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About this book

Multiphase systems dominate nearly every area of science and technology, and the method of volume averaging provides a rigorous foundation for the analysis of these systems. The development is based on classical continuum physics, and it provides both the spatially smoothed equations and a method of predicting the effective transport coefficients that appear in those equations. The text is based on a ten-week graduate course that has been taught for more than 20 years at the University of California at Davis and at other universities around the world. Problems dealing with both the theoretical foundations and the applications are included with each chapter, and detailed solutions for all problems are available from the author. The course has attracted participants from chemical engineering, mechanical engineering, civil engineering, hydrologic science, mathematics, chemistry and physics.

Table of Contents

Frontmatter

Chapter 1. Diffusion and Heterogeneous Reaction in Porous Media

Abstract
In this chapter we consider the process of bulk diffusion in a porous catalyst with heterogeneous, first order, irreversible reaction. Simultaneous diffusion and reaction occurs in such diverse systems as porous catalysts, (Jackson, 1977), soil aggregates (Rappoldt, 1990), and biofilms (Wood and Whitaker, 1998), and our objective in this chapter is to illustrate a general procedure by which governing point equations and boundary conditions for diffusion and reaction can be spatially smoothed to produce continuum models for multiphase systems.
Stephen Whitaker

Chapter 2. Transient Heat Conduction in Two-Phase Systems

Abstract
In this chapter we consider the problem of heat conduction in two-phase systems without the complications associated with adsorption, chemical reaction, phase change, etc. Our objectives in this chapter are two-fold:
1.
To study a process in which transport occurs in two phases.
 
2.
To indicate how a one-equation model can be developed in order to describe transport in a two-phase system.
 
Stephen Whitaker

Chapter 3. Dispersion in Porous Media

Abstract
In this chapter we will study the simplest possible convective transport process; that of passive convection and diffusion in a rigid, impermeable porous medium. The word passive is used to mean that there is no adsorption or reaction at the fluid-solid interface, nor is there any mass transfer from the fluid phase to the solid phase since the latter is impermeable. Very few real processes are passive in the sense used here; however, it is best to begin our studies of convective transport with as few complications as possible.
Stephen Whitaker

Chapter 4. Single-Phase Flow in Homogeneous Porous Media: Darcy’s Law

Abstract
The process of single-phase flow in rigid porous media is of importance to a variety of engineers and scientists who are concerned with problems ranging from the financial aspects of oil movement in petroleum reservoirs to the social problems of groundwater flows in polluted aquifers. In this chapter we will explore the simplest aspect of this problem i.e., incompressible flow in homogeneous porous media, while in Chapter 5 we will explore the problem of flow in heterogeneous media. Our treatment of homogeneous porous media is based on prior studies by Whitaker (1986d), Barrère et al. (1992), and Quintard and Whitaker (1994c).
Stephen Whitaker

Chapter 5. Single-Phase Flow in Heterogeneous Porous Media

Abstract
In the previous chapter we analyzed the process of single-phase flow in homogeneous porous media, and the result was a proof of Darcy’s law and a method of predicting the permeability tensor. In this chapter we consider porous media that are clearly heterogeneous, i.e., porous media in which there are abrupt and significant changes in the permeability. Such systems can be referred to as mechanically heterogeneous in order to distinguish them from porous media in which there are abrupt and significant changes in the chemical characteristics. These systems are referred to as chemically heterogeneous. Most geological systems tend to be both mechanically and chemically heterogeneous, but in this chapter we will be concerned only with the influence of mechanical heterogeneities.
Stephen Whitaker

Backmatter

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