Transport of passive solutes in heterogeneous isotropic porous formations

The paper deals with the transport of non-reactive tracers in heterogeneous aquifers with a view to the development of dispersion tensor in natural formations. A Monte Carlo numerical scheme is developed to discuss validity and limitations of the existing dispersion theories. The results suggest that quite different velocity of convergence with Monte Carlo runs holds for different orders of spatial moments. This has implications on the spatial extent of the spatial domain for single-realization numerical studies of same type. A comparison of the variance of plumes with the results of Dagan’s linear theory shows an unexpectedly broad validity of field for the theoretical solution (obtained upon a suitable linearization of flow and transport). Reformulation of the same problem with a linearization of the flow equation alone, an assumption commonly accepted in theoretical and numerical studies in this subject, yields deviations from linear theory larger than those induced by a fully nonlinear solution. The interesting consequence, besides casting some doubt on previous conclusions drawn on the limitation of the linear theory based on partially linearized equations, is that the effects on nonlinear terms in the flow and transport equations on the moments of dispersing plumes seem somewhat counteracting thereby yielding to globally consistent formulations.