Probabilistic approach for transport of contaminants through porous media

Abstract

AbstractThe channels formed between individual particles in porous media have variable dimensions and orientations. The porosity, permeability and its anisotropy exhibit random spatial distributions. The probabilistic approach can effectively describe the transport of contaminants through porous media and is analysed in this paper. Numerical results are obtained by considering (I) random dispersion coefficients without and with spatial structure, (II) random time distribution of concentration at the inlet boundary, (III) random velocity distribution in the flow field without and (IV) with variable dispersion coefficient, (V) non‐linearity of the governing equation and (VI) anisotropy of the dispersion coefficient. Two methods are used for probabilistic predictions: (1) Gaussian field approach in conjunction with Monte Carlo method and (2) random walk method. The input random parameters are assumed to have normal and log‐normal distributions according to available experimental data. The probability distribution functions of the contaminant concentration at different locations within the flow domain are calculated and compared with the input distributions as a function of the mean and fluctuation Peclet numbers. The one‐dimensional case is analysed in detail and the illustrative numerical predictions are compared with analytical and experimental results. The extension to a two‐dimensional domain is discussed in the last part of this paper.