Analysis of flow through heterogeneous random aquifers by the method of embedding matrix: 1. Steady flow

The statistical structures of the hydraulic conductivity, head gradient, specific discharge, and head fields are analyzed with the aid of a simplified model consisting of a collection of spherical (in three dimensions) and cylindrical (in two dimensions) blocks of different conductivity and diameter set at random and independently in space. Results of a previous work for the effective conductivity and unbounded formations (Dagan, 1979) are recovered and given a rational derivation. The influence of the aquifer boundary and nonuniform average flows are examined for the first time. The growth of the head variance with distance from boundary in two‐dimensional flows is compared with that of the Monte Carlo simulations of Smith and Freeze (1979).