A semianalytic approach to tracer flow modeling in heterogeneous permeable media

Abstract

A semianalytic approach for modeling tracer motion in heterogeneous permeable media is presented. The method is analytic along streamlines; the streamlines are derived from an underlying velocity field which is obtained numerically from a conventional fluid flow simulator. This generalizes the approach to any arbitrary configuration of wells and also to areally heterogeneous permeability fields. The semianalytic scheme is based on the observation that in a velocity field derived by finite difference, streamlines can be approximated by piecewise hyperbolic intervals. Along each of these intervals the evolution equation can be solved exactly. Thus, the approach is free from numerical time truncation error. Once tracer transit times to a producing well have been determined, the tracer response curve and the area swept by the tracer can be obtained from simple integral expressions. The transit time formalism allows for easy extension of the semianalytic approach to multiphase flow problems and the results are shown to be in excellent agreement with high resolution finite-difference simulations, but obtained at a fraction of the computation time. We have illustrated the semianalytic approach through application to tracer migration in homogeneous as well as heterogeneous quarter five spot patterns.