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Table of Contents
Preface; Acknowledgments; Contents; 1 Generalization of Darcy's Law: Non-Darcian Liquid Flow in Low-Permeability Media; Abstract; 1.1 Henry Darcy and His Law for Subsurface Fluid Flow; 1.2 Relationship Between Water Flow Flux and Hydraulic Gradient in a Capillary Tube; 1.3 Generalized Darcy's Law for Water Flow in Low-Permeability Media; 1.4 Correlation Between Permeability and the Threshold Gradient; 1.5 Relationship Between Parameter {\varvec \alpha} and Pore Size Distribution; 1.6 Multidimensional and Anisotropic Cases; 1.7 Case Studies.
1.7.1 Impact of Non-Darcian Flow on Performance of a Shale Repository for High-Level Nuclear Waste1.7.2 Influence of Non-Darcian Flow on Observed Relative Permeability; 1.7.3 Imbibition of Fracturing Fluids into Shale Matrix and a Methodology to Determine Relevant Parameters; 1.7.4 Non-Darcian Flow and Abnormal Liquid Pressure in Shale Formations; 1.8 Concluding Remarks; References; 2 Generalization of the Darcy-Buckingham Law: Optimality and Water Flow in Unsaturated Media; Abstract; 2.1 Edgar Buckingham and His Law for Water Flow in Unsaturated Soils.
2.2 Unsaturated Flow Constitutive Models Under Local Equilibrium2.2.1 Burdine Model for Relative Permeability and the Brooks-Corey Relation; 2.2.2 Mualem Model for Relative Permeability and the van Genuchten Relation; 2.3 Optimality Principles and the Euler-Lagrangian Equation; 2.4 Generalization of the Darcy-Buckingham Law Based on an Optimality Condition; 2.5 Verification with Field Observations of Unsaturated Water Flow in Soils; 2.5.1 Field Experiments; 2.5.2 Data Analysis Methods; 2.5.3 Results and Discussion; 2.6 The Active Fracture Model: An Equation for a Mountain.
2.6.1 Yucca Mountain Project2.6.2 The Active Fracture Model (AFM); 2.6.3 Verification of the AFM with Field Observations; 2.6.4 Comparisons with Fracture Network Modeling Results; 2.7 Optimality and Surface Water Flow; 2.8 Concluding Remarks; Appendix: An Alternative Derivation of Eq.ß2.48 Without Using the Lagrange Multiplier; References; 3 Two-Part Hooke Model (TPHM): Theory, Validation and Applications; Abstract; 3.1 Robert Hooke and His Law for Elastic Deformation; 3.2 Two-Part Hooke's Model; 3.2.1 TPHM for Isotropic Stress Condition.
3.2.2 TPHM-Based Constitutive Relationships for Isotropic Stress Condition3.2.2.1 Bulk Rock Compressibility; 3.2.2.2 Pore Compressibility; 3.2.2.3 Rock Porosity; 3.2.2.4 Relationship Between Permeability and Porosity for Low-Permeability Rock; 3.2.3 TPHM for Anisotropic Stress Condition; 3.2.4 TPHM-Based Constitutive Relationships for Anisotropic Stress Condition; 3.2.4.1 Rock Porosity; 3.2.4.2 Bulk Compressibility; 3.2.4.3 Shear Modulus; 3.2.5 Implementation of the TPHM in a Geomechanical Simulator; 3.3 Fracture Deformation and Properties.
1.7.1 Impact of Non-Darcian Flow on Performance of a Shale Repository for High-Level Nuclear Waste1.7.2 Influence of Non-Darcian Flow on Observed Relative Permeability; 1.7.3 Imbibition of Fracturing Fluids into Shale Matrix and a Methodology to Determine Relevant Parameters; 1.7.4 Non-Darcian Flow and Abnormal Liquid Pressure in Shale Formations; 1.8 Concluding Remarks; References; 2 Generalization of the Darcy-Buckingham Law: Optimality and Water Flow in Unsaturated Media; Abstract; 2.1 Edgar Buckingham and His Law for Water Flow in Unsaturated Soils.
2.2 Unsaturated Flow Constitutive Models Under Local Equilibrium2.2.1 Burdine Model for Relative Permeability and the Brooks-Corey Relation; 2.2.2 Mualem Model for Relative Permeability and the van Genuchten Relation; 2.3 Optimality Principles and the Euler-Lagrangian Equation; 2.4 Generalization of the Darcy-Buckingham Law Based on an Optimality Condition; 2.5 Verification with Field Observations of Unsaturated Water Flow in Soils; 2.5.1 Field Experiments; 2.5.2 Data Analysis Methods; 2.5.3 Results and Discussion; 2.6 The Active Fracture Model: An Equation for a Mountain.
2.6.1 Yucca Mountain Project2.6.2 The Active Fracture Model (AFM); 2.6.3 Verification of the AFM with Field Observations; 2.6.4 Comparisons with Fracture Network Modeling Results; 2.7 Optimality and Surface Water Flow; 2.8 Concluding Remarks; Appendix: An Alternative Derivation of Eq.ß2.48 Without Using the Lagrange Multiplier; References; 3 Two-Part Hooke Model (TPHM): Theory, Validation and Applications; Abstract; 3.1 Robert Hooke and His Law for Elastic Deformation; 3.2 Two-Part Hooke's Model; 3.2.1 TPHM for Isotropic Stress Condition.
3.2.2 TPHM-Based Constitutive Relationships for Isotropic Stress Condition3.2.2.1 Bulk Rock Compressibility; 3.2.2.2 Pore Compressibility; 3.2.2.3 Rock Porosity; 3.2.2.4 Relationship Between Permeability and Porosity for Low-Permeability Rock; 3.2.3 TPHM for Anisotropic Stress Condition; 3.2.4 TPHM-Based Constitutive Relationships for Anisotropic Stress Condition; 3.2.4.1 Rock Porosity; 3.2.4.2 Bulk Compressibility; 3.2.4.3 Shear Modulus; 3.2.5 Implementation of the TPHM in a Geomechanical Simulator; 3.3 Fracture Deformation and Properties.