FM.qxd 3/22/06 4:52 AM Page i RESERVOIR ENGINEERING H A N D B O O K Third Edition This Page Is Intentionally Left Blank FM.qxd 3/22/06 4:52 AM Page iii RESERVOIR ENGINEERING H A N D B O O K Third Edition Tarek Ahmed AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO Gulf Professional Publishing is an imprint of Elsevier FM.qxd 3/22/06 4:52 AM Page iv Gulf Professional Publishing is an imprint of Elsevier 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA Linacre House, Jordan Hill, Oxford OX2 8DP, UK Copyright © 2006, Elsevier Inc 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 Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone: (+44) 1865 843830, fax: (+44) 1865 853333, E-mail: permissions@elsevier.com You may also complete your request on-line via the Elsevier homepage (http://elsevier.com), by selecting “Support & Contact” then “Copyright and Permission” and then “Obtaining Permissions.” ϱ Recognizing the importance of preserving what has been written, Elsevier prints its books on acid-free paper whenever possible Library of Congress Cataloging-in-Publication Data Application submitted British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library ISBN 13: 978-0-7506-7972-5 ISBN 10: 0-7506-7972-7 For information on all Gulf Professional Publishing publications visit our Web site at www.books.elsevier.com 06 07 08 09 10 11 10 Printed in the United States of America FM.qxd 3/22/06 4:52 AM Page v This book is dedicated to my children, Justin, Brittany, Carsen, and Jennifer Ahmed I hope that at least one of them will grow up to be a petroleum engineer in the future This Page Is Intentionally Left Blank FM.qxd 3/22/06 4:52 AM Page vii CONTENTS Acknowledgments, xi Preface to the Third Edition, xiii Preface to the Second Edition, xiv Preface to the First Edition, xv Fundamentals of Reservoir Fluid Behavior Classification of Reservoirs and Reservoir Fluids, 1; Problems, 27; References, 27 Reservoir-Fluid Properties 29 Properties of Natural Gases, 29; Behavior of Ideal Gases, 30; Behavior of Real Gases, 36; Effect of Nonhydrocarbon Components on the Z-Factor, 44; Correction for High-Molecular Weight Gases, 49; Direct Calculation of Compressibility Factors, 54; Compressibility of Natural Gases, 59; Gas Formation Volume Factor, 65; Gas Viscosity, 67; Methods of Calculating the Viscosity of Natural Gases, 68; Properties of Crude Oil Systems, 75; Methods of Calculating Viscosity of the Dead Oil, 115; Methods of Calculating the Saturated Oil Viscosity, 117; Methods of Calculating the Viscosity of the Undersaturated Oil, 119; Properties of Reservoir Water, 124; Problems, 126; References, 133 vii FM.qxd 3/22/06 4:52 AM Page viii Laboratory Analysis of Reservoir Fluids 136 Composition of the Reservoir Fluid, 137; Constant-Composition Expansion Tests, 137; Differential Liberation (Vaporization) Test, 149; Separator Tests, 152; Extrapolation of Reservoir Fluid Data, 164; Laboratory Analysis of Gas Condensate Systems, 171; Problems, 184; References, 188 Fundamentals of Rock Properties 189 Porosity, 190; Saturation, 195; Wettability, 199; Surface and Interfacial Tension, 200; Capillary Pressure, 203; Permeability, 227; Rock Compressibility, 254; Net Pay Thickness, 260; Reservoir Heterogeneity, 261; Areal Heterogeneity, 274; Problems, 281; References, 286 Relative Permeability Concepts 288 Two-Phase Relative Permeability, 289; Relative Permeability Ratio, 308; Dynamic Pseudo-Relative Permeabilities, 311; Normalization and Averaging Relative Permeability Data, 313; Three-Phase Relative Permeability, 320; Problems, 329; References, 330 Fundamentals of Reservoir Fluid Flow 331 Types of Fluids, 332; Flow Regimes, 334; Reservoir Geometry, 336; Number of Flowing Fluids in the Reservoir, 339; Fluid Flow Equations, 340; Steady-State Flow, 342; Unsteady-State Flow, 373; Constant-Terminal-Pressure Solution, 384; Constant-Terminal-Rate Solution, 384; Pseudosteady-State Flow, 413; Principle of Superposition, 442; Transient Well Testing, 453; Problems, 476; References, 482 Oil Well Performance 484 Vertical Oil Well Performance, 484; Horizontal Oil Well Performance, 528; Problems, 542; References, 544 Gas Well Performance 546 Vertical Gas Well Performance, 546; Horizontal Gas Well Performance, 577; Problems, 580; References, 581 viii FM.qxd 3/22/06 4:52 AM Page ix Gas and Water Coning 583 Coning, 584; Coning in Vertical Wells, 587; Breakthrough Time in Vertical Wells, 620; After Breakthrough Performance, 624; Coning in Horizontal Wells, 629; Horizontal Well Breakthrough Time, 638; Problems, 646; References, 648 10 Water Influx 650 Classification of Aquifers, 651; Recognition of Natural Water Influx, 654; Water Influx Models, 655; Problems, 728; References, 731 11 Oil Recovery Mechanisms and the Material Balance Equation 733 Primary Recovery Mechanisms, 734; The Material Balance Equation, 752; Problems, 806; References, 809 12 Predicting Oil Reservoir Performance 810 Phase Reservoir Performance Prediction Methods, 811; Phase Relating Reservoir Performance to Time, 850; Problems, 853; References, 854 13 Gas Reservoirs 855 The Volumetric Method, 856; The Material Balance Method, 859; Material Balance Equation as a Straight Line, 874; Abnormally Pressured Gas Reservoirs, 880; Problems, 906; References, 908 14 Principles of Waterflooding 909 Factors to Consider in Waterflooding, 910; Optimum Time to Waterflood, 915; Effect of Trapped Gas on Waterflood Recovery, 917; Selection of Flooding Patterns, 927; Overall Recovery Efficiency, 932; I Displacement Efficiency, 934; II Areal Sweep Efficiency, 985; III Vertical Sweep Efficiency, 1041; Methods of Predicting Recovery Performance for Layered Reservoirs, 1058; Waterflood Surveillance, 1069; Problems, 1085; References, 1094 15 Vapor-Liquid Phase Equilibria 1096 Vapor Pressure, 1096; Equilibrium Ratios, 1099; Flash Calculations, 1103; Equilibrium Ratios for Real Solutions, 1107; Equilibrium Ratios for the Plus Fraction, 1120; Applications of the Equilibrium ix Appendix.qxd 3/15/06 1346 8:04 PM Page 1346 Reservoir Engineering Handbook Figure Heptane Conv press 5,000 psia Courtesy of the Gas Processors Suppliers Association Published in the GPSA Engineering Data Book, Tenth Edition, 1987 Appendix.qxd 3/15/06 8:04 PM Page 1347 Appendix 1347 Figure 10 Octane Conv press 5,000 psia Courtesy of the Gas Processors Suppliers Association Published in the GPSA Engineering Data Book, Tenth Edition, 1987 Appendix.qxd 3/15/06 1348 8:04 PM Page 1348 Reservoir Engineering Handbook Figure 11 Nonane Conv press 5,000 psia Courtesy of the Gas Processors Suppliers Association Published in the GPSA Engineering Data Book, Tenth Edition, 1987 Appendix.qxd 3/15/06 8:04 PM Page 1349 Appendix 1349 Figure 12 Decane Conv press 5,000 psia Courtesy of the Gas Processors Suppliers Association Published in the GPSA Engineering Data Book, Tenth Edition, 1987 This Page Is Intentionally Left Blank Index.qxd 3/15/06 8:07 PM Page 1351 INDEX A Absolute open flow, 488 permeability correlations, 250 porosity, 190 Absolute open flow, 488 Acentric factor, 25 correlations, 26 After-breakthrough production, 976 Ahmed’s splitting scheme, 1215 Alani-Kennedy equation, 1149 API gravity, 76 Apparent molecular weight, 32 Aquifer, 651 boundary conditions, 653 classification, 651 flow geometry, 653 flow regimes, 653 prediction models, 655 Areal sweep efficiency (EA), 985 Asymmetric mixture, 1179 Average reservoir pressure, 419, 770, 866 Averaging permeability, 241 porosity, 184 relative permeability, 313 saturation, 197 B Back pressure equation, 556 plot, 557 Behavior of real gases, 36 Binary interaction coefficient, 1172 Bottom-water drive, 669, 692 Breakthrough, 965 Bubble-point pressure, 86, 871 curve, definition of, 86 methods of determining, 86, 1125, 1198, 1201 phase equilibrium, 1179 Buildup testing, 467 Bulk compressibility coefficient, 255 C Campbell’s equilibrium ratio method, 1121 1351 Index.qxd 3/15/06 1352 8:07 PM Page 1352 Index Capillary pressure, 203 curve, 208 definition, 203 hysteresis, 209, 211 Carter-Tracy water influx model, 718 Carter type curve, 1291 Characterizing petroleum fractions, 25 Combination drive, 801 Component, 1096 Compressibility coefficient bulk, 255 definition, 59 formation, 256 gas, 59 matrix, 255 oil, 98, 148 pore, 255 Compressibility factor calculation, 38, 1159 definition, 37 Compressibility of natural gases, 59 Condensate liquid dropout, 182 retrograde, 171 Conductance ratio, 1016 Cone, 585 stable, 585 unstable, 585 Coning, 583 gas, 588 in horizontal wells, 629 in vertical wells, 587 water, 589 Constantcomposition tests, 137, 174 terminal pressure , 384 terminal rate, 384 volume depletion tests, 176 Convergence pressure, 1113 Hadden’s method, 1115 Rzasa’s method, 1118 Standing’s method, 1117 Correcting constant-composition data, 164 differential liberation date, 166 separator data, 169 viscosity data, 167 Counterflow, 945 Cox chart, 1097 Craig-Geffen-Morse oil recovery prediction method, 1065 Cricondenbar, Cricondentherm, Critical compressibility factor, 26 flow rate, 586 point, pressure, temperature, Crude oil density, 97,141,1142 gravity, 75 properties, 74 Cubic equation of state, 1158 D Dalton’s Law, 1099, 1107 Darcy’s Law, 228 Dead-oil viscosity, 115 Decline curve analysis, 1235 Exponential decline, 1237, 1241 Harmonic decline, 1238, 1249 Hyperbolic decline, 1238, 1250 Deliverability equation, 556 Density calculations, 1142 Depletion-drive mechanism, 735, 761 Index.qxd 3/15/06 8:07 PM Page 1353 Index Desaturating process, 210 Dew-point, 11, 1179 curve, Dew-point pressure, 3, 1179 definition of, 1123, 1195 methods of determining, 1195, 1201 Differential liberation, 149 Differential separation, 1130 Diffusivity equation, 381 Dimensionless diffusivity equation, 395 gravity number, 1039 pressure, 393 radius, 394 time, 394 Displacement efficiency (ED), 934 Downdip flow, 943 Drainage process, 293 Drawdown test, 454 Driving mechanisms, 761 combination, 752 depletion, 735 gas-cap, 787 gravity-drainage, 746 solution gas, 735, 761 water-drive, 792 Dry-gas reservoirs, 15 Dykstra-Parsons Modified, 1062 oil recovery prediction method, 1059 permeability variation method, 1042 sequencing technique, 1046 E Ei-function, 385 Edge-water drive, 669 Edmister correlation, 1178 1353 Effective permeability, 289 porosity, 191 wellbore radius, 437 End-point mobility ratio, 1050 Energy plots, 866 Equation(s) of state, 1134 applications, 1194 cubic, 1158 Peng-Robinson, 1182, 1203, 1295 Redlich-Kwong, 1160 Soave-Redlich-Kwong (SRK), 1169, 1205 Van der Waals, 1150 vapor pressure, 1205 Equilibrium ratio, 1099 applications, 1122 Campbell’s method, 1121 determination of, 1194 Katz’s method, 1122 phase equilibrium, 1179 for plus fractions, 1120 for real solutions, 1107 three-phase, 1199 Winn’s method, 1121 Equilibrium separation, 1130 Exponential integral, 385 Extrapolation of reservoir fluid data, 164 F Felsenthal, Cobb, and Heuer oil recovery prediction method, 1062 Fetkovich’s IPR equation, 509 method, 509 Type curve, 1275 Water influx, 722 Index.qxd 3/15/06 8:07 PM Page 1354 1354 Fill-up, 1027 Finite-radial reservoir, 398 Flash calculations, 1103, 1202 Flash separation, 1130 Flood patterns, 927 Confiment, 1080 Conformance, 1082 Flow equations, 340 Flow regimes, 334 Flowing material balance, 1308 Fluids classification of, injectivity, 1012 properties, 29 Formation compressibility, 254 Correlations, 259 Formation volume factor gas, 65 oil, 92 Fractional flow equation, 936 Fratures; Finite-condutivity, 1322 infinite-condutivity, 1322 Uniform-flux, 1323 Fractured wells, 1321 Free water level, 213 Frontal advance equation, 952 Frontal displacement theory, 936 Fugacity, 1175 coefficient, 1176 Fundamentals of reservoir fluid behavior, reservoir fluid flow, 331 rock properties, 189 G Gas coning, 583 dry gas, 10, 15 fugacity, 1175 Index material balance equation, 859 in place, 856 properties, 29 reservoirs, 10, 855 saturation, 873 solubility, 78 viscosity, 68 well performance, 546 wet gas, 10 Gas-cap drive reservoirs, 787 Gas-condensate reservoirs, 10 Gas-oil ratio, 372 Gas solubility correlations, 78 Gas well performance, 546 Geometric average permeability, 249 Gravity crude oil, 75 solution gas, 76 Gravity-drainage reservoirs, 746 H Hadden’s convergence pressure method, 1115 Hall Plot, 1071 Harmonic average permeability, 245 Havlena and Odeh, 772 Heptanes-plus fraction, 1191, 1207 Heterogeneity, 261 vertical, 261 High shrinkage oil, Hong’s mixing rules, 1222 Horizontal heterogeneity, 261, 274 well breakthrough, 624 gas, 577 oil, 528 Horner’s plot, 470 Hurst and van Everdingen, 668 Hurst’s steady-state method, 663 Index.qxd 3/15/06 8:07 PM Page 1355 Index I Image wells, 450 Imbibition process, 296 Incompressible fluids, 332 Infinite acting, 374, 396 Inflow performance relationships gas, 547 oil, 488 Injection rate, 1012 Interfacial tension, 200 Interference, 1012 IPR, 484, 488 Fetkovich’s, 509 Standing’s, 505 Vogel’s, 493 Inverse distance method, 276 Inverse distance squared method, 277 Isothermal compressibility coefficient gas, 59 oil, 98 rock, 254 1355 Laminar flow, 342 Laminar-Inertial-Turbulent, 558 Layers, minimum number of, 1043 Lee and Kessler correlation, 1178 Lee’s mixing rules, 1223 Leverett J-function, 224 Linear flow, 338 Liquid dropout, 12 LIT approach, 558 Lohrenz’s splitting scheme, 1212 Lorenz coefficient, 268 Lost oil saturation, 824 Low-shrinkage oil, Lumping schemes, 1218 Whitson’s, 1219 M Katz’s equilibrium ratio method, 1122 splitting scheme, 1210 Kay’s mixing rules, 1223 Klinkenberg effect, 234 m(p)-solution method, 405 Material balance equation (MBE), 733, 958 gas, 958 oil, 733 straight-line, 772 Material balance pseudo-time, 1301 Matrix compressibility coefficient, 254 Maximum liquid dropout, 13 Method of images, 450 Mixing rules, 1161, 1222, 1223 Mobility ratio, 987 Muskat’s material balance method, 838 L N Laboratory PVT tests, 136 routine, 136 special, 136 Natural gases, compressibility of, 59 Near-critical crude oil, J J-function, 224 K Index.qxd 3/15/06 8:07 PM Page 1356 1356 Near-critical gas condensate, 10 Non-Darcy flow, 438 Nonstabilized zone, 957 Normalized material balance pseudo-time, 1301 Normalizing relative permeability, 313 O Odeh and Havlena, 772 Oil formation volume factor, 92 for undersaturated oils, 103 Oil material balance equation, 773 Oil properties, 74 Oil recovery predicting, 81 Oil reservoirs, Oil saturation, 824 Oil saturation adjustment for combination drive, 822 for gas-cap expansion, 820 for water influx, 819 Oil viscosity, 115 Oil-water contact, 213 Oil well performance, 484 Optimum gas saturation, 922 Optimum separator pressure, 1131 Ordinary black oil, P p/z gas equation, 861 pattern balancing, 1079 Pedersen’s splitting scheme, 1214 Peng-Robinson equation of state, 1182, 1203, 1205 Permeability, 227 absolute, 227 averaging, 242 effective, 289 Index relative, 288 variation, 262 Permeability ordering, 1046 Phase diagram, Phase equilibrium, 1179 Plant products, 173 Plus fractions, 1191, 1207 lumping, 1218 splitting, 1208 Polygon method, 276 Pore compressibility coefficient, 255 volume, 192 Porosity, 190 absolute, 190 effective, 191 Porosity averaging methods, 194 Positional permeability variation, 1046 Pot aquifer, 655 Predicting oil reservoir performance, Craig-Geffen-Morse method, 1065 Dykstra-Parsons method, 1069, 1062 Felsenthal, Cobb, and Heuer method, 1062 Muskat’s method, 838 Tarner’s method, 843 Tracy’s method, 831 Pressure bubble-point, 3, 86, 1125, 1198, 1201 buildup, 467 drawdown, 454 drop due to skin, 472 capillary, 203 dew-point, 3, 1123, 1179, 1195, 1201 Index.qxd 3/15/06 8:07 PM Page 1357 Index Pressure (Continued ) pseudo-critical, 38 pseudo reduced, 37 separator, 1128 -squared approximation, 408 vapor, 1205 Pressure-approximation method, 404 Pressure-squared method, 404 Pressure-temperature diagram, Primary recovery mechanisms, 761 Probability-log scale, 264 Productivity index, 473 Properties of crude oil systems, 74 natural gases, 29 rocks, 189 water, 124 Pseudocritical pressure, 42 temperature, 42 Pseudoization, 1218 Pseudosteady-state flow, 413 R Radial diffusivity equation, 382 flow of gases, 429 Raoult’s Law, 1099, 1107 Real solutions, 1107 Redlich-Kwong equation of state, 1162 Reduced gas density, 56 Reduced pressure, 37 Reduced temperature, 37 Relative oil volume, 141 Relative permeability, 288 averaging, 313 concepts, 288 correlations, 296 1357 three-phase, 320 two-phase, 289 Relative total volume, 141 Reservoir apparent molecular weight, 32 composition of, 137 density, 33 fluid properties, 29 geometry, 336 heterogeneity, 261 ideal gases, 30 specific gravity, 34 specific volume, 33 standard volume, 33 water properties, 122 Reservoir drive mechanisms, combination, 752 gas-cap, 787 solution gas-drive, 735 water-drive, 792 Reservoirs, classification of, Residual oil saturation, 196 Retrograde gas reservoirs, 10 Riazi and Daubert correlation, 1191 Rock compressibility, 254 properties, 189 Routine laboratory PVT tests, 136 Rzasa’s convergence pressure method, 1118 S Saturated oil reservoirs, viscosity, 117 Saturation, 189 averaging, 195 critical oil, 196 movable oil, 196 Index.qxd 3/15/06 8:07 PM Page 1358 1358 Saturation (Continued ) pressure, 137 residual oil, 196 trapped gas, 873 water, 197 Schilthuis’s steady-state method, 655, 659 Semisteady-state, 336, 414 Separator tests, 146, 152 Shallow gas reservoirs, 900 Shape factor, 423, 466 Shock front, 967 Shrinking gas cap, 822 Skin factor, 431 Soave-Redlich-Kwong (SRK) equation of state, 1168 modifications of, 1178 Splitting schemes, 1108 Ahmed’s, 1215 Lohrenz’s, 1212 Pedersen’s, 1214 Stabilized zone, 957 Stage separation, 1128 Standing-Katz density calculation method, 1142 Standing’s convergence pressure method, 1117 correlation, 1108, 1166 IPR equation, 505 Steady-state flow, 334, 342 Stiles’ permeability variation method, 1050 Stone’s I model, 324 Stone’s II model, 326 Superposition, 442 Surface tension, 121, 200 Index T Tarner’s method, 843 Three-phase equilibrium, 1199 Three-phase relative permeability, 320 correlations, 322 Tight gas reservoirs, 866 Time end of infinite-acting, 465 Total formation volume factor, 159 Tounquing, 1038 Tracy’s form of the MBE, 803 method, 831 Transition zone, 213 Trapped gas saturation, 873 Turbulent flow factor, 437 Two-phase formation volume factor, 108, 159 relative correlations, 296 relative permeability, 289 z-factor, 178 Type-curve Anash, 1311 Carter, 1292 Fetkovich, 1275 Fractured wells, 1321, 1326 Palacio-Blasingame, 1299 Type-curve analysis, 1264 U Undefined petroleum fractions, 24 Undersaturated oil reservoirs, 4, 825 viscosity, 117 Unsteady-state flow, 373 Index.qxd 3/15/06 8:07 PM Page 1359 Index V Van der Waals equation of state, 1149 Van Everdingen-Hurst’s unsteadystate model, 668 Vapor pressure, 1096, 1205 Vertical gas well performance, 546 heterogeneity, 262 oil well performance, 484 sweep efficiency (EV), 1061 Viscosity dead oil, 115 gas, 67 oil, 114 saturated oil, 117 undersaturated oil, 119 water, 125 Vogel’s IPR equation, 493 Volatile crude oil, Volume translation method, 1180 Volumetric sweep efficiency, 934 Waterflooding Factors to consider, 910 optimum time, 915 patterns, 927 recovery factor (RF), 932 surveillance, 1069 trapped gas, 865 Water influx, 650 Carter-Tracy model, 718 Fetkovich’s model, 722 Water isothermal compressibility, 126 Water-oil ratio, 372, 946 Waterflood surveillance, 1069 Wellbore storage, 460 Wet-gas reservoirs, 14 Wettability, 199 Whitson and Torp correlation, 1119 Whitson’s lumping scheme, 1219 Wilson’s correlation, 1108, 1118 Winn’s equilibrium ratio method, 1121 X W Water properties, 124 viscosity, 125 Water coning, 589 Water-drive reservoirs, 792 gas, 870 oil, 792 Water fingering, 1038 1359 X-plot, 1075 Y Y-function, 143 Z Zonation problem, 1046 Z-factor, 37, 151 Index.qxd 3/15/06 8:07 PM Page 1360 ABOUT THE AUTHOR Tarek Ahmed, Ph.D., P.E., is a Reservoir Engineering Advisor with Anadarko Petroleum Corporation Before joining the corportion, Dr Ahmed was a professor and the head of the Petroleum Engineering Department at Montana Tech of the University of Montana He has a Ph.D from the University of Oklahoma, an M.S from the University of Missouri-Rolla, and a B.S from the Faculty of Petroleum (Egypt)—all degrees in petroleum engineering Dr Ahmed is also the author of other textbooks including Hydrocarbon Phase Behavior (Gulf Publishing Company, 1989), Advanced Reservoir Engineering (Elsevier, 2005), and is currently completing a textbook entitled EOS and PVT Analysis 1360 ... Tc of the reservoir fluid, the reservoir is classified as an oil reservoir Ch01.qxd 3/15/06 7:06 PM Page Reservoir Engineering Handbook • Gas reservoirs—If the reservoir temperature is greater... 7:07 PM Page 22 Reservoir Engineering Handbook Ch01.qxd 3/15/06 7:07 PM Page 23 Fundamentals of Reservoir Fluid Behavior 23 Ch01.qxd 3/15/06 7:07 PM Page 24 24 Reservoir Engineering Handbook (text... the reservoir is considered a gas reservoir Oil Reservoirs Depending upon initial reservoir pressure pi, oil reservoirs can be subclassified into the following categories: Undersaturated oil reservoir