Solute transport in sand and chalk: a probabilistic approach

Abstract

A probabilistic approach is used to simulate particle tracking for two types of porous medium. The first is sand grains with a single intergranular porosity. Particle tracking is carried out by advection and dispersion. The second is chalk granulates with intergranular and matrix porosities. Sorption can occur with advection and dispersion during particle tracking. Particle tracking is modelled 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 relationships between dispersivity and the elementary step are given using the central limit theorem. Particle tracking in the chalky medium is a non-Markovian process. The probability density function depends on a power of the distance. Experimental simulations 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. Copyright © 2006 John Wiley & Sons, Ltd.