Reservoir simulation is used to demonstrate the dynamic physical processes of rocks and fluid properties with high-order nonlinear equations. Currently, different types of simulation models used in the petroleum industry. These models are solved by numerical techniques to get a solution considering with lots of inherent assumption. In this paper, an extensive review is offered on the state-of-the-art literature with a focus on the nonlinearity in partial differential equations related to the petroleum reservoir simulation. A critical analysis is done on the different techniques for solving nonlinear governing equations in a petroleum reservoir. It is also addressed the inherent assumptions and properties, the significance of nonlinear solvers and their technical challenges. Finally, the article discusses the impact of a solution of these nonlinearity problems by following the different numerical techniques.
Contributors: Deb, P. K; Akter, F; Imtiaz. S. A.; Hossain, M. E.