Carbonate Reservoir Characterization: A Geologic-Engineering Analysis, Part II 0444821031, 9780444821034, 9780080528564

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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. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA tion: A Geologic - Engineering Analysis, Part II

Developments in Petroleum Science, 44

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

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. zyxwvutsrqponmlkjihgfedcb 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

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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 zyxwvutsrqp

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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

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

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xi zyxwvutsrqpo

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 .............................................................................................................. zyxwvutsrqponmlkj 107 Coring ............................................................................................................................................... 107 Introduction ................................................................................................................................. 107 Conventional whole coring ......................................................................................................... 108 Oriented whole coring ................................................................................................................ 110 Wireline retrievable whole coring ................................................................................................ 111 Containerized whole coring ......................................................................................................... 111 Pressure whole coring ................................................................................................................ 112 Sponge whole coring .................................................................................................................. 113 Wireline sidewall coring .............................................................................................................. 114 Core handling .................................................................................................................................... 115 W h o l e cores ................................................................................................................................ 115 Sidewall cores ............................................................................................................................. 116 Core analysis ..................................................................................................................................... 116 Introduction ................................................................................................................................. 116 Sampling ...................................................................................................................................... 117 Conventional (routine) core analysis ........................................................................................... 118 Petrographic core analysis .......................................................................................................... 139 Special considerations for core analysis o f carbonate reservoirs .................................................... 144 Heterogeneities ............................................................................................................................ 144 Multimineral composition ............................................................................................................ 145 L o w porosity and low permeability ............................................................................................ 145 Wettability .................................................................................................................................... 145 A c c u r a c y and reproducibility ...................................................................................................... 146 R o c k catalogs ................................................................................................................................... 146 Introduction ................................................................................................................................. 146 General rock properties catalogs ................................................................................................ 147 Specific formation rock properties catalogs ............................................................................... 147 S u m m a r y .......................................................................................................................................... 148 A c k n o w l e d g m e n t s ............................................................................................................................ 149 References ........................................................................................................................................ 149 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 ..............................................................................................................

155

155 155 155 156 156 157 157 159 159 159

160 162 164 164 165 167 167 168 178 178 179

xiii zyxwvutsrqponm 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 azzullo 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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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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GEOPHYSICS

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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). zyxwvutsrqpon

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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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2.0

3.0

4.0

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5.0

LOG NA. Fig. 1-3. Chart showing the relation between friction factor, f, and Reynolds number, NRe, for laminar, transitional and turbulent fluid flow in granular rocks and smooth fractures. (Modified after Lomiz6, 1951.) No.

e,cm

e/b

3 4 9

0.055 0.055 0.175

0.327 0.205 0.854

10 11 12 13 14 15 16

0.175 0.175 0.175 0.055 0.055 0.055 0.055

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0.15 0.10 0.05

0.00

0.05

O.10

O.15

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0.25

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPON 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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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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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 g9 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: N ( N - 1 ) (QN-Z)p2 + . . . . . NQN-,p + (Q + p ) N : QN + zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA lx2 N ( N - 1) ( N - 2 ) . . .

( N - r + 2)

(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" T I - zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA ', S.1

(1-14)

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 seand PS is the probability of intercepting at least the number of fractured quence is PC, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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

PC =

beds plus two fractured beds combination"

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

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(%)

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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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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. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLK

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) simple, multifractals. The singular fractals can be subdivided into two groups: (1) zyxwvutsrqponmlkjihg 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 ~

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272

The multifractals also are subdivided into two groups, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQP 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 ,

zyxwvutsr (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. zyxwvutsrqpon 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

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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. zyxwvutsrqponmlkjihgfedcbaZ

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. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFED 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) zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

Peritidal Supratidal Intertidal Subtidal

Reef (sup) (int) (sub)

Pinnacle Bioherm Atoll

Shallow shelf

(p) (b) (a) zyxwvutsrqponmlkjihgfedcbaZ

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. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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reservoir O'&

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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

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~

t

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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

Dlagenetlc Overprint

9 Lacustrine

9 CompactionCementation

9 Peritidal Sur~etJd~ 9 . bleftJdal . Sublidal

9 Shallow Shelf Open 9 Shell

SILICICLASTIC

I

"Ramp

Structural Compartmentalization 9 Unstructured

9 CompactionCementation 9 Grain Dissolution

9 Natural Fracture Porosity

9 Aulhigenic

9 Faulted

9 Dolomitization

9 Faulted

9 Alluvial F a n

B 9 un

Canter

zyxwvutsrqponml - Humid (Sveam-Dominaled) A 9 n d / S e m i Arid 9Fan Deltas

Clay

9 Folded

9 Chertificalion

9 Faulted/ Folded

9 Faulted/ Folded

9 Fluvial

Braided Sueams

.

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9

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Delta

9

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Reefs - Ptnnade Reels . Biohecml

Overprint

9 Natural Fracture Porosity

9 Massive Dissolution

I Dlagenetlc

System

9 Grain Enhancement

9 Folded

RESERVOIRS

......

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9 Unslructured

9 Dolomitization

9 Shelf M a r g i n mnmed 9 Sh~

!

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(Evaporites)

. ResVicled Shell

9

I RESERVOIRS

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- Wave-Domimlled F 9luvial.Dominamd

Silicification

- T~le- D o r n i n a t e d

-A ~

9 Strandp~ain 9 l~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 9 Pelagic

Fig. 5-299 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. zyxwvutsrqponmlkjihgfed

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.

zyxwvu 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.

zyxwvutsr

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. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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:

Omo =

(1 -- Swi) - Soc , ( 1 - zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA s.;,i)

(5-17) zyxwvutsrqp

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

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zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 30 40 50 60 70 WATER SATURATION,% PV 70

60

OIL

50

40

30

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: zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQP = 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 - S9 gl.) 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: zyxwvutsrqponm 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

zyxwvutsrqponmlkjihgfed

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 ).

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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

.,2., .o o

-

.............. ~ ~ o

.

~~-J"

.

,

~

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONML

0.7 n

no

0.6t

-------"-+i

~ " ~

". o.., o'~176176176 ~176176 "~176

~

......

~

~

_

13

== E3

0-5

~ -

.,..-.--

0

Unhoclurod Chalk~ .,,O~).SIXIIf I

I

2

:3

Homogeneous

. . . .

4

Data not avoiloblefor ~ s range ~*-- Of:ranShelf, Rofform--~ 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.) zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFE

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" zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

E =

v

Nu

,

(5-34)

7758 (A) (~b) (Soi/Boi zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA - Sor/Boa )

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

0.9

I

:

0.8

c

0.7-

I

I

I

I

- Low H I ( I_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). zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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 _0. The similarity dimension (D) is defined as: f(a)

~

Slope : 1 Stope q

Do

)) D,

f(a( q

I

I -r(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

zyxwvutsr zyxw

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 a priori. The pores to be altered were of all the pores in this range was specified zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIH 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 ==..,..,,,.,=.==

o~2 o -3

9

=,

.

,i

.

.

.

9 Arun Limestone O San Andres Dolomlle -- ~.i

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

~

y = 14.368x - 3.526 J r 2 = 0.722

~ . zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 2 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

,,

1

immq

,,

~

v

y = ~.979x

v

v,

9 2.619

O~ ~ e e r 2 = 0.642 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 2 o ........

~.

:3

(D 4)

@ 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.) zyxwvutsrqponmlk

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) zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDC

N=52 O o

0

1

~o I L

(/)

0

E A L _ -V

=,,

r

0"2

..J

,

-3

, - , ,

9 Norphlet Sandstone II Spraberry Sandstone O Arun Limestone E] San Andre$ Dolomlte -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. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHG

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

k5

OW

P=Z~P

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.....zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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 If the medium was anisotropic, then the resistances on four resistors enclosed in the dotted square is 89 k i.zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDC 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. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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

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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

~

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w3wl

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w4wl

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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 charand is defined by using Eq. acterized by the behavior of its generating function Xq(fi) zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONM 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)9 Each 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).

zyxwvu 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 Bx(6") vary with 6 when x is fixed? .... How does it vary if 6 is the medium enclosed in zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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)

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFED

A

kn(1) zyxwvutsrqponmlkjihgfedcbaZYXW

kn(1)

w+ kn(1)

w2

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= zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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) --

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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 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 .

(5-129)

432 Employing ko(~o) = 1, and eliminating n with ~n = 2-n yields: ~(q) = "n ,

(5-130)

where the scaling exponent zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA ~q)=-log2(). 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" zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONML D + t(q)- ~(q) ?(q)

= ~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. zyxwvutsrqponmlkjihgfedcbaZYXWVUTS

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCB

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). zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIH

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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

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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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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. zyxwvutsrqponmlkjihgfedcba

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

kg/k o c u r v e s with low equilibrium gas with nonuniform porosity typically have zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHG 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 90 of the reservoir, with enough oil draining downdip to resaturate the lower 88 of the zone during the shut-in periods to 90% liquid saturation; (3) comparable to case 2, but with the oil draining from the upper 89 of the reservoir to resaturate the lower 89 of the zone; and (4) comparable with cases 2 and 3, but with oil coming from the upper 88 of the reservoir to replenish the lower 90 of 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

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.

.

.

.

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

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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. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPO

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCB 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. homogeneous carbonate system having the following The first model tested was a zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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.

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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

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99 71 19

65.2 64.9 63.6

10.4 6.2 1.5

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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

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1000 500 100

10 7 5

99 71 19

64.0 63.2 62.3

11.1 5.4 1.4

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Layered Model Thick layer system

500 100

28 22

17 3.5

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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 -

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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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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.

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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) = zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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. cross-sectional model (Fig. 5-130A) had 10.8 MMSTB The differential depletion zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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) zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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. Apog (g)k(t)/(l.to [~b(1 - Slw They plotted the results graphically as: log (1-N)p vs. log zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQ 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) zyxwvutsrqponmlkj

1

41 70

0.19 0.25

0.14 0.15

0.11 0.12

0.21 0.14 zyxwvutsrqponmlkjihgfedc

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 satuS~ is ration at the end of the measurement (td -- 100); n is relative-permeability exponent in kro = k~ 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

-

.oo1

.ooo,

0

kro/

~/

k/F~r

L z

.0,

.ooool

I

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. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFE 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. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFE

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~

~

:

?

:

GASSING ZONE (SATURATED OIL)

CURRENT G/O LEVEL

EQUILIBRIUM GAS SATURATION LEVEL

zyxw

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

zyxwvu

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

.\ ]

I'--" t,L

TOP

OF

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

s )...

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. zyxwvutsrqponmlkjih

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 zyxwvutsrqpo 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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA (594)

1600

(S281

.075 1400 1~21

O

,ft r

o .u

13961

E

I,&J

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

I,.

~

U.I Q~

800

o Q.

12641

.15

~. j.".r-

u_

o

tJ')

~

600

~

11981

m

.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--

25

zyxwvutsrqp po(rv,to)='~[ln

+0.809071

toa < 0.1

P o (ro,t D) =

~

% - 1

(to +

)

72"-

(% - 1)

Closed

(3r~

-4r;

toA > 0.1

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

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. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

~P

1

Fig. 6-8. Pressure drop vs. 1 / ~t-for spherical flow pressure data.

562 k,

I I 111 I I l II

-Xf

~

,

].t.,

Ct

111 I I Ill Ix'

3_ bf

zyxwvutsrqponmlkjihgfedcbaZYXWVUTS

Fig. 6-9. Bilinear flow in a reservoir.

In terms of real variables, the pressure drop ApwI can be expressed as follows: zyxwvutsrqponmlk

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 ]. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCB

bP

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

]

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., zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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

(D

o I c~

I

,

I

I

I

I

k 87.67 c IxlO-4 s 9.194

10

zyxwvutsrqponmlkjih 0

v

"- 3600

t.f) t/') (1.)

-I

-C3 C)_

3 800 t.D Q_

,

100

I

c0

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFED tD/ CD, and multiplying by tD/ C D gives: zyxwvutsrqponm

to /

t~

-~P'D-Co

(6-13)

Taking logarithms: zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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 /

!

I

I

I

zyxwvutsrqponmlkj k 87.67 c 5xlO -2

--/,et ee~ee

_

I

100

'"

~ 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

!

zyxw f

]0

,

1000

tD/C

D

1 x 104

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.)

zyx

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

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

I

1 -

oi~l~ ~ o O~

*** , ~ l I

I

I

0.1

1

10

SHUT-IN TIME, At,HRS

~176 ,,

0.1 100

O. 1

zyxwvu

1

I

,

10

tD/C D

zyxwv I

I

100

1000

lxlO4

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.)

zyxwvu

Double Porosity T e s t

Double Porosity Test

Mi Iler- Dyes-Hutchinson plot 950

....

I

\

940

....

t

zyxwvutsrqponmlkjihgfedcba Stg & Skn DP StdySt [nf Actng One Q

'|

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

o

t__

O..

920 - -

k rn s w 1

910

49Z 1 10.18 -2.055 0.1051 8.94.x10-tO I

xlO - 3

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~

zyxwvutsrqpo

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

zyxwvutsrqponmlk C 0

O

m 4000 n SO00

1

!

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(I)

100

I

I

J

204.8 87.67 9.194 301.1

:3 oo

I

I

I

_

LC

1.549x1011

9

" " " T , ; ~

.. . .. . .. . .. . ... . .. . . . . ."... . .

~ x

zyxwvutsrqponmlkji 10

~~

oo 4 0 0 0 Q..

I

k 87.67 c 1.427x10-z s 9.194 .~

r~ 5000 ~.)

-

%

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

zyxw zyxwvutsrq ~

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 zyxwvutsrqpo 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,

Clr =

aoq tip 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. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHG

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: zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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

zyxwvutsrqpon

zyxwvutsr

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

.e+ r,-' 4]

LARGE TIME APPROXIMATION

SMALL TIME APPROXIMATION

GENERAL EQUATION

BOUNDARY CONDITIONS INNER OUTER

rD =l,

zyxwvutsrqponm 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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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

\

\ \\

zyxwvutsrqponmlkjihgfedcbaZYXWVUTS

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

(tD/ CD)P'D shows a notably In this figure note that the pressure derivative function zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQP 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

"noise" of instances of reservoirs with high mobility-thickness products, due to the zyxwvutsrqponmlkjihgfedcb 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 _> 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 ..

~1

tp zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQP , ~_.. ,. . . . .

I

t

--I ~

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 zyxwvutsrqponml 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: zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJ

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 zyxwvutsrqponmlkjihgfed (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 + log tP zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONML + At (DI2err2w

(6-84)

615

Pw~ o r (Ap)buildup VS. Ate, This expression suggests that a graph of buildup pressure, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSR 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:

Ikll

4

s = 1.115131Pw~ (At = 1)-Pws(Atm = O) zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFED log log (6-85) Cpctr: 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. zyxwvutsrqponmlkjihgfedcbaZYXW

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 zyxwvutsrqponmlkjihgfedcbaZYXW

Fig. 6-54. Variation of flow rate vs. time during the tests in well A. TABLE 6-XIII Reservoir and fluid data zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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

9

9

s,"

o D

%

9

s

~

t I. m_0.25

9 9

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

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 99

Oo

PWS, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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. zyxwvutsrqponmlkjihgfe

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 zyxwvutsrqpo

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 .~_..._ _ 3900- zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA I

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

~j

3600-

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

10-2

,

i

At

10-1

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA ~ ,,.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): zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

t dApwl dt

-

m zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA + m*t (6-86) 2.303

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 dAPw zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA s / 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

~

/

-.--t%

9 9

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA o 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. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJI '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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA derivativedApws/dAtvs, tp / At(tp + At) for the first buildup test, well B2. 0.5

9'

CASE

d~pws dAt

zyxwvutsrqponmlkjihgfedcbaZY

-

psi

~;

B-2

m

~ ~ -9 1 4 9

9149 9 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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA I I I i I 0.2 0.4 0.6 t p

(tp+ht) At

,

I

0.8

,

]

! hr_ ]

Fig. 6-71. Graph of the pressure derivative zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCB 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): zyxwvutsrqponmlkjihgfedcbaZYXWVU (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.

ANALYSIS OF W E L L I N T E R F E R E N C E TESTS

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 "active" well, creates a pressure interference in a previously-closed, nearby obseran zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA vation 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

PD

J

----/" 161

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

....

I0-z

I0-I

1

I0

0z

10 3

I04

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: zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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). F1(PD) and the ordinate F2(tD) correspond to the definitions of The abscissa zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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.) zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGF

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

]d ~ I

ld a

LINEAR

.

"

lFi, ~

.

' RADIAL~

/

I

/

!

1

I

~

SPHERICAL FLOW

#

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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

0

12

0

4

11-A

o 0

o

o5

~ zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA "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: zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIH 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) zyxwvutsrqpo w

639

PPD (rD,tD) =

{pp(pi)-pp(r,t)} h(p,) {1 - ~b(p,)} zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA (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)

dp PP(P) zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA = Po { 1 - ~ (p) } p (p)

(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,)} zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA ~, (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) zyxwvutsrqpon

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: zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHG

k(Pwf)

-1.1513a o

:l-~b(Pw:)}

1 9 ~ (,pwl)9 (6-101) h(Pi):l-qb(Pwl)} zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGF q i P (Pi)

P(,Pw:)(OPw~) ~

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIH (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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCB "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

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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

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.

Pwfq

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): zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGF

p~(t~)

=

f

l~ 98

Ap,D(tD- v)dv zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA (6-106) zyxwvutsrqponm

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 Ape(t) involved in Eq. 6-105 for infinite-acting radial flow that the influence function zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA conditions can be expressed, for units of the English system: zyxwvutsrqponmlkjihgfedcbaZYXWV 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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFED

-

~

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPO 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. zyxwvutsrqponmlkjihgfedcbaZYXWV

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 9 begins at time, t.. and ends at time t j, the zyxwvutsrqpo ,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, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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 l OAt). If this limitation is not satisfied, then data should be corrected. To time ( t > zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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" zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQP

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

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

(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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA tAft = C1L t 1/2

(6-123)

2 Bilinear flow t a p ' = Clbft 1/4 t2 Izap,,I

=

C

lbftl/4 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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 AzyxwvutsrqponmlkjihgfedcbaZYXW 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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJI 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

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

--.....

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-

~

~

'I000-.

-__o___~_~. C3

m-i

~_.._.......___-----

.---

~

-

1000~I

-

.

.

.

.

.

.

.

.

700J

Numbers indicate

t 350

conftning pressure

/,60

~

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

a 3 : 0 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA ~3 = I00 ~3:35 ~3 : 210 ~,,

case 1

_

1

v

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. zyxwvutsrqpon

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. zyxwvutsrqponmlkjihgfedcba 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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

sort o"3 domes zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQ

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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. zyxwvutsrqponml

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. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONM

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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 9 normal

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. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFED

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHG

\

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA [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 zyxwvutsrqp

|

|

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: LFD V = LFDZ = n /L Vertical fracture density = zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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. zyxwvutsrqpon

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) zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA and horizontal (b) fracture density9

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. zyxwvutsrqponmlkjihgfedcbaZ

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 = 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 zyxwvutsrqponmlkjihgfedcbaZYXWV

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) 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: laterally delineated by vertical fracture (1) Each single matrix block extension is zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHG 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

I . vn 3

2

"

lo 2

'/ /

,,,..

-

,'

n.

lO ,

E

1

4

vq

/ I

/'1

/ ~ ,i~//, \'-/ I

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA // //

i,

10' '" 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: zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFE (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 zyxwvutsrqpo

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


...

I,,,--

(3 Z

Z w 20 n,ILl r 15

. ~ . . _ -

.

80 W zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGF =)

BRECCIATED

0 Z I0 LU

0 LU rl," LL

(3

15~

O

60 ~ Z

U-W

~0 w ~ ~LU

.,

20

5

0

6

10

LfD(NUMBER

20 OF

30 FRACTURES

A0 PER

90 99


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

? Z

/I/, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

b

:

BL zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

r

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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" x,("S~ e f f e c t i v e "~: of a single fracture based on Fig. 7.29 is represented by: S ffectiv e - -

a*b

(7-16)

714

,,-

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQ 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: zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJI

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

9

. . . .

9

~.

.

".

.

.

.

.

9I ?" zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA .'" ." 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 layer9 Fractures and layers are parallel.

(2) zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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: / * (Jr / 2 ) 2* LFDZ] ~ = [29.6 * k / * LFDZ] ~ ~ / = [12 * kzyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

(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

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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

(..);


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,. -- zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

hTH

1 /

}

Block B o t t o m Face

,

n,.,

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA = Pc/(~'o-~'Q) |:(/GUO". O.:':.o-?.:W.:.> zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFED ..... ;,~,..-..o.~.., 6 0..t p!~:U.~.O,c?.~..i~~.! Po % I?:r ibo.a( ).o.:~ !,,4,,,'~ :o:.. "1,2' "v-. ;O: ""::L~.' ___IV~'.:'U ,V.',~:.'.o ....: 9..r ' '. o..- -~: .' .:,r ".~. I f-D:, ~o:~::~el',. I 10.:., :]:o..~ 1 ~....~l"a :o. "~.'Lr ".'d:v. :'" II I ! g: +;.+:,O. o o ~

!

I l...o. ~.!e~,T,+~.~ I

I~'.~ .":o "A. I/ "." f2:~:4"1:-

:( .*.0.M- ~ " . ' i ) : ,, ~:.., ;~ :.'.- ..,;r162

.~.,

I

ii

""

I ~--.--.--- - ~

PTHH] ~:i ::.'..

3! ......

3

I 7b

":':"

0 0

Sw

~o \\\~

~:~7

Equil.

~;', hTH=h3

!;~

~,.~: BOTTOM"

gas-oil ~...cont act

! !

i:~:

I~:~

L:~]

!

:~ :;=.

~.:""[

V/'

hTH

q-

2 ~

equilib.

oil press.I _\~

gas-oil

grad.

"capillary

100

"" ~

[ \ - ~ ~

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.

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

"

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONM

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: zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFED Q' BI , 0, GC = Q , o,o 9 M' 9 DF'oc

\(-7- _ . ,o . . s, ]~

zyxwvutsrqponm

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. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPON 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

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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 D F zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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 v

9

flowing

capacity

- Viscosity Kinetic viscosity

-

- Specific mass - Stress - Porosity -

C

o

n

s

t

a

n

t

r el at ed to f l o wi n g

direction

f.o zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA -Relative f r a c t u r e s t o r a g e c a p a c i t y zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHG

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

- Axis direction

1

- Matrix

2

- Fracture

- Interstitial water - Water-oil

This Page Intentionally Left Blank

773 zyxwvutsrqpon

Chapter 8 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUT

B

Fig. 8-1. (A) Scanning-electron micrograph of skeleton of coccolith zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPON (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 (notaInoceramus spp.), echinoderm fragments, bryozoans, and bone fragbly, those of zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA ments.

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

:i " S C 0

T L A

D

.....:~i~i~i!:ii:.ii:iiii::i:ii~ili~i~, ...............::...................... :: _ ....... : : ,/:

~

0

R

W

.A Y,~,~:

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDC

i r

.,

,,:

C.7~,

i.

,.o ,~o.

~

] /

,.,#

,

./

~

w E.S r e E R M ^ N V 1

I

d / ~'~,,~,~,,os/ ,

:.k

i 5,

~o~,

.4" /

......................~............~ ................... Fig. 8-3. Ekofisk Field in the Central Graben, southern part of the Norwegian sector of the North Sea. (From Van ddn Bark and Thomas, 1980; reprinted with permission from the American Association of Petroleum Geologists.)

777 zyxwvutsrqpo

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

C H A L K FORMATIONS |

.

.

.

.

.

.

.

E K O F I S K FORMATION , "'

STAGE ,

I

DANIAN

i

1 'i

MAASTRICHTIAN TOR FORMATION

9

13.. i ::3 i O n" ' (..9 ,,r -J < "1" O

. . . . .

L

9

CAMPANIAN

H O D FORMATION

SANTONIAN

CONIACIAN TURONIAN 9

i

9

1

l

P L E N U S M A R L FORMATION ,

i

J HIDRA FORMATION

CENOMANIAN 9

,,

|

Fig. 8-4. Stratigraphy of the North Sea chalk within the Central Graben. (From Feazel and Farrell, 1988; reprinted with permission from SEPM, the Society for Sedimentary Geology.)

778 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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

SONIC

/

9500'~2895m

/

2900m

/ / / /

9700~

/ /

I

/

9500' -2950m

9700' -

.,

n

t

I

,,r !,i :i

10,000'-l'-

.

:

~0.206' \

Laooom

11

i;

\ \

\

,

1

]

\ \ \\

11,000' 1 03

W

10,000'- 3050m

\

t

[

I

i

[ -1

I I:-

"

~

,

,

3100m

-o lO.2o~'

~LU

-,

12,000' -,

IUJ

,tr

I i

tr

i

_d

10,500'.-3200m

13,000'~

Fig. 8-5. Cretaceous and lower Tertiary lithostratigraphic nomenclature in the Ekofisk area, North Sea. (From Van den Bark and Thomas, 1980; reprinted with permission from the American Association of Petroleum Geologists.)

779

zy

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

\ \

\

~57"00'N \ I I

\ I

\

l

~

56 ~ 4O'N

\

~,W.~ISK~

2 c 40'E %

\ %

%~

$6 ~ 30'N

\ \

"/'\TJ-

'

"~'"

i

[

\,,,,i 1 ~ O0'E

3 o 40"N

Fig. 8-6. Location map of the Greater Ekofisk Area fields, central North Sea. (From Feazel and Farrell, 1988" reprintedwith permission from SEPM, the Society for Sedimentary Geology.)

2/4-3X 3 R O S S PAY 9 NET PAY 9 rIME INTERVAL

710' 295' 9

O. 1 1 0

SEC.

2/4-1AX 758' 620' O. 15O S E C . I n tqlrll ~ I r

2/4-4AX 698' 410'

o. 120 S E C . 11,680'

/ SEC.

--.I

zyxwvu 2.5

o9 Q z o o I.tl 3.0 r~ Z LU I-

0 F'3.5

Fig. 8-7. North-to-south seismic cross-section integrates borehole and seismic data to show the high porosity limits of the field. (From Van den Bark and t h o m a s , 1980; reprinted with permission from the American Association of Petroleum Geologists.)

781 zyxwvutsrqp

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).

I.Lu tu

t~ t~ iii

-9OOO

-10,000

280O

30OO

-11,000 - ~

5 ~

v

J

t

3200

~

..."-- 1 5

--..~

10 ~ ,, > - > 5

Fig. 8-8. Isometric projection of the Ekofisk Field. (From Van den Bark and Thomas, 1980; reprinted with permission from the American Association of Petroleum Geologists.)

782 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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).

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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). zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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

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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 w i t h the geomorphic developformed 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 ment of the geomorphic landscapes.

819

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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 zyxwvutsrqponmlkjihgfedcbaZYXW 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).

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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). zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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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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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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

I

! BR. AMER. FUSON

STRUCTURAl, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIH CROSS SECTION A 2 4 S 6 7 PHILLIPS

C.S.O.

lEGgIER

C.S.O.

WEST

I

--4000

WIERNIER-FARLEY COMPOSITE

LOG

EIGHT12.9

C.S.O. I.T.I.O.

TROSPIER FARLEY. w PARK r OKLAHOMA 9 CITY

JO H N S O N RiENO UNIT

9COMPOSITE

LOG

EAST --MILES

Kms

"---~ [ ~ 4 o o o -

--4500

~

- 6000

V_

-6000Z

& GILL

PROSPERITY ACRES

-

k-~~--,soo.~_ z

"

6ooo-~-

< I u

6soo-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)

zyxwvu (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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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

zyxwvutsrqponmlkji

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) components ofkarsted reservoirs in all types ofkarst-associated hydrocarbon as the main zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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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.

.

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.

.

.

.

.

.

.

.

9,--~;~,~;'.::_.....,,,+n:-.,-:,m~

_r - - T - - - ~ - _ ~ =

'--

Vici~clll

.

.

.

. . .

,,.,o

.

I

.....

zyxwvutsrqpo

zyxwvutsrqpo .

..,.,

,,,,o,..,

'

"

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONML 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 ~ T E R zyxwvutsrqponmlkjihgfedcbaZYXWV

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 zyxwvutsrqponmlkjihgfedc 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, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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) zyxwvutsrq

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

(C-22) zyxwvutsrqpon d d Api +zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 4or cos0a~

Therefore, when

Ap, >> P :

V1 dl 2 ~z~ V1 d22

(C-23)

and when @ i 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 ! zyxwvutsrqpon 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)

Z R s zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONM (SCF/STB)

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 zyxwvutsrqpo 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? zyxwvutsrqponmlkjih 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

+ C O 2 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJ

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, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFED 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 zyxwvutsrqp

A U T H O R INDEX

Aalund, L., 332, 333,534 Anderson, J.H., 804, 810, 840, 860 Abbit, W.E., 676 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Anderson, K.E., 93 7 Abernathy, B.F., 29, 30, 31, 35, 36, 37, 51,258, Anderson, R.C., 532 283, 534, 539 Anderson, T.O., 28, 51 Abou-Sayed, A.S., 354, 534 Anderson, W.G., 873, 899 Abrassart, C.P., 533 Anderson, W.L., 208, 221 Acuna, J.A., 433,534 Andresen, K.H., 235,502, 534 Adams, A.R., 41, 51, 676 Andrews, D.P., 541 Adams, R.L., 340, 344, 540 Andriasov, R., 949 Adams, W.L., 793 Angevine, C.L., 84, 98 Adler, EM., 393,394, 397, 534, 542 Anstey, N.A., 68, 98 Adolph, R.A.,227 Antonlady, D.G., 51 Agarwal, R.G., 612, 613,614, 650, 657, 676 Arab, N., 264, 534 Agtergerg, F.E, 100 Araktingi, U.G., 359, 384, 534, 535, 886, 891, Aguilera, R., 8, 9, 10, 11, 12, 13, 14, 15, 51, 899 880, 899 Archer, D.L., 902 Aharony, A., 388, 389, 392, 405, 534 Archer, J.S., 106, 108, 149 Ahr, W.H., 306, 545 Archie, G.E., 133, 147, 149, 155, 163, 164, 168, Aigner, T., 83, 98, 101 177, 178, 184, 186, 188, 189, 190, 196, AIME, 198,226 197, 210, 217, 219, 221,481,534 Akins, D.W. Jr., 532 Arifi, N.A., 681 A1-Hussainy, R., 592, 593,595,676 Arkfeld, T.E., 226 A1-Muhairy, A., 333,534 Armstrong, EE., 28, 51 A1-Shaieb, Z., 810,861 Armstrong, M., 902 A1-Zarafi, A., 332,534 Arnold, M.D., 9, 51 Alameda, G.K., 53 7 Aron, J., 224 Alberty, M., 166, 221 Aronofsky, J.S., 260, 501,504, 534, 741,753, Algeo, T.J., 456, 534 769 Alger, R.P., 228, 793 Arps, J.J., 18, 20, 21, 23, 38, 51, 189, 221,534 Allen, D., 158, 203,221 Arribas, J.R.F., 859 Allen H.H.,532 Arya, A., 534 Allen, W.W., 532 Atlas Wireline Services, 158, 169, 172, 180, 181, Alpay, O.A., 8, 28, 51 189, 197, 198, 200, 205,207, 214, 222 Alsharhan, A.S., 74, 90, 96, 98, 1O0 Aubry, M.P., 100 Aly, A., 544 Aud, W.W., 355, 356, 357, 534 Ambrose, R.W. Jr., 678 Aufricht, W.R., 887, 899 Ameri, S., 334, 534, 676 Ausburn, B.E., 158, 215,222 American Petroleum Institute, 118, 128, 149, Auzerais, E, 221 167, 178, 201,221 Avasthi, J.M., 55 Aminian, K., 594, 676 Aves, H.S., 813,856 Amott, E., 136, 149 Ayesteran, L., 644, 677, 679 Amthor, J.E., 48, 51,810, 838, 845, 856 Ayoub, J.A., 676, 677, 678 Anderson, A.L., 544 Ayral, S., 152 Anderson, B.I., 223 Aziz, K., 546, 641,676 Anderson, G., 108, 149

960 Berger, B.D., 937 Babson, E.C., 251,252, 253,534 Berggren, W.A., 100 Bachman, R.C., 896, 900 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Bergosh, J.L., 117, 141, 142, 149, 206, 222 Bachu, S., 888, 900 Bergt, D., 221 Back, W., 799, 856, 859 Bemthal, M.J., 83,102 Backmeyer, L.A., 897,900 Berry, V.J.Jr., 545 Bacon, M., 60, 101 Bertrand, J-P., 535 Badley, M.E., 64, 65, 66, 68, 98 Best, D.L., 221,229 Bagley, J.W., Jr., 28, 54 Betzer, ER., 858 Bajsarowicz, C., 151 Bevan, T.G., 8 Bakalowicz, M.J., 799, 800, 856 Beveridge, S.B., 489, 498, 499, 500, 501,535 Baker, R.I., 534 Beydoun, Z.R., 332, 333, 503, 535 Bakker, M., 8, 56 Bezdek, J., 99, 100, 101, 102 Baldwin, D.E., Jr., 28, 51 Bice, D., 83, 99 Balint, V., 812,856 Biggs, W.P., 169, 205, 226, 227 Ball, M.M., 86, 98 Bilhartz, H.L., 222 Bally, A.W., 60, 98, 101, 103 Bilozir, D.E., 898,900 Barbe, J.A., 302, 534 Binder, R.C., 940, 941,949 Barber, A.H.Jr., 285,302, 303,304, 305, 534 Bissell, H.J., 25, 52, 57, 536, 543, 901, 951,952 Barclay, W., 60, 101 Bissell, R.C., 52 Bardon, C., 52 Biswas, G., 99, 100, 101, 102 Bardossy, G., 797, 807, 856 Bitzer, K., 84, 99 Barenblatt, G.I., 741,769 Black, C.J.J., 52 Barfield, E.C., 257,534 Black, H.N., 335, 338, 339, 340, 341,343,344, Barham, R.H., 679 535 Baria, L.R., 90, 99 Black, J.L., Jr., 533 Barnum, R.S., 297, 534 Blair, P.M., 260, 501,535 Baron, R.P., 52 Blair, R.K., 52 Barr6n, T.R., 665, 676 Blanchet, EH., 8, 51 Barton, C.C., 433,535 Blanton, J.R., 532 Barton, H.B., 532 Bliefnick, D.M., 47, 51, 810, 838, 856 Bashore, W.M., 433, 534, 535, 899 Bock, W.D., 98 Baxendale, D., 679 Bocker, T., 797, 857 Baxley, ET., 228 Bogli, J., 797, 85 7 Bayer, J.E., 227 Bohannan, D.L., 532 Be, A.W.H., 49, 55 Bois, C., 832, 857 Beales, EW., 56 Bokn, I., 544 Beals, R., 225 Bokserman, A.A., 44, 47, 51 Beaudry, D., 93, 99 Bond, J.G., 144, 149 Bebout, D.G., 308, 309, 535, 538, 802, 813, Bonnie, R.J.M., 194, 222 840, 856, 857, 858, 860, 861,885, 900 Borg, I.Y., 535 Beck, D.L., 52 Borgan, R.L., 532 BEG, 32, 33, 34, 54, 287,289, 290, 292, 293, Bosak, P., 797, 798, 799, 800, 806, 834, 856, 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

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 Calvert, T.J., 192,222 Boynton, R.S., 46, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 51 Campa, M.E, 28, 52 Brace, W.F., 346, 535 Campbell, EL., 158, 197, 225 Bradley, M.D., 538 Campbell, R.L., Jr., 222 Brady, T.J., 48, 51, 813, 845, 857 Campbell, N.D.J., 51, 85 7 Braester, C., 678 Candelaria, M.P., 51,797, 856, 857, 858, 859, Bramkamp, R.A., 533 860, 861, 862, 863, 864, 865 Brandner, C.E, 897, 900 Cannon, R., 99, 100, 101, 102, 900 Bras, R.L., 540 Canter, K.L., 811,857, 865 Breland, J.A., 858 Carannante, G., 79, 102 Brewster, J., 781, 782, 793 Cardwell, W.T., 888, 900 Brice, B.W., 542 Cargile, L.L.,533 Bridge, J.S., 83, 99 Carlson, L.O., 897, 900 Brie, A., 223 Carlton, L.A., 55, 679 Briens, F.J.L., 57, 546 Carmichael, R.S., 128, 150, 168, 179, 193,222 Briggs, P.J., 46, 47, 52 Carnes, ES., 28, 52 Briggs, R.O., 207, 214, 222 Carpenter, B.N., 810, 85 7 Brigham, W.E., 680 Carroll, H.B., Jr., 56, 358, 539, 542, 901,903 Brimhall, R.M., 5 7, 546 Carslaw, H.S., 677 Brinkmeyer, A., 545 Carter, N.L., 535 Broding, R.A., 209, 222 Carter, R.D., 676 Bromley, R.G., 782, 784, 793 Carver, R.E., 139, 150, 167, 178, 202, 213,222 Brons, E, 51,534, 679 Cassan, J.P., 878, 880, 902 Brooks, J., 794 Castellana, ES., 152 Brooks, M., 60, 100 Castillo, E, 859 Broomhall, R.W., 45, 55 Castillo-Tejero, C., 813,820, 830, 832, 847, 864 Brown, A.R., 158, 215, 222, 851,854, 857 Castro Orjuela, A., 222 Brown, C.A., 790, 793, 794 Catacosinos, P.A., 810, 828, 849, 857 Brown, R.J.S., 181, 195,222, 466, 535 Caudle, B.H., 456,545 Brown, R.O., 207, 208, 222 Chace, D.M., 173,222, 224 Brown, S., 223 Chakrabarty, C., 432, 535 Brownrigg, R.L., 862 Chandler, M.A., 133,150 Bruce, W.A., 131,151, 177, 227, 253,533, 535 Chaney, ER., 260, 501,544 Bubb, J.N., 50, 52, 76, 99 Chang, D.M., 370, 539 Buchwald, R.W., 51, 534 Chang, J., 535 Buckley, J.S., 200, 222, 873, 900 Chang, M.M., 151, 312,315, 322, 323,324, 535, Buckley, S.E., 29, 52, 488, 489, 535 540 Bulnes, A.C., 233,256, 258, 535 Chapman, R.E., 537 Burchell, P.W., 532 Charlson, G.S., 160, 222 Burchfield, T.E., 871,899, 902 Chatas, A.T., 677 Burgess, R.J., 51,676 Chatzis, I., 879, 898, 900, 901 Burk, C.A., 151 Chauvel, Y., 207, 214, 222 Burke, J.A., 169, 222 Chayes, E, 265, 535 Chemali, R., 228 Burns, G.K., 540, 793 Busch, D.A., 810, 816, 825,840, 858 Chen, H-K., 332,333,535 Bush, D.C., 139, 149 Chen, H.C., 363, 535, 537 Butler, J.R., 222 Chen, H.Y., 544 Button, D.M., 545 Chen, M., 224 Chen, S., 28, 390, 535 Bykov, V.N., 812, 861 Byrd, W.D., 50, 52 Chen, Z., 133,150 Byrne, R.H., 858 Cheng, S.W.L., 862 Chenowith, P.A., 806, 857 Cady, G.C., 680 Cheong, D.K., 100 Caldwell, R.L., 5 7, 229 Cheung, ES., 223,227 Calhoun, J.C., Jr., 38, 57, 296, 547 Chichowicz, L., 41, 55 Callow, G.O., 256, 544 Chilingar, G.V., 24, 25, 52, 53, 54, 56, 57, 233,

962 390, 536, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 542, 543, 544, 546, 869, 877, Coufleau, M.A., 226 900, 901,909, 951,952, 953, 954, 956 Coulter, G.R., 334, 536 Chilingarian, G.V., 1, 4, 34, 47, 52, 54, 55, 231, Couri, F., 678 Cove de Murville, E., 52 254, 268, 274, 275, 280, 389, 390, 417, 466, 468, 536, 537, 539, 541, 543, 545, Crabtree, P.T., 152, 229, 546 Crabtree, S.J., 900 677, 681,834, 861,882, 901,937 Chopra, A.K., 435,544 Craft, B.C., 18, 52, 234, 245, 246, 282, 536, 956, 95 7 Choquette, P.W., 52, 254, 268, 536, 542, 793, 797, 798, 799, 801,802, 803, 805, 806, Craft, M., 141,151, 794 Crafton, J.W., 793 814, 832, 833,834, 845, 857, 858, 859, 860, 861,863 Craig, D.H., 52, 805,812, 831,832, 836, 837, 842, 844, 847, 856, 857 Chork, C.Y., 539 Chuber, S., 787, 793, 794 Craig, F.F., 35, 37, 48, 52, 56, 545, 870, 873, 874, 882, 900 Chuoke, R.L., 900 Crary, S., 208,209, 223 Cichowitz, L., 679 Crawford, D.A., 677 Cinco-Ley, H., 203, 210, 223, 317, 320, 321, Crawford, G.E., 611, 677 536, 545, 559, 563,575,584, 596, 601, Crawford, P.B., 28, 51, 52, 676 607, 615, 621,623,625,630, 633,638, Craze, R.C., 3, 52, 233, 247, 536 646, 651,652, 656, 657, 673,677, 678, Crevello, P.D., 99, 102, 794, 857 680 Crichlow, H.B., 363, 375,536 Cisne, J.L., 84,99 Criss, C.R., 533 Clark, B., 221 Cromwell, D.W., 51,856, 859, 861,862, 864 Clark, C.N., 545 Crookson, R.B., 55 Clark, D.G., 580, 581,677 Cross, T.A., 100, 101, 102 Clark, J.B., 297, 536 Crow, W.L., 345, 346, 536 Clark, K.K., 27, 41, 52, 677, 680 Crowe, C.W., 356, 536 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

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Drews, W.E, 677 de Waal, P.J., 226 Driscoll, V.J., 302, 537 de Witte, L., 394, 546 Dromgoole, E., 83, 99, 101 Dean, M.C., 224 Dubey, S.T., 150, 200, 224 Deans, H.A., 150, 158, 223,539 Dublyansky, V.N., 799, 858 Dees, J.M., 334, 536 Dubois, D., 363, 537 DeHaas, R.J., 810, 836, 837, 844, 858 Dubois, J., 546 Delaney, R.P., 882, 883, 900 Duchek, M.E, 222 Delaune, P.L., 199, 223 Dufurrena, C.K., 810, 811,830, 862 Delhomme, J.P., 365, 536 Dullien, EA.L., 875,900, 901 Dembicki, H., 225 Dumanoir, J.L., 169, 179, 205, 223,224 Demicco, R.V., 83, 99, 102 Dunham, R.J., 256, 537 DeMille, G., 800,858 Dunn, P.A., 100 Demko, S., 427, 537 Dunnington, H.V., 696, 697, 769 Dempsey, J.R., 536 Duns, H., 546 Dennis, B., 223 Duong, A.N., 658, 677 Denoo, S., 223 Dupuy, M., 543 Denoyelle, L., 11,52 Duran, R., 679 Deryuck, B.G., 677 Durbin, D., 229 Desbrisay, C.L., 42, 52 Durham, T.E., 861 Desch, J.B., 381,383,384, 537 Dussan, E., 221 Dewan, J.T., 158, 180, 197, 223 Dussert, P., 48, 53, 813, 831,838, 844, 858 D'Heur, M., 781, 783, 793 Dyer, R.C., 60, 100 Dickey, P.A., 240, 537 Dyes, A.B., 679 Dickson, J.A.D., 783, 794 Dykes, F.R.Jr., 532 Diederix, K.M., 139, 153 Dykstra, H., 34, 53, 290, 436, 537 Diemer, K., 535 Dzulynski, S., 797, 858 DiFoggio, R., 152, 229, 546 Dines, K., 158, 215,223 Ealey, P.J., 893, 902 Dixon, T.N., 677 Earlougher, R.C., Jr., 196, 203,224, 549, 553, Dobrin, M.B., 63, 69, 70, 99 563,584, 614, 632, 636, 677 Dodd, J.E., 98 Earlougher, R.C. Jr., Dodson, T., 151 Eaton, B.A., 39, 53 DOE, 277, 278, 280, 281,537 Ebanks, W.J., 811,830, 840, 858 Doe, P.H., 200, 224 Eberli, G.P., 84, 85, 99 Dogru, A.H., 659, 677 Economides, M.J., 539, 632, 678 Doh, C.A., 228 Edelstein, W.A., 134, 150, 152, 179, 184, 224, Doll, H.G., 168, 204, 223,227 229, 546 Dolly, E.D., 810, 816, 825, 840, 858 Edgar, T.F., 677 Domenico, S.N., 158, 223 Edie, R.W., 812, 814, 825, 858 Dominguez, A.N., 677 Edmunson, H., 128, 150, 168, 179, 193,224 Dominguez, G.C., 375,537, 545, 550, 677, 681 Edwards, C.M., 544 Donaldson, E.C., 136, 150 Effs, D.J.Jr., 538 Donohoe, C.W., 532 Egemeier, S.J., 799, 858 Donohue, D.A.T., 158, 223 Eggert, K., 535 Doolen, G.D., 535 Ehlers, E.G., 139, 150 Doughty, D., 545 Ehlig-Economides, C.A., 656, 658, 678 Douglas, A.A., 222, 676 Ehrlich, R., 55, 140, 150, 178, 224, 413,537, Douglas, R.G., 49, 56, 773, 793, 794 873,900 Dove, R.E., 53, 225 Eidel, J.J., 85 7 Dowdall, W., 94, 101 Eijpe, R., 436, 537 Dowling, P.L., 42, 52, 256, 537 Ekdale, A.A., 782, 784, 793 Doyle, M., 98, 101 Ekstrom, M.P., 207, 214, 224 EI-Ghussein, B.F., 52 Doyle, R.E., 376, 378, 537 Doyle-Read, F.M., 883,903 E1-Rabaa, A.W.M., 55 Dresser Atlas, 173,224 Elkins, L.F., 2, 8, 28, 44, 45, 53, 302, 486, 487,

964 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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 Goss, L.E., 532 Gale, J.E., zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 56 Gould, T.L., 285, 286, 538 ~: Galloway, W.E., 233,275,276, 538, 546 Gounot, M-T., 223 Gamson, B.W., 181, 195,222, 466, 535 Govier, G.W., 680 Garaicochea Petrirena, E, 538 Govorova, G., 949 Garat, J., 225 Gradstein, F.M., 85, 100 Garcia-Sineriz, B., 799, 812,859 Graham, J.W., 44, 53, 260, 501,502, 539 Gardner, G.H.E, 229 Graham, S.K., 542 Gardner, J.S., 169, 179, 224, 227 Grant, C.W., 436, 438, 439, 440, 452, 453,454, Garfield, R.F., 533 456, 539 Garfield, T.R., 811,840, 859 Grau, J., 53, 225 Garrett, C.M.Jr., 538, 546 Graus, R.R., 83, 100 Garrison, J.R.Jr., 267, 268, 269, 270, 271,272, Graves, E.D. Jr., 957 415, 417, 538 Gray, L.L., 54, 533 Garrison, R.E., 773, 793 Gray, R., 532 Gatewood, L.E., 810, 827, 831,832, 837, 859 Gray, T.A., 435, 539 Gealy, F.D.Jr., 532 Greaves, K.H., 151,226 Geertsma, J., 769 Grebe, J.J., 296, 539 Geesaman, R.C., 811,840, 857, 859, 865 Gregory, A.R., 229 Geffen, T.M., 52, 481,545 Grier, S.P., 151,228 Gehr, J.A., 56 Gries, R.R., 60, 100 Geldart, L.P., 102 Grine, D.R., 226 George, C.J., 33, 34, 53, 534 Gringarten, A.C., 203, 210, 224, 563,580, 597, George, C.P., 902 614, 641,656, 658, 678, 680 Georgi, D.T., 133, 140, 150, 201,211,212, 224 Grotzinger, J.P., 84, 100 Gevers, E.C.A., 85 7 Grover, G.A., 100 Gewers, C.W., 38, 53, 472, 473,538 Groves, D.L., 258, 539 Ghauri, W.K., 302, 538, 882, 901 Gryte, C.C., 152 Gianzero, M., 228 Guangming, Z., 48, 53, 806, 810, 825, 832, 837, Giger, F.M., 324, 538 838, 845, 859 Gilbert, L., 98 Guillory, A.J., 194, 225 Gildner, R.E, 99 Guindy, A., 223 Gill, D., 801, 811,830, 859 Guise, D.R., 900 Gillen, M., 223 Gulati, M.S., 680, 681 Gillson, J.L., 51 Gunter, J.M., 197, 199, 200, 224 Gilreath, J.A., 213,224 Gussow, W.C., 236, 237, 239, 240, 539 Gimatudinov, Sh., 949 Gustavino, Lic.L., 544 Ginsburg, R.N., 84, 85, 92, 99, 100 Guti6rrez, R.M.E., 633,678 Glaister, R.P., 868, 902 Gutman, S., 535 Glazek, J., 807, 834, 856, 857, 858, 859, 862, Gutschick, K.A., 46, 51 863, 864, 865 Guy, B.T., 863 Gleeson, J.W., 466, 468, 538 Guyod, H., 190, 224 Glenn, E.E., 5 7, 229 Guzman, E.J., 832, 859 Gnatyuk, R.A., 56 Gysen, M., 166, 224 Godbold, A.C., 54, 533 Goetz, J.F., 207, 214, 224 Hache, J-M., 221 Goggin, D.J., 150, 436, 538, 539 Hadley, G.F., 486, 539 Goldhammer, R.K., 84, 99, 100, 101 Hagerdom, A.R., 677 Golf-Racht, T.D. van, 141, 142, 150, 205,206, Hagoort, J., 498, 501,539 224 Haidl, EM., 860 Golson, J.G., 793 Halbouty, M.T., 48, 52, 53, 795, 806, 807, 857, Gonzales, H.T., 51 859, 860, 862, 863, 864, 865 Goode, P.A., 221,542 Haldorsen, H.H., 53, 358, 363, 370, 539, 884, Goodknight, R.C., 257, 538 886, 901 Goodman, A.G., 858 Halliburton Logging Services, Inc., 169, 170, Goolsby, J.L., 532 171,172, 180, 189, 190, 197, 198, 200, Goolsby, S.M., 794, 860, 862, 863

966 205,207, 214, 221,224 Henry, J.C., 532 Hallock, P., 77, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 100 Henry, W.E., 794 Halsey, T.C., 410, 423,430, 539 Hensel, W.M., Jr., 205,225 Ham, W.E., 537, 953 Hentschel, H.G.E., 410, 423,539 Herald, F.A., 533 Hammond, P., 221 Herbeck, E.F., 532 Hamon, G., 250, 539 Han, B., 799, 800, 859 Herchenroder, B.E., 100 Hancock, J.M., 782, 793 Herman, J.S., 856 Handford, C.R., 810, 834, 836, 837, 839, 843, Herriot, H.P., 532 844, 861 Herron, M.M., 54, 205,223,225 Herron, S.L., 27, 53, 181,225 Handy, L.L., 260, 486, 539 Hertzog, R.C., 27, 53, 173, 175, 181,195,225, Hansen, A., 534 229 Hansen, J.P., 414, 539 Hester, C.T., 45, 54 Hansen, K.S., 131 Heuer, G.J., 27, 32, 56 Hanshaw, B.B., 799, 856, 859 Haq, B., 82, 85, 98, 100 Hewett, T.A., 363, 364, 365, 366, 367, 368, Harbaugh, J.W., 84, 99, 102, 867, 901 369, 370, 371,378, 379, 387, 388, 433, 452, 534, 537, 539 Hardenbol, J., 100 Hewitt, R., 100 Hardie, L.A., 100 Hardman, R., 150, 224 Heymans, M.J., 857 Hardman, R.EP., 782, 793 Hickman, W.B., 544, 952 Hardy, H.H., 379, 387, 534, 535, 539 Hicks, P.J., Jr., 136, 150, 461,539 Harper, M.L., 50, 53 Hill, C.A., 799, 800, 805,859 Harris, A.J.P.M., 863 Hiltz, R.G., 532 Harris, J.D., 533 Hine, A.C., 100 Harris, J.F., 8, 53 Hingle, A.T., 169, 197, 225 Harris, M.T., 99 Hinkley, D.V., 901 Harris, P.M., 56, 99, 100, 103, 539, 793, 794, Hinrichsen, E.L., 534 800, 812, 840, 858, 859, 860, 861,863 Hirasaki, G.J., 136, 137, 150 Harrison, W., 234, 546, 85 7 Hnatiuk, J., 237, 238, 533, 540 Harvey, A.H., 540 Ho, T.T.Y., 225 Harvey, R.L., 811,814, 822, 831,859 Hobson, G.D., 865 Harville, D.G., 140, 141,150, 151, 167, 224, Hocott, C.R., 535, 540 Hodges, L., 537 227 Hashmy, K.H., 166, 221,224 Hoffman, L.J.B., 167, 225 Hohn, M.E., 363, 365,540 Hassan, T.H., 100 Hastings, B.S., 56 Holcomb, S.V., 57, 229 Holden, W.R., 956, 957 Haszeldine, R.S., 11O, 150, 213,223 Hatlelid, W.G., 50, 52, 76, 99 Holditch, S.A., 349, 540, 541 Havlena, D., 888, 889, 901 Holm, L.W., 44, 54 Hawkins, M.E, 18, 52, 234, 245,246, 282, 536 Hoist, P.H., 52 Hawkins, M.E Jr., 587, 588, 678 Holtz, M.H., 296, 298, 300, 540, 810, 830, 838, Haymond, D., 785, 786, 787, 793 859 Hazebroek, P., 39, 53, 679, 680 Honarpour, M.M., 17, 54, 290, 443,540 Hazen, G.A., 229 Hoogerbrugge, P.J., 225 Heard, H.C., 535 Hook, R.C., 810, 859 Heaviside, J., 435,539 Hoover, R.S., 340, 344, 540 Heifer, K.J., 8, 53 Hopkinson, E.C., 229 Heim, A., 223 Horacek, I., 856, 857, 858, 859, 862, 863, 864, Helland-Hansen, W., 83, 100 865 Heller, J.P., 150 Horkowitz, K.O., 537 Henderson, G., 223 Homby, B.E., 215,223,225 Henderson, J.H., 536 Home, R.N., 549, 580, 581,636, 642, 644, 645, Henderson, K.S., 810, 831,859 656, 657, 659, 677, 678, 680 Homer, D.R., 646, 678 Hendrickson, A.R., 334, 539 Hendrickson, G.E., 28, 32, 34, 35, 53 Horsefield, R., 200, 225,237, 413,533, 540

967 Horstmann, L.E., 329, 540, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 785, 793 860, 863 Hoss, R.L., 532 Jaminski, J., 534 Hotz, R.E, 537 Jantzen, R.E., 138, 151 Hovdan, M., 330, 542 Jardine, D.J., 255,256, 259, 496, 497, 541, 867, Hove, A., 136, 137, 150 869, 901 Hovorka, S.D., 811,859 Jardon, M.A., 542, 547 Howard, G.C., 297, 540 Jargon, J.R., 641,644, 678 Howard, J.J., 134, 150, 151,203,224, 225 Jasti, J.K., 457, 541 Howell, J.V., 861,864 Jeffers, D., 151, 228 Howell, W.D., 51 Jeffreys, P., 214, 222 Howes, B.J., 869, 895, 896, 901 Jenkins, R.E., 139, 149 Hoyle, W., 223 Jenkyns, H.C., 56, 794 Hrametz, A., 225 Jennings, J.N., 797, 860 Hriskevich, M.E., 78, 100 Jennings, J.W., 540 Hsu, K.J., 56, 223, 794 Jennings, H.Y., Jr., 188, 228 Hubbert, M.K., 39, 54 Jensen, J.L., 886, 901 Hudson, J.A., 10, 54 Jensen, M.H., 365, 539 Hudson, W.K., 148 Jenyon, M.K., 849, 860 Huijbregts, C.J., 363, 364, 365,541,891,901 Jesion, G., 541 Huinong, Z., 678 Jie, T., 100 Huitt, J.L., 3, 54 Jodry, R.L., 131,151, 177, 225, 250, 258, 282, Humphrey, J.D., 84, 100 475,481,541,801,860 Hunt, E.R., 227 Johnson, C.E., 480, 541 Hunt, P.K., 136, 151 Johnson, D., 223 Hunter, B.E., 55 Johnson, K.S., 797, 857, 859, 860, 861,863, Hurley, T.J., 28, 54 864,865 Hurst, H.E., 366, 387, 540 Johnson, M.C., 533 Hurst, J.M., 94, 100 Johnston, J.R., 542 Hurst, R.E., 334, 540 Johnston, L.K., 214, 215, 225 Hurst, W., 540, 553, 587, 644, 678, 681 Jones, M.W., 810, 836, 837, 844, 858 Hutchinson, C.A. Jr., 679 Jones, E, 584, 679 Hutfilz, J.M., 678 Jones, S.C., 133, 150, 201,224, 436, 541 Huxley, T.H., 793 Jones, T., 900 Huzarevich, J.V., 532 Jones, T.A., 4, 54 Hyland, G.R., 112,151 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

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,

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

319,320,321,324,541

Jossang, T., 534 Journel, A.G., 363, 364, 365, 541, 891,901

968 Kaveler, H.H., 20, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 54, 533 Kriss, H.S., 41, 56 Kaye, B.H., 273,541 Krohn, C.E., 264, 265,266, 409, 541 Kazi, A., 534 Kruger, J.M., 811,860 Keany, J., 793 Kuchuk, F.J., 542, 644, 645,658, 677, 679 Kearey, P., 60, 100 Kuich, N., 326, 328, 329, 542, 785, 786, 787, Keelan, D.K., 108, 119, 128, 130, 139, 141,151, 788, 794 887, 901 Kumar, A., 541,549, 563, 680, 681 Keith, B.D., 858 Kumar, S., 937 Kellan, D.K., 481,484, 485,541 Kunkel, G.C., 28, 54 Kendall, C.G.St.C., 50, 56, 59, 74, 82, 83, 97, Kupecz, J.A., 81 O, 860 98, 99, 100, 101, 102, 103, 383, 542 Kuranov, I.F., 681 Kennedy, J.E., 53 7 Kyle, J.R., 44, 55, 797, 860 Kennedy, S.K., 900 Kennedy, W.J., 782, 794 Lacaze, J., 858 Kent, D.M., 254, 258, 541, 812, 830, 860 Lacey, J.W., 532 Kent, D.V., 100 Lacik, H.A., 533 Kenworthy, J.D., 532 Ladwein, H.W., 812, 824, 860 Kenyon, W.E., 134, 151,203,225,226 LaFleur, R.G., 862 Lai, F.S.Y., 900 Kerans, C., 47, 54, 545, 810, 812, 830, 831,837, 838, 842, 844, 848, 851,859, 860, 902 Laidlaw, W.G., 874, 901 Kern, C.A., 215, 216, 225 Lair, G.H., 952 Kettle, R.W., 102 Lake, L.W., 56, 150, 358, 363,370, 371,378, Keys, D.A., 102 534, 538, 539, 541,542, 867, 884, 888, 901,903 Khutorov, A.M., 813,860 Lambeck, K., 99 Kidwell, C.M., 194, 225 Lanaud, R., 858 Kienitz, C., 221 Kimminau, S., 227 Landel, P.A., 678 King, E., 151,226 Lane, B.B., 28, 54 King, P.R., 368, 388, 392, 401,402, 403,404, Langdon, G.S., 75, 81,101 405,423,541,901 Langford, B.J., 952 Langnes, G.L., 17, 23, 54, 542, 544, 937 King, R.E., 55, 402, 769, 859, 861,863, 865 King, R.L., 898, 901 Langston, E.P., 679, 872, 883, 884, 885, 894, 901 Kinney, E.E., 532 Lanz, R.C., 85 7 Kirman, P.A., 679 LaPoint, P.R., 10, 54 Kittridge, M.G., 161,195,225,436, 438,439, 541 Lapre, J.F., 795, 885, 901 Larsen, E., 433,535 Klappa, C.F., 858 Larsen, G., 536, 909, 951 Klikoff, W.A., 538 Larsen, L., 330, 542 Klinkenberg, B., 263,541 Klitgord, K.D., 100 Larsen, W.K., 53 7 Klute, C.H., 257, 541 Larson, R.G., 534 Larson, V.C., 532 Kniazeff, V.J., 678 Lasseter, E., 229 Knox, S.C., 810, 831,859 Lasseter, T.J., 893, 901 Kochina, I.N., 769 Latham, J.W., 810, 831,860 Koederitz, L.E, 540 Latimer, J.R.Jr., 532 Koen, A.D., 325,541 Laughlin, B.A., 302, 310, 542, 547 Koerschner III, W.F., 83, 100 LaVigne, J., 227 Kolata, D.R., 857 Kopaska-Merkel, D.C., 542 Lawrence, D.T., 59, 82, 83, 98, 101 Le Lan, P., 227 Koplik, J., 546 LeBlanc, D.P., 158, 225 Kordos, L., 807, 856 Korvin, G., 366, 388, 541 Lee, J.E., 488, 489, 490, 492, 494, 496, 542 Kozic, H.G., 346, 347, 348, 349, 350, 351,541 Lee, J.I., 42, 54 Krajewski, S.A., 102 Lee, R.L., 595,679 Kretzschmar, J.L., 158, 215,225 Lee, W.J., 563,679 Krief, M., 172, 180, 225 Leeder, M.R., 83, 99

969 MacAllister, D.J., 458, 459, 461,542 Lefebvre du Prey, E.J., 875,901 MacDonald, I.F., 900 900 Legere, R.E, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA MacDonell, P.E., 900 Leibrock, R.M., 532 MacEachem, J.A., 860 Leighton, M.W., 857 Maclnnis, J., 226 Lemaitre, R., 542 Macintyre, I.G., 100 Lents, M.R., 36, 55 Mackenzie, F.T., 784, 794 Lerche, I., 9, 10, 11, 12, 13, 14, 15, 16, 55, 83, Macovski, A., 457, 542 99, 100, 101 Macrygeorgas, C.A., 680 Leroy, G., 710, 769 Maerefat, N.L., 151 Lesage, M., 221 Magara, K., 8, 54 Letton, W.III, 226 Maggio, C., 85 7 Leverett, M.C., 19, 20, 29, 52, 54, 131, 151, Magnuson, W.L., 538, 901 177,226 Maher, C.E., 51, 85 7 Levorsen, A.I., 236, 542, 806, 860 Mahmood, S.M., 133,151,468, 545 Levy, M., 535 Main, R., 536, 956 Lewis, W.B., 19, 20, 54 Maksimovich, G.A, 812, 861 Li, M., 810, 860 Malecek, S.J., 75, 81,101 Li, Y., 873,901 Maliva, R.G., 783, 794 Lichtenberger, G.J., 327, 328, 329, 330, 331,542 Malone, W.T., 545 Lieberkind, K., 794 Mamedov, Y.G., 51 Lindsay, J.E, 102 Mancini, E.A., 326, 359, 542 Lindsay, R.F., 383, 537, 542 Mandelbrot, B.B., 263,264, 270, 365, 366, 372, Lishman, J.R., 887, 901 407, 410, 422, 542, 543 Little, T.M., 226 Mann, J., 900 Littlefield, M., 2, 54, 533 Mann, M.M., 151,228 Liu, H., 864 Mann, S.D., 542 Liu, O., 223 Manning, M., 227 Lloyd, P., 223 Mannon, R.W., 52, 53, 289, 542, 543, 544, 546, Lloyd, R.M., 102 9O0 Locke, C.D., 56 Manual, T., 151 Locke, S., 224 Mapstone, N.B., 50, 54 Lockridge, J.E, 790, 792, 794 Marafi, H., 812, 830, 840, 861 Logan, R.W., 679 Marchant, L.C., 45, 46, 54 Lohman, J.W., 678 Marek, B.F., 150, 223 Lomando, A.J., 793, 859, 863 Maricelli, J.J., 213,224 Lomas, A.T., 225 Markowitz, G., 214, 215,225 Lomiz6, G.M., 4, 5, 6, 54 Marks, T.R., 149, 222 Longman, M.W., 291,542, 791,794, 811,840, Marrs, D.G., 532 859, 860, 862, 863 Marsden, S.S., 943,949 Lord, C.S., 501,542 Marshall, J.W., 44, 55 Lord, G.D., 142, 149, 151,206, 222, 226 Martell, B., 640, 679 Lorenz, P.B., 150 Martin, EG., 8, 55 Loucks, R.G., 804, 810, 813,834, 836, 837, Martin, J.C., 378, 543 839, 840, 843,844, 847, 856, 858, 860, Martin, J.E, 227 861 Martin, R., 48, 55, 98, 806, 812, 822, 823,861 Louis, C., 4, 54 Martin, W.E., 44, 5 7 Lovell, J., 223 Martinelli, J.W., 237, 238, 533, 540 Lowenstam, H.A., 811,840, 861 Martinez, A.R., 679 Lowry, D.C., 101 Martinez del Olmo, W., 847, 856, 861 Lucia, EJ., 177, 178, 184, 186, 190, 202,226, Martinez, R.N., 679 535, 541,545, 868,900, 901, 902 Maslov, V.E, 861 Luque, R.E, 546 Mass6, L., 534, 769 Lyle, D., 326, 542 Mast, R.F., 535 Lynch, M., 810, 861 Masters, C.D., 546 Lytle, R.J., 158, 215,223 Masuda, E, 101

970 Mesolella, K.J., 801, 811, 819, 840, 862 Mathews, M.A., 152, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 229 Metghalchi, M., 536 Mattar, L., 681 Meunier, D., 223,644, 645, 679 Mattavelli, L., 25, 26, 55 Meyer, L.J., 681 Mattax, C.C., 44, 55 Mezzatesta, A., 166, 226, 227 Matthews, C.S., 39, 53, 55, 203, 210, 226, 549, Miall, A.D., 865 584, 654, 679 Middleton, M.F., 88, 101 Matthews, R.K., 84, 101 Miller, A.E., 458,459, 461,543 Maute, R.E., 190, 226 Miller, B.D., 356,536 May, J.A., 89, 101 Miller, C.C., 679 Mayer, C., 166, 224, 226 Miller, D.N.Jr., 532 Mazzocchi, E.F., 44, 55 Miller, EG., 536, 677, 679, 680 Mazzullo, L.J., 811,830, 861 Miller, F.H.,532 Mazzullo, S.J., 1, 34, 47, 52, 54, 231,254, 256, Miller, G.K., 226 268, 280, 417, 468, 536, 537, 539, 541, Miller, J.A., 863 543, 545, 677, 681, 800, 802, 803, 804, Miller, K.C., 97, 100, 542 810, 811,812, 818, 825, 830, 834, 861, Miller, M.G., 36, 55, 223 862, 863, 882, 901 Miller, R.D., 102 McCaleb, J.A., 32, 45, 56, 359, 360, 361,362, Miller, R.T., 496, 543 533, 811,814, 830, 862 Miller, T.E., 856 McCammon, R., 900 Miller, W.C., 228 McCauley, J.L., 273, 391,392, 393,394, 395, Millheim, K.K., 41, 55, 679 396, 397, 398, 399, 400, 407, 409, 413, Mimran, Y., 783, 794 539, 543, 544 Mink, R.M., 542 McCleb, J.A., 546 Misellati, A., 52 McCord, J.R., 677 Miska, S.Z., 594, 680 McCormack, R.K., 102 Mitchell, ER., 227 McCormick, L.M., 862 Mitchum, R.M., Jr., 50, 55, 56, 103, 803, 862, McCormick, R.L., 533 864 McCoy, T.F., 304, 305, 306, 538, 543 Mitkus, A.E, 149, 222 McDonald, S.W., 662,665, 679 Miyata, Y., 102 McGee, P.R., 679 Mohanty, K.K., 458, 459, 461,543 McGhee, E., 584, 679 Mohanty, S., 405,543 McGill, C., 892,901 Monicard, R.P., 108, 136, 151 McGuire, W.J., 335,342, 543 Montiel, H.D., 680 Mclntosh, I., 615, 679 Moody, J.D., 797, 832, 862 Mclntosh, J.R., 678 Mooney, L.W., 862 Mclntyre, A., 49, 55 Moore, A.D., 389, 543 McKellar, M., 903 Moore, C.H., 858, 860, 861,867, 894, 902 McKeon, D., 53, 150 Moore, C.V., 197, 199, 200, 224 McKinley, R.M., 28, 55, 611,635,661,677, Moore, D., 546 679, 681 Moore, G.E, 93, 99 McKoen, D., 224, 225 Moore, P., 99, 100, 102 McLemore, J., 150 Moore, P.J.R.McD., 902 McLimans, R.K., 864 Moore, W.D., 22, 55, 534 McMahon, B.E., 533 Moran, J.H., 213, 226 McNamara, L.B., 868, 886, 887, 893,894, 902 Morgan, L., 94, 101 McQueen, H., 99 Morineau, Y., 436, 543 McQuillin, R., 60, 67, 78, 101 Moring, J.D., 532 Mear, C.E., 810, 811,830, 862 Morris, C.F., 182, 195,207, 214, 226 Medlock, P.L., 865 Morris, E.E., 258, 543 Meinzer, O.E., 638, 679 Morris, R.L., 205,208, 226 Meissner, F.F., 794 Morris, S.A., 152, 228 Meister, J.J., 543 Morrow, N.R., 136, 151,200, 222, 875,879, Meneveau, C., 426, 543 900, 901,902 Menzie, D.E., 45, 46, 54, 902 Morse, J.W., 784, 794 Mesa, O.J., 372, 435, 543

971

Morse, R.A., 52, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 56, 335,342, 543, 545 Norton, L.J., 5 7, 229 Mortada, M., 257, 544 Nuckols, E.B., 231,298, 544 Mosley, M.A., 863 Nute, A.J., 900 Mruk, D.H., 857 Nydegger, G.L., 790, 791, 792, 794 Mudd, G.C., 100 Nygaard, E., 782, 794 Muegge, E.L., 150, 223 Mueller, O.M., 150, 224 Obradovich, J., 100 Mueller, T.D., 585, 679 O'Brien, M., 53, 225 Muggeridge, A.H., 541 Odeh, A.S., 679 Muller, G., 769 Ogbe, D.O., 632, 678 Muller, J., 372, 407, 409, 412, 415,425,433, Ogg, J.G., 100 Oliver, F.L., 532 539, 544 Muller, P., 799, 862 Oltz, D.E, 857 Mullins, J.E., 209, 226 Onur, M., 658, 680 Ormiston, A.R., 862 Mundry, M., 51, 900 Mungan, N., 875, 902 Oros, M.O., 535 Muravyov, I., 947, 948, 949 Orr, EM., 546, 902 Murray, G.H., 713,716, 769 Orsi, T.H., 457, 544 Murray, R.C., 868, 901 Ortiz de Maria, M.J., 538 Muskat, M., 117, 151,201,226, 245,302,311, Osborne, A.E, 538, 901 544 Osborne, W.E., 810, 831,863 Musmarra, J.A., 544 Oshry, H.L., 229 Mussman, W.J., 798, 862 Ostrowsky, N., 539, 542 Myers, M.T., 147, 191, 192, 226 Overbey, W.K., Jr., 8, 55 Owen, L.B., 139, 140, 151, 178, 226 Nabor, G.W., 257, 544, 679 Owens, W.W., 902 Nadon, G.C, 810, 862 Nagel, R.G., 55 Pabst, W, 900 Nagy, R.M., 864 Pach, E, 812, 856 Najurieta, H.L., 634, 636, 679 Paillet, EL., 208, 226 Nakayama, K., 100, 1O1 Palacas, J.G., 794 Narayanan, K.R., 150, 539 Palisade Corporation, 217, 226 Narr, W., 9, 10, 11, 12, 13, 14, 15, 16, 55 Palmer, A.N., 797, 798, 799, 800, 856, 862 Natanson, S.G., 503,504, 534, 538, 751,753, Palmer, M.V., 798, 800, 856, 862 769 Paola, C., zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPO 84, 101 Nath, A.K., 222 Papatzacos, P., 672, 680 Naylor, B., 537 Pape, W.C., 55 Needham, R.B., 538, 543 Pariana, G.J., 56 Neidell, N.S.,lO1 Park, W.C., 696, 769 Nelson, D.E., 901 Parker, H.M., 893,902 Nelson, H.W., 858 Parra, J., 677 Nelson, R.A., 784, 794 Parsley, A.J., 415, 544 Neslage, F.J., 532 Parsley, M.J., 812, 831,860 Nettle, R.L., 537 Parsons, R.L., 34, 53, 290, 436, 537, 888, 900 Neuse, S.H., 540 Parsons, R.W., 3, 55, 260, 501,544 Partain, B., 8, 55 Newell, K.D., 810, 831,862 Pascal, H., 644, 680 Nichol, L.R., 38, 53, 472,473,538 Nicoletis, S., 227 Pasini, J., III, 8, 55 Niko, H., 150, 352, 353,354, 546 Pasternack, I., 802, 862 Nisle, R.G., 585,679 Patel, R.S., 45, 55 Niven, R.G., 542 Pathak, P., 457, 544 Nodine-Zeller, D.E., 858 Paul, A., 223 Nolan, J.B., 46, 55 Pautz, J.E, 312, 315, 535 Nolen-Hoeksema, R.C., 42, 55 Payne, D.A., 51,900 Nooteboom, J.J., 226 Payton, C.E., 52, 55, 56, 102, 103, 849, 862, 864 Nordquist, J.W., 533 Pearce, L.A., 223

972 Price, H.S., 363, 368, 546, 810, 864, 894, 903 Peam, W.C., 538 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Price, J.G.W., 200, 226 Peeters, M., 166, 226 Price, R.C., 861 Peggs, J.K., 55 Price, W.G., 541 Peitgen, H-O., 546 Procaccia, I., 410, 423, 539 Pelet, R., 85 7 Prothero, D.R., 100 Pellisier, J., 223 Pruit, J.D., 794 Pendexter, C., 802, 856, 885, 900 Pucci, J.C., 331, 544 Penn, J.T., 152, 228 Pugh, V.J., 146, 152, 481,484, 485, 541 Ptrez, A.A.M., 681 Pullen, J.R., 800, 863 Perez, G., 544 Purcell, W.R., 131,151, 201,226 Ptrez Rosales, C., 39, 40, 55, 538, 634, 679, 680 Pyle, T.E., 856 Perkins, A., 532 Perlmutter, M., 99 Qi, F., 48, 55, 810, 832, 837, 840, 845,846, 862 Permian Basin Chapter of the AIME, 226 Quanheng, Z., 48, 53, 806, 810, 825, 832, 837, Perry, R.D., 297, 298, 544 838, 845, 859, 863 Peters, D.C., 102 Querol, R., 859 Peters, E.J., 874, 902 Quinn, T.M., 84, 100, 101 Peterson, R.B., 532, 793 Quirein, J., 166, 227 Petrash, I.N., 56 Petricola, M.J.C., 53, 225 Rabe, B.D., 99 Pettitt, B.E., 28, 53 Raeser, D.E, 787, 794 Petzet, G.A., 325,544 Rafavich, F., 67, 68, 101 Phillips, C., 150, 224 Raffaldi, EJ., 152, 229, 546 Phillips, M., 534 Raghavan, R., 612, 638, 650, 672, 680, 681 Pickell, J.J., 481,544, 952 Rhheim, A., 794 Pickering, K.T., 100 Raiga-Clemenceau, J., 172, 180, 227 Pickett, G.R., 163, 164, 169, 180, 197, 208, 219, Rainbow, H., 53 226 Raleigh, C.B., 535 Pierce, A.E., 677 Ramakrishnan, T.S., 221 Pinter, N., 84, 101 Rainbow, EH.K., 209, 227 Pirard, Y.M., 222, 676 Ramey, H.J. Jr., 549, 553,563,565, 580, 585, Pirson, S.J., 29, 55, 486, 544, 956 590, 595, 596, 597, 606, 611,632, 636, Pittman, D.J., 223 656, 658, 659, 676, 677, 678, 680, 681 Plasek, R.E., 227, 229 Ramey, H.J., Jr., 51,536 Playford, P.E., 91, 94, 101 Randrianavony, M., 223 Plumb, R., 223 Rao, R.P., 840, 863 Plummer, L.N., 856 Raoofi, J., 534 Pocovi, A.S., 331,544 Rapoport, L.A., 677 Poggiagliolmi, E., 864 Rappold, K., 332, 333,534 Poley, J.P., 192, 226 Rasmus, J., 221 Pollard, P., 741,769 Rau, R.N., 192, 222, 227, 229 Pollastro, R.M., 790, 794 Ray, R.M., 279, 544 Pollock, C.B., 533 Raymer, L.L., 128, 150, 168, 172, 179, 180, 193, Polozkov, V., 949 224, 227 PoroTechnologies, 147 Raymond, D.E., 810, 831,863 Porter, J.W., 801,858 Read, D.L., 863 Posamentier, H.W., 56 Read, J.E, 83, 84, 99, 100, 101, 102, 798, 862 Poston, S.W., 57, 326, 327, 329, 330, 544, 546 Read, P.A., 150 Poulson, T.D., 534 Reeckmann, A., 254, 544 Poveda, G., 372, 435,543 Reed, C.L., 51,797, 856, 857, 858, 859, 860, Powers, R.W., 533 861,862, 864, 865 Pozzo, A., 544 Reese, D.E., 543 Prade, H., 363, 53 7 Reeside, J.B., 792, 793 r Prats, M., 680 Rehbinder, N., 224 Pray, L.C., 254, 268, 536, 802, 805, 834, 845, Reid, A.M., 810, 812, 818, 825,862, 863 857

973 Rothwell, W.P., 203,228 Reid, S.A.T., 812, 825,863 Rough, R.L., 8, 55 Reijers, T.J.A., 545 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Roulet, C., 221 Reinson, G.E., 801,864 Rowly, D.S., 141,151 Reiss, L.H., 702, 769, 880, 881,902 Ruessink, B.H., 141,151, 167, 227 Reitzel, G.A., 42, 54, 256, 544 Ruhland, R., 701,702, 703,712, 769 Reservoirs, Inc., 147, 148, 151, 164, 165, 184, Ruppel, S.C., 103, 540, 811,859 190, 202, 227 Russ, J.C., 370, 544 Reynolds, A.C., 658, 680, 681 Russell, D.G., 39, 55, 203, 210, 226, 549, 584, Reytor, R.S., 260, 261,262, 488, 489, 541,954 679, 680 Rice, D.D., 791, 794 Rust, D.H., 169, 223 Richardson, J.E., 162, 194, 227, 228 Ruzyla, K., 264, 545 Richardson, J.G., 44, 53, 260, 501,502, 539, 542, 885, 894, 902 Sabet, M.A., 549, 580, 645, 680 Rickards, L.M., 50, 55 Sabins, ES., 8, 56 Ricoy, U., 679 Sadiq, S., 473,545 Rieke, H.H. III, 1, 8, 38, 52, 53, 54, 231,233, Safinya, K.A., 207, 214, 227 240, 242, 258, 297, 298, 334, 466, 534, Sahuquet, B.C., 46, 56 536, 537, 539, 541,542, 543, 544, 545, Salathiel, R.A., 875,902 546, 677, 681, 861, 900 Saller, A.H., 800, 811,830, 863 Ringen, J.K., 150 Salt, H.J., 435,539 Rittenhouse, G., 48, 55, 806, 863 Samaniego, V.F., 203, 210, 223,282, 317, 536, Rivera, R.J., 677 537, 545, 550, 559, 563,575, 596, 598, Roach, J.W., 212, 227 603,638,639, 656, 677, 679, 680 Robert M. Sneider Exploration, Inc., 147, 148, Sandberg, G.W., 533 151, 164, 165, 184, 190, 202, 227 Sander, N.J., 533 Roberts, J.N., 267, 544 Sanders, J.E., 775, 783, 793 Roberts, T.G., 18, 20, 21, 23, 51 Sanders, L.J., 677 Robertshaw, E.S., 56 Sando, W.J., 798, 863 Robertson, J.O. Jr., 54, 542, 937 Sangree, J.B., 902 Robertson, J.W., 533 Sangster, D.E, 797, 863 Robinson, D.B., 680 Santiago-Acevedo, J., 813,830, 840, 863 Robinson, E.S., 59, 101 Santoro, G., 53, 858 Robinson, J.D., 862 Sanyal, S.K., 152, 229 Robinson, J.E., 363, 466, 544 Saraf, D.N., 456, 545 Rockwood, S.H., 952 Sarem, A.M.S., 285, 286, 538 Rodriguez, A., 679 Sarg, J.E, 50, 56, 82, 99, 101,861 Rodriguez, E., 166, 226, 227 Sass-Gustkiewicz, M., 797, 858 Rodriguez-Iturbe, I., 540 Saucier, A., 389, 401,403,405,415,421,422, Roehl, EO., 542, 793, 802, 803,804, 832, 833, 423,424, 425,427, 428, 430, 431,432, 834, 845, 859, 860, 861,863 545 Roemer, P.B., 150, 152, 224, 229 Saunders, M.R., 151 Roger, W.L., 496, 543 Saupe, D., 546 Rohan, J.A., 150 Savit, C.H., 69, 70, 99 Romero, R.M., 28, 52 Savre, W.C., 227 Rong, G., 860 Sawatsky, L.H., 177, 224 Root, P.J., 258, 546, 681,741, 769 Sawyer, G.H., 54 Rosa, A.J., 659, 680 Scala, C., 223,545 Roscoe, B.A., 227 Scaturo, D.M., 59, 82, 83, 99, 101 Rose, ER., 813, 863 Schafer-Perini, A.L., 594, 680 Rose, W.D., 131,151,177, 205,227,229, 389, Schatz, EL., 532 391,544, 547 Schatzinger, R.A., 540, 782, 783, 793, 794 Rosendahl, B.R., 97, 102 Schechter, D.S., 881,902 Rosman, A., 470, 544 Scheibal, J.R., 199, 227 Ross, C.A., 56 Schepel, K.J., 215, 216, 225 Ross, W.C., 101 Schilthius, R.J., 302, 545 Rossi, D.J., 224

974 Sherman, C.W., 535 Schipper, B.A., zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 150 Sherrad, D.W., 542 Schlager, W., 77, 100, 280, 281,545 Shirer, J.A., 901 Schlanger, S.O., 49, 56, 773, 794 Shirley, K., 330, 545, 810, 863 Schlee, J.S., 102 Shouldice, J.R., 858 Schlottman, B.W., 545 Shouyue, Z., 863 Schlumberger, 158, 213,227 Shraiman, B.I., 539 Schlumberger Educational Services, 169, 172, Sibbit, A., 166, 223,226 175, 180, 181,182, 189, 197, 198, 199, Siemens, W.T., 306, 545 201,205,207, 214, 221,227 Sieverding, J.L., 812, 859, 863 Schlumberger Limited, 207, 214, 227 Sikora, V.J., 335, 342, 543 Schlumberger, M., 227 Simandoux, P., 543 Schmidt, A.W., 222 Simmons, G., 150, 224 Schmidt, M.G., 222, 224 Simmons, J.F., 581,582, 644, 645, 678, 681 Schneider, EN., 545 Simon, R., 470, 544 Schneidermann, N., 793 Simone, L., 78, 102 Schnoefelen, D.J., 302, 534 Singer, J., 227 Scholle, P.A., 49, 50, 56, 81,102, 139, 151, Sinnokrot, A., 536, 954, 956 782, 783, 790, 793, 794, 858, 860, 861 Skinner, D.R., 937 Schott, E.H., 696, 769 Skjeltorp, A.T., 413,414, 539 Schreiber, J.E, 810, 859 Skopec, R.A., 136, 151,205, 206, 213, 228 Schuffert, J.D., 864 Skov, A.M., 8, 28, 44, 53, 486 Schwartz, L., 221 Skovbro, B., 415,545 Schweitzer, J., 54 Slider, H.C., 626, 681 Schweller, W.J., 535 Slingerland, R.L., 84, 102 Schweltzer, J., 225 Slobod, R.L., 457, 545 Scorer, D.T., 680 Slotboom, R.A., 897, 900 Scott, A.J., 811,840, 859 Slov, A.M., 487, 537 Scott, D.L., 97, 102 Smaardyk, J., 226 Scott, H.D., 53, 150, 173,225,227 Smagala, T.M., 790, 791,794 Scott, J.O., 681, 813,864 Smart, P.L., 798, 800, 858, 863, 865 Screenivasan, K.R., 426, 543 Smith, A.E., 51,534 Scriven, L.E., 544 Smith, D.G., 131,151, 183,212, 228, 800, 863 Seeburger, D.A., 222 Smith, G.L., 862 Seeman, B., 53, 223,225 Smits, J-W., 223 Seevers, D.O., 134, 151,203, 228 Smits, R.M.M., 150 Seidel, F.A., 545 Sneider, R.M., 141,146, 147, 152, 902 Sen, P.N., 394, 545 Snelson, S., 101 Sengbush, R.L., 60, 102 Snow, D.T., 769 Senger, R.K., 436, 438, 439, 440, 443,444, 446, Snowdon, D.M., 505, 507, 508, 536 449, 451,452, 454, 456, 545, 891,900, Snyder, R.H., 151, 787, 794 902 Soc. of Professional Well Log Analysts, 110, Serra, J., 370, 545 152, 208, 210, 221,228 Serra, K.V., 640, 681 Soewito, F., 102 Serra, O., 150, 208, 211,212, 213,224, 228 Sorenson, R.P., 545 Sessions, R.E., 245,532, 545 Soudet, H., 53, 858 Shalimov, B.V., 44, 51 Southham, J., 535 Shanmugan, G.S., 103 Spain, D.R., 138, 152, 158, 228 Shannon, M.T., 228 Spang, J., 52, 793 Sharma, B., 540 Spencer, R.J., 83, 99, 102 Sharma, M.M., 405,543 Spicer, P.J., 151 Sharma, P., 60, 102 Spirak, J., 862 Shaw, B.B., 50, 53 Spivak, A., 535 Sheikholeslami, B.A., 329, 545 Spronz, W.D., 536 Shell Development Company, 147 Srivastava, R.M., 893, 902 Shepler, J.C., 302, 536 Stahl, E.J., 28, 51 Sheriff, R.E., 60, 71, 72, 94, 102

975 Taira, A., 101 Stalkup, F.I., 222, 882, 902 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Taisheng, G., 860 Standing, M.B., 235,545, 588, 589, 593,681 Takamura, K., 900 Stanislav, J.F., 549, 580, 656, 681 Takao, I., 84, 102 Stanley, H.E., 539, 542 Talukdar, S.N., 813, 840, 863 Stanley, T.L., 533 Tang, Jie, 83, 102 Stapp, W.L., 326, 545, 787, 794 Tanguy, D.R., 228 Staron, P., 224 Tanner, C.S., 160, 228 Steams, D.W., 694, 695, 769 Tappmeyer, D.M., 813, 856 Steel, R., 100 Tariq, S.M., 679 Steeples, D.W., 102 Tarr, C.M., 27, 32, 56 Stegemeier, G.L., 542 Tatashev, K.K., 44, 56 Stehfest, H., 644, 681 Taylor, G.L., 53 Stein, M.H., 44, 56 Taylor, M.R., 151 Steineke, M., 533 Tek, M.R., 679 Stell, J.R., 542 Telford, W.M., 59, 102 Stellingwerff, J., 225 Teodorovich, G.I., 268, 400, 545 Stevenson, D.L., 811, 831,865 Tetzlaff, D.M., 84, 102, 227 Stewart, C.R., 21, 22, 56, 475, 477, 479, 480, Tew, B.H., 542 486, 488, 545 Theis, C.V., 584, 681 Stewart, G., 679 Theys, P., 223 Stiehler, R.D., 532 Thomas, D.C., 146, 152 Stiles, J.H. Jr., 901 Thomas, E.C., 118, 125, 146, 147, 152, 159, Stiles, L.H., 33, 34, 53, 302, 534, 882, 902 177,220,228 Stiles, W.E., 33, 34, 35, 37, 56 Thomas, G.E., 868, 902 Stockden, I., 151 Thomas, G.W., 593,681 Stoessell, R.K., 799, 864 Thomas J.B., 532 Stoller, C., 227 Thomas, O.D., 776, 778, 779, 780, 781, 783, Storer, D., 55 795 Stormont, D.H., 811,864 Thomas, R.D., 150 Stosser, S.M., 296, 539 Thomas, R.L., 539 Stoudt, D.L., 99, 100 Thomasson, M.R., 96, 102 Straley, C., 151,225,226 Thomeer, J.H.M., 106, 131,152, 155, 183, 201, Straus, A.J.D., 5 7, 229 228 Streltsova, T.D., 681 Thompson, A.H., 267, 270, 271,415, 541 Strickland, R., 228 Thompson, B.B., 534 Strickler, W.R., 680 Thompson, S., 55, 103, 864 Strobel, C.J., 681 Thorsfield, W., 101 Strobel, J.S., 83,100, 101,102 Thrailkill, J., 797, 844, 864 Strobl, R., 364, 369, 370, 371,547 Thrasher, R., 538 Strubhar, M., 586, 681 Thrasher, T.S., 538 Stubbs, B.A., 335,338, 339, 340, 341,343,344, Tiab, D., 563,681 535 Tillman, R.W., 541 Suinouchi, H., 102 Timmons, J.P., 226 Sullivan, R.B., 534 Timur, A., 181,205, 228, 390, 466, 545 Sutton, E., 533 Tiner, R.L., 545 Swanson, B.F., 131,152, 201,228, 544, 952 Tinsley, J.M., 335,342, 545 Swanson, R.G., 128, 152, 167, 178, 228 Tittman, J., 158, 179, 228 Sweeney, S.A., 188, 228, 480, 541 Tixier, M.P., 197, 208, 228 Sylvester, R.E., 98 Todd, T.P., 101 Syrstad, S.O., 151 Tomanic, J.P., 546 Syvitski, J.P.M., 102 Tomutsa, L., 462, 468, 540, 545 Szpakiewicz, M.J., 540 Torabzadeh, J., 536 Torres, D., 207, 214, 228 Taggart, I.J., 539 Torrey, P.D., 244, 246, 249, 296, 545, 546 Taijun, Z., 860 Tortike, W.S., 535 Taikington, G.E., 532

976 Vander Stoep, G.W., 535 Touchard, G., zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 546 Vargo, G.A., 100 Tracy, G.W., 258, 543 Vasilechko, V.E, 45, 56 Tran, T.T.B., 534, 899 Vela, S., 55, 297, 534, 635, 679, 681 Traugott, M.O., 186, 190, 209, 228 Velde, B., 433,546 Travis, B.J., 535 Vennard, J.K., 940, 941,949 Treiber, L.E., 902 Ventre, J., 225 Tremblay, A.-M.S., 423, 546 Vernon, ED., 799, 864 Tremblay, R.R., 546 Verseput, T.S., 864 Trocan, V.N., 45, 56 Vest, E.L., 82 l, 825, 831,840, 864 Troschinetz, J., 811,830, 832, 864 Vest, H.A., 860 Trouiller, J-C., 223 Videtich, EE., 813,864 Trube, A.S.Jr., 532 Vienot, M.E., 649, 678 Truby, L.G., Jr., 22, 55 Villegas, M., 227 Truitt, N.E., 680 Vinegar, H.J., 134, 135, 136, 137, 150, 152, 168, Tsang, P.B., 882, 883,900 178, 179, 184, 200, 203,224, 226, 228, Tsarevich, K.A., 681 229, 456, 457,458, 462, 466, 546 Tschopp, R.H., 813, 864 Viniegra, O.E, 813, 820, 830, 832, 847, 864 Tumer, K., 190, 228 Visser, R., 166, 226 Turcotte, D.L., 83, 98, 102, 103,264, 273, 401, Viturat, D., 677 407, 546 Vizy, B., 797, 857 Tutunjian, P.N., 134, 135, 150, 152, 184, 197, Voelker, J.J., 538 200, 224, 226, 228, 229, 546 Von Gonten, W.D., 335, 342, 543 Twombley, B.N., 100, 813,864 von Rosenberg, D.U., 538 Tyler, N., 276, 277, 280, 538, 546 Vorabutr, P., 937 Tyskin, R.A., 807, 832, 864 Voss, R.F., 365,366, 367, 546 Vrbik, J., 681 Uliana, M.A., 803,862 Vysotskiy, I.V., 807, 864 Ulmishek, G., 234, 546 Underschultz, J.R., 888, 900 Waddell, R.T., 810, 864 Waggoner, J.M., 901 Vadgana, U.N., 681 Waggoner, J.R., 901 Vague, J.R., 532 Wagner, O.R., 52 Vail, ER., 50, 55, 56, 82, 100, 103, 800, 802, Walker, J.W., 54 805,864 Walker, K.R., 103 Van Akkeren, T.J., 28, 52, 209, 223 Walker, R.D., 56 Van de Graaf, W.J.E., 893,902 Walker, T., 208, 221 Van den Bark, E., 776, 778, 779, 780, 781,783, Wall, C.G., 106, 108, 149 795 Waller, H.N., 677 Van Den Berg, J., 535 Wallis, J.R., 366, 372, 543 van der Hijden, J., 223 Walper, J.L., 53 van der Poel, C., 900 Walter, L.M., 99, 101 Van Der Vlis, A.C., 320, 321,546 Walters, R.E, 810, 815, 825, 831,864 Van Driel, J.J., 856 Waltham, D., 83, 99 Van Everdingen, A.E, 41, 51, 56, 534, 553,587, Wang, J.S.Y., 56 644, 681 Wang, S.Y., 136, 137, 152 Van Golf-Racht, T.D., 580, 581,677, 681, 710, Ward, R.F., 33, 56, 79, 103 769 Ward, W.C., 864 Van Horn, D., 863 Wardlaw, N.C., 801,864, 868, 872, 873,874, Van Kruyskijk, C.EJ.W., 352, 353, 354, 546 876, 877, 878, 880, 886, 887, 893,894, van Meurs, E, 900 901,902, 903 Van Ness, J.W., 365, 366, 543 Warembourg, P.A., 534 van Poollen, H.K., 64 l, 644, 678 Warme, J.E., 793 Van Schijndel-Goester, F.S., 795 Warren, J.E., 258, 363, 368, 546, 681,741, 769, van Straaten, J.U., 536 894, 903 Van Wagoner, J.C., 56 Washburn, E.W., 184, 229 Vandenberghe, N., 849, 85 l, 852, 855,864

977

Wasson, J.A., 56, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 533, 681 834, 835, 841,842, 858 Waters, K.H., 59, 103 Williams, R., 221 Watfa, M., 223 Willingham, R.W., 32, 45, 56, 533 Watkins, J.W., 51 Willis, D.G., 39, 54 Watney, W.L, 83, 99, 862 Willmon, G.J., 44, 56, 533 Watson, H.J., 830, 832, 837, 840, 865 Willmon, J.H., 615,679 Watson, H.K.S., 864 Wilshart, J.W., 256, 259, 496, 497, 541,867, 901 Wattenbarger, R., 294, 295,546, 595, 681 Wilson, D.C., 678 Watts, D.E., 101 Wilson, J.L., 99, 101, 807, 810, 812, 837, 865 Watts, G., 864 Winham, H.E, 533 Watts, N.L., 782, 784, 795 Winkler, K., 223 Watts, R.J., 44, 56 Winterer, E.L., 793 Wayhan, D.A., 360, 361,362, 533, 546, 811, Wishart, J.W., 255, 256 814, 830, 862 Witherspoon, P.A., 4, 56, 585, 679 Weber, K.J., 1, 8, 25, 56, 436, 537, 541,546, Withjack, E.M., 136, 137, 152, 457, 458, 546 883, 884, 885, 892, 903 Withrow, P.C., 814, 831,865 Weeks, W.C., 536 Witterholt, E.J., 158, 215,225 Wegner, R.E., 378, 543 Wittick, T.R., 222 Weidie, A.E., 856 Wittmann, M.J., 679 Weiland, J.L., 227 Wolf, K.H., 25, 56, 536 Welex, 207, 214, 229 Wong, P-Z., 390, 394, 395,397, 398, 546 Wellington, S.L., 135, 136, 152, 168, 178, 184, Wood, G.V., 860 229, 456, 457, 458, 462,546 Wood, L., 70, 103 Wells, L.E., 128, 152, 168, 179, 193,222,229 Woodland, A.W., 52 Welton, J.E., 140, 152 Woodward, J., 794 Wendel, F., 227 Woolverton, D.G., 60, 99, 856, 857, 862 Wendte, J.C., 101 Wooten, S.O., 54 Wesson, T.C., 57, 539, 899, 901,902 Works, A.M., 538 West, L.W., 883,903 World Oil Coring Series, 108, 110, 111, 112, West Texas Geological Society, 532 113, 116, 123, 124, 152, 158, 182, 183, Westaway, E, 195,229 229 Westermann, G.E.G., 100 Worrell, J.M., 199, 227 Wharton, R.E, 192, 229 Wortel, R., 84, 99 Whately, M.K.G., 100 Worthington, M.H., 158, 215,229 Wheeler, D.M., 857 Worthington, P.F., 1, 2, 5 7, 294, 295,546 Whitaker, F.F., 798, 800, 863 Wraight, P.D., 53, 221,225 White, D.A., 233,546 Wright, M.S., 52 White, F.W., 545 Wright, V.P., 280, 546, 797, 799, 845, 847, 858, White, R.J., 533 863, 865 Whiting, L.L., 811, 831,865 Wu, C.H., 42, 43, 57, 302, 310, 542, 546, 547 Whittaker, A., 108, 109, 120, 122, 123, 126, 127, Wunderlich, R.W., 137, 145, 146, 152 152 Wurl, T.M., 376, 378, 537 Whittle, G.L., 59 Wyatt, Jr., D.F., 195,225,229 Whittle, T.M., 222, 676 Wyllie, M.R.J., 172, 180, 205,229, 391,547 Widess, M.B., 103 Wyman, R.E., 138, 153, 227 Wigley, EL., 48, 56, 799, 800, 845, 857, 865 Wilde, G., 862 Xie-Pei, W., 48, 55, 810, 832, 837, 840, 845, Wilgus, C.K., 56, 101 846, 862 Wilkinson, D., 221 Xueping, Z., 860 Willemann, R.J., 83, 103 Willemsen, J.F., 151,225 Yamaura, T., zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQ zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHG 102 Williams, J.R.Jr., 545 Yang, C-T., 542 Williams, J.W., 901 Yang, D., 903 Williams, K.W., 223 Yapaudijan, L., 858 Williams, M.R., 228 Yen, T.E, 877, 900 Williams, P.W., 797,798, 799, 800, 801,806, Yortsos, u 432, 433,534, 535

978 Zemanek, J., 28, 5 7, 207, 214, 229 Youmans, A.H., 192, 193,229 Zheltov, Y.P., 769 Young, G.R., 436, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 547 Zhenrong, D., 860 Young, J.W., 541 Zhigan, Z., 807, 865 Young, M.N., 44, 5 7 Zhou, D., 902 Youngblood, W.E., 199, 200, 229 Ziegler, P.A., 782, 795 Yuan, H.H., 132, 139, 153 Zimmerman, L.J., 28, 5 7 Yuan, L-P., 364, 369, 370, 371,547 Zogg, W.D., 811, 831,863 Yuster, S.T., 38, 57, 296, 547 Zotl, J., 797, 865 Zwanziger, J.E., 326, 547 Zana, E.T., 593,681

979 zyxwvutsrqp

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 , bottom water, 490, 496, 510, 511, 514, Damme field (Kansas), 522, 528 515 Davis field (Kansas), 521 DST data, analysis of, 105, 158, 165 Davis Ranch field (Kansas), 525 Dubai (UAE), 80 Dawson field (Nebraska), 525 Dune field (Texas), 32, 33, 278, 299, 307-309, Dean-Stark extraction, apparatus, 126, 127, 134, 338, 339, 342, 344, 443,449, 452 137 Dupo field (Illinois), 525 Dean-Wolfcamp pay (Texas), 258 Dwyer field (Montana), 530 Debris flow deposits, 87, 89 Dykstra-Parsons coefficient, 290--292 Decline curve analysis, 42,293,326 D-I, D-2, D-3 zones (Devonian, Canada), 240, Deer Creek field (Montana), 525 242, 252 Deerhead field (Kansas), 530 Delaware Basin (USA), 310,338 Eagle Ford Formation, 326 Delphia field (Montana), 523 Eagle Springs field (Nevada), 526 Density logs, 16, 17, 27, 47 East Texas field (Texas), 248 -, spectral, 16, 27 ECLIPSE (reservoir simulation program), 449 Denver Basin (USA), 776-778 Edda field (North Sea), 781 Depletion, rate, 490, 492,496, 498 Edinburg West field (Illinois), 811, 831 Depositional sequences, 82 Edwards Group, 468 Devil's Basin field (Montana), 521 Egypt, 468 Devonian, 21, 44, 45, 74, 78, 79, 94, 239, 240, Ekofisk Formation, field (North Sea), 49, 50, 415, 490, 497,498, 501,505,506, 508, 801,805, 778, 779, 781 814, 827, 867, 869, 882, 896 E1Abra Limestone, 820 Diamond-M field (Texas), 821 Eldfisk field (North Sea), 415, 781,783 Diamond-M/Jack field (Texas), 43 Electrical array imaging logs, 56, 63, 64, 65 Diamond-M/McLaughlin field (Texas), 43 Electrical conductivity, 164, 186 Dielectric logs, 41 Electrofacies, 211 Differential entrapment, 236, 239, 240 Electromagnetic tomography, 158, 215 Digital production, 1 Elk Basin field (Wyoming), 359, 362, 52 l, 525, Diplogs/dipmeters, 56, 62, 65 811,830 Dispersivity (permeability), 367 Elkhorn field (Texas), 24 Dollarhide East field (Texas), 525 Ellenburger Dolomite, fields (Texas, New Mexico), Dollarhide field (Texas), 799, 800, 811,830 22-24, 56, 59,208, 210, 818, 827-830,838, Dolomites, radioactive, 18 848 Dorado field (Spain), 830 Embar field (Texas), 24 Dorcheat field (Arkansas), 522 Emma field (Texas), 848 Dorward field (Texas), 303,304 Enlow field (Kansas), 529 Eocene, 468, 469 Douthit unit, 305 Drawdown, analysis, 8, 583, 584 Epeiric seas, basins, 76, 95 -, curve matching, 649 Error propagation, in formation evaluation, 67 Drill stem tests, 4, 45 Ervay Member (Phosphoria Formation), 355 Drilling well, formation evaluation, 5 Etosha Basin, 94 Drive mechanisms (reservoir), 243-254, 276 Eubank field (Kansas), 519, 527 , combination drives, 250-253,528 Europe, 49, 775,776, 787, 792, 793, 853 , external gas drive, 475 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Eustasy, eustatic curves, 82-85, 73, 76, 77 gas-cap expansion, 243,246, 485, 502,510, Evaporites, 72, 74, 77, 79, 80, 276, 505, 786, 512, 513, 527, 867, 869 800, 885 - - , gravity drainage, drive, 243,249, 254, 489, Evaporitic drawdown, 800 494,497,498,500,502, 510, 511, 515,867, Excelsior D-2 (reef) pool, field (Canada), 250, 869, 885, 898 496, 497 solution-gas, 17, 20, 27,243,244, 340, 361, Expert systems, 167 383,470,475,477,478,485,488,502,510-, for formation evaluation, 13 516, 518, 867, 869 Extension drilling, 298 , undersaturated oil expansion, 502 , water drive, encroachment, 243, 247, 311, Fahud field (Middle East), 48,, 813,825 340, 489, 522, 867, 869 Fairplay field (Kansas), 526 ,

,

983 , flow units versus depositional facies, 439 Fairview field, 810 , fracture-fluid flow, 5 Fairway field (Black Warrior Basin), 278,520 , index, 15, 16 Fallon field (Texas), 346, 348, 351 , laminar, turbulent, 5, 6 Falls City field (Nebraska), 526 , models, 446 Fanglomerates, 97 , multiphase, 378 Fanska field (Kansas), 530 , paths, 459 Fateh field (Dubai, Middle East), 48, 80, 813,825, , radial, 330 830 , simulations, 440 Faults, 25 - - , single-phase, 4 -, sealing, non-sealing, 25 steady-state, 9 Feeley field (Kansas), 528 , storage-dominated, 565 F enn-B ig Valley field (Canada), 461-465 , units, 454 Fertile Prairie field (Montana), 530 , velocity, 4 Field A (Mediterranean Basin), 22, 813 Fluid injection, 27 Field development, 105, 231 Fluid saturation, 1, 106, 122, 182 Findlay Arch (USA), 810, 827 , irreducible, 1,124 Fingering, 459 Flushed zones, 188, 190 Fishook field (Illinois), 527 Formation evaluation, 1,155, 156, 232 Flanagan field (Texas), 43 , drilling wells, 5, 159 Floods, flooding , for flood process pilots, 7 -, alkaline, 275 , openhole wells, 159 -, brine pre-flood, 160 , production surveillance, 7 -, chemical, 42, 137, 162 , propagation of error considerations, 67 -, core, 137 - - , properties of interest, 2 -, CO 2, 44, 113, 137, 157, 160, 161,275,379 - - , situations, 5 -, cyclic, 44, 45 , tools, 4, 157 -, fire, 137, 275 Formation stimulation, 334, 335 -, immiscible gas, 896 Formation volume factor, 8, 17, 36, 116, 284, -, miscible, 42, 44, 45, 137,275,894, 896 289, 311,514 -, pilot, process pilot, 35, 159 Formation water, 195 - - , formation evaluation, 7 , salinity, 134 -, polymer, 162, 275,296, 298-300 Fort Jessup field (Louisiana), 325 -, solvent, 896-898 Foster field (Texas), 30, 36, 37, 519 -, steam, 46, 275 Fourier transform infrared spectroscopy (FTIR), -, tertiary, 195 14, 167 -, vertical, 896, 898 FRACOP model, 349--351 -, water, 23, 25, 27-29, 33, 34, 41, 42, 44, 45, Fractals, 364, 371,421 112, 113,137, 157,284, 287,290,293,296, -, analysis, 412 302,307-310, 332,356,357,378,380,384, -, dimensions and permeability, 415, 422, 426, 387, 436, 440, 444, 480, 496, 497, 869-430 871,874, 877, 878, 881 -, models, 399, 406 , displacement efficiency, 871,894 -, performance models, 371 - - , hot water, 137 -, relationships, 409 , performance, 883 -, reservoirs, 432 , versus vugs, 508, 874, 948 FRACTAM, 388,389 Florida, 301,468, 481,482, 484 Fractional water saturation, 36 Fluid displacement, 867 Fractures, fractured reservoirs, 2-6, 11, 14, 15, Fluid flow, 1,306, 232 23, 38, 39, 41, 44-46,50, 59, 81, 116, 141, , barriers, 25, 233, 257, 306, 363, 451,882, 142, 144, 208, 210, 250, 257,258,260, 264, 884, 887, 896, 898 296, 311, 313, 318, 319,326, 332,334, 342, , behavior, 258 390,457,487, 501,503,508, 615,796, 883, , capacity, 39, 40 887-, artifical versus natural fractures, 683 , channels, 46 , pressure gradient, 685 , compartmentalization, 456 , versus depth, 685 , diagnosis, 563,580 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA -, detection, 54 -, dynamics, 1,276 ,

-

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, -, resistivity, 27, 107, 168, 204 490-493,496, 501 -, shear versus compression travel time plots, 169 Leduc-Woodbend field (Canada), 238, 529 -, spectral density, 169 Lekhwair Formation, 95, 96 -, spontaneous potential (SP), 168, 204 Leonardian, 296,300 -, thermal neutron, 169, 180 Lerado field (Kansas), 526 , epithermal neutron, 169, 180 Lerado SW field (Kansas), 522 Loma de la Lata field (Argentina), 331,332 Levelland field (Texas), 338,342 Loring field (Mississippi), 527 Levelland Northeast field (Texas), 527 Louisiana, 20, 21,146, 208, 325,346, 519 Lower Clear Fork, 304 Libya, 74, 519, 802, 813, 831 Lima-Indiana trend (Indiana), 810, 827 Lower Fars Formation, 503 Lime, manufacture, 46 Low-permeability reservoirs, 2 Lineament analysis, 8 Lowstand, lowstand wedges, 73, 76-80 Liquid saturation, 17-19 Lucia classification, 178 Lithology, determination, 13 Lundgren field (Kansas), 523 Little Beaver East field (Montana), 522 Luther S.E. field (Texas), 519 Little Beaver field (Montana), 522 Little Knife field (Wyoming), 68, 381,383,385, M-N plots, 17 386 Maben field (Black Warrior Basin), 810, 831 Livengood field (Kansas), 523 Macedonia Dorcheat field (Arkansas), 24 Llanos field (Kansas), 522,523 Mackerel field (Australia), 851,854 Lockport Dolomite, 45 Madison Group, Limestone, 326, 359-362, 381, LOGIX, 167 383, 384 Log-inject-log process, 42 Magnolia field (Arkansas), 24, 248,522 Logs, logging Magutex field (Texas), 523,526 -, acoustical, 28, 168, 169, 179 Mardin Group, 498 , acoustic waveform, 207, 208 Marine pool (Illinois), 811,825 Martin field (Texas), 24 -, borehole televiewer, 28, 42, 209, 215 Matrix identification plots, 17 -, cased-hole logs, 159 Matrix porosity, permeability, 3, 44, 47 -, core gamma, 107 -, density, density-neutron, crossplots, 107, 108, Matzen field (Austria), 812 162, 165, 168-170 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Matzen-Schonkirchen-Reyersdorf field (Austria), 824 --, acoustic crossplots, 169 , photoelectric factor crossplots, 169 Maureen Formation, 778 Maydelle field (Texas), 527 -, dielectric, 192 McClosky Limestone, 240, 241 -, dipmeter, 208 -, gamma ray, 168, 172 McElroy field (Texas), 452, 519 ---, spectroscopy, 168, 172, 173, 175, 181, McFarland field (Texas), 523 McKamie field (Texas), 24 195 McKnight reservoir (Texas), 304, 305 -, geochemical, 25, 27, 175, 181 Means field (Texas), 33, 34, 43,286 -, grain density, 164 Measurement while drilling logs, 4, 60 -, Hingle plots, 169 Mediterranean Basin, 813 -, imaging logs, 208 Megabreccias, 87 , array resistivity, 215 Menger sponge, 267, 273, 415 -, Leverett "J" function, 494, 495 Mercury injection, 119, 120, 183 -, measurements while drilling, 159 Mesozoic, 72, 94 -, M-N plots, 169 Mexico, 39, 40, 48, 80, 326, 508, 510, 598, 664, -, mud logging, 158, 199 813,820, 825,830, 832, 837, 840, 847 -, neutron, 179 Miami Formation, 468 , pulsed neutron capture, 180, 192-196, 198 -, NML, 181, 195,466 Michigan, 522, 810, 811 Michigan Basin (USA), 49, 74, 79, 301,787, 810, -, NMR (magnetic resonance imaging), 179, 184, 811, 814, 819, 825,827, 828, 830,837, 844, 199, 462, 466, 468, 469 849 -, nuclear, 27, 168 Michigan Basin Pinnacle Reef trend (Michigan Ba-, photo-electric cross section log, 165 sin), 811 -, porosity-lithology crossplots, 168, 169

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 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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