Permeability, Percolation And Statistical Crack Mechanics

The permeability of sands and soils seems to be adequately de- scribed by Darcy's law, but the permeability of rocks is complicated by a number of factors related to the probability of crack intersections. During the last few years we have developed a statistical theory of fragmentation which has been successful in explaining the observed behavior of rocks. In this paper, a theory of permeability is developed which draws on the concepts employed in previous work. The permeability involves three factors, the average fluid flux per crack, the number of cracks per unit area, and the fraction of cracks that are not isolated. Probabilistic ideas are used in connection with the hydrodynamic theory of flow through a single crack to develop an integral expression for permeability. The result has the form of Darcy's law for anistropic media. Although the current work is motivated by the need to develop optimized oil-shale retorts, we believe that the theory can be applied to a variety of other problems.