CONTAMINANT TRANSPORT IN AQUIFERS WITH SPATIALLY-VARIABLE HYDRAULIC AND SORPTION PROPERTIES

We consider migration of contaminants in groundwater and wish to chara cterize transport globally using spatial and temporal moments. The spe cific problem addressed in this work is how to simultaneously account for the spatial variability of the hydraulic conductivity, K, and of o ne or several sorption parameters, P. The Lagrangian framework for rea ctive transport in aquifers of Cvetkovic and Dagan is extended to inco rporate the spatial variability in sorption parameters. For arbitrary sorption reactions, the general result can be used for simplified Mont e Carlo simulations, where a three-dimensional advection-sorption prob lem is reduced to a three-dimensional advection and one-dimensional ad vection-sorption problem. The first two spatial moments characterize t he spatial extent of a contaminant plume and are derived for ergodic t ransport, for cases of continuous and pulse injection. Expressions for the first three temporal moments which characterize field-scale conta minant discharge are derived for linear sorption reactions. All the de rived expressions for the global transport quantities are given in ter ms of Lagrangian statistics of the fluid velocity and the sorption par ameter(s) random fields. Analytical solutions are provided for a few s orption models which are most frequent in applications: nonlinear equi librium sorption and linear non-equilibrium sorption. Analytical resul ts are given in terms of Lagrangian statistics of the 'reaction flow p ath', mu, which integrates the sorption parameter along an advection f low path with time as the integration variable. Lagrangian statistics of mu, are related to the Eulerian statistics of the hydraulic conduct ivity, K, and the sorption parameter, P, analytically and using Monte Carlo particle-tracking simulations. The derived analytical expression s are robust for the considered range of variabilities when compared t o simulation results. For extraction of a contaminant subject to Langm uir sorption, the effect of spatial variability in the sorption capaci ty on the first two moments of the displacament front is supressed by the effect of nonlinearity. For linear non-equilibrium sorption, spati al variability in the forward rate coefficient has a more significant influence than in the backward rate on the first three temporal moment s.