TRANSPORT IN ORDERED AND DISORDERED POROUS-MEDIA - VOLUME-AVERAGED EQUATIONS, CLOSURE PROBLEMS, AND COMPARISON WITH EXPERIMENT

In this paper we consider transport in ordered and disordered rigid porous media. We define order and disorder in terms of geometrical integrals that arise naturally in the method of volume averaging and we show that dependent variables for ordered media must generally be defined in terms of the cellular average. This leads to the use of weighting functions to produce a generalized averaging procedure that is valid for any porous medium. The method of volume averaging leads to spatially smoothed transport equations and a closure problem that allows one to predict effective transport coefficients on the basis of a geometrical model of the porous medium under consideration. In order to develop a local closure problem, a spatially periodic model is used for both ordered and disordered systems. Comparison between theory and experiment suggests that this is an acceptable approach for many systems.