Two-Pressure Model of Particle-Fluid Mixture Flow with Pressure-Dependent Viscosity in a Porous Medium

Abstract

Equations governing the flow of a fluid-particle mixture with variable viscosity through a porous structure are developed. Method of intrinsic volume averaging is used to average Saffman’s dusty gas equations. A modelling flexibility is offered in this work by introducing a dust-phase partial pressure in the governing equations, interpreted as the pressure necessary to maintain a uniform particle distribution in the flow field. Viscosity of the fluid-particle mixture is assumed to be variable, with variations in viscosity being due to fluid pressure. Particles are assumed spherical and Stokes’ coefficient of resistance is expressed in terms of the pressure-dependent fluid viscosity. Both Darcy resistance and the Forchheimer micro-inertial effects are accounted for in the developed model