Preface |
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xiii | |
Acknowledgements |
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xvi | |
List of Symbols |
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xvii | |
1 Interfacial Curvature and Contact Angle |
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1 | (16) |
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1 | (3) |
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1.2 Young-Laplace Equation |
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4 | (3) |
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1.3 The Young Equation and Contact Angle |
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7 | (10) |
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1.3.1 The Young Equation as an Energy Balance |
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10 | (1) |
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1.3.2 Interfacial Tension, Roughness and Wettability |
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11 | (3) |
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14 | (2) |
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1.3.4 Historical Interlude: Thomas Young and the Marquis de Laplace |
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16 | (1) |
2 Porous Media and Fluid Displacement |
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17 | (56) |
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17 | (15) |
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2.1.1 Statistical and Process-Based Pore-Space Reconstruction |
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22 | (7) |
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2.1.2 Definition of a Porous Medium, Representative Volumes, Porosity and Saturation |
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29 | (3) |
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2.2 Pore-Scale Networks and Topological Description |
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32 | (24) |
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33 | (2) |
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2.2.2 Network Construction |
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35 | (10) |
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2.2.3 Generalized Network Models |
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45 | (5) |
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2.2.4 Topological Descriptors of the Pore Space |
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50 | (6) |
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2.3 Wettability and Displacement |
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56 | (17) |
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2.3.1 Thermodynamic Description of Displacement Processes |
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56 | (3) |
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2.3.2 Displacement Sequences |
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59 | (1) |
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2.3.3 Wettability and Wettability Change |
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60 | (5) |
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2.3.4 Surface Roughness and Contact Angle Hysteresis |
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65 | (4) |
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2.3.5 Effective Contact Angle and Curvature |
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69 | (4) |
3 Primary Drainage |
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73 | (42) |
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3.1 Entry Pressures and Fluid Configurations |
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74 | (11) |
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79 | (3) |
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3.1.2 Entry Pressures for Irregular Throats |
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82 | (3) |
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3.2 Macroscopic Capillary Pressure in Drainage |
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85 | (4) |
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3.3 Bundle of Tubes Model and the Throat Size Distribution |
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89 | (6) |
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3.3.1 Prediction of Capillary Pressure from Images |
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92 | (3) |
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95 | (15) |
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3.4.1 Scaling Relations in Invasion Percolation |
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99 | (6) |
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3.4.2 Displacement under Gravity and Gradient Percolation |
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105 | (4) |
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3.4.3 Invasion Percolation, Normal Percolation and Flow |
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109 | (1) |
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3.5 Final Saturation and Maximum Capillary Pressure |
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110 | (5) |
4 Imbibition and Trapping |
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115 | (73) |
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4.1 Layer Flow, Swelling and Snap-Off |
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116 | (10) |
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4.1.1 Roof Snap-Off during Drainage |
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122 | (4) |
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4.2 Piston-Like Advance and Pore Filling |
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126 | (19) |
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4.2.1 Piston-Like Throat Filling |
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126 | (2) |
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4.2.2 Cooperative Pore Filling |
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128 | (4) |
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4.2.3 Competition between Snap-Off and Cooperative Pore Filling |
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132 | (3) |
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4.2.4 Frequency of Different Filling Events |
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135 | (6) |
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4.2.5 Dynamics of Filling |
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141 | (3) |
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4.2.6 Displacement as a Series of Metastable States |
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144 | (1) |
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4.3 Displacement Patterns in Imbibition |
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145 | (16) |
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4.3.1 Percolation with Trapping |
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145 | (2) |
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4.3.2 Invasion Percolation with Trapping |
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147 | (1) |
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148 | (1) |
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149 | (1) |
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4.3.5 Phase Diagrams for Capillary-Controlled Displacement |
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149 | (8) |
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4.3.6 Infiltration or Unstable Imbibition under Gravity |
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157 | (4) |
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4.4 Macroscopic Capillary Pressure |
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161 | (4) |
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165 | (3) |
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4.6 Capillary Trapping and Residual Saturation |
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168 | (20) |
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4.6.1 Direct Imaging of Trapped Clusters and Percolation Theory |
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168 | (8) |
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4.6.2 Effect of Initial Saturation |
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176 | (12) |
5 Wettability and Displacement Paths |
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188 | (31) |
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5.1 Definitions and Capillary Pressure Cycles |
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188 | (6) |
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194 | (7) |
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5.2.1 Pinned Water Layers and Forced Snap-Off |
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194 | (2) |
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5.2.2 Forced Water Injection and Oil Layer Formation |
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196 | (4) |
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5.2.3 Recap of Displacement Processes |
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200 | (1) |
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5.3 Capillary Pressures and Wettability Indices |
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201 | (10) |
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5.3.1 Wettability Trends and Relationships between Indices |
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204 | (4) |
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5.3.2 Displacement Statistics in Mixed-Wet Systems |
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208 | (3) |
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5.4 Trapping in Mixed-Wet and Oil-Wet Media |
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211 | (8) |
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5.4.1 Layer Connectivity as a Function of Initial Water Saturation |
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213 | (3) |
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5.4.2 Pore-Scale Observation of Trapping in Mixed-Wet Systems |
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216 | (3) |
6 Navier-Stokes Equations, Darcy's Law and Multiphase Flow |
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219 | (96) |
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6.1 Navier-Stokes Equations and Conservation of Mass |
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219 | (17) |
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221 | (4) |
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6.1.2 The Washburn Equation |
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225 | (3) |
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6.1.3 Flow in Wetting Layers |
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228 | (5) |
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6.1.4 Reynolds Number and the Stokes Equation |
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233 | (3) |
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6.2 Darcy's Law and Permeability |
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236 | (18) |
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6.2.1 Permeability of a Bundle of Capillary Tubes |
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238 | (1) |
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6.2.2 Typical Permeability Values |
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239 | (4) |
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6.2.3 The Leverett J Function |
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243 | (4) |
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6.2.4 Computing Flow Fields on Pore-Space Images |
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247 | (7) |
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6.3 The Multiphase Darcy Law and Relative Permeability |
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254 | (3) |
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6.3.1 Historical Interlude: Muskat, Leverett and Buckingham |
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254 | (1) |
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6.3.2 Assumptions Inherent in the Multiphase Darcy Law |
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255 | (2) |
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6.4 Capillary Number and Pore-Scale Dynamics |
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257 | (41) |
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6.4.1 Macroscopic Flow Patterns for Imbibition |
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257 | (6) |
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6.4.2 Capillary Number and the Perturbative Effect of Flow Rate |
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263 | (2) |
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6.4.3 Layer Conductance and Viscous Effects |
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265 | (5) |
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6.4.4 Correlation Lengths for Percolation-Like Displacement |
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270 | (3) |
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6.4.5 Correlation Length and Residual Saturation |
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273 | (2) |
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6.4.6 Mobilization of Trapped Ganglia |
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275 | (4) |
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6.4.7 Ganglion Dynamics, Connectivity and Flow Regimes |
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279 | (6) |
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6.4.8 Viscous and Capillary Forces as an Energy Balance |
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285 | (3) |
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6.4.9 Direct Computation of Multiphase Flow |
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288 | (10) |
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6.5 Extensions to the Multiphase Darcy Law |
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298 | (6) |
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6.5.1 Infiltration and Phase Field Models |
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298 | (2) |
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6.5.2 Accounting for Non-Equilibrium Effects |
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300 | (1) |
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6.5.3 Averaged Equations from Energy, Momentum and Entropy Balance |
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301 | (2) |
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6.5.4 Consideration of Trapped Phases and Other Approaches |
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303 | (1) |
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304 | (11) |
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6.6.1 Dimensionless Numbers |
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305 | (1) |
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6.6.2 Viscous Fingering and DLA |
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306 | (3) |
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6.6.3 Summary of Regime Diagrams |
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309 | (6) |
7 Relative Permeability |
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315 | (39) |
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315 | (11) |
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315 | (3) |
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318 | (1) |
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7.1.3 Predictions of Relative Permeability |
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319 | (3) |
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7.1.4 Relative Permeabilities for Different Rock Types |
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322 | (3) |
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7.1.5 Effect of Initial Saturation |
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325 | (1) |
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7.2 Effect of Wettability |
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326 | (17) |
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327 | (2) |
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7.2.2 Cross-Over Saturation and Waterflood Recovery |
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329 | (1) |
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330 | (3) |
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7.2.4 Hysteresis in the Water Relative Permeability |
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333 | (3) |
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7.2.5 Hysteresis in the Oil Relative Permeability |
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336 | (2) |
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7.2.6 Features of Relative Permeability in Mixed-Wet Rocks |
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338 | (2) |
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7.2.7 Guidelines for Assessing Wettability |
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340 | (3) |
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7.3 Effect of Capillary Number and Viscosity Ratio |
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343 | (4) |
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7.3.1 Relative Permeability in the Viscous Limit |
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344 | (2) |
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7.3.2 Viscosity Ratio and Viscous Coupling |
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346 | (1) |
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347 | (7) |
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7.4.1 Relative Permeability of a Bundle of Tubes |
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348 | (2) |
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7.4.2 Functional Forms for Relative Permeability and Capillary Pressure |
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350 | (2) |
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7.4.3 Empirical Models in Hydrology |
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352 | (2) |
8 Three-Phase Flow |
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354 | (48) |
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354 | (4) |
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8.2 Contact Angles and the Bartell-Osterhof Equation |
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358 | (6) |
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8.2.1 Wetting and Spreading in Three-Phase Flow |
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360 | (1) |
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8.2.2 Why Ducks Don't Get Wet |
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361 | (2) |
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8.2.3 Wettability States in Three-Phase Flow |
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363 | (1) |
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364 | (9) |
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8.3.1 Mixed-Wettability and Layer Stability |
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365 | (1) |
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8.3.2 Three Phases in Capillary/Gravity Equilibrium |
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366 | (2) |
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8.3.3 Layer Conductance and Relative Permeability |
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368 | (5) |
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8.4 Displacement Processes |
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373 | (8) |
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8.4.1 Fluid Configurations |
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373 | (2) |
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8.4.2 Configuration Changes and Layer Stability |
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375 | (1) |
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8.4.3 Multiple Displacement |
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375 | (3) |
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378 | (3) |
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8.5 Three-Phase Relative Permeability |
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381 | (21) |
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8.5.1 Pore Occupancy and Saturation Dependence |
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386 | (3) |
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8.5.2 Predictions of Three-Phase Relative Permeability |
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389 | (2) |
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8.5.3 Trapping in Three-Phase Flow |
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391 | (6) |
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8.5.4 Direct Imaging of Trapped Phases in Three-Phase Flow |
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397 | (1) |
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8.5.5 Empirical Models in Three-Phase Flow |
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397 | (5) |
9 Solutions to Equations for Multiphase Flow |
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402 | (35) |
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9.1 Conservation Equations for Multiphase Flow |
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402 | (9) |
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9.1.1 Equations in One Dimension and the Fractional Flow |
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405 | (1) |
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9.1.2 Waterflooding and Spontaneous Imbibition |
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405 | (2) |
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9.1.3 Exemplar Relative Permeabilities and Capillary Pressures |
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407 | (4) |
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9.1.4 Boundary Conditions for One-Dimensional Flow Problems |
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411 | (1) |
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9.2 Buckley-Leverett Analysis for Two-Phase Flow |
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411 | (11) |
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9.2.1 Dimensionless Variables and Wavespeeds |
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413 | (1) |
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414 | (1) |
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9.2.3 Constructing a Solution for Saturation |
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415 | (3) |
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9.2.4 Recovery Calculations |
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418 | (1) |
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9.2.5 Example Recovery Curves |
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418 | (4) |
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9.3 Analysis of Imbibition |
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422 | (10) |
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9.3.1 Capillary Dispersion and Fractional Flow |
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422 | (5) |
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427 | (3) |
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9.3.3 Experimental Analysis of Spontaneous Imbibition |
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430 | (2) |
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9.4 Recovery, Imbibition and the Trillion-Barrel Question |
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432 | (5) |
Appendix Exercises |
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437 | (10) |
References |
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447 | (28) |
Index |
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475 | |