A comparison between the advection-dispersion and the Kolmogorov-Dmitriev model for groundwater contaminant transport

The growing interest of the scientific and public community in environmental problems has sparked the undertaking of several activities of protection from pollutants, of remediation of contaminated sites and of design of deposits for toxic or radioactive waste. The implementation and management of these activities require the use of mathematical models for predicting the behaviour of the pollutant in the geosphere; of particular interest is the study of the transport of contaminants in the groundwater system, which provides an important pathway of return of the hazard to the biosphere. In this paper a comparison is made between the traditional advection-dispersion model, which is the most widely used model of groundwater contaminant transport, and a stochastic model based on the Kolmogorov-Dmitriev theory of branching processes. The behaviour of the two models is analysed in the case of transport with and without retardation of contaminant in the solid matrix and, in the latter case, both equilibrium and non-equilibrium processes are considered. The results obtained show that for non-reactive contaminant and for reactive contaminant under equilibrium, the Kolmogorov-Dmitriev parameters are related by simple relations with the advection-dispersion parameters. Moreover, the Kolmogorov-Dmitriev model is capable of describing more realistic non-equilibrium phenomena, that the advection-dispersion cannot treat. This capability arises from the fact of treating explicitly the reactions of contaminant interchange between the liquid and solid phases.