Proposal for a probabilistic model of dispersion: A first validation

Abstract

The probabilistic approach is used to simulate the particle tracking for two types of porous media. The first one is sand grains with a single intergranular porosity. The particle tracking is carried out by advection and dispersion. The second one is chalk granulates with intergranular and matrix porosities. Sorption can occur with advection and dispersion during particle tracking. The particle tracking is simulated as the sum of elementary steps with independent random variables in the sand medium. An exponential distribution is obtained for each elementary step and shows that the whole process is Markovian. A gamma distribution or probability density function is then deduced. The relationship between dispersivity and the elementary step is given using the central limit theorem. The particle tracking in the chalky medium is a non-Markovian process. The probability density function depends of a power to the distance. Experimental simulation by dye tracer tests on a column have been performed for different distances and discharges. The probabilistic approach computations are in good agreement with the experimental data. The probabilistic computation seems an interesting and complementary approach to simulate transfer phenomena in porous media with respect to the traditional numerical methods.