A Review of Modeling Thermal Displacement Processes in Porous Media

The subject of heat transfer in oil reservoirs has gained huge attention, due to its diverse range of applications in petroleum reservoir management and thermal recovery for enhanced oil recovery. Thermal recovery methods entail the addition of heat energy into the reservoir through injection wells with the aim of reducing the in situ oil viscosity which is usually around several thousand centipoise cP (in S.I unit kg/m s) at reservoir conditions to very low values at steam temperatures. In addition, several other mechanisms are associated with thermal recovery methods. These include thermal expansion of oil, steam distillation, and relative permeability changes, which contribute to the ultimate recovery of the reservoir. In this article, a detailed review of non-isothermal modeling in an oil reservoir is presented. In addition, a few remarks regarding the momentum transport and the energy balance equations and its various modifications through the years are provided. Finally, a memory-based formulation is proposed to capture the alteration of rock and fluid properties with time as well as accounting for other phenomena not described by classic diffusion equations.