Displacement waves in saturated thermoelastic porous media. I. basic equations

Abstract

A complete set of macroscopic equations, the solution of which describes fluid and solid stresses, displacements and temperatures, evolving from an excitation of a saturated porous medium domain in the form of an abrupt pressure and temperature changes applied at the domain's boundary is presented. The tluid is a compressible Newtonian one and the solid is thermoelastic. Nonisothermal conditions prevail. The set of equations includes mass, momentum and energy balance equations, constitutive relations and definitions. A simple example indicates that the tluid and solid displacements are described by two coupled wave equations.

Weighted average flux method and flux limiters for the numerical simulation of shock waves in rigid porous media

“…This idea was advanced further by Levy et al [6], by performing a dimensional analysis on the resulting macroscopic balance equation developed by Sorek et al [4] and Bear et al [7]. This established a theoretical basis on which to model non-linear wave motion in a deformable porous media represented by a continuum of interacting solid and uid phases.…”

A model for solute transport following an abrupt pressure impact in saturated porous media

“…To address the transient period, we follow the methodology developed by Bear and Sorek (1990) who studied the evolution of fluid's mass and momentum balance equations following the onset of an abrupt pressure change in saturated porous media. Sequel papers emerged since, involving deformable porous media under nonisothermal conditions (Bear et al 1992;Sorek et al 1992).…”

Mathematical Formulation Requirements and Specifications for the Process Models

“…For an isotropic medium there is no preferred axis of symmetry the dispersion tensor D H has the well-known form (Bear, 1972b) Anisotropic Media. The dispersion tensor for anisotropic media has not received much attention, However, it has been shown that in an axi-symmetric medium with axis of symmetry λ s , the dispersion tensor takes the general form (Lichtner et al, 2002)…”

“…An alternative formulation for the coefficient for molecular diffusion in porous media is given by the formation factor, F f , defined as (Bear, 1972b) (4.15) in which case the diffusive flux in porous media becomes…”

“…Since water-rock interaction commonly takes place in porous materials, it is important to account for the effect of tortuosity (Figure 1), which is defined as the ratio of the path length the solute would follow in water alone, L, relative to the tortuous path length it would follow in porous media, L e (Bear, 1972b)…”