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Date of Award
Thesis-ISU Access Only
Master of Science (MS)
Department of Mathematics
Papa A. Sissokho
Almost every aspect of life and technology today requires reasonable amount of energy to run. This high energy consumption in turn places high demand on energy generation/production. Currently, the most predominant and prominent sources of nonrenewable energy are coal, crude oil and natural gas.
The entire process of nonrenewable energy exploration, processing and usage raises a lot of environmental concerns orchestrated by high level of carbon-dioxide generated by the process (burning of fossil fuels such as coal, oil and gas) which contributes so much to global warming. The other concerns are groundwater contamination and earthquake.
Since the mid 1940s, some oil and gas companies seem to have found a more efficient tool for their exploration activities. This tool is called hydraulic fracturing: a mechanism used in extracting oil and gas locked in rock deposits deep down the earth much more easily.
In this research work, we undertake a study on using partial differential equations to model hydraulic fracturing and analyze its impact on the environment, with respect to earthquakes and groundwater contamination. The model is a system of PDEs which can be solved using analytical or numerical methods. Our method is 3-D continuum modeling with direct and analytical solution technique. We conducted a numerical analysis of the solutions, which reveals a heavy dependence of rock deformation on stress generated by the fracturing fluid pressure. To ascertain the efficiency, reliability and safety or otherwise of fracturing against the backdrop of major environmental concerns, we analyze the fracturing process, results from studies and facts from governments/agencies. These analyses give results that could allay the associated environmental concerns, like earthquake and groundwater contamination. In this study, we do not venture into real life experiment or simulation method on the subject.
Ogu, Henry A., "Using Partial Differential Equations To Model Hydraulic Fracturing And Analyze Its Environmental Impact" (2019). Theses and Dissertations. 1151.