Fluid Flow in Fractured Rocks

FLUID FLOW IN FRACTURED ROCKS "The definitive treatise on the subject for many years to come" —Prof. Ruben Juanes, MIT Authoritative textbook that provides a comprehensive and up-to-date introduction to fluid flow in fractured rocks Fluid Flow in Fractured Rocks provides an authoritative introduction to the topic of fluid flow through single rock fractures and fractured rock masses. This book is intended for readers with interests in hydrogeology, hydrology, water resources, structural geology, reservoir engineering, underground waste disposal, or other fields that involve the flow of fluids through fractured rock masses. Classical and established models and data are presented and carefully explained, and recent computational methodologies and results are also covered. Each chapter includes numerous graphs, schematic diagrams and field photographs, an extensive reference list, and a set of problems, thus providing a comprehensive learning experience that is both mathematically rigorous and accessible. Written by two internationally recognized leaders in the field, Fluid Flow in Fractured Rocks includes information on: Nucleation and growth of fractures in rock, with a multiscale characterization of their geometric traits Effect of normal and shear stresses on the transmissivity of a rock fracture and mathematics of fluid flow through a single rock fracture Solute transport in rocks, with quantitative descriptions of advection, molecular diffusion, and dispersion Fluid Flow in Fractured Rocks is an essential resource for researchers and postgraduate students who are interested in the field of fluid flow through fractured rocks. The text is also highly suitable for professionals working in civil, environmental, and petroleum engineering.

Table of Contents:
Preface ix Author Biographies xi About the Companion Website xiii 1 Genesis and Morphology of Fractures in Rock 1 1.1 What Are Fractures, and Why Are They Important? 1 1.2 Formation of Fractures in Rock 2 1.3 Morphology of Single Fractures 5 1.4 Morphology of Fracture Networks 14 2 Fluid Flow in a Single Fracture 27 2.1 Introduction 27 2.2 The Navier–Stokes Equations and the Cubic Law 28 2.3 The Stokes Equations 32 2.4 The Reynolds Lubrication Equation 36 2.5 Effect of Contact Area 41 2.6 Accuracy of the Lubrication Model 43 2.7 Fracture in a Permeable Matrix 46 2.8 Fracture Filled with Porous or Granular Material 49 3 Effect of Stress on Fracture Transmissivity 57 3.1 Introduction 57 3.2 The Effect of Normal Stress on Fracture Deformation 58 3.3 Models for the Normal Stiffness of Rock Fractures 60 3.4 "Row of Elliptical Voids" Model for Fracture Transmissivity 63 3.5 Relation Between Transmissivity and Mean Aperture During Normal Compression 68 3.6 Effect of Shear Deformation on Fracture Transmissivity 70 4 Fluid Flow Through Fractures at Moderate to High Reynolds Numbers 75 4.1 Introduction 75 4.2 Approximate Analytical Solution for a Sinusoidal Fracture Aperture 76 4.3 Weak Inertia Regime and Forchheimer Regime 77 4.4 Verification of theWeak Inertia and Forchheimer Regimes 80 4.5 Experimental Data on Fluid Flow at Moderate to High Reynolds Numbers 84 4.6 Flow of Compressible Gases Through Fractures 85 5 Thermo-Hydro-Chemical-Mechanical Effects on Fracture Transmissivity 91 5.1 Introduction 91 5.2 Fracture Contact 92 5.3 Pressure Dissolution 94 5.4 Diffusion Rates 97 5.5 Solute Precipitation 98 5.6 Aperture Changes 99 5.7 Relationship Between Aperture, Contact Fraction, and Transmissivity 101 5.8 Numerical Simulations of Pressure Solution 103 5.9 Lehner–Leroy Model for Pressure Dissolution 104 5.10 Bernabé–Evans Model for Pressure Dissolution 106 5.11 Dissolution and Precipitation in Open and Closed Systems 109 6 Solute Transport in a Single Fracture 113 6.1 Introduction 113 6.2 Advection–Diffusion Equation 114 6.3 Taylor–Aris Problem in a Uniform Channel 118 6.4 Influence of Fracture Morphology on Solute Transport 121 6.5 Non-Fickian Transport in Rock Fractures 123 6.6 Influence of Adsorption, Matrix Diffusion, and Radioactive Decay 126 7 Analytical Models for the Permeability of a Fractured Rock Mass 133 7.1 Introduction 133 7.2 Snow's Model of Planar Fractures of Infinite Extent in an Impermeable Matrix 134 7.3 Upper and Lower Bounds on the Effective Permeability 136 7.4 Spheroidal Inclusion Model of a Fractured Rock Mass 137 7.5 Effective Permeability in the Regime (α/κ much less than) 140 7.6 Effective Permeability in the Regime (α/κ much greater than) 142 7.7 Semi-empirical Model of Mourzenko et al. 144 8 Fluid Flow in Geologically Realistic Fracture Networks 149 8.1 Introduction 149 8.2 Stochastically Generated Fracture Networks 150 8.3 Geomechanically Generated Fracture Networks 152 8.4 Intersections and Connectivity in Fracture Networks 155 8.5 Fracture Apertures in Discrete Fracture Networks 156 8.6 Numerical Computation of Fractured Rock Mass Permeability 159 8.7 Effect of Fracture Density on Equivalent Permeability 163 8.8 Effect of In Situ Stresses on Equivalent Permeability 166 8.9 Channels and Preferential Flow Pathways 170 9 Dual-Porosity Models for Fractured-Porous Rocks 177 9.1 Introduction 177 9.2 Pressure Diffusion Equation for the Fractured Continuum 178 9.3 Fracture/Matrix Fluid Interaction Term 180 9.4 Equation for the Evolution of the Mean Pressure in the Matrix Blocks 182 9.5 Warren–Root Solution for Flow to aWell in a Dual-Porosity Medium 184 9.6 Fully Transient model for Matrix-to-Fracture Flow 188 9.7 Nonlinear Matrix-Fracture Transfer Model 190 9.8 Multi-Phase Flow, Gravity Effects, and Other Extensions 193 10 Matrix Block Shape Factors 199 10.1 Introduction 199 10.2 Approaches to Choosing the Shape Factor 200 10.3 Some Specific Results and General Theorems 202 10.4 Upper and Lower Bounds on the Shape Factor 203 10.5 Methodology for Numerical Calculation of the Shape Factor 204 10.6 Scaling Laws for Irregularly Shaped Matrix Blocks 207 10.7 Shape Factor Under Constant-Flux Boundary Conditions 209 10.8 Constant-Flux Shape Factor for a Brick-like Matrix Block 213 11 Solute Transport in Fractured Rock Masses 219 11.1 Introduction 219 11.2 Advection–Dispersion and Solute Transport Equations 220 11.3 Numerical Solution of the Advection–Dispersion and Solute Transport Equations 222 11.4 Non-Fickian Transport 226 11.5 Channel Models 227 11.6 Particle Tracking Methods 230 11.7 Continuous Time RandomWalk Approach 232 11.8 Effects of Matrix Permeability 234 11.9 Effects of In Situ Stresses 235 12 Two-Phase Flow in Fractured Rocks 241 12.1 Introduction 241 12.2 Basic Concepts of Two-Phase Flow 242 12.3 Pruess–Tsang Model of Two-Phase Flow in a Single Fracture 246 12.4 Other Models and Observations of Two-Phase Flow in a Single Fracture 248 12.5 Dual-Porosity and Dual-Permeability Models for Two-Phase Flow 251 12.6 Discrete-Fracture Network Models for Two-Phase Flow in Fractured Rock Masses 254 Problems 256 References 256 List of Symbols 259 Index 265

About the Author :
Robert W. Zimmerman is Professor of Rock Mechanics at Imperial College London. He is the co-author, with J.C. Jaeger and N.G.W. Cook, of the authoritative monograph Fundamentals of Rock Mechanics (4th ed., Wiley, 2007). Adriana Paluszny is Reader in Computational Geomechanics, and Royal Society University Research Fellow, at Imperial College London. She was the inaugural recipient, in 2018, of the Chin-Fu Tsang Award for Coupled Processes in Fractured Rocks.

Review :
"Fractures are ubiquitous in geologic formations, and they are often the key determinants of fluid flow and transport in the subsurface, controlling processes that are critical in environmental flows and in the energy transition, such as geothermal energy extraction, in situ mining of metals and minerals, and migration of radionuclides from geological nuclear waste disposal facilities. Despite their fundamental role in subsurface technologies, modeling fluid flow in fractured rocks is notoriously challenging because of their multiscale (fractal) nature, and the complex behavior that emerges from their interconnected network structure. In this book, world-leading experts Zimmerman and Paluszny present a didactive and insightful synthesis of the physics, mathematics, and computational modeling of fluid flow in fractured rock, that is destined to become the definitive treatise on the subject for many years to come." (Ruben Juanes, Professor of Civil and Environmental Engineering, MIT, Cambridge, USA)