Prediction of solute spreading during vertical infiltration in unsaturated, bounded heterogeneous porous media

In this study we investigate the effect of a water table boundary on solute spreading during infiltration in the vadose zone of heterogeneous soils. It has been found recently that the presence of the water table significantly affects unsaturated flow in a heterogeneous vadose zone and causes the flow to be spatially nonstationary. Because a vadose zone is by definition bounded by the water table at the bottom and the contaminants present in the vadose zone migrate into the groundwater through the water table, it is of great interest to study the behaviors of a solute plume near the water table and the effects of flow nonstationarity caused by the water table on solute spreading. To do so, we develop a Lagrangian stochastic approach for predicting field-scale solute spreading in a spatially nonstationary velocity field. Through first-order approximations the statistical moments of particle displacement are related to the moments of the Eulerian velocity field. Closed form expressions are obtained for the special case of unidirectional but nonuniform mean flow such as vertical infiltration. We illustrate our theoretical developments with some one-dimensional examples of solute transport during steady state infiltration in bounded vadose zones. It is found that the inclusion of the water table significantly impacts the behaviors of the mean particle displacement and the displacement covariance, which quantify expected solute displacement and spreading about the expected value, respectively. At late times the particle displacement covariance is generally much smaller when the effect of the water table is included than when it is neglected. In particular, for the case of one-dimensional infiltration in a bounded vadose zone the particle displacement covariance decreases with time at late times. This finding is in contrast to the result that the particle displacement covariance increases linearly at late times as found by previous stochastic studies of solute transport in unbounded vadose zones. Hence macrodispersion may be greatly overestimated in previous stochastic studies that disregarded the presence of the water table. The validity of the theoretical approach developed in this paper is investigated and confirmed by Monte Carlo simulations.