Doctoral Degrees (Institute for Groundwater Studies (IGS))

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Browsing Doctoral Degrees (Institute for Groundwater Studies (IGS)) by Advisor "Atangana, Abdon"

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    Mathematical modelling of pressure build-in due to geological carbon dioxide storage in deep Saline Aquifers, using non-local operators: the context of groundwater protection in the climate change mitigation era
    (University of the Free State, 2023) Mbah, Hans Tah; Atangana, Abdon
    Man-caused Green House Gas (GHG) emissions have perturbed the earthโ€™s energy balance, and the need to achieve deep emission reduction is a pressing challenge, faced by humankind. Carbon Capture and Storage (CCS) in deep geological saline aquifers is a viable option for Green House Gas (GHG) mitigation. Industrial-scale scenarios may induce large-scale reservoir pressurization and displacement of native fluids. Especially in closed systems, the pressure buildup can quickly elevate beyond the reservoir fracture threshold and potentially fracture and or reactivate existing faults in the cap rock. This can create conduits for focused leakage and mobilization of heavy metals and harmful trace elements, into capture zones of freshwater wells. Risk assessment in CCS requires that careful safety and environmental impact evaluations be considered. Through sustainable pressure management, the reservoir's hydraulic integrity is maintained. This is theoretically achievable with the help of a numerical simulation, using robust mathematical models that provide consistent and effective ways to understand and predict pressure buildup in such complex systems. This thesis focuses on modelling two aspects: (๐‘–) the pressure buildup and (๐‘–๐‘–) COโ‚‚ saturation evolution in the two-phase flow zone, by extending the classical pressure diffusivity and the Buckley-Leverette fractional flow models to the framework of non-local differential and integral operators. The extended models describe the pressure behavior during COโ‚‚ injection through a vertical well, open in a saline aquifer. To include in the mathematical models the effect long-range, fading memory and weak crossover from stretched exponential to power-law, several differential operators were considered. For each extended model, different numerical schemes were adapted to derive numerical solutions. The presented numerical results provide an overview of subsurface transient pressure response and are useful tools for accurate risk assessment and sustainable reservoir management and operational safety during geo-sequestration in basins with shallow freshwater capture zones.
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    Quantification and modelling of heterogeneities in aquifers
    (University of the Free State, 2017-01) Ahokpossi, Dehouegnon Pacome; Atangana, Abdon; Vermeulen, Danie
    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.