Radial flow in heterogeneous porous media: An analysis of specific discharge


  • R. L. Naff


A perturbation solution to three-dimensional radial flow in heterogeneous porous media is reported on; the analytical solution is in terms of the first and second moments of the gradient in the radial direction and the specific discharge in this direction. The solution requires evaluation, numerically in the case of this paper, of some rather difficult integrals which compose its basic form. By proper adjustment of the statistical anisotropy of the medium, a solution for the two-dimensional flow problem can be emulated; the two-dimensional solution for the mean and variance in specific discharge resembles asymptotes reported earlier by another investigator. In general, the effective hydraulic conductivity, outside a few length scales of the well itself, is found to be nearly constant and dependent upon the value selected for the statistical anisotropy factor; the variance in specific discharge behaves nearly as the inverse square of the distance from the well in all cases.