Ahmed, Tarek - Reservoir Engineering Handbook PDF

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Summary

Splitting and lumping schemes of the plus-fraction ................................................. 1137 Splitting schemes ......................................... 1138 Lumping schemes ........................................ 1148 Problems ..................................................... 1155...

Description

Splitting and lumping schemes of the plus-fraction .................................................

1137

Splitting schemes ......................................... Lumping schemes ........................................

1138 1148

Problems .....................................................

1155

References ..................................................

1159

APPENDIX .................................................. 1165 INDEX ......................................................... 1177

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Second Edition

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Second Edition

Gulf Professional Publishing Boston • London • Auckland • Johannesbourg • Melbourne • New Delhi

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Gulf Professional Publishing is an imprint of Butterworth-Heinemann. Copyright © 2001 by Butterworth-Heinemann A member of the Reed Elsevier group Previously copyrighted © 2000 by Gulf Publishing Company, Houston, Texas All rights reserved. No part of this publication may be reproduced, stored in a retrival system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Recognizing the importance of preserving what has been written, Butterworth-Heinemann prints its books on acid-free paper whenever possible. Library of Congress Cataloging-in-Publication Data Ahmed, Tared H., 1946Reservoir engineering handbook / Tarek Ahmed. p.cm. Includes bibliographical references and index. ISBN 0-88415-770-9 (alk. paper) 1. Oil reservoir engineering. 2. Oil fields. 3. Gas reservoirs. I. Title. TN871 .A337 2000 622’.3382--dc21 99-005377 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. The publisher offers special discounts on bulk orders of this book. For information, please contact: Manager of Special Sales Butterworth-Heinemann 225 Wildwood Avenue Woburn, MA 01801–2041 Tel: 781-904-2500 Fax: 781-904-2620 For information on all Butterworth-Heinemann publications available, contact our World Wide Web home page at: http://www.bh.com 10 9 8 7 6 5 4 3 2 1 Printed in the United States

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To my gorgeous wife Shanna, And my beautiful children Jennifer Justin Brittany Carsen

ACKNOWLEDGMENTS .............................

xiii

PREFACE TO THE SECOND EDITION .....

xiv

PREFACE TO THE FIRST EDITION ..........

xv

1 FUNDAMENTALS OF RESERVOIR FLUID BEHAVIOR ......................................

1

Classification of reservoirs and reservoir fluids ............................................................

1

Pressure-temperature diagram .................... Oil reservoirs ................................................ Gas reservoirs ............................................. Undefined petroleum fractions .....................

2 4 10 24

Problems .....................................................

27

References ..................................................

28

2 RESERVOIR-FLUID PROPERTIES ........

29

Properties of natural gases .........................

29

Behavior of ideal gases ...............................

30

Behavior of real gases .................................

36

Effect of nonhydrocarbon components of the Z-factor ..................................................

44

Nonhydrocarbon adjustment methods ......... The Wichert-Aziz correction method ............

45 45

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

74

Crude oil gravity ........................................... Specific gravity of the solution gas .............. Gas solubility ............................................... Bubble-point pressure .................................. Oil formation volume factor .......................... Isothermal compressibility coefficient of crude oil ....................................................... Oil formation volume factor for undersaturated oils ...................................... Crude oil density .......................................... Crude oil viscosity ........................................

75 76 77 86 92

103 106 108

Methods of calculating viscosity of the dead oil ........................................................

109

Methods of calculating the saturated oil viscosity .......................................................

111

Methods of calculating the viscosity of the undersaturated oil ..................................

112

Surface/interfacial tension ...........................

115

Properties of reservoir water .......................

118

Water formation volume factor ..................... Water viscosity ............................................. Gas solubility in water .................................. Water isothermal compressibility .................

118 119 119 120

Problems .....................................................

120

References ..................................................

126

3 LABORATORY ANALYSIS OF RESERVOIR FLUIDS .................................

130

Composition of the resevoir fluid .................

131

98

Constant-composition expansion tests ........

131

Differential liberation (vaporization) test ......

143

Separator tests ............................................

146

Adjustment of differential liberation data to separator conditions ................................

151

Extrapolation of resevoir fluid data ..............

158

Correcting constant-composition expansion data ............................................ Correcting differential liberation data ........... Correcting oil viscosity data ......................... Correcting the separator tests data .............

158 160 161 163

Laboratory analysis of gas condensate systems .......................................................

165

Recombination of separator samples .......... Constant-composition test ........................... Constant-volume depletion (CVD) test ........

165 168 170

Problems .....................................................

178

References ..................................................

182

4 FUNDAMENTALS OF ROCK PROPERTIES .............................................

183

Porosity .......................................................

184

Absolute porosity ......................................... Effective porosity .........................................

184 185

Saturation ....................................................

189

Average saturation .......................................

191

Wettability ....................................................

193

Surface and interfacial tension ....................

194

Capillary pressure .......................................

197

Capillary pressure of reservoir rocks ........... Capillary hysteresis ......................................

200 203

Initial saturation distribution in a reservoir ... Leverett J-function ....................................... Converting laboratory capillary pressure data ..............................................................

206 218

Permeability .................................................

221

The Klinkenberg effect ................................. Averaging absolute permeabilities ...............

228 235

Weighted-average permeability .............................. Harmonic-average permeability .............................. Geometric-average permeability ..............................

221

236 239 243

Absolute permeability correlations ...............

244

Rock compressibility ....................................

248

Net pay thickness ........................................

254

Resevoir heterogeneity ...............................

255

Vertical Heterogeneity .................................

256

Areal heterogeneity .....................................

268

Problems .....................................................

273

References ..................................................

278

5 RELATIVE PERMEABILITY CONCEPTS ................................................

280

Two-phase relative permeability ..................

281

Drainage process ......................................... Imbibition process ........................................ Two-phase relatie permeability correlations .................................................. 1 Wyllie and Gardner correlation ................. 2 Torcaso and Wyllie correlation ................. 3 Pirson’s correlation ...................................

285 286 286 288 289 289

4 Corey’s method ......................................... 5 Relative permeability from capillary pressure data ............................................... 6 Relative permeability from analytical equations .....................................................

291

Relative permeability ratio ...........................

298

Dynamic pseudo-relative permeabilities ......

301

Normalization and averaging realtive permeability data .........................................

304

Three-phase relative permeability ...............

310

Three-phase relative permeability correlations .................................................. Wyllie’s correlations ..................................... Stone’s model I ............................................ Stone’s model II ........................................... The Hustad-Holt correlation .........................

312 313 314 316 316

Problems .....................................................

319

References ..................................................

320

6 FUNDAMENTALS OF RESERVOIR FLUID FLOW ..............................................

321

Types of fluid ...............................................

322

Flow regimes ...............................................

324

Resevoir geometry ......................................

326

Number of flowing fluids in the resevoir ......

329

Fluid flow equations .....................................

330

Darcy’s Law .................................................

331

Steady-state flow .........................................

332

Linear flow of incompressible fluids ............. Linear flow of slightly compressible fluids .... Linear flow of compressible fluids (gases) ...

333 339 341

292 294

Radial flow of incompressible fluids ............. Radial flow of slightly compressible fluids .... Radial flow of compressible gases .............. Horizontal multiple-phase flow .....................

344 350 352 360

Unsteady-state flow .....................................

363

Basic transient flow equation ....................... Radial flow of slightly compressible fluids ....

365 370

Constant-terminal-pressure solution ...........

374

Constant-terminal-rate solution ...................

374

The E-function solution ................................ The dimensionless pressure drop (Pd) solution ........................................................ Radial flow of compressible fluids ................ The m(p)-solution method (exact-solution) ............................................ The pressure-squared approximation method (p2-method) .................................... The pressure-approximation method ...........

375

Pseudosteady-state flow .............................

403

Radial flow of slightly compressible fluids .... Radial flow of compressible fluids (gases) ......................................................... Pressure-squared approximation method .... Pressure-approximation method .................. Skin factor .................................................... Turbulent flow factor ....................................

409

Principle of superposition ............................

431

Effects of multiple wells ............................... Effects of variable flow rates ........................ Effects of the reservoir boundary ................. Accounting for pressure-change effects ......

432 435 438 442

Transient well testing ...................................

442

Drawdown test .............................................

443

383 392 395 398 400

418 419 419 420 426

Pressure buildup test ...................................

456

Problems .....................................................

465

References ..................................................

471

7 OIL WELL PERFORMANCE ...................

473

Vertical oil well performance .......................

473

Productivity index and IPR ........................... Vogel’s method ............................................ Saturated oil reservoirs ................................ Undersaturated oil reservoirs ....................... Wiggins’ method .......................................... Standing’s method ....................................... Fetkovich’s method ...................................... The Klins-Clark method ...............................

473 482 483 485 491 494 498 514

Horizontal oil well performance ...................

515

Method I ....................................................... Method II ...................................................... Horizontal well productivity under steady-state flow .......................................... Borisov’s method ......................................... The Giger-Reiss-Jourdan method ............... Joshi’s method ............................................. The Renard-Dupuy method ......................... Horizontal well productivity under semisteady-state flow ..................................

516 517

Problems .....................................................

529

References ..................................................

531

8 GAS WELL PERFORMANCE .................

533

Vertical gas well performance .....................

533

Region I. High-pressure region .................... Region II. Intermediate-pressure region ......

536 537

519 520 520 521 522 527

Region III. Low-pressure region ................... The simpified treatment approach ............... The Laminar-Inertial-Turbulent (LIT) approach ...................................................... The Back-Pressure test ............................... Future inflow performance relationships ......

537 543

Horizontal gas well performance .................

562

Problems .....................................................

566

References ..................................................

568

9 GAS AND WATER CONING ...................

569

Coning .........................................................

570

Coning in vertical wells ................................

573

Vertical well critical rate correlations ............

573

The Meyer-Garder correlation ................................. The Chierici-Ciucci approach ... The Hoyland-Papatzacos-Skjaeve methods.................................... Critical rate curves by Chaney et al. ............................ Chaperson’s method ................ Schols’ method .........................

545 550 559

574 581 593 597 604 605

Breakthrough time in vertical wells ..............

606

The Sobocinski-Cornelius method ............... The Bournazel-Jeanson method ..................

606 609

After breakthrough performance .................

610

Coning in horizontal wells ............................

615

Horizontal well critical rate correlations .......

616

Chaperson’s method ................ Efros’ method ...........................

616 620

Karcher’s method ..................... Joshi’s method .........................

621 622

Horizontal well breakthrough time ...............

624

The Ozkan-Raghavan method ..................... Papatzacos’ method ....................................

624 627

Problems .....................................................

632

References ..................................................

634

10 WATER INFLUX ....................................

636

Classification of aquifers .............................

637

Degree of pressure maintenance ................ Outer boundary conditions ........................... Flow regimes ............................................... Flow geometries ..........................................

637...