Fluid Flow in Fractured Rocks

Authoritative textbook providing a rigorous and application-oriented introduction to fluid flow in fractured rocks

Fluid Flow in Fractured Rocks provides an authoritative introduction to the mechanics of fracture growth, flow in single fractures, and flow in fractured porous media, covering a multitude of topics within a single text and providing a holistic understanding of how these subjects interconnect.

Discussions of analytical, experimental, and numerical results illustrate and support the explained concepts. Each chapter comes with problems and summary tables, and contains schematic images as well as field photographs, thus providing a comprehensive learning experience that is both mathematically rigorous and accessible. Case studies from key areas such as petroleum geology, radioactive waste disposal, and geothermal energy aid in practical understanding of concepts.

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
• Coupled thermal, hydraulic, mechanical, and chemical (THMC) rock-water interactions
• 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.

Robert Zimmerman is Professor of Rock Mechanics at Imperial College, London. He obtained a BS and MS in mechanical engineering from Columbia University, and a PhD in solid mechanics from the University of California at Berkeley.

Adriana Paluszny is a Senior Lecturer and Royal Society University Research Fellow at Imperial College, London. She conducts research in the development of numerical methods for the multi-physical simulation of subsurface systems.

1 Genesis and Morphology of Fractures in Rock
1.1 What are Fractures, and Why are they Important?
1.2 Formation of Fractures in Rock
1.3 Morphology of Single Fractures
1.4 Morphology of Fracture Networks

2 Fluid Flow in a Single Fracture
2.1 Introduction
2.2 The Navier-Stokes Equations and the Cubic Law
2.3 The Stokes Equations
2.4 The Reynolds Lubrication Equation
2.5 Effect of Contact Area
2.6 Accuracy of the Lubrication Model
2.7 Fracture in a Permeable Matrix
2.8 Fracture filled with Porous or Granular Material

3 Effect of Stress on Fracture Transmissivity
3.1 Introduction
3.2 The Effect of Normal Stress on Fracture Deformation
3.3 Models for the Normal Stiffness of Rock Fractures
3.4 Row of Elliptical Voids Model for Fracture Transmissivity
3.5 Relation between Transmissivity and Mean Aperture during Normal Compression
3.6. Effect of Shear Deformation on Fracture Transmissivity

4 Fluid Flow through Fractures at Moderate to High Reynolds Numbers
4.1 Introduction
4.2 Approximate Analytical Solution for a Sinusoidal Fracture Aperture
4.3 Weak Inertia Regime and Forchheimer Regime
4.4 Verification of the Weak Inertia and Forchheimer Regimes
4.5 Experimental Data on Fluid Flow at Moderate to High Reynolds Numbers
4.6 Flow of Compressible Gases through Fractures

5 Thermo-Hydro-Chemical-Mechanical Effects on Fracture Transmissivity
5.1 Introduction
5.2 Fracture Contact
5.3 Pressure Dissolution
5.4 Diffusion Rates
5.5 Solute Precipitation
5.6 Aperture Changes
5.7 Relationship between Aperture, Contact Fraction, and Transmissivity
5.8 Numerical Simulations of Pressure Solution 5
5.9 Lehner-Leroy Model for Pressure Dissolution
5.10 Bernabé-Evans Model for Pressure Dissolution
5.11 Dissolution and Precipitation in Open and Closed Systems

6 Solute Transport in a Single Fracture
6.1 Introduction
6.2 Advection-Diffusion Equation
6.3 Taylor-Aris Problem in a Uniform Channel
6.4 Influence of Fracture Morphology on Solute Transport
6.5 Non-Fickian Transport in Rock Fractures
6.6 Influence of Adsorption, Matrix Diffusion, and Radioactive Decay

7 Analytical Models for the Permeability of a Fractured Rock Mass
7.1. Introduction
7.2. Snows Model of Planar Fractures of Infinite Extent in an Impermeable Matrix
7.3. Upper and Lower Bounds on the Effective Permeability
7.4. Spheroidal Inclusion Model of a Fractured Rock Mass
7.5. Effective Permeability in the Regime alpha/kappa << 1
7.6. Effective Permeability in the Regime alpha/kappa >> 1
7.7. Semi-empirical Model of Mourzenko et al.

8 Fluid Flow in Geologically Realistic Fracture Networks
8.1 Introduction
8.2 Stochastically Generated Fracture Networks
8.3 Geomechanically Generated Fracture Networks
8.4 Intersections and Connectivity in Fracture Networks
8.5 Fracture Apertures in Discrete Fracture Networks
8.6 Numerical Computation of Fractured Rock Mass Permeability
8.7 Effect of Fracture Density on Equivalent Permeability
8.8 Effect of in situ Stresses on Equivalent Permeability
8.9 Channels and Preferential Flow Pathways

9 Dual-Porosity Models for Fractured-Porous Rocks
9.1 Introduction
9.2 Pressure Diffusion Equation for the Fractured Continuum
9.3 Fracture/Matrix Fluid Interaction Term
9.4 Equation for the Evolution of the Mean Pressure in the Matrix Blocks
9.5 Warren-Root Solution for Flow to a Well in a Dual-Porosity Medium
9.6 Fully-Transient model for Matrix-to-Fracture Flow
9.7 Nonlinear Matrix-Fracture Transfer Model
9.8 Multi-phase Flow, Gravity Effects, and other Extensions

10 Matrix Block Shape Factors
10.1 Introduction
10.2 Approaches to Choosing the Shape Factor
10.3 Some Specific Results and General Theorems
10.4 Upper and Lower Bounds on the Shape Factor
10.5 Methodology for Numerical Calculation of the Shape Factor
10.6 Scaling Laws for Irregularly-Shaped Matrix Blocks
10.7 Shape Factor under Constant-flux Boundary Conditions
10.8 Constant-flux Shape Factor for a Brick-like Matrix Block

11 Solute Transport in Fractured Rock Masses
11.1 Introduction
11.2 Advection-Dispersion and Solute Transport Equations
11.3 Numerical Solution of the Advection-Dispersion and Solute Transport Equations
11.4 Non-Fickian Transport
11.5 Channel Models
11.6 Particle Tracking Methods
11.7 Continuous Time Random Walk Approach
11.8 Effects of Matrix Permeability
11.9 Effects of In Situ Stresses

12 Two-Phase Flow in Fractured Rocks
12.1. Introduction
12.2. Basic Concepts of Two-Phase Flow
12.3. Pruess-Tsang Model of Two-Phase Flow in a Single Fracture
12.4. Other Models and Observations of Two-Phase Flow in a Single Fracture
12.5. Dual-Porosity and Dual-Permeability Models for Two-Phase Flow
12.6. Discrete-Fracture Network Models for Two-Phase Flow in Fractured Rock Masses

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