Travel time analysis of tracers and reactive solutes in the unsaturated zone

This paper presents a Lagrangian stochastic approach for modeling field sca le contaminant transport in the heterogeneous unsaturated geological enviro nments. We derive the probability distribution function of the travel times of tracers and reactive solutes, without limiting it to be either normal o r log-normal, and show how it can be used for computing the moments of solu te fluxes and breakthrough curves. We also provide closed-form expressions for the travel time moments of tracers and reactive solutes characterized b y linear equilibrium and non-equilibrium sorption kinetics. These expressio ns are useful for prediction and for interpretation of field experiments. I n our derivation we account for soil heterogeneity by modeling the soil par ameters, such as the saturated hydraulic conductivity and the pore size dis tribution parameter, as weakly stationary random space functions. Unlike pr evious studies, we-account for the effect of the spatial variability of the water content and refrain from assuming that the saturation is practically constant in the unit gradient flow zone. The derivation is done using a fi rst-older perturbative expansion of the flow equation, and is thus limited to small variability of the input parameters. The effects of spatial variab ility on the displacement and travel time statistics are discussed and demo nstrated.