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Über dieses Buch

The main purpose of this book is to provide the theoretical background to engineers and scientists engaged in modeling transport phenomena in porous media, in connection with various engineering projects, and to serve as a text for senior and graduate courses on transport phenomena in porous media. Such courses are taught in various disciplines, e. g. , civil engineering, chemical engineering, reservoir engineering, agricultural engineering and soil science. In these disciplines, problems are encountered in which various extensive quantities, e. g. , mass and heat, are transported through a porous material domain. Often the porous material contains several fluid phases, and the various extensive quantities are transported simultaneously throughout the multiphase system. In all these disciplines, management decisions related to a system's development and its operation have to be made. To do so, the 'manager', or the planner, needs a tool that will enable him to forecast the response of the system to the implementation of proposed management schemes. This forecast takes the form of spatial and temporal distributions of variables that describe the future state of the considered system. Pressure, stress, strain, density, velocity, solute concentration, temperature, etc. , for each phase in the system, and sometime for a component of a phase, may serve as examples of state variables. The tool that enables the required predictions is the model. A model may be defined as a simplified version of the real (porous medium) system that approximately simulates the excitation-response relations of the latter.

Inhaltsverzeichnis

Frontmatter

General Theory

Frontmatter

Chapter 1. The Porous Medium

Abstract
Phenomena of transport in porous media are encountered in many engineering disciplines. Civil engineering deals, for example, with the flow of water in aquifers, the movement of moisture through and under engineering structures, transport of pollutants in aquifers and the propagation of stresses under foundations of structures. Agricultural engineering deals, for example, with the movement of water and solutes in the root zone in the soil. Heat and mass transport in packed-bed reactor columns and drying processes are encountered in chemical engineering. Reservoir engineers deal with the flow of oil, water and gets in petroleum reservoirs. In all these examples, one or more extensive quantities (i.e., quantities that are additive over volumes, with mass, momentum and energy as examples) are transported through the solid and/or the fluid phases that together occupy a porous medium domain. To solve a problem of transport in such a domain means to determine the spatial and temporal distributions of state variables (e.g., velocity, mass density and pressure of a fluid phase, concentration of a solute, stress in the solid skeleton), that have been selected to describe the state of the material system occupying that domain.
Jacob Bear, Yehuda Bachmat

Chapter 2. Macroscopic Description of Transport Phenomena in Porous Media

Abstract
The objective of this chapter is to develop the mathematical models that describe transport phenomena in porous media at the macroscopic level. As will be shown, a model consists of a balance equation for each extensive quantity that is being transported, constitutive relations, describing the properties of the particular phases involved, source functions of the extensive quantities, and initial and boundary conditions, all stated at the macroscopic level.
Jacob Bear, Yehuda Bachmat

Chapter 3. Mathematical Statement of a Transport Problem

Abstract
We now have all the elements needed in order to formulate the complete statement of a problem of forecasting the distribution of state variables within a porous medium domain at the macroscopic level. The statement includes two parts: a conceptual model and a mathematical one.
Jacob Bear, Yehuda Bachmat

Application

Frontmatter

Chapter 4. Mass Transport of a Single Fluid Phase Under Isothermal Conditions

Abstract
In this chapter we consider the transport of a Newtonian fluid that occupies the entire void space under isothermal conditions. The entire discussion is restricted primarily to the macroscopic level. The fluid is either of constant density, ρ = const., or compressible, i.e., ρ = ρ (p). The effect of possible changes in the concentration of (say, dissolved) components on the fluid’s density is assumed to be negligible. We shall return to this effect in Chap. 6. The flow obeys Darcy’s law (2.6.57), or (2.6.60).
Jacob Bear, Yehuda Bachmat

Chapter 5. Mass Transport of Multiple Fluid Phases Under Isothermal Conditions

Abstract
In Chap. 4, we assumed that a single fluid occupies the entire void space. In the present chapter we treat the simultaneous mass transport of a number of fluid phases that together occupy the void space. The fluids may be a liquid and a gas (e.g., water and air), two liquids (e.g., oil and water), or two liquids and a gas (e.g., water, oil and some gaseous hydrocarbon). At the microscopic level, i.e., within the void-space, each fluid occupies a distinct portion of the void-space, and is separated from other fluids (and from the solid) by boundary surfaces.
Jacob Bear, Yehuda Bachmat

Chapter 6. Transport of a Component in a Fluid Phase Under Isothermal Conditions

Abstract
In this chapter, we focus our attention on the transport of a component, e.g., a solute, contained in a fluid phase that occupies the entire void space, or only part of it. No special symbol will be used to denote the phase, unless more than one phase is being considered.
Jacob Bear, Yehuda Bachmat

Chapter 7. Heat and Mass Transport

Abstract
In this chapter, our primary objective is to construct models of heat transport in porous media. However, since advection (with a fluid moving through the void space), is one of the transport modes, any heat transport model must treat, simultaneously, also the transport of fluid(s) mass. As we shall see below, the coupling between the transport of these two extensive quantities is due also to the fact that both the fluid’s density, and, perhaps, more so, its viscosity, depend on the temperature.
Jacob Bear, Yehuda Bachmat

Chapter 8. Hydraulic Approach to Transport in Aquifers

Abstract
In Chaps. 4 through 7, we have discussed the complete mathematical statement of problems involving the transport of a single fluid phase, of a multiphase fluid system, of a component, or a multi-component system, and of heat, in a porous medium domain of any arbitrary shape. Usually, we had in mind a three-dimensional domain. In the present chapter, we discuss transport phenomena in a domain that has a special shape, viz., a thin domain. Such a domain has the shape of a thin slab, in which one dimension, referred to as thickness, is much smaller than the other two. An aquifer, which is a porous geological formation that contains and transmits groundwater, and an oil reservoir, may serve as examples. For the sake of making the presentation more practical, we shall present the methodology proposed in this chapter by applying it to the former example, namely, that of an aquifer.
Jacob Bear, Yehuda Bachmat

Backmatter

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