Doctoral Degrees (Institute for Groundwater Studies (IGS))

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Browsing Doctoral Degrees (Institute for Groundwater Studies (IGS)) by Author "Mbah, Hans Tah"

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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.