Tarek Ahmed. Reservoir engineering handbook
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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.....
Much of the material on which this book is based was drawn from the
publications of the Society of Petroleum Engineers. Tribute is due to the
SPE and the petroleum engineers, scientists, and authors who have made
numerous and significant contributions to the field of reservoir engineer-
ing. I would like to express my appreciation to a large number of my col-
leagues within the petroleum industry and academia who offered sugges-
tions and critiques on the first edition; special thanks go to Dr. Wenxia
Zhang with TotalFinaElf E&P USA, Inc, for her suggestions and encour-
agements. I am also indebted to my students at Montana Tech of the Uni-
versity of Montana, whose enthusiasm has made teaching a pleasure; I
think! Special thanks to my colleagues and friends: Dr. Gil Cady, Profes-
sor John Evans; and Dr. Margaret Ziaja for making valuable suggestions
for the improvement of this book. I would like to acknowledge and
express my appreciation to Gary Kolstad, Vice President and General
Manager with Schlumberger, and Darrell McKenna, Vice President with
Schlumberger; for their continued support.
I would like to thank the editorial staff of Butterworth-Heinemann and
Gulf Professional Publishing for their concise and thorough work. I
greatly appreciate the assistance that Karen Forster has given me during
my work on the second edition.
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ACKNOWLEDGMENTS
Reservoir Eng FOB 2001-10-29 16:18 Page xiii