Anomalous diffusion in heterogeneous porous media

Abstract

The dispersion of a passive tracer resulting from flow through heterogeneous porous media is studied. When the correlation length for the permeability fluctuations is finite, a normal diffusive process, with the mean-square displacement of the tracer growing linearly with time, is obtained at long times. However, it is shown that, when the correlation length diverges, anomalous diffusion occurs in which the mean-square displacement grows faster than linearly with time. The space–time evolution of the tracer’s concentration is calculated and shown to be universal—uniquely related to the covariance of the permeability field—in the anomalous regime.