Hard Rock Hydraulics: An Introduction to Modeling

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface
1 About modeling
	1.1 Introduction
		1.1.1 Scope and level of this book
		1.1.2 Modeling uncertainty
		1.1.3 Reducing uncertainty
		1.1.4 Practical examples
			1.1.4.1 Example of the difficulty to detect karstic features
			1.1.4.2 Example of the value of published information
			1.1.4.3 Example of the consequences of not detecting minor geologic features
			1.1.4.4 Example of anticipating future WT levels
			1.1.4.5 Example of pumping-rates predictions
		1.1.5 Concluding remarks
	Notes
2 Fundamentals
	2.1 Introduction
	2.2 Basic concepts
		2.2.1 Pseudo-continuity
		2.2.2 Porosity and permeability
		2.2.3 Volumetric and gravimetric relations
			2.2.3.1 Homogeneous and isotropic systems
			2.2.3.2 Homogeneous and anisotropic systems
			2.2.2.3 Heterogeneous systems
		2.2.4 Observation scales
		2.2.5 Description at different scales
	2.3 Hydraulic variables
		2.3.1 Scalars, vectors, and second-order tensors
		2.3.2 Groundwater flow description
		2.3.3 The specific discharge
		2.3.4 The hydraulic gradient
		2.3.5 The hydraulic conductivity
			2.3.5.1 Introduction
			2.3.5.2 Fractures and conduits
			2.3.5.3 Pseudo-continuity and pervious fractures
			2.3.5.4 Valid pseudo-continuity assumption
			2.3.5.5 Erratic discontinuities
		2.3.6 Assessment of the hydraulic conductivities
			2.3.6.1 Introduction
			2.3.6.2 Exploring at the “sample scale”: back to 1930
			2.3.6.3 Exploring old Lugeon tests: 1958 to 1968
			2.3.6.4 Exploring integral sampling: 1968 to 1978
			2.3.6.5 Exploring inverse solution methods: 1978 to 1988
		2.3.7 Governing equations of groundwater flow
			2.3.7.1 Preliminaries
			2.3.7.2 Energy conservation principle: Darcy’s law
			2.3.7.3 Mass conservation principle: continuity equation
			2.3.7.4 Boundary conditions
		2.3.8 Addenda
			2.3.8.1 Effective velocity and specific discharge
			2.3.8.2 Hydrodynamic gradient
			2.3.8.3 Hydraulic conductivity for a group of random fractures
			2.3.8.4 Energy conservation principle
			2.3.8.5 Mass conservation principle
	Notes
	References
3 Approximate solutions
	3.1 Overview
	3.2 Differential operators
	3.3 Uniqueness of solutions
	3.4 Approximate errors
	3.5 Approximation methods
		3.5.1 Preliminaries
		3.5.2 Collocation method
		3.5.3 Least squares method
		3.5.4 Galerkin’s method
			3.5.4.1 Orthogonality
			3.5.4.2 Galerkin’s approach
			3.5.4.3 “Weak” solutions
			3.5.4.4 Variational notation
		3.5.5 Time-dependent solutions
	3.6 Addenda
		3.6.1 Classes of second-order partial differential equations
		3.6.2 Minimizing squared residuals
		3.6.3 Minimizing squared residuals changed by differential operators
		3.6.4 The concept of orthogonality
	Note
	References
4 Data analysis
	4.1 Introduction
	4.2 Analyzing geological data
	4.3 Analyzing hydrologic data
	4.4 Analyzing flow rate data
	4.5 Analyzing hydraulic conductivity data
		4.5.1 Meaning of the hydraulic conductivity
		4.5.2 Mapping of eigenvalues and eigenvectors
		4.5.3 Interpolation of eigenvalues and eigenvectors
	4.6 Analyzing hydraulic head data
		4.6.1 Traditional analysis
		4.6.2 Integrated hydraulic head analysis
	Notes
	References
5 Finite differences
	5.1 Preliminaries
	5.2 Modeling hydrogeological systems
		5.2.1 Concepts
		5.2.2 Guidelines for conceptual models
	5.3 Finite difference basics
		5.3.1 Difference equations
		5.3.2 Finite differences
		5.3.3 Difference equations for steady-state systems
		5.3.4 Difference equations for unsteady-state systems
		5.3.5 Difference equations for boundary conditions
		5.3.6 Simultaneous difference equations
			5.3.6.1 Preliminaries
			5.3.6.2 Gauss–Seidel iterative routine
			5.3.6.3 Crank–Nicolson iterative routine
	5.4 Finite differences algorithms for hard rocks
		5.4.1 Preliminaries
		5.4.2 Steady-state solutions
			5.4.2.1 Dupuit’s approximation
			5.4.2.2 3D algorithms
		5.4.3 Transient solutions
	Notes
	References
6 Applications
	6.1 Preliminaries
	6.2 Fracture interconnectivity
		6.2.1 Interconnection between reservoirs
		6.2.2 Pollution bypassing a wide river
			6.2.2.1 The problem
			6.2.2.2 The anomalies
			6.2.2.3 The scanned images pieces of evidence
			6.2.2.4 The hydraulic properties of the megafractures net
			6.2.2.5 What happens during heavy rains
			6.2.2.6 The 3D model results
	6.3 Thermal waters without hot points
		6.3.1 Preliminaries
		6.3.2 Abridged geologic data
		6.3.3 Model premises
			6.3.3.1 Generalities
			6.3.3.2 Effective mean regional porosity
			6.3.3.3 Permeability
			6.3.3.4 The groundwater recharge discussion
			6.3.3.5 Fundamentals of heat transport
		6.3.4 Modeling results
			6.3.4.1 Dimensions and parameters
			6.3.4.2 The heat transfer processes
			6.3.4.3 Modeling the thermalism gradual decay
	Notes
Bibliography
Index