ON THE NATURE OF THE DISPERSIVE FLUX IN SATURATED HETEROGENEOUS POROUS-MEDIA

A method is presented for evaluating the mean transport of a tracer in saturated heterogeneous porous media when the hydraulic conductivity can be represented by a stochastic process; no assumption concerning stationarity of the concentration field is made. The analysis results in a transform‐space solution for the dispersive flux associated with the mean concentration in a mean uniform flow field when the tracer is conservative. For a pulse input of tracer, general forms for the first four moments in the longitudinal direction are presented; these forms are solved for specific cases of interest. A general form for the global dispersive flux, associated with mean transport, is presented for the case where local dispersion, relative to the length scale of heterogeneity, is negligible. The global dispersive flux takes the form of a convolution, over time, of the concentration gradient weighted by the correlation function of the velocity field; in large time, this integral asymptotically approaches a classical Fickian form. The convolution formulation of the global flux manifests itself in early time in the form of non‐Gaussian behavior of the mean tracer concentration. Beyond a travel distance equivalent to approximately 20 length scales of the hydraulic conductivity process, Gaussian behavior of the mean tracer cloud dominates. This paper is not subject to U.S. copyright. Published in 1990 by the American Geophysical Union.