Doctoral Degrees (Institute for Groundwater Studies (IGS))

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

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    A generic assessment of waste disposal at Douala City practice, prinicipals and uncertainties
    (University of the Free State, 2013-01) Atangana, Abdon; Botha, Joseph François
    English: One reason why groundwater, so often constitutes the main source of drinking water in many cities and towns around the world, is because it is frequently present in sufficient quantities at the point of demand. However, this seemingly advantage may sometimes be its greatest disadvantage, especially in situations where the groundwater occurs at shallow depths and the area overlying the aquifer is populated densely. This problem is particularly relevant in the present technological age with its vast quantities of waste that is often disposed in an uncontrolled manner. Such a situation occurs at Douala the economic capital of Cameroon in central Africa. The city not only host more than 80% of industries in the country, but also has the largest urban population of approximately 3 000 000 with a population density of approximately 350 persons per square kilometre, which continue to increase at a rate of approximately 120 000 migrants per year from the rural areas, while the groundwater level is very shallow and may sometimes rise above the soil surface, especially during floods, which occur not too infrequently. Although the pollution problem is not restricted to groundwater as such, it is aggravated here, because of the ancient belief that wastes are safely disposed of, if buried below the earth’s surface. It took disasters like Love Canal and the Price Landfill to discover the detrimental effects that this practice may have on the population living on or near polluted aquifers. Extreme care therefore should be exercised to prevent the pollution of any aquifer that may pose problems to living organisms or to try and restore a polluted aquifer threatening the natural environment. Groundwater pollution should therefore receive urgent attention when discovered. This thesis describes an attempt to develop a set of guidelines for the restoration of the groundwater resources at Douala, based on the relatively new technique of permeable reactive barriers for groundwater remediation—a technique that is also increasingly applied in the restoration of the Superfund sites in the United States of America. Modern attempts to clean up contaminated aquifers, relies heavily on the use of suitable computational numerical models. Such models have in the past always been based on the classical hydrodynamic dispersion equation. However, an analysis of the equation in this thesis has shown that the equation cannot account for the long‐tail contamination plumes characteristic of fractured rock aquifers. Fortunately, it is not too difficult to develop a more suitable equation. For, as shown in the thesis, all that one has to do is to replace the ordinary derivatives in the classical equation with fractional derivatives. Mechanistic modeling of physical systems is often complicated by the presence of uncertainties, which was in the past usually neglected in the models used in the restoration of aquifers.While these uncertainties have regularly been neglected in the past, it is nowadays imperative that any groundwater model be accompanied by estimates of uncertainties associated with the model. Although a large number of approaches are available for this purpose, they often require exorbitant computing resources. The present investigation was consequently limited to the application of the Latin Hypercube Sampling method applied to an analytical solution of the hydrodynamic dispersion equation. It has been known for years that the hydrodynamic dispersion equation discussed in Chapter 5, is not able to account for the long‐tail plumes often observed in studies of contaminated fractured‐rock aquifers. An approach frequently used to account for this is to replace the ordinary spatial and temporal derivatives in the hydrodynamic equation with fractional derivatives—a procedure confirmed in this thesis.
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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 earth’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: (𝑖) the pressure buildup and (𝑖𝑖) CO₂ 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 CO₂ 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.