Fractional derivatives and their applications in reservoir engineering problems: A review

• Published in: Journal of petroleum science & engineering 2017-08, Vol.157, p.312-327
• Main Authors: Obembe, Abiola D., Al-Yousef, Hasan Y., Hossain, M. Enamul, Abu-Khamsin, Sidqi A.
• Format: Article
• Language: English
• Subjects: Anomalous diffusion; Anomalous heat transport; Darcy law; Fractional derivatives
• ISSN: 0920-4105; 1873-4715
• DOI: 10.1016/j.petrol.2017.07.035

The use of fractional derivatives as a mathematical tool towards the development of more robust mathematical models in certain areas of reservoir engineering is gaining attention in both industry and academia alike. However, the main ideology and rationale for employing these fractional-based models are not fully understood. This expository paper carefully analyzes the literature on fractional calculus devoted to reservoir engineering applications. The review covers issues related to its history, definition, applications, and advantage over the classic reservoir engineering based approach. The potentials and challenges/limitation of some of the available approaches are highlighted where appropriate. Finally, some future potential research areas are proposed to fill the gap of the current state-of-the art in the area. This study contributes to the fundamental understanding and further development of fluid flow models that accurately describe the local and global phenomena. •Presents limitations of existing continuum fluid and heat transfer models employed for porous media.•Demonstrates the applications of fractional derivatives in reservoir engineering.•Provides numerical examples to demonstrate the nature of anomalous transport in porous media.•Critical investigation of the Hossain memory formalism via numerical simulation.•Enumerates potential future areas for research fractional derivative based models.