Preface |
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xv | |
1 Introduction |
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1 | (6) |
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1 | (1) |
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2 | (1) |
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1.3 The Need for a Knowledge-Based Approach |
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2 | (3) |
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5 | (2) |
2 Reservoir Simulation Background |
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7 | (32) |
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2.1 Essence of Reservoir Simulation |
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8 | (2) |
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2.2 Assumptions Behind Various Modeling Approaches |
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10 | (9) |
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2.2.1 Material Balance Equation |
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11 | (1) |
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12 | (1) |
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13 | (2) |
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15 | (1) |
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2.2.5 Finite-Difference Methods |
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16 | (3) |
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19 | (1) |
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2.3 Recent Advances in Reservoir Simulation |
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19 | (12) |
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19 | (2) |
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2.3.2 New Fluid-Flow Equations |
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21 | (5) |
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2.3.3 Coupled Fluid Flow and Geo-Mechanical Stress Model |
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26 | (3) |
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2.3.4 Fluid-Flow Modeling Under Thermal Stress |
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29 | (2) |
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31 | (2) |
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32 | (1) |
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2.4.2 Mathematical and Numerical Models |
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32 | (1) |
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2.5 Future Challenges in Reservoir Simulation |
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33 | (6) |
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2.5.1 Experimental Challenges |
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33 | (2) |
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2.5.2 Numerical Challenges |
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35 | (10) |
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2.5.2.1 Theory of Onset and Propagation of Fractures due to Thermal Stress |
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35 | (1) |
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2.5.2.2 Viscous Fingering during Miscible Displacement |
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36 | (3) |
3 Reservoir Simulator-Input/Output |
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39 | (46) |
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3.1 Input and Output Data |
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40 | (2) |
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3.2 Geological and Geophysical Modeling |
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42 | (3) |
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3.3 Reservoir Characterization |
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45 | (13) |
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3.3.1 Representative Elementary Volume, REV |
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46 | (3) |
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3.3.2 Fluid and Rock Properties |
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49 | (5) |
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49 | (5) |
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54 | (4) |
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58 | (7) |
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3.4.1 Power Law Averaging Method |
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59 | (1) |
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3.4.2 Pressure-Solver Method |
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60 | (2) |
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3.4.3 Renormalization Technique |
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62 | (1) |
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3.4.4 Multiphase Flow Upscaling |
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63 | (2) |
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3.5 Pressure/Production Data |
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65 | (1) |
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3.6 Phase Saturations Distribution |
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66 | (2) |
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3.7 Reservoir Simulator Output |
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68 | (2) |
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70 | (11) |
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3.8.1 History-Matching Formulation |
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72 | (3) |
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3.8.2 Uncertainty Analysis |
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75 | (12) |
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3.8.2.1 Measurement Uncertainty |
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76 | (2) |
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3.8.2.2 Upscaling Uncertainty |
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78 | (1) |
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79 | (1) |
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3.8.2.4 The Prediction Uncertainty |
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80 | (1) |
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81 | (4) |
4 Reservoir Simulators: Problems, Shortcomings, and Some Solution Techniques |
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85 | (32) |
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4.1 Multiple Solutions in Natural Phenomena |
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87 | (17) |
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4.1.1 Knowledge Dimension |
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90 | (14) |
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4.2 Adomian Decomposition |
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104 | (10) |
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4.2.1 Governing Equations |
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106 | (2) |
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4.2.2 Adomian Decomposition of Buckley-Leverett Equation |
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108 | (3) |
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4.2.3 Results and Discussions |
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111 | (3) |
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4.3 Some Remarks on Multiple Solutions |
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114 | (3) |
5 Mathematical Formulation of Reservoir Simulation Problems |
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117 | (38) |
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5.1 Black Oil Model and Compositional Model |
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119 | (1) |
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5.2 General Purpose Compositional Model |
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120 | (21) |
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120 | (2) |
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5.2.2 Primary and Secondary Parameters and Model Variables |
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122 | (3) |
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5.2.3 Mass Conservation Equation |
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125 | (3) |
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5.2.4 Energy Balance Equation |
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128 | (5) |
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5.2.5 Volume Balance Equation |
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133 | (1) |
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5.2.6 The Motion Equation in Porous Medium |
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134 | (5) |
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5.2.7 The Compositional System of Equations and Model Variables |
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139 | (2) |
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5.3 Simplification of the General Compositional Model |
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141 | (5) |
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5.3.1 The Black Oil Model |
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141 | (2) |
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5.3.2 The Water Oil Model |
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143 | (3) |
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5.4 Some Examples in Application of the General Compositional Model |
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146 | (9) |
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5.4.1 Isothermal Volatile Oil Reservoir |
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146 | (2) |
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5.4.2 Steam Injection Inside a Dead Oil Reservoir |
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148 | (2) |
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5.4.3 Steam Injection in Presence of Distillation and Solution Gas |
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150 | (5) |
6 The Compositional Simulator Using Engineering Approach |
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155 | (84) |
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6.1 Finite Control Volume Method |
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156 | (14) |
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6.1.1 Reservoir Discretization in Rectangular Coordinates |
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157 | (1) |
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6.1.2 Discretization of Governing Equations |
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158 | (10) |
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6.1.2.1 Components Mass Conservation Equation |
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158 | (8) |
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6.1.2.2 Energy Balance Equation |
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166 | (2) |
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6.1.3 Discretization of Motion Equation |
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168 | (2) |
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6.2 Uniform Temperature Reservoir Compositional Flow Equations in a 1-D Domain |
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170 | (5) |
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6.3 Compositional Mass Balance Equation in a Multidimensional Domain |
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175 | (15) |
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6.3.1 Implicit Formulation of Compositional Model in Multidimensional Domain |
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178 | (2) |
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6.3.2 Reduced Equations of Implicit Compositional Model in Multidimensional Domain |
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180 | (3) |
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6.3.3 Well Production and Injection Rate Terms |
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183 | (3) |
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183 | (2) |
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185 | (1) |
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6.3.4 Fictitious Well Rate Terms (Treatment of Boundary Conditions) |
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186 | (4) |
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6.4 Variable Temperature Reservoir Compositional Flow Equations |
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190 | (7) |
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6.4.1 Energy Balance Equation |
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190 | (4) |
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6.4.2 Implicit Formulation of Variable Temperature Reservoir Compositional Flow Equations |
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194 | (3) |
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197 | (6) |
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6.5.1 Solution of Model Equations Using Newton's Iteration |
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198 | (5) |
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6.6 The Effects of Linearization |
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203 | (36) |
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6.6.1 Case 1: Single Phase Flow of a Natural Gas |
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203 | (7) |
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6.6.2 Effect of Interpolation Functions and Formulation |
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210 | (1) |
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6.6.3 Effect of Time Interval |
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210 | (2) |
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6.6.4 Effect of Permeability |
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212 | (2) |
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6.6.5 Effect of Number of Gridblocks |
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214 | (1) |
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6.6.6 Spatial and Transient Pressure Distribution Using Different Interpolation Functions |
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214 | (4) |
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218 | (2) |
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6.6.8 Case 2: An Oil/water Reservoir |
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220 | (19) |
7 Development of a New Material Balance Equation for Oil Recovery |
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239 | (32) |
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239 | (2) |
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241 | (2) |
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7.3 Mathematical Model Development |
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243 | (1) |
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7.3.1 Permeability Alteration |
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243 | (1) |
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244 | (2) |
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246 | (4) |
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7.4.1 A Comprehensive MBE with Memory for Cumulative Oil Recovery |
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247 | (3) |
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250 | (8) |
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7.5.1 Effects of Compressibilities on Dimensionless Parameters |
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251 | (1) |
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7.4.2 Comparison of Dimensionless Parameters Based on Compressibility Factor |
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252 | (1) |
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7.4.3 Effects of M on Dimensionless Parameter |
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253 | (2) |
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7.4.4 Effects of Compressibility Factor with M Values |
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255 | (1) |
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7.4.5 Comparison of Models Based on RF |
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255 | (2) |
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7.4.6 Effects of M on MBE |
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257 | (1) |
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258 | (1) |
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Appendix Chapter 7: Development of an MBE for a Compressible Undersaturated Oil Reservoir |
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259 | (12) |
8 State-of-the-art on Memory Formalism for Porous Media Applications |
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271 | (30) |
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271 | (1) |
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272 | (1) |
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8.3 Historical Development of Memory Concept |
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273 | (4) |
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8.3.1 Constitutive Equations |
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274 | (1) |
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8.3.2 Application of Memory in Diffusion in Porous Media |
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274 | (3) |
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8.3.3 Definition of Memory |
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277 | (1) |
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8.4 State-of-the-art Memory-Based Models |
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277 | (7) |
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8.5 Basset Force: A History Term |
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284 | (3) |
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8.6 Anomalous Diffusion: A memory Application |
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287 | (10) |
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8.6.1 Fractional Order Transport Equations and Numerical Schemes |
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288 | (9) |
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297 | (1) |
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298 | (3) |
9 Modeling Viscous Fingering During Miscible Displacement in a Reservoir |
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301 | (58) |
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9.1 Improvement of the Numerical Scheme |
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302 | (15) |
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9.1.1 The Governing Equation |
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303 | (2) |
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9.1.2 Finite Difference Approximations |
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305 | (2) |
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9.1.2.1 Barakat-Clark FTD Scheme |
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305 | (2) |
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9.1.2.2 DuFort-Frankel Scheme |
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307 | (1) |
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9.1.3 Proposed Barakat-Clark CTD Scheme |
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307 | (2) |
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9.1.4 Accuracy and Truncation Errors |
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309 | (1) |
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9.1.5 Some Results and Discussion |
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309 | (7) |
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9.1.6 Influence of Boundary Conditions |
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316 | (1) |
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9.2 Application of the New Numerical Scheme to Viscous Fingering |
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317 | (42) |
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9.2.1 Stability Criterion and Onset of Fingering |
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318 | (1) |
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318 | (6) |
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324 | (6) |
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330 | (20) |
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9.2.4.1 Effect of Injection Pressure |
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331 | (4) |
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9.2.4.2 Effect of Overall Porosity |
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335 | (1) |
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9.2.4.3 Effect of Mobility Ratio |
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336 | (5) |
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9.2.4.4 Effect of Longitudinal Dispersion |
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341 | (2) |
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9.2.4.5 Effect of Transverse Dispersion |
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343 | (4) |
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9.2.4.6 Effect of Aspect Ratio |
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347 | (3) |
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9.2.5 Comparison of Numerical Modeling Results with Experimental Results |
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350 | (14) |
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9.2.5.1 Selected Experimental Model |
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350 | (1) |
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9.2.5.2 Physical Model Parameters |
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350 | (1) |
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9.2.5.3 Comparative Study |
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351 | (4) |
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9.2.5.4 Concluding Remarks |
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355 | (4) |
10 An Implicit Finite-Difference Approximation of Memory-Based Flow Equation in Porous Media |
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359 | (24) |
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359 | (1) |
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360 | (1) |
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361 | (3) |
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10.4 Theoretical Development |
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364 | (5) |
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365 | (1) |
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10.4.2 Composite Variable, η |
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366 | (1) |
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10.4.3 Implicit Formulation |
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367 | (2) |
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10.6 Numerical Simulation |
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369 | (1) |
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10.7 Results and Discussion |
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370 | (11) |
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381 | (2) |
11 Towards Modeling Knowledge and Sustainable Petroleum Production |
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383 | (82) |
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11.1 Essence of Knowledge, Science, and Emulation |
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384 | (13) |
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11.1.1 Simulation vs. Emulation |
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384 | (2) |
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11.1.2 Importance of the First Premise and Scientific Pathway |
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386 | (2) |
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11.1.3 Mathematical Requirements of Nature Science |
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388 | (4) |
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11.1.4 The Meaningful Addition |
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392 | (2) |
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11.1.5 "Natural" Numbers and the Mathematical Content of Nature |
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394 | (3) |
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11.2 The Knowledge Dimension |
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397 | (3) |
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11.2.1 The Importance of Time as the Fourth Dimension |
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398 | (2) |
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11.3 Aphenomenal Theories of Modern Era |
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400 | (12) |
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11.3.1 Examples of Linearization and Linear Thinking |
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408 | (1) |
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11.3.2 The Knowledge-Based Cognition Process |
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409 | (3) |
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11.4 Towards Modeling Truth and Knowledge |
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412 | (1) |
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11.5 The Single-Parameter Criterion |
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413 | (9) |
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11.5.1 Science Behind Sustainable Technology |
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413 | (2) |
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11.5.2 A New Computational Method |
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415 | (5) |
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11.5.3 Towards Achieving Multiple Solutions |
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420 | (2) |
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11.6 The Conservation of Mass and Energy |
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422 | (20) |
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11.6.1 The Avalanche Theory |
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423 | (5) |
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11.6.2 Aims of Modeling Natural Phenomena |
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428 | (2) |
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11.6.3 Challenges of Modeling Sustainable Petroleum Operations |
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430 | (3) |
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11.6.4 The Criterion: The Switch that Determines the Direction at a Bifurcation Point |
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433 | (19) |
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11.6.4.1 Some Applications of the Criterion |
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436 | (6) |
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11.7 The Need for Multidimensional Study |
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442 | (3) |
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11.8 Assessing the Overall Performance of a Process |
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445 | (7) |
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11.9 Implications of Knowledge-Based Analysis |
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452 | (13) |
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452 | (3) |
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11.9.2 Impact of Global Warming Analysis |
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455 | (3) |
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11.9.3 Examples of Knowledge-based Simulation |
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458 | (7) |
12 Reservoir Simulation of Unconventional Reservoirs |
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465 | (36) |
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465 | (1) |
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12.2 Material Balance Equations |
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466 | (10) |
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12.3 New Fluid Flow Equations |
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476 | (2) |
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12.4 Coupled Fluid Flow and Geo-mechanical Stress Model |
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478 | (2) |
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12.5 Fluid Flow Modeling under Thermal Stress |
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480 | (1) |
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12.6 Challenges of Modeling Unconventional Gas Reservoirs |
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481 | (8) |
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12.7 Comprehensive Modeling |
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489 | (12) |
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12.7.1 Governing Equations |
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489 | (1) |
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490 | (1) |
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12.7.3 Forchheimer's Model |
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491 | (3) |
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12.7.4 Modified Brinkman's Model |
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494 | (2) |
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12.7.5 The Comprehensive Model |
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496 | (5) |
13 Final Conclusions |
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501 | (4) |
References and Bibliography |
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505 | (40) |
Appendix A |
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545 | (24) |
Index |
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569 | |