Spanos The Thermophysics of Porous Media

Erscheinungsjahr 2010
ISBN: 978-1-4200-2612-2
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 230 Seiten

Reihe: Monographs and Surveys in Pure and Applied Mathematics

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.

Zielgruppe

Graduate students in theoretical physics, applied mathematicians and physicists, civil engineers working in fluid dynamics, the mechanics of solids, or geophysics.

Autoren/Hrsg.

Spanos, T.J.T.

Fachgebiete

• Naturwissenschaften Physik Thermodynamik Oberflächen- und Grenzflächenphysik, Dünne Schichten
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Naturwissenschaften Physik Thermodynamik Festkörperphysik, Kondensierte Materie
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde

Inhaltsverzeichnis

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