Fluid capacity distributions of random porous media

Abstract

As a quantitative measure of the microstructure in a statistically homogeneous porous material, we introduce the notion of thefluid capacity at a specified length scale λ. In two dimensions, fluid capacity is the void space per unit area for a square of side λ and in three dimensions it is the void space per unit volume for a cube of side λ. The most random distribution of fluid capacity, for a prescribed mean fluid capacity, corresponds to an exponential distribution. The distribution of fluid capacity is important during unstable fluid displacements in porous media where viscous fingering occurs. For a material with an exponential fluid capacity distribution, an unstable displacement process can be simulated by simple stochastic algorithms related to diffusion-limited aggregation. We measure the two-dimensional fluid capacity distributions of published cross-section photomicrographs of sandstone, salt, and packed beds of glass beads, for various length scales A. The form of the distribution depends upon the magnitude of the length scale λ. For the sandstone and salt packs, appropriate length scales are found on which the fluid capacity has, to a good approximation, an exponential distribution. An exponential distribution appears to be inappropriate for the packed bed of glass beads on all length scales.