Travel path uncertainty: a case study combining stochastic and deterministic hydrodynamic models in the Rhône valley, Switzerland

In the framework of waste storage in geological formations at shallow or greater depths and accidental pollution, the numerical simulation of groundwater flow and contaminant transport represents an important instrument to predict and quantify the pollution as a function of time and space. The numerical simulation problem, and the required hydrogeologic data, are often approached in a deterministic fashion. However, deterministic models do not allow to evaluate the uncertainty of results. Furthermore, the hydrogeologic data and hydrodynamic properties required to implement the flow-transport model are generally very scant, so that an essential part of the simulation effort needs to be devoted to building the different spatially distributed data through spatial interpolation, extrapolation, smoothing, etc. In this paper, deterministic (classic finite element hydrodynamic model) and stochastic approaches (geostatistics : kriging and conditional simulations) are used for evaluating groundwater flow patterns and pollutant trajectories for a site-specific application (Rhône valley aquifer in Switzerland, area of 6.5 km²). The stochastic approach, based on kriging and multiple conditional simulations, leads to a quantification of uncertainty of flow-transport simulations, which are due to the underlying uncertainty of hydrogeologic properties and their spatial distribution. The available data used in this case study are : 55 transmissivity, 791 permeability and 145 hydraulic potential values. In spite of the relative wealth of available data, our study shows that the uncertainty of pollutant migration pathlines and travel distances is relatively important. The distance traveled by a pollutant particle during 30 monthes varies between 3150 m and 4800 m over five different but equally plausible scenarios (conditional simulations). The uncertainty is about 42% relative to the average travel distance, or 55% relative to the smallest travel distance mentioned above.