Petroleum Reservoir Engineering Practice

Contents......Page 8
Preface......Page 24
Acknowledgments......Page 26
About the Author......Page 30
1.2 Total Porosity and Effective Porosity......Page 32
1.3.1 Direct Methods for Measurement of Porosity......Page 34
1.3.2 Indirect Methods for Derivation of Porosity......Page 35
1.4.1 Volumetric Calculation......Page 41
1.4.3 Reservoir Characterization......Page 42
Nomenclature......Page 43
References......Page 44
General Reading......Page 45
2.1 Introduction......Page 46
2.2 Sources of Permeability Data......Page 47
2.2.1 Permeability from Core Samples......Page 48
2.2.3 Permeability from Well Logs Based on Empirical Correlations......Page 49
2.3 Relative Permeability......Page 54
2.4.1 Laboratory Measurements of Relative Permeability Data......Page 56
2.4.3 Empirical Correlations......Page 57
2.6 Applications of Permeability and Relative Permeability Data......Page 63
Nomenclature......Page 64
References......Page 65
General Reading......Page 68
3.1 Introduction......Page 70
3.2.1 Clean Sands......Page 71
3.2.2 Shaly Sands......Page 75
3.2.3 Carbonate Rocks......Page 76
3.2.4 Water Saturations from Nuclear Magnetic Resonance Logs......Page 77
3.2.5 Uncertainties in Estimation of Water Saturation......Page 78
3.3.1 Net Sands, Net Reservoir, and Net Pay......Page 79
Nomenclature......Page 80
References......Page 81
General Reading......Page 83
4.2 Phase Diagrams......Page 84
4.2.1 Single Component Systems......Page 85
4.2.2 Binary Systems......Page 87
4.2.3 Multicomponent Systems......Page 89
4.2.4 Retrograde Behavior of Gas-Condensate Systems......Page 92
4.3.1 Ideal Gas Equation......Page 94
4.3.3 Gas Gravity......Page 95
4.3.4 Reduced Temperature and Pressure......Page 96
4.4.1 Composition of Gas Mixtures Known......Page 98
4.4.2 Correction for non-Hydrocarbon Gas Impurities......Page 99
4.4.3 Composition of Gas Mixture Unknown......Page 100
4.5.1 Recombination Method......Page 101
4.5.2 Correlation Method......Page 105
4.6 Correlations for Gas Compressibility Factor......Page 109
4.7 Gas Formation Volume Factor (FVF)......Page 110
4.8 Gas Density......Page 112
4.9 Gas Viscosity......Page 113
4.10 Gas Coefficient of Isothermal Compressibility......Page 114
4.11.1 Bubble Point Pressure......Page 124
4.11.3 Oil Formation Volume Factor (FVF)......Page 126
4.11.4 Coefficient of Isothermal Compressibility of Oil......Page 127
4.11.5 Oil Viscosity......Page 129
4.12.3 Coefficient of Isothermal Compressibility of Formation Water......Page 134
Nomenclature......Page 135
References......Page 137
General Reading......Page 139
5.1 Overview of Reservoir Fluid Sampling......Page 142
5.2.1 Undersaturated Oil Reservoirs......Page 147
5.2.2 Undersaturated Gas Condensate Reservoirs......Page 148
5.2.4 Saturated Gas Condensate Reservoirs......Page 149
5.4 Subsurface Sampling Methods and Tools......Page 150
5.4.3 Single-Phase Samplers......Page 151
5.5.1 Oil-Based Mud Contamination of WFT Samples......Page 152
5.5.2 Formation Pressures from WFT......Page 153
5.5.3 Capillary Effects on WFT Formation Pressures......Page 154
5.5.4 Effects of Supercharging on WFT Formation Pressures......Page 159
5.5.5 Comments on Applications of WFT Pressure Data......Page 160
5.6.1 Fluid Composition......Page 161
5.6.3 Differential Liberation (DL)......Page 162
5.6.5 Separator Tests......Page 164
5.7 Applications of Laboratory PVT Measurements......Page 165
5.7.2 Calculation of Gas Compressibility Factor, Gas FVF, and Total FVF......Page 166
5.7.3 Calculation of Oil Compressibility Factor......Page 167
Subscripts......Page 169
References......Page 170
General Reading......Page 171
5A.1 Reservoir Fluid Summary......Page 173
5A.2 Calculated Analysis of Reservoir Fluid......Page 174
5A.3 Pressure-Volume Properties at 212°F (Constant Composition Expansion)......Page 175
5A.4 Differential Liberation at 212°F......Page 176
5A.5 Gas Differentially Liberated at 212°F......Page 177
5A.7 Comparison of Reservoir Oil Flash Liberation Tests......Page 178
5B.1 Summary of Reservoir Data and Surface Sampling Conditions......Page 179
5B.2 Chromatograph Analysis of Separator Gas at 1140 psig and 92°F......Page 181
5B.3 Chromatograph Analysis of Separator Liquid at 1140 psig and 92°F......Page 182
5B.5 Measured Saturation Pressures from Stepwise Recombinations at 267°F......Page 183
5B.6 Pressure-Volume Properties of Reservoir Fluid at 267°F (or CCE)......Page 184
5B.7 Depletion Study at 267°F: Hydrocarbon Analyses of Produced Wellstream (Mole %)......Page 185
5B.8 Retrograde Condensation During Gas Depletion at 267°F......Page 186
6.1 Historical Introduction to Equations of State (EOS)......Page 188
6.2 van der Waals (vdW) EOS......Page 189
6.3 Soave-Redlich-Kwong (SRK) EOS......Page 190
6.5 Phase Equilibrium of Mixtures......Page 193
6.6 Roots from Cubic EOS......Page 195
6.7 Volume Translation......Page 196
6.8 Two-Phase Flash Calculation......Page 199
6.8.1 Generalized Procedure for Two-Phase Flash Calculations......Page 200
6.9 Bubble Point and Dew Point Pressure Calculations......Page 201
6.10 Characterization of Hydrocarbon Plus Fractions......Page 202
6.11 Phase Equilibrium Predictions with Equations of State......Page 205
Nomenclature......Page 209
Abbreviations......Page 210
References......Page 211
7.2 Derivation of the General Material Balance Equation (GMBE)......Page 214
7.2.1 Development of Terms in the Expression of Equation (7.1)......Page 215
7.3 The GMBE for Gas Reservoirs......Page 218
7.4 Discussion on the Application of the GMBE......Page 219
Abbreviations......Page 220
References......Page 221
8.1 Introduction......Page 222
8.2.1 Volumetric Calculations for Dry Gas Reservoirs......Page 223
8.2.2 Volumetric Calculations for Wet Gas and Retrograde Gas Condensate Reservoirs......Page 224
8.2.3 Material Balance for Volumetric Dry Gas, Wet Gas, and Retrograde Gas Condensate Reservoirs......Page 227
8.3 Gas Reservoirs with Water Influx......Page 229
8.3.1 Volumetric Approach......Page 230
8.3.3 The Cole Plot......Page 231
8.3.4 The Havlena-Odeh Straight Line Method......Page 232
8.4 Water Influx Models......Page 233
8.4.1 Fetkovich Aquifer Model......Page 235
8.4.2 Carter-Tracy Aquifer Model......Page 240
8.5 Geopressured Gas Reservoirs......Page 244
8.5.1 The Ramagost and Farshad Method......Page 245
8.5.2 The Roach Method......Page 248
8.6.1 The Case History of Red Hawk Reservoir......Page 252
8.6.2 The Case History of West Cameron 580 Reservoir......Page 264
Nomenclature......Page 278
References......Page 279
General Reading......Page 281
Appendix 8A: Correlations for Estimating Residual Gas Saturations for Gas Reservoirs under Water Influx......Page 282
Appendix 8B: Dimensionless Pressure for Finite and Infinite Aquifers......Page 283
Appendix 8C: Dimensionless Pressure for Finite and Infinite Aquifers......Page 284
9.2 Oil Reservoir Drive Mechanisms......Page 286
9.3 Gravity Drainage Mechanism......Page 288
9.4.1 Volume Calculations Above Bubble Point Pressure......Page 289
9.4.2 Volume Calculations Below Bubble Point Pressure......Page 294
9.5.1 Volume Method......Page 295
9.5.2 Material Balance Method......Page 296
9.6.1 Volume Method......Page 307
9.6.2 Material Balance Method......Page 308
9.8 Case History of Manatee Reservoirs......Page 310
9.8.1 Reservoir Geology......Page 311
9.8.3 Reservoir Pressure and Production Data......Page 313
9.8.4 Review Questions......Page 314
Subscripts......Page 323
References......Page 324
10.1 Introduction......Page 326
10.2.2 Slightly Compressible Fluids......Page 327
10.3.1 Transient Flow......Page 328
10.3.2 Pseudosteady-State (PSS) Flow......Page 330
10.3.3 Steady-State (SS) Flow......Page 331
10.4 Darcy Fluid Flow Equation......Page 332
10.5.1 Steady-State Flow, Incompressible Fluids......Page 333
10.5.2 Average Permeability of Parallel Beds......Page 334
10.5.3 Average Permeability of Serial Concentric Segments......Page 336
10.5.4 Pseudosteady State, Incompressible Fluids......Page 338
10.5.5 Steady-State Flow, Compressible Fluids......Page 340
10.6 Derivation of the Continuity Equation in Radial Form......Page 341
10.7 Derivation of Radial Diffusivity Equation for Slightly Compressible Fluids......Page 342
10.8.1 Constant Terminal Rate Solution......Page 344
10.8.2 Constant Terminal Pressure Solution......Page 350
10.9 Derivation of the Radial Diffusivity Equation for Compressible Fluids......Page 352
10.10 Transformation of the Gas Diffusivity Equation with Real Gas Pseudo-Pressure Concept......Page 353
10.11.1 Applications of Constant Terminal Rate Solutions with Superposition Principle......Page 358
10.11.2 Applications of Constant Terminal Pressure Solution with Superposition Principle......Page 363
10.13 Well Injectivity Index......Page 369
Nomenclature......Page 370
References......Page 371
General Reading......Page 372
Appendix 10A: Chart for Exponential Integral......Page 373
Appendix 10B: Tabulation of p[sub(D)] vs t[sub(D)] for Radial Flow, Infinite Reservoirs with Constant Terminal Rate at Inner Boundary......Page 374
Appendix 10C: Tabulation of p[sub(D)] vs t[sub(D)] for Radial Flow, Finite Reservoirs with Closed Outer Boundary and Constant Terminal Rate at Inner Boundary......Page 376
Appendix 10D: Tabulation of p[sub(D)] vs t[sub(D)] for Radial Flow, Finite Reservoirs with Constant Pressure Outer Boundary and Constant Terminal Rate at Inner Boundary......Page 381
Appendix 10E: Tabulation of Q[sub(D)] vs t[sub(D)] for Radial Flow, In. nite Reservoirs with Constant Terminal Pressure at Inner Boundary......Page 389
Appendix 10F: Tabulation of Q[sub(D)] vs t[sub(D)] for Radial Flow, Finite Reservoirs with Closed Outer Boundary and Constant Terminal Pressure at Inner Boundary......Page 392
11.1 Introduction......Page 398
11.2.1 Radius of Investigation......Page 399
11.2.2 Skin and Skin Factor......Page 400
11.2.4 Effective Wellbore Radius......Page 403
11.2.5 Drawdown Well Tests......Page 405
11.2.6 Buildup Well Tests......Page 406
11.2.7 Wellbore Storage......Page 408
11.3 Line Source Well, Infinite Reservoir Solution of the Diffusivity Equation with Skin Factor......Page 409
11.4.1 Slightly Compressible Fluids......Page 412
11.4.2 Compressible Fluids......Page 436
11.5.1 Multiphase Flow......Page 463
11.5.3 Wellbore Phase Redistribution Effects......Page 466
11.5.5 Multilayered Reservoirs......Page 467
Nomenclature......Page 470
Subscripts......Page 471
References......Page 472
General Reading......Page 475
12.2 What Are Type Curves?......Page 476
12.3 Gringarten Type Curves......Page 478
12.3.1 Unit-Slope Line......Page 479
12.4 Bourdet Derivative Type Curves......Page 480
12.5 Agarwal Equivalent Time......Page 481
12.6 Type-Curve Matching......Page 482
12.7 Procedures for Manual Application of Type-Curve Matching in Well Test Analysis......Page 483
12.8.1 Identification of the Interpretation Model......Page 485
12.8.3 Validation of the Interpretation Model Results......Page 486
Nomenclature......Page 490
Abbreviations......Page 491
References......Page 492
Appendix 12A: Characteristic Shapes of Pressure and Pressure-Derivative Curves for Selected Well, Reservoir, and Boundary Models......Page 494
Appendix 12B: Buildup Test Data for Example 12.1......Page 498
Appendix 12C: Calculation of Pressure Derivatives......Page 504
Reference......Page 505
13.2 Hydraulically Fractured Wells......Page 506
13.4.1 Fracture Linear Flow......Page 507
13.4.2 Bilinear Flow......Page 508
13.5 Fractured Well Flow Models......Page 509
13.5.3 Uniform Flux Vertical Fracture......Page 510
13.6.1 Bilinear Flow......Page 511
13.6.3 Formation Linear Flow......Page 514
13.6.4 Procedure for Application of Straightline Methods on Well Test Data During Formation Linear Flow Regime......Page 516
13.6.5 Pseudo-Radial Flow......Page 517
13.7 Fractured Well Test Analysis: Type-Curve Matching......Page 518
13.7.2 Calculation from Interpretation Model Parameters......Page 520
13.7.3 Validation of the Interpretation Model Results......Page 521
13.7.4 Procedure for Analysis of Well Test from Hydraulically Fractured Wells......Page 522
13.9 Naturally Fractured Reservoir Models......Page 528
13.9.1 Homogeneous Reservoir Model......Page 529
13.9.2 Multiple Region or Composite Reservoir Model......Page 530
13.9.4 Single Fracture Model......Page 532
13.9.5 Double Porosity Model......Page 533
13.10 Well Test Analysis in Naturally Fractured Reservoirs Based on Double Porosity Model......Page 536
13.11 Well Test Analysis in NFRs: Straightline Methods......Page 537
13.12 Well Test Analysis in NFRs: Type Curves......Page 540
13.13.3 Validation of Results with Straightline Methods......Page 543
Nomenclature......Page 551
Abbreviations......Page 552
References......Page 553
General Reading......Page 554
14.2 What Is Deconvolution?......Page 556
14.3 The Pressure-Rate Deconvolution Model......Page 557
14.3.1 The von Schroeter et al. Deconvolution Algorithm......Page 558
14.4 Application of Deconvolution to Pressure-Rate Data......Page 559
14.5 Examples on the Application of the von Schroeter Deconvolution Algorithm to Real Well Test Data......Page 560
14.6 General Guidelines for Application of von Schroeter Deconvolution Algorithm to Pressure-Rate Datafrom Well Tests......Page 565
References......Page 566
General Reading......Page 567
15.1 Introduction......Page 568
15.2.1 Rock Wettability......Page 569
15.2.2 Capillary Pressure......Page 570
15.2.4 Mobility and Mobility Ratio......Page 574
15.3 Fractional Flow Equations......Page 575
15.3.1 Fractional Flow Equation for Oil Displaced by Water......Page 576
15.3.2 Fractional Flow Equation for Oil Displaced by Gas......Page 579
15.4 The Buckley-Leverett Equation......Page 580
15.5.1 Water Saturation at the Flood Front......Page 584
15.5.3 Average Water Saturation after Water Breakthrough......Page 586
15.6 Summary......Page 590
Nomenclature......Page 591
References......Page 592
General Reading......Page 593
16.1 Introduction......Page 594
16.2.1 Waterflood Patterns......Page 595
16.2.3 Recommended Steps in Waterflood Design......Page 598
16.2.4 Waterflood Management......Page 599
16.3 Gasflooding......Page 606
16.3.2 Gasood Design......Page 607
16.3.3 Recommended Steps in Gasflood Design......Page 608
16.3.4 Gasflood Management......Page 609
16.3.5 Management of Gasflood Reservoirs......Page 610
References......Page 611
General Reading......Page 613
17.1 Introduction......Page 614
17.2 EOR Processes......Page 615
17.3.1 EOR Screening Criteria for Miscible Gas Injection Processes......Page 618
17.3.2 EOR Screening Criteria for Chemical Flooding Processes......Page 619
17.4.1 Basic Concepts on Miscibility for Gas Displacement Processes......Page 620
17.4.3 Multiple-Contact Miscibility (MCM)......Page 622
17.4.4 Vaporizing Gas Drive MCM Process......Page 623
17.4.5 Condensing Gas Drive MCM Process......Page 625
17.5 Methods for Determination of MMP or MME for Gasfloods......Page 626
17.5.1 Analytical Techniques for Estimation of MMP or MME......Page 627
17.5.2 Experimental Methods......Page 641
17.6.1 Nitrogen/Flue-gas Miscible Gas Flooding......Page 643
17.6.3 Carbon Dioxide Gas Flooding......Page 644
17.7 Chemical Flooding Processes......Page 645
17.7.2 Alkali/Surfactant/Polymer (ASP) Flooding......Page 646
17.8 Thermal Processes......Page 647
17.8.1 Steamflooding Methods......Page 648
17.8.2 Steamflood Models......Page 652
17.8.3 Management of Steamflood Projects......Page 653
17.8.4 In-Situ Combustion (ISC)/High Pressure Air Injection (HPAI)......Page 654
17.9.1 Process Screening and Selection......Page 655
17.9.3 Geologic and Reservoir Modeling of Selected Processes......Page 658
17.9.5 Pilot Testing......Page 659
17.9.6 Upgrade Geologic and Reservoir Models with Pilot Test Data/Results......Page 660
Abbreviations......Page 661
References......Page 662
General Reading......Page 669
18.2 Sources of Data for Geologic Modeling and Reservoir Characterization......Page 672
18.2.3 Well Log Data......Page 673
18.2.6 Pressure Transient Test Data......Page 674
18.4 Scale and Integration of Data......Page 675
18.5.1 Generation of Geologic Surfaces or Horizons......Page 676
18.5.4 Correlation and Assignment of Well Log Data......Page 677
18.5.5 Property Data Modeling......Page 678
18.5.6 Uncertainty Analysis......Page 689
18.5.7 Upscaling of Geologic Model to Reservoir Flow Model......Page 691
Abbreviations......Page 707
References......Page 708
General Reading......Page 709
19.1 Introduction......Page 712
19.2 Derivation of the Continuity Equation in Rectangular Form......Page 715
19.3 Flow Equations for Three-Phase Flow of Oil,Water, and Gas......Page 717
19.4.1 Grid Systems......Page 720
19.4.2 Timesteps......Page 727
19.4.3 Formulations of Simulator Equations......Page 728
19.4.4 Material Balance Errors and Other Convergence Criteria......Page 729
19.4.5 Numerical Dispersion......Page 730
19.4.6 Well Model......Page 731
19.4.7 Model Initialization......Page 733
19.4.8 History Matching......Page 734
19.4.10 Uncertainty Analysis......Page 736
19.5.1 Definition of Model and Simulator......Page 737
19.5.6 Well Data......Page 738
Nomenclature......Page 739
Abbreviations......Page 740
References......Page 741
General Reading......Page 745
20.1 Introduction......Page 748
20.2 Reservoir Management Principles......Page 749
20.2.3 Systematic and Sustained Practice of Data Collection......Page 750
20.3 Case Histories Demonstrating Applications of Reservoir Management Principles......Page 751
20.3.1 The Case History of 26R Reservoir (1976–1996)......Page 752
20.3.2 Application of Reservoir Management Principles to 26R Reservoir......Page 756
20.3.3 The Case History of MBB/W31S Reservoirs (1976–1999)......Page 759
20.3.4 Application of Reservoir Management Principles to MBB/W31S Reservoirs......Page 763
20.3.5 The Case History of the Shaybah Field......Page 766
20.3.6 Application of Reservoir Management Principles to the Shaybah Field......Page 767
References......Page 772
General Reading......Page 775
B......Page 776
C......Page 777
D......Page 779
E......Page 780
F......Page 782
G......Page 783
H......Page 785
I......Page 786
M......Page 787
N......Page 789
O......Page 790
P......Page 791
R......Page 792
S......Page 795
T......Page 797
U......Page 798
W......Page 799
Z......Page 801