Hydrodynamic Dispersion in Network Models of Porous Media

Abstract

We consider the longitudinal dispersion of dynamically neutral tracer placed in a fluid flowing within a porous medium. For a random tube network, we derive the exact rules for tracer motion under the combined action of molecular diffusion and convection, and we introduce an efficient "probability propagation" algorithm which permits an (in principle) exact calculation of the first-passage-time distribution of the tracer as it flows through the medium. With our formalism, we exhibit both linear and nonlinear dispersion phenomena in two-dimensional random networks.