THE RANDOM-WALK MODEL WITH AUTOCORRELATION OF FLOW THROUGH POROUS MEDIA

Abstract

In pursuit of the idea of applying statistical mechanics to the theory of flow through porous media, this paper reports an investigation of the implications of a random-walk model as opposed to random residence-time models. Although the random-walk model is physically not as satisfactory as other statistical models, it has the advantage of enabling one to introduce and to investigate easily the effect of autocorrelation between subsequent time steps. It is shown that, if autocorrelation exists, the mixing process in porous media is governed by a telegraph equation rather than by a diffusivity equation. Expressions for the constants occurring in the telegraph equation are deduced in terms of other dynamical variables.