Estimation of macrodispersion by different approximation methods for flow and transport in randomly heterogeneous media

We present two- and three-dimensional calculations for the longitudinal and transverse macrodispersion coefficient for conservative solutes derived by particle tracking in a velocity field which is based on the linearized flo w equation. The simulations were performed upto 5000 correlation lengths in order to reach the asymptotic regime. We used a simulation method which do es not need any grid and therefore allows simulations of very large transpo rt times and distances. Our findings are compared with results obtained from linearized transport, from Corrsin's Conjecture and from renormalization group methods. All calcu lations are performed with and without local dispersion. The variance of th e logarithm of the hydraulic conductivity field was chosen to be one to inv estigate realistic model cases. While in two dimensions the linear transport approximation seems to be very good even for this high variance of the logarithmic hydraulic conductivity , in three dimensions renormalization group results are closer to the numer ical calculations. Here Dagan's theory and the theory of Gelhar and Axness underestimate the transverse macrodispersion by far. Corrsin's Conjecture a lways overestimates the transverse dispersion. Local dispersion does not si gnificantly influence the asymptotic behavior of the various approximations examined for two-dimensional and three-dimensional calculations.