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fundamentals of reservoir engineering

498 Pages · 1999 · 7.25 MB · English

  • fundamentals of reservoir engineering

    Developments in Petroleum Science, 8


    fundamentals of


    reservoir engineering FURTHER TITLES IN THIS SERIES


    1 A. GENE COLLINS


    GEOCHEMISTRY OF OILFIELD WATERS


    2 W.H. FERTL


    ABNORMAL FORMATION PRESSURES


    3 A.P. SZILAS


    PRODUCTION AND TRANSPORT OF OIL AND GAS


    4 C.E.B. CONYBEARE


    GEOMORPHOLOGY OF OIL AND GAS FIELDS


    IN SANDSTONE BODIES


    5 T.F. YEN and G.V. CHILINGARIAN (Editors)


    OIL SHALE


    6 D.W. PEACEMAN


    FUNDAMENTALS OF NUMERICAL RESERVOIR SIMULATION


    7 G.V. CHILINGARIAN and T.F. YEN (Editors)


    BITUMENS, ASPHALTS AND TAR SANDS


    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 Developments in Petroleum Science, 8


    fundamentals of


    reservoir


    engineering


    LP. DAKE


    Senior Lecturer in Reservoir Engineering,


    Shell Internationale Petroleum Maatschappij B. V.,


    The Hague, The Netherlands


    ELSEVIER, Amsterdamuf8e7Londonuf8e7New Yorkuf8e7Tokyo ELSEVIER SCIENCE B.V.


    Sara Burgerhartstraat 25


    P.O. Box 211, 1000 AE Amsterdam, The Netherlands


    First edition 1978


    Second impression l979


    Third impression 1980


    Fourth impression 1981


    Fifth impression 1982


    Sixth impression 1982


    Seventh impression 1983


    Eighth impression 1985


    Ninth impression 1986


    Tenth impression 1988


    Eleventh impression 1990


    Twelfth impression 1991


    Thirteenth impression 1993


    Fourteenth impression 1994


    Fifteenth impression 1995


    Sixteenth impression 1997


    Seventeenth impression 1998


    ISBN 0-444-41830-X


    uf6d9 1978 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 U.S.A.-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 U.S.A. All other copyright questions,


    including photocopying outside of the U.S.A., 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.


    This book is printed on acid-free paper


    Printed in The Netherlands To Grace PREFACE


    This teaching textbook in Hydrocarbon Reservoir Engineering is based on various


    lecture courses given by the author while employed in the Training Division of Shell


    Internationale Petroleum Maatschappij B.V. (SIPM), in the Hague, between 1974 and


    1977.


    The primary aim of the book is to present the basic physics of reservoir engineering,


    using the simplest and most straightforward of mathematical techniques. It is only


    through having a complete understanding of the physics that the engineer can hope to


    appreciate and solve complex reservoir engineering problems in a practical manner.


    Chapters 1 through 4 serve as an introduction to the subject and contain material


    presented on Shell's basic training courses. They should therefore be of interest to


    anyone even remotely connected with the business of developing and producing


    hydrocarbon reserves.


    Chapters 5 through 8 are more specialised describing the theory and practice of well


    testing and pressure analysis techniques, which are probably the most important


    subjects in the whole of reservoir engineering. The approach is entirely general in


    recognising that the superposition of dimensionless pressure, or pseudo pressure


    functions, perm its the analysis of any rate-pressure-time record retrieved from a well


    test, for any type of reservoir fluid. To appreciate this generality, the reader is advised


    to make a cursory inspection of section 8.13 (page 295), before embarking on a more


    thorough reading of these chapters. The author hopes that this will serve as a useful


    introduction to the recently published and, as usual, excellent SPE Monograph


    (Advances in Well Test Analysis; by Robert C. Earlougher, Jr.), in which a knowledge is


    assumed of much of the theory presented in these four chapters.


    Chapter 9 describes the art of aquifer modelling, while Chapter 10, the final chapter,


    covers the subject of immiscible, incompressible displacement. The message here is-


    that there is but one displacement theory, that of Buckley and Leverett. Everything else


    is just a matter of "modifying" the relative permeability curves (known in the business


    as "scientific adjustment"), to account for the manner in which the fluid saturations are


    distributed in the dip-normal direction. These curves can then be used in conjunction


    with the one dimensional Buckley-Leverett equation to calculate the oil recovery. By


    stating the physics implicit in the generation of averaged (pseudo) relative


    permeabilities and illustrating their role in numerical simulation, it is hoped that this


    chapter will help to guide the hand of the scientific adjuster.


    The book also contains numerous fully worked exercises which illustrate the theory.


    The most notable omission, amongst the subjects covered, is the lack of any serious


    discussion on the complexities of hydrocarbon phase behaviour. This has al ready


    been made the subject of several specialist text books, most notably that of Amyx,


    Bass and Whiting (reference 8, page 42), which is frequently referred to throughout this


    text. PREFACE / ACKNOWLEDGEMENTS VIII


    A difficult decision to make, at the time of writing, is which set of units to employ.


    Although the logical decision has been made that the industry should adopt the SI


    (Système Internationale) units, no agreement has yet been reached concerning the


    extent to which "allowable" units, expressed in terms of the basic units, will be


    tolerated. To avoid possible error the author has therefore elected to develop the


    important theoretical arguments in Darcy units, while equations required for application


    in the field are stated in Field units. Both these systems are defined in table 4.1, in


    Chapter 4, which appropriately is devoted to the description of Darcy's law. This


    chapter also contains a section, (4.4), which describes how to convert equations


    expressed in one set of units to the equivalent form in any other set of units. The


    choice of Darcy units is based largely on tradition. Equations expressed in these units


    have the same form as in absolute units except in their gravity terms. Field units have


    been used in practical equations to enable the reader to relate to the existing AIME


    literature. PREFACE / ACKNOWLEDGEMENTS IX


    ACKNOWLEDGEMENTS


    The author wishes to express his thanks to SIPM for so readily granting permission to


    publish this work and, in particular, to H. L. Douwes Dekker, P.C. Kok and C. F.M.


    Heck for their sustained personal interest throughout the writing and publication, which


    has been a source of great encouragement.


    Of those who have offered technical advice, I should like to acknowledge the


    assistance of G.J. Harmsen; L.A. Schipper; D. Leijnse; J. van der Burgh; L. Schenk; H.


    van Engen and H. Brummelkamp, all sometime members of Shell's reservoir


    engineering staff in the Hague. My thanks for technical assistance are also due to the


    following members of KSEPL (Koninklijke Shell Exploratie en Productie Laboratorium)


    in Rijswijk, Holland: J. Offeringa; H.L. van Domseiaar; J.M. Dumore; J. van Lookeren


    and A.S. Williamson. Further, I am grateful to all former lecturers in reservoir


    engineering in Shell Training, and also to my successor A.J. de la Mar for his many


    helpful suggestions. Sincere thanks also to S.H. Christiansen (P.D. Oman) for his


    dedicated attitude while correcting the text over a period of several months, and


    similarly to J.M. Willetts (Shell Expro, Aberdeen) and B.J.W. Woods (NAM, Assen) for


    their efforts.


    For the preparation of the text I am indebted to G.J.W. Fransz for his co-ordinating


    work, and particulariy to Vera A. Kuipers-Betke for her enthusiastic hard work while


    composing the final copy. For the drafting of the diagrams and the layout I am grateful


    to J.C. Janse; C.L. Slootweg; J.H. Bor and S.O. Fraser-Mackenzie.


    Finally, my thanks are due to all those who suffered my lectures between 1974 and


    1977 for their numerous suggestions which have helped to shape this textbook.


    L.P. Dake,


    Shell Training,


    The Hague,


    October 1977. CONTENTS


    PREFACE VII


    ACKNOWLEDGEMENTS IX


    CONTENTS X


    LIST OF FIGURES XVII


    LIST OF TABLES XXVII


    LIST OF EQUATIONS XXX


    NOMENCLATURE LIX


    CHAPTER 1 SOME BASIC CONCEPTS IN RESERVOIR ENGINEERING 1


    1.1 INTRODUCTION 1


    1.2 CALCULATION OF HYDROCARBON VOLUMES 1


    1.3 FLUID PRESSURE REGIMES 3


    1.4 OIL RECOVERY: RECOVERY FACTOR 9


    1.5 VOLUMETRIC GAS RESERVOIR ENGINEERING 12


    1.6 APPLICATION OF THE REAL GAS EQUATION OF STATE 20


    1.7 GAS MATERIAL BALANCE: RECOVERY FACTOR 25


    1.8 HYDROCARBON PHASE BEHAVIOUR 37


    REFERENCES 41


    CHAPTER 2 PVT ANALYSIS FOR OIL 43


    2.1 INTRODUCTION 43


    2.2 DEFINITION OF THE BASIC PVT PARAMETERS 43


    2.3 COLLECTION OF FLUID SAMPLES 51


    2.4 DETERMINATION OF THE BASIC PVT PARAMETERS IN THE


    LABORATORY AND CONVERSION FOR FIELD OPERATING


    CONDITIONS 55


    2.5 ALTERNATIVE MANNER OF EXPRESSING PVT LABORATORY


    ANALYSIS RESULTS 65


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