Bounds on transport coefficients of porous media

James G. Berryman

berryman@sep.stanford.edu

ABSTRACT

Transport coefficients such as electrical conductivity, thermal conductivity, fluid permeability, etc., can all be treated in mathematically equivalent terms. So an analytical formulation of conductivity bounds by Bergman and Milton can be used in a different way to obtain rigorous bounds on, for example, the real thermal conductivity (which is the particular transport coefficient chosen for the present study) of a fluid-saturated porous material. These bounds do not depend explicitly on the porosity, but rather on two formation factors - one associated with the pore space and the other with the solid frame. The results are then applicable to other physical properties such as fluid permeability. In particular, the formation factors are measures of the microstructure (actually of the tortuosities) of the porous medium, and are therefore the same dimensionless numbers for all these transport processes within the same porous material.