Numerical evaluation of solute dispersion and dilution in unsaturated heterogeneous media

[1] We investigate flow and solute transport in a heterogeneous unsaturated soil under gravity-driven flow conditions using a direct simulation Monte Carlo method. We account for the cross correlation between the heterogeneous fields of unsaturated flow parameters representing a silty loam. We determine through particle tracking the statistical moments of the travel time distribution for nonpoint injection of a conservative tracer. The oneparticle mean and variance characterize the mean arrival time and spreading of solute integrated over an entire horizontal cross section of the domain, whereas the two-particle semivariogram characterizes the spreading observed at individual points. From these quantities we derive macrodispersivities and effective dispersivities. The latter reflect solute dilution. Owing to the nonlinearity of unsaturated flow the dispersivity values at a given depth vary with the mean infiltration rate. The two-particle semivariogram hardly differs from the one-particle variance of travel time at low infiltration rates, whereas dilution and macrodispersion rates differ significantly at high infiltration rates. We compare the dispersivities determined through particle tracking with approximations from linear stochastic theories based on the covariance of the Eulerian velocity field [Dagan, 1988; Fiori and Dagan, 2000]. These linear stochastic theories slightly underestimate both dispersivity types. We present parametric models for the two types of dispersivities as function of the infiltration rate and the depth.