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Abiola D. Obembe Sidqi A. Abu-Khamsin M. Enamul Hossain Kassem Mustapha 《Computational Geosciences》2018,22(5):1231-1250
The increasing applications of fractional calculus in simulating the anomalous transport behavior in disordered and fractured heterogeneous porous media has grown rapidly over the past decade. In the present study, a temporal fractional flux relationship is employed as a constitutive equation to relate the volumetric flow rate to the gradient of the pore pressure. The novelty of this paper entails interpreting the time fractional derivative operator in the flux relationship by the Grünwald-Letnikov (G-L) definition as opposed to the Caputo interpretation which has been widely considered. Subsequently, a numerical scheme based on the block-centered finite-difference discretization is formulated to handle the resulting non-linear fractional diffusion model. In addition, a linear stability analysis is successfully performed to establish the stability criterion of the developed numerical scheme. An expression for the modified incremental material balance index was derived to assess the effectiveness of the numerical discretization process. Finally, numerical experiments were performed to provide qualitative insights into the nature of pressure evolution in a hydrocarbon reservoir under the influence subdiffusion. In summary, the results establish that subdiffusion regime results in the development of higher pressure drop in the reservoir. This paper will provide a strong foundation for researchers interested in investigating anomalous diffusion phenomena in porous media. 相似文献
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Kalam Shams Khan Rizwan Ahmed Khan Shahnawaz Faizan Muhammad Amin Muhammad Ajaib Rameez Abu-Khamsin Sidqi A. 《Natural Resources Research》2021,30(2):1697-1717
Natural Resources Research - Low-salinity waterflooding (LSWF) has, in the past decade, attained a lot of attention to enhance oil recovery. In LSWF, diluted water is injected into an oil reservoir... 相似文献
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