MONTE-CARLO STUDIES OF FLOW AND TRANSPORT IN FRACTAL CONDUCTIVITY FIELDS - COMPARISON WITH STOCHASTIC PERTURBATION-THEORY

A Monte Carlo simulation of flow and transport is employed to study tr acer migration in porous media with evolving scales of heterogeneity ( fractal media). Transport is studied with both conservative and reacti ve chemicals in media that possess physical as well as chemical hetero geneity. Linear kinetic equations are assumed to relate the sorbed pha se and the aqueous phase concentrations. The fluctuating log conductiv ity possesses the power law spectrum of a fractional Brownian motion ( fBm). Chemical heterogeneity is represented as spatially varying react ion rates that also are assumed to obey fBm statistics and may be corr elated to the conductivity field. The model is based on a finite diffe rence approximation to the flow problem and a random walk particle-tra cking approach for solving the solute transport equation. The model is used to make comparisons with the nonlocal transport equations recent ly developed by Deng et al. [1993], and Hu et nl. [1995, 1997]. The re sults presented herein support these nonlocal models for a wide range of heterogeneous systems. However, the infinite integral scale associa ted with the fractal conductivity has a significant effect on the pred iction of the nonlocal theories, This suggests that integral scale sho uld play a role in stochastic Eulerian perturbation theories. The impo rtance of the local-scale dispersion depends to a great extent on the magnitude of the local dispersivities. The effect of neglecting local dispersion decreases with the decrease in local dispersivity.