Application of Memory Formalism and Fractional Derivative in Reservoir Simulation

Reservoir properties (e.g., porosity, permeability, surface tension, viscosity, fluid saturation, wettability, reservoir thickness, pressure, and temperature) are the function of time. Time variation of rock-fluid properties in a reservoir can be defined as memory concept in the field of petroleum engineering. Introducing memory formalism in reservoir simulation allows to account the time-varying nature of rock-fluid properties and enables reservoir simulator to provide more accurate reservoir flow forecast. The key purpose of this paper is to summarize the details for developing a memory formalism-based reservoir simulator. Within the context of the study, the key concept of memory formalism and fractional calculus are precisely explained. A complete roadmap in preparing a memory formalism-based reservoir simulator is shown with example and application.