In-place measurement of permeability in heterogeneous media: 1. Theory of a proposed method

Abstract

A method for in-place measurement of permeability in heterogeneous, saturated soils is presented. The method is based upon a general theory presented in three dimensions for saturated flow in a heterogeneous medium. When the permeability is considered to be the dependent variable, a first-order quasi-linear partial differential equation requires solution. It can be solved through an extension of Lagrange's method, in which a system of subsidiary differential equations is used. Through consideration of the identity of two of the Lagrange subsidiary equations with the three-dimensional stream function, a special interrelationship is shown. The interrelationship between the method of analytical solution and the stream function has special significance with respect to the boundary condition. If the arbitrary or boundary function satisfies part of the subsidiary differential equations, no unique solution exists. In the physical problem this requirement for uniqueness indicates that the permeability measurements used for a boundary condition cannot be measured along a stream tube.