LAGRANGIAN ANALYSIS OF TRANSPORT IN HETEROGENEOUS FORMATIONS UNDER TRANSIENT FLOW CONDITIONS

The coupled effects of porous media heterogeneity and flow unsteadines s on transport are investigated. We address the problem using a stocha stic-Lagrangian approach. The log condictivity is modeled as a space r andom function; however, the flow unsteadiness is considered as determ inistic, and it affects the magnitude and direction of the mean head g radient. 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 displ acement tensor, all as a function of the media heterogeneity and the u nsteady mean flow parameters. The model is applied to the case of a pe riodic variation in the flow direction. We show that the effects of un steadiness on the longitudinal spread are insignificant, while it affe cts strongly the transverse spread, in the form of an added constant d ispersivity. Results obtained in previous studies are discussed and ar e shown to be particular cases of the present results.