General theory of dispersion in porous media

TLDR

Nikolaevskii had already shown that in isotropic media the dispersivity tensor reduces to two constants. The study investigates the generalization of dispersion equations for flow through porous media. Using Bear's hypothesis that only velocity components parallel or normal to the mean flow matter, the authors deduce a general fourth‑rank dispersivity tensor and relate it to Bear’s earlier tensor. The dispersivity tensor is a fourth‑rank tensor with 36 independent components in general anisotropic media, reducing to two constants in isotropic media.

Abstract

The possibilities of generalizing the dispersion equations of flow through porous media are investigated. Based on the hypothesis (‘Bear's hypothesis’) that only that part of each velocity component is of significance which is either parallel or normal to the mean flow direction, the general form of the dispersion is deduced. The dispersivity becomes a tensor of the fourth rank. It has such symmetry properties that it contains only 36 instead of 81 independent components in the general case of an anisotropic porous medium. In isotropic media there are only two dispersivity constants. The latter result had already been deduced by Nikolaevskii. The connection of the dispersivity tensor with a tensor which had previously been constructed by Bear is demonstrated.