Effective conductivity in steady well-type flows through porous formations

摘要

A steady flow generated by a well of given strength takes place in a two-dimensional heterogeneous porous formation where the conductivity K is modeled as a random space function (RSF). As a consequence, the flow-variables become RSF s, and we wish to compute the effective conductivity (EC) by means of the self-consistent approximation. Toward this aim, the porous formation is sought as a collection of circular, non overlapping, inclusions with different (and statistically independent) conductivities. We compute the EC by adapting a procedure which was originally developed for mean uniform flows. Overall, the EC is found to be position-dependent, and therefore it can not be regarded as a medium's property (unless one is dealing with large distances from the well). Then, it is shown how results of the present study can be used for practical applications.