Utilization of memory concept to develop heat transfer dimensionless numbers for porous media undergoing thermal flooding with equal rock and fluid temperatures

Enhanced oil recovery (EOR) techniques are regaining interest as high oil prices have rendered such techniques economically attractive. Thermal EOR processes, which involve injection of heat into the reservoir, cause continuous alteration of the thermal characteristics of both reservoir rock and fluids that are seldom modeled in the heat and momentum transfer equations. In this study, the memory concept is employed to develop new dimensionless numbers that can characterize convective heat transfer between the rock and fluids in a continuous alteration phenomenon. The energy balance equation is employed to develop the heat transfer coefficient with the assumption that the rock achieves the fluid temperature instantaneously. The final form of the equation is written in terms of Peclet number and the three proposed dimensionless numbers. The results show that the proposed dimensionless numbers are sensitive to the absolute and effective thermal conductivities of the solid and fluids, average system heat capacity, and the hydraulic diffusivity of the fluid-saturated porous medium. One of the new numbers correlates with the Nusselt and Prandtl numbers, while the local Peclet number is found to be sensitive to memory. Since heat convection and conduction in porous media can now be explained through the proposed numbers with the memory concept, these numbers help characterize the rheological behavior of the rock-fluid system. This work will enhance understanding the effect of heat transfer on alteration of thermal conductivity during thermal recovery operations in a hydrocarbon reservoir.