Nonequilibrium sorption under physical and chemical heterogeneity

Aquifers are physically heterogeneous and they are also heterogeneous with respect to mineral chemistry and soil organic content. It is not feasible and possible to measure soil physical and chemical parameters in detail without disturbing the soil material even though supercomputers are available nowadays to process the detailed information. On the other hand, if spatial variability of physical and chemical properties of the medium is not taken into account, one cannot predict the contaminant concentrations in large-scale heterogeneous environments. It is possible to describe medium heterogeneities statistically by using a limited amount of data. If one can assume that aquifer physical and chemical properties are random variables in space and time, one ends up describing the process (such as transport of a contaminant) by a stochastic differential equation(s).; In this study, the ensemble average of the stochastic differential equations of advection/convection diffusion/dispersion with nonequilibrium sorption reaction is taken by using the cumulant expansion method and Lie operator property in order to obtain the mean behavior. The stochastic nature in the differential equations is imbedded as additive quantities in the averaged equations due to the cumulant expansion method. Those additive quantities are the statistical information about the aquifer heterogeneities.; The ensemble-averaged equations are used to calculate aqueous and sorbed phase concentrations under instantaneous contaminant release for a two-dimensional steady state confined aquifer problem with parameters resembling the Borden aquifer experiment. Ensemble-averaged equations' results are compared with Monte Carlo ensemble averaging. According to the comparison, ensemble average aqueous and sorbed phase plume concentration ranges, ensemble average sorbed phase plume behavior, and ensemble average aqueous phase plume centroid locations in the x-axis are predicted well by the ensemble-averaged equations. Longitudinal second central moments of the ensemble average aqueous phase plume are underestimated by the ensemble-averaged equations. The linear increase until t = 180 days in the transverse second central moments is predicted well by the ensemble-averaged equations. Ensemble-averaged equations predicted the same linear increase in the transverse second central moments after t = 180 days but Monte Carlo ensemble averaging yielded a reduced rate of linear increase after t = 180 days.