Lagrangian analysis of transport in heterogeneous formations under transient flow conditions

The coupled effects of porous media heterogeneity and flow unsteadiness on transport are investigated. We address the problem using a stochastic-Lagrangian approach. The log condictivity is modeled as a space random function; however, the flow unsteadiness is considered as deterministic, and it affects the magnitude and direction of the mean head gradient. Using a first-order solution in terms of the log conductivity variance, we developed a three-dimensional solution that includes the velocity covariances, the macrodispersion coefficients, and the displacement tensor, all as a function of the media heterogeneity and the unsteady mean flow parameters. The model is applied to the case of a periodic variation in the flow direction. We show that the effects of unsteadiness on the longitudinal spread are insignificant, while it affects strongly the transverse spread, in the form of an added constant dispersivity. Results obtained in previous studies are discussed and are shown to be particular cases of the present results.