Groundwater contaminant transport in presence of colloids I. A stochastic nonlinear model and parameter identification

In this paper we present an extension of a stochastic model of groundwater contaminant transport, previously proposed by the authors, to account for the presence of colloids in the system. These have been shown experimentally to facilitate significantly the transport of contaminants. The stochastic model is based on the Kolmogorov–Dmitriev theory of branching stochastic processes and is capable of explicitly accounting for the individual interactions, possibly nonlinear and not at equilibrium, which occur during the transport process. We tackle the problem by means of a Monte Carlo method properly devised to account for the nonlinearities introduced by the presence of colloids. For the determination of the model parameters an approach is followed which is based on a comparison of the stochastic model equations with those of the classical advection-dispersion one. This has enabled us to establish relationships which link the transition rates to the classically measurable quantities.