Contaminant transport in aquifers with spatially variable hydraulic and sorption properties

We consider migration of contaminants in groundwater and wish to characterize transport globally using spatial and temporal moments. The specific problem addressed in this work is how to simultaneously account for the spatial variability of the hydraulic conductivity, K, and of one or several sorption parameters, P. The Lagrangian framework for reactive transport in aquifers of Cvetkovic and Dagan is extended to incorporate the spatial variability in sorption parameters. For arbitrary sorption reactions, the general result can be used for simplified Monte Carlo simulations, where a three-dimensional advection-sorption problem is reduced to a three-dimensional advection and one-dimensional advection-sorption problem. The first two spatial moments characterize the spatial extent of a contaminant plume and are derived for ergodic transport, for cases of continuous and pulse injection. Expressions for the first three temporal moments which characterize field-scale contaminant discharge are derived for linear sorption reactions. All the derived expressions for the global transport quantities are given in terms of Lagrangian statistics of the fluid velocity and the sorption parameter(s) random fields. Analytical solutions are provided for a few sorption models which are most frequent in applications: nonlinear equilibrium sorption and linear non-equilibrium sorption. Analytical results are given in terms of Lagrangian statistics of the 'reaction flow path', mu, which integrates the sorption parameter along an advection flow path with time as the integration variable. Lagrangian statistics of mu, are related to the Eulerian statistics of the hydraulic conductivity, K, and the sorption parameter, P, analytically and using Monte Carlo particle-tracking simulations. The derived analytical expressions are robust for the considered range of variabilities when compared to simulation results. For extraction of a contaminant subject to Langmuir sorption, the effect of spatial variability in the sorption capacity on the first two moments of the displacament front is supressed by the effect of nonlinearity. For linear non-equilibrium sorption, spatial variability in the forward rate coefficient has a more significant influence than in the backward rate on the first three temporal moments.