Flow and Transport in Porous Formations
Published on 6. December 2012
XVII, 465 pages
978-3-642-75015-1 (ISBN)
Description
In the mid-seventies, a new area of research has emerged in subsurface hydrology, namely sto chastic modeling of flow and transport. This development has been motivated by the recognition of the ubiquitous presence of heterogeneities in natural formations and of their effect upon transport and flow, on the one hand, and by the vast expansion of computational capability provided by elec tronic machines, on the other. Apart from this, one of the areas in which spatial variability of for mation properties plays a cardinal role is of contaminant transport, a subject of growing interest and concern. I have been quite fortunate to be engaged in research in this area from its inception and to wit ness the rapid growth of the community and of the literature on spatial variability and its impact upon subsurface hydrology. In view of this increasing interest, I decided a few years ago that it would be useful to present the subject in a systematic and comprehensive manner in order to help those who wish to engage themselves in research or application of this new field. I viewed as my primary task to analyze the large scale heterogeneity of aquifers and its effect, presuming that the reader already possesses a background in traditional hydrology. This is achieved in Parts 3, 4 and 5 of the text which incorporate the pertinent material.
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Gedeon Dagan
Flow and Transport in Porous Formations
Book
08/1989
Springer
€53.49
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Content
1 Mathematical Preliminaries: Elements of Probability Theory and Random Functions.- 1.1 Random variables. Statistical moments.- 1.2 Joint probability distributions. Conditional probability. Multivariate normal distributions.- 1.3 Random functions. Stationarity. Isotropy.- 1.4 Differentiation and integration of random functions Microscale and integral scale.- 1.5 Differentiation of random discontinuous functions.- 1.6 Spectral methods.- 1.7 Random functions of stationary increments.- 1.8 Conditional Gaussian probability and interpolation by kriging.- 1.9 Spatial averages of random functions.- 1.10 The ergodic hypothesis.- 2 The Laboratory Scale (Homogeneous Media).- 2.1 Introduction.- 2.2 Geometry of porous media and space averaging.- 2.3 The microscopic equations of flow and transport.- 2.4 Averaging of derivatives of microscopic variables.- 2.5 Macroscopic variables and macroscopic equations of mass and energy conservation.- 2.6 The macroscopic equations of conservation of momentum.- 2.7 The constitutive equation of heat transfer (effective heat conductivity).- 2.8 The constitutive equation of mass transfer (effective diffusion coefficient).- 2.9 Darcy's law.- 2.10 Convective-diffusive transport (hydrodynamic dispersion).- 2.11 Summary of macroscopic equations of water flow.- 2.12 Summary of macroscopic equations of solute and heat transfer.- 2.13 Flow and transport boundary conditions.- 3 Water Flow at the Local (Formation) Scale.- 3.1 Introduction.- 3.2 The heterogeneous structure of aquifers at the local (formation) scale.- 3.3 General formulation of the direct problem and of the equations of flow.- 3.4 The effective hydraulic conductivity.- 3.5 Solutions of the mean flow equations (examples of exact solutions).- 3.6 Solutions of the mean flow equations(approximate methods).- 3.7 Second-order statistical moments of the flow variables.- 4 Solute Transport at the Local (Formation) Scale.- 4.1 Introduction.- 4.2 Afew field findings.- 4.3 The conceptual model.- 4.4 A few numerical simulations of solute transport in heterogeneous formations.- 4.5 Transport through stratified formations.- 4.6 Transport informations of three-dimensional heterogeneous structures.- 4.7 Two-dimensional transport and comparison with afield experiment.- 4.8 Effects of nonlinearity and unsteadiness.- 4.9 Transport of reactive solutes. Effect of parameters estimation errors..- 5 Flow and Transport at the Regional Scale.- 5.1 Introduction.- 5.2 Analysis of field data and statistical characterization of heterogeneity.- 5.3 Mathematical statement of the direct problem.- 5.4 Effective properties and the solutions of the equations of mean flow.- 5.5 Second-order statistical moments of the flow variables. The effect of conditioning.- 5.6 The inverse (identification) problem.- 5.7 Transport at the regional scale.- 5.8 Modeling transport by travel time approach.
