Séminaire d’Allen Hunt le 14 mars 2011
Dans le cadre des séminaires du LEESU, le professeur Allen Hunt, de l’université Wright State (USA) a fait une intervention intitulée "Solute dispersion in porous media" le lundi 14 mars à l’École des Ponts ParisTech, à Champs sur Marne.
Le résumé de son séminaire est :
Percolation cluster statistics and critical path analysis can be combined to generate the probability that a given volume of a porous medium can be covered by a network of paths with a given minimum conductance value. The topology of percolation clusters can then be applied to find the time required for solutes to cross such clusters. An appropriate probabilistic identity gives the probability that solute will arrive at, say, the right end of the volume if it enters the left end at a given time. The calculation yields the observed distribution of arrival times in simulations as well as the long-time tail of the distribution in fracture flow. The spatial moments are obtained from an analogous calculation for the spatial distribution at an instant in time. When the input distribution of local conductance values is monomodal with a single scale of heterogeneity and in the case that diffusive processes are explicitly neglected, the output distribution of dispersivity values matches a compilation of 2200 observation over ten orders of magnitude of length scale. This result requires a complete rethinking of the role of multiple scales of heterogeneity as well as a reevaluation of the appropriateness of stochastic subsurface hydrology and the role of diffusion-like processes in dispersion.