Local thermal equilibrium constraints for energy transport equations for thermal oil recovery processes

Abstract

The mathematical framework of reservoir thermal simulators typically relies on the assumption of local thermal equilibrium (LTE) when modeling energy transport through porous media for petroleum engineering applications, including Thermal Enhanced Oil Recovery (TEOR) processes. The LTE presupposes instantaneous exchange of energy between the injected hot fluids and the reservoir's rock and fluids. Nevertheless, it is essential to acknowledge that LTE's validity becomes questionable in specific scenarios, potentially resulting in an overestimation of oil recovery, e.g., when high fluid velocities arise. Under such conditions, the local thermal non-equilibrium (LTNE) formulation may offer a more accurate representation of the energy transport physics. In this study, we present the physical constraints that must be satisfied for the application of two distinct mathematical formulations (1) the one-equation model for the fluids and rock as a whole (LTE is assumed), and (2) the two-equation model, one equation assigned to the fluids and another one to the rock (pseudo-LTNE is assumed). Such constraints were derived by examining conductive and convective heat transport properties via the theory of the method of volume averaging, specifically applied to an oil-water-gas-rock system at the pore scale. It was found that the one-equation model requires that 18 physical constraints to be satisfied, while the pseudo-LTNE model needs to fulfill 9 physical constraints. A sensitivity analysis was conducted based on factor upon which accumulation, conduction and convection constraint equations depend, aiming to identify the conditions under which LTNE occurs within the porous medium. These influencing factors encompass the characteristic time, the Peclet number, the presence of external heat sources, the distribution of phases at the pore-scale, and the disparity between rock and fluid properties. The combinations of these factors can induce the existence of local thermal non-equilibrium. One significant property is the heat transfer coefficient in the reservoir. We recommend that the pseudo-LTNE approach is reliable as long as the rock-fluid heat transfer coefficients are at least one order of magnitude larger than the fluid-fluid heat transfer coefficients (1000−10000W/(m3K)). Contrarily, the OEM should be employed only when the heat transfer coefficients surpass a threshold value of 10000W/(m3K). When injector and producer wells are hydraulically interconnected, resulting in heightened fluid velocities, it is encouraged the use of the two-equations model. The predictability and reliability of the energy models were verified by comparison of predicted oil recovery against data from laboratory experiments. The equations presented in this study consistently demonstrate their utility in assessing the reliability of energy transport models for TEOR scenarios.