DIAGRAMMATIC THEORY OF EFFECTIVE HYDRAULIC CONDUCTIVITY

This work presents a stochastic diagrammatic theory for the calculatio n of the effective hydraulic conductivity of heterogeneous media. The theory is based on the mean-flux series expansion of a log-normal hydr aulic conductivity medium in terms of diagrammatic representations and leads to certain general results for the effective hydraulic conducti vity of three-dimensional media. A selective summation technique is us ed to improve low-order perturbation analysis by evaluating an infinit e set of diagrammatic terms with a specific topological structure that dominates the perturbation series. For stochastically isotropic media the selective summation yields the anticipated exponential expression for the effective hydraulic conductivity. This expression is extended to stochastically anisotropic media. It is also shown that in the cas e of non homogeneous media the uniform effective hydraulic conductivit y is replaced by a non-local tensor kernel, for which general diagramm atic expressions are obtained. The non-local kernel leads to the stand ard exponential behavior for the effective hydraulic conductivity at t he homogeneous limit.