Fundamentals of Reservoir Engineering

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
2.6 COMPLETE PVT ANALYSIS 69
REFERENCES 70

CHAPTER 3 MATERIAL BALANCE APPLIED TO OIL RESERVOIRS 71
3.1 INTRODUCTION 71
3.2 GENERAL FORM OF THE MATERIAL BALANCE EQUATION FOR
A HYDROCARBON RESERVOIR 71
3.3 THE MATERIAL BALANCE EXPRESSED AS A LINEAR EQUATION 76
3.4 RESERVOIR DRIVE MECHANISMS 77
3.5 SOLUTION GAS DRIVE 78
3.6 GASCAP DRIVE 86
3.7 NATURAL WATER DRIVE 91
3.8 COMPACTION DRIVE AND RELATED PORE COMPRESSIBILITY
PHENOMENA 95
REFERENCES 98

CHAPTER 4 DARCY'S LAW AND APPLICATIONS 100
4.1 INTRODUCTION 100
4.2 DARCY'S LAW; FLUID POTENTIAL 100
4.3 SIGN CONVENTION 104
4.4 UNITS: UNITS CONVERSION 104
4.5 REAL GAS POTENTIAL 110
4.6 DATUM PRESSURES 111
4.7 RADIAL STEADY STATE FLOW; WELL STIMULATION 112
4.8 TWO-PHASE FLOW: EFFECTIVE AND RELATIVE PERMEABILITIES 117
4.9 THE MECHANICS OF SUPPLEMENTARY RECOVERY 121
REFERENCES 125

CHAPTER 5 THE BASIC DIFFERENTIAL EQUATION FOR RADIAL FLOW IN A
POROUS MEDIUM 127
5.1 INTRODUCTION 127
5.2 DERIVATION OF THE BASIC RADIAL DIFFERENTIAL EQUATION 127
5.3 CONDITIONS OF SOLUTION 129
5.4 THE LINEARIZATION OF EQUATION 5.1 FOR FLUIDS OF SMALL
AND CONSTANT COMPRESSIBILITY 133
REFERENCES 135

CHAPTER 6 WELL INFLOW EQUATIONS FOR STABILIZED FLOW
CONDITIONS 136
6.1 INTRODUCTION 136
6.2 SEMI-STEADY STATE SOLUTION 136
6.3 STEADY STATE SOLUTION 139
6.4 EXAMPLE OF THE APPLICATION OF THE STABILIZED INFLOW EQUATIONS 140
6.5 GENERALIZED FORM OF INFLOW EQUATION UNDER SEMISTEADY
STATE CONDITIONS 144
REFERENCES 146

CHAPTER 7 THE CONSTANT TERMINAL RATE SOLUTION OF THE RADIAL
DIFFUSIVITY EQUATION AND ITS APPLICATION TO OILWELL TESTING 148
7.1 INTRODUCTION 148
7.2 THE CONSTANT TERMINAL RATE SOLUTION 148
7.3 THE CONSTANT TERMINAL RATE SOLUTION FOR TRANSIENT AND SEMI-STEADY STATE FLOW CONDITIONS 149
7.4 DIMENSIONLESS VARIABLES 161
7.5 SUPERPOSITION THEOREM: GENERAL THEORY OF WELL TESTING 168
7.6 THE MATTHEWS, BRONS, HAZEBROEK PRESSURE BUILDUP THEORY 173
7.7 PRESSURE BUILDUP ANALYSIS TECHNIQUES 189
7.8 MULTI-RATE DRAWDOWN TESTING 209
7.9 THE EFFECTS OF PARTIAL WELL COMPLETION 219
7.10 SOME PRACTICAL ASPECTS OF WELL SURVEYING 221
7.11 AFTERFLOW ANALYSIS 224
REFERENCES 236

CHAPTER 8 REAL GAS FLOW: GAS WELL TESTING 239
8.1 INTRODUCTION 239
8.2 LINEARIZATION AND SOLUTION OF THE BASIC DIFFERENTIAL EQUATION FOR THE RADIAL FLOW OF A REAL GAS 239
8.3 THE RUSSELL, GOODRICH, et. al. SOLUTION TECHNIQUE 240
8.4 THE AL-HUSSAINY, RAMEY, CRAWFORD SOLUTION TECHNIQUE 243
8.5 COMPARISON OF THE PRESSURE SQUARED AND PSEUDO PRESSURE SOLUTION TECHNIQUES 251
8.6 NON-DARCY FLOW 252
8.7 DETERMINATION OF THE NON-DARCY COEFFICIENT F 255
8.8 THE CONSTANT TERMINAL RATE SOLUTION FOR THE FLOW OF A REAL GAS 257
8.9 GENERAL THEORY OF GAS WELL TESTING 260
8.10 MULTI-RATE TESTING OF GAS WELLS 262
8.11 PRESSURE BUILDUP TESTING OF GAS WELLS 278
8.12 PRESSURE BUILDUP ANALYSIS IN SOLUTION GAS DRIVE RESERVOIRS 289
8.13 SUMMARY OF PRESSURE ANALYSIS TECHNIQUES 291
REFERENCES 295

CHAPTER 9 NATURAL WATER INFLUX 297
9.1 INTRODUCTION 297
9.2 THE UNSTEADY STATE WATER INFLUX THEORY OF HURST AND VAN EVERDINGEN 298
9.3 APPLICATION OF THE HURST, VAN EVERDINGEN WATER INFLUX THEORY IN HISTORY MATCHING 308
9.4 THE APPROXIMATE WATER INFLUX THEORY OF FETKOVITCH FOR FINITE AQUIFERS 319
9.5 PREDICTING THE AMOUNT OF WATER INFLUX 328
9.6 APPLICATION OF INFLUX CALCULATION TECHNIQUES TO STEAM SOAKING 333
REFERENCES 335

CHAPTER 10 IMMISCIBLE DISPLACEMENT 337
10.1 INTRODUCTION 337
10.2 PHYSICAL ASSUMPTIONS AND THEIR IMPLICATIONS 337
10.3 THE FRACTIONAL FLOW EQUATION 345
10.4 BUCKLEY-LEVERETT ONE DIMENSIONAL DISPLACEMENT 349
10.5 OIL RECOVERY CALCULATIONS 355
10.6 DISPLACEMENT UNDER SEGREGATED FLOW CONDITIONS 364
10.7 ALLOWANCE FOR THE EFFECT OF A FINITE CAPILLARY TRANSITION ZONE IN DISPLACEMENT CALCULATIONS 381
10.8 DISPLACEMENT IN STRATIFIED RESERVOIRS 389
10.9 DISPLACEMENT WHEN THERE IS A TOTAL LACK OF VERTICAL EQUILIBRIUM 402
10.10 THE NUMERICAL SIMULATION OF IMMISCIBLE,
INCOMPRESSIBLE DISPLACEMENT 405
REFERENCES 419
AUTHOR INDEX 422
SUBJECT INDEX 424

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