The Thermophysics of Porous Media: 1st Edition (Hardback) book cover

The Thermophysics of Porous Media

1st Edition

By T.J.T. Spanos

Chapman and Hall/CRC

230 pages

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Hardback: 9781584881070
pub: 2001-11-28
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Description

Models for the mechanical behavior of porous media introduced more than 50 years ago are still relied upon today, but more recent work shows that, in some cases, they may violate the laws of thermodynamics. In The Thermophysics of Porous Media, the author shows that physical consistency requires a unique description of dynamic processes that involve porous media, and that new dynamic variables-porosity, saturation, and megascale concentration-naturally enter into the large-scale description of porous media. The new degrees of freedom revealed in this study predict new dynamic processes that are not associated with compressional motions.

The book details the construction of a Lorentz invariant thermodynamic lattice gas model and shows how the associated nonrelativistic, Galilean invariant model can be used to describe flow in porous media. The author develops the equations of seismic wave propagation in porous media, the associated boundary conditions, and surface waves. He also constructs the equations for both immiscible and miscible flows in porous media and their related instability problems.

The implications of the physical theory presented in this book are significant, particularly in applications in geophysics and the petroleum industry. The Thermophysics of Porous Media offers a unique opportunity to examine the dynamic role that porosity plays in porous materials.

Reviews

"The book will be of interest … to researchers and postgraduate students in physics with strong knowledge in mathematics."

- Zentralblatt MATH, 1043

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Table of Contents

INTRODUCTION

Terminology and Objectives

Tensor Analysis

Coordinate Transformation

Tensor Calculus (summation convention back in effect

Conservation Laws

Energy Momentum Tensor and its Properties

Euler Lagrange Equations

Averaging

Automata Modeling

References

THERMOMECHANICS AND POROMECHANICS

Content of this Chapter

Previous Theories

Pore-Scale Equations

Construction of Megascale Equations for a Homogeneous Medium

Megascopic Potential Energy

Equations for a Homogeneous Medium

The Effect of Heterogeneity

Equations for a Spatially Varying Porosity

Implications for the Energy Momentum Tensor

References

THERMODYNAMICS - PORODYNAMICS OF DEFORMATION

Objectives of this Chapter

The Fluid Component

The Solid Component

Internal Energy for Porous Media

The Effect of Heterogeneity

Summary

References

THERMODYNAMIC AUTOMATA

Objectives of this Chapter

Cellular Automata Models

A Lorentz Invariant Lattice Gas Model

A Non Relativistic Model

Porous Media

Summary

References

SEISMIC WAVE PROPAGATION

Objectives of this Chapter

Construction of the Wave Equations

Reflection Transmission Problems

Effect of Thermomechanical Coupling

Breakdown of the Assumption of Interacting Phases

Surface Waves

Wave Propagation in an Inhomogeneous Medium

Summary

References

IMMISCIBLE FLOW

Objectives of this Chapter

Quasi-Static Two-Phase Flow in Porous Media

Flow Equations for Quasi-Static Flow

Multiphase Fluid Displacement

A Megascopic Capillary Pressure Equation

Boundary Conditions Associated with Fluid Displacement

Instabilities During Immiscible Displacement

Multiphase Flow with Phase Transitions

Summary

References

MISCIBLE DISPLACEMENT IN POROUS MEDIA

Objectives of this Chapter

Equation of Continuity

Convection Diffusion Theory

A Solution of The Dynamical Equations

Dispersion

Summary

References

POROSITY-PRESSURE PROPAGATION

Objectives of this Chapter

Megascopic Equations for Porosity-Pressure Propagation and Diffusion

Porosity Diffusion

Porosity Wave Propagation

Summary

References

GRANULAR FLOW

Objectives of this Chapter

Stability of a Porous Medium-Fluid Suspension Boundary

Stability of a Particulate Boundary in a Porous Medium

Flow of Suspensions in a Fluid

Summary

References

About the Series

Monographs and Surveys in Pure and Applied Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
SCI065000
SCIENCE / Mechanics / Dynamics / Thermodynamics
TEC009020
TECHNOLOGY & ENGINEERING / Civil / General