Atangana, AbdonVermeulen, DanieAhokpossi, Dehouegnon Pacome2017-09-082017-09-082017-01http://hdl.handle.net/11660/6847English: 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.Afrikaans: Die ontwikkeling van nuwe in situ toets (hidrouliese en massa vervoer) prosedures met nuwe ooreenstemmende wiskundige modelle is die toekoms van modellering van heterogeneteit in waterdraers. Nuwe tendense in die wiskundige differensiasies bied geleenthede om meer buigsaam, en praktiese wiskundige model oplossings te verken. Dit geld vir beide analitiese en numeriese modellering. Slegs 'n goeie begrip van die rots strukture kan die probleem duidelik stel wat dan gebruik word om die hidrouliese vergelykings te bepaal wat deur wiskundige modelle opgelos moet word. Die mees onlangse konsep van differensiasie gebaseer op die nie-plaaslike en niesinguliere kern wat bekend staan as die algemene Mittag-Leffler funksie, was gebruik om die model van gefraktuurde waterdraer fraktale vloei te hervorm. Die bestaan van 'n positiewe oplossing van die nuwe model was aangebied, en die uniekheid van die positiewe oplossing was gestig. Drie verskillende numeriese skemas was gebruik om die nuwe gefraktuurde fraktale model op te los. Die oplossing was daarna suksesvol toegepas op eksperimentele data wat van vier verskillende konstante vloei toetse versamel was. 'n Nuwe analitiese oplossing vir die fraktale vloei in 'n dubbele media sisteem was ook voorgestel, waar die media elasties; heterogeen; en visco-elasties kan wees. Die bestaande dubbele media fraktale vloeimodel was aangepas deur die vervanging van die plaaslike afgeleide met die nie-plaaslike operateur met krag. Twee nie-plaaslike operateurs was oorweeg - 'n operateur met Mittag-Leffler kern en Mittag- Leffler-Power wet kern. Vir elke model is 'n gedetailleerde studie van die bestaan en uniekheid van die sisteem oplossings met behulp van die vaste punt stelling aangebied. Die meer akkurate numeriese skema, bekend as windop, was gebruik om elke model numeries op te los. Die heterogeniteit in 'n tipiese Suid-Afrikaanse kristallyne rots waterdraer was geassesseer. Uit hierdie was 'n metodiese vlak vir die kwantifisering en modellering van heterogeniteit in 'n waterdraer afgelei. Dit was gedemonstreer hoe ruimtelike heterogeniteit in waterdraers gemodelleer kan word op grond van die mees algemeen beskikbare gereedskap en data in Suid-Afrikaanse mynbou omgewings. Ruimtelike variasie van hidrouliese parameters is gebruik om heterogeniteit in die waterdraer in ag te neem. Geostatistiese gereedskap was gebruik om die geskatte hidrouliese geleiding en herlaai waardes te analiseer.enGroundwaterHeterogeneityVariabilityFractalMittag-LefflerNumerical modelsQuantificationDiffusionAquifersThesis (Ph.D. ( Institute for Groundwater Studies))--University of the Free State, 2017ThesisUniversity of the Free State