The scaling concept is important, effective, and consistent in any application of science and engineering. Scaled physical models have inimitable advantages of finding all physical phenomena occurring in a specific process by transforming parameters into dimensionless numbers. This concept is applicable to thermal enhanced oil recovery (EOR) processes where continuous alteration (i.e., memory) of reservoir properties can be characterized by various dimensionless numbers. Memory is defined as the continuous time function or history dependency which leads to the nonlinearity and multiple solutions during modeling of the process. This study critically analyzed sets of dimensionless numbers proposed by Hossain and Abu-Khamsin in addition to Nusselt and Prandtl numbers. The numbers are also derived using inspectional and dimensional analysis (DA), while memory concept is used to develop some groups. In addition, this article presents relationships between different dimensionless numbers. Results show that proposed numbers are measures of thermal diffusivity and hydraulic diffusivity of a fluid in a porous media. This research confirms that the influence of total absolute thermal conductivities of the fluid and rock on the effective thermal conductivity of the fluid-saturated porous medium diminishes after a certain local Nusselt number of the system. Finally, the result confirms that the convective ability of the fluid-saturated porous medium is apparently more pronounced than its conductive ability. This study will help to better understand the modeling of the EOR process thus improving process design and performance prediction.

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