Looking at Monte Carlo simulation for describing nonlinear sorption in groundwater contaminant transport

The long-term behaviour of toxic and radioactive solutes in groundwater has become a subject of great interest in connection with investigation of environmental releases of hazardous chemicals and wastes. The transport, distribution and fate of contaminants in groundwater strongly depend on sorptive interactions with soils, sediments and aquifer solids. Most current transport models account for sorption by assuming a linear equilibrium distribution of contaminant between the sorbed and aqueous phases. However, it is recognised that nonlinear, nonequilibrium sorption plays an important role in contaminant transport. In this paper, a stochastic model of contaminant transport is expanded to include nonlinear sorption effects within a Monte Carlo framework. The model, based on the theory of branching stochastic processes of Kolmogorov and Dmitriev, considers the adsorption/desorption processes in an explicit manner, thus, allowing the introduction of nonequilibrium, nonlinear effects in a relatively simple way. The approach is methodological in nature and a case study is presented with reference to a simple monodimensional system in which the nonlinear sorption process is based on a conjecture for the dependence of the adsorption rates on the current adsorbed contaminant concentrations.