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