On the transport of reactive solutes in partially saturated heterogeneous anisotropic porous formations

First-order analysis, based on a stochastic continuum presentation of the Eulerian retarded velocity in heterogeneous, partially saturated porous formations and a general Lagrangian description of the transport, was used to investigate the effect of both the anisotropy of the formation and the texture of the soil materials constituting the formation, on the spreading of reactive (sorptive) solutes under unsaturated flow. The physically plausible situation in which the retardation factor is negatively correlated with log-unsaturated conductivity was considered in this study. Results of the analyses show that for a given water saturation and gravity-dominated unsaturated flow, both the physical and chemical heterogeneities of the formation enhance the spreading of the reactive solute in the longitudinal direction. This applies especially in formations with typical flow barriers which are small in a direction perpendicular to the mean flow, relative to their size in the direction parallel to the mean flow (large aspect ratio, e), and in formations of fine-textured soil materials with significant capillary forces (large macroscopic capillary length scale, lambda). The relative impact of the chemical heterogeneity of the formation on the spreading of the reactive solute, however, is expected to increase in formations of coarse-textured soil materials (small lambda) and in formations which exhibit a significant stratification (small e). This result stems from the fact that when the mean flow is vertical, small lambda and small e both diminish the impact of the heterogeneity in the physical properties of the formation on the variability of the flow in the longitudinal direction.