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

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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 ..................................................................................................................................... 116 116 Introduction ................................................................................................................................. 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

Probability of success**

Unfractured

Fractured

(%)

(%)

5 4 3 2 1 0

0 1 2 3 4 5

6.16 22.97 34.29 25.60 9.55 1.43

93.84 70.87 36.58 10.98 1.43

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

14 ....

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

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

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

244 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

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

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f

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PER CENT

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~ ;

60

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\

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,%

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

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IToo ~

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

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

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

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

~ ~

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Fig. 5-11. Typical gas-cap-driveperformance, Goldsmith San Andres Dolomite reservoir in west Texas. (After Craze, 1950, fig. 5; reprinted with the permission of the Society of Petroleum Engineers.)

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

A reservoir having high permeability (such as a fractured or cavernous limestone) in contact with an extensive aquifer will normally have an active water drive. The degree to which the reservoir withdrawals are replaced by water determines the efficiency of the water-drive mechanism. In complete water-drive systems, which are not common, substantially all the fluid withdrawals are replaced by intruding water. Some excellent examples of complete water-drive reservoirs in carbonate rocks are Arbuckle Dolomite fields in Arkansas and Kansas. If the reservoir is initially undersaturated, natural pressure maintenance by water influx may result in oil production above the bubble point pressure for an extended period. As a result of this production, a small portion of the reservoir pore space is replaced by expanding oil. Later in the life of the reservoir a free gas phase may form, which will provide part of the energy for the oil expulsion. The existence of the free gas will depend largely on the rate of withdrawal of fluids.

248 In all water-drive reservoirs, an initial pressure decline results in the necessary pressure differential at the reservoir boundary to induce water movement into the reservoir. Figure 5-12 illustrates this initial rapid production decline preceding water influx. The Schuler (Reynolds), Magnolia, Buckner, and Midway fields are Smackover limestone reservoirs, and the Hobbs and Yates reservoirs produce from a Permian dolomite. The remaining fields shown in Fig. 5-12 are sandstone reservoirs. All these reservoirs, except the solutiotr-gas-drive Schuler Jones Sand pool (which is included for comparison purposes) are subject to at least substantial, if not complete, water drive (Elliott, 1946). To summarize water-drive performance, the producing zone is in contact with a broad aquifer, normally of high permeability. A decrease in production capacity is minor until water begins to be produced. The produced gas/oil ratio is substantially constant. Figures 5-13 and 5-14 illustrate this type of performance. Recovery factor depends on reservoir rock characteristics such as pore size and fracture distribution,

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CUMULATIVE OIL PRODUCTION (PER CENT OF ULTIMATE RECOVERY) Fig. 5-12. Pressure-production performance of some water-drive reservoirs. (After Elliott, 1946, fig. 1" reprinted with the permission of the Society of Petroleum Engineers.)

249 I

I

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RESERVOIR PRESSURE

OIL PRODUCTIONRATE

f

i

-

GAS-OIL RATIO

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Fig. 5-13. Idealized water-drive performance. (After Torrey, 1961" reprinted with the permission of PrenticeHall, Inc.)

values for mobility ratio zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA (kPolkPw) and reservoir geometry. The rate at which the reservoir is produced also may affect recovery, particularly if the reservoir is subject to only partial water drive. Reservoir withdrawal rates greatly in excess of the rate of water influx can lead to performance similar to that of solution--gas-drive reservoirs. Free gas saturations in the reservoir can develop in the more permeable sections to the extent that incoming water will bypass tighter sections. The water will move preferentially into areas of high gas saturation, with a resulting loss in recovery.

Gravity drainage In oil reservoirs subject to gravity drainage, the gravity segregation of fluids during the primary production process is evident in the production history. Oil migrates downdip to maintain down-structure oil saturation at a high level, and free gas accumulates high in the structure. If a primary gas cap exists, then it will expand as a result of the segregation process. A reservoir without a primary gas cap will soon form a secondary gas cap. Early in the life of the reservoir, the gas/oil ratios of the structurally high wells will increase rapidly. A program of shutting-in wells with high gas/oil ratios and controlling individual well rates will maximize gravitational fluid movement. Figure 5-15 shows the two generalized performance cases of a gravity-drainage reservoir with and without such control. The oil gravity, permeability of the zone, and formation dip dictate the magnitude of the gravity drainage. The combination of low viscosity and low specific gravity values (high API gravity), high zone permeability, and steeply dipping beds accentuate the down-structure oil movement. Typically, in gravity-drainage reservoirs the water influx is minor and the down-dip wells produce at the lowest gas/oil ratios and have the highest oil recovery. In cases of strict gravity drainage, a major portion of the recovery occurs after complete pressure depletion. Gravity is the primary dynamic force moving the oil to the wellbore.

250

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2.54 2.74 2.75

7.19 7.11 7.33

15 > 10 33

Carbonates Arab D Bedford Limstone Austin Chalk Smackover Dolomite Smackover Limestone

Sandstones Navajo (red, fine-grained) St. Peter Navajo (red, coarse-grained) Berea Blackhawk (well s a m p l e - 188 m)

Shales Niobrara (well s a m p l e - 2 5 2 6 m) Maim (well sample - 2308 m) Mowry (well s a m p l e - 2780 m)

Source: Modified after Krohn, 1988b, table 2; courtesy of the American Geophysical Union. * L 2 marked with > denotes the lower limit for L 2 where the end of the fractal regime was not observed by Krohn.

266 E

-1.5

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-2.5

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Fig. 5-21. Fractal data for the Bedford Limestone showing the bifractal nature of the measured surface features. (Modified after Krohn, 1988b, fig. 12a; courtesy of the American Geophysical Union.)

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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~ i ~ ~ ~ ~ii..~...:---~i G

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

16

12

16

14

12

12

12

10

10

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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 ,

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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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Fig. 5-26. Heterogeneity scaling description of pore space with respect to a reservoir and surrounding geology (From Chilingarian et al., 1992a, fig. I-2; reprinted with the permission of Elsevier Science Publishers B.V.)

275

erogeneity in reservoirs (Chilingarian et al., 1992a). The necessity for proper reservoir characterization is driven by: the maturity of oil reservoirs worldwide; war damage to reservoirs in Kuwait; improper exploitation of Russia's reservoirs; and the United States' eroding light oil (>20 ~ API) reserve base. More crude has to be recovered from the existing reservoirs. In this section, quantitative and qualitative geological information at the interwell scale will be used to formulate a geological carbonate reservoir classification scheme. A practical application of this scheme will be made in evaluating the incremental recovery of unrecovered mobile oil in carbonate reservoirs. 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

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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

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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

I

I

I

0.5 O/

0.1 Z 0 1

~" 0.05 U >.-, F.J

I

1

~9

0.01 -.---

l.iJ IX

tu 0 0 0 5

1

IX.

l.iJ > I-.

/--

_J 14.1 n,,

0.001 - -

0.0005 2O

80

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 ).

286 IO0

-~.

90

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80

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0.01 ,.,

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.

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0.ol,,,I .... I , I , , I , , , , I , ~ , , I 0.01 0.0,5 0.1 0.2 0.,5 I

2

, , i,,,,L ......... li,,,l,,lll,l,, 5 I0 20 30 40 CUMULATIVE

i,lil,,,illllil,,, 50 (GO 70

FREQUENCY

X ~

80

i,,,lllt 90

ilst

I

hillhltill 98 99

I

I, 5.11,,a~ 99.8 99,9 99.99

K

Fig. 5-34. Examples showing the calculation of Dykstra-Parson coefficients using a log-normal plot of the cumulative distribution of core permeability values on log-probability paper. Core data from the "C" zone (subtidal depositional environment) of the Red River Formation, well Melby No. 4-1, Bush Lake Field, Sheridan County, Montana, U.S.A. No. 6: VDp = 0.74; 35.5 ft (11 m) of limestone composed of mudstone and wackestone containing some 12 different Archie classes (Oave = 3.9). No. 7: VDp = 0.50; 95 ft (30 m) of interbedded dolomite and limestone comprising a single Archie class (Oave = 1.8). (Core data and lithologic descriptions from Ikwuakor, 1992; courtesy of the U.S. Department of Energy.) The VDp results are very similar to values obtained from core data from the Red River Formation "D" zone (equal to the "C" Burrowed Member) in two wells (No. 1-25 Alexander and the No. 2-31 Hilton), South Horse Creek Field, Bowman County, North Dakota, U.S.A. The Dykstra-Parsons coefficients are 0.75 (well No. 1-25) and 0.53 (well No. 2-31). Higher values of VDp indicate less efficient water drive and/or waterflood systems when water displaces oil. (Modified after Longman et al., 1992, fig. 8; courtesy of the American Association of Petroleum Geologists.)

carbonate reservoirs to H v = 10 for very heterogeneous carbonate reservoirs. The following equations developed by Fassihi (1986) can be used to estimate the vertical sweep efficiency once the Dykstra-Parsons coefficient correlations are k n o w n either from direct measurements or using Fig. 5-35" x=-0.6891

+ 0.9735VDp+ 1.6453VZDp ,

(5-31)

292 i

A > v C

I

I

'

I

'

t

'a

I

i

0.9

.g

15

)

0.8

.,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_. I-.J .....

m

W CE

a. W ~ m

I-I

\ \ \ 0

_ 0

I 20

I 40

I 60

WATER SATURATION

I, 80

100

(Sw), %

Fig. 5-57. Variation in the relative permeability to gas with increasing water saturation in two Cotton Valley Limestone core samples from the Muse-Duke well No. 1; both cores show a similar trend. The relative permeability to gas is virtually unaffected by the presence of water up to 20% S . When S w is about 85%, relative permeability to gas approaches zero. (After Kozik et al., 1980, fig. 5; courtesy of the U.S. Department of Energy.)

laboratory at a reservoir temperature of 285 ~ F (141 o C) and at various water saturations (Fig. 5-57). Initial production rates, using standard 1970s stimulation technology, were moderately good (1 - 4 MMCF/D: 0 . 0 3 - 0.11 MMm3/D) in the Haynesville Limestone. Five of the first six wells completed received light acid stimulations and began to produce at about 1 MMCF/D per well and soon declined to 0 . 2 - 0.3 MMCF/D (0.006 - 0 . 0 0 8 MMm3/D). The Burleson No. 1 well received a hydraulic fracture treatment of 48,000 gal (182 m 3) of gelled water and 178,000 lb (80,741 kg) of sand. Initial production was 4.4 MMCF/D (0.125 MMm3/D), but declined to 0.5 MMCF/D (0.014 MMm3/D) in two years. The natural fracture system was not sufficient to maintain initial flow rates. The Muse No. 1 was the first well to receive the MHF treatment. As was the case in the mini-massive fracture stimulations, 100-mesh sand (48,000 lb: 21,773 kg) was

348 pumped ahead of the 2 0 - 4-mesh sand to control fluid loss. A total of 340,000 gal (1,287 m 3) of gelled water and 450,000 lb (204,120 kg) of 2 0 - 40-mesh sand was pumped (Kozik et al., 1980), resulting in an initial production rate in excess of 4 MMCF/D (0.113 MMm3/D) that declined to 1.1 MMCF/D (0.031 MMm3/D) after 28 months. A larger, or so called "super-massive hydraulic fracture stimulation treatment" was performed on the Muse-Duke No. 1 well following an acid stimulation of the well. This treatment consisted of using 95,000 gal (360 m 3) of treated-water prepad containing 10 lb/gal salt water; no 100-mesh sand was pumped. A total of 842,850 gal (3,190 m 3) of gelled water (Versagel) containing 2,800,000 lb (1,270,080 kg) of 2 0 - 40-mesh sand was displaced into the limestone. Initial production after fracturing was 6 MMCF/D (0.17 MMm3/D), which declined to 2.1 MMCF/D (0.06 MMm3/D) after 22 months. By 1980, four other wells were fractured using sand volumes ranging from 450,000 to 1,000,000 lb (204,120-453,600 kg). Kozik et al. (1980) reported that initial production rates indicate performance similar to the Muse No. 1 well. Figure 5-58 presents a comparison of the performance curves for the Muse No. 1, Muse-Duke No. 1, Burleson No. 1, and three best acidized wells (11year production history). 10,000-.. g,O00-~ e,O00|

FALLON

7,000~ 9. , o o

s,ooo ! 4,ooo !

AND NORTH PERSONVILLE LIMESTONE CO.. TEXAS 2-1-80

_..use-ouKt., ...s,v.

FIELDS

F..c,

. -= ,.0o0 r =E 1=

1,000. 900 800 700

URLESON ,F, 1 IONAL FRAC)

6O0

500 400 300

AVERAGE OF 3 WELLS (NOT FRACED)

200

100

I

.1

9

I 1

CUMULATIVE

i

I 2

PRODUCTION

ii

i

i

I 3

(BILLION

CU. FT.)

Fig. 5-58. A comparisonbetweendaily flow rates and cumulativeproduction for massive fracture stimulation, conventional fracture treatment, and non-fracturedwells in the Cotton Valley Lime (Haynesville Limestone). (After Kozik et al., 1980, fig. 7; courtesy of the U.S. Departmentof Energy.)

349 Reservoir simulation studies of the Muse No. 1 and Muse-Duke No. 1 wells consisted of varying formation permeability, fracture length, and fracture conductivity to match well performance and assess the sensitivity of costs (Kozik et al., 1980). Unfortunately, a unique history match was not obtained for the Muse No. 1 well owing to insufficient pressure buildup data. Definitive fracture half-length could be not determined for this well. A fracture half-length of 1500 ft (457 m) was determined for the Muse-Duke No. 1 well. From the reservoir simulation history matching analysis of these two wells, the formation gas permeability ranges from 0.01 to 0.04 mD (0.00001 - 0 . 0 0 0 0 3 9 ~m2). A computer model FRACOP (Holditch et al., 1978) was used to determine optimum fracture length and well spacing for a well similar to the Muse No. 1 and the MuseDuke No. 1. The model uses reservoir and well parameters, and fracture length values, to generate a production function, which is used to determine net cash flow and net present value for any specified discount rate. Results are presented in Fig. 5-59, which shows ultimate gas recovery as a function of permeability, fracture length, and drainage area (well spacing). At a 160-acre (65-ha) spacing, increase in the fracture halflength from 250 ft to 1250+ ft ( 7 6 - 381 + m) does not have a significant influence on 30-year ultimate recovery (Kozik et al., 1980). The effect of higher permeability values ...

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~

0

K-~ 0 . 0 1 ,

:12011r

4 8r

0

K ~ 0.01

I

,,

800 PROPPED

,

160at,

I

I

1000

1800

FRACTURE

LENQTH

,

I

2000

,,

2800

(FT.)

Fig. 5-59. The effect of permeability upon 30-year ultimate gas recovery per well as a function of fracture half-length. Ultimate recovery increases as permeability, fracture length, and well spacing increase. Higher permeability values, however, have a pronounced effect as the drainage area increases. Results are based on a FRACOP model study using Haynesville Limestone reservoir parameters and economic costs from the Muse No. 1 and Muse-Duke No. 1 wells. (After Kozik et al., 1980, fig. 19; courtesy of the U.S. Department of Energy.)

350 becomes more pronounced as the drainage area increases. This suggests that the best well spacing would be 4 wells per section (one sq. mile = 640 ac = 259 ha), inasmuch as this well density results in a maximum recovery efficiency. Kozik et al. (1980) stated that to properly optimize well spacing and fracture length from an economic viewpoint, the maximum discounted present value profit for each case must be determined. Figures 5-60 and 5-61 show the 10% profit per section for permeabilities of 0.01 and 0.04 mD (0.00001 -0.00039 ~tm2), respectively. Table 5XVII lists the economic parameters and fracturing costs used in the study. The optimum well spacing for these conditions is 320 acres (129 ha), and the propped fracture half-length is 1500 ft (457 m). zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

Massive hydraulicfracturing-horizontal drilling comparisons. As described above, tight gas reservoirs with matrix permeability values in the microdarcy range can contain zones of natural fractures having relatively high permeability. A major risk associated with the development of such reservoirs is the possibility of having water breakthrough as a result of fractures tapping underlying water zones. Van Kruysdijk and Niko (1988) assessed this risk using a reservoir prototype model based on Shell Oil Company's black oil simulator. The first phase of the study assumed single-phase compressible flow, and utilized Green's function theory to derive transient pressure response. Results from the model study (Fig. 5-62) indicated that a horizontal well 3.0

320 Acres. 1140 A c r e s

2.,5

~W ~

2.0 160 A c r e s

m

~- a0 1.5 0 n

Z) 1.0

0

NOTE: F i g u r e s a r e on a per s e c t i o n b a s i s

. m

0

-0.5 800

1000

1500

2000

2500

PROPPED FRACTURE LENGTH (FT,)

Fig. 5-60. Results from a FRACOP model study showing a comparison of the 10% discounted presentvalue profit per section (one square mile: 2.59 square kilometers) with propped fracture length for a formation having 0.01 mD permeability. (After Kozik et al., 1980, fig. 21; courtesy of the U.S. Department of Energy.)

351 zyxwvutsrqp

om IU m

8 820 Acres 640

c~ m

Acres

180 Acres

41 .9,0 N O T E : Figures are on a per section basis

I

I 500

.

lOOO PROPPED

I

.

18oo

FRACTURE

LENGTH

I 2000

,

2500

(FT.)

Fig. 5-61. Results from a FRACOP model study showing a comparison of the 10% discounted presentvalue profit per section (one square mile: 2.59 square kilometers) with propped fracture length for a formation having 0.04 mD permeability. (After Kozik et al., 1980, fig. 22; courtesy of the U.S. Department of Energy.)

TABLE 5-XVII Economic values and fracturing costs (1979 rates) used in the optimization of fracture length and well spacing evaluation from Mitchell Energy Corporation's Cotton Valley Lime (Haynesville Limestone) massive hydraulic fracturing test data, Fallon and North Personville fields, Limestone County, east Texas, U.S.A. Note that any economic evaluation or technical evaluation involving economic analyses is sensitive to each operator's economic parameters, such as current product price, price escalation or deflation, operating costs, initial investment, interest rates, and net working interest (data from Kozik et al., 1980) zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Economic parameters

Fixed investment: Product price: Operating expenses: Net revenue interest: Production Tax rate: Federal Income Tax rate:

$1,000,000 $1.52/MCF constant $8,400/yr constant 79.7% 13.0% 0%

Fracturing costs

Designed fracture-length radius, ft

Costs, $

250 500 750 1000 1250 1500 1750 2000

75,000 100,000 150,000 200,000 250,000 300,000 400,000 700,000

352

W.I E L. L B. O R. E

'I

y

!

I

Ze

//

Z

J ~

--X

L_ .

,,

RESIERVOIH ~

_1

A .

..-._.__

WELL|ORE

i I I I I

I I I I I

MASSIVE HYOA,tUUC FRACTURE

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

_ Z

~_7.T s

X'

~ / -

~

I

RLSE~K)In

B Fig. 5-62. Two semi-analytical models used to assess alternatives for draining tight naturally-fractured gas reservoirs: (A) Horizontal well reservoir model containing a naturally-fractured zone of finite width extending over the full height and width of the reservoir; (B) Double-fracture reservoir model showing a massive hydraulic fracture intersecting a vertical fracture plane. (Modified after Van Kruysdijk and Niko, 1988, figs. 1 and 5; courtesy of the Society of Petroleum Engineers.)

draining a natural fracture zone compares well with massive hydraulic fracture treatment, which connects the well to the fracture zones. Figure 5-63 presents typical pressure responses of both the horizontal well and a massive hydraulic fracture (MHF) intersecting a fracture zone. Inasmuch as the models used in Van Kruysdijk and Niko's (1988) assessment involve single-phase flow, additional advantages of the horizontal well with respect to water coning control were ignored. Table 5-XVIII presents the reservoir parameters used in this study.

353

L|

1(~

'

!~ !~ i-

'~ ..... ' "' ............... , ,, -

9U - - H- -r, C , t t=0' , " ' , , ' s

..r ~Hr uHr kIHu

cfo = CI0 s CIOCIO :

...... "

"'""

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

w

........

,

2.~ $ tO 1S

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 9

.......

,o-,

--.

y

V......-::

I0"*

o

I 0 "s

I0"

I 0 "s

I0"

10"

I 0~

Io'

1o'

OIMENSIONLESS TIME. I0

Fig. 5-63. Typical pressure responses of a horizontal well and a massive hydraulic fracture, both tapping a large natural fracture zone in a tight gas reservoir, with respect to dimensionless time. Cro is the dimensionless fracture conductivity and is equal to w(kf)/xf(k), where w is the fracture width, kf is the fracture permeability, Xf is the fracture wing length, and k is the reservoir (average) permeability. (After Van Kruysdijk and Niko, 1988, fig. 11; reprinted with the permission of the Society of Petroleum Engineers.)

TABLE 5-XVIII Basic reservoir parameters used in the model studies assessing the production performance of massive hydraulic fracturing and horizontal well scenarios in a naturally-fractured gas reservoir fractured zone width, w e reservoir thickness, z e reservoir width, ye wellbore length wellbore radius, r w fractured zone permeability, kns reservoir permeability, k fractured zone porosity, (I)f reservoir porosity, ~

9 30 ft 9 750 ft 9 1500 ft 9 1500 ft 9 0.3 ft 9 250 mD 9 20 I~D 9 0.01 9 0.07 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGF

Source." After van Kruysdijk and Niko, 1988, table 1" reprinted with the permission of the Society of Petroleum Engineers.

Van Kruysdijk and Niko (1988) pointed out that the horizontal well's early-time pressure response is considerably lower than that of a similar stimulation by the MHF (ignoring fracture linear flow), which is attributed to the horizontal well's direct entrance to the high-conductivity fracture zone. The MHF curve crosses the horizontal well response when the MHF conductivity is sufficiently high (above the

354 I.S

II

1.0

....

I

= C o ........ : ~. = 9

x..

-ll 0 o :. --0 I

o110=10 (x!=O.STe) oi tO 9100 (X! : O.S re) al ID 910 ( x l - 0.2S 'ire) ot ID = I 0 0 (X! : 0.2S Ye) ol 10 : I0 (XI : 0.125 Ye) ol 10 = 100 (Xl = 0.12S Ye)

O.S

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X

-O.S

b.

" ' ~ ' " t ~ -

-.---.._.__..__.....~.._._____.

I

"1.0

-I.~)

. 0.0

1.0

I

I

i

2.0

3.0

4.0

....

l

s.a

9

1

I

!

6.0

7.o

s.a

~.0

MHY r

1

~0.0

1

,I.0

1

12.0

i

13.0

|

14.0

i~.0

CfD

Fig. 5-64. Production improvements in a naturally-fractured tight gas reservoir. Both the horizontal well and the massive hydraulic fracture tap into the large zone of natural fractures as a function of the massive hydraulic fracture length, t D is dimensionless time and is equal to zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONM

k(t) O~tctY-----~,where k is reservoir permeability, t is the 2 time, t3 is the porosity, ~t is the gas viscosity, ct is the total compressibility, and yf is the fractured zone half-length. MHF fractured zone interaction at 0.5 Ye; Xf is the fracture wing length and Ye is the fractured zone length. (After Van Kruysdijk and Niko, 1988, fig. 12; reprinted with the permission of the Society of Petroleum Engineers.)

break-even point as shown in Fig. 5-64), so that the extra fracture surface compensates for the finite conductivity link to the fracture zone. The break-even point for the MHF intersecting a fracture zone with respect to a horizontal well is determined by the balance between extra fracture surface and pressure drop over the fracture wing (Fig. 5-62B) intersecting the fractured zone. Figure 5-64 illustrates the effect of MHF length and conductivity. Van Kruysdijk and Niko (1988) pointed out that short fractures (with respect to the fractured zone) require very high conductivities in order to be competitive with horizontal wells. Another drawback to massive hydraulic fracturing treatments is a lack of fracture direction control. The horizontal well can be considered then as having an advantage in the development of naturally-fractured carbonate reservoirs.

Refracturing About 80% of all active wells in the U.S.A. are producing at less than their potential. Results of recent advances in computer software, operational hardware, and materials have created opportunities to successfully refracture these existing wells. Abou-Sayed (1993) pointed out that most refracturing treatments have been applied to wells where original design parameters, materials, or operational procedures were

355 below current standards. Advance techniques, such as in the pumping of proppants, high overpressure perforating, and dynamic formation breakdown and fracture initiation are successful in improving the fracture-to-well connectivity and reducing fracture cornering and tortuosity in the near-wellbore region. An excellent example of applying refracturing technology to increase reserves was the acid refracturing of the Permian Ervay Member (dolomite), (Phosphoria Formation), in the Cottonwood Creek Unit, Washakie County, Wyoming, U.S.A. The reservoir covers about 60 mi2(155 km 2) in the Big Horn Basin and is not naturally fractured (Aud et al., 1992). The Cottonwood Creek Unit is developed on an 80 - 320 acre ( 3 2 - 130 ha) spacing. Early field development concentrated on the updip part of the reservoir owing to good production response from high-permeability streaks. At that time, the operator assumed that the field was producing from natural fractures. As development continued, poorer producing wells were drilled in lower-permeability zones. These wells were treated initially with a conventional acid fracture stimulation of 5 , 0 0 0 - 30,000 gal (19 - 114 m 3) of 15 - 28% HC1 pumped at 5 - 15 bbl/min (0.8 - 2.4 m3/min). The treatment evolved into one requiring 4 0 , 0 0 0 - 60,000 gal (151 - 2 2 7 m 3) of 28% HC1 with and without nitrogen gas. Large conventional acid fracture treatments used 125,000 gal (473 m 3) of 15% HC1 pumped at injection rates as high as 25 bbl/min (4 m3/min). Gelled acid with and without CO 2 was used as an economic alternative to the large acid treatments. Sand fracture treatments were unsuccessful owing to sand production problems associated with etched regions around the wellbore resulting from remedial matrix treatments (Aud et al., 1992). Typical porosity and permeability values are 8 - 10% and 1 mD (0.000987 ~tm2), respectively. Core analysis, however, revealed porosity values of 1 5 - 20% with associated permeabilities up to 800 mD (0.789 ~tm2). Reservoir modeling indicated that vertical permeability values are low (0.001 - 0.00001 mD: 0.00000001 - 0 ~tm2). The thin, high-permeability streaks constitute a low percentage of the reservoir, and have TABLE 5-XIX Average Phosphoria (Ervay Member) reservoir-fluid and formation properties in the Cottonwood Creek Unit, Washakie County, Wyoming, U.S.A. Original reservoir pressure, psi Original Pb, psia FVF at Pb' RB/STB Solution GOR at Pb' scf/STB Oil gravity, ~ Reservoir-fluid viscosity at Pb' cP Total compressibility at Pb, Psi-I Total compressibility at 800 psi, psiq Net pay, ft Connate water saturation, % Reservoir temperature, ~ Wetting characteristic Formation embedment strength, psi Acid solubility, %

:3608 : 1126 :1.14 : 313 :27 : 4.75 : 2.25 • 10-5 : 1.78 x 10-4 : 20 - 120 :10 : 125 :Oil :70,000 : 95 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHG

Source: After Aud et al., 1992, table 1" reprinted with permission of the Society of Petroleum Engineers.

356 values above 2 mD (0.00197 ktm2). Average reservoir parameters and their values are presented in Table 5-XIX. The reservoir originally contained an undersaturated crude with an average bubblepoint pressure of 1,126 psig (7.8 MPa). Reservoir pressure measurements indicated that the pressure, Pb, is slightly below the bubblepoint in most parts of the field (Aud et al., 1992). Waterflooding operations pressurized some areas of the reservoir, but this pressure is now dropping quickly because the waterflood is no longer operational. A detailed reservoir and geologic study involving a fully implicit, 3D, multiphase reservoir simulator with an acid fracture design program, indicated that many wells in the reservoir had short infinite-conductivity fracture half-lengths of 100 - 300 ft (30 91 m) (Aud et al., 1992). Reservoir simulation results suggested that an increase in the effective fracture half-length would increase the production rate and ultimate recovery. Five wells were retreated using 60,000 gal (227 m 3) of 15% HCI plus 60,000 gal (227 m 3) of 20% HC1. No significant incremental fracture half-lengths were obtained in these wells. The reason for the poor results was attributed to poor fracturingfluid efficiency caused by high fluid leakoff. Aud et al. (1992) pointed out that the free gas phase below the bubblepoint significantly increases reservoir fluid compressibility, and is an important parameter in the refracture treatment design. The fracture fluid encountered a highly compressible gas instead of a relatively incompressible liquid in the pores, therefore, resulting in a high leakoff. Refinement of the reservoir model resulted in a new treatment design. The wells were refractured using an external oil-emulsion acid system containing 70% by volume of 28% HC1 and 30% by volume of diesel oil and gelled water used in multiple alternating stages. Crowe and Miller (1974) developed the external oil-emulsion acid system for use in high-temperature limestone reservoirs. Fracture lengths of 250 ft (76 m) or longer were necessary to achieve reasonable economic results in wells having infinite-conductivity fracture half-lengths of 1 0 0 - 300 ft ( 3 0 - 91 m). Gelled acid treatments were not used owing to model predictions showing inadequate conductivity development in low-permeability regions. Table 5-XX presents results of the 1990 refracturing program, as well as data relative to treatment size and design. The program was successful. The sixteen wells, which were acid-fractured, showed an incremental production increase of 750 BOPD. Eleven wells of the 16 wells, which were refractured, contributed about 460 BOPD (73 m3/D) to the incremental production increase. The effective fracture half-lengths obtained by refracturing ranged from 300 to 800 ft (91 - 2 4 4 m). The refracturing treatments resulted in incremental reserves of about 105,000 bbl (16,694 m 3) of oil per well for these 11 wells. Aud et al. (1992) attributed the remaining difference of 290 BOPD (46 m3/D) of the production increase to five wells that had not been previously fracture-stimulated. Four of these wells were not stimulated on initial completion owing to high water production rates from high-permeability zones. Modeling for predicting post-fracture production response and reserves on these four wells was impossible (Aud et al., 1992). The wells were modeled only for fracture design purposes to ensure that proper flow capacity was accounted for in treatment design.

TABLE 5-XX Summary of the 1990 refracturing well stimulation results, Phosphoria Formation, Cottonwood Creek Unit, Washakie County, Wyoming, U.S.A. Acid volume (gal)

Gelled Gel load water (Ibm/ volume 1000 gal) (gal)

Well

Treatment date

Job type

165

22 Feb 90

RF

185

29 Mar 90

FR

180

24Apr90

RF

184

17May90

RF

183 190

5 June 90 20 June 90

RF RF

151

27June90

RF

172 173 163

11 July 90 25 July 90 8 Aug 90

RF RF FR

182

22 Aug 90

RF

201

5 Sept 90

FR

167 161 169

20 Sept 90 3 Oct 90 20 Oct 90

RF RF FR

88,000 E 40 40 75,000E 25 75,000 E 25 67,000E 40

168

31 Oct 90

FR

67,000 E 40

80,000 E 12,300 C 81,000 E 30,000 C 70,000 E 15,000 C 62,000E 15,000 C 80,000 E 19,000 E 10,000 C 61,000 E 11,000 C 72,000 E 74,000 E 65,000E

Interval Permeability thickness (mD) (ft)

Fracture half-length (ft) Initial Final

Pretreatment rate (BOPD/BWPD)

Post-treatment production rates (BOPD/BWPD) 30 days 60 days 90 days

14/0

122/50

58/4

54/3

9/0

80/15

40/3

34/0

15/0

95/15

55/3

50/0

19/0

106/50

60/3

55/0

zyxwvut

20

65,000 L

0.5

52

200

500

20

74,000 L

1.9

59

0

300

20

75,000 L

0.3

50

300

650

40 40 25 40

65,000X 42,000 L 117,000 L 95,000 L

100 1 1.2 0.3

5 35 52 60

150 200

300

30/0 6/0

198/29 33/5

130/7 18/10

120/5 17/0

40

99,000 L

1

40

100

70

6/0

127/2

83/9

73/9

20 20 40 40 80,000 E 25

119,000 L 122,000 L 19,000X 90,000 L 25,000 X 85,000 L 80,000 X 30,000 L 110,000 L 120,000 L 20,000 X 76,000 L 125,000 X

1 1.5 100 1 2.5

40 40 8 22 50

300 0

# 800 *

22/0 29/8 12/15

67/28 240/48 172/119

100

450

32/0

150/19

150 1 0.5 0.8

20 30 42 60

*

28/100

120/201

# 700 *

7/0 19/0 5/30

32/18 78/12 50/85

150 1

15 45

*

67/67

* *

0 300 400 0 0

37/15 110/8 180/110 80/2

35/13 90/6 91/60 62/5

zyxwv 125/180

Source: After Aud et al., 1992, table 6; reprinted with the permission of the Society of Petroleum Engineers. RF = refracture treatment; E = external oil-emulsion acid; L = linear gelled water; * = high-permeability streak; FR = initial fracture treatment; C =conventional acid: 15% HCI; X = crosslinked gelled water; # = not modeled yet.

-.z

358 CARBONATE RESERVOIR CHARACTERIZATION

This section will focus on the present-day use of various mathematical strategies in determining reservoir heterogeneity. The term heterogeneity, as described previously in geological terms, is a measure of the continuity of a particular reservoir property. In the previous sections, it was shown that heterogeneity in carbonate reservoirs is the critical overall productivity parameter for characterizing these reservoirs. Examples of present-day oil-field practice to overcome heterogeneity effects were presented earlier in the chapter. A discussion of the relationship between porosity and permeability, and their heterogeneity is a central premise in the development of fluid transport models for carbonate reservoirs. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCB

Reservoir heterogeneity models Carbonate reservoir heterogeneity is a challenge, which needs to be clearly defined not only geologically, but also from a reservoir mechanics viewpoint in order to increase well and reservoir productivity. This section acquaints the reader with some of the technical aspects by briefly discussing various approaches, with a focus on micro- to macro-scale applications to reservoir performance, used in attempting to mitigate reservoir heterogeneity problems. The production of hydrocarbon fluids from heterogeneous carbonate rocks depends on variations in reservoir and fluid properties and their spatial correlations. The concept of reservoir heterogeneity was revived in the late 1970s and early 1980s owing to advances in geoscience and engineering technology, and the political necessity to produce from complex reservoirs. There have been three (as of 1993) reservoir characterization technical conferences sponsored by The National Institute for Petroleum and Energy Research (NIPER), Bartlesville, Oklahoma, held to address reservoir heterogeneity. The first one was held in Dallas, Texas, U.S.A., in 1985 (Lake and Carroll, 1986). Haldorsen and Damsleth (1993) pointed out that despite many recent advances in reservoir characterization technology, its practice and accompanying publicity by the oil industry, there appears to be no sign of a general increase in productivity. Their statement was based on the observation that (1) there has been only a slight increase in province-average recovery factors, (2) production forecasts are still notoriously in error, and (3) the mainstream, day-to-day forecast modeling of reservoir behavior by a typical oil company has not changed appreciably since 1987. The writers do not completely agree with Haldorsen and Damsleth's statement. Our outlook is that productivity increases (or decreases) should be measured on a well-by-well basis and/or on an individual reservoir basis. Rationale for this opinion is given in the previous discussions on: (1) the classification of carbonate reservoirs based on their geological nature, and (2) the incremental recovery technology. These problems were shown to be solvable, and the solutions produced favorable returns to the operator. It should be noted that other factors have a strong influence on overall productivity of the older established reservoirs, such as: (1) present economic adversity, (2) oil price stability, (3) technology affordability and its acceptance, (4) management and staff education, (5) lack of technical and field personnel owing to company

359 downsizing, (6) sloppy practice, (7) poor planning and execution, (8) competing internal company reservoir development projects with better bottom-line returns, (9) lack of quality control, (10) large, long-term projects which are underway, and (11) the focus on higher investment returns from exploration efforts in less developed countries. These factors have a strong impact on the effectiveness of reservoir characterization "applications" to cure day-to-day production problems. The bottom-line, however, is that any approach to characterization has to be cost effective. Disregarding costs, however, it is technically possible to offer methods to the operator, whereby one can obtain precise and accurate reservoir information at various scales for reservoir modeling. These information acquisition methods could involve a 3-D seismic acquisition and processing that could provide a tomographical picture of the reservoir, interwell seismic definition of geological conditions, wellbore image analysis for fracture definition and magnitude of damage, and use of algorithms to help describe the reservoir by relating the measured petrophysical properties procured by advanced well-test and well-logging techniques. Analysis of this information involves the application of statistics and geostatistics. Such mathematical tools provide the foundation to evaluate and simulate conditions in and near the wellbore (at microscopic and mesoscopic scales) and between existing wells (at mesoscopic and macroscopic scales) (see Figs. 5-26 and 5-37) for primary recovery operations. Methods for integrating seismic data with well-log data in the construction of reservoir models, and potential pitfalls, were reviewed by Araktingi et al. (1991). A non-statistical method (Eq. 5-20) for determining interwell heterogeneity involving waterflood sweep efficiency was previously presented on page 282. Values determined in this manner are used in the design of advanced recovery operations. In present-day practice, macroscopic heterogeneity is usually addressed by using the previously discussed incremental recovery technology. Unfortunately, variability in geological aspects of carbonate reservoir heterogeneity is still a descriptive process in the minds of most geologists. Reservoir examples are frequently given in the literature using the classical descriptive approach. An example of this practice is illustrated by Mancini et al.'s (1991) study of Jurassic Smackover carbonate reservoirs in the southeastern U.S.A. This approach describes reservoir geology by portraying data variability for various geological properties as a series of generalized maps. The detail expressed in these maps depends on the amount of money spent to acquire and analyze the data and the spacing of the data both vertically and horizontally within the reservoir. In practice, it is normal not to address the vertical variations within a reservoir in great detail unless they strongly influence reservoir performance. Overall, this descriptive approach is one of defining anisotropic properties rather than dissimilar properties or heterogeneity occurring within the reservoir. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Elk Basin FieM case history

The following case history describes an early example of an effort to define several megascopic (field) scale heterogeneities in a large producing carbonate reservoir. Wayhan and McCaleb (1969) described reservoir heterogeneities in the lower Mississippian Madison Limestone (Elk Basin Field), Montana, U.S.A. They instituted appropriate corrections to production operations based on the obtained geological data.

360 The methodology used to handle these heterogeneities was based on classical geological and engineering analyses practiced in the 1960s. Whether or not Wayhan and McCaleb were successful in increasing the recovery of additional oil is a matter of opinion. The Elk Basin anticline is a giant oil field which contained more than a billion barrels of oil originally in place and produced at rates in excess of 70,000 bbl/D (11,129 ma/D) from seven horizons ranging in depth from 1,000 to 6,500 ft ( 3 0 5 1981 m) (Fig. 5-65). Production from the Madison Limestone began in 1946. The early conceptual model of a homogeneous reservoir (no zonation) was influenced by the operating practice of completing the wells open-hole through the entire 920 ft (280 m) Madison section. Any low-permeable streaks were thought not to be continuous. During the first 10 years of production, the reservoir exhibited a water drive with only a slight pressure decline (Wayhan and McCaleb, 1969). Wells were drilled near the crest of the anticline so that oil would be recovered as it moved updip ahead of the natural water drive. Flank wells were added as needed to accelerate production and to ensure good areal sweep of the reservoir. The operational strategy called for progressive plug-backs to minimize lift requirements as water cuts increased in the wells. In 1957, water cuts increased, affecting the overall reservoir productivity.

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Fig. 5-65. West-eastcross-section of the Elk Basin anticline showing seven producing horizons. (Modified after Wayhanand McCaleb, 1969, fig. 2; courtesy of the Society of PetroleumEngineers.)

361 A review of core analyses and well logs in 1957 revealed highly complex zonation in the Madison section. Four zones (A, B, C and D) were identified, all of which were still thought to be under a natural water drive. During the period 1 9 5 8 - 1961, singlezone completions were made in the Madison reservoir. The completions showed that the A zone exhibited solution-gas-drive, whereas the other three zones continued to show water-drive performance. In 1961, water was injected into the reservoir. The A and B zones, in early 1962, began to produce water. Wayhan and McCaleb (1969) stated that only minor waterflood response was observed and the producing rate continued to decline sharply. Operational modification in 1963 rerouted the available water to the reservoir's A-zone interior injection wells. Production rate began to improve immediately; however, by early 1965 water breakthrough occurred in the interior and production started to decline. Severe curtailment of production occurred owing to wellbore scaling of the interior offset production wells. A new integrated geological and engineering program was executed in 1965 to define the problem by gathering additional reservoir data using 12 new development wells. A detailed study was made to define the degree of continuity in the reservoir on a zone-by-zone basis. Interpretation of core and well-log data showed that the Madison reservoir has a fluid flow heterogeneity (low-permeability streaks) within its four Madison producing zones. The A zone, which for the most part was deposited in a high-energy environment, exhibited a very complex vertical and areal zonation. Zone A consists of three major oolitic pay sub-intervals with limited areal continuity. These sub-intervals are interspersed with layers of lime mud creating limited fluid communication between the subzones. The B, C, and D zones are blanket limestones deposited in a low-energy environment. The B zone was divided into two pay sub-intervals, the upper one of which has two sub-members. The C zone has a productive horizon only at its base. The D zone has only one-pay horizon. Varying degrees of dolomization in the zones occurred after lithification. Subsequent erosion, karst development giving rise to collapse features and dissolution breccias, and leaching of relict limestone by meteoric water greatly altered the original Madison heterogeneity and permeability of the A zone. A major permeability discontinuity discovered by additional drilling lies on the anticlinal crest of the A zone (Fig. 5-66). Collapse and remineralization was so severe at the crest that they created a barrier subdividing the A zone into east side and west side reservoirs. Natural water drive is from west to east in the B and D zones toward a permeability restriction in the crestal area and toward a fault on the east flank of the anticline (Wayhan and McCaleb, 1969). At the anticlinal axis, remineralization by anhydrite and calcite of the lower Madison zones reduced porosity and permeability, thereby destroying potential reservoirs. The original heterogeneity and flow characteristics of Madison section were greatly altered by erosion, solution, and diagenetic overprinting. A detailed integrated study resulted in production practice changes during the 1960s. Waterflooding changes consisted of returning water into only the A zone, and stopping water injection into the B zone. Wells were drilled on the east flank of the anticline to take advantage of lower water cuts of 1 0 - 50 % in the B and D zones. This is in contrast with the original production plan of drilling wells near the crest of the structure to recover the oil moving updip ahead of the natural water drive. Flank wells

362 PRODUCING ZONES /'-~ ~ maSOLUTION BRECCIA _ ___ '~1~ ZONE

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Fig. 5-66. Idealized west-to-east geological cross-section showing the axial collapsed A zone in the Elk Basin Madison reservoir. (After Wayhan and McCaleb, 1969, fig. 5; reprinted with the permission of the Society of Petroleum Engineers.)

were added as needed to accelerate production and to ensure good areal sweep efficiencies. Scaling was greatly diminished by shifting water injection to the periphery of the A zone. No definitive answer could be given by Wayhan and McCaleb on the potential magnitude of the increase in recovery that could be ascribed to the change in production practices. Their only answer is that the reservoir by 1968 has produced 5.4 million bbl of extra oil and that the current rate was 8,500 BOPD above the old trend. Numerical reservoir model studies were not performed at that time, owing to the assumption that the 'reservoir' was so complex that a model would not be beneficial (Wayhan and McCaleb, 1969).

Importance of models Weber (1982) stated that the value of having a geological/petrophysical model lies in estimating well drainage areas, completion design, and as input into the appraisal of development drilling pattems. Development of accurate reservoir performance models has been difficult owing to problems in extrapolating values for petrophysical properties between wells. The simulation of reservoir performance is now limited primarily by the petroleum industry's ability to numerically model geological uncertainty. The following discussion is a brief overview ofprobabilistic modeling presently in use by the petroleum industry. Attention is focused here on how fractal and multifractal distributions can be used to describe reservoir heterogeneity in reservoir simulation models. Application to carbonate reservoirs follows the overview discussion on fractal models. In the early development stage, knowledge of reservoir anisotropy and heterogeneity

363 is scarce. Fluid flow problems are usually solved by using volume-average approaches under conditions of minimal data. Flow characteristics in reservoirs are described by Darcy's law, which prescribes a linear relation between the pressure gradient and flow. In order to predict future reservoir performance behavior for the initial development plan, one has to use reservoir simulation models with a minimum of data. The accuracy of the model's predictions depends on the available data, which reflects the amount of investment made to procure information. It should be noted that the lack of "maximum" acquired data usually precludes accurate modeling; however, data estimation algorithms and sensitivity analyses, which evaluate various reservoir parameters relating to production, can be used in a "first pass". A statistical analysis of reservoir data is necessary to estimate the range of reservoir properties. Application of fuzzy set theory may be one way to obtain a more reliable estimation of values, inasmuch as it returns values closer to sensitivity specifications than those values fitting an exact Boolean (crisp) output. An example in the use of fuzzy set theory is given by Fang and Chen (1990). Their study on the estimation of petroleum volumes in prospect appraisals presented a comparison between the classical Monte Carlo probability approach and possibility approach (Dubois and Prade, 1988). The possibility method via fuzzy arithmetic method can handle uncertainties in the estimation of values for hydrocarbons in place when some of the data are missing, subjective, or vague. Chen and Fang (1993) pointed out that the possibility method is an appropriate alternative approach, but not a substitute for conventional methods based on probability theory. One advantage of applying either approach in numerical models is that these methods provide a low-cost, rapid procedure for preparing generalized maps and measuring risk for a "first pass" scenario. Ideally, a carbonate reservoir is envisioned to be deterministic if at every point in the reservoir true properties exist which can be measured. A resulting model description of the reservoir, however, would have to be of a statistical nature. Hewett and Behrens (1990) pointed out that incompleteness of available data and their spatial disposition, coupled with the intrinsic variability in the geology of the reservoir, would preclude deterministic mapping of properties between points. It is also more than a question of the scaling of flow processes and properties, and uncertainty resulting from missing information in reservoir descriptions. Also, the simulation has to address reservoir property continuity. These problems force one to describe the reservoir in a probabilistic manner. There are three probabilistic reservoir-property modeling techniques used in a Eulerian framework: (1) Monte Carlo simulation (Warren and Price, 1961), (2) models built up from genetic flow and lithological barrier units (Haldorsen and Lake, 1984), and (3) geostatistical interpolation using kriging (Journel and Huijbregts, 1978). There are important shortcomings in the first two techniques. The Monte Carlo approach ignores the spatial correlations in reservoir properties by assigning values to locations within the reservoir without regard to the values of the neighboring points (Hewett and Behrens, 1990). The genetic flow and lithological barrier unit model honors a stratified reservoir at each location. This technique, however, does not have variability included within the units, and the dispositions and sizes of successive units are completely independent (Hewett and Behrens, 1990). A variety of techniques are available for constructing reservoir parameter contour maps, which interpolate between data points (Crichlow, 1977; Robinson, 1982; Hohn,

364

1988). Two types of interpolation are used in geostatistics: universal kriging, and stochastic interpolation (Hewett, 1986). The choice of which one to use in modeling depends on the intended application. Kriging, which gives the minimum variance of distribution at each location, is used in reserve estimations and conditional simulations of fluid flow to predict the most likely value of concentration at a given location (Journel and Huijbregts, 1978). Stochastic interpolation intercalates between measured values using a realization of a random function having a variance structure similar to the original structure. Journel and Huijbregts (1978) stated that stochastic interpolation does not provide as good an estimate of values at any given location. It is appropriate to use stochastic interpolation in modeling the dispersion characteristics of a heterogeneous formation (Hewett, 1986). Unfortunately, the computer-generated maps give only information reflecting reservoir property variations that have a scale similar to, or larger than, the sample spacing. In most cases, well spacing controls sample spacing. Reservoir property variations at scales below the field's well spacing will be smoothed out. The variations, therefore, are not useful in the interpretation of properties at the macroscopic mapping scale. All three of the above probabilistic reservoir-modeling techniques have the same weakness attributed to deterministic interpolation schemes in that property variations at scales smaller than the data sample spacing are smoothed. Most reservoir-simulation models are based on transport equations derived for the interwell scale. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFE

Geostatistical modeling overview. Hewett and Behrens (1990) adopted the method of geostatistics for probabilistic modeling of reservoir-property distributions. Their model addressed the issue of resolution of interwell property variations on a scale where the rock-property variations are sufficiently resolved to reproduce the effect of permeability variations on fluid-displacement fronts. They employed two geostatistical strategies to achieve the desired results in their reservoir performance model. One geostatistical strategy employed a power-law variogram model (other models are spherical, exponential, and Gaussian) defining a fractal distribution of geologic properties, whereas the other geostatistical strategy used conditional simulations to determine effective flow properties at different scales. Journel and Huijbregts (1978) defined conditional simulation as a process of constructing unsmoothed realizations of the random function that honor data at the sample point, whereas unconditional simulation is one that does not necessarily honor data values at location points. Presently, experience in using conditional simulations of process performance in heterogeneous formations is limited, and is an adopted approach used by Hewett and Behrens (1986). The first strategy used by Hewett and Behrens (1990) was to generate a description of reservoir heterogeneity by creating fractal model property distributions having any desired resolution. This allowed for the scaling of reservoir properties and addressed the problem of incomplete effective flow property information. The strategy does not consider a fault, which excludes a large-scale heterogeneity. A variogram measures similarities in the values of a variable at various distances and is a type of size measure (Yuan and Strobl, 1991). Another previously-mentioned component is connectivity, which addresses property continuity within the reservoir, and it is not well captured in the variogram. The variogram of random fractals, which is based

365 on a measure of variability, is defined by Mandelbrot and Van Ness (1968), Delhomme (1978), and Hohn (1988) as:

E{[Z(x + h ) - Z(x)]2}, 2r(h) = zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

(5-48)

where r(h) measures the mean-square variation of property as a function of the spatial separation of its sample locations; Z(x) is the value of the variable at locationx; Z(x + h) is its value at a lag distance, h, away from x; and E{ } indicates the expected or mean value of a random variable, x. The greater the variogram value, 2 r(h), the less related are the two variables. When estimating values at unsampled locations, the function v(h) is regarded as the meansquare error incurred, if the value of a sample is used from one location as the estimate for the value at a distance h away. Delhomme (1978) stated that in most cases x and h are regarded as vectors; therefore, anisotropies in the distribution can be accommodated. The above variogram is based on the behavior of fractal Brownian motion, fBm, which is a good starting point for understanding anomalous diffusion and random walks on fractals (Voss, 1988). It was pointed out by Jensen et al. (1985) that it may be necessary to include other forms for a normalized cumulative probability distribution function in order to describe distributions of permeability and other reservoir properties having skewed marginal distributions. Geological properties often exhibit correlations that can be observed over a range of scales (i.e., microscopic to megascopic). Hewett and Behrens (1990) pointed out that distributions exhibiting this nested structure can be characterized by superimposing a series of transitional variograms with different ranges and sill values. A sill value is the semi-variance value where this value essentially does not change with increasing distance. On a semi-variance vs. distance plot, the resulting curve would increase until reaching a break-point value where it then becomes essentially constant. If the sill and range for each scale increase in a geometric progression, then the form of the variogram characterizing each variation scale is said to be geometrically similar to the others. The superposition of many variograms results in a power-law variogram (Delhomme, 1978). Distributions having the form of Eq. 5-48 for their increments are said to be statistically self-similar (Manelbrot and Van Ness, 1968). Fractal distributions are characterized by a power-law semivariogram (89 of 2v(h) of Journel and Huijbregts, 1978) model having the form:

v(h) = voh2H,

(5-49)

where Vo is a characteristic variance scale at a reference-unit lag distance; and H is known as either the Lipschitz-H61der exponent or Hurst exponent and characterizes the scaling behavior. Emanuel et al. (1989) called H an intermittency exponent, which quantifies the intermittent or "spotty" nature of the geometries of fractal distributions. Here it represents the fractal co-dimension equal to the difference between the Euclidean dimension in which the distribution is described and the fractal dimension of the distribution. The reader should be aware that there is a major drawback to the use of the Hurst exponent. The Hurst exponent is only a single scaling exponent. Most geologic analyses involve bivariant statistical conditions, which are effectively

366 examined using multiscaling statistics. The equality (Eq. 5-49) must be valid only in a statistical sense; that is, the functions r(h) and roh TM, should be realizations of the same stochastic process. Equation 5-49 implies that the variance at any scale can be determined from the variance measured at any other scale (Mandelbrot and Van Ness, 1968). As the scaling parameter H increases through the range of 0 < H < 1, the functions become smoother (Korvin, 1992). Figure 5-67 shows samples of the behavior offBm traces for different values of H and D, where D is the fractal dimension (see Eq. 5-11). When H is close to 0, the traces are roughest. As H increases in value toward unity, the persistence of correlations increases and the contribution of the smallest scales of variation (highest frequencies) decreases (Hewett, 1986). A value of H = 0.5 indicates a totally random structure. H values derived from measurements of topographic features of the earth's surface (roughness) typically fall in the range of 0.7 < H < 0.9, compared with the theoretically expected value of 0 . 5 - a Gaussian distribution (Hurst, 1957; Hewett, 1986; Emanuel et al., 1987). A class of functions known as fractional

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367 Brownian motion (fBm) is defined when H is not equal to 89 and r(h) is the error function, with: zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA H=d-D,

(5-50)

where d is the Euclidean dimension (Hewett, 1986). When r(h) is the probability distribution function of a log-normal distribution then Eq. 5-50 simply becomes: H/2 = d - D.

(5-51)

When distributions satisfy Eq. 5-48 with a non-Gaussian cumulative probability distribution, they are referred to as fractional motions (Hewett, 1986). In the case where the fractal dimension D (see Eq. 5-11) is related to H for a twodimensional Euclidean dimension, the D value is simply D = 2 - H . Voss (1988, p. 45) stated that fractals, like traditional Euclidean shapes, typically reduce their dimension by one under intersection with a plane. As an example, the intersection of a solid three-dimensional sphere with a plane is a two-dimensional circular area; an intersection of the circular area with another plane is a one-dimensional segment; and the intersection of this line with another plane is a zero-dimensional point. Unconditional simulations were used by Hewett and Behrens (1990) to simulate the continuity and regularity of distributions described by the variogram. The techniques available for constructing these realizations included the turning-bands method, lower/upper-triangular decomposition of the covariance matrix, and spectral methods. Hewett and Behrens (1990) chose the Weierstrass-Mandelbrot random function, which is based on a Fourier series that involves a geometric progression (see Voss, 1988, p. 57, for details). The Weierstrass-Mandelbrot function, which is continuous but not differentiable, is widely used to describe irregular surfaces. This method provides an analytical representation of the realization that can be used to calculate property values at arbitrary locations. The second geostatistical strategy deals with scale averaging of fluid flow properties. Transport equations were derived for the macroscopic scale in a Eulerian framework where local continuum properties can be defined. In a simulation model, where the simulation scale is larger than the interwell scale (scaled-up model), the property variations within the volume block to which flow properties must be assigned will generally require the definition of scale-effective flow properties and fluid compositions. Hewett and Behrens (1990) stated that the primary flow properties of interest are: (1) absolute permeability, (2) dispersivity, and (3) relative permeability. Hewett and Behrens (1990) stated that the primary factor influencing the definition of effective flow properties is heterogeneity in the permeability distribution. In response to a uniform pressure gradient, fluid velocities within a volume will be proportional to the local permeability. Any heterogeneity in the permeability distribution results in a nonuniform flow velocity field. Such a field can distort the shape of a displacement front during secondary and EOR operations creating by-passed oil pockets. Hewett and Behrens (1990) reviewed the effect of permeability heterogeneity on absolute permeability, dispersivity, and relative permeability.

368

absolute permeability has been studied The influence of heterogeneity on effective zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCB by petroleum engineers and groundwater hydrologists. In modeling, the terms 'effective' or 'pseudo' permeability were associated originally with finite-difference (or element) techniques used to solve the pressure equation in conventional numerical simulations. Effective has a special meaning that may not be obvious to the reader and is equivalent to the old term 'pseudo' used previously. Effective permeability is an average value of permeability of a grid block used in reservoir simulation. Those who work in reservoir modeling use the term 'pseudo' in a different context. This term is derived from pseudoization procedures used to correct for enhanced numerical dispersion (King et al., 1993, p. 245). King (1989) pointed out that it is necessary to use a suitable effective reservoir property value in numerical models, which is determined from reservoir core samples or logs. The effective value is a single value for an equivalent homogeneous grid block in a model. As an example, grid blocks are on the scale of hundreds of meters, whereas reservoir property heterogeneities occur over a wide range of scales (refer to Figs. 5-37 and 5-81). In the case of absolute permeability the size of fluctuation ranges over many orders of magnitude. King (1989) stated that this makes it difficult to assign a single effective value to absolute permeability that would give the same mean flow. Many attempts have been made to address the above stated problem of assigning an effective absolute permeability value. The analytical methods used are based on effective medium theory (EMT) or perturbation expansions. The effective permeability estimates, however, are accurate only when permeability fluctuations are small (King, 1989). In carbonate reservoirs this is rarely the case. Warren and Price's (1963) method is still taken as the petroleum industry standard. They used numerical simulations to show that the geometric mean usually gives the closest estimate to the effective permeability for a random, isotropic distribution. As King (1989) pointed out, there are many distributions for which this is not a good estimate. Dagan (1979), in numerical simulation of groundwater flow, presented an approach that placed upper and lower boundaries on effective permeability. He established the lower boundary to equal the harmonic mean, which corresponds to the effective permeability of a layered formation to flow perpendicular to the layering direction. The upper boundary equals the arithmetic mean, which corresponds to the effective permeability to flow parallel to a similarly layered formation. His approach avoided the geometric mean. Hewett and Behrens (1990) advocated the use of conditional simulations of permeability fields that honor measured data and mimic permeability variability and spatial correlations in the field of interest to derive effective permeabilities from flow simulations. The standard to which the effective permeability calculation must be compared to is the fine-scale flow simulation. From the groundwater literature, the effect of permeability heterogeneity on the dispersion of solutes in single-phase flows provides analytical procedures for deriving effective values ofdispersivity (Dagan, 1984). Araya et al. (1988) noted that when the permeability field has a finite range of correlations, the effective dispersion coefficient becomes constant when the length of the flow path is large compared with the range of correlations. Hewett (1986) and Araya et al. (1988) noted that field measurements of dispersivity derived from tracer tests show a scale dependence. These

369 results indicate that there is an influence of long-range correlations on the dispersion characteristics of heterogeneous reservoirs. The solutions of the convective-dispersion equation with an effective dispersion coefficient will be unsatisfactory for predicting dispersion effects in interwell flows. This statement is based on the observed scale effect occurring over large distances compared with typical well spacings in oil fields. Hewett and Behrens (1990) stated that more accurate predictions of dispersivity can be obtained by simulating the flow through conditional simulations of the heterogeneous permeability distribution. Several theoretical approaches have been proposed for generating pseudo (effective) relative permeabilities in layered systems, and are based on the assumption that there is a high degree of vertical communication existing in the reservoir (Coats et al., 1971). One would make the assumption that stratified flow or vertical equilibrium conditions exist. Problems arise due to the use of pseudo relative permeability values based on flow simulation through models that are more finely resolved than the scale for which effective properties are desired. The effective relative permeability values required to reproduce the observed behavior in the fine-scale simulation are backcalculated. Hewett and Behrens (1990) advocated that these values have to be validated, and described a method to do so. Reason for validation is that if a streamwise dependence for the pseudo relative permeability is indicated, then flow properties can no longer be defined locally. Flow properties depend on the simulation's boundary conditions and the position of the coarse gridblock (scaled-up model) along fluidflow paths, which violates the basic assumption of the Eulerian formulation of the transport equations. In order to be able to scale-up in the Eulerian formulation, it is necessary to use streamtube methods and front-tracking simulators. Emanuel et al. (1989) showed that streamtube scale-up of flows in conditional simulations of heterogeneous geology have been successfully used to match waterflood production history in carbonate reservoirs. The authors refer the reader to Hewett and Behrens (1991) for a complete discussion on scaling behavior of solutions to the transport equations for flow in permeable media. How is lateral and vertical property continuity exhibited in the fractal models? Connectivity of properties between wells is an important consideration in carbonate reservoir characterization. A variogram does not examine whether particular lithofacies or units with distinct permeability values are connected. As a result, stochastic simulations designed to reproduce a particular variogram usually produce cross-sectional areas having high proportion that are connected, and low proportion areas that are disconnected (Yuan and Strobl, 1991). Hewett (1986) provided an example of stochastic interpolation between neutron porosity well logs taken from three wells in an unidentified west Texas carbonate reservoir. Figure 5-68 shows the resulting synthetic pattern obtained in his study. The cross-section exhibits a variability between the wells that is quite representative of the actual lithological units. It was pointed out by Hewett (1986) that in any smooth interpolation scheme, contours beginning at one well must either connect with data at a neighboring well, or die out between wells. Other stipulations are that no new features can arise between the wells, and all of the bedding exhibited in the original three well logs are preserved in the interpolated field (Hewett, 1986). If low porosity or low permeability zones were discontinuous

370

FRACTAL INTERPOLATION OF POROSITY LOGS H =0.8]' I"-

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within the formation, however, then the model would not reflect their actual containment. This is analogous to having a proper description of whether or not shales exist within a reservoir (as an example of a flow barrier) as: (1) distinct and continuous shale beds; (2) discontinuous shale beds (non-continuous shale stringers); (3) shale casts; (4) randomly dispersed clay particles (shaly or clayey limestone); and (5) a combination of all these conditions. Haldorsen and Lake (1984) discussed this problem of managing flow barriers (shales) in field-scale models. Two flow barrier (or a reservoir property) types are distinguished based on whether the dimensions and spatial disposition of the barriers (properties) are known. Stochastic barriers or properties cannot be correlated between wells and appear to be scattered randomly within the reservoir. Deterministic barriers or properties are continuous between the observation points. Haldorsen and Chang (1986) addressed the generation of discontinuous shales beds having a lateral extent less than the well spacing for stochastic reservoir models. The reader needs to be aware of a recent effort to develop quantitative measures of variable connectivity for stochastic reservoir simulation studies. Yuan and Strobl (1991) proposed a unique but complex approach to measure reservoir continuity, which is essential for accurate reservoir characterization. Their approach defines reservoir continuity by quantifying the connectivity of reservoir variables, and is based on mathematical morphology and image analysis. The methodology consists of two proposed measures: the connectivity number and the connectivity indicator. The connectivity number (Serra, 1982) or Euler number (Russ, 1990) is equal to the number of disconnected objects minus the number of holes in those objects. Figure 5-24A provides an example of their concept. This measure can be used on both categorical variables and continuous variables such as permeability (Yuan and Strobl, 1991). The connectivity number, however, treats all objects with the same importance regardless of their size, making it highly sensitive to small objects and noises. The connectivity indicator is equal to the total amount of rough area divided by the total sand (matrix) area, and varies between 0 and 1. Zero indicates that all object areas are disconnected, whereas 1 indicates a high degree of connectivity. It is limited to cat-

371

egorical variables and is less affected by variation associated with small objects and noise. Yuan and Strobl (1991) tested these measures on synthetic images and on an outcrop. There are several limitations to implementing the two measures: (1) the measures rely on the availability and sedimentological study of appropriate outcrop analogues; (2) the outcrops need to be matched to nearby subsurface reservoirs producing from the same formation (facies); and (3) the requirement of complete two-dimensional data from the outcrop. Well and seismic data cannot be used directly. Generally, seismic data do not have the necessary resolution for detailed reservoir continuity studies (Yuan and Strobl, 1991). In order for the petroleum industry to have better reservoir performance prediction results, models need to address four issues: (1) flow-property scale-up, (2) incomplete property information, (3) uncertainty in the reservoir's description, and (4) connectivity. Development of a performance model that indirectly considers the difference between carbonate and sandstone reservoirs by accounting for porosity and permeability heterogeneities using fractal distributions is a new approach. zyxwvutsrqponmlkjihgfedcbaZYX Fractal-based reservoir performance model Emanuel et al. (1989) presented a reservoir performance prediction method incorporating many points of Hewett's (1986) fractal geostatistical methodology and using an approach developed by Lake et al. (1981). This developed approach consists of: (1) blending detailed geological, fluid-flow and fluid-property data; (2) creating fractal distributions of reservoir property data; (3) using generated interwell data in a finite-difference simulation to obtain a crosssection representing displacement efficiency and vertical sweep; and (4) incorporating this fractional-flow information into the areal coverage of a streamtube model to obtain fluid displacement values for the section, thereby completing calculation for the areal conformance. Their goal was to have the ability to make more accurate performance predictions for large-scale waterflood and EOR projects by detailed accounting of reservoir heterogeneity with a reduced history-matching effort at a lower overall simulation cost. A generalized logic schema of this procedure is presented in Figs. 5 - 6 9 A - D . The tasks and stepwise procedures, which are similar to Emanuel et al.'s (1989) methodology, were modified in order to provide the reader with an overview picture of the connectivity of geologic quantification, data integration, simulation of geological property distributions, the scaling of effective flow properties, and the possible extension of the procedure to infill drilling. Comments about the tasks that describe the major computational operations and decisions are necessary, inasmuch as different methodologies are coupled together (Figs. 5 - 6 9 A - D). Task 1 - Collect reservoir data. As in all reservoir analyses, one has to establish first the porosity-permeability character of the reservoir in order to analyze the data for statistical structure and to develop a heterogeneous reservoir cross-sectional model between two wells (Fig. 69A). The necessary points to be considered include: (1) using conventional methods to analyze well logs and core analyses for porosity and permeability and tying the data to depth;

372 (2) establishing empirical relationships between porosity and permeability so that missing data can be generated; (3) normalizing the data to zero mean, unit variance, and a unit interval; (4) establishing the probability density of the normalized values for the data sets; (5) calculating H values using the R/S rescaled adjusted range procedure (plot of R/ S vs. time) as applied to geophysical records is described in detail by Mandelbrot and Wallis (1968; 1969a). zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA R/S plot, variogram, and Fourier series are spectral functions used to analyze correlations defined by bivariant statistics. The procedure, which consists of analyzing random processes and time series with the help of the behavior of R(t,s)/S(t,s), is known as 'R/S analysis'. R is the sample sequential range of a stationary time series X(t) for its lag s, and S is the sequence variance, which scales as R/S -- (as) H, where a is a constant. This test evaluates the long-run behavior of statistical series and detects the presence of long-run correlations (statistical dependence) in fractal distributions (Mandelbrot and Wallis, 1969b). Dependence implies that what happened at a previous time has an after-effect in the future. Mesa and Poveda (1993) and Muller et al. (1992) provide thorough discussions on the Hurst effect and its limitations.

Task 2 - Establish fluid properties and fluid flow paths. It is necessary to have representative fluid-property and fluid-flow data from the candidate wells (Fig. 5-69B). This can be accomplished by: (1) choosing the appropriate fluid-flow path(s) for analysis based on the well pattem; (2) selecting the wells defining the flow path; (3) checking if fluid-property and fluid-flow data is available. If not, then obtain such information from corefloods from selected well cores and PVT measurements on reservoir fluids samples. Coreflood data from noncandidate wells would be suitable, if the cores are reasonably representative of the zone; (4) determining if the well pair is separated by average field spacing; and (5) establishing geological markers fi'om well logs for the wells. These markers should be correlatable not only between the well pair, but to the majority of other wells in the reservoir. If not, then either another well pair having universal correlatable markers has to be selected, or this simulation approach possibly is not applicable to the reservoir. Task 3-Perform interwell stochastic interpolation. In order to generate an interwell cross-sectional porosity-permeability map from the data sets, it is necessary to consider the following data preparations (Fig. 5-69B): (1) the property value distributions values have to exhibit a normal (Gaussian) distribution with mean zero and unit variance. If the distributions are skewed, they are transformed to normally-distributed variables before interpolation (Emanuel et al., 1989). After interpolation the distributions are transformed back to their skewed form; (2) the interpolation program starts with porosity and permeability well-log values for each of the two wells. Porosity and permeability values are selected on a foot-byfoot basis by the program for each well in the cross section and the intermediate values are generated using the fractal interpolation scheme. This process is accom-

373

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1 Fig. 5-69A. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA TASK 1 flow diagram presents the activities that define the steps necessary in the collection and the analysis of data for fractal statistical structure. Initial task in a fractal geostatistical-logic schema, which can be used to calculate the effect of waterflood, miscible gas injection, and infill drilling operations on reservoir performance.

plished by calculating the initial variance using the mean-square variation of values on a foot-by-foot basis between the wells. Emanuel et al. (1989) pointed out that this measures the scale of variations at the interwell distance. It is assumed that the value of H, derived from the well logs, applies to the reservoir. The interpolation equations reduce the magnitude of the variance through recursion according to a power law determined by the value of H. Emanuel et al.'s (1989) study provides an example of the interpolation equations for multiple iterations; and (3) the end results of Task 3 are porosity and permeability cross-section maps between the selected wells.

Task 4 - Develop finite-difference cross-sectional model. A vertical cross-sectional hybrid model has to be developed, which will represent interwell flow in the reservoir (Fig. 5-69C). The approach consists of: (1) Choosing the appropriate finite-difference schemes (explicit or implicit forms), creating a grid (block, lattice, or irregular pattern) having 2 0 - 100 blocks between

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Fig. 5-69B (continued). zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA TASKS 2 and 3 are shown in the flow diagram. Task 2 activities define the steps necessary to establish representative fluid property and flow data. Task 3 activities scope the stochastic interpolation procedure. Second and third tasks are part of a fractal geostatistical-logic schema, which can be used to calculate the effect of waterflood, miscible gas injection, and infill drilling operations on reservoir performance. the wells and testing the stability of the solution. Crichlow (1977) provides a good discussion on developing finite-difference models. (2) Creating a simulator model that is highly detailed in the vertical direction in order to represent measured log and/or core data as closely as possible (Emanuel et al., 1989). Simulation layers should be 1 - 2 ft ( 0 . 3 - 0.6 m) thick. The intent is to model heterogeneity near the same level of detail as that of the available data. (3) Setting the transverse (y) direction of the cross-section so it represents the shape of a stream channel. Emanuel et al. (1989) noted that this geometry is intended to model the transition from radial flow near the wellbore to more linear flow midway in the pattern. Additional discussion of finite-difference models was provided in Volume I by Dominguez et al. (1992). (4) The finite-difference model is run for the projected conditions. The results will correlate as fractional flow at the producer and average interwell saturation for each phase as a function of pore volumes injected. Task 5 - Develop Streamtube Map Model. The streamtube mapping approach can take the cross-sectional data and use it to estimate field-wide performance (Fig. 569D). The two-dimensional cross-sectional results and reservoir operating conditions are used as input to a streamtube program (or conformable mapping program) to account for pattern and areal confinement effects. Streamtube models can accurately calculate the positions of fluid banks (maintaining saturation discontinuities), thereby overcoming the effects of numerical dispersion. Emanuel et al. (1989) used a single-layer

376 I

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Fig. 5-69C. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA TASK 4 flow diagram presents the activities that define the steps necessary in the development of an appropriate finite-difference, cross-sectional model. Fourth task in the fractal geostatisticallogic schema, which can be used to calculate the effect of waterflood, miscible gas injection, and infill drilling operations on reservoir performance.

streamtube model, because the fractional flow generated by the cross-sectional simulation accounted for permeability distribution, layering and gravity override, and the model can accommodate large patterns. Streamtube maps, which are based on streamline networks, can be constructed according to Doyle and Wurl (1971): (1) Generate a streamline network having both the sides and axes of channels connecting to well pair(s) based on a combination of Darcy's law and the continuity equation for a homogeneous incompressible fluid where the effects of gravity can be

377 RUli MODEL EliD PROJECT

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Fig. 5-69D. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA TASK 5 flow diagram presents the activities that show the steps necessary in the use of a streamtube map model to forecast future reservoir performance. Final task in a fractal geostatistical-logic schema, which can be used to calculate the effect of waterflood, miscible gas injection, and infill drilling operations on reservoir performance.

378 neglected. Martin and Wegner (1979) expanded the approach to two-phase flow using the Buckley-Leverett theory to calculate the fluid displacement along streamlines. For details, Hewett and Behrens (1993) discussed the one-dimensional transport equation for multicomponent, multiphase flow in a porous medium and the applicable scaling laws in such a displacement process. Flow-diagrams for a streamline program, a shape-factor program, and Higgins-Leighton's waterflood program were presented by Doyle and Wurl (1971). The model used in Emanuel et al.'s (1989) study was more or less based on the streamtube model procedure discussed by Lake et al. (1981). (2) Map the fractional-flow solution onto each tube. The total mobility in each tube was determined by line integration as described by Martin and Wegner (1979). Emanuel et al. (1989) chose a timestep increment so that the injected volume is allocated among the streamtubes in proportion to tube mobility. The incremental pore volume injected for each tube is the injected volume divided by the tube's volume. The cumulative value of the injected pore volumes determines the fractional phases, such as oil, gas, water or solvent, comprising the employed recovery method. The gross fluid volume is equal to the incremental pore volume injected (Emanuel et al., 1989). The assumption is that the project is run on the basis of voidage balance between production and injection. (3) Check the model against known reservoir performance by adjusting the gross fluid voidage to the history value. (4) Repeat the calculation for each tube. Summation of all the contributions from the tubes results in the flow of each phase for each well at a given timestep (Emanuel et al., 1989). (5) Impose a planned injection rate to forecast future performance. Emanuel et al.'s (1989) above-described scale-up model is generally limited to: (1) waterflood or miscible gas injection, (2) injection/production voidage balance, and (3) Negligible pressure depletion. Hewett and Behrens (1991) pointed out that streamtube methods are not suitable for modeling primary depletion, because they are based on incompressible flow. A suggested addition of infill drilling to the overall schema (Figs. 5-69A- D) was made to show how fractal-generated interwell distributions can be used in forecasting incremental recovery of by-passed oil during primary production operations. Hewett and Behrens (1993) reviewed some of the inherent limitations to Emanuel et al.'s (1989) model. They discussed the effects of length dependency of the dispersion coefficients derived from simulations of miscible displacements. Such a length dependence precludes the definition of an effective dispersion coefficient or the use of numerical dispersion to represent the effects of permeability heterogeneity on miscible displacements. Problems arise in the application of effective relative permeabilities that change along the flow path when scaled up. Hewett and Behrens (1993) pointed out that the problems are caused by the streamwise dependence of the effective relative permeabilities, some of which are initial conditions preceding the displacement, nature of the displacement (water displacing oil, etc.), gridblock size, the streamwise position of the block to which the effective relative permeability value is assigned, making their assignment to fixed grids difficult. As shown by the flow-diagrams (Figs. 5-69A- D), complications are introduced into the model by the requirement that there be some knowledge of the flow paths before the problem can be analyzed. Numerical dispersion effects have to be kept negligible by keeping the number of cells large enough so that all the areal paths must pass

379

through the same number of cells (Hewett and Behrens, 1993). Still, such models are better than older ones and show the direction of future simulations. zyxwvutsrqponmlkjihgfedcbaZYX

Applications of Fractal Models to Carbonate Reservoirs There have been several published accounts on the application of fractal models in predicting waterflooding and enhanced oil recoveries in carbonate rocks (Emanuel et al., 1989; Beier and Hardy, 1991). Emanuel et al.' s (1989) results will be discussed as case histories. The validity of the above-discussed simulation method was tested by modeling a total of twelve reservoirs having waterflood and miscible flood projects with measured performance. Four field cases, having comparable results with the other reservoirs, were selected by Emanuel et al. (1989) for presentation. Reservoir fluid properties and model configurations are given for the four cases in Table 5-XXI. Of the four presented cases, only Quarantine Bay is a sandstone reservoir and is included in Table 5-XXI for comparison. Reef reservoir: CO 2pilot flood case history. An 800-acre (323-ha) CO 2 pilot flood in a high-water-cut carbonate reservoir, which is part of a Permian limestone reef complex, was used in Emanuel et al.'s (1989) validation study. Location of the limestone reef reservoir was not given, but it is probably either in west Texas or eastern New Mexico, U.S.A. The pilot flood involved between 40 and 50 wells. Figure 5-70 shows comparisons between reported and predicted oil and CO 2 production rates. The match between the predicted and actual oil production rate is reasonable. No adjustment was made to the geological data to match history. Emanuel et al. (1989) stated that discrepancy in the early oil production rates is partly a result of TABLE 5-XXI Reservoir properties and model dimensions for four field cases studied by Emanuel et al. (1989). Three of the fields are carbonate reservoirs, whereas Quarantine Bay is a sandstone reservoir Data for reservoir models

Grid dimensions nx n Y n_. Pressure, psi Temperature, ~ API gravity, ~ Oil FVF Solution GOR, scf/bbl Oil viscosity, cP k/k H

Model thickness (z direction), ft Model lengths (x direction), ft

Quarantine Bay

Carbonate CO 2 pilot

Waterflood test

Little Knife

100 1 40 3450 183 33 1.22 435 1.15 1.0 40 800

43 1 84 2500 130 40 1.5 1000 0.5 0.65 168 1800

43 1 84 500 85 32 1.14 320 2.7 1.0 84 1011

129 1 30 3500 245 33 1.68 1093 0.27 0.01 - 1.0 30 258

S o u r c e : After Emanuel et al., 1989, table 1" reprinted with the permission of the Society of Petroleum

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treating all wells used in the model as coming on at the project's start and that they deliver fluid at a constant average rate. Inherent to all production operations, there are going to be some of the wells shut-in from time to time and fluctuations in the fluid production rates. The average gross fluid injection/production in total reservoir barrels per day for each well, the injection volume of CO 2, and the injection water comprised the historical data used in the model. The streamtube model for the project is given in Fig. 5-71. Model and reservoir fluid data are presented in Table 5-XXI. zyxwvutsrqponmlk

Dolomite reservoir: waterflood case history. A mature waterflood in a large carbonate reservoir composed of a thick sequence of dolomites and siltstones of Permian age was evaluated using the fractal model. The probable location of this reservoir is west Texas. A selected section of the reservoir was chosen consisting of six inverted nine-spots covering about 250 acres (101 ha). Emanuel et al. (1989) used an 86 x 43-cell cross-sectional model to represent the interwell geology. The model consisted of an injector and producer spaced 1,000 ft (305 m) apart. Porosity and permeability values were interpolated from core data measured at one-foot intervals through the reservoir. Cell dimensions were 2 x 23.25 ft (0.6 x 7 m), with the y dimension shaped to conform to a streamtube (Emanuel et al., 1989). Figure 5-72 shows the total project response of cumulative oil with time and water cut. The cross-sectional simulation used average water injection rates over a 20-year period. Predicted and field data match closely without any adjustment of geological data (Emanuel et al., 1989).

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Little Knife field: CO: (WAG) minitest case history Emanuel et al. (1989) undertook this study to test the ability of the fractal distribution to predict a detailed measurement of the vertical saturation distribution. The test interval was in the Little Knife Field, located near the central part of the Williston Basin in Billings, Dunn and McKenzie counties, North Dakota, U.S.A. Production is from the Mississippian Mission Canyon Formation and is the middle member of the Madison Group (Desch et al., 1984). The formation: (1) is about 465 ft (142 m) thick, (2) the top of the formation is at an average depth of 9650 ft (2,941 m), (3) has porosity ranging from 8.5 to 27% and averaging 14% in the dolomitic zones,

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Fig. 5-72. A comparison between the reported field data and predicted values of water cut (%) and cumulative oil production rate for a mature waterflood in a dolomite reservoir. (After Emanuel et al., 1989, fig. 12; reprinted with the permission of the Society of Petroleum Engineers.)

383 (4) has permeability ranging from 1.0 to about 167 mD (0.000987- 0.165 ~tm2), and (5) has been subdivided into six informal zones defining a shallowing upward carbonate to anhydrite sequence. The zones are from top down: A - anhydrite, B - dolomitized packstone/wackestone, C - dolomitized wackestone, D - dolomitized wackestone, E dolomitized wackestone, and F - limestone (Lindsay and Kendall, 1985). Zones B, C, and D compose the reservoir. The original reservoir was undersaturated and had no free-gas-cap drive. Its drive mechanism is solution gas-drive with a limited edgewater drive (Desch et al., 1984). The reservoir has not been extensively waterflooded. The CO 2 non-producing minitest involved four wells drilled in an inverted fourspot configuration covering 5 acres (2 ha) with a radius of 250 ft (76 m) (Fig. 5-73), plus another well (ZAB OBS #4) drilled for pressure cores (Desch et al., 1984). The cores were used to measure oil saturation values, which in turn, were compared to calculated well-log saturation values. The central well (ZAB INJ #1) served as the injection well and remaining four wells served as non-producing observation wells. ZAB. ORS. o l

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Fig. 5-73. A fence diagram of zones C and D of the Mission Canyon Formation (Madison Group) through the WAG (water alternating with gas) minitest wells located in the Little Knife Field, North Dakota, U.S.A. (After Desch et al., 1984, fig. 5; reprinted with the permission of the Society of Petroleum Engineers.)

384

All observation wells were in good fluid communication with the injection well. The test consisted of a water-alternating-gas (WAG) type injection sequence with five alternating slugs of formation water and CO 2 into a 31 ft (9.4 m)-thick interval composed of lower basal C beds and upper D beds. Emanuel et al. (1989) revealed that the interval is characterized by persistent high permeability values of about 1 Darcy near its center, and diminishing to near zero at interval top and bottom. Desch et al. (1984) reported that the minitest was designed to provide the following information: (1) reduction in oil saturation due to water injection, (2) reduction in waterflood residual oil saturation due to alternate WAG, (3) extent of gravity segregation, (4) effect of stratification and crossflow, and (5) influence of reservoir heterogeneity. A numerical, three-dimensional, three-phase multicomponent compositional simulation provided a satisfactory history match of the pressures, saturations, and fluid compositions observed throughout the test. Vertical sweep by CO 2 was incomplete owing to stratification and the possible occurrence of viscous fingers; however, it was about 52%. The minitest's pattern sweep efficiency for CO 2 approached 52% of the original oil-in-place at the start of the project as compared to 37% for the waterflood (Desch et al., 1984). Emanuel et al.'s (1989) model consisted of a cross-section 250 ft (76 m) in length and 30 ft (9 m) in gross thickness. The cross-section distance is the same as the distance between the injection well and the observation well ZAB OBS No. 2 (Fig. 573). An H value of 0.65 was used in the simulation; however, cross-sectional permeability maps were generated for H values between 0.65 and 0.85. Emanuel et al. (1989) stated that these are typical values for reservoirs, which they have studied to date. The fractal permeability distribution for this zone is shown in Fig. 5-74. The predicted saturation minimum is about 3 ft (1 m) higher in the cross-section than that observed from the well logs. Vertical permeability values are much lower than the ratio from 1" 1 to horizontal ones. Measured core permeability showed a range of kh/k zyxwvutsrqponmlkjihgfedcbaZYXWVU 100:1 (Emanuel et al., 1989). The oil saturation profiles for ZAB OBS well No. 2 are matched with the fractal model's predicted profile (Fig. 5-75). The conclusion to this exercise was that the fractal model can represent the general trend of fluid movement; however, an exact match lies beyond the certainty of the available data in most instances (Emanuel et al., 1989).

Reservoir modelingprognosis As demonstrated, fractal interpolation methods using well-log and core data from carbonate reservoirs yield a new and effective means for handling reservoir heterogeneity in simulation studies. This technique has carried heterogeneity descriptions just beyond the verbal, qualitative stage of analysis. New modifications and approaches, which are appearing frequently in the literature suggest, however, that future quantitative refinement is possible. Araktingi et al. (1993) described a menu-driven workstation application program, GEOLITH, designed to analyze reservoir data and construct reservoir simulation models with a geostatistical approach. Numerical input from well logs, core analyses, and seismic data are used to construct realistic quantitative geological reservoir models that calculate the spatial distribution of reservoir flow properties. The GEOLITH program addresses Tasks 1 through 4 (Fig. 5-69A to C).

zyxwvutsrqponm zyxwvu HORIZONTAL

I--

1"-3 Above 600 mD

l

~

Below I.OmD

PERMEABILITY

MAP

3O

I,,1_25

(n'zo (/)15 LI.I Zlo

"1- ,3 0 I--

?_C

40

60

80

INJECTOR-

I O0

12 0

PRODUCER

i 40

160

180

200

220

240

DISTANCE, FT

Fig. 5-74. Cross-sectional map of horizontal permeability between the injection well and observation well No. 2 in the Little Knife Field, North Dakota, U.S.A. (After Emanuel et al., 1989, fig. 13; reprinted with the permission of the Society of Petroleum Engineers.)

OO

386 9845

S a t u r a t e d 011 Base Case 9850

. _ _ _ . . . S a t u r a t e d 011 Observed ......

Simulation

Top of Permeable Zone 9855

"

~

0

/ o

9 e

,(.

/./.9860

e

9

./..I. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA //"... 9

9865

",.

o\~

9870 Bottom

of

~'~~

Permeable Zone 9875 0

I .2

J .4

I .6

I .8

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I

Oil S a t u r a t l o n Fig. 5-75. A comparison between simulated and observed oil saturation values in observation well No. 2, Little Knife Field, North Dakota, U.S.A. (After Emanuel et al., 1989, fig. 14; reprinted with the permission of the Society of Petroleum Engineers.)

387

Beier and Hardy (1991) made a comparison between fractional Gaussian noise zyxwvutsrqpo fractional Brownian motion (fBm) in the generation of interwell distributions of reservoir properties as determined from well logs. As was previously discussed, Hewett (1986) reasoned that the fractal structure found in porosity well logs is fGn. Hewett (1986), however, postulated that the horizontal properties have a different spectral distribution, which is described by fBm. Well spacing is normally too large to determine the statistical structure in the horizontal distance. Hardy (1991) proposed an unique solution to this problem by analyzing the horizontal structure of sedimentary layers using distributions of dark and light regions from photographs of cores and outcrops. He found that the horizontal traces could be characterized as fGn. A comparison between the fGn and fBm methods was made using a carbonate reservoir located in southwestern New Mexico, U.S.A. This unnamed reservoir was undergoing a mature waterflood in the Permian Grayburg and San Andres dolomitic pay zones. Appropriate cross-sections using the field spacing of 20 acres (8 ha) were generated for both fGn and fBm. Performance data were calculated using a hybrid finite difference-streamtube model. Results showed that both methods matched field water cut data. The initial water saturation was the only property adjusted to obtain the match, and was made owing to initial water production from transition zones. The study revealed that the fGn distributions have lower effective permeabilities (linear flow) than thefBm distributions (Beier and Hardy, 1991). The fractals infGn are also known by the term 'fat' fractals. There were, however, only slight differences between the resulting cumulative oil vs. cumulative injection curves of the two methods. They conjectured that as the well spacing increases the simple linear interpolation and fBm will become poorer representations for reservoir heterogeneity. One interesting approach involving streamlines is conformable mapping (complex variables), which can be applied to the analysis of compressible fluids and transient behavior. A region of the reservoir or a region(s) around a well or wells can be mapped onto a conformable rectangle. The appropriate numerical analyses are then performed and transformed back to the region's original configuration. The application of conformable mapping principles to streamlines defining transient flow was discussed by Hurst (1981, 1982). Hewett and Behrens (1993) suggested that any difficulties associated with the above practical application of effective flow properties in Emanuel et al.'s (1989) model were due to their definition in an Eulerian framework. In such a framework, properties are distributed in space without regard to fluid flow paths or travel distances of fluid fronts. A Lagrangian framework, however, permits flow fronts to carry the appropriate flow properties with them, and the motion of displacing fronts is modeled explicitly. The integrated total mobility and phase fractional-flow distributions are scaled and mapped directly onto areal streamlines. The solution preserves the streamwise dependence observed in the cross-section simulation, and no new errors enter into the simulation owing to the definition of a grid. It was emphasized by Hewett and Behrens (1993) that the areal flow paths are determined by solving the streamlines corresponding to a unit mobility ratio displacement with the well rates and areal permeability thickness distribution of the reservoir. As with all new approaches there is a new set of restrictions.

(fGn) and

388 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

It was shown in this section that permeability values for macroscopic simulation modeling are either obtained by simple arithmetic, geometric or harmonic averages over the microscopic values, or by using advanced techniques such as perturbation expansions. None of these are valid when the distribution of local permeabilities is very wide, or when the distribution contains strong correlations. As mentioned above by Hewett and Behrens (1993), the effects of spatial anisotropies on permeability have not been addressed in detail. Another way to account for permeability values assigned to grid blocks was proposed by Aharony et al. (1991). Their approach involved a simple renormalization group scheme (method), which they termed FRACTAM. The term stands for fast renormalization (scale-up) algorithm for correlated transport in anisotropic media. The algorithm is based on real space renormalization group approach first used for the percolation bond probability (King, 1989; Aharony et al., 1991). Korvin (1992, p. 21) provides an excellent discussion on percolation theory. The idea is taken from statistical physics and is used to described the build-up of clusters to form an infinite cluster. In this section we refer to the build-up (percolate the lattice) being the construction of a connected porous network. Percolation threshold is defined (in the case of a porous network) as the point where a critical porosity and pore interconnectedness exist and fluids can flow through the pores. Below the threshold the pore system is 1

A

4 Ib

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.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

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.

.

.

9 9

........ ,

9

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.

.

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i

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Fig. 5-76. FRACTAM scheme showing how the upper left lattice is renormalized into the upper right one. Bonds 1,2, 3, 4 and 5, as shown below the lattice, are equivalent to the triangular graph and are used to determine the permeability value of the renormalized bond A. The permeability value of bond B is found similarly, from the original permeabilities of bonds 2, 3, 6, 7, and 8. (After Aharony et al., 1991, fig. 2; courtesy of Elsevier Science Publishers B.V.)

389

ineffective. Practically speaking, it is the point at which a rock is either permeable or essentially impermeable. A random resistor network can be used to describe the scaling-up of permeabilities as shown in Fig. 5-76. Here the permeability of bond A is determined by those of bonds 1, 2, 3, 4, and 5 by employing the Wheatstone bridge analogy. The permeability of bond B is found similarly, from the original permeabilities of bonds 2, 3, 6, 7, and 8. Aharony et al. (1991) then iterated FRACTAM for each of the specific squares until they were left with two effective permeability "tubes", one in the x- and one in the y-directions. Comparisons were made with "true" permeability values obtained from digitized core sample images and with generated fractal forgeries of core images. The authors found that FRACTAM was accurate to within less than 5% in all cases. Thorough background discussions on macro- and micro-scaled network models are given by Moore (1952), Fatt (1956a; 1956b; 1956c), and Rose (1957). Real space renormalization application will be discussed near the end of this section. The above deliberations reinforce the premise that oil and gas recovery applications rely on the functional relationship between the volume-average parameters described by Darcy's law and the microscopic processes occurring at the pore scale. Discussion will now focus with some detail on the numerical relations between porosity, permeability, and electrical conductivity. It is these transforms that control the input of permeability values into the macroscopic scale simulation models of carbonate reservoirs. zyxwvutsrqponmlkjihgfed

Microscopic heterogeneity: permeability- conductivity- porosity relationships Obtaining information on fluid flow properties inside carbonate oil reservoirs is complicated by high variability of permeability values. As pointed out previously in this chapter, one can observe intermittent variations of the absolute permeability over several orders of magnitude at a given scale, such as the core length scale. The permeability variations occur over a wide range of scales from microscopic to megascopic. Saucier (1992) emphasized that forecasting difficulties arise from the fact that the three-dimensional structure of the permeability field remains poorly defined due to the lack of information that comes from rather sparsely drilled wells. Geology and seismic data provide only poor guidelines about heterogeneity size, stratification, and fine-scaled structures. Theoretical, statistical, and empirical correlations among porosity, permeability, surface area, pore size, irreducible water saturation, and conductivity (resistivity) were discussed by Chilingarian et al. (1992c: Volume I, Chapter 7). Mathematical relationships were described based on capillary tube models and include the following factors: pore shape, tortuosity, electrical resistivity of rocks and fluids, sonic speed, and scaling. It should be remembered, however, that as any thin-section of a sedimentary rock would show, the pore space is connected in a complicated and random manner by pore throats.

Scaling exponents Unfortunately, permeability and porosity values do not closely track each other when rock samples are taken from carbonate formations having different geological histories. This is demonstrated by different samples with the same porosity values

390 exhibiting a wide range in permeability and conductivity values, especially due to fracturing. Chilingar (1964) demonstrated a reasonable correlation between porosity and permeability of cores, by considering the effect of irreducible fluid saturations, using the concept of effective porosity, ~be, which has a different physical meaning in contrast to the modeling effective properties just discussed. Effective porosity was defined by Chilingar (1964) as the fluid-saturated pore volume minus irreducible fluidsaturated volume. By taking into account specific surface area, which incorporates the influence of fractures, and irreducible fluid saturation, Chilingarian et al. (1992c) developed an excellent correlation between permeability and porosity. The differentiation of fluid flow properties inside carbonate reservoirs is complicated by the high variability of the permeability field. Two empirical equations are used generally by petroleum engineers and geologists to define the relationship between permeability and conductivity using porosity values. These empirical relationships are justified by the non-intersecting tube models of the pore space. The scaling law for permeability, k, and porosity, ~b, is: k =

(s-52)

where m is the slope of the line from a log-log plot of permeability vs. porosity. Theoretically, Eq. 5-52 follows from different capillary tube models as described by Chilingarian et al. (1992c), and cellular automata involving lattice gas hydrodynamic simulation models described by Chen et al. (1991). The cellular automata approach can be described, in a physics context, as a class of mathematical systems characterized by discreteness in space, time and state values, determinism, and local interaction. The empirical equation (Archie's formula) relating electrical rock conductivity, G, and porosity is: zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA (5-53)

G = aGwd~ m" ,

where a is an empirical parameter that varies with the lithology of the formation. It is generally assumed that a is unity. The conductivity of the pore water is Gw, and m^ is an exponent, which is defined by log-log plots of rock conductivity vs. porosity. Wong et al. (1984) mentioned that the power-law dependence in Eq. 5-53 resembles the behavior in the usual percolation problem, except that it suggests a conduction threshold at ~b= 0. According to Wong et al. (1984), the exponents m and mn are related as follows: m = mn(m n +

1),

(5-54)

for one-dimension, and m = 2m ^,

(5-55)

for higher dimensions. The relations used by well-log analysts to quantitatively obtain permeability values from porosity take two forms. Timur (1973) proposed the following equation, which is a variation of the Schlumberger empirical formula:

391

k=0.136

IO 44~1 kSwi~r2

,

(5-56)

where S i r r is the irreducible water saturation. The weakness of Eq. 5-56 is that k is dependent on 4.4th power of porosity and the second power of the irreducible water saturation. The determination of ~band S i r r values from well logs will most certainly be in error by a small amount. These errors will be magnified by being raised to the second and 4.4th powers, and can become large depending on the size of the error up to one order of magnitude. Also, Eq. 5-56 suggests that the pore space is connected at any finite porosity. Wyllie and Rose's (1950) empirical equation was derived from a plot of their "rock cb/k ~ and irreducible water saturation, S~rr" textural" function zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

(5-57) wirr

where c is a constant that must have the dimensions of a length, and c A is a dimensionless constant. For a clean sand c A = 0. This equation, however, has no theoretical basis. In addition, there is a wide scatter of data points in their abovementioned plot of ~ / k ~ vs. S~rr (Wyllie and Rose, 1950; see fig. 7, p. 115 and eq. 18, p. 116). An empirical equation was developed by Chilingar et al. (1963) relating surface area per unit of pore volume, S , cm2/cm3; porosity, ~b, fractional; permeability, k, mD; and formation resistivity factoPr, F (- Ro/R w, where R ~ is the electrical resistivity of formation 100% saturated with formation water andR wis the formation water resistivity): S = 2.11 • 105/(F22~"2k) ~ . P

(5-58)

This utilitarian equation deserves attention, because the formation resistivity factor embodies the effects of grain size, grain shape, grain size distribution, and grain packing. Fractal relations between internal surface area, porosity, and permeability are discussed in the section on multifractal analysis of porous media. Using all these equations poses a problem with the spatial distributions of porosity and permeability. Very little is known about the macroscopic permeability distributions in reservoirs. As shown by the previously discussed fractal simulation models, microscopic permeability distributions have to be scaled-up. In non-fractal reservoir performance models, "history matching" is used to attempt to correct the wrong assumptions. McCauley (1992) stated that geologists sometimes assume that the distribution of permeability transverse to direction of average fluid flow within the layer has a zero correlation length. The distribution of permeabilities parallel to this average flow direction has an infinite correlation length. The assumption of a log-normal distribution is in conflict with the assumption of an infinite correlation length (McCauley, 1992). The end results of simulation efforts are unrealistic predictions for the long-range performance of a carbonate reservoir.

392

Several investigators (King, 1989; Aharony et al., 1991; McCauley, 1992) pointed out that models of fluid flow through porous rocks, both on the microscale and macroscale, typically are equivalent to resistor networks. The scaling laws expressed by Eqs. 5-52 and 5-53, however, are in conflict with measured data for permeability and electrical conductivity. Comprehending this conflict will help us to delineate the geometry of the pore-space in carbonate reservoirs. At best, only a cursory review of this very complex problem can be given in this book. The reader will be exposed to various proposed mathematical approaches that accommodate pore-system heterogeneity. Starting with McCauley's (1992) approach using two simple models, one fractal-no disorder (Sierpinski carpet model) and the other nonfractal-disordered (bond-shrinkage model) are discussed here. It will be shown that these models follow zyxwvutsrqpo

:,

i

t

X

t.

_,

I

ry

Fig. 5-77. Parallel tube model constructed from Sierpinski carpets with b = 3 and L = 1. The area is b 2 subsquares, and L 2 of these subsquares are subdivided into four squares; each square is divided into zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIH removed in the center of the initial squares. The reader is referred to Eqs. 5-11 and 5- 12. The lattice shown is at the second construction stage (see Fig. 5-22). (After Adler, 1986, fig. 1; reprinted with the permission of the American Institute of Physics.)

393 from a more general model. Both models do not include the idea of pore-space connectivity and, therefore, they do not explain on their own the difference between measured conductivity and permeability data. The general fractal--disordered (composite) model developed by McCauley (1992) includes connectivity, and qualitatively explains the experimentally known non-universal scaling exponents for permeability and conductivity. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

Sierpinski carpet (parallel tubes) model. Adler's (1986) three-dimensional, fractal transverse pore-space model is based upon the geometry of the regular Sierpinski carpet constructed from parallel square cylinders (Figs. 5-77 and 5-22). In his analysis, McCauley (1992) compared a tube network model (parallel resistor network) with Adler's Sierpinski carpet model to show that the conductivity exponent m^ is completely wrong as predicted by both approaches. Parallel tube models, however, can be made to fit known permeability measurements. The tube model can be represented by an octal tree (Adler's tube model and tree models are approximately the same), where the parallel resistors are equivalent to the parallel tubes (Fig. 5-78) (McCauley, 1992). The tube equation for the effective permeability, k~, is: (5-59)

kff ~ 2nL4n '

where n is the number of generations on the tree (there are 2" branches in generation n); and L is the length of the side of a square tube so that the electrical conductivity, G 12, and the local permeability k z L 4. The volume flow rate through a pore is defined

(a) zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA (b)

Fig. 5-78. Resistor network models. ( A ) - Binary tree model exhibited for n = 3 generations. The third generation represents the smallest pore sizes. ( B ) - Octal tree model having 2" resistors in parallel equivalent to 2" tubes in parallel. The tree model of-A- reduces approximately to this case when the smallest pores (generation with the largest n) have lengths that are very large compared with those of the pores in the first n - 1 generations. (Modified after McCauley, 1992, figs. 3b and 5; courtesy of Elsevier Science Publishers B.V.)

394 as the local permeability times the local pressure gradient; therefore, k is analogous to G. Both obey the same laws of combination for the calculation of effective permeability (McCauley, 1992). The laws are: G ~ = G l + G2

(5-60)

for two tubes in series and, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA G ff= G I G 2 / ( G 1 +

G2)

(5-61)

for two tubes in parallel. If the model is built upon the assumption that the length of each tube segment is roughly the same for all tubes on the tree, then the electrical conductance for the tube model for large n is: Gelf ~ 2"L.2,

(5-62)

For a large n, the last generation of tubes dominate, which are the smallest pores and the same is true of the effective permeability given by Eq. 5-59. McCauley (1992) showed that the conductivity exponent, m 6 is" mA=(2-Do)/D

o,

(5-63)

where D o is the fractal dimension and the permeability exponent, m, is" m = (4 - D o ) / D ~ ,

(5-64)

where D o < 2 for both equations. For small sandstone samples, it is known that m ^ 3/2 ~ 1.5 (from the iterated dilute limit model of Sen et al., 1981) and m ~ 15/2 ~ 7.5 as an average, whereas for carbonates m A values range from 1.6 to as high as 2.8 (de Witte, 1972; Wong et al., 1984). McCauley (1992) suggested that for any model to be reasonably correct, the orders of magnitude of these numbers should at least be reproduced using Eqs. 5-63 and 5-64. As one can see, these numbers cannot be reproduced by the tree model. Adler's (1986) model gives the resulting conductivity exponent, m A = 1, inasmuch as G ~ = ~, and the permeability exponent, m, is: m = (4 - Do)/(2 - Do),

(5-65)

which can reproduce m ~ 15/2 ~ 7.5 for sandstones; however, it is impossible to reproduce the required conductivity exponent m A values in the range of 1.5 - 2.8 for sandstones and carbonates. McCauley (1992) observed that Adler did not compute the permeability for successive stages of construction of a Sierpinski carpet. Adler computed permeability for 23~ separate tubes in parallel with each other rather than 2 ~, because the Sierpinski carpet is organized onto an octal tree. The effective permeability, when an octal tree is taken, becomes:

395 kff ~ 23nL4. ,

(5-66)

and the pore-space area is equal to: ~b = Geff= 23"L 2. ,

(5-67)

which is the pore-space area of the 23n smallest pores connected in parallel, analogous to Fig. 5-78. The above suffer from the fatal defect that ~b= Geff; therefore, m ^ = 1. This conclusion is in strong disagreement with experimental results (McCauley, 1992). It should be noted that in the tree and Adler's models, only the cross-sectional area of the pore space is distributed fractally. McCauley (1992) has argued successfully that the conductivity exponent m 6 is completely wrong, as is predicted by both the tube and the Sierpinski carpet models. Models portraying tubes that are all merely mutually parallel did not remedy this problem. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJI Bond-shrinkage model. Wong et al.'s (1984) nonfractal model focused on the variation of pore space with porosity. It describes how pore-size distribution can influence the conductivity and permeability of brine-saturated rocks. The electrical conductivity is simulated by a random resistance network with a zero percolation threshold, which occurs at ~b= 0, and where all the resistors are in series. The rock model consists of a single, long pipe that is made by combining many tubes having different diameters (Fig. 5-79) (McCauley, 1992). Each tube segment has an area L 2, in series, and k ~ L 4. Porosity is varied by a random bond-shrinkage mechanism. Wong et al. (1984) used a binomial distribution of the different elements connected in series with each other in a one-dimensional model. To calculate porosity, the probability, p, for any particular tube to shrink n times is given by the binomial distribution"

= [1 + p ( L 2 - 1)] u ,

(5-68)

where is the average pore-space area over the network, and N is the different possible diameters for a section of pipe, each with the same length L i. McCauley (1992) showed that the electrical conductivity scaling exponent is: m^ = a 2 > 1 ,

(5-69)

forp ~ 1, and Eq. 5-69 yields m^--+ 1 asp ~ 1. Derivation of Eq. 5-69 is based on the fact that the inverse conductivity is additive for resistors connected in series. McCauley (1992) pointed out that this bond-shrinkage model was originally introduced from the qualitative standpoint of percolation theory to model the zero-percolation threshold. The probability that a section of tube is shrunken n times by the factor L = 1/a (L m = a -m) from unit radius to form a section with radius L m is pm, and (1 __p)N-m is the probability to find a segment of pipe of unit radius as described by the bond shrinkage model (McCauley, 1992). The bond shrinkage model was originally introduced by Wong et al. (1984) to model the zero-percolation threshold. Hence, with P(m ^) = pm^(1 --p)N-m^N! / m ^ ! ( N - m6)! resulted in Eq. 5-68.

396

L

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

Fig. 5-79. Disordered, nonfractal, one-dimensional model based upon tubes of different cross-sectional area in series. (After McCauley, 1992, fig. 11" courtesy of Elsevier Science Publishers B.V.) As indicated the shrinking procedure can be repeated indefinitely with the same L to reduce the network conductance and permeability, and the total volume of the tubes. The effective permeability for this binomial distribution is equal to" -1

kfr = [1 + zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA p(L -4 - 1)]N,

(5-70)

and m--

ln[1 + p ( L -~- 1)]

(5-71)

ln[1 + p ( L ~ - 1)] Whenever, p ~ 1, m = m^(m ^ + 1) > 2m ^, whereas m ~ 2, ifp --~ 1, which corresponds to a long pipe with constant diameter in Fig. 5-79 (McCauley, 1992). An a, o r p and a, can be chosen to fit m ^ z 3/2, but it is then impossible to obtain m ~ 15/2 as is suggested for sandstone. The predicted scaling exponent for the effective permeability is too small, which means that the fluid flows too easily (a too high permeability) through the pore-space of the bond-shrinkage rock model (McCauley, 1992).

397

.-,,...%,\\,~

,'N\\\\" ~. \ \ \ \ \ \ \

~ \\\" \

Fig. 5-80. Schematic ofMcCauley's (1992) combined model that is fractal and disordered. The model is a generalization of the model shown in Fig. 5-79 to include complete binary connectivity. The generalization to models with complete trees with order t = 3,4,5 . . . . is obvious. This new model reduces to the model presented in Fig. 5-78B where t = 2, whenever p approaches unity, but also reduces to the disordered, nonfractal one-dimensional model for the special case where t = 1. (After McCauley, 1992, fig. 12; courtesy of Elsevier Science Publishers B.V.) zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDC

Composite model. McCauley (1992) proposed that a rock model can be constructed by combining Wong et al.'s (1984) and Adler's (1986) models into a composite model having equations based on a single-scale fractal. This model would then be extended by McCauley (1992) to a general model based on multiscale fractal. The composite model corresponds to a simple parallel/series network of resistors where there is variation in both porosity and the number of pores from one thin-section to another (Fig. 5-80). The "thin-section" concept (McCauley used the term toy rock) is derived by taking multiple thin slices of a theoretical rock and stacking them so that the sections correspond to the above network. McCauley (1992) generalized results, which correspond to the binary organization of Fig. 5-80, yielding in the following relationships for porosity, permeability, and conductivity: = [1 + p(2L 2 - 1)] N,

(5-72)

398 -1

Gear = [1 + zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA p ( 2 - ' L -2 - 1)] N

(5-73)

and -1

k e~ = [1 + p ( 2 - ' L -4 - 1)]u.

(5-74)

From these equations, the composite model gives the following equations for conductivity and permeability, respectively: ln[1 + p(2-'L -2 - 1)] m^ =

(5-75)

ln[1 + p(ZL 2 - 1)]

and ln[1 + p ( 2 - ' L --4 - 1)] m=-

ln[1 + p ( Z L 2 - 1)]

,

(5-76)

Wong et al.'s (1984) exponent equations are obtained when p ~ 1 for electrical conductivity and permeability, respectively: m ^ ~ 89 2,

(5-77)

and

a2(89 4 - 1) m~

( a 2 - 2)

,

(5-78)

McCauley (1992, p. 43) showed that the limit p --~ 1 yields the parallel tube [or Adler (1986)-1ike Sierpinski carpet model] results: m ^ = 1, and m = ( 4 - D o ) / ( 2 - D o ) , where D o = ln2/lna (ln is the natural log). If a is set equal to 2, then m ^ = 2 and m~ m 6 - 7 from Eqs. 5-77 and 5-78 (McCauley, 1992). These results are very reasonable. In order to obtain an m ^ value of 2.5, p can be kept small and a increased in Eqs. 5-75 and 5-76. Also p and a can be varied. Manipulation of the values can be made to get m ^ = 1.4 by holding a constant and increasing p, because m ^ = 1 when p = 1. McCauley (1992) showed how to get larger values of the permeability exponent for a given value of conductivity exponent. He introduced connectivity (branching) of a complete binary tree. There is a limit in the composite model, as there was in Wong et al.'s (1984) model, where both the porosity and permeability are log-normally distributed (see McCauley, 1992, p. 44). By generalizing Eqs. 5-72 to 5-76 to a complete tree or order t, McCauley (1992) simply replaced the tree order of 2 by t, where t can take on values of 1, 2, 3 , . . . . resulting in m ^ and m exponents in the log-normal limit:

399 1 + [(1-p)/2](4-Do)lna m^ ~

(5-79) 1 - [(1 - p ) / 2 ] ( 2 - Do)lna

and zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

m/m ^ ~, (4 - Do)/(2 - Do).

(5-80)

Multifractal rock model. McCauley (1992) stated that the log-normal limit correctly reproduced the trivial limit of parallel tubes, where p = 1. Ifp is small, then the limit cannot be reproduced in the log-normal approximation. McCauley (1992, p.45) then discussed treating Eqs. 5-72 to 5-80, which are based upon a single-scale fractal, as a multiscale or nonuniform fractal. The transverse thin-sections of pore space o f the simplest multiscale fractal are a two-scale fractal. The reader is referred to the discussion on multifractal characterization later in this chapter. McCauley (1990) and Ijjasz-Vasquex et al. (1992) provided a complete background on multifractals and their applications in dynamic systems. The simplest case of a multifractal distribution of pore-space area can be envisioned where the porosity of a very thin slice of carbonate rock has a thickness that is small compared to the size of the largest pores, as being built by iterating two length scales L~ and L 2. McCauley (1992, p. 33) stated that in the first generation (n = 1) the scale L~ occurs b times, then L 2 occurs t - b times, where b is any integer between 0 and t - 1 and b = 0. Thus, for t" tubes connected in parallel, porosity and permeability are: = [tL 2, +

(5-81)

and G=

[bL 4 +

(5-82)

McCauley suggested that it is useful to introduce the canonical partition function, which is a generating function:

Z(fl) = [bl ~ + ( t - b)l~2 ]",

(5-83)

where g(fl) = - l n Z ( f l ) / n is analogous to the Gibbs potential per particle because n is analogous to the number of particles in ordinary statistical mechanics. Models like Eq. 5-83 follow from deterministic chaos (McCauley, 1992, p. 34). McCauley's (1992) Eqs. 5-72 to 5-78 are based upon a single-scale fractal. If the transverse thin-sections of pore space are represented by a multiscale fractal, then McCauley's simplest case is that of the two-scale fractal shown by the above Eqs. 581 to 5-83. Equations 5-72 to 5-76 restated for two-scale fractal are: = [1 + p(e -g(2)-- 1)IN,

(5-84)

400 -1

Gfr = [ 1 + p(e g~2)- 1)]u,

(5-85)

-1 keff = [1 + p ( e -g(4) - 1)]N,

(5-86)

resulting in In[ 1 + p(e -~z) - 1)] m^ = -

(5-87)

In[ 1 + p(e ~2) - 1)]

and In[ 1 + p(e -g~4)- 1)] m=

In[ 1 + p(e g~2)- 1)]

.

(5-88)

The general model explains two important facts: (1) connectivity (branching) is the way to obtain a large zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA m / m ^ ratio with m^ > 1, and (2) nonuniversality of the scaling exponents m and m ^ results by varying both the first generation length scale L~ = 1/a and the probability p. McCauley's (1992) approach and interpretation were not based upon ideas from equilibrium statistical mechanics having attributes of universal critical exponents and formal percolation theory, but are based upon ideas from chaos theory. Chaos theory describes transport far from thermal equilibrium using trees, weak universality, multifractals, and nonuniversal scaling laws. McCauley concluded that in the dynamic model, the tree order describes how different thin-sections with different porosity values connect with each other. The very small diameter pore throats provide the connections between the pores, and typically require large scale magnification of a thin-section in order to be observed. McCauley speculated that a sufficiently accurate photograph of a thin-section, which reveals the smallest pore throats, would lead to a connectivity parameter t that agrees with what is needed to explain the transport exponents. Again, the writers observe that Teodorovich's (1943, 1949, 1958) ideas on the structure of carbonate rocks and his approach to calculate permeabilities from thin-sections of carbonate rocks gain additional support. McCauley (1992) suggested that microscale scaling laws for conductivity and permeability with experimentally known exponents m and m ^ should be used as a constraint to test models ofmacroscale permeability distributions. If a resistance network used to model a permeability distribution cannot reproduce the experimentally known exponents for the microscale reservoir, then it is unlikely that the model will be correct in predicting the performance or other properties of the macroscopic reservoir from which the rock and fluid samples were taken (McCauley, 1992). At this time, the real space renormalization group method employing resistance networks needs to be considered. This method is an effective scaling-up, numerical tool that greatly improves conventional carbonate reservoir performance modeling. Permeability renormalization is discussed and is an averaging process that replaces a large array of small-scale effective permeabilities with a smaller array of larger-scale effective permeabilities.

401

Turcotte (1992) defined renormalization as the transformation of a set of equations from one scale to another by a change of variables. Advantages in using renormalization are: (1) A cost-savings computational technique over previous techniques, which compared coarse-grid simulations with fine-grid simulations. Saucier (1992) recounted that even if all the permeability data were actually available for a reservoir, then a complete three-dimensional picture of the permeability field at a mesoscopic scale of resolution could exceed the capacity of existing super computers or else be prohibitively expensive to process. These data, at present, are rather sparsely known for a reservoir and are expensive to process. (2) Higher resolution of details on a much finer scale than finite difference techniques. (3) Accurate estimates of the pressure drop across a heterogeneous system for fluid flow in oil reservoirs. Finally, the real space renormalization group method will be used to calculate scaling exponents in multifractal porous media. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFED

Real space renormalization group method The requirement to use average (effective or pseudo) property values for grid blocks in reservoir simulation was previously discussed in this section. King (1989) discounted the use of both perturbation theory and effective medium theory (EMT) as effective techniques to replace an inhomogeneous medium by an effective homogeneous medium when property fluctuations, such as permeability, become very large. If the fluctuations are small, then the perturbation theory or EMT give reliable estimates of the effective property. With respect to perturbation theory, the problem lies in the fact that when the property variance is large the result is invalid. The assumption behind EMT is that the mean fluctuations in the pressure field are negligible and average to zero (King, 1989). In the case of permeability, as permeability fluctuations increase, however, pressure fluctuations do not increase and effective medium approximations break down. The position-space renormalization approach originated in physics and the seed of its origin is attributed to Kadanoff (1966). This method can produce fractal statistics and explicitly utilizes scale invariance. King (1989) proposed the use of realspace renormalization to calculate effective absolute permeability values in a h e t e r o g e n e o u s medium. By adopting this method, the effective absolute permeabilities are rescaled in order to utilize the same system at the next larger scale. Figure 5-81 illustrates the scaling-up methodology. The process is repeated using larger and larger scaled-grid blocks until the initial grid is reduced to a singlegrid block (single effective value) for a small localized region. This process is repeated by combining various localized regions into blocks and reducing them to a single effective value, thereby coarsening the grid. Block renormalization of the grid is repeated until the desired part, or the entirety, of the reservoir has been realized. Application. King (1968) and King et al. (1993) discussed the renormalization procedure in detail. They showed that the procedure for isotropic media can be extended

402 NO

ROW

No Row

.~

No Flow

.~

K

22

K

K

K

K

K

K

13

p

1

31 3

14

32

K

34

23

K

1

43

K

24

K

42

P 2

P 1

P 2

P 1

K

eft

P 2

K

44

Fig. 5-81. The real space renormalization method is illustrated in two dimensions for an initial 4 x 4 grid, which coarsens from left to right. Assuming an isotropic medium, the effective permeability (kff) is calculated in only one direction (horizontal). Horizontal boundaries represent impermeable barriers (no flow). Fluid flow occurs in the x-direction from left to right (pressure in (P~,) > pressure out (Pout))"

to three-dimensions and immiscible flow. Here, only single-phase flow is discussed using permeability as an example. First, the properties have to be distributed on a fine grid. The scale-length of the grid has to be representative of the original data sample size. For example, if the permeabilities are derived from core samples at one-foot intervals, then the initial grid blocks should have dimensions of one foot (King, 1989). The only required input is a permeability probability distribution. The permeability distributions to be averaged are taken from the sample distributions determined from cores. Initially, the renormalization method involves averaging over small regions of the reservoir to form a new averaged permeability distribution with a lower variance than the original distribution. This pre-averaging is then repeated until a stable estimate is found. King (1989) considered only uncorrelated media in his examples so that the permeabilities are randomly distributed. This was done by King to avoid the separate issue of handling correlated media. In order to treat correlated media one needs statistical methods for generating large grids of correlated variables. Once the permeability grid has been established, the same renormalization techniques can be used for correlated media. King (1989) organized the initial grid block into blocks of four in two dimensions (for three dimensions there are eight blocks initially). The effective permeability of the four blocks is calculated and assigned to a new, coarser grid composed of one block (Fig. 5-81). A coarse-grid reservoir model can represent all scales of heterogeneity associated with the reservoir, whereas a fine-grid model can represent only small to medium scale heterogeneities. King et al. (1993) pointed out that the accuracy of the final coarse-grid simulation is only as accurate as the fine-grid simulations used to derive the pseudo properties. One drawback to this procedure is that the results of the coarse-grid simulations cannot be checked as no fine-grid model can reproduce all scales of property variation. The resulting effective permeability is a single value retaining the same flow as the initial blocks and the original pressure drop (King, 1989). The process is repeated many times until a stable effective permeability is

403 zyxwvutsrqp

P 2

A

B

C

Fig. 5-82. Modeling block permeabilities by using an equivalent resistor network. (A) Resistor network showing each block with a cross of resistors. (B) Resistor network that is identically equal to (A). The end edges were set to a uniform pressure. (C) An equivalent resistor network created by trimming off the dead-end edges of the four blocks and joining together those nodes with the same pressure.

found for the area (volume) being investigated. The variance in the permeability and the correlation length in correlated media are reduced as the permeability approaches the value of the whole region. King's (1989, p. 43) procedure involves the development of probability distributions by Monte Carlo sampling. In this manner the permeability distribution on the old grid is transformed to obtain an approximate Gaussian probability distribution on the new grid. The next step is to calculate the effective permeability of the renormalized block. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFE

Calculation of renormalized permeabilities. King (1989) and King et al. (1993) described how to calculate the effective permeability of the renormalized block. The block permeabilities are modeled using an equivalent resistor network with the boundary condition that the external edges of the blocks are at uniform pressure (Fig. 5-82). This is not true, however, for the internal edges, and is a source of error if the permeabilities are arranged in particular configurations (King, 1989). Such configurations are rare events, and even under those situations, the error is small. The permeability field can be estimated by using a resistor network, where each block is replaced by a resistor cross. The blocks of four in Fig. 5-81 were replaced with a cross of resistors as shown in Fig. 5-82A. Each equivalent resistor between the midpoints of the edges is 1/k for a block of permeability K. After hooking up the resistor crosses together, the boundary conditions are set so that the sides of the blocks are at constant voltage. This corresponds to a uniform pressure on both vertical boundaries as shown in Fig. 5-81. The inverse of the equivalent resistance of this circuit yields an estimate of the effective permeability field (Saucier, 1992). Figure 5-82B shows a resistor network that is identically equal to Fig. 5-82A. The dead end edges in Fig. 5-82B are trimmed off, and the nodes having the same pressure are joined together, resulting in the equivalent resistor network (Fig. 5-82C). King (1989) applied the star-triangle transformation (shown in Fig. 5-83A to the resistor relationships in Fig. 5-82C) to give a circuit composed of resistors in series and parallel (Fig. 5-83B). The star-triangle transformation is very useful for reducing resistor networks to a simpler form. The circuit in Fig. 5-83C is equivalent to the circuit in Fig. 5-83B. In two dimensions the effective permeability (K~r) of the four blocks is reduced to:

404 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA R

A

3

B

A

B

c p

C

C

e

11w

f~

//~

aL

IF

p

2

,Q A

B

C

C Fig. 5-83. Simplification of the resistor network. (A) Star-triangle transformation scheme used by King (1989). Examples of the resistor transformation equations are shown. (B) Transformation of Fig. 5-82C into a circuit having resistors in series and parallel. (C) Simplified circuit equivalent to B.

4(K~ + K3) (K 2 + K4) x zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFE Kff =

[K2K4(K 1 + K3) + K1K3(K 2 + K4) ] [K, + K 2 + K 3 + K41 +

[K~K4(X, + X~) + X.K~(K~ +/';,)1

(5-89)

3(K, + K2) (K 3 + K4) (K l + K3) (K 2 + K4) Not only can the effective permeability of the four blocks be calculated by Eq. 589, but also the current in the resistors (fluxes between the fine-grid cells) can be established in a similar manner. The reader is referred to King et al. (1993, p. 241) for a complete discussion. .. ... The effective permeability (K) of the four block permeabilities can be written as:

x =/(K., K~, X~, X,).

(5-90)

If the permeability distribution on the old grid is P(K), then the probability distribution (P(K)) on the new grid is: P ( K ) = 3 fi(K - f(K,, K 2, K 3, K4) x P(KI)P(K2)P(K3)(dKIdK2dK3dK4) ,

(5-91)

405

where the integrations are performed over all possible values of the original grid block permeabilities K ~ , . . . , K 4 (two dimensions) or K ~ , . . . , K 8 (three dimensions) (King, 1989, p. 43). The block renormalized permeability f({K}) is used in Eq. 5-91 in order to determine the renormalized probability for the permeability. King (1989) developed the probability distribution by Monte-Carlo sampling. K~, K 2, K 3, and K 4 are selected first from the original probability distribution so that the effective permeability can be calculated using Eq. 5-90. This is repeated until a satisfactory distribution P(K) is built up (King, 1989). King (1989) noted that the variability in permeability observed from small-lengthscale samples such as cores is not necessarily that which should be used at the reservoir simulator grid-block scale. He showed that the distribution parameters behave in the following manner under renormalization for the two-dimensions case. zyxwvutsrqponmlkjihgfe K n+l

= Kn

(5-92)

+ 1 "- d 2 n / 4 -

(5-93)

and d~

The mean of the distribution is unchanged and the variance is reduced by a factor of four. Figure 5-84 shows the effect of three repeated renormalizations on a uniform probability distribution. The result of repeated renormalization is to arrive at a single value. The probability distribution reduces to a delta function, which is the limit of a Gaussian distribution for a small variance. P(Ki) in Eq. 5-91 is considered by King (1989, p. 46) to be Gaussian. King (1989) and Saucier (1992) noted that there are several problems connected with the real space renormalization method. These drawbacks include: (1) the possibility of hooking the resistor crosses in many different arrangements, thereby leading to different estimates of Kfr; (2) the approximations involved are difficult to quantify; (3) the accuracy of the predictions remains unknown in actual field practice. Numerical experiments performed on various reservoir test cases by King (1989), Mohanty and Sharma (1990), and Aharony et al. (1991) have proved this method to be accurate; (4) if the flow paths are very contorted (have a high tortuosity), then the resistor network does not provide a good representation; (5) the estimate of effective permeability is poor, when there is a high contrast between neighboring permeabilities, such as exhibited by a shaley carbonate reservoir; and (6) King's (1989) approach will not give a direct realization of the flow paths. King et al. (1993) stressed two important attributes of the renormalization method: (1) this procedure is about 100 times faster (in terms of computer time) when compared with pseudoization, which is computationally intensive, and (2) the speed allows us to run a larger number of statistical realizations of permeability heterogeneity, which provides a better estimate of uncertainty in reservoir performance prediction. The following discussion of Saucier's (1992) work on effective permeability concentrates on how the real space renormalization group method can be used to calculate

406 1.5

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA ORIGINAL

A

DISTROBUTION SUCCESSIVE RENORMALIZATIONS

v ft.

I.o

:i

,IP .,,i ,,-t ,,e

,0 0.5 .o 0

i

:

'

i

~

.;

1

.......

2

.......

3

i

,../o:.............. ',\ ,....~

I.,

a,

..... /,

,, '_ 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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this condition is to use short ranges of correlation and high variances. Grant et al. (1994) recommended a sampling density of 1 - 2 in-field permeability measurements per foot (30 cm) in order to capture permeability trends. An inference that can be deduced from these field studies is that the short correlation lengths are probably what generally distinguish carbonate reservoir production behavior from that of sandstone reservoirs. With some exceptions, sandstone reservoirs tend to exhibit petrophysical properties with longer correlations. Further investigations are needed to clarify this point. As a word of caution, these two case studies provided only hypothetical results that showed similar results derived from active San Andres reservoir waterfloods in west Texas, U.S.A. Grant et al. (1994) noted that the uniform saturation profile, coupled

456 with the very low water processing rate exhibited by the layer cake model, had a water breakthrough that lagged 260 days behind the geostatistically generated models. This condition demonstrated that such a simplistic geologic model misrepresents the geological and petrophysical complexities needed to simulate accurately the effects of carbonate reservoir heterogeneity on fluid displacement and production. A visual examination of computer-generated water saturation profiles helps to clarify the impact of different lithofacies on fluid flow. Examples were provided by Grant et al. (1994, fig. 15, p. 43) which showed upward-increasing permeability trends as evidenced by high water saturations present in the bar-crest dolograinstone facies of the Lawyer Canyon depositional cycles 7 and 9 (Fig. 5-101C). Water saturations in cycle 8 lags behind the waterflood fronts in cycles 7 and 9 owing to a lack of grain-rich barcrest and bar-flank facies. Senger et al.'s (1991) and Grant et al.'s (1994) simulations showed that the basal dolomudstones act as baffles to vertical cross-flow. In Grant et al.'s (1994) realistic model, the dolomudstones were modeled as nearly continuous across the outcrop panel > 1, little crossflow occurred across the dolomudstone boundaries. There and with kv/kh zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA was considerable permeability streaking in the bar-crest and bar-flank dolograinstone lithofacies. Grant et al.'s (1994) simulations demonstrated that it is the thin, poorlydeveloped cycles lacking good dolograinstone layers, such as cycle 8, which resulted in the greatest compartmentalization of viscous-dominated fluid flow within a given succession of cycles. Most of the bypassed oil remained in these poorly-developed cycles. This was supported by Senger et al.'s (1991) facies-averaged waterflood simulations. Their model results showed a systematic stacking of poorly developed parasequences (cycles) that compartmentalized fluid flow into two distinct "flow horizons".

Radiological imaging applications New, cutting-edge, nondestructive imaging techniques such as computerized Xray tomography and nuclear magnetic resonance (NMR) microscopy are used in the laboratory to obtain three-dimensional visual information of the distribution of fluids in porous media. This visualization capability is of direct help in determining the oil displacement processes taking place at the micro- and mesoscopic scales (Fig. 5-37), aiding in the design of recovery processes, and assessment of sample heterogeneity. Saraf (1981) questioned the accuracy of other in-situ methods that were used previously to determine fluid saturations during coreflood experiments, such as (1) transparent models, (2) microwave absorption, (3) radioisotope injection, (4) neutron radiography, (5) resistivity, and (6) magnetic susceptibility. All the above methods imposed restrictions on the experimental technique and provided only areal average values for fluid saturations (Wellington and Vinegar, 1987).

X-ray computerized tomography (CT). Slobod and Caudle (1952) introduced the X-ray shadowgraph (radiograph) method for studying sweep-efficiency in five-spot and line-drive well patterns. The shadowgraph is restricted to two-dimensional investigations owing to the fact that an X-ray shadow projection onto a single plane obscures three-dimensional information. Recently, high-resolution X-radiography was used to decipher the depositional history of sedimentary rocks at the microscale (Algeo et al., 1994).

457 Although this technique might reveal millimeter-scale heterogeneities, it is the images of fluid-flow patterns obtained during corefloods that are deemed important in testing the overall effect of heterogeneity on flow in carbonate rocks. Carbonate reservoir engineering applications of computerized tomography include the investigation of CO 2 displacement in laboratory cores, studying viscous fingering, gravity segregation, miscibility, and mobility control. Computerized tomography differs from X-ray radiography in that image construction and its display are generated using a computer and proprietary software packages (Macovski, 1983; Orsi et al., 1994). This technique measures density and atomic composition inside opaque objects. Second- and later-generation medical CT scanners have the appropriate X-ray energy and dose for scanning cores and slab models. CT scanners produce two-dimensional cross-sectional image slices through an object by revolving an X-ray tube around the object and obtaining projections at various different angles (Wellington and Vinegar, 1987). A three-dimensional array is created from the two-dimensional transmission images. Recently, Jasti et al. (1993) described new CT technology that directly measures three-dimensional geometric and topological properties of porous rocks on a microscale using a microfocal X-ray imaging system. Petrophysical applications of CT scanning have aided in the three-dimensional determination along a core's length of: (1) bulk density and porosity patterns, (2) core-well log correlation by direct comparison of the density log's bulk density signature and one generated from the core, (3) drilling fluid invasion, (4) fractures (natural and induced), (5) complex mineralogies, (6) sand(carbonate)/shale ratios, (7) hydrocarbon/water/gas distributions, (8) sedimentological features such as thin flow-barriers, and (9) uniaxial compressibility of the rock under compression. It is important to remember that semivariograms of various rock and fluid properties, such as porosity, permeability and residual fluid saturations, can be calculated from CT data and are used to determine correlation lengths on the laboratory (micro- to meso-scopic) scales. Pathak et al. (1982) demonstrated that the topology of the matrix's pore system was critical for residual oil saturations. They measured connectivity between pores. Their study showed that when a matrix contains a larger number of pore interconnections, there is a greater number of alternative routes available for oil drainage resulting in a lower percolation threshold and a lower residual oil saturation. Pathak et al. (1982) concluded that flow properties in porous media not only depend on pore size and shape, but also on local connectivity. Porosity distributions can be measured with any two fluids as long as the fluids attenuate the CT X-rays differently. Dopants are sometimes added to the injection brines and oils in order to increase the difference between the X-ray attenuation of water and oil. Iodated oils, such as 1-iododecane, can be added to the oleic phase, and high-atomic number salts such as sodium iodide or tungstate to the brine. Sodium iodide was preferred by Withjack (1988) for the aqueous phase owing to its interaction with clay minerals, which is similar to the sodium chloride interactions with clays. Figure 5-111 illustrates CT-determined average porosity values of a porous, permeable, fine-grained dolomite sample (Silurian Guelph Formation from the J.E. Baker Co. quarry in Millersville, Ohio, U.S.A.). In making the porosity measurements, Withjack (1988) used a range of sodium iodide molar solutions of 0.25, 0.50, 0.75, and 1.00 and X-ray tube voltages of 80 and 120 kV. The 0.75 molar concentration

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provided a close agreement (within about + 1%) between CT and conventionally measured porosities (Withjack, 1988). MacAllister et al. (1993), Wellington and Vinegar (1987), and Withjack (1988) described the use of a CT scanner to measure in-situ gas-water and oil-water saturations (apparent relative permeabilities) during displacement studies in laboratory cores. Apparent oil-water relative permeability relations are presented in Fig. 5-112 for a fine-grained "Baker" dolomite core (~b = 0.226; kai r = 110 roD) under a wettability state altered to a mixed-wettabili~, condition (MacAllister et al., 1993). Most field mixed-wettability cores are also weakly wet (Mohanty and Miller, 1991). All relative permeability values were normalized relative to ko at initial water saturation. These test results show that the relative permeabilities for the oil and water phases were higher at 4-psi (0.03-MPa) Ap than at 100-psi (0.69-MPa) Ap. MacAllister et al. (1993) considered several possible causes for the sensitivity to pressure drop, such as capillary number, capillary end effect and non-Darcy flow. Mohanty and Miller (1991) discussed potential factors and how they could influence the flow in a mixed-wettability laboratory core and, hence, the relative permeability during an unsteady test. From Mohanty and Miller's (1991) CT scan results, it was concluded that the early part (.-

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west Texas core. The Fenn-Big Valley core porosity indicates a definite correlation with length. Both cores show that the variance is still increasing, which Hicks et al. (1992) attributed to the wider variation in matrix porosity in the San Andres samples. Hicks et al. (1992) also studied the effect of direction on the porosity semivariograms generated for the three carbonate cores (Fig. 5-117). The results demonstrated that a difference exists in the semivariograms across the bedding planes in the two San Andres cores (Fig. 5-117B, C). The laboratory scale of heterogeneity is on the order of 0.4 in. (1 cm). Hicks et al. (1992) pointed out that the optimal grid block sizes for laboratory-scale simulations were expected to be of this size. Three-phase flow experiments using a CT scanner to measure fluid saturations were carried out by Vinegar and Wellington (1987). Tomutsa et al. (1992) pointed out that for porosity and two-phase saturation measurements, CT scanning at one X-ray energy level is sufficient. For three-phases, however, fluid differentiation requires that scanning takes place at two different X-ray energy levels. Computerized tomography scanning can provide valuable information during laboratory testing on whether or not carbonate cores have been fully saturated before, during, or after displacement studies. Data from CT scans can be used to model petrophysical properties on the laboratory scale by using semivariograms. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHG

Magnetic resonance imaging microscopy (NMR). Porosities in carbonate rock reservoirs have been shown to be difficult to determine in situ using conventional

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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

I

0

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~

80,

a

60"

40"'

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9 4.6,5 CC/ SEC 0 0

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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.

zyxwvu B

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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

10 7 5

99 71 19

65.2 64.9 63.6

10.4 6.2 1.5

Homogeneous kh = 500 mD kV= 10 mD

500

7

71

63.8

8.6

100

5

19

62.2

2.8

Heterogeneous

1000 500 100

10 7 5

99 71 19

58.2 57.7 54.4

27.4 22.8 10.5

Tight lenses

1000 500 100

10 7 5

99 71 19

64.0 63.2 62.3

11.1 5.4 1.4

zyxwvutsrqponm

Leduc Coning Model

Layered Model Thick layer system

500 100

28 22

17 3.5

55.6 57.8

0.61 0.58

Thin layer system

500 100

28 22

17 3.5

59.2 57.8

3.06 0.24

Source: After Lee et al., 1973, table 2; reprinted with the permission of the Society of Petroleum Engineers.

Lee et al.'s (1974) fourth model was developed to study the sensitivity of recovery to production rate for tight lenses in an otherwise homogeneous carbonate matrix. Four lenses were included in the model to introduce areas of significantly reduced horizontal and vertical permeability. Results show that oil recovery increases uniformly from 62.3 to 64.0% OIP for rates of 100 and 1,000 BFPD (Table 5-XXVII). Lee et al. (1974) noted that the position of the lens in the reservoir, and the magnitude of its permeabilities, determine if increased rates have a beneficial or detrimental effect on oil recovery from the specific lens. The increase in water throughput offsets any slight reduction in recovery from some of the lenses (Lee et al., 1974). The coning model was used to investigate the effect on ultimate recovery of increased rates (100 BFPD to an economic limit and then the rate was increased to 1,000 BFPD) in a heterogeneous reservoir during late stages of depletion. Figure 5129A indicates that recovery is improved from 54.4% to 57.8% OIP as a result of the increased rate. Lee et al. (1974) noted that the rate increase, however, captured only 90% of the additional recovery, which would have been achieved by producing at

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INCREASED TERMINAL RATE MODEL RESULTS

,cam

BEAVERHILL LAKE

YODEL RESULTS

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54

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zyxwvutsrqponmlkjihgfedcbaZY 493 zyxwvutsrqponmlkjihgf

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

-

I

kro/

~/

k/F~r

L z

.0, .oo1

.ooo,

.ooool

//

0

10

20

I/ 30

/

r .....

40 SL

N

--

50

60

70

80

90

100

e/o

Fig. 5-132. Gas-oil relative permeability relationships used in the simulation of recovery sensitivities of the high-reliefcarbonate reservoirs subject to gravity drainage. Recoverypredictions: krbas e = 57.7%; krl - 62.9%; and krz - 47.0%. (After Beveridge et al., 1969, fig. 1; reprinted with the permission of the Petroleum Society of The Canadian Institute of Mining, Metallurgy and Petroleum.)

method did not give accurate relative permeability values in the low saturation range. Hagoort (1980) showed that the centrifuge method was an accurate and efficient method for measuring oil relative permeabilities. Beveridge et al. (1969) revealed that the limiting kro in the Upper Devonian Leduc D-3A pool, Alberta, Canada, is about 10 times smaller than the value of kro at the end of laboratory flood. The residual oil saturations obtained from flood tests on Leduc core were much higher than those indicated from actual field performance. Recoveries in high-relief, vuggy carbonate reservoirs are generally underestimated. 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

r~

(~o)

po(rv,to)='~[ln

+0.809071

toa < 0.1 P o (ro,t D) =

~

% - 1

(to +

)

toA > 0.1

72"-

(% - 1)

Closed

(3r~

-4r;

2 +r~)_4_ r;2o lnr o Po(ro,to) = r~ _----~(to (r,2o _ l)

In r o - 2 r 2 - 1)

4(r:o - 1) 2 (3r~

+~r'~-" e-'''~

[d:(fl"

ro)Jt(fl.)Y(fl

~ ro)-(fl.)do(fl.ro)] 2

-4r:v in

Same as infinite reservoir

r o -

2r~

4(r:o - 1) 2

:.H:(:.r~)-J,(p.)] ro=l

tDa

2 "0 e -ant~d ( ~ ) p o ( t o ) = l n ro __.T.~": o r o .=, ; ~ J : ( 2 . r o)

Same as infinite reservoir


0.1

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,

-Xf

I I 111 I I l II

~

,

].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 ]

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 /

!

100

'"

I

I

I

zyxwvutsrqponmlkj k 87.67 c 5xlO -2

--/,et ee~ee

_

I

~ 0

_

lO00 .m O0 Q_

4.727x I0 I1

9 tm

~

10

v c" (3

O (D

a

a.

l O0

1

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

-

I

I

I

I

k 87.67 c 1.427x10-z s 9.194 _

LC

1.549x1011

9

" " " T , ; ~

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

~ x

zyxwvutsrqponmlkji .~

10

r~ 5000 ~.) :3 oo

~~

oo 4 0 0 0 Q..

%

1

3000 zooo[ lx10 -2

,

,

t

,

0.1

1

10

100

Ti me, hrs

I 1000

o.1 _ 0.1

I

I

I

I

1

10

100

1000

lx104

t D/CD

Fig. 6-17. A linear i m p e r m e a b l e boundary shows as semilog straight line with a doubling o f slope on a semilog graph, and as a second flat region on a derivative graph. (After H o m e , 1990, fig. 3.8, p. 47.)

...3

Lab -...I

Finite Cond Froc Stg & Skn Homogeneous [nf Actng One Q

Finite Cond Frac Finite Conductivity Fmc 10'

I

I

J

I

,,

100

I

k 2004 Xf 197.3

l

i

i

k 20.04 c O.1025 s 9.194 10

1

PD

PD

0.1

- ,o.......,,,..,.,,,...,.,, ~

9

o ~176176176176176176176

zyxw zyxwvutsrq 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 t AP'

Log tAP'

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

o D

9

9

s,"

%

9

s

~ 9 9

t I. m_0.25

psi

~,

cycle

0O

2415

r

0-2

I

10-1

I

1

I

,

10

t, min Fig. 6-56. Semilog graph for the first drawdown test data, well A.

I

102

103

619

CASE A m- 0.4 x 10-4

6 AP w qN 4 psi STB/D x104

& a

q,STBID 7430 5300 o 6740

I

9 8980

-0.6

-0.4

-0.2

n qj-qj-I ~l

0.2

0

log (t-t].])

qN

Fig. 6-57. Multiple flow rate test graph, well A.

10

I

I

!

I

I

A p / q : 3.017 x 10 - 4 + 6.283 x 10 . 8 q m

ra

Ap = 3.017 x 10 -4 q , 6 .

rn

~-

O9

8

o/~

(tJ C~_

m =6.283 xt0 -8

o,.

1:9"

Y0: 3.017 x 10-4 psi / STB / D 5

I Z

000

I

I

6 000

q (STB/D) Fig. 6-58. Well performance curve for well A.

1

8 000

I

10 000

0.4

620

CASE A oo

2420

9

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 an zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA "active" well, creates a pressure interference in a previously-closed, nearby observation well. Such a pressure interference can be analyzed for reservoir properties. The term "interference test" refers to the pressure drop caused by the producing wells, including the active well, as the shut-in observation wells "interfere with" the pressure at the observation wells. There are several important advantages inherent in the analysis of interference tests. First, a greater area of the reservoir is influenced with respect to that affected during a single-well test, be that a drawdown or buildup test. Second, these tests can provide information on reservoir properties that are not available from single-well tests, e.g., the storativity ~ cth. Third, reservoir connectivity can be estimated. Questions such as: (a) is the nearby observation area drained by other wells? and if so, (b) how rapidly?, can be answered. Fourth, reservoir anisotropy, which can be directly related to preferential flow patterns, can be estimated. On the other hand, a disadvantage of this test is that pressure drops reaching the observation well or wells can be very small, and importantly, are affected by additional operational field producing variations. This problem is especially common in high-permeability carbonate reservoirs. However, presently available electronic gauges of high accuracy and resolution are capable of registering such small pressure drops (usually less than 1 psi over days or even weeks), and so interference testing can be successfully employed. Of special importance in new reservoirs, an interference test is not affected by other production in the field, and it serves to prove the presence of productive reservoir between the first two wells. The basic theory used in the analysis of interference tests is based on the flow of a constant-compressibility liquid, which is mathematically expressed by Eq.6-42. This

632 104

10 5

106

107

10 8

109

10

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)

PP(P) = Po { 1 -

~

(p) } p (p) dp

(6-95)

It has been found convenient (Samaniego, 1974; Samaniego et al., 1977) to express Eq. 6-95 in terms of a normalized pseudopressure p~p(p) defined by:

1 G(p)

{1 - ~ (p,)} 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

9 ~ (,pwl)9

q i P (Pi)

h(Pi):l-qb(Pwl)}

:l-~b(Pw:)}

1

P(,Pw:)(OPw~) ~

(6-101)

log t

Equation 6-101 is the expression that allows estimation of the pressure-dependent parameter k(p w/.) / {1 -~b ( pw/) } at any flowing time " It is assumed in this equation that the thickness h~pi ) and porosity ~b(pw l ) may be estimated from other sources (e " q," well logging). It has been demonstrated that currently available techniques provide accurate estimates of these parameters (Martell, 1989). In this expression and in all similar expressions in this section, the derivative c ~ w / ) / 0 log t is an instantaneous derivative (slope), at the time (or pressure) at which the pressure-dependent parameter is evaluated. Data on the pressure dependency of porosity indicate that, in most cases, its variation is small when compared to corresponding changes of permeability. Then, neglecting the dependence of porosity on pressure, Eq. 6-101 can be written as:

k(pws) = -1.1513ao

qi P(P)

~(Pwj)

1

(6-102)

c3log t Similarly, for a pressure buildup test in a pressure-dependent system, the necessary equation for analysis can be derived as previously described for drawdown tests. Again, if the pressure dependence of porosity is neglected then:

k~w~) = -1.1513a ~

qi P(Pi )

~(Pws)

h

p(pw)

1 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 t = O. 0 5 t . Here, deviation from the first derivative behavior occurs at approximately AzyxwvutsrqponmlkjihgfedcbaZYXW 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-

~

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

.---

~

-__o___~_~. C3

-

.

.

.

.

.

.

.

.

m-i

700J

Numbers indicate

t 350

conftning pressure

/,60

~

'I000-.

-

1000~I

~

210

\ 3s

0

j

in Kg/cm2

" ~ ~00 ,

,~

1

2

,

89 Strain,

,

•I ('I'1

Fig. 7-10. Differential stress 0-t- 0-2vs. strain for various confining pressures. 0 < 0"3 < 30 kg/cm 2 35 < 0"3 • 150 kg/cm 2 150 < o 3 < 400 kg/cm 2 0"3 ) 400 kg/cm 2

-

irregular fracture net and visible fracture abundant conjugate fractures no fractures

As shown, when confining pressures are around 2 5 0 - 400 kg/cm 2, conjugate fractures are developed for the same unique axial stress. If the fractures are observed on a folded structure as shown in Fig. 7-12, it may be stated that right lateral and left lateral fractures form at angles of 60 ~ This happens as a result of maximum shear

692 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 precipit at es MICROFRACTURES

MACROFRACTURES .

.

.

.

.

.

.

.

.

.

.

I .

.

.

9small width 9n o n extended

9w i d t h > ~t 9very extended

[FRACTURESLi

!

measurable

I

[ n~ ! .

(visible)

"ATUAL-, ,!

!

.

.

fractures

.

.

.

.

.

.

.

.

.

.

_

[ -.'NDUCED- ]

§

9 clean, fresh

9partlally.,,~ plugged 9t o t a l l y . ~ 9parallel w i t h other .

,

too small (Invisible)

.

9parallel-,~ to core axis 9normal .

.

.

.

.

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

/I/,

? Z

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,

eff

- Effective

f

- Fracture

drainage

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 HNS 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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__120 ~ (Treiber et al., 1972) or of mixed wettability (portions of surface more water-wet and portions more oil-wet). Four major mechanisms of oil trapping are recognized in water-swept reservoir rocks (Fig. 10-4). (1) Viscous fingering causes irregularities at the water-oil displacement front in systems with large water-oil mobility ratios (Craig, 1971). Viscous fingers cause early breakthrough of water, and the irregular advancing fronts leave residual pockets of oil which contribute to high residual saturations. Viscous fingering is not dependent on a porous structure in so far as it occurs between parallel plates in the absence of structure. (2) "Snap-off' of oil by capillary imbibition of water which forms collars of water at pore throats. These collars become unstable and snap-off in rocks which are strongly water-wet and have large pore-to-throat diameter ratios (Li and Wardlaw, 1986a, b). (3) Bypassing of oil related to differential travel of water-oil interfaces caused by V ISCOUS FINGERING

BYPASSING

CAR LLARY INSTABILIT Y

SURFACE TRAPPING

WATER WET

.

WATER O OIL 9

.

.

.

.

//

.

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFED

I

\

INTERMEDIATE WET

c OIL WET 1

2

3

4

Fig. 10-4. Four mechanisms of oil-trapping on the microscope scale for three wettability conditions. (After Wardlaw, 1990.)

874

differences in the effective sizes of adjacent pathways within the rock. This differential travel causes bypassing of oil in heterogeneous systems. The greater the size contrasts (heterogeneity) the larger will be the oil residuals. (4) In oil-wet systems, oil is the phase contacting rock surfaces, and surface trapping is likely to be particularly important in rocks with highly irregular pore surfaces and large surface areas. Of the four mechanisms of oil entrapment, all occur at the core scale during waterflooding, and mechanisms 1 and 3 also occur at larger (reservoir) scales. Optimizing oil recovery involves imposing conditions during production which will minimize oil entrapment. Thus, there may be advantages to identifying the fraction of the total trapped oil which is associated with each of the above mechanisms, because the conditions of displacement that would minimize trapping by one mechanism are not necessarily the same as those that would minimize trapping by one of the other mechanisms. Minimizing oil entrapment requires knowing both the mechanisms of oil entrapment and the conditions under which they occur. In the following, a qualitative assessment is made of the effects of fluid and rock properties on the four mechanisms of oil entrapment. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPON

Effects of fluid properties and wettability on trapping The relative effects of oil-water viscosity ratio, interfacial tension, wettability and waterflood velocity on the four trapping mechanisms are indicated in Table 10-I as being large or small. Large oil-water viscosity ratios cause large water-to-oil mobility ratios and promote viscous fingering (Craig, 1971) but have little effect on snap-off by capillary instability (Wardlaw, 1982) or oil trapping by bypassing (Laidlaw and Wardlaw, 1983). Large oil-water viscosity ratios may reduce recovery of oil from rough, oil-wet surfaces because of the large viscous resistance of the displaced phase and its relative inaccessibility in small surface spaces. Interfacial tension for water-oil interfaces during waterflooding generally is in the range of 15 to 30 mN/m, and these relatively small variations are not thought to affect significantly oil entrapment. Of course, interfacial tension lowering of several orders of magnitude does have important effects, and is of major importance in tertiary recovery where it is used to decrease capillary forces causing retention of oil in relation to viscous and gravity forces which promote oil mobilization. Increasing waterflood velocity increases instability and fingering at flood fronts. This causes earlier breakthrough of water and reduced recovery of oil (Peters and Flock, 1981). Increasing velocity causes an increase in viscous forces relative to capillary forces, and because snap-off requires the formation of a collar of water and is rate-dependent, oil may be displaced from a pore by viscous forces before snap-off has had time to break oil continuity in a downstream throat. Likewise, for water-wet systems, increasing flow rate can reduce trapping by bypassing (Laidlaw and Wardlaw, 1983). Although velocity has a potentially large effect on oil entrapment by three of the four mechanisms (Table 10-I), the extent to which this is the case for the relatively small range of velocity variations possible under field conditions of waterflooding is likely to be small.

875 TABLE 10-I Relative effects of fluid-wettability variables on trapping mechanisms under field conditions 1

2

3

4

Viscous fingering

Snap-off

Bypassing

Surface trapping

Viscosity ratio go/gw

L

S

S

L

Interfacial tension (~,)

S

S

S

S

Velocity (V)

S

S

S

S

Wettability

S

L

L

L

zyxwvutsrqponmlkjih

(0) L = large effect S = small effect

The effects of wettability on viscous fingering are small compared to the effects of mobility ratio and fluid velocity. Wettability differences, however, may have large effects on the other three trapping mechanisms. Strong water wetness favors extensive entrapment of oil by snap-off and by bypassing. Bypassing occurs with preferential advance of water in the finer oil-occupied pore spaces, leaving residual oil preferentially in the larger spaces. Oil wetness will favor larger residual oil saturations in rocks with large surface areas and rough pore walls. Inasmuch as oil continuity may be maintained across rough surfaces, such oil-wet systems do not have well defined oil-residual end points. With sufficient water throughput, oil flow may be maintained to low oil saturations but with diminishing oil-flow rates (Dullien et al., 1986). Surface area and surface characteristics vary widely in carbonate rocks and commonly are not well characterized (Fig. 10-5). Understanding the relationships of pore structure, wettability and mechanisms of oil entrapment is useful in understanding some of the apparent ambiguities in the published literature concerning the effects of wettability on displacement efficiency. For example, Salathiel (1973) presented evidence that strongly water-wet conditions caused high residual oil saturations compared with displacements conducted with mixed-wettability conditions. On the other hand, Mungan (1966) and Lefebvre du Prey (1973) provide evidence that strongly water-wet cores flooded more efficiently than cores of intermediate wettability. In contrast, Morrow (1978) presented evidence that there was less trapping at intermediate wettability than for strongly water-wet or strongly oil-wet conditions. Apparent contradictions of these kinds are, in part, related to the properties of porous media and can be expected if one considers the ways in which wettability changes affect trapping by the four mechanisms identified above. A change from strongly water-wet to strongly oil-wet conditions increases immobile oil for two of the mechanisms (surface trapping and viscous fingering), whereas it is expected to decrease immobile oil for the other two mechanisms (snap-off and bypassing) (Table 10-II).

876

zyxwvu

Fig. 10-5. Differences in surface characteristics and surface area. (A) Dolomite (D) with irregular surfaces associated with irregular grains of microspar (M). (B) Dolomite with smooth planar crystal faces; pore walls are smoother and with lower surface area than in A.

Effects of rock-pore properties on trapping

Table 10-III provides qualitative estimates of the effects of three rock attributes on the four trapping mechanisms. Carbonates commonly have relatively large secondary pores created by dissolution ("vuggy" carbonates). Such secondary pores are commonly accessed by throats which have sheet-like form, similar to spaces between sub-parallel plates (Wardlaw, 1976) and have large pore-throat size contrast (Fig.10-6). The "matrix" between large secondary pores or vugs commonly is relatively "tight" (porosity z 3 - 5%). Under water-wet conditions, large amounts ofoil would be trapped in the large pores by a combination of snap-off and bypassing. The vugs may represent a large fraction of the total pore volume, and if they remain filled with oil following TABLE 10-II Effects of wettability on trapping mechanisms Wettability condition

Viscous fingering

Snap-off

Bypassing

Surface trapping

Strongly water wet

S

L

L

S

Intermediate wettability

L

S

S

L

Strongly oil wet

L

S

S

L

S = smaller potential for trapping residual oil. L = larger potential for trapping residual oil. Arrows indicate increasing (1') and decreasing ($) potential for trapping by various mechanisms as a function of wettability.

zyxwvutsr 877

TABLE 10-III Trapping mechanisms

1

2

3

4

Viscous fingering

Snap-off

Bypassing

Surface trapping

Pore-throat size ratio

S

L

S

S

Surface roughness

S

L

S

L

Heterogeneity (spatial order)

S

S

L

S

L = Large effect S = Small effect

waterflooding, oil displacement efficiency would be low (Figs. 10-4A and 10-7A). Under intermediate to oil-wet conditions, however, oil is displaced from vugs and the residual oil saturation is much lower (Fig. 10-7B) (Wardlaw, 1980). Thus, the effects of large pore-throat size ratio on trapping and residual oil saturation can only be evaluated when the wettability of the system is known. Because most carbonates are thought to be intermediate to oil-wet (Chilingar and Yen, 1983), rather than strongly water wet, the effects of large pore/throat ratio on oil trapping may be minimized. The surface roughness of carbonates varies widely (Fig. 10-5). The combination of high surface area (large surface roughness) and oil wetness will contribute to high residual oil at the economic limit (Table 10-II) but high surface area need not cause high residual oil in water-wet rocks (Fig. 10-4A).

A

B

Fig. 10-6. (A) and (B): Etched dolomite crystals (D) and epoxy resin impregnated pores (P) connected by sheet-like throats (T) in reservoirs with large pore/throat size ratios.

878

Fig. 10-7. Etched glass micromodel with vugs and matrix porosity. Water (dark) and oil (light) at residual oil saturation following waterflood. (A) Water-wet model; residual oil fills vugs and residual oil saturation is large. (B) Intermediate to oil wet; oil was displaced from vugs and residual oil saturation is much lower than in A. Both A and B have small amounts of oil trapped in matrix. Thus, whether water-wetness or oil-wetness favors greater oil recovery efficiency can be evaluated only in the context of rock-pore properties. Conversely, the effects of rock-pore properties on recovery can be evaluated only if the wettability of the system is known. Generally, studies of wettability in the published literature are not accompanied by quantitative information about the pore structure of the rocks tested, and the apparent ambiguity of the results is not surprising. The presence of heterogeneities in cores from reservoirs tends to increase irregularities at the advancing fluid front and increases oil trapped by bypassing (Wardlaw and Cassan, 1979; Wardlaw, 1980). The end points of a two-phase displacement are an initial connate water saturation ( S ) and a final or residual oil saturation (Sr). These end points define the amount of oil which is recoverable, and have been shown in experimental studies with sandpacks to be affected more by the spatial order or clustering of pores and throats of particular types and sizes than by their lack of

879 uniformity or sorting (Morrow, 1971; Chatzis et al., 1983). This spatial order is usually referred to as heterogeneity. Local clustering of smaller pores and throats causes higher L i and, for water-wet conditions, local clustering of larger pores and throats causes higher S r (Fig. 10-8). The combination of high S i and high S r defines low oil recovery. For the same population of poorly sorted particles, S i and SOr both can be changed greatly by altering the arrangement from disordered to spatially ordered (i.e., local clustering of smaller and larger particles or crystals). On the other hand, degree of grain sorting does not appear to affect significantly either S or S for disordered packings. Thus, it is not so much degree of sorting or lack of uniformity of particle or crystal size which is the issue, but rather, the spatial arrangement (type and degree of heterogeneity) which affects oil recovery efficiency. Some common types of heterogeneity Wl

oF

WATER RETENTION AT I R R E D U C I B L E S A T U R A T I O N

DISORDERED S.~

10%

~Sal I I Oil D Water

ORDERED Sw~ ~ 35%

OIL R E T E N T I O N AT R E S I D U A L OIL S A T U R A T I O N

DISORDERED So, ~ 14%

ORDERED Sor -~40%

Fig. 10-8. (A) Initial connate water saturation (Swi) in a disordered sand. (B) Swi in a sand with clusters of smaller sand grains (ordered) as discontinuous domains in a continuous domain of larger grains. Sw~much larger in B thanA, although size frequency distribution of grains could be the same in both. (C) Residual oil saturation (So,.) following waterflood in a disordered sand. (D) S r following waterflood in a sand with clusters of larger grains as discontinuous domains in a continuous domain of smaller grains. S r is much larger in D than in C, although size frequency distribution of grains could be the same in C and D.

zy

880 and their effects on microscopic displacement efficiency are given in Wardlaw and Cassan (1978). Pore systems in carbonate reservoir rocks are thought to be more heterogeneous, as a group, than those of clastics and, if so, lower oil recovery efficiency can be expected. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

Effects of wettability on recovery from fractured carbonates Fractures in carbonates may create dual porosity-permeability systems which can be considered as an aspect of heterogeneity. Fractures tend to be more abundant in dolomites than in limestones (Aguilera, 1980) and have important effects on flow which are difficult to evaluate in core tests. Fracturing may contribute greatly to permeability but not much to porosity, whereas the matrix blocks between fractures may have low permeability but contain most of the pore volume (storage) of the system. Reiss (1980) presented a discussion of displacement in vug-matrix-fracture systems under water-wet and oil-wet conditions. The efficiency with which water or gas can displace oil is affected by the combined effects of gravity, capillary and viscous forces; gravity forces due to differences of density between oil and water or gas, capillary forces due to the interaction of surface forces within pores which is related to wettability, and viscous forces where the fluids are moving. The initial rate of expulsion of oil (qi) p e r unit cross-section, from an element of matrix suddenly immersed in water, can be derived from:

k a(Pw-Po)g + P o qi = 1.to a

(10-2)

where" k = matrix permeability to oil Pw,Po = water and oil specific gravities ~o = oil viscosity a = typical vertical dimensions of the matrix element P = capillary pressure The term a(p w - Po)g represents the magnitude of the gravity force, and is proportional to the dimensions of the matrix blocks. The necessary condition for oil expulsion to take place is qi > O"

a(Pw -- Po)g + P~ > 0

(10-3)

If a rock is water-wet, gravity reinforces capillary imbibition and both terms in Eq. zyxwvutsrqp 10-3 are positive, qi > O, and oil is displaced by water. Water travelling along fractures imbibes spontaneously into adjacent matrix displacing oil back into the fracture (counter-current imbibition) for transport out of the system. For an oil-wet matrix, capillary forces oppose the penetration of water into the matrix and displacement of oil from the matrix is possible only if gravity effects overcome the threshold capillary displacement pressure (Pd):

881 zyxwvutsrqpo a(p~ - Po)g > Pa

(10-4)

Invasion of matrix blocks by water is only possible if the size of the matrix blocks between fractures "a" is large (Reiss 1980). Viscous forces, as well as gravity forces, may contribute to the displacement of oil by water. Beliveau et al. (1991) provided an example from the Mississippian Midale carbonates of Saskatchewan of the importance of water-wetness to production from a matrix-fracture system. The total waterflood pressure gradients applied across the reservoir from injectors to off-trend row producers is about 1.5 psi/ft (~ 30 kPa/m). Fracture-matrix capillary pressure differences are of about the same magnitude. If the rocks are water-wet, viscous and capillary forces work together. Matrix blocks spontaneously soak up water by imbibition as well as expel oil by viscous drive due to the applied pressure gradient. Water breakthrough in such a water-wet system will be retarded, and performance may appear similar to a conventional unfractured reservoir. Evidence from wettability tests, as well as simulations of reservoir performance, indicate that the Midale carbonates are, at least in part, water wet (Beliveau et al. 1991). If these rocks were oil wet, however, then the matrix would repel water and the viscous forces would not be sufficiently large for oil to be displaced from one foot or larger (1/3 m) matrix blocks. Waterflooding would be less efficient and water breakthrough would occur earlier in an oil-wet fractured reservoir of this type than in their water-wet or unfractured counterparts. Moderate lowering of interfacial tension has been shown to have beneficial effects on oil recovery in matrix-fracture systems by altering the balance of gravity and capillary forces (Schechter et al., 1991). In summary, specific attributes of the pore system affect the different trapping mechanisms to varying degrees for different conditions of wettability. For example, in vuggy carbonates with large pore/throat size ratios, snap-off is of first order importance to trapping large amounts of oil under water-wet conditions but not under intermediate to oil-wet conditions. Heterogeneity, on the other hand, affects trapping by bypassing for any wettability condition. Surface roughness is important for surface trapping under strongly oil-wet conditions. From the above, it is apparent that wettability and pore structure are variables of first order importance to oil recovery and that whether water-wet or oil-wet is the more favorable wettability condition depends on the properties of the rock-pore system. Conversely, the significance of rock-pore properties can be evaluated satisfactorily only if the system wettability is known. For a system with conductive fractures which define matrix blocks with significant porosity and low permeability, oil recovery is likely to be greater for waterwet than for oil-wet conditions. The optimum wettability condition for a wide range of reservoir rock properties would appear to be one of weak water wetness (contact angles somewhat less than 90 ~) or weak water wetness combined with oil wetness for different portions of surfaces within the same rock (mixed wettability). This latter condition provides the benefits of spontaneous imbibition of water while providing continuous pathways for oil flow down to low saturations.

882 VOLUMETRIC SWEEP EFFICIENCY

Volumetric sweep efficiency is a measure of the three dimensional effect of larger scale reservoir heterogeneities, and is a product of the pattern areal sweep and vertical sweep efficiencies. Sweep efficiency is affected by mobility ratio, density contrasts amongst fluids, relative magnitudes of capillary and viscous forces, and heterogeneity (Craig, 1971; Stalkup, 1983). Permeability contrasts amongst adjacent units, the lateral continuity of these units in relation to well spacing, and the presence or absence of partial or complete permeability barriers which affect cross flow between units, all have important effects on volumetric sweep efficiency (Fig. 10-9). INJECTION WELL

PRODUCTION WELL

NON-LAYERED

,

NON-

.t co.,,,.

PARTIALLY

4,...e.o.....,,.u,!.:...,,,.,.,,..,3...

LAYERED

Fig. 10-9. Non-layered and layered reservoir models with communicating, non-communicating and partially communicating layers. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

Continuity of beds, wells spacing and position The geometry, internal arrangement and continuity of differing lithologies and petrophysical types within carbonate reservoirs depends on such factors as the biota present, sea-level fluctuations, rates of sedimentation and subsidence, and tectonic effects as well as all the diagenetic overprinting (Mazzullo and Chilingarian, 1992). The continuity or lack of continuity of permeable beds as a function of lateral distance is an important factor in determining optimum recovery schemes. Delaney and Tsang (1981) applied the methods of Ghauri et al. (1974) and Stiles (1976, 1977) to measuring reservoir continuity within the Devonian Judy Creek carbonate reef in Alberta. The fraction of the total section composed of continuous beds was plotted as a function of interwell distance for various reservoir facies (Fig. 10-10). Continuity was greater in the reef margin than in the reef interior. The decrease in continuity of layers as a function of distance can be used in defining optimum well spacing and in analyzing the potential benefits of infill drilling.

883

CONTINUITY vs INTERWELL DISTANCE

100 >"

I"

Z I-. Z

0

(=)

,~

806040-

I I I I I

I 0

INCREMENTAL 10%

CONTINUITY

"

8

uJ

6

o z 0

UJ

U.

4 2 0 40

50

60

70

80

90

100

U L T I M A T E RECOVERY, % O 0 1 P

Fig. 10-17. Ultimate recovery for 37 vertical hydrocarbon solvent floods have a mean of 74% OOIP compared with mean of 53% OOIP for 8 horizontal solvent floods. All floods are for carbonate reservoirs. Thirty-seven vertical solvent floods operating in Alberta have an average ultimate recovery factor of 74% OOIP, with standard deviation of 8%, which is significantly higher than the average ultimate recovery 53% OOIE with a standard deviation of 4% for 8 horizontal solvent floods (Howes, 1988) (Fig. 10-17). The average ultimate recovery factor of 59% OOIP for all solvent floods compares favorably with the average ultimate recovery of 32% for Alberta waterfloods. In vertical floods, the incremental recovery from miscible injection over waterflood recovery ranges from 1 5 - 40% OOIE In horizontal floods, the incremental recovery is smaller, being between 5 - 20% (Howes, 1988). The vertical floods have an area to pay thickness (height of oil column) ratio of less than 14 hectares per meter and, in most cases, the ratio was less than 2 hectares per meter. The horizontal solvent floods have equivalent ratios of greater than 70 hectares per meter.

zyxwvuts

Immiscible gas flooding

Westerose Field, Alberta, is an Upper Devonian dolomitized stromatoporoid reef with vug-fracture porosity. The original oil column was 74 m thick and was overlain by a 117-m gas cap (Bachman et al., 1988). The area-to-thickness ratio is 3.4 hectares per meter and the reservoir is being produced by an immiscible gas recycling scheme in which the water-oil contact is maintained in its original position. Since discovery, 67% OOIP has been produced and the ultimate recovery of oil is estimated as 84% OOIE This is a higher recovery factor than the average for the vertical miscible floods (75% OOIP). The absence of extensive horizontal permeability barriers within the reef, particularly in the reef interior area, facilitates high recovery. Although the matrix porosity is low (~ 4%), the vugs appear to be well connected throughout the reef by fractures and solution channels, and displacement of oil by gas is efficient. Oil

897 which is bypassed by advancing gas can drain by gravity and, provided the drainage rate for bypassed oil is large in relation to the rate at which the gas-oil contact is being driven down (contact movement ~ 1 cm per day), this oil can rejoin the main oil bank and be produced (Yang et al., 1990). Methane gas rather than nitrogen was used for the gas cycling scheme here following a multi-component mathematical characterization of the reservoir fluids and a field history match via a numerical reservoir simulator. Forecasts were generated for various gas injection schemes, and injection of nitrogen was found to cause significantly more coning in the oil leg because of its higher density. In a case such as this, one can ask how much additional oil would have been recovered had a solvent bank been emplaced and a miscible flood conducted. An attempt to answer this question was made by comparing recoveries from immiscible and miscible gas floods. Unfortunately, although there are some 23 carbonate reservoirs with associated gas caps in western Canada, vertical immiscible floods have been utilized only in two. These are Westerose and Bonnie Glen fields with recoveries of 84% and 68% OOIE respectively. Thus, there are insufficient cases of vertical immiscible gas drives for a comparison to be made. Because no two reservoirs are the same, it is difficult to make comparisons on an individual basis. However, the Wizard Lake D3A Pool, Alberta, is in geographic proximity and of a generally similar size and reef type and has been subjected to miscible floods (Backmeyer et al., 1984). The ultimate recovery here is estimated at 96% OOIP based on a 1.5 m "sandwich loss" (final oil layer not recoverable because of coning) at the end of flood, compared with the 84% OOIP for the Westerose Field vertical immiscible flood. The Wizard Lake Field recovery will be achieved with solvent slugs which total 15% of the hydrocarbon pore volume subject to solvent displacement. Compared with Westerose Field, an additional 12% pore volume of oil is being recovered from Wizard Lake by injecting 15% pore volume of solvent. This assumes that the entire Wizard Lake reservoir is subject to solvent flooding. The percentage of the solvent recovered is not specified. Evidence is also available from sandstone reservoirs of high recoveries under immiscible gas drive with gravity drainage. In the Hawkins Field, East Texas, recovery efficiency for gas drive is estimated at over 80% compared with about 50% for water drive (Carlson, 1988). This study showed that the minimum residual oil saturation from gas displacement of water-invaded oil column is essentially the same as that from gas displacement of original oil column. Thus, in reservoirs of the Hawkins type, potential exists for reducing the average residual oil saturation in the water invaded oil column by gas d r i v e - gravity drainage. Experiments by Brandner and Slotboom (1974), in physical models of vuggy carbonates, indicate that initial upward displacement of oil by water may be reversible during subsequent downward movement of oil. Water was the wetting phase in these scaled models. They concluded that vertical gas floods could be expected to give similar ultimate oil recovery with or without preceding waterfloods under the conditions of their experiments. Immiscible gas injection into a reservoir at residual oil saturation following waterflooding causes oil to spread at gas-water interfaces. As critical gas saturation is

898 reached and gas has continuity through the system, oil continuity is re-established and oil production can recommence. In reservoirs with large vertical to horizontal dimensions, oil recovery is further aided by gravity drainage of the denser oil in the presence of the less dense gas. Gravity-assisted immiscible gas injection has been the subject of several recent papers (Chatzis et al., 1988; Kantzas et al., 1988; King et al., 1970). In summary, horizontal and vertical solvent flooding are proven methods of enhanced oil recovery with vertical floods giving, on average, approximately 20% OOIP more oil recovery than horizontal floods. Vertical immiscible gas floods also can give high oil recoveries, but insufficient cases are available to allow statistical comparisons with recoveries by miscible flooding. Horizontal permeability barriers are the major cause of lower recovery efficiencies for both miscible and immiscible gas floods. Unswept oil retained on horizontal permeability barriers has been substantiated, in some cases, by recompletion of wells above the pool-wide solvent/oil contact and by the subsequent production of"perched" oil bypassed by the solvent front (Bilozir and Frydl, 1989). In the case of vertical floods, it is important that "sandwich loss" be minimized by reducing coning to a minimum consistent with an acceptable production rate, and simulation models have proved valuable in achieving this.

CONCLUSIONS

The recovery of oil from a reservoir is the product of the microscopic displacement efficiency in the rocks contacted by the displacing fluid and the volumetric sweep efficiency, that is the fraction of the total reservoir volume that is contacted by injected fluids. Thus, residual oil at the end of secondary recovery is of two types: (1) residual oil trapped on small (microscopic) scale in the swept portion of the reservoir; and (2) residual oil bypassed in larger regions which are unswept. Residual oil in the former category may be recovered by solvent floods, or other tertiary methods, utilizing existing injection and production wells, whereas residual oil in the latter category may require infill wells to access unswept regions. Volumetric sweep efficiency may be inferred if the microscopic displacement efficiency is known from core displacement tests on representative samples and if the ultimate recovery of the reservoir can be estimated by extrapolation of decline curves or, alternatively, by analogy with other similar reservoirs at more advanced stages of production. Neither method is satisfactory because long production time may be required before extrapolations to a recovery limit can be made reliably from pressure decline curves. Also, pressure decline curves reflect the effects of fluid and rock expansion and phase behavior related to substantial pressure changes, which usually are not incorporated in laboratory flood tests. That is, it may not be justifiable to "back out" volumetric sweep from Eq. 10-1. Alternatively, suitable analogues produced to economic limits may not be available. Field surveillance programs, such as temperature surveys, tracer surveys, flowmeter and noise logs and pressure transient well tests, are expensive to implement,

899 but provide indirect methods of estimating volumetric sweep efficiency and furnish a basis for injection balancing and optimizing sweep efficiency. These tests, if well chosen, usually repay their cost many times over. A further approach is to use a reservoir model and to simulate physical processes within the reservoir in order to forecast the rates and proportions of fluid recovery under various production schemes and well-placement patterns. Several of the petrophysical properties used in such models (porosity, permeability, relative permeability-saturation relationships) are measured at the core scale and have to be averaged to represent flow and displacement at larger (reservoir grid block) scales. Such averaging requires information about the spatial arrangement of reservoir units with differing properties (heterogeneity) and may be difficult because heterogeneity may occur on several different scales in a "nested" manner. The types, degrees and scales of heterogeneity present the most difficult problems for quantitative reservoir characterization. The success of various methods of averaging core scale measurements to represent permeability at larger scales can be evaluated by comparing estimates made from appropriately averaged core measurements with those derived from in-situ pressure transient well tests. Few published data of this type are available, but the indications are that correlations to date are poor and that averaging core data to represent flow at larger scales is, as yet, subject to considerable error. Numerical reservoir simulators can match past performance, usually after several changes of parameters, but have been less successful in making predictions about future performance, particularly for enhanced oil recovery schemes. Predictions concerning ultimate recoverable reserves, which are made early in the production history of a reservoir, have been notoriously in error. This is usually because some aspect of the "container" has not been correctly modelled. Further progress in predicting performance will require increased resolution of reservoir flow units. This will be achieved through better integration of higher resolution seismic methods and geological data with new in-situ pressure tests.

ACKNOWLEDGEMENTS The writer is grateful to Drs. S.J. Mazzullo, G.V. Chilingarian and R.J. Galway for their editorial and critical comments on the original version of the manuscript.

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905 zyxwvutsrqpon

Appendix A GLOSSARY OF SELECTED G E O L O G I C TERMS S.J. M A Z Z U L L O and G.V. CHILINGARIAN

A Abiogenic Accretion [sed] Aerobic

Aggradation [sed] Allochem Allochthonous [sed]

Argillaceous Atoll

Authigenic

Autochthonous [sed]

Products (minerals, sediments, or rocks) resulting from inorganic processes of formation. Cf: biogenic. Vertical buildup or lateral extension of deposits as a consequence of sedimentation or biotic activities. Physical, organic, or chemical processes operative in, or said of products formed in, the presence of oxygen. Cf: anaerobic, anoxic. Vertical accumulation of deposits as a consequence of sedimentation or biotic activities. Cf: degradation. Carbonate particle of either skeletal or non-skeletal origin. Sediments or rocks formed elsewhere than where they are ultimately deposited; of foreign or introduced origin. Syn: allogenous. Containing clay minerals as impurities in carbonate, siliciclastic, or evaporitic sediments. A ring-shaped reef, circular or elliptical or horseshoeshaped, generally encircling an interior lagoon, and surrounded by deeper water. Formed or generated in place; specifically said of minerals that have precipitated in place or which have replaced other minerals or particles in various diagenetic environments. Said of sediments or rocks that have accumulated in place. Cf: allochthonous, allogenous. Syn: autogenous. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGF B

Backstepping [sed]

Baffiestone

Bank [sed]

Referring to carbonate platforms that are being eroded or tectonically drowned such that their areal dimensions are progressively reduced in a landward direction. Reef rock that has accumulated as a result of the trapping or baffling of sediments amidst in-place organic frameworks. Limestone deposits consisting of skeletal matter formed by in-place organisms, or sediments deposited.

906

Barrier reef [sed]

Bindstone

Bioclastic Bioerosion

Biofacies [ecol] Biogenic Bioherm

Biolithite

Biostrome Biota Bioturbation

Bitumen

Boundstone

Brecciation

generally in shallow water; in both cases the deposit may be surrounded by deeper water. Long, linear reef oriented roughly parallel to shoreline and separated from it at some distance by a lagoon of considerable depth and width; generally occur along the margins of shallow-water platforms, and pass seaward into deeper-water environments. Reef rock that has accumulated as a result of the presence of tabular or lamellar fossils that entrusted or otherwise bound sediments during deposition. Partial syn: boundstone, biolithite. Skeletal-derived sediments. Syn: biogenic, skeletal, organic. Removal of generally consolidated sediments by the boring, scraping, chewing, and rasping activities of organisms. Distinctive assemblages of organisms formed at the same time but under different environmental conditions. Sediments or rocks, or mineral deposits whose origin is related to organic activity. Syn: organic. Mass of rock with varying amounts of topographic relief above the sea floor that has been constructed by organisms. General term for reef rocks that have accumulated as a result of the activity of organisms. Partial syn: boundstone. Bedded and widely extensive, or broadly lenticular, blanket-like mass of rock constructed by organisms. All organisms that are living or have lived in an area, including animals and plants. The disruption of sedimentary strata and included sedimentary/biotic structures by the burrowing or grazing activities of organisms. Syn: burrow mottling. A generic term for natural, inflammable substances that are composed of a mixture of hydrocarbons that are substantially free of oxygenated bodies. Great confusion exists in the literature on the definition of See T.F. Yen and George V. the term Bitumen. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDC Chilingarian, 1994. Asphaltenes andAsphalts. Elsevier, Amsterdam, for definitions of bitumen, bitumoid, etc. General term for reef rock that has accumulated as a result of the activity of organisms; or non-reef rock that has accumulated as a result of extensive syndepositional marine lithification. Disruption of strata, and development of fitted clasts

907

Buildup [organic] Buried hill

separated by fractures or of chaotic clasts with or without matrix, formed as a result of tectonism, carbonate dissolution and collapse, or evaporite dissolution and collapse. General term for reefal accumulation. Relict hill topography resulting from erosion, or specifically, karst weathering of carbonate terranes. Buried hills commonly composed hydrocarbon traps in karsted carbonate rocks. C

Calcite/Aragonite Compensation Depth Caliche

Calichification Caprock [petrol] Catagenesis

Cement

Chalk Circumgranular [sed] Clastic [sed]

Coated grain

Coccolith

Depth in the sea below which the rate of calcite or aragonite dissolution exceeds their rates of deposition. Authigenic deposit of calcium carbonate, generally low-magnesian calcite, that forms at the expense of (i.e., replacing) preexisting sediments, soils, or rocks. Syn: soilstone crusts, calcrete. Term describing the process of caliche or calcrete formation. An impervious body of rock that forms a vertical seal against hydrocarbon migration. Term applied to changes in existing sediments, or most commonly, rocks during deep burial at elevated temperatures and pressures short of metamorphism. Adj: catagenetic. Syn: mesogenesis, epigenesis. Naturally occurring (biogenic or abiogenic) precipitate of mineral material, usually calcite, aragonite, or dolomite in carbonate rocks, that binds particles together into a lithified framework. Carbonate rock of low-magnesian calcite composition composed dominantly of the remains of coccoliths and coccospheres. Cement which completely lines the pores in a rock. Syn: isopachous. Term used in reference to particles (carbonate, siliciclastic, or other mineralogies) that commonly are transported by fluids. Partial syn: hydroclastic. Carbonate particle consisting of nuclear fragment surrounded by cortex of chemically precipitated carbonate (e.g., ooids, pisoliths) or cortex composed of organic encrustation (e.g., oncolites, rhodolites). A button-like plate composed of calcium carbonate, generally about 3 microns in diameter, a number of which compose the outer skeletal remains of

908

Collapse breccia

Compaction [sed]

Composite grain Connate [sed]

Cross-stratification

Cryptalgal Cryptocrystalline [sed]

Crystal silt

Cyanobacteria

Cyclic sedimentation

coccospheres (skeletons of marine, planktonic protists). Sedimentary breccia formed as a result of collapse of indurated strata due to dissolution of underlying strata, or commonly, cave-roof collapse. Reduction in bulk volume and/or thickness of a sedimentary deposit resulting from either physical processes of grain readjustment (closer packing) in response to an increased weight of overburden (mechanical compaction), or chemical processes such as dissolution, grain interpenetration, and stylolitization (chemical compaction). Aggregate carbonate grain composed of discrete particles bound together by cement or organic mucilage. In reference to evolved waters ultimately of marine origin that have been entrapped in sediment pores after their burial, and which have been out of contact with the atmosphere for an appreciable period of geologic time. Cf: meteoric. Layers or laminae of sedimentary rock deposited at angles to the horizontal (not exceeding the angle of repose in air or water) as a normal consequence of transport by air or water. Syn: cross-bedding. Term used in reference to a presumed algal or cynaobacterial origin of certain carbonate rocks. Term used in reference to crystal components (e.g., cements or architectural elements of shells) of very fine size, generally not resolvable without the use of at least a petrographic microscope; also said of a rock with such texture. Syn: microcrystalline, nannocrystalline. Internal sediments found in cavities in rocks, composed of silt-size particles of crystals; generally form as a result of partial dissolution of host rock/sediment or boring by organisms. Biological/geological term for blue-green algae (cyanophytes), the association of blue-green algae and bacteria, or the bacterial affinity of blue-green algae. Sedimentation involving a vertical repetition of rock types representative of distinct depositional environments. Syn: rhythmic sedimentation. zyxwvutsrqponmlkjihgf D

Dedolomite Dedolomitization

Dolomite that has been replaced by calcite wherein the crystal form of the predecessor has been preserved. Process of replacement of dolomite by calcite with preservation of dolomite crystal form.

909 Deflation Depositional karst

Desiccation Detrital

Diagenesis

Diagenetic facies [carb]

Dissolution Dissolutionenlargement/enhancement

Dissolution-reprecipitation [carb]

Distally-fining [sed]

Doline

Dolomitization Dolostone Duricrust

Removal of loose, dry sediment by wind action. Term used in reference to various small-scale karst features (e.g., small dissolution caves and related speleothems and cave cements, dissolution-etched erosional surfaces) formed as a result of short periods of subaerial exposure during deposition. Loss of interstitial water from sediments as a result of drying. Term generally restricted to sediments derived from the erosion of preexisting rocks. Syn: terrigenous, siliciclastic. All chemical, physical, and biologic changes in sediments or rocks that have altered their original textures and mineralogies, operative from the time of their formation and deposition, exclusive of metamorphism. In carbonate studies, the term usually encompasses micritization, changes in mineralogy, cementation, recrystallization, dolomitization and dedolomitization, dissolution, etc. Adj: diagenetic. For various definitions of diagenesis zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONM found in the literature, see G. Larsen and G.V. Chilingar, 1979. Diagenesis in Sediments and Sedimentary Rocks. Elsevier, Amsterdam, 579 pp. (Also Catagenesis.) An assemblage of rocks with similar diagenetic attributes or which have been affected by similar diagenetic histories. Process of dissolving substances. Syn: leaching. In porosity studies, the process of enlarging or otherwise enhancing the size of preexisting pores by dissolution. Common process of carbonate dissolution and void formation at the microscale or macroscale, followed by the precipitation of another mineral phase. A sequence of rocks wherein sediment size decreases either away from shore, toward deeper water (marine), or from the point of sediment input (marine or terrestrial). General term for a closed depression of dissolutional origin in an area of karst topography. Partial syn: sinkhole. Replacement of a preexisting carbonate sediment or rock by dolomite. Synonym for dolomite rock. General term for a hard crust (carbonate, silica,

910

ferruginous, or aluminous) on the surface of land or as a replacive layer in the upper horizons of soils. zyxwvutsrqponmlkjihg E

Emergence

Eogenetic

Eolian Epeiric sea

Epibionts Epigenesis

Eustatic Euxinic Extraclasts [carb]

Fabric [sed] Facies [gen]

Fenestrae

Term used in reference generally to subaerial exposure of newly-deposited sediments or buried rocks as a result of tectonic uplift, unroofing by weathering, or relative or eustatic sea level fall. All diagenetic processes operative from the time of sediment formation, including marine and meteoric processes, until the sediments or rocks ultimately are buried and away from the influence of surface and near-surface processes. Referring to processes and products of sediment transport, erosion, or deposition by wind. A shallow sea on a broad continental shelf or an inland sea covering large portions of a continent; in the latter case, commonly considered to be tideless. Partial syn: epicontinental. In reference to encrusting organisms or that population of organisms that has encrusted various substrate. Diagenetic processes that have occurred, and resulting products that have formed, in the deep burial environment. Adj: epigenetic. Syn: mesogenesis, catagenesis. C f: eogenetic. Rise or fall in sea level due to global changes in the volume of the oceans. Cf: relative sea level change. An environment of restricted circulation, with stagnant or anaerobic conditions. Particles derived from outside the basin of carbonate deposition. Cf: intraclasts.

The orientation, or lack of orientation, of the elements (particles, crystals, cements) in a sedimentary rock. Sum of all lithologic, biologic, and diagenetic attributes in a rock or sequence of rocks from which the origin and environment of deposition can be inferred. The term can be restricted to lithologic facies (lithofacies), depositional facies, biotic facies (biofacies), or diagenetic facies. General term for penecontemporaneously formed shrinkage pores or gas-bubble pores in rocks, both larger than interparticle pore spaces; includes "birdseyes" and larger pores such as sheetcracks. Also in reference to

911

Floatstone

Fluvial

Framebuilder Framestone

pore types in carbonate rocks (see Porosity terms). Adj: fenestral. Reef rock composed of matrix-supported organic particles, the particles being of allochthonous (transported) rather than in-place origin. In reference to sediments transported or deposited by rivers or streams, or rocks interpreted to have been deposited in rivers or streams. Syn: fluviatile. Organisms capable of creating massive, generally wave-resistant buildups. Reef rock that has formed as a result of the accumulation of large, in-place fossils that formed the actual framework of the deposits. G

Gilsonite

Grainstone

A black, shiny asphaltite, with conchoidal fracture and black streak, which is soluble in turpentine. Syn: uintahite, uintaite. Grain-supported carbonate rock textural type, generally mud-free. Syn: sparite. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQP H

Hardground

Hemipelagic [sed] Hydrothermal Hypersaline

General term for a surficial or near-surficial layer of sediment that is cemented syndepositionally, close to or at the sediment-water interface. Deep sea sediments composed of the remains of pelagic organisms and a small amount of terrigenous material. Alteration of rocks or minerals by the action of heated waters. Sea water salinity elevated beyond values of normal salinity (e.g., greater than 34-38 o/oo); also used in reference to environments of excessively high salinity. I

Internal sediment

Interregional karst Interstitial Intrabasinal

Fine-grained sediment, including insoluble residue, that has collected in pores in sediments or rocks; such sediment is generated syndepositionally as a result of organic boring and micritization, or partial dissolution of soluble rocks. Widespread surface of karstification generally related to eustatic sea level fall or tectonic uplift. Interparticle (either pore space, cements, or fluids). Said of sediments or rocks formed within or derived from the basin of deposition. Cf: terrigenous.

912 Intracratonic Intrastratal Isopachous [sed]

Geologic features found on cratons, e.g., intracratonic basins, intracratonic seas. Formed or occurring within a given layer or layers. Syn: intraformational. Cement which completely lines the pores in a rock. Syn: circumgranular. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONML K

Karst

Karst towers Kerogen

Lacustrine Leaching [sed] Lithification Lithoclast

Lithofacies Lithographic texture

Lithohydraulic unit Lithology Lysocline

Topography (surficial and subsurface) formed as a result of the dissolution of soluble rocks such as limestones, dolomites, and evaporites, and characterized by closed depressions, caves, and underground drainage. Residual hills in karsted terranes. Syn: buried hills. Insoluble organic matter (fossilized), which can be converted by distillation into petroleum products.

Pertaining to lakes or deposits of lakes. Pertaining to dissolution of soluble minerals or rocks. Partial syn: dissolution. Process of converting unconsolidated sediments to rocks by the addition of mineral cements. Syn: cementation. Mechanically or biogenically formed and deposited fragment (larger than 2 mm) of a weakly lithified sediment or rock, formed within the basin of deposition. Cf: extraclast. See Facies. Compact, dense, homogeneous and exceedingly finegrained rock with conchoidal or sub-conchoidal fracture. Partial syn: micrite, carbonate mudstone. Layer or layers of rock with uniform fluid-flow properties distinct from adjoining layers. Descriptive, physical characteristics of rocks. Depth in the ocean at which the rate of dissolution of calcium carbonate increases significantly. M

Matrix [sed]

Maturation

The continuous material (sediment, cement) composing rocks; the continuous material enclosing interstices in rocks. [petroleum] Term pertaining to the thermocatalytic state of hydrocarbons or hydrocarbon source material; [sed] term pertaining to the mineralogic composition of siliciclastic or carbonate rocks as they approach a pure

913

Maturity Megabreccias [sed] Meniscus [sed]

Mesogenetic Metastable [sed]

Meteoric Micrite

Micritization Microbial Microcrystalline Microfacies Microspar

Mimetic Monominerallic Mound

Mud [carb sed] Mudbank Mudstone

quartz or calcite end-member composition, respectively. In reference to maturation, above. Generally thick bodies composed of large blocks of rock that are randomly oriented. The hour-glass shape of interparticle cements precipitated from fluids held by attraction at grain-tograin contacts; usually indicative of cement precipitation in the vadose environment. Diagenetic changes in rocks occurring in the deep burial environment. Syn: catagenetic, epigenetic. Said of minerals that are unstable at certain temperatures and pressures, or in fluids of certain compositions. Partial syn: unstable. Water derived ultimately from rain; water of recent atmospheric origin. [sed] Particulate, fine-grained matrix of carbonate rocks, by various definitions, the particles being less than 20 microns or 4 microns in size; a carbonate rock textural type composed dominantly of mud. Syn: carbonate mudstone; [crystal] pertaining to carbonate crystal size less than 4 microns. Organic or inorganic process of converting preexisting carbonate cements or grains to micrite. Pertaining to the presence, activities, or products of microbes such as algae, bacteria, fungi, yeasts. See Cryptocrystalline; said of a rock with such a texture. Petrologic term for the features, composition, and appearance of rocks, or of specific diagenetic features, as identified in thin sections. Fabric of carbonate crystals resulting from recrystallization of micrite-size crystals or grains that range in size from 5 microns to about 30 microns in size. Process of replacement (e.g., during dolomitization) wherein precursor textures and fabrics are preserved. Composed of one mineral species. Organic or inorganic sediment buildup with low depositional relief; or organic buildup composed of nonframework building (but commonly gregarious), in-place organisms or allochthonous organisms. Fine-grained particles, by various definitions less than 20 microns or 4 microns in size. Syn: particulate micrite. Accumulation of mud. Carbonate rock textural type composed dominantly of mud (micrite) with less than 10% grains. Partial syn: micrite.

914 N Nannofossil Neomorphism

General term for small fossils, the resolution of which is near the limits of the light microscope. General carbonate petrologic term that encompasses both recrystallization (increase in crystal size in cases where mineralogy is constant) and inversion (crystal fabric changes attending mineralogic conversions). O

Occlusion Offiap

Oncolite

Onlap

Ooid

Ooze [sed]

Overburden [sed] Overpressuring/ overpressured reservoirs

In reference to porosity reduction as a typical consequence of cementation or compaction. Progressive offshore migration of the updip terminations of sedimentary beds within a conformable sequence of rocks. Cf: onlap. An accretionary carbonate particle composed of a particulate nucleus surrounded by a cortex of algae and entrapped sediment and/or precipitated cement. Progressive onshore migration of the updip terminations of sedimentary beds within a conformable sequence of rocks. Cf: offiap. An accretionary, sand-size carbonate particle composed of a particulate nucleus surrounded by a laminated cortex of microcrystalline calcium carbonate; oolite is the term commonly used for rocks composed of ooids. Partial syn: oolite, oolith. Soft, soupy mud generally composed of at least 30% skeletal remains of pelagic organisms (calcareous or siliceous), the remainder being clay minerals. Section of rocks overlying a given stratum or strata.

Porous rocks characterized by greater than normal fluid pressures resulting, for example, from undercompaction due to rapid sedimentation. zyxwvutsrqponmlkjihgfedcbaZYXWVUT P

Packing [sed] Packstone Paleoenvironment Paleogeomorphic

Paleokarst Paleosol Pelagic

Three-dimensional arrangement of particles in a rock. Muddy, but grain-supported carbonate rock textural type. Ancient depositional (or diagenetic) environment. Term used in reference generally to a buried landscape; in reference to hydrocarbon reservoir traps in or along certain buried landscape features. Buried or relict karst. Fossilized soil. [oceanographic] Pertaining to open ocean water as an

915

Pellet Peloid

Pendant

Penecontemporaneous Periplatform

Peritidal

Permeability [geol] Petrophysics Phreatic

Pinnacle reef Pisolite

Planktonic Platform Playa Polycyclic Polygenetic Polyminerallic Polymorph [mini

Pore Porosity terms

environment; [sed] deep-sea sediments without terrigenous material (either inorganic red clays or organic oozes). A particle composed of fecal material. Partial syn: pelletoid, peloid. A cryptocrystalline carbonate particle of unrecognizable origin, most likely a completely micritized grain, less likely a fecal pellet. Partial syn: pellet. Cement fabric that is precipitated along the undersides of grains or cavities, usually indicative of precipitation in the vadose environment. Syn: stalactitic. Contemporaenous with deposition. Syn: syndepositional. Said of sediments or environments in deeper water immediately seaward of carbonate platforms, atolls, or banks. Inclusive term for supratidal and intertidal environments, or in some definitions, supratidal, intertidal, and upper subtidal environments. The ability of a medium to transmit fluids. The physical properties of reservoir rocks. Zone below the water table in an unconfined groundwater lens, or in an aquifer, where all the pores are filled with water. An isolated, long (thick), spire or column-shaped reef. An accretionary carbonate particle, usually larger than sand-size, composed of a particulate nucleus surrounded by a cortex, generally laminated, of precipitated calcium carbonate; term commonly used for rocks containing pisoids or pisoliths. Syn: pisolith, pisoid. In reference to pelagic organisms that float. A linear region of variable width of shallow-water calcium carbonate deposition. A desiccated, vegetation-free, fiat-floored area, commonly found in deserts, which represents a former shallow desert-lake basin. Syn: playa lake. Pertaining to more than one cycle of formation. Pertaining to an origin involving more than one process of formation, or superimposed processes of formation. Composed of more than one mineral. A mineral species with more than one crystal form, e.g., C a C O 3 calcite (hexagonal) and aragonite (orthorhombic). A hole, opening, or passageway in a rock. Syn: interstice. Fabric-selective porosity: pores that occur in regard to

916

Postdepositional Pressure- solution

Progradation

Protodolomite Pseudospar

specific elements in the rock. Cf: not fabric-selective; framework porosity: porosity in the matrix of rocks, exclusive of fractures. Syn: matrix porosity; porosityspecific: porosity occurrence within a given rock type or paleodepositional facies; pore system: the total petrophysical attributes of a porous unit; primary porosity: porosity inherited from the depositional environment. Cf: secondary porosity, that which develops after deposition as a result of dissolution. Physical or chemical changes in sediments or rocks after final deposition and burial. Process in which carbonate dissolution occurs at burial as a result of increased pressure due to overburden stress; usually results in the formation of stylolites and interpenetrative grain contacts. Syn: pressuredissolution. Tthe seaward accretion and migration of sedimentary bodies and corresponding depositional environments. Cf: regression. Term used in reference to dolomite that is poorly ordered and compositionally impure (i.e., calcic). Fabric of carbonate crystals, resulting from recrystallization of micrite-size crystals or grains, that are larger than 30 microns in size. zyxwvutsrqponmlkjihgfedcbaZYXW R

Ramp Recrystallization Reef Regression

Replacement [crys] Resedimentation

Rhizoconcretion, rhizolith Rhodolite

A carbonate depositional surface that dips very gently (less than 1~ in a seaward direction, passing imperceptibly from shallow to deep water. Term that refers to an increase in the size of existing crystals without a change in mineralogy. An organic buildup. The landward migration of sedimentary bodies and corresponding depositional environments. Cf: progradation. Situation where one mineral replaces another mineral or rock, e.g., dolomitization, silicification. Refers to sediments, originally formed and deposited in one environment and subsequently transported to a completely different environment. An accumulation of calcium carbonate around plant roots. An accretionary carbonate particle, larger than sand-size, with or without a nucleus surrounded by a laminated to massive cortex constructed by red (rhodophyte) algae;

917

Rimmed shelf/platform

Rudstone

term used for rocks composed of rhodoliths. Syn: rhodolith, rhodoid. A shallow-water platform of deposition, the seaward edge of which is defined by a submarine topographic high constructed by carbonate sands or reef buildups. Reef rock composed of grain-supported texture of allochthonous (transported) rather than in-place organic particles. S

Sabkha

Saddle dolomite

Sapropel

Schizohaline Seal Sea-marginal

Shoal Silcrete Siliciclastic Skewness

Sorting [sed] Spar

Sparite Strand, strandline Stromatolite

A deflation flat developed in coastal, arid-zone environments, typically associated with evaporites, and inundated occasionally by sea water. Syn: sebkha. A conspicuous habit of dolomite, generally precipitated in high-temperature environments, characterized by curved crystal faces. Material composed of plant remains, most commonly algae, that is or has macerated and putrefied in an anaerobic environment: source material for petroleum and natural gas. Said of a water body or environment of fluctuating salinity. An impermeable bed that acts as a barrier to the vertical or lateral migration of hydrocarbons. Environments close to the sea, such as lagoons, tidal fiats, beaches; or deposits in these environments. Syn: marine-transitional. Area of shallow water. A soil-replacive or sand and gravel-replacive deposit composed of silica. In reference to terrigenous detrital sediment composed of silicate mineral grains. A statistical measure of the state of asymmetry shown by a frequency distribution curve that is bunched on one side of the mean and tails out on the other side. A measure of the spread or range of particle size distributions about the mean in a sediment population. Term for coarse crystalline calcite; commonly used in reference to precipitated cements, but may be used for coarse crystalline, recrystallized micrite. Syn: sparry. Grain-supported, mud-free carbonate rock textural type. Syn: grainstone. The zone of contact between the sea and land, commonly represented by beach deposits. A laminated organo-sedimentary deposit, either planar

918

Stylolite

Stylolitization Subaerial Subsidence Subunconformity Sucrosic

Sulfuric acid karst

Supraunconformity Syndepositional

or dome-shaped, constructed by the sediment trapping and binding activities, together with some amount of syndepositional lithification, of blue-green algae (cyanobacteria). A pressure-solution feature, generally formed in moderately to deeply-buried rocks, characterized by a thin seam or suture of irregular, interlocking, sawtoothed appearance. Process of stylolite formation. Referring to exposure on land, to meteoric fluids. Local or regional downwarping of a depositional surface due to tectonism or sediment loading. Position of strata beneath an unconformity. General, non-genetic term for coarse crystalline texture, used mostly in reference to dolomites; a porosity term referring to intercrystalline pores within coarse crystalline dolomites. Dissolution, generally of carbonate strata, by sulfuric acid generated from the oxidation of upward migrating, H2S-bearing fluids from depth. Position of strata directly above an unconformity. Physical, biologic, or diagenetic processes occurring during sediment deposition. Syn: penecontemporaneous, synsedimentary. T

Telogenesis

Terrigenous Texture [sed]

Tidal flat

Transgression

Diagenetic alteration in the subaerial meteoric environment of rocks that once were deeply buried. Adj: telogenetic. Sediments, typically siliciclastic, derived from the erosion on land of preexisting rocks. Syn: detrital. General physical appearance or characteristics of a rock, including parameters such as size, shape, sorting, and packing of constituent particles. Environment, and deposits therein, formed in the intertidal zone (including neighboring supratidal and upper subtidal environments and deposits). Syn: peritidal fiat. Inundation of land by the sea. The term transgressive is used in reference to sediments deposited during a transgression. U

Unconformity

A substantial break or gap in the geologic record where a rock unit is overlain by another that is not next in the

919

Upward-shoaling [sed]

stratigraphic succession. A vertical section of deposits that records continually decreasing paleowater depths. V

Vadose

That zone in an unconfined groundwater lens wherein the pores in the sediments are filled mostly with air. Cf: phreatic. W

Wackestone

A mud-supported carbonate rock textural type with greater than 10% particles.

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921 zyxwvutsrqpon Appendix B zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

P E T R O L E U M ENGINEERING GLOSSARY J.O. ROBERTSON JR., G.V. CHILINGARIAN AND S.J. MAZZULLO

A Acidizing

fracture acidizing

matrix acidizing Air Balance Beam Air Drilling Alkanes (or paraffins)

Alkenes (see Olefins) Alkylation

Annular Space Aquifer Aromatics

API Gravity

The introduction of acid (hydrochloric, formic, and acetic, for carbonates; and hydrofluoric for sandstones) into a formation to dissolve rocks, thus opening passageways for fluids to flow through. Acid is injected into the formation at a high enough pressure to fracture the formation. The acid etches the new fracture. Enlargement of preexisting pores without fracturing. Acids can also enlarge (etch) the pre-existing fractures. Device using compressed air, rather than weights, to balance the weight of the sucker rods. Use of compressed air instead of liquid as the circulation medium in rotary drilling. Methane series, derived from petroleum, with carbon atoms arranged in a straight chain. It includes methane, ethane, propane, butane, pentane, hexane, heptane, and octane (C n Hzn+2). The reaction of alkenes or olefins with a branched chain alkane to form a branched, paraffinic hydrocarbon with high antiknock qualities. Space between the outside of the casing and the wellbore. A reservoir or portion of a reservoir containing water. Cyclic hydrocarbons found in oils. Contain a benzene ring nucleus in their structure, with a general formula of C n H2n_6. The standard method of expressing the gravity, or unit weight of oils. 141.5 oApI = ~ 131.5, SG60o

Automatic Tank Batteries

where SG6oo = the specific gravity at 60~ Lease tank batteries equipped with automatic measuring, gauging, and recording devices.

922 B

Ball Sealers Barefoot Barite Barrel Batch BPD, bbl/d or B/D Benzene

Bit Blowout

Blowout Preventer, BOP

Bottom Fraction Bottom Water Bridge Plug BS BS&W

Rubber balls dropped into a wellbore to plug perforations. Well completed without casing. A mineral often used as a component of drilling mud (or fluid) to add weight: barium sulphate, SG z 4.2 A unit of petroleum liquid measure equal to 42 gallons, US. A shipment of a particular product through a pipeline. Barrels per day. C6H6, an aromatic hydrocarbon found in petroleum. Used as a solvent for petroleum products. Used as a synonym for gasoline in many European countries. The rock cutting tool attached at the working end of the drilling string. Blowing out of gas and fluids when excessive well pressure exceeds the pressure of the drilling fluid head. Device consisting of a series of hydraulically controlled rams and inflatable bags to prevent the blowout of a well. This equipment allows control over volumes of fluid to be bled off from the wellbore through a choke manifold during drilling operations. There are several classifications of BOP. Heavier components of petroleum which remain after the lighter ends have been removed (distilled out). Water located at the bottom of reservoir. A mechanical device used to "seal-off" the wellbore below the point where it is set. Basic sediment. Basic sediment and water (often found at the bottom of tanks). C

A drilling device that uses percussion to make a hole. The upward and outward movement of fluids through the porous rock as a direct result of surface rock properties. (See Appendix C.) The minute openings between rock particles through Capillary which fluids are drawn. (See Appendix C.) A "soot" produced from natural gas. Carbon Black Pipe used to keep the wellbore walls from collapsing Casing zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA and to seal the borehole to prevent fluids outside the well from moving from one portion of the well to another. Cable Tool Drilling Rig Capillary Action

923 Casinghead Gasoline Catalysis Catalyst Catalytic ("Cat") Cracking Cathead Cellar

Cement slurry

Cementing

primary cementing secondary cementing squeeze cementing Centralizers

Choke

Christmas Tree Circulation System Collapse Resistance Completion

Compressor

Conductor Contact Angle

"Natural gasoline" is condensate from natural gas. Process in which the chemical reaction rate is affected by the introduction of another substance (catalyst). A substance that is used to slow or advance the rate of a chemical reaction without being affected itself. Breaking down of petroleum compounds into various subcomponents. Spool-shaped hub on a winch shaft around which a rope may be snubbed. Area dug out beneath the drilling platform to allow room for installation of blowout prevention equipment (BOP). A mixture of cement and water in a liquid form which is pumped behind the casing. The slurry is allowed to set until it hardens. Pumping of the cement slurry down the casing and then back up the annular space between the casing and the borehole. The cementing operation where casing is cemented in the borehole. Cementing operations in wells after the well has been completed. Placing cement by squeezing it under pressure. Devices fitted around the outside of casing as it is lowered down in the borehole to keep it centered in the hole, to achieve a good cement job. A restriction in a flowline that causes a pressure drop or reduces the rate of flow through the orifice. It provides precise control of wellhead flow rates in surface production applications involving oil and gas and in enhanced recovery. Array of valves, pipes, and fittings placed at the top of the well, on the surface. Portion of the rotary drilling system which circulates the drilling fluid (mud). The minimum extemal pressure necessary to collapse casing or a pipe. Finishing a well. Installation of all necessary equipment to produce a well. Includes placing the casing, cementing and perforation opposite the productive zone. Mechanical device used for increasing the pressure of gases, similar to a pump which is used to increase the pressure of gases or liquids. First pipe in a drilling well used to attach to the BOP. The angle which the oil-water interface makes with

924 the solid (rock). Usually, it is measured from the solid through the liquid phase (if the other phase is a gas) and through the water phase if oil and water are both present, to the oil-water interface. (See Appendix C.) Core conventional

A sample of the rock taken from the well during drilling operations. sampling Taking a sample of geological strata for examination. sidewall Cores generally one inch in diameter taken from the side of the wellbore, often by wireline. Corrosion Chemical reaction (mainly loss of electrons) that oxidizes metals, e.g., Fe ~ Fe § +2e-. Chemicals added to inhibit corrosion of metals. Corrosion Inhibitor Refinery process of breaking crude oil down into subCracking components. Lifting and placing the welded and wrapped pipeline Cradling into the trench. Critical Point (with A point at which one phase cannot be distinguished from another, and the material cannot be condensed corresponding zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA regardless of the amount of pressure applied. critical temperature There is no volume change when a liquid is vaporized critical pressure) at the critical point. Pulley at the top of the drilling rig which raises and Crown Block lowers the drill-string. Petroleum as it is produced from the formation. Crude Thick (sticky) oil with an ~ gravity of less than heavy crude 17~. Thin (light) oil with an ~ gravity greater than 25 ~ light crude Percentage (by volume) of water associated with a Cut particular crude oil. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPON D

Daily Drilling Report Darcy (D) Derrickman Deviation Drillstem Test (DST)

Distillation

Records kept of the drilling activities, completed every morning while well is being drilled, by the toolpusher. Unit of measurement of permeability (ease of fluid movement), named after its originator, Henry D'Arcy. Member of drilling crew who handles the pipe joints and works on the tubing board of the rig. Directional change of wellbore from vertical. Drillstem test employs equipment which allows a well to flow for a short period of time, gathering information on reservoir fluids and the ability of the reservoir to produce fluids. Boiling off various fractions of an oil at different temperatures.

925 Doodlebug Doubles Draw-works Drillstring Driller Drilling Mud

Drilling Program Drilling Ship Drip Drive Mechanism

bottom water combination drive gas cap expansion

gravity drainage

solution gas water drive Dry Hole DWT Dynamic Positioning

"Doodlebug Crew" makes seismographic measurements. Two joints of pipe (casing, tubing) fitted together. The hoisting equipment of a drilling rig. A long continuous string of tubular goods of tubing, drill collars, bit, and subsurface tools. Person in charge of the drilling crew on each tour. Fluid composed of water or oil, clays, chemicals and weighting materials used to lubricate the bit and to move cuttings out of the hole. Plan for assembling all the personnel, equipment and supplies for drilling and completing a well. Vessel especially designed for offshore drilling operations. Device for tapping off natural gasoline at the wellhead. The natural force present in a reservoir which causes the fluid to move toward the wellbore, the action of one fluid pushing another. Underlying water in the reservoir exerts pressure moving fluids toward the wellbore. Two or three natural drives moving the fluid toward the wellbore. Expansion of the gas cap, located in the upper portion of the reservoir, upon reduction of reservoir pressure, forces fluids toward the wellbore. Gravity force results in movement of oil downward as the gas migrates upward. This force is strong in steeply dipping reservoirs. Gas bubbles dissolved in the oil push the latter towards the wellbore. Water (part of an aquifer) in the reservoir exerts the force to push fluids towards the wellbore. A well that fails to produce oil or g a s - syn: "Duster". Dead weight tons. Means of keeping a drillship positioned exactly above the drillsite by transmitting position signals from the ocean floor to the ship's thrusters. zyxwvutsrqponmlkjihgfedcbaZYX E

Edgewater

Water around the edge of a reservoir- water presses inward. Effective Pressure Grain-to-grain stress, which is equal to the total (Pe' Pg' or c') overburden pressure (p, or c) minus the pore (fluid) pressure, pp. Electric Submersible Pump, An electric submersible pump system comprising a

926 ESP Electrodrills Environmental Impact Report (EIR)

Elevators Enhanced Recovery

downhole pump, motor, power cable and surface control system. Rotary drills powered downhole by electricity. To determine the impact upon the surrounding environment, a detailed report is required by the Environmental Protection Agency before any major construction project can begin. Clamps for lifting rods, tubing and casing. Techniques that supplement the natural primary recovery mechanism to increase the flow of fluids to the wellbore. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJ F

Flare Flow Fluid Loss Agent Formation Resistivity

Burning off excess natural gas at a well or other production site. Movement of fluids through the reservoir. Materials added to a drilling mud to reduce water loss into the formation. R F = o , where R is equal to the electrical resistivity R o w

Formation Volume Factor

(B)

Fourble Fraction

Fractionation Columns

Fracturing

fracture acidizing hydraulic fracturing

of a formation 100% saturated with formation water and R w is equal to the formation water resistivity. F = ~-~, where ~ is porosity and m is the cementation factor (varies from 1.3 for unconsolidated sands and oolitic limestones to 2.2 for dense dolomites). F embodies the effects of grain size, grain shape, grain distribution and grain packing. The volume of oil (and the solution gas dissolved in it) at reservoir pressure, p, and temperature, T, per unit volume of stock-tank oil (at surface, T= 60~ and p 1 atm). Four joints of pipe (casing, tubing) connected together. Percentage or fraction of a separate component of the crude oil having a certain boiling point range, or of a product of refining or distilling. Tall columns used in refineries to separate oil into its various components, e.g., gasoline, kerosene, gas-oil, etc. Artificial opening up (fracturing) of a formation, by pumping fluids under high pressure, to increase permeability and flow of oil to the well. The pumping in of acid solution to dissolve rocks in addition to fracturing the formation. Fracturing by pumping in liquid under pressure,

927

Frasch Process

exceeding fracturing pressure. Process to remove sulfur from a sulfur-bearing crude oil, by using cupric acid, developed by Herman Frasch. G

Gage Ticket Gager

Written record of the volumetric quantity of fluids in the tanks kept by gauger or pumper. Person who measures the amount of fluid in lease storage tanks and/or the quantity of material entering the sales line.

Gas

free gas gas cap natural gas solution gas sour gas Gas Drilling Geophones Go-Devil Gun Barrel Tank

Gum

Gas present in a vapor state. Pocket of free gas trapped in the reservoir. Gas associated with oil in a reservoir. Gas dissolved (in solution) in reservoir liquids. Natural gas containing hydrogen sulfide (H2S). Use of compressed natural gas instead of liquid as the circulation medium in rotary drilling. Microphones placed near the earth's surface to detect seismic waves. A device sent through a pipeline for cleaning purposes (see Pig). A settling tank placed between the pumping unit and other tanks, normally fitted with a trap at the top to separate gas from the liquids. Naturally-occurring or synthetic hydrophilic colloids used to control various properties of drilling fluids. zyxwvutsrqponm H zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

Head (fluid)

Holiday Horsehead

Hydrocracking Hydrophones Hydrostatic Head

h = P/7, where h = head of fluid (e.g., in ft), p = pressure (i.e., in lb/ft2), and 7 = specific weight of fluid (e.g., in lb/ft3). Gap left in the protective coating of painted tanks. End of a pumping beam to which the polished rod is attached, the sucker rods are screwed into the polished rod. Method of cracking or breaking up of long-chain hydrocarbons. Waterproof microphones used to detect seismic echoes at sea. Pressure (p) exerted at the bottom of a column of liquid, p = ~, x D, where 7 = the specific weight of liquid, e.g., in lb/cu ft; and D = depth, e.g., in ft.

928

Independent(s)

Companies engaged in a certain phase of the petroleum industry, without being a part of one of the larger oil companies. Inflow Performance Plot of the flowing bottomhole pressure versus the Relationship, flow rate (q), greatly influenced by the reservoir drive IPR mechanism. Injection Placing fluids into the reservoir under pressure. carbon dioxide injection Compressed CO 2 is injected into the formation to supply energy to push the oil toward the producing wells and also to improve recovery by mixing with both the oil and water. caustic injection Adding caustic to the water being injected to improve oil recovery by forming oil-water emulsions that help plug off the larger pore channels, giving a more even push to oil in moving it toward the producing wells. Also reduces interfacial tension and increases the relative permeability to oil. Irreducible Fluid Saturation Equilibrium saturation of the wetting phase, which cannot be lowered by flowing indefinitely a nonwetting phase through a porous medium, providing evaporation does not take place. In-Situ Combustion Enhanced recovery technique by starting a fire at the injector to generate heat and gas to drive oil toward the producing wells. Integrated Company An oil company engaged in several phases of petroleum industry, e.g., production, refining, marketing, and shipping. Internal Yield Minimum internal pressure to burst casing (pipe).

Jeep Joint

Device for detecting gaps in the protective coating of a pipeline. Single section of a pipe. K

A hollow 40-fl long pipe, having four or more sides Kelly zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA and threaded connections at each end to permit it to be attached to the swivel and to the drillpipe. It transmits torque from the rotary drilling table to the drillstring. L LACT (Lease Automatic Custody Transfer)

Fully automated tank battery that records and ships oil and gas into a gathering pipeline.

929 Latent Heat of Vaporization Btu's required to vaporize 1 lb of a liquid at its atmospheric boiling point. Lease Legal document which gives one party rights to drill and produce oil on real estate owned by another party. Various methods of lifting oil to the surface. Lift Mechanism(s) Any mechanism, other than natural, that lifts fluid to artificial lift the surface. Device using a cable, often from a tower, instead of a cable lift walking beam to lift the sucker rods. Downhole electric motor and pump, which are used electric submersible lift for high volumes of fluid production. Injection of gas into the well to lift fluids out of the gas lift wellbore. Use of hydraulic pressure to activate the downhole hydraulic lift pump. Use of solid metal rods to activate the downhole rod lift (or pumping) pump. Any lifting equipment at the surface such as a pumpsurface lift ing unit. Volatile components (or fractions) of petroleum. Lighter Ends Instructions that include names of owners of the Line List property, length of pipeline and any special instructions or restrictions. Pipeline inspector who examines the pipeline along its Linewalker extension, looking for evidence of leaks, corrosion, etc. Continuous record of certain data obtained from a Log logging tool lowered into the wellbore. Measurements of porosity, cement bonding and acoustic log lithology by use of sonic waves. Determination of the inside diameter of a wellbore or caliper log casing. Measurement of the formation conductivity. conduction log Measurement of formation porosity. Involves bomdensity log barding the formation with gamma rays, with detectors measuring the number of gamma rays that are reflected from the formation. Continuous recording of types of cuttings, gas and oil drillers log occurrences while drilling the well. Measures the electric characteristics of a formation; electric log the tool transmits signals to the surface. Measurement of the natural formation radioactivity to gamma ray log determine lithology. Measurement of the formation resistivity response to induction log an induced current. Measurements of porosity, type of fluids and/or gas, nuclear log

930

neutron log

pressure log production log

resistivity log

lithology, etc., by recording the nuclear properties of the formation. Measurement of porosity; also valuable information concerning rock composition and fluid content. The logging tool bombards the formation with neutrons. Measurement of the formation pressure at various depths. Measurement of the production status of a completed well. Yields information on the nature and movement of fluids within the well. Defines the reservoirs contents. Electric current flows in the formation between two electrodes on a logging tool and measures resistivity between those two points.

sonic log (see Acoustic Log) spontaneous potential, SP Measurement of the difference in potential between the formation and the earth's surface ~ identification of rock types. temperature log Measurement of the formation temperature at various depths. Recording of data (various physical, chemical, and Logging mechanical properties of a reservoir) obtained by lowering of various types of measuring tools into a wellbore. M

Device used to bend the pipe without deforming it. Shallow hole drilled on one side of a drilling rig to store the next joint of pipe to be added to the drilling string. See Drilling Mud. Mud Person who analyzes the cuttings brought up by the Mud Logger drilling mud while drilling the well. Plan of supplying and using drilling fluids and their Mud Program additives during the drilling process. Several producing zones completed for production Multiple Completions through one well. Fluid displacement in which the displacing fluid and Miscible Drive the displaced fluid become miscible in all proportions. Complete mixture of fluids: single phase. Miscible Mixture The ability of a fluid to move through a reservoir. Mobility zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

Mandrel Mouse Hole

N Naphtha

Petroleum distillate used as a cleaning fluid, for

931

Natural Gas

Natural gasoline

example. A naturally-occurring mixture of hydrocarbon and nonhydrocarbon gases found in porous media at depth. It is often associated with crude oil. Composed mainly (z 70 to 96%) of methane gas. A condensate of natural gas: "Casinghead gasoline". O

Occupational Health and Federal law covering working conditions and health Safety Act of 1971 (OSHA) and safety of workers in industry and business. Octane Number A measure of anti-knock quality of gasoline. The higher the rating the lower the knock. One hundred octane number indicates that gasoline will perform as a pure octane. Oil String The casing in a well that runs from the surface to the zone of production. Oil Treater (also Heater Equipment used to separate natural gas, BS&W and Treater) water from the oil by the use of heat. Olefins Class of unsaturated hydrocarbons (one double bond), such as ethene, (CznH4n). Organization of Petroleum Middle Eastern, South American and African counExporting Countries tries with large petroleum reserves that have joined (OPEC) together to control production and marketing (pricing) of oil. Override Additional royalty payment in excess of the usual royalty. Overburden pressure Total pressure, Pt, exerted on a reservoir by the weight of the overlying rocks and fluids. It is balanced by the pore pressure, pp, plus the grain-to-grain stress, pg (or effective pressure, p e ) " p t = rDp + rDe . Oxidation Process in which a given substance loses electrons or a share of its electrons. P

Packer

Mechanical device set in the casing (attached to the tubing) to prevent communication between the tubing and annulus. Paraffins Group of saturated aliphatic hydrocarbons (CnHzn+2). Paraffin also denotes a solid, waxy material. Pay Sand The zone of production where commercially recoverable oil and/or gas are present. Perforating Making holes in the casing (or liner) so that gas and fluids can enter the wellbore. knife perforating zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Holes are made in the casing by a mechanical device (kuife).

932

Perforating the casing by shooting bullets. Perforating the casing by jets. A measurement of the ease of flow of fluids through porous media. Permeability is equal to one Darcy if 1 c m 3 o f fluid flows through 1 cm 2 of cross-section of rock per second under a pressure gradient of 1 atm/ cm, the fluid viscosity being 1 cP. A measure of the ability of the porous medium to effective permeability transmit a particular fluid at the existing saturation, (of a porous medium which is normally less than 100%. to a fluid) Ratio of the effective permeability at a given saturarelative permeability tion of that fluid to the absolute permeability at 100% (k). The terms k ro (ko /k), k r g (k g /k) ~ and kr w saturation zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFED (k/k) denote the relative permeabilities to oil, to gas, and to water, respectively, k is the absolute permeability, often the single-phase liquid permeability. Working surface or deck of a drilling rig. Platform Device sent though pipelines to clean it. Pig (see Go-Devil) Pipeline crew who prepare and line up the pipe, and Pipe Gang make the initial welds. Device for bending small-diameter pipes without Pipe Shoe deforming them. Person who measures the amount and quality of oil Pipeline Gager entering the gathering lines from lease tanks. Pipelines from the lease tank batteries to the lease Pipeline - Gathering shipping line. The main line. Pipeline- Trunk Working area for cleaning, coating and storing pipe. Pipeyard Catalytic reforming unit to convert the low-quality oil Platforming to higher octane products. "Plugging off" or stopping production from a lower Plug Back portion of a producing oil well. Compounds having many repeated linked units. Polymers Primary Drive Mechanism The predominant reservoir drive mechanism when more than one drive mechanism is present. The difference in pressure at two given points, divided Pressure gradient by the distance between these two points. Period (time) that the lease covers. Primary Term Total removal of fluids using only the initial reservoir Primary Recovery energy, q where q = flow rate Productivity Index (PR or J) It is equal to PR = J = - - , Pr -- Pwl

gun perforating jet perforating Permeability

Pumper

(bbl/D); pr = average reservoir pressure (psia); and Pwf = flowing bottomhole pressure at the wellbore (psia). Person in charge of production and records for a

933

Pumping Pumping Rig, Standard Pumps ball pump centrifugal pump plunger lift pump

sonic pump

Pumping Off Pumping Stations

producing well or group of wells. Lifting fluids from the production well to the surface by an artificial lift method. Conventional pumping unit using a walking beam to raise and lower the sucker rods. Mechanical devices which lift fluids to the surface. Pump using a ball and seat to lift fluids. Pump using rotating impellers to lift fluids. A plunger that is driven up the tubing by the produced gas, and then falling by gravity to the bottom of the tubing to lift another load of fluid. Downhole pump that generates sound waves resonating on the tubing which lifts by opening and closing a series of check valves. Pumping the reservoir fluids out of the well faster than they can enter the wellbore. Pumps placed along a pipeline at intervals to maintain the pipeline pressure and flow. zyxwvutsrqponmlkjihgfedcbaZYXWV R

Radial Flow Rat Hole Rate of Penetration Recovery primary recovery secondary recovery tertiary recovery

Reduced Temperature

Two-dimensional flow from all points around a 360 ~ circle within a formation to a centered well. Shallow hole drilled next to a drilling rig where the Kelly is stored when not in use. Speed with which the drilling bit cuts through the formation. The petroleum produced from the reservoir in % (or fraction) of the total oil-in-place. The production obtained using the initial reservoir energy. The production obtained by introducing a second source of energy, i.e., waterflooding. The production obtained by introducing a third source of energy, i.e., enhanced oil recovery, such as thermal, CO 2 flooding, surfactants, polymers, alkaline flooding, in-situ combustion, and DC electrical current. The absolute temperature divided by the absolute T/T. critical temperature T = zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPO The absolute pressure at which the gas exists divided by the absolute critical pressure, P/Pc" Rearranging the carbon and hydrogen molecules by use of catalysts and heat. r

Reduced Pressure Reforming Relative Permeability (see permeability) Reservoir

r

A porous and permeable rock formation or trap

934

Residuals Residuum Rod Rotary Drilling Roughneck Royalty Run Run Ticket

holding an accumulation of gas and/or oil. "Left over" materials in boilers or refinery vessels. Sticky, black mass left in bottom of a refining vessel. Sucker rod is attached to the downhole pump, usually having a length of 1689ft. A drilling method that imparts a turning or rotary motion to the drill string to drill the hole. Member of a drilling crew who assists the driller. Fee paid to the owner of a lease based on the volume of production. Delivering (or transferring) oil from the lease tank battery to the pipeline or tank truck. Amount and quality of the run: a written record. S

SIDPP SI Samples bottom sample composite sample running sample

spot sample water and sediment sample Saturation Scratchers

Screen Liner

Scale Inhibitor

Sediment

Shut-in drillpipe pressure. Shut-in, term often used for wells that are no longer producing. Small volumes of oil drawn from a tank for testing. Sample obtained from the lowest point in the tank. Sample composed of equal portions of samples obtained from two or more points in the tank. Sample taken by lowering an unstoppered beaker from the top outlet level to the bottom outlet and returning it at a uniform rate of speed so that it is about three quarters full when returned. Sample obtained from a particular level of the tank. Sample of oil taken for obtaining the water and sediment content, usually by centrifuging. Percentage of a particular fluid in a porous medium, expressed as the percent of the pore volume. Mechanical devices placed on the outside of the casing to clean the drilling mud cake from the sides of the wellbore prior to cementing in order to improve the cement bond between the casing and the formation. Perforated pipe or wire mesh screen placed at the bottom of the well to prevent larger formation particles from entering the wellbore. Chemicals introduced into the producing well to prevent the buildup of scale, paraffin, etc. These can block off the flow of fluids and gas into the wellbore. Particulate material (clay, silt, etc.) that is carried along with the produced fluids and settles to the bottom of the tanks.

935 Secondary Recovery (see recovery) Separator

Equipment for separating the crude oil from the natural gas and water. The primary function of the Separator is to produce gas-free liquid and liquid-flee gas. Drilling a new section of wellbore parallel to a previSidetracking ously drilled hole but blocked with junk. Marine drilling rig that can either be anchored to the Semi-Submersible bottom of sea or maintained at a given position. Centrifuging to separate water, oil, and BS&W that Shaking Out may be present in a sample. Mechanical device for separation of rock cuttings Shale Shaker from the drilling fluid as it arrives at the surface. Sidetracked Well Well drilled out from the side of a previously drilled well. Sidewall Cock Valve placed on the side of a tank for the purpose of obtaining small oil samples. Solution Gas Gas dissolved so thoroughly in the oil that the solution formed is one phase. Sour Gas (or Oil) Gas or oil which contains hydrogen sulfide. Specific Heat Quantity of heat (e.g., in Btu' s) required to raise the temperature of a unit weight of material (e.g., 1 lb) one degree (temperature, e.g., I~ Specific Surface Surface of pores and pore channels per unit of pore volume (commonly), per unit of bulk volume, or per unit of grain volume. The above information zyxwvutsrqponmlkjihgfed m u s t be supplied by the investigator. Surfactants (in stimulation) Chemicals that prevent stimulation fluids from forming emulsions with reservoir oil. Swabbing Raising and lowering rubber cups in the tubing to recover liquids- "bicycle pump" action. Sweet Gas (or Oil) Gas or oil devoid of hydrogen sulfide. T Torque Tortuosity (~)

Turning or twisting force on a drilling string. Square of the ratio of the effective length, Le, to the length parallel to the overall direction of flow of the L pore channels, z = (_~__)2.

Tour

Shift of duty at well site (normally 8 hours and pronounced as "tower"). Arrangement of pulleys on the drilling rig with an attached hook, which moves up and down on cables running through the crown block.

Traveling Block

936 Trip Turbodrills

Process of pulling drillstring (or tubing) out of the borehole and then running it back in. A rotary drilling method in which fluid pumped down the tubing turns the drill bit. The downhole motor consists of multistage vane-type rotor and stator section, bearing section, drive shaft, and bit-rotating sub. V

Viscosity

Measure of the internal resistance of a fluid to flow. Viscosity is equal to the ratio of shearing stress, x, to the rate of shearing strain. Considering a flow be(F/A): (V/h), where: F = tween two parallel plates, ~t = zyxwvutsrqponmlkjihgfedcbaZYXWVUTSR force required to move the upper plate, having an area, A. V= velocity of upper plate; velocity of a thin layer of fluid adhering to the lower plate is zero. h = distance between plates. W

Water Shut-Off Test (WSO) A test that ensures there is no communication above and below a selected interval in a well. Weight Indicator Device that constantly measures the weight of the drillstring on a drilling rig. Wireline A rope made from steel wire. Workover Remedial work on a well, i.e., cleaning, repairing, servicing, stimulating, etc., after commencement of production. Z Zones of Lost Circulation

Openings in the formation (fractures, etc.) into which the drilling mud is lost without returning to the surface during the drilling operations.

937 RECOMMENDED REFERENCES Berger, B. D. and Anderson, K. E., 1978. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Modern Petroleum, A Basic Industry Primer. Petroleum Publishing Co., Tulsa, OK, 293 pp. Chilingarian, G. V., Robertson, J. O. Jr. and Kumar, S., 1987. Surface Operations in Petroleum Production, L Developments in Petroleum Science, 19A. Elsevier, Amsterdam, 821 pp. Chilingarian, G. V., Robertson, J. O. Jr. and Kumar, S., 1989. Surface Operations in Petroleum Production, II. Developments in Petroleum Science, 19B. Elsevier, Amsterdam, 562 pp. Chilingarian, G. V. and Vorabutr, P., 1981. Drilling and Drilling Fluids. Developments in Petroleum Science, 11. Elsevier, Amsterdam, 767 pp. Langnes, G. L., Robertson, J.O. Jr., and Chilingar, G. V., 1972. Secondary Recovery and Carbonate Reservoirs. Am. Elsevier, New York, 304 pp. Skinner, D. R., 1983. Introduction to Petroleum Production. Drilling, Well Completions, Reservoir Engineering. Vol. 1., Gulf Pub. Co., Houston, TX, 190 pp.

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939 zyxwvutsrqpon

Appendix C FUNDAMENTALS OF SURFACE AND CAPILLARY FORCES G.V. CHILINGARIAN, J.O. ROBERTSON JR., G.L. LANGNES and S.J. MAZZULLO

INTRODUCTION

Wettability may be defined as the ability of the liquid to "wet", or spread over, a solid surface. Figure C-1A shows a liquid wetting a solid surface, whereas Fig. C-1B shows the relationship between the liquid and solid when the liquid has little affinity for the solid. In Fig. C-1C, the liquid drop occupies an intermediate position. The fluid which wets the surface more strongly occupies the smaller pores and minute interstices in a rock.

e < 90-

o > 90-

SOLID

$

A

8

o

99 0 ,

C

Fig. C-1. Different degrees of wetting of solid by liquid.

INTERFACIAL TENSION AND CONTACT ANGLE

The angle which the liquid interface makes with the solid is called the contact angle, 0. Usually, it is measured from the solid through the liquid phase (if the other phase is a gas) and through the water phase if oil and water are both present. In a capillary tube, shown in Fig. C-2A, the angle between the side of the tube and the tangent to the curved interface (where it intersects the side of the tube) is less than 90 ~ For a capillary depression, shown in Fig. C-2B, the contact angle is greater than 90 ~ In the case of no rise or depression, the angle is 90 ~ (Fig. C-2C). Interfacial tension, 0, is caused by the molecular property (intermolecular cohesive forces) of liquids. It has the dimensions of force per unit length (lb/ft or dynes/ cm), or energy per unit area (ergs/cm2). On considering an element of a surface having double curvature (R~ and R2), the sum of the force components normal to the element is equal to zero (Fig. C-3). The pressure difference, pz-p~, is balanced by the

940 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

I A

B

C

Fig. C-2. Behavior of various fluids in glass capillary tubes. A = water, B = mercury, and C = tetrahydronaphthalene (when glass is perfectly clean and liquid is pure).

2~ 2 '

" "! I_

_1 dx

/'"'-,~ I'" N Crdx

Fig. C-3. Surface tension forces acting on a small element on the surface having double curvature, (P2 = Pl + yh). (See Binder, 1962, and Vennard, 1961.)

interfacial tension forces: (P2-P~) dydx = 2 a dy sin02 + 2 a dx sin0~

(C-l)

If the contact angles 0~ and 02 are small, then the following simplifications m a y be made:

@ sin01 = ~ 2R~ and:

(C-2)

94 1

Fig. C-4. Rise of water in glass capillary tube. (See Binder, 1962, and Vennard, 1961.)

zy

zyxwvut zyxwvut zyxwvutsr

Therefore, Eq. C- 1 becomes: 1

1

P 2 - P I = o(-+-) R2 R ,

For a capillary tube (Fig. C-4):

R, =R,=R d cose = 2R

and

P, = P,+ Yh

(A3-7)

942

.O' o

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHG

SOLID Fig. C-5. Shape of water drop resulting from interfacial tension forces. where ? = specific weight of fluid, d = diameter of capillary tube, and h = height of capillary rise. Thus, Eqs. C-4 through C-7 may be combined to yield the following expression for capillary rise, h" h=

4or cos0 ~,d

(C-8)

Equation C-8 can also be derived on considering the equilibrium of vertical forces. The weight of fluid in the capillary tube, W, which is acting downward, is equal to: W = zr d2hy 4

(C-9)

The vertical component of interfacial tension force acting upwards is equal to: F t r y = rcdcr cos0

(C- 10)

Equating these two forces and solving for h gives rise to Eq. C-8. In reference to Fig. C-5, the interfacial tensions can be expressed as O-ws+ Crwocos0+~o

(C-11)

where Crw~,Crwo,and %o = interfacial tensions at the phase boundaries water-solid, water-oil and solid-oil, respectively, or O-so cr zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA cos0 = - (C- 12) O'wo ws

As shown in Fig. C-6A, when a solid is completely immersed in a water phase, 0 = 0 ~ cos0 = 0, and consequently, "wo

=or s o - o r wzyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA (C-13) s

943 e : O*

O : 90 ~

e:180* 0

OIL

e W

W

8

C

9 WATER

A

Fig. C-6. Illustrations of 0~ 90~ and 180~contact angles. When half of the solid is wet by water and the other half by oil (Fig. C-6B), 0 = 90 ~ cos0 = 0 and thus ~o = Crws.

(C-14)

On the other hand, if the solid is completely wetted by oil (Fig. C-6C), 0 = 180 ~ zyxwvutsrqponmlkji cosO zyxwvutsrqp 1, and

-

crSO = crWS - crWO

(C-15)

If 0 < 90 ~ the surfaces are called hydrophilic and when 0 > 90 ~ they are called hydrophobic. An interfacial tension depressant lowers Crwo,whereas a wetting agent lowers 0 or increases cos0. A decrease in crw o does not necessarily mean an increase in cos0, or vice versa, because of the changes in crSO and crWS . I f a rock is completely water wet ( 0 = 0~ water will try to envelop all of the grains and force all of the oil out in to the middle of the pore channel. Even though some oil may still be trapped in this case, the recovery would be high. On the other hand, if all of the solid surfaces were completely oil wet (0 = 180~ oil would try to envelop all of the grains and force all of the water out into the center of the pore channel. In this extreme case, recovery would be very low by water drive. Many oil-wet reservoirs are known to exist. In the usual case (0 ~ < 0 < 180~ to improve waterflooding operations the contact angle 0 should be changed from > 90 ~ to < 90 ~ through the use of surfactants. This would move the oil from the surface of the grains out into the center of the pore channels, where they would be produced more readily. Contaminants or impurities may exist in either fluid phase and/or may be adsorbed on the solid surface. Even if present in minute quantities, they can and do change the contact angle from the value measured for pure systems (see Marsden, 1968).

944 EFFECT OF CONTACTANGLE AND INTERFACIAL TENSION ON MOVEMENT OF OIL For an ideal system composed of pure liquids, the advancing contact angle should equal the receding angle. Because of the presence of impurities within the liquids, however, the advancing contact angle is greater in most systems. The advancing contact angle is the angle formed at the phase boundary when oil is displaced by water. It can be measured as follows: the crystal plate is covered by oil and then the water drop is advanced on it. The contact angle is the limiting angle with time after equilibrium has been established (Fig. C-7). The contact angle formed when water is displaced by oil is called the receding angle (Fig. C-8). The contact angles during movement of a water-oil interface in a cylindrical capillary, having a hydrophilic surface, are shown in Fig. C-9. Inasmuch as a reservoir is basically a complex system of interconnected capillaries of various sizes and shapes, an understanding of flow through capillaries is very important. In Fig. C-10, a simple two-branch capillary system is presented. If a pressure drop is applied, then the water will flow more readily through the large-diameter capillary than it will through the small-diameter one. Thus a certain volume of oil may be trapped in the small capillary when water reaches the upstream fork. Poiseuille's law states that:

WA1 ER 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)

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 Chakrabarty, C., 432, 535 Brown, S., 223 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 Burns, G.K., 540, 793 Chemali, R., 228 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, Choquette, P.W., 52, 254, 268, 536, 542, 793, 956, 95 7 797, 798, 799, 801,802, 803, 805, 806, Craft, M., 141,151, 794 Crafton, J.W., 793 814, 832, 833,834, 845, 857, 858, 859, Craig, D.H., 52, 805,812, 831,832, 836, 837, 860, 861,863 842, 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., 532 100 Hallock, P., 77, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 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 Hammond, P., 221 Herald, F.A., 533 Hamon, G., 250, 539 Herbeck, E.F., 532 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 Hardie, L.A., 100 Hewitt, R., 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 Lee, J.E., 488, 489, 490, 492, 494, 496, 542 Korvin, G., 366, 388, 541 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 Pasini, J., III, 8, 55 Nicoletis, S., 227 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 -, spontaneous potential (SP), 168, 204 Lekhwair Formation, 95, 96 -, thermal neutron, 169, 180 Leonardian, 296,300 , epithermal neutron, 169, 180 Lerado field (Kansas), 526 Loma de la Lata field (Argentina), 331,332 Lerado SW field (Kansas), 522 Loring field (Mississippi), 527 Levelland field (Texas), 338,342 Louisiana, 20, 21,146, 208, 325,346, 519 Levelland Northeast field (Texas), 527 Lower Clear Fork, 304 Libya, 74, 519, 802, 813, 831 Lower Fars Formation, 503 Lima-Indiana trend (Indiana), 810, 827 Low-permeability reservoirs, 2 Lime, manufacture, 46 Lowstand, lowstand wedges, 73, 76-80 Lineament analysis, 8 Lucia classification, 178 Liquid saturation, 17-19 Lundgren field (Kansas), 523 Lithology, determination, 13 Luther S.E. field (Texas), 519 Little Beaver East field (Montana), 522 Little Beaver field (Montana), 522 M-N plots, 17 Little Knife field (Wyoming), 68, 381,383,385, Maben field (Black Warrior Basin), 810, 831 386 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 Maureen Formation, 778 , photoelectric factor crossplots, 169 Maydelle field (Texas), 527 -, dielectric, 192 McClosky Limestone, 240, 241 -, dipmeter, 208 -, gamma ray, 168, 172 McElroy field (Texas), 452, 519 McFarland field (Texas), 523 ---, spectroscopy, 168, 172, 173, 175, 181, 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 Michigan, 522, 810, 811 -, NML, 181, 195,466 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