Upscaling of solute transport in heterogeneous media : theories and experiments to compare and validate Fickian and non-Fickian approaches/

The classical Fickian model for solute transport in porous media cannot correctly predict the spreading (the dispersion) of contaminant plumes in a heterogeneous subsoil unless its structure is completely characterized. Although the required precision is outside the reach of current field characterization methods, the classical Fickian model remains the most widely used model among practitioners. Two approaches can be adopted to solve the effect of physical heterogeneity on transport. First, upscaling methods allow one to compute "apparent" scale-dependent parameters to be used in the classical Fickian model. In the second approach, upscaled (non-Fickian) transport equations with scale-independent parameters are used. This research aims at comparing upscaling methods for Fickian transport parameters with non-Fickian upscaled transport equations, and evaluate their capabilities to predict solute transport in heterogeneous media. The models were tested using simplified numerical examples (perfectly stratified aquifers and bidimensional heterogeneous media). Hypothetical lognormal permeability fields were investigated, for different values of variance, correlation length and anisotropy ratio. Examples exhibiting discrete and multimodal permeability distributions were also investigated using both numerical examples and a physical laboratory experiment. It was found that non-Fickian transport equations involving fractional derivatives have higher upscaling capabilities regarding the prediction of contaminant plume migration and spreading, although their key parameters can only be inferred from inverse modelling of test data.