Atangana, A.Kholotsa, Mathapelo Emely2023-10-132023-10-132022http://hdl.handle.net/11660/12300Dissertation (M.Sc.(Geohydrology))--University of the Free State, 2022The practice of carbon capture and storage effectively lowers greenhouse gas emissions and mitigates climate change and global warming. To determine whether long-term geological CO₂ sequestration is safe and practical, scientists have increasingly relied on model-based predictions of CO₂ behavior beneath the earth's surface in recent years. This investigation aims to get a firm grasp of the CO₂ dissolution trapping process and mathematical models depicting the behavior of the CO₂ convective dissolution process (Fingering) in saline aquifers. This comprehension will eventually help to ensure that the CO₂ plume stays inside the designated locations of CO₂ storage. The approach involved employing the concept of fractional differentiation by replacing the classical time derivative with the Caputo, Caputo Fabrizio, and Atangana Baleanu fractional derivative. To analyze the finger development process using three non-local operators: Power law, exponential law, and Mittag-Leffler function. Equally important, through performing linear stability analysis, we considered the stability evolution equation for the perturbation, which incorporated the exponential law and thus resulted in a memoryless function. We then replaced the exponential kernel with the Mittag-Leffler kernel to the perturbation equation to modify it into a process that has memory. By incorporating the Mittag-Leffler kernel into the perturbation equation, we suggest a new approach that provides a more accurate, robust, and efficient solution algorithm to capture finger development. In conclusion, we demonstrated some numerical simulations obtained using MATLAB.enCarbon Capture StorageGreenhouse gasesfractional differentiationlinear stability analysisDissertationUniversity of the Free State