Nonlinearity and solution techniques in reservoir simulation: A review

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 are used in the petroleum industry. These models are solved by numerical techniques to get a solution considering 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 also addresses the inherent assumptions and properties, the significance of nonlinear solvers and their technical challenges. Finally, the article discusses the impact of the solution of these nonlinearity problems by following the different numerical techniques.