displacements. Problems arise in the application of effective relative permeabilities that change along the flow path when scaled up. Hewett and Behrens (1993) pointed out that the problems are caused by the streamwise dependence of the effective relative permeabilities, some of which are initial conditions preceding the displacement, nature of the displacement (water displacing oil, etc.), gridblock size, the streamwise position of the block to which the effective relative permeability value is assigned, making their assignment to fixed grids difficult. As shown by the flow-diagrams (Figs. 5-69A- D), complications are introduced into the model by the requirement that there be some knowledge of the flow paths before the problem can be analyzed. Numerical dispersion effects have to be kept negligible by keeping the number of cells large enough so that all the areal paths must pass

379 through the same number of cells (Hewett and Behrens, 1993). Still, such models are better than older ones and show the direction of future simulations.

Applications of Fractal Models to Carbonate Reservoirs There have been several published accounts on the application of fractal models in predicting waterflooding and enhanced oil recoveries in carbonate rocks (Emanuel et al., 1989; Beier and Hardy, 1991). Emanuel et al.' s (1989) results will be discussed as case histories. The validity of the above-discussed simulation method was tested by modeling a total of twelve reservoirs having waterflood and miscible flood projects with measured performance. Four field cases, having comparable results with the other reservoirs, were selected by Emanuel et al. (1989) for presentation. Reservoir fluid properties and model configurations are given for the four cases in Table 5-XXI. Of the four presented cases, only Quarantine Bay is a sandstone reservoir and is included in Table 5-XXI for comparison. Reef reservoir: CO 2pilot flood case history. An 800-acre (323-ha) CO 2 pilot flood in a high-water-cut carbonate reservoir, which is part of a Permian limestone reef complex, was used in Emanuel et al.'s (1989) validation study. Location of the limestone reef reservoir was not given, but it is probably either in west Texas or eastern New Mexico, U.S.A. The pilot flood involved between 40 and 50 wells. Figure 5-70 shows comparisons between reported and predicted oil and CO 2 production rates. The match between the predicted and actual oil production rate is reasonable. No adjustment was made to the geological data to match history. Emanuel et al. (1989) stated that discrepancy in the early oil production rates is partly a result of TABLE 5-XXI Reservoir properties and model dimensions for four field cases studied by Emanuel et al. (1989). Three of the fields are carbonate reservoirs, whereas Quarantine Bay is a sandstone reservoir Data for reservoir models

Grid dimensions nx n Y n_. Pressure, psi Temperature, ~ API gravity, ~ Oil FVF Solution GOR, scf/bbl Oil viscosity, cP k/k H

Model thickness (z direction), ft Model lengths (x direction), ft

Quarantine Bay

Carbonate CO 2 pilot

Waterflood test

Little Knife

100 1 40 3450 183 33 1.22 435 1.15 1.0 40 800

43 1 84 2500 130 40 1.5 1000 0.5 0.65 168 1800

43 1 84 500 85 32 1.14 320 2.7 1.0 84 1011

129 1 30 3500 245 33 1.68 1093 0.27 0.01 - 1.0 30 258

S o u r c e : After Emanuel et al., 1989, table 1" reprinted with the permission of the Society of Petroleum

Engineers.

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Fig. 5-70. A comparison between the reported and model-predicted oil and carbon dioxide production rates for a pilot flood in a carbonate reservoir. (After Emanuel et al., 1989, fig. 10; reprinted with the permission of the Society of Petroleum Engineers.) treating all wells used in the model as coming on at the project's start and that they deliver fluid at a constant average rate. Inherent to all production operations, there are going to be some of the wells shut-in from time to time and fluctuations in the fluid production rates. The average gross fluid injection/production in total reservoir barrels per day for each well, the injection volume of CO 2, and the injection water comprised the historical data used in the model. The streamtube model for the project is given in Fig. 5-71. Model and reservoir fluid data are presented in Table 5-XXI.

Dolomite reservoir: waterflood case history. A mature waterflood in a large carbonate reservoir composed of a thick sequence of dolomites and siltstones of Permian age was evaluated using the fractal model. The probable location of this reservoir is west Texas. A selected section of the reservoir was chosen consisting of six inverted nine-spots covering about 250 acres (101 ha). Emanuel et al. (1989) used an 86 x 43-cell cross-sectional model to represent the interwell geology. The model consisted of an injector and producer spaced 1,000 ft (305 m) apart. Porosity and permeability values were interpolated from core data measured at one-foot intervals through the reservoir. Cell dimensions were 2 x 23.25 ft (0.6 x 7 m), with the y dimension shaped to conform to a streamtube (Emanuel et al., 1989). Figure 5-72 shows the total project response of cumulative oil with time and water cut. The cross-sectional simulation used average water injection rates over a 20-year period. Predicted and field data match closely without any adjustment of geological data (Emanuel et al., 1989).

381 Producing Well Injection Well - - T u b e C e n t e r L.in T u b e Borders --

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Little Knife field: CO: (WAG) minitest case history Emanuel et al. (1989) undertook this study to test the ability of the fractal distribution to predict a detailed measurement of the vertical saturation distribution. The test interval was in the Little Knife Field, located near the central part of the Williston Basin in Billings, Dunn and McKenzie counties, North Dakota, U.S.A. Production is from the Mississippian Mission Canyon Formation and is the middle member of the Madison Group (Desch et al., 1984). The formation: (1) is about 465 ft (142 m) thick, (2) the top of the formation is at an average depth of 9650 ft (2,941 m), (3) has porosity ranging from 8.5 to 27% and averaging 14% in the dolomitic zones,

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Fig. 5-72. A comparison between the reported field data and predicted values of water cut (%) and cumulative oil production rate for a mature waterflood in a dolomite reservoir. (After Emanuel et al., 1989, fig. 12; reprinted with the permission of the Society of Petroleum Engineers.)

383 (4) has permeability ranging from 1.0 to about 167 mD (0.000987- 0.165 ~tm2), and (5) has been subdivided into six informal zones defining a shallowing upward carbonate to anhydrite sequence. The zones are from top down: A - anhydrite, B - dolomitized packstone/wackestone, C - dolomitized wackestone, D - dolomitized wackestone, E dolomitized wackestone, and F - limestone (Lindsay and Kendall, 1985). Zones B, C, and D compose the reservoir. The original reservoir was undersaturated and had no free-gas-cap drive. Its drive mechanism is solution gas-drive with a limited edgewater drive (Desch et al., 1984). The reservoir has not been extensively waterflooded. The CO 2 non-producing minitest involved four wells drilled in an inverted fourspot configuration covering 5 acres (2 ha) with a radius of 250 ft (76 m) (Fig. 5-73), plus another well (ZAB OBS #4) drilled for pressure cores (Desch et al., 1984). The cores were used to measure oil saturation values, which in turn, were compared to calculated well-log saturation values. The central well (ZAB INJ #1) served as the injection well and remaining four wells served as non-producing observation wells. ZAB. ORS. o l

ZAB. INJ. o I

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ZAB. OBS. ,e 3

Fig. 5-73. A fence diagram of zones C and D of the Mission Canyon Formation (Madison Group) through the WAG (water alternating with gas) minitest wells located in the Little Knife Field, North Dakota, U.S.A. (After Desch et al., 1984, fig. 5; reprinted with the permission of the Society of Petroleum Engineers.)

384 All observation wells were in good fluid communication with the injection well. The test consisted of a water-alternating-gas (WAG) type injection sequence with five alternating slugs of formation water and CO 2 into a 31 ft (9.4 m)-thick interval composed of lower basal C beds and upper D beds. Emanuel et al. (1989) revealed that the interval is characterized by persistent high permeability values of about 1 Darcy near its center, and diminishing to near zero at interval top and bottom. Desch et al. (1984) reported that the minitest was designed to provide the following information: (1) reduction in oil saturation due to water injection, (2) reduction in waterflood residual oil saturation due to alternate WAG, (3) extent of gravity segregation, (4) effect of stratification and crossflow, and (5) influence of reservoir heterogeneity. A numerical, three-dimensional, three-phase multicomponent compositional simulation provided a satisfactory history match of the pressures, saturations, and fluid compositions observed throughout the test. Vertical sweep by CO 2 was incomplete owing to stratification and the possible occurrence of viscous fingers; however, it was about 52%. The minitest's pattern sweep efficiency for CO 2 approached 52% of the original oil-in-place at the start of the project as compared to 37% for the waterflood (Desch et al., 1984). Emanuel et al.'s (1989) model consisted of a cross-section 250 ft (76 m) in length and 30 ft (9 m) in gross thickness. The cross-section distance is the same as the distance between the injection well and the observation well ZAB OBS No. 2 (Fig. 573). An H value of 0.65 was used in the simulation; however, cross-sectional permeability maps were generated for H values between 0.65 and 0.85. Emanuel et al. (1989) stated that these are typical values for reservoirs, which they have studied to date. The fractal permeability distribution for this zone is shown in Fig. 5-74. The predicted saturation minimum is about 3 ft (1 m) higher in the cross-section than that observed from the well logs. Vertical permeability values are much lower than the horizontal ones. Measured core permeability showed a range of kh/k ratio from 1" 1 to 100:1 (Emanuel et al., 1989). The oil saturation profiles for ZAB OBS well No. 2 are matched with the fractal model's predicted profile (Fig. 5-75). The conclusion to this exercise was that the fractal model can represent the general trend of fluid movement; however, an exact match lies beyond the certainty of the available data in most instances (Emanuel et al., 1989).

Reservoir modelingprognosis As demonstrated, fractal interpolation methods using well-log and core data from carbonate reservoirs yield a new and effective means for handling reservoir heterogeneity in simulation studies. This technique has carried heterogeneity descriptions just beyond the verbal, qualitative stage of analysis. New modifications and approaches, which are appearing frequently in the literature suggest, however, that future quantitative refinement is possible. Araktingi et al. (1993) described a menu-driven workstation application program, GEOLITH, designed to analyze reservoir data and construct reservoir simulation models with a geostatistical approach. Numerical input from well logs, core analyses, and seismic data are used to construct realistic quantitative geological reservoir models that calculate the spatial distribution of reservoir flow properties. The GEOLITH program addresses Tasks 1 through 4 (Fig. 5-69A to C).

HORIZONTAL I-1"-3 Above 600 mD

l

~

Below I.OmD

PERMEABILITY

MAP

3O

I,,1_25

(n'zo (/)15 LI.I Zlo

"1- ,3 0 I--

?_C

40

60

80

INJECTOR-

I O0

12 0

PRODUCER

i 40

160

180

200

220

240

DISTANCE, FT

Fig. 5-74. Cross-sectional map of horizontal permeability between the injection well and observation well No. 2 in the Little Knife Field, North Dakota, U.S.A. (After Emanuel et al., 1989, fig. 13; reprinted with the permission of the Society of Petroleum Engineers.)

OO

386 9845

S a t u r a t e d 011 Base Case 9850

. _ _ _ . . . S a t u r a t e d 011 Observed ......

Simulation

Top of Permeable Zone 9855

"

~

0

/ o

./..I. //"...

9 e

,(.

/./.9860

e

9

9

9865

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o\~

9870 Bottom

of

~'~~

Permeable Zone 9875 0

I .2

J .4

I .6

I .8

I

I

Oil S a t u r a t l o n Fig. 5-75. A comparison between simulated and observed oil saturation values in observation well No. 2, Little Knife Field, North Dakota, U.S.A. (After Emanuel et al., 1989, fig. 14; reprinted with the permission of the Society of Petroleum Engineers.)

387 Beier and Hardy (1991) made a comparison between fractional Gaussian noise fractional Brownian motion (fBm) in the generation of interwell distributions of reservoir properties as determined from well logs. As was previously discussed, Hewett (1986) reasoned that the fractal structure found in porosity well logs is fGn. Hewett (1986), however, postulated that the horizontal properties have a different spectral distribution, which is described by fBm. Well spacing is normally too large to determine the statistical structure in the horizontal distance. Hardy (1991) proposed an unique solution to this problem by analyzing the horizontal structure of sedimentary layers using distributions of dark and light regions from photographs of cores and outcrops. He found that the horizontal traces could be characterized as fGn. A comparison between the fGn and fBm methods was made using a carbonate reservoir located in southwestern New Mexico, U.S.A. This unnamed reservoir was undergoing a mature waterflood in the Permian Grayburg and San Andres dolomitic pay zones. Appropriate cross-sections using the field spacing of 20 acres (8 ha) were generated for both fGn and fBm. Performance data were calculated using a hybrid finite difference-streamtube model. Results showed that both methods matched field water cut data. The initial water saturation was the only property adjusted to obtain the match, and was made owing to initial water production from transition zones. The study revealed that the fGn distributions have lower effective permeabilities (linear flow) than thefBm distributions (Beier and Hardy, 1991). The fractals infGn are also known by the term 'fat' fractals. There were, however, only slight differences between the resulting cumulative oil vs. cumulative injection curves of the two methods. They conjectured that as the well spacing increases the simple linear interpolation and fBm will become poorer representations for reservoir heterogeneity. One interesting approach involving streamlines is conformable mapping (complex variables), which can be applied to the analysis of compressible fluids and transient behavior. A region of the reservoir or a region(s) around a well or wells can be mapped onto a conformable rectangle. The appropriate numerical analyses are then performed and transformed back to the region's original configuration. The application of conformable mapping principles to streamlines defining transient flow was discussed by Hurst (1981, 1982). Hewett and Behrens (1993) suggested that any difficulties associated with the above practical application of effective flow properties in Emanuel et al.'s (1989) model were due to their definition in an Eulerian framework. In such a framework, properties are distributed in space without regard to fluid flow paths or travel distances of fluid fronts. A Lagrangian framework, however, permits flow fronts to carry the appropriate flow properties with them, and the motion of displacing fronts is modeled explicitly. The integrated total mobility and phase fractional-flow distributions are scaled and mapped directly onto areal streamlines. The solution preserves the streamwise dependence observed in the cross-section simulation, and no new errors enter into the simulation owing to the definition of a grid. It was emphasized by Hewett and Behrens (1993) that the areal flow paths are determined by solving the streamlines corresponding to a unit mobility ratio displacement with the well rates and areal permeability thickness distribution of the reservoir. As with all new approaches there is a new set of restrictions.

(fGn) and

388

It was shown in this section that permeability values for macroscopic simulation modeling are either obtained by simple arithmetic, geometric or harmonic averages over the microscopic values, or by using advanced techniques such as perturbation expansions. None of these are valid when the distribution of local permeabilities is very wide, or when the distribution contains strong correlations. As mentioned above by Hewett and Behrens (1993), the effects of spatial anisotropies on permeability have not been addressed in detail. Another way to account for permeability values assigned to grid blocks was proposed by Aharony et al. (1991). Their approach involved a simple renormalization group scheme (method), which they termed FRACTAM. The term stands for fast renormalization (scale-up) algorithm for correlated transport in anisotropic media. The algorithm is based on real space renormalization group approach first used for the percolation bond probability (King, 1989; Aharony et al., 1991). Korvin (1992, p. 21) provides an excellent discussion on percolation theory. The idea is taken from statistical physics and is used to described the build-up of clusters to form an infinite cluster. In this section we refer to the build-up (percolate the lattice) being the construction of a connected porous network. Percolation threshold is defined (in the case of a porous network) as the point where a critical porosity and pore interconnectedness exist and fluids can flow through the pores. Below the threshold the pore system is 1

A

4 Ib

~_

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

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5

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v ~

.

.

.

9 9

. . . . . . . . . . . . 9

........ ,

9

o ,

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.

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9

.......

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................

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Fig. 5-76. FRACTAM scheme showing how the upper left lattice is renormalized into the upper right one. Bonds 1,2, 3, 4 and 5, as shown below the lattice, are equivalent to the triangular graph and are used to determine the permeability value of the renormalized bond A. The permeability value of bond B is found similarly, from the original permeabilities of bonds 2, 3, 6, 7, and 8. (After Aharony et al., 1991, fig. 2; courtesy of Elsevier Science Publishers B.V.)

389 ineffective. Practically speaking, it is the point at which a rock is either permeable or essentially impermeable. A random resistor network can be used to describe the scaling-up of permeabilities as shown in Fig. 5-76. Here the permeability of bond A is determined by those of bonds 1, 2, 3, 4, and 5 by employing the Wheatstone bridge analogy. The permeability of bond B is found similarly, from the original permeabilities of bonds 2, 3, 6, 7, and 8. Aharony et al. (1991) then iterated FRACTAM for each of the specific squares until they were left with two effective permeability "tubes", one in the x- and one in the y-directions. Comparisons were made with "true" permeability values obtained from digitized core sample images and with generated fractal forgeries of core images. The authors found that FRACTAM was accurate to within less than 5% in all cases. Thorough background discussions on macro- and micro-scaled network models are given by Moore (1952), Fatt (1956a; 1956b; 1956c), and Rose (1957). Real space renormalization application will be discussed near the end of this section. The above deliberations reinforce the premise that oil and gas recovery applications rely on the functional relationship between the volume-average parameters described by Darcy's law and the microscopic processes occurring at the pore scale. Discussion will now focus with some detail on the numerical relations between porosity, permeability, and electrical conductivity. It is these transforms that control the input of permeability values into the macroscopic scale simulation models of carbonate reservoirs.

Microscopic heterogeneity: permeability- conductivity- porosity relationships Obtaining information on fluid flow properties inside carbonate oil reservoirs is complicated by high variability of permeability values. As pointed out previously in this chapter, one can observe intermittent variations of the absolute permeability over several orders of magnitude at a given scale, such as the core length scale. The permeability variations occur over a wide range of scales from microscopic to megascopic. Saucier (1992) emphasized that forecasting difficulties arise from the fact that the three-dimensional structure of the permeability field remains poorly defined due to the lack of information that comes from rather sparsely drilled wells. Geology and seismic data provide only poor guidelines about heterogeneity size, stratification, and fine-scaled structures. Theoretical, statistical, and empirical correlations among porosity, permeability, surface area, pore size, irreducible water saturation, and conductivity (resistivity) were discussed by Chilingarian et al. (1992c: Volume I, Chapter 7). Mathematical relationships were described based on capillary tube models and include the following factors: pore shape, tortuosity, electrical resistivity of rocks and fluids, sonic speed, and scaling. It should be remembered, however, that as any thin-section of a sedimentary rock would show, the pore space is connected in a complicated and random manner by pore throats.

Scaling exponents Unfortunately, permeability and porosity values do not closely track each other when rock samples are taken from carbonate formations having different geological histories. This is demonstrated by different samples with the same porosity values

390 exhibiting a wide range in permeability and conductivity values, especially due to fracturing. Chilingar (1964) demonstrated a reasonable correlation between porosity and permeability of cores, by considering the effect of irreducible fluid saturations, using the concept of effective porosity, ~be, which has a different physical meaning in contrast to the modeling effective properties just discussed. Effective porosity was defined by Chilingar (1964) as the fluid-saturated pore volume minus irreducible fluidsaturated volume. By taking into account specific surface area, which incorporates the influence of fractures, and irreducible fluid saturation, Chilingarian et al. (1992c) developed an excellent correlation between permeability and porosity. The differentiation of fluid flow properties inside carbonate reservoirs is complicated by the high variability of the permeability field. Two empirical equations are used generally by petroleum engineers and geologists to define the relationship between permeability and conductivity using porosity values. These empirical relationships are justified by the non-intersecting tube models of the pore space. The scaling law for permeability, k, and porosity, ~b, is: k =

(s-52)

where m is the slope of the line from a log-log plot of permeability vs. porosity. Theoretically, Eq. 5-52 follows from different capillary tube models as described by Chilingarian et al. (1992c), and cellular automata involving lattice gas hydrodynamic simulation models described by Chen et al. (1991). The cellular automata approach can be described, in a physics context, as a class of mathematical systems characterized by discreteness in space, time and state values, determinism, and local interaction. The empirical equation (Archie's formula) relating electrical rock conductivity, G, and porosity is: (5-53)

G = aGwd~ m" ,

where a is an empirical parameter that varies with the lithology of the formation. It is generally assumed that a is unity. The conductivity of the pore water is Gw, and m^ is an exponent, which is defined by log-log plots of rock conductivity vs. porosity. Wong et al. (1984) mentioned that the power-law dependence in Eq. 5-53 resembles the behavior in the usual percolation problem, except that it suggests a conduction threshold at ~b= 0. According to Wong et al. (1984), the exponents m and mn are related as follows: m = mn(m n +

1),

(5-54)

for one-dimension, and m = 2m ^,

(5-55)

for higher dimensions. The relations used by well-log analysts to quantitatively obtain permeability values from porosity take two forms. Timur (1973) proposed the following equation, which is a variation of the Schlumberger empirical formula:

391

k=0.136

IO 44~1 kSwi~r2

,

(5-56)

where S i r r is the irreducible water saturation. The weakness of Eq. 5-56 is that k is dependent on 4.4th power of porosity and the second power of the irreducible water saturation. The determination of ~band S i r r values from well logs will most certainly be in error by a small amount. These errors will be magnified by being raised to the second and 4.4th powers, and can become large depending on the size of the error up to one order of magnitude. Also, Eq. 5-56 suggests that the pore space is connected at any finite porosity. Wyllie and Rose's (1950) empirical equation was derived from a plot of their "rock textural" function cb/k ~ and irreducible water saturation, S~rr"

(5-57) wirr

where c is a constant that must have the dimensions of a length, and c A is a dimensionless constant. For a clean sand c A = 0. This equation, however, has no theoretical basis. In addition, there is a wide scatter of data points in their abovementioned plot of ~ / k ~ vs. S~rr (Wyllie and Rose, 1950; see fig. 7, p. 115 and eq. 18, p. 116). An empirical equation was developed by Chilingar et al. (1963) relating surface area per unit of pore volume, S , cm2/cm3; porosity, ~b, fractional; permeability, k, mD; and formation resistivity factoPr, F (- Ro/R w, where R ~ is the electrical resistivity of formation 100% saturated with formation water andR wis the formation water resistivity): S = 2.11 • 105/(F22~"2k) ~ . P

(5-58)

This utilitarian equation deserves attention, because the formation resistivity factor embodies the effects of grain size, grain shape, grain size distribution, and grain packing. Fractal relations between internal surface area, porosity, and permeability are discussed in the section on multifractal analysis of porous media. Using all these equations poses a problem with the spatial distributions of porosity and permeability. Very little is known about the macroscopic permeability distributions in reservoirs. As shown by the previously discussed fractal simulation models, microscopic permeability distributions have to be scaled-up. In non-fractal reservoir performance models, "history matching" is used to attempt to correct the wrong assumptions. McCauley (1992) stated that geologists sometimes assume that the distribution of permeability transverse to direction of average fluid flow within the layer has a zero correlation length. The distribution of permeabilities parallel to this average flow direction has an infinite correlation length. The assumption of a log-normal distribution is in conflict with the assumption of an infinite correlation length (McCauley, 1992). The end results of simulation efforts are unrealistic predictions for the long-range performance of a carbonate reservoir.

392 Several investigators (King, 1989; Aharony et al., 1991; McCauley, 1992) pointed out that models of fluid flow through porous rocks, both on the microscale and macroscale, typically are equivalent to resistor networks. The scaling laws expressed by Eqs. 5-52 and 5-53, however, are in conflict with measured data for permeability and electrical conductivity. Comprehending this conflict will help us to delineate the geometry of the pore-space in carbonate reservoirs. At best, only a cursory review of this very complex problem can be given in this book. The reader will be exposed to various proposed mathematical approaches that accommodate pore-system heterogeneity. Starting with McCauley's (1992) approach using two simple models, one fractal-no disorder (Sierpinski carpet model) and the other nonfractal-disordered (bond-shrinkage model) are discussed here. It will be shown that these models follow

:,

i

t

X

t.

_,

I

ry Fig. 5-77. Parallel tube model constructed from Sierpinski carpets with b = 3 and L = 1. The area is subdivided into four squares; each square is divided into b 2 subsquares, and L 2 of these subsquares are removed in the center of the initial squares. The reader is referred to Eqs. 5-11 and 5- 12. The lattice shown is at the second construction stage (see Fig. 5-22). (After Adler, 1986, fig. 1; reprinted with the permission of the American Institute of Physics.)

393 from a more general model. Both models do not include the idea of pore-space connectivity and, therefore, they do not explain on their own the difference between measured conductivity and permeability data. The general fractal--disordered (composite) model developed by McCauley (1992) includes connectivity, and qualitatively explains the experimentally known non-universal scaling exponents for permeability and conductivity.

Sierpinski carpet (parallel tubes) model. Adler's (1986) three-dimensional, fractal transverse pore-space model is based upon the geometry of the regular Sierpinski carpet constructed from parallel square cylinders (Figs. 5-77 and 5-22). In his analysis, McCauley (1992) compared a tube network model (parallel resistor network) with Adler's Sierpinski carpet model to show that the conductivity exponent m^ is completely wrong as predicted by both approaches. Parallel tube models, however, can be made to fit known permeability measurements. The tube model can be represented by an octal tree (Adler's tube model and tree models are approximately the same), where the parallel resistors are equivalent to the parallel tubes (Fig. 5-78) (McCauley, 1992). The tube equation for the effective permeability, k~, is: (5-59)

kff ~ 2nL4n '

where n is the number of generations on the tree (there are 2" branches in generation n); and L is the length of the side of a square tube so that the electrical conductivity, G 12, and the local permeability k z L 4. The volume flow rate through a pore is defined

(a) (b)

Fig. 5-78. Resistor network models. ( A ) - Binary tree model exhibited for n = 3 generations. The third generation represents the smallest pore sizes. ( B ) - Octal tree model having 2" resistors in parallel equivalent to 2" tubes in parallel. The tree model of-A- reduces approximately to this case when the smallest pores (generation with the largest n) have lengths that are very large compared with those of the pores in the first n - 1 generations. (Modified after McCauley, 1992, figs. 3b and 5; courtesy of Elsevier Science Publishers B.V.)

394 as the local permeability times the local pressure gradient; therefore, k is analogous to G. Both obey the same laws of combination for the calculation of effective permeability (McCauley, 1992). The laws are: G ~ = G l + G2

(5-60)

for two tubes in series and, G ff= G I G 2 / ( G 1 +

G2)

(5-61)

for two tubes in parallel. If the model is built upon the assumption that the length of each tube segment is roughly the same for all tubes on the tree, then the electrical conductance for the tube model for large n is: Gelf ~ 2"L.2,

(5-62)

For a large n, the last generation of tubes dominate, which are the smallest pores and the same is true of the effective permeability given by Eq. 5-59. McCauley (1992) showed that the conductivity exponent, m 6 is" mA=(2-Do)/D

o,

(5-63)

where D o is the fractal dimension and the permeability exponent, m, is" m = (4 - D o ) / D ~ ,

(5-64)

where D o < 2 for both equations. For small sandstone samples, it is known that m ^ 3/2 ~ 1.5 (from the iterated dilute limit model of Sen et al., 1981) and m ~ 15/2 ~ 7.5 as an average, whereas for carbonates m A values range from 1.6 to as high as 2.8 (de Witte, 1972; Wong et al., 1984). McCauley (1992) suggested that for any model to be reasonably correct, the orders of magnitude of these numbers should at least be reproduced using Eqs. 5-63 and 5-64. As one can see, these numbers cannot be reproduced by the tree model. Adler's (1986) model gives the resulting conductivity exponent, m A = 1, inasmuch as G ~ = ~, and the permeability exponent, m, is: m = (4 - Do)/(2 - Do),

(5-65)

which can reproduce m ~ 15/2 ~ 7.5 for sandstones; however, it is impossible to reproduce the required conductivity exponent m A values in the range of 1.5 - 2.8 for sandstones and carbonates. McCauley (1992) observed that Adler did not compute the permeability for successive stages of construction of a Sierpinski carpet. Adler computed permeability for 23~ separate tubes in parallel with each other rather than 2 ~, because the Sierpinski carpet is organized onto an octal tree. The effective permeability, when an octal tree is taken, becomes:

395 kff ~ 23nL4. ,

(5-66)

and the pore-space area is equal to: ~b = Geff= 23"L 2. ,

(5-67)

which is the pore-space area of the 23n smallest pores connected in parallel, analogous to Fig. 5-78. The above suffer from the fatal defect that ~b= Geff; therefore, m ^ = 1. This conclusion is in strong disagreement with experimental results (McCauley, 1992). It should be noted that in the tree and Adler's models, only the cross-sectional area of the pore space is distributed fractally. McCauley (1992) has argued successfully that the conductivity exponent m 6 is completely wrong, as is predicted by both the tube and the Sierpinski carpet models. Models portraying tubes that are all merely mutually parallel did not remedy this problem. Bond-shrinkage model. Wong et al.'s (1984) nonfractal model focused on the variation of pore space with porosity. It describes how pore-size distribution can influence the conductivity and permeability of brine-saturated rocks. The electrical conductivity is simulated by a random resistance network with a zero percolation threshold, which occurs at ~b= 0, and where all the resistors are in series. The rock model consists of a single, long pipe that is made by combining many tubes having different diameters (Fig. 5-79) (McCauley, 1992). Each tube segment has an area L 2, in series, and k ~ L 4. Porosity is varied by a random bond-shrinkage mechanism. Wong et al. (1984) used a binomial distribution of the different elements connected in series with each other in a one-dimensional model. To calculate porosity, the probability, p, for any particular tube to shrink n times is given by the binomial distribution"

= [1 + p ( L 2 - 1)] u ,

(5-68)

where <~> is the average pore-space area over the network, and N is the different possible diameters for a section of pipe, each with the same length L i. McCauley (1992) showed that the electrical conductivity scaling exponent is: m^ = a 2 > 1 ,

(5-69)

forp ~ 1, and Eq. 5-69 yields m^--+ 1 asp ~ 1. Derivation of Eq. 5-69 is based on the fact that the inverse conductivity is additive for resistors connected in series. McCauley (1992) pointed out that this bond-shrinkage model was originally introduced from the qualitative standpoint of percolation theory to model the zero-percolation threshold. The probability that a section of tube is shrunken n times by the factor L = 1/a (L m = a -m) from unit radius to form a section with radius L m is pm, and (1 __p)N-m is the probability to find a segment of pipe of unit radius as described by the bond shrinkage model (McCauley, 1992). The bond shrinkage model was originally introduced by Wong et al. (1984) to model the zero-percolation threshold. Hence, with P(m ^) = pm^(1 --p)N-m^N! / m ^ ! ( N - m6)! resulted in Eq. 5-68.

396

L

Fig. 5-79. Disordered, nonfractal, one-dimensional model based upon tubes of different cross-sectional area in series. (After McCauley, 1992, fig. 11" courtesy of Elsevier Science Publishers B.V.) As indicated the shrinking procedure can be repeated indefinitely with the same L to reduce the network conductance and permeability, and the total volume of the tubes. The effective permeability for this binomial distribution is equal to" -1

kfr = [1 + p(L -4 - 1)]N,

(5-70)

and m--

ln[1 + p ( L -~- 1)]

(5-71)

ln[1 + p ( L ~ - 1)] Whenever, p ~ 1, m = m^(m ^ + 1) > 2m ^, whereas m ~ 2, ifp --~ 1, which corresponds to a long pipe with constant diameter in Fig. 5-79 (McCauley, 1992). An a, o r p and a, can be chosen to fit m ^ z 3/2, but it is then impossible to obtain m ~ 15/2 as is suggested for sandstone. The predicted scaling exponent for the effective permeability is too small, which means that the fluid flows too easily (a too high permeability) through the pore-space of the bond-shrinkage rock model (McCauley, 1992).

397

.-,,...%,\\,~

,'N\\\\" ~. \ \ \ \ \ \ \

~ \\\" \

Fig. 5-80. Schematic ofMcCauley's (1992) combined model that is fractal and disordered. The model is a generalization of the model shown in Fig. 5-79 to include complete binary connectivity. The generalization to models with complete trees with order t = 3,4,5 . . . . is obvious. This new model reduces to the model presented in Fig. 5-78B where t = 2, whenever p approaches unity, but also reduces to the disordered, nonfractal one-dimensional model for the special case where t = 1. (After McCauley, 1992, fig. 12; courtesy of Elsevier Science Publishers B.V.)

Composite model. McCauley (1992) proposed that a rock model can be constructed by combining Wong et al.'s (1984) and Adler's (1986) models into a composite model having equations based on a single-scale fractal. This model would then be extended by McCauley (1992) to a general model based on multiscale fractal. The composite model corresponds to a simple parallel/series network of resistors where there is variation in both porosity and the number of pores from one thin-section to another (Fig. 5-80). The "thin-section" concept (McCauley used the term toy rock) is derived by taking multiple thin slices of a theoretical rock and stacking them so that the sections correspond to the above network. McCauley (1992) generalized results, which correspond to the binary organization of Fig. 5-80, yielding in the following relationships for porosity, permeability, and conductivity: <$> = [1 + p(2L 2 - 1)] N,

(5-72)

398 -1

Gear = [1 + p ( 2 - ' L -2 - 1)] N

(5-73)

and -1

k e~ = [1 + p ( 2 - ' L -4 - 1)]u.

(5-74)

From these equations, the composite model gives the following equations for conductivity and permeability, respectively: ln[1 + p(2-'L -2 - 1)] m^ =

(5-75)

ln[1 + p(ZL 2 - 1)]

and ln[1 + p ( 2 - ' L --4 - 1)] m=-

ln[1 + p ( Z L 2 - 1)]

,

(5-76)

Wong et al.'s (1984) exponent equations are obtained when p ~ 1 for electrical conductivity and permeability, respectively: m ^ ~ 89 2,

(5-77)

and

a2( 89 4 - 1) m~

( a 2 - 2)

,

(5-78)

McCauley (1992, p. 43) showed that the limit p --~ 1 yields the parallel tube [or Adler (1986)-1ike Sierpinski carpet model] results: m ^ = 1, and m = ( 4 - D o ) / ( 2 - D o ) , where D o = ln2/lna (ln is the natural log). If a is set equal to 2, then m ^ = 2 and m~ m 6 - 7 from Eqs. 5-77 and 5-78 (McCauley, 1992). These results are very reasonable. In order to obtain an m ^ value of 2.5, p can be kept small and a increased in Eqs. 5-75 and 5-76. Also p and a can be varied. Manipulation of the values can be made to get m ^ = 1.4 by holding a constant and increasing p, because m ^ = 1 when p = 1. McCauley (1992) showed how to get larger values of the permeability exponent for a given value of conductivity exponent. He introduced connectivity (branching) of a complete binary tree. There is a limit in the composite model, as there was in Wong et al.'s (1984) model, where both the porosity and permeability are log-normally distributed (see McCauley, 1992, p. 44). By generalizing Eqs. 5-72 to 5-76 to a complete tree or order t, McCauley (1992) simply replaced the tree order of 2 by t, where t can take on values of 1, 2, 3 , . . . . resulting in m ^ and m exponents in the log-normal limit:

399 1 + [(1-p)/2](4-Do)lna m^ ~

(5-79) 1 - [(1 - p ) / 2 ] ( 2 - Do)lna

and

m/m ^ ~, (4 - Do)/(2 - Do).

(5-80)

Multifractal rock model. McCauley (1992) stated that the log-normal limit correctly reproduced the trivial limit of parallel tubes, where p = 1. Ifp is small, then the limit cannot be reproduced in the log-normal approximation. McCauley (1992, p.45) then discussed treating Eqs. 5-72 to 5-80, which are based upon a single-scale fractal, as a multiscale or nonuniform fractal. The transverse thin-sections of pore space o f the simplest multiscale fractal are a two-scale fractal. The reader is referred to the discussion on multifractal characterization later in this chapter. McCauley (1990) and Ijjasz-Vasquex et al. (1992) provided a complete background on multifractals and their applications in dynamic systems. The simplest case of a multifractal distribution of pore-space area can be envisioned where the porosity of a very thin slice of carbonate rock has a thickness that is small compared to the size of the largest pores, as being built by iterating two length scales L~ and L 2. McCauley (1992, p. 33) stated that in the first generation (n = 1) the scale L~ occurs b times, then L 2 occurs t - b times, where b is any integer between 0 and t - 1 and b = 0. Thus, for t" tubes connected in parallel, porosity and permeability are: = [tL 2, +

(5-81)

and G=

[bL 4 +

(5-82)

McCauley suggested that it is useful to introduce the canonical partition function, which is a generating function:

Z(fl) = [bl ~ + ( t - b)l~2 ]",

(5-83)

where g(fl) = - l n Z ( f l ) / n is analogous to the Gibbs potential per particle because n is analogous to the number of particles in ordinary statistical mechanics. Models like Eq. 5-83 follow from deterministic chaos (McCauley, 1992, p. 34). McCauley's (1992) Eqs. 5-72 to 5-78 are based upon a single-scale fractal. If the transverse thin-sections of pore space are represented by a multiscale fractal, then McCauley's simplest case is that of the two-scale fractal shown by the above Eqs. 581 to 5-83. Equations 5-72 to 5-76 restated for two-scale fractal are: <~b> = [1 + p(e -g(2)-- 1)IN,

(5-84)

400 -1

Gfr = [ 1 + p(e g~2)- 1)]u,

(5-85)

-1 keff = [1 + p ( e -g(4) - 1)]N,

(5-86)

resulting in In[ 1 + p(e -~z) - 1)] m^ = -

(5-87)

In[ 1 + p(e ~2) - 1)]

and In[ 1 + p(e -g~4)- 1)] m=

In[ 1 + p(e g~2)- 1)]

.

(5-88)

The general model explains two important facts: (1) connectivity (branching) is the way to obtain a large m / m ^ ratio with m^ > 1, and (2) nonuniversality of the scaling exponents m and m ^ results by varying both the first generation length scale L~ = 1/a and the probability p. McCauley's (1992) approach and interpretation were not based upon ideas from equilibrium statistical mechanics having attributes of universal critical exponents and formal percolation theory, but are based upon ideas from chaos theory. Chaos theory describes transport far from thermal equilibrium using trees, weak universality, multifractals, and nonuniversal scaling laws. McCauley concluded that in the dynamic model, the tree order describes how different thin-sections with different porosity values connect with each other. The very small diameter pore throats provide the connections between the pores, and typically require large scale magnification of a thin-section in order to be observed. McCauley speculated that a sufficiently accurate photograph of a thin-section, which reveals the smallest pore throats, would lead to a connectivity parameter t that agrees with what is needed to explain the transport exponents. Again, the writers observe that Teodorovich's (1943, 1949, 1958) ideas on the structure of carbonate rocks and his approach to calculate permeabilities from thin-sections of carbonate rocks gain additional support. McCauley (1992) suggested that microscale scaling laws for conductivity and permeability with experimentally known exponents m and m ^ should be used as a constraint to test models ofmacroscale permeability distributions. If a resistance network used to model a permeability distribution cannot reproduce the experimentally known exponents for the microscale reservoir, then it is unlikely that the model will be correct in predicting the performance or other properties of the macroscopic reservoir from which the rock and fluid samples were taken (McCauley, 1992). At this time, the real space renormalization group method employing resistance networks needs to be considered. This method is an effective scaling-up, numerical tool that greatly improves conventional carbonate reservoir performance modeling. Permeability renormalization is discussed and is an averaging process that replaces a large array of small-scale effective permeabilities with a smaller array of larger-scale effective permeabilities.

401 Turcotte (1992) defined renormalization as the transformation of a set of equations from one scale to another by a change of variables. Advantages in using renormalization are: (1) A cost-savings computational technique over previous techniques, which compared coarse-grid simulations with fine-grid simulations. Saucier (1992) recounted that even if all the permeability data were actually available for a reservoir, then a complete three-dimensional picture of the permeability field at a mesoscopic scale of resolution could exceed the capacity of existing super computers or else be prohibitively expensive to process. These data, at present, are rather sparsely known for a reservoir and are expensive to process. (2) Higher resolution of details on a much finer scale than finite difference techniques. (3) Accurate estimates of the pressure drop across a heterogeneous system for fluid flow in oil reservoirs. Finally, the real space renormalization group method will be used to calculate scaling exponents in multifractal porous media.

Real space renormalization group method The requirement to use average (effective or pseudo) property values for grid blocks in reservoir simulation was previously discussed in this section. King (1989) discounted the use of both perturbation theory and effective medium theory (EMT) as effective techniques to replace an inhomogeneous medium by an effective homogeneous medium when property fluctuations, such as permeability, become very large. If the fluctuations are small, then the perturbation theory or EMT give reliable estimates of the effective property. With respect to perturbation theory, the problem lies in the fact that when the property variance is large the result is invalid. The assumption behind EMT is that the mean fluctuations in the pressure field are negligible and average to zero (King, 1989). In the case of permeability, as permeability fluctuations increase, however, pressure fluctuations do not increase and effective medium approximations break down. The position-space renormalization approach originated in physics and the seed of its origin is attributed to Kadanoff (1966). This method can produce fractal statistics and explicitly utilizes scale invariance. King (1989) proposed the use of realspace renormalization to calculate effective absolute permeability values in a h e t e r o g e n e o u s medium. By adopting this method, the effective absolute permeabilities are rescaled in order to utilize the same system at the next larger scale. Figure 5-81 illustrates the scaling-up methodology. The process is repeated using larger and larger scaled-grid blocks until the initial grid is reduced to a singlegrid block (single effective value) for a small localized region. This process is repeated by combining various localized regions into blocks and reducing them to a single effective value, thereby coarsening the grid. Block renormalization of the grid is repeated until the desired part, or the entirety, of the reservoir has been realized. Application. King (1968) and King et al. (1993) discussed the renormalization procedure in detail. They showed that the procedure for isotropic media can be extended

402 NO

ROW

No Row

.~

No Flow

.~

K 22

K

K

K

K

K

K

13

p 1

31 3

14

23

32

K

34

24

K 1

K

K

43

42

K P 2

P 1

P 2

P 1

eft

P 2

K

44

Fig. 5-81. The real space renormalization method is illustrated in two dimensions for an initial 4 x 4 grid, which coarsens from left to right. Assuming an isotropic medium, the effective permeability (kff) is calculated in only one direction (horizontal). Horizontal boundaries represent impermeable barriers (no flow). Fluid flow occurs in the x-direction from left to right (pressure in (P~,) > pressure out (Pout))"

to three-dimensions and immiscible flow. Here, only single-phase flow is discussed using permeability as an example. First, the properties have to be distributed on a fine grid. The scale-length of the grid has to be representative of the original data sample size. For example, if the permeabilities are derived from core samples at one-foot intervals, then the initial grid blocks should have dimensions of one foot (King, 1989). The only required input is a permeability probability distribution. The permeability distributions to be averaged are taken from the sample distributions determined from cores. Initially, the renormalization method involves averaging over small regions of the reservoir to form a new averaged permeability distribution with a lower variance than the original distribution. This pre-averaging is then repeated until a stable estimate is found. King (1989) considered only uncorrelated media in his examples so that the permeabilities are randomly distributed. This was done by King to avoid the separate issue of handling correlated media. In order to treat correlated media one needs statistical methods for generating large grids of correlated variables. Once the permeability grid has been established, the same renormalization techniques can be used for correlated media. King (1989) organized the initial grid block into blocks of four in two dimensions (for three dimensions there are eight blocks initially). The effective permeability of the four blocks is calculated and assigned to a new, coarser grid composed of one block (Fig. 5-81). A coarse-grid reservoir model can represent all scales of heterogeneity associated with the reservoir, whereas a fine-grid model can represent only small to medium scale heterogeneities. King et al. (1993) pointed out that the accuracy of the final coarse-grid simulation is only as accurate as the fine-grid simulations used to derive the pseudo properties. One drawback to this procedure is that the results of the coarse-grid simulations cannot be checked as no fine-grid model can reproduce all scales of property variation. The resulting effective permeability is a single value retaining the same flow as the initial blocks and the original pressure drop (King, 1989). The process is repeated many times until a stable effective permeability is

403

P 2

A

B

C

Fig. 5-82. Modeling block permeabilities by using an equivalent resistor network. (A) Resistor network showing each block with a cross of resistors. (B) Resistor network that is identically equal to (A). The end edges were set to a uniform pressure. (C) An equivalent resistor network created by trimming off the dead-end edges of the four blocks and joining together those nodes with the same pressure. found for the area (volume) being investigated. The variance in the permeability and the correlation length in correlated media are reduced as the permeability approaches the value of the whole region. King's (1989, p. 43) procedure involves the development of probability distributions by Monte Carlo sampling. In this manner the permeability distribution on the old grid is transformed to obtain an approximate Gaussian probability distribution on the new grid. The next step is to calculate the effective permeability of the renormalized block.

Calculation of renormalized permeabilities. King (1989) and King et al. (1993) described how to calculate the effective permeability of the renormalized block. The block permeabilities are modeled using an equivalent resistor network with the boundary condition that the external edges of the blocks are at uniform pressure (Fig. 5-82). This is not true, however, for the internal edges, and is a source of error if the permeabilities are arranged in particular configurations (King, 1989). Such configurations are rare events, and even under those situations, the error is small. The permeability field can be estimated by using a resistor network, where each block is replaced by a resistor cross. The blocks of four in Fig. 5-81 were replaced with a cross of resistors as shown in Fig. 5-82A. Each equivalent resistor between the midpoints of the edges is 1/k for a block of permeability K. After hooking up the resistor crosses together, the boundary conditions are set so that the sides of the blocks are at constant voltage. This corresponds to a uniform pressure on both vertical boundaries as shown in Fig. 5-81. The inverse of the equivalent resistance of this circuit yields an estimate of the effective permeability field (Saucier, 1992). Figure 5-82B shows a resistor network that is identically equal to Fig. 5-82A. The dead end edges in Fig. 5-82B are trimmed off, and the nodes having the same pressure are joined together, resulting in the equivalent resistor network (Fig. 5-82C). King (1989) applied the star-triangle transformation (shown in Fig. 5-83A to the resistor relationships in Fig. 5-82C) to give a circuit composed of resistors in series and parallel (Fig. 5-83B). The star-triangle transformation is very useful for reducing resistor networks to a simpler form. The circuit in Fig. 5-83C is equivalent to the circuit in Fig. 5-83B. In two dimensions the effective permeability (K~r) of the four blocks is reduced to:

404 R

A

3

B

A

B

c p

C

C

e

11w

f~

//~

aL

IF

p

2

,Q A

B

C

C Fig. 5-83. Simplification of the resistor network. (A) Star-triangle transformation scheme used by King (1989). Examples of the resistor transformation equations are shown. (B) Transformation of Fig. 5-82C into a circuit having resistors in series and parallel. (C) Simplified circuit equivalent to B.

4(K~ + K3) (K 2 + K4) x Kff =

[K2K4(K 1 + K3) + K1K3(K 2 + K4) ] [K, + K 2 + K 3 + K41 +

[K~K4(X, + X~) + X.K~(K~ +/';,)1

(5-89)

3(K, + K2) (K 3 + K4) (K l + K3) (K 2 + K4) Not only can the effective permeability of the four blocks be calculated by Eq. 589, but also the current in the resistors (fluxes between the fine-grid cells) can be established in a similar manner. The reader is referred to King et al. (1993, p. 241) for a complete discussion. .. ... The effective permeability (K) of the four block permeabilities can be written as:

x =/(K., K~, X~, X,).

(5-90)

If the permeability distribution on the old grid is P(K), then the probability distribution (P(K)) on the new grid is: P ( K ) = 3 fi(K - f(K,, K 2, K 3, K4) x P(KI)P(K2)P(K3)(dKIdK2dK3dK4) ,

(5-91)

405 where the integrations are performed over all possible values of the original grid block permeabilities K ~ , . . . , K 4 (two dimensions) or K ~ , . . . , K 8 (three dimensions) (King, 1989, p. 43). The block renormalized permeability f({K}) is used in Eq. 5-91 in order to determine the renormalized probability for the permeability. King (1989) developed the probability distribution by Monte-Carlo sampling. K~, K 2, K 3, and K 4 are selected first from the original probability distribution so that the effective permeability can be calculated using Eq. 5-90. This is repeated until a satisfactory distribution P(K) is built up (King, 1989). King (1989) noted that the variability in permeability observed from small-lengthscale samples such as cores is not necessarily that which should be used at the reservoir simulator grid-block scale. He showed that the distribution parameters behave in the following manner under renormalization for the two-dimensions case. K n+l

= Kn

(5-92)

+ 1 "- d 2 n / 4 -

(5-93)

and d~

The mean of the distribution is unchanged and the variance is reduced by a factor of four. Figure 5-84 shows the effect of three repeated renormalizations on a uniform probability distribution. The result of repeated renormalization is to arrive at a single value. The probability distribution reduces to a delta function, which is the limit of a Gaussian distribution for a small variance. P(Ki) in Eq. 5-91 is considered by King (1989, p. 46) to be Gaussian. King (1989) and Saucier (1992) noted that there are several problems connected with the real space renormalization method. These drawbacks include: (1) the possibility of hooking the resistor crosses in many different arrangements, thereby leading to different estimates of Kfr; (2) the approximations involved are difficult to quantify; (3) the accuracy of the predictions remains unknown in actual field practice. Numerical experiments performed on various reservoir test cases by King (1989), Mohanty and Sharma (1990), and Aharony et al. (1991) have proved this method to be accurate; (4) if the flow paths are very contorted (have a high tortuosity), then the resistor network does not provide a good representation; (5) the estimate of effective permeability is poor, when there is a high contrast between neighboring permeabilities, such as exhibited by a shaley carbonate reservoir; and (6) King's (1989) approach will not give a direct realization of the flow paths. King et al. (1993) stressed two important attributes of the renormalization method: (1) this procedure is about 100 times faster (in terms of computer time) when compared with pseudoization, which is computationally intensive, and (2) the speed allows us to run a larger number of statistical realizations of permeability heterogeneity, which provides a better estimate of uncertainty in reservoir performance prediction. The following discussion of Saucier's (1992) work on effective permeability concentrates on how the real space renormalization group method can be used to calculate

406 1.5 ORIGINAL

A

DISTROBUTION SUCCESSIVE RENORMALIZATIONS

v ft.

I.o

:i

,IP .,,i ,,-t ,,e

,0 0.5 .o 0

i

:

'

i

~

.;

.............

1

.......

2

.......

3

i

,../o:.............. ',\ ,....~

I.,

a,

..... /,

,, '<..

9

I

0.0

..." .... /"9

2.

0.

.,."

/

..... 9

.

I

_.,.._,,

/

~

'

,

~

, ,_

4. Permeability

"~

...

"\

"~ ...............

iS.

8.

4.6

e..

L.

B

10.

(K)

|

6.0

I

...

~.._

C

~L,

.Q......., o ..

... ....

4.6

"-~. "'....

o..

4.4, ...................................

9 .......

~

......

@

.......

9 .......

,41, . . . . . .

~

........

~7,

... ..

~..

4.0

... "o......

4.2

0 n

2. (no.

of

4. 6. 8. renormalizations)

tO.

--LL.

~.

o n

(no.

",,;. of

~'4.

"

~i.

renormailzattons)

to

Fig. 5-84. Examples of the effect of a successive renormalization on a uniform probability distribution and the scaling of two probability parameters in two dimensions. (A) Repeated renormalization of a uniform probability distribution; (B) Scaling of the mean; (C) Scaling of the variance. (After King, 1989, figs. 3 and 4; reprinted with the permission of Kluwer Academic Publishers.) analytically the scaling exponents of the effective absolute permeability in multifractal porous media. An insight into the process of calculating effective permeability ofrandom multifractal permeability fields helps one to become aware of the analytical foundation of this new modeling technology. Such an approach enhances reservoir performance prediction in carbonate reservoirs by increasing greatly the ability to characterize microscopic heterogeneity and to scale-up the results on a reservoir-wide basis.

Multifractal characterization A brief but concise orientation on the nature of multiscaling is in order before applying renormalization to multifractal porous media. This presentation provides direction and help in deciphering the mathematical thrust behind the multifractal pore space--permeability relationships and shows renormalization strategies used in threedimensional modeling.

407

Multifractals. By now, one has probably realized that fractals fall into two categories: geometrically self-similar (uniform) fractals, and nonuniform (multiscale) fractals called multifractals. McCauley (1990) pointed out that the fractals found in nature and in the analysis of nontrivial dynamic systems are statistically self-similar, but not geometrically self-similar. Multifractal theory was developed in order to manage nonuniform fractals and gives one the ability to analyze and to better model nature. The distribution of reservoir properties, such as pore space in sedimentary rocks, was shown previously to be fractal. By using the geometrically self-similar approach, the multifractal nature of pore space was not distinguishable over several decades of length scales from that of a two-scale Sierpinski carpet (a planar Cantor set). Information describing the detail of the differences between fractals and multifractals got lost. It was demonstrated previously that fractals are constructed by using a recursion formula. The next term of the fractal sequence is determined from one or more of the preceding terms and conditions. McCauley's (1992) approach to models of permeability and conductivity suggested that one should think of a fractal as a collection of fragments that can be organized into a hierarchy such as a tree model. A geometrically self-similar fractal is constructed by iterating a single first-generation length (L) repeatedly, so that all the L i will have the same value L" in the nth generation (McCauley, 1990). A multifractal, however, is constructed by repeated iteration of two or more first-generation length scales and the result is a nonuniform fractal. Multifractal statistics give both moments and correlations. Mandelbrot (1988) emphasized that the notion of self-similarity extends readily from fractal sets to multifractal measures. That is the passage from geometric objects characterized primarily by one number (fractal dimension) to geometric objects characterized by a function (in this case a limited probability distribution). A multifractal measure is a way of specifying a method of distributing probability, mass, or other material relationships over a supporting set, such as planar, uniform, and nonuniform Cantor sets. By knowing the multifractal spectrum one can compute all moments at all length scales for which the scaling holds (Muller et al., 1992). If scaling is observed, then the multifractal spectrum provides a wealth of statistical information. Turcotte (1992) has an excellent discussion on connecting fractal distributions to probability. Figures 5-85A and B portray a uniform Cantor set and a nonuniform Cantor set, respectively. The uniform Cantor set is constructed recursively by the iteration of a single length scale L = 1/3 (Fig. 5-85A), whereas a nonuniform Cantor-set's construction involved two rescaling parameters L~ = 1/4 and L 2 = 2/5 (Fig. 5-85B). These two types of Cantor sets were used by McCauley (1990) as examples for explaining support for generated probability distributions. McCauley, however, recognized that this approach is not the best either for the analysis of experimental data or for computations, and opted for a more direct formulation using the generating function X(q). McCauley (1990; 1992) proposed that we should think of a fractal as a collection of fragments that can be organized into a hierarchy, or tree. In this collection there are boxes N =].~n fragments with box sizes L~, L2,..., LNn in the nth generation. If the fractal is geometrically self-similar, then it can be constructed recursively by the repeated iteration of a single first-generation length scale L (McCauley, 1990, p. 229).

RANDOM

ORDERED ~=0

'n=O

III

=1

PI = I/2

P2=1/2

L I :1/3

L 2 = I/3

2

2

2

P2=n/4

-

-2

L 2 = I/9

I

=3

2

P2= n/4

PI=V4 Pl=l/4 = 2 ~ L2= 119

P 2"

Ll,l/4

L2=2/5

I

2 2 P 1=9/25,FI P2,,6/25 PI P'z's/'ZS, P I ' 4 / z 5 ~

LI~B=I/I6,LIL~I/IO

LIL2"I/IO ,Ltn~,4/25

P~=l/e m i U U L t = 1/27

P03 : lie am j a am I a L31=1/27

2/5

P I 315 9

= J

i

B

A

=3

=4 IllliillliiilllillilllllliLllilllililllllllililllllmillillllWBil C

NONUNIFORM

UNIFORM

VARIATIONS I

II i ii

nmmml / IN II Ii I1 Jl t

i

H

II II ii

oo

'n=O

I |0: I Wl

|1111 i

II

Ol II

III

i

I |

ilia i mi

6L: I / Z

w2 ill

Wl

64=l/Is . . . . . . . .

L i W2

Wl

L"''J"'"

D

E

F

UNIFORM

UNIFORM

UNIFORM

409 As shown by the Cantor set examples (Fig. 5-85), a multifractal requires an iteration of two or more different length scales of construction by recursion (Fig. 5-85B). McCauley (1990) pointed out that the resulting fractal is nonuniform, but statistically self-similar in that the relation N,, " L~ -~ holds. The generating function X(q) is defined by McCauley (1990, p. 229) for the partition width {Zi} as:

Nnq X(q) = Y~P~ , i=l

(5-94)

and is the sum over all boxes of the qth power of box probabilities P. N is the number of boxes (bins; cells) covering an image or object, n is the number of iterations, and q is a moment. So N is the number of cells required to resolved the dynamics after n iterations (McCauley, 1990, p. 231). The generalized dimension (Dq) is expressed by McCauley (1990) as: X(q) = L

n

(q - l ) D q ,

(5-95)

where L denotes the characteristic size of the N boxes (bins) with various widths Li for each generation n of coarse-graining of phase space in dynamic (chaotic) systems. Multifractal relationships. At this point in multifractal discussion, it is necessary to provide an expanded, but basic, description of multifractal spatial organization and scaling properties. Also this formalism leads to recent analyses which improve on the initial studies by Katz and Thompson (1985), Roberts (1986), and Krohn (1988a,b) (see page 264). It is not only the basis for differentiating multifractal pore-systems in carbonate reservoirs, but also in attempting to relate the multifractals to measured permeability (Muller, 1992; Garrison et al., 1993c). These investigations are also discussed here. The following approach will show how q, exponents, and other parameters are defined in the context of a multifractal spectrum. Fig. 5-85 (opposite). Cantor set constructions. ( A ) - Uniform Cantor set was constructed by removing the central third of each line segment, creating a triadic set. The set is constructed recursively by the iteration of a single-length scale ofL = 1/3. Each of the two intervals receives the same measure (probability)p = 1/2, I/4 . . . . . nth, each of length L = 1/3. Using Eq. 5-11 [D = log N/log (I/r)] the fractal dimension (D) can be calculated for all constructions except (B) - N is the number of identical line segments retained having a characteristic length (r), and the relation between L and r is r = 1/Ln; at r = 1/L~, where L = 1/3, r - 3; D = 0.6309. (B) Nonuniform (multifractal) Cantor set is constructed by using two rescalings LI = 1/ 4 and L2= 2/5 and the respective measure rescalings for each interval Pi = 3/5 andP 2 = 2/5. The multifractal dimension can be computed using Eq. 5-97. As indicated in examples (A) and (B), the values of P for each line segment of order n are obtained by using the binomial expression [(a + b)"]. (C) - Random Cantor set was constructed by removing randomly a third of each line. Examples (D) and (E) are uniform Cantor sets with the same D = 0.5, but each having different configurations. ( F ) - Saucier (1992) used a uniform fractal having four cascade steps (n 5 = ~4 = 4) and two different weights WI and W2 to study the effective permeability of a deterministic multifractal permeability field as a function of scale. The inner scale is S4 - (1/2)4/~o 9Horizontal brackets enclosed all the values of permeability in this interval which share the same multipliers at scales 61 and 62 (that is, w ( ~ ) = w E, and w(62) = wR). The reader is referred to page 426 for an explanation of the formulas used to describe the permeabilities generated by the cascade process. ((F) is after Saucier, 1992, fig. 7; courtesy of North-Holland.)

410 The concept of a multifractal spectrum (formalism) is expressed by: (5-96)

f ( a ) = p(a) + m a x f ( a ) ,

where f(a) is a fractal dimension (also known as the spectrum of singularity: Halsey et al., 1986) of the subset of boxes characterized by the exponent a. a is the crowding index or H61der exponent (Mandelbrot, 1988) (also known as the singularity strength: Halsey et al., 1986)), and p(a) is a limited probability distribution function. The curve resulting from a plot o f f ( a ) vs. a is known as the multifractal spectrum (Halsey et al., 1986). Figure 5-86 is a generalized diagram of a typical multifractal spectrum illustrating graphically the various relationships between exponents and parameters. The bell-shaped curve provides a picture of the full complexity of the scaling structure. The function t(q) is a standard probabilistic tool to represent measures, called the cumulant generating function (Mandelbrot, 1988). Exponents t(q) are related to the set of generalized fractal dimensions Dqby: D

q

- t(q)/(q-

1),

(5-97)

and these quantities are called the 'critical dimensions' by Mandelbrot (1988). Equation 5-97 implies multiscaling (different values of D q for every value of q). Hentschel and Procaccia (1983) noted that there exist a hierarchy of critical dimensions that are defined for any q >_0. The similarity dimension (D) is defined as: f(a)

~

Slope : 1 Stope q

Do

)) D,

f(a( q

I

I -r(q)

'

I I

~Q

el=IJa(q) a(O} Fig. 5-86. Schematic of a typical multifractal spectrum (orf(a) - a curve) diagram. Do is the Hausdorff dimension defined by the maximum value of a continuous functionf(a). The information dimension (D l) lies at the point wheref(a) = f ' ( a ) = a = 1. The reader is referred to McCauley (1990, fig. 2.3, p. 234) for the geometrical construction showing how to locate the correlation dimension (D2). r(q) is the ordinate of the intercept of the tangent of slope q by the vertical axis.

411 lim D q = D. q--+0

(5-98)

The information dimension (D~) is defined as: lim D q = D 1. q ---~ 1

(5-99)

D l measures how the information required to describe the measure scales with In(l/6) (refer to the elementary box counting technique mentioned on page 264). The correlation dimension (D2) is defined as: lim

Dq = D 2.

(5-100)

q-2 If the D q values are the same for every value of q, then the measure reflects simple scaling. For the case where box counting is used, f(a) would be the fractal dimension of the set of boxes with the same a value. This formalization has its basis in a relationship where a grid with boxes of size r is superimposed over an area of interest, such as a map or image displaying the distribution of a property of interest. Carbonate rock porosity images are such an example. Ijjasz-Vasquez et al. (1992, p. 298) gave an excellent discussion on how this part of the procedure is accomplished. The behavior of the probability measure Pr(X) with r showing the organization of the property of interest around the point x is described as: Pr(X) "~ (r/L) a,

(5-101 )

where r is the box length, L is the overall length of the area under investigation (L = rmax) , and a is the H61der exponent. A log-log plot of Pr(X) (cumulative value of the property in the box) vs. r/L results in a straight line whose slope is a. It is necessary to count the number of N ( a ) of grid boxes with common values o f a (Ijjasz-Vasquez et al., 1992). There are usually many boxes with the same index a. It was pointed out by Ijjasz-Vasquez et al. (1992) that these grid boxes are mixed and interwoven inside the domain of study. Their number depends on the size r of the grid boxes and scales as:

Nr(a ) ~ (r/L) -s(~ ).

(5-102)

A log-log plot of Nr(a ) vs. a results in a straight line whose slope is -f(a). The numerical calculation of the multifractal spectrum based on Eqs. 5-101 and 5-102 requires large amount of data and is affected by logarithmic prefactors that depend on the grid box size r. A direct procedure used by Ijjasz-Vasquez et al. (1992) to calculate the multifractal spectrum uses the cumulants of order q of Pr(X). Their method consists of three steps based on relating the scaling behavior of C ( r ) with r for different values of q with the multifractal spectrum. The procedure is:

412 (1) Find the cumulants C(r) from: C ( r ) = Zi[Pr(Xi)] q,

(5-103)

where the centers X i of the boxes have been indexed. (2) Calculate r(q); the scaling behavior of C(r) with box size r is expressed as:

C(r) ~ (i'lL) t(q).

(5-104)

The exponents r(q) are related to D by Eq. 5-97. When q = 0, Co(r) measures how many boxes of size r are occupied b~r the measure and D Ois the fractal dimension of the support set where the variable of interest is studied (if an entire reservoir map is used then D O= 2) (Ijjasz-Vasquez et al., 1992). The values of the moment q are integers (q = 0, + 1, +2, +3, . . . . ,). If the values of D are different for every value of q, then this is a condition known as multiscaling. Sir~ple scaling is where D q values are the same for every value of q. (3) Lastly, determine a and f ( a ) using the values of r(q). Ijjasz-Vasquez et al. (1992, p. 300) showed that it was possible to relate the three exponents by: (5-105)

t(q) = qa(q) - f(a(q)) ,

and taking the derivative with respect to q and using the relationship df(a(q))/da = q gives:

tit(q)

dq

- a +q

da

df

dq

dq

- a.

(5-106)

Equation 5-106 shows that a is the slope of the tangent to the curve r(q) vs. q. f ( a ) is the intercept of that tangent with the r(q) axis and-r(q) is the intercept of this tangent with the f ( a ) axis as demonstrated by Eq. 5-105. These relationships are shown graphically in Fig. 5-86. Muller et al. (1992) gave some advice on calculating a multifractal function. The calculations are carried out for n refinements of coarse-graining, with q ranging usually from qminequal to about-15 to qmaxequal to about + 15 with steps of 0.1. As a suggestion, the investigation of the scaling region in multifractal analysis of reservoir properties should have box sizes of 2, 4, 8, 16, 32, 64, 128, and 256 units. With a single fractal dimension, only 2, 4, 8, 16, 32, and 64 units should be sufficient.

Multifractal analysis of porous media. One practical application of multifractal scaling of rock microstructure, as discussed above, is the characterization of rock pore systems. As mentioned previously, the relation between porosity and permeability in rocks is a subject of great practical interest. Empirical equations, such as Eqs. 556 through 5-58, attempted to relate various reservoir parameters to permeability. The following discussion is built upon the important concept of very thin slices of rock

413 pore-space. McCauley (1992) pointed out that any photograph or digitized image of a rock's pore-space represents an infinitely thin section of the pore-space. The implications a description of the fractal structure may have on the comprehension of rock fluid flow properties are presented here. Ehrlich and Horkowitz (1984) made one of the earliest attempts to use petrographic image analysis data to study porosity and link some 24 petrographic image analysis variables to permeability. Hansen and Skjeltorp (1988) were the first to apply the box counting technique to digitized rock pore images in order to perform an analysis of random fractal scaling. In their detailed study, they determined the fractal dimensions of the microscopic geometry of rock surfaces (Ds) and of the pore space (D). The results indicated that the values of D s were less than Dv. Hansen and Skjeltorp (1988) stated that this result arises from a 'grain-filling procedure' of the pore space. They conceptualized the procedure as follows" (1) A porous medium can be created by introducing a fraction fl~ of grains with characteristic size L~. (2) The pore volume is then reduced when it is changed from V (initial volume) to /~VO~ (3) Next a fraction f12 of characteristic size L 2 is introduced and the process is repeated until reaching the smallest grain size L n. (4) The total surface area in the rock increases from S to r~§ ~S. ~'i is the fraction of surface area and the {7i} and {fl~} are a function of the grain structures and the packing of each grain size into the system of larger grain sizes (Hansen and Skjeltorp, 1988). The total volume and surface after the filling is expressed as:

V - I i=l fi ~il V~

(5-107)

and

S= I ~ ~1S o

(5-108)

Now the fractal-box counting dimension associated with the pore volume can be estimated. Hansen and Skjeltorp (1988) showed that by covering the pore volume, using Euclidean dimension (E) boxes of length Li, and counting the boxes containing pores space, the number of boxes N i can be calculated:

Ni•

(5-109)

j=l

cdp/S2,

Hansen and Skjeltorp (1988) used Kozeny's equation (k = where c is a rock dependent constant, as a model to study the impact of different fractal dimensions on

414 permeability. The relationship for the specific surface S is expressed by Hansen and Skjeltorp (1988) as follows:

S = So(Ll/Ln )(Ds - Es) + (Ev - Dv).

(5-110)

The rock's surface is covered with Es dimensional squares of the same sizes ( E = 2, the Euclidean dimension). By substituting into the well-known Kozeny equation (k = c~b/S2) the expression for permeability one gets k = c'~) ( L , / Z n ) 2[(Es - Ds) + (Dv - Ev)].

(5-111 )

The dimension Dv is always less than or equal to E v, and Ds is greater than E. Equation 5-111 indicates that permeability has a power-law dependence of D and D . As D s is increased, kr decreases, and as Dv is increased k increases. This is reasonable because D and D reflect the tortuosity of the rock structure (Hansen and Skjeltorp, 1988). Further it is revealed by Eq. 5-111 that the variations in permeability for different fractal dimensions can be large if the ratio (Li/Ln) also is large. Hansen et al. (1988) demonstrated that pore distributions in sedimentary rocks could be distinguished using a plot of f(a) vs. a. Figure 5-87 shows the digitized representations of optical micrographs of thin-sections cut from sandstone core samples collected from two different North Sea oil reservoirs. This approach is a natural s

s

. O,

1.6

v

v

"~ ...k '~.

"|

I

I

1

%

1.2

% % %

r

%

o.e

% %

0.4

0.0 1.5

2.3

3.0 (1

3.8

4.5

2 ~- -'F- m

Fig. 5-87. Results of a multifractal analysis (/(a) vs. a plot) of digitized images indicate that pore distributions are different for the two sandstone thin-sections (shown on the right-hand side). The analysis used the box-counting method. Thin-sections were cut from cores retrieved from two North Sea reservoirs. (After Hansen et al., 1988, fig. 1; reprinted with the permission of Kluwer Academic Publishers.)

415 extension to the previously discussed Katz and Thompson's (1985) use of the Hausdorff-Besicovitch fractal dimension in defining pore geometry. Muller (1992) applied multifractal characterization to samples of oil-bearing chalk, collected from four different North Sea formations, using digitized images. Allochthonous chalk deposits are widespread in the Upper Cretaceous to Lower Paleocene (Danian) rocks of the North Sea (Skovbro, 1983). In the North Sea's Central Graben, commercial oil production is limited to two narrow fairways (Parsley, 1986). Some of the major Norwegian oil fields producing from chalk reservoirs are Ekofisk, Tor, Eldfisk, Albuskjell, and Valhall. Muller (1992, fig. 2) used Eq. 5-94 to generate a plot of log X(q,L) vs. log L. This approach resulted in a linear relationship which illustrated the scaling of the multifractal generating function of the digitized picture for a typical positive value ofq. The measure Pi in Eq. 5-94 is the fraction of pore space area in each box (a box-counting method was used), and N is the number of boxes covering the digitized image. Figure 5-88A shows a typical D(q) multifractal spectrum with error bars for a North Sea chalk sample, and was generated using Eq. 5-97 from 10 different digitized images of the same rock thin-section. The error in the D(q) values increased with q; however, the error is small for q between 0 and 5. Muller (1992) noted that when comparing multifractal spectra of different rock samples one should only concentrate on the D(q) values calculated from these q values. Figure 5-88B displays the multifractal D(q) spectrum of four unidentified North Sea chalk samples. One can only guess from which formations the samples were taken" the most probable candidates are the Ekofisk, Tor, Hod and Hidra formations. The error bars for these samples are of the same order as in Fig. 5-88A (Muller, 1992). All four chalk samples at D(q = 0) have a value close to 2. These four samples have air permeabilities that are different from each other as shown in Fig. 5-88B. The rank order of the multifractal spectra for the different chalk samples changes over the range of q from 0 to 5. Muller (1992) pointed out that the deviation of the D(q > 0) exponents from the D(q = 0) value increases in the order of decreasing permeabilities for rh2 sample (1.8 mD) to rea2 sample (0.6 mD). The rgd9 sample (~ 0.4 mD) does not follow this pattern. Muller (1992) questioned the accuracy of rgd9's measured permeability value. These deviations were attributed by Muller to be related to the degree of clustering of the multifractal measure. Apparently, diagenetic evolution in the North Sea chalk caused a lowering of the chalk's permeability. n

Relationship of multifractal dimensions andpermeability. Before exploring Saucier' s (1992) three-dimensional model, the interrelationships among fractal dimensions, porosity, and permeability are discussed further. Garrison et al. (1992) (see discussion starting on p. 267) considered that reservoir rock/pore systems could be natural fractal objects and modeled as, and compared to, the regular fractals known as the Menger sponge and the Sierpinski carpet. Subsequently, it was shown that the physical properties of porous carbonate rocks are, in part, controlled by the geometry of the pore system. The rate at which a fluid can flow through a carbonate pore system is controlled by the path along which it must travel. Tortuosity is a measure of the length of the fluid path through the rock. The fluid pathway is a subset of the overall geometry of

416

2.2 2.1 2.0 1.0

n W W

O

1.8 1.7 1.I

1.5 -5

5

10

15

9

A 2.0

0

1.9 h

1.8

W

W

a

1.7 1.6

1.5

Fig. 5-88. MultifractalD(q) spectra of North Sea chalk sample rea2. (A) Multifractal spectrum with error bars computed from 10 different pictures of the same rea2 thin-section. (B) Multifractal spectrum of 4 chalk samples taken from different formations in the North Sea reservoirs. (After Muller, 1992, figs. 3 and 4; courtesy of North-Holland.)

417 the pore system. This geometry is described in terms of apparent fractal dimensions determined from pore diameter-number distributions (plots of log N(6), which are the number of holes, vs. log (6), which are the hole diameters: Garrison et al., 1992, p. 382). The distributions contain information about the nature, and number, of multiple fractal pore populations forming the rock/pore system. Garrison et al. (1993b) developed a computer algorithm that allows stochastic modeling of multifractal pore diameter distributions in order to study process relationships. The two cases considered are: (1) those systems having two or more fractal pore populations (processes) with different fractal dimensions, each scaling over a distinct range of lengths, and (2) systems having two or more fractal pore populations with the same fractal dimensions, each scaling over a distinct range of lengths, but with different integral abundances. The algorithm was used successfully by Garrison et al. (1993b) to evaluate and validate the Sierpinski carpet model (refer to discussion starting on p. 267) by being able to simulate: (1) the mixing of two or more of generated stochastic fractal pore diameter distributions, and (2) the alteration of the fractal pore size distributions by allowing a random, but systematic pore size increase and decrease, and coalescence of pores over a range of lengths. Previously, Mazzullo and Chilingarian (1992a) pointed out that there is no one single genetic (mechanical) or diagenetic (chemical) process responsible for forming pore space in carbonate rocks. The algorithm used by Garrison et al. (1993b), however, modified only the diagenetic processes of solution enhancement (increased pore size), cementation and compaction (decreased pore size), and coalescence (dissolution and recrystallization). In this study only a portion of the pores within a selected pore size range were altered. The percent fraction of all the pores in this range was specified a priori. The pores to be altered were selected at random from those pores in the specified range. Garrison et al.'s (1993b) schema contains a function for dual pore selection. The criterion is that "two" pores must be chosen for modeling coalescence. One pore is chosen from the specified size range, and the other is chosen at random from the entire population of pores. Their coalescence procedure used the conditional distribution Pn[~' I ~n)] to select pores to be altered. Pn represents the probability that the nearest neighbors of pores with size 6(n) will have sizes ~'. This nearest neighbor pore relation hypothesis is rough, but satisfies the criterion that the second pore chosen is near the first one chosen. The above approach established a basis for Garrison et al. (1993c) to relate certain fractal dimensions to the flow of fluids through pore space. Their study showed that for natural fractal reservoir rocks, the apparent effective surface fractal dimension D s' and the pore cross-sectional area shape factor S correlate highly with laboratory measured air permeabilities only in the case for process 2 pores. The fractal process with the smallest pore sizes is always referred to by Garrison et al. (1993c) as process 1. Process 1 pores are ineffective in conducting fluid and contribute little to the flow path geometry in the rocks. S was defined by Garrison et al. (1992, p. 387) as the ratio of the cross-sectional area of a non-square hole, either Euclidean or fractal, of diameter ~ to the cross-sectional area of an equivalent Euclidean square hole with the same diameter ~. Their definition takes into consideration the departure of the Sierpinski carpet's hole shape from the Euclidean square.

418 Garrison et al. (1993c) showed that for multifractal rock/pore systems, only the subset of geometry as defined by fractal systems having two or more fractal pore populations with the same fractal dimensions (each scaling over a distinct range of lengths, but with different integral abundances) are highly correlated with air permeability. This correlated fractal process (known as process 2) was designated as the controlling fractal process having the apparent surface fractal dimension Ds'(control) and the area shape factor S control) In Garrison et al ' s (1993c) study, the rock/pore systems have the following characteristics for disjunct singular fractal systems: (

"

.

m

Ds'(control) -- D s' a n d Sa o.t o,, -- S ;

and for multifractal systems: ?

?

Ds ( c o n t r o l )

Ds2 and

"-

S(control)

=

S

2

.

Figures 5-89 and 5-90 present the correlations between D s' and S and measured

- -

--

v

9

l

v

.

v .....

.

.

4

.

.

9

, l 1 .

:3

.

o

o

.

v

.

I

.

1 Q 59H

0 238

I J

Pe

C E

~4

A

9

O

9

O 24 ==..,..,,,.,=.==

9

o~2 o

=,

.

,i

.

.

.

9 Arun Limestone O San Andres Dolomlle -- ~.i

-3

1

.....

9

,&

" '"

~

-

-

1.5 2 2.5 3 3.5 4 4.5 Apparent Fractal Dirnensl0n Ds'

5

Fig. 5-89. Correlation between measured air permeability (core plugs) and mean apparent surface fractal similarity dimension, Ds', for the Arun Limestone (Indonesia) and San Andres Dolomite (west Texas, U.S.A.) samples. Correlation coefficient for the trend is low. Both carbonates are singular disjunct fractal rocks. (After Garrison et al., 1993c, fig. 7; reprinted with the permission of Marcel Dekker, Inc.)

419 core plug air permeability for Arun Limestone and San Andres Dolomite samples. There are many data point deviations from the regression line. All samples of both carbonates have disjunct singular fractal rock/pore systems (refer to p. 271). This is in contrast to the two sandstones studied by Garrison et al. (1993c), which exhibit multifractal rock/pore systems. By excluding pathologic samples, a better data correlation can be obtained for both the carbonates and sandstones (Figs. 5-91 and 592). A stepwise multiple linear regression analysis of various fractal characteristics identified by Garrison et al. (1993, tables 1 to 4) was performed using 52 nonpathologic carbonate and sandstone data points. Based on the results of this analysis, only Ds'(contro]) and Sa(control) are required to account for all of the variability in measured core plug air permeability (k, mD). From these data, an empirical equation was determined by Garrison et al. (1993c) to be: (5-112)

log(k) = -1.699 - 0.616Ds'(control) + 113.287Sa(control).

A plot of measured core plug permeability against the permeability calculated by Eq. 5-112 is shown in Fig. 5-93.

V

~.

I

2

y = 14.368x - 3.526 J r 2 = 0.722 28078

28067

9

8

~

1

~5

&2H

oal O8

0 O

E ._~-1

4~

O14 O 28142 024

i

'~-2 m

9 Arun Llmeston~ O San Andres Dolomite

o

. . . . . . .

,,|

,

-3 .1

.15 .2 .25 .3 .35 .4 .45 Pore Area S h a p e Factor S a

.5

Fig. 5-90. Correlation between measured air permeability (core plugs) and pore area shape factor S a for the singular disjunct fractal Arun Limestone (Indonesia) and San Andres Dolomite (west Texas, U.S.A.) samples. As in Fig. 5-89, the correlation coefficient for the trend is low. (After Garrison et al., 1993c, fig. 8; reprinted with the permission of Marcel Dekker, Inc.)

420

,ram

'

"v

-v

~

v

y = ~.979x

~ e

O~

e

v

v,

9 2.619

r 2 = 0.642

2

o

:3

(D 4)

,,

,,

1

immq

~.

v

........

@ e @e

0

E A

r v

9 Norphlet Sandstone i Spraberry Sandstone Arun Llmestone San Andres Dolomlle

..Ir

O~-2

O ..J

_

-3

"

0

.5

I I I I II II

__

1 1.5 2 2.5 3 3.5 4 4.5 Ds'(control)

5

Fig. 5-91. Plot of measured air permeability (core plugs) vs. Ds'(controt) for the pores of the controlling process in selected samples oftheArun Limestone (Indonesia), SanAndres Dolomite (west Texas, U.S.A.), Norphlet Sandstone (offshore Gulf of Mexico, U.S.A.), and Spraberry Sandstone (west Texas, U.S.A.). Correlation coefficient for the trend is low. (After Garrison et al., 1993c, fig. 9; reprinted with the permission of Marcel Dekker, Inc.)

The straight line in this figure represents a line of perfect correlation with a data point scatter about this line with a correlation of r 2 = 0.950. The equation suggests that D s' and S are simple, concise, quantitative descriptors of pore geometry and are independent of rock composition and texture. The writers believe this approach holds promise; however, several obstacles have to be resolved. First, more variety in the carbonate rock samples is needed in order to validate these fractal dimensionpermeability correlations. Second, the genetic component needs to be evaluated, inasmuch as it will involve on the whole the simple and disjunct component of carbonate rocks. Third, a way will have to be found to mathematically account for the nonrepresentative samples that exhibit large deviations from the "norm" (Figs. 5-89 and 5-90). Fourth, data point deviation for selected samples in the fractal dimension control scenario (Figs. 5-91 and 5-92) appear to be no better than the classical prediction methods. Lastly, when Figs. 5-89 to 5-92 are compared to previously presented examples of fractal analysis, the data point scatter around the trend lines is questionable. These issues will have to be resolved before Garrison et al.'s (1992, 1993a--c) permeability correlation results can be used effectively in carbonate reservoir performance modeling.

421

ol :3

y = 18.312x - 4.49 r 2 = 0.752

2

~.

e

k.,

e OE]

o O :3

0

e

G)

O

E

co

I

9 Norphlet Sandstone II Spmberry Sandstone O Arun Umestone E] San Andre$ Oolomlte

o "3

~

19

.15

.2

-

.25

.3

.35

.4

S a (control)

Fig. 5-92. Plot of measured air permeability (core plugs) vs. Sa(control) (the mean area shape factor of the cross-sectional area of pores in fractal process controlling fluid flow) in selected samples of the Arun Limestone (Indonesia), San Andres Dolomite (west Texas, U.S.A.), Norphlet Sandstone (offshore Gulf of Mexico, U.S.A.), and Spraberry Sandstone (west Texas, U.S.A.). Correlation coefficient for the trend is low. (After Garrison et al., 1993c, fig. 10; reprinted with the permission of Marcel Dekker, Inc.)

Modeling of effective permeability in multifractal (nonlacunar fractal) porous media Now the discussion returns to the application of the real space renormalization group (RSRG) method. Saucier (1992) showed theoretically how to calculate the scaling exponents of the effective absolute permeability in multifractal porous media using the RSRG method. As described previously, the permeability field is renormalized (also known as homogenization) before the fluid flow equation is solved directly by numerical methods. FRACTAM, also discussed previously on page 388, is an example of homogenization (Fig. 5-76). Saucier (1992) pointed out that this procedure allows the generation of effective permeabilities k(L) at any scale L, where L is the mesh-size length of the grid. The structure of the permeability field determines the dependence of k(L) on L. King (1989) related that if the permeability field is an uncorrelated noise, then k(L) converges rapidly to a constant value as L approaches infinity. This means that the renormalized permeability field is constant at large scale. In the case of correlated permeability fields, these fields can be variable even after homogenization (Saucier, 1992). The variance of k(L) can remain large even for large L values. Saucier (1992)

422

Permeability Calculated from Fractal Dimension and Shape Factor 3 O)

2

r 2 = 0.950 = _+ Iog(1.714)

N=52 O o

0

1

~o I L

(/)

0

E A L _ -V

=,,

, - , ,

9 Norphlet Sandstone II Spraberry Sandstone O Arun Limestone E] San Andre$ Dolomlte

r

0"2

..J

,

,

,

,

,

-3 -3

-2

-1

0

1

2

3

Log[ k (calculated)]

Fig. 5-93. Relationship between measured air permeability (core plugs) and calculated air permeability using Eq. 5-112 for selected samples of the Arun Limestone (Indonesia), San Andres Dolomite (west Texas, U.S.A.), Norphlet Sandstone (offshore Gulf of Mexico, U.S.A.), and Spraberry Sandstone (west Texas, U.S.A.). A good correlation coefficient exists for the trend. (After Garrison et al., 1993c, fig. 12; reprinted with the permission of Marcel Dekker, Inc.)

pointed out that a realistic modeling of reservoir properties at large scales requires a minimum definition of the variability of the poorly defined permeability field. He proposed that it is sensible to make the simplest and most natural assumptions as possible when considering poorly-known property distributions in reservoirs. Mandelbrot (1982) argued that structures involving self-similarity are among the simplest ones, and that they can often provide qualitatively reasonable approximations for many irregular geophysical fields.

Multifractal permeability fields. As discussed previously in the review of Garrison and his colleagues' work, it is possible that real permeability fields in carbonate and sandstone reservoirs can be characterized as being correlated and anisotropic owing to the nature of their sedimentation process (fluid flow and gravitational effects) and subsequent diagenetic modifications. Saucier (1992) noted that multifractal permeability fields are among the simplest correlated structures having no characteristic length scale. These fields, therefore, provide a good starting point for the study of

423 flow through inhomogeneous porous media, such as in carbonate rocks. The reader is referred to Hentschel and Procaccia (1983), Halsey et al. (1986), and Tremblay and Tremblay (1992) for an in-depth discussion of correlation lengths for multifractals. Saucier (1992) examined the scale dependence of the effective absolute permeability of both deterministic and random multifractal permeability fields and expanded King's (1989) two-dimensional model to three-dimensions. The three-dimensional structure of a reservoir's permeability field is poorly known owing to sparse information from widely-spaced well records. Well-site geology, two-dimenional seismic data, and well testing provide only rough guidelines to carbonate reservoir porosity and permeability trends, stratification, heterogeneity sizes, and structures. Renormalization equations, however, derived for the effective permeability, allow the linking of the statistics of the effective permeability field at the core scale to the statistics at the macroscale. King's (1989) main idea is that the permeability values are distributed on a D-dimensional cubic grid. The grid blocks, all having the same volume, are then grouped into blocks of 2 D and the effective permeability of each group is assigned to a new coarser grid as was shown in Fig. 5-81. The effective permeability of a cubic group of 2 D blocks is defined by Darcy's law, assuming that the pressure is uniform along both vertical boundaries and the horizontal boundaries of the block are impermeable (Fig. 5-94) (Saucier, 1992). Figure 5-95 illustrates an equivalent circuit for the model shown in Fig 5-94. Four 2 Dresistor crosses have been hooked together. The

k2

kl FI

P=O

OW

P=Z~P

k5

k4

impermeable boundary

L

Fig. 5-94. Boundary conditions used for the calculation of effective permeability of a group of 2 D cubic blocks. (After Saucier, 1992, fig. 2; courtesy of Elsevier Science Publishers B.V.)

424

11 ]............. ~:~ ~ ~! [I..... 1-~:~2 .... ..........i

. . . .

. . . . . . . .

~.............. "

. . . . . . .

. . . . . . . .

Fig. 5-95. An equivalent circuit schematic is obtained when four crosses are linked together with constant pressure (voltage) on both sides. Around each node, labelled 1, 2, 3 and 4, the value of each of the four resistors enclosed in the dotted square is 89k i. If the medium was anisotropic, then the resistances on the horizontal and vertical arms of the resistor cross would have different values. Refer to Fig. 5-82. (After Saucier, 1992, fig. 4; courtesy of Elsevier Science Publishers B.V.)

equivalent resistance between the midpoints of the edges is 1/k. For D-dimensional space it is 1 / k L D - 2, where L is the characteristic length of the block and that the viscosity ( ~ ) = 1 (Saucier, 1992). In the region of the reservoir space where the permeability is non-zero, the permeability field can be covered with a regularly-spaced cubic grid of mesh 6. For the case of a multifractal permeability field, Saucier (1992) proposed that this field can be characterized by the behavior of its multifractal generating function X q(5). A multifractal permeability field is defined by studying the cumulants or order q of ,tt{Si(6)} : L((~)-

.~[~t{Bi(~)}]q ,

1

(5-113)

where on a grid each D-dimensional cube of size 6 is denoted by B(6) and #B(6) is, therefore, the sum of the permeabilities of all the grid blocks contained in the region of the reservoir under consideration. It is possible to relate the scaling behavior of X ( 5 ) with 6 for different values of the moments of order q with the multifractual spectrum. The generating function for multifractal fields exhibits a scaling behavior over a wide range of scales and can be expressed as: L(6)

_ ~ x(q),

(5-114)

where in general, the mass exponents r ( q ) are a standard probabilistic tool representing measures, called cumulant generating function. This function (r(q)) depends nonlinearly on q.

425 The scaling properties of the effective absolute permeability of multifractal permeability fields is explored for two constructions (deterministic and random cases) using multiplicative processes.

Deterministic permeability fields. In the deterministic case (properties are measurable at any point), Saucier (1992) showed that the effective permeability k(6) of a region of size 6 centered about a point x was found to scale according to" k(~)-~ ~(x)-v,

(5-115)

where a(6) is the local point-wise scaling exponent of the permeability field, a is commonly known as the local singularity strength, and ), is an exponent determined by the weights used in the multiplicative process. One impact of multifractals has been the study of turbulence, where it was found that local dissipation of kinetic energy in experimental one-dimensional cuts of fully developed turbulence can be described by a simple multifractal spectrum (Muller et al., 1992). Following this approach, Saucier (1992) constructed a multifractal field using a multiplicative process, such as the multifractal cascade model (Fig. 5-96) for

t

I r=L

I-

It

i-

~., '

{I

I~

' I

r=

|

r :

L

L

I

I I I a,.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

~, .

.

.

.

.

r=q

Fig. 5-96. One-dimensional version of a cascade model of eddies. Each eddy breaks down into two new ones. The flux of kinetic energy to smaller scales is divided into nonequal fractions Pl and P2. This cascade terminates when the eddies are of the size of the Kolmogorov scale, rl. (After Meneveau and Sreenivasan, 1987, fig. 3; reprinted with the permission of the American Physical Society.)

426

n=O

8o=1

wl

w2

81 - 112

n=l w3

w4

wlwl

wlw2

~I

wlw3

wlw4

~

~4

w3wl

w3vv2

w4wl

w4w2

w3w3

v~w4

w4w3

w4w4

52 = 1/4

n=2

Fig. 5-97. First two steps of construction of a deterministic multifractal two-dimensional permeability field from top to bottom. (After Saucier, 1992, fig. 5; courtesy of Elsevier Science Publishers B.V.) turbulence presented by Meneveau and Sreenivasan (1987, 1989). This model reproduces the flux of energy from larger to smaller scales in turbulent fluid flow. Figure 5-97 illustrates the first two steps (n = 2) in the construction process for the two-dimensional permeability field. The multifractal permeability field can be characterized by the behavior of its generating function Xq(fi) and is defined by using Eq. 5-113. The summation extends over all the cubes in covering of the field. In Fig. 5-97, the unit cube B(6o) of size rio is shown to be divided into 2 D identical cubes B (i) (ill) of size fi~ = fio/2 (here Saucier used tim = fio2-m) 9Each of the sub-cubes has an assigned weight w i, i = 1, . . . . 2 D (the process involves 2 D weights w i >_ 0, i, . . . . 2D).

427 The process is repeated on each subcube: B(i)(61) is divided into 2D cubes of size 62, which were assigned the weights wiw~;j = 1 , . . . S a 2 ~. Saucier (1992) stated that this process is continued n times down scale until a scale 5, = 2-" is reached. 6 is known as the homogeneity or inner scale and is where the permeability field becomes homogeneous. For simplicity, Saucier chose this example of the multiplicative process to be conservative, that is, the total measure is conserved in the construction by imposing on the weights the constraint S,w~= 1. This implies that p{B(5o)} remains equal to unity at each cascade step and the measure of a cube B(Sm) takes the form: ri

u{B(6m)} = w(a,) w ( a 9 . . . W(~m) ,

(5-116)

where W(6k) denotes a multiplier at 6k (W(fik) can be equal to any of the 2 ~ values of w~). Different strings of multipliers w(5~) w(fiz) . . . W(~m) correspond, therefore, to different cubes B(6~) (Saucier, 1992, p. 386). Figure 5-98 shows a permeability field obtained by Saucier after 7 cascade steps with a two-dimensional multiplicative process. It should be noted that the construction is composed of a Sierpinski gasket pattern, which is based on the contraction mapping defined by Eq. 5-116. Demko et al. (1985) reviewed the feasibility of using iterated function systems (IFS) in computer generated graphics to geometrically model and render two- and three-dimensional fractal objects, such as the Sierpinski gasket and carpet.

Fig. 5-98. Sierpinski gasket generated from a two-dimensional permeability field constructed with 7 cascade steps and 4 different weights (w I = 0.35, w 2 = 0.05, w3 = 0.15, w4 = 0.45). Dark areas represent regions of low permeability, whereas the bright areas are regions of high permeability. The pattern represents a multifractal adaptation of a uniform Cantor set having different weights (multipliers). (After Saucier, 1992, fig. 6; courtesy of Elsevier Science Publishers B.V.)

428 Saucier (1992) also studied the effective permeability of the deterministic multifractal permeability field as a function of scale. He posed the following questions: "Given a cubic ball B(fi) of size 6 centered on a point x, how does the effective permeability of the medium enclosed in Bx(6") vary with 6 when x is fixed? .... How does it vary if 6 is fixed but when x varies?" Saucier's solution is similar to that of Eq. 5-116. The permeabilities at the homogeneity scale fin are designated by/6,, ) (Sn), V = 1, 2 , . . . , N(n), where N(n) = 2 nD. The effective permeability of the porous medium contained in Bx(Sm) is kn(fim) for a permeability field constructed with n steps (fi = 2-m and m < n). Referring to Fig. 5-85F, all the kn(Sn) contained in Bx(~n) share a string of common multipliers w ( f i , ) . . . W(~m). The permeabilities at the homogeneity scale (6n) are expressed as: (v) k(~n)

= w((~l) . . .

W(~m)k~V_m ' (~n_m) ,

(5-117)

(v)

where v = 1 , 2 , . . . , N ( n - m), and k_m(~n_m) are the permeabilities at the homogeneity scale generated by the same multiplicative process, but with only n - m cascade steps. Saucier's (1992) conceptual model shown in Fig. 5-85F is of the one-dimensional multiplicative process (D = 1) having four cascade steps and two different weights w~ and w 2. The permeability field enclosed by the horizontal bracket has an inner scale ((54 = ( 89 All the permeability values in this interval share the same multipliers at scales fi, and fie SO that w(fi,) = w2 and W((~2) = W 1. The permeabilities in the horizontal bracket can be expressed by the form: (v)

(v)

k,( fi2) w( fi,)w( fi2)k2( fi2) ,

(5-118) (v) where k4(82) is a permeability generated by only the part of the cascade process indicated by the vertical brackets, i.e., with only two cascade steps (Saucier, 1992, p. 390). The general equation where kn(fio) is the effective permeability of the whole permeability field constructed with n cascade steps is derived from Eq. 5-118: =

k(~m) -- js

} k _ m((~o) 9

(5-119)

Saucier (1992) showed that kn(~o) could be determined by using a recurrence relation between kn+ ,(rio) and kn(6o). The conceptual model for his approach is illustrated in Fig. 5-99. A two-dimensional permeability field -~n was constructed with n cascade steps. By rescaling and rearranging permeability values, a new effective permeability field ~n + 1 was created. The approach in constructing .~, § consists of: (1) constructing 2 D copies of ~n and scaling them down by a factor of 89(Fig. 599a); (2) multiplying all the permeabilities k(n) (fin) at the homogeneity scale fin by w i for each copy (# i, i = 1 , . . . , 2D); (3) arranging the new fields in a 2 D array with the same spatial order as the w ~sin ' the multiplicative process yielding a new permeability field "qn§ with n + 1 cascade steps (Fig. 5-99b); and

429

kn(1)

kn(1)

Xl/2 kn(1)

A

-

kn(1)

w+ kn(1)

w2

kn(1)

kn(1)

B w3 kn(1)

w4 k.(1 )

RSRG

kn, l(1)

C

Fig. 5-99. A two-dimensional permeability field constructed with n cascade steps. (A) Four copies of the permeability field (3n) are produced and scaled down by a factor of 89 (B) For each copy #i, i = 1, 2, 3, 4, all the values of permeabilities are multiplied by w~ to create the new effective permeabilities, and then arranged in a 2 x 2 array resulting in a new permeability field 3 n § l = 1 , constructed with n + 1 cascade steps. ( C ) - The real space renormalization group method is used to compute the new effective permeability according to k, +1= g(Wlk,(1), w2kn(1), w3k.(1), w4kn(1)). (After Saucier, 1992, fig. 8; courtesy of Elsevier Science Publishers B.V.)

430 (4) by using the RSRG method (Fig. 5-99c) to compute the effective permeability according to"

o f ~ n + 1'

k+

1(~o) --

f(Wl,W2,....

, WN(1))k(l~o) ,

(5-120)

which is a simple renormalization equation for the effective permeability kn(fio) (Saucier, 1992, p. 391). Iterating Eq. 5-120, setting ko(fio) = 1, and eliminating n using fin = 2-n results in: kn(fio) = finr,

(5-121)

where the scaling exponent y = - l o g 2 (f(w 1,w2 , . . . . ,wN(I) )) " Equation 5-121 shows that the effective permeability of the whole permeability field scales with the inner scale fin, and y is determined by the function f and by the 2 Dweights wj. Saucier (1992) stated that for multifractal measures a pointwise scaling exponent a(x) is usually defined such that p {Bx(fi) } ~ fi~ (x) as ~; --->0 (Halsey et al., 1986). If the inner scale fi is finite, this statement is expressed as" P{Bx(b-)} ~ fia(x),

(5-122)

when fin ~ fi ~ rio, and Eq. 5-119 becomes: a (x) - ~,

kn(6m) 6m

(5-123)

by using Eqs. 5-121 and 5-122, and fin- m = ~n/~m' when fin <
Random multifractalpermeabilityfields. Saucier (1992) expanded on the conservative multiplicative process showing how the random multiplicative process can also be constructed. Random permeability variations are expected for blocks of porous medium coming from different locations within the reservoir. In the random case, the permeability k(fi) is a scale-dependent random variable that is proportional to and satisfies the relationship: <[k(6)]q

> ,~ ~ D +t(q)-~,(q)

(5-124)

where < > denotes the averages over many samples of [ k ( 6 ) ] q, v(q) is the order-q exponent of the multifractal permeability field and y(q) is another nonlinear function determined by the joint probability distribution of the weights used in the multiplicative

431 process (Saucier, 1992). (The reader should refer to Figs. 5-85F and 5-99 for additional information and visual representations of the weights used in this procedure.) The transport properties are determined by the multifractal spectrum of the permeability field (Eq. 5-124). Saucier (1992) pointed out that in reservoir modeling, Eq. 5124 relates the variance of the permeabilities measured at the core scale to the variance of the effective permeabilities at the grid block scale used in the flow simulators. A proper description of the scaling properties of the permeability field in carbonate reservoirs is necessary in order to generate realistic effective permeabilities, and consequently, to predict with greater accuracy the large-scale flow through the rocks. Random variations in the permeability field are expected in core samples coming from different parts of a reservoir. The effective permeability k(L) at scale L can be regarded as a random variable that depends on a length scale parameter L (Saucier, 1992). In order to characterize the random variations of k(L) by the scaling behavior of its moments, one considers the quantities <[k(L)]q > as a function of L and the real parameter q. Saucier (1992) showed that for random multifractal permeability fields these moments satisfy: < [ k ( Z ) ] q > ,~, Z ~(q) ,

(5-125)

where ~(q) is a nonlinear function of q. Saucier's approach is twofold: (1) to derive an expression of ~(q) using the RSRG method, and (2) to adapt the formalism used to derive the effective permeability of deterministic multifractal permeability fields to random multifractal fields. The permeability fields for the deterministic case generated with the random multiplicative described by Eq. 5-114, and starting with Eq. 5-117, resulted in the following equation: k (6)

= w ( 6 , ) . . . W(

)kn_m(6o).

(5-126)

The random version of Eq. 5-126 is simply: d

kn(6m) =

w(6~)... W(6m)kn_m(6o),

(5-127)

d

where = stands for equality in probability distribution, and k m(6O)is a random variable independent of the W(fk)'s, where W signifies the weights in the random multifractal permeability fields. By raising Eq. 5-127 to the power q and averaging yields: <[k(t~m)]q > = < mq > m < [ k _ m(~o)] q >.

(5-128)

Pursuing the same logic and iteration as in his derivation for the deterministic case, Saucier arrived at the following simple renormalization equation for the moments of the effective permeability: <

> -

w , < , ) ] q > n <[ko(6o)]q >.

(5-129)

432 Employing ko(~o) = 1, and eliminating n with ~n = 2-n yields: ~(q) <[kn(6o)] q> = "n ,

(5-130)

where the scaling exponent ~q)=-log2(<[f(W~,W2, . . . . , WN~l))]q>).Compare Eq. 5130 with Eq. 5-121 for the deterministic case. By eliminating m in Eq. 5-128 with ~m = 2-m, using the relationship for the mass exponents r(q) = - D - 1og2(< Wq >), replacing Eq. 5-130 in this resulting expression, and using ~n-m = ~n/~mresults in an equation comparable to the deterministic Eq. 5-123" D + t(q)- ~(q) ?(q)

<[k(~m)lq> = ~m

~n"

(5-131)

Saucier (1992) states that Eq. 5-131 appears to be the first analytical derivation of the effective permeability of random multifractal permeability fields. The relation between the scaling exponents of the effective permeability, as defined by Eq. 5-125, is" ~(q) - D + v(q)- ~(q).

(5-132)

A multiscaling permeability field, therefore, gives rise to a multiscaling effective permeability field. Saucier (1992) commented that the mass exponents r(q) determined directly, but not completely, the permeability scaling exponents ~(q). He further stated that the permeability exponents ~(q) are not trivially related to the mass exponents r(q), because f is a non-linear function. Equations 5-115 and 5-124 are approximate results derived with the real space renormalization group method (Saucier, 1992). Measuring both r(q) and ~q) requires three-dimensional information about the permeability field (Saucier, 1992). This is a disadvantage to this method. Three-dimensional data usually are not available, inasmuch as most of the data come from wells that are one-dimensional vertical cuts through the reservoir. Saucier (1992) recognized that recovering three-dimensional information from one-dimensional cuts is a nontrivial problem. It has been shown in this chapter that information involving the anisotropy, stratification, and heterogeneity of carbonate reservoir properties is necessary to characterize the reservoir. If the permeability field was locally isotropic, or if the anisotropy could in some way be characterized, then there could be an effective solution to this problem. The role of anisotropy in fluid flow through porous carbonate rocks and the ability to extract information about anisotropy from one-dimensional cuts are the kernels to effective carbonate reservoir characterization and ability to increase productivity. Fractal reservoirs

The concept of fractal reservoirs has appeared in the recent literature (Chang and Yortsos, 1990; Beier, 1990; Chakrabarty et al., 1993). This term could lead to confusion and might not be appropriate, inasmuch as all reservoirs can be shown to contain properties that were described as fractal. Chang and Yortsos (1990) defined a fractal reservoir as consisting of a fracture network embedded in a Euclidean object (matrix). They envisioned such a reservoir as containing brittle and highly fractured rocks,

433 with fracture scales ranging from centimeters to micrometers. Using this concept, it is apparent that carbonate reservoirs can be classified as fractal reservoirs. Barton and Larsen (1985) first showed that complex two-dimensional fracturetrace networks can be described quantitatively using fractal geometry. Open-fracture networks are the primary avenues of transport for oil and gas through the reservoir's matrix. In contrast to fracture flow, matrix flow generally is significant only for very low transport rate values. Fracture flow dominates matrix flow in carbonate reservoirs owing to fracture permeabilities being up to 7 orders of magnitude greater than matrix permeabilities. Velde et al. (1991) showed that different failure modes, consisting of shear, tension and compressional relaxation, can give different fractal relations. The reader is referred to Chang and Yortsos (1990) and Acuna and Yortsos (1991) for further applications of fractal geometry to flow simulation in networks of fractures. The classical approach to determining the nature of fractured carbonate reservoirs and their properties are stressed in the present two volumes.

Concluding remarks In reservoir analyses, fluid-flow simulation results are used extensively as reservoir performance predictions upon which to base economics for reservoir management decisions (Bashore et al., 1993). It was shown in this section that the analysis of the productivity of carbonate reservoirs in the near future will be based on geostatistical measures when "good" reservoir geological and geophysical data, computational time, and the expertise are readily available to the operator. Creating an improved characterization of carbonate reservoirs helps to predict and decipher productivity problems. A basic assumption is that geological properties can be regarded as regionalized variables that are distributed in space and have an underlying structure in their apparent irregularity. Knowledge about fractal scaling exponents obtained from bivariant statistical methods is used in reservoir characterization as described in the above discussions. Geostatistical interpolation using kriging with a fractal variogram is a technique that regards the reservoir-property distribution as a random function. The random function is defined by a spatial law, which describes how similar values drawn from different locations will be a function of their spatial separation (Hewett and Behrens, 1990). The property distributions will have a prescribed spatial correlation structure (fractal model) and matched measured property values at the sampling points. Muller et al. (1992) made a very strong case for the use of multifractal scaling, rather than employing fractal scaling exponents obtained from bivariant statistical methods. Multifractal statistics gives both moments and correlations. By knowing the multifractal spectrum one can compute all moments at all length scales for which the scaling holds, offering a wealth of statistical information. Multifractals provide a powerful tool for the characterization of irregular signals (Muller et al., 1992). Geostatistical methods of preparing the reservoir property distributions for use in reservoir performance simulations involves scaling-up of the data and scaling within the simulator. The scaling-up procedure of a grid is diagramatically shown in Fig. 5100. At present, properties such as permeability at the interwell scale are being predicted using these advanced numerical techniques involving fractals and multifractals.

434

13

C Fig. 5-100. Successive scale-up (coarsening) procedure used in grid simulation models. (A)- Fine-grid model, representingsmall-scalereservoir-flowheterogeneities.(B) - Replacementof the fine-scaleblocks by a single-grid block at the medium scale after the effective properties were generated at the fine-grid scale. (C)- Coarse-grid reservoir model representing the fine- and medium-grid models. Saucier's (1992) study revealed that the multifractal scaling of a permeability field implies that the scaling of effective permeability can be generated by deterministic and random multiplicative processes (refer to Eqs. 5-115 and 5-124, respectively). Both equations give only approximate results with the real space renormalization group method. The effective transport properties of porous media are determined, via Eq. 5-124, by the multifractal spectrum of the permeability field. Scaling properties measured on the permeability field along wells at the core-plug scale can be used to predict the statistics, such as the variance, of effective permeabilities at larger scales in carbonate reservoirs. One can only hope that in the next five years the petroleum industry will have the ability to directly generate large-scale descriptions of a carbonate reservoir using multifractals. Lastly, it should be remembered that modeling does not have to produce an exact geologic numerical model, but rather, the flow-simulation only has to deliver resuits similar to the output of production data. If modeling forecasts do not match

435 future field performance data, then the operator needs to look not only at the geostatistical model and the application limits described by Perez and Chopra (1991), Gray et al. (1993) and Mesa and Poveda (1993), but also at production practices and equipment.

LABORATORY AND FIELD CHARACTERIZATION OF CARBONATE RESERVOIRS

The writers have taken the reader in this chapter from the basic descriptions of carbonate reservoirs to conceptual models, and finally to numerical models. Now, the focus will be on some methods of identifying, measuring, and evaluating microscopicand mesoscopic-scale heterogeneities (Fig. 5-37) in carbonate reservoir rocks using laboratory and field tests. The analysis of reservoir samples, such as fluids, rock cuttings and cores, involves procedures that can be complex and contain many stages between the reservoir and the final measurements and interpretation. Quality control in reservoir sampling, testing, and data analysis will help to ensure valid data as input into the economic prediction of performance. Such quality control procedures in core analysis were discussed by Heaviside and Salt (1988).

Laboratory~outcrop characterization of heterogeneity Carbonate reservoirs with large permeability contrasts are common and are difficult to evaluate in the outcrop and laboratory. Flow heterogeneity in laboratory core samples of carbonate rocks can significantly influence the experimental measurement of fluid flow and displacement characteristics used in evaluating oil recovery methods. There has been a great deal of speculation as to the influence of variations in pore size, shape, and degree of connectivity on oil recovery processes in carbonates. Also, a great deal of thought has been given to the interpretation of carbonate reservoir performance data. Previously, the only alternatives to using laboratory models and their generated test data was the extrapolation of primary recovery data obtained by partially depleting a field, or obtaining production information from pilot texts. As shown here, employing numerical models is another viable method, especially if the models can tie together reservoir properties and petrophysical data from outcrop studies. Conventional laboratory methods used in core analysis of carbonate rocks were discussed in Chapter 3. It has been recognized that predictions of reservoir performance based on displacement tests using small-diameter carbonate core samples (same size as sandstone cores) can often be misleading. This is due to the improbability of obtaining a representative sample in such small-diameter samples. Special core analysis using novel techniques such as petrographic image analysis from thin-sections, minipermeameter, and computerized tomographic scans appear to be one way to characterize anisotropic carbonates in the laboratory. The application of petrographic image analysis to generate fractal and multifractal characterizations of carbonate rocks was discussed in the previous section. A key to the usefulness of these applications is to tie their results into carbonate reservoir models, thereby improving the ability to forecast production.

436

Minipermeameter application The first documented use of an apparatus to measure local permeabilities was by Dykstra and Parsons (1950), followed by Morineau et al. (1965). Eijpe and Weber (1971) employed a minipermeameter to measure air permeabilities of consolidated rock and unconsolidated sand. The minipermeameter is a rapid and non-destructive method of measuring permeabilities in situ or using core samples. Goggin et al. (1988) performed a theoretical and experimental analysis of minipermeameter response, which included gas slippage and high-velocity flow effects. The minipermeameter (mechanical field permeameter) gauges gas-flow rates and pressure drop by pressing an injection tip against a smooth rock surface. The gas flow rate and tip pressure measurements of the minipermeameter are converted through the use of a shape factor depending only on an elliptical tip having different shape factor values and sample geometry. Determination of permeability anisotropy on a core plug was performed by Young (1989) using Goggin et al.'s (1988) permeameter. Jones (1994) described the development of a non-steady state probe (mini)-permeameter. A steady-state minipermeameter was modified by removing the flow controller and adding reservoirs of different calibrated volumes. The time rate of pressure decay as nitrogen flowed from any one or all of these reservoirs through the probe and into the rock sample yields a direct measure of the permeability. Time to measure permeability was reduced from 20 min per sample to around 35 sec (Jones, 1994). Caution must be expressed in using this permeameter to obtain accurate measurements of permeability in vuggy carbonates, carbonates with abundant moldic porosity, and/or microfractures. As Grant et al. (1994) pointed out, these conditions would violate the regular gas flow path geometry. The application of the "field" permeameter is useful for capturing fine-scale heterogeneity patterns in carbonate rocks lacking fracture and abundant vug porosity. Two separate field case studies employing a field permeameter are presented. These cases show the utility of using field-measured permeability data in statistical flow models to account for carbonate reservoir heterogeneity. Lawyer Canyon test site, New Mexico, U.S.A. Chevron Petroleum Technology Company (Grant et a1.,1994) and the Texas Bureau of Economic Geology (Senger et al., 1991; Kittridge et al., 1990) applied the mechanical field permeameter to the study of vertical and lateral spatial permeability variations in a continuous outcrop of the San Andres Formation on the Algerita Escarpment in the Guadalupe Mountains, Otero County, southeastern New Mexico, U.S.A. (Fig. 5-101A) Two broad goals of their studies were: (1) To establish a geologic framework for a reservoir model, which was compared by Kittridge et al. (1990) to the Wasson Field located some 140 miles (225 km) to the northeast in the Midland basin of west Texas, U.S.A. The regional geologic setting and correlation between the numerous San Andres/Grayburg reservoirs are poorly understood. Such correlations are important inasmuch as the reservoirs of the San Andres and overlying Grayburg Formations have a combined cumulative production of 7.7 billion bbl of oil (Grant et al., 1994). (2) To conceptualize a reservoir model and use this model as a basis for studying the results of hypothetical waterflood simulations and reservoir flow. These studies addressed the influence of lithofacies in the prediction of San Andres

O

o

(!" I > tu

~_%, 9..._

Loc~ro

o o

' . 11: , : :h. . : : .~ :.......::...: i .... ' fill::! :Ei~..:~::::

::::::::::::::::::::::

ii:'i:~i.~ii:i:~:~i:.:;-~i.:i~i~:~:i~i~~!ii!!~i~:~:'~!:~, ....~

~

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=

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.

.

.

.

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.

........ .~.-.-.-.-.-.-.-..:

San And . . . . . d Grayburg (undivided) Undifferentiated basin facies

~o ~,~,

m

8

,oo13o O-x-O

]

1000 DEPOSITAL FACIES (FLOW UNITS) ~ F I o o d e d shelf, tidal shelf (1) [-'-'] Shallow shelf II (5)

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.

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.................................. -:..l!!!!~:!~:!i!!!iiiiiiii~::ii::ili ............ :

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2000 M D

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1 ~ Shallow shelf II (6) ~ accreticrest on'Bar setsbar(10) 1"7;171Shallow shell I, Shallow shelf II, bar crest, bar top (7) ~ 1 Bar crest (11) ~ S h a l l o w shell II, bar top (4) ~ Shallow shelf II, bar crest, bar accretion sets (8)

1000

~

,t

300

Grainstone (10 - 100 m)

[-']Shallow shelf I (2) L---]Shallow shelf I (3) S

~ ~ I'~

...... .....

:::::::::::::::::::::::::::::::::: ......~ ! i : i i ~ - : ' ~ i ~ i ; ' - ....... 17-~"':':':':...............

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----:----- ......... -

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ft . . . . . . . . .

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600 m

D

D

Grain dominated packstone (1-10 m)

Mud dominated pack wackestone (< 1.0 m) Tight mudstone fenestral caps (< 1.0 m)

Separate vug grainstone (1 - 10 m)

C

200Q fl

.,

E]

Parasequencenumber

Fig. 5- 101. Location, regional geology, distribution and geometry of facies and rock-fabric flow units for the L a w y e r Canyon site, N e w Mexico, U.S.A. (A) - Location and geologic map of the test site in the Guadalupe Mountains. (B) - Distribution and geometry of depositional facies mapped in the upper San Andres parasequence window. (C) - Rock-fabric flow units of the upper San Andres parasequence window. (After Senger et al., 1991, figs. 1, 2 and 9; courtesy of the U.S. Department of Energy.)

4~ ---I

438 carbonate reservoir performance and reserves. The low recovery efficiency of 30% makes these reservoirs prime candidates for using improved field development strategies discussed previously in the incremental recovery section of this chapter.

Lithofacies and permeability heterogeneity. The San Andres Formation ranges in thickness from 1,100 to 1,200 ft (335 - 366 m) along the Algerita Escarpment. The geologic units are known to be continuous between the Lawyer Canyon outcrop and the Wasson Field. At both locations, the formation has similar attributes making the outcrop a good analog for the producing interval in Wasson Field (Kittridge et al., 1990, table 7). Senger et al.'s (1991) and Kittridge et al.'s (1990) field investigations were limited to study grids and a vertical transect at a specific site located on the north wall of Lawyer Canyon. Results from the study grids were integrated into Chevron's investigations by Grant et al. (1994). The largest sampling interval was 10 ft (3 m) in one grid area, whereas data were collected on 1-ft and 0.5-ft (0.3-m and 0.15-m) spacing in six smaller grids, and on a 2-in. (0.05-m) spacing for the vertical transect. Geological mapping of the San Andres dolomites and grainstones, which form a series of upward shallowing parasequences some 1 0 - 4 0 ft (3 - 12 m) thick (Fig. 5-101B), permitted depositional and diagenetic processes to be correlated with the variability in areal and vertical measured permeability values. The carbonate cycles at the Lawyer Canyon site coarsen upward. Parasequence boundaries at the site are typically denoted by low-permeability mudstone/wackestone beds displaying variable degrees of lateral continuity ranging from several hundred feet to more than 2,500 ft (762 m). The ramp-crest facies (dolograinstones) extends approximately 5 miles (8 km) in a dip direction, passing seaward into fusulinid dolopackstone-dominated outer ramp deposits and landward into algal-rich inner ramp dolomudstones and dolowackestones (Grant et al., 1994). The dolomudstone beds at Lawyer Canyon are potentially important as flow barriers (Fig. 5-101 C) (Senger et al., 1991). Three wells (Algerita Nos. 1, 2 and 3) were drilled by Chevron and cored adjacent to the outcrop. Algerita 2 and 3 were logged using gamma-ray and lithodensity tools. Grant et al. (1994) used a hand-held scintilometer to create gamma-ray log traces along four vertical transects. The logs were used for lateral correlation. A total of 1,584 permeability measurements using the field permeameter were made at the Lawyer Canyon site by the Texas Bureau of Economic Geology study groups. Grant et al. (1994) performed some 2,748 permeability measurements on the 1 Algerita core in order to evaluate sampling strategies and further investigate vertical permeability trends. Both Chevron's and BEG's investigations concentrated on cycles 7 through 9. In addition to 600 permeability measurements collected along a 288-ft (88m) horizontal transect in the bar-crest lithofacies of cycle 9, a total of 1003 permeability measurements were obtained by Grant et al. (1994) using four vertical transects across cycles 7 - 9 (Fig. 5-101C). Geostatistical analyses indicated that permeability correlation lengths decreased with decreasing sample spacing, and that different carbonate rock fabrics exhibited different mean permeabilities. Permeability variability in the outcrop was not confined to bed-to-bed changes, but there was substantial variability within individual units by as much as five orders of magnitude. Vertical transect data exhibited rapid

439 variation in permeability and porosity over a short vertical interval. Grant et al. (1994) noted an upward-increasing trend in geometric mean permeability and attributed the trend to the lithofacies arrangement within a depositional cycle (dolomudstones at the base and bar-crest dolograinstones at the top). They observed that these upwardincreasing permeability trends were consistently uniform from cycle to cycle. The cycles, however, are punctuated locally by low-permeability zones, even in the barcrest grainstone facies, and was attributed by Grant et al. (1994) to local subtle textural and diagenetic changes. The vertical correlation range as determined by Grant et al. (1994) was approximately 18 ft (5.5 m). This corresponded to the spacing between fine-grained mudstones and the grainstone lithofacies within and between cycles. The correlation range approximately equals the average cycle thickness and supports the conclusion that the depositional cycles may constitute a fundamental flow unit in analogous cyclic shelf- or ramp-carbonate reservoirs (Grant et al., 1994). At the site, Kittridge et al. (1990) observed two distinct scales of spatial correlation for San Andres permeability and porosity depending on the spacing of the data used. Predicted correlation lengths were 3 - 5 ft ( 0 . 9 - 1.5 m) for 1-ft and 0.5-ft (0.3-m to 0.15-m) data spacing and 0.25 ft (0.08 m) for the 1-in. and 0.5-in. ( 0 . 0 3 - 0.015 m) data. It is obvious from these results that, within the parasequences, there is a distinct variability of facies and petrophysical properties which are at scales well below those of interwell spacing of 6 6 0 - 1,330 ft (201 to 405 m) common in the San Andres reservoirs. Senger et al. (1991) extended Kittridge et al.'s (1990) outcrop/subsurface comparisons of heterogeneity study by: (1) characterizing the permeability of a grainstone parasequence (parasequence 1) of the Lawyer Canyon outcrop; (2) investigating the small-scale heterogeneities using waterflooding simulations of a hypothetical two-dimensional reservoir based on the grainstone facies that formed parasequence 1 at the outcrop; and (3) using the entire upper San Andres outcrop to conceptualize the reservoir-flow model. The upper portion is more typical of the large-scale complexity of subsurface reservoirs formed in a ramp-crest depositional environment than is a single parasequence, such as grainstone parasequence 1. Grant et al.'s (1994) permeability and fluid-flow modeling focused on cycles 7 - 9 by studying the effects of the heterogeneity pattern on uncontacted mobile oil (displacement efficiency) and on viscous, capillary, or gravitational crossflow (vertical sweep efficiency).

Permeability distributions. Characterization was accomplished by generating a series of"realistic" permeability distributions that accounted for the underlying permeability structure and the uncertainty of measurement data. To evaluate heterogeneity at different scales, permeability values from the different grids were analyzed using fitted spherical model variograms. The reader is referred to Hohn (1988, p. 25) for an explanation on modeling an observed semivariogram. Numerical waterflood flow simulations were performed using selected permeability realizations, which were designed to characterize interwell heterogeneity and to represent heterogeneity by appropriate average properties (Senger et al., 1991). A petrophysical/rock-fabric

440 approach was used to quantify the geologic framework of the reservoir-scale flow model. Figure 5-101C delineates the rock-fabric flow units of the upper San Andres parasequence window. These rock-fabric flow units exhibited significant differences in mean permeameter-measured permeability values, with the grainstone having the highest values and the mudstone having the lowest values. The bar-crest and baraccretion-set facies have the highest mean permeability of log k = 1.1 mD. The mapped parasequences are characterized by different fabric and facies combinations creating different hydraulic properties for each parasequence. Referring to Fig. 5-101 C, the mean permeabilities in grainstone-dominated parasequences 1, 2, 7, and 9 are greatly higher than those in the parasequences 3, 4, 5, 6, and 8 that consist of packstone and wackestone. A kriged permeability map was constructed for the northern half of parasequence 1 using fitted variogram models (vertical 5-ft grid horizontal and 50-ft horizontal variograms) (Fig. 5-102). A drawback to kriging is that it tends to average permeability over larger areas, ignoring small-scale heterogeneity. Senger et al. (1991), therefore, produced some 200 stochastic permeability realizations using simulations for the grainstone facies in parasequence 1 (Fig. 5-101 C) in order to account for small-scale permeability heterogeneity. Their model extended laterally from 0 to 1,050 ft ( 0 - 320 m) and is 17 ft (5.2 m) thick, with block sizes of 5 ft by 1 ft (1.5 by 0.3 m). The simulations were conditioned to permeabilities measured along vertical transects spaced about 25 ft apart and incorporated the correlation structure from the variograms. Two of the distributions were chosen for flow simulations. These two permeability distributions represented the maximum and minimum lateral continuity of domains having permeability values greater than 50 mD (0.049 ~m2). A comparison of the two permeability realizations shown in Fig. 5-103 does not reveal noticeable differences; however, the spatial variability exhibited in the grainstone variograms (Fig. 5-102) are preserved. Senger et al. (1991) pointed out that the permeability patterns appear in the variogram spatially uncorrelated because of a relatively high nugget value representing local random variability that is of the same magnitude as the sill value given in Figs. 5-102A and B. Grant et al. (1994) stated that the small-scale textural and diagenetic variations are reflected in the high nugget values at separation distances less than 1 ft (0.3 m) in vertical correlation. Two of the writers (Drs. Chilingarian and Rieke) would like to point out a very important fact, which should be kept in mind. Dedolomitization: CaMg(CO3) 2+ Ca 2§ ~ 2CaCO 3 + Mg 2§ which could occur in outcrops, will decrease porosity.

BEG's waterflood simulations (Parasequence 1). Waterflooding of the grainstone facies in parasequence 1 at the Lawyer Canyon site was simulated by Senger et al. (1991) using the reservoir simulator ECLIPSE (ECL Petroleum Technologies). The simulator was used to evaluate reservoir two-phase flow characteristics in a hypothetical two-dimensional reservoir. Water was injected along the right boundary of the hypothetical reservoir, and fluids were produced along its left boundary. Input data into the simulator included pressure data, stochastic permeability distributions, porosities, relative-permeability curves, and capillary-pressure curves. An injection pressure of 2,450 psi (17 MPa) and production pressure of 750 psi (5.2 MPa) were prescribed to control the water injection and fluid production in the model.

441 Verticol Correlotion of k Doto 0.8

.....

0.7

E

_

"i

=,.:,~u.=~,"-vv=, -~.'~ _ [

9

0.6

oI . . ,

A

l____=

Spherical m0de~, r a n q e : S f f

o ~9 0.5

A

_

9

.I,. ,;.

0.4

~d

9

0.3

'

9

O

l)

}

:

I

;

"i

0.2 i

1

O.I 0

5

I0

1,5

20

?.5

D I S T A N C E (ft)

S H O R T R A N G E C O R R E L A T I O N OF k DATA

'

] I I

I I 0"I "

0.8-

E o L_

B

~0.6

-

. = t _

_ V

0.4-

J

A v

_,r

o I0.2

0

......

-

0

10

20

30

40

50

60

70

80

DISTANCE (ft)

LO NG-RANGE CORRELATION OF k DATA O.8

9

0.7

-

~

~

. . . .

,, ! . ~ :

~

-

----'~"Nesled s ,

:

. . . . . .

,

~

9

E 0.6 -

C

~ 9~ _ .

L_

9

-

9 0.4-

o

-r

().3

0

200

400

6L~O

800

1000

DISTANCE (fl)

Fig. 5-102. Sample variogram models for the entire permeability transects from the grainstone facies in San Andres parasequence 1. ( A ) - Vertical fitted variogram model. ( B ) - Short-range horizontal fitted variogram model based on the 5-ft (1.5-m) grid. (C) - Long-range horizontal variogram model, based on all transects spaced about 50 ft (15 m) apart. (After Senger et al., 1991, fig. 14; courtesy of the U.S. Department of Energy.)

442

LOG P E R M E A B I L I T Y [ mD ] COND.SIMULATION:REAL!ZATION No.7 .

.

.

.

!6

1.:2

o

~,~

300

4~,

soo

750

900

........ ~.oso

LOG PERMEABILITY[ mD ] COND.SIMULAT!ON:REALIZAT!ON No.1 1 6. 129

0

1~ :

~

450

600

750

~

1050

B D i s t a n ~ in Feet

i-i..5 ~1.5-2

~ < 0

Fig. 5-103. Comparison of two conditional permeability distributions (see Table 5-XXII). (A)-Realization No. 7 represents the minimum lateral continuity of domains having permeability values greater than 50 mD. (B) - Realization No. 11 represents the maximum lateral continuity of domains having permeability values greater than 50 mD. (After Senger et al., 1991, fig. 17; courtesy of the U.S. Department of Energy.)

443 Fluid property input data assumed in the waterflood simulations are: (1) oil viscosity = 1 cP, (2) water viscosity = 0.804 cP, (3) oil specific weight = 55 lb/ft 3, (4) water specific weight = 64 lb/ft 3, (5) residual oil saturation = 0.25, and (6) residual water saturation = 0.1. The porosity-permeability relation was based on a linear transform representing intergranular pore characteristics in a grainstone: k = (5.01 • 10m)q~8.33,

(5-133)

where k is the intrinsic permeability (mD) and ~bis the fractional intergranular porosity. Equation 5-133 was established from core-plug analyses at the site. This equation was used to calculate porosity distributions from the stochastic permeability realizations shown in Fig. 5-103. The derived porosities typically ranged between 5 - 25%. Similarly, Senger et al. (1991) developed an empirical equation (for grainstone) relating the fractional water saturation (S), to the fractional intergranular porosity (~b), and capillary pressure (as the height in feet of the reservoir above the free-water level) (h): S = 68.581 h--~

-1.745

(5-134)

9

Honarpour et al. (1986) provided two equations for determining the relative-permeability functions for oil (ko) and water ( k ) : N k

rw

-k

~

rw

I 1 --S S

--Swr or

-S

Iw

(5-135)

wr

and N =k~

~o

I

1 - S

-S

w 1 -- Sr - Swr

1' ~

(5-135)

where Sor is the residual oil saturation, S r is the residual water saturation, and N w and N o are exponents having values of approximately 3. The values were derived from fitting relative permeability data (slope of regression line from a plot of the log of relative permeability vs. log of normalized saturations) obtained from grainstones of two cores from Dune Field in west Texas, U.S.A. The relative-permeability end points k~ and k~ are 0.266 and 0.484, respectively, and were derived from the intercepts of the log-log plots of measured relative-permeability data vs. saturation (Senger et al., 1991). Senger et al. (1991) performed a series of six numerical simulations to evaluate the different effects associated with the observed heterogeneity on production characteristics in parasequence 1 at the Lawyer Canyon site. Table 5-XXII presents the statistical results of the waterflood simulations of the grainstone facies in parasequence 1. Figure 5-104 presents four relative-permeability and capillary-pressure curves used

444 TABLE 5-XXII Waterflood simulations of grainstone facies in parasequence 1, San Andres Formation outcrop on the north wall of Lawyer Canyon, Otero County, New Mexico, U.S.A. Statistics

Mean horizontal continuity (Ch) w

No.

Permeability realization

Mean log-k (mD)

Variance log-k (mD 2)

Nugget (mD 2)

Sill (m 2)

1" 2 3 4 5 6"

7 7 11 45 kriged facies-averaged

1.219 1.219 1.219 1.219 1.219 1.219

0.42 0.42 0.45 0,38 0.46 N/A

0.2 0.2 0.2 0.0 0.2 N/A

0.2 0.2 0.2 0.4 0.2 N/A

(ft) 7.53 7.53 8.82 11.95 N/A N/A

Source: After Senger et al., 1991, table 1.

* Single relative-permeability and capillary-pressure curves.

in the flow simulations. The curves represent four different porosity intervals (5 to 10 %; 10 to 15 %; 15 to 20 %; and 20 to 25 %). Residual water saturations were calculated according to Eq. 5-134 for the four intervals, and then the Sw~values were used as input to compute the relative-permeability curves using Eqs. 5-135 and 5-136. Figure 5-105 shows that the effect of small-scale heterogeneity and associated capillary-pressure phenomena on cumulative production characteristics was relatively small, and accounted for less than a 2.5 increase in sweep efficiency. The computed water saturations exhibited sharp and vertical injection fronts despite large variations in permeability, initial saturations, and capillary pressures in some of the simulations (Table 5-XXII). Senger et al. (1991) remarked that for practical purposes, the observed heterogeneity within the grainstone facies (parasequence 1) can be represented by a geometric-mean permeability distribution employing an arithmetic-mean porosity in calculating uniform initial water saturation and accompanied capillary pressure values according to Eq. 5-134. The kriged permeability distribution in Fig. 5-105 (simulation 6 in Table 5-XXII) yields a similar production-rate pattern as the conditional permeability realizations. This indicates that small-scale permeability variability has a negligible effect on the production rate and only large-scale permeability patterns need to be incorporated into the flow model for history matching (Senger et al., 1991, p.27). One should be aware that the water (driving phase) to oil (driven phase) mobility ratio M (M = kw/k x po/Pw)in the above waterflood simulations was not discussed by Senger et al. (1991). If the mobility does not change in the model, then the fluid's velocity and flow rate also would remain unchanged. As in the above waterflood simulations, where both oil and water are flowing simultaneously, it is the ratio of the mobility of the water to that of the oil which determines their individual flow rates and, therefore, the water/oil ratio. The mobility ratio is an important factor affecting the displacement efficiency of oil by water. If M = 1, then the mobilities of the displaced and displacing phases are identical. An M < 1 is favorable and the areal displacement efficiency is usually high, whereas M > 1 is unfavorable. Detailed discussion on the mobility ratio and waterflooding of carbonate reservoirs is presented Langnes et al. (1972).

445 RELATIVE-PERMEABILITY CURVES I m

A -0.1

0.1-:.

p. =

5-10 }; P O R O S I T Y 10-15% P O R O S I T Y 15-?OX POROSITY 20-25% POROSITY

L] C~ ',

FACIES AVERAGEt~ DUNE F I E L D DAT~.

9

-O.Oi

o oi-

O.Otl

'

I =

I

'

'"

I

0.2

0

'

'

|

'

0.4

I

.

_O.OOI

i

0.8

0.6 Sw

CAPILLARY-PRESSURE CURVES 250 j

,

,

I

i

=

,

i

I

_i

;

,

__

__

~

\

200~

.......

I

,

5-10% 10-15% 15-20~ 20-25Y, FACIES

,

,

I

l

i

I

I

B

POROSITY POROSITY POROSITY POROSITY AVERAGED

=

150.

t,

I00

i \\

50

, 0

w

x I

I

02

9

.

=I

-I

i

i

0.4

,

I

0.6

'

I

v

I 0.8

Sw

Fig. 5-104. Relative-permeability and capillary pressure curves used in the different flow simulations (Table 5-XXII). (A) - Relative-permeability curves used for the six waterflood simulations in SanAndres parasequence 1. (B) - Capillary-pressure curves used for the six different waterflood simulations in parasequence 1. (After Senger et al., 1991, figs. 19 and 20; courtesy of the U.S. Department of Energy.)

446 Q u

a

70.0

6o.o.

..... :,ra.-~-'--~ : - 2 ~ - ' - ~ - ' -

--

0.

I

0 ,,eC

50.0

-

40.0

-

0 U

L O

veraged permeability 0

............ Conditional permeability realization 7

C

.9 .6U 0 L Q.

30.0 -

/

(single-capillary pressure curve) Conditional permeability realization 7

/ 20.0

(multiple-capillary pressure curve) Conditional permeability realization

-

0

:,T.

II

(multiple-capillary pressure curve)

Q

Unconditional permeability realization

Io.o -

0 ..,..

45

(zero nugget, multiple-capillary pressure curve) Kriged permeability (multiple-capillary pressure curve)

E 0.0

1 0.0

I

I

I 0.2

1

I

1

I 0.4

I

I

I

ir' 0.6

I

i

i

!

!

I

0.8

T'

i LO

I

!

i

I 1.2

I

i

i

i L4

i I. 5

Injected pore volume

Fig. 5 - 1 0 5 . Cumulative oil production as percentage of original oil-in-place for six waterflood simulations in San Andres parasequence 1. (After Senger et al., 1991, f i g . 2 5 " courtesy of the U.S. Department of Energy.)

Outcrop reservoir-flow model (11 flow units). The approach taken by Senger et al. (1991) to model the large-scale effects was an elaboration of the waterflood simulation. Both the geologic model of the Lawyer Canyon parasequence window (Fig. 5101B) and the rock-fabric characterization of the depositional facies (Fig. 5-101C) were used to define the conceptual reservoir-flow model. The model distinguishes 11 flow units (Fig. 5-101B) having different average permeability, porosity, initial water and residual oil saturation values (Table 5-XXIII), and uses the same fluid properties used in the waterflood simulations. A total of 4089 irregularly-shaped grid blocks compose the model. The blocks represent the spatial distribution and the petrophysical properties of the different rock fabrics and depositional facies. Block size is 100 ft (30 m) in the horizontal direction with a variable thickness in the vertical direction ranging from less than 0.5 ft (0.15 m) to several feet. The injection and production rates were controlled by selected pressures of 4,350 psi (30 MPa) and 750 psi (5.2 MPa), respectively. Simulations were run for 20-, 40-, and 60-year scenarios. Senger et a1.(1991) assigned three different petrophysical/rock-fabric classes for nonvuggy carbonates to the five productive flow units in Fig. 5-101. The three classes (grainstone, grain-dominated packstone, and mud-dominated, <20 ~tm) were distinguished based on porosity, permeability, and saturation relationships. The relationships between permeability and porosity are given in Fig. 5-106. The water saturations for the grain-dominated packstone and the mudstone-wackestone rock-fabric classes were established using empirical relationships similar to those used in defining Eq. 5-134.

447 TABLE 5-XXIII Rock-fabric flow unit properties used in the Lawyer Canyon outcrop reservoir-flow model Flow units Rock fabric

Depositional facies

Porosity (arithmetic average)

Permeability (geometric average, mD)

Residual oil saturation

0.9

0.01

Flooded shelf Tidal fiat

0.04

Wackestone

Shallow shelf I

0.105

0.30

0.405

0.4

Grain-dominated packstone

Shallow shelf I

0.085

4.50

0.214

0.35

4

Grain-dominated packstone

Shallow shelf II Bar top

0.129

1.80

0.40

0.35

5

Grain-dominated packstone

Shallow shelf II

0.118

5.30

0.243

0.35

6

Grainstone (moldic)

Shallow shelf II

0.145

0.7

0.091

0.40

7

Grainstone (moldic)

Shallow shelf I Shallow shelf II Bar crest Bar top

0.159

2.2

0.077

0.40

8

Grainstone (highly moldic)

Shallow shelf II Bar crest Bar-accretion sets

0.23

2.5

0.041

0.40

1

Mudstone

2 3

0.01

Initial water saturation

9

Grainstone

Bar flank

0.095

9.5

0.189

0.35

10

Grainstone

Bar crest Bar-accretion sets

0.11

21.3

0.147

0.25

11

Grainstone

Bar crest

0.135

44.0

0.103

0.25

Source" After Senger et al., 1991, table 2.

The equation for the grain-dominated packstone is" S = 106.524 h-~176 -1"440

(5-137)

and for the mudstone-wackestone, Sw= 161.023

h--~176176

(5-138)

where h is the height of the reservoir above the flee-water level in feet and ~bis the fractional porosity. The initial saturations for the different flow units were calculated using Eqs. 5-134, 5-137, and 5-138 for the three rock-fabric classes and average porosities. Rock-fabric, porosity, and water-saturation correlations based on capillary-pressure curves are shown in Fig. 5-107. The effect of vuggy porosity in the grainstones of parasequence 7 (Fig. 5-101 C) was accounted for by assigning a higher residual oil saturation to the unit,

448

Grainstone I00.0

100.0

e; o. E

Grain-dominated ,

packstone

100-

1o.o

Mud-dominated

< 2 0 I,t m

/]

I00.0

I0.0-

(

.~"

e; 9

.

41/O

1.o

/

1.09

9

o.1

T

l

2

[

T

I

I

5

IT

0.I

T

10

Interpart~cle

20

30

r

r

r

T

2

1.0-

[

t

5

o.1

t

0

InterpartJcle

porosity

!

20

30

i

i

2

poros0ty

i

i 1 ii

10

Interparticle

20

30

porosity

(percent)

(percent)

(percent)

I

5

Fig. 5-106. Lawyer Canyon San Andres outcrop porosity--permeability relationships from core-plug measurements for the three rock-fabric classes of nonvuggy carbonates. The large data scatter shows a poor correlation in these log-log plots. (After Senger et al., 1991, fig. 7; courtesy of the U.S. Department of Energy.)

.

_ ' _ . : . . ' _ , . . . . . . . . . . . ~...... . ~ . : ~ . ~ . . : ~ . . ~

...... ~................. _ ~ . ~

. . . .

.'.../_~.:'..

:::::::::::::::::::::::::::::::::::::::::::: ::i.:. ::::::::::::::::::::::: MD LIMESTONE ===================== :::::::::::!::'::::::::: ====================== ::l F I N E XL M D D O L O M I T E

...................-f-....... ! ....... i .......i ~ N " ~

........ ' ,

-t--~

~ ~::~i

........... ~.L. .... ~~..... :-----:-:---" !' i ~: \ ~\ :~ " :" ....",,~~~"~! ..... 7" ..... i; ... ....... \ : ........... .......

o~

0.1

............. ....... ' ..... iSi

.....

....:

o

-i

0.01 0.01

..

,.-.

'

i

,..

i

~! ":~

I

......-'i..... ::.... i i:,l

- ~: :::..:.:~ :i..:.:'~-:~:! . ~ " ! ! : ! " ! : I . . . . . . . -.-;' ..... ";: .... ' . . .:. . . . . .:. . ITE .. . .. ... ... ... .. . ~ 'm. -,--.:, 9 9] I. . . . . . . . . . . . . . . . . . ; : - ....:,j--..j...'~:.-~- .-.i-.l i 9 , MEDIUM XL MD DOLOMITE t GD PACKSTONE

GR/~INSTONE - -. .-. .I. ~ L A R G E XL D O L O M 9 ': " ! " " " : .... i " .... ,

O: I.U I--

~

o.

~,

-=

9

9

'"

I"~ I I '1 t

0.1

..... I

I

i

~

i

!i

:i i

lj

1

I

POROSITY

Fig. 5-107. Porosity, water saturation, and rock-fabric relationships derived from capillary-pressure curves used in the reservoir-flow model (refer to Table 5-XXIII). (After Senger et al., 1991, fig. 8; courtesy of the U.S. Department of Energy.)

449 and that the same porosity-saturation relationship exists as in the nonvuggy grainstones of parasequences 1, 2, 3, and 9 (Senger et al., 1991). The relative permeability values for the different flow units were obtained from the shapes of the relative-permeability curves derived from relative-permeability data from the two grainstone cores from Dune Field (west Texas, U.S.A.). These curves are similar to those shown in Fig. 5-104. Senger et al. (1991) pointed out that only the relative-permeability endpoints were adjusted according to the computed initial water saturations and assumed residual oil saturations. Table 5-XXIV summarizes the six outcrop simulation scenarios used to study the various factors affecting reservoir-flow behavior using the ECLIPSE reservoir simulator. Senger et al. (1991) used simulation EC-A to represent the base scenario in their hypothetical Lawyer Canyon outcrop carbonate reservoir model. Production characteristics of the six simulations were compared in order to evaluate: (1) capillary pressure effects (EC-B), (2) different production well locations (right, left and middle), and (3) different grid layouts (irregular and normalized). The production results of the simulations are shown for production rate (Fig. 5-108A), water cut (Fig. 5-108B), and cumulative production (Fig. 5-108C). Neglecting capillary pressure (simulation EC-B) results in a lower sweep efficiency except in the later stages of pore volume injection when it is about the same as simulation EC-A and lower than simulation EC-DP (Fig. 5-108C). Senger et al. (1991) noted that capillary pressure improves the sweep of the less permeable zones in parasequences 3 through 6 as was exhibited by EC-A data. Waterflooding in simulation EC-B was restricted to the more permeable grainstone facies in parasequences 1, 2, 7, and 9. In order to evaluate the effects of different injection schemes, the production and injection wells were varied as shown in Table 5-XXIV. The injection and production TABLE 5-XXIV Model scenarios for six waterflood simulations of the Lawyer Canyon outcrop model. Fluid properties are the same as used in the waterflood study of parasequence 1 Model scenario Sim. no.

Grid

Production well location

Capillary pressure

Permeability data

EC-A EC-B EC-N EC-DP EC-R EC-F

Irregular Irregular Normalized Normalized Irregular Irregular

Right Right Right Right Left Middle

Yes No Yes Single Yes Yes

Facies-averaged Facies-averaged Facies-averaged Linear interpolated between wells Facies-averaged Facies-averaged

Fluid properties: Oil viscosity Water viscosity Oil density Water density

1.000 cP 0.804 cP 55 lb/ft 3 64 lb/ft 3

Source: After Senger et al., 1991, table 3.

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Fig. 5-108. Reservoir performance results from six waterflood simulations using the Lawyer Canyon San Andres outcrop model. (A)-Oil-production rate vs. time; (B)-Water/oil ratio vs. injected pore volume; ( C ) - Cumulative oil production as a percentage of original oil-in-place. (After Senger et al., 1991, figs. 29, 30 and 31; courtesy of the U.S. Department of Energy.)

451 wells in the model were reversed for the simulation EC-R, changing the model's production characteristics. The model and reservoir-fluid properties are the same as used in the EC-A simulation. Simulation EC-F's configuration has the production well in the center of the model with two injections wells placed at either side of the production well. The prescribed pressures were adjusted in order to create the same pressure gradient between the injection wells and the production well. Results from the EC-R simulation indicated that after 40 years of waterflooding there will be a larger area of unswept oil at the model's center than in the simulation EC-A. Initial production rates are lower for EC-R than in EC-A. According to simulation EC-R, at later times the production will have a lower WOR (Fig. 5-108B) than EC-A. Simulation EC-A indicates a higher sweep efficiency than EC-R. This shows that the spatial distribution of permeable grainstone facies relative to the direction of the waterflood (Fig. 5-101B) is important for the overall reservoir-flow behavior (Senger et al., 1991). In simulation EC-R, cross flow occurred on the left side of the model toward the production well from parasequence 1 all the way down to parasequences 1 and 2. Cross flow did not occur on the left-hand side in simulation EC-A. This result was attributed by Senger et al. (1991) to the fact that cross flow on the left hand side of the model during simulation EC-R was facilitated by the existence of discontinuous mudstone layers, whereas on the right side the layers are continuous. They noted, however, that continuous mudstone layers are not always flow barriers as evidenced by the cross flow in simulation EC-A between parasequences 9 and 7 in the upper right of the model. Results of the EC-F simulation showed that the initial production rates are much higher in simulation EC-F than the other simulations. After 16,000 days, the production rate leveled off at slightly higher rate than was shown by simulation EC-A (Fig. 5-108A). The water cut rate for EC-F breaks at a lower WOR than that in simulation EC-A (Fig. 5-108B). Figure 5-108C shows that the sweep efficiency of EC-F is lower than in simulation EC-A, but slightly higher than in simulation EC-R (Senger et al., 1991). Different grid layouts were used to study the effect of irregular formation geometry (EC-N and EC-DP) with that of normalized formation geometry. In simulation EC-N, the nine parasequences were normalized to a constant thickness. When compared with the base case EC-A shown in Fig. 5-108A, the production rate is higher for EC-N and there is an earlier drop off of the rate. Figure 5-108B shows a steeper waterbreakthrough curve in simulation EC-N than in EC-A. This means that simulation EC-N results in a lower recovery efficiency. In the case of EC-DP, the constructed carbonate reservoir model used permeabilities of the individual flow units at the injection and production wells as endpoints. Permeabilities were linearly interpolated between these two wells using the normalized grid of EC-N. Only single capillarypressure and relative-permeability curves were used in the simulation (Senger et al., 1991). Results of this BEG model study verify what one would reasonably expect, that (1) the high-permeability grainstone units in parasequences 1, 2, and 9 are preferentially flooded with respect to the other parasequences, and (2) waterflooding was controlled by the low-permeable mudstone units separating most of the parasequences. Senger et al. (1991) noted that the spatial distribution of permeable grainstone facies relative

452 to the parasequence boundaries showed variable degrees of lateral continuity, which are crucial for understanding carbonate reservoir performance. This was documented by their flow simulations. The key is to predict the most permeable zones, such as bar-crest and bar-flank grainstones and packstones~ in a ramp-crest environment. As shown by parasequence 9 in Fig. 5-101B, the lateral dimensions of grainstone facies are highly variable in that the facies exhibits thick localized pods, rapid thinning, and sustained continuity. As shown by Fig. 5-108C, the recovery ofoil in the six simulations approached 45% of the total oil-in-place, which compares with oil-recovery data of the San Andres carbonate reservoirs in the Permian Basin, U.S.A. The San Andres reservoir model can be criticized for its limited two-dimensionality that overestimates sweep efficiency and which does not portray the potential effects of three-dimensional heterogeneity on flow. Chevron's F l o w Models. Fortunately, further model comparisons with the BEG's simulations using a very large Lawyer Canyon data set were performed by Grant et al. (1994). The goal of this study was to illustrate the relationship between fluid flow, carbonate cycles, and lithofacies variation. Grant et al. (1994) applied four different permeability models to delineate how permeability heterogeneity affects viscousdominated flow behavior and recovery efficiency in analogous cyclic ramp-crest carbonate reservoirs. Reservoir and flow parameters for the simulations were derived from an evaluation of the waterflood in the McElroy Field, which is located along the eastern edge of the Central Basin Platform, near Dune Field, in Crane and Upton counties, west Texas, U.S.A. (Table 5-XXV). The flow simulations were used to determine the level of detail required to represent the "effective" heterogeneity description for cycles 7 - 9 (Grant et al., 1994). The models used in the study are: (1) facies-averaged or "layer-cake" model, which incorporated the geometric mean permeabilities for the facies identified on the outcrop; (2) detailed geostatistical model, which consisted of 21,877 cells generated by using Hewett and Behrens' (1988) conditional simulation fractal technique; (3) coarse-grid model, which contained 3,068 cells and was designed to test scaling by using the averaging effects of fractal conditional simulations in the presence of detailed data; and (4) the realistic model included anisotropic permeability by facies and cycles, which were derived from whole core permeability data from the No. 1 Algerita well core. Fractures were not modeled in these simulations. Both the facies-averaged and the coarse-grid models used isotropic permeabilities in each cell ( k / k h = 1). The results of this study are shown in Fig. 5-109 and are not as optimistic as the BEG simulation results presented in Fig. 5-108C. Grant et al.'s (1994) horizontal variogram demonstrated a short correlation range that resulted in nearly uncorrelated permeability patterns in the detailed geostatistical, coarse-grid, and realistic models. Consequently, the nearly uncorrelated permeability patterns dominated the vertical sweep efficiency in these models resulting in very little difference in the recovery curves (Fig. 5-109). It was concluded by Grant et al. (1994) that a coarser-grid, fractal representation performs equally as well as fine-grid, geologically realistic, or geometrically-averaged facies models for estimating sweep efficiencies. An extremely

453 TABLE 5-XXV Model, reservoir, and fluid parameters and values used in waterflood simulations of cycles 7 - 9, Chevron's Lawyer Canyon, New Mexico, U.S.A., San Andres outcrop model Parameter

Simulator value

Displacement parameters (dimensionless)

Endpoint mobility ratio (M~ Gravity number (N~ Capillary number (NRL) Aspect ratio (L/H)

0.59 0.007 4980 7.77

Panel and cell dimensions

Length Height Depth Total number of cells "Detailed" model "Coarse" model Average cell dimensions "Detailed" model "Coarse" model

157.5 m (516.7 ft) 20.3 m (66.5 ft) 0.3 m (1 ft) 21,877 3068 0.2• 1.2m(0.5x 1 x4ft) 0 . 3 x 0 . 3 x 3 m ( 1 • 1 x lOft)

Boundary conditions

No-flow boundaries Perforated intervals (injector/producer) Injector Producer

top and bottom of panel all wellbore cells 1 bbl/day 2000 ps (max) 1550 psi (min)

Rock and fluid properties

Average total pore volume Average permeability Average porosity Connate water saturation Residual oil saturation Injected water viscosity at reservoir conditions Produced oil viscosity at reservoir conditions

985 bbl 11.0 mD 14% 25.8% 36.5% 0.62 cP 0.97 cP

Source: After Grant et al., 1994, table 2" reprinted with the permission of American Association of

Petroleum Geologists. favorable mobility ratio was used in their simulations (endpoint mobility ratio = 0.59). This ratio favored efficient fluid displacement in heterogeneous permeability fields. They did not, however, model the carbonate outcrop panel with more reasonable (higher) mobility ratios in order to study the effects of fine-scale heterogeneity on the sweep efficiency. Fine-scale heterogeneities should have a large impact in CO 2 floods with M > 20. Grant et al. (1994) noted important differences between the four models. Figure 5110 is a crossplot illustrating water injection (processing) rates for the models. The injection rates resulted in different oil recovery responses with respect to the water break-through times and oil production rate schedules. Differences observed in the injection rates reflect the variations of heterogeneity in each of the models. The detailed model has an overall effective permeability that is 1.2 times that of the coarse

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Fig. 5-109. Hypothetical San Andres cumulative oil production as a percentage of original oil-in-place for the four models used by Chevron. (After Grant et al., 1994, fig. 15" courtesy of the American Association of Petroleum Geologists.)

model, 1.4 times that of the realistic model, and 3.2 times that of the layer cake model (Grant et al., 1994). The team believed that refining the grid to smaller cell sizes improved the probability of connecting fine-scale permeability streaks.

Significance of the Lawyer Canyon outcrop studies. It was demonstrated in Senger et al.'s (1991) and Grant et al.'s (1994) case examples that acquired in-field permeability data can be applied to statistical flow models in characterizing heterogeneity in ramp-crest carbonate reservoirs. The field permeameter was shown to be a potent tool for capturing fine-scale heterogeneity patterns in carbonate rocks lacking fractures and vuggy porosity. Although permeability data were very heterogeneous at all scales of observation, permeability increased upward within the individual cycles (parasequences). The flow units, interpreted as mappable intervals with similar petrophysical properties, can be best defined in terms of rock-fabric facies. Grant et al. (1994) suggested that, in general, the individual depositional cycles at the Lawyer Canyon outcrop are probably equivalent to a flow unit. Each flow unit has distinct vertical permeability patterns, spatial statistics, and flow boundaries. Variations of cycle thickness and of the lithofacies within a cycle have a strong effect on permeability distribution and fluid flow. At another site, under different geologic depositional conditions, the flow unit could be composed of a series of thick or thin cycles, or a combination of both. As noted previously in this chapter, permeability in carbonate rocks can be highly uncorrelated laterally and vertically. One way of accommodating permeability under

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500

6(X)

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Days Injected Fig. 5-110. Water processing rates for the four models used by Chevron. Differences in the water processing rates for the San Andres reflect the variations of heterogeneity in each model. (After Grant et al., 1994, fig. 16; courtesy of the American Association of Petroleum Geologists.)

this condition is to use short ranges of correlation and high variances. Grant et al. (1994) recommended a sampling density of 1 - 2 in-field permeability measurements per foot (30 cm) in order to capture permeability trends. An inference that can be deduced from these field studies is that the short correlation lengths are probably what generally distinguish carbonate reservoir production behavior from that of sandstone reservoirs. With some exceptions, sandstone reservoirs tend to exhibit petrophysical properties with longer correlations. Further investigations are needed to clarify this point. As a word of caution, these two case studies provided only hypothetical results that showed similar results derived from active San Andres reservoir waterfloods in west Texas, U.S.A. Grant et al. (1994) noted that the uniform saturation profile, coupled

456 with the very low water processing rate exhibited by the layer cake model, had a water breakthrough that lagged 260 days behind the geostatistically generated models. This condition demonstrated that such a simplistic geologic model misrepresents the geological and petrophysical complexities needed to simulate accurately the effects of carbonate reservoir heterogeneity on fluid displacement and production. A visual examination of computer-generated water saturation profiles helps to clarify the impact of different lithofacies on fluid flow. Examples were provided by Grant et al. (1994, fig. 15, p. 43) which showed upward-increasing permeability trends as evidenced by high water saturations present in the bar-crest dolograinstone facies of the Lawyer Canyon depositional cycles 7 and 9 (Fig. 5-101C). Water saturations in cycle 8 lags behind the waterflood fronts in cycles 7 and 9 owing to a lack of grain-rich barcrest and bar-flank facies. Senger et al.'s (1991) and Grant et al.'s (1994) simulations showed that the basal dolomudstones act as baffles to vertical cross-flow. In Grant et al.'s (1994) realistic model, the dolomudstones were modeled as nearly continuous across the outcrop panel and with kv/kh> 1, little crossflow occurred across the dolomudstone boundaries. There was considerable permeability streaking in the bar-crest and bar-flank dolograinstone lithofacies. Grant et al.'s (1994) simulations demonstrated that it is the thin, poorlydeveloped cycles lacking good dolograinstone layers, such as cycle 8, which resulted in the greatest compartmentalization of viscous-dominated fluid flow within a given succession of cycles. Most of the bypassed oil remained in these poorly-developed cycles. This was supported by Senger et al.'s (1991) facies-averaged waterflood simulations. Their model results showed a systematic stacking of poorly developed parasequences (cycles) that compartmentalized fluid flow into two distinct "flow horizons".

Radiological imaging applications New, cutting-edge, nondestructive imaging techniques such as computerized Xray tomography and nuclear magnetic resonance (NMR) microscopy are used in the laboratory to obtain three-dimensional visual information of the distribution of fluids in porous media. This visualization capability is of direct help in determining the oil displacement processes taking place at the micro- and mesoscopic scales (Fig. 5-37), aiding in the design of recovery processes, and assessment of sample heterogeneity. Saraf (1981) questioned the accuracy of other in-situ methods that were used previously to determine fluid saturations during coreflood experiments, such as (1) transparent models, (2) microwave absorption, (3) radioisotope injection, (4) neutron radiography, (5) resistivity, and (6) magnetic susceptibility. All the above methods imposed restrictions on the experimental technique and provided only areal average values for fluid saturations (Wellington and Vinegar, 1987).

X-ray computerized tomography (CT). Slobod and Caudle (1952) introduced the X-ray shadowgraph (radiograph) method for studying sweep-efficiency in five-spot and line-drive well patterns. The shadowgraph is restricted to two-dimensional investigations owing to the fact that an X-ray shadow projection onto a single plane obscures three-dimensional information. Recently, high-resolution X-radiography was used to decipher the depositional history of sedimentary rocks at the microscale (Algeo et al., 1994).

457 Although this technique might reveal millimeter-scale heterogeneities, it is the images of fluid-flow patterns obtained during corefloods that are deemed important in testing the overall effect of heterogeneity on flow in carbonate rocks. Carbonate reservoir engineering applications of computerized tomography include the investigation of CO 2 displacement in laboratory cores, studying viscous fingering, gravity segregation, miscibility, and mobility control. Computerized tomography differs from X-ray radiography in that image construction and its display are generated using a computer and proprietary software packages (Macovski, 1983; Orsi et al., 1994). This technique measures density and atomic composition inside opaque objects. Second- and later-generation medical CT scanners have the appropriate X-ray energy and dose for scanning cores and slab models. CT scanners produce two-dimensional cross-sectional image slices through an object by revolving an X-ray tube around the object and obtaining projections at various different angles (Wellington and Vinegar, 1987). A three-dimensional array is created from the two-dimensional transmission images. Recently, Jasti et al. (1993) described new CT technology that directly measures three-dimensional geometric and topological properties of porous rocks on a microscale using a microfocal X-ray imaging system. Petrophysical applications of CT scanning have aided in the three-dimensional determination along a core's length of: (1) bulk density and porosity patterns, (2) core-well log correlation by direct comparison of the density log's bulk density signature and one generated from the core, (3) drilling fluid invasion, (4) fractures (natural and induced), (5) complex mineralogies, (6) sand(carbonate)/shale ratios, (7) hydrocarbon/water/gas distributions, (8) sedimentological features such as thin flow-barriers, and (9) uniaxial compressibility of the rock under compression. It is important to remember that semivariograms of various rock and fluid properties, such as porosity, permeability and residual fluid saturations, can be calculated from CT data and are used to determine correlation lengths on the laboratory (micro- to meso-scopic) scales. Pathak et al. (1982) demonstrated that the topology of the matrix's pore system was critical for residual oil saturations. They measured connectivity between pores. Their study showed that when a matrix contains a larger number of pore interconnections, there is a greater number of alternative routes available for oil drainage resulting in a lower percolation threshold and a lower residual oil saturation. Pathak et al. (1982) concluded that flow properties in porous media not only depend on pore size and shape, but also on local connectivity. Porosity distributions can be measured with any two fluids as long as the fluids attenuate the CT X-rays differently. Dopants are sometimes added to the injection brines and oils in order to increase the difference between the X-ray attenuation of water and oil. Iodated oils, such as 1-iododecane, can be added to the oleic phase, and high-atomic number salts such as sodium iodide or tungstate to the brine. Sodium iodide was preferred by Withjack (1988) for the aqueous phase owing to its interaction with clay minerals, which is similar to the sodium chloride interactions with clays. Figure 5-111 illustrates CT-determined average porosity values of a porous, permeable, fine-grained dolomite sample (Silurian Guelph Formation from the J.E. Baker Co. quarry in Millersville, Ohio, U.S.A.). In making the porosity measurements, Withjack (1988) used a range of sodium iodide molar solutions of 0.25, 0.50, 0.75, and 1.00 and X-ray tube voltages of 80 and 120 kV. The 0.75 molar concentration

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Fig. 5-111. Computerized tomography measured fractional average porosity values for a Silurian dolomite from the Guelph Formation of Ohio, U.S.A. Testing was done at 80 and 120 kV with four sodium iodide concentrations of 0.25, 0.50, 0.75, and 1.00 molar. (After Withjack, 1988, fig. 9; reprinted with the permission of the Society of Petroleum Engineers.)

provided a close agreement (within about + 1%) between CT and conventionally measured porosities (Withjack, 1988). MacAllister et al. (1993), Wellington and Vinegar (1987), and Withjack (1988) described the use of a CT scanner to measure in-situ gas-water and oil-water saturations (apparent relative permeabilities) during displacement studies in laboratory cores. Apparent oil-water relative permeability relations are presented in Fig. 5-112 for a fine-grained "Baker" dolomite core (~b = 0.226; kai r = 110 roD) under a wettability state altered to a mixed-wettabili~, condition (MacAllister et al., 1993). Most field mixed-wettability cores are also weakly wet (Mohanty and Miller, 1991). All relative permeability values were normalized relative to ko at initial water saturation. These test results show that the relative permeabilities for the oil and water phases were higher at 4-psi (0.03-MPa) Ap than at 100-psi (0.69-MPa) Ap. MacAllister et al. (1993) considered several possible causes for the sensitivity to pressure drop, such as capillary number, capillary end effect and non-Darcy flow. Mohanty and Miller (1991) discussed potential factors and how they could influence the flow in a mixed-wettability laboratory core and, hence, the relative permeability during an unsteady test. From Mohanty and Miller's (1991) CT scan results, it was concluded that the early part (
459

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Fig. 5-112. Computerized tomography measured relative oil and water permeabilities at 4- and 100-psi (0.03- and 0.69-MPa) differential pressures across a dolomite core (Silurian Guelph Formation, Ohio, U.S.A.) having a mixed wettability. (After MacAllister et al., 1993, fig. 5; reprinted with the permission of the Society of Petroleum Engineers.)

Fingering becomes less severe as the flow rate decreased: apparently, krw decreased and k~o increased. The capillary end effect was small in Mohanty and Miller's (1991) test cores and would be significant only at very low flow rates. Flow parameters, capillary end-effect number, macroscopic capillary number, heterogeneity number, and instability number affect unsteady relative permeability in weakly mixedwettability rocks having viscous oil. Figure 5-112 shows that at a given fractional flow in the dolomite core, the difference between the average phase saturation at 4 psi (0.03 MPa) and 100 psi (0.69 MPa) is small, whereas the difference in apparent relative permeability is large. MacAllister et a1.(1993) concluded, after examining CT scan slices along the core, that at 4 psi (0.03 MPa), high oil saturations appear at the top and right of each cross-section and very low oil saturations appear at the bottom and left in the dolomite core (Fig. 5113A). This condition leaves large connected flow paths for both oil and water with high relative permeability (MacAllister et al., 1993). At 100 psi (0.69 MPa), the high oil saturations at the top and right of each cross-section were reduced and the very low oil saturations at the core's bottom and left increased (Fig. 5-113B). Such a condition results in a reduction of fluid flow paths and, therefore, significantly lowers relative permeability. MacAllister et al. (1993) stated that the overall average oil saturation changed very little; however, the distribution of the oil was greatly changed. The assumption of a uniform saturation distribution in the dolomite core is shown not

460

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B Fig. 5-113. Computerized tomography scans showing the oil saturation distribution along a dolomite core having mixed-wettability (Silurian Guelph Formation, Ohio, U.S.A.) with a WOR of 0.5. ( A ) Differential pressure of 4 psi (0.03 MPa); (B) - Differential pressure of 100 psi (0.69 MPa). (After MacAllister et al., 1993, figs. 7 and 8; reprinted with the permission of the Society of Petroleum Engineers.)

to be the case. The point of these visual results presented in Fig. 5-113 is that substantial saturation redistributions would not be detected, and the cause of the large changes in the relative permeability would be difficult to infer owing to the fact that the average saturations change little. The oil-water relative permeability curves generated in

461 MacAllister et al.'s (1993) experiments were sensitive to pressure drop and fluid saturation, creating localized fluid heterogeneity patterns within the dolomite core. Laboratory results must be scaled to the field values of the flow parameters described above by Mohanty and Miller (1991). Unsteady-waterflood displacement tests in the laboratory should be conducted at or extrapolated to the field rate. Failure to use the appropriate relative permeability values derived using these guidelines would impact negatively the results from any simulated waterflood. MacAllister et al. (1993) obtained gas-water apparent relative permeabilities in four steady-state gas-water cycles using a "Baker" dolomite core at the end of an oilwater relative permeability test. The core was in its native water-wet state. No attempt was made by them to keep both Ap and injection rate constant. Test results showed significant gas trapping. Gas saturation decreased from residual gas at water floodout (4 psi [0.03 MPa] Ap) to a gas/water ratio of 3 (5 psi [0.035 MPa] Ap). The variation in their data was greater than the uncertainty in the laboratory measurements. CT scan comparisons of the gas distributions between the water flood-out and a GWR of 3 at 5 psi (0.035 MPa) indicated that the gas saturation in the core was affected by the heterogeneous nature of the core's front, which controlled fluid distribution. Greater fluid segregation occurred toward the core's front, which is the more heterogeneous portion of the core, than at the rear (MacAllister et al., 1993). Hicks et al. (1992) measured porosity and residual oil saturations using CT scans in three heterogeneous vugular carbonate cores having 4-in. (10-cm) diameters. The well cores were from the Fenn-Big Valley Field in Alberta, Canada, and the TaylorLink Field in Pecos County, west Texas, U.S.A., whereas an outcrop core was obtained from San Andres Formation near Carlsbad, New Mexico, U.S.A. All cores were taken perpendicular to the bedding planes. Average porosities of these cores are 6.7% (Fenn-Big Valley carbonate), 11.4% (San Andres Formation core), and 12.2% (San Andres Formation New Mexico core). The two San Andres cores have significantly different porosity distributions which resemble those from tested Berea and Boise sandstone cores, which were tested by Hicks et al. (1992). The reason why they resemble the sandstone distributions is because each core's average porosity happens to be the most common porosity present on the voxel size level (resolution of objects). Most of the porosity values in the Fenn-Big Valley core are quite low. Figure 5-114 illustrates the variations in fractional porosity along each core length. Hicks et al. (1992) calculated the residual saturations for each voxel, which were averaged over the entire core. The average residual oil saturations for the FennBig Valley and the west Texas San Andres Formation cores were 42.6 and 24.9%, respectively. They correlated porosity and residual fluid saturations as a function of position for both the Fenn-Big Valley and the Taylor-Link cores. Figure 5-115 compares the relation between the mean S in the Fenn-Big Valley carbonate core and Sor and Swr for the Taylor-Link San Andres core and porosity distributions. The Fenn-Big Valley carbonate shows less absolute variation, but much S scatter (dampened by using the mean values" Fig. 5-115A" Hicks et al., 1992). Similar scatter is shown by the west Texas, San Andres core (Fig. 5-115B). Semivariograms were calculated, and illustrate the variation of voxel size for a selected CT scan slice from the Fenn-Big Valley and the west Texas Sand Andres cores (Fig. 5-116). The Fenn-Big Valley core shows that the decreasing variances with increased voxel sizes are more pronounced than the variances in the

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Fig. 5-114. Relationship between fractional porosity and core length for three carbonate rocks (Fenn-Big Valley carbonate, Alberta, Canada; San Andres Formation, west Texas, U.S.A.; and San Andres Formation, New Mexico, U.S.A.) and two sandstones (Berea and Boise). Each longitudinal point is calculated by averaging all the pixels from a given computerized tomography scan slice. (After Hicks et al., 1992, fig. 6; reprinted with the permission of the Society of Petroleum Engineers.) west Texas core. The Fenn-Big Valley core porosity indicates a definite correlation with length. Both cores show that the variance is still increasing, which Hicks et al. (1992) attributed to the wider variation in matrix porosity in the San Andres samples. Hicks et al. (1992) also studied the effect of direction on the porosity semivariograms generated for the three carbonate cores (Fig. 5-117). The results demonstrated that a difference exists in the semivariograms across the bedding planes in the two San Andres cores (Fig. 5-117B, C). The laboratory scale of heterogeneity is on the order of 0.4 in. (1 cm). Hicks et al. (1992) pointed out that the optimal grid block sizes for laboratory-scale simulations were expected to be of this size. Three-phase flow experiments using a CT scanner to measure fluid saturations were carried out by Vinegar and Wellington (1987). Tomutsa et al. (1992) pointed out that for porosity and two-phase saturation measurements, CT scanning at one X-ray energy level is sufficient. For three-phases, however, fluid differentiation requires that scanning takes place at two different X-ray energy levels. Computerized tomography scanning can provide valuable information during laboratory testing on whether or not carbonate cores have been fully saturated before, during, or after displacement studies. Data from CT scans can be used to model petrophysical properties on the laboratory scale by using semivariograms.

Magnetic resonance imaging microscopy (NMR). Porosities in carbonate rock reservoirs have been shown to be difficult to determine in situ using conventional

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466 porosity logs (see Chapter 4). The nuclear magnetism well logging tool (NML) was developed initially to provide a prediction of in-situ, free-fluid porosity measurements in carbonate rocks (Brown and Gamson, 1960). The free fluid index (FFI) measured by NML is equivalent to the total porosity in a carbonate rock. Timur (1972) studied the use of NMR under laboratory conditions making measurements on some 100 carbonate rock samples from four oil fields in the U.S.A. Robinson et al. (1984) expanded NML's field applications to determine residual-oil saturation and permeability. The success of these investigations and developments in medical imaging techniques led to the application of NMR in the petrophysical laboratory. In NMR imaging, a rock sample is placed inside an intensely homogeneous magnetic field generated by a superconducting magnet (Vinegar, 1986). The direct proportionality of the NMR signal frequency to the magnetic field strength is the basis of NMR imaging (Gleeson et al., 1993). Radio frequency (RF) magnetic fields at the precise Larmor frequency are generated by RF coils, which causes a particular nuclear species to precess, and the RF coils then detect signals emanating from the precessing nuclei. Three-dimensional localization within the laboratory core is obtained by x, y, and z magnetic-field gradient coils. These coils cause nuclei in different parts of the sample to precess at slightly different frequencies (Vinegar, 1986). The spatial distribution of the nuclear-spin density is obtained from a Fourier transformation of the resulting frequency-modulated signal. Vinegar (1986) stated that unlike computerized tomography, an image is obtained of the entire core volume within the RF coil. NMR imaging can provide information on the same various rock and fluid properties as were described above in the CT discussion. In addition, NMR is a useful method used in determining grain density, oil viscosity, interstitial water salinity, wettability, diffusion coefficients, and carbonate pore types. 1H NMR spectroscopy has a particular advantage in measuring petrophysical properties of low-permeable, gypsum-bearing carbonates. Vinegar et al. (1991) reported that NMR eliminates laboratory problems of extremely slow and incomplete lowtemperature oil extraction in low-permeability carbonates, and the high-temperature dehydration of gypsum in core analysis. This creates large errors in water-saturation values, which can exceed the total pore volume of the rock. The weight loss of the core owing to gypsum dehydration is reported as oil (Vinegar et al., 1991). The phase change conversion of gypsum to anhydrite results in the increase of core's air permeability. The conversion reaction is similar to the dehydration of smectite, inasmuch as the latter process produces fluids at a constant rate under the proper dehydration conditions. There is no water signal detected from waters-of-hydration of gypsum. Anhydrite and gypsum are common minerals in the Permian carbonate and evaporite sections of west Texas and New Mexico, U.S.A. Gypsum is the hydrated form of anhydrite. These minerals may occur as nodules, pore-filling material, fracture-filling material, and as massive beds. The pressure-temperature relationship between gypsum and anhydrite in the subsurface is discussed by Rieke and Chilingarian (1974, p. 323). Vinegar et al. ( 1991 ) investigated the gypsum problem occurring in an oil-bearing dolomitic zone in the San Andres Formation from west Texas, U.S.A. They used 300 vile-sealed core plugs and 166 ft (51 m) of whole sponge core (3.25-in. [8.13-cm] diameter) from this zone. Figure 5-118A compares the plug and whole core NMR fluid-filled porosity vs. depth. Porosity appears to be less variable in the whole core

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468 than in the plug core samples, which Vinegar et al. (1991) attributed to a larger core sample size. A larger core sample results in better statistical smoothing of porosity. No gas was present in the whole core, which could result in the fluid-filled porosity to be less than the total porosity. Figure 5-118B compares the whole core and plug core NMR-determined oil saturation. The average oil saturation in the oil-bearing zone from 3,820 to 4,000 ft ( 1 1 6 4 - 1219 m) depth interval is 20%. Vinegar et al. (1991) attributed the highly variable oil saturation on a plug-by-plug basis to more numerous local saturation variations due to heterogeneity. The comparisons in Fig. 5-118 provide strong evidence that whole-core NMR spectroscopy gives more representative results than small core plugs having only a 1-in. (2.5-cm) diameter and a length of 1.5 in. (3.75 cm). NMR-determined oil viscosity in the core plugs was about 2 - 3 cP at room temperature. The assessment of this investigation indicates that the NMR measurements were accurate, rapid, and non-invasive, resulting in NMR whole-core analysis costs substantially lower than those of standard extraction (Vinegar et al., 1991). Mazzullo and Chilingarian (1992a) discussed the various classifications of pores in carbonate rocks based on their size, shape, and mode of formation. NMR imaging has been used to determine pore structures in rocks (Mahmood, 1990). Gleeson et al. (1993) demonstrated that NMR images of water-filled and drained pores in coarsegrained limestone samples from the U.S.A. and Middle East could be used to recognize various pore types such as: (1) growth-intraframework porosity in a Holocene coral boundstone from Florida, U.S.A., (2) intergranular porosity in a peloid grainstone from the Middle East and in an ooid grainstone from the Pleistocene Miami Formation, Florida, U.S.A., (3) moldic porosity in the Miami Formation and in a molluscan grainstone from the Cretaceous Whitestone Member of the Edwards Group in central Texas, U.S.A., (4) intraparticle porosity in an Eocene foraminiferal packstone from Egypt, and (5) vuggy porosity in an Eocene foraminiferal packstone from the Middle East. Three-dimensional NMR images have shown that in certain vuggy limestones the vugs can be so elongated that the porosity can be classified as channel porosity. Gleeson et al. (1993) stated that channel porosity is difficult, if not impossible, to identify in two-dimensional NMR images. Their NMR investigation was extended to examine carbonate pore connectivity. Pore casts are commonly used to characterize a carbonate rock's pore system. Plastic resin is injected into the pore system of a sample and allowed to harden, and then the carbonate is dissolved slowly in acid leaving a three-dimensional replica of the pore system. This technique does not always capture the small-pore-sized connectivity and is difficult to manipulate and interpret quantitatively. Another technique in establishing connectivity is to use two-dimensional petrographic image analysis, which was discussed previously in this chapter. The visual advantage to three-dimensional pore images is evident in Fig. 5-119. The incremental 30 ~ rotated views of the water-saturated limestone core plug show the vuggy opaque pore structure, which exhibits channeling, in a volume of transparent solid rock. These vuggy channels represent the dominant fluid-flow paths in the plug. Light gray shading denotes the optional (other pores than channel pores) part of the pore structure. These optional pores contribute very little to the fluid flow in the core (Gleeson et al., 1993). Tomutsa et al. (1992) proposed that real-time records of nuclear magnetic resonance imaging microscopy and computerized tomography analyses of fluid displacement tests in cores and thin-slab rock models can be created using video technology.

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470 High-quality, commercial-grade video equipment can not only capture high-velocity fluid behavior events in the pores during displacement tests, but also can be used to tape sequential events in lapsed time. Video technology as a teaching aid and technology transfer device eliminates the excessive costs associated with the mass reproduction of numerous high-quality photographs required to depict complex, dynamic fluid behavior in laboratory tests. Microscopic flow heterogeneity is related to pore size, shape, and location. The application of CT and NMR technologies to define pore structure overcomes uncertainty in estimating inherently three-dimensional properties from two-dimensional images. It is obvious that the adaptation of three-dimensional image rock- and fluidproperty data in two- and three-dimensional multifractal analysis of carbonate reservoirs will improve the ability to predict more accurately the production potential of a reservoir.

Determination of heterogeneity in carbonate pore systems from laboratory gasdrive tests Another means of defining heterogeneity in carbonate rocks is the application of laboratory tests, which measure deviations in dynamic fluid behavior in cores. Characterization of core-scale heterogeneities has been accomplished by using various gas flow tests, pressure transient analysis, and standard miscible displacement experiments.

Nitrogen/helium miscible displacement test Rosman and Simon (1976) used nitrogen to displace helium from limestone and sandstone cores and sand packs to determine the microscopic flow heterogeneity. This very rapid and nondestructive method was used in the laboratory to determine the extent of core damage. The nitrogen breakthrough and effluent composition was measured by the frontal chromatography methods. Nitrogen and helium were chosen by Rosman and Simon (1976) because their viscosity ratio (nitrogen/helium) approaches unity at room temperature, and both gases have sufficiently different thermal conductivities for chromatographic detection. Microscopic flow heterogeneity was expressed by breakthrough recovery during the displacement of helium by nitrogen. Nitrogen breakthrough ranged from 0.13 to 0.78 PV injected. An early nitrogen breakthrough indicates a higher degree of heterogeneity. The results were compared with measurements from liquid, equal-viscosity miscible displacements in the same cores, and agreed well. Cores were mounted vertically to avoid gravity segregation effects caused by density difference between the two gases. Nitrogen was injected into the bottom of the vertical core and the emerging gas flowed through the chromatograph so that the nitrogen breakthrough could be timed (Rosman and Simon, 1976). Reproducibility of vertical flow was within 1% of the recovery at breakthrough. It was not affected by flow direction, although horizontally tested cores had poor reproducibility. There was deviation in the heterogeneity values on the order of 1 - 5% when the core was inverted. A core damaged by NaC1 brine (which caused clay-particle movement) showed a difference in helium recovery of more than 25% by inverting the core. Flow rate

471 affected the displacement owing to diffusion. Figure 5-120 illustrates the flow rate effect on helium recovery, at nitrogen breakthrough for two limestone cores and five sandstone cores. Rosman and Simon (1976) pointed out that as the recovery levels off, the results are similar to those from the liquid miscible-displacement tests. Microscopic flow heterogeneity in cores decreased as the length of the cores increased, that is as the length/diameter EL~D)ratio of the cores increased. Rosman and Simon (1976) explained that the reason for the heterogeneity decrease is a result of the configuration of the three-dimensional, interconnected pore network of many flow paths having conductivities that tend to even out as the flow paths become longer. This was evident in the data for the Berea and Colorado sandstone cores presented in Fig. 5-

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472 120. As the L/D ratio increased in both cases, the percent of helium recovery at breakthrough in the longer core increased. The microscopic flow heterogeneity measurements can be used to separate the effects of diffusion in core flow tests by varying injection rates. Gas turbulence in microvugular carbonates Very little information has been presented in this chapter about heterogeneity of carbonate gas reservoirs and the effect it has on gas wells. The impact of gas turbulence in low-permeability carbonate rocks was studied in the laboratory by Gewers and Nichol (1969). Turbulence of gas flowing through porous solids with relatively narrow flow passages is characterized by an excessive pressure drop associated with the inertia effects of the gas travelling through these passages. This heterogeneity results from the high degree of pore inhomogeneity in the microvugular carbonate system. Although estimates of the turbulence effect can be obtained by gas-well tests, it is helpful to measure this parameter in the laboratory in order to establish turbulence factor-permeability correlations. The investigation had two goals: (1) to establish a turbulence factor-permeability correlation for microvugular carbonates, and (2) to determine the effect of a static second phase (interstitial water or condensate) in the pores on this correlation. The liquid saturation around the wellbore can be increased by mechanisms such as mud-filtrate invasion, water coning, acidizing, or retrograde condensation (Gewers and Nichol, 1969). Such knowledge will help to improve the predictability of gas-well performance in microvugular carbonate reservoirs by correctly evaluating the additional pressure drop resulting from turbulence. Turner Valley carbonates. Gewers and Nichol (1969) selected a suite of carbonate cores from the Turner Valley Member of the Mississippian Rundle Formation, Alberta, western Canada. The samples were chosen to cover the formation's permeability range. The dry flow test procedure consisted of measuring the stabilized flow rate of nitrogen for various input pressures ranging from 1 to 11 atmospheres (1.03 11.36 kg/cm2). Input pressures below 1 atm were found to give rise to laminar flow, and were used by Gewers and Nichol (1969) to evaluate the Klinkenberg effect. In a second set of tests, glycerine was chosen to be the stationary liquid phase in the cores. Glycerine has a low vapor pressure, high viscosity, proper wettability (it wets the mineral surface as does water), and a static spatial distribution during gas flow that is close to that of water. Water was rejected owing to the ability of a gas to pick up water (even if the gas is saturated) as it expands during flow through the core's pore system. The mathematical basis for the experiments is the Forchheimer's equation: dp

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k

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(5-139)

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473 Darcy term and holds for viscous flow. The second term is the one that corrects for the turbulence effects and is a constant for any given rock sample. Gewers and Nichol (1969) used the following integral of Eq. 5-139 to calculate the turbulence factor from measured laboratory data: 2

2

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Turbulence factor. Results of the liquid saturation tests are shown in Fig. 5-12 lB. The magnitude of the turbulence factor varies with the static liquid saturation. As the saturation of the static second phase increases, the turbulence factor first decreases (SL= 0 to 10%) and then rapidly increases (SL > 10%), whereas the permeability decreases (SL= 0 to 10%), remains essentially constant (SL= 10 to 20%), and then increases (SL= 20 to 30%). The behavior of the microvugular carbonate system suggests that the turbulence factor-permeability correlation should be tested for each reservoir. Gewers and Nichol (1969) remarked that it is fortunate that the linearity of the slope (as shown in Fig. 5121) indicates that the data can be obtained with a minimum of laboratory work. The significance of knowing the turbulence factor accurately is stressed by Gewers and Nichol (1969). If the value of the turbulence factor in evaluating a gas well is too low, then actual field tests (absolute open flow tests) will yield a lower flow capacity than predicted by calculation. In most cases, the well is often suspected of being damaged. If this damage is non-existent, then the well cannot be expected to show a better performance. The turbulence factor must be considered in evaluating acidizing techniques. Gewers and Nichol (1969) pointed out that it is not enough to look at the effect on permeability alone. In their study, an increase in permeability or a decrease in liquid saturation below 20% not only increased production but also reduced the turbulence factor. This tends to compound the increase in production. Any factor that damages the well or raises liquid saturation over 10% will decrease production by both reducing

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Fig. 5-121. Turbulence factor vs. permeability for low-permeable carbonate cores from the Turner Valley Member of the Rundle Formation, Alberta, Canada. (A) - Dry-air turbulence factors of vugular carbonates; (B) - Effect of a static liquid on turbulence factor. (After Gewers and Nichol, 1969, figs. 3 and 4; reprinted with the permission of Petroleum Society of the Canadian Institute of Mining, Metallurgy and Petroleum.)

475 permeability and increasing turbulence. Calculated gas-well productivity and hence the desirability of a workover can be seriously misjudged if the wrong correlation is used (Gewers and Nichol, 1969).

Solution and external gas-drive model flow tests Jodry (1992) in Volume 1 of this two-volume book explained in detail the use of capillary pressure data to obtain an accurate description of carbonate pore systems. Stewart et al. (1953 and 1954) performed model flow performance tests on limestone cores that also provide valuable information on carbonate pore structure and oil recovery. The degree of divergence between the gas-oil relative permeability relationships calculated from solution or extemal gas drive tests is an indication of pore structure heterogeneity. The results of their laboratory work are especially pertinent here in the light of foregoing discussions.

Laboratory andfield performance characteristics. In Stewart et al.'s (1953) laboratory investigation, solution gas-drive and extemal gas-drive tests were conducted on 2.5- to 3.5-in. (6.25-- 8.75-cm)-diameter limestone cores. The results of the flow tests showed minor divergence between the k / k curves calculated from the extemalgas-drive test and the solution-gas-drive tests. They found the extent of this divergence to be indicative of the carbonate rock type. With respect to intergranular limestones, the solution and external-gas-drive k/k data were in close agreement. g o For rock samples having vugular porosity or fracture-matrix porosity, the respective k/k curves diverged to varying degrees, depending on the nature of the multipleg o , porosity development. The flow tests also showed that dead-end or storage pores exist in some intergranular limestones. Figures 5-122, 5-123, and 5-124 (from Stewart et al., 1953), indicate gas-drive performance for limestone cores possessing intergranular-intercrystalline, vugular, and fracture-matrix porosities. The relation between the extemal-gas-drive and solution-gas-drive k/k curves for different rock types typifies the qualitative correlation g o between the gas drive and type of pore system. F~gure 5-122 shows a close agreement between the k/k curves for two different drives with an intergranular pore system. g o Model flow test data presented in Fig. 5-122 are also compared to k / k values calculated from solution-gas-drive field performance data. There is a close match. In Fig. 5-123, the two reef limestone cores having vugular porosity exhibit substantial deviation in the curves. The fractured limestone has the greatest divergence in the k/k curves as shown by the test results in Fig. 5-124. g o Results from this study show that the laboratory-measured gas-oil flow behavior of uniform-type porosity limestones is essentially the same for a test simulating a field solution-gas drive as for one simulating an external-gas drive. For non-uniform porosity type limestones, however, a significant difference in gas-oil flow behavior was observed by Stewart et al. (1954) during a Solution-gas-drive test. Effect of bubble formation on oil recovery by solution-gas drive. Stewart et al. (1954) analyzed laboratory results of gas-drive tests with respect to the formation of gas bubbles during the depletion process in limestones having non-uniform porosity. Oil recovery performance depended directly on the number of gas bubbles formed,

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GAS SATURATION, PERCENT PORE VOLUME Fig. 5-122. Comparison of gas-drive performance of a limestone core having intergranular porosity under laboratory external-gas- and solution-gas-drive tests and solution-gas- drive field data. (After Stewart et al., 1953, fig. 5; reprinted with the permission of the Society of Petroleum Engineers.)

and the displacement operation was shown to be contingent on the formation of gas bubbles within the pores of the limestone itself. Stewart et al. (1954) attributed the formation of gas bubbles to the oil containing more dissolved gas than would be predicted from PVT relationships (supersaturated state). Figure 5-125 shows data that are quite typical of this condition. The gas in the external-drive mechanism is injected from an outside source. Stewart et al. (1954) explained that in an external-gas-drive reservoir having fracture-matrix porosity, the gas will channel through portions of the fracture system, resulting in a highly inefficient displacement of oil. Under conditions of solution-gas drive, the gas will also channel through the fissures and larger

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Fig. 5-123. Comparison of gas-drive performance on two reef limestone cores under laboratory externalgas- and solution-gas-drive tests. (After Stewart et al., 1953, fig. 7; reprinted with the permission of the Society of Petroleum Engineers.)

pore throats as the bubbles unite to form a continuous free gas phase. As a result, a solution-gas drive will be more efficient than extemal-gas drive in rocks with vugs and fracture-matrix porosity. Stewart et al. (1954) also found that differences ranging up to twofold in oil recovery could be obtained by varying the test conditions. The variations in test results were substantial for rocks with vugs and fracture-matrix pores, and only minor for rocks with intergranular porosity. For limestones having nonuniform porosity, the following parameters influenced the gas-drive results: (1) rate of pressure decline, (2) original bubble point pressure of the gas-oil solution, (3) oil viscosity, and (4) gas

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solubility characteristics. The greater the rate of pressure decline, the larger the number of gas bubbles formed. Laboratory tests showed that an increase in the pressure rate decline by a factor of 10 results in the formation of 10 times as many bubbles. Solution-gas-drive recovery will increase in rocks having nonuniform porosity with an increase in the number of bubbles. The reasoning is that the oil recovery from storage pores of rocks with nonuniform porosity will occur only when gas bubbles form in the storage pores. Only a part of the total gas saturation is, therefore, responsible for the observed gas/oil ratio performance in non-uniform porosity limestones.

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Fig. 5-125. Relative permeability characteristics of a limestone core, from the midcontinent U.S.A., having a non-uniform pore system. Permeability is 1 mD and average porosity is 30%. Curve A is a methane and C~0-Ct2 mixture having a bubble point pressure of 200 psig (1.4 MPa), and curve B is a methane and C~0-C~2mixture having a bubble point pressure of 1000 psig (6.9 MPa). (After Stewart et al., 1954, fig. 2; reprinted with the permission of the Society of Petroleum Engineers.)

Significance of the modelflow tests. Laboratory solutions-gas-drive tests in carbonate rocks usually demonstrate more favorable recoveries than those anticipated in actual practice because fewer bubbles form at the rates of pressure decline that exist in the field. Increases in oil recovery by using this technique may be feasible under the proper conditions. This question is but one aspect of the issue of appropriate oil production rates in carbonate reservoirs. Stewart et al. (1954) realized that there is no practical test to measure, in the laboratory, the solution-gas-drive oil recovery performance at field rates of pressure decline. They postulated that laboratory external-gas-drive data can be

480 used to make a conservative prediction of field solution-gas-drive performance for limestone reservoirs with non-uniform porosity. Production rate effect on recovery is discussed in the following section, which presents some theoretical and practical aspects of carbonate reservoir performance. Stewart et al. (1953) also conducted similar gas-drive experiments on sandstone cores. The relative permeability relationships were identical under both extemalgas- and solution-gas-drive conditions in all cases. A comparison was made between a more uniform pore structure exhibited by the sandstones, to a less uniform pore structure in the limestones. It appears that in rocks having uniform porosity the pores act as fluid conductors as well as fluid storage spaces. It is not necessary, therefore, for gas bubbles to form in the pore spaces themselves, as the gas evolved upstream is able to enter essentially all the individual pores to achieve oil displacement. A close examination of the pore structure of the limestone sample, the k g/ k o curves of which are presented in Fig. 5-122, indicated intergranular porosity. Many of the passages between the original fragments, however, have been sealed off by cementation resulting in the formation of storage pores. As a result, the externalgas-drive k / k curve is slightly less favorable than the solution-gas-drive k / k curve shown in l~lg. 5-122. Similar k.g/ k o curves results were obtained by Johnson and Sweeney (1973) for limestones m their study on measuring flow heterogeneity quantitatively in these samples using air to replace refined kerosene. Their method for measuring and expressing the flow path heterogeneity of laboratory core samples was based on a conceptual cylindrical tube model. The model was composed of 50 parallel flow paths (tubes), each containing 2% of the pore volume and of constant cross-sectional area. Their model was similar to the tube model shown in Fig. 5-77, which was constructed from a Sierpinski carpet. No cross flow was assumed owing to the implementation of an equal viscosity, equal density piston-like miscible displacement in each tube. They concluded that there is a general correlation where the higher values of the relative permeability ratio accompany greater flow path heterogeneity. In conclusion the degree of divergence between the solution-gas-drive k g/ k o and external-gas-drive k g/ k o should be a good measure of heterogeneity of the pore system. Waterflooding operations in these limestone reservoirs will not be as successful as planned as the degree of divergence between the kg/ko values increases. The injected water will have a tendency to sweep out less oil from the pores due to the heterogeneity of the pore system.

Some theoretical and practical aspects of carbonate reservoir performance The prudent management of oil and gas reservoirs is crucial to judging risks and maximizing returns of exploration, development, and production operation investments. A continuous theme of these two volumes is that much of the theory and many of the practices acceptable for sandstone reservoirs do not always apply to carbonate reservoirs. Next discussion focuses on the application of this know-how to the fieldoriented solutions of production problems.

481

Trapped gas saturations in carbonate formations Both gas reservoirs with a naturally-occurring underlying aquifer and aquifer gas storage projects offer possibilities for large volumes of gas to be trapped and not recovered. This trapping has been documented to occur in various carbonate rock types (Kellan and Pugh, 1973) and sandstones (Geffen et al., 1952). Gas trapping results from gas-water capillary forces that become active as production occurs and water encroaches into pores that previously contained water and gas.

Testing configuration. Kellan and Pugh (1973) investigated trapped gas in the laboratory by testing suites of cores from five carbonate formations (Cretaceous Austin Chalk Formation, Jurassic Smackover Formation, Permian Abo Formation, Pennsylvanian Lansing-Kansas City Group and Silurian Niagaran Formation). The testing scheme for defining the magnitude of trapped gas, which could exist in these carbonate reservoirs, attempted to correlate this phenomenon with porosity, permeability, and carbonate rock type. The samples covered the porosity and permeability range within each field tested. Cores from five Smackover reservoirs located in the states of Arkansas, Florida, Mississippi and Texas, U.S.A., were selected in order to examine differences in trapped gas, which might occur within a stratigraphic unit distributed over a large geographical area. The core samples from the Smackover ranged from extremely fine-grained, uniform dolomite to a coarse-grained, poorlysorted oolitic limestone. Kellan and Pugh (1973) classified the carbonate samples from thin-sections based on Archie's rock type, where Type I is composed of a compact crystalline matrix, Type II is a rock with a chalky matrix, and Type III rock has a sucrosic matrix. Differentiation of the capillary pressure-saturation curves, obtained from core testing using both air-water restored state and air-mercury techniques, yielded histograms showing the distribution of pore-entry radii as a function of pore space. Pore sizes in the carbonate samples tested ranged from "A" (0.01 mm) to "D" (> 1.0 mm) sizes as defined in the Archie system (Archie, 1952; Jodry, 1992) (Table 5XXVI). The study employed Pickell et al.'s (1966) technique for determining the trapped gas saturation. Experimental results. Table 5-XXVI presents the results of Kellan and Pugh' s (1973) tests. Core samples, for the most part, were 1.5-in. (3.75-cm) in diameter; a few were only 1-in. (2.5-cm) in diameter. Figure 5-126 presents a cross-plot of porosity vs. trapped gas saturation for an initial gas saturation of 80% of pore space. Trapped gas saturations varied from 23% to 68% of the pore space in cores containing 80% initial gas saturations. The data show that the pore throat connections, as reflected by matrix characteristics, are more important than total porosity. Archie's rock types I and II have trapped gas essentially independent of porosity. Trapped gas values for mixed rock types were, in many cases, no higher ( 3 8 . 9 - 80%) than for those reservoirs that contained only one rock type (Table 5-XXVI). Type II carbonates had a favorable gas saturation of about 30% pore space, whereas Type I samples had saturations exceeding 52% pore space. Archie's Type III samples exhibited a greater dependence on porosity. The data showed that the trapped gas increased as porosity decreased within Type II sucrosic and oolitic reservoirs. Kellan and Pugh (1973) noted that there is a general trend of increasing

482 TABLE 5-XXVI Basic data on the core samples from various carbonate reservoir rocks located in the U.S.A. Samples without numbers are the previous samples tested at 20 and 50% initial gas saturation values. Rock type refers to Archie's classification of carbonate rocks, where L (large grains > 0.5 mm), M (medium grains: 0 . 2 5 - 0.5 mm), F (fine grains: 0 . 1 2 5 - 0.25 mm), VF (very fine grains: 0 . 0 6 2 5 - 0.125 mm), and XF (extremely fine grains <0.0625 mm). Visible porosity is divided into four classes: A, not visible under 10x magnification; B, visible under 10x magnification; C, visible to the naked eye; and D, pore size greater than most drill cuttings indicated by secondary crystal growth on faces of cuttings Sample number

Porosity (%)

Permeability (mD)

Gas saturation Initial Final 80 80 50 20 80 80 50 20 80

31.8 33.3 29.5 14.5 30.0 34.5 30.1 14.6 55.5

80 80 80 50 20 80 50 20 80

40.2 38.9 39.9 30.0 14.7 40.3 30.0 16.3 44.4

80 80 50 20 80 50 20 80 80

37.0 43.0 36.0 16.8 50 39 18.9 45.5 49.0

IIIfm B IIIfc B/IA

80 50 20 80 80 50 20 80 80 80

33.9 27.8 13.3 39.7 43.9 33.1 14.0 44.8 42.3 41.9

IIIxfvfB

Rock type

Smackover Formation (Texas) 1 2

34 31.1

549 313

3 4

26.7 23.8

108 59

5

20.9

14

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IIIfvfB IIIfm B

IIIvf/Ixf C

Smackover Formation (Arkansas) 6 7 8

21.7 21.7 20.6

302 35 116

9

19.9

6.1

10

17.5

1.0

IIIvf BC/IAB IIIxfBC/IA IIIvfBC/IA

IIIxf AB/IA

IIIxf A

Smackover Formation (Mississippi) 11 12

17.8 13.7

408 141

13

10.2

33

14 15

11.1 8.2

3.2 62

IA/IIIfc B

IIIfB/IA IA/IIIm B

Smackover Formation (Florida Area) 16

27.0

135

17 18

23.9 17.0

30 14

19 20 21

13.9 12.6 21.9

5.6 1.1 100

IIIxfvf A IIIxfvf A

IIIxfvf A IIIxfvf A IIIvfB

483 Sample number

Porosity

("/I

Permeability (mD)

Gas saturation Initial Final

22

21.3

245

23

19.2

40

24 25

15.0 10.2

60

80 50 20 80 50 20 80 80

46.1 34.3 16.9 44.5 32.9 16.2 49 53.8

80 80 50 20 80 50 20 80 80

30.5 30.4 26.0 12.3 29.8 30.0 12.2 23.4 30.4

IIxf AB IIxf BC

80 50 20 80 80 80 50 20 80

48.2 34.4 16.5 41.7 61.7 53.2 38.6 19.7 65.9

IIIf BCiIxf A

80 50 20 80 80 80 50 20 80

52.5 37.0 17.0 61.0 65.0 63.9 41.7 17.5 62.6

Ixf CD

80 50 20 80 50 20 80 80 80

68.5 44.2 17.9 66.8 43.6 17.3 62.3 67.2 68.1

Chalk Formation 26 36.5 27 32.3 28

30.7

29 30

28.9 21.8

4.1

59 104 15 7.1 1.7

Niagaran Formation 31 15.8

122

32 33 34

13.4 8.9 8.2

20 228 17

35

3.6

Abo Formation 36 13.0

5.7 500

37 38 39

11.7 10.1 6.3

39 45 4.3

40

5.7

9.4

Lansing-Kansas City Formation 41 28.9

222

42

25.1

39

43

24.9 22.4 22.1

550 5.7 9.0

44 45

Rock type IIIvf B IIIvf B IIIvf B IIIfvf BA

IIxf A IIxf A IIxf A

Ixf CiIIIf B Ixf CD Ixf CiIIIf B Ixf c

Ixf CD Ixf CD Ixf CD Ixf CD Ixf c Ixf CD Ixf c Ixf c Ixf c

Source: After Keelan and Pugh, 1973, table 2; reprinted with the permission of the Society of Petroleum Engineers.

484 40

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80

TRAPPEDGAS PERCENTPORESPACE Fig. 5-126. Laboratory-determined relationships between the trapped gas, porosity, and Archie's rock types (I, II, III, III/I and I/III) for various carbonate reservoirs in the U.S.A. Initial gas saturation was 80% o f the pore space. (After Keelan and Pugh, 1973, fig. 11; reprinted with the permission o f the Society o f Petroleum Engineers.)

trapped gas with decreasing porosity on both intra- and inter-reservoir scales (Table 5-XXVI and Fig. 5-126). Their laboratory data also indicated that trapped gas is a function of the initial gas saturation. Different correlations were attempted to relate trapped gas, as a function of the initial gas saturations, to porosity, permeability, and a combination of the two. None of these parameters were entirely satisfactory. However, two other approaches, where one corresponded to the irreducible water saturation and the other to common initial gas saturation, appeared to be viable. The latter approach improved the correlation as demonstrated by Fig. 5-126 (Kellan and Pugh, 1973). Each core sample had a variable irreducible water saturation (Sir) and the corresponding initial gas saturation depends upon the pore geometry. An initial water saturation of 20% pore space was

485 selected to remove the variable of irreducible water. Actual S i r values were, for the most part, within 10% (higher or lower) of the chosen 20% value. Kellan and Pugh (1973) extrapolated the trapped gas values to 20% initial water saturation using the initial vs. trapped gas saturation curve shapes available on two cores from each of the reservoirs studied. Their tests also yielded additional trapped saturation values for initial gas saturation at 50% of the pore space in each one of the cores.

Importance to carbonate reservoirs and aquifer gas storage projects. The application of Kellan and Pugh's (1973) results would be important to select the number of gas reservoirs where large amounts of gas could be trapped and not recovered. The results, however, are very important in aquifer gas storage projects. They tested two cores from each reservoirs to yield additional information on trapped gas saturations using initial gas saturation values of 20 and 50%. The carbonate reservoirs which exhibit gas trapping have a low permeability and a high capillary pressure, or limited structural relief where most of the reservoir is underlain by water. These conditions can result in an appreciable transition zone where variable amounts of gas will be trapped as water moves upward in the reservoir (Kellan and Pugh, 1973). If a relatively large portion of a naturally-occurring reservoir is at an irreducible water saturation and has a limited gas-water transition zone, it tends not to have a problem with trapped gas. The fluid configuration results from a large density difference between the two fluids and there has been a significant amount of geologic time to allow the separation of the gas and water. Under these conditions, most of the reservoir exists at the irreducible water saturation and the trapped gas values at other saturations are not important (Kellan and Pugh, 1973). The fluid distribution in gas storage aquifers tends to be more complex. Reasons for this condition are: (1) the equilibrium time between the two fluids is significantly shorter than geologic time, and (2) the injection-withdrawal sequence complicates the fluid distribution in the reservoir. Kellan and Pugh (1973) stated that the total reservoir may exist at varying gas saturations, with lower saturations at increasing distance from the injection wellbore. Water encroaches to replace the gas at the time of gas withdrawal resulting in variable trapped gas volumes, which would be less than if the carbonate reservoir was at an irreducible water saturation. Solution-gas-drive and gas-cap-drive reservoirs The performance of carbonate reservoirs under solution-gas-drive or gas-cap-drive varies over a wide range, depending on the nature of the producing zone. Figures 1-10 to 1-15 in Chapter I present the general field k / k behavior of reservoirs having (1) intergranular, (2) vuggy, and (3) fracture-matrix porosities. The performance of reservoirs with intergranular-intercrystalline porosity resembles closely that of sandstone reservoirs with similar k/k g o curves and ultimate oil recovery. Reservoirs with vuggy porosity may have lower ultimate recoveries owing to less favorable and more unpredictable kg/ko behavior. Finally, reservoirs having fracture-matrix porosity proved to be the most difficult to evaluate because of very erratic performance. These reservoirs generally have low ultimate recoveries owing to low-permeability host rock, even though the existence of fractures greatly increases permeabilities. Carbonate reservoirs

486 with nonuniform porosity typically have kg/k o c u r v e s with low equilibrium gas saturations that sometimes approach zero. The low recoveries are due in part to the inefficient displacement of the oil contained in the pores by the solution-gas bubbles and the gas coming from outside the oil zone. In addition, it appears that gravity segregation of fluids in the secondary channels, particularly the fractures, may play an important role in the production process. In a highly-fractured reservoir the fracture system may, at least at low withdrawal rates, act as an effective oil and gas separator. On emitting from the matrix, the oil and gas separate, with the gas migrating upward to form a secondary gas cap in some cases. Fluid segregation in the fractures may have a pronounced effect on reservoir performance.

Fractured reservoir performance. Pirson (1953), in considering the problem from a theoretical standpoint, assumed a highly-fractured reservoir model with a low matrix and high fracture permeability, both horizontally and vertically. Under these conditions, the nature of the fluid segregation and its effect on ultimate oil recovery were examined. Pirson calculated the theoretical reservoir performance for various types of fluid segregation. He used an average k / k curve for a group of dolomite reservoirs with an equilibrium gas saturation of about 7%. For slmphclty, the productmn process was viewed as a succession of depletion stages separated by shut-in periods. During these periods, the static and capillary pressures reached equilibrium in both the matrix and the fracture system.As a result, fluid saturation readjusts in the reservoir's pore system during the shut-in periods. Several degrees of segregation were considered in the theoretical calculations: (1) no segregation of oil and gas in a simple depletion performance; (2) segregation from the upper 90of the reservoir, with enough oil draining downdip to resaturate the lower 88of the zone during the shut-in periods to 90% liquid saturation; (3) comparable to case 2, but with the oil draining from the upper 89of the reservoir to resaturate the lower 89of the zone; and (4) comparable with cases 2 and 3, but with oil coming from the upper 88of the reservoir to replenish the lower 90of the zone. As expected, there is a decrease in calculated ultimate oil recovery and an attendant increase in peak gas/oil ratio in going from case 1 to case 4. The respective ultimate oil recoveries and peak gas/oil ratios, progressing from case 1 to case 4, are: 27.0% and 7,500 ft3/bbl, 20.8% and 12,000 ft3/bbl, 14.5% and 37,000 ft3/bbl, and 9.6% and 83,000 ft3/bbl. In view of the continuous fracture system assumed, a kg/ko curve with an equilibrium gas saturation approaching zero would be more realistic. Under this circumstance, Pirson's (1953) calculated ultimate recoveries would be reduced by one-quarter to one-half. Most of the kg/ko curves for carbonate reservoirs suggest lower values for equilibrium gas saturation than those in sandstones. Another phenomenon mentioned by Pirson (1953), Elkins and Skov (1963) and Stewart et al. (1953) is the possible reduction in oil recovery in fractured carbonate reservoirs caused by the capillary end effect. This condition develops at the effiux end of a core in the laboratory or at the end of matrix block in the reservoir. Hadley and Handy (1956), in a theoretical and experimental study, stated that the end effect is caused by the discontinuity in capillary pressure when the flowing fluids leave the 9

g

o

.

.

.

.

487 porous medium and abruptly enter a region with no capillary pressure. The capillary pressure discontinuity tends to decrease the rate of effiux of the preferentially wetting phase. They compared the amount of oil expelled from the core or matrix blocks to the rate of efflux of the nonwetting phase or the gas phase. Accordingly, oil tends to accumulate near the edges of the blocks. Laboratory experiments show that the end effect becomes less important at higher flow rates. Figure 5-127 presents a comparison between the observed and the calculated saturation distribution in a core at various flow rates under conditions approaching steady state. At higher flow rates, oil recovery increases and the oil saturation buildup becomes more localized toward the outlet end of the core. The overall effect of the capillary end effect in a fractured reservoir is to decrease oil recovery and to increase the average gas/oil ratio during the life of the reservoir. At the flow rates experienced in the field, the end effect is normally unimportant. It probably would be significant only in extensively fractured zones where the dimensions of the matrix blocks are on the order of several inches rather than several feet (Elkins and Slov, 1963). A possible solution to the problems of gravity segregation and end effect is to attempt to prevent them developing, which can be accomplished by producing the wells at high drawdown rates. High producing rates must be compatible with water aO0

I

0

l-Z L~ 0

80,

LLI IX.

a

60"

~

40"'

u') J

~ 20

9

GAS F L O W R A T E o .0~3~ CC/SEC A .189

CC/SEC

9 4.6,5 CC/ SEC 0 0

.2

DISTANCE

.4

FROM

~ .6

.8

1.0

INLET END OF CORE, FT

Fig. 5-127. Comparison of observed and calculated fluid distribution in a core for a gas-oil system at various flow rates. (After Hadley and Handy, 1956, reprinted with the permission of the Society of Petroleum Engineers.)

488 influx and market demand considerations. Under high horizontal pressure gradients, oil and gas flowing from the matrix blocks may move more directly to the producing wells, thus reducing fluid segregation and end effects.

Withdrawal Rate of Recovery- Solution-Gas-Drive The original concept of the maximum efficient rate of recovery was originally depicted by Buckley (1951). He stated that excessive rates of withdrawals lead to rapid decline of reservoir pressure, to the release of dissolved gas, and creation of an irregularity in the boundary between the invaded and non-invaded sections of the reservoir. Furthermore, (1) gas and water are dissipated, (2) trapping and by-passing of oil occurs, and (3) in extreme cases, there is a complete loss of demarcation between the invaded and non-invaded parts of the reservoir, with dominance of the entire recovery by inefficient dissolved-gas drive. Each of the above effects of excessive withdrawal rates reduces ultimate oil recovery. It was further pointed out by Buckley (1951) that for each reservoir there is (for the chosen dominant drive mechanism) a maximum production rate which will permit reasonable fulfillment of the basic requirements for efficient recovery. Lee et al. (1974) pointed out that Buckley's concept was formulated when conservation concepts were being developed. Enhanced recovery technology or pressure maintenance were not universally practiced by the industry. The only means by which to maintain efficient recovery was to exercise rate control to achieve the benefits of the most efficient natural drive mechanism. Additional field evidence is needed to support a broad conclusion that an increased oil recovery results from the high withdrawal rates (or maximum efficient rate) in carbonate reservoirs under solution-gas drive. Stewart et al. (1953) conducted similar gas-drive experiments on sandstone cores. The relative permeability relationships were identical under both extemal-gas- and solution-gas-drive conditions in all cases. It appears that in rocks having uniform porosity the pores act as fluid conductors as well as fluid storage spaces. It is not necessary, therefore, for gas bubbles to form in the pore spaces themselves, as the gas evolved upstream is able to enter essentially all the individual pores to achieve oil displacement. The recovery from carbonates can vary several-fold from 12 to 58% based on the laboratory solution-gas-drive tests (Stewart et al., 1953).Also carbonates exhibit great differences in gas-oil relative permeabilities between the solution- and gas-drives. These differences indicate the inadvisability of extrapolating field solution-gas-drive performance to predict the external gas-drive performance as shown in Fig. 5-122. Jones-Parra and Reytor (1959) mathematically modeled the effect of fluid segregation in the fracture system on carbonate reservoir production performance and ultimate recovery. The model consisted of an idealized network having a high-permeability matrix with no gravity segregation (Figure 5-20). The porosities of the reservoir were divided into two broad types in accordance with their assumed effects on fluid distribution and flow. The coarse porosity is presented on the left side, where gravity segregation is believed to take place freely and the resistance to flow is very low. Fine porosity is presented on the right-hand side, where there is a high resistance to flow with relative permeability characteristics similar to those of a low-permeable sandstone. Gravity segregation does not occur here. Using the model's assumptions, it is possible to recover more oil by producing at high rather than at low gas/oil ratios. In

489 this manner, the fine porosity is drained more effectively. Overall production declines less when producing at the higher k / k values in spite of the fact that at any given stage of depletion, the pressures areglower. Jones-Parra and Reytor's (1959) purely mathematical treatment supports the contention that higher withdrawal rates at increased gas/oil ratios may enhance oil recovery in some instances (Fig. 5-20). Needless to say, the validity of these conclusions depends, as in all simulation studies, on how well the particular model used represents actual carbonate reservoir conditions. Inasmuch as matrix porosity and fracture networks may exist as an integral system, such a model could be an oversimplification of the complex conditions existing in many carbonate reservoirs. In fact, Jones-Parra and Reytor's (1959) results appear to contradict the inferences drawn by Elkins (1946) on the basis of observations of a limited number of carbonate reservoirs. He stated that the faster production rate in the Harper Field (San Andres Formation), west Texas, U.S.A., probably caused less favorable recovery characteristics than did the slower production rate in the Penwell Field (San Andres Formation), west Texas, U.S.A. (see curves 8 and 9, Fig. 1-10). Water- and gravity-drive reservoirs The concept of the maximum efficient rate in water and gravity drives operating in carbonate reservoirs also has changed considerably since Buckley (1951) comments. This is due to significant advancements, which challenged and changed reservoir management techniques during the past 40 years. Current field practice assures control of the most efficient recovery mechanism throughout the life of a reservoir. Universally instituted EOR schemes can supplement or replace inefficient recovery mechanisms. In the previous discussions, the writers have shown that the greatest impact has come from advancements in quantifying complex fluid-flow problems associated with carbonate reservoirs. Computer simulations provide production data from the combined effects of pressure decline, gravity, imbibition, viscous forces, fluid properties, and fluid movement in the reservoir. Lee et al. (1974) showed that for the displacement mechanisms in typical westem Canadian carbonate reservoirs, there is no definable depletion rate, within the practical range, above which recovery begins to deteriorate. Doubling the withdrawal rates in the high-relief carbonate reservoirs, subjected to gravity control, has little effect on the ultimate recovery. The magnitude of the effect that permeability and relative permeability have on gravity drives in highrelief reservoirs is shown by Beveridge et al.'s (1969) computer model studies. Withdrawal rate of recovery - w a t e r drive. Multidimensional, multiphase mathematical simulator studies and performance analyses of western Canadian carbonate reservoirs indicated that recovery is improved when pool and well rates are increased, provided the desired water displacement mechanism is maintained (Lee et al., 1974). The increased recovery at increased production rates is attributed to the operator's ability to cycle more water through the reservoir prior to reaching the economic limit. In their model study, Lee et al. (1974) used depletion rates that varied from 1 - 50% of ultimate reserves per year. These rates far exceed the limits for normal withdrawal rates used in western Canadian carbonate reservoirs. It should be noted that whereas

490 better recoveries were obtained at low rates at a given water/oil ratio or a given water throughput, in all of Lee et al.'s model scenarios improved recovery to the economic limit was achieved at increased withdrawal rates. The models showed that there was no definable maximum rate within the practical economic depletion rates at which recovery begins to decrease for these carbonate reservoirs. Lee et al.'s (1974) mathematical model studies analyzed the sensitivity of ultimate recovery to well producing rates for selected reservoirs in the Upper Devonian Leduc and Beaverhill Lake formations of westem Canada. The majority of Canadian carbonate reservoirs are found in these two formations and have the greatest potential for future increases in production rates. These reservoirs, therefore, are significant and have to be considered in any assessment of the effect of rate on recovery. Different variations of the Leduc coning model were used to investigate the raterecovery relationship for bottom-water-drive pools. Reservoir conditions that could be indicative of water coning are: (1) high vertical permeability, (2) presence of a water contact across the entire reservoir, (3) high production rates; (4) high GOR or WOR ratios, and (5) the resulting high bottomhole pressure drawdowns. Oil production, controlled by water coning at the economic limit, determines when a well and, ultimately, when a reservoir is depleted. Reservoir parameters (obtained from field and laboratory tests) used in the three model studies are: ~ = 6.53%; Sw= 25%: OIP = 5.4 MMSTB; oil zone thickness = 100 ft; aquifer thickness = 100 ft; and 1973 actual field costs. The first model tested was a homogeneous carbonate system having the following permeability values: kh = 5,000 mD and k = 10 mD. Results are presented in Fig. 5128A. Ultimate recoveries, to the economic limit, carried from 65.8% oil-in-place (OIP) for the 5,000 bbl of total fluids produced per day (BFPD) to 63.6% OIP for the 100 BFPD. As expected, water breakthrough occurred earlier for the increased rates, which resulted in quite different water/oil ratio performance for each case as shown in Fig. 5-128A. Lee et al. (1974) pointed out that it is the level of water/oil ratio at a given oil rate that establishes the economic limit. Results showed that when larger volumes of water are cycled through the Leduc homogeneous reservoir, the ultimate recoveries are higher. The 5,000 BFPD case resulted in a 65.8% recovery, in contrast to 63.6% for the 100 BFPD case (Table 5-XXVII). A second homogeneous case investigated the sensitivity of recovery to the well rate as a function of the ratio of horizontal to vertical permeability (kh = 500 mD and k~ = 10 mD). The value of this ratio affects the coning characteristics of a well. Lee et al. (1974) reported that the water breakthrough occurred 15 - 20% OIP earlier for each producing rate than in the previous 5,000-mD case. Again, the results show that with higher production rate, a greater percentage of the oil is recovered, but not as much as in the first case (Table 5-XXVII). Lower ultimate recovery is due to an increase in water coning. The third Leduc coning case considered a heterogeneous carbonate system. The model was constructed with kh values ranging from 2 to 5,000 mD and k values ranging from 0.02 to 300 mD. Figure 5-128B summarizes the predicted performance for this case. Lee et al. (1974) attributed the early water breakthrough in the heterogeneous reservoir to lower overall permeability values, which increased the coning tendencies, as compared to the homogeneous cases. Better oil recoveries at increased producing rates are evident in Table 5-XXVII.

B

A ~

T

ECONOMIC LIMIT BFPD

m ,

I

ECONOMIC LIMIT BFPD

100

-

i

"\I

-.,.~ S000

I 1000

-

S01)

I

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;

t

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1000__

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-

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50

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H O M O G E N E O U S SYSTEM RESULTS (K h ,

"\

100

A

.

i

10

20

30

i

J

00

~0

CUik~Jl~kTlVE OIL PRODUCTION - % OIP !0

20

310 40 50 80 CUIIKJLATIV| OIL PIIOOUCTION - % OIP

70

Fig. 5-128. Effect of variable production rates on oil recovery based on a two-dimensional, two-phase water coning model (Leduc reef coning model). ( A ) Performance results for a homogeneous carbonate reservoir. The water breakthrough occurred early for the increased rates, which resulted in significantly :lifferent water/oil ratio performance for each case. ( B ) - Performance results for heterogeneous carbonate reservoir. Here, water breakthrough occurred earlier Lhan for the homogeneous system due to increased coning tendencies. (After Lee et al., 1974, figs. 2 and 3" reprinted with the permission of the Society of Petroleum Engineers.)

,D

492 TABLE 5-XXVII Recovery efficiencies at economic limit generated by different computer models in a western Canadian carbonate reservoir simulation study Fluid rate bfpd

Oil rate bopd

WOR bbl/bbl

Recovery % OIP

Water cycled MMSTB

Homogeneous kh = 5000 mD k = 10 mD

5000

26

192

65.8

21.4

1000 500 100

10 7 5

99 71 19

65.2 64.9 63.6

10.4 6.2 1.5

Homogeneous kh = 500 mD kV= 10 mD

500

7

71

63.8

8.6

100

5

19

62.2

2.8

Heterogeneous

1000 500 100

10 7 5

99 71 19

58.2 57.7 54.4

27.4 22.8 10.5

Tight lenses

1000 500 100

10 7 5

99 71 19

64.0 63.2 62.3

11.1 5.4 1.4

Leduc Coning Model

Layered Model Thick layer system

500 100

28 22

17 3.5

55.6 57.8

0.61 0.58

Thin layer system

500 100

28 22

17 3.5

59.2 57.8

3.06 0.24

Source: After Lee et al., 1973, table 2; reprinted with the permission of the Society of Petroleum Engineers.

Lee et al.'s (1974) fourth model was developed to study the sensitivity of recovery to production rate for tight lenses in an otherwise homogeneous carbonate matrix. Four lenses were included in the model to introduce areas of significantly reduced horizontal and vertical permeability. Results show that oil recovery increases uniformly from 62.3 to 64.0% OIP for rates of 100 and 1,000 BFPD (Table 5-XXVII). Lee et al. (1974) noted that the position of the lens in the reservoir, and the magnitude of its permeabilities, determine if increased rates have a beneficial or detrimental effect on oil recovery from the specific lens. The increase in water throughput offsets any slight reduction in recovery from some of the lenses (Lee et al., 1974). The coning model was used to investigate the effect on ultimate recovery of increased rates (100 BFPD to an economic limit and then the rate was increased to 1,000 BFPD) in a heterogeneous reservoir during late stages of depletion. Figure 5129A indicates that recovery is improved from 54.4% to 57.8% OIP as a result of the increased rate. Lee et al. (1974) noted that the rate increase, however, captured only 90% of the additional recovery, which would have been achieved by producing at

1 m -

I

I

I

I

I

I

B

INCREASED TERMINAL RATE MODEL RESULTS

,cam

BEAVERHILL LAKE YODEL RESULTS

im--

im

s

c

I w

f

< E 4

4

ECONOMIC LIMIT B P I 0

I

5

10

1-

_-

10

52

CUMULATIVE OIL

54

Id

Id

rnowcnm

60

62

1

- x OIC

493

Fig. 5- 129. Effect of variable production rates on oil recovery based on two different models. (A) - Leduc reef coning model performance results showing the effect of increased terminal rates on ultimate recovery during late stages of reservoir depletion; (B) -Cross-sectional model performance results on Beaverhill Lake Formation. (After Lee et al., 1974, figs, 5 and 7; reprinted with the permission of the Society of Petroleum Engineers.)

494 1,000 BFPD over the entire life of the well. Additional costs to accommodate the additional water produced could make the change in production practice unattractive. A Beaverhill Lake cross-sectional reservoir model (13 x 17 grid system) was developed by Lee et al. (1974). The model used horizontal and vertical permeability and porosity data, and fluid displacement functions obtained from core analyses of a specific Beaverhill reservoir. The parameters used in the model are: (1) horizontal permeabilities ranging from 5 to 1,900 mD, (2) vertical permeabilities ranging from 0.003 to 1.0 mD, (3) the total oil volume of 4.7 MMSTB, (4) actual field costs, and (5) economic limits ranging from 22 BOPD (100 BFPD) to 51 BOPD (1,000 BFPD). Figure 5-129B illustrates the predicted performance by the cross-sectional model. Water breakthrough occurred between 40% and 45% OIP and is consistent with the field-observed recoveries to water breakthrough (Lee at el., 1974). Ultimate recovery for the 1,000 BFPD is 5.8% OIP higher than the OIP at 100 BFPD. Another set of models was devised to consider the effect of thickness of lowpermeability carbonate layers on oil recovery in reservoirs where imbibition and gravity flow of water occur into these layers. The low-permeability layers may be sufficiently thick that complete drainage by imbibition will not occur prior to reaching the economic limit (Lee et al., 1974). The thick-layer model represented a reservoir 6,000 ft (1829 m) long, 100 ft (30 m) thick and 870 ft (265 m) wide having 6% porosity, S = 8%, and OIP of 4.7 MMSTB. The economic limits used were the same as those in the Beaverhill Lake model. Each layer was 16.7 ft (5 m) thick, and the layers were interbedded in a continuous lowpermeability layer and a continuous high-permeability layer. A capillary pressure function was applied to the footage-weighted average horizontal permeability of 16.8 mD. The capillary pressure function assigned by Lee et al. (1974) to each layer was modified by the Leverett "J" function for its permeability level. Horizontal permeabilities varied from 1.4 to 60.5 mD and were determined from a permeability capacity distribution curve. Lee et al. (1974) used one-tenth the harmonic average of the horizontal permeabilities to generate vertical permeability values. The thin-layer model was composed of layers only 5.6 ft (1.7 m) thick (1/3 the thickness of the thick-layer model). Results for the thick-layer case (Table 5-XXVII) show that recoveries range from 57.8% of the OIP at 100 BFPD, to 55.6% for the 500 BFPD. This case was the only one studied by Lee et al. (1974) where recovery did not improve with increased production rates. The thin-layer model showed the opposite effect. The 500 BFPD case recovered 59.2% OIP, which is 1.4% greater than the 100 BFPD scenario. Lee et al. (1974) used another cross-sectional model (18 x 13 grid system), and an areal model (10 x 14 grid system), to establish the effect of individual well rate restrictions and differential depletion due to selective withdrawal patterns on percent recovery of oil-in-place. Sketches of the grid models, showing the location of wells A and B, are presented in Fig. 5-130. The assigned parameter values are listed for each of the two models in Fig. 5-130. Each of these models was produced in accordance with the following three rate schedules (Lee et al., 1974): (1) Both parts of the reservoir were depleted at equal rates in order to achieve a peak rate of 10% of the ultimate reserves per year. Well rates were allowed to increase to a maximum fluid-producing capacity of twice the initial oil rate after water breakthrough; (2) Initially, only the well located in the high-permeability region was produced.

495

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B Fig. 5-130. Differential depletion model results showing the effects of individual well rate restrictions and differential depletion on reservoir performance. ( A ) - Cross-sectional system having two wells A and B, where J is the Leverett function {J(Sw) = Pc/6(k/~)~, where Pc is the capillary pressure in dynes/cm 2, is the interfacial tension in dynes/cm, k the is permeability in cm 2, and ~ is the fractional porosity}. (B) Areal system having two wells A and B. (After Lee et al., 1974, figs. 8 and 9; reprinted with the permission of the Society of Petroleum Engineers.)

Production from the low-permeability part commenced when oil productivity from the high-permeability well decreased below the production rate of 10% of ultimate recovery per year; and

496 (3) Similar to schedule 1, except that the total fluid production was restricted to the initial oil rate. The differential depletion cross-sectional model (Fig. 5-130A) had 10.8 MMSTB OIP. The economic limits were the same as used by Lee et al. in their Leduc coning model. Results from the simulation are given in Table 5-XXVIII. Target oil rate was 2,000 BOPD. Schedule 2 gave the highest recovery, whereas schedules 1 and 3 were 0.1% and 0.9% of schedule 2, respectively. The areal simulation (Fig. 5-130B) used a target oil rate of 1,600 BOPD, with 9.4 MMSTB OIP. Wells A and B in schedule 1 have maximum fluid production capacities of 1,600 BFPD. Results from the simulation are given in Table 5-XXVIII. Both differential depletion model variations demonstrated that the selective withdrawal patterns, which result in concentrating production in the higher-permeability portion of the reservoir, do not result in a loss of ultimate recovery for the bottom-water drive. Only rate restrictions will lead to a loss in ultimate recovery in these carbonate reservoirs (Lee et al., 1974). The results of the model study compared very well to performance analyses Lee et al. (1974). Four pools in Alberta, Canada (Redwater D-3, Leduc Formation; Excelsior D-2, Leduc Formation; Judy Creek A and Judy Creek B, Beaverhill Lake Formation), were chosen for analysis based on increases in their production rates within the previous 3 years. Both the Redwater and the Excelsior pools produce under a typical Leduc strong bottom-water drive. The Redwater Field is a very large bioherm (200 mi2; 520 klTl2), which rests on a drowned carbonate platform and is surrounded by the basinal shales. The Judy Creek bioherm reservoirs require pressure maintenance by waterflooding. Porosity is best developed in the reef, reef detritus along its perimeter, and in a detrital zone across the top of the reef (Jardine and Wilshart, 1987). Lee et al. (1974) observed no significant change in the recovery efficiency at increased withdrawal rates. They concluded that the ultimate recovery will be increased with increased production rates owing to the greater volume of water throughput before reaching the economic limit (Table 5-XXIX). These conclusions are similar to those reached by Miller and Roger (1973) for typical Gulf Coast reservoir conditions. TABLE 5-XXVIII Generated recovery efficiencies at economic limit using differential depletion models in a western Canadian carbonate reservoir simulation study

System

Maximum well capacity Target rate Oil rate WOR Schedule (bfpd) (bopd) (bopd/well) (bbls/bbl)

Recovery (% OIP)

Water cycled (MMSTB)

Cross-section 1 Cross-section 2 Cross-sectiop, 3

2000 2000 1000

2000 2000 2000

14 14 10

142 142 99

61.5 61.6 60.7

43.2 43.9 28.3

Areal Areal Areal

1600 1600 800

1600 1600 1600

60 60 46

26 26 16

66.0 66.0 64.3

7.7 7.4 4.6

1 2 3

Source: After Lee et al., 1974, table 3; reprinted with the permission of the Society of Petroleum Engi-

neers.

497 TABLE 5-XXIX Recovery efficiencies determined from performance analyses of four Canadian Devonian carbonate reservoirs located in Alberta, Canada (after Lee et al., 1974, table 4; reprinted with the permission of the Society of Petroleum Engineers) Redwater D-3 Pool

September 1964

September 1971

December 1973

Hydrocarbon volume invaded- MMSTB Net Water Influx- MMSTB Flushing Efficiency-% OIP

451.9 287.5 63.6

610.4 405.6 66.4

722.7 487.9 67.5

Excelsior D-2 Pool

December 1960

January 1968

June 1973

Hydrocarbon volume invaded- MMSTB Net Water Influx- MMSTB Flushing Efficiency- % OIP

14.2 8.5 59.4

19.6 12.3 62.7

24.7 16.1 65.2

Judy Creek BHL A Pool

December 1969

December 1973

Hydrocarbon volume invaded- MMSTB Net Water Influx- MMSTB Flushing Efficiency- % OIP

193.9 57.3 29.6

385.2 124.4 32.3

Judy Creek BHL B Pool

December 1969

December 1973

Hydrocarbon volume invaded- MMSTB Net Water Influx- MMSTB Flushing Efficiency- % OIP

43.4 17.8 41.0

94.7 39.3 41.5

Some 13 years later, Jardine and Wilshart (1987) reported the projected approximate recovery factor for the Redwater Field to be 65% and for the Judy Creek Field to be 45%. The Redwater recovery factor is just 2% lower than Lee et al.'s (1974) projection of 67.5%, whereas Judy Creek's recovery factor is much higher than the 1969 and 1973 projections (Table 5-XXIX). This increase is due to better definition of the flow heterogeneities in the reef. This heterogeneity problem was addressed by strategically placing water injection wells into discontinuous porous zones, and then establishing a pattern waterflood. The pattern waterflood, which was placed in operation in 1974, showed a dramatic improvement in reservoir pressure approximately one year later (Jardine and Wilshart, 1987). The validity of this production practice is demonstrated by the results. H i g h - r e l i e f reservoir recovery performance. One of the greatest challenges in reservoir engineering is a reliable determination of the expected performance of a highrelief, vuggy carbonate reservoir subjected to gravity control. An example of such a reservoir would be a pinnacle reef where the height of the reef is measured in hundreds of feet. Gravity drainage is where gravity acts as the main driving force, and where gas replaces the drained reservoir pore volume. It may occur in primary stages

498 of oil production (gas-expansion drive or segregation drive), as well as in supplemental stages when gas is injected into the reservoir. The displacement efficiency for gravity drainage can be as high as 87%, and it is especially effective in water-wet, water-bearing reservoirs (Hagoort, 1980). Beveridge et al. (1969) presented simulation results of a sensitivity study to determine the effects of withdrawal rate, permeability, and relative permeability on the recovery performance of high-relief carbonate reservoirs. Their study was carried out using a one-dimensional (assuming one-dimensional vertical flow), three-phase reservoir model of a typical Devonian Rainbow-Zama pinnacle reef reservoir. It was observed by Beveridge et al. (1969) that under gravity-controlled conditions, conventional relative permeability data obtained by the unsteady-state Welge displacement method in the laboratory do not cover the low oil saturation range needed for accurate recovery predictions. Relative permeability curves can be extrapolated beyond the terminal point of the unsteady-state Welge-determined curve. However, this extrapolation is exceedingly difficult because it is the character of the curve and not the mid point that controls recovery. A better method would be a steady-state determination of relative permeability at low oil saturations. Hagoort (1980) determined the relative permeability of a dolomite in the Middle Cretaceous Karababa carbonates (Mardin Group) in the Kurkan Field, southeastern Turkey, using steady-state centrifuge results. They plotted the results graphically as: log (1-N)p vs. log Apog (g)k(t)/(l.to [~b(1 - S lw Sorg)]L, where N is the cumulative oil production expressed as a fraction of the movable oil volume IV.(1 -Siw-Sor.)] during the core test, V is the pore volume, Siw is the initial water satura~tion, Srg_iS ti~e residual oil saturation " Pfor displacement by gas, L is the characteristic length of a core or reservoir, Apo g is the pressure differential between the oil and gas, g is the acceleration of gravity, k is the absolute permeability of the core, t is the time,/~o is the oil viscosity, and ~ is the porosity of the core. In most of Hagoort's (1980) core measurements, this plot resulted in a straight line allowing him to express the results as a Corey relative permeability. Table 5-XXX provides the results of oil relative-permeability measurements for two samples of dolomite from the Kurkan Field. The results show that there are low saturations after long drainage times and, apparently, low-permeablility dolomite cores may exhibit favorable oil relative permeabilities (Hagoort, 1980). As shown before, oil production from the high-relief reservoirs forms an appreciable part of the total oil production in Alberta, Canada. In many of these carbonate reservoirs, the primary recovery mechanism is gravity drainage. Gravity forces tend to segregate the fluids according to their densities, and segregation causes the oil to move vertically ahead of the displacing water or gas (Beveridge et al., 1969). Figure 5-131 shows the simulation results of the effect of withdrawal rate on the ultimate recovery. Even doubling the expected proration allocation rate of 800 BOPD had little effect (about a 3% reduction) on ultimate recovery (Beveridge et al., 1969). It was observed by Beveridge et al. (1969) that at equal times during the depletion of the reservoir, oil saturations in the top blocks of the model were the same regardless of rate. This finding suggests that the rate effect is related to depletion time and not to higher pressure gradients. At lower rates, model blocks in the secondary gas cap have more time to drain than at higher rates. Beveridge et al.' s (1969) simulations indicate that at the lower rates, top blocks of the model had 30 years longer to drain to their

499 TABLE 5-XXX Core-determined reservoir rock and saturation properties, and Corey relative permeability values for a dolomite in the Middle Cretaceous Karababa Formation, Kurkan reservoir, southeastern Turkey Core

k (mD)

~

Siw

Sw

SO (td= 100)

1

41 70

0.19 0.25

0.14 0.15

0.11 0.12

0.21 0.14

Siw 0.14 0.15

S*orange 0.13 - 0 . 4 0.07 - 0 . 4

2

Corey Relative Permeability Core 1 2

n 5.79 4.34

k~ 0.67 1.22

Sorg 0 0

Source: From Hagoort, 1980, table 1" courtesy of the Society of Petroleum Engineers. Note: k is absolute permeability; ~bis fractional porosity; Siw is initial water saturation; Sewis water saturation at the end of the measurement (td -- 100); n is relative-permeability exponent in kro = k~ S~ is average reduced oil saturation; Sorg is residual oil saturation for displacement by gas; td is dimensionless time and distance expression. effective residual oil saturations. Table 5 - X X X I presents the rock and fluid properties u s e d for the simulation. H i g h e r d i s p l a c e m e n t rates d o w n w a r d tend to offset the gas segregation u p w a r d o w i n g to the h i g h e r viscous pressure gradients i m p o s e d on the system. The gas cap m o v e s d o w n the r e e f with a lower average gas saturation; therefore, at h i g h e r rates, e c o n o m i c depletion is terminated by the high G O R p r o d u c t i o n at an earlier depletion stage. This termination will result in relatively higher residual oil saturations r e m a i n i n g in the h i g h - r e l i e f carbonate reservoir. B e v e r i d g e et al. (1969) p r o p o s e d that if the rates w e r e h i g h e n o u g h (a m a g n i t u d e h i g h e r than the p r o b a b l e rates), t h e n the TABLE 5-XXXI Rock and fluid properties used in the modeling of a pinnacle reef with 586 ft (179 m) of oil pay and no initial gas cap

Rock properties Porosity Vertical permeability Connate water saturation Maximum pay Oil originally in place

11.6% 29.2 mD 8.0% 586 ft 17,200,000 STB

Fluid properties @ Pb Saturation pressure Oil formation volume factor Solution gas--oil ratio Oil viscosity Oil gradient

1644 psig 1.2791 RB/STB 434 scf/STB 0.596 cP 0.31 psi/ft

Source: After Beveridge et al., 1969, table 1; reprinted with the permission of the Petroleum Society of Canadian Institute of Mining.

500

60

! 55 144

5O

5

T

2000

=-

9

9 9

1000 800

9

.

600

.

.

.

400

200

TOTAL PRODUCTION RATE - STB/D

Fig. 5-131. Effect of withdrawal rates on oil recovery in high-relief carbonate reservoirs subject to gravity drainage. (After Beveridge et al., 1969, fig. 2; reprinted with the permission of the Petroleum Society of The Canadian Institute of Mining, Metallurgy and Petroleum.)

segregation mechanism would break down and the depletion would revert to an ordinary solution-gas drive. However, none of the rates used in their simulation showed such a breakdown of the oil and gas segregation. At high rates, the upward gas migration through the oil column was slowed down, but never ceased. The magnitude of the rate effect depends upon the shapes of the relative permeability curves and absolute permeability. The effect of absolute permeability on recovery efficiency is that by increasing the vertical permeability, the percent recovery increased (by doubling the permeability (29 mD) the recovery increased by 3.5%). Beveridge et al. (1969) noted that if the effective permeability to oil in the gas-swept region is too low to appreciably allow further oil flow, then the rate effect will be small. Beveridge et al. (1969) made three simulation runs with different relative permeability to oil curves. The relative permeability to gas remained the same for all runs (Fig. 5-132). The largest predicted recovery of 62.9% was exhibited by the kro~curve; the least recovery was provided by the kro2 curve. It was noted that the effect of relative permeability on recovery is of a greater magnitude than that of absolute permeability. The relative permeability curves, particularly in the region of low oil saturation, far outweigh any other parameter in their influence on the performance of carbonate reservoirs being depleted under gravity drainage. The relative permeability values have to be accurately defined at low liquid saturations. The non-steady state Welge

501 1,0

-

I

kro/

~/

k/F~r

L z

.0, .oo1

.ooo,

.ooool

//

0

10

20

I/ 30

/

r .....

40 SL

N

--

50

60

70

80

90

100

e/o

Fig. 5-132. Gas-oil relative permeability relationships used in the simulation of recovery sensitivities of the high-reliefcarbonate reservoirs subject to gravity drainage. Recoverypredictions: krbas e = 57.7%; krl - 62.9%; and krz - 47.0%. (After Beveridge et al., 1969, fig. 1; reprinted with the permission of the Petroleum Society of The Canadian Institute of Mining, Metallurgy and Petroleum.) method did not give accurate relative permeability values in the low saturation range. Hagoort (1980) showed that the centrifuge method was an accurate and efficient method for measuring oil relative permeabilities. Beveridge et al. (1969) revealed that the limiting kro in the Upper Devonian Leduc D-3A pool, Alberta, Canada, is about 10 times smaller than the value of kro at the end of laboratory flood. The residual oil saturations obtained from flood tests on Leduc core were much higher than those indicated from actual field performance. Recoveries in high-relief, vuggy carbonate reservoirs are generally underestimated. Water invasion in fractured reservoirs During water influx into a fractured reservoir, oil displacement may result from: (1) the flow of water under naturally-imposed pressure gradients (viscous forces), and (2) imbibition, which is the spontaneous movement of water into the matrix under capillary forces. In fractured carbonate reservoirs capillary forces predominate over viscous forces. As a result, the tendency of water to channel through more permeable strata is offset by the tendency of water to imbibe into the tight matrix and displace the oil into fractures. Numerous investigators have examined imbibition behavior (Aronofsky et al., 1958; Graham and Richardson, 1959; Blair, 1964; Lord, 1971; Parsons and Chancy, 1966).

502 Graham and Richardson (1959), for example, found that in a fractured zone, imbibition is described as a condition of water imbibing from the fracture system into the matrix with simultaneous countercurrent movement of the oil from the matrix into the fractures. The rate of imbibition is directly proportional to the interfacial tension and the square root of permeability, and is dependent on wettability, fluid viscosities, and characteristics of the carbonate rock.

Examples of carbonate reservoir field performance The following case histories present a short synopsis of various carbonate reservoirs and their performance. They provide various examples of the producing mechanisms discussed in the preceding sections of this chapter. Asmari reservoirs in Iran. The producing zone in these reservoirs is the Asmari Limestone of Lower Miocene to Oligocene age. Characteristically, the reservoir is a fine- to coarse-grained, hard, compact limestone with evidence of some recrystallization and dolomitization. It generally has low porosity and permeability. The reservoir rock is folded into elongated anticlines and is extensively fractured into an elaborate pattern of separate matrix blocks. Andresen et al. (1963) have analyzed the Asmari reservoirs and their performance. During the depletion of a typical Asmari reservoir, the mechanisms of gas-cap drive, undersaturated oil expansion, solution-gas drive, gravity drainage, and imbibition displacement are all in operation at various times. Figure 5-133 is a schematic diagram of a typical Asmari reservoir, showing the distribution of fluids during production. At normal drawdown pressures, the gas-oil level moves downward and the water-oil level upward under the action of dynamic and capillary forces. The high-relief Asmari reservoirs have extremely thick oil columns with free gas caps as indicated in Fig. 5133. The oil columns consist of four sections: (1) the secondary gas cap, (2) the gassing zone, (3) the oil expansion zone, and (4) the water-invaded zone (Andresen et al., 1963). The secondary gas-cap zone is bounded by the original and the current gas-oil levels in the fissure system. Owing to the low permeability of the matrix, there is no significant segregation of fluids in the matrix blocks themselves. The gassing zone has the current gas-oil level as its upper boundary, and the lower boundary is the level at which the reservoir oil is at saturation pressure. Located within the gassing zone is the equilibrium gas saturation level. Above this position in the zone, the gas evolved from solution is mobile and flows from the matrix blocks to the fractures. It then migrates vertically through the fissure system to the gas cap. The free gas below the level of equilibrium gas saturation is immobile and is not produced from the matrix blocks. The oil expansion zone extends from the saturation pressure level to the current oil-water level. The water-invaded zone lies below the oil expansion zone. Water displaces oil in the invaded zone primarily by imbibition. The phenomenon of convection also occurs in Asmari reservoirs. At initial conditions, the reservoir is in a state of equilibrium, which is disrupted by the production process. According to Sibley (1969) saturation pressure increases with depth in most Asmari reservoirs at a rate of 4 - 5 psi/100 ft. The solution gas/oil ratio correspondingly shows an increase of 0.8 SCF/STB/100 ft of depth, which provides for convection in the highly-permeable fissure system. The above description illustrates the complexity

503 OR G. GAS CAP ~ i i i ~ i i i i i i i i i ~ i i : ~ ~ L':."i:.'i.'"!":. ORIGINAL G/O LEVEL r

EXPANSION~

~

:

?

: CURRENT G/O LEVEL

GASSING ZONE (SATURATED OIL)

EQUILIBRIUM GAS SATURATION LEVEL SATURATION PRESSURE LEVEL

)RIGINAL )IL ZONE

OIL EXPANSION ZONE (UNDER-SATURATED OIL)

CURRENT W/O LEVEL WATER INVADED ZONE ,

,....,,.3,.,.,

ORIGINAL W/O LEVEL

WATER ZONE

I Fig. 5-133. Fluid distribution in Asmari Limestonereservoirs in southern Iran during production. (After Andresen et al., 1963" courtesy of the Sixth World Petroleum Congress.) of production mechanisms in highly fractured, high-relief reservoirs. The analysis of such reservoirs can be extremely difficult.

Kirkukfield, Iraq. Kirkuk oilfield is a super-giant oil field (ultimate recovery around 10 billion barrels) discovered in Iraq in 1927 (Beydoun, 1988). The field consists of a very long, sinuous anticline that forms one of the Zagros foothill asymmetrical folds. There is superficial thrusting in the incompetent Miocene Lower Fars Formation, which is a caprock. Production is from the 'main' Asmari-equivalent (EoceneOligocene-Lower Miocene) limestone of the Kirkuk Group. The Kirkuk oilfield is another classic example of a complex reservoir system. Free water movement, pronounced gas segregation, and oil convection all occur in an extensively fractured, vuggy limestone (Freeman and Natanson, 1959). The degree of fracturing and vugginess is highest at the crest of the anticlinal structure. Temperature profiles of wells indicate that convection is substantial at the crest of the structure. In Fig. 5-134, the temperature profile of a well drilled on the crest is presented; the well had been idle for a long time. From the top of the fractured section of the oil zone to

504 0

~.t~~ '"',

I"'

I

400

9'

800

9

t200

9

.\ ]

TOP

I'--" t,L

s )...

OF

MAIN

1600

"

2000

-

LIMESTONE .

i =

I.iJ Q

2400

2800

3200 70

, 80

90

iO0

TEMPERATURE,

II0

120

,,, 130

*F

Fig. 5-134. Temperature profile of a well in the Kirkuk Field, Iraq. (After Freeman and Natanson, 1959, fig. 6; courtesy of the Fifth World Petroleum Congress.)

the water table, a distance of over 400 ft (122 m), there is virtually no change in temperature. At Kirkuk, imbibition is a major driving mechanism. Freeman and Natanson (1959) described two types of imbibition taking place in the Kirkuk reservoir. When the matrix block is totally immersed in water, countercurrent and direct flow types of imbibition should ideally yield the same ultimate recovery, even though there may be some trapping of the oil droplets in the water-filled fracture under countercurrent flow conditions. In any given time interval, however, the direct flow conditions will yield more oil if this imbibition process acts over a larger area. The reverse may also be true. Aronofsky et al. (1958) used a simple abstract model to examine the effect of water influx rate on the imbibition process. Their treatment is confined to the countercurrent imbibition.

Beaver River field, British Columbia, Canada - a high-relieffractured gas reservoir The Beaver River gas field is located in the Liard fold belt of northeastern British Columbia and the southern Yukon Territory, Canada. Gas production is from a

505 TABLE 5-XXXII Beaver River gas field, British Columbia, Canada, Middle Devonian carbonate reservoir data Reservoir

Area at G/W contact Reservoir volume (gross) Initial temperature Initial pressure Gas gravity Gas composition

Reservoir parameters Porosity cut-off Porosity average Sw: Matrix (from logs) Fracture-vugs Average h Volume (net) Recovery factor (with volumetric depletion) Gas deviation factor Recoverable reserves (raw)

10,700 acres 10.5 MM acre-ft 353~ 5,856 psig 0.653 6.9% CO 2 0.5% H2S 92.5% CH 4

2% 2.7% 25% 0% 20% 888 ft 7,210,664 acre-ft 90% 1.10 1470 BCF

Source: After Davidson and Snowdon, 1977, table 2; reprinted with the permission of the Society of Petroleum Engineers.

high-relief, massive, extensively fractured and altered dolomitic reservoir with water influx (Davidson and Snowdon, 1977). Original estimates of the recoverable gas reserves, based on log and core data from the producing horizon known as the "Middle Devonian carbonate", was in excess of 1 TCF. Initial production rates of over 200 MMCF/D from six deep wells (>11,500 ft; >3,500 m) were reduced to 5 MMCF/D after four years owing to influx of water into the wells. This condition resulted in a revised estimated ultimate recovery of only 176 BCF gas. The Middle Devonian section, a relatively monotonous carbonate and evaporite sequence, was deposited in a shallow subtidal to supratidal environment on a broad carbonate bank (Davidson and Snowdon, 1977). Reservoir heterogeneities were created by a high degree of diagenesis and tectonic alteration. Tectonism created secondary fracture porosity and permeability in the dolomites. According to Davidson and Snowdon (1977) the reservoir rock can be described as a two-porosity system; matrix porosity is about 2% or less, whereas fracture-vug porosity can range from 0% to 6% or greater. Table 5-XXXII presents reservoir data for this reservoir. The high formation temperature of 353 ~ F (177 ~ C) often exceeded the endurance limits of available well-logging tools. Water saturations could not be reliably calculated from resistivity logs owing to extremely low conductivities of the dolomites. Figure 5-135 presents the capillary pressure tests on the cores from the field. Results indicate that connate water saturations in the matrix porosity are in the range of 5 0 - 80%. Davidson and Snowdon (1977) pointed out that it was reasonable to expect the fracture-vug system to be essentially free of connate water. Initial reserve calculations, however, assumed

506 MATRIX & VUGGY POROSITY

MATRIX POROSITY ( W/OCCASIONAL VUG. )

18oo (594)

1600

(S281

.075 1400 1~21

O

,ft r

o .u

13961 I,&J

E

Q~ = : ) uIX a

.10

u~ I.iJ Q~

O..

U,J

Z

I~X

I.--

eLI

)--

13301

o~ u.i Q.

O~ U

u.J 0 Z

~

U.I Q~

800

o Q.

12641

I,.

.15

~. j.".r-

u_

o

tJ') m

~

600

~

11981

.20

.25

400 (1321

200 (66)

o-

2.0 4.0

4.3 = POROSITY o

~o

2o

WETTING

30

4o

so

6o

70

PHASE SATURATION

to

9o

I00

(percent)

Fig. 5-135. Mercury injection capillary pressure curves for the Middle Devonian carbonate in the Beaver River Field, northern British Columbia, Canada. Porosity values shown on the curves are in percent. The curves show that the irreducible water saturations in the matrix range from 50 to 80 %. (After Davidson and Snowdon, 1977, fig. 6; reprinted with the permission of the Society of Petroleum Engineers.) an average water saturation of 20% before core testing. Log estimates of 25% for the matrix and 0% in the fracture-vug system resulted in the overall Swave = 20%. The weighted average matrix permeabilities as determined from cores are extremely questionable owing to the formation of horizontal relaxation fractures created by coring the tectonically-stressed dolomites. Matrix permeabilities in the low-porosity zones

507 ranged from 2 to 20 mD for kh and from 0.1 to 5 mD for k.v In the high-porosity zones, matrix permeabilities ranged from 20 to 200 mD for kh and from 2 to 25 mD for k. Davidson and Snowdon (1977) remarked that within six months, decrease in production rate and flowing pressure were observed in two wells. Well testing showed that there was a high water/gas ratio of around 2000 bbl/MMSCF. Water coning was suspected because: (1) the completed zones were close to the water contact, (2) vertical permeability was high through the fracture system, (3) production rates were high, with (4) resulting high bottomhole pressure drawdowns. Water production commenced generally across the entire Beaver River Field with WOR's increasing from the water of condensation level of 5 bbl/MMSCF to 25 bbl/MMSCE After imposing rate limits, decrease in the gas production rate continued as water production increased. Evidence that formation water was entering the wells was based on the increase in the chloride content of produced water before the WOR increased in the wells. This was due to mingling of the invading water with the water of condensation (Davidson and Snowdon, 1977). After an increase in the WORs, the wells died from excessive water production within a year. The production history of the Beaver River Field is documented in Fig. 5-136. 240

240

o

200

200

.d an

160 ~

160

~ v

0

,/

uJ I--

<[ ~-

mz

/

I-

/

120

t~

120 t~ O Oa. ttl

w9~ o 80

80

40

40

~"

oL 1971

I 1972

I 1973

! 1974

I 1975

| 1976

~

0 1977

Fig. 5-136. Cumulative production history of the Beaver River Field, northern British Columbia, Canada. (After Davidson and Snowdon, 1977, fig. 7; reprinted with the permission of the Society of Petroleum Engineers.)

508 Subsequent well recompletions and computer modeling demonstrated that water coning was an insignificant factor, and that water influx across the entire reservoir through the fracture system was responsible for the water production (Davidson and Snowdon, 1977). The recovery problem was attributed to the extensive vertical and horizontal fractures, which prevented the establishment of the pressure distribution necessary for coning and resulted in a uniform influx of water through the fracture system. Davidson and Snowdon (1977) pointed out that with the type of fracture system present, water production would not be sensitive to the withdrawal rate until the water contact approached a well's perforations. A tactic used to take advantage of this situation was to create the largest possible pressure drop between the matrix and the fracture system by producing the wells at their maximum rates. This approach was to optimize the depletion of the matrix and dead-end fractures-vugs before they are isolated by the influx of water. (The writers find it interesting that in the case of waterflooding in oil reservoirs, vugs are "bad news" in water-wet rocks owing to oil trapping and "good news" in oil-wet rocks.) Davidson and Snowdon (1977) proposed the explanation that the water influx problem was a direct result of the general relation of the Beaver River Field to the regional Beaver River Aquifer (Fig. 5-137). Hydrodynamic analysis showed that the reservoir's pressure-depth relation is related to the aquifer's outcrop elevation. For the Beaver River Field the potentiometric-surface values are about 1,500 ft (457 m) above sea-level. This corresponds to the surface elevation of the Middle Devonian carbonate outcrops some 85 mi (137 km) to the north in the Yukon Territory. The aquifer increases in elevation by 13,000 ft (3,962 m) or 153 ft/mi (29 m/km) between the Beaver River Field and the South Nahanni River (Fig. 5-137). Such a high dip in the aquifer is conducive to a rapid influx of water into the reservoir as depletion occurs. The writers, however, question whether or not the major fault, shown in Fig. 5-137 just south of the South Nahanni River, could be a barrier to the movement of water downdip. Water influx into the reservoir could have just as well occurred from the Besa River Formation along the faults and extension fractures, which extend upward along the crest of the Beaver River anticline. Davidson and Snowdon (1977) did not discuss this alternative as a possible source of water. San Andres Field, Veracruz, M e x i c o - an extremely undersaturated oil reservoir. The Jurassic SanAndres Limestone reservoir of the SanAndres Field (State of Veracruz, Mexico) is an example of a highly undersaturated oil reservoir (Garaicochea Petrirena et al. 1963). The original reservoir pressure was 6,620 psi (45.6 MPa) and a bubble point pressure was 2,525 psi (17.4 MPa). The San Andres zone is chalky, oolitic limestone exhibiting intergranular porosity with occasional vugs and fissures. The average permeability is 2.5 mD. Reservoir performance, as illustrated in Fig. 5-138, has demonstrated a high degree of undersaturation with a rapid decrease in production rate and an essentially constant gas/oil ratio of 615 ft3/B (110 m3/m3) and a water cut of 1 - 2 % . An increase in the GOR in the middle of 1960 reflected a pilot gas injection test. The test was initiated in December, 1959, and terminated in the latter part of 1960 owing to an unfavorable response in the surrounding wells to the gas injection. By March, 1960, the reservoir pressure had declined sharply to 4,060 psi (28 MPa) with a cumulative recovery of 5% of the initial oil-in-place. Garaicochea

$

N Mil)OI.E DEVONIAN C A l U l O N A T [ OUTCROP .

AGE

L. CRET.

.

.

.

SOUTH NAHANNI RNER ~

r" A

|

ROCK UNIT FT. :. ST. JOHN GROUP ~

~__

7z

_o,,,T_.U~~A. t.~'VE__L

,

...................

o

~iiii::'"

,ooo

iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiil;i!iiiiiiiiii, -Iil i/ I~TTSON .'.:. Fm. ".'~"

-'.-.2

MISS.

BI~SA

.-----"

kT[

RNER

u.

0Ev.

VICIAN

ooo

PROPHE~ -_..-

MIDDLE DEV~omAN "MIDDLE DEV. SILURIANCARS" ORDO

!

-_.~

,L 16,000

l~ .....

,o,

.......

,,,o

Fig. 5-137. Cross-section of the Beaver River aquifer. (After Davidson and Snowdon, 1977, fig. 8; reprinted with the permission of the Society of Petroleum Engineers.)

510

% _

7

6

TION a.

RATE

4

3 2

Z I-

O

Z 0

WATER PRODUCTION

I,.-

I"1_

300

E

I

2O0

nO w p-

E p.

0 Ir

250

GAS -OIL

<

150

--J

ioo

RATIO

~:

O i

<

50

1956

1957

I958

I959

i960

1961

1962

Fig. 5-138. Performanceof the Jurassic San Andres Limestone reservoir,VeracruzState, Mexico. (After Garaicochea Petrirenaet al., 1963"courtesy of the Sixth WorldPetroleumCongress.) Petrirena et al. (1963) calculated a recovery of 7.4% to bubble point pressure under an oil expansion producing mechanism. By the middle of 1962, 8.4% of the oil-in-place had been produced, which should have lowered the reservoir pressure to slightly below bubble point pressure. Statistical studies on oil recovery efficiency The American Petroleum Institute (1967) presented a statistical study of oil recovery efficiency based on the case histories from 226 sandstone and 86 carbonate reservoirs in the U.S.A. The reservoirs were classified on the basis of their predominant drive mechanism: solution-gas drive without supplemental drive, solution-gas drive with supplemental drive, gas-cap drive, water drive, and gravity drainage. It is by far the most comprehensive and exhaustive study of oil pool performance ever published, and affords the opportunity for meaningful comparisons between sandstone and carbonate reservoirs under the various drive mechanisms mentioned. The results of the study are summarized below: Tables 5 - X X X I I I - 5-XXXVII show the range of values for the reservoir parameters under the five different producing mechanisms. The parameters for the solutiongas- and water-drive pools have been grouped on the basis of the type of reservoir rock: sandstone or limestone, dolomite, and other (chert, etc.). The gas-cap-drive and gravity-drainage reservoir data were more limited. The sandstone and carbonate reservoirs have been combined in the gas-cap-drive analysis. The gravity-drainage data

511 TABLE 5-XXXIII Range of values for reservoir parameters with solution-gas drive as a predominant drive mechanism without supplemental drives Parameters*

Sand and sandstone Minimum

Rock k, darcys 0.006 ~, fraction 0.115 S w, fraction 0.150 Fluids go, ~ 20 Pob' cP 0.3 Rsb, cf/bbl 60 Bood, ratio 1.050 Boor ratio 1.050 Boaa, ratio 1.000 Environment h , ft 3.4 a, deg 0-5 Db,, ft 1500 T, ~ 79 Pb' psig 639 pa, psig 10 Ultimate recovery BAF, bbl/AF 47 RE, % 9.5 S r, fraction 0.130

Limestone, dolomite, and other

Median

Maximum

Minimum

Median

Maximum

0.051 0.188 0.300

0.940 0.299 0.500

0.001 0.042 0.163

0.016 0.135 0.250

0.252 0.200 0.350

35 0.8 565 1.310 1.297 1.090

49 6 1680 1.900 1.740 1.400

32 0.2 302 1.200 1.200 1.060

40 0.4 640 1.346 1.402 1.120

50.2 1.5 1867 2.067 2.350 1.420

32.2 5-15 5380 150 1,750 150

772 >45 11,500 260 4,403 1,000

3.9 0-5 3,100 107 1,280 50

27 0-5 6300 174 2,383 200

425 5-15 10,500 209 3,578 1,300

154 21.3 0.229

534 46.0 0.382

20 15.5 0.169

88 17.6 0.267

187 20.7 0.447

Source: After Arps et al., 1967; courtesy of the American Institute of Petroleum. * Nomenclature for Tables X X X I I I - XXXVII: go = stock-tank oil gravity (~ /~o = reservoir oil viscosity (cP); R s = solution gas/oil ratio (SCF/bbl); B o = oil formation volume factor (reservoir bbl/ STB); h = net pay thickness (ft); a = formation dip (degrees); Dos =depth below the surface (ft); RE = recovery efficiency (% of initial stock tank oil-in-place)" S = residual gas saturation (fraction of pore space)" S = residual oil saturation (fraction of pore space). Subscripts: i = mmal conditions; b = bubble point conditions; a = abandonment conditions; d = differential liberation;f= flash liberation; k= arithmetic average of absolute permeability, D. '

gr

.

.

.

.

.

.

parameters are presented for sandstones only. Seventy-seven sandstone and 21 carbonate pools producing under essentially solution-gas-drive mechanisms were studied. Eighty-one pools (60 sandstone and 21 carbonate) had solution-gas drive as the predominant recovery mechanism, supplemented by water drive, gravity drainage, and, in a few cases, partial gas or water injection. Seventy-two sandstone and 39 carbonate water drive pools were examined. Only 14 gas-cap-drive and 6 gravity-drainage pools were included. The value of these data is primarily for comparison purposes. As expected, the solution-gas-drive pools have the lowest recovery efficiencies and the pools under water drive and gravity drainage show the highest recoveries. The sandstone reservoirs exhibit higher oil recoveries than the carbonate pools, and also have higher porosities and much greater permeabilities. The carbonates, however, are much more likely to be fractured and fissured, a factor which is not always reflected accu-

512 TABLE 5-XXXIV Range of values for reservoir parameters with solution-gas drive as a predominant drive mechanism with supplemental drives Parameters*

Sand and sandstone Minimum

Rock k, darcys 0.010 ~, fraction 0.120 Sw, fraction 0.100 Fluids go, ~ 15.5 l~ob, cP 0.4 Rsb, cf/bbl 10 Bobd, ratio 1 010 Bobr ratio 1.015 Boad, ratio 1.000 Environment h , ft 4 a, deg 0--5 Dbs, ft 300 T, ~ 77 Pb' psig 5 pa, psig 5 Ultimate recovery BAF, bbl/AF 109 RE, % 13.1 St, fraction 0.077

Limestone, dolomite, and other

Median

Maximum

Minimum

Median

Maximum

0.216 0.210 0.310

2.500 0.359 0.579

0.002 0.033 0.035

0.019 0.133 0.250

0.867 0.248 0.600

36 0.9 390 1.230 1.230 1.050

46 20 1010 1.580 1.845 1.220

22 0.3 60 1.050 1.050 1.020

38 0.8 615 1.328 1.310 1.110

46 2 1325 1.682 1.680 1.500

30 0-5 4237 146 1,360 100

714 >45 10,280 260 4,275 800

8 0-5 2800 88 530 40

31 0-5 6000 128 1,830 200 1,550

154 5--15 10,530 225 2,935

227 28.4 0.255

820 57.9 0.435

32 9.0 0.112

120 21.8 0.260

464 48.1 0.426

Source: After Arps et al., 1967; courtesy of the American Institute of Petroleum. Nomenclature as for Table XXXIII. *Data for gas-drive pools do not include any oil produced above bubble point.

rately in the stated values for porosity and permeability. In this connection, it should be borne in mind that fractures may form during the core recovery process. The wider range of recovery efficiencies in carbonates corresponds to the inherently greater authigenic and diagenetic complexity of carbonate rocks. In Table 5-XXXIII the median value for percentage recovery of initial oil-in-place for solution-gas drive without supplementary drive is 21.3% for sandstone pools, compared to 17.6% for carbonate reservoirs. The median values of 154 and 88 bbl/acre-ft for sandstones and carbonates, respectively, show, however, that actual recoveries in sandstones are almost twice as high as the carbonate values, partly owing to the much higher porosities in sandstones. Supplemental drives also appear to have benefitted sandstone reservoirs examined in this study (Table 5-XXXIV). The median values show that the effect of supplementation by additional drive mechanisms is about 1/3 for sandstones and 1/4 for carbonates. When gas-cap drive is the predominant mechanism, the average recovery efficiency is higher by about 2/3 than the comparable value for the solution-gas-drive mechanism (Table 5-XXXV). The median values for ultimate recovery (bbl/acre-ft) by water drive in sandstones exceed those for limestones and dolomites by a factor of 3 and, in terms of recovery

513 TABLE 5-XXXV Range of values for reservoir parameters with gas-cap drive as a predominant drive mechanism Parameters

All rock types combined

Rock k, darcys q~, fraction S w, fraction Fluids go, ~ Pob, cP Rsb, cf/bbl Boba, ratio Bobp ratio Boaa, ratio Environment h,ft a, deg Dbs, ft T, ~ Pb' psig pa, psig Ultimate recovery BAF, bbl/AF

RE, % S r, fraction

Minimum

Median

Maximum

0.047 0.086 0.150

0.600 0.225 0.262

1.966 0.358 0.430

34 0.3 226 1.116 1.116 1.040

40 0.6 703 1.374 1.350 1.159

43 2.3 1335 1.675 1.631 1.490

7 0-5 3300 108 854 0

15 0-5 5500 175 2213 500

35 15-45 7675 200 3583 2900

68 15.8 0.223

289 32.5 0.271

864 67.0 0.517

Source: After Arps et al., 1967; courtesy of the American Institute of Petroleum. Nomenclature as for Table XXXIII.

efficiency, by 17% (Table 5-XXXVI). Water drive seems to be about 2.5 times more efficient than unsupplemented solution-gas drive in both sandstone and carbonate reservoirs. Data for the water-drive cases in sandstones, and the solution-gas-drive cases in both sandstones and carbonate rocks, were subjected to regression analysis. For the water drive reservoirs the following regression equation for the recovery efficiency (RE, in % of initial oil-in-place) was found: 0.0422 RE

=

5 4 . 8 9 8

-.--

.

0.0770 .

- 0.1903 .

-0.2159 ,

where/~w~ = initial water viscosity (cP), jLgoi "- initial oil viscosity (cP), k = arithmetic average of absolute permeability (D), S = interstitial water content (fraction of the total pore space), ~b = porosity (fraction), Boi = initial oil formation volume factor (reservoir bbl/bbl tank oil), Pi = initial reservoir pressure (psig), and Pa = reservoir pressure at abandonment (psig).

514 TABLE 5-XXXVI Range of values for reservoir parameters with water drive as a predominant drive mechanism Parameters

Sand and sandstone Minimum

Rock k, darcys 0.011 ~b, fraction 0.111 S w,fraction 0.052 Fluids go, ~ 15.5 Poi, cP 0.2 Pw, cf/bbl 0.24 BoiI, ratio 0.997 Bobz, ratio 1.008 Bo,I, ratio 1.004 Pw- Po, g/cc 0.054 Environment h , ft 6.5 a, deg 0-5 Db,, ft 1400 T, ~ 84 Pi' psig 450 Pb' psig 52 Pa' psig 100 Ultimate recovery BAF, bbl/AF 155 RE, % 27.8 S r, fraction 0.114

Limestone, dolomite, and other

Median

Maximum

Minimum

Median

Maximum

0.568 0.256 0.250

4.000 0.350 0.470

0.010 0.022 0.033

0.127 0.154 0.180

1.600 0.300 0.500

35.3 1.0 0.46 1.238 1.259 1.223 0.241

50 500 0.95 2.950 2.950 1.970 0.490

15 0.2 . . . . . . . 1.110 . . . . . .

37 0.7 . . . . . . 1.321 . . . . . . . . . .

54 142

17.5 0-5 6260 163 2775 1815 1970

160 15-45 12,400 270 6788 5400 5010

9 50.2 . . . . . . . . . 2210 6790 90 182 700 3200 30 1805 . . . . . . . . .

185

571 51.1 0.327

1641 86.7 0.635

6 6.3 0.247

. . . .

172 43.6 0.421

11933

13,100 226 5668 3821 1422 80.5 0.908

Source: After Arps et al., 1967; courtesy of the American Institute of Petroleum. Nomenclature as for Table XXXIII.

The API subcommittee established the following regression equation for recovery efficiency below the bubble point in solution-gas-drive reservoirs: 0.1611

RE = 41.815

[~I-S)1 Bob

"

0.0979 I Pkoi b 1

"

0.3722 I Sw 1

"

0.1744 P[-~a 1 ,

(5-142)

where Bob = oil formation volume factor at bubble point pressure (reservoir bbl/bbl tank oil), Pob = oil viscosity at bubble point pressure (cP), and Pb = bubble point pressure (psig). An examination of Eqs. 5-141 and 5-142 shows the presence of four common variables: (1) oil-in-place under initial conditions for the water-drive reservoirs and at bubble point pressure for the solution-gas-drive reservoirs; (2) mobility factor: at initial conditions for the water-drive pools and at bubble point pressure for the solutiongas-drive pools; (3) interstitial water saturation; and (4) pressure drop ratio" initial/

515 TABLE 5-XXXVII Range of values for reservoir parameters with gravity drive as a predominant drive mechanism Parameters

Rock k, darcys ~, fraction Sw,fraction Fluids go, ~ l~ob, cP Rsb , cf/bbl Bobd, ratio Bobp ratio Boad, ratio Environment h, ft a, deg Dbs, ft T, ~ Pb' psig Pu' psig Ultimate recoxery BAF, bbl/AF RE, % S,., fraction

Sand and sandstone only Minimum

Median

Maximum

0.305 0.194 0.030

1.285 0.329 0.293

2.000 0.350 0.400

15 0.7 96 1.070 1.070 1.030

22.5 4 200 1.106 1.106 1.040

38.5 8 735 1.383 1.340 1.100

40 0-5 1,170 100 497 0

71 5-15 2,400 100 1,044 20

900 15-45 6,500 132 2,670 50

250 16 0.151

696 57.2 0.377

1,124 63.8 0.654

Source: After Arps et al., 1967; courtesy of the American Institute of Petroleum.

Nomenclature as for Table XXXIII.

abandonment pressure ratio for water-drive reservoirs and bubble point/abandonment pressure ratio for solution-gas-drive reservoirs. It is interesting to note that recovery efficiencies may either increase or decrease for both mechanisms when the oil-inplace and the mobility factor variables, respectively, are either high or low. On the other hand, low values for water saturation ( S ) and pressure drop rates result in higher recovery efficiencies in water-drive reservoirs, and lower recovery efficiencies in solution-gas-drive reservoirs. Even though high S values serve to increase recovery efficiency in solution-gas-drive reservoirs, the actual recoveries in barrels per acre-foot are usually less. Equations 5-141 and 5-142 can be of value to the geologist and the petroleum engineer in the estimation of ultimate recovery from carbonate reservoirs in instances where the data required for more detailed studies are lacking. In all cases, these equations are helpful for comparison purposes. To facilitate the use of Eqs. 5-141 and 5-142,Arps (1968) developed the nomographs shown in Figs. 5-139 and 5-140. In Table 5-XXXVIII, the writers have assembled limited data on reservoir characteristics and performance for selected carbonate reservoirs throughout the world.

516

Based On:

BAF = 3244 X

fiob

X

X

.Oil in

~oo~(~ - s , )

D r~r.r.r.r.r..~p_ Ratio

Bob in Per Cent

" - - - 2 . 20

Estimated Recovery. Facto__.__r in Bbls/AF

~

~

Interstitial Wate.~_z.r Saturation S in Per C e n t . - "~

-

'-

.S ,-

't

:XH -

,

I

:X)I--

Mobility.. Facto____~r

i"

SO

S ~ IS

Sw

EXAMPLE:

4~)|

i

.3

!

30

'

-

' .21 I

001-

i~-(~.

,.

- ~ "~" IWt':

-, - - " "

.I

~

9

30 "~ ....

7

~" )$~

(~,,

C); I format ion volume factor Bob - 1.40

~ = .020 da,c;es

Q 10~

00"-. """"

9

Water Ioturation S - .34

~O

III

-

Porosl l'y g = . 174

" ""'"

,...,04

Formot;on oil v;scosity ~c~= cp. Bubble point pretsure

- 6

gO -

I~-

" "

4

|1

2~

"

Pb :

"

Al~r~donment pressure Pa : 580 ps;

D3

S

3 6 6 0 psi

:)2

Z

- 4

.

:30 '--

3 !-

,o, -

2C

"

1.40

_ 8.2% -

/~ob;/;ty factor: (.020) .'- (.50) = .04

~. 3

0 ; I ;n place: (~oo)(. ~ r _ , ) ( ~ - . ~ )

2C aS ."

Pressure drop ratio: 3660 - 580 -- 6"--"~1.

.~3~ 2 A

I: B

C

s

F

,oo21-O

I . CONWCt 8.:7% on oil in place scale A with mobility factor .04 on scale G and find intercept b on scale B. 2. C ~ n e c t point b on scale I~ with ~ater toturatlon 34% on scale F and find intercept c on scale C. 3. Connect point c on scale C with p r e t ~ m drop ratio 6.31 on scale E and find estimated recovery factor a3 119 I~'rllls I ~ r acre foot at intercept with scale 0 9

Fig. 5-139. Nomograph for estimating recovery factor (bbl/acre-ft) by solution-gas drive (below bubble point) in sandstones and carbonates. (After Arps, 1968; reprinted with the permission of the Society of Petroleum Engineers.)

517

r~ (,- Sw)~ ".o,2 ( ~" 1" o77 i 'o, ~ x ~o,/ •

~'~~176 Q;I "n Place 100~(1 - s ) w

Pressure Drop_

Est i mated Recovery Factor in Bbls/'AF

B .

OI in Pe Cent __ _._j

Ratio

(s). -.190

- .216

Interstitial Water Saturation

M i _o. .b. i l ty. Factor

Sw

k IJwi i

i-~a

- 25

in Per Cent

'F

'~

31-

t

EXAMPLE:

2

Porosity It : .282

I

-20 IIi

Water Soturat;o~ S =.35

i

i

w

O i l formation volume factor B . :1.10 o!

t .S t$

Permeobl llty k : .250 d o t t l e s

.3 ~

Formation woter viscosity

.2

iJwi : ..$4 cp 14)0

x

FormGtion o;I v i ~ i t y

~.r

iJoi

= 1.31 cp

I n i t i a l pressure Pi : 1986 psi 9

,

Abandonment premium

4

Po :

800 psi

8

20<

7

,b

30

6 t-

-b

Q i l in Place: (loo)( .282)(I - .~) i .lO

.02

(.250)(.$4) 1.31

I0

A ! .

2. 3.

g

C

:

.103

P r e ~ u r e d,r,o~_rati___.__o: 19~-~ : 2.48

$

-4

16.7%

Mob; I;t~ factor:

.at

7 -

:

SOL l

f

.oo'zL G

C o n n e c t 1 6 . 7 % on o;I ;n place scale A with m o b i l i t y factor .103 on scale G oral find i n t e r c e p t b on scale !1. Connect point b on scale B with ~ofer saturation 35% on scale F and find intercept c o~ scale C . Cocmect p o i n t c on scale C with pressure drop ratio 2 . 4 8 on scale E and find estimated recovery factor $54 barrels per acre foot at intercept with scAIle O.

Fig. 5-140. Nomograph for estimating recovery factor (bbl/acre-ft) by water drive in sandstones. (After Arps, 1968; reprinted with the permission of the Society of Petroleum Engineers.)

Table 5-XXXVIII OO

Summary of reservoir characteristics and primary performance data, and references for selected carbonate reservoirs categorized on pore type and drive mechanism The following symbols are used in the table: 1. Exploration discovery methods: G Surface geology GS Surface geology and seismic survey R Redrill S Seismic survey SG Subsurface geology SGS Subsurface geology and seismic survey W Wildcat WS Wildcat and seismic survey 2. Geologic age: T Tertiary (e = Eocene, p = Paleocene) K Cretaceous J Jurassic P Permian IP Pennsylvanian M Mississippian D Devonian S Silurian O Ordovician C Cambrian

Field name

State, County country

A:

Solution Gas Drive

AA:

Intercrystalline-intergranular porosity - solution-gas drive

Exploration Productive Geologic Trap Reservoir discovery formation age mechanism rock type method

3. Trap mechanism: 1 Anticline 2 Fault 3 Unconformity 4 Reef 5 Pinch out 6 Monocline 7 Local porosity 8 Syncline 4. Reservoir rock type: D Dolomite (dolostone) L Limestone D-L Dolomite and limestone; dolomite predominates L-D Limestone and dolomite; limestone predominates 5. Porosity is normally given as an average value; some values are absolute maximums. 6. Most of the permeabilities reported represent an average value; some values are shown as ranges, and others are reported in relative descriptive terms 7. Footnotes: a Matrix has no porosity, b Oil viscosity in centipoises. c Cumulative oil production to date of publication, d Condensate reservoir. e Ultimate recovery in barrels per acre-foot, f STOP (stock tank oil-in-place, initial). Ultimate recovery is primary unless otherwise noted.

Productive Oil and acreage gas column (acres) (ft)

Pay thickness

Crude gravity

~

k

S;

(ft)

(~

(%)

(mD) (%)

P;

Ph

T

Solution Ultimate reGOR covery

(psi)

(psi) (~

(cu ft/bbl) (MMbbl)(%)

Ref. No.

1 Adell

Kansas Sheridan

W

2 Anton-

Texas

SGS

Irish

Lamb,

3 Block 31 4 Eubank

Hale, Lubbock Texas Crane Kansas Haskell

W

Eubank Eubank

Kansas Haskell Kansas Haskell

W W

LansingIP Kansas City Clear Fork P

1

L

1200

5

D

9000

L L

400 1280

25 20

5 14

35.8 34.4

235

42

47

Texas

Ector

Grayburg

P

5

D

15500

7 Fullerton

Texas

Andrews

Clear Fork P

5

L

16642

Ohara

M

5

L

725

Turner

M

5

D

23962

Valley Petit

K

1-5

L

11269

13 McElroy

LansingP Kansas City Fusselman S--D

1

L

60

5--6

D

3600

Crane,

Grayburg

P

1-5

D

30000

14 New Hope Texas 15 Panhandle Texas

Upton Franklin Carson, Gray

Bacon Brown

K P

1 3

L D

4609 200000

16 Parks 17 Pickton 18 Plainville 19 Rocker A 20 Slaughter

Midland Hopkins Daviess Garza Cochran

Bend Bacon McClosky Glorieta San Andres

P K M P P

1 1-5 1 1 5

L L D-L D D-L

Grayburg Dahra-B San Andres Petit

P T (p) P K

5 1 1 5

D D D L

21 22 23 24

Texas

Texas Texas Indiana Texas Texas

So. CowdenTexas Ector U m m F a r u d Libya Waddell Texas Crane West Louiana Claiborne

S SG

1

1-5 1-5

16000

S

15

M IP

L

Howard

46 37

185 11

5

12 Luther S.E. Texas

16.2

350 27

IP

SGS

9.4

6000 240

Odom

11 Hortonville Kansas Sheridan

30

L L

Coke

9Harmattan- Alberta,

400

1 1-5

Texas

Elkton Canada 10Haynesville Louisiana, Arkansas

30 - 41.5

D M

borne 6 Foster

W

140

Devonian Ste. Genevieve Cherokee LansingKansas City

5 Ft.Chad-

8 Gard's Pt.* Illinois Wabash

50--60

6400 7900 400 1120 87500

200 330

82

10

100125 550

215 220 60 60

3354 8000 4341

80 280

37

4145

44

600 1330

35-45

2230

2230 134

975

1

35

1140

371

24

38

7.7- 6.711.4 12.6 8--12 100

1581760 2980

36.4

216 6-12

2040

4-5 8

35

36

11.3

11.3

38-40

19-20 23

113

2-4

29-40

8-65

43.5

15

23

2764 139

1300

5c

1

39 c

2

69

25 t

1 1

96

2370

1590

26

246

28 z

4

13.6

5

26.5

6

8001200 3636

0.9 ~

7

3636 203

871

45--60

30--40 ~ 8

2440

2331 179

460

14.9 28.54

18 344

9 1

16 20

4246

13 ~

42.5

8.1 1200 f

19

11 1214 15 16 7 2 1719

32

13

30

1300

755

86

315

11 60

43 40-46

18.9 12

379 25

25.4 30--45

3425 440

907 203 440 85

256 275

21 8 20 40 40

45.5 50 38.5 34 29--32

6.8 20

2.6 250

33 25

4567 3578 375

3508 174 3578 209

1817 1915

3.9 6.66 4.07

17 19.4

13.2 12.2

4.6 10

11

1710

1710 108

465

275 ~

20

40

34.8 0.7 b 34 35

7.5 24 28.1 43 11.8 12.3 9--21 1-49

31 22 35.5

1760 1003 1650 2550

325 96 253 136 1134 88

150 8

3 1

160 90-100 484 395

2 10

10.4 75 f 33 ~ 1.4

21 14

20 21 22 23

Lisbon * Composed of four small oil pools. ~Total recovery with miscible displacement is 50§ 2 Total recovery with water flood is 54%. 3 Total with gas-cap cycling and water injection; in addition 75% of condensate will be recovered. 4 Including secondary recovery (water flooding); this field has some vugular porosity and gas-cap drive. 5 Plus 17.5 MMbbl secondary. 6 Total recovery with gas injection is 61.7%. 7 Includes No. 36;

t.~

induced water drive,

q~

t,O Field name

State, County country

Exploration Productive Geologic Trap Reservoir discovery formation age mechanism rock type method

AB: Vugular-solution porosity - solution-gas drive 25 Aneth Utah San Juan Paradox 26 Bar-Mar 27 Bateman Ranch Bateman Ranch 28 Big Eddy

Texas Texas

Crane King

SG G

Texas

King

G

New Eddy Mexico Texas Henderson Texas Gaines Alberta, Canada

29 Fairway* 30 GMK 31 Golden Spike South, D-3A 32 KellyTexas Snyder 33 Morrow Ohio County 34 North New Anderson Mexico Ranch 35 Nunn Kansas 36 Plainville 37 Pleasant Prairie 38 Pollnow

Scurry

GS SG SGS

SGS

Morrow

Productive Oil and acreage gas column (acres) (ft)

Pay thickness

Crude gravity

~b

k

S;

Pi

Ph

T

Solution Ultimate reGOR covery

(ft)

(~

(%)

(mD)

(%)

(psi)

(psi) (~

(cu ft/bbl) (MMbbl) (%).

40-42

10.2

20

22

2200

1780 132

IP

4-5

L

55000

250

D IP

2-5 1

D L

80 1700

60 28

68 28

35.8 34-38

25 11

103

1532 2265

0.3 9.1

14.3- 24 18.5 52 e 2 2

IP

1

L

1450

14

14

36

7.7

172

2390

2.0

2

IP

4

L

640

50

50.1

7.5

100

James Lime K San Andres P Leduc D

4 1 4

L D L

23000 1280 1390

624

75 86 477

46--48 32 37

11 9.6 8.8

3 320

Canyon IP Reef TrempealeauC

4

L

51000

775

233

43

7

1

D

100

42

Tubb Strawn B-Zone Strawn C-Zone Strawn

Lea

GS

Wolfcamp

P

1

L

920

35

Finney

S

Marmaton

IP

1

L

I100

8

Indiana Daviess Kansas Haskell

S W

Aux Vases Morrow

M IP

1 5

D L

400 10000

Kansas Decatur

S

LansingKansas City Canyon Reef Marmaton Greenbrier

IP

5

L

800

IP

4

L

11000

IP M

5 8

L D

300 6000

39 SharonTexas Scurry Ridge 40 Sun City Kansas Barber 41 Sycamore- West Calhoun Millstone Virginia

G W

75

3--13

20 5-10

37

5875 4225

11.7

5211 2040 2093

15

28

3122

7.8

49

25

1080

41.7

9.6

124

20

3569

33-35

17.8

38

20.5

176

98

44

8.8

44

17

0.57

32.8

1050

28

3135

38

1570 300

48

0.12 '

25

1608

70 5.1 320 f

11

26 2 27

1820 130

885

670

23.6

28

1045

307

90140 e 3.6 ~

30

29

1393 154

88

1500

2.53.Oct 4.0c~

300 983

38

34.4 46

170

50.8

38.5 29--32.5

4

10-12 13

667

Ref. No.

0.3 c 1900 128

* Considerable gas-cap drive, t Includes No. 208. ~ Includes No. 18. w Plus 10.95 MMbbl owing to water injection; estimated ultimate recovery under water injection is over 50%.

1153

25

1 7 1 1

51.9w

30

1.6 c

31 32

AC: Fracture-matrix porosity - solution-gas drive 42 Bitter Lake New Chaves South and Mexico West 43 Brown Texas Gaines 44 CottonwoodWyWashakie Creek oming 45 Devil's Mon- Mussel-

San Andres P

1-7

D

680

SGS S

Giorieta P Phosphoria P

6 5-6

D D

960 14200

G

Van Duzen M

1

L

80

Basin 46 Elk Basin

tana Mon-

shell Park-

Madison

M

1

D

8960

Carbon

A-Zone

47 Reeves 48 Yellow

tana, Wyoming Texas Texas

San Andres P San Andres P

5 6

D-L D

5480 3230

Fusselman Viola Strawn

5 5 4

L D L

1840 40 80

House AD: Undefined porosity 49 Big Spring Texas 50 Cairo North Kansas 51 Camp Texas Springs 52 Chaveroo

53 Davis 54 Gove

Yoakum Hockley

S S

- solution-gas drive Howard SG Pratt W Scurry SG

S O IP

New Chaves, Mexico Roosevelt

GS

San Andres P

5

D

11000

Kansas Wabaunsee Kansas Gove

G SG

Kansas IP LansingIP Kansas City Laurel S

1 1

L L

160

55 Greensburg Kentucky 56 Hanson Texas 57 Huat Texas 58 Lamesa Texas

Green, Taylor Crockett Gaines Dawson

10

20

13

2.5

38

0.07 c

44 21

33.8 30

7 10.4

16 16

35

5-10

28.2

17

13

28

12

47-368

20

33 32

11.6 12.1

2.7 0.5

14 4 5

48.3 37 43.5

11.9

4.7

40

26

6

0.7

25

1340

15

31

15

41.5

50

645

W SG SGS S

Grayburg Wolfcamp

168 55

920

88 20 40

20

80

4--6

2900 85 125 11261810

20-51

2264 700

200

2000 825 1540

106

D

14953

15

30

41.8

12

560

45

P P M

1-5 1-5 1

D L L

160 550 800

12

15 16 20

27 31.2 35

5 4.5 9

0.4 3

4600 4800

S M IP

1-2 1 4

D L L

1600 160 1160

106 20 162 22

29 37.5 42.6

9.5

0.75

3692

40 400

7.6

1.85

Fallon

GS

S

1

D

1760

185

180

33

11

1

3794

Fallon

GS

Stoney Mt. O

1

D

1760

210

62

33

1!

1

3794

Fallon

GS

Red River

1

D

2589

270

67

31

12.6

1

Barber Garza

W SG

M San Andres P

5 1

* Plus 1.9 MMbbl secondary, t Includes No. 144. ~ Intergranular porosity.

L D

6000 1740

0-50 250

10

34

1000 f

361

21 25

2 2

4.5

2 31 2

0.02 110

4001000

35

50 e

1.6 ~ 1.3 x 109 Mcf 3.0c-t-

18-26 34

25

36 1

62 Pennel

63 Rhodes 64 Rocker A

0.03'

36-39

3

O

2 33

2644

Salem Canyon Reef and Strawn Interlake

Pennel

62

4495

S S SG

Pennel

150 3.0* 313-452 182 f

64

West 59 Monarch Mont. Fallon 60 Montgomery~IndianaDaviess 61 Ocho Jaun Texas Scurry, Fisher Montana Montana Montana Kansas Texas

25

~J

23.6

3.6

45

2435

283

18

60 e

7

0.13 1.1 0.96

53 e

2 2 2

2.0 0.8 5.1

34 7 2

34 0.4 c

34 24

30 2.1 c 3.0

34 31 2

L~

Field name

State, County country

Exploration Productive Geologic Trap Reservoir discovery formation age mechanism rock type method

65 Rojo Caballos 66 Snyder North

Texas

Pecos

S

Morrow

IP

1-2

L

Texas

Scurry

R

IP

5

L

1000

66

Texas

Scurry

R

Strawn Upper B Zone Strawn Lower B Zone Strawn C Zone San Andres

IP

5

L

1000

65

95

Snyder North

Snyder Texas North 67 Welch Texas North 68 Westbrook Texas

Scurry

R

Dawson Terry Mitchell

S

Westbrook Texas

Mitchell

R

Productive Oil and acreage gas column (acres) (ft)

Pay thickness

Crude gravity

~b

k

S,

P~

Ph

T

Solution Ultimate reGOR covery

(ft)

(~ 53

(%)

(mD)

(%)

(psi)

(psi) (~

(cu ft/bbl) (MMbbl) (%)

5.5

0.1

40

40

16

3337

40

40

16

3337

13221

5.6

IP

5

L

P

6

D

6500

35

Upper ClearP Fork Lower ClearP Fork

5

D

480

5

D

20010

40

16

34

10

0.3

2100

450

25-26

5.75

3.5

420

270

255

600

24

6.34

4.9

1100

133

500

250

42

40

Ref. No.

140'

3401 3.6 c

2 2

51

2

B: Water Drive BA: Intercrystalline-intergranular porosity - water drive 69 Beaver Creek 70 Buckner 71 Coldwater 72 Damme 73 Dorcheat

WyFremont oming Arkan- Union sas Michiganlsabella

Kansas Finney Arkan- Union sas 74 Gila Illinois Jasper 75 Grayson Texas Reagan 76 Lerado SW Kansas Reno Lerado SW Kansas Reno 77 Little MontanaFallon Beaver 78 Little MontanaFallon Beaver East 79 Llanos Kansas Sherman Llanos Kansas Sherman 80 Magnolia Arkan- Columbia sas 81 Mt. Holly Arkan- Union sas

Madison

2-6

L

1260

Smackover J

1

L

1610

Rogers City D

1

D

3200

St. Louis M Smackover J

1 1

L L

2130

SG W SG SG GS

McClosky San Andres Lansing Viola Red River

M P P O O

5 1 1 1 1

L D L D L

540 320 200 200 1100

GS

Red River

O

1

L

500

SGS SGS W

Marmaton P Cherokee P Smackover J

1 1 1

L L L

160 40 4494

Smackover J

1

L

360

SG

M

15 3 10

308

8.7

10

20

50

30-35

49

7.1

01368

10-18

30-32 43.5

14

155

10

15

8 14 3 11 95

38.6 32 41 41 29

12

1.3

35

65

30

13.6

4.5

1500

170

5300

673 232

288

3250 1453

1190

4250

4250

512

20

1130

20

49

38

20.1 c

70

39 1 38

21.8 r

270

35.9-41.4 20.2-23.5 39 18.5

6

1.27 1.2

293" 117 e

3828

0.14 1.64

61 e 12

7 2 31 31 34

35

3828

0.85

5

34

20

1373 1115 3465

3465

220

38,

3405

3405

50 40 35

700

10.5 r

38

L~ I'~ I'O

82 New Texas Navarro W Richland 83 Ross Ranch Texas King G 84 Schuler Arkan- Union W sas BB: Vugular-solution porosity - water drive 85 Acheson

1-2

L

10

Strawn IP Smackover J

1 1

L L

650 1200

62 26

Leduc

D

4

L

3640

234

1460

159

40

26

Rodessa

K

86 Amrow

Alberta, Canada Texas Gaines

S

Devonian

D

1

D

87 Ashburn

Kansas Wabaunsee

SG

Viola

O

1

D-L

88 Bannatyne MontanaTeton 89 Bateman Texas King Ranch 90 Bonnie Alberta, Glen Canada 91 Bough New Lea Devonion Mexico 92Breedlove Texas Martin 93 Bronco Texas Yoakum 94 Comiskey Kansas Morris 95 Comiskey Kansas Morris Northeast 96 Coming MissouriHolt 97 Delphia MontanaMusselshell 98 Glen Park Alberta, Canada 99 Homeglen- Alberta, Rimbey Canada 100 Lea Texas Crane 101 Livengood Kansas Brown 102 Llanos Kansas Sherman

G G

Sun River Bunger

M IP

1 4

D L

100 680

25 20

Leduc

D

4

L

8800

711

S

Devonian

D

1

D

240

S S G SGS

Devonian Devonian Viola Viola

D D O O

1 1-2 1 1

D D D-L D-L

W S

Kimmswick O Amsden IP

1 1

Leduc

D

Leduc

D

103 Lundgren 104 Lundgren South 105 Magutex 106 McFarland

Kansas Gove Kansas Gove

GSG GSG

Eilenburger Hunton LansingKansas City Spergen Spergen

Texas Texas

145 265

D D

480

245

4

L

433

421

4

L

14053

553

2066 240 440

430 18

185

17

O S-D IP

1-2 1-5 1

D D L-D

M M

I 1

D D

S S

Devonian D Eilenburger O

1 1

D-L D

5760 400

107 Mill Creek Kansas Wabaunsee 108 Mound LakeTexas Terry

W SG

Viola O Fusselman S

1 5

D-L D

80 880

109 Newbury

W

Viola

1-3

D-L

160

Andrews Andrews

Kansas Wabaunsee

S W SGS

3520 1080 0 240

O

20

23

40

37 36-38

40

35.4 22-25

5 20

27 33

0.01 r 10 16.7

19 1200

9.1

3100

1085

0.03 ~

285 1631

2.7

9.4

350

6

2560

625ft

43

26

4580

0.09 r

25

41.3 43.4 19 22

9 6

150

200-250

31.5 33.6

46 47.5

120

4--8 17-25

24 38

3-5

24

2 38, 42

10.1

35 140 6 4

40 2(?)

40

5455

400

150 78

4.7 13

2-280 (20) 4 . 8 - 0.126-86 25.5 3890 10-20 2-25 43 16.5 115

10

4

6

21 16

930

149 f"

43

43 25-27 33.8-39.5 35 35

3530 200

2530

78

75 15-20

2360 3530

41

28 f

43

250

10

2570

1.8

v.h.

3730

505000

* Plus 10 Bcfgas-in-place (GiP). t Plus 430 Bcf GiP. ~ Plus 1.3 Tcf GiP. (B = billion = 109; T = trillion = 10t2.) r Oringinal reservoir volume, oil zone.

30

ll0f~

1320

20.9 0.1 c 0.03 r

1820 1120

0.005 c 0.1 r

5350 5702

253 r 166~

34 2

36 34

7.6

6-15

40 198~

0.7

2560

6--7 41 3.9--6 612670

36

1195 2800 7.6

54

2

31.2 25 0 0.2 ~

1604

15

164

203 '

5600 4789 1015 1030

9.6

13

0.1

43

750

367

635

46 2.0

2 2 36 36

43 135 e

2 36 1 1 1

200 e

2 2

1000 4680

0.3 c 1.9

36 2

1178

0.3 ~

36

Field name

State, County country

110 Outlook and MontanaSheridan South Outlook Outlook and South Outlook Outlookand South Outlook 111 Rocker A 112 Rosedale

Exploration Productive Geologic Trap Reservoir discovery formation age mechanism rock type method

S

WinnipegosisD

1

D

Productive Oil and acreage gas column (acres) (ft) 2240 ] [

Pay thickness

Crude gravity

~b

k

S i

P,.

Ph

T

Solution Ultimate reGOR covery

(ft)

(~

(%)

(mD)

(%)

(psi)

(psi) (~

(cu ft/bbl) (MMbbl) (%)

60

40

1.5-8

1

125

34 3.8

t MontanaSheridan

S

lnterlake

S

1

D

2240

MontanaSheridan

S

Red River

O

1

D

2240

Texas Garza Kansas Kingman

SG S

1 1

D L

113 Sabetha

Kansas Nemaha

S

Clear Fork P LansingIP Kansas City Hunton D

1

Sabetha

Kansas Nemaha

Viola

1

O

18

40

1.5-8

4186

20

20

33

5

4486

0.3

34

280 320

70 6

15 19

32-34 43

14

165

1229 1540

0.3 r

2 31

D

40

31

26.7

1000

0.05 r

36

D

30

12

2.56- 0--843 37.6 23.40 7.61- 0--6.0662.9 14.30

0.2 r

36

114 Strahm

Kansas Nemaha

S

Hunton

D

1

D

200

None

65

Strahm

Kansas Nemaha

S

Viola

O

1

D

80

25

20

S

Hunton Amsden

D IP

1 1

D D

80 200

48

65 5-10

D

1

D-L

210

58

12

44.1

S D

1 1-3

D D

1200 2700

167 45

15 0--50

40.2 39--41

100

46.1

0-350 (2) 10.5-- 3.615.8 45 7 25.3 6.5-- 0.119.8 110 10.2 267 15

950

18.3 9.4

1018 700

115 Strahm East Kansas Nemaha 116 Sumatra, MontanaRosebud North West 117 Terre-Haute Indiana Vigo East 118 Tex-Hamon Texas Dawson 119 Unger Kansas Marion 120 Vealmoor East 121 Wapella East 122 Wellman 123 Wilmington 124 Wizard Lake

Ref. No.

Texas

Howard, Borden Illinois De Witt

Texas Terry Kansas Wabaunsee Alberta, Canada

SG

23.226.9 27.428.6 24 27.3

S SGS

Fusselman Hunton

S

Cisco-Wolf- P camp Niagaran S

4

L

3600

610

1--4

D

400

48

22

30.5

Wolfcamp Viola Leduc

4 1 4

L D L

1200 320 3250

738 17 646

280 33

41-44 20.5

W

W

P O D

34

1180 910

14.1

2.66130.4

2-25

1340

35

0.003 c 228 e

640 1981 630

35 51.391.4

5066 620

1.8 154

3362

9001000

360

48 7

4150 985 2510

25

350 50

7

1.1 c 4.1 c

35

2 36

37.8

105 e

2

1.5 1290 150

36 34

13.4 r 380 r

7 2 36 43

I'Q "~

BC: Fracture-matrix p o r o s i t y - water drive 125 Woman's Pocket Anticline 126 Big Wall

MontanaGolden Valley

MontanaMusselshell 127 Black Leaf MontanaTeton 128 Cabin MontanaFallon Creek 129 Crossroads New Lea South Mexico 130 Deer Creek MontanaDawson Deer Creek MontanaDawson 131 Dupo Illinois St. Clair 132 Elk Basin WyPark oming 133 Richey MontanaDawson, McCone 134 Sumatra, MontanaRosebud Northwest 135 Wolf MontanaYellowSprings stone

G

Amsden

IP

1

D

10

11

WS

Amsden'

IP

1

D

600

60

S S

Madison Madison

M M

1 1-2

D D

6700

S-D

1-5

D-L

1-2 1-2 1 1

D D L D

160 480 1020 8960

S

lnterlake S Red River O KimmswickO Madison B M Zone Madison M

1

D

1700

S

Piper

J

1

L

3260

S

Amsden

IP

1

D

2560

M IP

1-5

D L

480

20

D M M

1 1 1

D D-L D-L

200 320

P

4

D

680

S-O

1-2

D

6700

1

L

120 7

S S S G

19

1500

25

4867

35 35

4500

34 34

33

7.5 12

25

52

10

38 90 100 24

43 41 32.7 28

53

39

7 6.7 14 1011.5 4

40

27.3

5-30

31

3 12

33.3 27

15 47

30 19 18

29 40 38

6 6

146

95

36.8

4.5

695

33

2

24.8

7

19.3

61

20

29.5 23 23 41

7

28

4564

0.7 c

44 44 2

45

5

30

4609

1.9 c

2

10

800 4180

30

80(?) 25

100 920

20

34

16

600

1250

25

19

3.25

35

0.4 ~

17

7.7 3-11

168

350

1400 30

500 135 9 83 e 2.9 1000 f

25 24

34 34 7 35

4

25

34

5.4

50

34

3539 1973

1.64.8

0.11000

25

2758

BD: Undefined porosity - water drive 136 Ash Grove Kansas Dickinson 137 Bantam NebraskaHarlan

SG Kansas City Hunton Charles Madison

138 Barada 139 Bredette 140 Bredette North 141 Brown

NebraskaRichardson MontanaRoosevelt S MontanaDaniels, S Roosevelt Texas Gaines SG

142 Cabin Creek 143 Cary

MontanaFallon

S

Miss- Sharkey issippi Kansas Wabaunsee

S G

Hunton

D

!

D

40

Kansas Wabaunsee

G

Viola

O

1

D

680

144Davis Ranch Davis Ranch 145 Dawson Dawson 146 Dollarhide East Dollarhide East

WichitaAlbany

Selma

0.2 c

56 53

3110 3125

2.6 ~ 0.2 0.5

79

30

3043

12

3.25

20

4180

30

O-

45

361

131

254

36 44

50 50

3.0 51 0.2 c

44 34 34 2

30

34 45

1124

NebraskaRichardson NebraskaRichardson Texas Andrews S

Hunton D Viola O Fusselman S

! 1 1-2

D L L

800

100

20 13 62

Texas

Ellenburger O

1-2

D

1680

250

107

Andrews

880

S

992 12

188

64

36

1120 0.5 c

t.~ t,~

Field name

147 Eagle Springs Fairplay Falls City Fradean Gingrass Goodrich

148 149 150 151 152

State, County country

Exploration Productive Geologic Trap Reservoir discovery formation age mechanism rock type method

Productive Oil and acreage gas column (acres) (fl)

Nevada Nye

W

Sheep Pass T (e)

2

L

Kansas Marion NebraskaRichardson Texas Upton Kansas Harvey Kansas Sedgwick

G GS SG SG W

Hunton Hunton Ellenburger Hunton LansingKansas City

S-D S-D O S-D IP

1 1-2 1 1-5 1

D D D D L

120 1080 800 30 600

M S-D S-D O IP P

1 1 1-5 1-5 1 1

L D D D L D

600 600 400 80 7120

IP-P

4

L

850

Goodrich Kansas Sedgwick Goodrich Kansas Sedgwick 153 Greenwich Kansas Sedgwick Greenwich Kansas Sedgwick 154 HaussermanNebraskaHarlan 155 Howard Texas Howard, Glasscock Glassock, Sterling Mitchell

W W W W G

Hunton Hunton Arbuckle Kansas City GlorietaClear Fork

Pay thickness

Crude gravity

~

k

S.

Pi

Pb

T

Solution Ultimate reGOR covery

(ft)

(~

(%)

(mD)

(%)

(psi)

(psi) (~

(cu ft/bbl) (MMbbl) (%)

200

26-29 14 93 370 11

7 23 35 52

35

30 18 35 2-3 12

36-37 30 50 34 34.2

2.0 c 0.3 ' 5.0 c 6.0 0.04 c

820

8

4200 975

5

46

197 ~

52 c 39 41.5 36.5 36 27.4

10

4

115

37.6

6.7

61

7.715 815.6 10.518.1 14.618.7 14-18 4-7 9

0.30.8 0.64.5 0.8-5.4 1.522 3.85.4 12-76 135

2-3 12 12 12

7

13~*

40

J'39 x 106 Mcf 156 Huat Canyon 157 Hugoton Hugoton 158 Hugoton Hugoton

Texas

Gaines

SGS

500

Morton, Kansas ,ifStevens,

W

Herington

P

5

L-D

2560000

5--10

Gas

[Seward,

w

Krider

P

5

L-D

2560000

25-35

Gas

Kansas

] Staunton, Kansas ] Grant,

Kansas ] Haskell, Hamilton, / Hugoton Kansas [Kearney, Finney 159 Hutex Texas Andrews 160 John Creek Kansas Morris 161 Lerado Kansas Reno Lerado Kansas Reno Lerado Kansas Reno 162 Magutex Texas Andrews 163 Pine Montana ~Fallon Pine Montana{Prairie Pine Montana LWibaux 164 Shubert NebraskaRichardson 165 Snethen NebraskaRichardson 166 Tex-Hamon Texas Dawson

W

Winfield

P

5

L-D

2560000

20--35

Gas

W

Towanda

P

5

L

2560000

25-40

Gas

W

Fort Riley

P

5

L

2560000

15-20

Gas

S G W W W S GS GS GS

Devonian Viola Lansing

1 1 1 1 1 1 1 1 1 1 1 1

D-L D L L D D D D D-L D L D

60 18

44 25.5 43.2 Gas 43.2 45.1 34 34 34 23 27 39

S

D O IP M Viola O Ellenburger O Interlake S Stoney Mt. O Red River O Hunton D Viola O Montoya O

4480 1960 750 750 750 2160 8380 8380 8380

270 75 3 40 10 70

400

67

19 140 80 225 7 113

361

4539 50-65

435

!

Ref. No.

36 36 2 36 36 36 36 36 36 44 2

2

"9.6

1

4.4 x 109

1

Mcf~

1

350 1

24.838 31.642.5 22.839.6 27

1

34 63.5

5400 1050

23 3.78 3.78 3.78

30 30 30

6013 4160 4160 4160

23.1

20

1055 5051

322

157

25.4 2 1,3 c 36 2.4 31 2.2 x 106 Mcf31 31 10c 2 } 34 55 30 34 34 44 0.12 c 44 35 2

L~ bO

167 Valley Kansas Sedgwick Center 168 Wells Texas Dawson Devonian 169Willowdale Kansas Kingman

S-D

SGS S

0-113

1-5

W

D-L

1200

175

3.36

5180

7-11

2

41.1

840

Viola

34-35

* Includes No. 228.

C: Gas-Cap Drive CA: Intercrystalline-intergranular porosity - gas-cap drive 170 Eubank

Kansas Haskell

W

171 Maydelle 172 Novinger 173 Opelika

Texas Cherokee Kansas Meade Texas Henderson

G SG

174 Plainville 175 Wilde 176 Wilsey

Indiana Daviess Kansas Morris Kansas Morris

LansingKansas City - E Zone Rodessa Marmaton Rodessa

IP

1-5

960

K IP K

1 4 1-2

1200 2400 11200

Salem Lansing Lansing

M IP IP

36

14

Gas

40

20 15.3 20

52 42 44

200 1080 640

100

13300 5000 1100

1068

16000

16

1105

61

4035

41 1 20--30 41, 47 3.4 x 106 Mcf 7 36 36

2.0 c 3400

11-17 59

3400

1400

550

Gas Gas Gas

CB: Vugular-solution porosity-- gas-cap drive 177 Coyanosa 178 Fishook 179 Wichita

Texas Pecos SGS Illinois Adams, Pike W Kansas Sedgwick W

Devonian D Edgewood S Viola O

1-2 1 1

Ellenburger O

1-2

10 54 0.84240

20

5.6 x 106 McF 2 3 Bcf 7 0.8 c 36

20

162 14 4

53.4 Gas 38

8.1 20 7.814.6

5OO

135

Gas

6.7

1-100 35

6648

1.5 x 108Mcf~

1715

790

51.2 d

1.33

0.56

6964

4.3 x 106 Mcf ~ 2

58O

140

56 d

12

1

3000

65

Gas

1 . 0 + 3 x 107 Mcf 109 Mcf

44.375.9

5937 119 1280

CC: Fracture-matrix p o r o s i t y - gas-cap drive 180 BrownBassett 181 Coyanosa

Texas Texas

Terrell, Crockett Pecos

S

D

Ellenburger O

1-2

D

8960

SG

Devonian

1

L

8OO

W

Greenwood IP

5-6

L

160000

SGS

Strawn

1-5

D-L

1440

40

44

10

S

Smackover

1

D-L

1280

361

49.4

14

SG SG

Devonian D Ellenburger O

1-2 1-2

L-D D

12160 23680

180 1030

49.5 d 53 d

SGS

10

2

CD: Undefined p o r o s i t y - gas-cap drive 182 Fradean

Texas

Upton

183 Greenwood Kansas, Morton, CoioradoBaca 184 Levelland Texas Hockley Northeast 185 Loring Miss- Madison issippi 186 Puckett Texas Pecos 187 Puckett Texas Pecos

D

IP

181 1600

435

O27.9

27

3250

25

5890

21000

0.8 c 1.9 x 10s McF 7.9 x lOs Mcft

2 1

45 2 2

q~ t'~

Field name

State, County country

Exploration Productive Geologic Trap Reservoir discovery formation age mechanism rock type method

Pi

Ph

T

Solution Ultimate reGOR covery

(roD) (%)

(psi)

(psi) (~

(cu ft/bbl) (MMbbl) (%)

500

3395

2520

950

Productive Oil and acreage gas column (acres) (ft)

Pay thickness

Crude gravity

~

k

(ft)

(~

(%)

89300

200

29-38

22

S.

Ref. No.

D: Open-Combination Drive DA: Intercrystalline-intergranular porosity - open combination drive 188 Abqaiq 189 Adell Northwest 190 Aden Consolidated and Aden South Aden Consolidated and Aden South Aden Consolidated and Aden South Aden Consolidated and Aden South Aden Consolidated and Aden South 191 Bahrain 192 Dale Consolidated Dale Consolidated Dale Consolidated

Saudi "Arabia Kansas Decatur Illinois Wayne, Hamilton

Arab D W S

J

2700

Rosiclare

2700

1170

31-39

320

LansingIP Kansas City Ohara M

7-8

38-41.5

8700

48

0.8 c

1

15.5

7

5-12 Illinois Wayne, Hamilton

S

Illinois Wayne, Hamilton

S

Illinois Wayne, Hamilton

S

Illinois Wayne, Hamilton

S

Bahrain Illinois Hamilton, Saline Illinois Hamilton, Saline

M

700

McClosky

M

2700

Salem

M

6001040

7.5

8-27

2700 1750

8-20

Warsaw

M

2700 I10

Second Pay K Ohara M

20000

S

Rosiclare

20000

Illinois Hamilton Saline

S

McClosky

M

193 Damme

Kansas Finney

SG

Marmaton

IP

194 Feeley

Kansas Decatur

W

Lansing

IP

2030

40

14

S

M

2.2 b

t 5

160

124

96

140

142

[125"

1150

23

49

7

800

34.837.2 3031 3439 39

278

800

5-15

20000

1236

340

1632 222

510

0.6 c

!

0.3 c

1

149

50, 51

t,~ OO

195 GhwarSaudi Ain-Dar Arabia 196 GhwarSaudi Fazran Arabia 197 GhwarSaudi Harah Arabia 198 GhwarSaudi Hawiyan Arabia 199 GhwarSaudi Shedgum Ambia 200 GhwarSaudi Uthmaniyan 201 Howard Texas Howard, Glasscock Glasscock, Sterling, Mitchell

G

Arab D

J

1

L-D

4000

1140

143

35

22

290

Amb D

J

1

L-D

136500

987

150

35

23

270

Amb D

J

1

L-D

110100

1369

103

33

21

220

Arab D

J

1

L-D

298600

1094

61

33

19

68

1126

60

33

16

52

80

31.7

10.5

Arab D

J

1

L-D

4100

Arab D

J

1

L-D

47400

San Andres P Grayburg

1

D

15620

Pleasant Prairie

KentuckyOhio Kansas Finney Kearney, Haskell Kansas Finney Kearney, Haskell

570

7515

1910 215

570

6443

1830 215

520

10989

1715 215

450

83

1595 215

420

429

50, 51 50, 51 50, 51 50, 51 50, 51

40 2 7

82 202 Jingo 203 Pleasant Prairie

5

1920 215

SG W

W

Salem M LansingIP Kansas City St. Louis

5 5

L L

8--27

90

41.5

8-27 12.5

0.1125

280

64.5

46.1

12 5--38

33 32-36

14.3

8 18

34 33.9

10

35.2

39

8.0

39.4

M

1-5

L

10000

Lansing Amsden

IP IP

1 1-5

L D

160 320

Leduc

D

4

L

21640

SG

S

4

L

320

161

S

M

5

L-D

1100

15

t

DST 1025 1045

1.2c'1 9 1

DB: Vugular-solution porosity - open-combination drive 204 Enlow 205 Gage

Kansas Edwards MontanaMusselshell 206 LeducAlberta, Woodbend Canada 207 New Baden, Illinois Clinton East 208 Nunn Kansas Finney 209 Ozona, East

Texas

Crockett

210 Pegasus

Texas

Midland, Upton

Alberta, Canada 212 Ropes and Texas Hockley South Ropes 213 Shallow Kansas Scott Water

S G

SG

Alberta, Canada

15

26-28

Ellenburger O

2

D

Ellenburger O

1-2

D

10000

800

Leduc

D

4

L

37833

101

S

Canyon

IP

4

L

1320

100

S

St. Louis

M

1-5

L

500

100

26-28

Leduc

D

4

L

1757

589

42

211 Redwater

214 Westerose

232

101

0.09 c 0.5

48 1000

15

1894

1894 150

553

655 DST 9.5-

22-

11.9

166

41267 55 0 Bcf 0.02

43, 52 7 1

7.4

45

3391

53

2-8

30

5668

2.7 b

6.5

500

25

1050

42

8.5

66

26.9

3754

1934

31 34

23

54--72 d

9.3

25

7

2570

275 Mcf/ac-ft 3386 485 94

2570 178

1556

2

40

53

64

54

195

817

368

59

2

2.0 c

1

650

121 77~ { 117 Bcf

43

L/I b9

Field name

State, County country

Exploration Productive Geologic Trap Reservoir discovery formation age mechanism rock type method

Productive Oil and acreage gas column (acres) (fl)

Pay Crude thickness gravity (fi)

(~

(%)

(mD)

(%)

Pl

Ph

T

Solution Ultimate reGOR covery

(psi)

(psi) (~

(cu ft/bbl) (MMbbl) (%)

Ref. No.

DC: Fracture-matrix porosity - open-combination drive 215 Blackfoot 216 Gypsy Basin 217 Waterloo 218 West Brady 219 West Edmond

MontanaGlacier MontanaPondera, Teton Illinois Monroe MontanaPondera Okla- Canadian homa

S W

Sun River Madison

M M

1-7 2

D-L L-D

GW SG W

Kimmswick O Sun River M Bois d'Arc M

I 1-5 3-6

L D L

SG

Devonian

D

2-3

L

S

St. Louis

M

1

L-D

6-15 133

40

25 34.5

14.2 14

264 305

230 !0 29240

50 !0 600

30 15 70

30.2 28.1 41

7.4 5.3

40 0-20

15

3145

5420

500

0-100

42

20

3.5

40

2500

440

955 1038

34 34

2770 145150

I010

0.24 7 0.005 34 ~I05 25-35 55, t961Bcf 56

DD: Undefined porosity - open-combination drive 220 Crosset South-El Cinco 221 Dale Consolidated 222 Deerhead 223 Dwyer 224 Fanska 225 Fertile Prairie 226 Gas City 227 Giendive

Texas

Crockett

Illinois Hamilton, Saline Kansas Barber MontanaSheridan Kansas Marion MontanaFallon

G S W S

Viola Madison Warsaw Red River

O M M O

2-5 1 1 1

D L D L-D

MontanaDawson MontanaDawson

S S

Red River Red River

O O

1-2 1-2

D L

1080 1040

320

MontanaDawson

S

Stony Niybtaub

O

1-2

D

1040

228 Greenwich Kansas Sedgwick Kansas Decatur 229 Hardesty

W W

1-5 l

L L

230 Neva West Texas Schleicher MontanaPondera, 231 Pondera Teton Kansas Sedgwick 232 Valley Center Valley Kansas Sedgwick Center 233 Warner Kansas Decatur

S W

M LansingIP Kansas City Strawn IP Madison M

4 3-6

L D

LansingIP Kansas City Viola O

l

L

160

12

2-14

34-35

5

D

1800

76

20-30

34-35

1-2

L

360

4

34.6

Glendive

W W SGS

LansingIP Kansas City

5-15

20000 880

65

7 0.8c:

32 32.9 33 33.4

5---6

38.2 38

II 6.5

30 35

60

31 f ~150 [

38

6.5

35

1400 160

16

60 4-15

44 29-39

2052 6000

166 58

30

45 27-38

* Includes No. 221. t Includes No. 37. :[:Efficient gravity-segregation drive; with some gas injection. w Plus 1.4 x 103 Mcfgas.

17

200

15 (?) 50 13 49

240 240

750

I0 24

3O

750 3520

0.3c I.I

160

4.0 f ~mo.4 [

24 25

7 14

2.5 82

28 45

2551

34

14.0 19.0 l }23.fF J

930

36

0.3 c

849

34 34

24

13.0 c I 170

31 34 36 34

I

35

2 34 36 36 1

t.~

E: Closed-Combination Drive EA: lntercrystalline-intergranular porosity- closed-combination drive 234 Turner Valley

Alberta, Canada

G

Turner Valley

M

1-2

1050f

9.812.8

6.84

10

2775

47--49

7.07

200

26

3363

154

180302

36.140

7-11

159-- 5.6460 8.2

25012623

187- 355195 765

483

172

32

7

32

49.1

6.5-7

2921

146

O.IY

16275

156

12175

10.5 500

800

758

149

880

EB: Vugular-solution porosity- closed-combination drive 235 Alison Northwest 236 Rainbow Area (typical) 237 Zama Area (typical)

New Lea, Mexico Roosevelt Alberta, Canada Alberta, Canada

S

Cisco

IP

S

Keg River

D

S

Keg River

D

Strawn

IP

1

L

80

IP

1

D

34000

M IP M D

1-5 2-5

L-D

978

19

F: Unknown Drive FA: Vugular-solution porosity - unknown drive 238 Tex Hamon Texas

Dawson

S

70

FB: Fracture-matrix porosity - unknown drive 239 Indian Basin

New Eddy Mexico

SGS

207

4.3

0.11780

25

FC: Undefined porosity - unknown drive 240 241 242 243

Bear's Den Otto Tex-Hamon Valley Center

MontanaLiberty Texas Schleicher Texas Dawson Kansas Sedgwick

SG SG S W

Madison Strawn Hunton

Source: After Langnes et al., 1972; courtesy of Elsevier Publ. Co.

1

250 480 240

30

18 6

39 38-41 37.5

15

470 137

6-18

0.1 O.OY 0.09 c

5 L~ L~ l,-,,,a

532 References to Table XXXVIII 1. Kansas Geological Society, 1959. Kansas Oil and Gas Fields, Vol. II, Western Kansas. Kansas Geol. Soc., p. 207. 2. West Texas Geological Society, 1966. Oil and Gas Fields in West Texas. West Texas Geol. Soc., Midland, Tex., p. 398. 3. Herbeck, E.F. and Blanton, J.R., 1961. Ten years of miscible displacement in Block 31 Field. J. Pet. Tech., 13(6)i 5 4 3 - 549. 4. Goss, L.E. and Vague, J.R., 1962. Pressure maintenance operations-Fort Chadbourne Field-Odom Lime Reservoir. Paper SPE 406, 3 7th Annual Fall Meeting, Los Angeles, Calif.., Oct. 5. Gealy, F.D.Jr., 1967. North Foster U n i t - evaluation and control of a Grayburg-San Andres waterflood based on primary oil production and waterflood response. Paper SPE 1474 presented at SPE Permian Basin Oil Recovery Conference Midland, Tex., May. 6. Hoss, R.L., 1948. Calculated effect of pressure maintenance on oil recovery. Petrol. Trans. AIME, 174:121 130. 7. Miller, D.N.Jr., 1968. Geology and Petroleum Production of the Illinois Basin. Illinois and Indiana-Kentucky Geol. Socs., p. 301. 8. Donohoe, C.W. and Bohannan, D.L., 1965. Harmattan-Eikton F i e l d - a case for engineered conservation and management. J. Pet. Tech., 17(9): 1171 - 1178. 9. Akins, D.W.Jr., 1951. Primary high pressure water flooding in the Pettit Lime Haynesville Field. Pet. Trans. AIME, 192:239 - 248. 10. Goolsby, J.L. and Anderson, R.C., 1964. Pilot water flooding in a dolomite reservoir, the McElroy Field. J. Pet. Tech., 16(12): 1345- 1350. 11. Trube, A.S.Jr., 1950. High-pressure water injection for maintaining reservoir pressures, New Hope Field, Franklin County, Texas. Pet. Trans. AIME, 189:325 - 334. 12. Gray, R. and Kenworthy, J.D., 1962. Early results show wide range of recoveries in two Texas Panhandle water floods. J. Pet. Tech., 14(12): 1323-1326. 13. Henry, J.C. and Moring, J.D., 1968. Flood evaluation yields vital guidelines. Pet. Eng., Aug.: 5 7 - 59. 14. Neslage, F.J., 1951. Gas injection in Dolomite reservoir, West Pampa Repressuring Association Project as of January 1, 1951. Proc., Second Oil Recovery Conference, Texas Petroleum Research Committee, pp. 142. 15. Marrs, D.G., 1961. Field results of miscible-displacement program using liquid propane driven by gas, Parks Field Unit, Midland County, Texas. J. Pet. Tech., 13(4): 3 2 7 - 332. 16. Barton, H.B. and Dykes, F.R.Jr. Performance of the Pickton Field. Pet. Trans. AIME, Reprint Series 4:83 88. 17. Sessions, R.E., 1960. How Atlantic operates the Slaughter Flood. Oil and Gas J., July: 91 - 98. 18. Hiltz, R.G., Huzarevich, J.V. and Leibrock, R.M., 1951. Performance characteristics of the Slaughter Field Reservoir. Proc. Second Oil Recovery Conference, Texas Petroleum Research Committee, pp. 1 4 6 - 157. 19. Sessions, R.E., 1963. Small propane slug proving success in Slaughter Field Lease. J. Pet. Tech., 15(1 ): 31 -36. 20. Fickert, W.E., 1965. Economics of water flooding the Grayburg Dolomite in South Cowden Field. Proc. Twelfth Annual Meeting of the Southwestern Petroleum Short Course, Texas Technological College, Lubbock, Tex, April pp. 22-23. 21. Allen, W.W., Herriot, H.P. and Stiehler, R.D., 1969. History and performance prediction of Umm Farud Field, Libya. J. Pet. Tech., 21(5): 5 7 0 - 578. 22. Borgan, R.L., Frank, J.R. and Taikington, G.E., 1965. Pressure maintenance by bottom-water injection in a massive San Andres Dolomite reservoir. J. Pet. Tech., 17(8): 883 - 888. 23. Miller, F.H. and Perkins, A., 1960. Feasibility of flooding thin, tight limestones. Pet. Eng., Apr.: B55 B75. 24. Burchell, P.W. and Coonts, H.L., 1964. Review of secondary recovery operations in the Greater Aneth area, San Juan County, Utah. Producers Monthly, July: 1 0 - 14. 25. Kinney, E.E. and Schatz, F.L., 1967. The Oil and Gas Fields of Southeastern New Mexico. Roswell Geol. Soc., Roswell, N.M., p. 185. 26. Latimer, J.R.Jr. and Oliver, F.L., 1963. The Fairway Field of East Texas: its development and efforts toward unitization. Paper SPE 703 presented at SPE 38th Annual Fall Meeting, New Orleans, La. 27. Larson, V.C., Peterson, R.B. and Lacey, J.W., 1967. Technology's role in Alberta's Golden Spike Miscible Project. Paper P.D. 12 (9) presented at the Seventh Worm Pet. Cong., Mexico City. 28. Allen H.H. and Thomas J.B., 1959. Pressure maintenance in SACROC Unit operations, January 1, 1959.,]. Pet. Tech., 11(11 ): 42 - 48. -

119

-

533 29. Sutton, E., 1965. Trempealeau reservoir performance, Morrow County Field, Ohio. J. Pet. Tech., 17(12): 1391- 1395. 30. Lacik, H.A. and Black, J.L.Jr., 1961. Pressure maintenance operations in the Sharon Ridge Canyon Unit, Scurry County, Texas, J. Pet. Tech., 13(7): 645-648. 31. Kansas Geological Society: 1956. Kansas Oil and Gas Pools, Vol 1, South Central Kansas. Kansas Geol. Soc., p. 97. 32. Wasson, J.A., 1967. Secondary oil-recovery possibilities in the basal Greenbrier Dolomite Zone, Sycamore-Millstone Field, Sherman District, Calhoun County, W.Va. USBM Rept. Invest. 7049, p. 20. 33. Willingham, R.W. and McCaleb, J.A., 1967. The influence of geologic heterogeneities on secondary recovery from the Permian Phosphoria Reservoir, Cottonwood Creek, Wyoming. Paper SPE 1770 presented at SPE Rocky Mountain Regional Meeting, Casper, Wyo. 34. Abrassart, C.P., Nordquist, J.W. and Johnson, M.C. 1958. Montana Oil and Gas Fields Symposium. Billings Geol. Soc., p. 247. 35. Wayhan, D.A. and McCaleb, J.A., 1969. Elk Basin Madison heterogeneity- its influence on performance. J. Pet. Tech., 21(2)" 153-159. 36. Curtis, G.R., 1960. Kansas Oil and Gas Fields, Vol. III, Northeastern Kansas. Kansas Geol. Soc., p. 220. 37. Pollock, C.B., 1960. Beaver Creek Madison, Wyoming's deepest water injection project. J. Pet. Tech., 12(1): 3 9 - 4 1 . 38. Bruce, W.A., 1944.A study of the Smackover Limestone Formation and the reservoir behavior of its oil and condensate pools. Pet. Trans. AIME, 155:88 - 119. 39. Criss, C.R. and McCormick, R.L., History and performance of the Coldwater Oil Field, Michigan. Pet. Trans. AIME, Reprint Series 4" 5 5 - 63. 40. Winham, H.F., 1943. An engineering study of the Magnolia Field in Arkansas. Pet. Trans. AIME, 151" 15 34. 41. Herald, F.A., 1951. Occurrence of Oil and Gas in Northeast Texas. Univ. of Texas, Bureau of Economic Geology, Austin, Tex., p. 449. 42. Kaveler, H.H., 1944. Engineering features of the Schuler Field and unit operations. Pet. Trans. AIME, 155" 58-87. 43. Hnatiuk, J. and Martinelli, J.W., 1967. The relationships of the Westerose D-3 Pool to other pools of the common aquifer. J. Can. Pet. Tech., Apr-June: 4 3 - 4 9 . 44. Finch, W.C., Cullen, A.W., Sandberg, G.W., Harris, J.D. and McMahon, B.E., 1955. The Oil and Gas Fields of Nebraska. Rocky Mt. Assoc. Geologists, Denver, Colo., p. 264. 45. Frascogna, X.M., 1969. Mesozoic-Paleozoic Producing Areas of Mississippi and Alabama. Mississippi Geol. Soc. Jackson, Miss., p. 139. 46. Garfield, R.F., 1969. International Oil and Gas Development. Intern. Oil Scouts Assoc, Austin, Tex. Part 1, XXXIX: 496. 47. Clay, T.W. Pressure maintenance by gas injection in Opelika Field of Henderson County, Texas. Oil and Gas J. Reprint Series on Secondary Recovery, pp. 54 - 57. 48. Stanley, T.L., 1960. Approximation of gas-drive recovery and front movement in the Abqaiq Field, Saudi Arabia. Pet. Trans. AIME, 219: 274. 49. Cotter, W.H., 1962. Twenty-three years of gas injection into a highly undersaturated crude reservoir. J. Pet. Tech., 14(4): 361 - 365. 50. Bramkamp, R.A. and Powers, R.W., 1958. Classification of Arabian carbonate rocks. Bull. GSA, 69(10): 1305- 1318. 51. Steineke, M., Bramkamp, R.A. and Sander, N.J., 1958. Stratigraphic relations of Arabian Jurassic oil.habitat ofoil. Bull. Am. Assoc. Pet. Geol., pp. 1294- 1329. 52. Horsfield, R., 1962. Performance of the Leduc D-3 Reservoir. Pet. Trans. AIME, Reprint Series 4: 6 5 - 72. 53. Cargile, L.L., 1969. A case history of the Pegasus Ellenburger Reservoir. J. Pet. Tech., 21(10): 1 3 3 0 1336. 54. Willmon, G.J., 1967. A study of displacement efficiency in the Redwater Field. J. Pet. Tech., 19(4): 449 456. 55. Elkins, L.F., 1969. Internal anatomy of a tight, fractured Hunton Lime Reservoir revealed by performance - West Edmond Field. J. Pet. Tech., 21(2): 221 - 232. 56. Littlefield, M., Gray, L.L. and Godbold, A.C. A reservoir study of the West Edmond Hunton Pool, Oklahoma. Pet. Trans. AIME, Reprint Series 4: 8 9 - 107. 57. White, R.J., 1960. Oil Fields of Alberta. Alberta Soc. Pet. Geol., p. 272. 58. Robertson, J.W., 1969. New life begins for Alberta's Keg River Pinnacle Reefs. World Oil., Sept.: 8 7 90.

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ACKNOWLEDGEMENTS

Dr. H. Rieke would like to thank the following people for assistance in preparing Chapters 1 and 5. Thanks go out to Mr. Nawaz Ahmed (Sialkor, Pakistan) for his continuing encouragement and help; Mr. M. Waseem Saleem (Jeddah, Saudi Arabia) for his help in many of the necessary odd jobs in putting manuscripts together; Mr. Abdul H. Afandi and his staff at the Directorate General of Mineral Resources in Jeddah for some of the drafting and Pat Vavrock for the rest; Mrs. Claudia Moe (West Virginia University Librarian, Morgantown, WV) and Mr. George J. Vranas (Director) of USGS Library in Jeddah for their assistance in searching and obtaining publications; Mr. Khalid M. Hajraf (Director) and his staff at the DGMR Publications Department in Jeddah for their support; Professor Kinji Magara (U.A.E. University, A1-Ain), and Drs. Assadullah Kazi and Leif Carlson at the DGMR for their advice and support. To Mr. E.B. Nuckols (Texas A & M University at Corpus Christi, Texas) and Mr. William Gwilliam (Department of Energy, Morgantown, WV) for reading and commenting on the manuscript. Lastly, to his son Henry Rieke for maintaining the computers, typing, and preparing electronically some of the large tables and figures.

This Page Intentionally Left Blank

549 Chapter 6

W E L L TEST ANALYSIS IN CARBONATE RESERVOIRS FERNANDO SAMANIEGO V. and HEBER CINCO LEY

INTRODUCTION

Forecasting reservoir performance requires, among other parameters, complete information on reservoir definition and rock and fluid properties. A reliable method for estimation of both rock properties and characterization of some reservoir heterogeneities, when using an integrated approach, is pressure transient testing. Over the last four decades, several hundred technical papers have been written on well test analysis; this material includes solutions for transient flow problems, methods of analysis, and practical aspects of testing procedures. This wealth of information is a result of the increasing interest among engineers in the determination of reservoir characteristics under in situ conditions, which is the essential objective of pressure transient analysis. An excellent treatment of different techniques currently available has been presented by Matthews and Russell (1967), Ramey, Kumar and Gulati (1973), Energy Resources Conservation Board (1975), Earlougher (1977), Home (1990), Stanislav and Kabir (1990) and Sabet (1991). Analysis of pressure transient data allows estimation of the following information (symbols and units are defined in the Nomenclature section at the end of this chapter): - formation conductivity (kh), well damage (s), - average formation pressure (p-), - formation storage capacity (O~c h), - parameters of double porosity 'behavior (w, ~, r/maO,AIo, Smao), -- hydraulic fracture parameters (klbl) o, k l b p x I, and s I, and detection of: - barriers and discontinuities, - layering, water drive conditions, permeability anisotropy, and interference between wells and reservoirs. -

-

-

-

Although this list is not complete, it highlights the most important information that can be acquired through this analysis. Experience on the application of pressure transient methods of interpretation has shown that, in some cases, the uniqueness dilemma arises especially when dealing with heterogeneous systems. In other words, it is implied that different reservoir situations yield the same pressure behavior. However, the uniqueness dilemma can, in many cases, be solved through an integrated approach, that is, a combination of pressure transient data and geological and geophysical information, well logging, pro-

550

q vs t

)

ADDITIONAL INFORMATION

( Pw vs t

PRESSURE RECORDER INTERPRETATI ON MODELS -------~-

DAMAGED ZONE

( RESERVOIR

WELL CONDITIONS

Fig. 6-1. Interpretation of a transient pressure test. duction data, core analysis, etc. Figure 6-1 shows a schematic of this approach where it is indicated that analysis of all information available provides the interpretation model(s), which defines well conditions and formation characteristics that are used as an input into reservoir simulation studies. A transient pressure test consists of recording the variation of pressure vs. time after a change of well flow rate. The pressure response can be measured either at the well where the change of flow rate takes place, in a single well test, or at nearby wells in a multiple well test. Table 6-I presents the most frequently used tests in the oil industry. Transient pressure tests have been successfully performed in all kinds of formations, but usually a special effort has to be made in applications to carbonate reservoirs due to their inherently more heterogeneous nature as compared to sandstones (Dominguez et al., 1992; Samaniego et al., 1992). Information on transient pressure analysis is vast, and would require many volumes to present a complete discussion of different aspects. This, indeed, is not the objective of the present chapter. Rather, the aim of this chapter is to discuss specific aspects of well test analysis as applied to carbonate reservoirs. First, the basic theory of transient flow in reservoirs is introduced, followed by a detailed discussion on the most commonly used techniques of interpretation. A special effort is made to present applied examples whenever possible.

551 T A B L E 6-I P r e s s u r e t r a n s i e n t a n d f l o w tests

TABLE

6.I

Pressure

transient

and flow RATE

TYPE SINGLE WELL TESTS

PRESSURE

qt,

1. Pressure Drowdown

(PBV)

l

qz

q

q' I

=.._

v t

to : t E

Pwf I

I q'

to

t~

~

4. I n j e c t i o n Test

v t

tz

w -q

=,..-

t

L~t

v t

o

J

tl tz ts

9

I

-q

-q

t4 ~ t

I

o il

to

o

tl

~---t Pwf ~t

Pwf

i

qT,,

i to

o

,

7. Deliverability Test

tz

t3

t4 "-t

-t -

" - t

Pw

~

w t

l

v t Pw Ii

qz q'

10. Repeat Formation Test (RFT) ,

=,.._

to

~---t

Drillstem Testing (DST)

i

t=

Pw

6. Constant Pressure Test

9.

l

tl

v t

Pwf

Testing

i

to

-q

q~176

5. Fall Off Test

--t

to:tp

=.=

8. Vertical

v t

to

ow , , . . f ~

;

3. Variable Flow Rate Test

=,=

v t

to

2. Pressure Buildup

tests

|

!

'~.~

tl

tz

to

I to -q

tl

Pw

11. Step Rate Test

~

"~ t

s

= .r~";-'F-

I

tz

tz

i

o

t~

t~

T

Active Well

t4

v t

,k ; i ~ I .= o -t~ -tz -ts -t4 v _ t & P || Observation Well .._

12. Interference Test

r JL

,

v t

Active Well q q q

to

v

t

p ,L Observation Wells

13. Pulse Testing "-t

v t

552 P R E S S U R E T R A N S I E N T B E H A V I O R OF R E S E R V O I R S

Analysis of pressure and flow test information has been performed since its introduction in the petroleum industry, by matching data to reservoir flow models. Such matching has been possible through the use of graphical and computer historymatching techniques. Undoubtedly, complete knowledge of the characteristics and limitations of flow models allows correct application of the methods of analysis, resulting in high level of confidence in the estimation of reservoir parameters. Traditionally, the cylindrical radial flow model has been used as a basis for pressure transient interpretation. This practice is based on the fact that, in general, flow towards a well follows this geometry. However, there are some cases where this flow geometry is not appropriate, and the analyst must apply other types of flow models such as linear, spherical radial, elliptical and bilinear. In the foregoing discussion a brief presentation is made of the main features and limitations of these flow models. Classical pressure transient analysis theory assumes a system with the following characteristics: the permeability (k) and the porosity (~b) of the medium are constant, the porous medium is homogeneous and isotropic, the fluid saturating the medium has constant viscosity (/~) and a small compressibility (c), - the flow is isothermal and Darcy's Law is valid, pressure gradients are small everywhere within the porous medium, and - gravity forces are negligible. Under these conditions, flow phenomenum in a porous medium can be described by the diffusivity equation: -

-

-

-

V2p -

k

9

(6-1)

where p and t represent pressure and time, respectively. Particular solutions of Eq. 61 require definition of specific boundary and initial conditions. The usual initial conditions consider a uniform pressure distribution throughout the medium, that is,

p(t = O) = pi for all domains

(6-2)

The boundary conditions are defined for both the inner and outer boundaries. The inner boundary represents the surface through which fluid is either produced or injected (i.e., the well). The outer boundary is the surface limiting extemally the porous medium saturated by hydrocarbons (i.e., sealing faults, pinch outs, oil-water and gas-water contacts, etc.). Generally, two types of conditions are considered along the boundary: a) prescribed flux, and b) prescribed pressure. The first case is expressed using Darcy's law:

! 9 ds On

qp k

(6-3)

553 where s represents the boundary surface; n, the direction normal to the surface; and q, the total flow rate produced (injected) through this surface. This condition includes the impermeable boundary case, that is q = 0. The second case is expressed as:

p(t) Is = Po

(6-4)

where Po is the prescribed pressure at the boundary. Sometimes, the flow problem is solved for a porous medium of infinite extent, and the boundary condition at the outer boundary is:

lim p(s,t)

S----~oo

(6-5)

= Pi

such that pressure never changes at the extemal boundary (infinity). In order to generalize the solution for different flow problems in reservoirs, dimensionless variables have been introduced (van Everdingen and Hurst, 1949; Ramey et al., 1973; Earlougher et al., 1977). The definition of dimensionless groups varies according to the geometry of flow as shown in Table 6-II. A characteristic of these TABLE 6-11 Dimensionless variables Flow geometry

Variable

Symbol

Liquid

Definition Gas

Linear

Distance

xo

x /L

x / L

~,kt

Radial

Spherical

12 ctZ2

~,kt ~) (12 ct)iL2

Time

tD

~

Pressure drop

POE

kbh(p i - p ) aoLB lzL

kbh(p ) - (Pp(Pwi) ) aoLB IuL

Distance

ro

r / rw

r / rw

Time

tD

flt k t ~ p c, r2w

qb (12 ct) i

Pressure drop

PD

kh ( P i -- P ) aoqB p

kh (pp (p i) - lap(Pw/) ) ag qsc T

Distance

ro

r / rw

r / rw

~,kt

~,kt

Time

to

~) ]lJ C t r 2

(~ (p c ) i r~

Pressure drop

k rw(Pi--p) aosph q B p

k rw(Pp(Pi)-Pp(Pw]))

PDsph

flt k t r~

tXgsphqsc T

The definitions of dimensionless variables for these cases include the variable, which represents the length of the medium for finite systems and has any arbitrary value for infinite systems. Although in practice a medium of infinite extent does not exist, every finite system behaves as infinite for times before boundary and or interference effects are present.

554

11111" ' I 1

b.,// f"

X=O

/A I "

//

, I

X

I I-r__/

"

1 h X

Fig. 6-2. Linear flow.

groups is that the dimensionless variables are directly proportional to the real parameters and appear naturally in the derivation of solutions.

L I N E A R F L O W BEHAVIOR

Many flow tests in reservoirs exhibit linear flow behavior; that is the case of some naturally-fractured reservoirs and hydraulically fractured wells. Figure 6-2 shows the system for a linear flow geometry. A porous medium of thickness h and width b is considered. The outer boundary of the medium can be either located at a finite or an infinite distance, depending on the case under study. The inner boundary is located at x = 0,where the medium is produced at either constant pressure or constant rate conditions. All other characteristics of the medium are those defined for Eq. 6-1. The solutions for all possible combinations of boundary conditions are summarized in Table 6-Ill. Both small and large time approximations are included, because they appear to be the basis of some methods of interpretation. Next, we discuss the main pressure and flow rate characteristics for the constant flow rate. Similar expressions could be written for constant pressure cases. Figure 6-3 shows the pressure distribution for this inner boundary condition. At an early time in flow both the closed and the constant pressure flow behavior period are sometimes referred to as infinite acting or "transient" period. The pressure behavior in dimensionless form for these particular conditions, and x D ~ O, is presented in Fig. 6-4 in terms of the groups PD / xD and tDL/ XD" 2 This figure shows a single curve and appears to be useful in the analysis of interference tests when linear flow prevails in the reservoir. It can be observed in Fig. 6-4 that as time increases the pressure-drop curve asymptotically approaches a one-half straight line. At the producing well, the dimensionless pressure change from Table 6-II1 for liquid flow may be expressed in terms of real variables as follows: Ap = moL ~

where the slope moL is defined by:

(6-6)

TABLE 6-Ili

Linear flow equations for homogeneous reservoirs

BOUNDARY CONDITIONS IN.NER OUTER

GENERALEQUATION

Infinite

Flow Rate

Reservoir

x o =0 "Pot

=2~'~

(l-xo) 2

1

co, (xo.to,) - ---T-F

!

I

i

Closed

LARGE TIME APPROXIMATION

tDL < 0 . 2 5

e ca~ ) - x o erfc (--~t~)

PoL (xo 'toL) = 2

Comtant

SMALL TIME APPROXIMATION

2 ~

6 + to, + - ~

e(-.'. 'to,)

.=

(1 - xo)2

,,

Pt~ (xo,toz)

-

2

1 + 6 t~

9

Same as infinite reservoir

• cos (n x x o )

N I

1

'

T E

x o=O'poL

2

~ e-(n'f~ toL)

I

1 x o = 0 " POL = tOL + - ~

=t~+~'+

R

E S E R V O

8 ~-, ( - / ) " P D, (x~,to, ) = ( 1 - xo ) - _-:7Z ~ - ~ n - - : , 2 ff

.=o

Pressure

i R S

xe

~

XD =O'PoL

8 =1--77"

.I

(%-+'3

sin

~

Comtant

Infinite

Pressure

Reservoir R I E FS

I x o = 0 9qoL =

* After Miller (1962),

~r ( l -

Same as infinite reservoir t DL > 2.5

x o)

x D =0

"PoL =1

xo =0

9q z ~

x o =0

"qoL =1

n2

1 ~toL _ n~r z tot

Closed

x D = 0 " q z~ = 2

I E

R S

POt. ( X o 'tOL) = 1 -- X o

+1)

~** e-(nzx ~ tD,/~r nodd

NR IV TO El

(d

Constant

e Same as infinite reservoir

nodd

co~

Pressure

x o = 0 " q~

= 1+ 2

e -'~'" t~ n=l

** After Nabor and Barham (1964),

+ After Carslaw'a~l Jaeger (1959)

Same as infinite reservoir

(x~ttu = 2 e - ---7-)

t~

556

T

X-0

X=L

f InitialPressure to=0 (D ::D oO (.f)

C3_

~t~

F

. - - - - - t pss

(o)

l

to

f

Initiel Pressure I

II

I

I

::D cr~ c/') (D

(3_

.....__

(b) Fig. 6-3. Pressure distribution for a linear system producing at constant flow rate: (a) closed outer boundary, (b) constant pressure outer boundary.

557

m~ =

2aoL qB / fl, p bh ~/ ~-~-~C t

(6-7)

where aoL and fit are unit conversion constants. According to Eq. 6-6 a graph of Ap vs. x/Tyields a straight line through the origin, as shown in Fig. 6-5. This type of graph is commonly referred to as a "linear flow graph ", "square root of time graph" or a "Millheim and Cichowicz's graph ". The linear flow graph is appropriate for wells with highly conductive fractures and, in some cases, for wells in naturally-fractured reservoirs.

RADIAL C Y L I N D R I C A L FLOW

The traditional model used most often to interpret well tests has been that based on the flow towards a well in a reservoir bounded by upper and lower impermeable layers, representing radial cylindrical flow (Fig. 6-6). The cylindrical coordinates (r, 0, z)are appropriate to study the flow process in this case, because the flow lines follow the direction of one of the system coordinates (r). The solutions for all possible combinations of boundary conditions are summarized in Table 6-IV. Both small and large time approximations are included, because they are fundamental to the methods of interpretation. Table 6-II includes the definitions of dimensionless groups for this case of cylindrical radial flow. The pressure behavior in an infinite reservoir corresponding to a well producing at a constant rate can be obtained by solving Eq. 6-1, written for radial flow, with initial and boundary conditions given previously by Eqs. 6-2, 6-3, and 6-5. However, this solution is not simple enough to be used in well test analysis. Thus, an approximation that yields a simple equation has been preferred: the line source solution. This flow problem will be discussed in detail in the Pressure Drawdown Analysis section of this chapter.

SPHERICAL FLOW BEHAVIOR

There are field conditions where spherical radial flow takes place in the producing formation, among them being: (a) a well only partially penetrating a thick formation, (b) a reservoir with water drive from the flanks and from the bottom, (c) a Repeat Formation Test, etc. The system under consideration is a reservoir with a sphere (or a semi-sphere for case (a) above, producing at the top of the formation) as the inner boundary, through which fluid is produced as indicated in Fig. 6-7. For conditions of spherical radial flow, the dimensionless wellbore pressure change for transient flow, presented in Table 6-V for liquid flow, may be expressed in terms of real variables as:

a o,ph qB APwl = k r where:

m o,ph t~

(6-8)

558

r~ X

1/2 r~

c3n o _J

/ /

/

2

Log ( t DL / XD ) Fig. 6-4. Dimensionless pressure behavior for constant-rate production in an infinite-acting linear reservoir.

Q.

G.) tO t-.

Ibgt) gt)

~D

t3_

mol 1

Square Root of T i m e , ~ Fig. 6-5. Linear flow graph.

559

q

I

I

J

f

h k, 9b,,tz , ct

-I.

Fig. 6-6. Radial flow.

_ ao~ph q B ( r ct) 1/2 ([z.~/ k) 3/2 m

osph

(7~flt) 1/2

(6-9)

Equation 6-8 indicates that pressure drop Apw p vs. the inverse of the square root of time is a straight line, as shown in Fig. 6-8. The slope of the straight line in this figure, given by Eq. 6-9, is inversely proportional to k 2/~.

BILINEAR FLOW BEHAVIOR

Hydraulically-fractured wells exhibit several types of flow. Among them is bilinear flow (Cinco Ley and Samaniego, 1981), where expansion occurs in the formation, generating a linear flow toward the fracture and feeding another linear flow which takes place inside the fracture (Fig. 6-9). In this case, flow inside the fracture can be considered as incompressible because the fracture volume is very small. The fracture has a half length ~.

L~

TABLE 6-IV Radial flow equations for homogeneous reservoirs BOUNDARY CONDITIONS INNER OUTER Con.Ctant

Infinite

Flow Rate

Reservoir

GENERAL EQUATION

SMALL TIME APPROXIMATION

2 f | ( 1 - e-U2t~ ) [ J , ( u ) Y ( u % ) - Y , ( u ) J o (uro)ldu Po (ro 'to ) = ~r J-~ u' [ J : (u)+ ri' (u)l 1

ro > 20 " p o ( r o , t o ) = ~ E ,

LARGE TIME APPROXIMATION

(to/r ~) >25

r~

(~o) po(rv,to)='~[ln

+0.809071

toa < 0.1 P o (ro,t D) =

~

% - 1

(to +

)

toA > 0.1

72"-

(% - 1)

Closed

(3r~

-4r;

2 +r~)_4_ r;2o lnr o Po(ro,to) = r~ _----~(to (r,2o _ l)

In r o - 2 r 2 - 1)

4(r:o - 1) 2 (3r~

+~r'~-" e-'''~

[d:(fl"

ro)Jt(fl.)Y(fl

~ ro)-(fl.)do(fl.ro)] 2

-4r:v in

Same as infinite reservoir

r o -

2r~

4(r:o - 1) 2

:.H:(:.r~)-J,(p.)] ro=l

tDa

2 "0 e -ant~d ( ~ ) p o ( t o ) = l n ro __.T.~": o r o .=, ; ~ J : ( 2 . r o)

Same as infinite reservoir

<

0.1

toa > 0.1

Constant Pressure

Constant

Infinite

Pressure

Reservoir

rD=l

ro=1, t o > 8 x I O '

Vo(x)

2 qo (to) = In t o + 0.80907

4t~ f| x -x't~ / 2 + tan ( - ~ - ~ ) l d x P o ( t o ) = ---l;- o o ro=l R E I

PD ( t o ) = lnr, o

toA < O.I

ro = l, tin> 0.1 21 t m e-CZ",,~ )

Closed

FS I E NR I V i TO E I

Conmma

R S

Pressure

rfo-I qo(to) = --~-

|

e-("~to)dt(a ro )

Same as infufite reservo~

2 ~ a2[d2~ (a ) - d: ( a r o ) ]

qo (to) = ln r o - 3 / 4

toA < 0.1

ro = l, toA > 0.1

Same as infinite reservoir

1 qo - In r,o

+ After Jacob and Lohman (1952), ++ After Ehlig-Economides ~ d R a n ~ (1981), * After van Everdingen and H u m (1949), ** After Ramey (1967)

- 1)

561

Fig. 6-7. Spherical flow.

~P

1

Fig. 6-8. Pressure drop vs. 1 / ~t-for spherical flow pressure data.

562 k,

-Xf

I I 111 I I l II

~

,

].t.,

Ct

111 I I Ill Ix'

3_ bf

Fig. 6-9. Bilinear flow in a reservoir.

In terms of real variables, the pressure drop ApwI can be expressed as follows:

APw! = mobs t 1/4

(6-10)

where mob/ =

8~/qB~ h(k/b/1'/2 (~)~UCtk)'/2

(6-11)

From Eq. 6-10 one can conclude that a graph of the pressure drop Apw I vs. t 1/4 yields a straight line that goes through the origin, as indicated in Fig. 6-10. The slope of this straight line, mob: given by Eq. 6-10, is inversely proportional to the square root of the fracture conductivity [(kibl)S/2 ].

bP ]

V~ Fig. 6-10. Graph for bilinear flow pressure data.

563 FLOW DIAGNOSIS

Experience has shown that during the analysis of a test, it is always possible to draw a straight line through some data points in a specific graph of interpretation (e.g., APwi vs. f/2; APwsvs. t1/4;APwlvs. log t; APwlvs. t, etc.), and this straight line may not be correct for the flow model under consideration. Such a situation makes it necessary to discem the type of flow that dominates a test before using a specific graph of analysis. Thus, it is essential to have a flow regime identification process for the correct interpretation of a pressure test. Next, a discussion introducing the concepts needed to carry out this process is presented. The term "type curve" (Ramey, 1970), refers to a log-log graph of a specific solution to the flow equation (e.g., the diffusivity equation). These solutions are plotted in terms of two groups, one involving the dimensionless pressure for the vertical axis and the other involving the dimensionless time for the horizontal axis. Most type curves are a family of pressure drawdown solutions. Type curve matching techniques offer the advantage that data can still be analyzed even if the drawdown test is too short for the semilog straight line to develop. The general type curve matching method applies to many kinds of well tests for any specific physical fluid flow problem, with known dimensionless solution in terms of po vs. to. Among the tests where currently type curve matching techniques are being successfully used are drawdown, buildup, interference, and constant pressure testing. The general type curve matching method has been thoroughly discussed elsewhere (Earlougher, 1977; Gringarten et al., 1979; Lee, 1982; Bourdet et al., 1983) and will not be discussed in this chapter. The first type curve presented in the petroleum engineering literature was that of Ramey (1970), and was generated for the situation of a constant rate drawdown test in a reservoir containing a slightly compressible single-phase liquid; wherein the well produces at a constant flow rate q, in an infinite, isotropic, homogeneous, horizontal reservoir. The porous medium has a permeability k, porosity ~b, thickness h, and uniform initial pressure pi. If one or more of these assumptions does not correspond to a specific physical situation, then the type curve interpretation is not expected to render useful results. The log-log graph of Ap w f vs " t has been used to detect wellbore storage effects, linear and bilinear flow, etc. However, when an incorrect value of initial pressure is used, this graph can not be used for flow diagnosis. The same problem also exists when skin damage influences linear and bilinear flow (Cinco Ley and Samaniego, 1977, 1981). The introduction to the petroleum industry in the early 1980s of the pressure derivative with respect to time (Tiab and Kumar, 1980a, b; Bourdet et al., 1983) solved the above-mentioned problem. It has been stated that this function offers several advantages over the previous log-log Ap vs. t method already mentioned: (a) It accentuates the pressure response, allowing the analyst to observe true reservoir response (which is somewhat hidden in the response). It facilitates, among other things, the identification and interpretation of reservoir heterogeneities, which are often not readily identifiable through existing methods. (b) It displays in a single graph, different separate characteristics that would

0%

Infinite Acting

Infinite Acting

Miller-Dyes- Hutchinson plot 4000

I

Stg & Skn Homogeneous Inf Actng One Q ,

100

I

-I

o I c~

t.D Q_

0

,

I

I

I

I

k 87.67 c IxlO-4 s 9.194

-C3 C)_

3 800

I

10

v

(D

"- 3600

c0

t.f) t/') (1.)

C3

13_

3400[-

3 200

I

m 204.8 k 87.67 s

IxlO-z

9.194

I 0.1

I

I

1

10

Time,

hrs

~,

O.l 100

0.1

!

I

I

1

1

10

100

1000

I lxlO 4

1 lx105 lx106

tD/C D

Fig. 6-11. Infinite-acting radial flow shows as semilog straight line on a semilog graph, and as a flat region on a derivative graph. (After Home, 1990, fig. 3.2, p. 45.)

565 otherwise require several plots. These characteristics are shown in Figs. 6-11 through 6-18, which are discussed further later in this section. It has been shown that for wellbore storage-dominated flow conditions, the dimensionless wellbore pressure behavior can be expressed as (Ramey, 1970): Po = to / Co

(6-12)

Deriving this expression with respect to tD/ CD, and multiplying by tD/ C D gives:

to /

t~

-~P'D-Co

(6-13)

Taking logarithms:

tog

(6-14)

Equation 6-14 clearly indicates that for wellbore storage conditions, a graph of the pressure derivative function (to/PD) P'o vs. to / Co retains the unit slope on the log-log graph. In terms of real variables, it can be demonstrated based upon the previous discussion that, for wellbore storage-dominated pressure data, a log-log graph of the pressure difference and of the pressure derivative function vs. time exhibit a common unit slope straight line (Fig. 6-9). In case of an error in the value of the initial pressure, the Ap curve will approach the unit slope straight line from above or from below, depending on the sign of the error in Pi" From Eq. 6-12, for the conditions just described:

APwI= C~wst + APerror

(6-15)

Taking the pressure derivative function of this expression gives:

t dApw/ dt

= C~wst

(6-16)

Thus, the effect of the APerror disappears in the pressure derivative function, yielding the correct unit slope straight line in a log-log graph. For infinite-acting radial flow, the dimensionless wellbore pressure behavior can be written (Table 6-IV) as follows: 1

Po = --~-[ln(tz~ / Co) + 0.80907 + In Co eZq

(6-17)

This semilog approximation is valid only after the wellbore storage effect is negligible. Deriving this equation with respect to tD/ CD, and rearranging, one gets:

Storage

Storage

Stg & Skn Homogeneous Inf Actng One O

Log - log plot IxlO 4

I

'

C 5.129xlO-Z

1 /

!

100

'"

I

I

I

k 87.67 c 5xlO -2

--/,et ee~ee

_

I

~ 0

_

~

lO00 .m O0 Q_

4.727x I0 I1

9 tm

10

v c" (3

O

a

a.

l O0

1

(D

rn

10

|

,

,

I

,

1 x 10 -z

I

1 SHUT-IN

TIME ,At,HR

0.1

I

100

,,

0.1

I

I

!

f

]0

,

1000 tD/C

1 x 104

D

Fig. 6-12. Storage shows as a unit straight-line on a log-log graph, and as a unit slope line plus a hump on a derivative graph. (After Home, 1990, fig. 3.3, p. 45.)

Finite Cond Frac

Finite Cond Frac Stg & Skn Homogeneous [nf Actng One Q

Finite Conductivity Froc 10

u

I

|

100

=

I

k 20.04 Xf 197.3

I

!

t

k 20.04 c O.1025 s 9.194 A

1

10

PD v "t3 r

0.1

d:3

1

-

Q.

oeo .~ 1~10 -4

,

I lx10 -2

,

I

i

1

,.

I 100

tDXf

0.1

i 1x

104

o ~

0.1

ooo~o ~ 1 7 6 I

I

I

!

1

10

100

1000

lxlO4

tD/CD

Fig. 6-13. A finite conductivity fracture shows a 1/4 slope line on a log-log graph, and the same on a derivative graph. (After Home, 1990, fig. 3.4, p. 46.)

O~ OO

lnl'lnlte t.;ona I-rac

I n f i n i t e Cond Frac

Stg 8t Skn Homogeneous Inf Act.ng One Q

L o g - log plot lxlO4

100 Xf

I

I

I

I

k 20.04 c 0.1025

192.2

s

r

9.194

10

1000 .m CO Q.

1.)

c~ 13 .=.

100

c~

==

o[

lx10"z

1 -

oi~l~ ~ o O~

*** , ~ l I

I

I

0.1

1

10

SHUT-IN TIME, At,HRS

~176 ,,

0.1 100

O. 1

1

I

,

10

I

I

100

1000

lxlO4

tD/C D

Fig. 6-14. An infinite conductivity fracture shows a 1/2 slope line on a log-log graph, and the same on a derivative graph. (After Home, 1990, fig. 3.5, p. 46.)

Double Porosity T e s t

Double Porosity Test

Mi Iler- Dyes-Hutchinson plot 950

....

I

....

t

Stg & Skn DP StdySt [nf Actng One Q

\

940

100

'|

-

I

{3.

10 -

to

I

I

I

k 497.1 c I x10-3 s -2.055 w O.1051 1SS 8.94x10 -I~

I

I

L~

145.4 .........

_~.~ax~**~x-

-

m~ 930 Xl

to to

E

t__

O..

920 - -

k rn s w 1

910

I xlO - 3

o

49Z 1 10.18 -2.055 0.1051 8.94.x10-tO I 0.1

I 1

1

:

0.1 10

100

1000

L

0.1

1

,

1

10

,

,,

i

t

100

1000

_

~

I

1 xlO 4

lxlO 5

, , ~

lxlO 6

T i m e , hrs tD/Co Fig. 6-15. Double-porosity behavior shows as two parallel semilog straight lines on a semilog graph, and as a minimum on a i:lerivative graph. (After Home, 1990, fig. 3.6, p. 46.)

%tl

L~

C Iosed Boundary Cartesian plot 7000

I

'

I

I

Closed Boundary Stg & Skn Homogeneous Clsd Crcl One Q 100 '

I

I

k c s Re

6000Ea.

!

i

I

87.67 1.427x 10-z 9.194 400.7

1.54gx1011

oloa I0 o~ 5 0 0 0

c~

v

~3

C 0

O

m 4000

1

n SO00

!

2ooo1 0

,

i

,

,

5

I0

15

20

T i m e , hrs

0.1 25

!

0.1

1

,

I

10

,

I

100

,

I

1000

1x104

t D/CD

Fig. 6-16. A closed outer boundary (pseudosteady state) shows as a straight line on a cartesian graph, and as a steep-rising straight line on a derivative graph. (After Home, 1990, fig. 3.7, p. 47.)

Foult B o u n d a r y Stg & Skn Homogeneous Clsd Fit One Q

Fault Boundary Miller - Dyes- Hutchinson plot

70ooI

I

I

m k s L

6OOO1-

100

I

I

J

204.8 87.67 9.194 301.1

I

I

I

I

k 87.67 c 1.427x10-z s 9.194 _

.~

(I)

-

LC

1.549x1011

9

" " " T , ; ~

.. . .. . .. . .. . ... . .. . . . . ."... . .

~ x

10

r~ 5000

~~

~.) :3 oo

oo 4 0 0 0

%

Q..

1

3000 zooo[ lx10 -2

,

,

t

,

0.1

1

10

100

Ti me, hrs

I 1000

o.1 _ 0.1

I

I

I

I

1

10

100

1000

lx104

t D/CD

Fig. 6-17. A linear i m p e r m e a b l e boundary shows as semilog straight line with a doubling o f slope on a semilog graph, and as a second flat region on a derivative graph. (After H o m e , 1990, fig. 3.8, p. 47.)

...3

Lab -...I

Finite Cond Froc Stg & Skn Homogeneous [nf Actng One Q

Finite Cond Frac Finite Conductivity Fmc 10'

I

I

J

I

,,

100

I

k 2004 Xf 197.3

l

i

i

k 20.04 c O.1025 s 9.194 10

1

PD

PD

0.1

- ,o.......,,,..,.,,,...,.,, ~

9

o ~176176176176176176176

oooOO~ I xld 2

l

IxlO '4

I

IxlO-2

,

I

i

I

I

I00 tDXf

o~

0.I

~

Ixi04

0.1

I

I

I

I

10

100

,

I

1000

Ix104

tD/CD

Fig. 6-18. A constant-pressure boundary shows as flat region on p vs. t graphs, and as a continuously decreasing line on a derivative graph. (After Home, 1990, fig. 3.9, p. 47.) On the right-hand side figure, the ordinate also shows (t D / CD)PD.

573

Log AP

------

AP - tAP'

or

Log t AP'

I

ff 7

Error in 6P

Log t Fig. 6-19. Log-log graph for identification of wellbore storage.

P'D = 0.5

(6-18)

Eqs. 6-14 and 6-16 indicate that the end points of the most used flow problem with regard to transient pressure analysis (i.e., infinite acting radial flow toward a well under the influence of wellbore storage), are fixed by two common asymptotes with a hump-shaped transition, which is a function of the wellbore condition group CD e2s

For this case of radial flow, real variables can be used to express Eq. 6-17, and a be introduced in a similar way as previously discussed for the wellbore storage case, reaching the same conclusion. The resulting equation is:

APerror c a n dAp wS t

dp _

-

Clr

(6-19)

where, aoq tip Clr = 2 kh

(6-20)

Thus, a graph of the field data for radial flow conditions would look like that shown in Fig. 6-20. For infinite acting linear flow conditions (Table 6-III), the pressure drop behavior in terms of dimensional variables can be expressed as follows:

APwf = CIL %ft--[- APski n "Jr"APerror Taking the pressure derivative yields:

(6-21)

574

Log AP or

Log tAP'

t AP'

Log t Fig. 6-20. Log-log graph for radial flow identification.

dAPw/ t

dt

-

C

(6-22) ~L

This expression yields a one-half slope straight line in a log-log graph, as indicated in Fig. 6-21. It can be observed that the pressure drop falls above the pressure derivative curve, and may also exhibit a one-half straight line slope in cases where APski n and AP~rro~ are zero. It is important to notice that the distance between the two one-half slope straight lines of this figure is 2.

Log2 Log &P or

Log t 8P'

/// AP ,

Log t Fig. 6-21. Log-log graph for linear flow identification.

t

AP'

575

/

Log AP

'

~

~

Log 4

or

Log t AP' AP

tAP'

Log t Fig. 6-22. Log-log graph for bilinear flow identification.

For bilinear flow in a hydraulically fractured well (Cinco Ley and Samaniego, 1981), the pressure drop behavior in terms of dimensional variables can be expressed as follows:

APwf

.

-

Clbf 4~"+ APskin + APerror

(6-23)

Taking the pressure derivative yields: t

dAPwl dt

Clbf ~4

(6-24)

As already mentioned for the previous cases, the effects of skin and error in the initial pressure measurement are eliminated when the pressure derivative function is used. Figure 6-22 shows a log-log graph for bilinear flow conditions of the pressure drop and of the pressure derivative function, the latter exhibiting a straight line of one quarter slope and located at a distance log 4 in the case where Apse, and Z~errorboth are zero. For infinite acting spherical flow conditions (Table 6-V), the pressure drop behavior is inversely proportional to the square root of time:

APwl = C"Ph

qsph ~17

(6-25)

Taking the pressure derivative yields: t

dApwl dt

C2~ph 2~

(6-26)

576

Log &P or _og t tiP'

/

/

~ t & p , Loa t Fig. 6-23. Log-log graph for spherical flow identification.

This equation indicates that a log-log graph of the pressure derivative function for spherical flow yields a straight line of slope equal to-1/2, as shown in Fig. 6-23. Finally, for pseudo-steady state radial flow conditions (Table 6-IV), the pressure behavior can be expressed as:

Log AP

I/

or

Logt AP'

tAp,~

1

Log t Fig. 6-24. Log-log graph for pseudosteady flow identification.

TABLE 6-V Spherical f l o w equations for h o m o g e n e o u s reservoirs*

-' [er~r~ e":~ Constant

Infinite

Flow Rate

Reservoir

LARGE TIME APPROXIMATION

SMALL TIME APPROXIMATION

GENERAL EQUATION

BOUNDARY CONDITIONS INNER OUTER

rD =l,

.e+ r,-' 4] po,~(to) = 1 - ~ ro >> 1 P,o,a, (ro'tD):-~DI erfc ( - ~r~ o)

,o,o.t,.i,.o~ Closed

,

_2(%_ ( % - 1)

[,

1)2 7 ( , ~ _ ~)2 + % (r D - 1/+

2 ( r ~ - 1)2 s ro

]

Same as infinite reservoir

Infinite

Pressure

Reservoir

['

-L~J ~n t~

2 ( r D - 1) ~-, + ~ B e r v ro ro .:,

E IS

Closed

E

v TO E I R S

2omtant

Po - ro r o

1

1 q D = l + ~--~O

2 ~ % = ( % _ 1-J) ~.=

r~- r

Same as infinite reservoir

ro = I qD --

rD=l,

22 w rw + ( r D - I ) ' 2 2 ._ .( %. ._ w.rD

1)

[ "~'~ ] -[~j

%=

e

2

w, ro + (r D - ~j

--

~

. . . . . .

(rz, - 1) L w , r o - ( t o

e

- 1)

%=1,

rD=], ~ n~tD

Same as infinite reservoir

red

~'essurc

qD = r D - - l + r D * After Chatas (1966)'

]

)

rD=l, R

(%-1) 2 + %

A e-[r: t~/(,,o-,)']

( .2

Constant

2

n=i

r o - ro po(to)=

-2(%-1)

( r D - 1) 3 ( r w - l ) ' + 2rD(r D - l) 2 + 3r~

2 % ( r D - 1) 2 + 3 r ~

Constant

Pressure

,o,,.t =i,r.o+,r.o-,,'l[

l[~o-,:(,.o.,).to]

-1

.--t e

qo--

%

- 1

".-..I

578

APw ! = C l~psst + C 2rpss+ APse. n + Z~Perror

(6-27)

Taking the pressure derivative yields:

dApwI t dt - C~st

(6-28)

Figure 6-24 presents a log-log graph of Ap and MAp /dt vs. time t. It can be observed that the line for the pressure derivative function is a straight line of slope equal to unity, and the pressure drop behavior follows a concave upward curve, which approaches the pressure derivative straight line. In summary, the pressure derivative function for the different flow regimes can be expressed as:

t

dAPwI - Ct" dt

(6-29)

where C, as indicated in the previous discussion of this section, is a constant that depends on the flow rate and on reservoir properties, and n has different values depending on the flow regime, as follows: Flow type

n

Wellbore storage Linear flow Bilinear flow Spherical flow Pseudo-steady state flow

1 1/2 1/4 -1/2 1

Figure 6-25 presents a graph that summarizes the previous discussions with regard to the pressure derivative function, for the most common flow regimes encountered in well tests. The derivative function in terms of dimensional parameters can be expressed as:

lto )

= P'o

kh t Ap wl OtoqBp f

where the derivative

AP'wl

]dp wl

(6-30)

AP'wlis given by Eq. 6-31"

dAp wl

(6-31)

Figure 6-26 presents the combined pressure and derivative function type curve for infinite acting radial flow toward a well under the influence of wellbore storage (Bourdet et al., 1983).

579

Wellbore Storage or

Pseudo-Steady-State

/~t/2 ~

Log tAP'

Line~

1

Bilinear

, ,,~

Radial

Spherical

Fig. 6-25. Pressure derivative function for six different flow regimes.

10 2

,

I ......

I

J

I'

CD

I0 60 1020

,.-,..

--.-,

,---

-.-,.,

-'--

"-"

....,,,

,,.

~0

I01

,,...=

....,,,

...,..,,

....,

u

I0 I0

m

0

\

,,i,-,,

\

"0 E o

\

\

oi0 0

\ a

lO-I/

i0"I

I I0 0

I IO I DIMENSIONLESS

\

\ \\

I ....... IO 2

I IO 3

TIME , | D/CD

Fig. 6-26. Pressure and pressure derivative function type curves for a homogeneous reservoir. (After Bourdet et al., 1983, fig. 7, p. 102.)

580 In this figure note that the pressure derivative function (tD/ CD)P'D shows a notably different behavior than that of pressure, because all the curves merge to a constant value of 0.5 regardless of the early-time storage-dominated pressure behavior. This is an important point to realize because pressure behavior alone presents the uniqueness problem with regard to flow diagnosis as is widely discussed in the literature. As mentioned above, early-time derivative function data are represented by a unit-slope line, which is also valid for the pressure data response. The late-time horizontal line described by Eq. 6-26 represents radial flow conditions. From the previous discussions in this section, it can be concluded that a combination of the pressure derivative function and of the conventional pressure graph presents the currently most powerful diagnostic tool available. It has been widely discussed in the literature that obtaining a constant flow rate during a test (especially at early times), is very difficult.Accordingly pressure buildup tests, when flow rate is equal to zero after the end of afterflow, are frequently preferred. The pressure change measured during a buildup test is the difference between the shut-in pressure Pws and the flowing pressure immediately before shutin ((Pws (At = 0)). Thus, the amplitude of the pressure drop at shut-in limits the magnitude of the buildup response. Therefore, the buildup type curve shape is a function of well and reservoir behavior and previous flow history. When the Homer method is applied to a test (i.e., infinite acting radial flow regime has been reached during drawdown), it is possible to match buildup pressure data on the derivative function drawdown type curves. This can be done provided the derivative of buildup data is taken with respect to the natural logarithm of the Homer ratio, instead of lnt which is used for drawdown (Bourdet et al., 1983). The expression for this case is given by the equation:

apws d In[At / ( t + At)]

_

(t + at) at

tP

AP'w,

(6-32)

where

AP'w"

dpw~ dAt

(6-33)

In summary, under the conditions just stated, the pressure derivative type curves of Fig. 6-26 also present the variation of the slope of the buildup data, graphed on a Homer semilog scale vs. time. Many studies have presented different methods for estimation of the pressure derivative of field data (Bourdet et al., 1983; 1984; Clark and van Golf-Racht, 1985; Home, 1990; Stanislav and Kabir, 1990; Sabet, 1991). The quality of the pressure data has a major influence on the calculation of the derivative function. It is the experience of the authors; and others (Clark and van Golf-Racht, 1985; Gringarten, 1985; Gringarten, 1987a, b; Ehlig-Economides et al., 1990; Home, 1990; Ramey, 1992) that data from electronic gauges are normally of sufficient density and of high enough resolution to be easily derived. However, the estimation becomes difficult in some

581 instances of reservoirs with high mobility-thickness products, due to the "noise" of some gauges being of the same magnitude as the pressure gradient. Crystal gauges have been successfully used in these cases (Clark and van Golf-Racht, 1985). As previously mentioned, there are different methods available for the estimation of pressure derivative. One such method has been proposed by Bourdet et al. (1989), who recommended this algorithm based on the finding that it best reproduces a complete type curve. It simply uses one point before (left) and one point after (right) the point of interest, calculates the two corresponding derivatives, and then places their weighted mean at the point of interest. The noise effect can be reduced by choosing the left and right points sufficiently distant from the point where the pressure derivative is to be calculated. However, the points should not be too far away because this will affect the shape of the pressure response. A compromise has to be made. The minimum distance L between the abscissas of the left and right points, and that of the point of interest, is expressed in terms of the time function being used, i.e., lnAt, Homer time, or the superposition time. If the data are distributed in geometric progression (the time difference from adjacent points increases with time), then the noise in the derivative estimation can be reduced by using a logarithmic numerical differentiation with respect to time (Bourdet et al., 1984; Home, 1990):

In (tj+ 1 tj_ 1 / tj2.)Apj t

-

din,

In (t.+ , / t.) In (tj / t._ 1)

= ln(L-+;-/Liln--~j-+;-/tj_l)

(6-34)

In ( tj.+l / tj) Apj _ l In (tj/tj_l)In (t.+l/t._l ) Using second-order finite differences, Simmons (1986) derived from a Taylor series expansion the following expressions; for the ith point:

At~-I Pj+ I "~" (Atff-- Ate_ l)Pj-- AtYpj_l ,2 < j _
Zlt}_lAt j + At~Atj_,

(6-35)

For the first pressure point, Simmons (1986) used a forward-difference expansion:

I (At1 At2)2 ] +

dp

At 2

1

(At I + Zlt2)2

P2 + P3

1 [(At~ + At2 )2 / A t I - ( A t I + At2) ]

Similarly, for the last point, a backward-difference expansion gives:

(6-36)

582

(Atn_ 1 + Atn_2)2

(Atn_ 1 4- Atn_2)2 J At 2

I(atn ,

"{"

atn-2)

-

P,

At 2n - 1

P. +

n-1

-

(At_ I + Atn_2)2 3 / At _ 1 J

1

"]" P. - 2

(6-37)

Simmons (1986) stated that the two main advantages of his algorithm is that it can handle unequal time-step pressure data, and also the second-order formulation improves the accuracy of the pressure derivative. One simple method that has proved through field use its usefulness, is based on a central difference aproximation to the pressure derivative, as given by Eq. 6-38 and presented graphically in Fig. 6-27:

+

1/2

,1 < j < n

t'+l--tj

(6-38)

The estimation of this derivative is assigned to the mid-time t between any pair of pressure points:

t.j.~=t.+(t.+,-9/2,1<j
(6-39)

Pcofj

i tof (P~f) j, I

,,\

i

i

'

t

(P~of) j + 2

i

i

i

,

tj

~i

tj+1

i

tj+z t

t j-1/2 Fig. 6-27. Central difference approximation to the pressure derivative.

583 Field experience has shown that this central difference aproximation method, when preceded by a proper smoothing pressure data procedure (e.g., moving average method, described later), works well. Table 6-VI presents, in general, the necessary calculations that have been previously described for the estimation of the pressure derivative function for a drawdown test. Figure 6-28 presents an example of how field data taken with a Bourdon type TABLE 6-VI Estimation of the pressure derivative function for a drawdown test Time t t o= O

Pwj

t

Pw/t

te

Pwz 2

t3

Pw! 3

Mid time t. +1/2

Pressure Change, Ap

At

Pressure derivative, Ap'

(tAp')j +1/2

t, +1/2

Ap,

At,

Ap', +,/e

(t

t2 + v2

AP2

At2

AP'2

+ v2

(t AP')2

0

0

A p ' ) , + l/2

10 3

o /Xp 9 tAp'

o

0

o

r

0

0

10 2 o oo

o

9

10

10 -1

1

10

Fig. 6-28. Example of field data taken with a Bourdon type gauge.

10 2

+ ,/2

584 gauge would appear when graphed in logarithmic scales in terms of the pressure difference Ap = (Pi--Pwf ) and of the pressure derivative function tdp /dt vs. time t. The noise present in the pressure derivative function is typical of field data. It must be kept in mind that the discussion of this section with regard to flow diagnosis has considered the simplest case of constant rate. If rate varies during a test, then the flow diagnosis process must be based on the influence function, which will be discussed later in the section entitled Analysis of Variable Flow Rate Using Superposition, Convolution, and Deconvolution (Desuperposition).

PRESSURE DRAWDOWN ANALYSIS

A pressure drawdown test consists of bottomhole pressure measurements made over a period of time, with the flow rate constant. Besides this constant rate condition, the simplest type of these tests considers that pressure throughout the reservoir is uniform (static). If the constant rate production and the static pressure condition are not met, then other tests are available which can be used (Matthews and Russell, 1967; Earlougher, 1977; Cinco et al., 1985). According to the purpose for which they are performed, there are two such types of tests: (1) short-term drawdown tests are used to estimate, among other parameters, formation permeability and the skin effect; and (2) long-term or reservoir limit tests (Jones and McGhee, 1956) are used to estimate the reservoir volume in communication with the well. For radial flow conditions, the pressure at a point P(r,t) in the reservoir may be expressed as follows:

kh(p,-p (r,t)) aoqBp

=pD(ro,tD)

(6-40)

where Po is the dimensionless pressure solution for a specific radial flow problem. The dimensionless pressure solutions, Po, for the most common fluid flow situations have been thorougly discussed in the literature (Earlougher, 1977). For conditions of the wellbore, where % = 1, Eq. 6-40 can be written as follows:

(6-41)

kh(Pi- Pwj) = Po (1,to) = Pwz~ aoqBp

The pressure behavior of a well producing at a constant rate, located in the center of a radial infinite reservoir, may be expressed by the line source solution (also called the exponential-integral solution or the Theis, 1935, solution) (Matthews and Russell, 1967; Earlougher, 1977):

kh(pi-pwj) - 1 aoqBp 2 E, -go

( 1 1 1:1

4

w

(6-42)

585 where the exponential integral E 1 (x) is defined by:

~u du

E, (x) = - E i (-x) =

(6-43)

Equation 6-42 considers that the wellbore radius is negligible and, consequently, it is only valid for to> 25 (Mueller and Witherspoon, 1965). Values of this integral may be taken from various data tables (Nisle, 1956; Ramey et al., 1973). If the argument of the exponential integral is small enough then:

E, (x) z - I n (1.781 x) = In

( ~ - - ) - 0.5772, for x < O.O1

(6-44)

where ~/= 0.5772; the exponential of the Euler constant is denoted by ~/~= 1.781. The logarithmic approximation to the exponential integral given by Eq. 6-44 may be used when x > 100 (t D> 25). It can be easily shown that for average rock and fluid properties, this time limit occurs within seconds or minutes and consequently, the logarithmic approximation may be used for most practical purposes. Using this approximation, Eq. 6-42 can be written as follows:

kh(Pi-Pwl) aoqB p

l(~zl~)]Actr2 I In w 2

(6-45)

4 fl, kt

The flowing bottom-hole pressure Pwl can be expressed as"

Pwj

=Pi -

1.1513a qBp o kh

log

~].Actr2w

+ log

~/1

(6-46)

Equation 6-46 describes a straight-line relationship between Pwl and log t as shown schematically in Fig. 6-29. A drawdown graph, or in general any pressure graph, can be divided into three portions: (a) short time data or front-end effects (pressure behavior is under the influence of wellbore storage, damage, unstable flow conditions in the tubing string, etc.); (b) the semilog straight line portion applicable to the analysis by the semilog methods; and (c) boundary effects, which include boundaries and interference effects. The straight-line portion of this semilog pressure graph has a slope m defined by: m = 1.1513 a

qBu o kh

(6-47)

It is clear that if proper identification of the semilog straight line is possible, then an estimation of the formation conductivity (kh) may be obtained through the use of Eq. 6-47.

586 o

_

_

o-b b-c (b)c-d

FRONT END EFECTS SEMILOG STRAIGHT LINE BOUNDARY EFECTS

=3

Q_ t o 1 - .

0 LL 0 -1--

'

I'X

I

J

I

i

E

I I

0

0

~

I I I I I I

,

r'n

,

,I

,

(telt)d

,

d

I I l

(telt)dd

Logt Fig. 6-29. Typical bottomhole pressure semilog graph for a drawdown test. SKIN F A C T O R

The flow capacity of the producing formation in the vicinity of the wellbore commonly is reduced due to formation damage during drilling and completion. Reduced permeability is usually caused by partial plugging or mudding off of the region immediately surrounding the rock face during drilling. In some cases, the pore openings are large enough (in high-permeability formations) to permit entrance of mud solids provided the difference between the drilling fluid hydrostatic pressure and formation pressure is large enough. This physical problem is illustrated in Fig. 6-30a. Permeability reduction can be particularly important in formations having clay content. On the other hand, permeability close to the wellbore can be higher than that of the formation when acid is used to stimulate carbonate formations. In addition to the alteration of formation permeability near the well described above, there are other factors that affect fluid flow from the formation to the wellbore. Figure 6-30 shows the most usual flow restrictions to fluid flow towards a well. Figure 6-30b presents the physical situation of a filter cake adhered to the rock face of a formation, which commonly results in waterflooding operations. Among the materials that can filter out on a formation face, either in an openhole completion or through perforations, are silts, clays, scale, ferric hydroxide, and ferrous and ferric sulfides (Strubhar, 1972). Figures 6-30c to 6-30i illustrate other factors that can affect fluid the flow towards a well, e.g., partially penetrating well, flow through perforations, and slanted well.

587

h

I

k

lI

I ks

a)

(-

FILTER CAKE

, ks

I

rw

rs

k

rw

b) rw CASING CEMENT

hc ..______.~..--~

c)

rw

d)

LJ 'i

h

CONDENSATE OR GAS SATURATION

LL

{.i.~~ ~ o~,.

I

I I I L rw

e)

Q

o

~

9

~ o

| (b

ool

o o

o oo o

9

~

o 0

rw

f)

8w CEMENT SHEET

GRAVEL

o~

1

g)

h)

FRACTURE

h k I "

-xf

k'

k, rw

1 k xf

i) Fig. 6-30. Flow restrictions to the flow of fluids toward a well.

There are two classic mathematical visualizations for the skin factor : (1) mainly those of van Everdingen (1953) and Hurst (1953) on one hand, and (2) that of Hawkins (1956) on the other. The first two authors presented the skin factor concept as a constant s, which relates the pressure drop experienced by the fluid flowing toward the well to the rate of flow:

588

aoqBp Ap, = ~ s kh

(6-48)

This method represents wellbore damage by the steady-state pressure drop at the well face given by Eq. 6-48, which if added to the normal transient pressure drop in the reservoir, would result in the wellbore pressure. The additional pressure drop, referred to as the skin effect, is thought to occur in an infinitesimally thin skin zone located at the well face. Thus, the additional pressure drop caused by the different flow restrictions occurs at the well face. The degree of damage (or stimulation) is expressed in terms of the skin factor, s. This parameter ranges in value from about - 6 (Standing, 1972) for a hydraulically fractured well, to + oo for a highly-damaged well. According to the visualization of Hawkins (1956), the additional pressure drop caused by flow restrictions is thought to occur as the fluid flows through an adjacent finite zone of radius r~ with permeability ks. It can be demonstrated that the following relation exists for s:

S l sll,nlrl,

,649,

An expression for the bottomhole flowing well pressurep w/ may be written considering two pressure drops: a "natural" pressure drop imposed by reservoir and fluid properties, and the additional pressure drop caused by flow restrictions" aoqBp Pi-Pw/ = ~ [Po (ro' to, g e o m e t r y , . . . ) + s]

(6-50)

An important particular case of this equation is that of radial flow:

Pw/ = P i

-

1.1513 a~ kh

ii , l l4.tllooq . log

+ log

~ p c tr w 2

+~

?;

s

(6-51)

kh

or:

Pw/ = Pi -

1.1513 a~ kh

log

+ log ~ lA ct r 2w

~/1

+ 0.86859 s

(6-52)

From this equation, considering t = 1 an expression for the skin factor may be obtained: s = 1.1513

Pi--Pl _ log m

(6-53)

--log ~ctr2 w

~/

589

r•

.~ DAMAGED ZONE Oo

,~ .

o

9

h

T---

.

I,oog 0 o

O

o

o0o

Fig. 6-31. Flow toward a damaged well.

The skin factor s, estimated from the analysis of transient tests, is a total factor in that it includes all the factors (restrictions) that affect fluid flow toward the well (Fig. 6-30). It is the algebraic sum of the true skin factor S,r caused by damage to the completed portion of the well, and all the other pseudo-skin factors due to flow restrictions discussed with regard to Figs. 6-30b to 6-30i. Consider the situation in Fig. 6-31, where a partially completed well in the interval h c in a formation of thickness h is shown. It is assumed that the formation is damaged through a limited distance. Fluids flowing from the formation toward the well will flow as follows: (a) first under radial conditions over the full zone thickness in the region away from the wellbore; (b) will converge into the completed interval in the region near the wellbore; (c) essentially as radial flow through the damaged zone of thickness h; and (d) flow through perforations. Writing expressions for the pressure drops associated with the three flow restrictions, in addition to considering the possibility of the well being slanted and hydraulically fractured, an expression for the skin factor may be obtained (Standing, 1972)" h S -'~

hr

(Str -J- Sp) "1" S c "l" Sswp "~ S f

(6-54)

If a stimulation job is considered, then the true skin factor or formation damage must be calculated. From Eq. 6-54 one obtains: hc

Str = - - ~ (S -- S c - - Ssw p -- S f) -- Sp

Str

(6-55)

Table 6-VII shows a relation of recommended references for the estimation of the pseudo-skin factors. Throughout the literature several additional relationships among well producing conditions have been introduced, including those related to flow efficiency (also called

590 TABLE 6--VII Recommended references for the estimation of the pseudo-skin factors Pseudo-skin factor

Reference Hong (1975); Locke (1981); Karakas and Tariq (1991) Martin and Brons (1961); Odeh (1968); Cinco Ley et al. (1975); Papatzacos (1987); Vrbik (1991) Cinco-Ley et al. (1975) Prats (1961); Standing (1972); Cinco Ley et al. (1978)

Sp

Sc Sswp S/

the condition ratio or completion effectiveness) which denotes the fraction of a well with undamaged producing capacity. This concept is defined as the ratio of actual productivity index of a well ( J ) to its productivity index if there were no flow restrictions (s = 0), J/de,t: FE

=

Lctual

=

J'deal

ff -Pw:- Ap~

(6-56)

P--Pw!

In an approximate form this expression is usually written as: FE = P * - P w : - APs

(6-57)

P*-Pw/ The pressure drop resulting from the skin, Ap: is obtained from Eq. 6-58 using the expression for the slope m: Aps = 0.87 ms

(6-58)

Another relationship used to relate well-producing conditions is the damage factor, DF, which is obtained by subtracting flow efficiency from 1" DF = 1 - FE =

~Ps

(6-59)

P* -Pw/ It can be readily concluded from Eq. 6-57 that flow efficiency depends on the producing time because Pwt is a function of time. Thus, FE is not a constant. There are two possible conditions under which the FE could be a constant: (a) at pseudosteady state, the pressure difference p - - P w / i s constant, and (b) at steady state, p - should be replaced by p : the pressure at the well's drainage area. For a damaged well, flow efficiency is less than unity; for a stimulated well, flow efficiency is greater than unity. Flow efficiency is a convenience for discussing well condition (Ramey et al., 1973). For instance, for a damaged well ifFE is 0.33, then the well is producing one third as much fluid for a fixed pressure drawdown, the rate it would have if it was not damaged. From the previous discussion, one can conclude that flow efficiency provides an easier way to visualize the well condition than the dimensionless skin factor.

591

-

i e

I i

i two

I Pwf

',

i i

i i

i i

i i

rw

rs

Inr Fig. 6-32. Visualization of the apparent wellbore radius.

One last useful relationship to express well producing conditions is the apparent (effective) wellbore radius, r w . This concept is defined as the radius that would produce the calculated pressure drop in an ideal formation, equal to that in an actual formation, with flow restrictions (skin). Then, from Darcy's law:

'nllrwa 'nlw)

+s

(6-60)

or

r

wa

= r e -s

(6-61)

w

Figure 6-32 shows a visualization of the apparent wellbore radius r for conditions of a damaged well (s > 0), resulting in a smaller radius than actual r w, implying that fluids must theoretically flow through additional formation ( r w - rwa ) to give the required pressure drop. On the other hand for a stimulated well (s < 0), the apparent wellbore radius rwa is greater than rw. This concept has been found to be quite useful in discussing results of hydraulic fracturing. wa

PRESSURE T R A N S I E N T ANALYSIS FOR GAS W E L L S

During the last few years, an important effort has been made to study the flow of gases through porous media. In deriving the fundamental flow equation that describes gas flow, one considers the gas as real, and in doing this two of the assumptions stated previously with regard to the diffusivity equation are released: (a) pressure gradients are considered, and (b) the variation of gas viscosity (p) and gas compressibility factor (z) with pressure are taken into consideration. Analogous to the discussion of liq-

592 uid flow, the fundamental flow equation for the description of this problem, neglecting high velocity effects is:

v.

_ kVp ) r p(p)z(p) =

p Op k

(6-62)

Uz a t

This expression can be transformed to a form similar to the diffusivity equation (Eq. 6-1) by making use of a transformation called pseudopressure or real gas potential pp(p) defined by A1-Hussainy et al. (1966)"

pp(p) = 2

P o

(6-63)

dp

where Po is a low base pressure. In all problems involving gas flow through porous media, it is recommended that the first step be the evaluation of the relationship of pseudopressure pp(p) vs. pressure. Once the pp(p) function has been evaluated, any pressure may be converted to pp(p) and vice versa. There are basically two methods for the evaluation Ofpp(p)" (a) Using experimental PVT analysis of a representative sample of the gas produced by the reservoir includes information regarding variations in viscosity (p) and the gas compressibility factor (z) as a function of pressure, at reservoir temperature conditions. A numerical integration procedure can be used to estimate pp(p) as shown in general in Table 6-VIII. Usual values for the number of data points range between 7 and 11. The pressures pj, 1 < j < n, may be either equally spaced or at different pressure spacings. Figure 6-33 shows the variation of the argument 2p / l-t z vs. pressure. The most commonly used numerical integration technique to estimate pp(p) (the area under the curve from the reference pressure Po to p) is the trapezoidal rule, stated as follows: (6-64)

pp(p) = pp(,pj_ 1) + App(.pj_,), 2 < j < n

where TABLE 6-VIII Estimation of the potentialpp (p) using experimental PVT data p

p

z

2p/laZ

Pp(p)

Pl = Po P2

Pl P2

zl z2

2pl / pl z I 2P2 / P2 z2

0 Pp (P2)

2p._,/U._,z_, 2p, / p z

p~(p._,) pp(p,,)

P,_, P. = Pi

.

.

.

.

.

.

.

.

U._, P,,

z_, . z

593

T

z p/tt z

I ,,I,,

P~ Pz

I i

I I

Ps P4 p -----~ a) p = - 0

T

2 p/,= z

f

I

I I I

I I I I

I

I

I I,

I I

Pz

P3 b)

p

P,>O

Fig. 6-33. Graph of 2p / #z vs. pressure for a real gas.

Ap(pj_ ,) = (2pj / /..ljzj -b 2pj_I / [LIj_I ~_I)Apj_, / 2

(6-65)

Figure 6-34 shows a typical p.(p) vs. p curve for a gas reservoir. (b) Using published correl~tions. There are two basic correlations for the estimation ofp p (p). First, the A1-Hussainy et al. (1966) correlation for sweet gases, based on Carr et al. (1954) for It and Standing and Katz (1942) for z, using p = 0.2 as the reference pressure. Second, the correlation of Zana and Thomas (1970)Pfor sour gases using Robinson et al. (1960) correction ratios to calculate z. The reference pressure

594

t O..

v

Po

P "''~

Fig. 6-34. Graph of pseudopressure vs. pressure for a real gas. used wasp = 1. Other recent correlations of mathematical form are those of SchafferPerini and PlVIiska (1986) and Aminian et al. (1991). Substituting the definition of the real gas potential pp(p) into Eq. 6-62, and considering the formation compressibility yields:

wp (p) =

/~ (p)c, (p) Opp(p)

(6-66)

k

where the total system compressibility compressibility, are defined as follows:

c,(p),

and the modified pore volume

ct(P) = S cg (p) Jr"S Cw "l- C f~

(6-67)

c 1' =--~ --~p = (1-d?)c I

(6-68)

It is common practice to approximate the total system compressibility c, given by Eq. 6-67 by the gas saturation-gas compressibility product Sg cg (p). A comparison of the fundamental equation that describes the flow of real gases through porous media (Eq. 6-66) with Eq.6-1 shows that the form of the diffusivity equation is preserved if the flow of real gases is expressed in terms of the pp(p) function. There are important differences between the two equations, among them the non-linear nature of Eq. 6-66, because diffusivity is a function of potential (or pressure), and pressure gradients are not considered to be negligible.

595 An important particular case of Eq. 6-66 is that which corresponds to radial flow according to the equation:

10 r

Or

(~pp(p)]~[l.l(P)Ct(p)~pp(p) r = Or k c3t

(6-69)

The case of a well producing at a constant mass flow rate, located at the center of a radial reservoir, has been numerically solved by A1-Hussainy et al. (1966). It was concluded that for transient flow conditions (infinite acting period), the flow of real gases correlates extremely well with liquid flow solutions obtained by solving the diffusivity equation, provided the dimensionless time is evaluated at initial values of viscosity and compressibility. Thus, for the transient flow conditions to < t o , one can write the following engineering approximation: (6-70)

PpD (l"tD) = PD (l'tD)

It has been shown (A1-Hussainy and Ramey, 1966; Wattenbarger and Ramey, 1969) that Eq. 6-70 can be generalized to Consider the effects of skin damage and high velocity, resulting in: (6-71)

PpD (1,to) = 1.1513(log to + 0.3513) + s + D(~)qce

where the first term on the right-hand side is the line source solution, and the last term represents the non-Darcy flow pressure loss due to high velocity effects (Ramey, 1965). As a first approximation, the non-Darcy flow coefficient is usually assumed to be constant, neglecting its dependency on fluid viscosity. In dimensional form, Eq. 6-71 can be expressed as follows:

q~cP~cT Pp (Pw:) = Pp (P) - 1.1513a ~ [ l o g ( g khT sc

14fit I rl

log ~

d-0.86859

(s + Dqsc) ]

kt

) +

~) [IA (dOi)Ct (Pi)r w2

(6-72)

This expression provides the basis for the interpretation of drawdown tests in gas wells. Lee et al. (1985) studied the main limitations of this equation with regard to the dependency of D on fluid viscosity. They concluded that the approximation of Wattenbarger and Ramey (1969), given by:

D(I~)

].,t i = O(lAi)~

(6-73)

[Alan

may be improved if the flow velocity-dependent skin is considered as the product C1D[I.Ii Iq~l, where C~ is a constant that depends on the flow regime prevailing during the test (laminar or Darcy, transition or high velocity). In the above expression, the i

596 index represents evaluation of the parameter at initial conditions, and ]'~lam is the viscosity that would occur at the wellbore if flow were laminar or Darcy. From this discussion, it seems that the most one can obtain from the analysis of a gas well test regarding the rate-dependent skin is D or the product C~D(IAi) in the conventional way (when information for at least two different drawdown and/or buildup tests, at two different constant flow rates, is available: Ramey, 1965). This procedure clearly assumes that the parameter D is a constant. A promising method for the analysis of gas well tests influenced by high-velocity effects was presented by Fligelman et al. (1981). The authors suggested a trial-anderror procedure that results in proper estimations of formation conductivity, skin factor and non-Darcy flow coefficient.

Example 6-1. Pressure buildup test in naturally-fractured gas well A-1 (Samaniego V. and Cinco-Ley, 1989) Well A-1 is located in a naturally-fractured gas reservoir whose main fractures run along the crest of a structure, and resulted from folding. This well is geographically located in northem M6xico, and is completed in the vicinity of the reservoir crest. Gas production from the reservoir is due mainly to the presence of fractures because the matrix has very low permeability. The lower Cretaceous reservoir in the well is composed of an altemating sequence of microdolomites and limestones. Usually, porosity of the microdolomites is good and permeability is low, but the latter has been increased by the presence of fractures. Well logging and core analysis evidently show the intersection of one of these fractures whose height is approximately 7 ft (2.1 m). Table 6-IX illustrates reservoir and fluid data pertinent to this well. The gas produced is fairly dry, with a specific gravity of 0.56. A routine pressure buildup was run on the well, with the main purpose of checking its drainage volume average pressure conditions for reserve estimations. Table 6-X presents the transient pressure data recorded during the test in terms of pseudo-time At and of the real gas potential pe(pw). Due to the relatively high flow rate of this well (10, 800 Mscf/D through a 2.7/8 in. tubing) the bottom-hole pressure must be corrected by TABLE 6 - I X Reservoir and fluid data for well A-1 T(~ ~b, fraction c t (at average shut--in pressure conditions), psi -l

169 0.06 3.8 x 10-4

Component

Volume %

Cl C2 C3 N2 CO 2 Total

97.75 0.39 0.02 1.68 0.16 100

Type o f completion: openhole 9.5 in. diameter from 1950 - 2328.5 m

597 TABLE 6-X Buildup test data for well A-1 q, Mscf/D Element depth, m

10,800 1900

At

At a

Pp(P)

(hours)

(hr-psi/cp x 10-4)

psi2/cP • 104

0 0.25 0.50 0.75 1 1.50 2 3 4 5 6 7 8 12 16 20 24 28 32 36 40 44 48 52 56 60 68

3.38 11.27 15.15 18.60 25.61 33.51 48.80 63.76 79.14 93.26 109.50 123.08 183.90 242.88 306.03 365.00 425.47 486.65 546.65 607.83 670.98 732.16 794.13 850.27 913.43 1043.66

379.0 380.2 382.6 384.8 385.8 387.6 389.4 392.0 395.4 397.9 400.5 402.3 404.1 409.5 414.4 418.0 422.9 425.8 428.7 432.1 434.9 436.9 439.8 442.2 444.1 446.1 447.5

the friction and turbulent effects involved. With the above purpose in mind, Fig. 6-35 shows a graph of potential drop Ap (p) [= Pp(Pws)-Pp. (Pwl (At = 0))] vs. pseudo-time Ate. The circles show the full datfrecorded during the test, and the triangles are an enlargement of the information up to At = 200 x 1 0 4 h r - p s i / c P . It is shown, as expected because shut-in occurred at the surface, that the early data (At = 30 x 104 hr -psi / c P ) follow a straight line whose extrapolation to the origin is Ap (Pwl (At = O)correcte) , which is equal to 44.5 x 104 psF / cP. Adding this value to t~e potential evaluated at the flowing measured pressure conditions, a corrected flowing potential before shut-in would be 379 x 1 0 6 psi 2 /cP. Using the corrected value of flowing potential, the log-log graph of Fig. 6-36 was constructed in terms of potential drop and pseudo-time. It is observed that after a transition period following the early time wellbore storage-dominated pressure behavior, data follow up to the end of the test, a half-slope straight line for more than a log cycle. The data of Fig. 6-36 can be matched to the Ramey and Gringarten's (1975) type curve for infinite-conductivity, vertically-fractured wells, with the curve a

598 PSEUDO 200

- TIME

sat=

400

, HR-PSI/CPxlO 6()0

"4 800

lOOO 140

,=

I0

o ,...= 100

U

J

U N 0

r

0

-

if)

0

-

100

.-7 0 J!

0 I!

O-L

80

i

r

o[ 0 O.

0o m

3=

0

0

o

Q.

&

A

-

60

== I

O.

60 r

Q.

- 20

Q.

(~t-Ol}correcte d 40 0

a.

4.5 x IO s P S I Z / C P

t

1

t

40

80

120

PSEUDO - T I M E

160

, At,~HR-PSI/CP

200

z 10 - 4

Fig. 6-35. Graph o f pseudopressure drop vs. pseudotime for the buildup test in w e l l A-1.

of dimensionless wellbore storage ( CD)f = 0 05 From match point data and the deftnitions of dimensionless potential and dimensionless time, estimates of formation conductivity kh and the ratio k / x 2 are 116.5 mD/ft and 1.02 x 10-5 mD-ft 2, respectively. From these values, kx2h2 is 1.3 x 109 mD-ft 4. Further analysis could not be carried out because formation thickness was not known (see Table 6-IX). Figure 6-37 shows a graph Ofpp(pws) vs. x/-~a. The linear flow straight-line slope is 2.29 x 104 psi: / c P ( h r - p s i /cP) z/2, and passes through the corrected wellbore flowing pseudopressure. As indicated by the type curve analysis, the first data points are influenced by wellbore storage. Analysis of the information provided by this graph yields kx2h: = 2.4 x 109 mD-ft 4, which agrees with the value estimated from type curve analysis. Figure 6-38 is a graph of the buildup data in terms ofp ( p ) and At. The use of this Miller-Dyes-Hutchinson graph is appropriate because of the long production period (several months) of the well before shut-in. Semilog analysis could not be carried out and, consequently, an estimate of the average pressure (the main objective of the test) can not be obtained. Neverthless, an upper limit for formation conductivity kh can be obtained tracing the semilog straight-line through the last data points, which results in a value of kh = 152.3 m D - f t . m

9

"

"

p_

ws

a

Example 6-2. Pressure analysis for exploratory well A-1 (Samaniego et al., 1985) Well A-1 is a gas condensate producer located in northern Mexico. The producing formation is a naturally-fractured packstone of lower Cretaceous age. All information

599 TRACING PAPER ~ i0 s 10

i i.o

....

Match

point

(Ato) M = !0 ~ HR-PSI/CP N~

[App(p )]

10 2 I

-

I" i"

, (%D)M = 4 . 5 x 1 0

"I~

: 100 xlO s PSlZ/CP ,(PPD)M = 1 . 2 1 _

M ( C Df )M = 0.05

J

f

i~ I

'

Io-'!

I I i

i

! I

i

l

04

)5

t

I

1()6

107

'

1

10-3 Ato

, HR - PSI

i

. I0

/ CP

toxf

Fig. 6-36. Match of the pressure data for the buildup test in wellA-1 to the infinite-conductivity, verticalfracture solution of Ramey and Gringarten (1975).

available indicates that the fractured zone is very localized, and it resulted from tectonic stresses of the Laramide orogeny. Well logging and petrophysical information clearly show the presence of the fracture system, and a tight matrix. Production from this well is due mainly to the presence of these fractures. Table 6-XI shows reservoir and fluid data pertinent to this well. The fluid produced has a specific gravity of 0.902, a dew point pressure of 3015 psig, and contains a small portion of nitrogen and carbon dioxide. A four-rate test was run in this well to determine formation parameters of interest, well potential, and reserves. Table 6-XII partially presents transient pressure data recorded during the test for the three first flow rates. Data for the fourth-rate test are disregarded because a reliable flow rate estimate could not be obtained. A high-sensitivity quartz crystal, pressure-sensing gauge was used in the test. Figure 6-39 is a cartesian graph of the pressure data registered during the test. One important aspect shown by these data is the linear relationship between pressure and time, especially observed in the longer third flow period, which is characteristic of pseudosteady-state flow. It is important to notice that the bottom-hole flowing pressure was always higher than the PVT-determined dew point pressure.Another key point is the pressure buildup data registered for a period of about 9 hr, showing an apparent pressure stabilization far below the initial pressure prevailing at the start of the test. This is the first clear indication of the small size of the reservoir discovered by this well.

600 450

//

440 i

0 ~,r

LINEAR FLOW STRAIGHT L I N E ' ~

420-

~3

,,

n (,.)

400 .~

o,I m.

. ~ i

0

0

PSI~/cP ( HR- PSI/CR ~/2

qmtf = 2.29 x104

n =,

Q.

-380. ~ ~

oSWELLBORE STORAGE oo~,.~Eo o ~

I

o.

__ ~ P p

,~

(Pw f 1 A t = 0 1 1 = 5 7 8

I

C)

10

,

-i 5 x l 06

!

20

" PSI2/CP

t

:30

, ~ 6 t O , , ( HR - PSI /CP)'/2

40 xlO"

5~

2

Fig. 6-37. Square-root-data graph for the drawdown test in well A-1. TABLE 6--XI Reservoir and fluid data for well A-1 T(~ #, fraction Specific gravity Type of completion:

138 0.07 0.902 openhole

Gas Composition Component

Mole %

CO2 N2 Methane Ethane Propane

0.0013 0.0061 0.6932 0.0900 0.0519 0.0192 0.0282 0.0199 0.0108 0.0192 0.0602

iso-Butane

n-Butane iso-Pentane

n-Pentane Hexane Heptane plus

For a moment, let us approach the analysis of this test in the conventional way, that is using a multiple rate test analysis technique. The results of this analysis are shown in Fig. 6-40. It should be clear that this is an approximation because of the long three-

601

_)

/

440 ~) I

o o~ 'j n t)

420

!

0

r

o

or) n

m= 7 3 xlO6

]

PSIa/CP

CYCLE

0 0

(n

0

400 0

0

c1. 0 0

Q.

0 0

0

380 0 4

10 5 Pseudo-

10 6 time

A t a , HR-PSl

10 7

10 8

/CP

Fig. 6-38. MDH graph for the buildup test in well A-1.

time intervals corresponding to the different flow rates. It is obvious from the results that no straight line is shown by the data, which is expected in light of our previous comments regarding Fig. 6-39. In relation to the discussion regarding the possibility of pseudosteady-state flow conditions affecting the test, Figs. 6-41 and 6-42 present graphs of the pressure derivative function tdpo(p wJ,,) / d t vs. t for the pressure data registered during the first and third flow rates. Tl~e results of Fig. 6-39, and especially those of Fig. 6-42, indicate the presence of pseudosteady-state flow affecting the test, starting at a time of about 2 - 4 hours. Figure 6-41 provides the possibility to obtain a value of formation conductivity kh, because an approximate horizontal portion is shown by the curve. Based on this information, the definition of tD dpp D /dto, and using a value of 0.5 for the dimensionless pressure derivative function (which corresponds to radial infiniteacting flow), a kh of 657 mD-ft is calculated. The data of the second flow period will be discussed later in reference to operating problems experienced during the test, which resulted in important variations of flow rate. A point that deserves to be stressed is that even though a high-sensitivity pressure gauge was used in the test, the data of Fig. 6-41 showed such scatter that an analysis was practically impossible. To improve this situation a smoothing data routine was programmed which involved a variable number of data points. This procedure is discussed further by Cinco et al. (1985). Without the use of this routine, the raw data for the first flow rate did not show any clear indication of the flow regime affecting the test. The data presented in this figure were calculated using 11 points (5 forward and 5 backward

602 TABLE 6-XII Three-rate flow test for well A-1 t

(hr) 0 0.083 0.10 0.42 0.67 0.92 1.17 1.42 1.67 1.92 2.17 2.42 2.67 2.92 3.17 3.42 3.67 3.92 4.17 4.42 4.67 4.92 5.17 5.42 5.67 5.92 6.17 6.42 6.67 7.17 7.67 8.17 8.67 9.17 9.67 10.17 10.67 11.17 11.67 12.00 12.25 13.17 13.67 14.17 14.67 15.17 15.67 16.17

t

q

(Mscf/D) ql ~ 1158

q2 ~ 1518

siE/cp) x 10-9 1.08288 1.08161 1.08146 1.08144 1.08137 1.08118 1.08101 1.08081 1.08074 1.08060 1.08049 1.08044 1.08027 1.08016 1.08006 1.08005 1.07995 1.07988 1.07981 1.07973 1.07967 1.07963 1.07958 1.07955 1.07951 1.07935 1.07930 1.07921 1.07918 1.07894 1.07888 1.07877 1.07864 1.07862 1.07851 1.07844 1.07832 1.07820 1.07807 1.07799 1.07652 1.07611 1.07606 1.07584 1.07572 1.07565 1.07550 1.07528

(hr) 22.17 22.67 22.92 23.67 24.17 24.67 25.17 25.67 26.17 26.67 27.17 27.67 28.17 28.67 29.17 29.67 30.17 30.67 31.17 31.67 32.17 32.67 33.17 33.67 34.67 35.67 36.67 37.77 38.77 39.77 40.77 41.77 42.77 43.77 44.77 45.77 46.77 47.77 48.77 49.77 50.77 51.77 52.77 53.77 54.77 55.77 56.77 57.77

(Mscf/D)

p(pO

siVcP) x 10-9

1.07355 1.07341 q3 ~ 3120

1.07336 1.06819 1.06710 1.06678 1.06658 1.06643 1.06615 1.06596 1.06575 1.06553 1.06530 1.06509 1.06486 1.06458 1.06435 1.06412 1.06388 1.06364 1.06340 1.06318 1.06295 1.06250 1.06204 1.06160 1.06111 1.06065 1.06020 1.05974 1.05929 1.05882 1.05837 1.05790 1.05743 1.05701 1.05651 1.05607 1.05559 1.05510 1.05464 1.05423 1.05372 1.05330 1.05283 1.05241 1.05191

603

TABLE 6-XII

t (hr)

(contd.)

q (Mscf/D)

si2/cp)

x

t (hr)

10-9

1.07525 1.07514 1.07503 1.07548 1.07471 1.07457 1.07442 1.07427 1.07413 1.07390 1.07373

16.67 17.17 17.67 18.17 18.67 19.17 19.67 20.17 20.67 21.17 21.67

q (Mscf/D)

P(p(P

si2/cp)

58.77 59.77 60.77 61.77 62.77 63.77 64.77 65.77 66.77 67.77 68.77 69.77

x

10-9

1.05143 1.05095 1.05047 1.05004 1.04951 1.04912 1.04869 1.04820 1.04775 1.04734 1.04685 1.04643

4 400 F

1/8' ~,.

5/32" i i

3/16"

li i i i i i i i i i

4 550 (.D Q._

**%. OO%o 4 300

1/8" _, 1 SHUT-IN

.._,

i i

%o

i i

i i i i i i i i 00000

,-

.

4250 0

20

40

60

80

100

t, HR Fig. 6-39. Pressure data registered during the test in well A-1.

of the center point) in the smoothing process. On the other hand, the data of the third flow period could be analyzed without the need of being smoothed beforehand. Figure 6-43 exhibits the results of this test for the first three flow periods according to the graphical pseudosteady-state high-velocity flow technique discussed by Samaniego et al. (1985, their fig. 1). The pseudopressure drop for these flow conditions, considering variable flow, was expressed by these authors as follows:

604 15

--"

! 0 X

0 0 0 0 I

0

....

0

13-

0

oo

o4

0

C~

0

0

Z

0 v

/ 0 I 0

I

~b

0

oa ~

0

0

0

|

-1

0

1

~ (qi-qJ-1) ~o(j (t-t j_1) qN

d=l

Fig. 6-40. Graph for the multiple-rate drawdown test in well A-1. l0 T

13_ r

oo/

r

10 6

10s 10-1

1

10 t, HR

Fig. 6-41. Pressure derivative function for the first flow rate, well A-1.

lO 2

605 10 8

Sj

n I.=...4 f.r) n

10 7

L/ 1

10 6

o 9

10 -1

1

10

t,

10 2

HR

Fig. 6-42. Pressure derivative function for the third flow rate, well A-1.

1.5

9- - ,

|

" ' I

,ql Aqz oq3

I

o >(

L.L..

(.3 C~

1.0 f

f "-'

2

~

0.5 ~I I

~**~

<3 0 0

10

20

30

40

50

60

f(t) Fig. 6-43. Normalized graph of bottomhole pressure for the multiple-rate drawdown test in well A-1.

606

pp (pi)--pp (pwf) qN =

2rcag fl, p~cT

q~-qi-t

~

l~(Pi)Ct(Pi)Lc

( qN

I/A1 /22458/

+ agPscT kh T c

In ~ + In rw2

+ (s + DqN)

CA

) (t- ti_,)

1

(6-74)

It is clear that this is the equation of a straight line with slope m* and intercept b* given by Eqs. 6-75 and 6-76: m* =

2 rCag fl, P~cT

(6-75)

Ahd? ~ (Pi)Ct(Pi)Lc

E/A//22458/ -khrsc

b* - agP~cT

In

+ In

+ (s + DqN)

1

(6-76)

Thus, multiple-rate pseudosteady-state test data should appear as a straight line when plotted as:

pp (pi)__pp (pwf) qN

N

vs. Z ( i-1

qi--qi qN

-') ( t - t~l )

The author's fig. 1, and Eq. 6-74, indicate that shifting of the straight-line behavior predicted by this equation is due to high-velocity effects affecting the test. This being the case, the intercepts can be used provided a value for the skin factor is available, through a graph of [APe(p) / q]i,, vs. q. This procedure is similar to that used in the semilogarithmic analysis of high-velocity flow tests (Ramey, 1965). One can observe in Fig. 6-43 that the parallel straight-line portions are well defined only for the first and third flow periods because as already mentioned, the flow rate of the second flow period could not be kept approximately constant. The function fit) on the horizontal axis is given by the summation of the first term on the right-hand side of Eq. 6-74. Using Eq. 6-75 for slope m*, using customary units (see the Nomenclature section), a value for the hydrocarbon pore volume V or gas volume at reservoir conditions V of 3.36 x 106 ft 3 is obtained, or expressed at standard conditions, the G value is 89~ MMscf. Figure 6-44 shows a graph of the intercepts of the two well-defined straight line portions of Fig. 6-43. Assuming independent estimates for the formation conductivity kh and the skin factor s are available, then the shape factor CA and the high-velocity coefficient D can be calculated. Unfortunately, this is not the case for the subject test, even if a great effort was made to get this information. It was expected that the estimate for kh could be acquired through transient flow analysis of the data, but this behavior shows during a very short period for these tests. Additional discussion re9

o

P

607

'o ~ C:3

0.4

LL (.J rE')

:E

EL (j

,-, or)

J

0.3

J

CL

m~l~ = PSIZ/CP 0.459 (MSCF/ D )2

I..Z -4---I

E)"

~.

0.2 ) 1

J

f

f

f

I

J

f

EL ,..._..,, EL

EL <:3

0.1 0

1000

20(~Z)

3000

4000

q, MSCF / D Fig. 6-44. Graph of intercepts of the straight line portions of the normalized graph ofbottomhole pressure vs. flow rate, well A-1.

garding this aspect is presented later. It has been discussed regarding Figs. 6-39 and 6-43 that data for the third flow rate show the best linear relationship between pressure and time. An alternative method for presenting these data can be through the use of the principle of superposition, considering that pseudosteady-state flow conditions applies. Then the resulting expression is essentially Eq. 6-74 if multiplied by qN" Figure 6-45 presents the data registered for this flow period in accordance to this method and, as expected, the alignment of the data is excellent. It should be clear that the slope of this graph and that of Fig. 6-43 have to be the same; this is approximately the case because the two values of 150 and 146.86 psiE/cP/Mscf/D hr compare well. Using this last figure one can estimate a value for the original gas volume G of 914 MMscf. The previous discussion has addressed the important point of smoothing pressure data to obtain a better analysis of tests. Figure 6-46 is a cartesian graph of the pressure derivative function tdp.(p ,)/dt, using the raw data vs. t in accordance with the method presented by Cinco e(alW~(1985), for the analysis of pressure data taken under the influence of an unknown trend. An analysis of the non-smoothed (raw) data is practically impossible. One can clearly see the improvement shown by the smoothed data; better results are obtained when 11 points (Fig. 6-48) instead of 5 (Fig. 6-47) are used. According to the method of these authors, one could expect the data to follow a straight line portion of intercept m/2.303 when graphed in this manner. This is not evidently the case due, among other factors, to the variation of flow rate during this portion of the test.

608 1070 0

*% 0

Q_

1060 In

m = 146.86

3 Q.

PSIz/CP MSCF/D-HR

Q..

1050

--

4-

5

10

15

$

~l

(qjL-qj_l) ( t- tj_l) , MSCF/D-HRxlO'*

Fig. 6-45. Pseudosteady-state flow superposition graph for the third flow rate, well A-1. u 0 0

0 Q_

o t,

,

o

I.,--4

r 12.

o o

o

o

o

0

~ o

0

0 0

o

o

000

--~ ..........

0

n-~ 0

o

0

0

0

O0

0

0

o 0

0

0

O0 0

00

o

o~

2.5

5.0

7.5

10.0

t, HR Fig. 6-46. Cartesian graph of the pressure derivative function based on raw data of the second flow rate, well A- 1.

609

0

O

o

X

0 o

o

r---

o

o

o

o

o

9

i

(3_ 0

0

I i

0

o

i i

i O

0 0

OO OO

0 0

!

O

i

O

O O

O

o

O O O

q: D O

I

O

o O OD

0

O ---~O'O--

OO

o

OO

0

O

O O

2.5

5.0

7.5

10.0

t,HR Fig. 6-47. Cartesian graph of the pressure derivative function based on five-point smoothed data, second flow rate, well A-1.

4, o O OO

O

O

O r'--.-

L

O

O0

3,

0 OU 0

O 0

~'O

0

0

OO

0

OO O

O O

0000000

.+..J ID

oO. oO O

o Oo

o o

O

D O O O O O (~

0 0

2.5

5.0

7.5

10.0

t,HR Fig. 6-48. Cartesian graph of the pressure derivative function based on 11-point smoothed data, second flow rate, well A-1.

610 10 r

b

i,,-,.-,X

n (._)

g

O0 CL 0

,,,,.

106

0

0

.......................

.0

1,v

0 0

0 0

0

@

o 0

O~

lO s

10"1

1

10

t, HR Fig. 6-49. Pressure derivative function for the second flow rate, well A-1.

106.2ool o o 10/6.

'

'

1

d

o

o o

GO o

Z '

o

0

o

10/6.1

o

o

I

0

0

0

0

,~'***

| o

o I) 0

0

0

0

0

O0

0

i

0 o 0

IO?E 1.150

1.100

t+ 9 At

q2

Log~ At ) + ~

1.200

Log At

Fig. 6-50. Graph for the two-rate flow test, well A-1.

10 2

611 Smoothed data for the second flow period of Fig. 6-48 are shown in a double logarithmic scale in Fig. 6-49. As it is expected, one can not identify the flow regime prevailing during the test. This graph is based on partial data registered during the test, and it could be concluded that a short radial infinite acting period, represented by the horizontal behavior of the curve, is present in the test between 1.7 and 2.0 hr. This being the case, the data can in principle be analyzed as a two-rate flow test. Figure 6-50 shows the results of this analysis considering more data points. There is no alignment of the pressure data and, consequently, a two-rate flow test interpretation can not be made. In this test the flow rate measurement was practically continuous, which explains the oscillation of the two-rate semilogarithmic graph of this figure.

A G A R W A L ' S (1980) M E T H O D TO ACCOUNT F O R P R O D U C I N G - T I M E E F F E C T S IN THE ANALYSIS OF BUILDUP TESTS

Since its introduction in the petroleum engineering literature in the early 1970s by Ramey and co-workers (1970), type curves for the interpretation of early time data have prompted profound changes in the techniques of analysis. A type curve is prepared for the specific flow problem in the field, considering a given set of inner and outer boundary conditions. Most of the type curves which have been developed and published to date consider drawdown solutions. The application of drawdown type curves in analyzing pressure buildup (or fall off) data is adequate when the following time criterion is met: if producing time to prior to shut-in is sufficiently long compared to the shut-in time At, that is, ( t -~ At) / t 1) for liquid systems, pressure buildup data can be analyzed using draffdown typ~ curves. If this criterion is not met, or in other words the producing time prior to shut-in is of the same order of magnitude or only slightly larger than the shut-in times At [ that is, (to + At) / t >> 1], then the use of drawdown type curves to analyze pressure buildup data is not P justified. Typical field situations where the time criterion is not met would include drillstem tests and pre-frac tests on low-permeability gas wells. It is clear that accounting for the duration of producing time is necessary, and some papers have addressed this matter. McKinley (1971) published buildup type curves for the analysis of pressure data. These, however, closely resemble drawdown type curves, because the producing time range used was long, and obviously can not be used to analyze pressure data registered under short producing conditions. Later, Crawford et al. (1977) discussed the previous limitations of the McKinley type curves, and presented new type curves for short producing times. An excellent discussion of the effect of producing time on type curve analysis has been presented by Raghavan (1980), who clearly states the limitations involved in the use of drawdown type curves. Agarwal (1980) developed a method for radial flow to overcome the difficulties involved and to eliminate dependence on producing time. This method permits one to account for the effects of producing time, and also data are normalized in a way that instead of utilizing a family of type curves with producing time as a parameter, available drawdown type curves may be used. The principle of superposition has to be applied to pressure drawdown solutions to

612

Pi

t (AP)drawdown

Pws(tp+At)--~.~..

(t)~

IJ_l OC :Z:) r 03 ILl Or" n

I*.I* (Al~)buildup

l/

(AP)difference"

' ~- pwf(fp+ At ) -~-

.7 l - -

CONSTANT RATE DRAWDOWN

'"

. . . .BUILDUP ..

tp ~_.. ,. . . . .

I

t

--I ~

~1 ,

At . . . . . . .

i

!

TIME Fig. 6-51. Schematic of pressure buildup behavior obtained after a constant rate drawdown.

obtain a pressure buildup solution. The result is buildup pressures at shut-in time At after a production time t. Figure 6-51 is a schematic of pressure buildup behavior obtained after a constant rate drawdown for a production period t.P Buildup pressures, . pw~(t + At), are shown in terms of shut-in time At. This figure also shows the pressure behavior of the well if it had continued open to production beyond t.p. Applying the principle of superposition to drawdown solutions results in the following expression:

kh[p,-pw

aoqBp

+ At)]

=

[(t + AO

]-pwo[(at)o]

(6-77)

An expression can be obtained for the dimensionless flowing pressure corresponding to Pws(t ) (or pw~(At - 0)) which, if substracted from Eq. 6-77, gives:

kh[Pw~ (t + At)-pw~(At = 0)] = pwo[(t)z~]-Pwz~[(t + At)D] + pwo[(At)o] aoqBp

(6-78)

613 This isAgarwal's (1980) equation 5, which provides the basis for buildup type curves. A simplification of this equation is commonly used to justify the use of drawdown type curves to analyze buildup data. If producing time tP is sufficiently longer than shut-in time At, then Eq. 6-78 can be written as:

kh[Pws (t + At)-pw~(At = 0)] = Pwo[(AtD)] aoqBp

(6-79)

A comparison of Eq. 6-79 and the pressure drawdown equation of Eq. 6-41 implies that (Ap)d~awdow,flowing time t is equivalent to (AP)buitdup VS. shut-in time At where: (6-80)

(AP)drawdown = P i - P w j

and (6-81)

(AP)buildup = Pws( t -I- At) --Pws (At =0)

It should be clear that because Eq. 6-79 has been derived from general buildup Eq. 6-78, based on the assumption of a long producing period t, the difference between the first two terms of Eq. 6-78 should be equal approximately to zero. Figure 6-51 shows this difference as the cross-hatched area which is defined as follows: (AP)difference = Pws(At =

(6-82)

O)-Pwj (t + At)

It can be shown that as producing time t gets smaller, or if At gets larger, then the difference expressed by Eq. 6-82 can not l~e ignored. Hence, drawdown type curves should not be used to analyze pressure buildup data. This difference is visualized in an easier manner through a graph of (Ap)d~awdow,VS. flowing time t, compared with (Ap)buildu p VS. shut-in time At, for different producing times tp (Fig. 6-52). It can be concluded that the limitations of using drawdown type curves for analyzing pressure buildup data where producing time, tp, is small, are especially important in the following situations: (a) for this producing time range the difference between (Ap)d~wdow, and (Ap)buitd,p is significant and gets smaller as producing time, tp, increases; and (b) for long shut-in times, At, the difference between the (Ap)'s gets larger. The basis of Agarwal's (1980) method is Eq. 6-78. Substituting the line source solution into this equation, and considering the skin effect, the following expression is obtained:

k h [ P w s ( t + A t ) - P w s ( A t = O ) ] l l t p D A t pIn ~ aoqB p 2 ( t + At)

+ 0.80907 ]

(6-83)

Agarwal (1980) demonstrated that this pressure buildup solution gives essentially the same results as those generated by the drawdown solution. Furthermore, it is possible to normalize a family of buildup curves into a single curve, which is as

614

UCING

TIME,t or At Fig. 6-52. Comparison of drawdown and buildup pressure drop behavior vs. shut-in time, for different producing times. mentioned, practically coincident with the drawdown curve. In conclusion, if pressure buildup data are to be analyzed by pressure drawdown type curves, then (Ap)buitdup data should be graphed as a function of a new time group At e = tp At / (tp + At) rather than just the shut-in time, At. The utilization of this group was successfully tested for different conditions, such as the presence of skin and wellbore storage, applicability to the type curves of Earlougher and Kersch (1974) and Gringarten et al. (1979), tworate testing, multiple rate testing, and in fractured wells. This method has the implicit assumption that producing time tp was long enough for the radical flow semilog straight line to be reached prior to shut-in of the well. Besides its use for type curve analysis, Agarwal's (1980) equivalent drawdown time, At e, is also useful in the semilog analysis of pressure buildup data. In dimensional form, Eq. 6-83 can be written as follows:

Pw, ( t + At)-Pw~ (At = O)= m

+ log

(4b,/ 7~

+ 0.86859 s

1

log

P tP + At

+ log (DI2err2w

(6-84)

615 This expression suggests that a graph of buildup pressure, Pw~ o r (Ap)buildup VS. Ate, should show a straight line portion of slope m on semi-log paper. This graph in terms of At is similar to the Homer graph, because it also accounts for the effect of producing time t.e This equation also indicates that for long producing times as compared with the shut-in time At, when (t. + At) / t ~ 1, then At ~ At. This expression justifies the use of the Miller-Dyes-Hutc~ainson graph p for long eproducing times. Similar to conventional analysis techniques, skin effects may be estimated through the following expression: s = 1.115131Pw~ (At = 1)-Pws(Atm = O)

Ikll -

log

-

Cpctr:

log

4

(6-85)

w

It can easily be demonstrated that the false pressure p*, corresponding to shut-in time At close to infinity, or the initial pressure,p~, can be directly read from the straight line portion of the semi-log graph Of Pw~ vs. Ate, if the Ate value equals to t.p P R E S S U R E T R A N S I E N T ANALYSIS F O R H I G H - P E R M E A B I L I T Y R E S E R V O I R S

It is well known that many carbonate reservoirs are high-permeability formations (Mclntosh et al., 1979; Kabir and Willmon, 1981; Cinco Ley et al., 1985). These systems show special characteristics that makes the application of conventional techniques of analysis difficult. For instance, in very high-permeability reservoirs, inertial effects appear to be important, because of high flow rates involved in tests. Furthermore, wellbore temperature effects and interference of neighboring wells produce pressure changes at the tested well, which are of the same order of magnitude as pressure changes generated by variations in flow rate in the test itself. This situation requires that the effects of different phenomena be detected and evaluated in order to perform comprehensive analyses. The discussion that follows will focus on the presentation of field cases. The reservoirs tested are in calcareous rocks of Cretaceous age, and all are highly fractured and include vugs and cavems. These characteristics provide good formation flow conductivity (kh), yielding high flow rates (20,000- 40,000 STB/D) during the first years of production. At the time these tests were conducted, the reservoirs were undersaturated.

Example 6-3. Pressure and flow test in oil well A-1 (Cinco-Ley et al., 1983) Well A-1 is an offshore openhole completion (Fig. 6-53). Figure 6-54 shows the tests carried out in February 1980, starting with a drawdown test followed by a buildup test. Next, the well was open through three different choke sizes for a period of half an hour each and, finally, it was shut-in for a second pressure buildup test of 16.5 hr duration. Figure 6-55 presents pressure data registered during the test. These results indicate that inertia effects strongly affected the pressure response of the well, both drawdown and buildup tests showing water-hammer effects. It is important to point out that

616

]

CASE A

PRESSURE GAUGE AT I170 m

1240 m 3PEN HOLE ,273 m Fig. 6-53. Completions details of well A.

these were the first tests conducted in this high-permeability prolific field and, consequently, the water-hammer effect had not been previously identified. In the analysis of the pressure-flow rate data obtained for this well, two types of tests can be considered: (a) a variable flow-rate test including the first flow period, the first shut-in period and subsequent flow periods through three different choke sizes; and (b) another test that includes the second buildup period.

Variable flow rate test The first flow period of this test can be considered a constant-rate drawdown test. Table 6-XIII shows the reservoir and fluid data for this well and also for wells B-1 and B-2 (discussed later). Figure 6-56 presents a semilog graph of the pressure data for the first flow period, which shows a straight line of slope 0.25 psi/cycle, resulting in a conductivity kh = 19.2 x 106 mD-ft and s z 3.5. Assuming radial flow conditions, Fig. 6-57 shows a multiple-rate data graph for this test. It can be observed that the slope of these four graphs, is approximately 0.23 psi/cycle found in the constant-rate semilog graph of Fig. 6-56, but the straight lines are displaced due to the friction losses which, for all conditions remaining constant, depend on flow rate. Using the approximately "stabilized" pressure information of Fig. 6-57 and the rate data of Fig. 6-54, Fig. 6-58 shows a graph of Ap / q vs. q. It can be observed that

617

CASE A

q,STB/D 7 430 5:500 6740 8980

q STB/D

lO,O00

4

,IF

_z

0

I

0

|

2

4

I

I

6 t, hours

8

I

I

10

Fig. 6-54. Variation of flow rate vs. time during the tests in well A. TABLE 6-XIII Reservoir and fluid data Well A- 1

Bubble point pressure, psi System total compressibility, psi -l Oil viscosity, cP Formation volume factor, RB/STB Well radius, ft Porosity, fraction Type of completion

2133 3 x 10-5 3 1.22 0.4 0.12 openhole

Wells B-1 and B-2

Bubble point pressure, psi System total compressibility, psi -t Oil viscosity, cP Formation volume factor, RB/STB Well radius, ft Porosity, fraction Type of completion of well B-1 Type of completion of well B-2

2532.8 1.7• 10-5 0.532 1.5 0.5 0.06 openhole perforated single completion

the data do n o t f o l l o w a h o r i z o n t a l straight line, thus i n d i c a t i n g h i g h - v e l o c i t y f l o w in the f l o w s y s t e m .

618

CASE A 2420

Pw ,psi

D

2415

,,i

I

I

I

I

I

i

,

i

5

i

I

I

10

15

t, hours Fig. 6-55. Pressure response for tests in well A.

"

IIl~

CASE A

2420

Pwf, psi

9

o D

9

9

s,"

%

9

s

~ 9 9

t I. m_0.25

psi

~,

cycle

0O

2415

r

0-2

I

10-1

I

1

I

,

10

t, min Fig. 6-56. Semilog graph for the first drawdown test data, well A.

I

102

103

619

CASE A m- 0.4 x 10-4

6 AP w qN 4 psi STB/D x104

& a

q,STBID 7430 5300 o 6740

I

9 8980

-0.6

-0.4

-0.2

n qj-qj-I ~l

0.2

0

log (t-t].])

qN

Fig. 6-57. Multiple flow rate test graph, well A.

10

I

I

!

I

I

A p / q : 3.017 x 10 - 4 + 6.283 x 10 . 8 q m

ra

Ap = 3.017 x 10 -4 q , 6 .

rn

~-

O9

8

o/~

(tJ C~_

m =6.283 xt0 -8

o,.

1:9"

Y0: 3.017 x 10-4 psi / STB / D 5

I Z

000

I

I

6 000

q (STB/D) Fig. 6-58. Well performance curve for well A.

1

8 000

I

10 000

0.4

620

CASE A oo

2420

9 --o" ~ 1 7 6 1 7 6 1 7 6 1 7 6 1 7 6 1 7 6

9 9 9 9 9 9 9 9

9 9 9 9 9

9 9

9 Oo

PWS,

psi iI

2410

i

0

I

I

1

2

,

I

I

,

5

4

5

At,min Fig. 6-59. Cartesian graph of the first five minutes of the buildup pressure response data, well A.

The best-fitted straight line of the data gives an interception at q = 0 of 3.017 • 10-4 psi/B/D, the inverse being the productivity index equal to 3,315 STB/D/psi.

Second buildup test The second buildup test includes two shut-in periods. However, the first test did not last long enough for the inertia and fluid segregation effects to become negligible, and, therefore, allow the recognition of analyzable data. The early-time data of the second buildup test were also under the influence of inertia and fluid segregation effects during the first 45 minutes. Figure 6-59 shows the pressure behavior of the well for the first 5 minutes, indicating a water-hammer effect with an initial 24-second cycle, which tends to dampen as a result of several factors, among them frictional forces. The water-hammer effect is the result of the sudden surface valve shut-in. As a final comment, it is useful to say that the experience gained through this test was used to improve the design of subsequent tests in the area. For instance, the inertia effects could be minimized by slowly opening or closing the surface valves. Longer test times were recommended in order to obtain more complete data for a proper analysis. In addition, design of future tests called for an accurate definition of pressure decline in the volume of drainage of the well before the start of the test. This aspect of test design was not quite important at the time the test was carried out, because this giant field was at the initial stage of development.

621

Example 6-4. Pressure drawdown and buildup test in oil well B-1 (Cinco-Ley et al., 1985) Well B-1 is an offshore openhole completion (Fig. 6-60). The producing formation is a Paleocene breccia in Cretaceous age rocks. At the time this test was conducted, the reservoir was undersaturated. Figure 6-61 shows the pressure variation during two drawdown and buildup tests carried out in August 1984. These tests started under shut-in conditions of the well so as to obtain measurement of pressure decline in the volume of drainage before the beginning of the test. Actually, for this test rather than dealing with a pressure decline, the field was under a pressure recovery because of a decrease in production rate of about 150,000 STB/D. Once this pressure recovery tendency was accurately defined, two drawdown tests followed by their corresponding pressure buildup tests were carried out. Both pressure and flow rate measurements were taken simultaneously and recorded at the surface. A quartz crystal recorder and a spinner were located at a depth of 3200 m. Unfortunately, flow rate data were not recorded because a fragment of rock from the producing formation prevented proper operation of the spinner. An average flow rate of 23,000 STB/D was handled during the test. Before every drawdown test, the gas column within the wellbore was purged to minimize inertial

CASE B-I

200 m

~

3779 m

Fig. 6-60. Completion details of well B 1.

622 3950

I

CASE B-1 r .~_..._ _

3900I

1

3850n itl r

k,..,__J

3800

~lllll~lllllll~ I

::D 03 t..tJ or" n

3750-~

!

9 IL--

J

3700 ,L I

.L

3650

3600-

~j i

0

20

40

60

8O

100

120

TI ME, HR Fig. 6-61. Pressure response for the tests in well B 1.

effects when the well was subsequently fully opened. The reliability of the drawdown test is limited because: (a) the pressure noise was of the order of the pressure variation during the test; and (b) of difficulties in the continuous flow rate measurements. Due to the location of the pressure recorder (463 m above the top of the producing interval), it was necessary to correct the bottomhole flowing pressure by adding the fluid column pressure difference plus frictional pressure losses. To make this possible, the pressure recorder was lifted 200 m right before the second buildup test so as to calculate the pressure gradient under flowing conditions. The results of the first pressure buildup test are shown in Fig. 6-62. Inertial oscillations are present at short shut-in times as was discussed for the test of Example 6-3. Analysis of the test indicates that apparent semilog straight lines are exhibited and explained by the double-porosity behavior. However, this situation could be erroneous in this type of field because similar behavior can be caused by rate variation in neighboring wells. A confident analysis of the buildup test can be obtained when both test results are analyzed simultaneously. Comparison of the Homer graphs for the first and second

623

CASE B-I 3924

Pw$ psia 5922

,%

3920

m o o

9

9

9

9

9

9 9 9

-o

9 9 9

~t

10-3

i

,

i

10-2

10-1

At

tp+At Fig. 6-62. Homer graph for the first buildup test, well B 1.

buildups (Figs. 6-62 and 6-63, respectively) indicates that the double porosity-like behavior of the first test does not represent the reservoir characteristics. Instead, it was caused by neighboring well effects. The period oscillations for both tests are identical; however, the oscillation amplitudes for the second buildup results (pressure recorded at lower depth) are higher than those observed in the first buildup. This situation can be explained by considering that the oscillation amplitude is related to frictional effects. The correct semilog straight line appears to be better defined in the second buildup test and has a slope of 1.46 psi/cycle (Fig. 6-63). According to data presented in Table 6-XIII for this well, the formation flow conductivity is 2.12 • 106 mD-ft. The pressure at At equal to 1.0 hr on the semilog straight line is 3736.75 psi. After correcting the measured bottomhole flowing pressure for the friction pressure drop, calculation of the skin effect gives a value of 16.7. Based on geological and geophysical information, it is believed that this skin value is due to the partial penetration condition of the well. Finally, Fig. 6-63 clearly shows that the final portion of the test was under the influence of the reservoir pressure trend.

Example 6-5. Pressure drawdown and buildup tests in oil well B-2 (Cinco Ley et al., 1985) This well was tested by using a bottomhole shut-in tool with simultaneous pressure recording at the surface. Both devices were installed as part of the production string. Figure 6-64 shows the pressure recorded for this well. Initially there was an observation

624

CASE B-1

3738

Pws, psia 3736

-oo 9

9

9~ ,,.It

9

oo 9

9

9

9

9 9

9

|

9 9 9 9 9

9

3734

3732

.

.

.

.

.

10-3

J lO-a

i

10-]

At tp+At

Fig. 6-63. Homer graph for the second buildup test, well B 1.

4140

o

CASE B-2

4155

DD

13_

DD

oo rr- 4150 1:3_ OBS DD BU 4125

I

24

I

I

Observation Drawd0wn Buildup ,

72

48

TIME, Hours Fig. 6-64. Pressure response for the tests in well B2.

I

96

12o

625 period to determine pressure variation at the wellbore, and next, the well was opened for a drawdown test followed by a buildup period. Finally, another drawdown and a buildup completed the test sequence. Figure 6-64 shows that the whole test sequence was under the influence of a changing reservoir pressure trend. However, the pressure trend is approximately linear for each particular test. It has been demonstrated that for a drawdown test under the influence of linear reservoir pressure trend, m* can be interpreted through equation A-4 of Cinco Ley et al. (1985):

t dApwl dt

-

m + m*t 2.303

(6-86)

This equation indicates that a graph of MAp wl/ dt vs. t, as shown in Fig. 6-65, yields a straight line whose slope is m* and intercept is m/2.303, where m is the semilog straight line slope. Thus, this method allows the simultaneous estimation of reservoir decline pressure trend m* and the semilog straight line m. On the other hand, a pressure buildup test under the influence of linear reservoir linear pressure trend m* can be analyzed through equation A-6 of Cinco Ley et al. (1985):

t dAPws dAt

m t = --P - m* 2.303 At ( t + At)

(6-87)

Drawdown Test

/ t

/

/

dAp /

dt

]

m / 2.303

TIME dAPwf

Fig. 6-65. Graph of the pressure derivative function t dt of an unknown linear pressure trend.

vs. t for a drawdown test under the influence

626

Buildup Test dAPws dAt m/2.303

m-~ i

tp (tp + At )At Fig. 6-66. Graph of the pressure derivative dAPws / dAt vs. tp / At(tp + At) for a buildup test under the influence of an unknown linear pressure trend. This equation shows that a graph ofdAPws/dAt vs. t / A t (t~ + At), as shown in Fig. 666, yields a straight line whose slope is m/2.303 ~nd intercept is m*. It should be mentioned that this method does not require the use of the desuperposition (negative superposition) suggested by Slider (1971). These methods of analysis are appropriate for the cases discussed in this section. Unfortunately, data of continuous flow rate measurements are not available. Hence, a reliable analysis of the drawdown test cannot be provided. It should be mentioned that the well was opened at the surface, and pressure data exhibited rather irregular behavior as a result of flow rate variations. The average flow rate used in these tests was 5,400 STB/D according to specifications of shut-in tool, and the pressure recorder was a high-resolution strain gauge (0.01 psi). Figure 6-67 is a Homer graph for the first buildup test. Note that this test was not under the influence of a reservoir pressure trend alone. Additionally, non-programmed changes in the production rate of some neighboring wells had to be made due to failure of production facilities. The shut-in pressure at the final portion of the buildup shows a decline resulting from pressure trend effects. Figure 6-68 presents a graph plotted in accordance with the method previously discussed, applied to the first buildup test. Data are rather scattered, and a smoothing process becomes necessary before calculating pressure derivatives. A simple method that produces excellent results for such a smoothing process is based on the equation:

627 4159

CASE B- 2 Pws, psia

.,/~

oe

9

~~176

4158 .. 9

9

o

9 ~

~

/

-.--t%

9 9

O ~

9

9

/

9O

".%j

4157

1

10-5

10-4

I

I

10-5

10-2

,

1

10-I

&t tp+&t Fig. 6-67. Homer graph for the first buildup test, well B2. 'A t + 8 t / 2

fiw~(At)

=

t-6,/2

Pws(tldt

(6-88)

or in discretized form for equally-spaced points: n-1

1

P---w~i -

n

(-7-)

Z Pw,(i+j)

(6-89)

j = -(~)

where n is an odd number. It has been found, for the cases presented in this work, that n = 11 produces satisfactory results, as seen in Fig. 6-69. Results are not reliable because field pressure trend changed during the test. Figure 6-70 is a Homer graph for the second buildup test; the effect of reservoir pressure trend is evident at long shut-in times. No apparent semilog straight line seems to be present. Figure 6-71 shows the application of the method previously described that considers a pressure decline, applied to the test after pressure data smoothing. The straight-line portion of the curve has a slope of 0.812 and intercept of -0.14. These data mean that the reservoir pressure trend during the test was -0.14 psi/ hour, and the slope of the semilog straight line is 1.87 psi/cycle, which produces a kh value of 3.7 x 105 mD-ft.

628

0.5

CASE B-2

dAPws

dAt

psi 0

~ ' ~ r

-0.5

, 0

9

. . I 0.2

.., . . . . .

o

I 0.4

oo

9

,

J 0.6

tp

(tp,At)At

I

1

0.8

, hr - I

Fig. 6-68. Graph of the pressure derivativedApws/dAtvs, tp / At(tp + At) for the first buildup test, well B2. 0.5

9'

CASE

d~pws dAt

-

psi

~;

B-2

m

~~- 9149

9149 99 00

O

~

9

9

9

9

o

-O.5~

. L , 0

! 0.2

A

I 0.4

( tp+

I

t p At ) At

! 0.6 t

l

,,I,, 0.8

I

hr_l

Fig. 6-69. Graph o f the pressure derivative dApws / dAt vs. tp / At(tp + At) obtained through an l 1-point smoothing process; first buildup test; well B2.

629

4138

CASE B-2 4157

Pws,psia ...............

4136

4135

4154

I

10-5

I

10-4

,

I

10-3

I

10-2

10-1

At

tp. At Fig. 6-70. Homer graph for the second buildup test, well B2.

0.5

CASE B- 2

dA Pwsld~,t. psilhr

2.505 - 0.812

j

. . . . . .

0 0 0 O0 9 0

9

9

9

m - o.14 psi/hour

-0.5

J

0

I

0.2

I

I

i

0.4

I

,

0.6 t p

(tp+ht) At

I

0.8

,

]

! hr_ ]

Fig. 6-71. Graph of the pressure derivative dApw s / dAt vs. tp / At(tp + At) obtained through an 11-point smoothing process; second buildup test; well B2.

630 In addition, the Homer graph corrected for pressure trend can be obtained by using the principle of superposition, that is (Cinco Ley et al., 1985): (6-90)

(Pws(AO)corrected--Pws (AO "l- m* At

In Figure 6-72 one can detect the semilog straight line at the final portion of the test. An important point in this test was to determine if the reservoir exhibits doubleporosity behavior, which becomes evident in the corrected Homer graph. Methods available for double-porosity analysis can be applied to the corrected data. It should be pointed out that the bottomhole shut-in tool was effective in eliminating wellbore storage and inertial effects. The shut-in pressure increases abruptly after closing the well. However, abnormal behavior occurs after 1.8 minutes. It appears that the wellbore pressure decreases with time. This anomaly is readily explained by vertical movement of the pressure recorder caused by temperature changes in the wellbore after shut-in. The production string did in fact move freely through the packer and no attempt was made to correct for this effect. The cases described above were selected to illustrate different types of unusual behavior of the pressure recorded in tests of high-permeability reservoirs. It is stressed that the use of high-resolution pressure gauges is a must in order to obtain good information. The first case described above showed the effect of inertia and friction pressure drop on bottomhole pressure, when the pressure recorder was located inside the tubing. As was mentioned, small flow rates must be used to avoid lifting

4138

.

.

.

.

.

.

i

CASE B-2

!

4137

Pws,psia 41:56

.. ......... .-.-..~....,.,.~ J "

J'"

4135

4134 . . . . . . . . 10-5

I

10-4

I

I

10-3

10-2

A t / ( t o + 6t ) Fig. 6-72. Corrected Homer graph for the second buildup test, well B2.

,

I

10-]

631 of the pressure element which indeed can be a major problem in detecting the semilog straight line because of small pressure variation. This situation should be avoided in this type of reservoir. The second case pointed out that changes of flow rate in neighboring wells can completely distort the pressure behavior of the tested well, and any analysis performed is unreliable under such conditions. It is important to have strict control on the production conditions of the wells when a particular well is being tested, and tests should be planned to obtain repeatability in pressure behavior. The third case showed the advantage of using a bottomhole shut-in tool in this type of reservoir. Both inertial and wellbore storage effects are almost eliminated under these conditions, but one should be aware of the possibility of having the pressure measurement affected by temperature changes if the pressure recorder is not anchored. Another point that deserves particular attention is the possibility of using the spinner to measure the flow rate continuously in order to analyze pressure drawdown data properly. The third case illustrated the application of a method of interpretation of data influenced by the reservoir pressure trend and a method for data smoothing.

A N A L Y S I S OF W E L L I N T E R F E R E N C E T E S T S

An interference test is a multiple-well transient test that involves more than one well. In an interference test, a long-duration rate or pressure change in one well, called an "active" well, creates a pressure interference in a previously-closed, nearby observation well. Such a pressure interference can be analyzed for reservoir properties. The term "interference test" refers to the pressure drop caused by the producing wells, including the active well, as the shut-in observation wells "interfere with" the pressure at the observation wells. There are several important advantages inherent in the analysis of interference tests. First, a greater area of the reservoir is influenced with respect to that affected during a single-well test, be that a drawdown or buildup test. Second, these tests can provide information on reservoir properties that are not available from single-well tests, e.g., the storativity ~ cth. Third, reservoir connectivity can be estimated. Questions such as: (a) is the nearby observation area drained by other wells? and if so, (b) how rapidly?, can be answered. Fourth, reservoir anisotropy, which can be directly related to preferential flow patterns, can be estimated. On the other hand, a disadvantage of this test is that pressure drops reaching the observation well or wells can be very small, and importantly, are affected by additional operational field producing variations. This problem is especially common in high-permeability carbonate reservoirs. However, presently available electronic gauges of high accuracy and resolution are capable of registering such small pressure drops (usually less than 1 psi over days or even weeks), and so interference testing can be successfully employed. Of special importance in new reservoirs, an interference test is not affected by other production in the field, and it serves to prove the presence of productive reservoir between the first two wells. The basic theory used in the analysis of interference tests is based on the flow of a constant-compressibility liquid, which is mathematically expressed by Eq.6-42. This

632 104

10 5

106

107

10 8

109

10 3

I04

10

PD

J

----/" 161

....

I0-z

I0-I

1

I0

0z

tD/rDz Fig. 6-73. The line-source solution type curve.

line source solution is quite useful for interference data analysis (Ramey et al., 1973; Earlougher et al., 1977; Economides and Ogbe, 1987). For interpretation purposes it is desirable to have a log-log graph of the line source solution, such as that illustrated in Fig. 6-73. Because both ordinate and abscissa dimensionless parameters are directly proportional to real variables (Ap and t), a field graph plotted on the same size log-log coordinates must appear very similar to this line source solution (shown in Fig 6-73). For instance, from the definition of dimensionless pressure given in Table 6-11, taking logarithms, one obtains: log Pz~ = log

kh(p i -p(r,t)) kh = log ~ + log(p/-p(r,t)) aoqBt.t aoqBp

(6-91)

It can be observed from the above expression that the first log term contains all constants, whereas the variable pressure drop is contained in the second term. A similar expression can be written starting from the definition of dimensionless time (Table 6-11). Thus, as already stated, a log-log graph of the real pressure drop Ap vs. time t must look like a log-log graph of dimensionless pressure pz~vs. dimensionless time to. Frequently, the starting point for an interference test is to open the active well, which causes a pressure drop at the observation well. Next, the active well is shutin, creating a second pressure drop at the observation well. Figure 6-74 reproduces the Ramey's (1980) type curve. The graph includes the drawdown line source solution of Fig. 6-73, followed by buildup interference behavior described by various deviations,

633 10 tpD/rDz DIM. PROD. TIME

PD

\

161

162 10-1

1

10 2

103

104

(tp + At)D Ir~ Fig. 6-74. Ramey's combineddrawdown/builduptype curve for radial flow interference tests. each one of them corresponding to a particular producing time. Thus, combined drawdown/buildup interference test data should follow one of these combinations. It can be observed from this graph that there are important differences in pressure behavior for small and large producing times, resulting in a marked increase in resolution and a substantial reduction of the uniqueness of the interpretation problem. The above discussion, with specific regard to the interpretation of interference tests, has considered a radial flow case. Other possibilities are linear and spherical flows. Guti6rrez (1984) and Guti6rrez and Cinco Ley (1985) have presented a unified theory of interpretation for interference tests which consider the three main flow types mentioned above. These authors have presented, similar to Fig. 6-74, combined drawdown/buildup solutions for linear and spherical flows. Figure 6-75 illustrates their results for the linear case. Figure 6-76 shows drawdown interference solutions for the three flow types considered by the authors (i.e., linear, radial and spherical). The abscissa F1(PD) and the ordinate F2(tD) correspond to the definitions of dimensionless pressure and time for the three flow types considered as defined in Table 6-II. Figure 6-76 shows that for small times, the different flow geometries exhibit essentially the same pressure drop, and as time increases, pressure behaviors differ from each other. For example, for large times the linear dimensionless pressure drop shows a log-log linear behavior with a slope of 0.5, whereas spherical flow shows a constant pressure drop. In summary, Fig. 6-76 can be used as a type curve for the interpretation of drawdown interference tests, providing the information on the flow geometry prevailing during the test is given.

634

10 2 -

PDL_ k,bhAp 2XDL 2r B/~x tpD L /3kt p x--T=

10

(tp*At)D _ /3k(tp,At)

,~ x~ x

Od

ct ~---~---~

r

x2

I

..J C~

10-1

1

10

10 2

103

104

2

( tp + At )D I X o Fig. 6-75. Gutirrrez and Cinco Leys' combineddrawdown/builduptype curves for linear flow interference tests. (After Gutirrrez and Cinco Ley, 1985, fig. 5.)

Example 6-6. Transmissivity and diffusivity mapping from interference test data The information coming from a series of single-well tests (drawdowns and buildups) and of interference tests conducted in a heterogeneous, anisotropic reservoir was used to obtain a two-dimensional description of this system in terms of transmissivity and diffusivity (Najurieta et al., 1995). A mapping procedure was used to produce a regular mesh of grids from the scattered field information acquired from well testing. Two mapping methods were used during the study, and these gave similar results. The first calculates the minimal tension surface with a commercially available contouring program. A normal analysis was also used (Perez-Rosales, 1979). In the present example, a 4850 grid of points was calculated from the scattered data points. The final step was to interpolate between adjacent grid points and determine the contour lines. To obtain the desired property map, the following procedure can be used: (1) The area under study must be evaluated performing interference tests between adjacent wells. Each interference test must be analyzed to have a pair of apparent transmissivity and diffusivity values, which correspond to a specific measurement ellipse (area influenced during an interference test).

635 102

" Ji

10'.

1

.

.

J

LINEAR

.

/

"

lFi, ~

.

' RADIAL~

/

~

!

SPHERICAL FLOW

]d ~ I

I

1 I

ld a

#

I

10-1

1

10

102

103

104

F2 (to) Fig. 6-76. Drawdown interference-type curves for linear, radial, and spherical flows. (2) A scattered data set of each parameter is made by assigning calculated values to the corresponding measurement ellipses. The transmissivity map can be improved using data from single-well tests. In this case, transmissivity data are assigned to the corresponding measurement circle (area influenced during a single well test). (3) The high-to-low data exclusion rule is applied, in order to obtain the higher measured transmissivity and diffusivity in common regions. (4) Depending on the objectives of the mapping, transmissivity and diffusivity, values must be assigned to the external contour of the map by extrapolation to a weighted average of the measured values. Finally the map is calculated by means of the user's preferred method. In order to calculate higher resolution maps, it is recommended to design the test in such a way as to obtain narrow measurement ellipses between adjacent wells. The number of data points in each ellipse must be sufficient to ensure that the calculated surface fits the data. This number can be used to assign different statistical weights to each test, taking into account the data quality or input from other synergetic sources. An injection pilot test was carried out in the Abkatun field during 1986. To improve reservoir characterization, a series of interference tests were perfomed as shown by the arrows in Fig. 6-77. The interpretation of these tests was made in accordance with techniques already available in the literature (McKinley et al., 1968; Vela and

636

0

12

0

4

~

0

11-A

o 0

o

o5

84

Fig. 6-77. Interference tests carried out in the pilot injection project of the Abkatun field.

McKinley, 1970; Lescarboura et al., 1975; Ramey, 1975; Earlougher, 1977; Grader and Home, 1988) and were earlier reported by Najurieta et al. (1995). In the following example, a set of six transmissivity and diffusivity values shown in Table 6-XIV were used. The properties of the southem and western limits of the map were fixed using data obtained from other interference tests. The northern and eastern limits were established to constant values corresponding to the representative values of average field parameters. To enhance the preferential water injection TABLE 6 - X I V Transmissivity and diffussivity data of the Abkatun injection pilot test area Active well

Observation well

T [ m D - m / c P ] x 10-6

1/[cm 2 /sec] x 10-6

20 ll-A 43 62 64 43

4 20 20 20 20 62

1.2 0.803 0.0017 1.02 0.97 0.376

1.36 1.233 0.08 6.75 5.33 0.586

637 APPARENT DIFUSSIVITY (I0 A6 cmA2 / sec ) It

/

---- z

2132000

2131000

213oooo

2129000

2128000

2127000

584000

586000

588000

590000

Fig. 6-78.Apparent diffusivity map from the results of the interference test, Abkatun field. (After Najurieta et al., 1995, fig. 9, p. 183.)

APPARENT TRANSMISSIVITY[10^6 md-m/cp] 2133000

X

14

2132000

2131000

2130000

2129000

2128000

2127000

2126000 584000

586000

588000

590000

Fig. 6-79. Apparent transmissivity map from the results of the interference tests, Abkatun field. (After Najurieta et al., 1995, fig. 10, p. 183.)

638 flow in the reservoir, early-time transmissivity and diffusivity data were used as input in the scattered data input map, thus producing narrow-measuring ellipses. A total of 137 scattered data points were used in the mapping process in this example. The results are shown in Figs. 6-78 and 6-79. A preferential permeability trend can be seen from well 62 to well 20, and a low-diffusivity, low-permeability zone appears in the northeast. Permeability and porosity maps calculated from the diffusivity and transmissivity distributions were used as a convenient input to a bidimensional, two-phase numerical simulation of the pilot test previously discussed.

DETERMINATION OF THE PRESSURE-DEPENDENT CHARACTERISTICS OF A RESERVOIR

It has long been recognized that porous media are not always rigid and nondeformable (Meinzer, 1928; Jacob, 1940). This problem is usually handled by means of properly chosen "average" properties. This method only reduces the errors involved and generally does not totally eliminate them. A review of the literature indicates that most of the effort toward the solution of this pressure-dependent flow problem, has been focused on the direct problem (i.e., predicting the pressure behavior of the reservoir from knowledge of pertinent reservoir parameters). Raghavan et al. (1972) derived a flow equation considering that rock and fluid properties vary with pressure. This equation, when expressed as a function of a pseudopressurep.(p), resembles the diffusivity equation. Samaniego and Cinco (1989) have presented a s~olution for the inverse problem (i.e., identifying a pressure-dependent reservoir from test data, and evaluating reservoir parameters). In order to properly predict reservoir behavior, it is important to identify the pressure-dependent characteristics of the reservoir early in its life. The method of these authors is based on the analysis of drawdown and buildup tests, both for oil and gas wells. It allows the estimation of the pressure-dependent characteristics of the reservoir in terms of k(p) / (1 - ~ (p)), or if porosity is considered constant in terms of permeability. The basic case for drawdown testing is that of constant rock-face mass flow rate in a radial system. It has been demonstrated (Samaniego, 1974; Samaniego et al., 1977) that the transient well behavior for flow in a pressure-dependent system can be expressed, for all practical purposes, by: 1

PPD(l'to) = -~--(ln to + 0.80907)

(6-92)

where po and ppo are the definitions for the dimensionless time and pseudopressure, respectively given by Eqs. 6-93 and 6-94: to =

flk(Pi)t

r

(p)c,

(6-93) w

639

PPD (rD,tD) =

h(p,) {1 - ~b(p,)} {pp(pi)-pp(r,t)} (6-94)

ao qi P (Pi)

and r o (Table 6-II) and p.(p) are the dimensionless distance and pseudopressure, respectively, the latter defi~ed by Eq. 6-95: ,~

k(p) p (p)

PP(P) = Po { 1 -

~

(p) } p (p) dp

(6-95)

It has been found convenient (Samaniego, 1974; Samaniego et al., 1977) to express Eq. 6-95 in terms of a normalized pseudopressure p~p(p) defined by:

1 G(p)

{1 - ~ (p,)} ~, (p)

k(p,) p (p,)

=

pp(p)

(6-96)

Then, Eq. 6-92 can be written as:

P~ (Pwl)

+ log

=

pip(p)_ 1.1513ao

71

qi P ~i)

log

k~i)h(Pi)

~)(Pi)P (p,)c,(p)r2w

+ 0.86859 s

(6-97)

The slope m of the semilog straight line is defined as:

m =

OPlp (Pwf) -

1.513a

9 log t

q i ].1 (P i)

o k(Pi)h(Pi)

(6-98)

This slope can be re-written as:

dP~p(Pw/) 8Pw/

@w:

_

1.513a

o tog t

qi P (Pi) o k(p,)h(p,)

(6-99)

Deriving the definition of the normalized pseudopressure given by Eq. 6-96 yields:

@~' (pw:) _ {1 - O(p,)} u(p).

Op w/

k(p,) p (pi)

k(pw:)P (Pw:)

{ 1 - r (Pw:)} P (Pw:)

(6-100)

640 Substituting Eq. 6-100 into Eq. 6-99 yields:

k(Pwf)

-1.1513a o

9~ (,pwl) 9

q i P (Pi)

h(Pi):l-qb(Pwl)}

:l-~b(Pw:)}

1

P(,Pw:)(OPw~) ~

(6-101)

log t

Equation 6-101 is the expression that allows estimation of the pressure-dependent parameter k(p w/.) / {1 -~b ( pw/) } at any flowing time " It is assumed in this equation that the thickness h~pi ) and porosity ~b(pw l ) may be estimated from other sources (e " q," well logging). It has been demonstrated that currently available techniques provide accurate estimates of these parameters (Martell, 1989). In this expression and in all similar expressions in this section, the derivative c ~ w / ) / 0 log t is an instantaneous derivative (slope), at the time (or pressure) at which the pressure-dependent parameter is evaluated. Data on the pressure dependency of porosity indicate that, in most cases, its variation is small when compared to corresponding changes of permeability. Then, neglecting the dependence of porosity on pressure, Eq. 6-101 can be written as:

k(pws) = -1.1513ao

qi P(P)

~(Pwj)

1

(6-102)

c3log t Similarly, for a pressure buildup test in a pressure-dependent system, the necessary equation for analysis can be derived as previously described for drawdown tests. Again, if the pressure dependence of porosity is neglected then:

k~w~) = -1.1513a ~

qi P(Pi )

~(Pws)

h

p(pw)

1

(6-103)

~ Pws

+ At. O log (tp At ) An example of application of this method to simulated transient pressure data has been presented by the authors. It has been demonstrated that problems arise in the application of the proposed method at short times, because of the influence of effects such as wellbore storage and wellbore damage. In this respect, it is important to keep in mind that drawdown and buildup results are complementary (Serra et al., 1987). Drawdown analysis yields good estimates of the pressure-dependent parameter (k(p) / {1 - q~(p)} or k(p) at low values of pressure, and the buildup analysis yields good estimates of the parameter at high values of pressure. Consequently, by combining drawdown and buildup test results, one can obtain a good definition of the pressure-dependent parameter. The best way to obtain the stress-sensitive characteristics of the reservoir is to perform a drawdown

641 test at a high rate, one that results in an important pressure decrement, which then allows the estimation of the pressure-dependent parameter in a wide range of pressure. Once this test is concluded, it is recommended to carry out a buildup test to complement the drawdown results. Another way to circumvent this problem of estimation of the pressure-dependent parameter at early times during a test, due to the influence of wellbore storage and damage, is to apply the methods of "convolution" analysis to be discussed later. Such analysis makes use of rock-face rate measurements.

ANALYSIS OF VARIABLE FLOW RATE USING SUPERPOSITION, CONVOLUTION AND DECONVOLUTION (DESUPERPOSITION)

The analysis of a well test under variable rate contributes much information about the reservoir. This matter is strictly related to the "black box" problem discussed elsewhere (Gringarten, 1982; Aziz, 1989), which is gradually overcome as the "input" (rate) variation increases. The main difficulty with variable rate analysis is that it is no longer possible to perform a flow diagnosis by examining standard graphs because the usual characteristics may not appear. Thus, for flow diagnosis purposes, a process of desuperposition has to be used to calculate pressure response if the rate had been constant. This response has also been referred to as the "influence function" (Coats et al., 1964; Jargon and van Poollen, 1965). Figure 6-80 illustrates the constantrate pressure representation of variable rate test data. Next, a pressure drawdown test is considered under variable flow rate conditions (Fig. 6-81), where the flowing bottomhole pressure is a function of both flow rate and time. As mentioned before, the original theory for interpretation assumes constant flow rate conditions; hence, it is necessary to take into consideration the variation of the flow rate. Using the principle of superposition, an expression for the pressure drop APw(t) = Pi-Pw: (t) can be written as:

t

l

[I

v

Fig. 6-80. Constant-rate pressure representation of a variable rate test data. (After Home, 1990, fig. 3.25, p. fig. 63.)

642

Pi

wf

TIME Fig. 6-81. Variable flow rate test. N

Ap(t) = E

(qi - q i - , ) A p , (t --

t~_,)

(6-104)

i=l

where N is the number of flow rates for time t, and Apl(t) is the influence function (Coats et al., 1964), or in other words, is a unit flow rate pressure response. Multiplying and dividing by the time increment, At, and if N in this step-wise approximation goes to infinity (N --~ oo) and At likewise goes to 0 (At --~ 0), then one obtains:

APw(t) = f 'o 0q(r r) APl(t "c)d'r -

-

(6-105)

where ~ is a variable of integration. This integral given by Eq. 6-105 is known under several names: superposition integral, convolution integral, and the Duhamel principle. Generally speaking, the methods of interpretation for a test with variable rate involve a correction of pressure (Fig. 6-82) or/and a correction of the time scale (Fig. 683). Both types of corrections are based on the principle of superposition and can be referred to as deconvolution and convolution, respectively. This convolution integral is the basis of the method of calculating the variable rate from the constant rate response (Home, 1992). Deconvolution is the process of determining the influence function from the variable rate pressure response, APw(t), and the data about the rate variation, q(t). Deconvolution does not assume the flow model, whereas convolution is a method based on a predefined reservoir model.

643

Pi (AP)corr (AP)corr

Pwf

Pwfq

0 TIME Fig. 6-82. Pressure correction for variable rate.

Pi

/~(At)corr

(Pwf)q

Pwf

TIME Fig. 6-83. Time correction for variable rate.

644 Excellent papers have been published in recent years dealing with these two methods of deconvolution and convolution (Jargon and van Poollen, 1965; Bostic et al., 1980; Pascal, 1981; Kuchuk and Ayesteran, 1985; Meunier et al., 1985; Kuchuk, 1990; Simmons, 1990; Home, 1992). The writers will briefly describe the procedure presented by Home (1992) to solve the deconvolution problem. First, Eq. 6-105 is written in dimensionless form (Table 6-II):

p~(t~)

=

f

l~ 89

Ap,D(tD- v)dv

(6-106)

Taking the Laplace transform of Eq. 6-106 (van Everdingen and Hurst, 1949) tums the convolution integral into a simple multiplication:

p~ (s) = s ~-~(s) A~,~ (s)

(6-107)

The Laplace transform of the unit flow rate solution can be obtained from the previous variable rate solution:

SAp~D (S) =

s ~ (s) s~(s)

(6-108)

The inversion to real time can be done using the Stehfest (1970) inversion algorithm. It has been pointed out (Kuchuk, 1990; Bourgeois and Home, 1992) that this technique based on Laplace space deconvolution, expressed by Eq. 6-108, is often unstable at early time because the variable flow rate due to wellbore storage gives the following deconvolution equation:

S~ S A P ,D (S) =

(S)

- c~ s ~

(s)

- s

(6-109)

For the wellbore storage dominated period, fiwDis given by"

P~o (S) -

(6-11 O) S~C~

resulting in the denominator of Eq. 6-109 being zero, or oscillates around zero due to computation inaccuracies. The solution found by the authors is to add a small amount of wellbore storage CrD to stabilize the deconvolution of Eqs. 6-108 or 6-109"

Spwo (S) S@,~ (S)

=

- =

S ~ (S) + CrD$2

(6-111)

Kuchuk (1990) presented two well test examples which he refered to as "well-run field experiments compared with well tests we usually encounter". This comment

645 goes along with the conclusions of Sabet (1991) that deconvolution, although theoretically grounded, is about to become practical with present-day technology. Fair and Simmons (1992) reached similar conclusions, mainly, that deconvolution depends on extreme accuracy of rate measurement. They showed two examples, proving that small errors in the rate data may significantly alter the deconvolved response. One of these examples is taken from the paper of Meunier et al. (1985), showing that measured pressure data and deconvolved results using measured rate differ substantially. Example A in the paper by Kuchuk (1990) is analyzed by Bourgeois and Home (1991) using the Laplace transform technique previously outlined, and the results are also included in the work of Home (1992). Going back to Figs. 6-82 and 6-83, it can be stated that in cases where there is a skin effect, a correction is necessary in both pressure and time. It can be demonstrated that the influence function Ape(t) involved in Eq. 6-105 for infinite-acting radial flow conditions can be expressed, for units of the English system: APl (t) = 162.6

ooB Elog t + log kh

k

~ l.t c r 2 - 3.2275 + 0.86859 s w

(6-112)

For this case, in accordance with Eq. 6-104, Fig. 6-84 can be used to estimate the reservoir parameters and well condition (damage). As stated in previous comments, the influence function ZlP l(t ) depends on the reservoir flow model, that is, it is represented by the main terms t, t 1/4, t 1/2, and 1 / t 1/2 for radial, bilinear, linear and spherical

Z

{z~r

|

1

v

I

|

i

N ( q -i q ) i-i .Z

t:t

qN

Ap I ( t - t

i-i )

Fig. 6-84. Cartesian graph of the normalized pressure drop [pi-Pwf(t)] / qNVS. ~ [qi--qi-l) / qN] APi (t--

ti_l).

646

Pi Pw Pwf

/ Pws

Pwf&t: 0

-

~

At

i

t

P

TIME

Fig. 6-85. Pressure buildup for constant rate.

flows, respectively. In a more general way, the influence function APl(t) can be represented by a Pz~-tD relationship corresponding to a given reservoir system. The pressure buildup test is the most frequently used test because bottomhole pressure theoretically is measured under constant flow rate (q = 0) conditions (Fig. 6-85). It can be shown (Cinco Ley et al., 1989) that, for a buildup test: (1) the early shut-in time pressure data are dominated by the last flow rate; (2) the middle time data depend on both flow rate variation and producing time; and (3) the long time data depend exclusively on cumulative production during the flowing period (Fig. 6-86). Hence, the flow rate history before the shut-in should be known for a proper analysis. Conventional methods of interpretation (Homer and M-D-H plots) assume that the flow rate before shut-in is constant, and that the flow regime exhibited by the reservoir system is radial. For an infinite-acting reservoir, the M-D-H plot method produces a straight line in a graph Of Pws vs. log t at the beginning of the test. However, the data deviate because this technique does not take into account the effect of producing time (Fig. 6-87). The Homer plot method considers the effect of tP in such a way that a graph OfPw~vs. log At / ( t + At) produces a straight line that goes through all of the data free of wellbore storage effects. In other words, the Homer time includes a "correction" for the producing time effect. Other types of graphs also have been used to consider flow regimes other than radial, such as Pw~ vs. [(t + At) 1/2(At)l/2] ' Pw~ vs. [(t + At) '/4- (At)'/4], and Pws vs. [(At) -1/2- ( t + At)-'/2], for linear,

647

Pi

f(Q)

f(q,tp)

Pw

f ( q last) '

q(t)

--"

| Pwf

A

At=-2tp

t 2tp

o

t TIME

Fig. 6-86. Pressure buildup for variable rate and long shut-in time Pwfat At = O.

t cor r Horner M-D-H

Pws

log (6t) or log

[ At/Ctp

Fig. 6-87. A comparison of Homer and MDH graphs.

9L~t )]

648 bilinear and spherical flow, respectively. However, a flow-diagnostic process must be carried out for proper application of any of these types of graphs.

The superposition time graph For the case of variable flow rate before shut-in, buildup pressure can be expressed as"

tp Pws (At) =pi--lo q(v) Ap~ (tp + At- r) dr

(6-113)

where kp~ is the time derivative of the unit flow rate pressure response of the well-reservoir system. If the flow rate history is discretized, then Eq. 6-113 becomes: N

Pws (At) = P i - s

qi [AP l (tp d- A t - ti_l)- Ap, ( t + A t - ti) ]

(6-114)

i=l

This summation is called "superposition time function" tup and depends on the flow regime that dominates the pressure behavior of the system. Sometimes, summation of the superposition time includes the flow rate ratio qi / qN and the simplified form of the function Api, in such a way that Eq. 6-114 is given by: N

Pws (At) = Pi-- m (qN)

= ~ qi [g ( t Zil

+ At-- ti_l) -- g ( t + A t - tl) ]

(6-115)

where the function g is presented by the main terms already mentioned for different flow regimes that could prevail during a test. This equation shows that a graph Of Pws vs. the summation yields a straight line of slope--m(qN) and intercept Pi (Fig. 6-88). The slope is a function of the last flow rate qN and depends on reservoir parameters. The Homer method is a special case of this graph, that is, the superposition time reduces to the Homer time group when the flow is radial and the flow rate before shut-in is constant. Determination of the nature of the function g (i.e., log(t), t 1/2, t 1/4, U 1/2) requires a TABLE 6-XV Slope of the superposition time graph based on models

Model

mp D

Linear

aot"qNB pL kbh

Bilinear or radial

~,f=r, kh

Spherical

Or! qN

Bp

bf

aosphqNB p kr w

i

649

Pi

Pws

m

0 q i g ( t i ,At) Fig. 6-88. Superposition time graph.

flow diagnosis process through the first or second-derivative functions. The beginning and the end of the proper straight line can be found as shown in Fig. 6-89. On assuming that a flow j regime detected 9begins at time , t.. and ends at time t j, the ,oj . starting point of the straight-line portion m the superposmon time graph occurs at t p corresponding to At 9= t b j and ends at ts u p for tp + At = t e.j This last point will depend on both the flow rate history and the flow model exhibited by the reservoir. The superposition time can also be defined by using a P D - tD reservoir model (Fetkovich and Vienot, 1984)" N

Pw~ (At) = p,--mpD Z

qi [PD (tD + AtD--tDi-,)--PD (tD + AtD--tDi)]

(6-116)

i=l

where mpDc o m e s from the definition of PD (see Tables 6-II and 6-XV). The application of the superposition time graph requires a trial and error procedure to be able to identify the relationship between tD and t that produces a straight line. D r a w d o w n type c u r v e m a t c h i n g

The application of the type-curve analysis technique as a diagnostic process allows determination of the initial point of the semilog straight line and the detection of reservoir heterogeneities. Usually, drawdown type curves (pressure drop and time derivative of pressure) are used to analyze pressure buildup data, because of their

650

REGION OF VALIDITY OF THE SUPERPOSITION TIME GRAPH &t

&tej

&tbj J,

O

l

FLOW d

tbj

I

[tej

TIME SCALE FOR THE BEHAVIOR OF THE INFLUENCE FUNCTION 0

|

II

v

tp TIME

Fig. 6-89. Beginning and end of the straight line.

simplicity as compared to a buildup type curve which involves producing time as an additional parameter match. The application of drawdown type curves is valid under a certain condition, that is, the producing time must be large compared to the shut-in time ( t > l OAt). If this limitation is not satisfied, then data should be corrected. To match the drawdown type curves, a correction on the time scale can be made using the "effective time", At, as defined by Agarwal (1980), based on the radial flow equations that were previously discussed. This correction is similar to that involved in the Homer graph, and yields excellent results if the drawdown data before shut-in are free of wellbore storage, and the flow exhibited by the reservoir is radial. The effective time method can not be used for the pressure derivative analysis to correct the time scale. Another method used in the analysis of pressure buildup data to match the drawdown pressure drop type curves involves the desuperposition of the drawdown effects (Raghavan, 1980). This technique assumes constant flow rate during the producing period, and requires the initial and the bottomhole flowing pressures before shut-in. A proper application of some of the methods already discussed requires a diagnosis of the flow regimes exhibited by the reservoir during tests. The process becomes complex if the flow rate changes during the producing period. There are two techniques that allow identification of flow rates under these conditions: (a) the superposition time pressure derivative, and (b) the instantaneous source method.

651 Although the application of these techniques is well documented, there are some aspects related to the first method that deserve further consideration. The definition of the superposition time, as suggested by Bourdet et al. (1983, 1989), is based on radial flow equations and is given by"

tsup =

qN In "=

t

+At-it~l

(6-117)

p

Hence, the derivative of pressure with respect to tsup can be expressed as"

dPws dPw~

dAt

dtsup

zNq i { i=lqu

1

1

(6-118)

m

tp + A t - t .

l

tp + A t - t . t - I

At early shut-in times this equation becomes: dPws

dPws

-

dt sup

At~ dAt

(6-119)

Thus, as mentioned by Bourdet et al. (1983, 1989), the derivative of the shut-in pressure with respect to the superposition time approaches the first derivative function tAp'for pressure drawdown corresponding to the last flow rate. At large values of shut-in time Eq. 6-118 reduces to: dPws _ dtsup

qs (At)2 dPws 24 Q dAt

(6-120)

where Q is cumulative production during the flow period. According to the instantaneous source theory, the time derivative of the pressure buildup at long times is: dpws

n

dAt

24Q

d2Ap(qN)

qN

d(At) 2

(6-121)

where Ap(qN ) is pressure drawdown corresponding to rate qu" A combination of Eqs. 6-120 and 6-121 gives" dpw~ dtup

-

d2Ap(q N) (At) 2 ~ d(At) 2

(6-122)

It appears, therefore, that the superposition time derivative of the pressure buildup at large values of time approaches the drawdown second derivative function as defined by Cinco Ley et al. (1986). (See Cinco Ley and Samaniego, 1989.)

652 Equations 6-119 and 6-122 are valid for any flow regime. Thus, in Eq. 6-119 the superposition time pressure derivative of buildup data behaves, at early time, as the drawdown first derivative function; and at large shut-in times it follows the drawdown second derivative function. The first and second derivative functions for different flow regimes, in terms of real variables are as follows (Cinco Ley et al., 1986): Linear flow tAft = C1L t 1/2

(6-123)

2 Bilinear flow t a p ' = Clbft 1/4 t2 Izap,,I

=

C

lbftl/4

4

(6-124)

Radial flow tap'=

Clr

t2 Izap" I = c,~

(6-125)

Spherical flow t a p ' = Clsph t - m 3 t2 IAp"I = --~Clspht '/2

(6-126)

Wellbore storage and pseudosteady state flow t a p ' = Czw t t 2 ]Aff'l = 0

(6-127)

According to Eqs. 6-123 through 6-127, the first derivative is, in general, not equal to the second derivative function except for the radial flow case. Regardless of the flow model, the analysis of pressure buildup data can be performed through the use of type-curve matching of the superposition time derivative. However, two sets of drawdown type curves are required: the first and the second derivative function type curves. Figure 6-90 presents the first and the second derivative function type curves for radial flow under the influence ofwellbore storage and skin. It can be observed that they are completely different at early time, but both sets of type curves approach a single line when wellbore storage effects disappear. If the producing time is large, then pressure

653 10:'

C e2 s

10 ...

r

Q .,..1

O

FIRST DERIVATIVE

~

~~

,....

x

,.

D DERIVATIVE

161; I0 -l

9

1

.

10

,

10z

10 3

10 4

to/CD

Fig. 6-90. Type curves for the first and the second derivative function for radial flow condition, with skin and wellb0re storage.

buildup data match the entire drawdown type curve; however, if the producing time is small (i.e., flowing pressure before shut-in is still affected by wellbore storage), then the superposition time derivative follows at early time the first derivative type curve and after a transition period it follows the second derivative curve (see Fig. 6-91). Analysis of pressure buildup tests through the application of the superposition time derivative, Eq. 6-118 can lead to serious errors of interpretation. This occurs when the reservoir exhibits flow regimes other than radial. For instance, if the system is dominated by linear flow during the entire test, then the analyst can erroneously conclude that the system exhibits double-porosity behavior, because the superposition time derivative shows two parallel straight lines having slopes of 0.5. According to Eq. 6-118, the duration of the transition period between the first and second derivative behaviors depends on flow rate history and producing time. The deviation from the first derivative behavior occurs at approximately A t = O. 0 5 t . Here, P. a 5% difference between the curves is considered. The superposition time derivative follows the second derivative curve after A t = 2 t . Hence, the transition period extends for about two log cycles. P

A GENERAL APPROACH TO WELL TEST ANALYSIS

Undoubtedly, a key problem in the interpretation of well tests in carbonate formations is due to the extremely heterogeneous nature of these reservoirs. Pore space in such reservoirs is more complex than in sandstones. This problem presents a difficult

654

t

tD PD

dP w

dt sup

/~t

tD/C 0

Fig. 6-91. Schematic of match of pressure buildup derivative.

but challenging test to the well test interpreter. Sources of additional information, as indicated in Fig. 6-1, include: petrophysical studies, well logging (electric, sonic, and nuclear logs), and geological and geophysical studies. Thus, it is concluded that one must approach the interpretation of tests through an integrated approach. The discussion presented by Matthews and Russell (1967), with regard to state-ofthe-art of test analysis, is still valid in a general sense. Under favorable circumstances, present theories and analyses permit one to characterize a reservoir system, and good estimates of main damage and average pressure in the drainage volume of wells can be obtained by transient pressure test analysis. This is particularly true if the steps of the general approach of this section are followed. In regard to the question related to the identification of heterogeneities in a reservoir through the interpretation of pressure behavior, the answer is pretty much the same. It is not possible at this time to infer heterogeneity type and distribution solely from pressure data. Thus, there is a uniqueness problem in the interpretation of pressure analysis techniques. It is not possible for even the most experienced reservoir engineer to analyze a well test and in the absence of other additional information (geological, geophysical, petrophysical, etc.) to give a unique interpretation. Of course, this is not the correct approach to well test interpretation. Instead, the analyst must accomplish this task through an integrated reservoir characterization approach. The result is that in many cases one can obtain unique interpretations. The writers firmly agree with Matthews and Russell (1967) that when well test analyses are used in conjunction with all other additional information, the uniqueness problems are minimized. Different authors have addressed the question of a general approach to the analysis

655 TABLE 6-XVI General methodology of analysis 1. Estimation of unit flow rate response 2. Diagnosis of flow regimes 3. Application of specific graphs of analysis 4. Non-linear regression of the pressure data and simulation

TABLE 6-XVII Estimation of the unit flow rate response PRESSURE AND FLOW RATE DATA DECONVOLUTION OR IMPULSE INFLUENCE FUNCTION AND DERIVATIVES

TABLE 6-XVIII Flow diagnosis INFLUENCE FUNCTION AND DERIVATIVES Ap , ,

t A p'1 ,

t2 l A p7 [

TYPE OF FLOW AND DURATION

of well tests (e.g., Gringarten, 1985; Gringarten, 1987a; Ehlig-Economides, 1988; Cinco Ley and Samaniego, 1989; Ehlig-Economides et al., 1990; Horne, 1990; Stanislav and Kabir, 1990; Ramey, 1992). Such an approach consists of several steps, as indicated in Table 6-XVI: (1) Estimation of the influence function or unit flow rate response through the deconvolution process (Table 6-XVII). (2) Diagnosis offlow regime, which is usually accomplished through the use of the pressure derivative function (Fig. 6-24), and the second derivative as defined by Cinco Ley et al. (1986) and discussed herein. Figure 6-92 is a general graph of the second derivative for the main flow regimes encountered in a well test. Table 6-XVIII also illustrates the main parts of this flow diagnosis process. Figures 6-11 to 6-18 presented specific response characteristics that could be identified during a well test. It is strictly necessary to identify each portion of the response during a well test because specific portions are used to estimate specific reservoir parameters. As pointed out by Home (1990), often a good indication of reservoir response can be obtained by considering the responses preceding and following it, because the various responses follow a certain chronological order, as shown in Table 6-XIX. It is useful to verify that particular responses (e.g., wellbore storage, semilog

656

LINEAR

<1

BILINEAR

v

O9 m

o ._1

RADIAL

~

-1/2

SPHERICAL Log

t

Fig. 6-92. Second pressure derivative function for four different flow regimes. TABLE 6-XIX

Chronological order of the pressure responses during a well test

Radial flow

Early time

Intermediate time

Storage

Infinite acting radial flow

Closed boundary Sealing fault; Constant pressure Closed boundary Sealing fault; Constant pressure

Fracture

Storage

Bilinear flow

Radial flow

Double porosity

Storage

Double porosity behaviour

Transition

Radial flow

Late time

Closed boundary Sealing fault; Constant pressure

Source: After Home, 1990, table 2.2, p.35.

straight line, and boundary effect) appear in the correct order, and do not overlap each other (Fig. 6-93). One must remember those useful indicators in relation to transitions between flow regimes; for example, the 1.5 log cycles between the end of wellbore storage-dominated flow and the beginning of the infinite acting radial flow. Such cyclicity has become known as the 1.5 log cycle rule. With regard to this methodology steps in interpretation, one can use Agarwal's (1980) method to account for producing time effects in the analysis of buildup tests,

657 100

I

k c s

1

'

/

!

I

87. 67 1.427 x 10 -2 9.194

LCF 800

1.~9x1011

lO

PD

Storage

Boundary

1.5 log cycles

0.1 0.1

i

~

i

J

1

10

100

1000

.....

I

1x10 4

,,

I

1xlO 5

lx106

tDlC D Fig. 6-93. Correctly ordered pressure response for a well located in a bounded area. (AfterHome, 1990, fig. 3.12, p. 52.) as was discussed in the previous section related to deconvolution. In that section, the writers emphazised the correct interpretation of the superposition time pressure derivative of buildup data, one that behaves at early time as the drawdown first derivative function, and at late shut-in times, as the drawdown second derivative function. New derivative type curves have been presented by Onur and Reynolds (1988) and Duong (1989), their main advantage being that type-curve matching becomes a onedimensional, horizontal and vertical (respectively) movement of the field data on the type curve. This feature is especially important when hand-matching is attemped, because of the degree of freedom needed to obtain a match is reduced. Currently, during many tests the downhole rate is measured together with pressure, allowing the use of the convolution derivative (Ehlig-Economides et al., 1986; Joseph et al., 1986; Kuchuk, 1990). The convolution-derivative response reveals the earlytime, near-wellbore information, which normally is masked by wellbore storage effects. (3) Application of Specific Graphs of Analysis. Once the flow regime diagnosis process is completed, specialized or straight-line analysis may be used which is appropriate to the particular flow regime. The specific straight-line graphs of analysis and the correspondent estimation of parameters of interest have been previously discussed in this chapter, for the main flow regimes encountered during a well test (e.g., linear, radial cylindrical, spherical and bilinear flows: Figs. 6-5, 6-29, 6-8 and 6-10, respectively).

658 (4) Non-Linear Regression of the Pressure Data. This last portion of the methodology has to do with verification of the interpretation model. An excellent discussion on model verification has been presented by Gringarten (1985, 1987). First, a consistency check is needed to test that the model parameters estimated through the different methods of analysis (i.e., type curve and the specialized analysis), provide the same numerical values within a fixed tolerance. Second, a more stringent test consists of comparing a Homer graph of the pressure data with one predicted from information from the matched type curve. Third, test pressure history is simulated taking into account the actual rate data, using the selected model and the numerical values of the parameters computed from the analysis. In other words, the interpretation model selected from the analysis of a specific flow period must be valid for the entire test, and not for only that flow period. This procedure is very important with regard to revealing errors in flow diagnosis. When using computer-aided interpretation, analysis and possible model verification is done through non-linear regression. Home (1990, 1992) presented clear, excellent discussions of this subject. This method is different from graphical analysis techniques in that it employs mathematical algorithms to match measured data directly to a chosen reservoir model. The algorithm itself does not select the appropriate model. Instead, nonlinear regression requires specification of the reservoir model to be matched. This means that steps one and two of this procedure have to be taken at least before the start of this regression. Several of the main advantages of using non-linear regression are: (1) The procedure is free from the usual restrictions considered in graphical techniques (constant rate production and instantaneous shut-in) and can, therefore, be used to interpret more modem tests with variable rates and with downhole rate measurements. (2) This method fits all the data simultaneously, thus avoiding the problem of inconsistent interpretation of separate portions of the data, as can happen with the specific graphical analysis. (3) More complex models with more unknown reservoir parameters may be used for the matching process. (4) The method matches data that lie in the transition regions usually ignored by conventional specific graphical analysis, thus allowing interpretation of tests that would not have enough data for traditional analysis. (5) Last and very important (Ramey, 1992), mathematical fitting procedure allows statistical determination of the goodness of fit, thus,providing (in addition to the estimation of the reservoir parameters) a quantitative evaluation of the validity of the interpretation through the confidence limits or intervals. The matching process is carried out by changing the values of unknown reservoir parameters (e.g., permeability, skin factor, initial pressure, etc.) until the model and the data fit as closely as possible, by minimizing the sum of squares of the differences between measured pressure and model (calculated) pressure: N

Min E = ~ i-1

[Pmeasured(ti)--Pmodel (~-/i)]2

(6-128)

659 where the vector ~ includes the unknown reservoir parameters, and E is the objective function. Confidence intervals, in the manner described by Dogru et al. (1977) and Rosa and Home (1983), are functions of: (a) the objective function, (b) the degree of correlation between the unknowns, (c) the noise in the data, and (d) the number of data points relative to the number of unknowns. Usually with regard to modem well tests, which include much data available as compared to unknown parameters, the confidence interval depends mainly on E (i.e., how well the model fits the data, or the noise level of the data) or the correlation between parameters (i.e., a change in one parameter can be compensated by a change in another, still resulting in a good match). Confidence intervals are also helpful in illustrating the goodness of a chosen model, as well as an aid to resolve model ambiguity. In other words, matching a reservoir model that is inappropriate for the field data should result in confidence limits that are unacceptable for most (or all) of the estimates. Home (1992) presented an example where an infinite-acting radial flow response is used to match a double slope response caused by a sealing fault. His example emphasizes an important fact; that confidence limits obligate the interpreter to reject the analysis, even though the match is visually perfect to both pressure and pressure derivative functions. Ramey's (1992) findings could easily strike the conventional-oriented well-test analyst. Based on analysis of simulated and field cases, he firmly stresses the need for non-linear regression. One important conclusion is that the apparent Homer straight line is rarely the correct one. Ramey (1992) also states that it is not wise to depend on straight-line hand methods when regression with a proper model is possible. The confidence limits provide a superb quantitative measure of quality. In summary, non-linear regression with confidence limits on model reservoir parameters is a most powerful tool which provides important interpretation information, that otherwise is not available in conventional graphical well test analysis. This process should be followed by a final simulation of the test through the model and reservoir parameters obtained so as to prove that the interpretation was reasonable. On using the general methodology for the interpretation of a well test just described, following an integrated or synergy-oriented approach, the goal of characterizing a reservoir system and obtaining good estimates of its main parameters can, in most cases, be achieved under favorable circumstances.

A D D I T I O N A L W E L L TEST E X A M P L E S

Example 6-7. Pulse test in well pair A4-A8 (McKinley et al., 1968) A pulse test program was conducted in a dolomitic limestone having mainly vugular permeability. Formation oil has a gravity of 29 ~ API with negligible amounts of dissolved gas; all wells were on pump completed at the top of an anticline. Figure 6-94 shows the location of wells in the field. The dashed line on the right-hand side of the figure represents the approximate position of a fault limiting the reservoir. The pump was unseated at the observation well, the tubing was filled with LPG (to provide a liquid column to the surface), and a pressure gauge was attached directly to

660 C5.C

C]

C2

A5'

A9 A4

ARROWS CONNECT PULSE-TESTED WELL PAIRS POINT TO RESPONDING WELL

A6

A 2 ~'

AI

~.

A5 A

w

B]

B5 I

Fig. 6-94. Pulse test survey. (After McKinley et al., 1968, fig. 1, p. 313.)

the top of the tubing string. To keep pressure variation conditions in the test area unaltered, all neighboring wells were left on pump. The pressure response in well A4 to a pulse sequence at well A8 is shown in Fig. 6-95. Flow at well A8 was shut off at time t = 0 for 90 min, then opened to production for 90 min, etc. This flow rate sequence is shown by the dashed lines in Fig. 6-95. This pressure response at observation well A4 located 1867 ft (569 m) from the pulsing well (A8) is shown by the solid points in Fig. 6-95. The time lag, tL for the different pulses ranges between 3 0 40 min. The other parameter of interest in the analysis, the pressure amplitude Ap, ranges between 0 . 1 8 3 - 0.223 psi. The analysis method used each time lag tLi and amplitude APi to estimate the reservoir parameters of interest r/, T, and S. The analysis of the three-part results shown in Fig. 6-95 gives the following estimates:

661 0.60 9

PRESSURE

FLOW RATE 0.50

-

0.40

-

or) 13. Z

/

J J W I--

9 AP..

I

AP2"

/~-"~

",,

"

I

2"1" I :

0.50-

LLI (.9 Z "r"

a 13.. m

-

0.20

Z oo
bJ 0.10

-

-

800

b.I 1

O-

-IO0

f .......

I

I~

i I

I I

' I

-O.lO

9

9,-1, ".FF--I

0

I tL, I i

II

I

,,/

C--

I

I

I i

I I

'l:t / i 2

s I

lO0

200

I

',F

;

, tL| i 3 i

...J ....I I,I

I 300

- 4O0

LLI

or"

I

, I i I

I

I

0

400

-"J ii

500

TIME AFTER STARTING PULSE IN MINUTES Fig. 6-95. Pressure response at well A 4 to a pulse sequence at well A8. (After M c K i n l e y et al., 1968, fig. 2, p. 314.)

Part o f response curve First valley Second peak

r / = k / $/~c (mD-psi/cP) 2.44 x 109 2.44 x 109

T = kh / la (mD-ft/cP) 34,000 33,000

S = $ ch (ft/psi) 13.7 x 10-6 13.5 x 10 -6

Example 6-8. Pressure buildup test in well South Dome IS-21

South Dome well IS-21 was the first one to be fractured and acidized in the Shuaiba chalk reservoir, located in offshore Qatar (McDonald, 1983). Most of this reservoir is a low-permeability formation, with nonimpaired well productivity indices of about 0.1 bbl/D/psi or less. Consequently, to obtain commercial production the wells had to be stimulated. Results of studies have shown that massive acid-fracturing give good production enhancement results for this type of formation.

662

l 000-

0

Match Point

PwD :7.2 ~ Ap : I000 psi

cCr: I0

tDxf: 1.58 (~ or)

lO0-

u

.,::3

o

/ ,,

10 0.01

Time to start of semi-log si.line-50 hrs I 0.1

I 1

I I0

, I00

8t,hr Fig. 6-96. Pressure buildup data for well IS-21, PT-l-log-log graph. (After McDonald, 1983, fig. 1, p.

500.) Following the fracture stimulation of this well and an extended clean up, HRT (High-Resolution Thermometer) logs indicated the height of the fracture near the wellbore to be 76 ft (23 m). Immediately after, production test 1 was carried out and consisted of a 5.5 day flowing period during which time the productivity index declined from 5 bbl/D/psi to 1.9 bbl/D/psi, followed by a 2-day pressure buildup. Buildup and related additional data for this test are shown in Table 6-XX. The log-log graph of Ap vs. At for the early-time data from the buildup test in this well (Fig. 6-96) shows the characteristic shape of a highly conductive fracture, with a log-log slope of slightly less than 0.5. The data were matched using the type curves presented by Cinco-Ley et al. (1978), with a dimensionless fracture conductivity of (k:/5~o) = 10re. From the match shown in this type curve, the Homer semilog straight line appears to begin after 30 hr of shut-in time. Based upon this information, Fig. 697 shows the semilog analysis of the pressure data for this test. The slope m is 186 psi/ cycle. Using Eq. 6-47, the formation conductivity kh is (see Table 6-XIX):

kh =

162.6 (870 STB / D) (1.22) (1.5 cP) (186 psi / cycle)

= 1,390mD-ft

Assuming that the producing interval, h, is the height of the fracture inferred from HRT logs (76 ft; 23 m), then the average permeability is calculated as 18.3 mD. The skin factor can be calculated by means of Eq. 6-85, and the P~h~value of 1853 psi is estimated from Fig. 6-97" s = 1.1513

F 1853L

1850

186

(18.3mD)

]

)

- log I 0.21 (1.5cP)(10.4 x 10-6 psi-')(0.51 ft)2 + 3.2275

This value is considered as indicative of a satisfactorily stimulated well.

=-4.7

663 TABLE 6-XX Buildup data for well IS-21, PT-1 Reservoir thickness, h, ft Porosity, $, fraction Viscosity, p, cP Total formation compressibility, c,, psi -~ Formation volume factor, Bo Wellbore radius, rw, ft Effective production time, tp, hr Well flow rate, q, STB/D Depth of pressure reading, D, ft subsea

76 0.21 1.5 10.4 • 104 1.22 0.51 263 870 4618

At (min)

Pw~(psi)

At (hr)

pw~(psi)

0 1 3 5 7 10 15 20 25 30 40 50 60 70 80 90 105 120 150 180 240 330

1850 1870 1879 1884 1889 1896 1905 1912 1917 1922 1930 1938 1942 1949 1953 1957 1963 1967 1977 1986 1998 2013

8 9 10 13 16 20 24 30 36 42 48

2032 2041 2047 2063 2077 2093 2106 2121 2135 2146 2154

Source: After McDonald, 1983; courtesy of SPE of AIME.

From the type curve pressure match of the log-log graph of Ap vs. At [(PwD)M= 7.2 at (Ap) M = 1000 psi] formation flow conductivity is calculated through the use of the definition of dimensionless pressure (Table 6-11):

kh = 141.2(870 STB / D)(1.22) (1.5cP)

7.2 1000 psi

/

= 1620 mD - ft

This value is reasonably close to the kh derived from the Homer graph; therefore, enhancing confidence in the analysis. The permeability estimated in this case is 21.3 mD. Another parameter of interest, the fracture half-length, is calculated through use of the definition of dimensionless time and the type curve time match of the log-log graph (Fig. 6 - 9 6 (tDxy)M = 1.58 at (At)M = 10 hr).

664 2 200

2 100

-

n

~

(/)

"

3 C~

2 000

-

o o

m - 186 psi,/cycle

0 0

1 900

_o

0

~176

Pl~hr /

At, hr 10

I I

1 800

J

looo

20 J

48 I

lb

( tp§ At)/ t Fig. 6-97. Pressure buildup data for well IS-21, PT-1-Homer graph. (After McDonald, 1983, fig. 2, p.

500.) 2.637 • 10-4 (21.3mD)(10 hr) X/ =

0.21( 1.5cP)(10.4 x 10-6 psi-')(1.58)

7. ~/2 = 104 ft = 31.7m

J

This value differs notably from the design value for of x l of 1600 ft (488m) The fracture conductivity is computed from the type curve match and the definition for the dimensionless fracture conductivity (k/b:)D (= (k/b//kx:)"

k/b/= 10re (21.3mD) (104 ft) = 69,592.6 mD - ft This completes the analysis. Two final comments are worthwhile. First, the analysis was presented as discussed by McDonald (1983), prior to introduction by Bourdet et al. (1983) of the pressure derivative function. Results can be improved if this technique is used in the analysis. Second, the real life fact is that fracture design characteristics often differ from estimates obtained through analyses of well tests, a problem that commonly is also emphasized by differences in well productivity design projections with respect to field measured flow rate behavior.

Example 6-9. Pressure buiMup test in a partially penetrating oil well (Barr6n, 1991) A pressure buildup test was carried out in well Tecominoac~in 446, which produces from a carbonate formation in southeastern Mexico. Computer-aided analysis of this test was performed through the use of the SAPP system (Martinez et al., 1991). The

665 4.88

4.85

j

(-9

J

C/3 -

-

rn

O

4.80

i

o r162 Q.

4,75

i

4.72

I 0

I 0.004

i

I 0.008

SHUT-IN

0.012

0.016

0020

TIME , A t , H R

Fig. 6-98. Cartesiangraph ofbottomhole shut-inpressure, Tecominoac~in446 well. (AfterBarr6n, 1991, fig. 6, p. 89.) main reservoir and fluid data, in addition to the pressure data recorded, are presented in Table 6-XXI. Figure 6-98 is a cartesian graph of the bottomhole shut-in pressure Pws vs. shut-in time At, indicating that the correct flowing pressure just before shut-in Pw/(At = 0) is approximately 4722.35 psig. Figure 6-99 is a graph of the pressure derivative function vs. shut-in time, observing four different flow periods, listed in chronological order as follows: (a) wellbore storage-dominated flow, (b) early radial flow influenced by the perforated interval, h,(c) a transition flow period, and (d) pseudoradial flow governed by the formation thickness h. This graph completes the flow diagnosis process for the test. Figure 6-100 shows a log-log graph of the pressure drop and of the pressure derivative function vs. shut-in time. These results were automated type-curve matched with an infinite-acting radial flow model and fully penetrating well as indicated by continuous curves, which explains the poor fit of the field data corresponding to the first three flow periods mentioned. The oscillations shown at the end of the test are believed to be due to reservoir temperature being too close to the maximum gauge operating temperature of 300 ~ F (Table 6-XXI). Figures 6-101 and 6-102 present Miller-Dyes-Hutchinson graphs of the pressure buildup data, which emphasize the early radial flow and the late radial flow, respectively. These graphs are justified based on the very large production time: t = 34,824 hr. The semilog straight lines are traced based on the flow diagnosis results already discussed with regard to Fig. 6-99.

666 2.8

000. 0 o

2.5

oj

<::!

_ o

q)

0 ~ %~176176176176

2.0 o

1.5

,

I

-2.5

i

o

1

-1.5

-0.5 LOG

1.5

0.5

At

Fig. 6-99. Log-log graph of the pressure derivative function vs. shut-in time, Tecominoac~in 446 well. (After Barr6n, 1991, fig. 27, p. 90.)

10 4

RESULTS FLOW CAPACITY, kho a d - f t

TRACING PAPER-

PER,tASILITY.,,

FIELD DATA Q.

-~ c

= 2042

r.16

.~

SKIN FACTOR M[LLBORE STORAGE, C, DIMENSIONLESS WELLBORE STORAGE. CD BEGINNING SEMIL06 STRAIGHT LINE. tbssL . HRS

:

~Type curve f-~

0.82 30.4 = 1947.6

:

0.70

10 3

.....

,l~k. . . . . .

Q.

102 ~

~

....

.... - ! , -

_

A .,,,

xxl~ax~

10 10-3

10-2

10 -1

SHUT-

10 ~

IN

10

10 2

TIME, At,HR

Fig. 6-100. Log-log graph of the pressure drop and the pressure derivative function vs. shut-in time, Tecominoac~in 446 well. (After Barr6n, 1991, fig. 28, p. 91.)

667 5 830

I

'

I

DATA: RATE,q, STB/D

5 720

= 4641 1.73 = 0.23 . 20.96x10 "~ : 0.27 = 0.03 131.20 = 4720.82

FOR~TION voL.F.,Bo

56]0

VISCOSITY, /~o' cp i CONPRESSIBILI T Y , - c t , p s i " I~LLBORE RADIUS, - r . , FT POROSITY, O, FRACTION" THICKNESS,h c ! f t pwf(&t=O), psi

I !I

Jr"

5500 , 5390

/

5 280 ,

3= 0.

tbssl = 0.203 HRS

it x

5 170 ,

~x

5 060

~

•

4950

RESULTS FORMATION CONDUCTIVITY, k h , m d - f t = PERMEABILITY, k, md = SKIN FACTOR, S : (Ap)s, psi SLOPE m, psi/cycle = pws(1HR), psi :

x~

4840 . /

Ixx~ x

4730 l _

x

1099 8.38 -2.64 -612.6 266.4 5609.5

x

l

10-2

10-3

10-]

10 o

SHUT-IN

TIME,

6L,

10 ]

10 2

HR

Fig. 6-101. MDH graph of the pressure buildup data, early radial flow, Tecominoac~in 446 well. (After Barr6n, 1991, fig. 29, p. 92.)

5 830 I 5 720 5 610

DATA:

l

RATE,q, STB/D = 4441 FORMATION VOL.F. ,B 0 1.73 -VISCOSITY, cp 1 = 0.23 2 0 . 9 6BXLx I TY, l OVct, ' 6 pCs i "O N P R= E S S I I MELLBORE RADIUS, r , FT = 0.27 I POROSITY, r FRACTIONW = 0.03 I - THICKNESS, h , f t = 285.20 puf(kt=O), psi = 4720.82

._,

5 500

~

/ ' ~ x

~

/

xx

x

x xlx

t bsst = 3 4 . 5 5

HRS

I x

xx xx

" 5 390 x

i#i

3 5

280

'Y

x x

5 170 x x

5 060 4

x

950

xx

RESULTS FORMATION CONDUCTIVITY, kh, m d - f t = 2388 PERMEABILITY, k , md : 8.37 SKIN FACTOR, s 2.16 (4p)s, psi 230.5 SLOPE m, p s i / c y c t e 122.6 Pws(At=IHR), psi = 5641.4

x x

4 840

x

x-~

4 730 lO-

3

, 0 -z

10-1 SHUT - I N

lO 0 TIME

, At,

1 101

10 2

HR

Fig. 6-102. MDH graph of the pressure buildup data, late radial flow, Tecominoacan 446 well. (After Barr6n, 1991, fig. 30, p. 92.)

668 5 830

DATA: RATE,q,STB/D FORMATION VOL.F.,B 0 VISCOSITY, ~n, cp CONPRESSIBILITY,-ct, psi "1 IdELLBORE RADIUS, - r , FT POROSITY, 4, FRACTIONw THICKNESS, h 9 pwf(&t=O), psi t p , HRS

5 720 5 610

= = = = = =

4441 1.73 0.23 . 20.96x10 "6 0.27 0.03 131.20 4720.82 34824

//J_x

5 500 -

J

u*J

5 390 u~

3= 5280

x xxxXXXXXXX~~

t bss~,= 0 . 6 9 4 HRS

-

J

C2.

5170

J

J

5 060

x .x

I1 x

xx

4950

x

x

RESULTS FORMATION CONDUCTIVITY, PERMEABILITY, k, SKIN FACTOR, s (Ap)s, psl FLOW EFFICIENCY, FE p~, psi SLOPE m, p s i / c y c l e t

X

X

4 840 '

x= x

X

x

4 730

I0- r

I0- 6

kh, m d - f t = 1094 = 8.33 -2.66 = -618.9 1.29 = 6825.8

267.7

I0- 4

I0- 5

i0-3

( tp + A t ) / A L

Fig. 6-103. Homer graph of the pressure buildup data, early radial flow, Tecominoacfin 446 well. (After Barr6n, 1991, fig. 31, p. 93.) 5 830

f

5 720

5 610 x

5 500 a.

~=

5 390

J

x x

x

x

x

t b s s l = 14.251

x

HRS

x x x

x

x xx

5 280

x

DATA: RATE,q,STB/D FORMATION VOL.F.,B o VISCOSITY, ~_, cp

x

5 170

= = ,

CONPRESSIBILITY,UCt, psi " l

UELLBORE RADIUS, - r , FT POROSITY, 4, FRACTION~ THICKNESS, h, f t p w f ( l t = O ) , psi t p , HRS

5 060 X X

l

4 950

RESULTS FORMATION CONDUCTIVITY, kh, ~ - f t PERNEABILITY, k, SKIN FACTOR, s (Ap)s, psi FLOW EFFICIENCY, FE p ~ psi SLOPE m, p s i / c y c L e i

X

x x

4 840

x

x

9

xx

4 730

i0-7

10-6

10-5 ( tp *bt

10-4

= =

=

4441 1.73 0.23 -6 20.96x10 0.27 0.03 285.20 4720.82 34826

= 2389 = 8.38 : 2.17 230.9 : 0.81, = 6198.0 = 122.5

10-3

)/At

Fig. 6-104. Homer graph of the pressure buildup data, late radial flow, Tecominoac~in 446 well. (After Barr6n, 1991, fig. 32, p. 94.)

669 Figures 6-103 and 6-104 show Homer graphs of the pressure buildup data, which again emphasize early and late radial flows, respectively. The semilog straight lines are traced based on the flow diagnosis results discussed with regard to Fig. 6-99. Table 6-XXII is a summary of the results obtained from the interpretation of this test. It can be concluded that results from the type curve analysis, and the results of the specialized Miller-Dyes-Hutchinson and Homer analyses are in agreement with regard to permeability. The skin factor, and its strictly related pressure drop due to the skin damage, APs, do not agree from the type curve match to those of the specialized semilog methods. This is due to the fact that the partially-penetrating well behavior was matched with a fully-penetrating well pressure response solution. The nearby formation presents stimulation conditions, as indicated by the negative true skin factor, Str, caused by stimulation to the completed portion of the well. Another important piece of information that can be obtained from this test is the effective formation thickness of the well, information that is of particular use when the well does not fully penetrate the formation. The writers use estimations for the early m e and late radial m I flOWS (266.4 psig and 122.6 psig, respectively, in the following expression derived by Raghavan and Clark (1975): mih

- 1

(6-129)

me hc

m~

(6-130)

h = ---5~h c

ml

Substituting values in this expression yields" h =

266.4 / 122.6

131.2 = 285.2 ft = 87 m

The estimate for h derived from well logging is 360 ft (110 m). It is believed that the value estimated from the analysis of the test, 285.2 ft (87 m), is more reliable because it was computed under dynamic flow conditions of the reservoir. For the flow conditions of this well, Eq. 6-54 for the skin factor can be simplified, resulting in the following expression: h s = s c- ~ s h tr

(6-131)

c

Thus, h s = s-~s c h '~ r

Evaluating this expression:

(6-132)

670

TABLE 6-XXI Pressure buildup data for well Tecominoacdn 446 Reservoir and fluid data

Initial pressure, Pi Temperature, T, ~ Bubble point pressure, Pb Initial solution gas--oil ratio, Rsi Formation volume factor, Bo Viscosity,/~o Oil compressibility, c o Porosity, Water saturation, S Wellbore radius, r w Perforated interval, h c Flow rate, q Producing time, t Depth (of the middle point of the perforated interval), D

9812 psig 289 3545 psig 196 fi3 / ft 3 1.725 0.235 cP 20.9610 -6 (psi) -I 0.032 0.106 0.27 fi 131.2 ft 4441 STB/D 34824 hr 5995 m

Buildup data

Time, At (hr)

Pressure, Pws (psi)

Time, At (hr)

Pressure, Pws (psi)

0 0.0050 0.0111 0.0119 0.0138 0.0161 0.0180 0.0211 0.0249 0.0268 0.0310 0.0329 0.0386 0.0441 0.0496 0.0566 0.0663 0.0805 0.0901 0.0952 0.1152 0.1402 0.1566 0.1775 0.1983 0.2230 0.2483 0.2810 0.3150 0.3520 0.3966 0.4466 0.5294

4753.64 4765.12 4808.12 4815.59 4833.90 4852.71 4871.73 4901.86 4938.12 4958.06 4993.04 5009.06 5053.58 5095.76 5135.04 5178.35 5230.32 5271.67 5302.94 5328.29 5353.28 5379.79 5394.15 5408.75 5420.95 5435.15 5447.92 5462.98 5476.42 5489.02 5503.10 5516.90 5536.03

1.4811 1.6811 1.9477 2.0811 2.2811 2.4811 2.7144 2.9144 3.1644 3.4144 3.7144 3.9144 4.1144 4.4144 4.6114 4.9144 5.4477 6.7841 6.9175 8.1494 8.9397 9.9064 10.9063 11.9897 12.9063 13.9064 14.7397 15.4111 15.9111 16.9111 17.9111 18.9111

5639.23 5649.38 5661.26 5666.27 5672.89 5678.82 5685.04 5690.12 5695.02 5700.36 5705.23 5708.45 5711.63 5715.71 5718.57 5722.20 5728.66 5740.19 5741.31 5751.86 5757.54 5763.16 5768.94 5773.43 5777.28 5781.37 5784.52 5787.06 5788.82 5792.04 5795.06 5798.06

671 TABLE 6-XXI Buildup data (continued) Time, At (hr) Pressure, Pws (psi) 0.6325 0.7325 0.8841 0.8241 1.0408 1.1811 1.3477

5555.46 5571.37 5583.13 5594.81 5607.05 5618.74 5630.72

Time, At (hr)

Pressure, Pw~(psi)

19.9858 20.9025 21.9183 22.8927 24.0180 24.1680

5800.76 5802.90 5805.74 5808.13 5810.69 5811.03

TABLE 6-XXII Results obtained from the analysis of the buildup test in well Tecominoac~in446 Parameter k h (mD-ft) (mD) s (Ap)s, psig FE kr

Type Curve (Fig. 6-100)

MDH analysis (Fig. 6-102)

Homer analysis Fig. 6-104)

2042 7.16 0.82 102.1

2388 8.37 2.16 230.5 --

2389 8.38 2.17 230.9 0.84

Str

Other results

- 2.64 285.2 /

s

c

= 2.16-

(-2.64) = 7.90 13112

Now, using the Papatzacos (1987) method for the estimation of the partial penetration pseudoskin factor, an estimate of the vertical permeability can be obtained. Dimensionless thickness hwo is defined as:

hwD -

he j .kr rw

(6-133)

k

The vertical permeability, k, can be expressed from the above definition:

( c/2

k=k~

(6-134)

hwDr w

The Papatzacos expression for the estimation of the pseudoskin, s c, is given by the expression:

Sc=

l;

where:

-1

In

~

~

+--ffln

I

2+b

B

1

(6-135)

672 b=h/h

(6-136)

A = lc/(ZID + b / 4 ) B = 1/(zn~ + 3 b / 4 ) Zl D

=z1/h

(6-137)

and z~ is the height from the top of reservoir to the top of the producing interval. For the conditions of this well:

zl -

h

h

2

2

w

(6-138)

From the previous expression for s"

1Eb(A-111]

2b hwz ~ -

s - ~ In c b

2+b

B

1

exp

(6-139)

(1/b-l)

Substituting values yields: 285.2 Z 1 --~

2

131.2 --

"- 77

2

77 zlz~ =

= 0.27 285.2

A = 1 / (0.27 + (0.25)(0.46)) = 2.597 B = 1 / (0.27 + (0.75)(0.46)) = 1.626

7.90hwz~ =

2(0.46)

(1 / E~ In

0.46

2+0.46

exp (1 / 0 . 4 6 - 1)

hwz~ = 2297 (131.2) k

-

(8.38)

/2 -

(2297) (0.27)

o.38 mO

1)11

1.626- 1

673 The vertical permeability can also be estimated using the method of Cinco Ley et al. (1975).

C O N C L U D I N G REMARKS

This chapter reviews relevant aspects of pressure transient analysis theory. It is hoped that this discussion will provide the reader with the basic knowledge necessary to apply the theory of pressure transient analysis to well tests in carbonate reservoirs. Undoubtedly, a key problem in the interpretation of well tests in carbonate formations is due to the extremely heterogeneous nature of these formations. Pore space systems in carbonate reservoirs are usually more complex than in sandstones. This introduces a difficult but challenging problem to the well test interpreter. It is imperative to approach this task through an integrated effort as discussed with specific regard to Fig. 6-1, where the interpreter evaluates the test using all related information of interest available: geophysical, well logging data, geological, and petrophysical. It is expected that this area of petroleum engineering that has experienced very dynamic growth for the last 30 years will continue its fast development, giving as a result better interpretation techniques that will greatly help the characterization of complex carbonate reservoirs. The latter is an imperative step to be taken in an optimization study of a reservoir, and is of special current importance when drilling is carried out under more hostile conditions.

NOMENCLATURE

A An

b B

c~

cy Ct

CA Clws

Clr C1L

Cbj Clsp C2w C l rpss C2rpss

D DF

= drainage area = Table 6-V, parameters of the dimensionless pressure response for spherical flow at constant rate producing conditions, in a finite closed reservoir = )/~P.2eD "~" (reD-- 1)2 / {~2,[~t2p.2, eD -[- (l"2eD "1- re D _ 1 ) 2 ] } = linear reservoir width = formation volume factor = pore volume compressibility = modified pore volume compressibility, Eq. (6-68) = total system compressibility, Eq. (6-67) = shape factor = constant for wellbore storage-dominated flow, Eq. (6-15) = constant for radial flow, Eq. (6-20) = constant for linear flow, Eq. (6-21) = constant for bilinear flow, Eq. (6-23) = constant for spherical flow, Eq. (6-25) = interception constant for spherical flow, Eq. (6-25) = constant for pseudosteady state flow, Eq. (6-27) = interception constant for pseudosteady state floF, Eq. (6-27) non-Darcy flow coefficient = (sJ3kmps c / h Tc)rJ"~(1/pr2)dr = damage factor, Eq. (6-59)

674

E Ez (x) FE h h k k Ja Ji N c

s

m m* mobf moL

m osph n P P p*

Pw! Pws

Pp(P) plp (p)

Pe

r?'o r

skin

Ap' Ap" Po q

Q I" rs rw r wa

S s sr s! sp Str

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

objective function, Eq. (6-128) exponential integral, Eq. (6-43) flow efficiency, Eq. (6-56) thickness thickness of completed interval, Fig. 6-30c permeability permeability of the damaged region, Fig 6-30a actual productivity index ideal productivity index total number of different flow rates, Eq. 6-104 slope of the semilogarithmic radial flow pressure behavior, Eq. (6-47) reservoir linear pressure trend, Eq. (6-86) slope of the bilinear flow graph, Eq. (6-11) slope of the linear flow graph, Eq. (6-7) slope of the spherical flow graph, Eq. (6-9) direction normal to the surface, Eq. (6-3), or exponent of the pressure derivative function, Eq. (6-29) pressure average pressure extrapolated Homer graph pressure for infinite shut-in time flowing bottomhole pressure shut-in bottomhole pressure pseudopressure or real gas potential, for gases, Eq. (6-63), and for liquids, Eq. (6-95) normalized liquid pseudopressure, Eq. (6-96) pressure drop influence function, Eq. (6-104) pressure drop error due to wrong initial pressure estimation pressure drop due to the skin factor pressure derivative function, Eq. (6-31) second pressure derivative function dimensionless pressure dimensionless gas pseudopressure = kh [pp(pi) --Pp(Pwf)] / Otg qsc T, Eq. (6-71) flow rate cumulative production, Eq. (6-120) radial distance radius of the damaged region, Eq. (6-49) wellbore radius apparent wellbore radius, Eq. (6-61) Laplace space variable, or formation storage skin factor, Eqs. 6-48, 6-49 and 6-53, or external boundary, Eq. (6-3) pseudoskin factor due to partial completion pseudoskin factor due to a hydraulic fracture pseudoskin factor due to perforations true skin factor due to damage of the formation

675

ss

wp

t tD

t

Ate T W w

n

O~g

= pseudoskin factor due to well inclination = time = dimensionless time = producing time = shut-in time = Agarwal's (1980) effective time = temperature or transmissivity = gas compressibility = roots of Eq. 47 of Chatas (1966), p. 106 = Table 6-V, roots of Eq. 47 of Chatas (1966), p. 106 = pseudopressure unit conversion constant for radial flow, Eq. (6-72), 5.03332 x

r

n

a o Ot

osph

aoL

8t

17 //

/./ Y r,

10 4

- Table 6-IV, roots of Eq. VII-7 of van Everdingen and Hurst, 1949, p. 319 = pressure unit conversion constant for radial flow, Eq. (6-40), 141.2 = pressure unit conversion constant for spherical flow, Eq. (6-8) = pressure unit conversions factor for linear flow, Eq. (6-7), 887.1 = Table 6-IV, roots of Eq. VII-15 of van Everdingen and Hurst, 1949, p. 322 = time unit conversion constant, 2.637 x 10-4 = pressure unit conversion factor for bilinear flow, Eq. (6-11), 34.97 --- total interval used in the smoothing pressure, symmetrically located with respect to the point of interest, Eq. 6-88 - porosity = diffusivity = Table 6-IV, roots of Eq. VII-21 of van Everdingen and Hurst, 1949, p. 322 = viscosity = variable of integration, Eq. (6-105) = Euler constant, Eq. ( 6 - 4 4 ) , - 0.5772 = Table 6-V, roots ofeq. 52 of Chatas (1966), p. 108

Subscripts

t

= -= = = = = =

unit time reference beginning or bilinear dimensionless effective or end initial or index index late laminar oil radial standard conditions total

tr

-

true

1 0 b D e i

J l lam o r sc

676

Superscripts . , "

= e x p o n e n t (Eq. 6 - 2 9 ) = first d e r i v a t i v e = second derivative

Si Metric Conversion Factors b b l x 1 . 5 8 9 873 cP x 1.0" flx 3.048* ft 3 x 2 . 8 3 1 6 8 5 mD x 9.869 233 psi x 6 . 8 9 4 7 5 7 p s i -1 x 1 . 4 5 0 3 7 7 psi 2 x 4.753 8 ~

x 5/9

E-01 = m 3 = Pa.s E-01 = m E-02 = m 3 E-04 = gm 2 E+00 = kPa E - 0 1 = k P a -1 E+01 -kPa 2 E-03

E+00 = K

REFERENCES

Adams, A.R., Ramey, H.J.Jr. and Burgess, R.J., 1968. Gas well testing in a fractured carbonate reservoir. J. Petrol. Techn., 28(10): 1187 - 1194. Agarwal, R.G., 1979. Real gas pseudo-time- a new function for pressure buildup analysis of MHF gas wells. Paper SPE 8279, 54th Annual Fall Technical Conference and Exhibition, Las Vegas, NV, Sept. 23-26. Agarwal, R.G., 1980. A new method to account for producing time effects when drawdown type curves are used to analyze pressure buildup and other test data. Paper SPE 9289, 55th Annual Fall Technical Conference and Exhibition, Dallas, TX, Sept. 21 - 24. A1-Hussainy, R., Ramey, H.J.Jr. and Crawford, P.B., 1966. The flow of real gases through porous media. J. Petrol. Techn., 18(5): 637 - 642. Aminian, K., Ameri, S., Abbit, W.E. and Cunningham, L.E., 1991. Polinomial approximations for gas pseudopressure and pseudotime. Paper SPE 23439, Eastern Reg. Mtg., Lexington, Kentucky, Oct. 22 -25. Aziz, K., 1989. Ten golden rules for simulation engineers. J. Petrol. Techn., 41 (11): 1157 - 1158. Barr6n T.R., 1991. Factores de da~o en pozos desviados parcialmente penetrantes. M.Sc. report, School of Engineering, National University of Mexico, 139 pp. Bostic, J.N., Agarwal, R.G. and Carter, R.D., 1980. Combined analysis of postfracturing performance and pressure buildup data for evaluating an MHF gas well. J. Petrol. Techn., 32(10): 1 7 1 1 - 1 7 1 9 . Bourdet, D., Whittle, T.M., Douglas, A.A. and Pirard, Y.M., 1983. A new set of type-curves simplifies well test analysis. World Oil, 196(4): 9 5 - 106. Bourdet, D., Ayoub, J.A. and Pirard, Y.M., 1989. Use of pressure derivative in well test interpretation. SPE Formation Eval., 4(2): 2 9 3 - 302. Bourgeois, M.J. and Home, R.N., 1993. Well test model recognition using Laplace space. SPE Formation Eval., 8(1): 17 - 25. Chatas, A.T., 1966. Unsteady spherical flow in petroleum reservoirs. Soc. Pet. Eng. J., 6(2): 1 0 2 - 114. Carslaw, H.S. and Jaeger, J.C., 1959. Conduction of Heat in Solids. Oxford University Press, London, 510 pp. Cinco Ley, H. and Samaniego, V.F., 1977. Effect of wellbore storage and damage on the transient pressure behavior of vertically fractured wells. SPE Paper 6752, presented at SPE 52nd Annual Fall Meeting, Denver, CO, Oct. 9 - 12.

677

Cinco Ley, H. and Samaniego, V.F., 1981. Transient pressure analysis for fractured wells. J. Petrol. Techn., 33(9): 1749 - 1766. Cinco Ley, H. and Samaniego, V.F., 1982. Pressure transient analysis for naturally fractured reservoirs. Paper SPE 11026, 58th Annual Fall Technical Conference and Exhibition, New Orleans, LA. Cinco Ley, H. and Samaniego, V.F., 1989. Use and misuse of the superposition time function in well test analysis. Paper SPE 19817, 64th Annual Technical Conference and Exhibition, San Antonio, TX, Oct. 8-11. Cinco Ley, H., Ramey, H.J.Jr. and Miller, F.G., 1975. Pseudo-skin factors for partially penetrating directionally drilled wells. Paper SPE 5589, 50th Annual Fall Technical Conference and Exhibition, Dallas, TX, Sept. 2 8 - Oct. 1. Cinco Ley, H., Samaniego, V.F. and Dominguez, A.N., 1978. Transient pressure behavior for a well with a finite conductivity vertical fracture. Soc. Pet. Eng. J., 18(4): 253 - 264. Cinco Ley, H., Samaniego, V.F., Parra, J., Dominguez, V.G.C. and Rivera R.J., 1984. Aspectos pr~cticos del an~ilisis de pruebas de presi6n en yacimientos de alta permeabilidad. Area Cantarell. Ing. Petrolera, XXIV(2): 3 7 - 4 6 . Cinco Ley, H., Samaniego, V.F. and Viturat, D., 1985. Pressure transient analysis for high-permeability reservoirs. Paper SPE 14314, 60th Annual Conference and Exhibition, Las Vegas, NV., Sept. 22 -25. Cinco Ley, H., Kuchuk, F., Ayoub, J., Samaniego, V.F. and Ayesteran, L., 1986. Analysis of pressure tests through the use of instantaneous source response concepts. Paper SPE 15476, 61st Annual Technical Conference and Exhibition, New Orleans, LA, Oct. 5 - 8. Clark, D.G. and van Golf-Racht, T.D., 1985. Pressure-derivative approach to transient test analysis: a high-permeability North Sea reservoir example. J. Petrol. Techn., 37(11): 2023 - 2039. Clark, K.K., 1968. Transient pressure testing of fractured water injection wells. J. Petrol. Techn., 20(6): 639 - 643; Trans. AIME, 243. Coats, K.H., Rapoport, L.A., McCord, J.R. and Drews, W.P., 1964. Determination of aquifer influence functions from field data. J. Petrol. Techn., 16(12): 1417- 1424. Crawford, D.A., Waller, H.N. and Sanders, L.J., 1981. Comparison of conventional and type curve analysis of pressure falloff tests for a west Texas carbonate reservoir. Paper SPE 10639, Production Technology Symposium, Lubbock, TX. Crawford, G.E., Hagerdorn, A.R. and Pierce, A.E., 1976. Analysis of pressure buildup tests in a naturally fractured reservoir. J. Petrol. Techn., 28(11): 1295- 1300. Crawford, G.E., Pierce, A.E. and McKinley, R.M., 1977. Type curves for McKinley analysis of drillstem data. Paper SPE 6754, 52nd Annual Fall Meeting, Denver, CO, Oct. 9 - 12. Deryuck, B.G., Bourdet, D.E, DaPrat, G. and Ramey, H.J.Jr., 1982. Interpretation of interference test in reservoirs with double porosity behavior-theory and field examples. Paper SPE 11025, 57th Annual Fall Technical Conference and Exhibition, New Orleans, LA, Sept. 26-29. de Swaan, O.A., 1976. Analytic solutions for determining naturally fractured reservoir properties by well testing. Soc. Pet. Eng. J., 16(2): 117- 122. Dogru, A.H., Dixon, T.N. and Edgar, T.F., 1977. Confidence limits on the parameters and predictions of slightly compressible, single phase reservoirs. Soc. Pet. Eng. J., 17(1): 4 2 - 56. Dominguez, V.G.C., Samaniego, V.F. and Chilingarian, G.V., 1992. Simulation of carbonate reservoirs. In: G.V. Chilingarian, S.J. Mazzullo and H.H. Rieke, III (Editors), Carbonate Reservoir Characterization: A Geologic-Engineering Analysis, Part I. Elsevier, New York, pp. 4 3 9 - 503. Duong, A.N., 1989. A new set of type curves for well test interpretation using the pressure derivative ratio. SPE Formation Eval., 4(2): 2 6 4 - 272. Earlougher, R.C.Jr., 1977. Advances in Well Test Analysis. Monograph Series, Society of Petroleum Engineers of AIME, Dallas, TX. Economides, M.J. and Ogbe, D.O., 1987. How to analyze interference well tests, part 2. World Oil, 205(2): 5 4 - 57. Ehlig-Economides, C.A. 1988. Use of the pressure derivative for diagnosing pressure-transient behavior. J. Petrol. Techn., 40(10): 1280- 1282. Ehlig-Economides, C.A. and Ramey, H.J.Jr., 1981. Transient rate decline analysis for wells produced at constant pressure. Soc. Pet. Eng. J., 21 (1): 98 - 104. Ehlig-Economides, C.A., Joseph, J.A., Ambrose, R.W.Jr. and Norwood, C.F., 1990. A modem approach to reservoir testing. J. Petrol. Techn., 42(12): 1554- 1563.

678 Energy Resources Conservation Board, 1975. Theory and Practice of the Testing of Gas Wells, 13rd ed., Pub. ERCB-75-34, Calgary, Canada, 505 pp. Fair, ES. and Simmons, J.F., 1992. Novel well testing applications of Laplace transform deconvolution. Paper SPE 24716, 67th Annual Technical Conference and Exhibition, Washington, DC, Oct. 4 - 7 . Fetkovich, M.J. and Vienot, M.E., 1984. Rate normalization of buildup pressure by using afterflow data. J. Petrol. Techn., 36(12): 2211-2224. Fligelman, H., Cinco Ley, H. and Ramey, H.J.Jr., 1981. Drawdown Testing for High Velocity Gas Flow. SPE Paper 9904, California Regional Meeting, Bakersfield, CA, March 25 - 27. Fligelman, H., Cinco Ley, H., Ramey, H.J.Jr., Braester, C. and Couri, F., 1989. Pressure-drawdown test analysis of a gas well-application of new correlations. SPE Formation Eval., 4(3): 4 0 6 - 4 1 2 . Gringarten, A.C., 1982. Interpretation of tests in fissured reservoirs with double porosity behavior: Theory and practice. Paper SPE 10044, SPE International Petroleum Exhibition and Technical Symp., Beijing, China, March 18 - 26. Gringarten, A.C., 1984. Interpretation of tests in fissured reservoirs and multilayered reservoirs with double porosity behavior: Theory and practice. J. Petrol. Techn., 36(4): 5 4 9 - 564. Gringarten, A.C., 1985. Interpretation of transient well test data. In: R.A. Dawe and D.C. Wilson (Editors), Developments in Petroleum Science- 1, Elsevier Applied Science Publishers, London, 297 pp. Gringarten, A.C., 1987a. Type-curve analysis: what it can and cannot do. J. Petrol. Techn., 39 (1): 11 13. Gringarten, A.C., 1987b. How to recognize "double-porosity" systems from well test. J. Petrol. Techn., 39 (6): 631 - 633. Gringarten, A.C., Bourdet, D.P., Landel, P.A. and Kniazeff, V.J., 1979. A comparison between different skin and wellbore storage type-curves for early-time transient analysis. Paper SPE 8205, 54th Annual Technical Conference and Exhibition, Las Vegas, NV, Sept. 23 - 26. Guti6rrez, R.M.E., 1984. Uso de curvas tipo en el an~lisis de pruebas de interferencia y de un solo pulso. B.Sc. report, School of Engineering, National University of Mexico, M6xico, DF, 84 pp. Guti6rrez, R.M.E. and Cinco Ley, H., 1985. Uso de curvas tipo en el an~ilisis de pruebas de interferencia y de un solo pulso. Ingenieria Petrolera, XXV (10): 2 4 - 4 7 . Hawkins, M.F.Jr., 1956. A note on the skin effect. Trans. AIME, 207:356 - 357. Home, R.N., 1990. Modern Well Test Analysis. Petroway Inc., Palo Alto, CA, 183 pp. Home, R.N., 1992. Advances in computer-aided well test interpretation. Paper SPE 24731, 67th Annual Technical Conference and Exhibition, Washington, D.C., Oct. 4 - 7. Homer, D.R., 1951. Pressure build-up in wells. Proc. Third World Pet. Congr., The Hague, Sec. I: 503 - 523. Huinong, Z., 1984. Interference testing and pulse testing in the Kenl carbonate oil p o o l - A case history. J. Petrol. Techn., 36(6): 1009 - 1017. Hurst, W., 1953. Establishment of the skin effect and its impediment to fluid flow into a wellbore. Pet. Eng. (Oct.): B-6-B-16. Hutfilz, J.M., Cockerham, P.W. and Mclntosh, J.R., 1982. Pulse testing for reservoir description in a high permeability environment, dr. Petrol. Techn., 34(9): 2179 - 2190. Jacob, C.E., 1940. On the flow of water in an elastic artesian aquifer. Trans. Amer. Geophys. Union: 574 - 586. Jacob, C.E. and Lohman, J.W., 1952. Nonsteady flow to a well of constant drawdown in an extensive aquifer. Trans. AGU: 559-569. Jain, A. and Ayuob, J.A., 1983. Pressure buildup in gas-lift oil wells, Falah field, offshore Dubai. Paper SPE 11446, Middle East Oil Technical Conference, Manama, Bahrain. Jargon, J.R. and van Poollen, H.K., 1965. Unit response function from varying-rate data. J. Petrol. Techn., 17(8): 965 - 969. Jones, P. and McGhee, E., 1956. Gulf Coast wildcat verifies reservoir limit test. Oil and Gas dr., 196(54): 1 8 4 - 196. Kabir, C.S. and Willmon, J.H., 1981. Pressure transient testing in high transmissibility reservoirs: design and analysis considerations. J. Can. Pet. Tech., 20(2): 6 4 - 73. Karakas, M. and Tariq, S.M., 1991. Semianalytical productivity models for perforated completions. SPE Production Eng., 6(1):73 - 82. Kuchuk, F.J., 1990. Applications of convolution and deconvolution to transient well tests. SPE Formation Eval., 5(4): 375 - 384.

679 Kuchuk, F.J. and Ayesteran, L., 1985. Analysis of simultaneously measured pressure and sandface flow rate in transient well testing. J. Petrol. Techn., 37(2): 323 - 334. Kuchuk, F.J. and Kirman, P.A., 1987. New skin and wellbore storage type curves for partially penetrated wells. SPE Formation Eval., 2(4): 5 4 6 - 554. Langston, E.P., 1976. Field application of pressure buildup test, Jay-Little Escambia crack fields. Paper SPE 6199, 51st Annual Fall Technical Conference and Exhibition, New Orleans. LA. Lee, W.J., 1967. Analysis of hydraulically fractured wells with pressure buildup tests. Paper SPE 1820, 42nd Annual Fall Meeting, Houston, TX. Lee, W.J., 1982. Well Testing. Textbook Series. Society of Petroleum Engineers, Dallas, TX, 159 pp. Lee, R.L., Logan, R.W. and Tek, M.R., 1987. Effect of turbulence on transient flow of real gas through porous media. SPE Formation Eval., 1(1): 1 0 8 - 120. Martinez R.N. and Ricoy, U., 1989. Sistema de an~.lisis de pruebas de presi6n en pozos petroliferos. Mexican Petroleum Institute, Internal Report, 75 pp. Martell, B., 1989. Personal communication, Pemex, M6xico, D.F. Matthews, C.S. and Russell, D.G., 1967. Pressure Buildup and Flow Tests in Wells. Monograph Series, Society of Petroleum Engineers of AIME, Dallas, TX. Matthews, C.S., Brons, F. and Hazebroock, P., 1954. A method for determination of average pressure in a bounded reservoir. Trans. AIME, 201: 182 - 191. McDonald, S.W., 1983. Evaluation of production tests in oil wells stimulated by massive acid fracturing offshore Qatar. J. Petrol. Techn., 35(3): 4 9 6 - 506. McGee, P.R., 1980. Use of a well model to determine permeability layering from selective well test. J. Petrol. Techn., 32(11): 2023 - 2028. Mclntosh, I. and Baxendale, D., 1986. Offshore reservoirs-a different engineering approach is required. J. Can. Pet. Tech., 25(1): 28 - 38. McKinley, R.M., 1971. Wellbore transmissibility from after flow dominated pressure buildup data. J.Pet. Tech., 23(7): 863 - 872. McKinley, R.M., Vela, S. and Carlton, L.A., 1968. A field application of pulse-testing for datailed reservoir description. J. Petrol. Techn., 20(3): 3 1 3 - 321. Meinzer, O.E., 1928. Compressibility and elasticity of artesian aquifers. Econ. Geol., 23:263 - 271. Meunier, D., Wittmann, M.J. and Stewart, G., 1985. Interpretation of pressure buildup test using in-situ measurement of afterflow. J. Petrol. Techn., 37(1): 1 4 3 - 152. Millheim, K.K. and Cichowitz, L., 1968. Testing and analyzing low-permeability fractured gas wells. J. Pet. Tech., 20(2): 1 9 3 - 198; Trans. AIME, 243. Miller, C.C., Dyes, A.B. and Hutchinson, C.a.Jr., 1950. The estimation of permeability and reservoir pressure from bottom hole pressure build-up characteristics. Trans. AIME, 189:91 - 104. Miller, F.G., 1962. Theory of unsteady-state influx of water in linear reservoirs, J. Inst. Petrol. 48(467): 365-379. Mueller, T.D. and Witherspoon, P.A., 1965. Pressure interference effects within reservoirs and aquifers. J. Petrol. Techn., 17(4): 4 7 1 - 4 7 4 ; Trans. AIME, 234. Nabor, G.W. and Barham, R.H., 1964. Linear aquifer behavior. J. Petrol. Techn., 16(5): 561 - 563. Najurieta, H., 1980. A theory for pressure transient analysis in naturally fractured reservoirs. J. Pet. Tech., 32(7): 1241 - 1250. Najurieta, H.L., Duran, R., Samaniego V.F., Rodriguez, A., Martinez A.R. and P6rez Rosales, C., 1991. Transmissivity and diffusivity mapping from interference test data: a field example. SPE Formation Evaluation J., 10(3): 1 8 0 - 185. Nisle, R.G., 1958. The effect of partial penetration on pressure buildup in oil wells. Trans.AIME, 243:85 90. Odeh, A.S., 1965. Unsteady-state behavior of naturally fractured reservoirs. Soc. Pet. Eng. J., 5(1): 60 66. Onur, M. and Reynolds, A.C., 1988. A new approach for constructing type curves for well test analysis. SPE Formation Eval., 3(1): 197 - 206. Papatzacos, P., 1987. Approximate partial-penetration pseudoskin for infinite-conductivity wells. SPE Reservoir Eng., 2(2): 2 2 7 - 235. Pascal, H., 1981. Advances in evaluating gas well deliverability using variable rate tests under nonDarcy flow. Paper SPE 9841, SPE/DOE Low Permeability Gas Reservoirs Symposium, Denver, CO, May 27 - 29. -

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683

Chapter 7

NATURALLY-FRACTURED

CARBONATE

RESERVOIRS

T.D. VAN GOLF-RACHT

INTRODUCTION

A carbonate reservoir is defined as being "fractured" only if a continuous network of various degrees of fracturing is distributed throughout the reservoir. Such fractures formed naturally during the specific geological circumstances of reservoir history. On the other hand, the presence of some dispersed fractures induced by engineering stimulations in a carbonate rock will never transform a carbonate reservoir into a natural "fractured carbonate reservoir" (Fig. 7-1). The identification of a continuous fracture network in carbonate reservoirs is indicated by:

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684 (1) significant mud losses during drilling operations, (2) special behavior of transient pressure analysis (e.g., double-slope curves), (3) cores examination, etc. But the true confirmation of the fractured character of a given reservoir results from certain specific features observed during the initial stage of field discovery as well as during the field development and production phase.

Specific features of the fractured carbonate reservoir Absence of the transition zone The transition zone, which is a key characteristic of low-permeable conventional limestone reservoirs (Fig. 7-2A), is absent in a fractured reservoir; nevertheless, the matrix is always of very low permeability. This is the direct consequence of the fact that the water-table and the gas-oil contact are both referred to fracture network fluids equilibrium where capillary pressure is negligible and the equilibrium of the two phases is controlled by gravity forces. The consequence is that in the absence of capillary forces, the two-fluid contact in the fracture network will always be horizontal and without any transition zone (Fig. 7-2B). On the contrary, in the presence of important capillary pressure the saturation distribution of various fluids in the matrix is totally different from that found in the fracture network. As a consequence, the "original" two-phase contacts in fractures can not be obtained through log data, which reflect essentially the matrix saturation distribution. Thus, the original gas-oil and water-oil contacts can be obtained only from the fluid levels monitored in observation wells. During the reservoir production history the levels have to be further determined through the same observation wells.

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685 ~

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O

+"

000

I,~ D_ 4~. o

--,~-~ "

t'-"-,

c a p

9

C) O ,

~.~..~.

, r -~r

'

~" dPb - (-)

"

~-

dPI

Pb = const.

- . . . . . (+) dh

dh Fig. 7-3. Variation o f bubble point pressure (PB) vs. depth in a fractured reservoir.

The possibility of constant P VTproperties with depth In a reservoir's PVT properties the bubble point pressure gradient vs. depth relationships show a gradient ApB / Ah, which can be positive or negative. In the case of a fractured reservoir, if the fracture network has very good continuity (vertically and horizontally) a convection process may take place as a result of the combined effect of fluid thermal expansion and gravitational compression. With geologic time this convection process may make the hydrocarbon composition of the oil phase uniform, and thus, the bubble point pressure as well as all PVT properties may remain constant with depth as shown in Fig. 7-3. Pressure drop around a producing well is small for high rates In a fractured limestone reservoir the pressure drop around the wellbore is low (Fig. 7-4A) when compared with the large pressure drop in the absence of fractures, due to the usually very small permeability of the matrix (Fig. 7-4B). This behavior is due to the fact that: (1) fluid-flows toward the well in a fractured reservoir occur only through the fracture network because the matrix blocks feed only the fractures with fluid; (2) due to very high intrinsic permeability of fractures compared with that of matrix, high rates can be assured with very small pressure drops; and (3) small pressure drops required for high rates will favor the free gas buoyancy over a very large area (with the exception of a very restricted area around the wellbore).

686 g

itl

l

IL -

-F~cct

; ,.,i~,

..,'

i'.,"..;i. ....-.,. ~'~,-."

~

A

S~a1,cp ~ ~ , . . - - - . . - - . - - . .

----

9 '~.~." - . . I .....

. .:~;',~

l " : - :" .;. ...'a.'-,-'." FRACTURED RESERVOIR

.

-'..'

....

..?'.-:

.,,~

, , .9 ,":; ' . . ' # ;

.

. ' .'.

. ,. ... ' !

4

:,..': ". ::'.r ..':" ":.:i~

CONVENTIONAL RESERVOIR

13

Fig. 7-4. Pressure distribution around the wellbore in: (a) fracture carbonate reservoir and (b) non-fractured carbonate reservoir.

Fracture network gas-cap

Flow toward the well only through fractures with very low pressure gradients (Fig. 7-4A) facilitates a segregation of liberated gas toward the upper part of fracture networks, forming a "fracture gas-cap". In fact, with the exception of a zone of 10 m around the wellbore, in the entire drainage area the average density difference between oil and gas A~,g,o = 0.5.10 -3 {(kg/cm 2)/cm} is substantially higher than pressure gradients in the fractures. On the other hand, the flow of oil toward the well through rock matrix having low permeability (k = 1 mD.), in the absence of fractures, requires a high pressure drop, which gives rise to viscous forces substantially higher than gravity forces. Thus, the liberated gas will flow toward the well (Fig. 7-5B), without any gas segregation toward the gas-cap. Pressure decline

The rate of pressure decline per unit of oil produced ( A p / A N p ) is normally low in a fractured reservoir produced below bubble point pressure, when compared to the behavior of the same reservoir in the absence of fractures (Fig. 7-6, curve A). Such an improved behavior in a non-fractured reservoir (similar to a pressure maintenance) may be obtained only if a large amount of produced gas is reinjected back into the reservoir. If, for a given reservoir, one assumes two cases: (1) the reservoir is fractured, and (2) the reservoir is not fractured, then the last case may show a behavior similar to a fractured reservoir only if up to 80% of produced gas has been reinjected (Fig. 7-6, curve B).

687

G AS

CAP

w

C~

0~- O~

C~

0,, C~

0..~ C ~

0-,~. O-e, C)-~. O § C~

o~0-~

O~

0..~. ~

0...

o.~

0.~

o-~o-e

0-~

0-,-

O~

0"~" 0,~.

o-~

O + 0-~

o-~o.~ 0 " ~ (3~"

Fig. 7-5. Gas segregation is: possible in fractures (a) and impossible in the absence of fractures (b).

The explanation of this dramatic improvement of fractured reservoir behavior is the result of the additional different production mechanisms developing in a doubleporosity reservoirs. In the specific case of depletion (below bubble point pressure PB), such a substantial increase in recovery is the result of a "gas-gravity drainage" production mechanism developed by the segregation of liberated gas. Gas/oil ratio

The reservoir gas-oil ratio (GOR) vs. recovery is substantially lower in a fractured carbonate reservoir than in an unfractured reservoir (Fig. 7-7B). This difference is due mainly to the tendency of the liberated gas to rapidly segregate through fractures towards the top of the reservoir (Fig. 7-5A), instead of flowing toward the well together with the oil (Fig. 7-5B). If the wells are then completed in only the lower part of the reservoir, the gas will be retained in the upper part and the GOR will remain very small when compared to the equivalent values found during conventional reservoir depletion. Water~oil ratio

The water/oil ratio or the water-cut during the production life of a fractured carbonate reservoir is essentially a function of production rate (Fig. 7-8A), whereas in the case of a non-fractured reservoir both ratios will depend on rock characteristics, fluid characteristics, displacement behavior and, evidently, on production rate (Fig. 7-8B).

FRACTURING VS. GEOLOGICAL HISTORY

The evaluation of fracturing in carbonate reservoirs requires examination of the present information obtained from field work (wells, cores, etc.) and the attempt to

688

IRESERVOIR 9

N

[AP/ANp] r~ON-F~CrUREDRESERVOIR

i

,

Non fractured

Fractured

J Pressure decline becomes equivalent to fractured pressure decline IF Gas produced

NIILlll."

.... oo_] ~'~njelted

Fig. 7-6. Variation of pressure decline vs. recovery [Ap / ANp ] in: (a) fractured carbonate reservoir and (b) non-fractured carbonate reservoir. correlate them with the past history of a reservoir. The main aspects on which the work has to be directed are: (1) geological conditions of fracturing; and (2) influence of stylolites and joints.

689

t

t

0

0

%RECOVERY

--~

A

%RECOVERY --~

B

Fig. 7-7. GOR vs. recovery in: (a) fractured carbonate reservoir and (b) non-fractured carbonate reservoir.

Geological condition offracturing From a geo-mechanical point of view, fractures in a fractured carbonate reservoir correspond to a solid surface in which a loss of cohesion has taken place and a rupture with no noticeable displacement is observed. Under the same stresses, fracturing resuiting from tectonic events will be different in different types of rocks. Fracturing will be more efficient, for example, in brittle reservoir rocks of low porosity and low permeability, where the fractures are relatively extended and have large openings. These are called macrofractures. In less brittle rocks of high porosity, the fractures are of limited extent and have relatively small openings. These are called "microfractures" or "fissures". Fractures which are generated as a result of the stress that reduces rock cohesion can be attributed to various geological events, such as: (1) diastrophism in the case of folding and/or faulting; (2) expansion of upper part of sediments as a result of consistent erosion associated with the removal of the overburden, which causes a differential stress on the rock through the planes of weakness; (3) rock volume shrinkage as a result of water loss in shale or shaly sands; and (4) rock volume shrinkage in the case of temperature variation in igneous rocks.

Review of classic laboratoryfracturing experiments In classic laboratory testing, a cylindrical sample is subjected to the axial maximum principal stress (eye) acting along the cylinder axis, and tO a lateral confining pressure (so that the two minimum stresses (3"2 and cy3 are equal) directed normal to the cylinder axis (Fig. 7-9). A hydrostatic pressure equal to the confining pressure is initially applied and then the axial loading is increased while the confining pressure is kept constant. This combined state of stress vs. deformation has been extensively debated in the literature. The main result of this procedure is that the yield and ultimate strength increase as the

690 A 100% f

/

/

/

WATER CUT (WC)

/

/ / I , I

,

q (rate) B

100%

/

WATER CUT (WC)

/

/I

I i

I I

I / I //, / // I/7 lJ,

/

/

/

!

Breakthrough

Water encroachment (We)

wc = f (Po, law,ko, kw) Fig. 7-8. Water-cut vs. recovery in: (a) fractured carbonate reservoir and (b) non-fractured carbonate reservoir. confining pressure increases. An example is shown in Fig. 7-10 where, for different confining pressures, the differential stress o~ - o 3 is plotted vs. longitudinal strain. As illustrated, the shape of the curves cr~- o 3 vs. e I is influenced by confining pressure. At a low confining pressure a brittle fracture is obtained with an evident strength drop when failure occurs, whereas for a high confining pressure a large deformation may occur without any strength drop. As illustrated in Fig. 7-11, fracture patterns are very much influenced by the confining pressure ~3, when the principal stress cr~ initiates the fracturing of the sample. The fractures are developed at cr3 > 35 kg/cm 2, whereas conjugate fractures are developed when o 3 > 210 kg/cm 2. This can be summarized as follows:

691

0 1

--.....

f

J

f \.____.J

l Fig. 7-9. Triaxial test for a cylindrical specimen (axial compression 0"1 and fluid confining pressure 0"2 = 0"3)-

2500~

o,

2O:X)-

b-

IS00-

~

~_.._.......___-----

.---

~ -

C3

-

.

.

.

.

.

.

.

.

m-i

700J

Numbers indicate

t 350

conftning pressure

/,60

~

'I000-.

-__o___~_~.

1000~I

~

210

\ 3s

0

j

in Kg/cm2

" ~ ~00 ,

,~

1

2

,

89 Strain,

,

•I ('I'1

Fig. 7-10. Differential stress 0-t- 0-2vs. strain for various confining pressures. 0 < 0"3 < 30 kg/cm 2 35 < 0"3 • 150 kg/cm 2 150 < o 3 < 400 kg/cm 2 0"3 ) 400 kg/cm 2

-

irregular fracture net and visible fracture abundant conjugate fractures no fractures

As shown, when confining pressures are around 2 5 0 - 400 kg/cm 2, conjugate fractures are developed for the same unique axial stress. If the fractures are observed on a folded structure as shown in Fig. 7-12, it may be stated that right lateral and left lateral fractures form at angles of 60 ~ This happens as a result of maximum shear

692

~3:35

a3:0

~3 = I00 ~,,

_

~3 : 210 1

v

case 1

cose

o 3 = 350 \

,

.

2

case

(x 3 : 700 .

.

.

3

cy3 : 1000 /

v -

case

C

case

5

Fig. 7-11. Triaxial testing results for various confining pressures cr3 in kg/cm 2.

stress which makes an angle of 30 ~ (angle of intemal friction) with each lateral conjugate fracture. The important advantage of such a fracture pattem is that it is sufficient to know only one orientation of a single fracture system in order to define the entire pattern of stress distribution during fracturing over geological time. On the contrary, orthogonal fractures having an intersection angle of 90 ~ will be the result of more than one single state of stress, even if it is not excluded that the fracturing occurred at the same geological time for both orthogonal fracture groups.

Folding vs. fracturing In a folded structure, fractures can not be associated with a single state of stress (as in the case of faulting), but rather, to several states of stress which may occur during

693

/,..Right lateral

0~

Conjugate

/

Transversal fracture

'

Left lat

/_.__._ Orthogonal

fractures

fractures

/Folding axis

Fig. 7-12. Conjugate and orthogonal fractures referred to the folding axis.

the folding history. The folding examples shown in Figs. 7-13 and 7-14 represent the greatest principal stress acting parallel and acting normal to formation bedding. In Fig. 7-13 the lateral stress 01 acts only on one side of the bed (Y) and is practically immobile on the other side (Y'). The folding will, therefore, generate a series of fractures as a result of both stresses (compression and tension). Figure 7-14 presents the case where a 1 acts vertically as a result of salt dome rising. The structure is uplifted and the reservoir layers are under compressional and tensional stresses. During the folding process a series of fracture patterns are generated under various conditions of distribution of the principal stress. Of these patterns, two have been retained as the most important and are described below. Pattern 1

In the case of pattern 1 (Fig. 7-15) the three principal stresses work in the following directions: a 1 and o 3 along the bedding plane and a 2 normal to the bedding plane.

O'2 or o"3

/o r 5"2.

0"i

Fig. 7-13. Folding compression.

694

sort domes

o"3 1

Fig. 7-14. Folding due to salt dome uplift. Due to the direction of the greatest principal stress o I along structural dip, a series of transversal fractures and respective conjugate fractures will develop. This observation is of major interest when studying outcrop data in a folded structure. Based on the observed conjugate fractures, it becomes possible to understand what direction o, had during folding, and also to establish the normal direction in the same bedding plane where a 1 was applied. The dip of the anticline is then given by o~ and the strike is given by the direction of o 3.

Pattern 2 Fracture pattern 2 (Fig. 7-16) is similar to pattern 1, with a 2 being normal to the bedding plane and a~ and a 3 acting in the bedding plane. The only difference is that the greatest principal stress a, acts in a direction parallel to the folding axis. Therefore, the result will be a series of conjugate fractures which will indicate that a~ is

~o I

.0" 3

Fig. 7-15. Fracture pattern 1: cr1, cr3is acting in the bedding plane and o-2acting normal to the bedding plane (not shown) tyl is in the dip direction; ty3is in the strike direction. (From Steams and Friedman, 1972.)

695

Fig. 7.16. Fracture pattern 2: 0-1,0-3acting in the beding plane and 0-2acting normal to the bedding plane (0-3is in a dip direction and % is in a strike direction). (From Steams and Friedman, 1972.) along the longitudinal direction (strike), whereas the lowest principal stress 0" 3 will indicate the direction of dip. A shortening and elongation will occur on the anticline folding in these two cases. The shortening due to o~ will be in a dip direction in pattern 1 and in a strike direction in pattern 2, and vice-versa for the elongation. Except for fracturing, no change such as shortening or elongation normal to bedding will occur.

Examples Steams and Friedman (1972) have mentioned a series of examples of these two patterns and have made a number of observations: (1) The two pattems may be developed in the same bed. (2) In general, pattern 1 will precede pattern 2, which means that folding must develop to a sufficient degree so that fracturing can occur. In such a case fractures will be normal to the anticline trend. (3) The fractures of pattern 1 are often developed on long distances such as single breaks. In general, the fractures are large, with a homogeneous orientation, a feature which may aid fluid movement over large areas. (4) The fractures of pattern 2 are of reduced length, often varying between a few inches and a few feet. The fractures are aligned with the folding axis and usually contain fractures in all three principal directions. (5) The extension fractures in pattern 1 may terminate in lateral fractures (left or right), and the shear fractures may terminate in extension fractures or in their conjugates. (6) Without being demonstrated, it seems that there are more chances of having a better continuity of a single or very few fractures in the case of pattern 1, but a larger fracture density and more effective fluid flow in the case of pattern 2. (7) In a well which may intersect pattern 1 fractures, there are three possible directions for the well to intersect the fractures, whereas if a well intersects pattern 2 the direction parallel to the structural trend will be the most probable communication direction between the well and the fractures.

696

Role of stylolites and joints In fractured carbonate reservoirs, both joints and stylolites have considerable influence on reservoir quality. Stylolites occur as irregular planes of discontinuity passing through the rock matrix, generally roughly parallel to bedding (Fig. 7-17 illustrates the main types), and their presence normally reduces the intercommunicability of the reservoir fracture system (Park and Schott, 1968). Understanding the importance of stylolites to fractured reservoirs depends more on understanding the timing of their origin relative to that of fracturing and hydrocarbon migration than on their actual origin. Joints are more common than stylolites, and are normally associated with the structural history of the area and may be used successfully for the interpretation of angularity to the principal stresses, resulting in regional folding and faulting trends.

Stylolites and stylolitization The presence of stylolites in carbonate rocks is a common feature independent of rock facies and geological age. In general, they are easily recognizable as irregular planes of discontinuity or sutures, along which two rock units appear to be interlocked or mutually interpenetrating (Dunnington, 1967). These planes are usually characterized by the accumulation of insoluble residue which forms the stylolite seams; they may terminate laterally or converge into residual clay seams. The presence of stylolites and reprecipitated cements, especially if continuous, causes considerable reduction in reservoir quality because they act as barriers to the

a

i 1

3

I

I HORIZONTAL TYPE

4

TYPE

HORIZONTAL- INCLINED

5

< VERTICAL TYPE

INTERCONNECTED TYPE

VERTICA L -INCLINED

Fig. 7-17. Classification of stylolites vs. bedding. (Park and Schott; reprinted with permission of the American Association of Petroleum Geologists.)

697 A

C

B

Fig. 7-18. Schematic diagram of stylolitization with thinning. hydrodynamic system, intergranular pores, and fracture networks. Although the origin of stylolites has in the past given rise to considerable debate, it is now generally accepted as being the result of either a contraction-pressure process or a pressure-dissolution process. In the case of a pressure-dissolution process, stylolitization could be simplified as shown in Fig. 7-18. The original grains of phase "A", due to increasing fluid pressure (as a result of increasing overburden with deepening burial), will reach a state of high solubility which will be greatest at the grain extremities and point-to-point contacts between grains. Phase "B" in Fig. 7-18 represents the carbonate material which will be transported, and if dissolution continues, the new phase "C" will be reached.

Stylolitization vs. compaction As discussed, stylolitization is the only process other than erosion which introduces changes in volume and shape of carbonate rocks after initial induration. Stylolites influence bulk volume, porosity, and often permeability. In addition, they may be often a source of microfractures (Dunnington, 1967). In hard rocks such as limestones, after initial rock induration when fluid (water) reaches a critical pressure, the stylolitization process could be developed as a function of burial depth. Joints and their formation Joints are considered to be structural features, but their origin remains controversial. In general, theories concerning their formation are associated with the observation and interpretation of the more obvious features, such as parallelism, angular relations between joint sets, and other structural features (folds and faults). Joints are systematic when they occur in sets where the respective composing joints are parallel or sub-parallel. In addition, one joint set may intersect other joint sets. Joints can also be non-systematic, in which case they are less oriented and more randomly distributed. Curvilinear patterns are the most representative of non-systematic joints. The following list helps to distinguish systematic and non-systematic joints: Systematic Joints occur as planar traces on surfaces - occur as broadly curved surfaces - occur on oriented surface structures

-

Non-systematic Joints meet but do not cross other joints are strongly curved in plan view terminate at bedding surfaces

-

-

-

698 Joints are roughly equidistant, and in thin-bedded rocks, they extend across many layers. Very few of them, however, completely extend through very thick units. The main characteristic of joints is their parallelism, i.e., they are grouped into sets, with each joint being parallel or sub-parallel to the other.

Fracture evaluation Evaluation of fractures in fractured carbonates are carried out continuously, starting during the exploration phase and continuing during the production phase. The material for observation is in general provided by outcrops (whenever such is the case) and cores obtained from drilling. The examination of fractures requires a certain definition and classification in relation to purely descriptive criteria, and with the relationship of fracturing to geological history. The classification shown in Table 7-I is based on descriptive criteria, where fractures are defined and classified according to the following categories: - open/closed fractures - macro/micro fractures natural/induced fractures -

The open and closed fractures depend mainly on circulating water and subsequent cement precipitation, which may plug the open fracture. It is also very important to remember that due to rock compressibility, closed fractures in outcrops may often be open in the subsurface reservoir as a result of high reservoir pressure-fluid action on keeping the fracture walls separated. The fractures and fissures, called macro- and microfractures, respectively, are of different lengths and widths, the first group being of larger extension and opening. In qualifying fractures it is extremely important to recognize natural fractures from artificially induced ones: clean, fresh fractures have less chances of being natural fractures than oil-impregnated ones, which are certainly natural ones. Table 7-11 presents a classification of fractures based on geological criteria. Inasmuch as an essential role in generating fractures is played by tectonic events, fractures are dependent on folding processes and type of folding history, including stratigraphical conditions and stress state, as well as the actual folding characteristics. The various types of fractures generated by folding and stress are shown in Fig. 7-19. The totality of the fractures (Table 7-11 and Fig. 7-19) could be associated with their direction and, therefore: (1) the fracture system is formed by all fractures having mutually the same parallel direction; and (2) the fracture network results from the presence of several fracture systems.

Basic characterization of a "single fracture" and of a "group of fractures "' The main differences between a single fracture and group of fractures are related to the direct characteristics of a single fracture such as size, width, orientation, etc., and to combined characteristics of matrix/fractures in the case of a group of fractures (such as fracture distribution, fracture density, fracture intensity, etc.).

699 TABLE 7-I Classification of fractures based on descriptive criteria

OPEN

i c,o o 1

i

free for fluid flow I

plugged w i t h p re ci p i ta te s MICROFRACTURES

MACROFRACTURES .

.

.

.

.

.

.

.

.

.

.

I .

.

.

9small width 9n o n extended

9w i d t h > ~t 9very extended

[FRACTURESLi

!

measurable

I

[ n~ ! .

(visible)

"ATUAL-, ,!

!

,

_

too small (Invisible)

[ -.'NDUCED- ]

§

9 clean, fresh

9partlally.,,~ plugged 9t o t a l l y . ~ 9parallel w i t h other

9parallel-,~ to core axis 9normal

fractures .

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

A group of fractures implies the following two main categories: (1) fracture systems formed by a comprehensive set of parallel fractures; and (2) fracture networks formed by two or several associated systems. Often in an idealized reservoir the network is structured through two or three orthogonal fracture systems. Single fracture parameters refer to intrinsic characteristics, such as opening (width), size and nature of the fracture. If the single fracture is associated with the reservoir environment, another essential characteristic, such as fracture orientation, has to be defined. The multi-fracture parameters refer to fracture arrangement (geometry) which further generates the matrix bulk unit, called the "matrix block". The number of fractures and their orientation are directly related to fracture distribution and density. When fracture density is related to lithology, another parameter of particular interest, called "fracture intensity", is obtained.

Single fracture parameters Fracture opening or fracture width is represented by the distance between fracture walls. The width of the opening may depend (in reservoir conditions) on depth, pore pressure, and type of rock. Fracture width varies between 1 0 - 200 microns, but statistics have shown that the most frequent range is between 1 0 - 40 microns. Fracture orientation is the parameter which connects the single fracture to the

TABLE 7-II

Classification of fractures based on geological criteria

.

.

.

LONGITUDINAL TRANSVERSAL DIAGONAL

.

/ STRESS STATE

ASSOCIATED WITH

CONJUGATE NON-CONJUGATE

STRATIGRAPHY ~ F I R S T ORDER SECOND ORDER i

.

.

.

.

i

.

i

.

.

.

.

.

.

.

_~

i

_

i

along the ~- perpendicular lo conjugate to the

folding axis

forming an angle of 60" with stress orthogonal

cutting several layers cutting one

layer

701 CONJUGATE RIGHT DIAGONAL FRACTURE

\

CONJUGATE LEFTr, DIAGONAL FRACTURE

TRANSVERSE IFRACTURE

LONGITUDINAL FRACTURE

HORIZONTAL STYLOLITE VERTICAL STYLOLITE

Fig. 7-19. Various types of fractures generated by folding.

environment. The fracturing plane can be defined (as in classic geological practice) by two angles, dip azimuth and dip angle (Fig. 7-20). From examination of the orientation of various single fractures it follows that all parallel fractures belong to a single fracture system. If more intercommunicating fracture systems are recognized in a reservoir, then those systems together will constitute the fractured reservoir network.

Group offractures parameters In a fracture network which contains two or more fracture systems, each system has been generated by a different stress (except in the case of conjugate fractures). Fracture distribution is then expressed by a fracturing degree factor. This factor is stronger if there is a continuous intercommunication among the fractures in a system and if the systems are equivalent to each other. In addition, the fracturing degree will be weaker if the intercommunication among the fracture systems is interrupted and if the fracturing of one system prevails over the other (Ruhland, 1975). Figure 7-21 shows several cases where two orthogonal fracture systems can be equivalent as in case 1, or with the predominance of one of the systems as in cases 2 and 3. The magnitude of predominance or its absence can be expressed by an equivalent fracturing degree in examples of Fig. 7-21. In addition, the fracture density delineates matrix blocks of different sizes as a

702

y+ b-

fracture

width

L-

fracture

length

co - d i p a n g l e / /

8 - azimuth

ABC - p l a n e c o n t a i n i n g the fracture

SINGLE FRACTURE Fig. 7-20. Single fracture orientation.

result of fracture distribution (case 1 compared with case 2) (Ruhland, 1975). Fracture density expresses the frequency of fractures along a given direction, and reciprocally, the extension of the matrix delimited by fractures encountered. The intersection of several orthogonal fracture systems results in single matrix blocks of different sizes and shapes. In fact, along the direction X the linear fracture density (LFD) is [LFD]x = number of fractures / length (along a certain direction) = n / / L x

(7-1)

and, reciprocally, the block length between two fractures L x can be determined as follows: Lx = n//[LFD]x

(7-2)

Based on this approach, some idealized block shapes (Reiss, 1966) resulting from various distributions of fractures in an orthogonal fracture network gives several fracture density values (Fig. 7-22). The blocks can be structured as elongated slides (No. 1) or matches offering only one permeability direction (Nos. 2 and 3), and finally, cubes having one flowing direction (Nos. 4 and 5) or two flowing directions (No. 6) When a single-layer productive zone is small, in order to discern the tectonic effect vs. lithology it is necessary to refer all fractures (vertical and subvertical) to the singlelayer pay. If the pay is larger and fractures are vertical (or sub-vertical) and horizontal (or sub-horizontal), the notion of fracture intensity can be introduced as the ratio between the vertical and horizontal fracture densities: FINT = (LFD V / LFDH) =

= Linear fracture density (vertical) / Linear fracture density (horizontal)

(7-3)

703

|

|

Q

\/ \J

J x J

/

f\

/\/

/

EQUIVALENT SYSTEM

-~ / \

\

\J

/ EQUIVALENT SYSTEM

PREDOMINANT SYSTEM

.........

WEAK

FRACTURING DEGREE

Fig. 7-21. Various combinations of orthogonal fracture systems and the qualitative evaluation of the fracturing degree. (From Ruhland, 1975.) where vertical and horizontal fractures may in certain cases be interpreted also as fractures that are normal and parallel to the stratification. In an orthogonal fracture network oriented along the three orthogonal axes, the fracture intensity will be the ratio of fracture density in the plane XOY to the fracture density in the plane XOZ. The number of fractures can be observed and counted along a plane normal to fracture direction. As an example, the number of fractures oriented in direction Z (Fig. 7-23A) are counted in the plane XOY so that: Vertical fracture density = L F D V = L F D Z = n / L and the number of fractures oriented in direction X (Fig. 7-23B) is counted in the plane YOZ, which will give: x

x

Horizontal fracture density = L F D H = L F D X = n / L z

z

This will further result in fracture intensity: (7-4)

F I N T = L F D Z / L F D X = (n x / Lx) / (n / Lz)

and the matrix block dimensions: Zbt = L z / n z = 1 / L F D X = 1 / L F D H Xbz = L x / n x = 1 / L F D Z = 1 / L F D V

or expressed as a ratio of matrix dimensions: F I N T = L F D Z / L F D H = (1 /

Xbl )//(1

/ Zbt)

= Zbl // Xbl

(7-5)

704 L.F.D. Slides Matches Matches Cube Cube Cube

I ! [ 2 [ 3 4_ 5

I I i I

1/a 1/a 2/a 2/a ] 1/a 2/a

/ SLIOES

MAICHES

@

CuBE 5

Fig. 7-22. Simplified geometrical matrix blocks. (From Reiss, 1966.)

FINT values show a relationship between vertical and horizontal fracture distributions and also give an indication about the matrix block shape as presented on Table 7-III: vertically elongated ("match" shape), horizontally elongated ("slab" shape), and/or cubes.

Simplified correlation and procedures A complex fracture-matrix structure geometry could be modified to a simplified geometrical shape of matrix block (parallelepipeds, cubes, spheres, etc.), which is evidently surrounded by uniform fractures. Various block geometries are shown in Fig. 7-22 (named slides, matches, and cubes) with their sizes and shapes related to

705

nX 9 9 1 4 99 1 7 69

A ~

~ ~149176

~176

9~

9

9176

o 9176176176 9 9

9

V e r t i c a l f r a c t u r e density

u

LFD V = L F D Z X

--~

LFDZ = n

x / LX

i LFDH = LFDX

NF

--~

LFDX = n

z

/

LZ

9176176176176176149176176

76149 9 9 1 4 9 1 7 6 1 7 6 1... ~ ~

nz

9 9

~ ~

~ ~

I Z

Fig. 7-23. Vertical (a) and horizontal (b) fracture density 9

fracture density at various fracturing directions. For example, if the horizontal fracture density is smaller than vertical fracture density, then the block will be an elongated parallelepiped, and if vice-versa, the block will be a flat parallelepiped.

Shape and block magnitude The dimension of a matrix is directly related to fracture density and intensity because an increase of fracture density in one direction represents a reduction of block dimensions along the same direction. The block shape vs. fracture intensity is expressed through a comprehensive diagram (Fig. 7-24) where the basic relationship in two directions is expressed as follows:

706 TABLE 7-11I Relationship between vertical/horizontal fracture density and matrix block shape. ,,

i

CASE 1

CASE 2 i

Vertical Horizontal Vertical Denslty ) Denslty Density

i

i

i

CASE 3 i

i

i i

i

Horizontal Vertical Horizontal Density Density < Density

i

LFDZ > LFDX

LFDZ = LFDX

LFDZ

<

FINT >

FINT = 1

FINT

< 1

ZBL,

< I

1

ZBL >

ZBL

= 1

.,

XBL

XBL

I / ! ! J l

i l

l l

/ / / / .

.

.

.

z at 2 2 2 ) .

/"

.

.

i"

.

J"

XBL

zoL

l

l

LFDX

J"

XBL

Xat.

VERTICALLY

ELONGATED

XBL

ELONGATED

MRTClt ....

j

II

L F D V = L F D Z = 1/Xbt L F D H = L F D X = 1/Zbt F I N T = L F D Z / L F D X = Zbt / Xbt

(7-6)

where Zbt and Xbt are representing block height and extension, respectively. By using a double logarithm diagram and plotting in the same scale LFDV on the ordinate and LFDH on the abscissa (Fig. 7-24), the diagonal lines will represent the FINT values. This is a simple way to generalize the relationship of shape to size of matrix blocks.

707 The cube is on the diagonal if both scales have the same basic values. For constant values of LFDV, the increase in LFDH represents the increase in the horizontal fracture density, which corresponds to the same block base and a reduction of the block height (block will become increasingly flatter) and FINT is <1. Inversely, if the LFDH frequency remains constant but the vertical fracture LFDV increases, then the blocks will become more and more elongated with increasing LFDV (FINT is > 1) and thus, their height will be kept constant while their base is reduced as an effect of the abundance of vertical fractures. At limit their shape is that of a thin column similar to a pencil. The shape/size relationship of an idealized block unit, related to a single-layer pay and a variable vertical fracture density, shows the variation between vertically elongated and horizontally extended block elements. The idealization of a block unit is developed under the following procedure: (1) Each single matrix block extension is laterally delineated by vertical fracture density (assuming that subvertical fractures are vertical) and vertically delineated either by the matrix height between two consecutive horizontal fractures or by the layer height in the absence of horizontal fractures in the single layer. 10

.Ivn 3

2

"

lo 2

'/ /

,,,..

-

,'

n.

lO ,

E

1

4

vq

/ I

/'1

/ ~ ,i~//, \'-/ //

I

//

10' '"

i,

U3 c" (:D

--J

(J 03

//

6'

//

//

(D ::3 LL_

/

/// iO ~

/

,,, 1 0 .2

,q,

//

//

/ i /

///

// c_ a3

/

/// /

/

// (.D ..t-J

'10-1

//

10-':"

-

// // // -2'l~

I0

/

~r_ 2

I0

i

/// o

10

/

///

j,,"

-,

10

//

//

/

,,,'10

,m

,

I0

'

2

10

LFDH Horizontal

fracture

density

Fig. 7-24. Block of matrix resulting from the intersection of an orthogonal fracture system.

FINT

708 (2) The vertical number ( n ) of fractures estimated through observations on cores, I if combined with number (nh) of layer of different pay, can be used for a preliminary approximation of the matrix block shape: (7-7)

FINT = LFDV/ LFDH = nI / n h Q u a n t i t a t i v e f r a c t u r e evaluation

Based on the diagram Fig. 7-18, the matrix block magnitude can be evaluated for various cases: The c u b e ' s m a g n i t u d e :

(1) If FINT = 1 ==>> then it is normal to find a cube because F I N T = 1 means L F D V = L F D Z = 1

Xbt = Zbt = 1

(7-8)

(2) The cube could change its dimensions if fracture density is changed as shown in the examples presented below: if F I N T = 1 but L F D V = L F D Z = 10-'

Xbl = Zbt = 10

(7-9)

The cube in this case is 10 times greater, whereas: if F I N T = 1 but L F D V = L F D Z = 10

Xbt = Zbl = O. 1

(7-10)

the cube in this case is 10 times smaller. The c u b e ' s deformation: The transformation of cubes into matches corresponds to the case of a constant LFDH and increasing LFDZ, which results in blocks of constant height but with reduced base related to the growing LFDV values. By analogy, the cubes become slabs when LFDV remains constant and LVDH increases, which resuits in slabs having the same base but with continuous reduction of block height as a result of LFDH growth. Qualitative f r a c t u r e evaluation through F I N T

Based on FINT definition, a qualitative interpretation could be made for shape and fracturing: Shape

FINT > 1 [Matches]

FINT = 1 [Cubes]

FINT < 1 [Slabs]

Degree of fracturing

FINT FINT FINT FINT FINT

> = = = =

0.05 0.1 5 - 10 2 0 - 50 > 100

==> ==> ==> ==> ==>

Fractured zone Average fractured zone Strongly fractured zone Very fractured zone Breccia

709

Data processing of fractures The observations of fractures gathered from cores are tabulated and then processed through various criteria. The characteristics to be gathered are: Lithology vs. hardness

- - - > rock hardness

Lithology vs.

--->

Fracture Characteristics

=> => -> =>

Soft Medium-hard Hard Very-hard

Presence of shales Presence of stylolites Orientation of the bedding planes ==> ==> ==> ==> ==>

fracture opening, size fracture orientation (dip, azimuth, angle) fracture density fracture intensity matrix block dimensions

Statistical representation The information obtained from core examination (to which may be added the results obtained from indirect measurements) can be processed through statistical diagrams or pure geometric representations. The data which usually are processed are: fracture width, size, nature, orientation, distribution, block unit, fracture density, and fracture intensity. The criteria through which various results are examined may be: depth, lithology, shaliness, pay magnitude, etc. The most representative models are the following: (1) statistical models, which include histograms and statistic stereograms. The histogram based on single-parameter values selected through adequate criteria indicates the most probable average parameter by using a frequency curve. The stereograms are used mainly for fracture orientation parameters (strike, dip angle, etc.), through which the preferential directions of the fractures are shown; (2) geometric models (especially in the case of matrix block units), using a stereographic projection approach for magnitude and shape. Polar stereograms and various other schematic representations are particularly useful in the identification of the preferential trends of certain parameters, which often help in the description of the properties for large groups of fractures; (3) histograms, which are used for the evaluation of the most frequent range of the variations of a given parameter. The data are generally collected in relation to a given criterion, such as lithology, or pay interval, or number of cores, or types of fractures, etc. Histograms are applied to almost all parameters which define single fracture or multi-fractures characterization. From the frequency curve and cumulative frequency curve the range of average values of a given parameter is obtained by a conventional procedure. A typical example is given in Fig. 7-25 where the cumulative frequency vs. fractured density LFDV is examined for shaly and non-shaly samples. As can be

710 SHALY SAMPLES 11021

25 z w 0

I00 >." o z 80 w

i

I,--

20

0

w Q- 15 >.. Z ill

I0

0 W

S

6(1 "-

Z

U-w L)

~0 w ~ 20

m

<

LL 0

0

0

3.5

2O

,0

40

3O

99

NON-SHALY SAMPLES (2601 ,,

25

100 >... (3 Z

I,,,--

Z w 20 n,ILl r 15

. ~ . . _ -

.

BRECCIATED

0 Z I0 LU

0 LU rl," LL

(3

15~

80 W =) O

60 ~ Z

U-W

~0 w ~ ~LU

.,

20

5

0

6

10

LfD(NUMBER

20 OF

30 FRACTURES

A0 PER

90 99

<

0

FOOT)

Fig. 7-25. Example of frequency curves of linear fracture density, for shaly and non-shaly samples.

observed, for 50% cumulative frequency of fracture density in non-shaly samples (6 fractures/foot) is greater than the one observed in shaly samples (3 fractures/foot). In addition, breccia develops only in non-shaly samples; and (4) stereograms, a representation using circles in order to define over 360 ~ the spatial position of the fractures, whereas the magnitude of fracture characteristics is measured on circle radii (Fig. 7-26).

PHYSICAL

PROPERTIES

OF FRACTURES

AND MATRIX

The physical characteristic of fractures and matrix are essentially contrasting since fractures have low porosity and high permeability, whereas matrix shows high porosity and low permeability. As a result, in dynamic conditions the fracture network will exhibit a small storage capacity, and thus, a very short transient time owing to its high permeability, whereas the matrix will exhibit a large storage capacity associated with a long transient time resulting from its low permeability. In addition, if the flow includes several phases, the fluid properties and complex reservoir rock characteristics, such as relative permeabilities and capillary pressure vs. saturation relationships (Leroy, 1976; Van Golf-Racht, 1982), makes the process very complex for the double-porosity systems, requiring new reservoir dynamic concepts.

711

O*

0 = 25% 1"=

N 270 ~ 2 5 " / . ~ 2 0

15 ,

10

10%

1 0 - - - - - - 15 ~ ' - - - 2 0 - - - - - 2 5 "/. 90 ~ E

/

r i - - ~ - 25 "/, ItS0~

2Fig. 7-26. Example o f fracture strike projected in a statistic stereogram (example).

Porosity and permeability in fractured carbonate reservoirs Porosity The double porosity of a fractured reservoir is formed by matrix "intergranular porosity" (similar to the conventional porosity of a porous media) and by "fracture porosity" often called "secondary porosity" (expressing the void volume of vugs and/ or fractures). The secondary porosity is developed in a later phase, after the porosity is in place as a result of mechanical geological processes (discussed above) or/and chemical geological processes (i.e., dissolution, diagenesis, etc.).

712

Porosity of matrix and fractures." Total and single porosity are related by the classic definition: Total porosity = Matrix porosity + Fracture porosity (Primary porosity) + (Secondary porosity) Total voids/Total bulk = Matrix voids/Total bulk + Fracture voids/Total bulk

CY- r "[" r

(7-11)

(7-12')

Inasmuch as secondary porosity ~2 = r << Cm Total bulk volume = matrix bulk volume VB = VBm

(7-12")

or CT~r

(7-13)

Storage capacity of matrix and fractures." In transient flowing conditions the term which plays an impor/ant role is not the single porosity (r m or r f ), but rather, the storage capacity expressed by the association of porosity and compressibility. In this case the product r becomes: Cm*C m--------~>~>for the matrix storage capacity r *CI ====>> for the fracture storage capacity

Order of magnitude of fracture porosity: In general, fracture porosity is very small compared to matrix porosity. As a general rule it could be stated that fracture porosity is below 1% and in only very exceptional cases may reach a value of 1%. However, in very tight rocks having a primary porosity r •10% and a very extended network of macrofractures and microfractures, a fracture porosity between 0.5% and 2% may occur. As a consequence, for reservoirs with high matrix porosity, and thus very small fracture porosity, it is practically impossible by conventional logging tools to evaluate fracture porosity. Representative fracture porosity values can be obtained only from observations and direct measurements on cores (Ruhland, 1975). Fracture porosity from direct measurements: A direct measurement of fracture porosity requires" (1) fracture width [b] from cores; and (2) fracture density [LFD] from core examination, so that in idealized case (Fig. 7-27)"

713

/I/,

? Z

b

:

BL

r

A,.-

OL

. . . .

Fig. 7-27. Idealized matrix/fracture unit. Porosity = Void fracture surface / Total surface

d?/= n/ *b*Xb,/Xb, *Zbl = b*LFD = n/* b/Zb,

(7-14)

Fracture porosity from structural geological data (Murray, 1977): The presence of fractures in the case of a folded structure could be related to the bed thickness (h) and structural curvature expressed by [d2z/dx 2] for the cross-section shown in Fig. 7-28. Fracture porosity in this case is approximated by the equation:

C/= h [d2z / dx z]

(7-15)

Permeability In principle, the permeability established in the case of a conventional porous media remains valid in the case of a fractured reservoir. But in the presence of two systems (matrix and fractures), permeability has to be redefined in relation to matrix ("matrix" permeability), to fractures ("fracture" permeability) and to the fracture-matrix system ("fracture-matrix" permeability). This redefinition could create some confusion in relation to a fractured reservoir and fracture permeability, which could be referred to the "single fracture permeability" or to the "fracture network permeability" or to the entire "fracture-bulk volume permeability". The resulting expression of permeability is, therefore, examined in more detail. Fracture permeability. The matrix permeability remains the same as in a conventional reservoir, but the fracture permeability requires a review of its basic definition. (1) Single fracture case. The difference resulting from the flowing cross-section could be: The effective "real flow cross-section" ("S "~: of a single fracture based on Fig. x, ~ e f f e c t i v e 7.29 is represented by: S ffectiv e - -

a*b

(7-16)

714

,,-

X

Fig. 7-28. Cross-section of a reservoir.

and the "pseudo-cross flow section" based on the Darcy concept, which includes matrix and fractures, will result from Fig. 7-29 as:

SDarcy a*h =

=

A

(7-17)

Inasmuch as the flow along the length l, through parallel plates (very close to each other), could be extended to the flow in fractures, it may be written that:

q/= a*b (b 2/ 12 *u)*(Ap /A/)

(7.18)

whereas for the flow in a porous media based on Darcy law, the same rate is expressed as:

q:= a'h*. (k// #) * (Ap /Al)

(7-19)

From Equations 7-18 and 7-19 it follows that: b 3 / 12 = h'k/

(b / h ) *b 2 / 12 = k/

(7-20)

(7-20')

As may be observed the term (b 2 / 12) could be considered as a "pseudopermeability", which physically represents the "intrinsic permeability" (k::) of the fracture, while the term (b / h ) represents the fracture porosity (~:). In ttns case a number of basic correlations can be expressed as:

~:. k::

= k:

d~l = b / h 12 * k l / b 2 b = (12. k/* h) T M = (12" k//d?/) ~

(7-21)

715

l-

9 ..

9 .

~

9

.

.

9 .

.

I

9

9I ?"

. 9

. . . .

9

9

~.

.

.

".

.

.

.'"

.

'o

.

."

".

"

h FLOW ...9

..-.

'" 9 .

.

~ / 9

.

"'. 9 "'"

0

".

~._.,

. ..."

L=-

"

.

t

.

. '.

"" .

..'.""

.

DIRECTION

I "

".-"

""

" "

t

Fig. 7-29. Matrix block containing two fractures. Fracture 1 (or =0). Fracture 2 (or >0).

AL r

~

~

~

FLOW DIRECTION

,,

Fig. 7-30. Multi-fracture layer 9Fractures and layers are parallel.

(2) Multifracture case. If, instead of a single fracture, the flow is examined through a fracture system formed by several parallel fractures (n) as shown in Fig. 7-30, separated by matrix of height "e", then the flowing equation (similar to the case of single fracture) will give"

Q = n*ab*(b 2 / 12 ~) (A p / A / ) = ah* (k: / ~) (A p / A l)

(7-22')

or

nb*b2/12 = h ' k /

or

( n * b / h ) * (b2/12) = k/

(7-22")

n b / h = LFD *b = ~/ Thus:

k/r

b 2 / 12 = k// * ~/ = k// * b * LFD = (b 3 / 12)* LFD

~ / = 12 * k / / b 2 = (12 * k / * LFDO ~ b = [12 * k / / ~ : ]0.5 = [ 12 k / / L F D ]0.333

(7-22'")

716 For a random distribution of fractures, a correction factor for porosity could be written through (n/2) 2 as follows: ~ / = [12 * k / * (Jr / 2 ) 2* LFDZ] ~

= [29.6 * k / * LFDZ] ~

(7-23)

Fracture permeability measurements and evaluation. The fracture permeability can be measured as follows: (1) by special equipment (Kelton), where the core is oriented so that the flow takes place along the fracturing direction, between the two ends of fracture contained in the lateral cylindrical surface of the core; (2) by measuring the fracture opening, b, and counting the number n of the fractures for estimating of LFD; thus: k / = b 3 / 12 * LFD = (1 / 12) * (b 2 * ~/)

(7-24)

(3) if structural geologic data are available (Murray, 1977), then when reservoir fracturing occurs as a result of structural folding for a layer having a pay "h" (Fig. 729), the fracture permeability k/(in mD) can be estimated through the equation: k / = (0.2)

* 10 9 *

e 2 * [h * (dez /dx2)] 3

(7-25)

where the distance between the two fractures e is in cm. (4) from well testing in conditions of steady-state flow: k z = PI * {t.1~ * B o. [ln(r /rw) + S]} /[2 * zc * h]

(7-26)

because the flow toward the wellbore is taking place through the fracture network. The fracture porosity in the case of a random distribution of fractures becomes: ~: = [29.6 * k z where: PI is in fractional.

* LFDe] ~

=

STM3/D/atm,

0.00173 [PI p~176In re/rw LFD2]0.333 h ~t~

(7-27)

is in cP.; h is in m; and LFD is in 1/cm; and ~ / i s

Correlation between field data and idealized fracture~matrix system. Inasmuch as the permeability and porosity of a fracture network are physically different from those of an intergranular porous system, a special approach is proposed. The philosophy and the procedure are as follows: (1) During stabilized flow toward a well in a fractured reservoir, the productivity index is directly correlated to fracture permeability: k z = f (PI) ==>> k z calculated using Eq. 7-26. (2) If the observation of the cores has been carried out and processed, the estimation of fracture density LFD from core observations makes possible the evaluation of the fracture porosity as a function of productivity index:

717 TABLE 7-IV

Correlation of parameters for idealized matrix blocks (Reiss, 1966).

~ 0OEL

DINENSIONLESS

,io ~ L.F.D

~f

kfl~f a

13 a '

r 2

m

~

UJ

'

2b

T

i a2@ 3 12 !

"

]6

L,,

b2(~ I

1

2

~6 a (~f

3

I

X

b2

~f

"

2

2~ a

.

I

I

I

1

kfCQf,b)

kf (~f,a)

~/ ,,.

EQUATIONS

9 o

darcy

,

,,

b

dorcy ,,:

,,

,

6.33 a2q)f 3

8,~3~~o~,

1.04 a2q) f 3

z,,!6xi0-~-b2qbf

I/

(..);

<

LED

kf(~f,b)

u"l

-J

OlNENSIONAL

EQUATIONS

-6II'"

r

i ~ef3

1

2b

2.08a2~)f 3

8,33• 10""b2~ f

I

2b

1,0L a2(~f3

4,16•

2.0~m2(~ f3

8,33xlO'Lb2~ l

0.62 a2(~f3

5,55x 10' b2 .@i

~T I

I

i' !

2~

4

a

i 2~13

96

I

6 b2q)f

L 5

U3 LU

_.2

2,.b_ a

' -~, I'

1__a2(~f3' ~ b 2 & 48

2

1 2~3

~s~

f

UNITS" K [ D a r c y ) , o ( c m )

b(microns)

,~/=f(PI, LFD) = = = > > ~,/calculated through Eq. 7-27. (3) Assuming the six simplified and idealized models of matrix blocks as shown in Fig. 7-22, it is possible to correlate the basic data of idealized blocks as: a - block dimension; b - fracture width; k / - fracture permeability; ~)/- fracture porosity; and L F D - fracture density. The theoretical correlations are given in Table 7-IV for various idealized block shapes. The block dimensions (a) and fracture opening (b) can be estimated if permeability (k/) and porosity (~/) have been evaluated from well testing results.

Example 7-1 Evaluation of the matrix block from production data In a fractured reservoir, from production testing data a rate of 12,260 STB/D was measured, and the formation pressure drop was 68 psi. Other reservoir data are: oil viscosity Po = 1.1 cP; oil volume factor B ~ = 1.36; total reservoir pay h = 86 m;

718 drainage radius r = 1200 m; and well radius r = 10 cm. From core examination an average fracture density LFD was estimated to be 2/m. Question: Assuming the model 5 of Fig. 7-22 (cube with 2 flowing directions), evaluate: (1) the fracture permeability; (2) the fracture porosity; and (3) the block size (a) and the fracture opening (b) by using the field production data. Solution: Evaluation o f k t and d~tfrom field data. (1) The productivity index PI (STM3/D/atm) is given by e

w

PI = A Q / A p = 12660 (STB/D) / 68 (psi)= 186.17 (STB/D/psi)= 435 (STm3/D/atm) = 5034 (STcm 3 / D/atm) (2) The fracture permeability is equal to (Eq. 7-20):

k / = PI * B ~ * Po" (In r / rw) / 6.28 h = 5034 (STcm 3 / D/atm)* * 1.36 * 1.1 * In 12000 / 6.28 * 8600 = 1.31 D The porosity (Eq. 7-27) is: ~: = 1.73.10 -3 [PI. Po* Bo * In ( r / r ) * LFD2/h

]0.333

~I = 1.73.10 -3 [435 * 1.36 * 1.1 * In (12000) * 0.022 /

8 6 ] 0.3333 =

0.00025 = 0.025%

Evaluation of" block size a and fracture opening b. Based on Table 7-IV for cubeshaped matrix blocks (Model 5). (3) The cube dimension is equal to" a = [ k / / 2 . 0 8 * ~/3]0.5= [1.31/2.08*0.025 3]0.5 = 200 cm. = 2 m(4) The fracture width is equal to" b (~tm)= 100*a(cm) x ~(%)/2 = 100"200" 0.025/2 = 250 ~tm

Rock compressibility in fractured limestone reservoirs In a fractured reservoir, the compressibility of a system plays an important role, especially if there is a great contrast between the two porosities of matrix and fractures (~/<< Cm)"The role of compressibility is essential in the interpretation of the transient pressure behavior resulting from well testing. In this case, compressibility associated with the double-porosity system could express the storage capacity parameter which could be estimated through transient pressure behavior. The compressibility could be defined as the change in volume A F referred to the total volume F as a result of an applied pressure Ap:

719 (7-28)

C= (1/V) * (AV/Ap)

Depending on the reference volume used, the compressibility will represent a behavior of a certain volume subjected to compression, such as the bulk volume (VB), pore volume (Vp), or fracture volume (Vf). The change in volume due to the variation of effective net pressure p~ is the result of a change either in overburden stress o (while the pore pressure p remains constant), or a change in pore pressure p. (while the overburden pressure remains constant). The usual case during reservoir production history is given by the depletion, which is associated with the drop in pore pressure P during reservoir depletion: P p~ = o - - p p

(7-29)

and thus, an increase in p. The direct effect is a reduction in porosity related to the formation compressibility C" Cp = (1 / r * (de / dp~)

(7-30)

The compaction and the resulting reservoir subsidence are directly associated with the decrease of pore volume, due to continuous growth in Pe as a result of reservoir depletion. The effective compressibility of fractures can be written as: C = CI-C

(7-31)

where C I = fracture compressibility and C m -" matrix compressibility. In general, the fracture compressibility for a carbonate reservoir is higher than the matrix compressibility: C I - (10 to 100) C m

Effective compressibility in a fractured limestone reservoir In the case of a double-porosity reservoir, oil saturation S m = f (Sw~,m)in the matrix is related to the magnitude of interstitial water saturation, whereas in the fracture network S = 1, since the interstitial water saturation is zero. Thus" S

i,J

=1

wi,j" -- 0 Soi,m = 1 - S w i

m

Inasmuch as the fracture porosity is very small Ct << Cm' it may be approximated that the effective compressibility for matrix in the oil zone C o is: Ceo -- C O "~- C w * Swi m /(1 --Swim) "~" C

/ (1 --Swim)

(7-32)

720 where" C = 2 - 5 . 1 0 -4 (1/psi) and C = 3.10 .-6 (1/psi) and

C-- Cm-I- Cf~ C m In the case of double-porosity with an impervious matrix:

Sm--Si --1 Therefore, it follows that"

Co--C+ [C,(~m/l~s ] -I-[Cm. (~m/~S ] "~"Cf

(7-33)

where

Cm+ Cf = Cp In the double-porosity system the total storage capacity is associated with the compressibilities of the fractures and the matrix so that: ~,. C = ~l * C~ + ~/* C 2

(7-34)

where ~ and ~2 are expressed by ~, = ( 1 - ~ 2 )

(7-35')

* ~m" ( 1 - S w i )

~2 = if/

(7-35")

and respective compressibilities from Eq. 7-32 are C 1 = C + C * S i + [ C / (1 - S i ) C2 = C

]

(7-36) (7-37)

Relative permeability and capillary pressure curves in fractured carbonate reservoirs Relative permeability Relative permeabilities in a conventional reservoir are obtained from special core analysis. In a fractured reservoir, the evaluation of relative permeability curves is complicated because of the nature of double-porosity system, where the fracturing plane between two matrix units develops a discontinuity in the multi-phase flowing process. At the present time, it may be stated that due to difficulties involved in the

721 attempt to present a "unique relative permeability curve" for the entire fracture/matrix system, it is more recommendable to characterize the fractured reservoir by two relative permeability curves: one for the matrix and another for the fracture network. Matrix Relperm curves. The relative permeability of the matrix for two or three phases is evaluated by the procedure used for any intergranular rock sample. The results have to be representative in relation to the shape of Relperm curves and the magnitude of their endpoints (irreducible saturation in the wetting and non-wetting phases and the respective relative permeability values at these critical saturations). Fracture Relperm curves. The fracture network Relperm curves are basically different from matrix Relperm curves as a consequence of the very high intrinsic permeability of fractures. This very high permeability will have as a main consequence the predominant control of gravity forces in multiphase flow in fractures. As a result of gravity equilibrium, the relative permeability curves will essentially be reduced to two straight lines (diagonals) as shown in Fig. 7-31A. At certain conditions, especially when drops of oil are moving in the fracture saturated with water, it is more correct to adjust the wetting phase Relperm curve (Fig. 7-31B) by a different relationship:

ketting = [Sett ]n

(7-38)

where often n = 3 and dimensionless saturation, Sett, is equal to:

Swett = (Swett- Swett,i ) / (l -

Swi)

(7-39)

Capillary pressure curve In a fractured matrix system, the capillary pressure curve plays a much more important role than in a conventional reservoir. In fact, in a single-porosity reservoir the role of capillary pressure at static conditions is associated with the transition zone, whereas at dynamic conditions the capillary forces (and thus the capillary pressure curve shape and magnitude) play a more limited role because the fluid displacement process in all conventional reservoirs is mainly controlled by viscous forces. On the contrary, in a fractured reservoir where the displacement process is essentially controlled by gravity and capillary pressure forces, the examination of capillary pressure curve behavior becomes essential for a correct understanding of the displacement process. Capillary pressure behavior with both "drainage" and "imbibition" displacement processes, if combined with gravity displacement behavior (through similar relationship), make possible evaluation of matrix-fractures fluid exchange. Wettability role. Wettability is the result of interaction of the solid / fluid under given temperature and pressure conditions where one fluid which is preferentially wetting the solid represents the "wetting phase" and the other fluid wetting the solidless is called the "non-wetting-phase". There are a series of conditions which contribute to increasing or decreasing preferential wettability of one or the other of the phases:

722 A

Knw Kwy

1

I

K

Knv,/

l

, T

0

0

Sw

"~

o 0

Sw ~ ' ~ "

"1

Fig. 7-31. Relative permeabilities in fractures: a =vertical equilibrium; b = optimized curves.

(1) higher temperature increases the wettability for water phase; and (2) certain compounds, such as asphaltene, reduce the wettability for water and increase the wettability for oil. The various phases encountered in a hydrocarbon reservoir under preferential wettability for one phase compared with other are: Wetting

Wetting phase

Non-wetting phase

Number of phases

Water-wet case Water-wet case Water-wet case Oil-wet case Oil-wet case

Water Water Water Oil Oil

Oil and gas Oil Gas Water and gas Gas

three two two three two

Capillary displacement vs. wettability. The displacement of oil from the matrix, and the role of capillary pressure, are dependent on fluid saturations in the fracture/matrix system, as well as on fluid wettability and saturation history. In fact, the displacement process could be a drainage or an imbibition process if the behavior of saturation variation in the matrix and fractures is similar to those described in Table 7-V Initially (@ t = 0) the matrix blocks are fully saturated with the "wetting-phase" ( S e t t "- 1) and the surrounding fractures fully saturated with "non-wetting-phase " ( S e t t = 0). The displacement of "wetting-phase" (contained in matrix blocks) by "nonwetting-phase" (contained in fractures) requires a higher pressure in fractures than in matrix (Pl > Pmatrix) and is called "drainage displacement". The resulting capillary pressure vs. saturation relationship is known as the "drainage capillary pressure curve" (Fig. 7-29). Inversely, if initially (@ t = 0) the matrix block is saturated with a "nonwetting-phase" ( S e t t = 0 ) , whereas the fractures are saturated with the "wetting-phase"

723 TABLE 7-V Initial conditions of drainage / imbibition displacement.

. . . . .

TIME

I

ii

' FRACTURE

/i i

ii

i

i

ii

i

ii

!

i

SWETT : 0

att=O

i DISPLACEMENT PROCESS

MATRIX

SWETT : I 1.

,

Pfr

>

,

P Matrix

DRAINAGE t >0

S WETT = 0

S WETT < 1 (decreases)

SWETT : I

SWETT = 0

att=O Pfr

= ,,

t >0

S WETT < 1

P Matrix

IMBIBITION

:,,

SWETT > 0 (increases) ill

i

1), then an "imbibition displacement" drive mechanism takes place (see Fig. 7-32). This displacement is controlled by a capillary pressure vs. saturation relationship known as "imbibition capillary pressure" curve.

(Set t =

Description of drainage and imbibition displacementprocess. In order to describe the drainage and imbibition processes, the desaturation in a wetting-phase (drainage), and saturation increases in a wetting-phase (imbibition) are schematically illustrated between initial conditions (@ t= 0) and final conditions (t ~ oo) in Fig. 7-33. If a "non-wetting phase" initially saturating the matrix block is displaced by a "wetting phase", then the result will be an "imbibition capillary pressure vs. saturation curve". If this "wetting-phase" in the block is further displaced by a "non-wetting phase", a "drainage process" will take place. This displacement is controlled by the "drainage capillary pressure vs. saturation curve" (Fig. 7-33) The essential characteristics obtained from the two driving histories, which resuited in two capillary pressure curves (drainage and imbibition) indicated in Fig. 733, suggest the following: (1) the minimum saturation of a wetting phase, which is the same in both processes and is called "irreducible saturation of wetting phase," corresponds to an infinitely large "displacing capillary pressure"; (2) the shape of a drainage capillary pressure curve shows the distribution of pores and reflects the homogeneity of pore dimensions; (3) the existence of a residual saturation in the non-wetting phase is obtainable only in an imbibition displacement process, when the trapped non-wetting phase fills

724

aP Or)

r

C.D

100% w e t t i n g - phase s a t u r a t i o n

Fig. 7-32. Drainage and imbibition capillary pressure curves. large-diameter pores which intersect with clusters of small-diameter pores; (4) in the case of capillary and gravity forces controlling a drainage process, the displacement of a wetting phase by a non-wetting phase can take place only if the threshold height is smaller than the block height; (5) the drainage process can start only if the pressure difference p /.,.,.t ~o~ - p ..... is .... t.i,. higher than "threshold pressure" Pthreshold (which is very close to the pore throat pressure); and (6) capillary forces are opposing the entrance of a non-wetting-phase in the matrix during the drainage process, whereas capillary forces help the entrance of the wetting phase in the matrix during imbibition.

Dimensionless drainage capillary pressure curve. A dimensionless curve can be elaborated by using a "normalization" approach for cores of the same reservoir but of different physical properties (porosity, permeability, etc.) and for which the capillary-saturation relationship was evaluated under different laboratory conditions (pressure, temperature, fluid characteristics, etc.). The dimensionless function J (Sw) expresses the ratio between capillary pressure and a pressure term expressed by parameter group formed by k, ~, o, and O: J (Sw) = Pc / o * cosO * (~) / k) '/2

(7-40)

where J (Sw) represents the Leverett dimensionless capillary pressure; ~ and k are

725

Pfr = Pmatrix

F I

MAT;IX SWETT = o

IMBIBITION MATRIX SATURATION HISTORY

J

+

~

FRACTURE l SWETT = 1 J

INIT1AL SWETT = 0

IMBIBITION PROCESS

DURING DISPL ACEMENT 0 < SWETT< MAX

FINA L SWETT = MAXIMUM

0 SWETT 1

0 SWETT I

pc !

CAPILLARY FORCES DIRECTED TOWARD MATRIX

o SWETT 1

CAPILLARY FORCES HELP DISPLACEMENT

-)

1

CAPILLARY FORCES DIRECTED TOWARD FRACTURES _1

1'

t

SWETT = 1

i SWETT o FRACTURE i

[ MATRIXA

t I I

CAPILLARY FORCES OPPOSE DISPLACEMENT

,I,

Pc 0 SWETT t

0 SWEIT

0 SWETT_1

, .

=

L

MATRIX [ WETTING PHASE SATURATION[ SWETT

SWETT = 0

'DRAINAGE PROCESS

t

INITIAL

0 < SWETT< MINIMUM SWETT= MINIMUM DURING DISPLACEMENT

FINAL

f Prr > Pmatrix

]

DRAINAGE MATRIX SATURATION HISTORY

Fig. 7-33. Imbibition/drainagecapillary displacementprocess. core porosity and permeability, respectively; and c and 0 are the interfacial tension and contact angle, respectively.

Schematization of drive mechanism by capillary and gravity forces. In a fractured reservoir, the imbibition will take place whenever the wetting phase (water) in fractures displaces the matrix block non-wetting phase (oil). A simplified scheme of the displacement process controlled by gravity and/or capillary forces is shown in Fig. 734, where the oil displacement is due to: (1) only capillary forces which imbibe the matrix with water (case a), and (2) additional gravity effects (case b) as a result of level difference h between water-oil contacts in fractures and matrix. By examining the two matrix blocks saturated with oil in Fig. 7-34, if the water-oil contact is at the matrix bottom face (Fig. 7-34A), then the forces displacing the oil are only the capillary forces. But if the water-oil contact in fractures is above the matrix block bottom face (Fig. 7-34B), the difference in the specific weight of water-oil generates a gravitational force G = (h.AT), which acts as a displacement gravitational driving force in addition to driving capillary forces. The magnitude of gravitational forces depends on the magnitude of level difference h between water-oil contacts in fractures and matrix: G = h * Ay

(7-41)

726 whereas the capillary forces are proportional to the average capillary height h c" P = h * A),

(7-42)

Composite capillary pressure curve. The capillary forces vs. water saturation curve ( P - S ) displays the distribution and magnitude of capillary forces during the displacement process of oil by water. If an analysis of gravity forces displacement is carried out, a similar curve (PG vs. Sw) could represent the relationship between gravity forces and oil desaturation (oil recovery). The "gravity forces" during the displacement are acting more in medium to large pores, whereas "capillary forces" displace the non-wetting phase more from medium to small pores. But the capacity of gravity to displace the non-wetting phase (oil) depends on the diameter of pore interconnections. In fact, a part of the displaced fluid might be trapped as a result of connection of medium to large pores with small pores leading to the blockage of oil in the large pores as result of contrasting pore size. As a result, the relation PG vs. S wwill reflect its dependence on two key elements" pore size distribution and pore intercommunication. The experimental PG vs. S wcurve may be considered similar to a capillary pressure curve, and it is therefore acceptable to consider gravity force Pc to be equivalent to a negative capillary pressure P (the negative sign of P is a conventional sign):

(7-43)

PG = - Pc

OIL IN

FRACTURES

"'"

""

9

.

9

"

9

" W A T E R ' ' -

.,,.,

A

B

Fig. 7-34.Typeof displacementfor matrixblock: (A) displacementundercapillaryforces; (B) displacement under capillary and gravity forces.

727

capillary

Pc

0

100"/,

gravity

1

forces

/

Fig. 7-35. Composite capillary pressure curve including the role of gravity vs. desaturation in water,

A S w.

During the imbibition process if the necessary conditions occur, then both gravity and capillary forces may displace the fluid saturating the matrix. Thus the gravity and capillary imbibition roles may be represented by a "composite curve" as shown in Fig. 7-35.

FRACTURED CARBONATE RESERVOIR EVALUATION THROUGH WELL PRODUCTION DATA

A fractured carbonate reservoir may have only one porosity type (only fractures) wherein the blocks delimited by fractures are impervious (Fig. 7-36A) or may have dual-porosity system when both the fractures and the matrix are porous and permeable (Fig. 7-36B). In the single-porosity case where the continuum is formed only by the fracture network, the solid impervious blocks play a similar role as the solid grains of a conventional intergranular reservoir, whereas the fracture network is similar to the intergranular voids. Based on this analogy, some basic laws and flowing equations established for flow in conventional intergranular limestone can be extended to the case of flow in a fracture network. The "continuum" formed by the totality of intercommunicating fractures is, in principle, described by fracture permeability and fracture density which could be evaluated from well test analysis.

728 In a case of double porosity formed by fractures and matrix, a different approach is introduced where only the fracture network represents a continuum, whereas all single isolated matrix blocks represent the discontinuity. Inasmuch as these single matrix blocks are characterized by large porosity and small but sufficient permeability, to assure the exchange of fluid with the fractures they could be considered as sources of fluids. These sources, containing large volumes of fluid when compared with the volume contained in the adjacent fractures, can feed the fractures with fluid during well production, or can receive fluid for storage during pressure build-up or during fluid storage. With this role played by matrix blocks, it becomes clear that their role is equivalent to "fluid supply sources" or "fluid storage sources", whereas the role of fracture networks is to "carry the fluid" from these sources toward the well during production and, inversely, toward the sources (matrix blocks) during storage.

Single porosity case (impervious matrix) In the case of impervious matrix blocks, the flow through high to very high-permeability fractures will be stabilized in a relatively short time either after initiation of production or after well production is shut in. As in the flow in pipes or in an intergranular porous reservoir, it was shown that the flow in a fractured reservoir presents a laminar state at low flow rates and a turbulent state at high flowing rates. In the flow of a fluid through a pipe of small diameter, through intergranular pores, or through a fracture network, viscous forces play a predominant role. Between the fracture networks with their very small openings (baverag e -" 30 microns) and intergranular pores it is possible to present a general physical analogy between the flow in fractures and flow in porous media.

Flow through single fractures In the narrow space of a single fracture (Fig. 7-29), the steady-state flow rate can be expressed by Eqs. 7-18 and 7-19, in the following forms: q/= q = a*b*(b 2 / 12" ~t) * (dp/d/) = a * b * (k/i~ ~t) * (dp / dO

(7-44')

where b z/12 = k//

(7-44")

and k is considered "intrinsic" fracture permeability. If ~n / the single fracture case (Fig. 7-29), the flow is expressed by Darcy's law, then overall cross-flow area a h has to be introduced with the fracture permeability (k/):

Q

=

a ' h * (k/I Ix) * (dp / dO

(7-45)

Combining Eqs. 7-44 and 7-45, a number of correlations as shown in Eq. 7-21 is obtained.

Flow through multi-fractures In fracture systems having an idealized geometries, the flow rate Q (Fig. 7-30) will

729

A

Fig. 7-36. Fracture-matrix system: (A) impervious matrix (k = 0) and (B) porous matrix (k = 0). have to include the effective cross-flow area (n.a.b):

Q = n*a*b*(b 2/12~)

*

(@/dO = n*a*b*k H (1/~)

*

(@/dO

(7-46)

or if based on Darcy's law, the fracture permeability (kj) and the total flowing crosssection (a.h) are introduced in the rate expression:

Q

=

a*h (ks/It) * (dp /

dO

(7.47)

On the other hand, the fracture network can be idealized through simple geometrical

730

Y

THE VELOCITY PROFILE

__7~ 8 4

! I ! I I I

It

/

/ Fig. 7-37. Schematic presentation of flow through two walls delimiting a fracture.

models as elaborated in Fig. 7-22 and in Tables 7-IV, 7-VI and 7-VII. The results obtained from field data could be reviewed in the light of this relationship, as shown in the Example 7-1.

Transition from laminar to turbulent flow in fractures From the experience of flow in pipes it is known that turbulent flow depends on pipe roughness, the magnitude of which is directly related to the friction factor. The transition from the laminar state to turbulent state of flow is controlled by the Reynolds number which is the ratio of the inertia to viscous forces: Re=2V*D* p/p=2VD/v

(7-48)

where V is the average velocity in the pipe, D is the length of the pipe, P and p are, respectively, the density and viscosity of the fluid transported, and v is the kinematic viscosity. For flow between parallel walls delimiting a fracture (Snow, 1965), the Reynolds number is given by:

Re=2*p*V*b/p=2* V*b/v

(7-49)

731

TABLE 7-VI Idealized geometrical models o f fractured reservoirs i,

i

i

Vx - 0

Vy= O;Vz - 0

HODEL 1 9

HODEL 2

9

9

SLIDES

HODEL 3 s

9

HATCHES

Vz= 0; Vy-O

9

Vx- O. Vy-O

s

HATCHES

Vx = O;Vy=O

MODEL z, IZUBES

MODEL 5 IZUBES

s

9

9

Velocity

L.F.D.

Cf

Vx= 0

1/a

Vy = 0; V z = 0

1/a

3. Matches

V x - 0; Vy - 0

4. Cubes

Vy- 0

MODEL 6 IZUBES

9

9

r

a

b

b/a

12*Kf*LFD 2

1/LFD

(12*Kf/dpf) ~

2b/a

96*Kf*LFD 2

1/LFD

(24*Kf/~r) ~

2/a

2b/a

12*Kf*LFD 2

2/LFD

(12*Kf/~f)~

V z - 0; Vy - 0

1/a

2b/a

96*Kf*LFD 2

2/LFD

(12*Kfh~f)~

5. Cubes

V x - Vy - 0

2/a

2b/a

12*Kf*LFD 2

1/LFD

(12*Kf/,f) ~

6. Cubes

Vy = 0

2/a

3b/a

40.5*Kf*LFD 2

2/LFD

(18*K/,# o.'

Model TYPE 1. Slides 2.

Matches

732 "Relative roughness" values for an average fracture opening of 20 gm are around 0.0015 - 0.025 for limestones and 0.004 - 0.007 for dolomites. In the event the fracture network is treated similar to a porous medium, it is necessary to introduce permeability and, thus, the critical Reynolds number is: Recr =

1

where the Reynolds number is expressed by a semi-empiric equation:

Re=lO*9* V*k ~

(7-50)

Basic equations describing flow in fractures If the flowing process in a fractured limestone network is considered analogous to the flow in an intergranular limestone, then the relationship between pressure drop Ap and rate Q will be:

Ap=A * Q+Bv* Q2 This corresponds to a linear flow for low rates when B T. Q 2 << A. Q, and to turbulent flow for high rates when B T . Q 2 > A.Q. Both constants A and BT in these cases depend on flow geometry and physical properties of rock and fluids. Thus, the analogy between a conventional reservoir and a fracture network is based on the similarity between the parameters of the fracture system (kp krp qbp b, n, LED) and the parameters of a conventional reservoir (k, ~, h). Such relati6nsliips for various simplified geometries of fracture networks are given in Tables 7-IV, 7-VI and 7-VII.

TABLE 7-VII Evaluation of permeability kj and rate Q for idealized geometrical models of fractured reservoirs. |

i

L

|

Rate

MODELS* ~f?12 LFD 2

Q = (A* ~)f 3 / 12 LFD 2) ( @ / d O

~f~96 LFD 2

Q = (A* ~)f 3 / 96 LFD 2) (dp/dl)

~r-~48 LFD 2

Q = (A* , f 3 / 48 LFD 2) (dp/dl)

~f~96 LFD 2

Q = (A* , f 3 / 96 LFD 2 ) ( d p / d / )

~f~162 LFD 2

Q = (A* ~)f 3 / 162 LFD 2) (dp/dl)

* Similar to the models of Table 7-VI

733

Steady-state radial symmetrical flow (toward a well) General analogy criteria. In a fractured network, as in a conventional intergranular reservoir, as soon as the well starts to produce the pressure will drop in the producing well and the fluid will move toward the well along the radial symmetrical flow lines. In three dimensions, the flow takes place through cross-sections represented by lateral surfaces of cylinders (which are co-axial with cylinder-shaped wellbore, see Fig. 7-38). Due to the same analogy between the flow through interconnected channel systems (fracture network) and the flow through intergranular pores (porous media), it is physically correct to express the flowing equation as Ap = A Q at low flowing rates. A non-linear relationship Q2 vs. Ap exists when flow rates are high, so that the total pressure drop becomes:

(7-51)

Ap =A * Q + B T* Q2

which is presented in a diagram Q vs. Ap (Fig. 7-39). As may be observed, the laminar flow Ap = A * Q is valid until a critical rate Qer is reached. If the rates continue to increase beyond a certain transition zone, the second right-hand term of Eq. 7-51 becomes predominant, and the flow is almost completely controlled by a turbulent flow state, expressed by Ap = B * QZ.

Radial flow analogy. In case of a radial symmetrical flow and based on the analogy discussed (Snow, 1965), the constants A and B are equal to:

WELL

MATRIX km,O

FRACTURE Fig. 7-38. Flow toward a well through fracture network.

734

AP=

f

ill

Fig. 7-39. Relationship between Q and AP obtained in a radial flow toward a well, through a fracture network. A = [~o* Bo (ln r / r + S)] / 2 * rt * k: * h

(7-52)

Bx=I3 * kto* B o ( 1 / r w - 1 / r ) / 4 *

(7-53)

r~' * h 2

where 13 is expressed as a function of permeability and porosity: 13 (1 / ft) = 2.23.109 / [k/. dp/(mD.fraction)] 1~

(7-54)

The use of the above equations can help two objectives: (1) to express the flowing equation:

Ap =A * Q + Bv * Q2 This is possible if the physical parameters (d~: k/, ~t, h, Bo) and geometrical data (rw, re) are available, in order to estimate the parameters A and B T through Eqs. 7-52 and 7-53. (2) To estimate the reservoir characteristics:

k/, dp/, [3, a and b. This is possible if the production data (Q and p) recorded during well testing are available.

735

t AP/Q A

Q Fig. 7-40. Relationship between AP and Q for the evaluation of parameters A and Br. Procedure f o r f i e l d parameters evaluation. By using the well stabilized rate [Q] and

pressure difference [Ap] during the steady-state conditions of flow, a linear relationship Ap / Q vs. Q is obtained when data are plotted as in Fig. 7-40. From the straight-line relationship Ap / Q vs. Q, the parameters A and B are directly obtained: A = as the value Ap / Q @ Q = 0 and B T = as the slope of straight-line Ap / Q vs. Q. The constantsA andB can be further used for evaluation of reservoir characteristics. Permeability. Permeability ks from Eq. 7-26 and using parameter A equal to 1 / PI,

gives: ks = {~o * Bo * [ln ( r / r ) + S]} / 6.28 * h * A

(7-55)

Porosity ~s can be estimated only if the fracture density LFD is known from core observations. Equation 7-27 requires the knowledge of productivity index (P/) and of fracture density LFD: ~I = 1.73.10 -3 {PI*B ~ * kt~ [In (r e /rw) + S)] * LFD2 / h] u3

(7-56)

where productivity index (PI) and parameter A are related by the expression PI = 1 / A. Turbulence. Turbulence factor 13, could be obtained from Eq. 7-53 by using the parameter BT:

736

= 4 * rc2 h 2 . r * B x~ 9o* Bo

(7-57)

Permeability. Permeability k: can be obtained from the turbulence factor fl by using Eq. 7-54:

k/(mD) = (1 / r

* [(2.2.10 9) / ]~ (1 / ft)] 0"922

(7-54')

Idealized model characterization. Based on parameters as k/, d?/and LFD for a given idealized block shape, the block size a and fracture opening b can be obtained from Table 7-VI:

a = f (LFD) b = f(k, r

Example 7-2 Fractured reservoir characterization from well testing data In a fractured limestone reservoir, from well production testing the following rates and pressure drop data rates were obtained: TEST 1

==>

Q = 5600 STB/D

Ap = 127.7 psi

TEST 2

==>

Q = 11300 STB/D Ap = 318.5 psi

TEST 3

==>

Q = 16700 STB/D Ap = 556.0 psi

In addition, the following data are known: Oil viscosity Oil gravity Oil volume factor Fracture density Average pay Drainage radius Well radius

kt~ )'o B~

= = = LFD = h = re = rw =

0.4 cP 0.814.10 -3 kg/cm 3 1.41 2/m 96 m 350 m 10 cm

Determine: (1) flowing parameters A and B x by plotting Ap / Q vs. Q obtained by the well testing; (2) the flowing equation Ap vs Q; (3) the limestone fracture permeability, k:; (4) the limestone fracture porosity, if/.; (5) the turbulence factor, 13; (6) a simplified / idealized matrix block, assuming a cubic matrix block where the

737

0.03 9-0.0175 1::13 I.--O0

0.02 -

/

= 9 . 4 x 1 0 -7 ( p s i / S T B / D ) 2 )

rd3 Q. v

0 13..

<~

A= 1.75x 10-2 [(psi/STB/D)] 0.01 '-J

i

I

I

I

I

5,000

10,000

I

I

I

15,000

Q(STB/D) Fig. 7-41. Relationship between AP / Q and Q obtained from well testing data in a fractured reservoir.

flow takes place in all three cartesian directions (model 6 of Fig. 7-22).

Solution (1) Based on well testing data: Q STB/D Ap psi Ap / Q psi/STB/D

5600 127.7 0.0228

11,300 318.5 0.02818

16,700 556 0.0332

These data are plotted in Fig. 7-41 as a straight-line (Ap / Q vs. Q), from which constants A and B v can be obtained: IfQ=0 A = 1.75" 10-2 psi/STBD = 6.49.10 -4 atm / STcm 3/ sec = 7.51.10 -3 a t m / S T m 3 / D The slope B T = [(Ap / Q)] / AQ = 9.4.10 -7 psi / STBD 2 = 2* 10-8 a t m / ( S T c m 3 / sec) 2 (2) The flowing equation is: AP (psi) = 1.75.10 -2 * Q (STBD) + 9.4.10-7Q z (STBD) 2

738 (3) The permeability k z is determined from linear relationship Ap vs. Q (Eq. 7-55) k / = [~to* Bo* In ( r / r ) ] / 6.28 * h * A =

0.4 * 1.41 * In (3500) / 6.28 * 96.102 * 6 . 4 9 . 1 0 -4 = 0.117 D = 117 mD where: h (cm); ~t~ (cP); A ( a t m / S T c m 3/sec). (4) Fracture porosity ~/is obtained from Eq. 7-56, assuming a random distribution of the fractures" ~: = 1.73.10 -3 [PI * B ~ * ~t~ * In (r e / r ) * LDF2/ h] ~/3 where" P I = 1/A (STm 3/ D / atm); ~/fraction; ~t o is in cP; h is in m and L F D is in 1 / cm. ~: = 1.73. 10 -3 * [(1 / 7.51. 10-3) * 1.41 * 0.4 * In (3500) * 0.022 / 96] v3 ~ / = 0.00023 = 0.023 % (5) The turbulence factor can be obtained from Eq. 7-57"" 13 = B T [4 rc 2 h 2 rw/9oBo ] = 2* 10-8 . *[4 * (3.14 * 9600) 2 10 / 0.83.10 -6 * 1.4] = 0.625*

10 9

(1/cm) = 19"

10 9 (l/ft)

where" h is in cm; r is in cm; 90 (kg * sec 2/cm4); B T is in atm / (cm 3 / sec)2. (6) Evaluation of the idealized matrix block Using the matrix block having a cube shape and where the flow takes place in all three flowing directions, from Table 7-IV one obtains the matrix block size: a = [ k / / 0 . 6 2 * ff/3]0.5 = [0.117(D) / 0.62 * 0.018 3]o.5= 179 cm = 1.79 m The fracture opening b = [100 if//3a(cm)] = [100 * 0.018 / 3 * 179] o.5 = 0.0033 cm = 33 ~tm C o n i n g in f r a c t u r e d reservoirs

The general considerations concerning the formation and development of coning in a conventional porous reservoir will not change in the case of a fractured reservoir, but the flowing conditions must be reviewed with regard to the specific conditions which govern flow in fractures. The basic equations are almost the same and can be extended to fractured reservoirs, so long as the continuity of the fracture network is developed throughout the oil and water zones, or oil and gas-cap zones. The fractured reservoir, producing either through an open-hole well or through a cased and perforated well, will have a certain producing pay delimited by two, upper and lower, boundaries (Fig. 7-42):

739 _~.--~,";-o:e~.o::::~:.C~4 9 '!r162 " ~ ' ~ " ~"~.:~:.~, - .... :o-~""-~176 .~.,-.~-'.. ..... * ~ O "" ":

:0. "".'0

!~ih:~gl ~'!~"':C:::2.=.0 ~ - . ~ : :

..........

:"

I~.'..:~:--<: o-:.-:~: ~-.:,,.~:. ,:~:~.:o:-.~ .:-o:0,. '.~",,. ~ . " o i~,:~,..... - ..

E.s:

"2'//

GOL

LFEy/:

/

WOL

Fig. 7-42. Sketch o f water-oil and gas-oil contacts vs. LFEP and HFEP.

HFEP: the highest fluid entry point, and LFEP: the lowest fluid entry point The evaluation of HFEP and LFEP and respective gas-oil and water-oil contacts in the fracture network (GOL and WOL) will indicate the "non-completed" height (hg and h w, Fig. 7-42) equivalent to the gas-coning and water-coning heights, respectively. The coning is thus associated with a certain critical radius r cr' which will correspond to the limit over which the water will arrive toward the well. Inasmuch as during production of oil through a fractured reservoir the flow toward the well is radial-symmetrical, the pressure distribution will follow a logarithmic variation along the flowing streamline. Around the wellbore, a critical zone of radius rcr is associated with the possibility of coning as an effect of high pressure gradient (as shown in Fig. 7-43). As a consequence, for both contacts (gas-oil and water-oil) the coning criteria values will always be represented by a critical and a safe coning value. Critical coning is obtained in relation to the laminar flow (BT = 0) and thus is expressed by:

hcr =

mPlaminar/m'y * In (r e / rw) = A * Q / Ay * 6.9

(7-58)

where it is assumed that ( r / rw) = 1000. Safe coning height in both flowing states, i.e., laminar and turbulent, is equal to hSAFE -- mPtotal 6.9 * A7 = (A * Q +B T * Q 2) / 6.9 * Ay

(7-59)

As a general rule, the coning criteria have to be associated with the reservoir pay thickness. For pay 200 ft < h < 1000 ft Eq. 7-58 is used for coning evaluation. For pay h < 200 ft, Eq. 7-59 is used for coning evaluation.

740

ii

\

~--~ W~QZ~L ~WOLI

---:c l rc

Fig. 7-43. Water coning, function of movable water-oil contact position.

The explicit coning evaluations for gas-oil and water-oil are" Water-oil coning hwo _ Water-oil coning hwo Gas-oil coning hg ~ _

_

c r ----

S A F E

cr =

Gas-oil coning hg~ - S A F E

A *Q/6.9 * A?w~ --"

[A *Q+B T * Q'] / 6.9 * A?w~

A * Q / 6.9 * Aqtg~ "-

[A

*

Q + B T * Q'] / 6.9 * A?g~

(7-60a) (7-60b) (7-60c) (7-60d)

FRACTURED LIMESTONE RESERVOIR EVALUATION THROUGH TRANSIENT FLOW

WELL DATA

The conventional reservoir having intergranular porosity is studied under the simplified assumption that it is homogeneous, and the physical properties such as

741 porosity and permeability are showing overall certain trends in the field. In a naturally-fractured reservoir, as a result of fracturing processes there are a series of discontinuities throughout the reservoir, a situation that results in two distinct porosities (matrix porosity and fracture porosity) and sometimes a third one, vuggy porosity (as shown in Fig. 7-44). The matrix region with fine pores and high storage capacity, but a low flowing conductivity, is connected with the fractured network region which has a low storage capacity but a high to very high flowing conductivity. Such contrasting conditions require different reservoir engineering procedures from those used in conventional intergranular reservoirs. The proposed procedures have as objectives the interpretation of transient recorded well pressure data vs. time in order to estimate reservoir characteristics such as porosity and permeability of both fracture and matrix regions, fracture density, matrix block shapes and sizes, etc. From all procedures discussed in the literature (Aronofsky and Natanson, 1958; Pollard, 1959; Barenblatt et al., 1960; Warren and Root, 1963), the most representative by its correct physical approach and proposed solution remains the Warren-Root (1963) method.

VUGS

MATRIX

FRAC TURE

Fig. 7-44. Real fractured reservoir rock.

Basic discussion of Warren-Root method The Warren-Root (1963) method proposes and uses a simplified representation of a fractured reservoir by an idealized system, where single matrix blocks are identical rectangular parallelipipeds separated by an orthogonal network of fractures (Fig. 745). The flow toward the wellbore is considered to take place only in the fractured network, whereas the expanded fluid contained in the single matrix block, as a result of fracture network pressure depletion, will feed the fractures network as shown in Fig. 7-46. The method can be summarized as follows:

742 ~ m N

~

~-_'_

\

\ MATRIX

'/-

FRACTURES

Fig. 7-45. Idealized fractured reservoir.

eee@@DDDe@eD @~N@@eeN~~Ge q~~D~

~Des

E] E] Q D D

~G 89

,/

Fig. 7-46. Matrix-fractures fluid exchange during the flow toward a well.

743 Log t..~ ,,

~f~

"-4

'Qt

~.P

., ....... %

,I,

,

I I

FIRST STAGE

FIRST STAGE

! SECOND STAGE

i

?

i

SECOND STAGE

m,',

I THIRDSTAGE

!

A

THIRD STAGE

,

i ~.."

! I

I .,. I.."

&P

.."" / /

/

Z V

Log [At/(to+~t)] ~

-

B

Fig. 7-47. Double slope of transient pressure in a well during pressure drawdown and pressure build-up. (1) The procedure of reservoir evaluation proposed by Warren-Root (1963) is based on a similar processing approach as is used in a conventional reservoir: the well data are plotted as pressure variation vs. log time either for pressure drawdown (Fig. 747A) or for pressure build-up (Fig. 7-47B). (2) In all transient behavior analyses of a "one-porosity reservoir" (non-fractured limestone), the well pressure vs. log time is represented axiomatically by a straightline in both conditions: pressure drawdown or pressure build-up. (3) In the case of a "double porosity" (fractured) reservoir, the pressure plotted vs. log time will exhibit in both cases of pressure drawdown and buildup: a double straight-line (double-slope) over three stages of different behavior (Fig. 7-47).

744 (4) The three stages in the variation of pressure with log time are represented by: (1) in a first one a straight line called early stage; (2) a second one called transition or intermediate stage; and (3) a third one, again a straight-line, called final stage. Each of them reflects the fluid exchange between the matrix and fracture network whenever a well starts to produce at a constant rate (Fig. 7-47A) or production stops, and the pressure starts to build up (Fig. 7-47).

Basic physics of transient flow analysis A pressure vs. log time diagram reveals the presence of two parallel straight lines instead of only one (as is usually obtained in a non-fractured reservoir). This will be the first step in recognizing the existence of a fractured reservoir. The specificity of the pressure vs. log time behavior in the case of a fractured reservoir requires a physical analysis of flowing conditions. For this analysis, the case of well pressure drawdown under a constant production rate is presented here: (1) After starting to produce a well at a constant rate Q, the well pressure decreases because the fracture pore volume is small and the supply of liquid from the matrix has not yet started. The linear pressure decline vs. log time reflects the flowing capacity of the fracture network as shown in Fig. 7-48 along the straight-line between points 1 and 2. This phase is called the "early stage" of transient pressure behavior. (2) By continuing to produce fluid at a constant rate from the fracture network (Fig. 7-46) the pressure in the fractures p ! declines continuously, developing a pressure difference between the matrix and fracture (p m - p f ") Thus the fluid from matrix blocks will start to flow toward the fracture network. By feeding the fracture network with expanded fluid from matrix, the result is similar to an "injection of liquid" in Log t ..~

0

, l\ ' T vX\

AP x

\\\\

1,

FIRSTSTAGE

I SECONDSTAGE l THIRDSTAGE

Fig. 7-48. Pressure drawdown behaviour (Dp vs. log time) in a producing well.

745 fractures, and consequently, the well pressure decline is reduced. This second phase (representing the "transition stage ") is shown in Fig. 7-48 where: (i) the decline reduction corresponds to the time when the "feeding rate" arriving from matrix blocks starts to compensate a part of fracture "production rate" at point 2 (corresponding to initial transition time tt) of Fig. 7-48; (ii) the reduction of pressure decline will continue until the pressure decline becomes practically zero at point 3 (time tt0 of Fig.7-48. At this inflection point, the pressure drop (Ap0 is constant for a short period of time. (3) While the well production continues at constant rate, the pressure decline will start again to grow from point 3 to point 4 (ti,me tt~ and tt.) as a result of a transitional non-equilibrium developed between a lower 'fluid supptied rate" (by matrix blocks) and the "well fluid produced rate" from fracture networks. (4) The end of the transition time (ttj) corresponds to point 4 representing the time when a quasi-equilibrium is installed in the reservoir flowing process, between the "fracture fluid production rate" and "matrix fluid feeding rate". The difference between these two rates becomes practically constant after time tq, and from point 4 to point 5 (Fig. 7-48) results in a "quasi-steady-state" well pressure decline.

Basic interpretation of the results The pressure difference (APw) between the "early" and "later" parallel straight line separation (Fig. 7-48) is associated with the relative storage capacity of the fracture represented by (l) "~ ~f * C f / (~m * C

(7-61)

and is evaluated through co = 1 / e 2"3. APco /

m,

(7-62)

The transition period of the pressure from the "early" to the "late" straight line will be a function of the fracture-matrix interflow capacity L. This capacity could be evaluated from pressure drop (Apm) at the time tt~ as shown in Fig. 7-48: Z = (1 -03) / 1.78 * e 2"3 * ~P~./m,

(7-63)

where the parameter could be associated with the matrix-fracture contact surface (or) through which the matrix fluid flows toward the fractures: ot = )~ (k2 / k,) * (i / taw)

(7-64)

The matrix-fracture contact surface (a) is dependent on matrix block specific size L. If contact surface ot is small, the block size L is big, and vice-versa. The relationship can be expressed as follows: L ~= W / ct where for n = 3, 2, and 1; and flowing directions q~ = 60, 32, and 12.

(7-65)

IFROM FIG: 7-471

-.4

,

II

l

,AI

PERMEABILITY Kf

INTERPOROSITY

[Equation 7-67]

Flowing capacity

9

,

~f = 1.15xqx/,t/2 :rr xhxm'

~, [Eq. 7-63]

FRACTURE

=(1-w )/1.78e 2.3 AP ~/m'

Relative Storage capacity #.) => [Eq. 7-62]

r.,d= 1/e 2.3/XPO)/m'

Matrix -fracture surface contact O( [Eq. 7 - 6 4 ]

o~= ~(K2/K1)x(1/r2w) q~

FRACTURE POROSITY ~f = ~2

[Eq.7-611

~f = ~mCm ~ / c f

Matrix-block size L[Eq. 7-65]

L2

~/o~

Fig. 7-49. "Flow-chart" for quantitative evaluation of transient pressure behavior in a well producing from a fractured reservoir.

747 The slope m' of the two parallel straight lines is a function of the flowing capacity (permeability) of only the fracture network, and is independent of matrix capacity. During the final stage, between point 4 (time ttf ) and point 5 (a later time), the fracture permeability k; = k2 can be obtained from the slope of pressure vs. log time straightline: m ' = 1.15 * q *kt / 2 * re* k 2 * h

(7-66)

k2= 1.15 * q * kt/2" rc * h * m '

(7-67)

Warren-Root procedure f o r the evaluation o f a fractured limestone reservoir

Quantitative evaluation of a fractured reservoir could be carried out by plotting, on a semilog diagram, the recorded pressure drop (Ap) vs. log time. A similar procedure has to be used for both pressure drawdown and pressure build-up cases (Fig. 7-47). The calculation procedure is presented as a "flow-chart" in Fig. 7-49, where the first step is the evaluation of parameters m', APo~and Ap~ directly from the pressure vs. log time diagrams (Fig. 7-47). With these data, using equations shown in the "flow chart" it becomes possible to evaluate: (1) fracture relative storage capacity, co; (2) fracture porosity, ~/; (3) interporosity flowing capacity, ~,; (4) matrix-fractures contact surface, or; and (5) matrix block dimension, L Example 7-3." Evaluation o f fractured carbonate reservoir characteristics through transient pressure drawdown

In a natural fractured limestone reservoir a well had produced oil at a constant rate, whereas the pressure had been recorded vs. time in the first days of production. The pressure variation Ap vs. log time was plotted in Fig. 7-50. Other basic data given are: Production rate, Q = 3200 STB/D Total pay, h = 240m. Well radius, r w = 7.5 cm Matrix permeability, k = 0.1 mD. Interstitial water saturation, S i -~- 0.3

Oil viscosity, ~o = 4.6 cP Compressibility, C 1 "" 13.5.10 -6 (1/psi) C 2 = 7.2.10 -6 (1/psi) Oil volume factor, B ~ = 1.23 Fracture density, LFD = 2 / m Matrix porosity, ~m "- 0 . 2 0

Determine: (1) following the procedure described in Fig. 7-49, determine the basic data: m', Ap~, Ap~ from Fig. 7-50; and (2) using the flow chart of Fig. 7-49, determine"

748

cO "T3 cO 0

"s

4

e~

e

~o

qf

I

:o

ql,

m

-

i

./

~'

r-

0

/

~

. 9 I'M. ll

/ ..

j/.-

..

~

,..-.....=.

E-

,

' I

--'--'--

-"--"--"

0

,

-J

14

0

,,,

,,,.,,

/,~"

,

T .-

.o

o*

,

..

e"

,

,;~,,

j

0

~

0

/..x

(!sa)

,

d 7

o ,,,.

o

c~

|!

,.-

'& ,,,..

a

0 0

0

0

0 p,.

0

~D

r.~

0 0

0

r-T-I

~b

t~

749 (a) fracture network permeability (k2 = kr (b) fracture relative storage capacity, o3, and fracture porosity (~j = ~2); (c) dimensionless interporosity flowing capacity, ~; (d) matrix-fractures contact surface, c~; and (e) average block size when, due to a radial-symmetrical flow, one flowing direction can be assumed. Solution Point 1 (1) The examination of Fig. 7-50 indicates that the characteristics of this reservoir are: (a) The presence of two slopes and a relatively long transition time (second stage) qualify the reservoir as a fractured reservoir. In other words, a reservoir having both matrix and fractures, with contrasting properties. (b) From Fig. 7-50, the basic parameters are:

m' = 16.2 psi/cycle; Apo' = 24.5 psi; AP~ = 84 psi Point 2 (a) Based on m' = 16.2 (psi/cycle) = 1.102 ( a t m / c y c l e ) , and Q = 3200 STB/ D =5890 STem 3/ s the permeability based on Eq. 7-67 is"

k2 = ki= 1.15 Q * goBo / 2 * ~:* h * m ' = 1.15 * 5890 * 4.6 * 1.23 / 6.28 * 24000 * 1.102 = 0.23 (D) = 230 (mD) (b) The relative fracture storage capacity based on Eq. 7-62 gives: co = 1 /

e 2"3. 24.5/16.2

--- 0.031

and the fracture porosity using Eq. 7-61"

*f-" *m * Cm * c o / C ; = 020 * 135. 10-6 * 0.031 / 7.2. 10-6=0.0117 (c) The dimensionless interporosity flowing capacity, )~, is obtained through Eq. 7-63 (as indicated in the Fig. 7-49 flow chart): 9~= (1 - 0 . 0 3 1 ) / 1.78 e 2-3 ,84/16.2

=

8.1 . 10-6

(d) The matrix-fracture contact surface, a, based on Eq. 7-64, is equal to: ct = 8.1. 10 -6 * (0.23 / 10 -4) * (1 / 55)= 3.37 (1 / cm 2) (e) Assuming one flowing direction, the equivalent length of the blocks is given by Eq. 7-65"

750 L z = 12/3.37 (l/m) = 3.56 m :, and L = 1.88 m

EVALUATION OF MATRIX-FRACTURES IMBIBITION FLUID EXCHANGE

The fractured reservoir is much more complex than the classical non-fractured reservoir as a result of the coexistence and interaction between matrix and fractures, which are saturated with different fluids. Inasmuch as the dynamic equilibrium in the fractured reservoir is controlled by gravity and capillary forces, a more detailed examination of fluid exchange behavior between the single matrix block and its surrounding fractures is required. In principle, a "single matrix block" of a fractured reservoir represents an isolated matrix unit surrounded only by fractures and without direct communication with other matrix units (similar to the Warren-Root idealized model as shown in Fig. 7-45). In this case the fluid displacement, and in more general terms matrix / fractures fluid exchange, will depend on rock and fluid characteristics and fluid types saturating the matrix and fractures. With different fluid saturations in the matrix and fractures there will be either a drainage or imbibition displacement history depending on the wettability of the rocks. In the first analysis, a matrix block of simplified (regular) geometry (parallelipiped) is used, where both fractures and matrix are saturated with oil. Then, the effect of gas or water has to be examined. The invasion of fractures by gas will result in a downward advancement of the gas-oil displacement front in the matrix, whereas the water invasion in the fractures will have, as a consequence, an upward advancement of the water-table (water/oil contact). In the case of gas invading the fractures: (a) i.e., as shown in Fig. 7-51, the block could be partially surrounded by gas (Fig. 7.51A); or (b) completely invaded by gas (Fig. 7-51B). In the matrix, due to the difference in specific weights of gas and oil, the oil will move downward by gravity forces, whereas the capillary forces will oppose fluid exchange because the entrance of gas into the matrix as a non-wetting phase is opposed by capillary forces. This process is known as "gravity drainage displacement". A

B J. O . ~ ! .

.....

9

"~.

, ...'.'P'l:9"-'u"

:.:~ ' ~

~ "". . . .

I ~ : ~_',

~o0(~. , . .-

.. ".~(~

.

:

9 0i .'

9o " ' o - ' ~ ' . k . J .

..,.,

9~ ' " o" ...o _. .. o. ...

'-

W. ....

o

:'

...L.3....LI', .o ...........

"u-

9 ..

9

..

Fig. 7-51. Matrix block saturated with oil, with the surrounding fracture: (A) partially invaded by gas, and (B) totally invaded by gas.

751 A

[3

LEGEND ~/~'~ oil matrix ~oil

fractures

|*-'-**! water, fractures and matrix ~gas.

fractures and matrix

Fig. 7-52. Matrix block saturated with oil, with the surrounding fractures being (A) partially invaded by water, and (B) totally invaded by water.

In the case of water invading the fractures (water injection or expansion of an aquifer), the water-oil contact rises in the fracture network, partially or completely surrounding the oil-saturated matrix block with water (Fig. 52A and B). Similar to the previous case, the difference between water and oil densities will develop an upward movement of oil in the matrix. Capillary forces and gravity could both work in the favor of an upward displacement of the oil, and the production mechanism in this case is called "imbibition displacement". In cases of gravity drainage and/or imbibition, the displacement history shows the role of wettability in determining the occurrence of drainage/imbibition. Experimental studies have shown that, in the drainage case if the contact angle 0 is below 49 ~ the capillary pressure will remain unchanged. Consequently, the threshold pressure (level) or critical block height remains constant. On the contrary, imbibition is very much influenced by the magnitude of contact angle, 0. This relationship can be summarized as follows: - spontaneous imbibition is observed when 0 < 49 ~ - limited imbibition is observed when 49 ~ < 0 < 73 ~ - no imbibition is observed when 0 >73 ~ In addition, for the evaluation of displacement processes, it is necessary to know both capillary pressure vs. saturation and relative permeability vs. saturation. These relationships play a key role in displacement saturation history, and in the type of displacement process (drainage or/and imbibition). The drainage applies to the

752 TABLE 7-VIII Cases of drainage/imbibition displacement Fluid saturation Case Matrix block Fracture network

Wetting phase in matrix

Oil displacement process

Displacement history

1

oil

water

water

imbibition

Reservoir production

2

oil

water

oil

drainage

Reservoir production

3

oil

gas

oil

drainage

Reservoir production

4

gas

water

water

imbibition

Reservoir production

5

water

oil

water

drainage

Reservoir migration

6

water

gas

water

drainage

Reservoir migration

displacement processes in which the wetting phase saturation in the matrix block decreases, whereas imbibition applies to all those processes where wetting phase saturation inside the matrix increases. In the single matrix block, the displacement process is related to the type of fluid which saturates the matrix and the fractures, as well as to their reciprocal preferential wettability. The preferential wettability, the type of displacement (drainage or imbibition), and displacement history are schematized in a simplified way for six cases in Table 7-VIII. The relative permeability curves have a similar trend in both cases (drainage and imbibition displacement), whereas the capillary pressure curves have a substantially different trend in the two cases (Fig. 7-32). As a result, the combined effect of gravity-capillary forces under imbibition displacement will show a totally different behavior in the displacement history of the drainage or imbibition field process.

Single-block imbibition process An imbibition process will take place when the matrix is saturated by a non-wetting phase (oil, gas) and the fracture network is saturated by a wetting phase (water). If both capillary and gravitational forces contribute to the displacement, then the saturation of "non-wetting" phase decreases and the "wetting phase" saturation increases. The imbibition takes place when the fractures are partially saturated with water (Fig. 7-52A) or completely invaded by water (Fig. 7-52B), often called "total immersion" of matrix block. The examination of imbibition was carried out through theoretical and experimental

753 work, in order to obtain a more correct description of the process, and further to assure an acceptable convergence (matching) between experimental and theoretical results.

Empirical approach In theoretical terms, principal attention had been given to the forces involved in the imbibition process, when a matrix block is saturated with oil and the surrounding fractures with water. Aronofsky and Natanson (1958) suggested a model where the variation of recovery with time i~ based on the assumption that oil production from a small volume is a continuous, monotonic function of time and that this recovery converges to a finite limit. To this assumption is added the principle of conservation of properties during the pro cegs, which necessitates that nothing affects the rate and its limits. This function has/the following expression: R = Roo ( l - e -Bt)

(7-68)

where R is oil recovery; B is a constant indicating the rate of convergence; and R is the recovery towards which R converges (Fig. 7-53).

Simplified behavior evaluation of imbibition process Objectives In a simplified evaluation, it is assumed that the matrix block is a parallelipiped of height h, the pores of which contain oil and an irreducible water. The objective of the evaluation is to estimate the role of the gravity and capillary forces controlling the imbibition displacement of oil, when the oil-water contact in fractures is rising at various rates. Behavior evaluation is expected to obtain, for a given matrix block, the following relationship: (1) recovery vs. time; (2) single matrix block rate vs. recovery; and

r'r

>.: rT" LU

>

9 (D ill

Q:

0

TIME

Fig. 7-53. Relationship between recovery and time.

754 (3) single matrix block rate decline vs. time. Inasmuch as the imbibition process can be govemed by both gravity and capillary forces, or only by one of them, the evaluation will have to consider three cases: (1) flow controlled only by gravity forces; (2) flow controlled only by capillary forces; and (3) flow controlled by both gravity and capillary forces.

Basics of simplified model Model structure. The matrix block is assumed to be a cylinder (Fig. 7-54) where lateral walls are coated, so that fluid exchange will take place only through the lower or the upper face of the block. The "water-table" (water-oil contact in the fractures) could rise at a given height (Hw), which corresponds to a fracture oil height ( H ) so that the block height can be expressed as: HB~ock = H = H + H . The "water-front" refers to water advancement height (Z) in matrix, while the remaining oil column in matrix is H - Z. In the matrix block, the water-invaded zone of height Z and the oil zone H - Z are in contact through a horizontal cross-section A. w

Z

l /

o

LEGEND 1

~

OtL IN FRACTURES O,L ,N M T ,X

FRACTURE Oil ZONE

WATER TABLE

'-!~i-",L.,W~TE, ,., ":"---:::----- 2;i::!

FRACTURE WATER ZONE

Q Fig. 7-54. Matrix block saturated with oil and surrounded by water-saturated fractures in the case of displacement of oil by water.

755

Recovery formulation. Recovery = A * Z * ~):: = A * Z * ~ : : * AS = A * Z * ~ (1 - S i - Sr, imb)

(7-69)

where S could be considered as resulting from a piston-like displacement similar to fractional-flow oil saturation behind the front (pseudo-Buckley-Leverett). The recovery in this case is directly proportional to the displacement front distance Z.

Forces governing the flow. The capillary and gravity forces when referring to Fig. 760 are expressed by: PTota, = Pc + G = h * AT + ( H -

Z) * AT

where Pe = J ( S ) * o cos 0 * (~ / k) ~

(7-70) (7-71)

In the case where the block is surrounded by water ( H = H), the total pressure, dimensional, and dimensionless, is equal to: PTotal -- [he+ ( H - Z)] * A~/= H [(h c / H) + (1 - Z D)] * A~/

(7-72)

where Z D = Z / H

(7-73)

Displacement front velocity. The Darcy velocity considering the two zones of "oil non-invaded" and "oil invaded by water", can be written as follows: V= [h e + ( H - Z)] * AT / [(~tw/ k ) * Z + (~t~ / k ) * ( H - Z)]

(7-74)

and if the mobility M and dimensionless height are introduced in Eq. 7-74: (7-75)

M = (k w / ~tw) / (k ~ / ~to)

the velocity of Eq. 7-74 becomes: v = (k ~ / ~to) * A~, * M *

*[(h e / H) +1

-ZD] / [ZD + M,

(1

-ZD)]

(7-76)

Matrix block rate. Based on continuity of the flow in matrix" Q = A * V = A * ( k / ~to) * Ay * M* *[(he/H) + 1 - Z D ] / [ Z o + M * ( 1 - Z o ) ]

(7-77')

Time vs. recovery (general formulation). Associating the rate expressed by continuity (A *V) with the displacement front rate (dZ / dt):

756 Q = A * V = A * ~eH* dZ / dt = A * ff~H* H * d Z D/ dt

(7-77")

the time is: dt = [((Des,,* H) / ( k / Ixo) ] (M * AO* * {[ZD + M (1 - ZD)] / [(h / H + (1 - ZD)]} * dZD

(7-78)

Simplified model results Time vs. recovery. The basic relationship presented in Eq. 7-78 includes capillary and gravity forces. A better definition of the role played by each of the two forces requires an analysis of the predominance of only one or the role of both of these parameters. Case 1: Predominance of gravity forces: If capillary forces are very small compared with gravity forces, then the term h / H is negligeable in Eq. 7-78, and so, the gravity-controlled flow equation through integration becomes:

J [Zo / ( 1 -

ZDI]* dZo + M J[(1 / (1-ZD)] * d Z D - M ~ [Zo / (1 --ZD) ] * dZ o

and tD,G = (M-- 1) * Z D- I n (1 -ZD)

(7-79)

where: to.c

=

[(k / ~to)] * A~, * M * t / ~ss * H

(7-80)

The role of mobility M in accelerating or delaying the recovery may be seen in Figs. 7-55 and 7-56, indicating the variation of recovery (ZD) VS. dimensionless time tDS"Comments: In the case of gravity forces predominating as expressed in geometric terms, the block height is very big when compared with capillary height (H >> h ) as shown in Fig. 7-57A. Inversely, if the block is small and capillary height very important ( h >> H) (Fig. 7-57B), the capillary forces are predominant. Case 2: Predominance of capillary forces In the case where the capillary forces are very big as shown in case B of Fig. 7-57: hc/ H > > l - Z Dsothath / H + I - Z D - h / H

Following the same procedure as in the case of predominant gravity forces, dimensionless time is equal to: tD,PC= M * Z D+ (1 - M ) * ZD2 / 2

(7-81)

The recovery vs. dimensionless time expressed in capillary terms is plotted in Fig. 7-58.

1.0

.9

!

.8

.7 --

//

.6

ZO

.5

.4 .3

.2

m

-i

.1

o o

1

2

3 t

Fig. 7-55. Relationship between recovery

(ZD) and dimensionless

time

4

5

D,G

(too) under predominance

of gravity forces.

"--..I

"-.,1

10

ZD

OO

5

0.1

1.0

tqG Fig. 7-56. Relationship between recovery (Zo)and log dimensionless time

(to~) under predominance of gravity forces.

10

759

B

A

(

)o )o oQ )

)ooo

)C or

Oo~ | o o o r )o Oo|

0 0

t

)o o ' o )o ~

o

o

o

|

oc| o

: oo ~

,J

,oOOooi oo o oo , i , oo ~

0r

|

dlb

o~ oo o| OoO (| o o o o| o Oo' | ' oo o|

o

i

:O;O5to

o o

~ o

o

~ o

1

ooo:l

)o o

o

Oo~ | o oc| o

o50 ! h c -T

Ooo

[.

O'OoO~~ ,t~ Oo~ oOoo:oo:l H o. OoOoO~Oj 4,'

Fig. 7-57. Comparison between block height (H) and capillary height (hc) in case of gravity predominance (A) and capillary predominance (B). Case 3" Capillary and gravity forces In the presence of both forces, capillary ( h / H ) and gravity (1 -ZD), by using the same procedure a relationship between recovery (Zo) and time can be obtained: tD,G,Pc= Z D * ( M - 1) - [M + 8 * (1 - M)] * In (8 - ZD)

(7-82)

where the dimensionless time is similar to that of the gravity case: tD,G,Pc= tD,G = ( k / ~to) * (AT) * M * t~ dde//* H

(7-83)

and where 8 = 1 + hc / H

(7-84)

B l o c k rate vs. recovery. By using Eq. 7-16 where both the capillary and gravity forces

are involved in displacement of oil:

QBI, o, GC = QG,0 *

M * DFGC

(7-85)

where, based on the Muskat equation, the gravity rate could be expressed in terms of oil phase flow rate (QG0) or in terms of water phase flow rate (QGw) as follows"

QG0 = A* (k/~to) * (AT)

(7-86)

760 o. S,,.

,,

1.0

"i zD

.1

0'T

I

. . . .

0

1

2

"

I 3

tO, Pc Fig. 7-58. Variation of recovery (Zn) with dimensionless time (to,e) expresed in capillary terms. QGw = A * (l/M) * ( k / ~ w ) * (AT) The decline factors D I for various predominant forces are as follows:

DF~ = (1 -ZD) / D DF c = ( h / f 0

= (~:- 1) / D

(7-87)

DF~c = ( h / H + 1 - ZD) = (~: -- ZD) / D where

D = ZD + M ( 1 - Z D)

(7-88)

Comments: (1) the rate variation with recovery is a function of the decline factor (DF) vs. recovery (Z D) found in Eq. 7-87; and (2) since the block rate decline depends on decline factor (DF) which is related to recovery by Eq. 7-87, the association with the time will require, in addition, the introduction of recovery-time relationship of Eqs. 7-80, 7-82 and 7-83.

761

Conditions requiredfor an imbibition experiment Role of impermeablefaces. If all lateral faces in a matrix block are impermeable, and the lower and upper faces of matrix block are not, then the following scenarios of displacement could be envisaged: (1) if the lower face is kept in contact with the water (Fig. 7-59a), then the only displacing force will be the capillary force; (2) if the water level increases (Fig. 7-59b) and lateral faces remain impermeable, then both capillary and gravity forces will assist the oil displacement process; and (3) in cases where the lateral faces are permeable (Fig. 7-59c) the capillary forces will remain constant and will act over all the lateral faces where fracture water is in contact with the matrix oil. The gravity forces on the other hand will grow with depth. This may influence the shape of water-oil displacement contact in slim blocks.

Development of counterflow. If the blocks are all impermeable with exception of the lower face, then the counterflow takes place when, on the same face of the matrix block, the production of a non-wetting phase has an opposite direction of flow to that of the imbibing wetting phase. On the contrary, when the "displacing" fluid (wetting phase) and "displaced" fluid (non-wetting phase) have the same direction, the production phase indicates a direct flow. The inflow of water and the outflow of the produced oil are shown in Fig. 7-60 for the case of a permeable lower face (case "A") and for an permeable upper face (case "B"). The main difference between these two cases is the role of oil buoyancy: in case "A" the oil buoyancy opposes the capillary controlled counterflow, whereas in case "B" it supports the flow toward the permeable upper face of the block.

Influence of block size. If the blocks are large, then the fluid exchange in the vicinity of the lateral faces is reduced to a "local effect "compared with the vertical displacement through the horizontal cross-section (Fig. 7-61A). On the other hand, if the blocks are elongated (matches), then the capillary effect on the lateral faces may play a certain role (Fig. 7-61B). In laboratory imbibition experiments which have to simu~,,r

,Z

oe

e 9

9 9 e

9

/-

oe e

eoeeooe

9

i--~

9

'

|

|

r

:

"

j

I

o

I

'

~._

A

L

,,~i~ t

~

9 Fig. 7-59. Role of forces in the case of impermeable lateral faces (cases a and b) and permeable lateral faces (case c): (a) capillary forces; (b) capillary and gravity forces on bottom face and (c) gravity and capillary forces on lateral faces and on bottom face.

762

B

A ~lil@lll~li~ll~,

~N,/ / / / / / /

% *

~149149

i ~

9

,~ !! 7//2.4.//1~ I / / i ~ - / / I ill i /////,'

','.'.V / / / / / / ~ ",r

/////./.,'ill

IIJ / /

9 . ::(.'":.

i11"//'-~111//illJ///

Fig. 7-60. Examples of: (A) counterflow through bottom face and (B) direct flow through top face of matrix block. (Legend as in Fig. 7-61.)

late the imbibition behavior of medium to large block size, the lateral faces of the core used in laboratory have to be made impermeable.

Evaluation of gravity drainage matrix-fracturefluid exchange Drainage displacement takes place when the wetting phase, which saturates the matrix, is displaced by a non-wetting phase, thus saturating the fracture network. A common case will be represented by the expansion of the gas-cap so that the gas (nonwetting phase) invades the fractures while the matrix blocks are saturated with oil. Similar behavior patterns occur throughout the oil migration history when the frac-

A

B Oil

9....-

. . :w: .-.... ,..

9

"

"

""

;

LEGEND

{~]

".

"--

, "

woter oil

".."

on

rr~trnx

"

. . . . "

""

Longitudinal section

.

9

.

9

oi|

zone

9

9

9

"

Transversal section

I ~ oll in floctutes /~_-//Ir,~permeol:,le

Fig. 7-61. Role of lateral and vertical displacement vs. block dimension: (A) large blocks and (B) narrow blocks.

763 tures initially saturated with water (wetting phase) are invaded by oil (as a non-wetting phase) which will displace the water from the matrix blocks. A less common case of drainage may be that of an oil-wet reservoir, where oil (wetting phase) saturating the matrix is displaced by the water (non-wetting phase) saturating the fractures. In general, it may be stated that production mechanisms such as expansion, solution-gas drive, water imbibition, and gas gravity drainage all may contribute to production of oil at different stages of the production life of a fractured reservoir. But the gas gravity drainage takes place mainly when gas from gas-saturated fractures displaces the oil of the matrix. The free gas may be internal gas (liberated from oil as a result of reservoir depletion) which has segregated in fractures forming a fracture gas-cap, or external gas injected into the reservoir. In both cases, the advancement of gas in fractures and the difference in density resulting between the fracture gas and matrix oil will provide the energy for the gas-gravity-drainage process. What is unique in the gas-gravity-drainage production mechanism is that oil production can take place without any pressure decline (depletion) if the field rate is not higher than field gravity-drainage rate.

Single-block gravity-drainage process In a classic gravity-drainage process it is expected that the free gas would invade the fractures surrounding the oil-saturated matrix blocks. Oil starts to drain downward because of the gravity difference between gas and oil, while gas enters on the top of the block to replace the produced oil.

Simplified analysis Geometrical-physical aspects. Considering a single block as in Fig. 7-62, its particularities for a gravity-drainage flow are" (1) the top of the matrix block is the reference level; (2) the lateral faces of the block are impermeable; (3) the gas front position is at a distance Z from the reference plane (Z = 0, corresponding to the top of matrix block); and (4) if the block height is H and the threshold height is hTw the maximum Z value is Zax = H-hTH. Block height vs. threshold height relationship. Inasmuch as in drainage conditions the non-wetting phase (gas) has to displace the wetting phase (oil), the gravity force is opposed by capillary force. In general, this relationship, based on Fig. 7-62, could be written as: pG - Pc = ( H - Z) * A7 - hvH * A7

(7-89)

The initial rate corresponds to initial conditions (Z = 0), and the final production rate takes place when the front reaches the threshold level Zax = H-hTH. For an understanding of this mechanism, three cases are presented in Fig. 7-63 during the advancement of gas-oil displacement front. In all these cases capillary pressure is constant with depth, whereas gravity force increases with depth. Furthermore, on this face of the block in cases "a" and "b" oil is produced since on the bottom face the gravity forces > threshold capillary forces (G > P ) . In case "c", where pressure P =

764

~

:::.'//,

: .:..g

**,

* 9

,* *

******

IMPERMEABLE rA'

. :o o ::o o.:. o.:. ,oli..o:.o.:0 .o,: ~176176176

:i:il

OIL IN FRACTURE

g! !

R ,

OIL IN MATRIX

[2.'2"2~~ GAS

***~

Fig. 7-62. Displacement of oil from a block where fractures are totally surrounded by gas. G, the flow (at the bottom face of the block) stops and the oil remaining in the block represents the "oil hold-up zone". Inasmuch as both forces have the same fluid density difference (Ay), the dynamic cases "a" and "b" could be expressed as ( H - Z ) > her , whereas in case "c" (the static condition), H - Z max-- hrH" Equilibrium vs. gas-oil contact in matrix and fractures. By using the representation indicated in Fig. 7-64, and referring to the bottom of the matrix through which the block production takes place, the level 3 of the block (Fig. 7-64B) reflects the threshold height her= hTH of capillary pressure curve (Fig. 7-64A). As observed in Fig. 764C, the gravity is higher than threshold gradient when the displacement front is in positions 1 and 2, which represent a non-equilibrium gas-oil contact. A static equilibrium will be reached when the displacement front arrives in position 3, where both threshold gradient and gravity are equal. Thus, the block will retain a column of unrecoverable oil due to capillary forces. It is called a capillary holdup zone having height h 3 = hra. From the initial condition of non-equilibrium to the final equilibrium condition, it is easy to conclude that if the block height H < h = h TH' then the recovery of oil is not possible at all just because the block height is srmaller than the capillary holdup height. Role o f block height vs. recovery. For a better understanding of the role of block height (H), a capillary pressure curve is presented in Fig. 7-65. For single matrix blocks (1,2,3,4) of different heights, the recovery will depend on block height. Block 1 (the smallest) will contain unrecoverable oil, block 2 (higher) oil will be slightly recovered, and more oil will be recovered in blocks 3 and 4. This means that in taller blocks the gravity forces could overcome (for a certain part of the block height) the capillary resistance to gas entrance and, therefore, would displace the oil. Role o f rock characteristics vs. recovery. If the matrix blocks have the same height

765

--

*AT,. --

hTH

1 /

}

,

n,.,

Block B o t t o m Face

o

,,,~,

o

o

.,,

..

t,

G>>P c

Flow assured by

./$-/= /

-

Z" L

Block B o t t o m Face Flow assured by

,,

G~P C

o-

-o

~o

o

oo

,o~ f

o

oo

4,

~o0--

K~

, o o~176176176

Block B o t t o m Face Flow is s t o p p e d b e c a u s e

G=P c

Fig. 7-63. Oil produced from an oil-saturated matrix block, if the surrounding fractures are saturated with gas, by examining the relative magnitude of gravity and capillary forces.

but are of different petrophysical characteristics, then recovery will depend on the capillary pressure curves of blocks A, B and C (Fig. 7-66). Considering the following characteristics:

766

),c = Pc/(~'o-~'Q)

|:(/GUO". O.:':.o-?.:W.:.>

..... ;,~,..-..o.~.., 6 0..t p!~:U.~.O,c?.~..i~~.!

I?:r

ibo.a( ).o.:~

!,,4,,,'~ :o:.. "1,2' "v-. ;O: ""::L~.' ___IV~'.:'U ,V.',~:.'.o ....: 9..r

' '. o..- -~:

.' .:,r ".~.

f-D:, ~o:~::~el',. I 10.:., :]:o..~ 1 ~....~l"a :o. "~.'Lr

".'d:v. :'"

! g: +;.+:,O. o o ~ I l...o. ~.!e~,T,+~.~ I

I~'.~ .":o "A. I/ "." f2:~:4"1:-

:( .*.0.M- ~ " . ' i ) : ,, ~:.., ;~ :.'.- ..,;r162

.~.,

3! ......

3

ii

0 0

Sw

!

":':"

~o \\\~

~:~7

Equil.

~,.~: BOTTOM"

gas-oil ~...cont act

! !

~;', hTH=h3

!;~

L:~]

q-

2 ~

i:~:

I~:~

I 7b

I

I

""

:~ :;=.

~.:""[

V/'

hTH

% I

II

I ~--.--.--- - ~

PTHH] ~:i ::.'..

Po

!

"capillary

100

"" ~

equilib.

oil press.I _\~

gas-oil

grad.

contact

[ \ - ~ ~

....

hold-up zone

Po:Pg FPc~

A

B

C

Fig. 7-64. Relationship between gravity and capillary forces in drainge displacement: (A) capillary curve, (B) drainage displacement in the block, (C) equilibrium of gas-oil contact at matrix-fracture interface. Zone hrHis equal to capillary hold-up zone.

<3 o.o H

o

?_

'.~P"f t'3 | \'2F

,.'t'~o-;-zd:7 " .'0" i

: ~ ;

il

:9"

"

9

~,

'~I~'.,i(7.]:~ .."

o..-a..' .~.~--

,.

0

;

100

Sw

capillary hold-up zone Fig.

"..

7-65. Capillary hold-up zone for various block heights.

-.

767 which correspond to hTH A < hTr~B < hrH c, it may be stated that because block C height is smaller than the capi|'|ary hold-up ~eight, oil recovery is impossible, whereas the oil in block A is largely recovered, and only with a very limited hold-up zone because its height is substantially greater than hold-up height.

Basic simplified evaluation In the simplified model of Fig. 7-62, the displacement of oil by gas could be carried-out through the same procedure used in case of water imbibition. The displacement forces expressed by the difference between gravity and capillary pressures could be written as: (7-90)

G - Pc = ( H - Z - hTn) * Aqt'

because Pc = PTH = hTH * Aqt' and where A~/' = 3'o- 3' 9 Inasmuch as the threshold height (htH) is equal to ]he hold-up zone, the recoverable column of oil has the height H - hTn , which corresponds to Z=Z max" The drainage time (t') vs. recovery (ZD) relationship based on the displacement front rate can be expressed as: [(k / kto)* M'* A~/' / (~e;; */4)] * dt = (7-91)

{[ZD + m'* (1 --ZD) ] / [1 --(hTH / H ) - Z D ] }*dZ D which by integration will give:

(7-92)

t'D= Z D * ( M ' - 1 ) - [M' + e' * ( 1 - M')]* In (d--ZD)

K A > KB >K C

(DA > (])B > (Dc hBLOCK > hTH,A I

hBLOCK > hTH,B

,B

tO' PTH.C

hBLOCK < hTH,C

:".':"'.~:,~"." ~'.--'*.~*'0"~'Ud ".-. ~. :o.~,..*:-. ~, 9 .",e"*. ~O.*.' ~..o...0.O~ r r 0

Sw

PTH,B

~.'1

"ii: ~ ,

9

"

PTH,A

100

A

B

C

Fig. 7-66. Blocks A,B,C of equal size but having different properties. Heights of displaced oil and oil hold-up zones depend on capillary pressure curve characteristics.

768 where: M' = ( k / ~s) (ko / ~o). The dimensionless drainage time (Eq. 7-92) is similar to imbibition gravity dimensionless time: t'D,G,PC = t'D,G = (Ko / ~o) * AT' * ~

t;' = 1 -

hTH

*

(I /

H * 0eii) * t'

/H

(7-93) (7-94)

The block drainage rate is equal to: Q' BI , 0, GC = Q , o,o 9 M'

9

DF'oc

\(-7- _ . ,o . . s, ]~

where Q'~,o = A * ( k / ~to) * AT'

(7-96)

Q'G,w = A * (1/3//') * ( k / law) * AY'

(7-97)

and the decline factor is: DF'c, c = ( 1 - - Z D - - h l H) I D ' = (~' - ZD)/D'

(7-98)

where: D ' = Z D +M'. (1--ZD)

(7-99')

and 5' = 1 - h / H

(7-99")

In a case where the block is very tall and capillary force is negligible, the hold-up zone will not play any role and the flow will be controlled only by the gravity force. The above relationship will result in the following: (1) Dimensionless time vs. recovery relationship will change from Eq. 7-92 of drainage displacement to an equation similar to Eq. 7-80 (obtained at imbibition conditions): t'D,C,pc = t'D,G = (M' - 1)* Z D- In (1 - ZD)

(7-100)

(2) A decline factor similar to that obtained during imbibition when flow is controlled by the gravity forces: DF' G = (1 -ZD) / D'

(7-101)

769 CONCLUDING REMARKS

Taking into account the findings of Festoy and Van Golf-Racht (1989) that the matrix is much more continuous in the reservoir than what appears from core examinations, the single-block model of Warren and Root (1963) can be often substituted by a stack of blocks model resulting from a tortuously continuous matrix. Physically, the 'stack-of-blocks' will represent a stack of matrix blocks separated by fractures, but with additional connections through matrix over a limited crosssectional area between the blocks. In this case, the oil produced from the base of one block reinfiltrates into the block below and the gas-invaded zone is represented by a number of single blocks stacked on each other. Oil drains downward from block to block to the gas-oil contact.

ACKNOWLEDGEMENT

The author is greatly indebted to Professor George V. Chilingarian for his invaluable help.

REFERENCES Aronofsky, J.S., Mass6, L. and Natanson, S.G., 1958. A model for the mechanism of oil recovery from the porous matrix due to water invasion in fractured reservoir. Trans. AIME, 213:17 - 19. Barenblatt, G.I., Zheltov, Y.P. and Kochina I.N., 1960. Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks. J. Appl. Math. Mech., 24(5): 852 - 864. Dunnington, H.V., 1967. Aspects of diagenesis and shape change in stylolitic limestone reservoirs. Proc. VII World Petrol. Congress, Mexico, 2, Panel Discussion, 3:13 - 22. Festoy, S. and Van Golf-Racht, T.D., 1989. Gas gravity drainage in fractured reservoirs through new dual-continuum approach. SPE Res. Engr. J., 4(Aug.): 271 - 278. Geertsma, J., 1974. Estimating coefficient of inertial resistance in fluid flow through porous media. J. Petrol. Techn.26(10): 445 - 449. Leroy, G., 1976. Cours de g6ologie de production. Inst. Franfais du P~trole, Paris, pp. 1 1 2 - 163. Murray, G.H., 1977. Quantitative fracture study, Sanish Pool: Fracture-controlled production.Am. Assoc. Petrol. Geologists, Reprint Series, 21:117 - 125. Park, W.C. and Schott, E.H., 1968. Stylolitisation in carbonate rocks. In: G. Muller and G.M. Friedman (Editors), Recent Developments in Carbonate Sedimentology in Central Europe. Springer-Verlag, Heidelberg, pp. 3 4 - 63. Pollard, P., 1959. Evaluation of acid treatment from pressure build-up analysis. Trans. AIME, 2 1 6 : 3 8 - 4 3 . Reiss, L.H., 1966. Reservoir Engineering en Milieu FissurO. French Institute of Petroleum, Paris, Ed. Technip, pp. 7 6 - 95 Ruhland, R., 1975. M6thode d'6tude de la fracturation naturelle des roches, associ6 a divers mod61es structuraux. Bull. Geol. Soc. Frangais, 26, ( 2 - 3 ) : 91 - 113. Snow, D.T., 1965. A Parallel Plate Model of Fractured Permeable Media. Ph.D. Thesis, University of Califomia, Berkley, 330 pp. Steams, D.W. and Friedman, M., 1972. Reservoir in fractured rock. In: R.E. King (Editor), inStratigraphic Oil and Gas Fields, Classification, Exploration Methods and Case Histories. Am. Assoc. Petrol. Geologists, Mem., 16:82 - 106. Van Golf-Racht, T.D., 1982. Fundamentals of Fractured Reservoir Engineering. Elsevier, Amsterdam: pp. 5 1 - 109. Warren, J.E. and Root, P.J., 1963. The behavior of naturally fractured reservoirs. Trans. AIME, 228:245 -255.

770

SYMBOLS

Latin letters a

dimension, fracture extension Constant of laminar flowing equation Fracture opening - Oil volume factor Constant of turbulent flow equation - Capillary c - Compressibility C Diameter D - Decline factor DF FINT - Fracture intensity G - Gravity G O R - G a s / o i l ratio h - Formation pay hvn - Threshold height H - Block height H - Horizontal J ( S w) - L e v e r e t t f u n c t i o n k - Permeability l,L - Length LFD - Linear fracture density M - Mobility Np -Cumulative oil p r o d u c e d n - Number of fractures p - Pressure PI - Productivity index Q - V o l u m e t r i c rate o f f l o w Re - Reynolds number S - Area S, S - O i l and water saturation, percent of pore space r - Radius tD - Dimensionless time t - Production time ~" - Velocity WC - W a t e r cut W - encroached water x,y,z - Cartesian axis Z - Height A b Bo B~

- B l o c k -

G r e e k letters

Matrix-fracture surface contact - Turbulence factor -

771

Density

-

A

- Difference Strain

-

-Interporosity ~t

- Viscosity

v

-

9

flowing

capacity

Kinetic viscosity

- Specific mass - Stress - Porosity -

f.o

C

o

n

s

t

a

n

t

-Relative

r el at ed to f l o wi n g

direction

fracture storage capacity

Subscripts BL

- Block

cr

- Critical

c

- Capillary

D

- Dimensionless

DG

-Dimensionless

in gravity terms

DP c

- Dimensionless

in capillary terms

e

- External,

drainage

eff

- Effective

f

- Fracture

ff

- Intrinsic fracture

m

- Matrix

o

- Oil

or

- Oil, residual

or, i m b - O i l i m b i b i t i o n , T

residual

- Turbulence

Th

- Threshold

w

- Well

w

- Water

wett wi w-o x,y,z

- Wetting - Interstitial water - Water-oil - Axis direction

1

- Matrix

2

- Fracture

This Page Intentionally Left Blank

773

Chapter 8

C H A L K RESERVOIRS GERALD M. FRIEDMAN

"In worla'ng over the soundings collected by Captain Dayman, I was surprised to find that many of what I have called "granules" of that mud were not, as one might have been tempted to think at first, the mere powder and waste of Globigerinae, but that they had a definite form and size. I termed these bodies "coccoliths." '7 have recently traced out the development of the coccoliths from a diameter of 1/7000 of an inch up to their largest size (which is about 1/1600) and no longer doubt that they are produced by independent organisms." Thomas H. Huxley (1825-1895) On a piece of chalk (1868)

GENERAL STATEMENT

Electron microscopy has revealed that many fine-textured, apparently unfossiliferous limestones of deep-sea origin consist almost entirely of the remains of pelagic nannofossil coccoliths (Figs. 8-1A, B and 2). Each coccolith consists of an intricately organized structure composed of calcite crystals between 0.25 and 1.0 ~tm in diameter, which together form spherical to oval disks about 2-20 ~tm broad in the plane of flattening. Coccoliths are known in sedimentary rocks of Jurassic to Recent age. Chalk is a friable, fine-textured limestone composed dominantly of coccoliths, but in which pelagic foraminifera also occur. Coccoliths accumulate initially as oozes, and later become chalk when lithified (Schlanger and Douglas, 1974; Garrison, 1981). Modem oceans abound in coccoliths (Fig. 8-2). The Upper Cretaceous Chalk, for example, which is 2 0 0 - 400 m or more in thickness, is so distinctive and so widely distributed in western Europe that it inspired the name for a geologic period: the Cretaceous (creta, from the Latin, meaning chalk). These rocks are considered to be open sea-type deposits that accumulated on the bottom of a moderately deep (+ 250 m), tropical shelf sea. Many of the sedimentologic and compositional characteristics of this chalk closely match those of modem, pelagic deep-sea oozes (Friedman and Sanders, 1978). The European Cretaceous chalk contains abundant chert beds and nodules. The centers of many of the chert nodules commonly contain non-replaced chalk which, when dissolved in hydrochloric acid, contains insoluble residues with abundant siliceous sponge spicules. In contrast, outside chert nodules few such spicules are found. Presumably, the spicules were in fact formerly present within unsilicified chalk in as

774

A

B

Fig. 8-1. (A) Scanning-electron micrograph of skeleton of coccolith (Coccolithus cfi C. barnesae), Isfya Chalk (Upper Cretaceous), Mount Carmel, Israel (A. Bein). (From Friedman and Sanders, 1978; reprinted with permission from the authors.) (B) "Coccoliths now known to be the remnants of unicellular algae". (From T.H. Huxley, 1868.)

775

Fig. 8-2. Scanning-electron micrograph of tiny suspended particles filtered from surface water of the western Atlantic Ocean at 34~ 77~ 30 December 1971. The prominent particle in the upper left consists of bound-together coccospheres; coccospheres in the right area of photograph have been bound to unidentified particle, probably organic matter (J.W. Pierce). (From Friedman and Sanders, 1978; reprinted with permission from the authors.)

great an abundance as within chalk remnants in chert nodules. It is likely that most or all of these spicules were dissolved so as to provide silica that subsequently was reprecipitated as chert. This chert probably was precipitated initially as opal and subsequently converted to cristobalite and, ultimately, to stable quartz (Friedman and Sanders, 1978). In addition to sponge spicules and chert, minor constituents in the European Cretaceous chalks include radiolarians, pelecypod shell fragments (notably, those of Inoceramus spp.), echinoderm fragments, bryozoans, and bone fragments.

RESERVOIRS IN CHALKS

Significant hydrocarbon reservoirs, which are developed in chalks, occur mainly in Cretaceous to Paleocene deposits in the North Sea, and in Cretaceous deposits in the Gulf Coast and western interior seaway provinces in North America. These important sites of hydrocarbon production are discussed below. North sea reservoirs Background

In 1969, the writer taught a short course in England on carbonate reservoirs. One of the participants in this course was the manager for Philips Petroleum Company. All his questions related to chalk because, at that time, Philips was drilling a structure in the North Sea whose objective was chalk. As of 1969, two hundred dry holes had already been drilled in the North Sea, and the exploration community derided Philips

776 b e c a u s e conventional " w i s d o m " at the time was that there was no oil to be found in the region. The writer also was skeptical and explained to the Philips m a n a g e r that a l t h o u g h the micron-size coccoliths w h i c h c o m p o s e chalk m a y exhibit g o o d intercoccolith porosity, such pores were only o f micron size (micropores: 1 - 5 lam) and

.

i N

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777

thus closer to narrow pore throats than to the open pores which typically give rise to good permeability in reservoirs. However, the writer felt that the large structures which were indicated on company seismic sections likely resulted from the movement of low-density salt through overlying strata, probably of Miocene age, which domed the chalk and created abundant fractures which could provide for excellent permeability. It turned out that fracturing indeed has contributed to the excellent reservoir characteristics that make the North Sea chalk so economically important. Three months after completion of the short course the writer received a communication from Philips Petroleum in London, announcing the discovery of Ekofisk Field, now known to be one of the world's giant petroleum reservoirs (Fig. 8-3). Yet, even as late as the spring of 1970 Sir Eric Drake, then chairman of British Petroleum, remarked that "... there won't be a major (oil) field out there (in the North Sea) but BP had obligation to show themselves as explorers, and so work would continue." (Alger, 1991). The first North Sea oil which came ashore in 1971 was from the chalk of Ekofisk Field. Mapping by the common reflection-datapoint system led to the discovery of Ekofisk Field. The Ekofisk Formation, of Danian (Paleocene) age, caps a thick section of

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778 Cretaceous chalks and other carbonates (Fig. 8-4). A seismic reflector located just above the top of the Ekofisk Formation (the Maureen Formation: Fig. 8-5) showed 244 m of closure over an area of 49 km 2 in and around the field. The first well drilled encountered mechanical problems and had to be abandoned. A second well yielded flow rates in excess of 10,000 BOD (barrels of oil per day). The subsequent third, fourth and fifth wells tested 3850 BOD, 3788 BOD, and 3230 BOD, respectively. GAMMA L I T H RAY OLOGY

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779

After installation of a permanent platform the next well encountered 315 m of pay in the chalk section (Van den Bark and Thomas, 1980). Since the discovery of Ekofisk Field in 1969, six other fields have been discovered that produce oil, gas, and condensate from chalk reservoirs (Fig. 8-6). The productive units in this area include the Tor Formation (Maastrichtian, Upper Cretaceous) and the Ekofisk Formation (Danian, Paleocene) (Figs. 8-4 and 8-5). The fields lie within

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781

the Central Graben in the southern part of the Norwegian sector of the North Sea (Fig. 8-3). Ekofisk, Eldfisk, Edda, Tor, West Ekofisk, and Albuskjell fields are collectively known as the "Greater Ekofisk Complex." Of these fields, however, Ekofisk is the largest in terms of size (Figs. 8-7 and 8-8) and reserves: estimated in-place reserves are 5.3 MMMBO (billions of barrels), 6.68 TCFG (trillion cubic feet of gas), and 63 MMB (million barrels) of condensate at the time of discovery. Together, the seven fields contain recoverable reserves in excess of 1.8 MMMBO and 6.6 TCFG (D'Heur, 1984; Brewster et al., 1986).

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782

Geology The Central Graben is a rift of Late Permian to Early Triassic age that was active until the Early Cretaceous (Ziegler, 1975). Permian, Triassic, and Jurassic sediments filled the graben and responded to intermittent fault movement prior to Cretaceous sedimentation (Ziegler, 1982). The Jurassic Kimmeridge Clay is the source rock for the chalk reservoirs in the Greater Ekofisk Complex. Beginning in the late Jurassic, and continuing into the Miocene, salt flowage and diapirism of the underlying Permian Zechstein beds, together with basement faulting, created domed low-amplitude folds that became the traps for hydrocarbons in the chalk reservoirs (Brewster et al., 1986). Rifting may have accelerated active salt movement. During the Cretaceous and Paleocene pelagic coccoliths accumulated to form the reservoir facies in an environment devoid of terrigenous input. Subsidence of the graben continued into later Tertiary time, and approximately 3000 m of now overpressured shale was deposited over the chalk, serving as a seal to the reservoir. The oil in the chalk is in an abnormallypressured environment.

Reservoir facies and diagenesis Two types of chalk deposits that compose the reservoirs in this area are recognized: (1) autochthonous (in-place) chalk, interpreted as being strictly of pelagic origin and which was not subjected to postdepositional resedimentation. This chalk typically is argillaceous and either laminated or burrow-mottled; and (2)allochthonous (reworked) chalk, that is, chalks which after initial deposition were resedimented into deeper-water environments by sliding, slumping, transport by turbidity currents, and mass-transport as debris flows facilitated by sediment instability caused by tectonism in the graben rift zone. The distinction between autochthonous and allochthonous chalks is of importance in reservoir development and performance. For example, the allochthonous chalk has higher porosity, and typically composes better reservoirs, than the autochthonous chalks because: (1) particles of pore throat-clogging siliciclastic clay have been winnowed out; (2) the sediment is relatively well-sorted in terms of particle and pore size; and (3) rapid deposition did not allow for subsequent bioturbation which facilitates porosity-occluding cementation (Hancock and Scholle, 1975; Kennedy, 1980, 1987; Watts et al., 1980; Hardman, 1982; Nygaard et al., 1983; Schatzinger et al., 1985; Jorgensen, 1986; Bromley and Ekdale, 1987; Feazel and Farrell, 1988). The coccoliths which compose chalks consist mineralogically of low-magnesian calcite, which is stable at surface and near-surface pressures and temperatures. Hence, it would seem that chalk would not undergo significant diagenetic changes through time. With progressive burial, however, chalk is known to be affected by a consistent sequence of diagenetic changes that cause reservoir development. Diagenetic hardgrounds resulting from early, submarine cementation are responsible for local lack of interparticle porosity and declines in productivity in some chalk reservoirs. In the absence of such hardgrounds, the original high-porosity, water-saturated oozes became progressively less porous with early, shallow burial below the sediment-water interface as a result of mechanical compaction and dewatering. Primary interparticle porosity was reduced by as much as 50 - 80% in some cases. Cores of some chalks have porosities near 50%, which means that only minor porosity occlusion by later

783 chemical compaction and cementation (discussed below) has occurred subsequent to early mechanical compaction. With increased burial depths, chemical compaction (i.e., pressure-solution) occurred, the effects ranging from small-scale (e.g., interpenetrative grain contacts) to the extensive development of stylolites. The process of stylolitization is believed to liberate vast quantities of CaCO3,which can be reprecipitated as interparticle pore-filling calcite cements that further reduce porosity. Cementation by calcite derived from this process has occurred throughout the Eldfisk Field chalk reservoir. Oxygen isotopic compositions of the calcite cements in these rocks suggest a pore-water temperature of 5 0 - 80~ during chalk dissolution and cement reprecipitation. Values of 5~3C PDB of these cements increase with depth, indicating an associated cementation process involving bacterial methanogenesis (Maliva et al., 1991). On the smaller scale, substantial reduction of interparticle porosity in chalks commonly also results from related dissolution along the contacts of adjoining coccolith plates in reservoir zones in which overburden stresses were high. Such a process involves calcite dissolution along grain-to-grain contacts, with resulting interpenetration of grains and an increase in bulk volume and density. The calcite liberated by dissolution likewise can be reprecipitated in nearby pores, or as overgrowths on adjoining coccolith plates, both processes reducing total interparticle porosity. Where this process has been dominant, a tightly interlocking mosaic of calcite crystals generates chalks with littleeffective porosity (van den Bark and Thomas, 1980). Despite burial to depths in excess of 3000 m, however, many chalks still have interparticle porosities as high as 30-40%. The preservation of high primary porosities is due to four inter-related factors: (1) the chalks are characterized by over-pressured pore fluids which reduce the grain-to-grain stresses and, hence, additional mechanical and chemical compaction; (2) pore fluids are relatively rich in dissolved magnesium which retards carbonate dissolution and subsequent cementation; (3) in this vein, because of their stable low-magnesian calcite composition chalks have a limited diagenetic potential for dissolution-cement reprecipitation as do sediments dominated by aragonitic mineralogies; and (4) early arrival of hydrocarbons into the pores. When hydrocarbons are trapped in pores, all cementation ceases (Scholle, 1975, 1977; Friedman and Sanders, 1978; D'Heur, 1984; Feazel et al., 1985; Feazel and Schatzinger, 1985; Maliva et al., 1991; Maliva and Dickson, 1992). A combination of the great thickness of overburden sediment (> 3,000 m), together with a high heat flow related to continuing rifting and graben development in the North Sea, caused salt diapirism and piercement in the productive area during the Tertiary. These salt movements not only generated extensive fracture systems, which became avenues for hydrocarbon migration, but the fractures also contribute extensively to the effective porosity and permeability of the chalk reservoirs here (Mimran, 1977). Large fractures may be related to the Tertiary tectonic history, whereas small fractures may represent minor tectonic adjustments to stylolitization. Fracturing increases with depth, and this general trend is coincident with increases in effective porosity. Also, effective porosity increases towards the structural crests of fields as a result of the higher incidence of fractures (Van den Bark and Thomas, 1980).

784

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Fig. 8-9. Sketch illustrating the relationship between the major fracture types and the principal stress axes in cores of the North Sea chalk. (FromFeazel and Farrell, 1988; reprinted with permission from the SEPM, the Society for Sedimentary Geology.) Fractures create reservoir permeabilities of up to 200 mD, and are of three kinds" (1) healed fractures; (2) tectonic fractures; and (3) stylolite-associated fractures (Fig. 8-9). Healed fractures are not porous; oil-staining, however, suggests that they may have once been open to hydrocarbon flow, but now are filled with carbonate that looks like chalk. Tectonic fractures are open to fluid flow, their formation being a response to vertical, maximum principal stress. These fractures actually are small faults that dip between 6 0 - 70 ~ Stylolite-associated fractures form contiguous to stylolites, and tend to be vertical (Nelson, 1981; Watts, 1983; Feazel and Farrell, 1988). The development of fractures, open stylolites, and microstylolitic seams is necessary to permit pressure-solution (Ekdale and Bromley, 1988; Morse and Mackenzie, 1990). North American reservoirs Austin Chalk The Austin Chalk is Upper Cretaceous in age (Fig. 8-10) and underlies much of east and central Texas as well as the Texas Gulf Coast. The structural strike of this formation is to the northeast-southwest, and extends approximately 520 km along strike (Fig. 8-11). The dip of the Austin Chalk into the Gulf Coast Basin is 1 - 4 ~ The thickness of the chalk varies from approximately 70 - 170 m. Its composition is similar to that of the North Sea chalk, but commonly present are pyrite, glauconite, tephra, and skeletal fragments. In contrast, however, porosity is low, ranging from 3 - 9 %, and permeabilities are generally less than 0.5 mD, most commonly, less than 0.1 mD.

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Porosity and permeability decrease with increasing burial depth. The best chalk production is from a depth of 1 5 0 0 - 3200 m. Production from the Austin Chalk dates to the 1920s. However, it was not until after the prolific North Sea discoveries in the early to middle 1970s that the Austin Chalk became a primary target for exploration. Although Pearsall Field in south Texas was discovered in 1936, the middle 1970s spurred further exploration, and by the late 1980s, approximately 1600 wells had produced in excess of 60 MMBO from this field. One of these wells, which gauged 18,000 BOD while drilling, is still making 600 BOD. An exciting discovery of the 1970s was the Giddings Field (Fig. 8-11), which has produced more than 185 MMBO from approximately 3,000 wells (Horstmann, 1977; Haymond, 1991). In the middle 1980s, a new approach to Austin Chalk exploration was inaugurated when Exxon completed a well in the Giddings Field from a horizontal borehole. Through 1987, fourteen horizontal wells were drilled here, resulting in an anticipated

786

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i Fig. 8-11. Location map illustrating Giddings Field relative to regional features: Balcones, Luling and Mexia-Talco fault zones, Austin Chalk outcrop. (From Kuich, 1990 after Corbett et al., 1987; reprinted with permission from WorldOil.) ultimate recovery of 80,000 BO per well. Thirty-four horizontal wells were completed in 1988, 56 in 1989, and 548 in 1990. At least 50 horizontal wells are completed each month. In December 1990 alone, 122 horizontal wells were permitted (Haymond, 1991). One of the companies in this play, Union Pacific Resources (UPRC), claims to be a leader in horizontal drilling in the Austin Chalk trend:

"Since late 1989, we have drilled 251 wells and currently have interests in 24 operated rigs and two non-operated rigs. This activity helps make us the leading driller in the United States today. This activity has generated 53000 BOED net to UPRC with 29000 BOD, 16000 BNGLD and 78 MMCFD. Our current leasehold in the trend totals 467000 acres and 36 MMBO reserves proven to date on these leases, with expected ultimate to be in excess o f l O0 MMBOE. Full-cycle economics generate internal rates o f return in the range o f 30-35 percent. The Chalk helped UPRC have another record year in 1991. Production was up, reserves were up andprofits were up. Look at the numbers: 66.5 MMBOE production. Up 6.17 MMBOE: $243 million earnings, up $3 million from 1990." (Adams, 1992).

787 Horizontal drilling connects multiple vertical fractures with a single wellbore, resuiting in drainage of a larger area and, hence, in higher rates of production (Fig. 812) (Snyder and Milton, 1977; Stapp, 1977; Corbett et al., 1987; Raeser and Collins, 1988; Haymond, 1991). Horizontal drilling is now the routine technique for Austin Chalk exploration and production (Chuber, 1991; Kuich, 1990). A horizontal well may recover three to five times more oil than a comparable vertical well. Before the advent of horizontal drilling, success had been claimed for seismic techniques finding fault zones and tracing them up into the fractured chalk (Fig. 8-13). Other techniques have included properly supervised fracture programs and use of circulating muds with proper properties.

Fracture trend NE-SW

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Fig. 8-12. Geologic model of fracture development in the Austin Chalk. Small-scale faulting and associated fracturing trend in a NE-SW direction in response to regional tension. Fracture swarms generally do not communicate in a dip direction. Horizontal wells attempt to interconnect the hydrocarbons isolated in these fractures. (From Kuich, 1990; reprinted with permission from Worm Oil.)

Comparison to European chalk One intriguing difference between European chalks and the Austin Chalk is the color of the rocks. European chalks are as white as expressed in the famous song on the white, chalk cliffs of Dover. By comparison, the Austin Chalk (and other North American chalks, discussed below) are medium and dark gray to black (Fig. 8-14). Apparently, North American chalks are internally sourced and, accordingly, their dark colors are related to the presence of organic matter. In fact, inexperienced mud loggers and geologists often have mistakenly identified subsurface samples of the Austin Chalk as shale.

788

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Fig. 8-13. (A) Seismic line shows typical fracture indicators: breakup of base Austin Chalk, top Austin Chalk and Pecan Gap reflectors (circled). The highly productive ECF 1-1 well is located on a base Austin Chalk indicator whereas the unsuccessful ECF 1-2 well is not. (B) Map view of seismic line relative to well locations. (From Kuich, 1990; reprinted with permission from Worm Oil.) A recent experience with an Austin Chalk core relates the following: (1) There are oil shows throughout the chalk interval (API gravity 17 - 26~ (2) The chalk ranges in color from medium gray to black. The basal part of the core is similar in appearance to the Devonian black shales of the Appalachians. (3) Primary permeability is less than 0.01 mD, and in contrast to North Sea chalk reservoirs, porosity is only 6 - 10%. (4) Fracturing is minor and the decision on whether or not productivity can be enhanced by a "frac job" is pending. In contrast, fractures are ubiquitous in the highly productive North Sea chalk reservoirs.

789

Fig. 8-14. Core of Austin Chalk (Champlin Petroleum #1 Lancier Brinkman, Burleson County, Texas). Black color results from the presence of a high concentration of organic matter. The well from which this core was taken had an initial production in excess of 400 BOPD and a large amount of gas. Width of core 15cm.

Niobrara Chalk The Niobrara Formation was deposited as a chalk in the westem interior seaway of North America during the Late Cretaceous (Fig. 8-15). Reservoirs that produce from this chalk were deposited during periods of maximum transgression when, like in the settings of the North Sea and Austin Chalk, influx of terrigenous material was at a

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_._j--Fig. 8-15. Distribution of Niobrara Chalk in western interior seaway. (Modified from U.S. Geological Survey, Panel # G-245-D, 1980.).

790 minimum (Smagala, 1981; Brown et al., 1982; Lockridge and Pollastro, 1988). Like North Sea chalks and the Austin Chalk, the Niobrara Chalk consists almost entirely of coccolith plates (Fig. 8-16) with only subordinate planktonic foraminifera, Inoceramus fragments, and oyster shells (Scholle, i977). This chalk occurs in the subsurface of eastern Colorado and Wyoming, and is exposed in South Dakota, Nebraska and Kansas. Farther to the west, it grades into calcareous mudstones and shales. Deltaic to nearshore-marine sandy facies along the westernmost margin of the western interior seaway are correlative with the pure chalk. All of these facies and lithologies of the Niobrara are productive. The chalk is up to 200 m thick in the Denver Basin of eastern Colorado (Lockridge and Scholle, 1978; Nydegger, 1991).

Fig. 8-16. Scanning-electronmicrographof Niobrara Chalk composedentirely of coccoliths. (Modified from U.S. Geological Survey,Panel # G-245-D, 1980.) Scale bar = 10 ~tm. The color of the chalk in subsurface cores is generally dark gray to black (Fig. 817) signifying a high concentration of organic matter; in fact, cores of chalk stink like propane even after several months of storage. Hence, the Niobrara is an excellent source rock. In the central Denver Basin its total organic carbon content averages 3.2

791

Fig. 8-17. Core of Niobrara Chalk. Black color of chalk results fromthe presence of a high concentration of organic matter. (Modified from U.S. Geological Survey, Panel #G-245-D, 1980.) Length of scale approximately 20 cm. weight percent (Rice, 1984). In areas of thermal maturity, such as the Denver Basin, the chalk is highly oil saturated (Smagala et al., 1984; Nydegger, 1991). Once again, as with the North Sea and Austin chalks, fracture patterns are the key to exploration for productive reservoirs in the Niobrara. Vertical fractures, confined to brittle interbeds between plastic and impermeable shales, form the reservoirs which are trapped between the overlying Pierre and underlying Carlile shales (Fig. 8-18). Both pervasive forces, such as regional tectonic stress and the history of burial and uplift, together with local features, such as bed-stretching, bed bending, thermal expansion at bed contacts, and elastic versus ductile bed contrasts, control the fracture pattern (Longman, 1991, quoting Fred Meissner). Resistivity logs are important in mapping potentially productive areas, and a need exists for improved drilling techniques, including the use of freshwater gels to prevent formation damage in horizontal wells (Longman, 1991, quoting Charles Brown). Before the advent of horizontal drilling, some companies employed remote sensing to determine fault and fracture patterns and drilled successful wells on the hade of the intersection of such features. Even after the technological revolution of horizontal drilling, however, aerial photography and satellite imagery retain their importance. In Silo Field in Wyoming, sets of northeast- and northwest-trending lineaments may guide exploration efforts (Longman, 1991). The Niobrara Chalk and its stratigraphic correlatives have produced over 56.5 MMBO or gas equivalent through 1990. On the eastern flank of the Denver Basin, accumulations are normally on low-relief anticlinal and fault anticlinal closures. Vertical wells have been stimulated with a foam-fracturing treatment; the estimated recovery per well normally is 1 0 0 - 500 MMCFG, although a few exceptionally good wells recover more than 1,000 MMCFG. Although production from Niobrara gas

792

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100 Fig. 8-18. Stratigraphy of western interior seaway. (From Cobban and Reeside, 1952; reprinted with permission from the Geological Society of America.)

wells is relatively limited, the low cost of drilling and completion makes them attrac' tive exploration targets for small independent producers (Lockridge, 1983). Cumulative Niobrara production from the Denver Basin is more than 4.5 MMBOE from 36 fields. Silo field in Wyoming has been the most active field for horizontal drilling, with cumulative Niobrara production of 1.3 MMBOE from 40 wells. The production of recent horizontal wells yielded 2,000 and 1,670 BOE per day (Nydegger, 1991).

EPILOGUE

As pointed out in the preceding narrative, the European chalk is white in color, even at great depth in the subsurface. Its source rock is generally indicated to be the underlying Jurassic Kimmeridge Clay, although overlying Paleocene shales likewise have been suggested as source rocks. By contrast, even in the shallow subsurface, North American chalks are dark and, commonly, as black as Appalachian black shale. Cores of North American chalk are often mistaken for shale. The source of the black color is the high concentration of organic matter present. In as much as the organic matter is derived from the original coccolith ooze and would also have been present originally in the European chalk, an unknown process in an unknown geologic setting

793

must have removed the European chalk's original organic matter. In other words, the European chalk has undergone a diagenetic history which did not affect the North American chalk. What could that have been? One can speculate how plate tectonic movements, as part of the opening of the Atlantic Ocean, affected the European chalk. But then the writer has seen subsurface chalks from the Middle East that likewise are as white as those from Europe.

REFERENCES

Adams, W.L., 1992. Geologists need business sense.Am. Assoc. Petrol. Geologists, Explorer, April 1992: 36. Alger, P., 1991. The UK sector of the North Sea is 25 years young. Bull. Houston Geol. Society, 33, 5:16 -19. Brewster, J., Dangerfield, J. and Farrell, H.E., 1986. The geology and geophysics of the Ekofisk Field waterflood. Mar. and Petrol. Geology, 3" 1 3 9 - 169. Bromley, R.G. and Ekdale, A.A., 1987. Mass transport in European Cretaceous chalk: fabric criteria for its recognition. Sedimentology, 34: 1079- 1092. Brown, C.A., Crafton, J.W. and Golson, J.G., 1982. The Niobrara gas play: exploration and development of a low pressure, low permeability gas reservoir. J. Petrol. Technol., 24:2862 - 2870. Chuber, S. (Editor), 1991. Austin Chalk Exploration Symposium. South Texas Geol. Society, 131 pp. Cobban, W.A. and Reeside, J.B., 1952. Correlation of the Cretaceous formations of the western interior of the United States. Bull. Geol. Soc. Am., 63: 1011- 1044. Corbett, K.P., Friedman, M. and Spang, J., 1987. Fracture development and mechanical stratigraphy of Austin Chalk, Texas. Bull. Am. Assoc. Petrol. Geologists, 71" 17 - 28. D'Heur, M., 1984. Porosity and hydrocarbon distribution in the North Sea chalk reservoirs. Mar. and Petrol. Geology, 1" 211 - 238. Ekdale, A.A. and Bromley, R.G., 1988. Diagenetic microlamination in chalk. J. Sed. Petrology, 58:857 -861. Feazel, C.T. and Farrell, H.E., 1988. Chalk from the Ekofisk area, North Sea: nannofossils + micropores = giant fields. In: A.J. Lomando and P.M. Harris (Editors), Giant Oil and Gas Fields, Soc. Econ. Paleont. Mineralogists, Core Workshop, 12, 1" 155-178. Feazel, C.T. and Schatzinger, R.A., 1985. Prevention of carbonate cementation in petroleum reservoirs. In: N. Schneidermann and P.M. Harris (Editors), Carbonate Cements. Soc. Econ. Paleont. Mineralogists, Spec. Publ., 36" 9 7 - 106. Feazel, C.T., Keany, J. and Peterson, R.M., 1985. Cretaceous and Tertiary chalks of the Ekofisk Field area, central North Sea. In: P.O. Roehl and P.W. Choquette (Editors), Carbonate Petroleum Reservoirs. Springer-Verlag, New York, pp. 4 9 5 - 507. Friedman, G.M. and Sanders, J.E., 1978. Principles of Sedimentology. John Wiley & Sons, New York: 792 pp. Garrison, R.E., 1981. Diagenesis of oceanic carbonate sediments: a review of the DSDP perspective. In: J.E. Warme, R.G. Douglas and E.L. Winterer (Editors), The Deep Sea Drilling Progress: A Decade of Progress. Soc. Econ. Paleont. Mineralogists, Spec. Publ., 32" 181 - 2 0 7 . Hancock, J.M. and Scholle, P.A., 1975. Chalk of the North Sea. In: A.W. Woodland (Editor), Petroleum Geology and the Continental Shelf of Northwest Europe, v. 1, Geology. Applied Science Publishers, London, pp. 413 - 427. Hardman, R.F.P., 1982. Chalk reservoirs of the North Sea. Bull. Geol. Soc. Denmark, 30' 1 1 9 - 137. Haymond, D.,1991. The Austin c h a l k - a n overview. Bull. Houston Geol. Society, 33" 2 7 - 34. Horstmann, L.E., 1977. Giddings Field. In: G.K. Bums (Editor), Typical Oil and Gas Fields of Southeast Texas. Houston Geol. Society, II, pp. 2 3 5 - 241. Huxley, T.H., 1868. On a piece of chalk. British Assoc. for the Advancement of Science, Norwich, England: no pagination. Jorgensen, N.O., 1986. Geochemistry, diagenesis and nannofacies of chalk in the North Sea Central Graben. Sed. Geology, 48: 2 6 7 - 294.

794 Kennedy, W.J., 1980. Aspects of chalk sedimentation in the southern Norwegian offshore. The Sedimentation of the North Sea Reservoir Rocks, Geilo, Norwat. Norwegian Petrol. Soc. Conference, 29 pp. Kennedy, W.J., 1987. Sedimentology of Late Cretaceous-Paleocene chalk reservoirs, North Sea Central Graben. In: J. Brooks (Editor), Petroleum Geology of Northwest Europe. Graham and Trotman, London, pp. 469 - 481. Kuich, N., 1990. Seismic and horizontal drilling unlock Austin Chalk. Worm Oil, 211(3): 47 - 54. Lockridge, J.P., 1983. Shallow gas fields in high porosity chalk: an independent's exploration strategy. Bull. Am. Assoc. Petrol. Geologists, 67: 2156. Lockridge, J.P. and Pollastro, R.M., 1988. Shallow Upper Cretaceous Niobrara gas fields in the Eastern Denver Basin. In: S.M. Goolsby and M. Longman (Editors), Occurrence and Petrophysical Properties of Carbonate Reservoirs in the Rocky Mountain Region. Rocky Mountain Assoc. Geol. Societies, 1988 Carbonate Symposium, pp. 6 3 - 74. Lockridge, J.P. and Scholle, P.A., 1978. Niobrara Gas in eastern Colorado and northwestern Kansas. In: J.D. Pruit and P.E. Coffin (Editors), Energy Resources of the Denver Basin. Rocky Mountain Assoc. Geol. Societies, Guidebook, pp. 3 5 - 49. Longman, M., 1991. Niobrara workshop reviewed. Outcrop, 40(7): 1 4 - 15. Mimran, Y., 1977. Chalk deformation and large-scale migration of calcium carbonate. Sedimentology, 24:333 - 360. Maliva, R.G. and Dickson, J.A.D., 1992. Microfacies and diagenetic controls of porosity in Cretaceous/ Tertiary chalks, Eldfisk field, Norwegian North Sea. Bull. Am. Assoc. Petrol. Geologists, 76:1825 1838. Maliva, R.G., Dickson, J.A.D. and R~iheim, A., 1991. Modelling of chalk diagenesis (Eldfisk Field, Norwegian North Sea) using whole rock and laser ablation stable isotopic data. Geol. Magazine, 128:43 - 4 9 . Morse, J.W. and Mackenzie, F.T., 1990. Geochemistry of Sedimentary Carbonates. Elsevier Publ. Co., Amsterdam, 707 pp. Nelson, R.A., 1981. Significance of fracture sets associated with stylolite zones. Bull. Am. Assoc. Petrol. Geologists, 65: 2 4 1 7 - 2425. Nydegger, G.L., 1991. Overview of the Rocky Mountain fractured Niobrara. In: S. Chuber (Editor), Austin Chalk Exploration Symposium. South Texas Geol. Society, pp. 111 - 117. Nygaard, E., Lieberkind, K. and Frykman, P., 1983. Sedimentology and reservoir parameters of the Chalk Group in the Danish central graben. Geol. en Mijnbouw, 6 2 : 1 7 7 - 190. Raeser, D.F. and Collins, E.W., 1988. Style of faults and associated fractures in Austin Chalk, northern extension of the Balcones Fault Zone, Central Texas. Trans., Gulf Coast Assoc. Geol. Societies, 38: 267-276. Rice, D.D., 1984. Occurrence of indigenous biogenic gas in organic-rich, immature chalks of Late Cretaceous age, eastern Denver Basin. In: J.G. Palacas (Editor), Petroleum Geochemistry and Source-Rock Potential of Carbonate Rocks. Am. Assoc. Petrol. Geologists, Studies in Geology, 18: 1 3 5 - 150. Schatzinger, R.A., Feazel, C.T. and Henry, W.E., 1985. Evidence of resedimentation in chalk from the Central Graben, North Sea. In: P.D. Crevello and P.M. Harris (Editors), Deep Water Carbonates. Soc. Econ. Paleont. Mineralogists, Core Workshop, 6: 3 4 2 - 385. Schlanger, S.O. and Douglas, R.G., 1974. Pelagic ooze-chalk-limestone transition and its implications for marine stratigraphy. In: K.J. Hsu and H.C. Jenkyns (Editors), Pelagic Sediments on Land and Under the Sea. Intl. Assoc. Sedimentologists, Spec. Publ., 1:117 - 148. Scholle, P.A., 1975. Application of chalk diagenetic studies to petroleum exploration problems. Bull. Am. Assoc. Petrol. Geologists, 59: 2 1 9 7 - 2198. Scholle, P.A., 1977. Chalk diagenesis and its relation to petroleum exploration: oil from chalks, a modem miracle? Bull. Am. Assoc. Petrol. Geologists, 61: 9 8 2 - 1009. Smagala, T.M., 1981. The Cretaceous Niobrara play. Oil and Gas J., 79, 10:204 - 218. Smagala, T.M., Brown, C.A. and Nydegger, G.L., 1984. Log-derived indicator of thermal maturity, Niobrara Formation, Denver Basin, Colorado, Nebraska, Wyoming. In: J. Woodward, F.F. Meissner and J.L. Clayton (Editors), Hydrocarbon Source Rocks of the Greater Rocky Mountain Region. Rocky Mountain Assoc. Geol. Societies, Guidebook, pp. 355 - 363. Snyder, R.H. and Craft, M., 1977. Evaluation of Austin and Buda formation cores and fracture analysis. Trans., Gulf Coast Assoc. Geol. Societies, 27: 3 7 6 - 385. Stapp, W.L., 1977. The geology of the fractured Austin and Buda formations in the subsurface of South Texas. Trans., Gulf Coast Assoc. Geol. Societies, 27:208 - 229.

795

Van den Bark, E. and Thomas, O.D., 1980. Ekofisk: first of the giant oil fields in Western Europe. In: M.T. Halbouty (Editor), Giant Oil and Gas Fields of the Decade: 1 9 6 8 - 1978. Am. Assoc. Petrol. Geologists, Mem., 3 0 : 1 9 5 - 224. Watts, N.L., 1983. Microfractures in chalks of Albuskjell Field, Norwegian Sector, North Sea: possible origin and distribution. Bull. Am. Assoc. Petrol. Geologists, 67:201 - 234. Watts, N.L., Lapre, J.F., Van Schijndel-Goester, F.S. and Ford, A., 1980. Upper Cretaceous and Lower Tertiary chalks of the Albuskjell area, North Sea: deposition in a base-of-slope environment. Geology, 8: 2 1 7 - 2 2 1 . Ziegler, P.A., 1975. Geologic evolution of the North Sea and its tectonic framework. Bull. Am. Assoc. Petrol. Geologists, 59:1073 - 1097. Ziegler, P.A., 1982. Geological Atlas of Western and Central Europe. Elsevier Publ. Co., Amsterdam, 130 pp.

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797

Chapter 9 HYDROCARBON RESERVOIRS IN KARSTED CARBONATE ROCKS S.J. MAZZULLO AND G.V. CHILINGARIAN

INTRODUCTION

Hydrocarbon reservoirs in which substantial porosity and permeability have resuited from karstification of carbonate rocks, or where trap configurations and some secondary porosity in preexisting porous carbonates are related to karstification, are common in many petroliferous basins in the world. The formation of most such karst reservoirs commonly is ascribed to extensive dissolution of carbonate rocks beneath and along subaerial unconformities. Additionally, reservoirs also are associated with various paleogeomorphologic (paleolandscape) features in weathered carbonate terrains. These processes, and the products of karstification, are generally, although not exclusively, indicative of prolonged periods of subaerial meteoric exposure along unconformities. In fact, upwards of 30% of recoverable hydrocarbons in Precambrian and Phanerozoic age reservoirs (both siliciclastic and carbonate) are intimately related to unconformities (Moody et al., 1970), and this percentage probably is greater for hydrocarbon reservoirs in carbonate rocks that have been affected by weathering along unconformities (Esteban, 1991). Although not discussed in this chapter, karsted carbonates also are host to many other economically valuable mineral deposits throughout the world. Karst associated with lead and zinc, copper, fluorite, antimony, mercury, vanadium, uranium, bauxites, ores of nickel, iron and manganese, phosphorites and phosphates, clays, coal, and of course, potable water are discussed in Kyle (1983), Sangster (1988), Bardossy (1989), Bardossy et al. (1989), Bocker and Vizy (1989), Bosak (1989a), Bourrouilh-Le Jan (1989), Dzulynski and Sass-Gustkiewick (1989), Ford and Williams (1989), Fuchs (1989) and Zotl (1989). This chapter reviews some basic geologic aspects of unconformity-related hydrocarbon reservoirs in karsted carbonate rocks. In particular, it concerns their global occurrence, contribution to global oil and gas reserves, subsurface recognition, and reservoir petrophysics. Readers interested in general aspects of karst formation in carbonate rocks should consult the works of Thrailkill (1968) Jennings (1971), Bogli (1980), James and Choquette (1984, 1988), Palmer (1984), Ford andWilliams (1989), and Wright et al. (1991), and the many references contained therein. Papers in Bosak et al. (1989a) provide excellent examples ofkarsts of different ages from around the world. Compilations that deal specifically with karsted hydrocarbon reservoirs include James and Choquette (1988), Esteban (1991), Johnson (1991), Wright et al. (1991), and Candelaria and Reed (1992).

798 KARSTS AND THEIR RELATIONSHIPTO UNCONFORMITIES

Karst origins Karst features of both surficial meteoric dissolution and precipitation origin within and transecting carbonate strata (vugs, caves, caverns, enlarged fractures, joints, and faults; flowstones, dripstones, and associated cements), and of geomorphic origin developed on weathered carbonate landscapes (dolines, residual hills, dissolution valleys), constitute the most common type ofkarst recognized in modem and ancient settings. That is, karst formed at and below unconformity surfaces of subaerial exposure (Fig. 91: James and Choquette, 1984; Choquette and James, 1988). Such karst typically is characterized as distinctive terranes whose landforms, hydrology, and diagenetic facies result from dissolution, mainly by carbonic acid (Smart and Whitaker, 1991). According to Esteban (1991, p. 96), karst is "... the product ofsubaerial exposure in carbonates consisting of an integrated drainage system including conduit flow. The drainage system is formed by dissolution and mechanical erosion of carbonates by meteoric w a t e r s . . , enhancing preexisting permeability networks (fractures, bedding planes, primary porosity and secondary porosity).", and " . . . with well-developed secondary porosity." (Ford and Williams, 1989, p. 1). Perhaps a more inclusive definition is that of Esteban and Klappa (1983), paraphrased as "a diagenetic facies, an overprint on subaerially exposed carbonates, produced and controlled by dissolution, and migration and precipitation of calcium carbonate in meteoric waters, occurring in a wide variety of climatic and tectonic settings and generating a recognizable landscape". This type ofkarst occurs throughout the stratigraphic record (e.g., Mussman and Read, 1986; Sando, 1988; Bosak, 1989b; Palmer and Palmer, 1989; papers in Bosak et al., 1989a), and despite the fact that not all aspects of karstification as defined above are always readily apparent in the subsurface, it has strongly affected the formation of most subunconformity-trap hydrocarbon reservoirs around the world. Tower

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799

Other types ofkarst-forming systems are known to occur in nature, some of which do not involve meteoric waters (for a general review see papers in Bosak et al., 1989a; Ford and Williams, 1989; Wright, 1991). Their relative contributions to the development of hydrocarbon reservoirs, however, appear to be vastly subordinate to reservoirs associated with subunconformity, subaerial and surficial meteoric karsts. The following six other types ofkarst systems are recognized: (1) Karst dissolution of emergent and shallow buried carbonate rocks by mixed meteoric-marine groundwaters in modem coastal settings (Back et al., 1979, 1986; Hanshaw and Back, 1980; Stoessell et al., 1989). Some hydrocarbon reservoirs are known to occur in this type of subunconformity-related karst. For example, reservoir porosity formation in Amposta Marino Field in offshore Spain was polygenetic in that this type of subunconformity-related karst overprinted a preexisting meteoric karst system (Garcia-Sineriz et al., 1980; Wigley et al., 1988; Bouvier et al., 1990). (2) Karst porosity in the submarine environment resulting from reflux of evolved meteoric waters through rocks buried under submerged continental shelves (Stoessell et al., 1989; Fanning et al., 1981). Hydrocarbon reservoirs are not presently known from such settings. Although such systems are not in direct contact with subaerial unconformities, it must be remembered that karstification may extend hundreds of meters or more below unconformity surfaces (Choquette and James, 1988). Hence meteoric, as well as mixed meteoric-marine fluids as discussed in (1) above, may result in extensive karstification of carbonate rocks in the subsurface (Fig. 9-1), whether the strata are on land (e.g., Vemon, 1969) or under the sea (Fanning et al., 1981; Stoessell et al., 1989). (3) Likewise, megascopic karst dissolution features (i.e., caverns) also are known to form as a result of interaction of carbonates and ascending hydrothermal fluids, wherein dissolution either overprints a preexisting subaerial karst system or which itself generates the bulk of the porosity (Dublyansky, 1980; Egemeier, 1981; Bakalowicz et al., 1987; Muller, 1989). Such karsts may be associated with subaerial unconformities in that fluids expelled from depth cause extensive near-surface dissolution. Reservoir examples of this type of karst also are not presently known. This type of karst commonly is related to "intrastratal karst", which forms by subsurface dissolution along lithologic boundaries, the products of which can be confused for surface karst (Choquette and James, 1988; Bosak et al., 1989b). (4) Extensive modem and older karst cavern systems, such as Carlsbad Caverns, New Mexico, many caves in Romania, and possibly some large oil fields around the world (e.g., Yates and Dollarhide fields, Permian Basin, Texas; Agha Jari, Kirkuk, Asmari, Rumaila, and Zubair fields in the Middle East; Renqiu Field in China) may represent "sulfuric acid oil-field karsts" (Han, 1990; Hill, 1990, 1992). Carbonate dissolution in this type ofkarst system occurs in the burial environment, as rocks are being uplifted, or in those rocks already telogenetically exposed. Dissolution is caused by ascending evolved connate fluids that are enriched in sulfuric acid as a consequence of oxidation of HzS in evaporite-rich, hydrocarbon environments and/or by mixing of waters of different H2S content (Hill, 1990, 1992; Palmer, 1991). These karsts likewise may not be associated with subaerial unconformities, particularly if they have formed in the deep burial (mesogenetic) environment. In fact, mesogenetic dissolution of carbonate rocks by evolving burial fluids of various chemistry is known to have caused

800

extensive secondary porosity development in many hydrocarbon reservoirs, and may locally result in the formation of intrastratal, karst-like unconformities in this environment (Mazzullo and Harris, 1992). Possible criteria for the recognition and distinction of meteoric subaerial, hydrothermal, and oil-field karsts are given by Bakalowicz et al. (1987), Ford and Williams (1989), Hill (1991, 1992), Palmer (1991), and Smart and Whitaker (1991). (5) Cold seawater-dissolution of extant carbonate platforms may also result in the formation of some karst-like cavities in carbonate rocks (Smart and Whitaker, 1991). (6) Collapse and brecciation of carbonate strata as a result of intrastratal dissolution of evaporites (not considered in this chapter because it's not related to subunconformity, meteoric processes: refer to several papers in Bosak et al., 1989a, specifically, Palmer and Palmer, 1989; and DeMille et al., 1964, and Smith and Pullen, 1967). The fact is that karst formation can be, and commonly is, "polycyclic" (sensu Ford and Williams, 1989) in that a specific cycle of karstification is overprinted by one or more successive cycles, each possibly having been related to different processes as discussed above: that is, they can be polycyclic as well as polygenetic. The Amposta Marino Field in Spain is an example of polycyclic and polygenetic karst, and likely, many other examples exist in karsted carbonate reservoirs (for example, Yates and Dollarhide fields in the Permian Basin of Texas: Hill, 1990, 1992; Sailer et al., 1991). In fact, with few exceptions (Garcia-Sineriz et al., 1980; Wigley et al., 1988; Bouvier et al., 1990; Han, 1990; Hill, 1990, 1992) most studies ofkarsted carbonate reservoirs have tacitly assumed that the karsted unit under consideration formed as a result of subaerial meteoric exposure. Unfortunately, the subsurface recognition of other types of karsts is a difficult task in reservoirs because of the common paucity of definitive regional information accompanying most oil-field studies that is required for their identification. Hence, virtually by default, the main topic of concern in this chapter is karsted carbonate reservoirs that have actually, or are assumed to have, formed as a result of subaerial meteoric exposure along unconformities. This constraint appears to be justified, however, because according to Ford and Williams (1989), the majority of studied occurrences of karsts are, in fact, of subaerial meteoric origin. Karsts and causative mechanisms of subaerial exposure

The most common types of karsts, those of subaerial meteoric origin, form as a result ofwholescale dissolution of carbonates. A major consideration in studies of this type ofkarst is the causative mechanism for subaerial exposure.As discussed below, it has been demonstrated or at least tacitly assumed in many studies that karstification in the stratigraphic record resulted from subaerial exposure due to sea level drops: either relative drops caused by situations in which rates of sedimentation exceeded subsidence, or resulting from local tectonic uplift; or of global scale due to eustatic falls (e.g., Vail et al., 1977). A special situation of karsting occurs in large, intracratonic basins associated with thick evaporites, wherein eustatic and or relative sea level lowstands are not necessarily indicated. This mechanism, referred to as "evaporative drawdown", involves periodic desiccation ofintracratonic basins and concurrent deposition ofevaporites. Carbonates

801

deposited during previous sea level highstand cycles become emergent and can be subject to karst dissolution. Such a mechanism apparently resulted in karstification of some Silurian reefs in the Michigan Basin and some Devonian reefs in the Alberta and Williston basins of Canada (Fuller and Porter, 1969; Jodry, 1969; Wardlaw and Reinson, 1971; Mesolella et al., 1974; Gill, 1985). Only the examples described by Mesolella et al. (1974) and Gill (1985) are included in later compilations of karsted reservoirs, however, because either there is no hydrocarbon production associated with the affected carbonates or karsting was not specifically mentioned in these other quoted references to have significantly contributed to reservoir porosity and permeability. For purposes of simplicity, specific causative mechanisms of subaerial exposure will not be considered in ensuing discussions. Instead, reference will be made only to local or global, eustatic or relative sea levels drops attending karstification.

Relationships to unconformities Controls on karstification The most common style of karstification (Fig. 9-1) occurs when carbonate strata are exposed to meteoric fluids along and beneath unconformities that represent periods of subaerial exposure. Several intrinsic and extrinsic factors affect karstification (Table 9-I). According to Ford (1988), Ford and Williams (1989) and others, karstification is promoted in wet climates and when the affected carbonate strata are moderately thick bedded, relatively impermeable, and with widely spaced joints. In

TABLE 9-I Factors that influence the development ofkarst terranes EXTRINSIC Climate

Rainfall and evaporation Temperature

Base level

Elevation and relief Sea level or local water bodies

Vegetation Time duration INTRINSIC Lithology

Mineralogy Bulk purity Fabric and texture Bedding thickness Stratal permeability Fractures

Structure and stratigraphy

Attitude of strata Confined or unconfined aquifers Structural conduits

Source: From James and Choquette, 1988; reprinted with permission from Springer-Verlag.

802

the absence of these conditions, subaerial exposure along unconformities will not always lead to karstification. Hence, not all subunconformity carbonate reservoirs can be considered to be karsted. In fact, there are many examples in the stratigraphic record of carbonate rocks that have been subaerially exposed, and which have developed secondary dissolution porosity, but which do not necessarily qualify as karst by the definitions given earlier (e.g., Zelten Field in Libya: Bebout and Pendexter, 1975; Seminole Southeast Field, Permian Basin, Texas: Mazzullo, 1985; Mississippian fields on the Sweetgrass Arch in Montana: Pasternack, 1988; and others in Roehl and Choquette, 1985, and the fields listed in encl. 3.1 in Esteban, 1991). At best, such examples may represent only incipient karsts because there clearly is a gradation in nature between meteoric diagenesis that causes cementation and only minor dissolution, and meteoric diagenesis that resuits in extensive karstification. Every effort was made to exclude non-karst examples from the compilations of karsted carbonate reservoirs that are presented later in this chapter, particularly when no mention ofkarst was indicated in original published references. In addition to climatic and geologic controls, the duration and timing ofsubaerial exposure exert strong influence on the style of karstification that will be produced along unconformities. In this regard, the type of unconformity present above a carbonate sequence is relevant to studies ofkarsted carbonate reservoirs. Esteban (1991) presented a definitive summary of unconformity types and their relationships to karstification and hydrocarbon reservoirs in karsted carbonate rocks (Fig. 9-2).

Caribbean style karst According to Esteban (1991), fifth-order conformities, represented by bedding plane contacts with perhaps as much as 0.001 million years time gap between beds, typically are not associated with karst features. In contrast, fourth-order disconformities commonly cap upward-shoaling, carbonate depositional cycles within the larger-scale depositional sequences of Vail et al. (1977). These disconformities typically represent up to 0.01 million years time gap, and generally do not imply exposure due to global or local sea level fall. Such disconformities often are referred to as "intraformational unconformities". Meteoric diagenesis along such boundaries is considered to be essentially syndepositional ("eogenetic" of Choquette and Pray, 1970) and relatively shortlived, and usually involves alteration of only a limited thickness of mineralogically unstable (for example, aragonitic and high-magnesium calcite composition in Pleistocene and Holocene deposits), unlithified to weakly lithified carbonate sediments. This style of early diagenetic alteration is referred to by Esteban (1991) as "Caribbean type karst" (Table 9-11). As discussed below, however, the use of this term is misleading and, in fact, may be erroneous. There simply is not enough time in most cases for dissolution attending shortlived subaerial exposure along parasequence boundaries to create true karsts. In fact, dissolution in such cases most commonly results in the development of secondary fabric-selective porosity (for example, by dissolution of aragonitic particles) superimposed on an existing depositional porosity system of primary interparticle and intraparticle pores in newly deposited sediments. In most cases, megascopic karst features such as caves, cavem systems, and relict dissolutional landforms do not develop. Instead, reservoir petrophysical properties show a marked control by

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facies-selective: Mazzullo, 1986) rather than being controlled by karst features. Hence, reservoirs formed in such situations can not be considered as being karst-altered. Representative hydrocarbon reservoirs of this type include Zelten and Seminole Southeast fields (references cited above), several fields in Upper Jurassic to Lower Cretaceous carbonates in the Neuquen Basin in Argentina (Mitchum and Uliana, 1985), and fields listed in encl. 3.1 in Esteban (1991). In other cases, subaerial exposure along parasequence boundaries has also resulted in the formation of incipient karst surfaces known as "depositional paleokarsts" (Choquette and James, 1988) or"diagenetic terranes" (Roehl, 1967). Such incipient karsts generally are limited to single, relatively thin layers in a stratal sequence (although there may be vertical stacking of such units, discussed below), and the affected strata lack the megascopic, well-developed drainage patterns and dissolution features characteristic of more mature karsts. Such depositional paleokarsts occur in many carbonate hydrocarbon reservoirs (e.g., fields listed in encl. 3.1 in Esteban, 1991), and these commonly are associated with relatively thin, laterally discontinuous units of carbonate dissolution-collapse breccia (such as those which result from the dissolution of evaporites and/or carbonates), small caves, and associated primary and secondary porosity. Likewise, the extent to which such incipient karstification has significantly affected reservoir porosity and permeability systems in these cases varies. For example, relatively high porosities (as much as 12%) and permeabilities (as much as 169 millidarcys)

804

TABLE 9-11 Subaerial diagenesis involving"Caribbean Model" versus "General Model" ofkarstification CARIBBEANMODEL 1. Short exposure time 2. Unstable carbonate mineralogy 3. Shallowburial 4. Minor tectonics 5. Minor deep phreatic zone 6. Primaryand fabric-selective pore types dominate 7. Only in tropical to semi-arid environments 8. Diffuse recharge-diffuse flow only 9. Affected by marine mixing zone 10. Absence ofhydrothermal mixing GENERALMODEL 1. Longer exposure time 2. Stable mineralogy(calcite, dolomite) 3. Deep burial 4. One or several tectonic events 5. Important deep phreatic zone 6. Secondary and fracture porosities predominate 7. Widerrange of environments 8. Confluent recharge, pipe, and confined flow 9. Absence of marine mixing zone effects 10. Presence ofhydrothermal mixing

Source: From Esteban, 1991" reprinted with the permission of Postgraduate Research Institute for Sedimentology and the author. occur in Puckett Field (Ordovician) in the Permian Basin ofTexas (Loucks andAnderson, 1985) partly, but not entirely, as the result of periodic, but short-lived, early subaerial exposure and attendant dissolution. Although small karst caves and associated breccias contribute to the overall reservoir porosity and permeability systems here, reservoir petrophysical properties remain strongly controlled by depositional facies, pre-exposure diagenetic facies (e.g., syndepositional dolomitization and associated porosity), depositionally-controlled diagenetic facies created during the subaerial meteoric exposure event (sensu Mazzullo, 1986), and to the presence of fractures. In contrast, despite early brecciation and attendant dissolution, such a style ofkarstification ultimately contributed little or nothing to the reservoir petrophysical system in, for example, Cabin Creek Field (Ordovician) in the Williston Basin (Roehl, 1985). Individual porous and productive karstic units in fields associated with unconformities along parasequence boundaries typically are thin. However, depositional stacking of such units and interbedded porous but not karsted beds, due to repeated transgression and regression, locally may result in the accumulation of thick gross pay sections. Likewise, successive episodes of short-lived subaerial exposure may cumulatively enhance previously-formed dissolutional pore systems throughout the affected section.Although thick, however, such sections typically compose vertically compartmentalized reservoirs unless the gross pay section is transected by a system of pervasive fractures (e.g., see Loucks and Anderson, 1985).

805

Field examples wherein meteoric alteration along parasequence boundaries did not result in any karsting, or where although formed, depositional paleokarsts did not contribute to reservoir porosity and permeability systems as per the original published references, are not included in later compilations ofkarsted carbonate reservoirs. General karst model Single unconformities of regional extent represent the third-order stratigraphic discontinuities (Fig. 9-2) of Esteban (1991), and as defined, are coincident with depositional sequence boundaries of Vail et al. (1977). Exposure in such cases normally results from global, eustatic sea level drops, although tectonic uplift rather than eustasy may result in local, relative sea level drops. Time gaps represented by these boundaries are on the order of 1.0 million years. According to Esteban (1991), only minor karsting usually occurs along depositional sequence boundaries, although major karst surfaces are known in a few cases (for example, Yates Field, Permian, in the Permian Basin of Texas: Craig et al., 1986 and Craig, 1988 [although this field may be an example of the sulfuric acid oil-field karsts of Hill, 1990, 1992]; and some Devonian reef fields in Canada). Such unconformities and associated hydrocarbon reservoirs generally are not associated with extensively structured (i.e., complexly folded or faulted) strata. In at least the upper portion of affected strata, where essentially newly-deposited carbonate sediments are exposed, diagenesis will be of"Caribbean style" as described above. In contrast, composite unconformities represent first-order and second-order stratigraphic discontinuities of Esteban (1991 ), with durations of exposure being from 4 million to 200 million years (Fig. 9-2). Exposure in such cases is due in large part to global, eustatic sea level drop, although regional tectonic uplift also cannot be ruled out. According to Esteban (1991), major karst systems of regional scale form along composite unconformity surfaces (the "interregional paleokarsts" of Choquette and James, 1988), which commonly affect tectonically deformed strata as well as regionally low-dipping strata. Most karsts associated with single and composite unconformities developed as a result of the meteoric dissolution of already mineralogically stabilized rocks (limestones and dolomites) during successive cycles of uplift after burial. Hence, dissolution generally is not fabric selective, rather than being strongly controlled by the presence of unstable (readily soluble) mineralogies in newly-deposited carbonate sediments (i.e., fabric-selective) as in Caribbean style karsts. This style of karstification, referred to by Esteban (1991) as the "general model" (Table 9-11) and which would be included as "telogenetic" in the Choquette and Pray (1970) classification, and associated karsted hydrocarbon reservoirs are very common in the stratigraphic record, discussed below. In contrast to reservoirs associated with early karsting along parasequence boundaries, the petrophysical characteristics of hydrocarbon reservoirs formed along most composite unconformities and some single unconformities (e.g., Yates Field) are strongly controlled by the presence of vertically and laterally extensive, not fabric-selective karst porosity such as caves, cavems, and dissolution-enlarged fractures and faults. These pore systems can extend hundreds of meters below unconformity surfaces, particularly in karsts associated with composite unconformities.

806

Additional karst definitions Numerous definitions ofkarsts in terms of relationship to timing of formation exist in the literature (e.g., Choquette and James, 1988; Bosak et al., 1989a; Ford and Williams, 1989), some of which have been presented in preceding discussions. The definitions of Choquette and James (1988) are followed throughout this paper. According to these authors, the general term "karst" includes those forming at the present time as well as "paleokarsts", a term that refers to ancient karsts that were buried by younger sediments or rocks. Two specific types ofpaleokarsts are recognized: (1) relictpaleokarsts, which are once-buried, ancient karst landscapes or features that subsequently have been exhumed by erosion so as to be components of present-day landscapes; and (2) buried paleokarsts, which are ancient karst landscapes or features that remain buried beneath younger sediments or rocks. Examples ofkarsted hydrocarbon reservoirs discussed in this chapter necessarily refer to buried paleokarsts; throughout this chapter they will simply be referred to as paleokarsts.

CLASSIFICATION OF KARST RESERVOIRS

Previous classifications Hydrocarbon reservoirs in karsted carbonate rocks occur in one of several trapping configurations, which collectively, are grouped into the general category of subunconformity paleogeomorphic traps (Fig. 9-3) as defined in the trap classification schemes of Levorsen (1936, 1967), Martin (1966), Chenowith (1972), Halbouty (1972), and Rittenhouse (1972). These authors did not propose specific classifications ofkarsted carbonate reservoirs. Implicit, although not necessarily implied in these classifications, however, are the "buried hill" traps (Fig. 9-3) which are but one specific example wherein reservoir porosity and permeability may have been created or enhanced as a result of meteoric karst dissolution. Guangming and Quanheng (1982) proposed a classification of fault-associated, buried hill traps from their studies in China. Martin (1966) specifically mentioned karsted carbonate reservoirs in his example of "indirect, leached reservoirs" located beneath unconformities. A classification scheme specific for karsted carbonate reservoirs was proposed by Esteban (1991) wherein five types of paleokarst reservoirs (Fig. 9-4) are related to structure and the unconformity types discussed in the preceding section. Type 5 paleokarst reservoirs are represented by fiat-lying to gently-structured strata in which upwardshoaling cycles and/or stacked carbonate mounds or buildups are associated with fourthorder disconformities along parasequence boundaries. These may grade to type 2b reservoirs wherein multiple, convergent unconformities are present within the productive section (Fig. 9-4). Karsted reservoir types 1 through 3 represent single and composite unconformities associated with broad arches, remnant depositional and erosional highs, and linear trends of folds and faults. Type 4 reservoirs are, in reality, supraunconformity traps associated with buffed karst topography. In essence, Esteban's (1991) reservoir types 2, 3, and 4 also may include examples of "buried hills" as described by Martin (1966), Halbouty (1972), and Rittenhouse (1972).

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809

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TABLE 9-III Examples of hydrocarbon reservoirs in karsted carbonate rocks ~ Field/trend

Location

Reservoir age (unit)

Field type 2

Reservoir lithology

Reference(s)

Various fields

Waverly Arch (Ohio)

U. Cambrian

IB

Dolomite

Dolly and Busch (1972)

Kraft-Prusa Trend (Kansas)

Central Kansas Uplift (Arbuckle Group)

Cambrian-L. Ordovician

I A,B

Dolomite Waiters (1946, 1958); Waiters and Price (1948); Newell et al. (1987)

Cottonwood Creek, Healdton, Oklahoma Wilburton fields (and others)

Anadarko and Arkoma Basins (Oklahoma)

Cambrian-L. Ordovician, (Arbuckle Group)

IV B; V A

Dolomite

Gatewood (1970); Latham (1970); Wilson ( 1980a,b; 1985); Shirley (1988); Hook (1990); Bliefnick and Belfield (1991); Carpenter and Evans (1991); Lynch andA1-Shaieb (1991); Waddell et al. (1991); Wilson et al. (1991, 1992); Bliefnick (1992)

Various fields (e.g., Renqiu)

North China-Bohay Bay Cambriatr-M. Ordovician I B; IV A-C Basins (China) Precambrian (various units)

Dolomite, limestone

Guangming and Quanheng (1982); Li et al. (1982); Qi and Xie-Pei (1984); Quanheng (1984)

Various fields

Permian Basin (Texas)

L. Ordovician (Ellenburger Group)

IB;IVB,C; V A,B; VII

Dolomite

Mear and Dufurrena (1984); Loucks and Anderson (1985); Mazzullo and Reid (1986); Ijirigho and Schreiber (1988); Kerans (1988, 1989, 1991); Amthor and Friedman (1989); S.J. Mazzullo (1989a, b: 1990); Mear (1989a); Verseput (1989); Holtz and Kerans (1992); Kupecz (1992); Loucks and Handford (1992)

Various fields (e.g., New Hope, Fairview, Maben)

Appalachian Region, Black Warrior Basin (Alabama, Mississippi, Tennessee)

L.-M. Ordovician (Knox Group)

IVB

Dolomite, limestone

Fritz (1991 ); Henderson and Knox (1991); Raymond and Osborne (199 l)

Various fields

Michigan Basin (Michigan)

L.-M. Ordovician (Prairie du Chien Group)

I A,B

Dolomite

Nadon and Smith (1992)

Lima Indiana and Albion-Scipio-Pulaski trends; Northville, Stoney Point, Trenton fields

Cincinnati and Findley Arches (Ohio, Indiana)

U. Ordovician (Trenton Fm., Black River Fm./Group)

VI

Dolomite

Wilson (1980 a,b; 1985); DaHaas and Jones (1988); Catacosinos et al. (1990)

Dollarhide Field

Central Basin Platform (Permian Basin, Texas)

L. Ordovician-Devonian (Ellenburger Group, Fusselman Fm., Thirtyone Fm.)

Various fields

Midland Basin and Central Basin Platform (Permian Basin, Texas and New Mexico)

L.-M. Silurian (Fusselman and Wristen Fms.)

I B; IV A--C

V A,B

Dolomite

Stormont (1949)

Dolomite; some limestone and locally tripolitic chert

Mear and Dufurrena (1984); Garfield and Longman (1989); Geesaman and Scott (1989); L.J. Mazzullo (1989; 1990 a,b); S.J. Mazzullo (1989b); Mear (1989b); Canter et al. (1992); Entzminger and Loucks (1992); Mazzullo and Mazzullo (1992); Troschinetz (1992 a,b)

Dolomite

Mesolella et al. (1974); Gill (1985)

No. and So. Michigan Michigan Basin Basin Pinnacle Reef (Michigan) Trend (e.g., Belle River Hills, Rapid River fields)

M. Silurian (Niagara Group)

Various fields (e.g., Marine Pool, ColmerPlymouth, Edinburg West)

Illinois Basin and Sangamon Arch (Illinois)

Silurian (Niagaran, some associated Devonian)

II; IV B

Dolomite, limestone

Lowenstam (1948); Whiting and Stevenson (1965); Kruger (1992)

Star, Lacey, West Campbell, NE Alden fields

Anadarko Basin (Oklahoma)

Silurian-Devonian (Hunton Group)

I B; III

Dolomite

Harvey ( 1972); Withrow ( 1972); Carpenter and Evans (1991)

Various fields

Permian Basin (Texas, New Mexico)

L.-U. Devonian

IB; IV A,B; V A,B

Dolomite, Hovorka and Ruppel ( 1990); Sailer et al. ( 1991); Canter et al. (1992) local limestone and tripolitic chert

Grant Canyon Field

Basin and Range (USA)

Devonian (Simonson and Guilmette Fms.)

IVC

Dolomite

Read and Zogg (1988)

Bindley Field

Central Kansas Uplift (Kansas)

L. Mississippian

Dolomite

Ebanks et al. (1977)

Big Horn Basin (Wyoming)

U. Mississippian (Madison Fm.)

Dolomite, some limestone

McCaleb and Wayhan (1969); McCaleb (1988)

Elk Basin Field (and others)

(Thirtyone Fm.)

(Warsaw Fm.) IB

oo

TABLE 9-III (Contd.) Reservoir age (unit)

Field type 2

Reservoir lithology

Alida, Daly, Newburg, Williston Basin Nottingham, Parkman, (Canada and USA) South Westhope, Virden fields (and others)

U. Mississippian (Mission Canyon and Madison Groups)

I B; III;

IVA

Limestone, dolomite

Edie (1958); Martin (1964, 1966); Illing et al. (1967); Marafi (1972);Wilson (1985); Kent etal. (1988)

Carter Creek and Whitney Canyon fields

Wyoming Overthrust Belt

U. Mississippian

IVB

Dolomite

Harris et al. (1988); Sieverding and Harris (1991)

Various fields

Central Kansas Uplift (Kansas)

Mississippian (Miss. Lime and "Chat")

IB

Limestone, Wilson (1980 a,b) chert residuum

Crossfield, Harmatton East, Harmattan Elkton, Sundre, Westward Ho fields

Alberta Basin (Canada)

Mississippian (Elkton Fm.)

IB;IVA

Limestone

Martin (1964, 1966)

Various fields (including those on Horseshoe Atoll)

Midland Basin (Permian Basin, Texas)

M.-U. Pennsylvanian (Strawn, Canyon, Cisco Fms.)

I A,B; II

Limestone, some dolomite

Vest (1970); Reid and Mazzullo (1988); Reid et al. ( ! 990, 1991); Reid and Reid ( 1991)

Central Basin Platform Yates and Taylor Link West fields (and others) (Permian Basin, Texas)

U. Permian (San Andres Fm.)

IA,B

Dolomite

Craig et al. (1986); Kerans and Parsley (1986); Craig (1988)

Various fields (including Ishimbay)

Ural Foredeep (U.S.S.R.)

Permian (various units)

Limestone

Maslov (1945); Maksimovich and Bykov (1978)

Malzen, Schonkirchen, Reyersdorf fields

Vienna Basin (Austria)

U. Triassic

IVA

Dolomite

Ladwein (1988)

Nagylengyel Field

Hungary

Triassic, some Cretaceous

1V

Limestone, dolomite

Balint and Pach (1984)

Casablanca Field (and others)

Tarragona Basin (Spain)

U. Jurassic

IVC

Limestone, some dolomite

Garcia-Sineriz et al. (1980); Watson (1982); Esteban ( 199 l)

Un-named

Bresse Basin (France)

Jurassic

VB

Limestone

Fontaine et al. (1987)

Field/trend

Location

Reference(s)

(Madison Group)

Amposta Marino Field (and others)

Tarragona Basin (Spain)

L. Cretaceous (Montsia Fm.)

IB

Limestone

Garcia-Sineriz et al. ( 1980); Wigley et al. (1988); Bouvier et al. (1990)

Field "A"

Mediterranean Basin

L. Cretaceous

IVC

Limestone

Fontaine et al. (1987)

Stuart City Trend

San Marcos Arch and Texas Gulf Coast (USA)

L. Cretaceous (Edwards Fm.)

IB;II; IVB

Dolomite, limestone

Rose (1972); Bebout and Loucks ( 1974); Wilson (1980a,b; 1985)

North Field

Qatar (Persian Gulf)

L.-M. Cretaceous (MishrifFm.)

IVB

Limestone

Aves and Tappmeyer (1985)

Golden Lane Trend

Tampico Embayment (Mexico)

M. Cretaceous (El Abra Fm.)

I A,B; II

Limestone

Viniegra and Castillo-Tejero (1970); Coogan et al. (1972)

Campeche-Reforma Trend

Mexico

L.-U. Cretaceous, U. Jurassic locally

IVB;V

Dolomite, some limestone

Santiago-Acevedo (1980)

BuHasa, Fahud, Fateh, and Natih fields

Saudi Arabia, United Arab Emirates (Persian Gulf area)

Cretaceous (Wasia Group)

II; IV C

Limestone

Tschopp ( 1967); Twombley and Scott ( 1975); Wilson (1980) a,b; 1985); Harris and Frost (1984); Jordan et al. ( 1985); Videtich et al. (1988)

Rospo Mare Field

Italy

Cretaceous

?IA

Limestone

Dussert et al. (1988)

Intisar "D"

Sirte Basin (Libya)

Paleocene (Intisar Fm.)

Limestone

Brady et al. (1980)

Kirkuk Field

Iraq

Eocene-Oligocene (Fars Fm.)

II; IV B

Limestone, dolomite

Daniel (1954)

Bombay High Field

India

Miocene

II; IV A; V: VI

Limestone

Rao and Talukdar (1980)

South Alamyshik Field

U.S.S.R.

Paleogene

IVA

Limestone

Khutorov (1958)

All examples are in subunconformity reservoirs. 2 See Figure 9-5.

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814

Reservoirs in buried hills Review of available published literature (Table 9-111) indicates that the most common occurrence of hydrocarbon reservoirs in karsted carbonates is as buried hills, which compose reservoir types I through IV of the present classification scheme. Implicit in the recognition of this type ofkarsted reservoirs are the following: (1) that karst dissolution has created or significantly enhanced preexisting reservoir porosity and permeability; and (2) that the geomorphic development of now-buried landforms is largely, but not necessarily entirely, attributed to karst erosion.Accordingly, the following types and examples of reservoirs in karsted buried hills are recognized, with additional examples and specific references listed in Table 9-1II: Type I - Karst erosion of regional horizontal to gently-dipping strata, which leads to the geomorphic development of residual hills (including "karst towers" of Choquette and James, 1988: Fig. 9-1) with megascale karst dissolution porosity. The residual hills compose the reservoir and trap beneath impermeable sealing beds. One of the betterknown examples of this type of reservoir are fields in Arbuckle (Cambrian to Ordovician) dolomites in the Kraft-Prusa Trend of central Kansas. Here, reservoirs occur mostly in karsted carbonates of buried hills and along the truncated edges of dissolution valleys at the top of the Arbuckle (Fig. 9-6). Other notable examples are: (1) fields in karsted Cambrian dolomites on the Waverly Arch in Ohio (Fig. 9-7); (2) fields in karsted Ordovician dolomites in the Permian Basin of Texas (Fig. 9-8); and (3) Yates Field (Permian dolomites) in the Permian Basin. Type I I - Karst erosional (geomorphic) modification of, and development of megascale dissolution within, depositional topographic features such as massive bedded reefs and organic mounds, which likewise, compose the reservoir and trap beneath sealing beds. Notable examples are the fields in karsted reefs of Silurian age in the Michigan Basin (Fig. 9-9), the giant Golden Lane (Cretaceous) Trend in Mexico (Fig. 9-10), and the Pennsylvanian HorseshoeAtoll in the Permian Basin, Texas (Fig. 9-11). In reality, many such field reservoirs clearly are hybrid traps, that is, combinations of at least two disparate trap types. For example, although both the Golden Lane and Horseshoe Atoll trends (Figs. 9-10 and 9-11) at least partly represent karst-modified reefs, individual fields within these trends also reflect production from buried hills that are not entirely coincident with actual reefal accumulations. Type I I I - This type represents a special category of buried hill reservoirs in which, although karst erosion has resulted in the geomorphic development of residual hills in gently-dipping strata, the reservoir had a preexisting porosity-permeability system that was not appreciably enhanced by karst dissolution. Rather, the lateral isolation of lenses of porous carbonate rocks within adjoining hills, which subsequently were overlain by impermeable strata, define the essential trap configuration of producing fields (Fig. 9-5). Notable examples of this type of trap are some of the productive fields in Silurian to Devonian carbonates (Hunton Group) in the Anadarko Basin in Oklahoma, and in Mississippian carbonates (Mission Canyon and Madison Groups) in the Williston Basin in Canada and the United States (Fig. 9-12). Specific references to these types of traps include Edie (1958), Illing et al. (1967), McCaleb and Wayhan (1969), Harvey (1972), Withrow (1972), and McCaleb (1988). Unconformities associated with buried hill reservoir types I, II, and III typically are

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Fig. 9-6. Cross sections illustrating Type I reservoirs associated with buried hills and edges of dissolution-valleys in karstedArbuckle (Ordovician) dolomites on the Central Kansas Uplift. (From Waiters, 1946; reprinted with permission from the American Association of Petroleum Geologists.)

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Fig. 9-7. (A) Buried hill paleotopography in karsted sub-Knox carbonates, WaverlyArch, Ohio, shown by isopach map of overlying Lower and Middle Chazy rocks; (B). Portion of Fig. 7A illustrating relationship between hydrocarbon production and buried hills as shown by Knox unconformity subcrop map. (From Dolly and Busch, 1972; reprinted with permission from the American Association of Petroleum Geologists.)

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Fig. 9-8. Buried hill paleotopography (structure, top ofEllenburger, CI = 25 feet) and Type I reservoirs in Ellenburger (Ordovician) dolomites in a portion of Borden County, Permian Basin, Texas. Black dots refer to wells that currently produce or which have produced from the Ellenburger. (Modified from Mazzullo and Reid, 1986.)

single unconformities which occur along sequence boundaries, although some composite u n c o n f o r m i t i e s also may be represented (i.e., the third-and s e c o n d - o r d e r unconformities, respectively, of Esteban, 1991). Excluding Type III reservoirs, karst dissolution and reservoir porosity-permeability systems in these buried hill reservoirs formed d u r i n g s u b a e r i a l e x p o s u r e a n d a r e c o i n c i d e n t w i t h the geomorphic development of the geomorphic landscapes.

819

i MODEL NO. 3 FOR REEF DEVELOPMENT i

i ii

[STAGE i] Development of coral pinnacle during Niogaran J ........ time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hieh ~_* _tEV~L 1 I . . . . . . . . . . . . leverol tens of feet

1

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[STAGE2] Cessation of reef development during Salina A-I

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[STAGE 3] Rejuvenation of reef development during Salina A-1 Carbonate deposition. H i c k SEA LEVEL

A-I CARBONATE

A-I CARBONATE

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/ ~N I AGARA INTERREEF

I

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CARBONATE

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Fig. 9-9. Sequential stages in the development of Type II buried hill reservoirs in karsted Silurian pinnacle reefs in the Michigan Basin. Location of typical pay zone indicated in diagram of stage 4. (Modified from Mesolella et al., 1974; reprinted with permission from the American Association of Petroleum Geologists.)

820

GoJden Lane Trend

.N.~

e~.~

L UPPER

CRETACEOUS

- MIOCENE

STRATA

8 km Fig. 9-10. Northeast-to-southeast cross section through Golden Lane Trend in Mexico illustrating karst topography developed on Middle Cretaceous El Abra Limestone, which includes production from reservoirs in Type I and Type II buried hills. (Modified from Viniegra and Castillo-Tejero, 1970.)

Type I V - Buried hills in structured strata are represented by karst-modified cuestas or hogbacks (some of which may be the limbs of breached antiforms or synforms), breached antiforms, and horst blocks (Fig. 9-5). Fields in such geologic settings commonly have been classified as structural traps. In this type of carbonate reservoir, however, the geomorphic formation of residual hills is largely the result ofkarst erosion of structural features rather than solely reflecting structural form. In the simplest case, formation of residual hill landscapes occurs during the last period of subaerial exposure subsequent to structuring. However, such traps alternatively may represent older buffed hills, formed during a previous cycle of karst weathering, which later have been deformed structurally, and perhaps, erosionally modified during a subsequent karst erosional cycle prior to final burial and onlap by impermeable strata. Such traps clearly are polycyclic in terms of origin. In these types of reservoirs, megascale karst dissolution beneath unconformities is, by definition, the primary process responsible for reservoir porosity and permeability. Likewise, however, karst dissolution and reservoir formation can also be polycyclic. That is, because composite unconformities (first- and second-order types of Esteban, 1991) are the most common unconformities associated with these types ofkarsted reservoirs, it follows that several episodes of karst dissolution and attendant reservoir porosity-permeability formation usually are indicated: for example, when karst dissolution along the youngest unconformity enhances porosity in previously-formed paleokarst facies. Several periods of karsting may also enhance depositional paleokarsts associated with disconformities along parasequence boundaries (in these as well as other karst types). In many cases, one can not easily differentiate the separate cycles of karstification in subsurface occurrences. In any event, however, reservoirs in this type ofkarsted carbonate commonly directly underlie associated unconformities (Fig. 9-5), although porous and productive zones may extends hundreds of meters below the unconformity. Notable examples of these types of traps are Renqiu and associated fields (pay in Precambrian to Ordovician carbonates) in China and South Alamyshik (Paleogene) Field in the former Soviet Union (Fig. 9-13), fields in mostly Cretaceous dolomites in the Campeche-Reforma Trend in Mexico, and fields in complexly thrust-faulted areas such as in the Wyoming Overthrust Belt (Whitney Canyon and Carter Creek Fields: Mississippian) and the Triassic of the Vienna Basin, Austria (Fig. 9-14).

821

TOP OF HORSESHOE REEF COMPLEX SCURRY-COGDELL

FIELD

BORDEN- SCURRY- KENT WEST C- I

TEXAS 91000

O |

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APPROXIMATE O I L - W A T E R CONTACT OF MAJOR FIELDS

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OF

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Fig. 9-11. Structure map on top of Pennsylvanian limestones in a portion of the Horseshoe Atoll Trend, Permian Basin, Texas, illustrating karst paleotopography and production from Type I and Type II buried hills. (FromVest, 1970; reprinted with permission from theAmericanAssociation of Petroleum Geologists.)

822

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Fig. 9-12. Type III buried hills. (A) Isopach map of strata overlying karsted Mississippian carbonates, showing production (in gray) from buried hills in a portion of the Williston Basin, Canada. (From Martin, 1966; reprinted with permission from the American Association of Petroleum Geologists.). (B) Erosional development of Type III reservoirs in dolomite with preexisting porosity, an example from the Anadarko Basin, Oklahoma. (From Harvey, 1972; reprinted with permission from the American Association of Petroleum Geologists.)

823

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Fig. 9-13. Type IV buried hill reservoirs in structured strata. (A) Development of Renqiu Field, China. Key: Q-N = Quaternary to Neogene, E - Paleogene, Ek = Eocene, Cm-O 2- Cambrian to Middle Ordovician, Zn = late Precambrian. (From Qi and Xie-Pei, 1984; reprinted with permission from the American Association of Petroleum Geologists.). (B) Cross-section through South Alamyshik Field, former U.S.S.R. (From Martin, 1966; reprinted with permission from the American Association of Petroleum Geologists.)

824

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Fig. 9-14. Type IV buried hill trap associated with complex thrusted strata, Matzen-Schonkirchen-Reyersdorf Field, Vienna Basin, Austria. (From Ladwein, 1988; reprinted with permission from the American Association of Petroleum Geologists.)

825

Combination traps in structured buried hills are also common, for example, where such buried hills are partly or entirely coincident with reef mounds (Marine Pool field, Silurian, Michigan Basin; Stuart City Trend, Cretaceous, Texas Gulf Coast; and the giant Bu Hasa, Fahud, Fateh, and Natih fields, Cretaceous, in the Middle East). Erosional relief developed on productive buried hills varies from 50 ft (15 m) or less (Waiters, 1946; Edie, 1958; Vest, 1970; Dolly and Busch, 1972; Mazzullo and Reid, 1986; Reid and Mazzullo, 1988; Reid and Reid, 1991) to as much as 820 ft (250 m) in the Golden Lane Trend in Mexico (Coogan et al., 1972). Structural enhancement of erosional relief in the Renqiu Field in China has resulted in a buried hill height of 5900 ft (1800 m: Guangming and Quanheng, 1982). Structurally expressed reservoirs This type of trap (Type V) is the most complex, polycyclic type recognized. As shown in Fig. 9-15, it is characterized by tectonically deformed strata wherein the initial formation of karsted reservoirs occurred along a second-order or third-order unconformity; or more likely, as a result of karsting along a third-order unconformity, followed by renewed deposition, and then another period of karsting along a secondorder unconformity. In either case, the main karsted reservoir zone (usually paleocaverns) is located at some distance below the associated unconformity (unless exhumed by later deep erosion), and is overlain by non-productive or poorlyproductive strata within the same stratigraphic formation or group. This relationship arises either because a second cycle of karstification did not result in the formation of significant porosity, or such porosity subsequently was occluded; or because a single cycle of karsting only affected strata well below the actual unconformity surface. Following was deposition of successive strata, possibly concurrent with ongoing tectonic deformation, and in tum, the entire section is further tectonically deformed and then breached by a second-order or first-order unconformity, and perhaps, also later restructured. Accordingly, reservoir formation in this type of trap is considered to have been related mainly to karstification along the oldest unconformity, although such a relationship can be misleading (in fact, karsted horizons can form at significant distances below unconformity surfaces in all types of karst reservoirs, and their true temporal relationships to specific unconformities can easily go unrecognized). In this type of trap, although formation of karsted reservoir horizons conceivably may have been coincident with development of residual hills along the oldest unconformity, there is no definitive evidence that the trap actually has a component of buried hill topography. Rather, it is mainly of structural configuration (usually with paleocavem reservoirs), despite the fact that there may be buried hill topography along the youngest unconformity which has accentuated tectonic relief on the breached structure (Fig. 9-5). Any erosional topography along that unconformity, however, may not have any relationship to reservoir occurrence. Topographically flat paleokarst surfaces that have been tectonically uplifted into horst blocks are also included in this trap type (Fig. 9-5). Admittedly, in some cases it may be difficult to distinguish this type of trap from other types of traps. In fact, this trap type actually may inherently be of hybrid nature in terms of the timing of main reservoir porosity formation. For example, if karstification and geomorphic development of residual

826

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i

1

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Fig. 9-15. Sequential model for the development of structurally expressed, Type V karsted reservoirs where the productive zone is not directly associated with, and occurs at a level well below, the youngest unconformity. Deposition of marine strata (1), followed by emergence and karstification along a second or third-order unconformity (2). Renewed carbonate deposition (3), followed by a second period of emergence wherein possible karsting along a second-order unconformity may not have affected the older karst system (4). Structuring may occur during stage 4 and/or stage 5.

hills also occurred along the youngest unconformity, then such a trap would be classified as a structured buried hill (Type IV) if it could be demonstrated that reservoir porosity was formed, or preexisting karst reservoir porosity was enhanced, at this time. Conversely, if only karstification and reservoir formation occurred at this time without the development of residual hills, then the trap is considered to be a type V structurallyexpressed karst reservoir. Likewise, exhumation of porosity in a preexisting but nonporous karst system would be considered either a type IV structured buried hill trap or a type V structurally expressed reservoir depending on whether or not depositional topography was present.

827

! BR. AMER. FUSON

STRUCTURAl, 2 PHILLIPS

C.S.O.

lEGgIER

C.S.O. <> WEST

I

--4000

WIERNIER-FARLEY COMPOSITE

LOG

EIGHT12.9

I

CROSS SECTION 4 S 6 C.S.O. I.T.I.O.

TROSPIER FARLEY. w PARK r OKLAHOMA 9 CITY

A 7 JO H N S O N RiENO UNIT 9COMPOSITE

LOG

EAST --MILES

Kms

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PROSPERITY ACRES

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CROSS

SECTION

Fig. 9-16. Cross section through Oklahoma City Field, Oklahoma, an example of a Type V karst trap. Note unconformity at the top of the Arbuckle (arrow, bottom left) and at the top of the Ordovician. Arbuckle pay (not shown) is 200 - 250 ft (61 - 76 m) below the unconformity at the top of the Arbuckle. (From Gatewood, 1970; reprinted with permission from the American Association of Petroleum Geologists.)

Notable examples of this type of trap (specifically, type VA), perhaps with some porosity formed in connection with younger unconformities, are: (1) Heal&on Field and the giant Oklahoma City Field in the Anadarko Basin of Oklahoma (Fig. 9-16), both of which produce from Ordovician dolomites; (2) numerous Ellenburger (Ordovician dolomite) fields in the Permian Basin of Texas (type VB); and (3) various fields in Silurian and Devonian carbonates in the Permian Basin.

Reservoirs associated with linear, subregional trends of fractures or faults This type of trap (Type VI) includes reservoirs associated with karst dissolutionenlarged, subregional fault or fracture trends that transect subunconformity strata (Fig. 9-5). The best-known examples of this type of trap are the Albion-Scipio-Pulaski and Lima-Indiana trends (Ordovician) on the Cincinnati and Findlay Arches (southern Michigan Basin) in Ohio and Indiana (Fig. 9-17).

828

0

6 ml

0

10 km

Fig. 9-17. Structure map (CI = 40 ft) on top of Trenton Limestone inAlbion-Scipio-Stoney Point field area, Michigan Basin, showing occurrence of non-structurally expressed reservoirs (Type VI) related to karstification along sub-regional fracture/fault trend. (From Catacosinos et al., 1990; reprinted with permission from the American Association of Petroleum Geologists.)

Non-structurally and non-paleotopographically expressed reservoirs This type of trap (Type VII) is the most subtle, karst-related subunconformity (truncation) trap recognized. It occurs in regionally gently-dipping strata beneath unconformities, where karsted reservoir zones transect bedding, or less commonly, are contained within individual strata (Fig. 9-5). Examples of this type of trap occur in some Ellenburger (Ordovician) fields in the Permian Basin of Texas (Fig. 9-18).

HYDROCARBONS PRODUCED FROM KARSTED CARBONATE RESERVOIRS

Volumes of hydrocarbons stored in and/or produced from karsted carbonate reservoirs are as varied as from any other type of reservoir. Data in Table 9-IV show that combined producible field reserves can be as low as 7.0 MMBO (million barrels of oil)

SE University 53 Field

NW

I IRION COUNTY

I SCHLEICHER COUNTY

PAY

I

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~-

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m)

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Fig. 9-18. Cross section illustrating occurrence of subtle, Type VII reservoirs in karsted (cavernous) Ellenburger (Ordovician) dolomites in the Permian Basin, Texas.

c~ l,,J

oo ta4

Table 9-IV Reserve data for selected fields in karsted carbonates (from Table 9-Ili). Key: ~Proved reserves; 2estimated original oil-in-place; 3ultimate recovery. Asterisks denote associated production from weathered cherts. Field/Trend

Location

Discovery

Reservoir

Cumulative

Reserves

References

Albion-Scipio-Pulaski

Michigan Basin

1957 (earliest)

Ordovician

123 MMBO 212 TCFG

200 MMBO 3

Catacosinos et al. (1990)

Alida, Nottingham, Parkman fields

Williston Basin

1954 (earliest)

Mississippian

>31.7 MMBO

>41 MMBO 3

Illing et al. (1967); Kent et al. (1988)

Amposta Marino, Casablanca, Tarraco, Dorado, Montanazo fields

Tarragona Basin Spain

1970's

Jurassic, Cretaceous

Up to 270 MMBO 3

Watson (1982); Bouvier et al. (1990); Esteban (1992)

Belle River Mills Field

Michigan Basin

1961

Silurian

21.4 BCFG

0

Gi11(1985)

Bindley Field

Central Kansas Uplift

1972

Mississippian

983 MBO

Brahaney Northwest, West Garrett, Buckwheat, Corrigan East, Crittendon, Dollarhide*, Midland Farms*, Patricia, Wells, Tex-Hamon, Seminole fields

Permian Basin

1945 (earliest)

Siluriarv-Devonian

115 MMBO 19.1 BCFG

>90 MMBO 3

Mear and Dufurrena (1984); Mazzullo et al. (1989); L.J. Mazzullo (1990b); Saller et al. (1991); Troschinetz (1992a,b)

Campeche-Reforma Trend

Mexico

1972

Cretaceous-Jurassic

945 MMBO 698.5 TCFG

15.3 MMBO 1

Santiago-Acevedo (1980)

Elk Basin, Newburg, South Westhope fields

Williston Basin

1946 (earliest)

Mississippian

145 MMBO

213.6 MMBO 3

McCaleb and Wayhan (1969); Marafi (1972); McCaleb (1988)

Ellenburger fields (149 of the largest)

Permian Basin

1939 (earliest)

Ordovician

1.4 MMMBO

3.7 MMMBO 2(a)

Holtz and Kerans (1992)

Fateh Field

United Arab Emirates

1966

Cretaceous

398 MMBO

1.02 MMMBO 3

Jordan et al. (1985)

Golden Lane Trend

Mexico

1908

Cretaceous

1.42 MMMBO

182.5

Viniegra and Castillo-Tejero

Ebanks et al. (1977)

MMMBO2(b)

(1970); Coogan et al. (1972); Enos (1977)

Grant Canyon Field

Basin and Range (USA)

1983

Devonian

7.48 MMBO

Healdton, Oklahoma City fields

Anadarko Basin

1928 (earliest)

Ordovician

19.3 MMBO 70 BCFG

>75.5 MMBO 2(e)

Gatewood (1970); Latham (1970)

Horsehoe Atoll Trend

Permian Basin

1948

Pennsylvanian

>529 MMBO

2.54 MMMBO2(,j)

Vest (1970)

lntisar "D" Field

Sirte Basin, Libya

1%7

Paleocene

812 MMBO

1.0 MMMBO 3

Brady et al. (1980)

Kincaid, Mt. Aburn, Colmar-Plymouth, Edinburgh West fields

Illinois Basin

Silurian, some Devonian

18 MMBO

Whiting and Stevenson (1965)

Krafl-Prusa Trend; ChaseSilica, Hall-Gurney, Trapp fields

Central Kansas Uplift (and adjoining areas)

1929 (earliest)

Ordovician

1.4 MMMBO

Waiters (1946); Newell et al. (1987)

Maben and New Hope fields

Black Warrior Basin

1953 (earliest)

Ordovician

7.8 MBO 850 MCFG

Henderson and Knox (1991); Raymond and Osborne (1991)

Rospo Mare Field

Italy

1975

Cretaceous

4.5 MMBO

25.4 MMBO 3

Dussert et al. (1988)

Star, West Campbell fields

Anadarko Basin

1958 (earliest)

Silurian-Devonian

4.6 MMBO 50.6 BCFG

7.0 MMBO 3 110 BCFG3

Harvey (1972); Withrow (1972)

Taylor Link West Field

Permian Basin

1929

Permian

15 MMBO

Kerans and Parsley (1986)

Yates Field

Permian Basin

1926

Permian

1.07 MMMBO

Craig et al. (1986)

TOTAL: 8.45 MMMBO 911 TCFG M = thousands of barrels MM = millions of barrels MMM = billions of barrels BCFG = billions cubic feet of gas TCFG = trillions cubic feet of gas

Read and Zogg (1988)

TOTAL: 111.0 MMMBO (~)

aproducible remaining reserves using a 40% recovery efficiency (Kerans and Parsley, 1986) bproducible remaining reserves using a 60% recovery efficiency (Coogan et al., 1972) CProducible remaining reserves using a 24% recovery efficiency (Gatewood, 1970) dproducible remaining reserves using a 52% recovery efficiency (Vest, 1970)

oo

832

in, for example, Star and West Campbell fields in the Anadarko Basin, to as high as 182.5 MMMB (billion barrels) of original oil-in-place in the Cretaceous Golden Lane Trend in Mexico. Wells drilled into karsted carbonate reservoirs are among the most prolific, in terms of daily production, of wells drilled into other reservoir types. As of 1970, for example, the world's most prolific oil well was the Cerro Azul No. 4 well drilled in 1916 in the Golden Lane Trend in Mexico, which flowed at a daily rate of 260,000 barrels of oil (Guzman, 1967; Viniegra and Castillo-Tejero, 1970). Typical high daily flow rates of some of the other early wells drilled in this area range from 15,000 to 100,000 barrels of oil. Very high daily flow rates are quite common from other karsted carbonate reservoirs as well (e.g., Gatewood, 1970; Guanming and Quanheng, 1982;Watson, 1982; Qi and Xie-Pei, 1984; Craig, 1988;Troschinetz, 1992a). In Yates Field (Permian) in the Permian Basin of Texas, some wells flowed at rates of 4833 BO in 34 minutes (Craig et al., 1986). Likewise, many individual wells in karsted carbonate reservoirs commonly are characterized by very high cumulative production figures. For example, cumulative production from three wells in the Golden Lane Trend, the Juan Casiano No. 6, Cerro Azul No. 4, and the Potrero del Llano No. 4 wells, was 70, 87 and 95 MMBO, respectively (Viniegra and Castillo-Tejero, 1970). Two wells in Casablanca Field in Spain are expected to ultimately produce a total of as much as 90 MMBO (Watson, 1982). Published estimates of the percentage of hydrocarbons produced or ultimately producible from karsted carbonate reservoirs relative to total reserves in all types of traps in carbonate and/or siliciclastic rocks do not exist. Nevertheless, an attempt was made to derive such a figure based on the hydrocarbon reserve data listed in Table 9IV, from the sources in Table 9-Ill. These data, however, clearly are far from inclusive of all hydrocarbon reserves in karsted carbonate reservoirs from around the world. Likewise, production data provided by the authors listed in Table 9-IV are current only up to the date of publication of individual references. Nevertheless, with these constraints clearly understood, available data indicate that an absolute minimum of 8.45 MMMB of oil and 911 TCF gas already have been produced from discovered, identified karsted carbonate reservoirs. More importantly, these data suggest that estimated total ultimate producible reserves at current technology from such reservoirs amounts to a minimum of at least 111 MMMB of oil; published data are too scanty to derive similar estimates for ultimately producible gas reserves. According to Bois et al. (1982), total ultimately producible (at current technology), global oil reserves from Phanerozoic carbonate and siliciclastic rocks amount to 1025 MMMBO. Hence, minimum ultimately recoverable oil from karsted carbonate rocks alone amounts to no less than 11% of total global hydrocarbon reserves from all types of rocks. This figure is close to that of Tyskin (1989), who suggested that about 8% of the oil reserves in the former U.S.S.R., for example, are associated with paleokarst carbonate traps. According to Roehl and Choquette (1985, p. 1), about 60% of recoverable global oil reserves in rocks of all ages occur in carbonate reservoirs. Using this figure, and the 11% estimate derived above, simple calculation suggests that karsted carbonate reservoirs account for a minimum of 18% of the hydrocarbon reserves stored in different types of traps in all carbonate reservoirs. An identical value is generated using the estimate of Moody et al. (1970) that upwards of 30% of recoverable hydrocarbons in

833

Precambrian and Phanerozoic siliciclastic and carbonate reservoirs (multiplied by 60% of these reservoirs being in carbonate rocks: from Roehl and Choquette, 1985, p. 1) are associated with unconformities.

GEOLOGIC AND PETROPHYSICAL CHARACTERISTICS OF KARSTED RESERVOIRS

Reservoir systems

There are many specific megascopic and microscopic features that are associated with and which characterize karsted carbonates and karsted carbonate reservoirs (Table 9-V). The subsurface recognition of these features is discussed in a later section of this chapter. Of these features, the two that are most relevant to hydrocarbon production obviously are karst-related porosity and permeability. With the exception of Type III buried hill reservoirs (described above), effective fluid transmission in most karsted carbonate reservoirs results from the presence of four main types of karst-related, porosity-permeability systems: (1) megascopic (i.e., not fabric-selective) dissolution porosity, (2) fractures and/or joints and dissolution-enlarged fractures and/or joints, (3) porosity associated with various types of breccia, and (4) preexisting matrix porosity in the affected rocks that has been enhanced or exhumed by karst dissolution. TABLE 9-V Features associated with paleokarst STRATIGRAPHIC-GEOMORPHIC Karst Landforms - Residual hills, dolines (sinkholes), dissolution valleys Unconformities MACROSCOPIC Surface karst Karren, kamenitzas, phytokarst Terra rosa and other soils Caliche (calcrete) Nonsedimentary channels Lichen structures Boxwork structure Brown-red fracture fillings Mantling breccias Chert residuum

Subsurface karst Vugs, caves, cavems In-place brecciated and fractured strata Collapse structures Dissolution-enlarged fractures Breccias Intemal sediments Speleothems MICROSCOPIC

Eluviated soil in small pores Etched carbonate cements Reddened and micritized grains Meniscus, pendant, and needle-fiber vadose cements Extensive dissolution-enlarged, preexisting porosity Source: Modified from Choquette and James, 1988.

834

Types 1 - 3 above occur together as the principal components ofmegaporosity associated with paleocaves and caverns (e.g., Choquette and James, 1988; Ford andWilliams, 1989). In fact, these three types are most frequently cited in the published literature (Table 9-111) as the main components ofkarsted reservoirs in all types ofkarst-associated hydrocarbon traps (Fig. 9-5). Accordingly, such occurrences indicate that, by far, most karsted carbonate reservoirs produce mainly from paleocaves and caverns.Accordingly, the discussions that follow focus heavily on karsted reservoirs developed in paleocaves and caverns. Such porosity-permeability systems can be: (1) primary, that is, formed and preserved during a single cycle of karstification or (2) secondary in that due to numerous cycles of karsting (which may in fact be polygenetic), previously-formed porosity may be enhanced, or previously formed but subsequently occluded karst porosity may be exhumed. Needless to say, porosity formed as a consequence of karstification can be substantially reduced, or in some cases, may not even be preserved in paleokarsts (e.g., Roehl, 1985; Entzminger and Loucks, 1992; and several papers in James and Choquette, 1988). Porosity reduction results from: (1) cementation by cave cements and later burial cements, and by infilling by sediments (Fig. 9-19); and (2) cave or cavern collapse (Fig. 9-20) (Ford, 1988). The subject of porosity reduction will not be considered further here because, in fact, this chapter is concerned with porous karst reservoirs. Readers interested in details of karst porosity preservation or destruction should consult the papers by Ford (1988), Bosak (1989b), Glazek (1989b), and Loucks and Handford (1992), and the book by Ford and Williams (1989). Megascopic dissolution porosity and fractures~joints Newly-deposited carbonate sediments and subunconformity, meteoric-altered but not karsted, older carbonate rocks commonly contain several different fabric-selective pore types: interparticle, particle-moldic, and particularly in dolomites, intercrystalline pores (terminology of Choquette and Pray, 1970). These pore types may be preserved primary, or depositional, porosity (e.g., interparticle) or secondary porosity owing to leaching (e.g., particle-moldic) (see Mazzullo and Chilingarian, 1992, for details). These matrix pore systems can be enhanced, exhumed, or in some cases, newly-created in rocks during wholescale karst dissolution. Such pores commonly occur as components of karsted carbonate reservoirs, although in many cases they largely represent preexisting matrix porosity (in some cases, perhaps karst-dissolution modified to some extent). By themselves, however, they are not diagnostic of karst dissolution processes. Rather, the most common occurrence of porosity in karsted carbonate rocks, including hydrocarbon reservoirs, is the development of megascopic porosity in the form of caves, caverns, and enlarged fractures and joints. Whereas megascopic vuggy porosity commonly is a component of many karsted reservoirs, by itself it also is not diagnostic of karst dissolution because it can also form in meteoric-altered rocks that have not been karstified. Cave and cavernous porosity in unfilled and filled caves, associated with dissolution-enlarged fractures or joints (which can be expressed as "solution pipes") and landforms such as dolines and residual hills (Fig. 9-20), are very common in many

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of the karsted reservoir examples listed in Table 9-111 and illustrated in Fig. 9-5. Several examples of the numbers of caves and caverns in specific hydrocarbon fields are provided in published sources. According to Craig (1988), for example, there are 285 caves identified in 142 out of the 898 wells that were drilled to 1983 in Yates Field (Permian) in the Permian Basin of Texas (Fig. 9-21). DeHaas and Jones (1988) re:..

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837

ported 170 caves in a 6500 square mile (16,834 square kilometer) region associated with hydrocarbon production in theAlbion-Scipio-Pulaski Trend in the southern Michigan Basin. Caves and caverns that appear to be at least mostly open, and associated dissolution-enlarged fractures, account for huge hydrocarbon storage volumes and production from, for example, the Precambrian to Ordovician Renqiu Field in China, the PermianYates Field and Pennsylvanian HorseshoeAtoll Trend in the Permian Basin of Texas, and the Cretaceous Golden Lane Trend in Mexico (Table 9-IV). The presence of such open megapores commonly is noted by sudden bit drops, rapid drilling breaks, and tremendous losses of circulating mud during drilling (e.g., Gatewood, 1970; Guangming and Quanheng, 1982; Watson, 1982; Qi and Xie-Pei, 1984; Craig, 1988; DeHaas and Jones, 1988). Reported heights of individual caves and caverns in such situations vary from 1 - 124 ft (<1 - 38 m) high (Gatewood, 1970; Guangming and Quanheng, 1982; Qi and Xie-Pei, 1984; Craig, 1988; DeHaas and Jones, 1988; Entzminger and Loucks, 1992). Porosity associated with breccias By far, however, the majority of paleocaves and caverns identified in karsted carbonate reservoirs are mostly or entirely filled dominantly by breccia and subordinate amounts of associated cave sediments, and locally, cements (Figs. 9-19 and 9-20). When porous, such cave-fill deposits also are identified during drilling by the criteria listed above. Kerans (1988, 1989) described a specific model of hydrocarbon reservoirs in filled cave/cavern systems that, with local minor variation, has been applied to many karsted carbonate reservoirs (Fig. 9-22). Filled caves/caverns are recognized by the presence of dominantly carbonateclast breccias that overlie intact host carbonates, and in turn, are overlain by highly brecciated carbonates. Basal breccias in such sequences are referred to as "lower collapse zone breccias" that formed as a result of wall and roof collapse during cave/cavern formation. They consist of chaotic, clast-supported breccias that typically are 5 0 - 60 ft ( 1 5 - 18 m) thick. Voids between clasts are partly filled to completely occluded by internal sediments (carbonate mud, shales) and later cements. In the Ordovician examples given by Kerans (1988, 1989), inter-clast porosity in this zone varies from less than 1% to 15% (some porosity may be contributed by matrix pores in the clasts themselves). Overlying "cave fill" breccias result from ultimate cave collapse due to the weight of overlying deposits. Breccias consist dominantly of carbonate clasts, the textures being both clast-supported and matrix-supported. Interstices between clasts generally are mostly occluded by internal sediments (sandstone and shale) and some cements, and porosity in such zones generally is low (1 - 3%). The overlying "cave roof' facies represents collapsed cave roofs, characterized mostly by in-situ brecciation textures, that may grade upward into intact roof rocks. This facies has upwards of 20% porosity (between the clasts and some matrix pores within the clasts) in the examples described by Kerans (1988, 1989). General aspects of cave/ cavern-filling breccias are described and illustrated in Loucks and Handford (1992) (Fig. 9-23) and Wilson et al. (1992). According to Kerans (1988, 1989), the thickness of individual, filled paleocave/ cavern sequences in the Ordovician examples described are as much as 650 ft (198 m). Associated breccia-plugged, dissolution-enlarged fractures or joints may extend

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vertically as much as 900 ft (275 m) below unconformities. Reported heights of individual, filled paleocaves and caverns, from other published sources wherein specific heights are given, range from 2 ft to as much as 985 ft ( 0 . 6 - 300 m) (Guangming and Quanheng, 1982; Dussert et al., 1988; Amthor and Friedman, 1989; Bliefnick, 1992; Holtz and Kerans, 1992). In many cases these heights, whether they occur in filled or

839

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840

unfilled paleocaves and caverns, closely approximate the thicknesses of individual pay zones in the gross productive sections. On the other hand, gross thicknesses of productive strata in karsted reservoirs, including filled and unfilled paleocaves and caverns and associated dissolutionenlarged fractures and karst-enhanced matrix porosity in nearly horizontal to relatively low-dipping strata, can be quite thick. Casablanca Field in Spain, Puckett Field inTexas, Renqiu Field in China, and Cactus Field in the Campeche-Reforma Trend in Mexico, for example, are developed in relatively gently-dipping strata on horst blocks and within anticlines. Gross pay thicknesses in these fields are 5 0 0 - 6 0 0 ft (153 - 183 m), 1600 ft (488 m), 2300 ft (702 m), and a maximum recorded thickness of 3280 ft (1000 m), respectively (Santiago-Acevedo, 1980; Watson, 1982; Qi and Xie-Pei, 1984; Loucks and Anderson, 1985). Such thick, gross productive sections result from extensive karstification during multiple periods of erosion along parasequence boundaries, during single cycles of exposure, and more commonly, from superimposed polycyclic karsting along composite unconformities. Many such reservoirs also are highly fractured. Of course, karsted beds in more strongly deformed strata such as anticlines likewise may also compose thick gross productive sections by virtue of high angles of dip and the presence of fractures: for example, 1000 ft (305 m) in Kirkuk Field in Iraq (Daniel, 1954). Karst reservoirs not associated with paleocaves and caverns

As mentioned earlier, the bulk of the reservoirs listed in Table 9-III are associated with paleocaves and caverns. Some of the sources listed in this table, however, did not mention a component of karst reservoir porosity-permeability contributed specifically by paleocaves and caverns (Lowenstam, 1948; Vest, 1970; Dolly and Busch, 1972; Marafi, 1972; Bebout and Loucks, 1974; Mesolella et al., 1974; Ebanks et al., 1977; Rao and Talukdar, 1980; Harris and Frost, 1984; Garfield and Longman, 1989; Geesaman and Scott, 1989). That is not to say, however, that such features are not present in these reservoirs as much as they simply might not have been recognized. In some of these cases, for example, the presence ofpaleocaves and caverns can reasonably be inferred on the basis of the presence of porous zones associated with bedded breccias occurring at some distance beneath unconformities and/or sand- or breccia-filled, dissolution-enlarged fissures (e.g., Lowenstam, 1948; Bebout and Loucks, 1974; Mesolella et al., 1974; Garfield and Longman, 1989; Geesaman and Scott, 1989), features that typically are associated with caves and caverns. In other cases, evidence of their likely existence is provided by the occurrence of an increasing frequency of large dissolution vugs in strata beneath unconformities, especially when they coincide with the presence of buried hills and other karst landforms (e.g., Vest, 1970; Dolly and Busch, 1972; Rao and Talukdar, 1980). In the few remaining cases there simply is no definitive evidence for the existence of paleocaves and caverns, although the reservoirs were still considered to have been karsted (Marafi, 1972; Ebanks et al., 1977; Harris and Frost, 1984). These authors indicated that porosity systems in these reservoirs include vugs (some of which are dissolutionenlarged biomolds), interparticle pores, and intercrystalline pores in dolomites rather than megapore systems as described above. These three cases represent only a small percentage ofkarsted carbonate reservoirs.

841

continuity

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842

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Fig. 9-26. Cave/cavern occurrence: highly anastomosing cave systems. The numbers 1, 2, and 3 refer to large caves, elongated in direction of paleoflow; 4 refers to caves associated with soil processes. (From Craig, 1988; reprinted with permission from Springer-Verlag.) smallest scale individual, filled p a l e o c a v e s / c a v e r n s typically are vertically compartmentalized because, as described in Kerans' (1988, 1989) model, relatively nonporous and nonpermeable cave-fill breccias separate reservoirs that occur in overlying, porous brecciated cave roof and underlying lower collapse zone facies (Fig. 922). On a larger scale, stacking ofpaleocaves/caverns in a stratigraphic section, whether filled or unfilled, can result in a thick gross pay section that likewise is vertically compartmentalized into a series of reservoir galleries (Fig. 9-27). In such a case, the occurrence ofnonpermeable beds both between individual cave levels (Fig. 9-27) and within individual caves (Fig. 9-22) results in complex vertical reservoir heterogeneity (compartmentalization). Production from associated buried hills, dolines, and dissolu-

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Fig. 9-27. Vertical compartmentalization due to the presence of stacked cave levels. On the figure on the right, also note finer-scale reservoir :ompartmentalization within individual caves-compare to Fig. 9-22. (From Loucks and Handford, 1992; reprinted with permission from the Permian Basin Section SEPM.)

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tion-enlarged fractures and joints further complicates reservoir characteristics in paleocave and cavem systems (Fig. 9-28). Although all included karst facies (porous and nonporous) may be laterally persistent, at least for some distance (Kerans, 1988, 1989), cave and cavem systems are notoriously laterally heterogeneous (Thrailkill, 1968). Reservoirs in such systems likewise are most commonly laterally restricted and heterogeneous because of (1) variations in effective porosity and permeability reflecting the occurrence of different specific facies within karst profiles, and (2) transitions from porous karst to impermeable nonkarst facies (e.g., see Figs. 9-19, 9-20, and 9-26). Such reservoirs are excellent candidates for horizontal drilling, which increases ultimate hydrocarbon recovery (e.g., Dussert et al., 1988). Most of the karsted hydrocarbon reservoirs listed in Table 9-III are both vertically and laterally heterogeneous and compartmentalized. Field examples associated with productive paleocaves and caverns, however, are known wherein reservoir transmissibility and production characteristics are quite homogeneous both vertically and laterally; for example, Yates Field in the Permian Basin of Texas (Craig, 1988) and Trenton Limestone production in the Michigan Basin (DeHaas and Jones, 1988). Amposta Marino Field in Spain is a reservoir with well-connected matrix and cavem-

845 STAGE I

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Fig. 9-29. Polygenetic, polycyclic karst, Amposta Marino Field, Spain: an earlier cycle of meteoric karst (stage I) was overprinted by mixed meteoric-marine karstification (stage II) which resulted in the occurrence of a well-connected zone of horizontal matrix and cavernous reservoir porosity. (From Wright, 1991; reprinted with permission from Postgraduate Research Institute for Sedimentology.)

ous porosity developed as a result of the superposition of meteoric karst and later mixed meteoric-marine karst (Fig. 9-29) (Wigley et al., 1988). Another well-known example is the Renqiu buried hill field in China, in which reservoir pressure, the oilwater contact, and its hydraulic regime are unified across the field (Fig. 9-30) (Guangming and Quanheng, 1982; Qi and Xie-Pei, 1984). Such reservoirs very commonly are highly fractured. Porosity-permeability and recovery efficiency in karst reservoirs

Data provided by selected sources cited in Table 9-III were summarized to indicate the range of porosity and permeability that typify karsted carbonate reservoirs (Fig. 931). Although a wide range of values are indicated, many karsted carbonate reservoirs clearly have values of porosity and permeability that far exceed average values for typical carbonate reservoirs (which are, according to data from fields described in Roehl and Choquette, 1985, 13.4% and 72.3 mD, respectively; Choquette and Pray, 1970, reported that typical carbonate reservoirs have 5 - 15% porosity). Dissolution-enlarged fractures are virtually ubiquitous in all karsted carbonate reservoirs. Likewise, karsted carbonate reservoirs are characterized by some of the highest recovery efficiencies of all reservoirs. Values reported in the sources in Table 9-III range from 21% (Amthor and Friedman, 1989) to a high of 80% (Brady et al., 1980).

846

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Fig. 9-31. Averages and ranges of porosity and permeability in selected karsted carbonate reservoirs, from data provided by sources listed in Table 9-II1.

847

SUBSURFACE RECOGNITION OF KARSTED CARBONATES The many distinguishing macroscopic and microscopic features of karst listed in Table 9-V are relatively easy to identify in outcrops and along present-day landscapes. In the subsurface, however, many of these features can be readily recognized, some can be recognized with difficulty, and others can not. For example, the karst identity of macroscopic and microscopic features (such as karren, boxwork and lichen structures, speleothems and other cave-related cements, and eluviated soil in small pores) often are extremely difficult to recognize even with detailed petrographic studies of core samples, and especially so if only drill cutting samples are available for study. For this reason, the real or imagined absence of such features has, in many cases, undoubtedly resulted in karst reservoirs going unrecognized. Notable exceptions in which some of these features have been identified are described by, for example: (1) Viniegra and Castillo-Tejero (1970), who reported that " . . . great pieces of stalactites..." (p. 316) from a cavern that was encountered in the Cerro Azul No. 4 well in the Golden Lane Trend in Mexico were blown out of that well during drilling; and among others, (2) by Craig (1988) and Entzminger and Loucks (1992), who reported the presence of recognizable cave cements in cores from Yates Field (Permian) and in Devonian karsted carbonates, respectively, in the Permian Basin of Texas. The recognition of karst in the subsurface proceeds in two ways: (1) recognition on seismic sections and by subsurface geologic mapping prior to drilling, and (2) recognition during and subsequent to drilling a well by analysis of drilling rates, drilling characteristics, and well logs. Several methods of recognizing karsted carbonates, at least on the gross scale, are briefly considered in this section; aspects are summarized in Martinez del Olmo and Esteban (1983), Wright ( 1991 ), and the specific references provided below.

Seismic and subsurface geologic mapping prior to drilling The stratigraphic-geomorphic features listed in Table 9-V, specifically, karst landforms and unconformities, often are resolvable in the subsurface by geologic mapping and on seismic sections. In mature basins, available well control commonly is dense enough to allow geologists to map paleotopography along known unconformities by means of structure and/or isopach maps. Such maps are useful in the identification of buried hills and areas in which the presence of abundant dolines (sinkholes) may be indicative of buried paleocaves and caverns (Figs. 9-7, 9-8, 911, 9-12. 9-32). In immature basins, however, remote sensing methods instead are used in a predictive exploration sense because of the paucity of well control. The most commonly used remote sensing method is analysis of conventional twodimensional and three-dimensional seismic sections.

Applications of two-dimensional seismic surveys A summary of the use of conventional two-dimensional seismic sections in the exploration for karsted carbonate reservoirs is given by Fontaine et al. (1987). The first step toward exploring for such reservoirs involves the location of unconformities on

848

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Fig. 9-32. Recognition ofkarsted carbonates from available well data: (A) Structure map, top of Ellenburger (Ordovician) unconformity, Emma Field, Permian Basin, Texas. (B) Isopach map of post-Ellenburger strata showing occurrence of sinkholes indicative of cavernous zones in Ellenburger. (From Kerans, 1988; reprinted with permission from the American Association of Petroleum Geologists.) seismic sections, below which karsted carbonates are anticipated to be present. In most cases, unconformity recognition is relatively easy following the methods of seismic sequence stratigraphic analysis presented in several papers in Payton (1977) (Fig. 93 3). Yet, the problem often remains that specific porous and permeable zones beneath these unconformities inherently are difficult to precisely define and locate because they

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849

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Fig. 9-34. Narrow, porous dolomite reservoir inAlbion-Scipio-Pulaski Trend (TypeVI reservoirs associated with fracture/fault trends, southern Michigan Basin: see Fig. 9-17) defined by subtle changes in waveform and attenuation of amplitudes between 0.715 and 0.760 sec. (From Catacosinos et al., 1990; reprinted with permission from the American Association of Petroleum Geologists.) generally do not have seismic facies patterns that are distinct from compact, nonporous carbonates (Fontaine et al., 1987). Catacosinos et al. (1990) have shown that subtle porosity zones can in some cases be defined by changes in seismic waveforms and attenuation of reflector amplitudes beneath unconformities (Fig. 9-34). Jenyon (1984) demonstrated that dissolutional collapse structures in buried strata can be recognized on conventional seismic sections by the presence of abundant reflector irregularities (Fig. 9-35). Vandenberghe et al. (1986) demonstrated the application of offset-dependent seismic reflector amplitude analysis on conventional seismic sections to the location and extent of porous zones in karsted, water-bearing limestone reservoirs of Early Carboniferous age in Belgium. This procedure relates amplitude analysis as a function of porosity (Fig. 9-36), such that porous zones can be distinguished from adjoining nonporous zones (Fig. 9-37). Fontaine et al. (1987) applied this method to the recognition of porous zones in Barremian karsted limestones in Europe (Fig. 9-38).

Applications of three-dimensional seismic surveys Analysis of more sophisticated three-dimensional seismic sections has proven to be most useful in karst recognition. Bouvier et al. (1990), for example, showed that there is a marked change from positive to negative acoustic impedance contrasts with increasing degrees of cavernous porosity and brecciation development, so that

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anomalously high amplitudes occur on three-dimensional seismic sections. Such characteristics allowed recognition of porous and cavernous karsted zones in the Amposta Marino Field in Spain (Fig. 9-39). Brown (1985) illustrated the occurrence of karst sinkholes on seiscrop sections generated from three-dimensional seismic in Mackerel Field in Australia (Fig. 9-40).

Karst recognition from drilling characteristics and well data Several methods of identifying karsted zones during or subsequent to drilling and on various downhole logs are available: 1) Dipmeter data locally may indicate drape of overlying strata on topographically irregular karst surfaces (Fig. 9-41) (Vandenberghe et al., 1986). (2) As mentioned in a preceding section of this chapter, rapid increases in drilling rates, lost circulation (mud loss), and drilling bit drops commonly occur when drilling through karsted carbonate rocks. (3) Various downhole logs can be useful to identify zones with exceptionally high porosities suggestive of karst dissolution. For example, Kerans (1988) showed that different gamma ray/spontaneous potential and resistivity signatures assist in defining cave roof and cave-filling deposits in karsted, Ordovician dolomites in Texas (Fig. 9-22). Sonic, density, and caliper logs likewise often display uphole gradients that relate to the degree of fissuring, brecciation, and cavernous porosity developed in karsted carbonate strata (Martinez del Olmo and Esteban, 1983; Craig, 1988). (4) Of course, analysis of cores provides important visual documentation on the occurrence of vuggy porosity, cave-filling breccias, and cave cements in karsted reservoirs.

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854

Fig. 9-40. Sinkholes recognized on seiscrop sections from 3-Dseismic data, Mackerel Field, Australia. (From Brown, 1985; reprinted with permission from the American Association of Petroleum Geologists.)

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856

CONCLUSIONS

Hydrocarbon production from karsted carbonate rocks accounts for huge volumes of already produced oil and gas, and existing reserves, in Precambrian and Phanerozoic reservoirs from around the world. At least 11% of total global hydrocarbon reserves in both siliciclastic and carbonate rocks are stored in karsted carbonate reservoirs. Reservoirs occur dominantly in buffed paleocaves in subunconformity karsts related to surficial, meteoric dissolution. Reservoir traps most commonly represent buried hills (structured and unstructured) that reflect residual karst landforms, and also in more subtle types of subunconformity traps. Average porosity and permeability in karsted carbonate reservoirs are considerably higher than in non-karsted carbonate reservoirs, although such reservoirs typically are highly compartmentalized and laterally and vertically heterogeneous. Karsted carbonates can be recognized in the subsurface by geologic mapping, on seismic sections, during drilling, and on several types of downhole logging tools.

REFERENCES Amthor, J.E. and Friedman, G.M., 1989. Petrophysical character of Ellenburger karst facies: Stateline (Ellenburger) field, Lea County, southeastern New Mexico. In: B.K. Cunningham and D.W. Cromwell (Editors), The Lower Paleozoic of West Texas and Southern New Mexico- Modern Exploration Concepts. Permian Basin Section Soc. Econ. Paleont. Min., Publ., 89 - 31: 133 - 144. Aves, H.S. and Tappmeyer, D.M., 1985. The use of synthetic sonic logs derived from seismic data in the interpretation of stratigraphic variation in Cretaceous carbonates of the North Field area, Qatar. In: O.R. Berg and D.G. Woolverton (Editors), Seismic Stratigraphy 11: An Integrated Approach to Hydrocarbon Exploration. Am. Assoc. Petrol. Geologists, Mem., 39:241 - 253. Back, W., Hanshaw, B.B., Herman, J.S. and Van Driel, J.J., 1986. Differential dissolution of a Pleistocene reef in the groundwater mixing zone of coastal Yucatan, Mexico. Geology, 14: 1 3 7 - 140. Back, W., Hanshaw, B.B., Pyle, T.E., Plummer, L.N. and Weidie,A.E., 1979. Geochemical significance of groundwater discharge and carbonate solution to the formation of Caleta Xel Ha, Quintana Roo, Mexico. Water Resources Res., 15:1531 - 1535. Bakalowicz, M.J., Ford, D.C., Miller, T.E., Palmer, A.N. and Palmer, M.V., 1987. Thermal genesis of dissolution caves in the Black Hills, South Dakota. Bull. Geol. Soc. America, 99: 7 2 9 - 738. Balint, V. and Pach, F., 1984. Depletion experiences and modeling of mixed-porosity, fractured, cavernous reservoirs in Hungary. Soc. Petrol. Engineers, Preprint, 13186, 11 pp. Bardossy, G., 1989. Bauxites. In: P. Bosak, D.C. Ford, J. Glazek and I. Horacek (Editors), Paleokarst: A Systematic and Regional Review. Elsevier Publ. Co., Amsterdam, pp. 399 - 4 1 8 . Bardossy, G. and Kordos, L., 1989. Paleokarst of Hungary. In: P. Bosak, D.C. Ford, J. Glazek and I. Horacek (Editors), Paleokarst: A Systematic and Regional Review. Elsevier Publ. Co.,Amsterdam, pp. 1 3 7 - 153. Bardossy, G., Fuchs, Y. and Glazek, J., 1989. Iron ore deposits in paleokarst. In: P. Bosak, D.C. Ford, J. Glazek and I. Horacek (Editors), Paleokarst: A Systematic and Regional Review. Elsevier Publ. Co., Amsterdam, pp. 419 - 429. Bebout, D.G. and Loucks, R.G., 1974. Stuart City Trend, Lower Cretaceous, south Texas. Bur. Econ. Geology, University of Texas-Austin, Rep. Investigations, 78:80 pp. Bebout, D.G. and Pendexter, C., 1975. Secondary carbonate porosity as related to Early Tertiary depositional facies, Zelten Field, Libya. Bull. Am. Assoc. Petrol. Geologists, 59:665 - 6 9 3 . Bliefnick, D.M., 1992. Karst-related diagenesis and reservoir development in the Arbuckle Group, Paschall #2 core, Wilburton Field, Oklahoma. In: M.P. Candelaria and C.L. Reed (Editors),Paleokarst, Karst Related Diagenesis and Reservoir Development: Examplesfrom Ordovician-Devonian Age Strata of West Texas and the Mid-Continent. Permian Basin Section Soc. Econ. Paleont. Min., Publ., 9 2 - 3 3 : 137-152. Bliefnick, D.M. and Belfield, W.C., 1991. The OrdovicianArbuckle Group of Oklahoma- a karsted dolomite reservoir. In: A. Bosellini et al. (Editors), Abstracts, Dolomieu Conference on Carbonate Plat-

857

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Chapter 10 FACTORS A F F E C T I N G OIL R E C O V E R Y F R O M C A R B O N A T E RESERV O I R S AND P R E D I C T I O N OF R E C O V E R Y N O R M A N C. WARDLAW

INTRODUCTION

This chapter reviews factors which affect oil recovery, and primary, secondary and tertiary recovery processes are considered. Emphasis is on examining the effects of pore structure and larger scale heterogeneities on oil recovery. The rock-pore part of the system (the "container") must be considered in the context of the effects of important fluid variables (viscosity, interfacial tension, density) and fluid-rock interaction (wettability). However, fluid phase behavior is not included. Examples used are mainly from carbonate reservoirs in Alberta, Western Canada. Many petrophysical properties are measured from cores or core plugs and have to be averaged at larger (reservoir grid-block) scales in order to be used in reservoir models. Methods of averaging and representing the effects of heterogeneity and scale are reviewed. Reservoir models provide the basis for simulating fluid displacement and production under a variety of imposed conditions, and are necessary for forecasting the rates and proportions of fluid recovery and for selecting optimal recovery schemes and patterns of well placement. Recovery of oil from a reservoir may be referred to as primary, secondary or tertiary. Primary recovery is recovery by natural depletion processes only, and includes oil recovered by natural water drive, solution-gas drive, gas cap expansion and gravity drainage. Secondary recovery involves injection of fluids, usually water or gas, in order to maintain reservoir pressure and to displace oil. Tertiary recovery refers to techniques applied after secondary recovery and includes injection of solvents, surfactants and polymers. Enhanced oil recovery (EOR) is used here to refer to artificially improved depletion processes and includes secondary and tertiary recovery processes (Energy Resources Conservation Board, 1986). Others have used a more restrictive definition of EOR for recovery of oil by the injection of materials not normally present in the reservoir (Lake, 1989). Such a definition would exclude from EOR waterflooding and all pressure maintenance processes. Local and regional variability of petrophysical properties (porosity, permeability, connate water saturation, residual oil saturation, etc.) are commonly related to depositional trends of different sediment types and/or diagenesis (Harbaugh, 1967; Moore, 1989). Thus, depositional trends and diagenesis may be useful in reservoir description, for optimal well placement and for prediction of oil recovery. For example, several of the Devonian stromatoporoid reefs in the Swan Hills area of Alberta have high porosity and permeability rocks near reef margins, and low porosity and permeability rocks in reef interiors where directional patterns of porosity may be related to depositional patterns (Jardine and Wilshart, 1982). The Westerose reef, a stromatoporoid reef of Devonian age in Alberta, also has

868 porosity and permeability distribution related to reef morphology but here, the highest porosity and permeability rocks are in the lower portions of the reef interior (McNamara and Wardlaw, 1991). The Westerose reef is elongate and is little more than 1 km wide compared with over 10 km for the Judy Creek field in the Swan Hills area, Alberta. The lack of a well-developed back-reef facies at Westerose may be related to the narrowness of the reef structure and the consequent lack of space to accommodate wave-sheltered environments. Thus, although petrophysical properties are related to depositional sediment patterns, these relationships may vary from reef to reef depending on local conditions at the time of deposition and among sedimentary facies and subsequent diagenetic events. In some cases, sediments which have the highest porosity and permeability at the time of deposition are transformed during diagenesis to rocks with the lowest porosity and permeability, and vice versa. Such porosity reversals resulting from diagenesis are common. Well-sorted, coarse, crinoid-rich sediments with original high inter-fragmental porosity, for example, may be completely occluded with calcite cement during early diagenesis, whereas poorly sorted carbonates with finegrained matrices and lower primary porosities may resist early cementation and later be replaced partially by dolomite. Subsequent dissolution of residual calcite in this dolomite may then create substantial porosity. An example of this type of porosity, from the Mississippian of Western Canada, has been described by Thomas and Glaister (1960). A somewhat similar case of dissolution of calcite following dolomitization is reported by Lucia and Murray (1967) from the Mississippian Harmattan field, Alberta, which is producing from a dolomite formed by the selective dolomitization of mud matrix in a crinoidal sediment. They also observed that in the Turner Valley Formation, exposed at Moose Mountain, Alberta, dolomite distribution is controlled by distribution of lime mud. Those limestones which contain less than 15% dolomite were deposited as mud-free carbonate sands, where powerful local tidal currents probably were instrumental in removing lime mud. Selectivity of dolomitization may be related to the greater reactivity of fine-grained sediment relative to more coarsely crystalline material such as crinoid debris. In summary, although petrophysical properties such as original porosity and permeability are extensively altered during diagenesis, spatial patterns of rocks with distinctive petrophysical properties commonly are related to patterns of different sediment types within the original environments of deposition. It follows that reconstruction of depositional patterns is valuable in making reservoir models of reservoir flow units. These models are essential for history matching of reservoir production and for predictions of future reservoir performance and ultimate recovery.

PRIMARY RECOVERY

Primary recovery is driven by potential energy sources within the reservoir which move oil to the wellbore. These include the energies of expansion of free gas in a gas cap or of solution gas dissolved in the oil or water, as well as expansion of oil, water and rock as pressure declines. Gravitational energy of the oil acting over the vertical

869 distances of the productive column also may contribute to the driving energy (Chilingar et al., 1972, p. 266). Solution-gas drive, gas-cap expansion drive, water drive and gravity drainage are major drive mechanisms and give rise to characteristic pressure decline and oil, water and gas production curves (Chilingar et al., 1972). Rock and fluid compressibilities, fluid phase behavior, and the extent of communication with contiguous water zones all are of major importance to pressure decline rates and to primary oil recovery. Primary recovery is not as sensitive to pore structure as is EOR and is not considered further here except to provide an example of the importance of contiguous water to the duration and extent of primary production. Judy Creek and Redwater fields are both in carbonate stromatoporoid reefs of Upper Devonian age in Alberta. They have generally similar internal patterns of reservoir facies with the more productive reservoir rocks in the reef margin regions and across the upper portions of the reefs (Jardine et al., 1982). About 75% of the Judy Creek reef field is filled with oil and the down-dip portion of the pool is water-bearing but the aquifer is too small to be effective. The reservoir behaves as a somewhat "closed" system and pressure declined rapidly with an estimated primary recovery of z 18% of original-oil-in-place (OOIP). Pressure maintenance by peripheral waterflood was initiated only three years after the start of production. Redwater field, in contrast, had 95% of the reef volume occupied by water, but the reef is connected to a large regional aquifer. The reservoir also has a strong natural water drive and produced 62% (OOIP) on primary production which extended over a period of about 30 years (Fig.

10-1). Thus, the extent of contiguous water in regional aquifers, and their ability to recharge an oil reservoir during production, are geological attributes which can affect the duration and extent of primary oil recovery. Primary recovery ranges from 0 to over 60% (OOIP) but averages ~ 19% for carbonate reservoirs in Alberta (Energy Resources Conservation Board, 1986; Howes, 1988).

JUDY CREEK

REDWATER

3

30

16

62

Years on Primary % Recovery ( OOIP )

0

0 W

W "CLOSED" .....

~///////~ High Permeability

[

]Low Permeability

Fig. 10-1. Large differences in primary production related to small and large effect of bottom-water drive in Judy Creek and Redwater reefs, respectively.

870 WATERFLOODING AND RESIDUAL OIL

Injection of water is the most widely used method of secondary recovery. Water injected in an injection well eventually breaks through into a production well. Thereafter, water production increases and oil production declines until oil recovery becomes uneconomic. At this stage, on average, approximately two thirds of the OOIP remains as residual oil in the reservoir and becomes a target for further recovery. The amount of residual oil varies widely from one reservoir to another as does the manner of its distribution. Both the amount and distribution of residual oil must be known for the design of effective strategies for further production. Residual oil occurs in the water-contacted portions of the reservoir trapped on small scales down to single oil droplets in individual pores. There is also the residual oil in macroscopic portions of the reservoir which were bypassed during the advance of the flood waters (Fig. 10-2). These macroscopic regions are related to heterogeneities within the reservoir and to local permeability barriers which obstruct the advance of water. The total recovery at the end of waterflooding (Re) is the product of the flood displacement efficiency in the waterswept regions (De) (oil recovered as a fraction of initial oil in place) and the volumetric sweep efficiency (V) which can be defined as the pore volume contacted by the injected water divided by the total pore volume of a reservoir or of a portion of a reservoir of interest (Craig, 1971). Thus:

SWEEP EFFICIENCY PRODUCERI

INJECTOR

Ea, AREAL SWEEP EFFICIENCY

INJECTOR

Ev,VERTICAL SWEEP EFFICIENCY PRODUCER t

Evol, VOLUMETRIC SWEEP EFFICIENCY Regions BB Swept Regions ! 1Unswept i Fig. 10-2. Areal, vertical and volumetric sweep efficiencies in a reservoir block.

871

Re-DeXVe

(10-1)

V can be considered as the product of vertical and horizontal components of sweep (Fig. 10-2). Oil trapped or immobilized on small scales in the water-swept regions of a reservoir may be mobilized by injection of tertiary fluids. These fluids change the viscosities, densities, interracial tensions, volumes, wettability or other properties of the fluids in the reservoir. Oil in portions of the reservoir unswept during waterflooding generally requires additional infill wells to improve continuity of oil-beating units between injection and production wells and to allow further production. It follows that different strategies are required to produce the remaining oil from the swept and unswept zones of a reservoir. The amounts of oil in these categories are difficult to assess, but global estimates for reserves totalling 513 billion barrels in the United States are presented in Fig. 10-3. An average of 33% (OOIP) is recovered at the end of secondary recovery, leaving 31% as immobile (residual) oil in swept zones and 36% bypassed in unswept zones. Of the latter, 19% is potentially mobile, and 17% is immobile. Immobile oil in water-swept zones and waterflood displacement efficiency (De) can be determined by tests under reservoir conditions on representative samples of reservoir rocks. Oil remaining in unswept zones and volumetric sweep efficiency (V) can be estimated indirectly i f D e is known and if ultimate recovery R can be estimated from pressure decline curves or, alternatively, by analogy with other similar reservoirs.

TOTAL :513 BILLION BARRELS (AS OF 87/12/:51)

CONVENTIONAL RECOVERY 33%

MOBILE IN UNSWEPT ZONES 19%

IMMOBILE IN U NSWEPT ZONES 17% IMMOBILE IN SWEPT ZONES 31% Source: BPO/Toris, API/AGA 1979, EIA 1987 (T. BURCHFIELD) Fig. 10-3. Primary and secondary recovery (conventional recovery) and categories of residual oil (T. Burchfield, pers. comm., 1987).

872 Estimation of R from decline curves is unsatisfactory because significant pressure decline may require long production times. A further problem is that the range of pressure changes and related changes of fluid viscosities and interfacial tensions which occur in the reservoir and affect the left hand side of Eq. 10-1 (R) commonly are not the same as those which occur in the core tests performed to estimate D . Furthermore, estimation by analogy is unsatisfactory because of uncertainties in identifying similar reservoirs produced to their limits. Alternative methods of assessing volumetric sweep require detailed reservoir description data combined with comprehensive surveillance programs using continuous flow meters and noise logs. Such methods may be combined with radioactive tracer tests, reservoir pressure data and interference tests (Langston et al., 1981). In summary, to assess the potential benefits of infill drilling and to estimate the amounts and distribution of residual oil requires that displacement efficiency (D) from core tests and volumetric sweep efficiency (V) from field tests and production data be known. D can be determined more easily and directly than can V and the importance of reliable core tests data should be emphasized. In the following sections, factors affecting microscopic displacement efficiency and volumetric sweep efficiency of oil by waterflooding are reviewed. e

e

D I S P L A C E M E N T EFFICIENCY

As water displaces oil at the pore scale, oil becomes disconnected and immobilized by one, or a combination, of several mechanisms. The properties of the rockpore system, the properties of the fluids, and the interaction of the fluids with the pore walls (wettability) all are important. A reservoir rock consists of larger spaces (pores), which are connected by smaller spaces or constrictions (throats). Thus, pores are, by definition, larger than the throats which connect them. However, larger pores may be connected by larger throats and smaller pores by smaller throats. That is, pore sizes and throat sizes may be arranged in a correlated rather than random or disordered manner. In the case of a correlated pore-throat structure, the smallest pore is not necessarily larger than the largest throat (Wardlaw, 1989). Throat size can be defined in terms of a plane of minimum cross-section between two adjacent pores. Pore size can be defined as a plane of maximum cross-section within a pore and also as the volume between the throats which define the pore. Thus, throats are defined in terms of diameter and pores in terms of diameter and volume. Pores represent the capacity of the rock to contain fluids but, in rocks where throats are much smaller than pores, it is the throats which have the major effect on fluid flow. Properties affecting multiphase fluid flow include the size-frequency distribution of pores and throats, the size correlation of directly connected throats and pores, and the spatial arrangement of pores and throats (Wardlaw, 1989). Throats and/or pores may have preferred orientations which confer preferred directions of flow within a pore system. A further pore property is that of irregularities or roughness of pore walls and their surface areas and characteristics. The most effective means of obtaining quantitative information about microscopic structure is through a combination of

873 mercury porosimetry and petrographic image analysis (PIA) (Ehrlich et al., 1984; 1988; Wardlaw, 1989; 1990). In addition to the properties of porous rocks, viscosities of displacing and displaced fluids, and their arrangement or configuration within the pore spaces (wettability), affect the relative flow and efficiency with which one fluid can displace another. Wettability is an expression of the relative affinities of immiscible fluids (brine, oil, gas) for mineral-rock surfaces, and can be evaluated external to the rock, as is the case with contact angle measurements; or within a rock sample, as is the case with Amott and USBM tests (Anderson, 1986; Buckley et al., 1989). Carbonate rocks appear to be mainly intermediate (water advancing contact angles of ~ 80 ~ 120 ~ to oil-wet (contact angles >__120 ~ (Treiber et al., 1972) or of mixed wettability (portions of surface more water-wet and portions more oil-wet). Four major mechanisms of oil trapping are recognized in water-swept reservoir rocks (Fig. 10-4). (1) Viscous fingering causes irregularities at the water-oil displacement front in systems with large water-oil mobility ratios (Craig, 1971). Viscous fingers cause early breakthrough of water, and the irregular advancing fronts leave residual pockets of oil which contribute to high residual saturations. Viscous fingering is not dependent on a porous structure in so far as it occurs between parallel plates in the absence of structure. (2) "Snap-off' of oil by capillary imbibition of water which forms collars of water at pore throats. These collars become unstable and snap-off in rocks which are strongly water-wet and have large pore-to-throat diameter ratios (Li and Wardlaw, 1986a, b). (3) Bypassing of oil related to differential travel of water-oil interfaces caused by V ISCOUS FINGERING

BYPASSING

CAR LLARY INSTABILIT Y

SURFACE TRAPPING

WATER WET .

WATER O OIL 9

.

.

.

.

//

.

I

\

INTERMEDIATE WET

c OIL WET 1

2

3

4

Fig. 10-4. Four mechanisms of oil-trapping on the microscope scale for three wettability conditions. (After Wardlaw, 1990.)

874 differences in the effective sizes of adjacent pathways within the rock. This differential travel causes bypassing of oil in heterogeneous systems. The greater the size contrasts (heterogeneity) the larger will be the oil residuals. (4) In oil-wet systems, oil is the phase contacting rock surfaces, and surface trapping is likely to be particularly important in rocks with highly irregular pore surfaces and large surface areas. Of the four mechanisms of oil entrapment, all occur at the core scale during waterflooding, and mechanisms 1 and 3 also occur at larger (reservoir) scales. Optimizing oil recovery involves imposing conditions during production which will minimize oil entrapment. Thus, there may be advantages to identifying the fraction of the total trapped oil which is associated with each of the above mechanisms, because the conditions of displacement that would minimize trapping by one mechanism are not necessarily the same as those that would minimize trapping by one of the other mechanisms. Minimizing oil entrapment requires knowing both the mechanisms of oil entrapment and the conditions under which they occur. In the following, a qualitative assessment is made of the effects of fluid and rock properties on the four mechanisms of oil entrapment.

Effects of fluid properties and wettability on trapping The relative effects of oil-water viscosity ratio, interfacial tension, wettability and waterflood velocity on the four trapping mechanisms are indicated in Table 10-I as being large or small. Large oil-water viscosity ratios cause large water-to-oil mobility ratios and promote viscous fingering (Craig, 1971) but have little effect on snap-off by capillary instability (Wardlaw, 1982) or oil trapping by bypassing (Laidlaw and Wardlaw, 1983). Large oil-water viscosity ratios may reduce recovery of oil from rough, oil-wet surfaces because of the large viscous resistance of the displaced phase and its relative inaccessibility in small surface spaces. Interfacial tension for water-oil interfaces during waterflooding generally is in the range of 15 to 30 mN/m, and these relatively small variations are not thought to affect significantly oil entrapment. Of course, interfacial tension lowering of several orders of magnitude does have important effects, and is of major importance in tertiary recovery where it is used to decrease capillary forces causing retention of oil in relation to viscous and gravity forces which promote oil mobilization. Increasing waterflood velocity increases instability and fingering at flood fronts. This causes earlier breakthrough of water and reduced recovery of oil (Peters and Flock, 1981). Increasing velocity causes an increase in viscous forces relative to capillary forces, and because snap-off requires the formation of a collar of water and is rate-dependent, oil may be displaced from a pore by viscous forces before snap-off has had time to break oil continuity in a downstream throat. Likewise, for water-wet systems, increasing flow rate can reduce trapping by bypassing (Laidlaw and Wardlaw, 1983). Although velocity has a potentially large effect on oil entrapment by three of the four mechanisms (Table 10-I), the extent to which this is the case for the relatively small range of velocity variations possible under field conditions of waterflooding is likely to be small.

875 TABLE 10-I Relative effects of fluid-wettability variables on trapping mechanisms under field conditions 1

2

3

4

Viscous fingering

Snap-off

Bypassing

Surface trapping

Viscosity ratio go/gw

L

S

S

L

Interfacial tension (~,)

S

S

S

S

Velocity (V)

S

S

S

S

Wettability

S

L

L

L

(0) L = large effect S = small effect

The effects of wettability on viscous fingering are small compared to the effects of mobility ratio and fluid velocity. Wettability differences, however, may have large effects on the other three trapping mechanisms. Strong water wetness favors extensive entrapment of oil by snap-off and by bypassing. Bypassing occurs with preferential advance of water in the finer oil-occupied pore spaces, leaving residual oil preferentially in the larger spaces. Oil wetness will favor larger residual oil saturations in rocks with large surface areas and rough pore walls. Inasmuch as oil continuity may be maintained across rough surfaces, such oil-wet systems do not have well defined oil-residual end points. With sufficient water throughput, oil flow may be maintained to low oil saturations but with diminishing oil-flow rates (Dullien et al., 1986). Surface area and surface characteristics vary widely in carbonate rocks and commonly are not well characterized (Fig. 10-5). Understanding the relationships of pore structure, wettability and mechanisms of oil entrapment is useful in understanding some of the apparent ambiguities in the published literature concerning the effects of wettability on displacement efficiency. For example, Salathiel (1973) presented evidence that strongly water-wet conditions caused high residual oil saturations compared with displacements conducted with mixed-wettability conditions. On the other hand, Mungan (1966) and Lefebvre du Prey (1973) provide evidence that strongly water-wet cores flooded more efficiently than cores of intermediate wettability. In contrast, Morrow (1978) presented evidence that there was less trapping at intermediate wettability than for strongly water-wet or strongly oil-wet conditions. Apparent contradictions of these kinds are, in part, related to the properties of porous media and can be expected if one considers the ways in which wettability changes affect trapping by the four mechanisms identified above. A change from strongly water-wet to strongly oil-wet conditions increases immobile oil for two of the mechanisms (surface trapping and viscous fingering), whereas it is expected to decrease immobile oil for the other two mechanisms (snap-off and bypassing) (Table 10-II).

876

Fig. 10-5. Differences in surface characteristics and surface area. (A) Dolomite (D) with irregular surfaces associated with irregular grains of microspar (M). (B) Dolomite with smooth planar crystal faces; pore walls are smoother and with lower surface area than in A.

Effects of rock-pore properties on trapping Table 10-III provides qualitative estimates of the effects of three rock attributes on the four trapping mechanisms. Carbonates commonly have relatively large secondary pores created by dissolution ("vuggy" carbonates). Such secondary pores are commonly accessed by throats which have sheet-like form, similar to spaces between sub-parallel plates (Wardlaw, 1976) and have large pore-throat size contrast (Fig.10-6). The "matrix" between large secondary pores or vugs commonly is relatively "tight" (porosity z 3 - 5%). Under water-wet conditions, large amounts ofoil would be trapped in the large pores by a combination of snap-off and bypassing. The vugs may represent a large fraction of the total pore volume, and if they remain filled with oil following TABLE 10-II Effects of wettability on trapping mechanisms Wettability condition

Viscous fingering

Snap-off

Bypassing

Surface trapping

Strongly water wet

S

L

L

S

Intermediate wettability

L

S

S

L

Strongly oil wet

L

S

S

L

S = smaller potential for trapping residual oil. L = larger potential for trapping residual oil. Arrows indicate increasing (1') and decreasing ($) potential for trapping by various mechanisms as a function of wettability.

877 TABLE 10-III Trapping mechanisms 1

2

3

4

Viscous fingering

Snap-off

Bypassing

Surface trapping

Pore-throat size ratio

S

L

S

S

Surface roughness

S

L

S

L

Heterogeneity (spatial order)

S

S

L

S

L = Large effect S = Small effect

waterflooding, oil displacement efficiency would be low (Figs. 10-4A and 10-7A). Under intermediate to oil-wet conditions, however, oil is displaced from vugs and the residual oil saturation is much lower (Fig. 10-7B) (Wardlaw, 1980). Thus, the effects of large pore-throat size ratio on trapping and residual oil saturation can only be evaluated when the wettability of the system is known. Because most carbonates are thought to be intermediate to oil-wet (Chilingar and Yen, 1983), rather than strongly water wet, the effects of large pore/throat ratio on oil trapping may be minimized. The surface roughness of carbonates varies widely (Fig. 10-5). The combination of high surface area (large surface roughness) and oil wetness will contribute to high residual oil at the economic limit (Table 10-II) but high surface area need not cause high residual oil in water-wet rocks (Fig. 10-4A).

A

B

Fig. 10-6. (A) and (B): Etched dolomite crystals (D) and epoxy resin impregnated pores (P) connected by sheet-like throats (T) in reservoirs with large pore/throat size ratios.

878

Fig. 10-7. Etched glass micromodel with vugs and matrix porosity. Water (dark) and oil (light) at residual oil saturation following waterflood. (A) Water-wet model; residual oil fills vugs and residual oil saturation is large. (B) Intermediate to oil wet; oil was displaced from vugs and residual oil saturation is much lower than in A. Both A and B have small amounts of oil trapped in matrix. Thus, whether water-wetness or oil-wetness favors greater oil recovery efficiency can be evaluated only in the context of rock-pore properties. Conversely, the effects of rock-pore properties on recovery can be evaluated only if the wettability of the system is known. Generally, studies of wettability in the published literature are not accompanied by quantitative information about the pore structure of the rocks tested, and the apparent ambiguity of the results is not surprising. The presence of heterogeneities in cores from reservoirs tends to increase irregularities at the advancing fluid front and increases oil trapped by bypassing (Wardlaw and Cassan, 1979; Wardlaw, 1980). The end points of a two-phase displacement are an initial connate water saturation ( S ) and a final or residual oil saturation (Sr). These end points define the amount of oil which is recoverable, and have been shown in experimental studies with sandpacks to be affected more by the spatial order or clustering of pores and throats of particular types and sizes than by their lack of

879 uniformity or sorting (Morrow, 1971; Chatzis et al., 1983). This spatial order is usually referred to as heterogeneity. Local clustering of smaller pores and throats causes higher L i and, for water-wet conditions, local clustering of larger pores and throats causes higher S r (Fig. 10-8). The combination of high S i and high S r defines low oil recovery. For the same population of poorly sorted particles, S i and SOr both can be changed greatly by altering the arrangement from disordered to spatially ordered (i.e., local clustering of smaller and larger particles or crystals). On the other hand, degree of grain sorting does not appear to affect significantly either S or S for disordered packings. Thus, it is not so much degree of sorting or lack of uniformity of particle or crystal size which is the issue, but rather, the spatial arrangement (type and degree of heterogeneity) which affects oil recovery efficiency. Some common types of heterogeneity Wl

oF

WATER RETENTION AT I R R E D U C I B L E S A T U R A T I O N

DISORDERED S.~

10%

~Sal I I Oil D Water

ORDERED Sw~ ~ 35%

OIL R E T E N T I O N AT R E S I D U A L OIL S A T U R A T I O N

DISORDERED So, ~ 14%

ORDERED Sor -~40%

Fig. 10-8. (A) Initial connate water saturation (Swi) in a disordered sand. (B) Swi in a sand with clusters of smaller sand grains (ordered) as discontinuous domains in a continuous domain of larger grains. Sw~much larger in B thanA, although size frequency distribution of grains could be the same in both. (C) Residual oil saturation (So,.) following waterflood in a disordered sand. (D) S r following waterflood in a sand with clusters of larger grains as discontinuous domains in a continuous domain of smaller grains. S r is much larger in D than in C, although size frequency distribution of grains could be the same in C and D.

880 and their effects on microscopic displacement efficiency are given in Wardlaw and Cassan (1978). Pore systems in carbonate reservoir rocks are thought to be more heterogeneous, as a group, than those of clastics and, if so, lower oil recovery efficiency can be expected.

Effects of wettability on recovery from fractured carbonates Fractures in carbonates may create dual porosity-permeability systems which can be considered as an aspect of heterogeneity. Fractures tend to be more abundant in dolomites than in limestones (Aguilera, 1980) and have important effects on flow which are difficult to evaluate in core tests. Fracturing may contribute greatly to permeability but not much to porosity, whereas the matrix blocks between fractures may have low permeability but contain most of the pore volume (storage) of the system. Reiss (1980) presented a discussion of displacement in vug-matrix-fracture systems under water-wet and oil-wet conditions. The efficiency with which water or gas can displace oil is affected by the combined effects of gravity, capillary and viscous forces; gravity forces due to differences of density between oil and water or gas, capillary forces due to the interaction of surface forces within pores which is related to wettability, and viscous forces where the fluids are moving. The initial rate of expulsion of oil (qi) p e r unit cross-section, from an element of matrix suddenly immersed in water, can be derived from:

k a(Pw-Po)g + P o qi = 1.to a

(10-2)

where" k = matrix permeability to oil Pw,Po = water and oil specific gravities ~o = oil viscosity a = typical vertical dimensions of the matrix element P = capillary pressure The term a(p w - Po)g represents the magnitude of the gravity force, and is proportional to the dimensions of the matrix blocks. The necessary condition for oil expulsion to take place is qi > O"

a(Pw -- Po)g + P~ > 0

(10-3)

If a rock is water-wet, gravity reinforces capillary imbibition and both terms in Eq. 10-3 are positive, qi > O, and oil is displaced by water. Water travelling along fractures imbibes spontaneously into adjacent matrix displacing oil back into the fracture (counter-current imbibition) for transport out of the system. For an oil-wet matrix, capillary forces oppose the penetration of water into the matrix and displacement of oil from the matrix is possible only if gravity effects overcome the threshold capillary displacement pressure (Pd):

881 a(p~ - Po)g > Pa

(10-4)

Invasion of matrix blocks by water is only possible if the size of the matrix blocks between fractures "a" is large (Reiss 1980). Viscous forces, as well as gravity forces, may contribute to the displacement of oil by water. Beliveau et al. (1991) provided an example from the Mississippian Midale carbonates of Saskatchewan of the importance of water-wetness to production from a matrix-fracture system. The total waterflood pressure gradients applied across the reservoir from injectors to off-trend row producers is about 1.5 psi/ft (~ 30 kPa/m). Fracture-matrix capillary pressure differences are of about the same magnitude. If the rocks are water-wet, viscous and capillary forces work together. Matrix blocks spontaneously soak up water by imbibition as well as expel oil by viscous drive due to the applied pressure gradient. Water breakthrough in such a water-wet system will be retarded, and performance may appear similar to a conventional unfractured reservoir. Evidence from wettability tests, as well as simulations of reservoir performance, indicate that the Midale carbonates are, at least in part, water wet (Beliveau et al. 1991). If these rocks were oil wet, however, then the matrix would repel water and the viscous forces would not be sufficiently large for oil to be displaced from one foot or larger (1/3 m) matrix blocks. Waterflooding would be less efficient and water breakthrough would occur earlier in an oil-wet fractured reservoir of this type than in their water-wet or unfractured counterparts. Moderate lowering of interfacial tension has been shown to have beneficial effects on oil recovery in matrix-fracture systems by altering the balance of gravity and capillary forces (Schechter et al., 1991). In summary, specific attributes of the pore system affect the different trapping mechanisms to varying degrees for different conditions of wettability. For example, in vuggy carbonates with large pore/throat size ratios, snap-off is of first order importance to trapping large amounts of oil under water-wet conditions but not under intermediate to oil-wet conditions. Heterogeneity, on the other hand, affects trapping by bypassing for any wettability condition. Surface roughness is important for surface trapping under strongly oil-wet conditions. From the above, it is apparent that wettability and pore structure are variables of first order importance to oil recovery and that whether water-wet or oil-wet is the more favorable wettability condition depends on the properties of the rock-pore system. Conversely, the significance of rock-pore properties can be evaluated satisfactorily only if the system wettability is known. For a system with conductive fractures which define matrix blocks with significant porosity and low permeability, oil recovery is likely to be greater for waterwet than for oil-wet conditions. The optimum wettability condition for a wide range of reservoir rock properties would appear to be one of weak water wetness (contact angles somewhat less than 90 ~) or weak water wetness combined with oil wetness for different portions of surfaces within the same rock (mixed wettability). This latter condition provides the benefits of spontaneous imbibition of water while providing continuous pathways for oil flow down to low saturations.

882 VOLUMETRIC SWEEP EFFICIENCY

Volumetric sweep efficiency is a measure of the three dimensional effect of larger scale reservoir heterogeneities, and is a product of the pattern areal sweep and vertical sweep efficiencies. Sweep efficiency is affected by mobility ratio, density contrasts amongst fluids, relative magnitudes of capillary and viscous forces, and heterogeneity (Craig, 1971; Stalkup, 1983). Permeability contrasts amongst adjacent units, the lateral continuity of these units in relation to well spacing, and the presence or absence of partial or complete permeability barriers which affect cross flow between units, all have important effects on volumetric sweep efficiency (Fig. 10-9). INJECTION WELL

PRODUCTION WELL

NON-LAYERED

,

NON-

.t co.,,,.

PARTIALLY

4,...e.o.....,,.u,!.:...,,,.,.,,..,3...

LAYERED

Fig. 10-9. Non-layered and layered reservoir models with communicating, non-communicating and partially communicating layers.

Continuity of beds, wells spacing and position The geometry, internal arrangement and continuity of differing lithologies and petrophysical types within carbonate reservoirs depends on such factors as the biota present, sea-level fluctuations, rates of sedimentation and subsidence, and tectonic effects as well as all the diagenetic overprinting (Mazzullo and Chilingarian, 1992). The continuity or lack of continuity of permeable beds as a function of lateral distance is an important factor in determining optimum recovery schemes. Delaney and Tsang (1981) applied the methods of Ghauri et al. (1974) and Stiles (1976, 1977) to measuring reservoir continuity within the Devonian Judy Creek carbonate reef in Alberta. The fraction of the total section composed of continuous beds was plotted as a function of interwell distance for various reservoir facies (Fig. 10-10). Continuity was greater in the reef margin than in the reef interior. The decrease in continuity of layers as a function of distance can be used in defining optimum well spacing and in analyzing the potential benefits of infill drilling.

883

CONTINUITY vs INTERWELL DISTANCE

100 >"

I"

Z I-. Z

,~

806040-

I I I I I

INCREMENTAL 10%

CONTINUITY

<1

0 (=)

20-

I 0

0

It 500

9

I

i t 1000

I 1500

I 2000

I 2500

I 3000

INTERWELL DISTANCE (m) Fig. 10-10. Percentage of continuous strata as a function of distance. (After Delaney and Tsang, 1981.)

For reservoirs formed in particular paleogeographic settings, there are characteristic shapes and orders of deposition of genetic units and these units may have characteristic width/thickness/length relationships (Weber, 1986). Relationships of these types have been defined for clastic sequences, but few data are available for carbonates. In addition to differences between horizontal and vertical permeabilities, there may be preferred horizontal flow paths within layers, and the presence of such flow paths must be known for optimal siting of injection and production wells. These directional permeabilities may be related to depositional, diagenetic or tectonic events. Permeability anisotropy may be inferred from a depositional model, or in the case of fractures, from observations of wellbore ellipticity and breakouts (Bell, 1989). Waterflood performance in carbonates can be dominated by natural sub-vertical fractures with preferred orientations. Such is the case in the Midale Formation (Mississippian) of Saskatchewan, where production wells located "on trend" from injectors (aligned with the fractures) showed early water breakthrough from waterflooding (Beliveau et al., 1991). In contrast, response of"offtrend" producers was smooth and delayed. Similarly, in the Norman Wells carbonate reef reservoir, waterflood injection and production wells were placed to take advantage of the directional permeabilities associated with fracture systems (West and Doyle-Read, 1988). In order to make effective use of reservoir description data of the above types on, for example, a waterflood, it is necessary to have waterflood surveillance programs. The results of these programs can be used to ensure the best possible volumetric sweep efficiency. Langston et al. (1981 ) considered such surveillance programs within the Jay/Lec field, in the Smackover and Norphlet Formations of the Gulf Coast, U.S.A., in two categories depending on whether the primary measurement was concerned with vertical sweep or areal (horizontal) sweep.

884 Vertical sweep

The total section in injection wells was opened by conducting multistage acidfracture treatments through spaced sets of perforations. Temperature surveys, tracer surveys, continuous flow meters and noise logs were used to define the degree of vertical conformance. The noise log was selected as the basic surveillance tool because it could detect flow behind pipe and provide an order of magnitude injection profile (Langston et al., 1981). The continued use of these surveys confirmed that water injection profiles are generally proportional to core permeability-thickness. Evaluation tools used to determine the success of conformance workovers in production wells included flowmeter/ gradiomanometer surveys, noise logs and pressure build-up tests. Areal sweep

Three procedures were used to define and control areal sweep (Langston et al., 1981). These methods involved the use of radioactive tracers, interference testing between injection and production wells and the monitoring of bottomhole pressure in key wells. These procedures were successful in defining injection wells responsible for water breakthrough, and for determining the source of water breaking through into producers. Principal conclusions of Langston et al. (1981) in the Jay/Lec field were that areal sweep generally was effective because of the favorable water-oil mobility ratio, but that vertical sweep in areas of high permeability contrast was poor. Based on the above information, infill wells were completed to improve vertical and areal conformance. Additional oil was recovered from discontinuous zones and vertical sweep was improved by selectively completing low-permeability zones which had been flooded more slowly. Areal sweep efficiency was improved by locating wells outside existing waterflood patterns. Injection balancing was implemented to optimize volumetric sweep efficiency by achieving waterfront closure in all zones from opposite directions on all producing wells while maintaining balanced zonal pressures to prevent wellbore crossflow. These measures delayed production decline until 75% of the estimated ultimate recovery had been produced and resulted in production in excess of 86% of the reserves in this carbonate reservoir. Shales and other permeability barriers

Shales and other permeability barriers exist on all scales up to that of the entire reservoir, and have important effects as baffles during displacement. Efforts have been made to collect data on shale continuity as a function of environment of deposition from which trends of continuity distribution could be derived. Most of this information, however, is for clastic and not for carbonate systems (Weber, 1986). Haldorsen and Lake (1984) modeled the continuity and spatial disposition of shales from North Sea reservoirs and elsewhere using statistical techniques. With the assumption of random distribution in space, models can be generated with a computer

885 and conditioned to fit the well data. Such models have been used to calculate the effective permeabilities of grid blocks. Carbonate reservoirs commonly have permeability barriers other than shales. Evaporites, tight carbonates, and stylolitic zones may be common and of variable continuity. Such barriers may be breached locally by fractures or solution channels. Lapre (1980) has given an overview of reservoir potential as a function of geologic setting for carbonate rocks. Detailed facies mapping both vertically and laterally is required to delineate the type and distribution of permeability barriers (Bebout and Pendexter, 1975). Permeability is subject to different errors and influences depending on the scale at which it is evaluated and any evaluation, deterministic or stochastic, requires geological input. In addition to geological input, vertically isolated zones of lower permeability can be defined by measuring detailed pressure profiles in newly drilled wells using wireline formation tester measurements. Flowmeter surveys and other production monitoring methods also may indicate the presence and position of baffles (Weber, 1986). If zones of a reservoir are separated by areally extensive permeability barriers, then each zone should be open to production and injection to ensure drainage of oil from the zone. Where barriers are of limited areal extent, calculations can be made to evaluate the potential coning of water or gas to aid in the location of completion intervals. For example, completion in the interval above a barrier could limit coning of water from below. Oil beneath the barrier will gravitate up around the barrier and be recovered if the barrier width is not too large (Richardson et al., 1987). Coning can be controlled by working wells over to reperforate above a shale barrier to avoid water coning or below a barrier to avoid gas coning. In the case of vertical gas drives, barriers are important in retaining oil above the gas-oil interface. As the gas-oil interface falls below a thin permeability barrier, oil is retained above the barrier. This oil is subject to gravity drainage and may rejoin the main oil body and be produced. Barriers may not significantly affect oil recovery if their lateral dimensions are small, but drainage times increase with the barrier width squared, and large barriers may retain significant amounts of oil beyond the lifetime of the field (Richardson et al., 1987). Estimation of volumetric sweep is necessary in order to evaluate the amounts of oil which are in the water-contacted portion of a reservoir and in the unswept portions. This information is required for decisions about infill drilling and/or the implementation of EOR procedures. If the ultimate recovery (Re) of a field can be projected from production decline data, and if the recovery efficiency is known for the contacted portion of a field (D) based on reliable and representative core displacement tests, then the volumetric sweep efficiency can be obtained indirectly (lie). Direct methods of obtaining volumetric sweep are not generally available, but a variety of field surveillance programs, such as those used in the Jay/LEC field described above (Langston et al., 1981), provide additional ways of acquiring data about sweep efficiency. It should be noted, however, that pressure decline curves may reflect the effects of fluid and rock expansion and phase behavior related to substantial pressure changes. These changes commonly are not incorporated in routine laboratory flood tests. That is, the right-hand side of Eq. 10-1 may not represent the same conditions as those which apply for the left-hand side of the equation.

886 A third method of assessing sweep efficiency requires a reservoir model and simulations of fluid displacements for a variety of imposed conditions. The challenges of constructing models are reviewed in the following section.

RESERVOIR MODELS FOR SIMULATION OF PRODUCTION

Reservoir models are necessary for forecasting the rates and proportions of fluid recovery and for selecting optimal recovery schemes and patterns of well placement. Forecasts of recoverable reserves are still notoriously in error in spite of recent advances in reservoir characterization (Haldorsen and Damsleth, 1991). A model of the spatial distribution and intercommunication of major reservoir units with assigned average petrophysical properties is required. Properties of interest inelude porosity, permeability, and relative permeability-fluid saturation relationships. Seismic data, pressure transient well test data and geological-petrophysical data from cores and from well logs all are used in building such reservoir models. Seismic data can be integrated with well log and core data for purposes of defining reservoir flow units with distinctive petrophysical properties in inter-well regions. The areal sampling of seismic data far exceeds the relative lack of data available from wells (Araktingi et al., 1991). The conditioning of seismic data for this integration, however, is difficult, and the resolution, both areally and, particularly, in depth is presently inadequate for delineating reservoir units and their properties at the necessary scale. The focus here is on the integration of well data and pressure well test data in the construction of reservoir models. Core and well logs in conjunction with a knowledge of possible genetic models, may be used to delineate major distinctive chronostratigraphic and facies units. Where obvious differences are not apparent, or these units require further and finer subdivision, a reservoir or reservoir unit can be segmented arbitrarily in both the vertical and horizontal directions. Statistical tests can then be applied to determine whether differences exist in reservoir quality among the segments. The null hypothesis that each sample was drawn from an identical parent population can be tested. A population can be defined as a volume of reservoir rock that has undergone similar depositional and diagenetic processes (Jensen et al., 1987). Combinations of adjacent segments can be tested for equality of means, and larger homogeneous data sets within the reservoir can be defined. Figure 10-11 provides an example of a reef which was divided into 16 segments of arbitrary thickness. Statistical testing of horizontal core permeability measurements within each segment allowed definition of reservoir blocks each with significantly different core permeabilities, at the 5% significance level, from adjacent blocks (McNamara and Wardlaw, 1991). Similar procedures can be followed for porosity, vertical permeability or other core-measured properties. Following definition of reservoir blocks with significantly different petrophysical properties, it is then necessary to provide average properties for each block in the reservoir model. Taking the example of permeability, how can an average permeability for a reservoir grid block be obtained from the permeability distribution function of core measurements from that block? The problem is one of scaling-up core-scale flow measurements in order to represent flow at larger (grid block) scales.

887

INTERIOR

MARGIN 059

.079

FLANK

.040

.033

..........................

.093

.

.040

-.

. . . . . . . . . . . . . . . .

1

.o .

.

.

""I

.

.

.

.

.

.

.

.

.

9

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

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.

.072

.044

......................................

.

.082

. . . . . . . 9. 1. .0. .9. . . . . . . . . . . . . . . .1. .0. .4.6. . . . . . . .

.051

....................................

.099

.04

ra-" ,

1.059 x .037

Fig. 10-11. Arithmetic averages and standard deviations of porosity (fraction) for position and layer groupings belonging to the same populations. Boxes enclose regions having statistically equivalent distribution of porosity. For each box, averagevalues are on the left and standard deviation is on the right. Arrows indicate increasing porosity. (After McNamara and Wardlaw 1991.) Biases of core measurements

Before the question of scale is addressed, possible biases in the core permeability measurements should be evaluated and, where possible, corrected. A number of factors (Aufricht, 1968; Keelan, 1972; McNamara and Wardlaw, 1991) may contribute to bias horizontal permeability (kH) measurements towards higher values: (i) measurements are not made at overburden pressure; (ii) measurements are not corrected for gas slippage; (iii) vugs and fractures are large in relation to core size and transect core; (iv) additional fractures are induced by coring; and (v) single-phase gas permeability measurements are likely to be higher than effective permeability of gas or oil in the presence of connate water. Average values of kH may be unrealistically low in certain cases: (i) core with the largest vugs and most frequent open fractures has been broken up and has not been recovered; (ii) experimental equipment cannot detect small pressure drops associated with the highest permeability samples; (iii) open fractures linking high permeability units in the subsurface have not been adequately sampled and measured in core; and (iv) drilling mud invasion has restricted communication. Several of these factors may also affect core measurements of vertical permeability (kv). As pointed out by Lishman (1969), the practice of making measurements on core samples, which are longer than their diameter, magnifies the contrast between horizontal and vertical permeability. The factor k v may also be influenced by the horizontal permeability barriers which are continuous at the core scale but discontinuous at larger scales, thus making the core k v unrealistically low.

888 Aside from the above difficulties associated with core permeability measurements, there is the problem of averaging these measurements to represent flow at some larger (grid block) scale in the reservoir. In order to be of use as input in simulating reservoir behavior, permeability must be averaged at the grid-block scale. Averaging core data to represent flow at the grid-block scale

The writer will assume that permeability measurements are available from continuous full-diameter core samples from the reservoir interval of interest. Permeability variability in the vertical sequence of cores may represent volumes of rock in the inter-well region which have: (i) differing permeabilities with high and low permeability blocks arranged parallel to each other (layer cake); (ii) or in series; (iii) or in a partially or completely disordered spatial array. The appropriate means for the permeability frequency distribution, which should be used to represent the average permeability of the interwell rock in each of these three cases, are the arithmetic, harmonic and geometric means, respectively (Havlena, 1966) (Fig. 1012). X 1 "]-X 2 + ....

Arithmetic Mean

-.1-X n

(10-5)

n

Harmonic Mean

(10-6)

1 .

n

x 1

Geometric Mean n ~/ X 1 X 2

x 2

....

X n

.

.

.

n

(10-7)

Thus, before averaging is undertaken, information is required about the spatial distribution of volumes of rock with differing permeabilities. Estimating effective permeability requires a frequency distribution of permeabilities as well as a model of their spatial distribution. As pointed out by Cardwell and Parsons (1945), the equivalent permeability of a heterogeneous portion of a reservoir lies between a harmonic volume average and an arithmetic volume average of the permeability measurements made at some smaller (core) scale. Core permeability measurements commonly are log-normally or near to being lognormally distributed (Bachu and Underschultz, 1992). If permeability is log-normally distributed but the total permeability variance is small, then errors introduced by not using an averaging technique (arithmetic, harmonic, geometric mean) appropriate to the spatial distribution of permeability units are small (Lake et al., 1986). However, carbonate reservoirs commonly are very heterogeneous and may have permeability differences of 10,000 times or more over short distances (Fig. 10-13). In such cases, the differences between arithmetic means for layer-cake models and geometric means for disordered arrangements of permeability units become very large (illustrated in Table 10-IV). Because permeability measured at the core scale is commonly log-normally dis-

889

ARITHMETIC MEAN FOR PARALLEL ~ - ~

K1

n

~1

~: K~ i

KA = K3

n

~3

HARMONIC MEAN FOR SERIES K.

~ K i

i

GEOMETRIC MEAN FOR RANDOM K~ =

Ki

n

WHERE

After HAVLENA, D. 1966

9"tr = Product of n terms one for each i positive integer from i to n

Fig. 10-12. The appropriate mean depends on the spatial arrangement (order) of blocks with differing permeability. (After Havlena, 1966.)

tributed and has large variance, it is concluded that information about the spatial arrangement of units with differing permeability and the choice of an averaging technique appropriate to the spatial order are important. Spatial order implies local clustering of units with similar properties in a non-uniform system and commonly is referred to as heterogeneity. Both the scale and type of heterogeneity have important effects on multiphase fluid flow and recovery efficiency. The variogram provides a quantitative measure of the scale of heterogeneity and is widely used in reservoir modeling. TABLE 10-IV Comparison of arithmetic, geometric and harmonic means; log-normal distributions with geometric means of 100 and variances (%) of from 0.1 - 3.0

%= 0.1

%= 0.5

%= 1.0

%= 2.0

%= 3.0

Arithmetic mean

100.52

113.39

164.68

727.45

7928.22

Geometric mean

100.02

100.12

100.24

100.47

100.71

Harmonic mean

99.52

88.25

60.19

12.77

1.10

Source: After McGill et al., 1991

890

.

.

.

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.

.

.

1630 i

-

~ii~i!!i~iiigiii!i!ii~!iiii!i~iii~ii!i~ii~i~i!!!!!.!!!!i!!!!!!!i!!i!ii!!!~i!!ii~i!i~!~:!:~..

......

E 3:: 1640- :!~i~i~N I-13. ILl ,.,,=

1650-

0.01

0.1

1

10

100

1000 10000

PERMEABILITY (mD) Fig. 10-13. Permeability in millidarcies from full-diameter core measurements from a dolomitized stromatoporoid reef (Keg River, OO Pool, 15-16-110-06W6 Alberta, Canada). Permeability is highly variable in vertical profile.

The variogram, kriging and conditional simulation One may consider a vertical outcrop face with core plugs taken on a regular grid and permeability measured from the plugs. Altematively, one could consider a vertical core with permeability measurements made at specified spacings. The variogram describes variability as a function of the distance between measurements. The average variance of a number (N) of measurement pairs (Y) within certain distance intervals (S) may show increasing variability (~,) with increasing interval distance (Fig. 1014); N(s)

1 ~i = ! 2 r (s) = N (S)

[Y(xi)- Y(xidr S)] 2

(10-8)

891

/SILL _0.2

_

,.

I

I

, .

I

1

I

.

.

I

.

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I

,I

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123 S (Distance) S=1

S-2 S-3 Fig. 10-14. Diagrammatic representation of a variogram showing variability (c) of a property (e.g., permeability) as a function of distance between measurements (1S, 2S, 3S, etc.). Beyond a certain distance, referred to as the range or the correlation length, T may no longer increase. The variance that corresponds with the range is the sill and typically corresponds to the variance for the entire data set. Kriging is a technique of estimating properties at unsampled points or blocks distributed over an area of interest by taking a weighted average of sample measurements surrounding a regularly spaced grid point or block. Kriging incorporates the spatial correlation structure contained in the variogram model. Conditional simulation uses the underlying permeability structure obtained from kriging and adds a component associated with the uncertainty of the limited permeability data.A large number of permeability realizations then can be made for the inter-well region of interest and a "realistic" permeability distribution selected from within a range of uncertainty. These realizations honor the permeability measurements made from core at specific sites. For full discussion of these procedures see Journel and Huijbregts (1978), and for examples of applications to carbonate sequences and reservoirs, see Fogg et al. (1990, 1991 ) and Senger et al. (1991). Ranges or correlation lengths can be from distances of meters or less to distances of hundreds or even thousands of meters (Araktingi et al., 1991; Senger et al., 1991). Spatial order also can be "nested" with several different scales of heterogeneity within the same group of rocks (Fig. 10-15). Correlation lengths for subsurface reservoirs which are derived from core or log data measurements will usually be approximately vertical and perpendicular to

892

'.'........:..~,:.'t... -'' .) . . . . . . . t~ " ' " "L . . . . . . . . . . . . . . : . ' 1 . ' . . ' . " ." .':'~'J'.'." .'.'.'.'.'." : - ' . ' . ' . ' . r . ' . ; . . . ." ~ .1.~...3..~...:.':~ :~.'.":'.".".'[ [.': ~'i'." i .-." .'.._ [ . . i.i v

," ." ,"_'-rT-J."

~ . . , ~ ~ . ' . i . ' - c . ~

,

9 . !t

i

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9 "'''"'"

,

,

,

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q

9 ~

lO0's m .."

lO's m "

.

'

o

.

'

'

10-100 ~

9

"

'

1-10 m

10-100

After Weber (4986) Fig. 10-15. Spatial order can occur on scales from that of small clusters of pores to dimensions approaching that of an entire reservoir. This can be the case for carbonates and siliciclastics alike. (After Weber, 1986.) stratification. Correlation lengths parallel to stratification might be obtained from horizontal wells but, more commonly, are obtained from analogous rocks in outcrop. It is to be expected that horizontal correlation lengths will be greater than vertical correlation lengths, because sedimentary sequences tend to be stackings of tabular units. McGill et al. (1991) studied the effects of increasing horizontal correlation length on effective permeability (k) using various averaging procedures. They used data sets with horizontal correlation lengths from zero (completely disordered) up to more than twice the length of the system being studied (inter-well spacing). Vertical correlation lengths were maintained constant. They noted that as the horizontal correlation length increases, the system effectively becomes more highly layered and the arithmetic mean of the "layers" provides the best estimate of k. On the other hand, where the correlation lengths are much smaller than the size of the system, the system behaves as though it were uncorrelated and the geometric mean provides the most appropriate estimate o f k e. Thus, there is a spectrum of means lying between the arithmetic mean and the geometric mean which are related to the correlation lengths. Variograms are useful in providing measures of the scale of heterogeneity (Fig. 1015) but may not contain information about the t y p e of heterogeneity. It is t y p e of

893

Fig. 10-16. A. Lower-permeability regions are discontinous and higher-permeability regions (denser symbol) are continuous. B. Lower-permeability regions are continuous and higher-permeability regions discontinous. A and B would not have the same permeabilities or residual oil saturations, but vertical variograms would be similar because spatial ordering occurs on similar scales.

heterogeneity which greatly affects the efficiency of displacement of one fluid by another. For example, variograms for core data through the heterogeneities in Figs. 10-16A and 10-16B could have similar ranges and sills but, in Fig. 10-16A, the higher permeability rocks are continuous and the lower permeability rocks are discontinuous compared with the reverse relationships in Fig. 10-16B. These differences in continuity or "type" of heterogeneity could cause differences of sweep efficiency, the nature of which would depend on the fluid properties and wettability. There are other problems in using the variogram as a measure of spatial continuity. Data sets from reservoirs tend to be relatively sparse, irregularly spaced, and may or may not be random samples. For example, samples may have been taken preferentially from areas with high values. Also, Srivastava and Parker (1989) have shown that variograms given by Eq. 10-8 often produce erratic and unreliable results when applied to positively skewed data such as are typical for permeability. They are also unreliable where the dispersion of values increases with an increase of mean value as also may be the case for permeability (McNamara and Wardlaw, 1991). Srivastava and Parker (1989) considered covariance measures and the correlogram as more robust measures of spatial continuity than is provided by the simple variogram. Lasseter et al. (1986) have addressed the fundamental problem, which is inherent in the preceding section, that heterogeneities causing differences in petrophysical properties at small scales can be effectively included in large-scale simulations by use of pseudo-functions. They describe a pseudo-function generation process in which the effects of smaller scale heterogeneities can be included without an inordinately large number of grid blocks. Van de Graft and Ealey (1989) discussed the hierarchical nature of heterogeneity and the types of quantification, which are required for numerical simulation studies. In summary, averaging measurements of permeability made at small (core) scales to represent flow at larger (reservoir grid-block) scales requires, not only permeability frequency distributions for suitably sampled rocks, but also information about the

894 types and scales of spatial order (heterogeneity). The success of various methods of averaging core scale measurements to represent average permeability at larger scales can be evaluated by comparing estimates made from core with permeability derived from in-situ pressure transient well tests. This topic is considered in the following section.

Comparison of permeability-derived from core and from pressure well tests Pressure transient well tests provide a means of obtaining permeability averaged for the test interval and drainage radius of the test. Where core measurements of permeability are available within this interval and radius, the averaging procedure for the core data, which gives the best match with the permeability derived from the well test, can be obtained (Warren and Price, 1961). The averaging technique, which gives the best match, should be consistent with the geological model for the region tested (layer-cake, disordered, etc.). If the core-measured permeabilities are reliable and representative of the test interval, and if the spatial arrangement of permeability units of differing permeability is known (geological model), then the core data can be averaged in an appropriate manner to predict flow at larger scales. Differences between this average and the permeability derived from the pressure well tests then could be attributed to contributions to permeability occurring at scales larger than those measured in core. Fractures would be a common example of this type, and the contribution of fractures to flow at larger scales in the reservoir then could be evaluated. Published reports in which comparisons are made between permeability derived from pressure transient well tests and that measured in cores are relatively few in number. Langston (1976) stated that buildup tests have provided the basis for arithmetic averaging of core data used to determine effective reservoir permeability, and are a significant guide in the planning and evaluation of workovers leading to better conformance. Richardson et al. (1987) observed that arithmetic averages of foot-byfoot horizontal permeabilities measured parallel to bedding planes are consistent with permeabilities calculated from well tests. This is a surprising result considering the common lack of lateral continuity of thin units at the scale of well spacings. Harmonic averages were used to obtain a best estimate of vertical permeability. On the other hand, Moore (1989) concluded that geometric mean permeability estimates were the most reliable for wells which had not been hydraulically fractured in Barque and Clipper sandstone reservoirs of the southern North Sea Basin. McNamara and Wardlaw (1991) reported that the geometric mean of core-measured permeability, corrected for truncation of high-permeability values, provided the best correspondence with permeability estimated from a pressure buildup test. These data were consistent with a reservoir model in which blocks of differing permeability were arranged in a disordered manner when viewed at the scale of inter-well spacing. The quality of the data from a pressure buildup test and the reliability of a derived permeability-thickness (kh) estimate can be assessed with some confidence. With high quality data, the major difficulty is in assigning appropriate values to h in order to derive an average k. Whether it is better to use the perforated interval only, or the net or gross total porous-permeable interval, may depend on local circumstances such as

895 the degree of communication of layers or the importance and extent of sub-vertical fractures. With attention to these matters, a large-scale, average permeability can be derived and used for comparison with core-averaged permeability. Without some independent measurement of large-scale permeability, it is difficult to evaluate the confidence that can be placed in core measurements and the various procedures that are used to average core measurements in order to assign permeability values to large reservoir grid-blocks.

TERTIARY OIL RECOVERY IN CANADA

Oil reserves in Canada have been declining for twenty years, and many reservoirs, which have been on primary and secondary recovery for long periods of time, have become candidates for tertiary recovery. Over fifty commercial tertiary projects are operating in the Province of Alberta, the majority being hydrocarbon miscible floods in carbonate reservoirs (Howes, 1988). Recovery factors for primary recovery of OOIP range from 0 - 50%, averaging about 19% for Alberta (Energy Resources Conservation Board, 1986). Secondary recovery involves pressure maintenance by injection of water or gas. At the economic limit of waterflood recovery, from 2 5 - 45% OOIP has been recovered with an average recovery of 32%. The waterflood displacement efficiency, or the portion of the original oil saturation that can be recovered from rock that is flooded by injected water, ranges from 4 0 - 70%. The volumetric sweep efficiency or portion of the total reservoir volume that is contacted by injected water ranges from 2 0 - 90% (Howes, 1988).

Miscible solvent flooding Miscible flooding is the main commercially applied method of tertiary recovery for light and medium gravity oil in Canada. Where solvent is miscible with in-place oil, interfacial forces are reduced to zero and displacement efficiency is nearly 100%. However, solvent is less viscous and more mobile than the oil being displaced and sweep efficiency may be low because of bypassing of oil by viscous fingering. Also, the low-density solvent tends to move to the top of the reservoir and override oil in the case of horizontal solvent floods. Sweep efficiency is related to the volume of solvent injected, but economic factors place limits on this volume. In Canada, the main solvents in commercial use are hydrocarbons in contrast to the USA, where carbon dioxide is the common solvent. Vertical solvent floods have higher average recoveries (Fig. 10-17), because the effects of both viscous fingering and gravity override are reduced where the solventoil interface is approximately horizontal and being driven vertically downward. In these gravity stabilized floods, the main impediment to efficient recovery is the presence of horizontal permeability barriers on which solvent and oil may be bypassed during downward advance of the flood front. In horizontal miscible floods, water can be injected alternately with solvent and with chase gas in a water-alternating-gas (WAG) injection which reduces the mobility of the injected fluids and reduces viscous fingering and gravity override.

896

H

-

C SOLVENT FLOODS, CARBONATES, ALBERTA 12 -

-

VERTICAL (37)/ M E A N 74

10 >"

8

uJ

6

o z 0

UJ

4

U. 2 0 40

50

60

70

80

90

100

U L T I M A T E RECOVERY, % O 0 1 P

Fig. 10-17. Ultimate recovery for 37 vertical hydrocarbon solvent floods have a mean of 74% OOIP compared with mean of 53% OOIP for 8 horizontal solvent floods. All floods are for carbonate reservoirs. Thirty-seven vertical solvent floods operating in Alberta have an average ultimate recovery factor of 74% OOIP, with standard deviation of 8%, which is significantly higher than the average ultimate recovery 53% OOIE with a standard deviation of 4% for 8 horizontal solvent floods (Howes, 1988) (Fig. 10-17). The average ultimate recovery factor of 59% OOIP for all solvent floods compares favorably with the average ultimate recovery of 32% for Alberta waterfloods. In vertical floods, the incremental recovery from miscible injection over waterflood recovery ranges from 1 5 - 40% OOIE In horizontal floods, the incremental recovery is smaller, being between 5 - 20% (Howes, 1988). The vertical floods have an area to pay thickness (height of oil column) ratio of less than 14 hectares per meter and, in most cases, the ratio was less than 2 hectares per meter. The horizontal solvent floods have equivalent ratios of greater than 70 hectares per meter.

Immiscible gas flooding Westerose Field, Alberta, is an Upper Devonian dolomitized stromatoporoid reef with vug-fracture porosity. The original oil column was 74 m thick and was overlain by a 117-m gas cap (Bachman et al., 1988). The area-to-thickness ratio is 3.4 hectares per meter and the reservoir is being produced by an immiscible gas recycling scheme in which the water-oil contact is maintained in its original position. Since discovery, 67% OOIP has been produced and the ultimate recovery of oil is estimated as 84% OOIE This is a higher recovery factor than the average for the vertical miscible floods (75% OOIP). The absence of extensive horizontal permeability barriers within the reef, particularly in the reef interior area, facilitates high recovery. Although the matrix porosity is low (~ 4%), the vugs appear to be well connected throughout the reef by fractures and solution channels, and displacement of oil by gas is efficient. Oil

897 which is bypassed by advancing gas can drain by gravity and, provided the drainage rate for bypassed oil is large in relation to the rate at which the gas-oil contact is being driven down (contact movement ~ 1 cm per day), this oil can rejoin the main oil bank and be produced (Yang et al., 1990). Methane gas rather than nitrogen was used for the gas cycling scheme here following a multi-component mathematical characterization of the reservoir fluids and a field history match via a numerical reservoir simulator. Forecasts were generated for various gas injection schemes, and injection of nitrogen was found to cause significantly more coning in the oil leg because of its higher density. In a case such as this, one can ask how much additional oil would have been recovered had a solvent bank been emplaced and a miscible flood conducted. An attempt to answer this question was made by comparing recoveries from immiscible and miscible gas floods. Unfortunately, although there are some 23 carbonate reservoirs with associated gas caps in western Canada, vertical immiscible floods have been utilized only in two. These are Westerose and Bonnie Glen fields with recoveries of 84% and 68% OOIE respectively. Thus, there are insufficient cases of vertical immiscible gas drives for a comparison to be made. Because no two reservoirs are the same, it is difficult to make comparisons on an individual basis. However, the Wizard Lake D3A Pool, Alberta, is in geographic proximity and of a generally similar size and reef type and has been subjected to miscible floods (Backmeyer et al., 1984). The ultimate recovery here is estimated at 96% OOIP based on a 1.5 m "sandwich loss" (final oil layer not recoverable because of coning) at the end of flood, compared with the 84% OOIP for the Westerose Field vertical immiscible flood. The Wizard Lake Field recovery will be achieved with solvent slugs which total 15% of the hydrocarbon pore volume subject to solvent displacement. Compared with Westerose Field, an additional 12% pore volume of oil is being recovered from Wizard Lake by injecting 15% pore volume of solvent. This assumes that the entire Wizard Lake reservoir is subject to solvent flooding. The percentage of the solvent recovered is not specified. Evidence is also available from sandstone reservoirs of high recoveries under immiscible gas drive with gravity drainage. In the Hawkins Field, East Texas, recovery efficiency for gas drive is estimated at over 80% compared with about 50% for water drive (Carlson, 1988). This study showed that the minimum residual oil saturation from gas displacement of water-invaded oil column is essentially the same as that from gas displacement of original oil column. Thus, in reservoirs of the Hawkins type, potential exists for reducing the average residual oil saturation in the water invaded oil column by gas d r i v e - gravity drainage. Experiments by Brandner and Slotboom (1974), in physical models of vuggy carbonates, indicate that initial upward displacement of oil by water may be reversible during subsequent downward movement of oil. Water was the wetting phase in these scaled models. They concluded that vertical gas floods could be expected to give similar ultimate oil recovery with or without preceding waterfloods under the conditions of their experiments. Immiscible gas injection into a reservoir at residual oil saturation following waterflooding causes oil to spread at gas-water interfaces. As critical gas saturation is

898 reached and gas has continuity through the system, oil continuity is re-established and oil production can recommence. In reservoirs with large vertical to horizontal dimensions, oil recovery is further aided by gravity drainage of the denser oil in the presence of the less dense gas. Gravity-assisted immiscible gas injection has been the subject of several recent papers (Chatzis et al., 1988; Kantzas et al., 1988; King et al., 1970). In summary, horizontal and vertical solvent flooding are proven methods of enhanced oil recovery with vertical floods giving, on average, approximately 20% OOIP more oil recovery than horizontal floods. Vertical immiscible gas floods also can give high oil recoveries, but insufficient cases are available to allow statistical comparisons with recoveries by miscible flooding. Horizontal permeability barriers are the major cause of lower recovery efficiencies for both miscible and immiscible gas floods. Unswept oil retained on horizontal permeability barriers has been substantiated, in some cases, by recompletion of wells above the pool-wide solvent/oil contact and by the subsequent production of"perched" oil bypassed by the solvent front (Bilozir and Frydl, 1989). In the case of vertical floods, it is important that "sandwich loss" be minimized by reducing coning to a minimum consistent with an acceptable production rate, and simulation models have proved valuable in achieving this.

CONCLUSIONS

The recovery of oil from a reservoir is the product of the microscopic displacement efficiency in the rocks contacted by the displacing fluid and the volumetric sweep efficiency, that is the fraction of the total reservoir volume that is contacted by injected fluids. Thus, residual oil at the end of secondary recovery is of two types: (1) residual oil trapped on small (microscopic) scale in the swept portion of the reservoir; and (2) residual oil bypassed in larger regions which are unswept. Residual oil in the former category may be recovered by solvent floods, or other tertiary methods, utilizing existing injection and production wells, whereas residual oil in the latter category may require infill wells to access unswept regions. Volumetric sweep efficiency may be inferred if the microscopic displacement efficiency is known from core displacement tests on representative samples and if the ultimate recovery of the reservoir can be estimated by extrapolation of decline curves or, alternatively, by analogy with other similar reservoirs at more advanced stages of production. Neither method is satisfactory because long production time may be required before extrapolations to a recovery limit can be made reliably from pressure decline curves. Also, pressure decline curves reflect the effects of fluid and rock expansion and phase behavior related to substantial pressure changes, which usually are not incorporated in laboratory flood tests. That is, it may not be justifiable to "back out" volumetric sweep from Eq. 10-1. Alternatively, suitable analogues produced to economic limits may not be available. Field surveillance programs, such as temperature surveys, tracer surveys, flowmeter and noise logs and pressure transient well tests, are expensive to implement,

899 but provide indirect methods of estimating volumetric sweep efficiency and furnish a basis for injection balancing and optimizing sweep efficiency. These tests, if well chosen, usually repay their cost many times over. A further approach is to use a reservoir model and to simulate physical processes within the reservoir in order to forecast the rates and proportions of fluid recovery under various production schemes and well-placement patterns. Several of the petrophysical properties used in such models (porosity, permeability, relative permeability-saturation relationships) are measured at the core scale and have to be averaged to represent flow and displacement at larger (reservoir grid block) scales. Such averaging requires information about the spatial arrangement of reservoir units with differing properties (heterogeneity) and may be difficult because heterogeneity may occur on several different scales in a "nested" manner. The types, degrees and scales of heterogeneity present the most difficult problems for quantitative reservoir characterization. The success of various methods of averaging core scale measurements to represent permeability at larger scales can be evaluated by comparing estimates made from appropriately averaged core measurements with those derived from in-situ pressure transient well tests. Few published data of this type are available, but the indications are that correlations to date are poor and that averaging core data to represent flow at larger scales is, as yet, subject to considerable error. Numerical reservoir simulators can match past performance, usually after several changes of parameters, but have been less successful in making predictions about future performance, particularly for enhanced oil recovery schemes. Predictions concerning ultimate recoverable reserves, which are made early in the production history of a reservoir, have been notoriously in error. This is usually because some aspect of the "container" has not been correctly modelled. Further progress in predicting performance will require increased resolution of reservoir flow units. This will be achieved through better integration of higher resolution seismic methods and geological data with new in-situ pressure tests.

ACKNOWLEDGEMENTS The writer is grateful to Drs. S.J. Mazzullo, G.V. Chilingarian and R.J. Galway for their editorial and critical comments on the original version of the manuscript.

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905

Appendix A GLOSSARY OF SELECTED G E O L O G I C TERMS S.J. M A Z Z U L L O and G.V. CHILINGARIAN

A Abiogenic Accretion [sed] Aerobic

Aggradation [sed] Allochem Allochthonous [sed]

Argillaceous Atoll

Authigenic

Autochthonous [sed]

Products (minerals, sediments, or rocks) resulting from inorganic processes of formation. Cf: biogenic. Vertical buildup or lateral extension of deposits as a consequence of sedimentation or biotic activities. Physical, organic, or chemical processes operative in, or said of products formed in, the presence of oxygen. Cf: anaerobic, anoxic. Vertical accumulation of deposits as a consequence of sedimentation or biotic activities. Cf: degradation. Carbonate particle of either skeletal or non-skeletal origin. Sediments or rocks formed elsewhere than where they are ultimately deposited; of foreign or introduced origin. Syn: allogenous. Containing clay minerals as impurities in carbonate, siliciclastic, or evaporitic sediments. A ring-shaped reef, circular or elliptical or horseshoeshaped, generally encircling an interior lagoon, and surrounded by deeper water. Formed or generated in place; specifically said of minerals that have precipitated in place or which have replaced other minerals or particles in various diagenetic environments. Said of sediments or rocks that have accumulated in place. Cf: allochthonous, allogenous. Syn: autogenous. B

Backstepping [sed]

Baffiestone

Bank [sed]

Referring to carbonate platforms that are being eroded or tectonically drowned such that their areal dimensions are progressively reduced in a landward direction. Reef rock that has accumulated as a result of the trapping or baffling of sediments amidst in-place organic frameworks. Limestone deposits consisting of skeletal matter formed by in-place organisms, or sediments deposited.

906

Barrier reef [sed]

Bindstone

Bioclastic Bioerosion

Biofacies [ecol] Biogenic Bioherm

Biolithite

Biostrome Biota Bioturbation

Bitumen

Boundstone

Brecciation

generally in shallow water; in both cases the deposit may be surrounded by deeper water. Long, linear reef oriented roughly parallel to shoreline and separated from it at some distance by a lagoon of considerable depth and width; generally occur along the margins of shallow-water platforms, and pass seaward into deeper-water environments. Reef rock that has accumulated as a result of the presence of tabular or lamellar fossils that entrusted or otherwise bound sediments during deposition. Partial syn: boundstone, biolithite. Skeletal-derived sediments. Syn: biogenic, skeletal, organic. Removal of generally consolidated sediments by the boring, scraping, chewing, and rasping activities of organisms. Distinctive assemblages of organisms formed at the same time but under different environmental conditions. Sediments or rocks, or mineral deposits whose origin is related to organic activity. Syn: organic. Mass of rock with varying amounts of topographic relief above the sea floor that has been constructed by organisms. General term for reef rocks that have accumulated as a result of the activity of organisms. Partial syn: boundstone. Bedded and widely extensive, or broadly lenticular, blanket-like mass of rock constructed by organisms. All organisms that are living or have lived in an area, including animals and plants. The disruption of sedimentary strata and included sedimentary/biotic structures by the burrowing or grazing activities of organisms. Syn: burrow mottling. A generic term for natural, inflammable substances that are composed of a mixture of hydrocarbons that are substantially free of oxygenated bodies. Great confusion exists in the literature on the definition of the term Bitumen. See T.F. Yen and George V. Chilingarian, 1994. Asphaltenes andAsphalts. Elsevier, Amsterdam, for definitions of bitumen, bitumoid, etc. General term for reef rock that has accumulated as a result of the activity of organisms; or non-reef rock that has accumulated as a result of extensive syndepositional marine lithification. Disruption of strata, and development of fitted clasts

907

Buildup [organic] Buried hill

separated by fractures or of chaotic clasts with or without matrix, formed as a result of tectonism, carbonate dissolution and collapse, or evaporite dissolution and collapse. General term for reefal accumulation. Relict hill topography resulting from erosion, or specifically, karst weathering of carbonate terranes. Buried hills commonly composed hydrocarbon traps in karsted carbonate rocks. C

Calcite/Aragonite Compensation Depth Caliche

Calichification Caprock [petrol] Catagenesis

Cement

Chalk Circumgranular [sed] Clastic [sed]

Coated grain

Coccolith

Depth in the sea below which the rate of calcite or aragonite dissolution exceeds their rates of deposition. Authigenic deposit of calcium carbonate, generally low-magnesian calcite, that forms at the expense of (i.e., replacing) preexisting sediments, soils, or rocks. Syn: soilstone crusts, calcrete. Term describing the process of caliche or calcrete formation. An impervious body of rock that forms a vertical seal against hydrocarbon migration. Term applied to changes in existing sediments, or most commonly, rocks during deep burial at elevated temperatures and pressures short of metamorphism. Adj: catagenetic. Syn: mesogenesis, epigenesis. Naturally occurring (biogenic or abiogenic) precipitate of mineral material, usually calcite, aragonite, or dolomite in carbonate rocks, that binds particles together into a lithified framework. Carbonate rock of low-magnesian calcite composition composed dominantly of the remains of coccoliths and coccospheres. Cement which completely lines the pores in a rock. Syn: isopachous. Term used in reference to particles (carbonate, siliciclastic, or other mineralogies) that commonly are transported by fluids. Partial syn: hydroclastic. Carbonate particle consisting of nuclear fragment surrounded by cortex of chemically precipitated carbonate (e.g., ooids, pisoliths) or cortex composed of organic encrustation (e.g., oncolites, rhodolites). A button-like plate composed of calcium carbonate, generally about 3 microns in diameter, a number of which compose the outer skeletal remains of

908

Collapse breccia

Compaction [sed]

Composite grain Connate [sed]

Cross-stratification

Cryptalgal Cryptocrystalline [sed]

Crystal silt

Cyanobacteria

Cyclic sedimentation

coccospheres (skeletons of marine, planktonic protists). Sedimentary breccia formed as a result of collapse of indurated strata due to dissolution of underlying strata, or commonly, cave-roof collapse. Reduction in bulk volume and/or thickness of a sedimentary deposit resulting from either physical processes of grain readjustment (closer packing) in response to an increased weight of overburden (mechanical compaction), or chemical processes such as dissolution, grain interpenetration, and stylolitization (chemical compaction). Aggregate carbonate grain composed of discrete particles bound together by cement or organic mucilage. In reference to evolved waters ultimately of marine origin that have been entrapped in sediment pores after their burial, and which have been out of contact with the atmosphere for an appreciable period of geologic time. Cf: meteoric. Layers or laminae of sedimentary rock deposited at angles to the horizontal (not exceeding the angle of repose in air or water) as a normal consequence of transport by air or water. Syn: cross-bedding. Term used in reference to a presumed algal or cynaobacterial origin of certain carbonate rocks. Term used in reference to crystal components (e.g., cements or architectural elements of shells) of very fine size, generally not resolvable without the use of at least a petrographic microscope; also said of a rock with such texture. Syn: microcrystalline, nannocrystalline. Internal sediments found in cavities in rocks, composed of silt-size particles of crystals; generally form as a result of partial dissolution of host rock/sediment or boring by organisms. Biological/geological term for blue-green algae (cyanophytes), the association of blue-green algae and bacteria, or the bacterial affinity of blue-green algae. Sedimentation involving a vertical repetition of rock types representative of distinct depositional environments. Syn: rhythmic sedimentation. D

Dedolomite Dedolomitization

Dolomite that has been replaced by calcite wherein the crystal form of the predecessor has been preserved. Process of replacement of dolomite by calcite with preservation of dolomite crystal form.

909 Deflation Depositional karst

Desiccation Detrital

Diagenesis

Diagenetic facies [carb]

Dissolution Dissolutionenlargement/enhancement

Dissolution-reprecipitation [carb]

Distally-fining [sed]

Doline

Dolomitization Dolostone Duricrust

Removal of loose, dry sediment by wind action. Term used in reference to various small-scale karst features (e.g., small dissolution caves and related speleothems and cave cements, dissolution-etched erosional surfaces) formed as a result of short periods of subaerial exposure during deposition. Loss of interstitial water from sediments as a result of drying. Term generally restricted to sediments derived from the erosion of preexisting rocks. Syn: terrigenous, siliciclastic. All chemical, physical, and biologic changes in sediments or rocks that have altered their original textures and mineralogies, operative from the time of their formation and deposition, exclusive of metamorphism. In carbonate studies, the term usually encompasses micritization, changes in mineralogy, cementation, recrystallization, dolomitization and dedolomitization, dissolution, etc. Adj: diagenetic. For various definitions of diagenesis found in the literature, see G. Larsen and G.V. Chilingar, 1979. Diagenesis in Sediments and Sedimentary Rocks. Elsevier, Amsterdam, 579 pp. (Also Catagenesis.) An assemblage of rocks with similar diagenetic attributes or which have been affected by similar diagenetic histories. Process of dissolving substances. Syn: leaching. In porosity studies, the process of enlarging or otherwise enhancing the size of preexisting pores by dissolution. Common process of carbonate dissolution and void formation at the microscale or macroscale, followed by the precipitation of another mineral phase. A sequence of rocks wherein sediment size decreases either away from shore, toward deeper water (marine), or from the point of sediment input (marine or terrestrial). General term for a closed depression of dissolutional origin in an area of karst topography. Partial syn: sinkhole. Replacement of a preexisting carbonate sediment or rock by dolomite. Synonym for dolomite rock. General term for a hard crust (carbonate, silica,

910 ferruginous, or aluminous) on the surface of land or as a replacive layer in the upper horizons of soils. E

Emergence

Eogenetic

Eolian Epeiric sea

Epibionts Epigenesis

Eustatic Euxinic Extraclasts [carb]

Fabric [sed] Facies [gen]

Fenestrae

Term used in reference generally to subaerial exposure of newly-deposited sediments or buried rocks as a result of tectonic uplift, unroofing by weathering, or relative or eustatic sea level fall. All diagenetic processes operative from the time of sediment formation, including marine and meteoric processes, until the sediments or rocks ultimately are buried and away from the influence of surface and near-surface processes. Referring to processes and products of sediment transport, erosion, or deposition by wind. A shallow sea on a broad continental shelf or an inland sea covering large portions of a continent; in the latter case, commonly considered to be tideless. Partial syn: epicontinental. In reference to encrusting organisms or that population of organisms that has encrusted various substrate. Diagenetic processes that have occurred, and resulting products that have formed, in the deep burial environment. Adj: epigenetic. Syn: mesogenesis, catagenesis. C f: eogenetic. Rise or fall in sea level due to global changes in the volume of the oceans. Cf: relative sea level change. An environment of restricted circulation, with stagnant or anaerobic conditions. Particles derived from outside the basin of carbonate deposition. Cf: intraclasts.

The orientation, or lack of orientation, of the elements (particles, crystals, cements) in a sedimentary rock. Sum of all lithologic, biologic, and diagenetic attributes in a rock or sequence of rocks from which the origin and environment of deposition can be inferred. The term can be restricted to lithologic facies (lithofacies), depositional facies, biotic facies (biofacies), or diagenetic facies. General term for penecontemporaneously formed shrinkage pores or gas-bubble pores in rocks, both larger than interparticle pore spaces; includes "birdseyes" and larger pores such as sheetcracks. Also in reference to

911

Floatstone

Fluvial

Framebuilder Framestone

pore types in carbonate rocks (see Porosity terms). Adj: fenestral. Reef rock composed of matrix-supported organic particles, the particles being of allochthonous (transported) rather than in-place origin. In reference to sediments transported or deposited by rivers or streams, or rocks interpreted to have been deposited in rivers or streams. Syn: fluviatile. Organisms capable of creating massive, generally wave-resistant buildups. Reef rock that has formed as a result of the accumulation of large, in-place fossils that formed the actual framework of the deposits. G

Gilsonite

Grainstone

A black, shiny asphaltite, with conchoidal fracture and black streak, which is soluble in turpentine. Syn: uintahite, uintaite. Grain-supported carbonate rock textural type, generally mud-free. Syn: sparite. H

Hardground

Hemipelagic [sed] Hydrothermal Hypersaline

General term for a surficial or near-surficial layer of sediment that is cemented syndepositionally, close to or at the sediment-water interface. Deep sea sediments composed of the remains of pelagic organisms and a small amount of terrigenous material. Alteration of rocks or minerals by the action of heated waters. Sea water salinity elevated beyond values of normal salinity (e.g., greater than 34-38 o/oo); also used in reference to environments of excessively high salinity. I

Internal sediment

Interregional karst Interstitial Intrabasinal

Fine-grained sediment, including insoluble residue, that has collected in pores in sediments or rocks; such sediment is generated syndepositionally as a result of organic boring and micritization, or partial dissolution of soluble rocks. Widespread surface of karstification generally related to eustatic sea level fall or tectonic uplift. Interparticle (either pore space, cements, or fluids). Said of sediments or rocks formed within or derived from the basin of deposition. Cf: terrigenous.

912 Intracratonic Intrastratal Isopachous [sed]

Geologic features found on cratons, e.g., intracratonic basins, intracratonic seas. Formed or occurring within a given layer or layers. Syn: intraformational. Cement which completely lines the pores in a rock. Syn: circumgranular. K

Karst

Karst towers Kerogen

Lacustrine Leaching [sed] Lithification Lithoclast

Lithofacies Lithographic texture

Lithohydraulic unit Lithology Lysocline

Topography (surficial and subsurface) formed as a result of the dissolution of soluble rocks such as limestones, dolomites, and evaporites, and characterized by closed depressions, caves, and underground drainage. Residual hills in karsted terranes. Syn: buried hills. Insoluble organic matter (fossilized), which can be converted by distillation into petroleum products.

Pertaining to lakes or deposits of lakes. Pertaining to dissolution of soluble minerals or rocks. Partial syn: dissolution. Process of converting unconsolidated sediments to rocks by the addition of mineral cements. Syn: cementation. Mechanically or biogenically formed and deposited fragment (larger than 2 mm) of a weakly lithified sediment or rock, formed within the basin of deposition. Cf: extraclast. See Facies. Compact, dense, homogeneous and exceedingly finegrained rock with conchoidal or sub-conchoidal fracture. Partial syn: micrite, carbonate mudstone. Layer or layers of rock with uniform fluid-flow properties distinct from adjoining layers. Descriptive, physical characteristics of rocks. Depth in the ocean at which the rate of dissolution of calcium carbonate increases significantly. M

Matrix [sed]

Maturation

The continuous material (sediment, cement) composing rocks; the continuous material enclosing interstices in rocks. [petroleum] Term pertaining to the thermocatalytic state of hydrocarbons or hydrocarbon source material; [sed] term pertaining to the mineralogic composition of siliciclastic or carbonate rocks as they approach a pure

913

Maturity Megabreccias [sed] Meniscus [sed]

Mesogenetic Metastable [sed]

Meteoric Micrite

Micritization Microbial Microcrystalline Microfacies Microspar

Mimetic Monominerallic Mound

Mud [carb sed] Mudbank Mudstone

quartz or calcite end-member composition, respectively. In reference to maturation, above. Generally thick bodies composed of large blocks of rock that are randomly oriented. The hour-glass shape of interparticle cements precipitated from fluids held by attraction at grain-tograin contacts; usually indicative of cement precipitation in the vadose environment. Diagenetic changes in rocks occurring in the deep burial environment. Syn: catagenetic, epigenetic. Said of minerals that are unstable at certain temperatures and pressures, or in fluids of certain compositions. Partial syn: unstable. Water derived ultimately from rain; water of recent atmospheric origin. [sed] Particulate, fine-grained matrix of carbonate rocks, by various definitions, the particles being less than 20 microns or 4 microns in size; a carbonate rock textural type composed dominantly of mud. Syn: carbonate mudstone; [crystal] pertaining to carbonate crystal size less than 4 microns. Organic or inorganic process of converting preexisting carbonate cements or grains to micrite. Pertaining to the presence, activities, or products of microbes such as algae, bacteria, fungi, yeasts. See Cryptocrystalline; said of a rock with such a texture. Petrologic term for the features, composition, and appearance of rocks, or of specific diagenetic features, as identified in thin sections. Fabric of carbonate crystals resulting from recrystallization of micrite-size crystals or grains that range in size from 5 microns to about 30 microns in size. Process of replacement (e.g., during dolomitization) wherein precursor textures and fabrics are preserved. Composed of one mineral species. Organic or inorganic sediment buildup with low depositional relief; or organic buildup composed of nonframework building (but commonly gregarious), in-place organisms or allochthonous organisms. Fine-grained particles, by various definitions less than 20 microns or 4 microns in size. Syn: particulate micrite. Accumulation of mud. Carbonate rock textural type composed dominantly of mud (micrite) with less than 10% grains. Partial syn: micrite.

914 N Nannofossil Neomorphism

General term for small fossils, the resolution of which is near the limits of the light microscope. General carbonate petrologic term that encompasses both recrystallization (increase in crystal size in cases where mineralogy is constant) and inversion (crystal fabric changes attending mineralogic conversions). O

Occlusion Offiap

Oncolite

Onlap

Ooid

Ooze [sed]

Overburden [sed] Overpressuring/ overpressured reservoirs

In reference to porosity reduction as a typical consequence of cementation or compaction. Progressive offshore migration of the updip terminations of sedimentary beds within a conformable sequence of rocks. Cf: onlap. An accretionary carbonate particle composed of a particulate nucleus surrounded by a cortex of algae and entrapped sediment and/or precipitated cement. Progressive onshore migration of the updip terminations of sedimentary beds within a conformable sequence of rocks. Cf: offiap. An accretionary, sand-size carbonate particle composed of a particulate nucleus surrounded by a laminated cortex of microcrystalline calcium carbonate; oolite is the term commonly used for rocks composed of ooids. Partial syn: oolite, oolith. Soft, soupy mud generally composed of at least 30% skeletal remains of pelagic organisms (calcareous or siliceous), the remainder being clay minerals. Section of rocks overlying a given stratum or strata. Porous rocks characterized by greater than normal fluid pressures resulting, for example, from undercompaction due to rapid sedimentation. P

Packing [sed] Packstone Paleoenvironment Paleogeomorphic

Paleokarst Paleosol Pelagic

Three-dimensional arrangement of particles in a rock. Muddy, but grain-supported carbonate rock textural type. Ancient depositional (or diagenetic) environment. Term used in reference generally to a buried landscape; in reference to hydrocarbon reservoir traps in or along certain buried landscape features. Buried or relict karst. Fossilized soil. [oceanographic] Pertaining to open ocean water as an

915

Pellet Peloid

Pendant

Penecontemporaneous Periplatform

Peritidal

Permeability [geol] Petrophysics Phreatic

Pinnacle reef Pisolite

Planktonic Platform Playa Polycyclic Polygenetic Polyminerallic Polymorph [mini

Pore Porosity terms

environment; [sed] deep-sea sediments without terrigenous material (either inorganic red clays or organic oozes). A particle composed of fecal material. Partial syn: pelletoid, peloid. A cryptocrystalline carbonate particle of unrecognizable origin, most likely a completely micritized grain, less likely a fecal pellet. Partial syn: pellet. Cement fabric that is precipitated along the undersides of grains or cavities, usually indicative of precipitation in the vadose environment. Syn: stalactitic. Contemporaenous with deposition. Syn: syndepositional. Said of sediments or environments in deeper water immediately seaward of carbonate platforms, atolls, or banks. Inclusive term for supratidal and intertidal environments, or in some definitions, supratidal, intertidal, and upper subtidal environments. The ability of a medium to transmit fluids. The physical properties of reservoir rocks. Zone below the water table in an unconfined groundwater lens, or in an aquifer, where all the pores are filled with water. An isolated, long (thick), spire or column-shaped reef. An accretionary carbonate particle, usually larger than sand-size, composed of a particulate nucleus surrounded by a cortex, generally laminated, of precipitated calcium carbonate; term commonly used for rocks containing pisoids or pisoliths. Syn: pisolith, pisoid. In reference to pelagic organisms that float. A linear region of variable width of shallow-water calcium carbonate deposition. A desiccated, vegetation-free, fiat-floored area, commonly found in deserts, which represents a former shallow desert-lake basin. Syn: playa lake. Pertaining to more than one cycle of formation. Pertaining to an origin involving more than one process of formation, or superimposed processes of formation. Composed of more than one mineral. A mineral species with more than one crystal form, e.g., C a C O 3 calcite (hexagonal) and aragonite (orthorhombic). A hole, opening, or passageway in a rock. Syn: interstice. Fabric-selective porosity: pores that occur in regard to

916

Postdepositional Pressure- solution

Progradation

Protodolomite Pseudospar

specific elements in the rock. Cf: not fabric-selective; framework porosity: porosity in the matrix of rocks, exclusive of fractures. Syn: matrix porosity; porosityspecific: porosity occurrence within a given rock type or paleodepositional facies; pore system: the total petrophysical attributes of a porous unit; primary porosity: porosity inherited from the depositional environment. Cf: secondary porosity, that which develops after deposition as a result of dissolution. Physical or chemical changes in sediments or rocks after final deposition and burial. Process in which carbonate dissolution occurs at burial as a result of increased pressure due to overburden stress; usually results in the formation of stylolites and interpenetrative grain contacts. Syn: pressuredissolution. Tthe seaward accretion and migration of sedimentary bodies and corresponding depositional environments. Cf: regression. Term used in reference to dolomite that is poorly ordered and compositionally impure (i.e., calcic). Fabric of carbonate crystals, resulting from recrystallization of micrite-size crystals or grains, that are larger than 30 microns in size. R

Ramp Recrystallization Reef Regression

Replacement [crys] Resedimentation

Rhizoconcretion, rhizolith Rhodolite

A carbonate depositional surface that dips very gently (less than 1~ in a seaward direction, passing imperceptibly from shallow to deep water. Term that refers to an increase in the size of existing crystals without a change in mineralogy. An organic buildup. The landward migration of sedimentary bodies and corresponding depositional environments. Cf: progradation. Situation where one mineral replaces another mineral or rock, e.g., dolomitization, silicification. Refers to sediments, originally formed and deposited in one environment and subsequently transported to a completely different environment. An accumulation of calcium carbonate around plant roots. An accretionary carbonate particle, larger than sand-size, with or without a nucleus surrounded by a laminated to massive cortex constructed by red (rhodophyte) algae;

917

Rimmed shelf/platform

Rudstone

term used for rocks composed of rhodoliths. Syn: rhodolith, rhodoid. A shallow-water platform of deposition, the seaward edge of which is defined by a submarine topographic high constructed by carbonate sands or reef buildups. Reef rock composed of grain-supported texture of allochthonous (transported) rather than in-place organic particles. S

Sabkha

Saddle dolomite

Sapropel

Schizohaline Seal Sea-marginal

Shoal Silcrete Siliciclastic Skewness

Sorting [sed] Spar

Sparite Strand, strandline Stromatolite

A deflation flat developed in coastal, arid-zone environments, typically associated with evaporites, and inundated occasionally by sea water. Syn: sebkha. A conspicuous habit of dolomite, generally precipitated in high-temperature environments, characterized by curved crystal faces. Material composed of plant remains, most commonly algae, that is or has macerated and putrefied in an anaerobic environment: source material for petroleum and natural gas. Said of a water body or environment of fluctuating salinity. An impermeable bed that acts as a barrier to the vertical or lateral migration of hydrocarbons. Environments close to the sea, such as lagoons, tidal fiats, beaches; or deposits in these environments. Syn: marine-transitional. Area of shallow water. A soil-replacive or sand and gravel-replacive deposit composed of silica. In reference to terrigenous detrital sediment composed of silicate mineral grains. A statistical measure of the state of asymmetry shown by a frequency distribution curve that is bunched on one side of the mean and tails out on the other side. A measure of the spread or range of particle size distributions about the mean in a sediment population. Term for coarse crystalline calcite; commonly used in reference to precipitated cements, but may be used for coarse crystalline, recrystallized micrite. Syn: sparry. Grain-supported, mud-free carbonate rock textural type. Syn: grainstone. The zone of contact between the sea and land, commonly represented by beach deposits. A laminated organo-sedimentary deposit, either planar

918

Stylolite

Stylolitization Subaerial Subsidence Subunconformity Sucrosic

Sulfuric acid karst

Supraunconformity Syndepositional

or dome-shaped, constructed by the sediment trapping and binding activities, together with some amount of syndepositional lithification, of blue-green algae (cyanobacteria). A pressure-solution feature, generally formed in moderately to deeply-buried rocks, characterized by a thin seam or suture of irregular, interlocking, sawtoothed appearance. Process of stylolite formation. Referring to exposure on land, to meteoric fluids. Local or regional downwarping of a depositional surface due to tectonism or sediment loading. Position of strata beneath an unconformity. General, non-genetic term for coarse crystalline texture, used mostly in reference to dolomites; a porosity term referring to intercrystalline pores within coarse crystalline dolomites. Dissolution, generally of carbonate strata, by sulfuric acid generated from the oxidation of upward migrating, H2S-bearing fluids from depth. Position of strata directly above an unconformity. Physical, biologic, or diagenetic processes occurring during sediment deposition. Syn: penecontemporaneous, synsedimentary. T

Telogenesis

Terrigenous Texture [sed]

Tidal flat

Transgression

Diagenetic alteration in the subaerial meteoric environment of rocks that once were deeply buried. Adj: telogenetic. Sediments, typically siliciclastic, derived from the erosion on land of preexisting rocks. Syn: detrital. General physical appearance or characteristics of a rock, including parameters such as size, shape, sorting, and packing of constituent particles. Environment, and deposits therein, formed in the intertidal zone (including neighboring supratidal and upper subtidal environments and deposits). Syn: peritidal fiat. Inundation of land by the sea. The term transgressive is used in reference to sediments deposited during a transgression. U

Unconformity

A substantial break or gap in the geologic record where a rock unit is overlain by another that is not next in the

919

Upward-shoaling [sed]

stratigraphic succession. A vertical section of deposits that records continually decreasing paleowater depths. V

Vadose

That zone in an unconfined groundwater lens wherein the pores in the sediments are filled mostly with air. Cf: phreatic. W

Wackestone

A mud-supported carbonate rock textural type with greater than 10% particles.

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921 Appendix B

P E T R O L E U M ENGINEERING GLOSSARY J.O. ROBERTSON JR., G.V. CHILINGARIAN AND S.J. MAZZULLO

A Acidizing

fracture acidizing

matrix acidizing Air Balance Beam Air Drilling Alkanes (or paraffins)

Alkenes (see Olefins) Alkylation

Annular Space Aquifer Aromatics

API Gravity

The introduction of acid (hydrochloric, formic, and acetic, for carbonates; and hydrofluoric for sandstones) into a formation to dissolve rocks, thus opening passageways for fluids to flow through. Acid is injected into the formation at a high enough pressure to fracture the formation. The acid etches the new fracture. Enlargement of preexisting pores without fracturing. Acids can also enlarge (etch) the pre-existing fractures. Device using compressed air, rather than weights, to balance the weight of the sucker rods. Use of compressed air instead of liquid as the circulation medium in rotary drilling. Methane series, derived from petroleum, with carbon atoms arranged in a straight chain. It includes methane, ethane, propane, butane, pentane, hexane, heptane, and octane (C n Hzn+2). The reaction of alkenes or olefins with a branched chain alkane to form a branched, paraffinic hydrocarbon with high antiknock qualities. Space between the outside of the casing and the wellbore. A reservoir or portion of a reservoir containing water. Cyclic hydrocarbons found in oils. Contain a benzene ring nucleus in their structure, with a general formula of C n H2n_6. The standard method of expressing the gravity, or unit weight of oils. 141.5 oApI = ~ 131.5, SG60o

Automatic Tank Batteries

where SG6oo = the specific gravity at 60~ Lease tank batteries equipped with automatic measuring, gauging, and recording devices.

922 B

Ball Sealers Barefoot Barite Barrel Batch BPD, bbl/d or B/D Benzene

Bit Blowout

Blowout Preventer, BOP

Bottom Fraction Bottom Water Bridge Plug BS BS&W

Rubber balls dropped into a wellbore to plug perforations. Well completed without casing. A mineral often used as a component of drilling mud (or fluid) to add weight: barium sulphate, SG z 4.2 A unit of petroleum liquid measure equal to 42 gallons, US. A shipment of a particular product through a pipeline. Barrels per day. C6H6, an aromatic hydrocarbon found in petroleum. Used as a solvent for petroleum products. Used as a synonym for gasoline in many European countries. The rock cutting tool attached at the working end of the drilling string. Blowing out of gas and fluids when excessive well pressure exceeds the pressure of the drilling fluid head. Device consisting of a series of hydraulically controlled rams and inflatable bags to prevent the blowout of a well. This equipment allows control over volumes of fluid to be bled off from the wellbore through a choke manifold during drilling operations. There are several classifications of BOP. Heavier components of petroleum which remain after the lighter ends have been removed (distilled out). Water located at the bottom of reservoir. A mechanical device used to "seal-off" the wellbore below the point where it is set. Basic sediment. Basic sediment and water (often found at the bottom of tanks). C

Cable Tool Drilling Rig Capillary Action

Capillary Carbon Black Casing

A drilling device that uses percussion to make a hole. The upward and outward movement of fluids through the porous rock as a direct result of surface rock properties. (See Appendix C.) The minute openings between rock particles through which fluids are drawn. (See Appendix C.) A "soot" produced from natural gas. Pipe used to keep the wellbore walls from collapsing and to seal the borehole to prevent fluids outside the well from moving from one portion of the well to another.

923 Casinghead Gasoline Catalysis Catalyst Catalytic ("Cat") Cracking Cathead Cellar

Cement slurry

Cementing

primary cementing secondary cementing squeeze cementing Centralizers

Choke

Christmas Tree Circulation System Collapse Resistance Completion

Compressor

Conductor Contact Angle

"Natural gasoline" is condensate from natural gas. Process in which the chemical reaction rate is affected by the introduction of another substance (catalyst). A substance that is used to slow or advance the rate of a chemical reaction without being affected itself. Breaking down of petroleum compounds into various subcomponents. Spool-shaped hub on a winch shaft around which a rope may be snubbed. Area dug out beneath the drilling platform to allow room for installation of blowout prevention equipment (BOP). A mixture of cement and water in a liquid form which is pumped behind the casing. The slurry is allowed to set until it hardens. Pumping of the cement slurry down the casing and then back up the annular space between the casing and the borehole. The cementing operation where casing is cemented in the borehole. Cementing operations in wells after the well has been completed. Placing cement by squeezing it under pressure. Devices fitted around the outside of casing as it is lowered down in the borehole to keep it centered in the hole, to achieve a good cement job. A restriction in a flowline that causes a pressure drop or reduces the rate of flow through the orifice. It provides precise control of wellhead flow rates in surface production applications involving oil and gas and in enhanced recovery. Array of valves, pipes, and fittings placed at the top of the well, on the surface. Portion of the rotary drilling system which circulates the drilling fluid (mud). The minimum extemal pressure necessary to collapse casing or a pipe. Finishing a well. Installation of all necessary equipment to produce a well. Includes placing the casing, cementing and perforation opposite the productive zone. Mechanical device used for increasing the pressure of gases, similar to a pump which is used to increase the pressure of gases or liquids. First pipe in a drilling well used to attach to the BOP. The angle which the oil-water interface makes with

924 the solid (rock). Usually, it is measured from the solid through the liquid phase (if the other phase is a gas) and through the water phase if oil and water are both present, to the oil-water interface. (See Appendix C.) Core conventional sampling sidewall Corrosion Corrosion Inhibitor Cracking Cradling Critical Point (with corresponding critical temperature critical pressure) Crown Block Crude heavy crude light crude Cut

A sample of the rock taken from the well during drilling operations. Taking a sample of geological strata for examination. Cores generally one inch in diameter taken from the side of the wellbore, often by wireline. Chemical reaction (mainly loss of electrons) that oxidizes metals, e.g., Fe ~ Fe § +2e-. Chemicals added to inhibit corrosion of metals. Refinery process of breaking crude oil down into subcomponents. Lifting and placing the welded and wrapped pipeline into the trench. A point at which one phase cannot be distinguished from another, and the material cannot be condensed regardless of the amount of pressure applied. There is no volume change when a liquid is vaporized at the critical point. Pulley at the top of the drilling rig which raises and lowers the drill-string. Petroleum as it is produced from the formation. Thick (sticky) oil with an ~ gravity of less than 17~. Thin (light) oil with an ~ gravity greater than 25 ~ Percentage (by volume) of water associated with a particular crude oil. D

Daily Drilling Report Darcy (D) Derrickman Deviation Drillstem Test (DST)

Distillation

Records kept of the drilling activities, completed every morning while well is being drilled, by the toolpusher. Unit of measurement of permeability (ease of fluid movement), named after its originator, Henry D'Arcy. Member of drilling crew who handles the pipe joints and works on the tubing board of the rig. Directional change of wellbore from vertical. Drillstem test employs equipment which allows a well to flow for a short period of time, gathering information on reservoir fluids and the ability of the reservoir to produce fluids. Boiling off various fractions of an oil at different temperatures.

925 Doodlebug Doubles Draw-works Drillstring Driller Drilling Mud

Drilling Program Drilling Ship Drip Drive Mechanism

bottom water combination drive gas cap expansion

gravity drainage

solution gas water drive Dry Hole DWT Dynamic Positioning

"Doodlebug Crew" makes seismographic measurements. Two joints of pipe (casing, tubing) fitted together. The hoisting equipment of a drilling rig. A long continuous string of tubular goods of tubing, drill collars, bit, and subsurface tools. Person in charge of the drilling crew on each tour. Fluid composed of water or oil, clays, chemicals and weighting materials used to lubricate the bit and to move cuttings out of the hole. Plan for assembling all the personnel, equipment and supplies for drilling and completing a well. Vessel especially designed for offshore drilling operations. Device for tapping off natural gasoline at the wellhead. The natural force present in a reservoir which causes the fluid to move toward the wellbore, the action of one fluid pushing another. Underlying water in the reservoir exerts pressure moving fluids toward the wellbore. Two or three natural drives moving the fluid toward the wellbore. Expansion of the gas cap, located in the upper portion of the reservoir, upon reduction of reservoir pressure, forces fluids toward the wellbore. Gravity force results in movement of oil downward as the gas migrates upward. This force is strong in steeply dipping reservoirs. Gas bubbles dissolved in the oil push the latter towards the wellbore. Water (part of an aquifer) in the reservoir exerts the force to push fluids towards the wellbore. A well that fails to produce oil or g a s - syn: "Duster". Dead weight tons. Means of keeping a drillship positioned exactly above the drillsite by transmitting position signals from the ocean floor to the ship's thrusters. E

Edgewater

Water around the edge of a reservoir- water presses inward. Effective Pressure Grain-to-grain stress, which is equal to the total (Pe' Pg' or c') overburden pressure (p, or c) minus the pore (fluid) pressure, pp. Electric Submersible Pump, An electric submersible pump system comprising a

926 ESP Electrodrills Environmental Impact Report (EIR)

Elevators Enhanced Recovery

downhole pump, motor, power cable and surface control system. Rotary drills powered downhole by electricity. To determine the impact upon the surrounding environment, a detailed report is required by the Environmental Protection Agency before any major construction project can begin. Clamps for lifting rods, tubing and casing. Techniques that supplement the natural primary recovery mechanism to increase the flow of fluids to the wellbore. F

Flare Flow Fluid Loss Agent Formation Resistivity

Burning off excess natural gas at a well or other production site. Movement of fluids through the reservoir. Materials added to a drilling mud to reduce water loss into the formation. R F = o , where R is equal to the electrical resistivity R o w

Formation Volume Factor

(B)

Fourble Fraction

Fractionation Columns

Fracturing

fracture acidizing hydraulic fracturing

of a formation 100% saturated with formation water and R w is equal to the formation water resistivity. F = ~-~, where ~ is porosity and m is the cementation factor (varies from 1.3 for unconsolidated sands and oolitic limestones to 2.2 for dense dolomites). F embodies the effects of grain size, grain shape, grain distribution and grain packing. The volume of oil (and the solution gas dissolved in it) at reservoir pressure, p, and temperature, T, per unit volume of stock-tank oil (at surface, T= 60~ and p 1 atm). Four joints of pipe (casing, tubing) connected together. Percentage or fraction of a separate component of the crude oil having a certain boiling point range, or of a product of refining or distilling. Tall columns used in refineries to separate oil into its various components, e.g., gasoline, kerosene, gas-oil, etc. Artificial opening up (fracturing) of a formation, by pumping fluids under high pressure, to increase permeability and flow of oil to the well. The pumping in of acid solution to dissolve rocks in addition to fracturing the formation. Fracturing by pumping in liquid under pressure,

927

Frasch Process

exceeding fracturing pressure. Process to remove sulfur from a sulfur-bearing crude oil, by using cupric acid, developed by Herman Frasch. G

Gage Ticket Gager

Written record of the volumetric quantity of fluids in the tanks kept by gauger or pumper. Person who measures the amount of fluid in lease storage tanks and/or the quantity of material entering the sales line.

Gas

free gas gas cap natural gas solution gas sour gas Gas Drilling Geophones Go-Devil Gun Barrel Tank

Gum

Gas present in a vapor state. Pocket of free gas trapped in the reservoir. Gas associated with oil in a reservoir. Gas dissolved (in solution) in reservoir liquids. Natural gas containing hydrogen sulfide (H2S). Use of compressed natural gas instead of liquid as the circulation medium in rotary drilling. Microphones placed near the earth's surface to detect seismic waves. A device sent through a pipeline for cleaning purposes (see Pig). A settling tank placed between the pumping unit and other tanks, normally fitted with a trap at the top to separate gas from the liquids. Naturally-occurring or synthetic hydrophilic colloids used to control various properties of drilling fluids. H

Head (fluid)

Holiday Horsehead

Hydrocracking Hydrophones Hydrostatic Head

h = P/7, where h = head of fluid (e.g., in ft), p = pressure (i.e., in lb/ft2), and 7 = specific weight of fluid (e.g., in lb/ft3). Gap left in the protective coating of painted tanks. End of a pumping beam to which the polished rod is attached, the sucker rods are screwed into the polished rod. Method of cracking or breaking up of long-chain hydrocarbons. Waterproof microphones used to detect seismic echoes at sea. Pressure (p) exerted at the bottom of a column of liquid, p = ~, x D, where 7 = the specific weight of liquid, e.g., in lb/cu ft; and D = depth, e.g., in ft.

928

Independent(s)

Companies engaged in a certain phase of the petroleum industry, without being a part of one of the larger oil companies. Inflow Performance Plot of the flowing bottomhole pressure versus the Relationship, flow rate (q), greatly influenced by the reservoir drive IPR mechanism. Injection Placing fluids into the reservoir under pressure. carbon dioxide injection Compressed CO 2 is injected into the formation to supply energy to push the oil toward the producing wells and also to improve recovery by mixing with both the oil and water. caustic injection Adding caustic to the water being injected to improve oil recovery by forming oil-water emulsions that help plug off the larger pore channels, giving a more even push to oil in moving it toward the producing wells. Also reduces interfacial tension and increases the relative permeability to oil. Irreducible Fluid Saturation Equilibrium saturation of the wetting phase, which cannot be lowered by flowing indefinitely a nonwetting phase through a porous medium, providing evaporation does not take place. In-Situ Combustion Enhanced recovery technique by starting a fire at the injector to generate heat and gas to drive oil toward the producing wells. Integrated Company An oil company engaged in several phases of petroleum industry, e.g., production, refining, marketing, and shipping. Internal Yield Minimum internal pressure to burst casing (pipe).

Jeep Joint

Device for detecting gaps in the protective coating of a pipeline. Single section of a pipe. K

Kelly

A hollow 40-fl long pipe, having four or more sides and threaded connections at each end to permit it to be attached to the swivel and to the drillpipe. It transmits torque from the rotary drilling table to the drillstring. L

LACT (Lease Automatic Custody Transfer)

Fully automated tank battery that records and ships oil and gas into a gathering pipeline.

929 Latent Heat of Vaporization Btu's required to vaporize 1 lb of a liquid at its atmospheric boiling point. Lease Legal document which gives one party rights to drill and produce oil on real estate owned by another party. Various methods of lifting oil to the surface. Lift Mechanism(s) Any mechanism, other than natural, that lifts fluid to artificial lift the surface. Device using a cable, often from a tower, instead of a cable lift walking beam to lift the sucker rods. Downhole electric motor and pump, which are used electric submersible lift for high volumes of fluid production. Injection of gas into the well to lift fluids out of the gas lift wellbore. Use of hydraulic pressure to activate the downhole hydraulic lift pump. Use of solid metal rods to activate the downhole rod lift (or pumping) pump. Any lifting equipment at the surface such as a pumpsurface lift ing unit. Volatile components (or fractions) of petroleum. Lighter Ends Instructions that include names of owners of the Line List property, length of pipeline and any special instructions or restrictions. Pipeline inspector who examines the pipeline along its Linewalker extension, looking for evidence of leaks, corrosion, etc. Continuous record of certain data obtained from a Log logging tool lowered into the wellbore. Measurements of porosity, cement bonding and acoustic log lithology by use of sonic waves. Determination of the inside diameter of a wellbore or caliper log casing. Measurement of the formation conductivity. conduction log Measurement of formation porosity. Involves bomdensity log barding the formation with gamma rays, with detectors measuring the number of gamma rays that are reflected from the formation. Continuous recording of types of cuttings, gas and oil drillers log occurrences while drilling the well. Measures the electric characteristics of a formation; electric log the tool transmits signals to the surface. Measurement of the natural formation radioactivity to gamma ray log determine lithology. Measurement of the formation resistivity response to induction log an induced current. Measurements of porosity, type of fluids and/or gas, nuclear log

930

neutron log

pressure log production log

resistivity log

lithology, etc., by recording the nuclear properties of the formation. Measurement of porosity; also valuable information concerning rock composition and fluid content. The logging tool bombards the formation with neutrons. Measurement of the formation pressure at various depths. Measurement of the production status of a completed well. Yields information on the nature and movement of fluids within the well. Defines the reservoirs contents. Electric current flows in the formation between two electrodes on a logging tool and measures resistivity between those two points.

sonic log (see Acoustic Log) spontaneous potential, SP Measurement of the difference in potential between the formation and the earth's surface ~ identification of rock types. temperature log Measurement of the formation temperature at various depths. Recording of data (various physical, chemical, and Logging mechanical properties of a reservoir) obtained by lowering of various types of measuring tools into a wellbore. M

Mandrel Mouse Hole

Mud Mud Logger Mud Program Multiple Completions Miscible Drive Miscible Mixture Mobility

Device used to bend the pipe without deforming it. Shallow hole drilled on one side of a drilling rig to store the next joint of pipe to be added to the drilling string. See Drilling Mud. Person who analyzes the cuttings brought up by the drilling mud while drilling the well. Plan of supplying and using drilling fluids and their additives during the drilling process. Several producing zones completed for production through one well. Fluid displacement in which the displacing fluid and the displaced fluid become miscible in all proportions. Complete mixture of fluids: single phase. The ability of a fluid to move through a reservoir. N

Naphtha

Petroleum distillate used as a cleaning fluid, for

931

Natural Gas

Natural gasoline

example. A naturally-occurring mixture of hydrocarbon and nonhydrocarbon gases found in porous media at depth. It is often associated with crude oil. Composed mainly (z 70 to 96%) of methane gas. A condensate of natural gas: "Casinghead gasoline". O

Occupational Health and Federal law covering working conditions and health Safety Act of 1971 (OSHA) and safety of workers in industry and business. Octane Number A measure of anti-knock quality of gasoline. The higher the rating the lower the knock. One hundred octane number indicates that gasoline will perform as a pure octane. Oil String The casing in a well that runs from the surface to the zone of production. Oil Treater (also Heater Equipment used to separate natural gas, BS&W and Treater) water from the oil by the use of heat. Olefins Class of unsaturated hydrocarbons (one double bond), such as ethene, (CznH4n). Organization of Petroleum Middle Eastern, South American and African counExporting Countries tries with large petroleum reserves that have joined (OPEC) together to control production and marketing (pricing) of oil. Override Additional royalty payment in excess of the usual royalty. Overburden pressure Total pressure, Pt, exerted on a reservoir by the weight of the overlying rocks and fluids. It is balanced by the pore pressure, pp, plus the grain-to-grain stress, pg (or effective pressure, p e ) " p t = rDp + rDe . Oxidation Process in which a given substance loses electrons or a share of its electrons. P

Packer

Paraffins Pay Sand Perforating knife perforating

Mechanical device set in the casing (attached to the tubing) to prevent communication between the tubing and annulus. Group of saturated aliphatic hydrocarbons (CnHzn+2). Paraffin also denotes a solid, waxy material. The zone of production where commercially recoverable oil and/or gas are present. Making holes in the casing (or liner) so that gas and fluids can enter the wellbore. Holes are made in the casing by a mechanical device (kuife).

932 Perforating the casing by shooting bullets. Perforating the casing by jets. A measurement of the ease of flow of fluids through porous media. Permeability is equal to one Darcy if 1 c m 3 o f fluid flows through 1 cm 2 of cross-section of rock per second under a pressure gradient of 1 atm/ cm, the fluid viscosity being 1 cP. A measure of the ability of the porous medium to effective permeability transmit a particular fluid at the existing saturation, (of a porous medium which is normally less than 100%. to a fluid) Ratio of the effective permeability at a given saturarelative permeability tion of that fluid to the absolute permeability at 100% saturation (k). The terms k ro (ko /k), k r g (k g /k) ~ and kr w (k/k) denote the relative permeabilities to oil, to gas, and to water, respectively, k is the absolute permeability, often the single-phase liquid permeability. Working surface or deck of a drilling rig. Platform Device sent though pipelines to clean it. Pig (see Go-Devil) Pipeline crew who prepare and line up the pipe, and Pipe Gang make the initial welds. Device for bending small-diameter pipes without Pipe Shoe deforming them. Person who measures the amount and quality of oil Pipeline Gager entering the gathering lines from lease tanks. Pipelines from the lease tank batteries to the lease Pipeline - Gathering shipping line. The main line. Pipeline- Trunk Working area for cleaning, coating and storing pipe. Pipeyard Catalytic reforming unit to convert the low-quality oil Platforming to higher octane products. "Plugging off" or stopping production from a lower Plug Back portion of a producing oil well. Compounds having many repeated linked units. Polymers Primary Drive Mechanism The predominant reservoir drive mechanism when more than one drive mechanism is present. The difference in pressure at two given points, divided Pressure gradient by the distance between these two points. Period (time) that the lease covers. Primary Term Total removal of fluids using only the initial reservoir Primary Recovery energy, q Productivity Index (PR or J) It is equal to PR = J = - - , where q = flow rate Pr -- Pwl

gun perforating jet perforating Permeability

Pumper

(bbl/D); pr = average reservoir pressure (psia); and Pwf = flowing bottomhole pressure at the wellbore (psia). Person in charge of production and records for a

933

Pumping Pumping Rig, Standard Pumps ball pump centrifugal pump plunger lift pump

sonic pump

Pumping Off Pumping Stations

producing well or group of wells. Lifting fluids from the production well to the surface by an artificial lift method. Conventional pumping unit using a walking beam to raise and lower the sucker rods. Mechanical devices which lift fluids to the surface. Pump using a ball and seat to lift fluids. Pump using rotating impellers to lift fluids. A plunger that is driven up the tubing by the produced gas, and then falling by gravity to the bottom of the tubing to lift another load of fluid. Downhole pump that generates sound waves resonating on the tubing which lifts by opening and closing a series of check valves. Pumping the reservoir fluids out of the well faster than they can enter the wellbore. Pumps placed along a pipeline at intervals to maintain the pipeline pressure and flow. R

Radial Flow Rat Hole Rate of Penetration Recovery primary recovery secondary recovery tertiary recovery

Reduced Temperature

Two-dimensional flow from all points around a 360 ~ circle within a formation to a centered well. Shallow hole drilled next to a drilling rig where the Kelly is stored when not in use. Speed with which the drilling bit cuts through the formation. The petroleum produced from the reservoir in % (or fraction) of the total oil-in-place. The production obtained using the initial reservoir energy. The production obtained by introducing a second source of energy, i.e., waterflooding. The production obtained by introducing a third source of energy, i.e., enhanced oil recovery, such as thermal, CO 2 flooding, surfactants, polymers, alkaline flooding, in-situ combustion, and DC electrical current. The absolute temperature divided by the absolute critical temperature T = T/T. The absolute pressure at which the gas exists divided by the absolute critical pressure, P/Pc" Rearranging the carbon and hydrogen molecules by use of catalysts and heat. r

Reduced Pressure Reforming Relative Permeability (see permeability) Reservoir

r

A porous and permeable rock formation or trap

934

Residuals Residuum Rod Rotary Drilling Roughneck Royalty Run Run Ticket

holding an accumulation of gas and/or oil. "Left over" materials in boilers or refinery vessels. Sticky, black mass left in bottom of a refining vessel. Sucker rod is attached to the downhole pump, usually having a length of 16 89ft. A drilling method that imparts a turning or rotary motion to the drill string to drill the hole. Member of a drilling crew who assists the driller. Fee paid to the owner of a lease based on the volume of production. Delivering (or transferring) oil from the lease tank battery to the pipeline or tank truck. Amount and quality of the run: a written record. S

SIDPP SI Samples bottom sample composite sample running sample

spot sample water and sediment sample Saturation Scratchers

Screen Liner

Scale Inhibitor

Sediment

Shut-in drillpipe pressure. Shut-in, term often used for wells that are no longer producing. Small volumes of oil drawn from a tank for testing. Sample obtained from the lowest point in the tank. Sample composed of equal portions of samples obtained from two or more points in the tank. Sample taken by lowering an unstoppered beaker from the top outlet level to the bottom outlet and returning it at a uniform rate of speed so that it is about three quarters full when returned. Sample obtained from a particular level of the tank. Sample of oil taken for obtaining the water and sediment content, usually by centrifuging. Percentage of a particular fluid in a porous medium, expressed as the percent of the pore volume. Mechanical devices placed on the outside of the casing to clean the drilling mud cake from the sides of the wellbore prior to cementing in order to improve the cement bond between the casing and the formation. Perforated pipe or wire mesh screen placed at the bottom of the well to prevent larger formation particles from entering the wellbore. Chemicals introduced into the producing well to prevent the buildup of scale, paraffin, etc. These can block off the flow of fluids and gas into the wellbore. Particulate material (clay, silt, etc.) that is carried along with the produced fluids and settles to the bottom of the tanks.

935 Secondary Recovery (see recovery) Separator

Equipment for separating the crude oil from the natural gas and water. The primary function of the Separator is to produce gas-free liquid and liquid-flee gas. Drilling a new section of wellbore parallel to a previSidetracking ously drilled hole but blocked with junk. Marine drilling rig that can either be anchored to the Semi-Submersible bottom of sea or maintained at a given position. Centrifuging to separate water, oil, and BS&W that Shaking Out may be present in a sample. Mechanical device for separation of rock cuttings Shale Shaker from the drilling fluid as it arrives at the surface. Sidetracked Well Well drilled out from the side of a previously drilled well. Sidewall Cock Valve placed on the side of a tank for the purpose of obtaining small oil samples. Solution Gas Gas dissolved so thoroughly in the oil that the solution formed is one phase. Sour Gas (or Oil) Gas or oil which contains hydrogen sulfide. Specific Heat Quantity of heat (e.g., in Btu' s) required to raise the temperature of a unit weight of material (e.g., 1 lb) one degree (temperature, e.g., I~ Specific Surface Surface of pores and pore channels per unit of pore volume (commonly), per unit of bulk volume, or per unit of grain volume. The above information m u s t be supplied by the investigator. Surfactants (in stimulation) Chemicals that prevent stimulation fluids from forming emulsions with reservoir oil. Swabbing Raising and lowering rubber cups in the tubing to recover liquids- "bicycle pump" action. Sweet Gas (or Oil) Gas or oil devoid of hydrogen sulfide. T Torque Tortuosity (~)

Turning or twisting force on a drilling string. Square of the ratio of the effective length, Le, to the length parallel to the overall direction of flow of the L pore channels, z = (_~__)2.

Tour

Shift of duty at well site (normally 8 hours and pronounced as "tower"). Arrangement of pulleys on the drilling rig with an attached hook, which moves up and down on cables running through the crown block.

Traveling Block

936 Trip Turbodrills

Process of pulling drillstring (or tubing) out of the borehole and then running it back in. A rotary drilling method in which fluid pumped down the tubing turns the drill bit. The downhole motor consists of multistage vane-type rotor and stator section, bearing section, drive shaft, and bit-rotating sub. V

Viscosity

Measure of the internal resistance of a fluid to flow. Viscosity is equal to the ratio of shearing stress, x, to the rate of shearing strain. Considering a flow between two parallel plates, ~t = (F/A): (V/h), where: F = force required to move the upper plate, having an area, A. V= velocity of upper plate; velocity of a thin layer of fluid adhering to the lower plate is zero. h = distance between plates. W

Water Shut-Off Test (WSO) A test that ensures there is no communication above and below a selected interval in a well. Weight Indicator Device that constantly measures the weight of the drillstring on a drilling rig. Wireline A rope made from steel wire. Workover Remedial work on a well, i.e., cleaning, repairing, servicing, stimulating, etc., after commencement of production. Z Zones of Lost Circulation

Openings in the formation (fractures, etc.) into which the drilling mud is lost without returning to the surface during the drilling operations.

937 RECOMMENDED REFERENCES Berger, B. D. and Anderson, K. E., 1978. Modern Petroleum, A Basic Industry Primer. Petroleum Publishing Co., Tulsa, OK, 293 pp. Chilingarian, G. V., Robertson, J. O. Jr. and Kumar, S., 1987. Surface Operations in Petroleum Production, L Developments in Petroleum Science, 19A. Elsevier, Amsterdam, 821 pp. Chilingarian, G. V., Robertson, J. O. Jr. and Kumar, S., 1989. Surface Operations in Petroleum Production, II. Developments in Petroleum Science, 19B. Elsevier, Amsterdam, 562 pp. Chilingarian, G. V. and Vorabutr, P., 1981. Drilling and Drilling Fluids. Developments in Petroleum Science, 11. Elsevier, Amsterdam, 767 pp. Langnes, G. L., Robertson, J.O. Jr., and Chilingar, G. V., 1972. Secondary Recovery and Carbonate Reservoirs. Am. Elsevier, New York, 304 pp. Skinner, D. R., 1983. Introduction to Petroleum Production. Drilling, Well Completions, Reservoir Engineering. Vol. 1., Gulf Pub. Co., Houston, TX, 190 pp.

This Page Intentionally Left Blank

939

Appendix C FUNDAMENTALS OF SURFACE AND CAPILLARY FORCES G.V. CHILINGARIAN, J.O. ROBERTSON JR., G.L. LANGNES and S.J. MAZZULLO

INTRODUCTION

Wettability may be defined as the ability of the liquid to "wet", or spread over, a solid surface. Figure C-1A shows a liquid wetting a solid surface, whereas Fig. C-1B shows the relationship between the liquid and solid when the liquid has little affinity for the solid. In Fig. C-1C, the liquid drop occupies an intermediate position. The fluid which wets the surface more strongly occupies the smaller pores and minute interstices in a rock.

e < 90-

o > 90-

SOLID

$

A

8

o

99 0 ,

C

Fig. C-1. Different degrees of wetting of solid by liquid.

INTERFACIAL TENSION AND CONTACT ANGLE

The angle which the liquid interface makes with the solid is called the contact angle, 0. Usually, it is measured from the solid through the liquid phase (if the other phase is a gas) and through the water phase if oil and water are both present. In a capillary tube, shown in Fig. C-2A, the angle between the side of the tube and the tangent to the curved interface (where it intersects the side of the tube) is less than 90 ~ For a capillary depression, shown in Fig. C-2B, the contact angle is greater than 90 ~ In the case of no rise or depression, the angle is 90 ~ (Fig. C-2C). Interfacial tension, 0, is caused by the molecular property (intermolecular cohesive forces) of liquids. It has the dimensions of force per unit length (lb/ft or dynes/ cm), or energy per unit area (ergs/cm2). On considering an element of a surface having double curvature (R~ and R2), the sum of the force components normal to the element is equal to zero (Fig. C-3). The pressure difference, pz-p~, is balanced by the

940

I A

B

C

Fig. C-2. Behavior of various fluids in glass capillary tubes. A = water, B = mercury, and C = tetrahydronaphthalene (when glass is perfectly clean and liquid is pure).

2~ 2 '

" "! I_

_1 dx

/'"'-,~ I'" N Crdx

Fig. C-3. Surface tension forces acting on a small element on the surface having double curvature, (P2 = Pl + yh). (See Binder, 1962, and Vennard, 1961.)

interfacial tension forces: (P2-P~) dydx = 2 a dy sin02 + 2 a dx sin0~

(C-l)

If the contact angles 0~ and 02 are small, then the following simplifications m a y be made:

@ sin01 = ~ 2R~ and:

(C-2)

94 1

Fig. C-4. Rise of water in glass capillary tube. (See Binder, 1962, and Vennard, 1961.)

Therefore, Eq. C- 1 becomes: 1

1

P 2 - P I = o(-+-) R2 R ,

For a capillary tube (Fig. C-4):

R, =R,=R d cose = 2R

and

P, = P,+ Yh

(A3-7)

942

.O' o

SOLID Fig. C-5. Shape of water drop resulting from interfacial tension forces. where ? = specific weight of fluid, d = diameter of capillary tube, and h = height of capillary rise. Thus, Eqs. C-4 through C-7 may be combined to yield the following expression for capillary rise, h" h=

4or cos0 ~,d

(C-8)

Equation C-8 can also be derived on considering the equilibrium of vertical forces. The weight of fluid in the capillary tube, W, which is acting downward, is equal to: W = zr d2hy 4

(C-9)

The vertical component of interfacial tension force acting upwards is equal to: F t r y = rcdcr cos0

(C- 10)

Equating these two forces and solving for h gives rise to Eq. C-8. In reference to Fig. C-5, the interfacial tensions can be expressed as O-ws+ Crwocos0+~o

(C-11)

where Crw~,Crwo,and %o = interfacial tensions at the phase boundaries water-solid, water-oil and solid-oil, respectively, or O-so cr cos0 = - O'wo

ws

(C- 12)

As shown in Fig. C-6A, when a solid is completely immersed in a water phase, 0 = 0 ~ cos0 = 0, and consequently, "wo

=or s o - o r w s

(C-13)

943 e : O*

O : 90 ~

e:180* 0

OIL

e W

W

8

C

9 WATER

A

Fig. C-6. Illustrations of 0~ 90~ and 180~contact angles. When half of the solid is wet by water and the other half by oil (Fig. C-6B), 0 = 90 ~ cos0 = 0 and thus ~o = Crws.

(C-14)

On the other hand, if the solid is completely wetted by oil (Fig. C-6C), 0 = 180 ~ cosO 1, and

-

crSO = crWS - crWO

(C-15)

If 0 < 90 ~ the surfaces are called hydrophilic and when 0 > 90 ~ they are called hydrophobic. An interfacial tension depressant lowers Crwo,whereas a wetting agent lowers 0 or increases cos0. A decrease in crw o does not necessarily mean an increase in cos0, or vice versa, because of the changes in crSO and crWS . I f a rock is completely water wet ( 0 = 0~ water will try to envelop all of the grains and force all of the oil out in to the middle of the pore channel. Even though some oil may still be trapped in this case, the recovery would be high. On the other hand, if all of the solid surfaces were completely oil wet (0 = 180~ oil would try to envelop all of the grains and force all of the water out into the center of the pore channel. In this extreme case, recovery would be very low by water drive. Many oil-wet reservoirs are known to exist. In the usual case (0 ~ < 0 < 180~ to improve waterflooding operations the contact angle 0 should be changed from > 90 ~ to < 90 ~ through the use of surfactants. This would move the oil from the surface of the grains out into the center of the pore channels, where they would be produced more readily. Contaminants or impurities may exist in either fluid phase and/or may be adsorbed on the solid surface. Even if present in minute quantities, they can and do change the contact angle from the value measured for pure systems (see Marsden, 1968).

944 EFFECT OF CONTACTANGLE AND INTERFACIAL TENSION ON MOVEMENT OF OIL For an ideal system composed of pure liquids, the advancing contact angle should equal the receding angle. Because of the presence of impurities within the liquids, however, the advancing contact angle is greater in most systems. The advancing contact angle is the angle formed at the phase boundary when oil is displaced by water. It can be measured as follows: the crystal plate is covered by oil and then the water drop is advanced on it. The contact angle is the limiting angle with time after equilibrium has been established (Fig. C-7). The contact angle formed when water is displaced by oil is called the receding angle (Fig. C-8). The contact angles during movement of a water-oil interface in a cylindrical capillary, having a hydrophilic surface, are shown in Fig. C-9. Inasmuch as a reservoir is basically a complex system of interconnected capillaries of various sizes and shapes, an understanding of flow through capillaries is very important. In Fig. C-10, a simple two-branch capillary system is presented. If a pressure drop is applied, then the water will flow more readily through the large-diameter capillary than it will through the small-diameter one. Thus a certain volume of oil may be trapped in the small capillary when water reaches the upstream fork. Poiseuille's law states that:

WA1 ER SOLID OIL Fig. C-7. Contact angle: plate is first immersed in oil followed by the placement of water drop on top.

W&TER

Fig.C-8. Contact angle: plate is first immersed in water followed by placing a drop of oil underneath.

945

OIL

I~i IN,

-

/O

/

W~TER

9o

Fig. C-9. Changes in contact angle as a result of movement of water-oil interferface. 0 = contact angle at static position; O = contact angle when oil is displaced by water (advancing angle); and 0b = contact angle when water is displaced by oil (receding angle).

TRAPPED

OiL Gt ORtJl F

- - .

W~,T ER

/-... Fig. C- 10. Flow through a two-branch capillary and trapping of oil in a small-diameter capillary.

~d4 ~Pt q =

128 ,uL

(C-16)

and q d 2 Ap, v= ~ = ~ A 32/.tL

(C-17)

w h e r e q = v o l u m e t r i c rate o f flow, cm3/sec; d = d i a m e t e r o f capillary, cm; A P t -- total p r e s s u r e drop, dynes/cm2; A = cross-sectional area, cm2; ~t = viscosity, cP; L = flow path length, cm; v = velocity, cm/sec. The capillary pressure, Pc, is equal to:

946 p = 4rrcos0 c d

(C-18)

where rr = interfacial tension between oil and water, dynes/cm; d = diameter of capillary, cm; and 0 = contact angle, degrees. The total pressure drop, APt, is equal to: (C- 19)

APt -- APi + P

where APi-" applied pressure, dynes/cm 2. Solving for v in each capillary, by combining Eqs. C- 17, C- 18 and C- 19 gives: all2

vl

=

32/.tiLl

(APi+ 4or cos0)

(C-20)

dI

and

d22 (APi+

v2 = 32~t2L2

4rr cos0 dE )

(C-21)

Setting L~ = L 2 and/.t~ =/~2, and dividing Eq. C-20 by Eqs. C-21 gives the following relationship: V1

v~

=

d12 APi + 4 o r c o s 0 d

1

d d Api + 4or cos0a~

Therefore, when

(C-22)

Ap, >> P :

V1 dl 2 ~z~ V1 d22

(C-23)

and when @ i << Pc" v~ d~ ~z~ v~ d 2

(C-24)

As shown in Fig. C-11, the sum of forces acting on the trapped oil globule may be expressed as"

~] F = F, + G - G

(c-25)

where: F = rd2 zip, 4

(C-26)

947

9

, ,

.

WATER ~

.

~Fz --~ ,

.

.

OIL

,,

,,

F3 ,,

WATER

,,,

db

f

o"o Fig. C-11. Forces acting on a trapped oil globule in a capillary.

zrd2

F, = ---4- Ap~

(C-27) a)

(C-28)

F 3 = 1rd2(4or bCOS0b)

(C-29)

F 2 = ffd 2 (40"aCOS0

Thus: Apt = Ap/-~-

(4o-acos0 a) d

-

(4or bCOS0b) d

(C-30)

Because the receding angle is usually less than the advancing angle, the capillary pressure not only does not help, but hinders the flow. The term (4or bCOS0 b/d) is usually greater than (4or acos0/d) because 0b < 0a. If a surfactant were added at the left to reduce era, APt would become less and the oil globule may eventually move to the left in Fig. C- 11 when APtbecomes negative. The quantity of trapped oil is dependent upon the value of cr cos 0 at each end of the globule as well as upon z~pi (imposed pressure drop). Inasmuch as the contact angle depends upon the interfacial tensions, which, in turn, may be influenced by surfactants, these chemicals may alter recovery by altering both the contact angle and interfacial tension. As the oil is displaced by water, which wets the rock surfaces, capillary pressure is a driving force. If, on the other hand, water does not wet the rock surface, then the capillary pressure is a retarding force which must be overcome. The magnitude of capillary pressure in pores having a radius of around 15 microns is not large and, therefore, capillary pressure is not an important force during the movement of oil-water contact, providing there is no mixing. The movement of oil and water in a reservoir, however, results in the formation of water-oil and gas-wateroil mixtures (see Muravyov et al., 1958). The amount of gas coming out of solution

948

SOLID

P2

/

\a2

\

P,

SOLID

Fig. C-12. Movementof gas globule through a constriction. (After Muravyovet al., 1958.) during migration is greater with increasing amount of dissolved active substances, with increasing surface area of porous medium (i.e., with decreasing permeability), and with decreasing temperature. As the oil-water-gas mixtures move through pores, the gas bubbles and water droplets are deformed on passing through constrictions (Fig. C-12) (see Muravyov et al., 1958). In order to move, the gas globule as shown in Fig. C-12 must overcome the capillary pressure equal to: _ 20"

Ap = Pl--P2

Rl

20" _ 2 o " ( 1 - 1 )

R---~

R1

(C-31)

R2

Although the Ap may be very small for a single globule, the cumulative resistance of many bubbles may be large (Jamin effect). Additional resistance to flow is created by the polymolecular layers of oriented molecules of surface-active components in the oil, which are adsorbed on the rock surface and may be quite thick (10 -3 to 10-4 cm). At a constant pressure differential, the rate of oil filtration through porous media diminishes with time and is more pronounced in the case of higher content of polar compounds in the oil. In water-wet carbonate rocks, vugs are "bad news" because during the waterflooding operations oil is trapped in the vugs. On the other hand, in oil-wet rocks, vugs are "good news" because water (non-wetting phase) will displace oil from the vugs. It should be remembered that the non-wetting phase preferably flows through larger pores.

949 WATER BLOCK

The minimum pressure, Pcwb,required for oil to displace a globule of water stuck in a pore throat between the rock grains, providing the oil is the wetting phase, is equal to:

Pwb = Cr@ + 1---)c~

(c-32)

where cr = interfacial tension between oil and water; r~ and r 2 = radii of capillary in two perpendicular directions; and 0 = contact angle. The above equation can be derived from Eq C-4" (C-33) R 1 R2 where Ap is the pressure difference across the oil-water interface, and R 1 and R 2 are the curvatures of interface in two perpendicular directions, by substituting rl/cosO for R~ and r2/cosOfor R 2. If cr = 25 dynes/cm, 0 = 30 ~ r 1 = 0.0001 cm and r 2 = 0.00001 cm, then Pwb = 34.5 psi. By reducing interfacial tension between oil and water to 0.5 dynes/cm, using a surface-active agent (surfactant), for example, Pwb will be lowered to 0.69 psi, and the water block can be easily broken.

REFERENCES Binder, R. C., 1962. Fluid Mechanics, 4th ed. Prentice-Hall, Englewood Cliffs, N.J.,453 pp. Marsden, S. S., 1968. "Wettability": The elusive key to waterflooding. Pet. Engr., (Apr.):82-87. Muravyov, I., Andriasov, R., Gimatudinov, Sh., Govorova, G. and Polozkov, V., 1958. Development and Exploration of Oil and Gas Fields. Peace (Mir) Publishers, Moscow, 503 pp. (in English.) Vennard, J. K., 1961. Elementary Fluid Mechanics, 4th Ed. Wiley, New York, N.Y., 570 pp.

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951

Appendix D SAMPLE QUESTIONS AND PROBLEMS G.V. CHILINGARIAN, J.O. ROBERTSON JR. AND S.J. MAZZULLO

GENERAL GEOLOGY

1. Before using compressibility data, what questions should be answered? 2. How would you predict abnormally high formation pressures in carbonate reservoirs? 3. (a) In an anticline, draw the oil-water contact if shaliness in a carbonate reservoir increases towards the flank, whereas porosity decreases. (b) If the oil-water contact in this particular reservoir tilts in the opposite direction, what would be the possible reasons? Explain why. 4. Show diagrammatically, the classification of carbonate rocks based on intercommunicating porosity and speed of sound. 5. Based on differential entrapment theory, if a reef contains water (1/3), oil (1/3), and gas (1/3), what could the reef updip contain? 6. How would you predict abnormally high formation pressures using chemistry of interstitial solutions? 7. Explain differential entrapment of oil and gas theory. Draw a schematic diagram. 8. According to Chilingar's classification, what would you call a carbonate rock having Ca/Mg ratio of 40? 10. What does decrease in Ca/Mg ratio of carbonate rocks during diagenesis and catagenesis indicate? List all possibilities. 11. Name the following carbonate rocks: (a) containing 60% skeletal fragments and 40% micrite; (b) containing 91% coated grains (oopellets) and 9% micrite; and (c) GMR = 7.2/2.5, with detrital grains. 12. Define epigenetic dolomites and explain the Ca/Mg ratio distribution in such rocks. Reference: Larsen, G. and Chilingar, G.V. (Editors), 1967. Diagenesis in Sediments, Elsevier Publ. Co., Amsterdam.

SOURCE ROCKS

1. Do you believe that carbonate rocks could act as source rocks? Why? 2. Compare carbonates and shales as source rocks of petroleum, and list all differences. Reference: Chilingar, G.V., Bissel, H. J. and Fairbridge, R.W. (Editors), 1967. Carbonate Rocks (Physical and Chemical Aspects), 9B Elsevier Publ. Co., Amsterdam, pp. 225 - 251.

3. What relationship exists between insoluble residue and organic matter in carbonate rocks?

952 Reference: Chilingar, G.V., Bissel, H.J. and Fairbridge, R.W. (Editors), 1967. Carbonate Rocks (Origin, Occurrence and Classification), 9A Elsevier Publ. Co., Amsterdam, pp. 8 7 - 168.

4. Discuss in detail all geochemical techniques for recognizing carbonate source rocks. Reference: Chilingar, G., Bissel, H.J. and Fairbridge, R.W. (Editors), 1967. Carbonate Rocks (Origin, Occurrence and Classification), 9A Elsevier Publ. Co., Amsterdam, pp. 8 7 - 168.

CAPILLARY PRESSURE

1. What effect does dolomitization have on capillary pressure correlations? 2. For two different cores having the same Pc 5~(pressure necessary to fill 50% of the pores with the nonwetting phase) draw a schematic diagram of pressure versus precentage wetting phase saturation curves if one core has better sorting than the other. Explain! 3. What relationship exists between Pd (pressure at which nonwetting phase is present in the pore system as a continuous phase), ps0, permeability, and mean pore throat size. Discuss! 4. What does a capillary pressure hysteresis loop show? Reference: Pickell, J.J., Swanson, B.E and Hickman, W.B., 1966. Application of air-mercury and oil-air capillary pressure data in the study of pore structure and fluid distribution,./. Pet. Tech, 237(3):55 -61.

5. What effect does dolomitization have on capillary pressure correlations? Reference: Rockwood, S.H., Lair, G.H. and Langford, B.J., 1957. Reservoir volumetric parameters defined by capillary pressure studies, J. Pet. Tech, 210(9): 2 5 2 - 259.

6. Outline regularities in the relationship between the shape of capillary pressure curves and pore configuration (size and shape of pores, type and width of intercommunicating channels, etc.). 7. Draw mercury capillary pressure curves (schematic diagrams) which are representative of a poor and a good carbonate reservoir rock. Label and explain all parts of the curves. 8. Draw approximate schematic diagrams of capillary pressure versus wetting phase saturation curves for: (a) Dolomite: intercrystalline porosity = 20%, mean pore throat size = 0.0021 mm, size of pores (avg.) = 0.3 mm, sorting = 2.6 ~ units, and permeability = 98 mD. (b) Oolitic limestone: Intergranular porosity = 19%, mean pore throat size = 0.0035 mm, size of pores (avg.) = 0.19 mm, sorting = 6.6 ~ units, and permeability = 40 mD. (c) Oolitic limestone: Intergranular to vuggy porosity = 14%, mean pore throat size = 0.0004 mm, size of pores (avg.) = 0.3 mm, sorting = 3.5 ~ units, and permeability = 9 mD.

PERMEABILITY AND POROSITY

1. Draw the relative permeability curves for polar and nonpolar oil. Discuss the magnitude of oil and water recovery in the case of polar and nonpolar oil. 2. Derive Kozeny's Equation.

953 3. What are stylolites? Do they improve permeability or not? Why? 4. List all processes by which secondary porosity may form. Also show their favorable and unfavorable effects upon oil recovery. 5. Show imbibition relative permeabilities for a spectrum of wetting conditions (for different contact angles, 0). 6. Show relationship between the relative permeability and capillary pressure curves. Show location of water, oil+water, water-free oil, etc. zones. 7. Estimate the porosity of chalk at a depth of 1000 m (assume normal compaction). 8. During drilling operations in dolomitized Asmari Limestone, Iran, only granular material was recovered. How would you estimate the porosity? 9. Define "effective" permeability. How closely does it approach absolute permeability? Why? 10. Compare simulator-calculated permeabilities with and without considering capillary pressure. 11. A carbonate reservoir has a porosity of 16% (diagenetic dolomitization is evident). Vugs and fractures are present. What is the percentage porosity due to: (a) dolomitization, (b) fractures, (c) vugs? Why? Estimate the primary porosity. 12. What is the reason for high porosity (>30%) of chalk reservoirs at a depth where porosity due to normal compaction should be around 10%? 13. Define "effective porosity" as used in Russia. What are the advantages? 14. Determine the permeability of a given thin section using both Teodorovich's and Lucia's methods. Expalin the difference. Thin section should be provided by the Professor. 15. Discuss dissolution porosity and compare it with dolomitization porosity. What is the effect of dissolution and dolomitization on insoluble residue content and Ca/Mg ratio? Reference: Chilingar, G.V., 1956. Use of Ca/Mg ratio in porosity studies, Am. Assoc. Petrol. Geol. Bull., 40: 2256- 2266.

16. If total secondary porosity (vugs + fractures) is equal to 3%, estimate the porosity due to fractures. Show all calculations. 17. Why are porosity and permeability insensititive to percent mud-size matrix when a rock is 50-75% dolomite? Reference: Ham, W.E. (Editor), 1962. Classification of carbonate rocks (A Symposium),Am. Assoc. Pet Geol., Tulsa, OK.

18. Diagramatically show the relationship between porosity, permeability and percent dolomitzation. 19. Estimate the permeability of arenaceous dolomite, containing finely porous conveying channels, by using Teodorovich's method. The fine elongate pores are abundant, and the rock has an effective porosity of 10%. 20. Calculate permeability, using Teodorovich's method, if porosity = 13% and size of elongated pores = 0.25-1 mm (Type II good porosity, with pores of different sizes). 21. Would replacement of calcite by dolomite theoretically result in an increase or decrease in porosity? Show all calculations. The specific gravity of dolomite = 2.87 and of calcite = 2.71. 22. Is there an increase or decrease in porosity as aragonite is replaced by (a) calcite and (b) dolomite? Show all calculations. The specific gravity of aragonite = 2.95,

954 of calcite = 2.71, and of dolomite = 2.87. 23. Would relative permeabilities to oil and to water be higher or lower if sandstone contains considerable amount of carbonate particles? Explain for both krw and k ! Reference: Sinnokrot, A.A. and Chilingar, G.V., 1961. Effect of polarity and presence of carbonate particles on relative permeability of rocks, Compass of Sigma Gamma Epsilon, 38:115- 120.

24. Do oil-wet reservoirs tend to have higher or lower recovery than water-wet reservoirs? Explain! 25. Explain the criteria used to suggest the occurrence of cavernous porosity while a well is drilling. 26. Explain the concept of"depositional-facies specificity" of porosity. 27. What relationship exists between porosity, insoluble residue, and Ca/Mg ratio in carbonate rocks? Explain! Reference: Chilingar, G.V., 1956. Use of Ca/Mg ratio in porosity studies. Am. Assoc. Petrol. Geol. Bull., 40:2256 - 2266.

PRODUCTION

1. In relating pressure to H (fraction of coarse porosity occupied by gas) would the curves for high c o n s t a n t Rp/Rsi , ratio lie higher or lower than those for l o w e r Rp/Rsi 9. Why? 2. Diagramatically show the difference between Darcy and non-Darcy flow, relating velocity and pressure gradient. 3. What are the most and least efficient drive mechanisms in carbonate reservoirs? 4. Give Forchheimer's equation describing non-Darcy flow. How does one determine the turbulence factor? 5. Draw performance curves for closed and open combination-drive pools and discuss the differences. 6. Discuss the theoretical proposals of Jones-Parra and Reytor regarding the effect of withdrawal rates on recovery from reservoirs having the fracture-matrix type of porosity. Reference: Jones-Parra, Juan and Reytor, R.S., 1959. Effect of gas-oil rates on the behavior of fractured limestone reservoirs, Trans, AIME, 216(5):395- 397.

7. Estimate the initial oil- and gas-in-place for the "XYZ" pool given the following data. Can you explain the apparently anomalous GOR behavior? Reservoir D a t a - XYZ Pool Average porosity Average effective oil permeability Interstitial water saturation Initial reservoir pressure Reservoir temperature Formation volume factor of formation water Productive oil zone volume (net) Productive gas zone volume (net)

16.8% 200 mD 27% 3,480 psia 207~ 1.025 bbl/STB 346,000 acre-ft 73,700 acre-ft

955 Pressure-Production Data Average reservoir pressure (psia)

Cumulative oil production (STB)

Cumulative GOR (SCF/B)

Cumulative water production (STB)

3,190 3,139 3,093 3,060

11,170,000 13,800,000 16,410,000 18,590,000

885 884 884 896

224,500 534,200 1,100,000 1,554,000

Flash Liberation Data (pertains to production through one separator at 100 psig and 75~ Pressure (psia)

B (I~bl/STB)

Rs (SCF/STB)

Z

3,480 3,200 3,200 2,400

1.476 1.448 1.407 1.367

857 792 700 607

0.925 0.905 0.888 0.880

ENHANCED RECOVERY

1. In the case of waterflooding, what range of contact angles is favorable? Why? 2. List problems involved in predicting secondary recovery of oil from reservoirs with a well-developed fracture-matrix porosity system. 3. List the three porosity type systems that are commonly present in carbonate reservoir rocks. How do these systems differ from one another? What type of secondary recovery technique would you use in each case? Why? 4. Discuss the factors that affect the sweep efficiency of a miscible flood. Why would one anticipate sweep efficiencies to be lower for a miscible displacement in a massive limestone than for waterflooding? 5. Is the recovery of oil from vugular carbonates higher or lower if the rock is oil-wet or water-wet? Why? 6. Discuss the major operational problems associated with the waterflooding of carbonate reservoirs. 7. Discuss the problems associated with gas injection in carbonate reservoirs.

LOGGING

1. By using density logs, calculate S on assuming (a) limestone and (b) dolomite, when R w= 0.02, Rf= 20, and m = 2.2. Explain the difference in the values obtained forS. 2. What is the porosity of a clastic limestone that shows a sonic transit time on the log of 90 ~tsec/ft? w

956 3. When using Archie's formula (F = ~-") for determining porosity from log analysis, what values of cementation factor, m, are appropriate for carbonate rocks? Reference: Pirson, S.J., 1963.Handbook of Well Log Analysis, Prentice-Hall, Englewood Cliffs, N.J., pp. 23 - 24.

ACIDIZING

1. Given the following information, calculate the weight of dissolved pure limestone (or dolomite) and the radial distance acid will penetrate until it is spent: (a) Matrix acidizing of 40-ft-thick limestone producing section; (b) porosity = 0.16; (c) volume of acid = 600 gal of 15% hydrochloric acid; (d) spending time = 30 sec; (e) specific gravity of acid = 1.075; (f) pumping rate = 9 bbl/min.; and (g) wellbore radius = 4 in. Given also: chemical equation for the reaction between HC1 and calcite: CaCO 3 + 2HC1 ~ GaG12 + H 2 0 100 73 111 18

+ CO 2

44

(relative weights)

One thousand gallons of 15% by weight HC1 solution contains 1344.8 lb. of hydrochloric acid (1000 x 8.34 x 1.075 x 0.15). Chemical equation for the reaction between HC1 and dolomite: CaMg(CO3) 2 + 4HC1 ~ CaC12 + MgC12 + 2H20 + 2 C O 2 184.3 146 111 95.3 36 88 Reference: Craft, B. C., Holden, W.R. and Graves, E.D., Jr., 1962. WellDesign (Drilling and Production). Prentice-Hall, Englewood Cliffs, N. J., pp. 5 3 6 - 546.

2. What effect does enlargement of pores have on acid velocity and the surface/ volume ratio? Are these effects opposite in significance or not? Explain! 3. How are acid volumes and pumping rates determined for acidizing operations? 4. How much deeper would later increments of acid penetrate before being spent? Why? 5. On using stronger acid, does spending time decrease or increase? Why? 6. Is sludge formation more or less likely with stronger acid? Why? How can it be prevented? 7. In acidizing operations, what are the functions of (a) intensifier, (b) surfactant, and (c) iron retention additive? 8. How are pumping pressure and necessary horsepower determined in acidizing operations? 9. Is the spending time of acid lower or higher in the case of lower specific surface area? Why? 10. Calculate the specific surface area of a carbonate rock with porosity = 15%. permeability = 8 mD, and cementation factor, m = 1 (matrix acidizing). Use at least two different formulas. References: (1) Chilingar, G.V., Main, R. and Sinnokrot, A., 1962. Relationship between porosity,

957 permeability and surface areas of sediments, J. Sediment. Petrol., 33(3):7759 - 7765. (2) Craft, B.C., Holden, W.R. and Graves, E.D., Jr., 1962. Well Design (Drilling and Production), Prentice-Hall, Englewood Cliffs, N.J., pp. 5 3 6 - 546.

FRACTURING

1. Prove (using calculations) that fractures alone do not contribute much to reservoir rock porosity. 2. Calculate porosity (~), permeability (k) and fracture height (b), given the following data: J = 5 m3/d/atm; re= 600 m; B - 1.2; m = 9 cP, h - 15 m; and r w = 0.2 m. 3. The initial net overburden pressure is 2000 psi, whereas the final overburden pressure is 8000 psi. What is the final fracture capacity? 4. If the permeability of matrix is equal to 12 mD, whereas permeability of the whole large core is 35 mD, determine the width of the fracture present. Total width of the core - 5 cm. 5. Determine the pressure drop in a horizontal (and also vertical) fracture given the following data: (a) specific gravity of fluid flowing - 0.8; (b) NRe -- 5 , 0 0 0 ; (C) q = 10 ml/min.; (d) a - 9 mm; (e) b = 0.268 mm; (f) l - 15 cm; and (g) absolute roughness (e) -- 0.054. 6. Give a formula for determining porosity due to fractures using two saturating solutions having different resistivities. 7. Calculate the productivity ratio for a horizontal fracture if fracture width - 0.1 in., net pay zone thickness = 60 ft, permeability of propping agent in place = 32,000 mD, horizontal permeability = 0.6 mD, re/r w = 2 , 0 0 0 , and fracture penetration, rf/r e = 0.3. Reference" Craft, B.C., Holden, W.R. and Graves, E.D., Jr., 1962. Well Design (Drilling and Production), Prentice-Hall, Englewood Cliffs, N.J., pp. 483 - 546.

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959

A U T H O R INDEX

Aalund, L., 332, 333,534 Abbit, W.E., 676 Abernathy, B.F., 29, 30, 31, 35, 36, 37, 51,258, 283, 534, 539 Abou-Sayed, A.S., 354, 534 Abrassart, C.P., 533 Acuna, J.A., 433,534 Adams, A.R., 41, 51, 676 Adams, R.L., 340, 344, 540 Adams, W.L., 793 Adler, EM., 393,394, 397, 534, 542 Adolph, R.A.,227 Agarwal, R.G., 612, 613,614, 650, 657, 676 Agtergerg, F.E, 100 Aguilera, R., 8, 9, 10, 11, 12, 13, 14, 15, 51, 880, 899 Aharony, A., 388, 389, 392, 405, 534 Ahr, W.H., 306, 545 Aigner, T., 83, 98, 101 AIME, 198,226 Akins, D.W. Jr., 532 A1-Hussainy, R., 592, 593,595,676 A1-Muhairy, A., 333,534 A1-Shaieb, Z., 810,861 A1-Zarafi, A., 332,534 Alameda, G.K., 53 7 Alberty, M., 166, 221 Algeo, T.J., 456, 534 Alger, R.P., 228, 793 Allen, D., 158, 203,221 Allen H.H.,532 Allen, W.W., 532 Alpay, O.A., 8, 28, 51 Alsharhan, A.S., 74, 90, 96, 98, 1O0 Aly, A., 544 Ambrose, R.W. Jr., 678 Ameri, S., 334, 534, 676 American Petroleum Institute, 118, 128, 149, 167, 178, 201,221 Aminian, K., 594, 676 Amott, E., 136, 149 Amthor, J.E., 48, 51,810, 838, 845, 856 Anderson, A.L., 544 Anderson, B.I., 223 Anderson, G., 108, 149

Anderson, J.H., 804, 810, 840, 860 Anderson, K.E., 93 7 Anderson, R.C., 532 Anderson, T.O., 28, 51 Anderson, W.G., 873, 899 Anderson, W.L., 208, 221 Andresen, K.H., 235,502, 534 Andrews, D.P., 541 Andriasov, R., 949 Angevine, C.L., 84, 98 Anstey, N.A., 68, 98 Antonlady, D.G., 51 Arab, N., 264, 534 Araktingi, U.G., 359, 384, 534, 535, 886, 891, 899 Archer, D.L., 902 Archer, J.S., 106, 108, 149 Archie, G.E., 133, 147, 149, 155, 163, 164, 168, 177, 178, 184, 186, 188, 189, 190, 196, 197, 210, 217, 219, 221,481,534 Arifi, N.A., 681 Arkfeld, T.E., 226 Armstrong, EE., 28, 51 Armstrong, M., 902 Arnold, M.D., 9, 51 Aron, J., 224 Aronofsky, J.S., 260, 501,504, 534, 741,753, 769

Arps, J.J., 18, 20, 21, 23, 38, 51, 189, 221,534 Arribas, J.R.F., 859 Arya, A., 534 Atlas Wireline Services, 158, 169, 172, 180, 181, 189, 197, 198, 200, 205,207, 214, 222 Aubry, M.P., 100 Aud, W.W., 355, 356, 357, 534 Aufricht, W.R., 887, 899 Ausburn, B.E., 158, 215,222 Auzerais, E, 221 Avasthi, J.M., 55 Aves, H.S., 813,856 Ayesteran, L., 644, 677, 679 Ayoub, J.A., 676, 677, 678 Ayral, S., 152 Aziz, K., 546, 641,676

960 Babson, E.C., 251,252, 253,534 Bachman, R.C., 896, 900 Bachu, S., 888, 900 Back, W., 799, 856, 859 Backmeyer, L.A., 897,900 Bacon, M., 60, 101 Badley, M.E., 64, 65, 66, 68, 98 Bagley, J.W., Jr., 28, 54 Bajsarowicz, C., 151 Bakalowicz, M.J., 799, 800, 856 Baker, R.I., 534 Bakker, M., 8, 56 Baldwin, D.E., Jr., 28, 51 Balint, V., 812,856 Ball, M.M., 86, 98 Bally, A.W., 60, 98, 101, 103 Barbe, J.A., 302, 534 Barber, A.H.Jr., 285,302, 303,304, 305, 534 Barclay, W., 60, 101 Bardon, C., 52 Bardossy, G., 797, 807, 856 Barenblatt, G.I., 741,769 Barfield, E.C., 257,534 Barham, R.H., 679 Baria, L.R., 90, 99 Barnum, R.S., 297, 534 Baron, R.P., 52 Barr6n, T.R., 665, 676 Barton, C.C., 433,535 Barton, H.B., 532 Bashore, W.M., 433, 534, 535, 899 Baxendale, D., 679 Baxley, ET., 228 Bayer, J.E., 227 Be, A.W.H., 49, 55 Beales, EW., 56 Beals, R., 225 Beaudry, D., 93, 99 Bebout, D.G., 308, 309, 535, 538, 802, 813, 840, 856, 857, 858, 860, 861,885, 900 Beck, D.L., 52 BEG, 32, 33, 34, 54, 287,289, 290, 292, 293, 294, 298, 299, 302, 307, 308, 309, 310, 540

Behrens, R.A., 363, 364, 365,367, 368, 369, 378, 379, 387, 388, 433,452, 537, 539 Beier, R.A., 379, 387,432,535 Belfield, W.C., 810,856 Beliveau, D., 44, 51, 881,883,900 Bell, A.H.,240,535

Bell, J.S., 883,900 Benimeli, D.,223 Benson, D.J., 326, 542 Bereskin, S.R., 151,226 Berg, O.R., 60, 99, 856, 857, 862 Bergan, R.A., 229

Berger, B.D., 937 Berggren, W.A., 100 Bergosh, J.L., 117, 141, 142, 149, 206, 222 Bergt, D., 221 Bemthal, M.J., 83,102 Berry, V.J.Jr., 545 Bertrand, J-P., 535 Best, D.L., 221,229 Betzer, ER., 858 Bevan, T.G., 8 Beveridge, S.B., 489, 498, 499, 500, 501,535 Beydoun, Z.R., 332, 333, 503, 535 Bezdek, J., 99, 100, 101, 102 Bice, D., 83, 99 Biggs, W.P., 169, 205, 226, 227 Bilhartz, H.L., 222 Bilozir, D.E., 898,900 Binder, R.C., 940, 941,949 Bissell, H.J., 25, 52, 57, 536, 543, 901, 951,952 Bissell, R.C., 52 Biswas, G., 99, 100, 101, 102 Bitzer, K., 84, 99 Black, C.J.J., 52 Black, H.N., 335, 338, 339, 340, 341,343,344, 535

Black, J.L., Jr., 533 Blair, P.M., 260, 501,535 Blair, R.K., 52 Blanchet, EH., 8, 51 Blanton, J.R., 532 Bliefnick, D.M., 47, 51, 810, 838, 856 Bock, W.D., 98 Bocker, T., 797, 857 Bogli, J., 797, 85 7 Bohannan, D.L., 532 Bois, C., 832, 857 Bokn, I., 544 Bokserman, A.A., 44, 47, 51 Bond, J.G., 144, 149 Bonnie, R.J.M., 194, 222 Borg, I.Y., 535 Borgan, R.L., 532 Bosak, P., 797, 798, 799, 800, 806, 834, 856, 857, 858, 859, 862, 863, 864, 865

Bosellini, A., 856 Bosence, D., 83, 99 Bosscher, H., 281,535 Bostic, J.N., 644, 676 Botset, H.G., 19, 20, 51 Bouche, P., 85 7 Bourdet, D.P., 203,222, 563, 578, 580, 581, 651, 665, 676, 677, 678 Bourgeois, M.J., 644, 645, 677 Bourrouilh-Le Jan, EG., 797, 857 Bouvier, J.D., 56, 799, 800, 830, 851,857, 865 Bowen, B., 100

961 Boyeldieu, C., 214, 222,223 Boynton, R.S., 46, 51 Brace, W.F., 346, 535 Bradley, M.D., 538 Brady, T.J., 48, 51, 813, 845, 857 Braester, C., 678 Bramkamp, R.A., 533 Brandner, C.E, 897, 900 Bras, R.L., 540 Breland, J.A., 858 Brewster, J., 781, 782, 793 Brice, B.W., 542 Bridge, J.S., 83, 99 Brie, A., 223 Briens, F.J.L., 57, 546 Briggs, P.J., 46, 47, 52 Briggs, R.O., 207, 214, 222 Brigham, W.E., 680 Brimhall, R.M., 5 7, 546 Brinkmeyer, A., 545

Broding, R.A., 209, 222 Bromley, R.G., 782, 784, 793 Brons, E, 51,534, 679 Brooks, J., 794 Brooks, M., 60, 100 Broomhall, R.W., 45, 55 Brown, A.R., 158, 215, 222, 851,854, 857 Brown, C.A., 790, 793, 794 Brown, R.J.S., 181, 195,222, 466, 535 Brown, R.O., 207, 208, 222 Brown, S., 223 Brownrigg, R.L., 862 Bruce, W.A., 131,151, 177, 227, 253,533, 535 Bubb, J.N., 50, 52, 76, 99 Buchwald, R.W., 51, 534 Buckley, J.S., 200, 222, 873, 900 Buckley, S.E., 29, 52, 488, 489, 535 Bulnes, A.C., 233,256, 258, 535 Burchell, P.W., 532 Burchfield, T.E., 871,899, 902 Burgess, R.J., 51,676 Burk, C.A., 151 Burke, J.A., 169, 222 Burns, G.K., 540, 793 Busch, D.A., 810, 816, 825,840, 858 Bush, D.C., 139, 149 Butler, J.R., 222 Button, D.M., 545 Bykov, V.N., 812, 861 Byrd, W.D., 50, 52 Byrne, R.H., 858 Cady, G.C., 680 Caldwell, R.L., 5 7, 229 Calhoun, J.C., Jr., 38, 57, 296, 547 Callow, G.O., 256, 544

Calvert, T.J., 192,222 Campa, M.E, 28, 52 Campbell, EL., 158, 197, 225 Campbell, R.L., Jr., 222 Campbell, N.D.J., 51, 85 7 Candelaria, M.P., 51,797, 856, 857, 858, 859, 860, 861, 862, 863, 864, 865

Cannon, R., 99, 100, 101, 102, 900 Canter, K.L., 811,857, 865 Carannante, G., 79, 102 Cardwell, W.T., 888, 900 Cargile, L.L.,533 Carlson, L.O., 897, 900 Carlton, L.A., 55, 679 Carmichael, R.S., 128, 150, 168, 179, 193,222 Carnes, ES., 28, 52 Carpenter, B.N., 810, 85 7 Carroll, H.B., Jr., 56, 358, 539, 542, 901,903 Carslaw, H.S., 677 Carter, N.L., 535 Carter, R.D., 676 Carver, R.E., 139, 150, 167, 178, 202, 213,222 Cassan, J.P., 878, 880, 902 Castellana, ES., 152 Castillo, E, 859 Castillo-Tejero, C., 813,820, 830, 832, 847, 864 Castro Orjuela, A., 222 Catacosinos, P.A., 810, 828, 849, 857 Caudle, B.H., 456,545 Chace, D.M., 173,222, 224 Chakrabarty, C., 432, 535 Chandler, M.A., 133,150 Chaney, ER., 260, 501,544 Chang, D.M., 370, 539 Chang, J., 535 Chang, M.M., 151, 312,315, 322, 323,324, 535, 540

Chapman, R.E., 537 Charlson, G.S., 160, 222 Chatas, A.T., 677 Chatzis, I., 879, 898, 900, 901 Chauvel, Y., 207, 214, 222 Chayes, E, 265, 535 Chemali, R., 228 Chen, H-K., 332,333,535 Chen, H.C., 363, 535, 537 Chen, H.Y., 544 Chen, M., 224 Chen, S., 28, 390, 535 Chen, Z., 133,150 Cheng, S.W.L., 862 Chenowith, P.A., 806, 857 Cheong, D.K., 100 Cheung, ES., 223,227 Chichowicz, L., 41, 55 Chilingar, G.V., 24, 25, 52, 53, 54, 56, 57, 233,

962 390, 536, 542, 543, 544, 546, 869, 877, 900, 901,909, 951,952, 953, 954, 956 Chilingarian, G.V., 1, 4, 34, 47, 52, 54, 55, 231, 254, 268, 274, 275, 280, 389, 390, 417, 466, 468, 536, 537, 539, 541, 543, 545, 677, 681,834, 861,882, 901,937

Chopra, A.K., 435,544 Choquette, P.W., 52, 254, 268, 536, 542, 793, 797, 798, 799, 801,802, 803, 805, 806, 814, 832, 833,834, 845, 857, 858, 859, 860, 861,863

Chork, C.Y., 539 Chuber, S., 787, 793, 794 Chuoke, R.L., 900 Cichowitz, L., 679 Cinco-Ley, H., 203, 210, 223, 317, 320, 321, 536, 545, 559, 563,575,584, 596, 601, 607, 615, 621,623,625,630, 633,638, 646, 651,652, 656, 657, 673,677, 678, 680

Cisne, J.L., 84,99 Clark, B., 221 Clark, C.N., 545 Clark, D.G., 580, 581,677 Clark, J.B., 297, 536 Clark, K.K., 27, 41, 52, 677, 680 Clausing, R.G., 306, 536 Clavier, C., 164, 169, 198, 223 Clay, T.W., 533 Claycomb, E., 329, 536 Clayton, J.L., 794 Clerke, E.A., 28, 52, 165,209, 223 Cloetingh, S., 84, 99 Coalson, E.B., 534 Coates, G.R., 182, 195,203,205,223 Coats, K.H., 369, 536, 641,642, 677 Cobban, W.A., 792, 793 Cochrane, J.T.H., 542 Cockerham, P.W., 678 Coffeen, J.A., 59, 99 Coffin, P.E., 794 Cohen, M.H., 545 Coles, M.E., 135, 150, 168, 179, 223 Collins, E.W., 787, 794 Colson, L., 53, 225 Conley, F.R., 19, 53 Connally, T.C., 860 Coogan, A.H., 241,242, 536, 813, 825, 831, 85 7 Cook, H.E., 858 Coonts, H.L., 532 Corbett, K.P., 8, 52, 786, 787, 793 Core Laboratories, 123, 132, 136, 139, 140, 144, 145,150 Coruh, C., 60, 101 Cotter, W.H., 533 Cottrell, T.L., 536

Coufleau, M.A., 226 Coulter, G.R., 334, 536 Couri, F., 678 Cove de Murville, E., 52 Crabtree, P.T., 152, 229, 546 Crabtree, S.J., 900 Craft, B.C., 18, 52, 234, 245, 246, 282, 536, 956, 95 7

Craft, M., 141,151, 794 Crafton, J.W., 793 Craig, D.H., 52, 805,812, 831,832, 836, 837, 842, 844, 847, 856, 857 Craig, F.F., 35, 37, 48, 52, 56, 545, 870, 873, 874, 882, 900 Crary, S., 208,209, 223 Crawford, D.A., 677 Crawford, G.E., 611, 677 Crawford, P.B., 28, 51, 52, 676 Craze, R.C., 3, 52, 233, 247, 536 Crevello, P.D., 99, 102, 794, 857 Crichlow, H.B., 363, 375,536 Criss, C.R., 533 Cromwell, D.W., 51,856, 859, 861,862, 864 Crookson, R.B., 55 Cross, T.A., 100, 101, 102 Crow, W.L., 345, 346, 536 Crowe, C.W., 356, 536 Crump III, J.J., 228 Cullen, A.W., 533 Cunningham, B.K., 51,856, 859, 861,862, 864 Cunningham, L.E., 676 Curtis, G.R., 533 Cussey, R., 858 Dagan, G., 368, 536 Dake, L.P., 18, 27, 312, 536 Damsleth, E., 53, 358, 539, 886, 901 Dangerfield, J., 793 Daniel, E.J., 3, 52, 813, 840, 858 Daniels, P.A., 85 7

DaPrat, G., 677 Dauben, D.L., 53 7 Davidson, D.A., 505,507, 508, 536 Davies, D.H., 214, 215,223 Davies, D.K., 140, 150, 178, 184, 202, 223,224 Davies, R., 227 Davis, E.F., 302, 536 Davis, H.T., 544 Davis, J.A., 42, 52 Davison, I., 11O, 150, 213,223 Dawans, J.M., 56, 865 Dawe, R.A., 678 Day, P.I., 151,225 de Graaf, J.D., 150 de Figueiredo, R.J.P., 103 de Swaan, O.A., 677

963 de Waal, J.A., 133, 150 de Waal, P.J., 226 de Witte, L., 394, 546 Dean, M.C., 224 Deans, H.A., 150, 158, 223,539 Dees, J.M., 334, 536 DeHaas, R.J., 810, 836, 837, 844, 858 Delaney, R.P., 882, 883, 900 Delaune, P.L., 199, 223 Delhomme, J.P., 365, 536 Dembicki, H., 225 Demicco, R.V., 83, 99, 102 DeMille, G., 800,858 Demko, S., 427, 537 Dempsey, J.R., 536 Dennis, B., 223 Denoo, S., 223 Denoyelle, L., 11,52 Deryuck, B.G., 677 Desbrisay, C.L., 42, 52 Desch, J.B., 381,383,384, 537 Dewan, J.T., 158, 180, 197, 223 D'Heur, M., 781, 783, 793 Dickey, P.A., 240, 537 Dickson, J.A.D., 783, 794 Diederix, K.M., 139, 153 Diemer, K., 535 DiFoggio, R., 152, 229, 546 Dines, K., 158, 215,223 Dixon, T.N., 677 Dobrin, M.B., 63, 69, 70, 99 Dodd, J.E., 98 Dodson, T., 151 DOE, 277, 278, 280, 281,537 Doe, P.H., 200, 224 Dogru, A.H., 659, 677 Doh, C.A., 228 Doll, H.G., 168, 204, 223,227 Dolly, E.D., 810, 816, 825, 840, 858 Domenico, S.N., 158, 223 Dominguez, A.N., 677 Dominguez, G.C., 375,537, 545, 550, 677, 681 Donaldson, E.C., 136, 150 Donohoe, C.W., 532 Donohue, D.A.T., 158, 223 Doolen, G.D., 535 Doughty, D., 545 Douglas, A.A., 222, 676 Douglas, R.G., 49, 56, 773, 793, 794 Dove, R.E., 53, 225 Dowdall, W., 94, 101 Dowling, P.L., 42, 52, 256, 537 Doyle, M., 98, 101 Doyle, R.E., 376, 378, 537 Doyle-Read, F.M., 883,903 Dresser Atlas, 173,224

Drews, W.E, 677 Driscoll, V.J., 302, 537 Dromgoole, E., 83, 99, 101 Dubey, S.T., 150, 200, 224 Dublyansky, V.N., 799, 858 Dubois, D., 363, 537 Dubois, J., 546 Duchek, M.E, 222 Dufurrena, C.K., 810, 811,830, 862 Dullien, EA.L., 875,900, 901 Dumanoir, J.L., 169, 179, 205, 223,224 Dunham, R.J., 256, 537 Dunn, P.A., 100 Dunnington, H.V., 696, 697, 769 Duns, H., 546 Duong, A.N., 658, 677 Dupuy, M., 543 Duran, R., 679 Durbin, D., 229 Durham, T.E., 861 Dussan, E., 221 Dussert, P., 48, 53, 813, 831,838, 844, 858 Dyer, R.C., 60, 100 Dyes, A.B., 679 Dykes, F.R.Jr., 532 Dykstra, H., 34, 53, 290, 436, 537 Dzulynski, S., 797, 858 Ealey, P.J., 893, 902 Earlougher, R.C., Jr., 196, 203,224, 549, 553, 563,584, 614, 632, 636, 677 Earlougher, R.C. Jr., Eaton, B.A., 39, 53 Ebanks, W.J., 811,830, 840, 858 Eberli, G.P., 84, 85, 99 Economides, M.J., 539, 632, 678 Edelstein, W.A., 134, 150, 152, 179, 184, 224, 229, 546 Edgar, T.F., 677 Edie, R.W., 812, 814, 825, 858 Edmunson, H., 128, 150, 168, 179, 193,224 Edwards, C.M., 544 Effs, D.J.Jr., 538 Egemeier, S.J., 799, 858 Eggert, K., 535 Ehlers, E.G., 139, 150 Ehlig-Economides, C.A., 656, 658, 678 Ehrlich, R., 55, 140, 150, 178, 224, 413,537, 873,900 Eidel, J.J., 85 7 Eijpe, R., 436, 537 Ekdale, A.A., 782, 784, 793 Ekstrom, M.P., 207, 214, 224 EI-Ghussein, B.F., 52 E1-Rabaa, A.W.M., 55 Elkins, L.F., 2, 8, 28, 44, 45, 53, 302, 486, 487,

964 489,533,537

Elliott, G.R., 248, 537 Ellis, D., 54, 128, 150, 158, 168, 179, 193, 224, 225 Elrod, J.A., 100 Emanuel, A.S., 365, 366, 369, 371,372, 373, 375, 378, 379, 380, 381,382, 384, 387, 537

Enderlin, M.B., 224 Energy Resources Conservation Board, 38, 53, 549, 678, 867, 869, 895, 900 Engler, P., 151 Enos, P., 177, 224, 858 Entzminger, D.J., 811,834, 837, 847, 858 Eremenko, N.A., 234, 537 Ertekin, T., 158, 223 Esteban, M., 797, 798, 802, 803, 804, 805,806, 807, 808, 812, 818, 820, 847, 856, 858, 861, 863, 865

Euwer, R.M., 858 Evans, D.M., 56 Evans, M.E., 810, 811,857 Ewing, T.E., 538, 546 Eyles, D.R., 89, 101 Fair, ES., 645, 678 Fairbridge, R.W., 57, 901,951,952 Faivre, O., 223 Falconer, I., 221 Fanchi, J.R., 322, 537 Fang, J.H., 363, 535, 537 Fanning, K.A., 799, 858 Faraguna, J.K., 207, 214, 224 Farid, E.A., 333,534 Farouq Ali, S.M., 535 Farrell, H.E., 777, 779, 782, 784, 793 Fassihi, M.R., 284, 285, 289, 291,292, 293, 537 Fast, C.R., 297, 540 Fatt, I., 257, 389, 537, 538 Feazel, C.T., 777, 779, 782, 783, 784, 793, 794 Feder, J., 534 Feldkamp, L., 541 Felsenthal, M., 3, 8, 9, 18, 19, 20, 21, 22, 27, 28, 29, 30, 32, 34, 35, 36, 38, 39, 41, 44, 53

Fenwick, M., 534 Ferreira, A.E., 223 Ferrell, H.H., 3, 8, 9, 18, 19, 20, 21, 22, 27, 28, 29, 30, 32, 34, 35, 36, 38, 39, 41, 44, 53 Ferrier, J.J., 46, 56 Ferris, J.A., 152, 228 Ferris, M.A., 545, 902 Fertal, T.G., 542 Fertl, W.H., 8, 53, 235,537 Festoy, S., 769 Fetkovich, M.J., 304, 306, 538, 649, 678

Fetkovich, R.B., 543 Fickert, W.E., 532 Finch, W.C., 533 Finke, M., 227 Firoozabadi, A., 473,538 Fisher, W.L., 275, 538 Fitting, R.U.Jr., 233,256, 258, 535 Flaum, C., 150, 224 Flemmings, P.B., 84, 99, 100 Fligelman, H., 596,678 Flis, J.E., 861 Flock, D.L., 874, 902 Flores, D.P., 57, 546 Flynn, J.J., 100 Flynn, P.E., 859 Foed, D.C., 859 Fogg, G.E., 535, 541,891,900 Folk, R.L., 258, 538 Fong, D.K., 55 Fons, L., 213,224 Fontaine, J.M., 812, 848, 849, 851,858 Ford, A., 795 Ford, B.D., 864 Ford, D.C., 797, 798, 799, 800, 801,806, 834, 835, 841,842, 856, 857, 858, 859, 862, 863, 864, 865

Fordham, E., 221 Forgotson, J.M., 864 Fortin, J.P., 207, 214, 215,224 Frank, J.R., 532 Frascogna, X.M., 533 Fraser, C.D., 28, 53 Freedman, R., 226 Freeman, B.E, 543 Freeman, D.L., 140, 150, 167, 224 Freeman, H.A., 503,504, 538 French, J.A., 83, 99, 101 Frey, D.D., 56 Frick, T.C., 536 Friedman, G.M., 48, 50, 51,254, 544, 769, 775, 783, 793, 810, 838, 845,856 Friedman, M., 52, 694, 695, 769, 793 Frisinger, R., 223 Fritz, M., 810, 858 Fritz, R.D., 865 Frohlich, C., 84, 101 Frost, E., 226, 227 Frost, S.H., 813,840, 859 Frydl, P.M., 56, 898, 900 Frykman, P., 794 Fu, C., 535 Fuchs, Y., 797, 856, 858 Full, W.E., 59, 900 Fuller, J.G.C.M., 801,858, 860 Fulleylove, R.J., 52 Furlong, K.P., 84, 102

965 Gale, J.E., 56 Galloway, W.E., 233,275,276, 538, 546 Gamson, B.W., 181, 195,222, 466, 535 Garaicochea Petrirena, E, 538 Garat, J., 225 Garcia-Sineriz, B., 799, 812,859 Gardner, G.H.E, 229 Gardner, J.S., 169, 179, 224, 227 Garfield, R.F., 533 Garfield, T.R., 811,840, 859 Garrett, C.M.Jr., 538, 546 Garrison, J.R.Jr., 267, 268, 269, 270, 271,272, 415, 417, 538

Garrison, R.E., 773, 793 Gatewood, L.E., 810, 827, 831,832, 837, 859 Gealy, F.D.Jr., 532 Geertsma, J., 769 Geesaman, R.C., 811,840, 857, 859, 865 Geffen, T.M., 52, 481,545 Gehr, J.A., 56 Geldart, L.P., 102 George, C.J., 33, 34, 53, 534 George, C.P., 902 Georgi, D.T., 133, 140, 150, 201,211,212, 224 Gevers, E.C.A., 85 7 Gewers, C.W., 38, 53, 472, 473,538 Ghauri, W.K., 302, 538, 882, 901 Gianzero, M., 228 Giger, F.M., 324, 538 Gilbert, L., 98 Gildner, R.E, 99 Gill, D., 801, 811,830, 859 Gillen, M., 223 Gillson, J.L., 51 Gilreath, J.A., 213,224 Gimatudinov, Sh., 949 Ginsburg, R.N., 84, 85, 92, 99, 100 Glaister, R.P., 868, 902 Glazek, J., 807, 834, 856, 857, 858, 859, 862, 863, 864, 865

Gleeson, J.W., 466, 468, 538 Glenn, E.E., 5 7, 229 Gnatyuk, R.A., 56 Godbold, A.C., 54, 533 Goetz, J.F., 207, 214, 224 Goggin, D.J., 150, 436, 538, 539 Goldhammer, R.K., 84, 99, 100, 101 Golf-Racht, T.D. van, 141, 142, 150, 205,206, 224 Golson, J.G., 793 Gonzales, H.T., 51 Goode, P.A., 221,542 Goodknight, R.C., 257, 538 Goodman, A.G., 858 Goolsby, J.L., 532 Goolsby, S.M., 794, 860, 862, 863

Goss, L.E., 532 Gould, T.L., 285, 286, 538 ~: Gounot, M-T., 223 Govier, G.W., 680 Govorova, G., 949 Gradstein, F.M., 85, 100 Graham, J.W., 44, 53, 260, 501,502, 539 Graham, S.K., 542 Grant, C.W., 436, 438, 439, 440, 452, 453,454, 456, 539 Grau, J., 53, 225 Graus, R.R., 83, 100 Graves, E.D. Jr., 957 Gray, L.L., 54, 533 Gray, R., 532 Gray, T.A., 435, 539 Greaves, K.H., 151,226 Grebe, J.J., 296, 539 Gregory, A.R., 229 Grier, S.P., 151,228 Gries, R.R., 60, 100 Grine, D.R., 226 Gringarten, A.C., 203, 210, 224, 563,580, 597, 614, 641,656, 658, 678, 680 Grotzinger, J.P., 84, 100 Grover, G.A., 100 Groves, D.L., 258, 539 Gryte, C.C., 152 Guangming, Z., 48, 53, 806, 810, 825, 832, 837, 838, 845, 859 Guillory, A.J., 194, 225 Guindy, A., 223 Guise, D.R., 900 Gulati, M.S., 680, 681 Gunter, J.M., 197, 199, 200, 224 Gussow, W.C., 236, 237, 239, 240, 539 Gustavino, Lic.L., 544 Guti6rrez, R.M.E., 633,678 Gutman, S., 535 Gutschick, K.A., 46, 51 Guy, B.T., 863 Guyod, H., 190, 224 Guzman, E.J., 832, 859 Gysen, M., 166, 224 Hache, J-M., 221 Hadley, G.F., 486, 539 Hagerdom, A.R., 677 Hagoort, J., 498, 501,539 Haidl, EM., 860 Halbouty, M.T., 48, 52, 53, 795, 806, 807, 857, 859, 860, 862, 863, 864, 865

Haldorsen, H.H., 53, 358, 363, 370, 539, 884, 886, 901 Halliburton Logging Services, Inc., 169, 170, 171,172, 180, 189, 190, 197, 198, 200,

966 205,207, 214, 221,224 Hallock, P., 77, 100 Halsey, T.C., 410, 423,430, 539 Ham, W.E., 537, 953 Hammond, P., 221 Hamon, G., 250, 539 Han, B., 799, 800, 859 Hancock, J.M., 782, 793 Handford, C.R., 810, 834, 836, 837, 839, 843, 844, 861

Handy, L.L., 260, 486, 539 Hansen, A., 534 Hansen, J.P., 414, 539 Hansen, K.S., 131 Hanshaw, B.B., 799, 856, 859 Haq, B., 82, 85, 98, 100 Harbaugh, J.W., 84, 99, 102, 867, 901 Hardenbol, J., 100 Hardie, L.A., 100 Hardman, R., 150, 224 Hardman, R.EP., 782, 793 Hardy, H.H., 379, 387, 534, 535, 539 Harper, M.L., 50, 53 Harris, A.J.P.M., 863 Harris, J.D., 533 Harris, J.F., 8, 53 Harris, M.T., 99 Harris, P.M., 56, 99, 100, 103, 539, 793, 794, 800, 812, 840, 858, 859, 860, 861,863 Harrison, W., 234, 546, 85 7 Harvey, A.H., 540 Harvey, R.L., 811,814, 822, 831,859 Harville, D.G., 140, 141,150, 151, 167, 224, 227 Hashmy, K.H., 166, 221,224 Hassan, T.H., 100 Hastings, B.S., 56 Haszeldine, R.S., 11O, 150, 213,223 Hatlelid, W.G., 50, 52, 76, 99 Havlena, D., 888, 889, 901 Hawkins, M.E, 18, 52, 234, 245,246, 282, 536 Hawkins, M.E Jr., 587, 588, 678 Haymond, D., 785, 786, 787, 793 Hazebroek, P., 39, 53, 679, 680 Hazen, G.A., 229 Heard, H.C., 535 Heaviside, J., 435,539 Heifer, K.J., 8, 53 Heim, A., 223 Helland-Hansen, W., 83, 100 Heller, J.P., 150 Henderson, G., 223 Henderson, J.H., 536 Henderson, K.S., 810, 831,859 Hendrickson, A.R., 334, 539 Hendrickson, G.E., 28, 32, 34, 35, 53

Henry, J.C., 532 Henry, W.E., 794 Hensel, W.M., Jr., 205,225 Hentschel, H.G.E., 410, 423,539 Herald, F.A., 533 Herbeck, E.F., 532 Herchenroder, B.E., 100 Herman, J.S., 856 Herriot, H.P., 532 Herron, M.M., 54, 205,223,225 Herron, S.L., 27, 53, 181,225 Hertzog, R.C., 27, 53, 173, 175, 181,195,225, 229 Hester, C.T., 45, 54 Heuer, G.J., 27, 32, 56 Hewett, T.A., 363, 364, 365, 366, 367, 368, 369, 370, 371,378, 379, 387, 388, 433, 452, 534, 537, 539 Hewitt, R., 100 Heymans, M.J., 857 Hickman, W.B., 544, 952 Hicks, P.J., Jr., 136, 150, 461,539 Hill, C.A., 799, 800, 805,859 Hiltz, R.G., 532 Hine, A.C., 100 Hingle, A.T., 169, 197, 225 Hinkley, D.V., 901 Hinrichsen, E.L., 534 Hirasaki, G.J., 136, 137, 150 Hnatiuk, J., 237, 238, 533, 540 Ho, T.T.Y., 225 Hobson, G.D., 865 Hocott, C.R., 535, 540 Hodges, L., 537 Hoffman, L.J.B., 167, 225 Hohn, M.E., 363, 365,540 Holcomb, S.V., 57, 229 Holden, W.R., 956, 957 Holditch, S.A., 349, 540, 541 Holm, L.W., 44, 54 Hoist, P.H., 52 Holtz, M.H., 296, 298, 300, 540, 810, 830, 838, 859

Honarpour, M.M., 17, 54, 290, 443,540 Hoogerbrugge, P.J., 225 Hook, R.C., 810, 859 Hoover, R.S., 340, 344, 540 Hopkinson, E.C., 229 Horacek, I., 856, 857, 858, 859, 862, 863, 864, 865

Horkowitz, K.O., 537 Homby, B.E., 215,223,225 Home, R.N., 549, 580, 581,636, 642, 644, 645, 656, 657, 659, 677, 678, 680 Homer, D.R., 646, 678 Horsefield, R., 200, 225,237, 413,533, 540

967 Horstmann, L.E., 329, 540, 785, 793 Hoss, R.L., 532 Hotz, R.E, 537 Hovdan, M., 330, 542 Hove, A., 136, 137, 150 Hovorka, S.D., 811,859 Howard, G.C., 297, 540 Howard, J.J., 134, 150, 151,203,224, 225 Howell, J.V., 861,864 Howell, W.D., 51 Howes, B.J., 869, 895, 896, 901 Hoyle, W., 223 Hrametz, A., 225 Hriskevich, M.E., 78, 100 Hsu, K.J., 56, 223, 794 Hubbert, M.K., 39, 54 Hudson, J.A., 10, 54 Hudson, W.K., 148 Huijbregts, C.J., 363, 364, 365,541,891,901 Huinong, Z., 678 Huitt, J.L., 3, 54 Humphrey, J.D., 84, 100 Hunt, E.R., 227 Hunt, P.K., 136, 151 Hunter, B.E., 55 Hurley, T.J., 28, 54 Hurst, H.E., 366, 387, 540 Hurst, J.M., 94, 100 Hurst, R.E., 334, 540 Hurst, W., 540, 553, 587, 644, 678, 681 Hutchinson, C.A. Jr., 679 Hutfilz, J.M., 678 Huxley, T.H., 793 Huzarevich, J.V., 532 Hyland, G.R., 112,151

860, 863

Jaminski, J., 534 Jantzen, R.E., 138, 151 Jardine, D.J., 255,256, 259, 496, 497, 541, 867, 869, 901 Jardon, M.A., 542, 547 Jargon, J.R., 641,644, 678 Jasti, J.K., 457, 541 Jeffers, D., 151, 228 Jeffreys, P., 214, 222 Jenkins, R.E., 139, 149 Jenkyns, H.C., 56, 794 Jennings, J.N., 797, 860 Jennings, J.W., 540 Jennings, H.Y., Jr., 188, 228 Jensen, J.L., 886, 901 Jensen, M.H., 365, 539 Jenyon, M.K., 849, 860 Jesion, G., 541 Jie, T., 100 Jodry, R.L., 131,151, 177, 225, 250, 258, 282, 475,481,541,801,860 Johnson, C.E., 480, 541 Johnson, D., 223 Johnson, K.S., 797, 857, 859, 860, 861,863, 864,865

Johnson, M.C., 533 Johnston, J.R., 542 Johnston, L.K., 214, 215, 225 Jones, M.W., 810, 836, 837, 844, 858 Jones, E, 584, 679 Jones, S.C., 133, 150, 201,224, 436, 541 Jones, T., 900 Jones, T.A., 4, 54 Jones-Parra, J., 260, 261,262, 488, 489, 541, 954

ICE 32, 33, 34, 54, 256, 287, 289, 290, 292, 293,294, 298, 299, 301,302, 307, 308, 309, 310, 540 IHRDC, 108, 115, 116, 151 Ijirigho, B.T., 810, 859 Ijjasz-Vasquez, E.J., 399, 411, 412, 540 Ikwuakor, K.C., 540 Illing, L.V., 812, 814, 830, 860 IOCC, 282, 284, 285,286, 287, 288, 540 Iwai, K., 56

Jossang, T., 534 Journel, A.G., 363, 364, 365, 541, 891,901

Jaap, W.C., 100 Jackson, S.R., 540 Jacob, C.E., 638, 678 Jacobson, L.A., 173, 181,195,225,229 Jaeger, J.C., 677 Jain, A., 678 Jain, K.C., 103 James, N.P., 52, 92, 100, 797, 798, 799, 801, 803,805, 806, 814, 833, 834, 857, 858,

Kaasscheiter, J.P.H., 545 Kabir, C.S., 549, 580, 615,656, 679, 681 Kadanoff, L.P., 401,539, 541 Kaluza, T.J., 54 Kansas Geological Society, 532, 533 Kantzas, A., 898, 900, 901 Karakas, M., 679 Katz, A.J., 267, 270, 271,415, 541 Katz, D.L., 473,538, 541, 593, 681

Jordan, C.F., 813, 830, 860 Jordan, J.K., 534 Jordan, T.E., 84, 99, 1O0 Jorden, J.R., 158, 197, 221,225,227 Jorgensen, N.O., 782, 793 Joseph, J.A., 658, 678 Joshi, S.D., 296, 311,312, 313, 316, 317, 318, 319,320,321,324,541

968 Kaveler, H.H., 20, 54, 533 Kaye, B.H., 273,541 Kazi, A., 534 Keany, J., 793 Kearey, P., 60, 100 Keelan, D.K., 108, 119, 128, 130, 139, 141,151, 887, 901 Keith, B.D., 858 Kellan, D.K., 481,484, 485,541 Kendall, C.G.St.C., 50, 56, 59, 74, 82, 83, 97, 98, 99, 100, 101, 102, 103, 383, 542 Kennedy, J.E., 53 7 Kennedy, S.K., 900 Kennedy, W.J., 782, 794 Kent, D.M., 254, 258, 541, 812, 830, 860 Kent, D.V., 100 Kenworthy, J.D., 532 Kenyon, W.E., 134, 151,203,225,226 Kerans, C., 47, 54, 545, 810, 812, 830, 831,837, 838, 842, 844, 848, 851,859, 860, 902 Kern, C.A., 215, 216, 225 Kettle, R.W., 102 Keys, D.A., 102 Khutorov, A.M., 813,860 Kidwell, C.M., 194, 225 Kienitz, C., 221 Kimminau, S., 227 King, E., 151,226 King, P.R., 368, 388, 392, 401,402, 403,404, 405,423,541,901 King, R.E., 55, 402, 769, 859, 861,863, 865 King, R.L., 898, 901 Kinney, E.E., 532 Kirman, P.A., 679 Kittridge, M.G., 161,195,225,436, 438,439, 541

Klappa, C.F., 858 Klikoff, W.A., 538 Klinkenberg, B., 263,541 Klitgord, K.D., 100 Klute, C.H., 257, 541 Kniazeff, V.J., 678 Knox, S.C., 810, 831,859 Kochina, I.N., 769 Koederitz, L.E, 540 Koen, A.D., 325,541 Koerschner III, W.F., 83, 100 Kolata, D.R., 857 Kopaska-Merkel, D.C., 542 Koplik, J., 546 Kordos, L., 807, 856 Korvin, G., 366, 388, 541 Kozic, H.G., 346, 347, 348, 349, 350, 351,541 Krajewski, S.A., 102 Kretzschmar, J.L., 158, 215,225 Krief, M., 172, 180, 225

Kriss, H.S., 41, 56 Krohn, C.E., 264, 265,266, 409, 541 Kruger, J.M., 811,860 Kuchuk, F.J., 542, 644, 645,658, 677, 679 Kuich, N., 326, 328, 329, 542, 785, 786, 787, 788, 794

Kumar, A., 541,549, 563, 680, 681 Kumar, S., 937 Kunkel, G.C., 28, 54 Kupecz, J.A., 81 O, 860 Kuranov, I.F., 681 Kyle, J.R., 44, 55, 797, 860 Lacaze, J., 858 Lacey, J.W., 532 Lacik, H.A., 533 Ladwein, H.W., 812, 824, 860 LaFleur, R.G., 862 Lai, F.S.Y., 900 Laidlaw, W.G., 874, 901 Lair, G.H., 952 Lake, L.W., 56, 150, 358, 363,370, 371,378, 534, 538, 539, 541,542, 867, 884, 888, 901,903

Lambeck, K., 99 Lanaud, R., 858 Landel, P.A., 678 Lane, B.B., 28, 54 Langdon, G.S., 75, 81,101 Langford, B.J., 952 Langnes, G.L., 17, 23, 54, 542, 544, 937 Langston, E.P., 679, 872, 883, 884, 885, 894, 901

Lanz, R.C., 85 7 LaPoint, P.R., 10, 54 Lapre, J.F., 795, 885, 901 Larsen, E., 433,535 Larsen, G., 536, 909, 951 Larsen, L., 330, 542 Larsen, W.K., 53 7 Larson, R.G., 534 Larson, V.C., 532 Lasseter, E., 229 Lasseter, T.J., 893, 901 Latham, J.W., 810, 831,860 Latimer, J.R.Jr., 532 Laughlin, B.A., 302, 310, 542, 547 LaVigne, J., 227 Lawrence, D.T., 59, 82, 83, 98, 101 Le Lan, P., 227 LeBlanc, D.P., 158, 225 Lee, J.E., 488, 489, 490, 492, 494, 496, 542 Lee, J.I., 42, 54 Lee, R.L., 595,679 Lee, W.J., 563,679 Leeder, M.R., 83, 99

969 Lefebvre du Prey, E.J., 875,901 Legere, R.E, 900 Leibrock, R.M., 532 Leighton, M.W., 857 Lemaitre, R., 542 Lents, M.R., 36, 55 Lerche, I., 9, 10, 11, 12, 13, 14, 15, 16, 55, 83, 99, 100, 101

Leroy, G., 710, 769 Lesage, M., 221 Letton, W.III, 226 Leverett, M.C., 19, 20, 29, 52, 54, 131, 151, 177,226 Levorsen, A.I., 236, 542, 806, 860 Levy, M., 535 Lewis, W.B., 19, 20, 54 Li, M., 810, 860 Li, Y., 873,901 Lichtenberger, G.J., 327, 328, 329, 330, 331,542 Lieberkind, K., 794 Lindsay, J.E, 102 Lindsay, R.F., 383, 537, 542 Lishman, J.R., 887, 901 Little, T.M., 226 Littlefield, M., 2, 54, 533 Liu, H., 864 Liu, O., 223 Lloyd, P., 223 Lloyd, R.M., 102 Locke, C.D., 56 Locke, S., 224 Lockridge, J.E, 790, 792, 794 Logan, R.W., 679 Lohman, J.W., 678 Lomando, A.J., 793, 859, 863 Lomas, A.T., 225 Lomiz6, G.M., 4, 5, 6, 54 Longman, M.W., 291,542, 791,794, 811,840, 859, 860, 862, 863

Lord, C.S., 501,542 Lord, G.D., 142, 149, 151,206, 222, 226 Lorenz, P.B., 150 Loucks, R.G., 804, 810, 813,834, 836, 837, 839, 840, 843,844, 847, 856, 858, 860, 861

Louis, C., 4, 54 Lovell, J., 223 Lowenstam, H.A., 811,840, 861 Lowry, D.C., 101 Lucia, EJ., 177, 178, 184, 186, 190, 202,226, 535, 541,545, 868,900, 901, 902 Luque, R.E, 546 Lyle, D., 326, 542 Lynch, M., 810, 861 Lytle, R.J., 158, 215,223

MacAllister, D.J., 458, 459, 461,542 MacDonald, I.F., 900 MacDonell, P.E., 900 MacEachem, J.A., 860 Maclnnis, J., 226 Macintyre, I.G., 100 Mackenzie, F.T., 784, 794 Macovski, A., 457, 542 Macrygeorgas, C.A., 680 Maerefat, N.L., 151 Magara, K., 8, 54 Maggio, C., 85 7 Magnuson, W.L., 538, 901 Maher, C.E., 51, 85 7 Mahmood, S.M., 133,151,468, 545 Main, R., 536, 956 Maksimovich, G.A, 812, 861 Malecek, S.J., 75, 81,101 Maliva, R.G., 783, 794 Malone, W.T., 545 Mamedov, Y.G., 51 Mancini, E.A., 326, 359, 542 Mandelbrot, B.B., 263,264, 270, 365, 366, 372, 407, 410, 422, 542, 543 Mann, J., 900 Mann, M.M., 151,228 Mann, S.D., 542 Manning, M., 227 Mannon, R.W., 52, 53, 289, 542, 543, 544, 546, 9O0

Manual, T., 151 Mapstone, N.B., 50, 54 Marafi, H., 812, 830, 840, 861 Marchant, L.C., 45, 46, 54 Marek, B.F., 150, 223 Maricelli, J.J., 213,224 Markowitz, G., 214, 215,225 Marks, T.R., 149, 222 Marrs, D.G., 532 Marsden, S.S., 943,949 Marshall, J.W., 44, 55 Martell, B., 640, 679 Martin, EG., 8, 55 Martin, J.C., 378, 543 Martin, J.E, 227 Martin, R., 48, 55, 98, 806, 812, 822, 823,861 Martin, W.E., 44, 5 7 Martinelli, J.W., 237, 238, 533, 540 Martinez, A.R., 679 Martinez del Olmo, W., 847, 856, 861 Martinez, R.N., 679 Maslov, V.E, 861 Mass6, L., 534, 769 Mast, R.F., 535 Masters, C.D., 546 Masuda, E, 101

970 Mathews, M.A., 152, 229 Mattar, L., 681 Mattavelli, L., 25, 26, 55 Mattax, C.C., 44, 55 Matthews, C.S., 39, 53, 55, 203, 210, 226, 549, 584, 654, 679 Matthews, R.K., 84, 101 Maute, R.E., 190, 226 May, J.A., 89, 101 Mayer, C., 166, 224, 226 Mazzocchi, E.F., 44, 55 Mazzullo, L.J., 811,830, 861 Mazzullo, S.J., 1, 34, 47, 52, 54, 231,254, 256, 268, 280, 417, 468, 536, 537, 539, 541, 543, 545, 677, 681, 800, 802, 803, 804, 810, 811,812, 818, 825, 830, 834, 861, 862, 863, 882, 901 McCaleb, J.A., 32, 45, 56, 359, 360, 361,362, 533, 811,814, 830, 862 McCammon, R., 900 McCauley, J.L., 273, 391,392, 393,394, 395, 396, 397, 398, 399, 400, 407, 409, 413, 539, 543, 544

McCleb, J.A., 546 McCord, J.R., 677 McCormack, R.K., 102 McCormick, L.M., 862 McCormick, R.L., 533 McCoy, T.F., 304, 305, 306, 538, 543 McDonald, S.W., 662,665, 679 McGee, P.R., 679 McGhee, E., 584, 679 McGill, C., 892,901 McGuire, W.J., 335,342, 543 Mclntosh, I., 615, 679 Mclntosh, J.R., 678 Mclntyre, A., 49, 55 McKellar, M., 903 McKeon, D., 53, 150 McKinley, R.M., 28, 55, 611,635,661,677, 679, 681

McKoen, D., 224, 225 McLemore, J., 150 McLimans, R.K., 864 McMahon, B.E., 533 McNamara, L.B., 868, 886, 887, 893,894, 902 McQueen, H., 99 McQuillin, R., 60, 67, 78, 101 Mear, C.E., 810, 811,830, 862 Medlock, P.L., 865 Meinzer, O.E., 638, 679 Meissner, F.F., 794 Meister, J.J., 543 Meneveau, C., 426, 543 Menzie, D.E., 45, 46, 54, 902 Mesa, O.J., 372, 435, 543

Mesolella, K.J., 801, 811, 819, 840, 862 Metghalchi, M., 536 Meunier, D., 223,644, 645, 679 Meyer, L.J., 681 Mezzatesta, A., 166, 226, 227 Miall, A.D., 865 Middleton, M.F., 88, 101 Miller, A.E., 458,459, 461,543 Miller, B.D., 356,536 Miller, C.C., 679 Miller, D.N.Jr., 532 Miller, EG., 536, 677, 679, 680 Miller, F.H.,532 Miller, G.K., 226 Miller, J.A., 863 Miller, K.C., 97, 100, 542 Miller, M.G., 36, 55, 223 Miller, R.D., 102 Miller, R.T., 496, 543 Miller, T.E., 856 Miller, W.C., 228 Millheim, K.K., 41, 55, 679 Mimran, Y., 783, 794 Mink, R.M., 542 Misellati, A., 52 Miska, S.Z., 594, 680 Mitchell, ER., 227 Mitchum, R.M., Jr., 50, 55, 56, 103, 803, 862, 864

Mitkus, A.E, 149, 222 Miyata, Y., 102 Mohanty, K.K., 458, 459, 461,543 Mohanty, S., 405,543 Monicard, R.P., 108, 136, 151 Montiel, H.D., 680 Moody, J.D., 797, 832, 862 Mooney, L.W., 862 Moore, A.D., 389, 543 Moore, C.H., 858, 860, 861,867, 894, 902 Moore, C.V., 197, 199, 200, 224 Moore, D., 546 Moore, G.E, 93, 99 Moore, P., 99, 100, 102 Moore, P.J.R.McD., 902 Moore, W.D., 22, 55, 534 Moran, J.H., 213, 226 Morgan, L., 94, 101 Morineau, Y., 436, 543 Moring, J.D., 532 Morris, C.F., 182, 195,207, 214, 226 Morris, E.E., 258, 543 Morris, R.L., 205,208, 226 Morris, S.A., 152, 228 Morrow, N.R., 136, 151,200, 222, 875,879, 900, 901,902

Morse, J.W., 784, 794

971 Morse, R.A., 52, 56, 335,342, 543, 545 Mortada, M., 257, 544 Mosley, M.A., 863 Mruk, D.H., 857 Mudd, G.C., 100 Muegge, E.L., 150, 223 Mueller, O.M., 150, 224 Mueller, T.D., 585, 679 Muggeridge, A.H., 541 Muller, G., 769 Muller, J., 372, 407, 409, 412, 415,425,433, 539, 544

Muller, P., 799, 862 Mullins, J.E., 209, 226 Mundry, M., 51, 900 Mungan, N., 875, 902 Muravyov, I., 947, 948, 949 Murray, G.H., 713,716, 769 Murray, R.C., 868, 901 Muskat, M., 117, 151,201,226, 245,302,311, 544

Musmarra, J.A., 544 Mussman, W.J., 798, 862 Myers, M.T., 147, 191, 192, 226 Nabor, G.W., 257, 544, 679 Nadon, G.C, 810, 862 Nagel, R.G., 55 Nagy, R.M., 864 Najurieta, H.L., 634, 636, 679 Nakayama, K., 100, 1O1 Narayanan, K.R., 150, 539 Narr, W., 9, 10, 11, 12, 13, 14, 15, 16, 55 Natanson, S.G., 503,504, 534, 538, 751,753, 769

Nath, A.K., 222 Naylor, B., 537 Needham, R.B., 538, 543 Neidell, N.S.,lO1

Nelson, D.E., 901 Nelson, H.W., 858 Nelson, R.A., 784, 794 Neslage, F.J., 532 Nettle, R.L., 537 Neuse, S.H., 540 Newell, K.D., 810, 831,862 Nichol, L.R., 38, 53, 472,473,538 Nicoletis, S., 227 Niko, H., 150, 352, 353,354, 546 Nisle, R.G., 585,679 Niven, R.G., 542 Nodine-Zeller, D.E., 858 Nolan, J.B., 46, 55 Nolen-Hoeksema, R.C., 42, 55 Nooteboom, J.J., 226 Nordquist, J.W., 533

Norton, L.J., 5 7, 229 Nuckols, E.B., 231,298, 544 Nute, A.J., 900 Nydegger, G.L., 790, 791, 792, 794 Nygaard, E., 782, 794 Obradovich, J., 100 O'Brien, M., 53, 225 Odeh, A.S., 679 Ogbe, D.O., 632, 678 Ogg, J.G., 100 Oliver, F.L., 532 Oltz, D.E, 857 Onur, M., 658, 680 Ormiston, A.R., 862 Oros, M.O., 535 Orr, EM., 546, 902 Orsi, T.H., 457, 544 Ortiz de Maria, M.J., 538 Osborne, A.E, 538, 901 Osborne, W.E., 810, 831,863 Oshry, H.L., 229 Ostrowsky, N., 539, 542 Overbey, W.K., Jr., 8, 55 Owen, L.B., 139, 140, 151, 178, 226 Owens, W.W., 902 Pabst, W, 900 Pach, E, 812, 856 Paillet, EL., 208, 226 Palacas, J.G., 794 Palisade Corporation, 217, 226 Palmer, A.N., 797, 798, 799, 800, 856, 862 Palmer, M.V., 798, 800, 856, 862 Paola, C., 84, 101 Papatzacos, P., 672, 680 Pape, W.C., 55 Pariana, G.J., 56 Park, W.C., 696, 769 Parker, H.M., 893,902 Parra, J., 677 Parsley, A.J., 415, 544 Parsley, M.J., 812, 831,860 Parsons, R.L., 34, 53, 290, 436, 537, 888, 900 Parsons, R.W., 3, 55, 260, 501,544 Partain, B., 8, 55 Pascal, H., 644, 680 Pasini, J., III, 8, 55 Pasternack, I., 802, 862 Patel, R.S., 45, 55 Pathak, P., 457, 544 Paul, A., 223 Pautz, J.E, 312, 315, 535 Payne, D.A., 51,900 Payton, C.E., 52, 55, 56, 102, 103, 849, 862, 864 Pearce, L.A., 223

972 Peam, W.C., 538 Peeters, M., 166, 226 Peggs, J.K., 55 Peitgen, H-O., 546 Pelet, R., 85 7 Pellisier, J., 223 Pendexter, C., 802, 856, 885, 900 Penn, J.T., 152, 228 Ptrez, A.A.M., 681 Perez, G., 544 Ptrez Rosales, C., 39, 40, 55, 538, 634, 679, 680 Perkins, A., 532 Perlmutter, M., 99 Permian Basin Chapter of the AIME, 226 Perry, R.D., 297, 298, 544 Peters, D.C., 102 Peters, E.J., 874, 902 Peterson, R.B., 532, 793 Petrash, I.N., 56 Petricola, M.J.C., 53, 225 Pettitt, B.E., 28, 53 Petzet, G.A., 325,544 Phillips, C., 150, 224 Phillips, M., 534 Pickell, J.J., 481,544, 952 Pickering, K.T., 100 Pickett, G.R., 163, 164, 169, 180, 197, 208, 219, 226 Pierce, A.E., 677 Pinter, N., 84, 101 Pirard, Y.M., 222, 676 Pirson, S.J., 29, 55, 486, 544, 956 Pittman, D.J., 223 Plasek, R.E., 227, 229 Playford, P.E., 91, 94, 101 Plumb, R., 223 Plummer, L.N., 856 Pocovi, A.S., 331,544 Poggiagliolmi, E., 864 Poley, J.P., 192, 226 Pollard, P., 741,769 Pollastro, R.M., 790, 794 Pollock, C.B., 533 Polozkov, V., 949 PoroTechnologies, 147 Porter, J.W., 801,858 Posamentier, H.W., 56 Poston, S.W., 57, 326, 327, 329, 330, 544, 546 Poulson, T.D., 534 Poveda, G., 372, 435,543 Powers, R.W., 533 Pozzo, A., 544 Prade, H., 363, 53 7 Prats, M., 680 Pray, L.C., 254, 268, 536, 802, 805, 834, 845, 857

Price, H.S., 363, 368, 546, 810, 864, 894, 903 Price, J.G.W., 200, 226 Price, R.C., 861 Price, W.G., 541 Procaccia, I., 410, 423, 539 Prothero, D.R., 100 Pruit, J.D., 794 Pucci, J.C., 331, 544 Pugh, V.J., 146, 152, 481,484, 485, 541 Pullen, J.R., 800, 863 Purcell, W.R., 131,151, 201,226 Pyle, T.E., 856 Qi, F., 48, 55, 810, 832, 837, 840, 845,846, 862 Quanheng, Z., 48, 53, 806, 810, 825, 832, 837, 838, 845, 859, 863 Querol, R., 859 Quinn, T.M., 84, 100, 101 Quirein, J., 166, 227 Rabe, B.D., 99 Raeser, D.E, 787, 794 Rafavich, F., 67, 68, 101 Raffaldi, EJ., 152, 229, 546 Raghavan, R., 612, 638, 650, 672, 680, 681 Rhheim, A., 794 Raiga-Clemenceau, J., 172, 180, 227 Rainbow, H., 53 Raleigh, C.B., 535 Ramakrishnan, T.S., 221 Rainbow, EH.K., 209, 227 Ramey, H.J. Jr., 549, 553,563,565, 580, 585, 590, 595, 596, 597, 606, 611,632, 636, 656, 658, 659, 676, 677, 678, 680, 681 Ramey, H.J., Jr., 51,536 Randrianavony, M., 223 Rao, R.P., 840, 863 Raoofi, J., 534 Rapoport, L.A., 677 Rappold, K., 332, 333,534 Rasmus, J., 221 Rau, R.N., 192, 222, 227, 229 Ray, R.M., 279, 544 Raymer, L.L., 128, 150, 168, 172, 179, 180, 193, 224, 227 Raymond, D.E., 810, 831,863 Read, D.L., 863 Read, J.E, 83, 84, 99, 100, 101, 102, 798, 862 Read, P.A., 150 Reeckmann, A., 254, 544 Reed, C.L., 51,797, 856, 857, 858, 859, 860, 861,862, 864, 865

Reese, D.E., 543 Reeside, J.B., 792, 793 r Rehbinder, N., 224 Reid, A.M., 810, 812, 818, 825,862, 863

973 Reid, S.A.T., 812, 825,863 Reijers, T.J.A., 545 Reinson, G.E., 801,864 Reiss, L.H., 702, 769, 880, 881,902 Reitzel, G.A., 42, 54, 256, 544 Reservoirs, Inc., 147, 148, 151, 164, 165, 184, 190, 202, 227 Reynolds, A.C., 658, 680, 681 Reytor, R.S., 260, 261,262, 488, 489, 541,954 Rice, D.D., 791, 794 Richardson, J.E., 162, 194, 227, 228 Richardson, J.G., 44, 53, 260, 501,502, 539, 542, 885, 894, 902 Rickards, L.M., 50, 55 Ricoy, U., 679 Rieke, H.H. III, 1, 8, 38, 52, 53, 54, 231,233, 240, 242, 258, 297, 298, 334, 466, 534, 536, 537, 539, 541,542, 543, 544, 545, 546, 677, 681, 861, 900 Ringen, J.K., 150 Rittenhouse, G., 48, 55, 806, 863 Rivera, R.J., 677

Roach, J.W., 212, 227 Robert M. Sneider Exploration, Inc., 147, 148, 151, 164, 165, 184, 190, 202, 227 Roberts, J.N., 267, 544 Roberts, T.G., 18, 20, 21, 23, 51 Robertshaw, E.S., 56 Robertson, J.O. Jr., 54, 542, 937 Robertson, J.W., 533 Robinson, D.B., 680 Robinson, E.S., 59, 101 Robinson, J.D., 862 Robinson, J.E., 363, 466, 544 Rockwood, S.H., 952 Rodriguez, A., 679 Rodriguez, E., 166, 226, 227 Rodriguez-Iturbe, I., 540 Roehl, EO., 542, 793, 802, 803,804, 832, 833, 834, 845, 859, 860, 861,863 Roemer, P.B., 150, 152, 224, 229 Roger, W.L., 496, 543 Rohan, J.A., 150 Romero, R.M., 28, 52 Rong, G., 860 Root, P.J., 258, 546, 681,741, 769 Rosa, A.J., 659, 680 Roscoe, B.A., 227 Rose, ER., 813, 863 Rose, W.D., 131,151,177, 205,227,229, 389, 391,544, 547 Rosendahl, B.R., 97, 102 Rosman, A., 470, 544 Ross, C.A., 56 Ross, W.C., 101 Rossi, D.J., 224

Rothwell, W.P., 203,228 Rough, R.L., 8, 55 Roulet, C., 221 Rowly, D.S., 141,151 Ruessink, B.H., 141,151, 167, 227 Ruhland, R., 701,702, 703,712, 769 Ruppel, S.C., 103, 540, 811,859 Russ, J.C., 370, 544 Russell, D.G., 39, 55, 203, 210, 226, 549, 584, 679, 680

Rust, D.H., 169, 223 Ruzyla, K., 264, 545 Sabet, M.A., 549, 580, 645, 680 Sabins, ES., 8, 56 Sadiq, S., 473,545 Safinya, K.A., 207, 214, 227 Sahuquet, B.C., 46, 56 Salathiel, R.A., 875,902 Saller, A.H., 800, 811,830, 863 Salt, H.J., 435,539 Samaniego, V.F., 203, 210, 223,282, 317, 536, 537, 545, 550, 559, 563,575, 596, 598, 603,638,639, 656, 677, 679, 680 Sandberg, G.W., 533 Sander, N.J., 533 Sanders, J.E., 775, 783, 793 Sanders, L.J., 677 Sando, W.J., 798, 863 Sangree, J.B., 902 Sangster, D.E, 797, 863 Santiago-Acevedo, J., 813,830, 840, 863 Santoro, G., 53, 858 Sanyal, S.K., 152, 229 Saraf, D.N., 456, 545 Sarem, A.M.S., 285, 286, 538 Sarg, J.E, 50, 56, 82, 99, 101,861 Sass-Gustkiewicz, M., 797, 858 Saucier, A., 389, 401,403,405,415,421,422, 423,424, 425,427, 428, 430, 431,432, 545

Saunders, M.R., 151 Saupe, D., 546 Savit, C.H., 69, 70, 99 Savre, W.C., 227 Sawatsky, L.H., 177, 224 Sawyer, G.H., 54 Scala, C., 223,545 Scaturo, D.M., 59, 82, 83, 99, 101 Schafer-Perini, A.L., 594, 680 Schatz, EL., 532 Schatzinger, R.A., 540, 782, 783, 793, 794 Schechter, D.S., 881,902 Scheibal, J.R., 199, 227 Schepel, K.J., 215, 216, 225 Schilthius, R.J., 302, 545

974 Schipper, B.A., 150 Schlager, W., 77, 100, 280, 281,545 Schlanger, S.O., 49, 56, 773, 794 Schlee, J.S., 102 Schlottman, B.W., 545 Schlumberger, 158, 213,227 Schlumberger Educational Services, 169, 172, 175, 180, 181,182, 189, 197, 198, 199, 201,205,207, 214, 221,227 Schlumberger Limited, 207, 214, 227 Schlumberger, M., 227 Schmidt, A.W., 222 Schmidt, M.G., 222, 224 Schneider, EN., 545 Schneidermann, N., 793 Schnoefelen, D.J., 302, 534 Scholle, P.A., 49, 50, 56, 81,102, 139, 151, 782, 783, 790, 793, 794, 858, 860, 861

Schott, E.H., 696, 769 Schreiber, J.E, 810, 859 Schuffert, J.D., 864 Schwartz, L., 221 Schweitzer, J., 54 Schweller, W.J., 535 Schweltzer, J., 225 Scorer, D.T., 680 Scott, A.J., 811,840, 859 Scott, D.L., 97, 102 Scott, H.D., 53, 150, 173,225,227 Scott, J.O., 681, 813,864 Screenivasan, K.R., 426, 543 Scriven, L.E., 544 Seeburger, D.A., 222 Seeman, B., 53, 223,225 Seevers, D.O., 134, 151,203, 228 Seidel, F.A., 545

Sen, P.N., 394, 545 Sengbush, R.L., 60, 102 Senger, R.K., 436, 438, 439, 440, 443,444, 446, 449, 451,452, 454, 456, 545, 891,900, 902

Serra, J., 370, 545 Serra, K.V., 640, 681 Serra, O., 150, 208, 211,212, 213,224, 228 Sessions, R.E., 245,532, 545 Shalimov, B.V., 44, 51 Shanmugan, G.S., 103 Shannon, M.T., 228 Sharma, B., 540 Sharma, M.M., 405,543 Sharma, P., 60, 102 Shaw, B.B., 50, 53 Sheikholeslami, B.A., 329, 545 Shell Development Company, 147 Shepler, J.C., 302, 536 Sheriff, R.E., 60, 71, 72, 94, 102

Sherman, C.W., 535 Sherrad, D.W., 542 Shirer, J.A., 901 Shirley, K., 330, 545, 810, 863 Shouldice, J.R., 858 Shouyue, Z., 863 Shraiman, B.I., 539 Sibbit, A., 166, 223,226 Siemens, W.T., 306, 545 Sieverding, J.L., 812, 859, 863 Sikora, V.J., 335, 342, 543 Simandoux, P., 543 Simmons, G., 150, 224 Simmons, J.F., 581,582, 644, 645, 678, 681 Simon, R., 470, 544 Simone, L., 78, 102 Singer, J., 227 Sinnokrot, A., 536, 954, 956 Skinner, D.R., 937 Skjeltorp, A.T., 413,414, 539 Skopec, R.A., 136, 151,205, 206, 213, 228 Skov, A.M., 8, 28, 44, 53, 486 Skovbro, B., 415,545 Slider, H.C., 626, 681 Slingerland, R.L., 84, 102 Slobod, R.L., 457, 545 Slotboom, R.A., 897, 900 Slov, A.M., 487, 537 Smaardyk, J., 226 Smagala, T.M., 790, 791,794 Smart, P.L., 798, 800, 858, 863, 865 Smith, A.E., 51,534 Smith, D.G., 131,151, 183,212, 228, 800, 863 Smith, G.L., 862 Smits, J-W., 223 Smits, R.M.M., 150 Sneider, R.M., 141,146, 147, 152, 902 Snelson, S., 101 Snow, D.T., 769 Snowdon, D.M., 505, 507, 508, 536 Snyder, R.H., 151, 787, 794 Soc. of Professional Well Log Analysts, 110, 152, 208, 210, 221,228 Soewito, F., 102 Sorenson, R.P., 545 Soudet, H., 53, 858 Southham, J., 535 Spain, D.R., 138, 152, 158, 228 Spang, J., 52, 793 Spencer, R.J., 83, 99, 102 Spicer, P.J., 151 Spirak, J., 862 Spivak, A., 535 Spronz, W.D., 536 Srivastava, R.M., 893, 902 Stahl, E.J., 28, 51

975 Stalkup, F.I., 222, 882, 902 Standing, M.B., 235,545, 588, 589, 593,681 Stanislav, J.F., 549, 580, 656, 681 Stanley, H.E., 539, 542 Stanley, T.L., 533 Stapp, W.L., 326, 545, 787, 794 Staron, P., 224 Steams, D.W., 694, 695, 769 Steel, R., 100 Steeples, D.W., 102 Stegemeier, G.L., 542 Stehfest, H., 644, 681 Stein, M.H., 44, 56 Steineke, M., 533 Stell, J.R., 542 Stellingwerff, J., 225 Stevenson, D.L., 811, 831,865 Stewart, C.R., 21, 22, 56, 475, 477, 479, 480, 486, 488, 545 Stewart, G., 679 Stiehler, R.D., 532 Stiles, J.H. Jr., 901 Stiles, L.H., 33, 34, 53, 302, 534, 882, 902 Stiles, W.E., 33, 34, 35, 37, 56 Stockden, I., 151 Stoessell, R.K., 799, 864 Stoller, C., 227 Storer, D., 55 Stormont, D.H., 811,864 Stosser, S.M., 296, 539 Stoudt, D.L., 99, 100 Straley, C., 151,225,226 Straus, A.J.D., 5 7, 229 Streltsova, T.D., 681 Strickland, R., 228 Strickler, W.R., 680 Strobel, C.J., 681 Strobel, J.S., 83,100, 101,102 Strobl, R., 364, 369, 370, 371,547 Strubhar, M., 586, 681 Stubbs, B.A., 335,338, 339, 340, 341,343,344, 535

Suinouchi, H., 102 Sullivan, R.B., 534 Sutton, E., 533 Swanson, B.F., 131,152, 201,228, 544, 952 Swanson, R.G., 128, 152, 167, 178, 228 Sweeney, S.A., 188, 228, 480, 541 Sylvester, R.E., 98 Syrstad, S.O., 151 Syvitski, J.P.M., 102 Szpakiewicz, M.J., 540 Taggart, I.J., 539 Taijun, Z., 860 Taikington, G.E., 532

Taira, A., 101 Taisheng, G., 860 Takamura, K., 900 Takao, I., 84, 102 Talukdar, S.N., 813, 840, 863 Tang, Jie, 83, 102 Tanguy, D.R., 228 Tanner, C.S., 160, 228 Tappmeyer, D.M., 813, 856 Tariq, S.M., 679 Tarr, C.M., 27, 32, 56 Tatashev, K.K., 44, 56 Taylor, G.L., 53 Taylor, M.R., 151 Tek, M.R., 679 Telford, W.M., 59, 102 Teodorovich, G.I., 268, 400, 545 Tetzlaff, D.M., 84, 102, 227 Tew, B.H., 542 Theis, C.V., 584, 681 Theys, P., 223 Thomas, D.C., 146, 152 Thomas, E.C., 118, 125, 146, 147, 152, 159, 177,220,228 Thomas, G.E., 868, 902 Thomas, G.W., 593,681 Thomas J.B., 532 Thomas, O.D., 776, 778, 779, 780, 781, 783, 795

Thomas, R.D., 150 Thomas, R.L., 539 Thomasson, M.R., 96, 102 Thomeer, J.H.M., 106, 131,152, 155, 183, 201, 228 Thompson, A.H., 267, 270, 271,415, 541 Thompson, B.B., 534 Thompson, S., 55, 103, 864 Thorsfield, W., 101 Thrailkill, J., 797, 844, 864 Thrasher, R., 538 Thrasher, T.S., 538 Tiab, D., 563,681 Tillman, R.W., 541 Timmons, J.P., 226 Timur, A., 181,205, 228, 390, 466, 545 Tiner, R.L., 545 Tinsley, J.M., 335,342, 545 Tittman, J., 158, 179, 228 Tixier, M.P., 197, 208, 228 Todd, T.P., 101 Tomanic, J.P., 546 Tomutsa, L., 462, 468, 540, 545 Torabzadeh, J., 536 Torres, D., 207, 214, 228 Torrey, P.D., 244, 246, 249, 296, 545, 546 Tortike, W.S., 535

976 Touchard, G., 546 Tracy, G.W., 258, 543 Tran, T.T.B., 534, 899 Traugott, M.O., 186, 190, 209, 228 Travis, B.J., 535 Treiber, L.E., 902 Tremblay, A.-M.S., 423, 546 Tremblay, R.R., 546 Trocan, V.N., 45, 56 Troschinetz, J., 811,830, 832, 864 Trouiller, J-C., 223 Trube, A.S.Jr., 532 Truby, L.G., Jr., 22, 55 Truitt, N.E., 680 Tsang, P.B., 882, 883,900 Tsarevich, K.A., 681 Tschopp, R.H., 813, 864 Tumer, K., 190, 228 Turcotte, D.L., 83, 98, 102, 103,264, 273, 401, 407, 546 Tutunjian, P.N., 134, 135, 150, 152, 184, 197, 200, 224, 226, 228, 229, 546 Twombley, B.N., 100, 813,864 Tyler, N., 276, 277, 280, 538, 546 Tyskin, R.A., 807, 832, 864 Uliana, M.A., 803,862 Ulmishek, G., 234, 546 Underschultz, J.R., 888, 900 Vadgana, U.N., 681 Vague, J.R., 532 Vail, ER., 50, 55, 56, 82, 100, 103, 800, 802, 805,864 Van Akkeren, T.J., 28, 52, 209, 223 Van de Graaf, W.J.E., 893,902 Van den Bark, E., 776, 778, 779, 780, 781,783, 795

Van Den Berg, J., 535 van der Hijden, J., 223 van der Poel, C., 900 Van Der Vlis, A.C., 320, 321,546 Van Driel, J.J., 856 Van Everdingen, A.E, 41, 51, 56, 534, 553,587, 644, 681

Van Golf-Racht, T.D., 580, 581,677, 681, 710, 769

Van Horn, D., 863 Van Kruyskijk, C.EJ.W., 352, 353, 354, 546 van Meurs, E, 900 Van Ness, J.W., 365, 366, 543 van Poollen, H.K., 64 l, 644, 678 Van Schijndel-Goester, F.S., 795 van Straaten, J.U., 536 Van Wagoner, J.C., 56 Vandenberghe, N., 849, 85 l, 852, 855,864

Vander Stoep, G.W., 535 Vargo, G.A., 100 Vasilechko, V.E, 45, 56 Vela, S., 55, 297, 534, 635, 679, 681 Velde, B., 433,546 Vennard, J.K., 940, 941,949 Ventre, J., 225 Vernon, ED., 799, 864 Verseput, T.S., 864 Vest, E.L., 82 l, 825, 831,840, 864 Vest, H.A., 860 Videtich, EE., 813,864 Vienot, M.E., 649, 678 Villegas, M., 227 Vinegar, H.J., 134, 135, 136, 137, 150, 152, 168, 178, 179, 184, 200, 203,224, 226, 228, 229, 456, 457,458, 462, 466, 546 Viniegra, O.E, 813, 820, 830, 832, 847, 864 Visser, R., 166, 226 Viturat, D., 677 Vizy, B., 797, 857 Voelker, J.J., 538 Von Gonten, W.D., 335, 342, 543 von Rosenberg, D.U., 538 Vorabutr, P., 937 Voss, R.F., 365,366, 367, 546 Vrbik, J., 681 Vysotskiy, I.V., 807, 864 Waddell, R.T., 810, 864 Waggoner, J.M., 901 Waggoner, J.R., 901 Wagner, O.R., 52 Walker, J.W., 54 Walker, K.R., 103 Walker, R.D., 56 Walker, T., 208, 221 Wall, C.G., 106, 108, 149 Waller, H.N., 677 Wallis, J.R., 366, 372, 543 Walper, J.L., 53 Walter, L.M., 99, 101 Walters, R.E, 810, 815, 825, 831,864 Waltham, D., 83, 99 Wang, J.S.Y., 56 Wang, S.Y., 136, 137, 152 Ward, R.F., 33, 56, 79, 103 Ward, W.C., 864 Wardlaw, N.C., 801,864, 868, 872, 873,874, 876, 877, 878, 880, 886, 887, 893,894, 901,902, 903

Warembourg, P.A., 534 Warme, J.E., 793 Warren, J.E., 258, 363, 368, 546, 681,741, 769, 894, 903 Washburn, E.W., 184, 229

977 Wasson, J.A., 56, 533, 681 Waters, K.H., 59, 103 Watfa, M., 223 Watkins, J.W., 51 Watney, W.L, 83, 99, 862 Watson, H.J., 830, 832, 837, 840, 865 Watson, H.K.S., 864 Wattenbarger, R., 294, 295,546, 595, 681 Watts, D.E., 101 Watts, G., 864 Watts, N.L., 782, 784, 795 Watts, R.J., 44, 56 Wayhan, D.A., 360, 361,362, 533, 546, 811, 814, 830, 862 Weber, K.J., 1, 8, 25, 56, 436, 537, 541,546, 883, 884, 885, 892, 903 Weeks, W.C., 536 Wegner, R.E., 378, 543 Weidie, A.E., 856 Weiland, J.L., 227 Welex, 207, 214, 229 Wellington, S.L., 135, 136, 152, 168, 178, 184, 229, 456, 457, 458, 462,546 Wells, L.E., 128, 152, 168, 179, 193,222,229 Welton, J.E., 140, 152 Wendel, F., 227 Wendte, J.C., 101 Wesson, T.C., 57, 539, 899, 901,902 West, L.W., 883,903 West Texas Geological Society, 532 Westaway, E, 195,229 Westermann, G.E.G., 100 Wharton, R.E, 192, 229 Whately, M.K.G., 100 Wheeler, D.M., 857 Whitaker, F.F., 798, 800, 863 White, D.A., 233,546 White, F.W., 545 White, R.J., 533 Whiting, L.L., 811, 831,865 Whittaker, A., 108, 109, 120, 122, 123, 126, 127, 152

Whittle, G.L., 59 Whittle, T.M., 222, 676 Widess, M.B., 103 Wigley, EL., 48, 56, 799, 800, 845, 857, 865 Wilde, G., 862 Wilgus, C.K., 56, 101 Wilkinson, D., 221 Willemann, R.J., 83, 103 Willemsen, J.F., 151,225 Williams, J.R.Jr., 545 Williams, J.W., 901 Williams, K.W., 223 Williams, M.R., 228 Williams, P.W., 797,798, 799, 800, 801,806,

834, 835, 841,842, 858 Williams, R., 221 Willingham, R.W., 32, 45, 56, 533 Willis, D.G., 39, 54 Willmon, G.J., 44, 56, 533 Willmon, J.H., 615,679 Wilshart, J.W., 256, 259, 496, 497, 541,867, 901 Wilson, D.C., 678 Wilson, J.L., 99, 101, 807, 810, 812, 837, 865 Winham, H.E, 533 Winkler, K., 223 Winterer, E.L., 793 Wishart, J.W., 255, 256 Witherspoon, P.A., 4, 56, 585, 679 Withjack, E.M., 136, 137, 152, 457, 458, 546 Withrow, P.C., 814, 831,865 Witterholt, E.J., 158, 215,225 Wittick, T.R., 222 Wittmann, M.J., 679 Wolf, K.H., 25, 56, 536 Wong, P-Z., 390, 394, 395,397, 398, 546 Wood, G.V., 860 Wood, L., 70, 103 Woodland, A.W., 52 Woodward, J., 794 Woolverton, D.G., 60, 99, 856, 857, 862 Wooten, S.O., 54 Works, A.M., 538 World Oil Coring Series, 108, 110, 111, 112, 113, 116, 123, 124, 152, 158, 182, 183, 229 Worrell, J.M., 199, 227 Wortel, R., 84, 99 Worthington, M.H., 158, 215,229 Worthington, P.F., 1, 2, 5 7, 294, 295,546 Wraight, P.D., 53, 221,225 Wright, M.S., 52 Wright, V.P., 280, 546, 797, 799, 845, 847, 858, 863, 865

Wu, C.H., 42, 43, 57, 302, 310, 542, 546, 547 Wunderlich, R.W., 137, 145, 146, 152 Wurl, T.M., 376, 378, 537 Wyatt, Jr., D.F., 195,225,229 Wyllie, M.R.J., 172, 180, 205,229, 391,547 Wyman, R.E., 138, 153, 227 Xie-Pei, W., 48, 55, 810, 832, 837, 840, 845, 846, 862 Xueping, Z., 860 Yamaura, T., 102 Yang, C-T., 542 Yang, D., 903 Yapaudijan, L., 858 Yen, T.E, 877, 900 Yortsos, u 432, 433,534, 535

978 Youmans, A.H., 192, 193,229 Young, G.R., 436, 547 Young, J.W., 541 Young, M.N., 44, 5 7 Youngblood, W.E., 199, 200, 229 Yuan, H.H., 132, 139, 153 Yuan, L-P., 364, 369, 370, 371,547 Yuster, S.T., 38, 57, 296, 547 Zana, E.T., 593,681

Zemanek, J., 28, 5 7, 207, 214, 229 Zheltov, Y.P., 769 Zhenrong, D., 860 Zhigan, Z., 807, 865 Zhou, D., 902 Ziegler, P.A., 782, 795 Zimmerman, L.J., 28, 5 7 Zogg, W.D., 811, 831,863 Zotl, J., 797, 865 Zwanziger, J.E., 326, 547

979

S U B J E C T INDEX*

Abkatun field (Middle East), 635 Abo Formation, 481,483,484 Abqaiq field (Saudi Arabia), 332,528 Abu Dhabi, 95, 96, 332, 333 Acheson field (Canada), 523 Acheson-Homeglen-Rimbey trend (Canada), 237, 238,247 Acid stimulation, 1 , acidizing technology, 27 Acoustic logs, 17, 17, 28, 59, 65 , waveforms, 56, 64 Acoustic tomography, 158 Adair field (Texas), 43 Adell field (Kansas), 519 Adell Northwest field (Kansas), 528 Aden Consolidated and Aden South fields (Illinois), 528 Advanced fracture treatments, 337 Africa, 91, 94 Aggradation, 59, 60 Agha Jari field (Iran), 799 Airborne radar imagery, 8 Alabama 325, 810 Alberta Basin (Canada), 801 Albion-Scipio-Pulaski trend (Michigan), 49, 810, 827, 828, 830, 837, 849 Albuskjell field (North Sea), 415, 781 Alden Northeast field (Oklahoma), 811 Algal-plate buildups, 74 Alison Northwest field (New Mexico), 531 Allen field (Texas), 24 Amposta Marino field (Spain), 48,799, 800, 813, 830, 844, 845, 851,853 Amrow field (Texas), 523 Anadarko Basin (USA), 49, 810, 811,814, 822, 827, 831,832 Aneth field (Utah), 520 Anhydrite, 145, 165, 169, 173, 259, 304, 309, 361,383,466 Anisotropy (reservoir), 3, 8, 9, 231 Anton-Irish field (Texas), 519 APEX models, 132

*Prepared by S.J. Mazzullo and C.S. Teal.

API gravity (oil), 240-242, 246, 249 Appalachian Basin (USA), 242 Arab-D Formation, 265,266, 332 Arbuckle (limestone, dolomite, formation, group), 247, 814, 815, 827 Archie's factor, equation, law, 10, 34, 67133, 147, 163,164, 168, 178, 184, 186-189, 196,217, 219, 267 Archie parameters, 190 Archie reservoir classes, 291 Archie rock types, classification, 481,482,484 Argentina, 326, 331,803 Arkansas, 20, 23, 24, 247, 253, 346, 481,482, 519, 522, 523 Arkoma Basin (USA), 810 Artesian flow, 22 Artificial lift, 17 Arun Limestone, 272, 418--422 Ashburn field (Kansas), 24, 523 Ash Grove field (Kansas), 525 Asmari Limestone, reservoir, field (Iran), 23,235, 502, 799 Atlanta field (Arkansas), 24 Atolls, 76, 91, 94, 95, 292 Austin Chalk, 44, 45, 56, 59, 81,208, 2!0, 278, 325-331, 481,784-791 Australia, 94, 851,854 Austria, 812, 820, 824 Austrian Chalk, 265 Authigenic clay, 256 Axeman Formation, 12 A4 Formation, 45 Bab field (Abu Dhabi), 333 Bahamas, 83-85 Bahrain, 528 Bahrain field (Bahrain), 528 Band method, 35 Bangestan Limestone, 235 Bannatyne field (Montana), 523 Bantam field (Nebraska), 525 Banyak Shelf, 93 Barada field (Nebraska), 525 Bar Mar field (Texas), 520 Basin and Range (USA), 811, 831

980 Bateman Ranch field (Texas), 520, 523 Bear's Den field (Montana), 531 Beaver Creek field (Wyoming), 522 Beaverhill Lake Formation, sub-group, 239,490, 493,494, 496 Beaver River field (Canada), 504-509 Bedford Limestone, field (Texas), 24, 265,266 Belle River Hills field (Canada), 811,830 Berea Sandstone, 133 Bemouli equation, 7 Berri field (Middle East), 332 Besa River Formation, 508 Big Creek field (Arkansas), 24 Big Eddy field (New Mexico), 520 Big Horn Basin (USA), 301,355, 811 Big Spring field (Texas), 521 Big Wall field (Montana), 525 Bimini Bank, 83, 84 Bindley field (Kansas), 811,830 Bioherms, biostromes, 23 Bitter Lake South and West fields (New Mexico), 521 Blackfoot field (Montana), 530 Black Leaf field (Montana), 525 Black oil, 235 Black Warrior Basin (USA), 810, 831 Blanket (infill) development, 307-310 Block 31 field (Texas), 24, 278, 519 Block 56 field (Texas), 829 Bloomer field (Kansas), 815 BOAST model, 322 Bohay Bay Basin (India), 810 Bois D'Arc-Hunton, 21,45 Bombay High field (India), 813 Bond shrinkage, 395 Bonnie Glen field(s)(Canada), 237,238,523,897 Boquillas Formation, 326 Borehole televiewer logs, 58, 64, 65 Bough Devonian field (New Mexico), 523 Boyle's Law, 119, 120, 123,266 Brahaney Northwest field (Texas), 830 Breakthrough, 883 -, of water, 350, 490, 494 Bredette field (Montana), 525 Bredette North field (Montana), 525 Breedlove field (Texas), 523 Bresse Basin (France), 812, 848 Bronco field (Texas), 523 Brown-Bassett field (Texas), 527 Brown Dolomite, 29, 36, 37, 325 Brown field (Texas), 521,525 Bubble point, 18, 44, 235, 242, 244, 356, 510, 514 Buckner field (Arkansas), 24, 248, 522 Buckwheat field (Texas), 830 Buda Limestone, 44, 325

BuHasa Formation, field (Middle East), 48, 74, 80, 813, 825 Buried hill traps (see Karst) Burro-Picachos Platform (Mexico), 326 Bush Lake field (Montana), 291 Bypassing, 27 -, bypassed oil, 287, 289, 456, 488, 873-877, 897 Cabin Creek field (Williston Basin), 525,804 Cactus field (New Mexico), 840 Cairo North field (Kansas), 521 California, 20 Caliper logs, 53 Cambrian, 814 Campeche-Reforma trend (Mexico), 48, 813, 820, 830, 840 Camp Springs field (Texas), 521 Canada, 38, 44, 74, 78, 237, 239, 240, 242,247, 250, 252,254, 326, 461-465,472,489, 490, 492,496--498, 501,504-507, 519,520,523, 524, 529, 531,801,805,812,818, 822, 867, 868, 890, 895,897 Canning Basin (Australia), 94 Capillary end effect, 486 Capillary pressure curves, 31, 33, 51, 62 Capillary pressure, forces, 1,131,132, 144, 145, 183,939-949 Carbonate play types , buildups, organic buildups, reefs, 59, 60, 74, 76-78, 82, 89, 91, 95 , clinoform, shelf margin, 59, 60, 79, 80, 82, 86-97 , sheets, sand sheets, sand shoals, 59, 60, 72-75, 82, 91, 95 Carlile Shale, 791 Carson Creek field (Canada), 239, 240 Carson Creek North field (Canada), 239, 240 Carter Creek field (Wyoming), 812, 820 Cary field (Mississippi), 525 Casablanca field (Spain), 812, 830, 832, 840 Catch-up sedimentation, 59, 76-78, 82 Cato field (New Mexico), 258 Caves, caverns (paleocaves, paleocavems), 47 (see Karst ) -, cave-filling breccias, 47 (see Karst) Central Basin Platform (Texas-New Mexico), 33, 300, 310, 338, 811,812 Central Kansas Uplift (Kansas), 810-812, 815, 830, 831 Chalk, chalky reservoirs, 49, 59, 81, 86, 292, 415, 416, 508, 773-793 -, burial diagenesis, 782, 789 -, effective porosity and permeability, 783 -, facies, 782 , autochthonous, 782

981 , allochthonous, 782 -, fractures, 783, 788, 791 -, horizontal drilling, 785-787, 791,792 -, North American versus European chalks, 784792 -, overpressured fluids, 783 -, permeability, 783,788 -, primary versus secondary porosity, 772, 783, 788 -, source rocks, 792 -, stimulation, 791 Chalk Group, 777 Channeling, 2, 42,259,468 -, channel porosity, 468 Chaos theory, 400 Chase Group, 302, 306 Chase-Silica field (Kansas), 831 Chaveroo field (New Mexico), 258, 521 Chazy Group, 816 Chert, 20, 21, 96, 169, 173,759, 779 Chihuido de la Sierra Negra field (Mexico), 331, 332 China, 48, 785, 806, 810, 820, 823, 825, 837, 840, 845, 846 Cincinnati Arch (USA), 810,827 Circular drawdown, 8 Clear Fork Formation, 18, 33, 42, 43, 165, 303 Coccoliths, coccospheres, 49, 773-776, 790 Cogdell field (Texas), 821 Coldwater field (Michigan), 522 Colmer-Plymouth field (Illinois), 811, 831 Colorado, 527,790 Comiskey field (Kansas), 24, 523 Comiskey North-East field (Kansas), 523 Compaction, 4, 49, 50, 83,256, 272 Compartmentalization (see Reservoir) Compressibility (oil),9 Computer -, forward modeling, 50, 83 -, modeling, 1, 8, 17, 329, 492, 508, 884 -, simulations, 59, 82, 84, 85,489 Collapse breccias, 96 Confocal microscope, 26 Coning, 296, 332, 490-493,507, 508, 738-740, 885 Contact angle, 725, 873,939, 943,944 Controls on carbonate productivity, 85 Cores, coring -, analysis, 3, 4, 13, 31, 48, 49, 54, 60, 62, 105, 106, 116, 158, 159 -, bottomhole cores, 109 -, capillary pressure testing, 129 -, containerized whole coring, 111 -, core fluids, 108 -, core gamma scans, 116, 133 -, CT scans, 116, 118, 128, 135, 136'~ 142

-, -, -, -, -, -, -, -, -, -, -,

electrical resistivity, 116 geochemical analysis, 116 handling, preservation, 108, 115 horizontal wells, 54 NMR scans, 116, 118, 128, 129, 134, 135 oriented cores, 110, 213 percussion sidewall cores, 115 photos, 129, 130 pressure coring, 112 resistivity, 133 sidewall cores, 105, 107, 111, 114, 116, 165, 199 -, slimhole cores, 138 -, sponge whole coring, 113, 183 -, stress analysis, 129 -, whole coring, cores, 105, 107, 108, 110, 115 Coming field (Missouri), 523 Corrigan East field (Texas), 830 Cotton Valley Limestone, Group, 346-348, 351 Cottonwood Creek field, unit (Wyoming), 32, 45, 355, 357, 521,810 Coulommes-Vaucourtois field (France), 10 Council Grove Group, 302, 206 Coyanosa field (Texas), 527 CO 2 -, displacement, 11,457 -, injection, 44, 380 -, production rates, 379 -, saturation, 162, 195 C-Pool (Swan Hills North field, Canada), 240 Craig-Stiles method (performance), 35-37 Cretaceous, 38, 40, 44, 46, 48, 49, 72, 80, 81, 86, 95, 208, 240, 301,325, 331-333,415, 468, 481,498,499, 596, 599, 615, 621,773, 775,778,779,784, 789, 803,814, 820, 825, 832, 837 Cretaceous chalk, 773,775 Cretaceous limestones (Louisiana and Mississippi, 56 Cristobalite, 775 Critical oil saturation, 31 Crittendon field (Texas), 830 Crosset South-E1 Cinco fields (Texas), 530 Crossfield field, 812 Cross-flow, 37, 384 Crossroads South field (New Mexico), 525 CT scans, 15, 27, 32, 168, 178, 179, 184, 456462 Cuttings samples, 165, 167, 178, 200, 329, 482 Cyclicity in carbonates, 59, 73, 74, 78, 84, 300, 306, 308, 439 Cyclic oil, 45 Cyclic steam stimulation, 45 DAK (dolomite-anhydrite-potassium) model, 165 Dale Consolidated field (Illinois), 528,530

982 Daly field (Williston Basin), 812 Damme field (Kansas), 522, 528 Davis field (Kansas), 521 Davis Ranch field (Kansas), 525 Dawson field (Nebraska), 525 Dean-Stark extraction, apparatus, 126, 127, 134, 137 Dean-Wolfcamp pay (Texas), 258 Debris flow deposits, 87, 89 Decline curve analysis, 42,293,326 Deer Creek field (Montana), 525 Deerhead field (Kansas), 530 Delaware Basin (USA), 310,338 Delphia field (Montana), 523 Density logs, 16, 17, 27, 47 -, spectral, 16, 27 Denver Basin (USA), 776-778 Depletion, rate, 490, 492,496, 498 Depositional sequences, 82 Devil's Basin field (Montana), 521 Devonian, 21, 44, 45, 74, 78, 79, 94, 239, 240, 490, 497,498, 501,505,506, 508, 801,805, 814, 827, 867, 869, 882, 896 Diamond-M field (Texas), 821 Diamond-M/Jack field (Texas), 43 Diamond-M/McLaughlin field (Texas), 43 Dielectric logs, 41 Differential entrapment, 236, 239, 240 Digital production, 1 Diplogs/dipmeters, 56, 62, 65 Dispersivity (permeability), 367 Dollarhide East field (Texas), 525 Dollarhide field (Texas), 799, 800, 811,830 Dolomites, radioactive, 18 Dorado field (Spain), 830 Dorcheat field (Arkansas), 522 Dorward field (Texas), 303,304 Douthit unit, 305 Drawdown, analysis, 8, 583, 584 -, curve matching, 649 Drill stem tests, 4, 45 Drilling well, formation evaluation, 5 Drive mechanisms (reservoir), 243-254, 276 , combination drives, 250-253,528 , external gas drive, 475 gas-cap expansion, 243,246, 485, 502,510, 512, 513, 527, 867, 869 - - , gravity drainage, drive, 243,249, 254, 489, 494,497,498,500,502, 510, 511, 515,867, 869, 885, 898 solution-gas, 17, 20, 27,243,244, 340, 361, 383,470,475,477,478,485,488,502,510516, 518, 867, 869 , undersaturated oil expansion, 502 , water drive, encroachment, 243, 247, 311, 340, 489, 522, 867, 869 ,

,

, bottom water, 490, 496, 510, 511, 514, 515 DST data, analysis of, 105, 158, 165 Dubai (UAE), 80 Dune field (Texas), 32, 33, 278, 299, 307-309, 338, 339, 342, 344, 443,449, 452 Dupo field (Illinois), 525 Dwyer field (Montana), 530 Dykstra-Parsons coefficient, 290--292 D-I, D-2, D-3 zones (Devonian, Canada), 240, 242, 252 Eagle Ford Formation, 326 Eagle Springs field (Nevada), 526 East Texas field (Texas), 248 ECLIPSE (reservoir simulation program), 449 Edda field (North Sea), 781 Edinburg West field (Illinois), 811, 831 Edwards Group, 468 Egypt, 468 Ekofisk Formation, field (North Sea), 49, 50, 415, 778, 779, 781 E1Abra Limestone, 820 Eldfisk field (North Sea), 415, 781,783 Electrical array imaging logs, 56, 63, 64, 65 Electrical conductivity, 164, 186 Electrofacies, 211 Electromagnetic tomography, 158, 215 Elk Basin field (Wyoming), 359, 362, 52 l, 525, 811,830 Elkhorn field (Texas), 24 Ellenburger Dolomite, fields (Texas, New Mexico), 22-24, 56, 59,208, 210, 818, 827-830,838, 848 Embar field (Texas), 24 Emma field (Texas), 848 Enlow field (Kansas), 529 Eocene, 468, 469 Epeiric seas, basins, 76, 95 Error propagation, in formation evaluation, 67 Ervay Member (Phosphoria Formation), 355 Etosha Basin, 94 Eubank field (Kansas), 519, 527 Europe, 49, 775,776, 787, 792, 793, 853 Eustasy, eustatic curves, 82-85, 73, 76, 77 Evaporites, 72, 74, 77, 79, 80, 276, 505, 786, 800, 885 Evaporitic drawdown, 800 Excelsior D-2 (reef) pool, field (Canada), 250, 496, 497 Expert systems, 167 -, for formation evaluation, 13 Extension drilling, 298 Fahud field (Middle East), 48,, 813,825 Fairplay field (Kansas), 526

983 Fairview field, 810 Fairway field (Black Warrior Basin), 278,520 Fallon field (Texas), 346, 348, 351 Falls City field (Nebraska), 526 Fanglomerates, 97 Fanska field (Kansas), 530 Fateh field (Dubai, Middle East), 48, 80, 813,825, 830 Faults, 25 -, sealing, non-sealing, 25 Feeley field (Kansas), 528 F enn-B ig Valley field (Canada), 461-465 Fertile Prairie field (Montana), 530 Field A (Mediterranean Basin), 22, 813 Field development, 105, 231 Findlay Arch (USA), 810, 827 Fingering, 459 Fishook field (Illinois), 527 Flanagan field (Texas), 43 Floods, flooding -, alkaline, 275 -, brine pre-flood, 160 -, chemical, 42, 137, 162 -, core, 137 -, CO 2, 44, 113, 137, 157, 160, 161,275,379 -, cyclic, 44, 45 -, fire, 137, 275 -, immiscible gas, 896 -, miscible, 42, 44, 45, 137,275,894, 896 -, pilot, process pilot, 35, 159 - - , formation evaluation, 7 -, polymer, 162, 275,296, 298-300 -, solvent, 896-898 -, steam, 46, 275 -, tertiary, 195 -, vertical, 896, 898 -, water, 23, 25, 27-29, 33, 34, 41, 42, 44, 45, 112, 113,137, 157,284, 287,290,293,296, 302,307-310, 332,356,357,378,380,384, 387, 436, 440, 444, 480, 496, 497, 869-871,874, 877, 878, 881 , displacement efficiency, 871,894 - - , hot water, 137 , performance, 883 , versus vugs, 508, 874, 948 Florida, 301,468, 481,482, 484 Fluid displacement, 867 Fluid flow, 1,306, 232 , barriers, 25, 233, 257, 306, 363, 451,882, 884, 887, 896, 898 , behavior, 258 , capacity, 39, 40 , channels, 46 , compartmentalization, 456 , diagnosis, 563,580 -, dynamics, 1,276 -

, flow units versus depositional facies, 439 , fracture-fluid flow, 5 , index, 15, 16 , laminar, turbulent, 5, 6 , models, 446 , multiphase, 378 , paths, 459 , radial, 330 , simulations, 440 - - , single-phase, 4 steady-state, 9 , storage-dominated, 565 , units, 454 , velocity, 4 Fluid injection, 27 Fluid saturation, 1, 106, 122, 182 , irreducible, 1,124 Flushed zones, 188, 190 Formation evaluation, 1,155, 156, 232 , drilling wells, 5, 159 , for flood process pilots, 7 , openhole wells, 159 , production surveillance, 7 , propagation of error considerations, 67 - - , properties of interest, 2 - - , situations, 5 , tools, 4, 157 Formation stimulation, 334, 335 Formation volume factor, 8, 17, 36, 116, 284, 289, 311,514 Formation water, 195 , salinity, 134 Fort Jessup field (Louisiana), 325 Foster field (Texas), 30, 36, 37, 519 Fourier transform infrared spectroscopy (FTIR), 14, 167 FRACOP model, 349--351 Fractals, 364, 371,421 -, analysis, 412 -, dimensions and permeability, 415, 422, 426, 430 -, models, 399, 406 -, performance models, 371 -, relationships, 409 -, reservoirs, 432 FRACTAM, 388,389 Fractional water saturation, 36 Fractures, fractured reservoirs, 2-6, 11, 14, 15, 23, 38, 39, 41, 44-46,50, 59, 81, 116, 141, 142, 144, 208, 210, 250, 257,258,260, 264, 296, 311, 313, 318, 319,326, 332,334, 342, 390,457,487, 501,503,508, 615,796, 883, 887-, artifical versus natural fractures, 683 , pressure gradient, 685 , versus depth, 685 -, detection, 54 ,

984 -, displacement versus wettability, 722 -, drainage and displacement, 750, 752 , imbibition, 722, 723,725,750, 752 -, flow capacity, 335,339 -, flow through, 714-720 -, fluid supply (storage) sources, 714 -, fracture compressibility, 719 -, fracture conductivity, 317 -, fracture coning, 724-726 -, fracture continuity, 3 -, fracture detection, 205 -, fracture evaluation, 698, 708, 721 -, imbibition, 722, 723,725,750, 752 , intensity, density, 699, 702, 706, 710, 727 , Relperm curves, 721 , role of wettability, 721 , single versus groups of fractures, 699, 701 , statistical representation, 709 , through transient-flow well data, 740, 747 , through well production data, 727, 736 -, fracture formation , experimental, 689 , folding versus fracturing, 692, 701 , horizontal versus vertical, 703,705-707 , influence of stylolites and joints, 688,690, 697, 701 , joint formation, 697 - - - , microfractures, macrofractures, 689, 699, 712 , relation to geologic history, 687 -, fracture geometry, 329 -, fracture gradient, 39 -, fracture index, 12, 14-16 -, fracture-matrix system, 3, 143,259, 260, 475, 477, 485,615, 881 -, network gas cap, 686 -, orientation, directionality, 8, 28, 143 -, pitch angle, 16, 17 -, planes, 16 -, spacing, 3, 9, 10, 12 -, stimulation, 325 -, fractured chert, 20, 21 -, frequency, 32 -, gas-gravity drainage, 687 -, gas segregation, 687 -, gravity-drainage matrix-fracture fluid exchange, 763 -, induced fractures, 27, 28 -, patterns, 10 -, porosity and permeability of fractures, 4, 711, 713 , magnitude of, 712 , matrix, 713 , measurement, 716 , productivity index, 716 , single versus double porosity, 711,727, 728

-, pressure decline rates, 686 -, refracturing, 354, 355 -, roughness, 5 -, storage capacity, 710 -, treatment, 345 -, two-phase contacts, 684 Fradean field (Texas), 526, 527 France, 11, 46, 812, 848 Free fluid index, 181 Free water level, 62 Fresnel zone, 66 Friction factor 0r in fractures, 4--6 Frio Formation, 33 Frobisher Limestone, 240, 242 Ft. Chadborne field (Texas), 519 Fuhrman-Mascho/Block 9 field (Texas), 43 Fullerton field (Texas), 18, 33, 34, 43,285,286, 303,519 Gage field (Montana), 529 Gamma ray logs, 18 -, induced spectroscopy, 18, 29, 44 -, natural spectroscopy, 18, 22 Gamma ray spectral evaluation, 8 Gard's Point field (Illinois), 519 Gas bubble, 11 Gas cap, 235-237, 240, 243,246, 253,332 Gas City field (Montana), 530 Gas expansion, 236, 243,252 Gas injection, 28 Gas/oil ratio, 17, 244, 245 Gas shrinkage, 243 Gas turbulence, 472 Gela field (Italy), 26 Geochemical logs, 21, 29, 53 GEOLITH program, 384 Geotomography, 4, 64, 158, 215,217 Ghawar field (Middle East), 332 Ghwar-Ain-Dar field (Middle East), 529 Ghwar-Fazran field (Middle East), 529 Ghwar-Harah field (Middle East), 529 Ghwar-Hawiyan field (Middle East), 529 Ghwar-Shedgum field (Middle East), 529 Ghwar-Uthmaniyan field (Middle East), 529 Giddings field (Texas), 326-330, 785,786 Gila field (Illinois), 522 Gingrass field (Kansas), 526 Give-up sedimentation, 76, 77, 82 Glendive field (Montana), 530 Glen Park field (Canada), 238, 523 Glorieta Formation, 33 GMK field (Texas), 520 Golden Lane trend (Mexico), 48, 813, 814, 820, 825, 830, 832, 837, 847 Golden Spike field (Canada), 254, 257, 520 Goldsmith field(s)(Texas), 18, 246, 247

985 Goodrich field (Kansas), 526 Gove field (Kansas), 521 Grain density, 116, 128, 167, 168 Grant Canyon field (Nevada), 811, 831 Gravitational compaction, 3 Gravity segregation, 384, 457, 486, 487 Grayburg-Brown Dolomite, 30, 36, 37 Grayburg Formation, 18, 33,307, 308, 387,436 Grayson field (Texas), 522 Greater Ekofisk Complex (North Sea), 781,782 Greenland, 94 Green River Formation, 280 Greensburg field (Kentucky), 521 Greenwich field (Kansas), 526, 530 Greenwood field (Kansas, Colorado, Oklahoma), 527 Guadalupian, 308 Guelph Formation, 457-459 Gulf Coast (USA), 22, 49, 81, 90, 326,496, 775, 784, 813,825,883 Gulf of Mexico, 80, 420, 422 Gypsum, 145, 169, 173, 179, 466 Gypsy Basin field (Montana), 530 Hadriya reservoir (Middle East), 332 Halite, 145, 173 Hall-Gurney field (Kansas), 831 Hanifa reservoir (Saudi Arabia), 332 Hanson field (Texas), 521 Hardesty field (Kansas), 530 Harmattan East field (Canada), 812 Harmattan field (Canada), 868 Harmattan-Elkton field (Canada), 519, 812 Harper field (Texas), 18,489 -, San Andres pool (Texas), 262 Hasmark Dolomite, 281 Hausserman field (Nebraska), 526 Hawkins field (Texas), 897 Haynesville field, limestone (Louisiana), 21,346, 348, 351,519 Healdton field (Oklahoma), 810, 831 Heavy oil, 46, 47, 123 Hidra Formation, 777 Highstand systems tract, 59, 76, 77, 80, 90 Hingle plots, 17, 46, 197 Hith Anhydrite, 96 Hobbs field, reservoir (New Mexico), 248, 338 Hod Formation, 415,777 Holocene, 94, 468, 802 Homeglen-Rimbey field (Canada), 237,238,523 Horizontal wells, drilling of, 45, 48,295,296, 310, 313-316, 318-325,329, 331-333,350, 353 , slant horizontal drilling, 295,296, 310, 320, 321,324, 325 Horseshoe Atoll (reef) trend, field (Texas), 48, 812, 814, 821,831,837

Hortonville field (Kansas), 519 Howard Glasscock field (Texas), 340, 345,526, 529 Huat Canyon field (Texas), 526 Huat field (Texas), 521 Hugoton Embayment (USA), 306 Hugoton field (Kansas, Oklahoma, Colorado), 297, 302, 304-307, 526 Hungary, 812 Hunton Limestone, Group, 2, 3, 21,302, 814 Hutex field (Texas), 526 Huxford field (Alabama), 325 Hydraulic fracturing, 296, 297, 313, 333, 334, 336, 340, 344, 346, 347, 350, 353 Hydrocarbon recovery, 17, 23 Hydrodynamic, hydrostatic pressure, 21, 22 H2S, 113 Illinois, 519, 522, 524, 525,527-530, 811 Illinois Basin (USA), 240, 241, 301, 811, 831 Image analysis, 26, 32, 51, 61, 178, 184, 202, 271,435 Imaging logs, 56, 65 Imbibition, 27, 28, 44, 47, 260, 489, 494, 501, 502, 504, 722, 723,880 Impression packer tests, 28 India, 813 Indiana, 266, 519, 520, 521,527, 810, 827 Indiana Limestone, 281,345 Indian Basin field (New Mexico), 531 Indonesia, 272, 418, 419, 421,422 Induced gamma ray spectroscopy logs, 18, 29, 44 Infill drilling, wells, development, 41, 42, 234, 295-300, 302-304, 307-310,324, 871,884 Injected water, 24, 27, 194, 362, 380, 384, 497, 511,870 , injectant loses, 162 - - , injection balancing, 884 , rate, tests, 38, 194 , thief zones, 28 Interfacial tension, 939, 940, 942, 944 Interference tests, 28, 631 Internal (reservoir) energy, 23 Intisar "D" field (Libya), 813, 831 Invasion (mud filtrate), 52, 53 Invasion (water), 123, 124, 182, 188, 203,204, 260, 488, 501,502, 881 Iran, 23,235, 502 Iraq, 503, 813,840 Irion 163 field (Texas), 829 Irreducible water, 18, 19, 31, 38, 182, 390, 484, 485 Irvine-Fumace field (Kentucky), 45 Ishimbay field (former Soviet Union), 812 Italy, 26, 813, 831

986 Jamin effect, 948 Jay field (Florida), 883,885 Jingo field (Kentucky), 529 J.M. field (Texas), 59, 210 John Creek field (Kansas), 24, 526 Johnson/Grayburg field (Texas), 43 Johnson/J.L. "AB" field (Texas), 43 Jordan field (Texas), 24 Judy Creek field, pool, reef (Canada), 239, 240, 496, 497, 868, 869, 882 Judy Creek South field (Canada), 239, 240 Jurassic, 72, 90, 325, 331,332, 345, 359, 481, 508, 510, 782, 792, 803 Kansas, 24, 74, 247,297, 301,302, 304-306, 519531,790, 810-812, 814 Kansas City Group, 96 Karabala carbonates, 498, 499 Karst, 797-856 -, associated mineral deposits, 797 -, controls on karstification, 801 , karst-forming systems, 799, 800, 805 , polygenetic, polycyclic karsts, 799,800, 834, 840, 845 , sulfuric acid oil-field karsts, 799, 805 -, karstic carbonates, dolomite, 46, 47 -, pay thickness, continuity, heterogeneity, 840844 -, petrophysical characteristics, 833-846 , megascopic dissolution, 834 , numbers of caves, caverns, 834, 836, 837 , porosity associated with breccias, 837840, 851 - - - , porosity preservation, loss, 834, 835 , porosity types, 834, 837 , recovery efficiency, 845 , transmissability, 844 -, porosity, permeability, 259, 361,797,804, 818, 820, 833,846 , facies selectivity, non-selectivity, 803,806 , timing of porosity formation, 825 -, relation to fractures, faults, joints, 806, 827, 828, 837, 844 -, relation to sea level, 800 -, relation to unconformities, 797-799, 801,804, 806, 807, 818, 826, 828, 840 -, reserves , producible, 828, 830-832 , rates of production, 832 , recovery efficiency, 845 , ultimate recoverable, 797, 832 - , reservoir compartmentalization, 805, 842845 -, reservoir relief, 825 -, structural expression, 825 -, subsurface recognition, 797, 837, 847

, bit drops, 837, 851 cave cements, 847, 851 , drill cuttings, 847 , drilling breaks, rates, 837, 847 , from dipmeter, 851 , from well data, 848, 851 , loss of circulation, mud, 838, 851 , seismic, 847-853 - - - , subsurface mapping, 847 -, topography, 95 -, trap types, classification, 807-814 , buried hills, 806, 807, 814-816, 818--825, 833, 840, 844, 847, 853 - - - , paleogeomorphic, subunconformity, 792, 797, 807, 818 , supraunconformity, 793 -, types, classification , buried paleokarsts, 806 , Caribbean style, 802, 804, 805 , depositional paleokarsts, 803 , diagenetic terranes, 803 , general model, 804, 805 , interregional karsts, 805 , paleokarsts, 806 , relict paleokarsts, 806 Keep-up sedimentation, 59, 73, 80, 82 Keg River pool (Canada), 890 Kelly-Snyder field (Texas), 278,520, 821 Kentucky, 45,326, 521,529 Keystone field (Texas), 24 Khami Limestone, 235 Kimmeridge Clay, 782,792 Kincaid field (Illinois), 831 Kirkuk Group, field (Iraq), 502, 504, 799, 813, 840 Klinkenberg effect, corrected permeability, 121, 145, 146, 201,472 Knowledge-based systems, for formation evaluation, 13 Knox carbonates, 816 Komi Republic (former Soviet Union), 47 Kraft-Prusa field, trend (Kansas), 810, 814, 815, 831 Kriging, 363,364, 890, 891 Kurkan reservoir, field (Turkey), 498, 499 Kuwait, 275

---,

Lacq Superieur field (France), 46 Lacunarity, 271 Lacey field (Oklahoma), 811 Lake Tanganyika, 97 Lamesa West field (Texas), 521 LANDSAT, 8 Lansing-Kansas City Group, 302, 481,483,484 Lea field (New Mexico), 523 Lec field (Florida), 885

987 Leduc Formation, pool, reef (Canada), 237,253, 490-493,496, 501 Leduc-Woodbend field (Canada), 238, 529 Lekhwair Formation, 95, 96 Leonardian, 296,300 Lerado field (Kansas), 526 Lerado SW field (Kansas), 522 Levelland field (Texas), 338,342 Levelland Northeast field (Texas), 527 Libya, 74, 519, 802, 813, 831 Lima-Indiana trend (Indiana), 810, 827 Lime, manufacture, 46 Lineament analysis, 8 Liquid saturation, 17-19 Lithology, determination, 13 Little Beaver East field (Montana), 522 Little Beaver field (Montana), 522 Little Knife field (Wyoming), 68, 381,383,385, 386 Livengood field (Kansas), 523 Llanos field (Kansas), 522,523 Lockport Dolomite, 45 LOGIX, 167 Log-inject-log process, 42 Logs, logging -, acoustical, 28, 168, 169, 179 , acoustic waveform, 207, 208 -, borehole televiewer, 28, 42, 209, 215 -, cased-hole logs, 159 -, core gamma, 107 -, density, density-neutron, crossplots, 107, 108, 162, 165, 168-170 --, acoustic crossplots, 169 , photoelectric factor crossplots, 169 -, dielectric, 192 -, dipmeter, 208 -, gamma ray, 168, 172 ---, spectroscopy, 168, 172, 173, 175, 181, 195 -, geochemical, 25, 27, 175, 181 -, grain density, 164 -, Hingle plots, 169 -, imaging logs, 208 , array resistivity, 215 -, Leverett "J" function, 494, 495 -, measurements while drilling, 159 -, M-N plots, 169 -, mud logging, 158, 199 -, neutron, 179 , pulsed neutron capture, 180, 192-196, 198 -, NML, 181, 195,466 -, NMR (magnetic resonance imaging), 179, 184, 199, 462, 466, 468, 469 -, nuclear, 27, 168 -, photo-electric cross section log, 165 -, porosity-lithology crossplots, 168, 169

-, -, -, -, -,

resistivity, 27, 107, 168, 204 shear versus compression travel time plots, 169 spectral density, 169 spontaneous potential (SP), 168, 204 thermal neutron, 169, 180 , epithermal neutron, 169, 180 Loma de la Lata field (Argentina), 331,332 Loring field (Mississippi), 527 Louisiana, 20, 21,146, 208, 325,346, 519 Lower Clear Fork, 304 Lower Fars Formation, 503 Low-permeability reservoirs, 2 Lowstand, lowstand wedges, 73, 76-80 Lucia classification, 178 Lundgren field (Kansas), 523 Luther S.E. field (Texas), 519 M-N plots, 17 Maben field (Black Warrior Basin), 810, 831 Macedonia Dorcheat field (Arkansas), 24 Mackerel field (Australia), 851,854 Madison Group, Limestone, 326, 359-362, 381, 383, 384 Magnolia field (Arkansas), 24, 248,522 Magutex field (Texas), 523,526 Mardin Group, 498 Marine pool (Illinois), 811,825 Martin field (Texas), 24 Matrix identification plots, 17 Matrix porosity, permeability, 3, 44, 47 Matzen field (Austria), 812 Matzen-Schonkirchen-Reyersdorf field (Austria), 824 Maureen Formation, 778 Maydelle field (Texas), 527 McClosky Limestone, 240, 241 McElroy field (Texas), 452, 519 McFarland field (Texas), 523 McKamie field (Texas), 24 McKnight reservoir (Texas), 304, 305 Means field (Texas), 33, 34, 43,286 Measurement while drilling logs, 4, 60 Mediterranean Basin, 813 Megabreccias, 87 Menger sponge, 267, 273, 415 Mercury injection, 119, 120, 183 Mesozoic, 72, 94 Mexico, 39, 40, 48, 80, 326, 508, 510, 598, 664, 813,820, 825,830, 832, 837, 840, 847 Miami Formation, 468 Michigan, 522, 810, 811 Michigan Basin (USA), 49, 74, 79, 301,787, 810, 811, 814, 819, 825,827, 828, 830,837, 844, 849 Michigan Basin Pinnacle Reef trend (Michigan Basin), 811

988 Micrologs, 53 Microresistivity logs, 39 Midale field, trend, carbonates (Williston Basin), 44, 881,883 Midcontinent (USA), 96 Middle East, 3, 13, 21, 27, 48, 53, 72, 167, 176, 205, 231,262,326, 332,468,469,793,799, 825 Midland Basin (Texas), 44, 80, 338, 436, 811, 812 Midland Farms field (Texas), 830 Midway field (Kansas), 24, 248 Mild Creek field (Arkansas), 24 Mill Creek field (Kansas), 523 Mineral identification plots, 171 Minipermeameter, 50, 61,436 Miocene, 20, 74, 146, 502, 503,782 Mishrif Formation, 80 Mission Canyon Formation, 381,383, 814 Mississippi, 208, 481,482,484, 525,527 Mississippian, 38, 39, 41, 44, 96, 240, 326, 345, 359, 381, 472, 802, 814, 820, 822, 868, 881,883 Mississippian "chat", 96 Mississippi-Solid Formation, 258 Missouri, 523 Mobile oil, gas, 32-34, 41,233, 275,283, 289, 298 Monahans field (Texas), 24 Monarch field (Montana), 521 Montana, 291, 301,359, 521-526, 529-531,802 Montanazo field (Spain), 830 Monte Carlo method, sampling, 216, 217, 363, 403,405 Montgomery field (Indiana), 521 Morrow County field (Ohio), 520 Mound Lake field (Texas), 523 Mounds, mudmounds (carbonate), 76, 90 Mount Holly pool (Arkansas), 253,523 Moveable oil, 3 Mt. Auburn field (Illinois), 831 Mudcake, 204 Mud filtrate invasion, 168, 182, 189, 199, 203 Mud logging, 4, 47, 60 Mud-skeletal banks, 76, 91, 92 Nagylengyel field (Hungary), 812 Natih field(s)(Middle East), 48, 813,825 Native energy, 17 Nebraska, 525, 526, 790 Net formation thickness, determination, 59 Neuguen Basin (Argentina), 331,789 Neutron logs, 16, 17, 29, 47 Neva West field (Texas), 530 Nevada, 526 Newbaden (New Baden) East field (Illinois), 529

Newburg field (Williston Basin), 812, 830 Newbury field (Kansas), 24, 523 Newhope (New Hope) field (Black Warrior Basin), 519, 810, 831 New Mexico, 18, 19, 33, 49, 72, 96, 258, 290, 293,299--301,338,379, 387,436, 444, 453, 461,462,466, 520, 521,523,525, 531, 811 New Richland field (Texas), 523 Niagara Formation, 481,483,484 Niobrara Chalk, 789-792 Nitrogen injection, 44 Norman Wells field (Canada), 883 Norphlet Formation, 883 North Anderson Ranch field (New Mexico), 520 North China Basin, 810 North Cowden field (Texas), 18 North Dakota, 291,326, 381,383,385, 386 North field (Qatar), 813 North Personville field (Texas), 346, 348, 351 North Sea, 49, 80, 81, 137, 415, 416, 775-777, 769, 781,783-785,788,789, 790, 850, 884, 894 Northville field (Ohio-Indiana), 810 Norway, 762 Nottingham field (Williston Basin), 812,830 Novinger field (Kansas), 527 Nuclear magnetic resonance, 27, 34, 46, 48, 49, 51 Nuclear magnetism logs, 30, 44, 52 Nunn field (Kansas), 520, 529 Ocho Juan field (New Mexico), 521 Ohara Limestone, 240, 241 Ohio, 457-459, 520, 810, 827 Oil-in-place, 2, 4, 33, 42,296 Oil saturation, 18, 25, 112, 123, 141, 159, 182, 384 , fractional, 18 , residual, 112, 123, 136, 196 Oil viscosity, 8 Oil-water relative permeabilities, 31, 38 Oklahoma, 2, 20, 21, 45, 49, 74, 258, 276, 293, 299, 301,304, 306, 530, 810, 811, 814, 822, 827 Oklahoma City field (Oklahoma), 49, 810, 827, 831 Oligocene, 33,502, 503 Oman, 332 Opal, 775 Opelika field (Texas), 527 Ordovician, 12, 20, 48, 49, 290, 302, 326, 804, 814, 815,818, 820, 827-829, 837, 848 Otto field (Texas), 531 Outlook and South Outlook fields (Montana), 524 Overburden, 3, 23,236 -, gradient, 24

989 Overpressuring, 50, 81 Ownby Clear Fork field (Texas), 43 Oxfordian, 75 Ozona East field (Texas), 529 Paleocene, 49, 74, 415, 621,775, 777, 779, 782, 792 Paleogene, 86, 820 Paleozoic, 72, 94 Palo Pinto reef, 23 Panhandle field (Texas-Oklahoma), 29, 36, 37, 519 Paris Basin, 11 Parkman field (Williston Basin), 812, 830 Parks field (Texas), 519 Patch reefs, 76, 94 Patricia field (Texas), 830 Pays de Bray fault, 11 Pearsall field (Texas), 327-331,785 Pegasus field (Texas), 529 Pennel field (Montana), 521 Pennsylvania, 12 Pennsylvanian, 23, 48, 74, 92,302,481,814, 821, 837 Penwell (SanAndres) field (Texas), 18,262,489 Perched oil, 898 Performance decline, testing, 232 Permeability -, absolute, 30, 290, 367, 498, 500 -, anisotropy, heterogeneity, 1, 17,389, 438, 454 -, barriers, 882, 884, 885, 887, 896, 898 -, capacity, 38 -, conductivity, 389 -, determination, 49, 201 , from drilling data, 210 , from empirical correlations, 204 , from invasion profiles, 203 , from samples, 201,205, 887, 888, 894 , from testing, 203, 210, 894 , from thin sections, 400 , from well logs, 203,207 - - , modeling blocks, 403 - - , renormalized, 403 -, directional, 8, 28, 122, 144, 201,257, 259, 883 -, dual systems, 880 -, effective, 9, 47, 201,257, 368, 394, 396, 421, 423,430, 431,500, 783,885 -, fracture, 326, 329, 344, 353 -, horizontal, vertical, 3,201,291, 311, 313,322, 324, 325,490, 494, 507, 883,887, 894 -, intrinsic, 443 -, matrix, 3, 41,505 -, minimum/maximum ratios, 8 -, of cores, 107, 121, 122 --, relative, 17, 29-31, 38, 106, 132, 201, 367, 479, 489, 498, 500, 501

-, total, 3, 7 -, variation, 17 Permian, 19, 29-32, 34-37, 39, 41-45, 48, 80, 96, 248, 302, 304, 306-308, 325, 355, 379, 380, 387,466,782, 805, 814, 818, 821,827829, 832, 836, 837, 847 Permian Basin, 42, 48, 49, 72,296, 300-302,340, 342, 344, 780, 782, 799, 804, 805, 810812,814, 818,821,827, 828-831,832, 836, 837, 844, 847, 848 Persian Gulf, 326, 813 Petrophysical models, 155, 162, 164, 167, 179, 180, 232 -, definition, 7 -, deterministic models, 12 -, error minimization models, 12 -, simple models, 13 Petrophysics, 1 Pettit Formation, 21 Phosphoria Formation, reservoir, 32, 45,355,357 Pickett plots, 10, 46, 68, 163, 164, 197, 219 Pickton field (Texas), 519 Pierre Shale, 791 Pine field (Montana), 526 Pinnacle reefs, 44, 74, 76, 94, 95, 819 Plainville field (Indiana), 519, 520, 527 Pleasant Prairie field (Kansas), 520, 529 Pleistocene, 468, 802 Plenus Marl Formation, 777 Pokrovsk field (Russia), 45 Pollnow field (Kansas), 520 Pondera field (Montana), 530 Pore combination modeling, 39 Pore fluids, saturation, 165, 166, 168, 179, 182 , determination, 196 , formation water thermal neutron capture, 198 , hydrocarbon type, density, 198, 200 , oil viscosity, chemistry, 200 - - , properties, determination, 44 , saturation, determination, 31 , water properties, 196, 197 Porosity -, cavernous, 257 -, channel, 468 -, classifications, 254, 258 -, depositional, 72, 74 -, determination, measurement, 26, 178,264 , from well logs, 107 , in cores, 107, 118, 119 -, diagenetic, 72, 254 -, double (dual) porosity systems, 259, 330, 331, 880 -, effective, 47, 390, 783, 892 -, fractal measurements of, 254, 263,267 -, fractional, 9, 496 -, fracture, 1, 4, 67, 353, 505

990 dissolution-enlarged fractures, joints, 48 growth-framework, 468 heterogeneity, 470, 480 in carbonate rocks versus sandstones, 257 intercrystalline, 47, 254, 258, 306, 475, 485, 834, 840 -, intergranular, interparticle, 21, 22, 47, 50, 80, 144, 191,202,256, 258,468,475,477,480, 485,508, 782, 783,834, 840 -, intraparticle, 468 -, matrix, 505 -, micropores, microporosity, 47, 144, 145, 191, 258 -, moldic, biomoldic, oomoldic, 47, 167,266,468, 834, 840 -, pore casts, 468 -, pore combination modeling, 191, 192 -, pore fluid-rock interaction, 867 -, pore geometry, interconnectiveness, 254 -, pore size distribution, 107 -, pore structure, microstructure, 264, 867 -, pore throats, 872, 876-879, 881 -, porosity reversal, 868 -, primary, 81,254 -, secondary, 27, 33, 72, 254, 258 -, single-porosity behavior, 11 -, storage porosity, 257, 480, 488 -, total, 178, 184, 191 -, versus depositional facies, setting, lithology, 255,256, 447, 448, 867-869 -, versus dolomitization, 868 -, versus permeability, 389, 390, 398,412, 448 -, versus reservoir flow, 256 -, vuggy, vugs, 47, 144, 167, 178, 186, 191,202, 205,209,254, 257-259,266, 461,469,475, 477,485, 501,503,508,784, 834, 840,844, 851,876, 887 Porosity/lithology log crossplots, 16, 47 Poza Rica trend (Mexico), 80 Prairie du Chien Formation, 146 Precambrian, 48, 49, 820, 833,837 Prentice field (Texas), 43 Pressure buildup tests, 3, 9, 38, 39 -, drop, 7 -, falloff analysis, 27, 39 Pressure cycling steam recovery, 47 Pressure interference tests, 8 Pressure maintenance, 24, 296, 869 Pressure monitoring, 1 Pressure transient tests, testing, 549 , analysis of variable flow rates, 641 , bilinear flow, 559 , for gas wells, 591 - - - , for high-permeability reservoirs, 615 , for oil wells, 615 , linear flow, 554 ,

-, -, -, -,

- - - , pressure-dependent character of reservoirs, 638 producing-time effects, 611 , radial cyclindrical flow, 557 , spherical flow, 557 Producing water level, 62 Production rates, testing, 156, 158, 165,254, 357 - - , design, history, 105,234 Production surveillance, formation evaluation, 7 Production tests, 4, 45, 52, 59 Productivity index, 342 Progradation, 60 Propagation of error considerations, in formation evaluation, 67 Puckett field (Texas), 527, 804, 840 Pulsed neutron capture logs, 56, 64, 65 Pyrite, 164 Pyrobitumen, 259 Pyrolysis analysis, 49 ,

Qatar, 96, 661, 813 Quantitative fluorescence technique, 47, 199 Quaternary, 94 Quintico Formation, 332 Radiological imaging, 456 Rainbow field, area (Canada), 78, 79, 531 Rainbow-Zama reservoir (Canada), 498 Ramps, 75 Rapid River field (Michigan Basin), 811 Recovery -, contiguous water, 869 -, conventional techniques, 231 -, cumulative, 319 -, displacement efficiency, 872, 877 -, efficiency, 48, 275--277, 296, 451,496, 510, 512, 514, 515, 878 -, enhanced, enhancement, EOR, 1, 25, 33, 42, 105,144, 232,233,257,263,275,367,489, 867, 869, 898 -, estimates, 17 -, factor, 248, 252, 253,497, 516, 517, 894 -, from different reservoir classes, 231,232 -, incremental, 295,297 -, oil retention, 879 -, oil trapping, 874-876 -, primary, 1, 17, 25, 28, 105, 233, 275, 287, 867, 868, 871 -, rate, 253,262 -, recoverable reserves, 2, 231 -, residual oil, saturation, 870, 897 -, secondary, 1, 23, 28, 32, 33, 105, 275, 284, 295,296, 307, 367, 867, 870, 871,894 -, tertiary, 1, 156, 867, 895 -, thermal, 42, 45 -, ultimate, 2, 4, 41,233, 246, 253, 302, 329,

991 356,485,486,488,490,494, 496,505,512, 515, 871, 884, 885, 896, 897-, unrecovered oil, gas, 289 -, versus rate of withdrawal, 488-496 -, water retention, 879 Red River Formation, 290, 291 Redwater (D-3) reservoir, field (Canada), 252, 496, 497, 529, 869 Reefs, 50, 60, 74, 76, 77, 90-92, 257-259, 280, 339, 340, 379,497, 805,867, 869, 882, 883, 896 Reeves field (Texas), 521 Renqiu field (China), 48, 49, 799, 810, 820, 823, 825, 837, 840, 845, 846 Reserve estimation, 1, 33, 105, 157, 232 , global reserves, 48, 871 Reservoirs -, analysis, 2 -, anatomy, geometry, 275 -, anisotropy, heterogeneity, 1, 25, 34, 231,233, 358, 362 -, characterization, 1,106, 232-234, 358, 435 -, classifications, environments, 1,234, 243,254, 274, 276-279 , atoll/pinnacle reef, 277, 287, 292 , barrier, strand, 277 , debris flows, fans, 277 , deltaic, 277 - - , fluvial, 277 , peritidal, 277, 279, 280, 287 , platform, 277 , ramp, 277 , reef, 277, 279, 280, 287 , shelf, 277, 279, 280, 287, 292 , shelf margin, 277, 279, 281,287 , slope, basin, 277, 279, 281,287 , turbidites, 277 , unconformity-related, 277 -, communication, 369 -, compartments, compartmentalization, 25, 47, 332 -, continuity, 25,285,289, 361,882, 883 -, decline, depletion, 1,233,249 -, energy, 234 -, homogeneity, uniformity, isotropic, 1, 8, 34, 360 -, management, 160, 232 -, models, modeling, 1,362, 364, 886 -, oolitic, 23 -, performance, 1, 2, 3, 136, 231,233,256, 480 -, production, 233 -, scaling, 389, 401 -, simulation, 362, 364 -, stimulation, 28 -, stratified, 33 -, water-wet, 27

-, withdrawal rates, 249 Residual oil saturation, 36, 38, 443 Resistivity logs, 16, 39, 53 Reyersdorf field (Austria), 812 Rhodes field (Kansas), 521 Richey field (Montana), 525 Robertson Clear Fork field (Texas), 32-34, 43, 286 Rock catalogs, 10, 39, 51, 146, 164, 165 Rocker A field (Texas), 519, 521,524 Rojo Caballos field (Texas), 522 Romania, 799 Ropes and South Ropes fields (Texas), 529 Rosedale field (Kansas), 524 Rosiclare Limestone, 240, 241 Rosiwal intercept method, 265 Rospo Mare field (Italy), 813, 831 Ross Ranch field (Texas), 523 Roughness, fracture surfaces, 4, 6, 7, 266, 269 Rumaila field (Middle East), 799 Rundle Formation, 38,472, 474 Russel Clear Fork field (Texas), 43 Russia, 45,275 Sabetha field (Kansas), 524 Sacatosa field (Texas), 302 Safah field (Middle East), 332 Saih Rawd field (Middle East), 332 Salem Limestone, 345 Salt domes, 694 Salt Flat field (Texas), 44 Sample examination, 13, 31, 48, 51, 54, 62 SanAndres Formation, Dolomite, fields (in TexasNew Mexico), 18, 31, 33-36, 42, 43, 80, 245-247,258,272,282,283,304, 310, 335, 338-342,344, 345,387, 418-422,436,438, 440, 441,444, 450, 453-455, 461-467,489 San Andres Limestone, field (Mexico), 508, 510 San Angelo Formation, 304 Sand Hills field (Texas), 303-305 Sandstones, 19, 20, 21, 37, 133, 164, 165, 173, 233,240, 241,248,254, 257-259, 262,265, 267, 276, 298,302,332,334, 379, 414,420422, 455, 461, 462, 471,485, 488, 510517, 653,894, 897 Sangamon Arch (USA), 811 San Marcos Arch (USA), 813 Saratoga Chalk, 325 Saudi Arabia, 75, 80, 96, 332, 528, 529, 813 Sehonkirchen field (Austria), 812 Schuler-Jones pool (Arkansas), 248 Schuler (Reynolds) field (Arkansas), 24, 248,523 Seal capacity, 157 Sealing faults, 25 Seismic, 5, 64, 215 -, absorption, 63

992 -, -, -, -, -, -, -, -, -, -,

acoustic impedance, 61, 63, 64, 72 acoustical properties, 106, 157 bulk density, 68 conventional, 3-D, 49, 158 fresnel zone, 66 imaging, 28 interference, 65 interval seismic velocity, 62 modeling, 70, 71 offset-dependent reflector amplitude analysis, 49 -, reflection coefficient tree, 71 -, synthetic traces, seismograms, 59, 68, 83 -, velocity, 68 -, wavelet, 71 -, Weiner filtering, 66 Seminole field (Texas), 43,830 Seminole SE field (Texas), 802, 803 Sequence stratigraphy, 85,275 - - , seismic, 50 Shafter Lake field (Texas), 24, 43 Shallow Water field (Kansas), 529 Shannon Sandstone, 133 Sharon Ridge field (Texas), 520 Shuaiba Formation, 80, 90, 332 Shubert field (Nebraska), 526 Sicily, 26 Sierpinski carpet, 267-269, 273, 392-394, 407, 415-417, 427,480 Silicification, 256 Silo field (Wyoming), 791,792 Silurian, 45, 74, 79,302,457--459,481,801,814, 819, 825, 827 Sirte Basin, 74, 813,831 Sitio Grande field (Mexico), 39, 40 Skaggs-Grayburg field (Texas), 18 Skin factor, 584, 586, 669 -, pseudo-skin factor, 589, 590 Slaughter field (Texas), 18, 245,338, 519 Slaughter-Levelland field (Texas), 278, 338, 342 Smackover Formation, Limestone, fields (Gulf Coast USA), 22-24, 90,248,253,265, 301, 325, 359, 481,482,484, 883 Snethen field (Nebraska), 526 Snyder North field (Texas), 522 Sonic logs, 16, 17, 28, 59 -, waveforms, 56, 64 Source rock, 157, 173 -, delineation, 18 -, richness evaluation, 49 South Alamyshik field (former Soviet Union), 813, 820, 823 South China Sea, 74, 93 South Cowden field (Texas), 519 South Cowden-Foster field (Texas), 18 South Dakota, 790

South Fullerton field (Texas), 24 South Horsecreek field (North Dakota), 291 South Swan Hills field (Canada), 239, 240 South Westhope field (Williston Basin), 812,830 Southwest Lacey field (Oklahoma), 258 Soviet Union (former), 47, 820 Spain, 48, 797, 798, 812, 813, 830, 832, 840, 844, 845, 851,853 Spontaneous potential logs, 16, 53 Spraberry-Driver field (Texas), 8 Spraberry field, trend (Texas), 44, 45 Star field (Oklahoma), 811, 831,832 Ste. Genevieve Formation, 240 Stillstands (sealevel), 59, 76, 77 Stoltenberg field (Kansas), 815 Stoney Point field (Ohio-Indiana), 810, 828 Strahm East field (Kansas), 524 Strahm field (Kansas), 24, 524 Strawn reef (Texas), 23 Structural and stratigraphic, determination, 61 Stuart City trend (Texas), 813,825 Stylolites, 3, 74, 885 Submarine fans, 88 Sulfur, 46, 333 Sumatra Northwest field (Sumatra), 524, 525 Sun City field (Kansas), 520 Sundre field (Canada), 812 Swan Hills field, trend (Canada), 237,239, 240 Swanson method, 201 Sweep, sweeping -, areal, 883,884, 293 -, efficiency, 25, 27, 282, 284, 285, 287, 289, 292,293,449--456, 870, 872, 882-886, 894 , fracture areal, 36 -, vertical, 162, 384, 883,884 -, volumetric sweep, 872 Sweetgrass Arch (USA), 802 Sweety Peck field (Texas), 24 Sycamore-Millstone field (West Virginia), 520 Tampico Embayment (Mexico), 813 Tank oil-in-place, 4 Taormina Formation, Sicily, 26 Tar, 123, 195 Tarraco field (Spain), 830 Tarragona Basin (Spain), 812, 813,830 Taylor-Link field (Texas), 461 Taylor-Link West field (Texas), 812, 831 Tennessee, 810 Terre Haute East field (Indiana), 524 Tertiary, 48 Texarkana field (Texas-Arkansas), 24 Texas, 2, 3, 8, 18-20, 22-24, 29-37, 41, 42, 44, 45, 48, 49, 72, 80, 96, 133, 146, 165,208, 210, 245,246,258,262,272,276, 277,280, 283,285,287,290, 293,299,300-302,304-

993 310, 325-328, 331,338--340, 344-246, 348, 351,369, 379, 380, 418-422,436,443,449, 452,455,461--468,481,482,484, 489,519-527, 529-531,784, 785,789-791,799, 804, 805,810-812,814, 818,821,827-829, 832, 836, 837, 840, 843, 844, 847, 848, 897 Tex-Hamon field (Texas), 524, 526, 531,830 Texture, rock, 26 Thamama Limestone, Group, 332, 333 Thermal expansion, 46 Thermal extraction chromotography, 49, 200 Thomeer method, 201 Todd field (Texas), 24 Tor Formation, field (North Sea), 415,777, 779, 781 TORIS database, 276, 286, 287, 293, 298, 301, 309 Tortuosity, 415 Tracer tests, testing, 1, 4, 28, 158, 293 Trapp field (Kansas), 831 Trenton fields (Ohio-Indiana), 810 Trenton Limestone, 828, 844 Triassic, 85, 768, 820 Triple-N/Grayburg field (Texas), 43 Tubb reservoir (Texas), 304 Turbidites, 87-89, 199 Turbulence, factor, 38, 473, 474 Turkey, 488, 499 Turkey Creek Formation, 248 Turner Valley field (Canada), 531 Turner Valley Member, Formation, 38,472-474, 868 TXL field (Texas), 24 Uinta Basin (USA), 280 Umm Farud field (Libya), 519 Uncontacted oil, gas, 289, 298 Unger field (Kansas), 524 United Arab Emirates (UAE), 80, 90, 333,830 University-Waddell field (Texas), 24 University 53 field (Texas), 829 Ural foredeep (former Soviet Union), 812 Usa field (former Soviet Union), 47 Utah, 280, 520 USSR (former), 812, 813,832 Vacuum field (New Mexico), 338,342 Valhall field (North Sea), 415 Valley Center field (Kansas), 527, 530, 531 Van Der Vlis equation, 321 Vealmoor East field (Texas), 524 Vicksburg Formation, 146 Video camera imaging logs, 56, 58, 65 Vienna Basin (Austria), 812,820, 824 Viking Sandstone, 240, 242 Village field (Arkansas), 24

Viola Limestone, 22, 24 Virden field (Williston Basin), 812 Virginia Hill(s) field (Canada), 239, 240 Vug, detection, 54 Waddell field (Texas), 519 Wapella East field (Illinois), 524 Warner field (Kansas), 530 Warren-Root method, 741,747, 750 Wasson field (Texas), 18, 43,278,285,286, 338340, 342,436, 438 Water block, 949 Water catalogs, 46 Waterloo field (Illinois), 530 Water level, definitions, 61 Water saturation, 29--31, 164, 184, 192 Waverly Arch, 810, 814, 816 Welch field (Texas), 31, 34-36, 283 Welch North field (Texas), 522 Wellman field (Texas), 524 Well placement, spacing, 867, 882 Wells (Devonian) field, 527, 830 West Brady field (Montana), 530 Westbrook field (Texas), 522 West Campbell field (Oklahoma), 811, 831,832 West Edmond field (Oklahoma), 2, 21, 45,530 West Ekofisk field (North Sea), 781 Western Canada Basin, 257 Westerose field, reef (Canada), 237, 238, 529, 867, 868, 896, 897 Westerose South field (Canada), 237, 238 West Garrett field (Texas), 830 West Lisbon field (Louisiana), 519 West Ranch field (Texas), 32, 33 West Virginia, 520 Westward Ho field (Canada), 812 Wettability, 106, 116, 132, 136, 145, 157, 187, 188, 192, 200, 458, 459, 502, 873-875,878, 881,939 -, in fractured carbonates, 880 -, versus oil trapping, entrapment, 874 Wheeler field (Texas), 21, 24 White Dolomite, 29, 36, 37 Whitestone Member, 468 Whitney Canyon field (Wyoming), 812,820 Wichita field (Kansas), 527 Wichita Formation, 24 Wilburton field (Oklahoma), 810 Wilcox Formation, 148 Wilde field (Kansas), 527 Williston Basin (USA, Canada), 68, 72, 301, 381, 801,804, 812, 818, 822, 830 Willowdale field (Kansas), 527 Wilmington field (Kansas), 24, 524 Wilsey field (Kansas), 527 Wilshire field (Texas), 24

994 Wireline logs, 4, 60 Wireline tests, 4, 33, 45, 47, 48 Wizard Lake pool, field (Canada), 524, 897 Wolfcamp limestone, 281 Wolf Springs field (Montana), 525 Woman's Pocket Anticline field (Montana), 525 Woods formula, 130 Wyoming, 20, 32, 45, 355, 521,522, 790-792, 811 -, Overthrust Belt, 812, 820 X-ray diffraction, 14

Yarbrough field (Texas), 24 Yates field, reservoir (Texas, New Mexico), 48, 248,799, 800, 805,812, 814, 831,832, 836, 837, 844, 847 Yellow House field (Texas), 521 Yemen, 146 Zama area (Canada), 531 Zechstein beds, 782, 850 Zelten field (Libya), 802,803 Zubair field (Middle East), 799

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