A note on the orientation of the macrodispersion tensor in partially saturated heterogeneous porous formations

Abstract

The general situation in which the mean gradient vector, J, is not necessarily aligned in a direction perpendicular to the bedding of a partially saturated heterogeneous formation, is considered. Previous results of first-order analyses, based on a stochastic continuum presentation of unsaturated flow and a general Lagrangian description of the transport 15 and standard tensor transformation relationships, were used to evaluate the orientation of the principal axes of the asymptotic macrodispersion tensor as a function of the inclination of J, and to assess its impact on solute spreading in partially saturated heterogeneous formations of three-dimensional anisotropic structure. The main results obtained in this study suggest that under unsaturated flow, for given statistics of the formation properties and given mean water saturation, and when the inclination of J is relatively small, coarse-textured soil material with negligibly small capillary forces may compensate for the enhanced lateral displacement (in the same direction as that of J relative to the longitudinal axis of the formation heterogeneity) and the enhanced lateral spreading of the solute plume due to increasing anisotropy (smaller e = I yv I yh where I yv and I yh are the correlation length scales of log-unsaturated conductivity in the vertical (longitudinal) and horizontal directions, respectively). On the other hand, when the inclination of J is relatively large, such soil material may enhance lateral displacement of the solute plume in a direction opposite to that of J relative to the longitudinal axis of the formation heterogeneity.