Dispersion and Dispersivity Tensors in Saturated Porous Media with Uniaxial Symmetry

TL;DR

This paper analyzes the dispersion and dispersivity tensors in saturated porous media with uniaxial symmetry, revealing their structure, constraints, and experimental requirements for parameter determination.

Contribution

It provides a detailed tensor analysis for axially symmetric porous media and establishes the minimum experiments needed to determine these coefficients.

Findings

Dispersivity in uniaxial media is governed by 6 independent moduli.

Constraints on the moduli are derived.

At least two experiments are necessary to determine the coefficients.

Abstract

The coefficients of dispersion, D_{ij}, and the dispersivity, a_{ijkl}, appear in the expression for the flux of a solute in saturated flow through porous media. We present a detailed analysis of these tensors in an axially symmetric porous medium and show that in such a medium, the dispersivity is governed by 6 independent moduli. We present also the constraints that have to be satisfied by these moduli. We also show that at least two independent experiments are required in order to obtain the values of these coefficients for any three-dimensional porous medium domain.