A Model for Tracer Flow in Heterogeneous Porous Media

Abstract

A tracer model utilizing scale dependent dispersion coefficient applicable to heterogeneous porous media is presented. Being a fractal model, it integrates the effects of the many length scales of heterogeneities and can be used for the prediction of fluid flow and mixing during tracer and unit mobility miscible displacements. A random field theory was used to describe the dispersion coefficient in terms of a scaling parameter~. The resulting convection-dispersion equation with the scaledependent dispersion coefficient was solved numerically by a Dual Reciprocity Boundary Element (DR-BEM) technique to generate type-curves of tracer concentration with time. This can be used in conjunction with data from field tracer tests, to determine the characteristic value of~representative of a field. A simple equation is provided to calculate the dispersion coefficient at any Icngth scale in terms of the~so determined and the field velocity correlation function. The accuracy of the model was tested by comparing its results for a range ofṽ alues representing asymptotically Fickian dispersion with analytical results and excellent agreement was obtained.