Application of Continuous Time Random Walk Theory to Tracer Test Measurements in Fractured and Heterogeneous Porous Media

We examine a set of analytical solutions based on the continuous time random walk (CTRW) approach, which can be evaluated numerically and used to analyze breakthrough data from tracer tests. Practical application of these solutions, with discussion of the physical meaning of the relevant model parameters, is emphasized. The CTRW theory accounts for the often observed non-Fickian (or scale-dependent) dispersion behavior that cannot be properly quantified by using the advection-dispersion equation. The solutions given here, valid for a wide range of dispersive behaviors of conservative tracers, and useful for both characterization and prediction, have been integrated into a library of external functions for use with the GRACE graphical display and analysis package. Example applications of these solutions are presented. The library and graphics software are freely accessible from a Web site.