1 FUNDAMENTALS OF RESERVOIR
FLUID BEHAVIOR...................................... 1
Classification of reservoirs and reservoir
fluids ............................................................ 1
Pressure-temperature diagram.................... 2
Oil reservoirs ................................................ 4
Gas reservoirs ............................................. 10
Undefined petroleum fractions ..................... 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 ......... 45
The Wichert-Aziz correction method............ 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 ........................................... 75
Specific gravity of the solution gas .............. 76
Gas solubility ............................................... 77
Bubble-point pressure .................................. 86
Oil formation volume factor .......................... 92
Isothermal compressibility coefficient of
crude oil ....................................................... 98
Oil formation volume factor for
undersaturated oils ...................................... 103
Crude oil density .......................................... 106
Crude oil viscosity ........................................ 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..................... 118
Water viscosity............................................. 119
Gas solubility in water .................................. 119
Water isothermal compressibility ................. 120
Problems ..................................................... 120
References .................................................. 126
3 LABORATORY ANALYSIS OF
RESERVOIR FLUIDS................................. 130
Composition of the resevoir fluid ................. 131
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 ............................................ 158
Correcting differential liberation data ........... 160
Correcting oil viscosity data ......................... 161
Correcting the separator tests data ............. 163
Laboratory analysis of gas condensate
systems ....................................................... 165
Recombination of separator samples .......... 165
Constant-composition test ........................... 168
Constant-volume depletion (CVD) test ........ 170
Problems ..................................................... 178
References .................................................. 182
4 FUNDAMENTALS OF ROCK
PROPERTIES ............................................. 183
Porosity ....................................................... 184
Absolute porosity ......................................... 184
Effective porosity ......................................... 185
Saturation .................................................... 189
Average saturation....................................... 191
Wettability .................................................... 193
Surface and interfacial tension .................... 194
Capillary pressure ....................................... 197
Capillary pressure of reservoir rocks ........... 200
Capillary hysteresis...................................... 203
Initial saturation distribution in a reservoir ... 206
Leverett J-function ....................................... 218
Converting laboratory capillary pressure
data .............................................................. 221
Permeability................................................. 221
The Klinkenberg effect ................................. 228
Averaging absolute permeabilities ............... 235
Weighted-average
permeability .............................. 236
Harmonic-average
permeability .............................. 239
Geometric-average
permeability .............................. 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......................................... 285
Imbibition process ........................................ 286
Two-phase relatie permeability
correlations .................................................. 286
1 Wyllie and Gardner correlation ................. 288
2 Torcaso and Wyllie correlation ................. 289
3 Pirson’s correlation ................................... 289
4 Corey’s method......................................... 291
5 Relative permeability from capillary
pressure data ............................................... 292
6 Relative permeability from analytical
equations ..................................................... 294
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 .................................................. 312
Wyllie’s correlations ..................................... 313
Stone’s model I ............................................ 314
Stone’s model II ........................................... 316
The Hustad-Holt correlation ......................... 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 ............. 333
Linear flow of slightly compressible fluids .... 339
Linear flow of compressible fluids (gases) ... 341
Radial flow of incompressible fluids ............. 344
Radial flow of slightly compressible fluids.... 350
Radial flow of compressible gases .............. 352
Horizontal multiple-phase flow ..................... 360
Unsteady-state flow ..................................... 363
Basic transient flow equation ....................... 365
Radial flow of slightly compressible fluids.... 370
Constant-terminal-pressure solution ........... 374
Constant-terminal-rate solution ................... 374
The E-function solution ................................ 375
The dimensionless pressure drop (Pd)
solution ........................................................ 383
Radial flow of compressible fluids ................ 392
The m(p)-solution method
(exact-solution) ............................................ 395
The pressure-squared approximation
method (p2-method) .................................... 398
The pressure-approximation method ........... 400
Pseudosteady-state flow ............................. 403
Radial flow of slightly compressible fluids.... 409
Radial flow of compressible fluids
(gases) ......................................................... 418
Pressure-squared approximation method.... 419
Pressure-approximation method.................. 419
Skin factor.................................................... 420
Turbulent flow factor .................................... 426
Principle of superposition ............................ 431
Effects of multiple wells ............................... 432
Effects of variable flow rates ........................ 435
Effects of the reservoir boundary ................. 438
Accounting for pressure-change effects ...... 442
Transient well testing ................................... 442
Drawdown test ............................................. 443
Pressure buildup test ................................... 456
Problems ..................................................... 465
References .................................................. 471
7 OIL WELL PERFORMANCE................... 473
Vertical oil well performance ....................... 473
Productivity index and IPR........................... 473
Vogel’s method ............................................ 482
Saturated oil reservoirs ................................ 483
Undersaturated oil reservoirs....................... 485
Wiggins’ method .......................................... 491
Standing’s method ....................................... 494
Fetkovich’s method...................................... 498
The Klins-Clark method ............................... 514
Horizontal oil well performance ................... 515
Method I....................................................... 516
Method II...................................................... 517
Horizontal well productivity under
steady-state flow .......................................... 519
Borisov’s method ......................................... 520
The Giger-Reiss-Jourdan method ............... 520
Joshi’s method ............................................. 521
The Renard-Dupuy method ......................... 522
Horizontal well productivity under
semisteady-state flow .................................. 527
Problems ..................................................... 529
References .................................................. 531
8 GAS WELL PERFORMANCE ................. 533
Vertical gas well performance ..................... 533
Region I. High-pressure region.................... 536
Region II. Intermediate-pressure region ...... 537
Region III. Low-pressure region................... 537
The simpified treatment approach ............... 543
The Laminar-Inertial-Turbulent (LIT)
approach...................................................... 545
The Back-Pressure test ............................... 550
Future inflow performance relationships ...... 559
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................................. 574
The Chierici-Ciucci approach ... 581
The
Hoyland-Papatzacos-Skjaeve
methods.................................... 593
Critical rate curves by
Chaney et al. ............................ 597
Chaperson’s method ................ 604
Schols’ method......................... 605
Breakthrough time in vertical wells .............. 606
The Sobocinski-Cornelius method ............... 606
The Bournazel-Jeanson method.................. 609
After breakthrough performance ................. 610
Coning in horizontal wells............................ 615
Horizontal well critical rate correlations ....... 616
Chaperson’s method ................ 616
Efros’ method ........................... 620
Karcher’s method ..................... 621
Joshi’s method ......................... 622
Horizontal well breakthrough time ............... 624
The Ozkan-Raghavan method..................... 624
Papatzacos’ method .................................... 627
Problems ..................................................... 632
References .................................................. 634
10 WATER INFLUX.................................... 636
Classification of aquifers ............................. 637
Degree of pressure maintenance ................ 637
Outer boundary conditions........................... 639
Flow regimes ............................................... 639
Flow geometries .......................................... 639
Recognition of natural water influx .............. 640
Water influx models ..................................... 641
The pot aquifer model .................................. 642
Schilthuis’ steady-state model ..................... 645
Hurst’s modified steady-state model............ 649
The Van Everdingen-Hurst
unsteady-state model .................................. 653
The edge-water drive ............... 654
Bottom-water drive ................... 677
The Carter-Tracey water influx model ......... 703
Fetkovich’s method...................................... 707
Problems ..................................................... 713
References .................................................. 716
11 OIL RECOVERY MECHANISMS
AND THE MATERIAL BALANCE
EQUATION ................................................. 717
Primary recovery mechanisms .................... 718
Rock and liquid expansion ........................... 718
The depletion drive mechanism................... 719
Gas cap drive............................................... 721
The water-drive mechanism ........................ 726
The gravity-drainage-drive mechanism ....... 730
The combination-drive mechanism .............. 735
The material balance equation .................... 736
Basic assumptions in the MBE .................... 751
The MBE as an equation of a straight line... 753
The straight-line solution method to the
MBE ............................................................. 755
Case 1. Volumetric undersaturated-oil
resevoirs ...................................................... 755
Case 2. Volumetric saturated-oil
reservoirs ..................................................... 760
Case 3. Gas-cap-drive reservoirs ................ 762
Case 4. Water-drive reservoirs .................... 766
The pot-aquifer model in the
MBE.......................................... 768
The steady-state model in
the MBE.................................... 769
The unsteady-state model in
the MBE.................................... 770
Tracy’s form of the material balance
equation ....................................................... 774
Problems ..................................................... 778
References .................................................. 781
12 PREDICTING OIL RESERVOIR
PERFORMANCE........................................ 782
Phase 1. Reservoir performance
prediction methods ...................................... 783
Instantaneous gas-oil ratio........................... 783
The resevoir saturation equations ............... 789
Undersaturated-oil reservoirs ...................... 797
Saturated-oil reservoirs ................................ 801
Tracy’s method ............................................ 803
Muskat’s method.......................................... 810
Tarner’s method........................................... 815
Phase 2. Relating reservoir performance
to time.......................................................... 822
Problems ..................................................... 825
References .................................................. 826
13 GAS RESERVOIRS............................... 827
The volumetric method ................................ 828
The material balance method ...................... 831
Volumetric gas reservoirs ............................ 832
Form 1. In terms of p/z ................................. 833
Form 2. In terms of Bg ................................. 838
Water-drive gas reservoirs........................... 840
Material balance equation as a straight
line ............................................................... 842
Abnormally pressured gas reservoirs .......... 847
Effect on gas production rate on ultimate
recovery ....................................................... 853
Problems ..................................................... 854
References .................................................. 856
14 PRINCIPLES OF WATERFLOODING .. 857
Factors to consider in waterflooding............ 858
Reservoir geometry ..................................... 859
Fluid properties ............................................ 859
Reservoir depth ........................................... 859
Lithology and rock properties....................... 860
Fluid saturations .......................................... 861
Reservoir uniformity and pay continuity ....... 861
Primary reservoir driving mechanisms......... 861
Optimum time to waterflood ........................ 863
Effect of trapped gas on waterflood
recovery....................................................... 865
First theory ................................................... 865
Second theory.............................................. 866
Selection of flooding patterns ...................... 875
Irregular injection patterns ........................... 875
Irregular injection patterns ........................... 875
Peripheral injection patterns ........................ 876
Regular injection patterns ............................ 878
Crestal and basal injection patterns ............. 879
Overall recovery efficiency .......................... 880
I. Displacement efficiency............................ 881
II. Areal sweep efficiency ............................. 932
III. Vertical sweep efficiency ........................ 989
Calculation of vertical sweep efficiency ....... 997
Methods of predicting recovery
performance for layered reservoirs ............. 1006
Simplified Dykstra-Parsons method............. 1006
Modified Dykstra-Parsons method ............... 1010
Craig-Geffen-Morse method ........................ 1013
Problems ..................................................... 1016
References .................................................. 1024
15 VAPOR-LIQUID PHASE
EQUILIBRIA ............................................... 1026
Vapor pressure ............................................ 1026
Equilibrium ratios ......................................... 1029
Flash calculations ........................................ 1033
Equilibrium ratios for real solutions ............. 1037
Wilson’s correlation...................................... 1038
Standing’s correlation .................................. 1038
Convergence pressure method ................... 1043
Whitson and Torp correlation....................... 1049
Equilibrium ratios for the plus fraction ......... 1050
Campbell’s method ...................................... 1051
Winn’s method ............................................. 1051
Katz’s method .............................................. 1052
Applications of the equilibrium ratio in
reservoir engineering................................... 1052
Dew-point pressure...................................... 1053
Bubble-point pressure .................................. 1055
Separator calculations ................................. 1058
Density calculations ..................................... 1072
Equations of state........................................ 1084
The Van der Waals equation of state .......... 1084
Redlick-Kwong equation of state ................. 1092
Soave-Redlick-Kwong equation of state
and its modifications .................................... 1098
Modifications of the SRK EOS..................... 1108
Peng-Robinson equation of state and its
modifications ................................................ 1112
Applications of the equation of state in
petroleum engineering................................. 1124
Determination of the equilibrium ratios ........ 1124
Determination of the dew-point pressure ..... 1125
Determination of the bubble-point
pressure....................................................... 1128
Three-phase equilibrium calculations .......... 1129
Vapor pressure from equilibrium of state ..... 1135
Splitting and lumping schemes of the
plus-fraction ................................................. 1137
Splitting schemes......................................... 1138
Lumping schemes........................................ 1148
Problems ..................................................... 1155
References .................................................. 1159
APPENDIX.................................................. 1165
INDEX ......................................................... 1177