Stochastic analysis of macrodispersion in gravity-dominated flow through bimodal heterogeneous unsaturated formations

[1] First-order analysis, based on a stochastic continuum presentation of the flow and a general Lagrangian description of the transport, was used to investigate the effects of a few characteristics of a bimodal, heterogeneous, partially saturated formation, on the principal components of the time-dependent macrodispersion coefficient, under steady state, unsaturated flow conditions. Results of the present analysis show that generally, a bimodal distribution of the formation properties, characterized by a relatively complex spatial correlation structure, contributes to the variability in water velocity and, consequently, may considerably enhance solute spreading. This applies especially in formations in which (1) the correlation length scales and the variances of the soil properties associated with the embedded soil are much larger than those of the background soil, (2) the contrast between mean properties of the two subdomains is large, (3) mean water saturation is relatively small, and (4) the volume fraction of the flow domain occupied by the embedded soil is relatively large. One of the major findings of this study is the important role played by the formation parameter α under unsaturated flow conditions. Consequently, the macrodispersion in a bimodal, unsaturated formation may be larger than its counterpart in a saturated formation, especially when the degree of saturation decreases, when the volume fraction of the flow domain occupied by the embedded soil increases, when the disparity between the correlation length scales of the two subdomains is relatively small, and when the texture of the embedded soil is coarser than that of the background soil.