Quantification and modelling of heterogeneities in aquifers

English: The future of modelling of heterogeneity in aquifers is definitively in the designing of new in situ testing (hydraulic and mass transport) procedures with new corresponding mathematical models. New trends in mathematical differentiation offer opportunity to explore more flexible and practical mathematical model solutions. This applies to both analytical and numerical modelling. Only a sound understanding of rock structures can clearly pose the problem which will then be used to define hydraulic equations to be solved by mathematical models, and numerical software. The most recent concept of differentiation based on the non-local and non-singular kernel called the generalized Mittag-Leffler function, was employed to reshape the model of fractured aquifer fractal flow. The solution was successfully applied to experimental data collected from four different constant discharge tests. Additionally, a new analytical solution to the fractal flow in a dual media was proposed, where the media could be elastic; heterogeneous; and visco-elastic. The existing dual media fractal flow model was modified by replacing the local derivative with the nonlocal operator (operator with Mittag-Leffler kernel, and Mittag-Leffler-Power law kerne)l. The more accurate numerical scheme known as Upwind was used to numerically solve each model. Heterogeneity in a typical South African crystalline rock aquifer was assessed. From this, a methodical level for quantifying and modelling heterogeneity in an aquifer was deduced. It was demonstrated how spatial heterogeneity in aquifers can be modelled based on the most commonly available tools and data in mining environment. The capability of selected numerical geohydrological softwares were assessed using spatial variability of hydraulic parameters (hydraulic conductivity and recharge). Geostatistical tools were specifically applied. Focus was also given to hydro-geochemical characterization by using bivariate scatter plots, Piper and Expanded Durov diagrams, and PHREEQC hydro-geochemical model as complimentary tools to analyse the groundwater chemistry data to describe different hydro-geochemical process which prevail in the monitored groundwater system. Three manuscripts have been submitted out this thesis, in top tier journals of the Natural and Applied Sciences.