Investigation of the Influence of Heterogeneous Porosity on Matrix Diffusion: a Novel Approach Using Adaptive Tree-Multigrid Technique and Real Porosity Data

Last year we developed a two-dimensional deterministic heterogeneous matrix diffusion model, which is capable of utilising porosity information originating from real drill-core samples. The results of numerical infiltration experiment we had performed with the model displayed substantial spatial variations in the penetration depth. Because it is practically impossible to verify experimentally those two-dimensional penetration profiles we had computed, this time we decided to try modelling of measured leaching curves. Unfortunately we have not succeeded in acquiring such curves for the exact same samples, which we have used in numerical leaching experiments. Nevertheless it can be seen, that the shape of leaching curves computed with the heterogeneous model is clearly closer to the shape of measured curves, than the shape of curves provided by the standard model. These differences can be utilised as a basis for an approximate numerical method of assessing the geometric factor, which has traditionally been a purely empirical parameter.

The results of the new numerical experiments agree with our older results from last year: the heterogeneity of the rock matrix has highly significant impact on the diffusion. However, when interpreting the results, one must not neglect numerous limitations of the model, and hence, one should not attempt to overgeneralise the conclusions.