A geostatistical approach to the estimation of a solute trajectory through porous formations

When dealing with groundwater flows, many difficulties arise in the characterization of an aquifer and in the identification of the solute trajectories, due to the natural heterogeneity of the porous formations. Transmissivity spatial variability is the main source of uncertainty in an aquifer system in the study of two-dimensional flows and as detailed knowledge of its values is not possible, the flow and transport phenomena are subject to uncertainty. This manuscript deals with the problem of the estimation of a solute trajectory and it presents the combined use of piezometric head, transmissivity and solute trajectory displacement data for the estimation of the solute path. The work is carried out in a stochastic framework and linear theory tools are used. The proposed methodology is a cokriging application and it has been tested by means of two Monte Carlo experiments carried out for two degrees of heterogeneity, one has been performed considering weakly heterogeneous aquifers, the other highly heterogeneous aquifers. A numerical application, based on a real transmissivity heterogeneous field, has been proposed. The results of the computation show the important impact of trajectory displacement data on the estimation of the solute path.