Mixing in Multidimensional Porous Media: A Numerical Study of the Effects of Source Configuration and Heterogeneity

We investigate transport of an inert solute in multidimensional porous media characterized by spatially variable hydraulic conductivity. Through the use of a GPU-accelerated solute transport simulator based on the Random Walk Particle Tracking technique, we show how different factors such as the degree of heterogeneity, flow dimensionality and source zone configurations impact mixing. Solute mixing is quantified in terms of the temporal evolution of the plume's statistics (mean, variance and probability density function) and the dilution index. Our analysis show that mixing is strongly affected by the above mentioned factors. We also compare the probability distributions obtained from the numerical simulations with the beta distribution. Despite the discrepancies at very low concentrations, our results show that the fitting with the beta distribution is improved for transport in three-dimensional settings originating from a vertical planar source. To improve the fit at low concentrations, we utilize two one-to-one variable transformation, namely the logarithm and power law transformations. Results demonstrate that the Pareto-type IV and the uniform distributions are capable to capture the lower tail of the cumulative distribution function. Numerical results are validated against existing analytical solution for both homogeneous and heterogeneous media.