Well Test Analysis for Fractured Reservoir Evaluation Developments in Petroleum Science, 27 DEVELOPMENTS in PETROLEUM SCIENCE Advisory Editor: G.V
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Developments in Petroleum Science, 27 well test analysis for fractured reservoir evaluation Developments in Petroleum Science, 27 DEVELOPMENTS IN PETROLEUM SCIENCE Advisory Editor: G.V. Chilingarian Volumes 1,3,4,7 and 13 are out of print. 2. W.H.FERTL ABNORMAL FORMATION PRESSURES 5. T.F. YEN and G.V. CHILINGARIAN (Editors) OIL SHALE 6. D.W. PEACEMAN FUNDAMENTALS OF NUMERICAL RESERVOIR SIMULATION 8. L.P.DAKE FUNDAMENTALS OF RESERVOIR ENGINEERING 9. K.MAGARA COMPACTION AND FLUID MIGRATION 10. M.T. SILVIA and E.A. ROBINSON DECONVOLUTION OF GEOPHYSICAL TIME SERIES IN THE EXPLORATION FOR OIL AND NATURAL GAS 11. G.V. CHILINGARIAN and P. VORABUTR DRILLING AND DRILLING FLUIDS 12. T.D. VAN GOLF-RACHT FUNDAMENTALS OF FRACTURED RESERVOIR ENGINEERING 14. G. MOZES (Editor) PARAFFIN PRODUCTS 15A 0.SERRA FUNDAMENTALS OF WELL-LOG INTERPRETATION 1. THE ACQUISITION OF LOGGING DATA 15B O.SERRA FUNDAMENTALS OF WELL-LOG INTERPRETATION 2. THE INTERPRETATION OF LOGGING DATA 16. R.E. CHAPMAN PETROLEUMGEOLOGY 17A E.C. DONALDSON, G.V. CHILINGARIAN and T.F. YEN ENHANCED OIL RECOVERY, I FUNDAMENTALS AND ANALYSES 18A A.P. SZILAS PRODUCTION AND TRANSPORT OF OIL AND GAS A. FLQW MECHANICS AND PRODUCTION second completely revised edition 18B A.P. SZILAS PRODUCTION AND TRANSPORT OF OIL AND GAS B. GATHERING AND TRANSPORTATION second completely revised edition 19A G.V. CHILINGARIAN, J.O. ROBERTSON Jr. and S.KUMAR SURFACE OPERATIONS IN PETROLEUM PRODUCTION, I 19B G.V. CHILINGARIAN, J.O. ROBERTSON Jr. and S. KUMAR SURFACE OPERATIONS IN PETROLEUM PRODUCTION, I1 20. A.J. DIKKERS GEOLOGY IN PETROLEUM PRODUCTION 21. W.F. RAMIREZ APPLICATION OF OPTIMAL CONTROL THEORY TO ENHANCED OIL RECOVERY 22. E.C. DONALDSON, G.V. CHILINGARIAN and T.F. YEN (Editors) MICROBIAL ENHANCED OIL RECOVERY 23. J. HAGOORT FUNDAMENTALS OF GAS RESERVOIR ENGINEERING 24. W. LITTMANN POLYMER FLOODING 25. N.K. BAIBAKOV and A.R. GARUSHEV THERMAL METHODS OF PETROLEUM PRODUCTION 26. D.MADER HYDRAULIC PROPPANT FRACTURING AND GRAVEL PACKING t we11 test analysis for fractured reservoir evaluation GIOVANNI DA PRAT Reservoir Department Manager Latin America Division Hallibutton Reservoir Services Caracas, Venezuela ELSEVIER - Amsterdam - Oxford - New York - Tokyo 1990 ELSEVIER SCIENCE PUBLISHERS B.V. Sara Burgerhartstraat 25 P.O. Box 211,1000 AE Amsterdam, The Netherlands Distributors for the United States and Canada: ELSEVIER SCIENCE PUBLISHING COMPANY INC. 655 Avenue of the Americas New York, NY 10010, U.S.A. Library of Congress Cataloging-in-Publication Data Da Prat. G. Well test analysis for fractured reservoir evaluation / G. Da Prat. p. cm. -- (Developments in petroleum science . 27) Includes bibliographical references and index. ISBN 0-444-88691-5 'I. Oil wells--Testing. 2. Oil reservoir engineering. I. Title. 11. Series. TN871.03 1990 622'.3382--dC20 90-49214 CIP ISBN 0-444-88691 5 0 Elsevier Science Publishers B.V., 1990 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or trans- mitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Science Publishers B.V./Physical Sci- ences & Engineering Division, P.O. Box 330,1000 AH Amsterdam, The Netherlands. Special regulations for readers in the USA - This publication has been registered with the Copyright Clearance Center Inc. (CCC), Salem, Massachusetts. 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 publisher. 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. Printed in The Netherlands Dedication This book is dedicated to the memory of John S. Rodgers This Page Intentionally Left Blank VII Preface When I decided to write a book on a complex subject such as naturally fractured 'reservoirs, I was aware that the technology is improving continuously and through time new methods for well-test interpretations are becoming available while existing models can be verified through te use of high-resolution pressure and spinner gauges. This book does not introduce an new model for well-test interpretation in wells completed in fractured reservoirs. Rather it may be considered as a guide to what has been done so far regarding analysis of pressure and flow-rate transients for these systems. Basically, the contents can be divided into three important topics related to transient test interpretations: - Interpretation of pressure transient tests at constant flow rate - Decline curve analysis, and - Interpretation of interference tests. In Chapter 1 a summary of well-test analysis is presented. It includes a review on the pressure-derivative method and the analysis of simultaneous measurements of pressure and flow rate (convolution and deconvolution techniques). The reader already familiar with the subject may skip this chapter. In Chapter 2 the characteristics of fractured reservoirs are presented and the tech- niques used to identify fractured reservoirs are analyzed. It includes a summary on the different models introduced over the past 30 years for well-test interpretations. A comparison of the different models from a practical point of view. Chapter 3 is a fundamental chapter regarding pressure-transient analysis for fractured reservoirs. The partial differential equations used to generate the dimen- sionless wellbore pressure solutions are presented. Both pseudo-steady-state and transient interporosity fluid flows are considered. The use of the type curves is illustrated through examples of their application. Chapter 4 is an application chapter and is dedicated basically to the most popular method used in well-test interpretation: the Horner plot. A practical procedure for analyzing build-up data from fissured formations is also given. Chapter 5 presents the solutions for dimensionless fractured and matrix pressures in the formation or the line-source solution for fissured reservoirs. The use of the type curves is illustrated with both a simulated and a field case. Chapter 6 discusses the fundamentals of decline-curve analysis for fractured reservoirs. This topic has not received much attention in the literature even though it is related to a key factor regarding economics: production-forecast analysis. The dimensionless transient rate solutions in the estimation of the fissured-reservoir pa- rameters w and A, using transient rate data due to the lack of pressure data, makes VIII Preface the method worthy of use for practical purposes following the improvement in the present-day resolution of flowmeters and their accuracy. Chapter 7 presents the dimensionless matrix- and fracture-pressure solutions needed to study the data from interference tests conducted in fractured reservoirs when the wells are producing under constant pressure. Chapter 8 describes and lists a basic computer program (in FORTRAN) that solves the general two-porosity system. With this program, the user can generate type curves for specific cases. The appropriate changes to be made to this program to include transient interporosity fluid flow and the pressure derivative are also explained. Chapter 9, a contribution by Luis Prado, deals with the use of pressure-transient tests to determine the fracture system extensions and fracture trends. The solution for unsteady liquid flow in a uniformly fractured zone around a well is also provided. Chapter 10, finally, discusses the design of production, interference and build-up tests to be conducted in wells completed in fractured reservoirs. The planning and design of each test is illustrated with a numerical example. GIOVANNI DA PRAT M Acknowledgements I would like to thank Mr. Luis R. Prado, presently working with K.S.E.P.L., The Netherlands, who is the author of Chapter 9 and parts of Chapter 1. I am grateful to the Petroleum Engineering Department of Stanford University, specially to Dr. Henry J. Ramey, Jr. and Heber Cinco-Ley, who oriented me in the area of well test analysis during my career. Finally, I would like to thank Mr. Rafael Zapata and Luis Ignacio for the typing of the original manuscript. This Page Intentionally Left Blank XI Contents Preface . , . VII Acknowledgements .. .. .. .. .. .. , . M Chapter 1. Well-Test Analysis . 1 1.1. introduction . 1 1.2. Wellbore storage and skin effect . 1 1.3. Outer boundaries and discontinuities . , . 2 1.4. Well-test interpretation . .. .. .. .. .. .. .. .. .. ., .. .. 4 1.4.1. Partial differential equations . ......................................... 4 1.4.2. Dimensionless pressure solutions . 5 1.4.3. Infinite reservoir solution . ............... 5 1.4.4. Type-curve matching techniques . 9 1.4.5. Semi-logarithmic analysis . ................................ 10 1.4.6. Example of an interference test . ....................... 11 1.4.7. Identification of flow regimes .. 13 1.4.8. Superposition principle-build-up testing . 15 1.5. Pressure-derivative analysis . 16 1.6. Interpretation using simultaneously measured pressure and sandface 23 1.6.1. Convolution . ................................... 24 1.6.2. Deconvolution . ....................... 27 1.6.3. Examples of application . , . 29 1.7. Wellbore storage deconvolution . ...............................