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

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.