Modelling of fluid flow through porous media using memory approach: A review

Reservoir simulator is widely known in the petroleum industry for analysing and predicting the fluid flow behaviour through porous media. Conventional mathematical approach, which is the mostly used approach in reservoir simulation, assumes several unrealistic assumptions. Introducing the memory formalism with classical mathematical approach can eliminate this shortcoming. Because, the assumptions of fundamental laws (e.g., mass conservation, equation of state, and constitutive equation) used in reservoir simulation are reduced through incorporation of memory formalism. Memory-based flow model accounts the time varying nature of rock-fluid properties. To date, flow models do not yet exist where all the possible reservoir properties are considered as a function of time and space. The present study shows a comprehensive workflow in developing a memory-based reservoir simulator. The fundamentals of memory formalism and fractional calculus along with the use of fractional order derivative to formulate memory formalism are summarized. The proposed memory approach is validated using an application. A comparison of memory approach and multi-continuum approach is shown to depict the significance of the memory formulation for anomalous diffusion. This research is expected to open a door for introducing non-linear solvers in reservoir simulation study where cloud points solutions will be obtained instead of a single point solution. The outcome of this study will help engineers and researchers to develop more transparent simulator instead of creating a black box.