Modeling Transport Phenomena in Porous Media

Abstract

The paper¹ reviews the continuum approach to modelling the transport of mass, momentum and energy, of phases and of their components in a porous medium domain. The review begins with the definition of a porous medium, making use of the concept of a Representative Elementary Volume (REV) as a tool for overcoming the effect of the microscopic heterogeneity resulting from the presence of a solid matrix and a void space. The microscopic and macroscopic levels of description are defined. By averaging the description of a transport phenomenon at the microscopic level over an REV, using certain ‘averaging rules’, the macroscopic or continuum description of the same phenomenon is obtained. This methodology is first introduced in general terms for any extensive quantity, and then demonstrated for the transport of mass, momentum and energy.

In the process of deriving the macroscopic models, expressions are presented also for the advective, dispersive and diffusive fluxes of extensive quantities that appear in them, in terms of averaged, measurable values of state variables.