| Preface |
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ix | |
| Acknowledgments |
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xi | |
| Nomenclature |
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xiii | |
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1 | (8) |
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1.1 Need for Reservoir Modeling |
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1 | (1) |
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1.2 Purpose of Reservoir Modeling |
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2 | (1) |
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1.3 Classical Reservoir Engineering Protocols versus Numerical Modeling |
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2 | (1) |
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1.4 Basic Components of a Reservoir Model |
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3 | (3) |
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1.4.1 Fundamental Equations of the Mathematical Model |
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3 | (2) |
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1.4.2 The Numerical Model |
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5 | (1) |
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5 | (1) |
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1.5 Why Model the Reservoir? |
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6 | (1) |
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1.5.1 Newly Discovered Fields |
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6 | (1) |
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6 | (1) |
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6 | (1) |
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1.5.4 Modeling as a Dynamic Process |
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6 | (1) |
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7 | (2) |
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7 | (2) |
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2 Mathematics of Reservoir Engineering |
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9 | (26) |
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2.1 The Generalized Transport Equation (GTE) |
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10 | (5) |
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2.1.1 The Lagrangian View |
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10 | (2) |
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2.1.2 Divergence Theorem and Differential Operators |
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12 | (2) |
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2.1.3 Reynolds Transport Theorem, Euler Formulations, and Generalized Transport Equation |
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14 | (1) |
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2.2 General Transport Equation Applied to Porous Media |
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15 | (2) |
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2.3 Review of Equations of Flow in Porous Media |
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17 | (18) |
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2.3.1 Single-Phase Flow Equations |
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17 | (6) |
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2.3.2 Extension of Flow Equations to Multiphase Flow |
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23 | (2) |
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2.3.3 Extension of Flow Equations to Compositional Flow |
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25 | (3) |
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2.3.4 Coordinate Transformations |
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28 | (7) |
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3 Reservoir Engineering Fundamentals |
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35 | (32) |
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3.1 The Porous Medium as a Continuum |
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35 | (1) |
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3.2 The Fundamental Equations |
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35 | (1) |
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3.3 Fluid and Rock Compressibility Concepts |
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36 | (6) |
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3.3.1 Liquids and Fluid Compressibility |
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37 | (2) |
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3.3.2 Gases and Real Gas Law |
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39 | (2) |
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3.3.3 Rock Compressibility and Total Compressibility |
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41 | (1) |
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3.4 Porosity and Porosity Distribution |
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42 | (3) |
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3.5 Permeability and Permeability Distributions |
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45 | (2) |
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3.5.1 Characteristics of Darcy's Equation |
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45 | (2) |
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3.6 The Flow Potential Concept |
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47 | (2) |
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3.7 Permeability as a Symmetric Tensor of a Second Rank |
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49 | (3) |
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3.8 Wettability and Interfacial Tension |
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52 | (1) |
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3.9 The Relative Permeability Concept |
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53 | (6) |
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3.10 Capillary Pressure in Porous Media |
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59 | (3) |
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3.11 Skin Factor and Wellbore Flow |
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62 | (5) |
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65 | (2) |
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4 Hydrocarbon Fluid Models and Thermodynamics |
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67 | (30) |
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4.1 Reservoir Fluid Modeling Choices |
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67 | (3) |
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4.2 Compositional Fluid Modeling: The Nc-Component Fluid |
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70 | (6) |
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4.2.1 Thermodynamic Equilibrium and Ki Ratios |
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73 | (1) |
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4.2.2 Compositional Modeling and Flash Calculations |
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74 | (2) |
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4.3 Black-Oil Fluid Model and its PVT Properties |
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76 | (21) |
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4.3.1 Compositional Calculations in Black-Oil Models |
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81 | (5) |
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4.3.2 Black-Oil Fluid Thermodynamics and Flash Calculations |
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86 | (6) |
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4.3.3 Black-Oil PVT Data from Compositional and Density Information |
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92 | (4) |
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96 | (1) |
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5 Reservoir Engineering Transport Equations |
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97 | (38) |
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5.1 Mass Conservation in Compositional Reservoir Engineering Models |
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97 | (9) |
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5.1.1 Overall (across-all-phases) Compositional Equations |
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103 | (3) |
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5.2 Incompressible Fluid (e.g., water) Flow Problem: Single-Phase (Np = 1), Single-Component (Nc = 1) |
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106 | (2) |
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5.3 Slightly-Compressible Fluid (e.g., oil flow): Single-Phase (Np = 1), Single-Component (Nc = 1) |
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108 | (3) |
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5.4 Compressible Fluid (e.g., dry gas) Flow Problem: Single-Phase (Np = 1), Single-Component (Nc = 1) |
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111 | (3) |
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5.5 Immiscible Liquid/Liquid (e.g., oil/water) Flow Problem: Two-Phase (Np = 2), Two-Component (Nc = 2) |
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114 | (2) |
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5.6 Standard Black-Oil Formulation for Oil/Gas How: Two-Phase (Np = 2), Two-Component (Nc = 2) |
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116 | (2) |
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5.7 Extended Black-Oil Formulation for Oil/Gas/Water Flow: Three-Phase (Np = 3), Three-Component (Nc = 3) |
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118 | (17) |
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134 | (1) |
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6 Analytical Reservoir Engineering Solutions |
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135 | (106) |
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6.1 Analytical Reservoir Solutions and Systems Analysis |
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135 | (1) |
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6.2 Classical Formulations and Hydraulic Diffusivity Concept |
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136 | (2) |
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6.3 Analytical Models in Well Test Analysis and Purpose of Well Testing |
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138 | (2) |
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6.4 Derivation of Classical 1-D Radial Cylindrical Flow Equation |
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140 | (3) |
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6.5 Liquid Flow Analytical Formulation |
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143 | (2) |
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6.6 Compressible Flow Analytical Formulations |
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145 | (7) |
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6.6.1 Compressible Flow Equations: Pressure Approach |
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147 | (1) |
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6.6.2 Compressible Flow Equations: p2-Approach |
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148 | (1) |
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6.6.3 Compressible Flow Equations: Real Gas Potential Approach |
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149 | (3) |
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6.7 Dimensionless Groups and Dimensionless Form of the Governing Equations |
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152 | (7) |
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6.7.1 Derivation of Dimensionless Groups |
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153 | (4) |
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6.7.2 Dimensionless Form of the Well Test Model |
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157 | (2) |
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6.8 Reservoir Boundary Idealizations in Classical Analytical Solutions |
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159 | (2) |
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6.9 Analytical Solutions of the Dimensionless Formulation |
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161 | (12) |
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6.9.1 Infinite-Acting Analytical Solution |
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161 | (6) |
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6.9.2 Finite Reservoir Analytical Solutions |
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167 | (6) |
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6.10 Important Well-Test Analysis Concepts |
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173 | (6) |
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6.11 Deviations from Idealized Behavior |
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179 | (27) |
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6.11.1 Variable Rates and Superposition Principle |
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179 | (7) |
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6.11.2 Noncircular Drainage Areas: Method of Images |
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186 | (15) |
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6.11.3 Multiphase Flow Effects |
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201 | (1) |
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6.11.4 Skin and Inertial-Turbulent Effects |
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202 | (1) |
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6.11.5 Skin Due to Restricted Entry |
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203 | (1) |
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6.11.6 Wellbore Storage Effects |
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204 | (2) |
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6.12 Basic Pressure Transient Data Analysis (PTA) Techniques |
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206 | (22) |
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6.12.1 Pressure Buildup (PBU) Analysis |
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207 | (11) |
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6.12.2 Pressure Drawdown (PDD) Analysis |
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218 | (10) |
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6.13 Conformal Mapping Techniques |
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228 | (13) |
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239 | (2) |
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7 Numerical Reservoir Engineering Solutions |
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241 | (60) |
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7.1 Taylor Series and Numerical Schemes |
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242 | (2) |
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7.2 Finite-Volume Method Representations of Flow Equations |
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244 | (1) |
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7.3 FVM Representations of Single-Phase How Equations |
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245 | (18) |
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7.3.1 Single-Phase Incompressible Flow |
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245 | (7) |
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7.3.2 Single-Phase Slightly Compressible Flow |
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252 | (7) |
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7.3.3 Single-Phase Compressible Flow |
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259 | (4) |
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7.4 Newton-Raphson and Single-Phase Numerical Solutions |
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263 | (7) |
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7.5 FVM Representations of Multiphase Flow: Black-Oil Equations |
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270 | (8) |
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7.5.1 Immiscible Liquid/Liquid (Oil/Water) Flow |
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270 | (4) |
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7.5.2 Extended and Standard Black-Oil Formulations |
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274 | (4) |
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7.6 Solution of Black-Oil Multiphase Numerical Equations |
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278 | (9) |
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7.6.1 Implicit Pressure, Explicit Saturation (IMPES) Method |
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279 | (3) |
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7.6.2 Generalized Newton-Raphson Procedure |
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282 | (5) |
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7.7 FVM Representations of Multiphase Flow: Compositional Equations |
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287 | (5) |
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7.8 Solution of Compositional Multiphase Numerical Equations |
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292 | (9) |
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7.8.1 Pressure-Overall I-th Composition Solutions |
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292 | (4) |
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7.8.2 Pressure-Overall I-th Mass Solutions |
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296 | (3) |
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299 | (2) |
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8 Proxy and Hybrid Models in Reservoir Engineering |
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301 | (36) |
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8.1 Use of Artificial Intelligence-Based Models in the Upstream Petroleum Industry |
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301 | (4) |
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8.2 ANN-Based Toolboxes for Decision Making in Reservoir Engineering |
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305 | (18) |
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8.2.1 Enhanced Oil Recovery Screening Toolbox |
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306 | (1) |
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8.2.2 Well Test Analysis Toolbox |
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306 | (5) |
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8.2.3 General Reservoir and Production Engineering Analysis Toolbox |
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311 | (12) |
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8.3 Overview of Mathematical Manipulations in ANNs |
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323 | (14) |
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335 | (2) |
| Index |
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337 | |
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