Development of dimensionless numbers for heat transfer in porous media using a memory concept

Various dimensionless numbers such as the Nusselt, Prandtl, and Peclet numbers, play a significant role in the analysis of heat transfer in any non-isothermal physical system. This transport phenomenon is modeled by a very complex set of differential equations that could involve a large number of variables and for which analytical solutions may be unattainable. Therefore, the model equations are often linearized by neglecting one or more terms (such as convection) or by employing simplifying assumptions.With the advent of advanced computational tools, it is possible to tackle such mathematical challenges numerically. Using a mathematical model based on nonlinear energy balance equations, new dimensionless numbers were developed to describe the role of various heat transport mechanisms (such as conduction and convection) in thermal recovery processes in porous media. The results show that the proposed numbers are sensitive to most of the reservoir rock/fluid properties such as porosity, permeability, densities, heat capacities, etc. Therefore, the proposed dimensionless numbers help to characterize the rheological behavior of the rock-fluid system. This work will enhance the understanding of the effect of heat transfer on the alteration of effective permeability during thermal recovery operations in a hydrocarbon reservoir.