New Definition and Numerical Analysis of Local Thermal Non-Equilibrium (LTNE) Conditions in Porous Media: Considering Convection and Conduction Processes for Darcy Scale Problems

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2023-11-22

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Doğan, Mehmet Onur
Tavakkoli Osgouei, Yashar

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New Definition and Numerical Analysis of Local Thermal Non-Equilibrium (LTNE) Conditions in Porous Media: Considering Convection and Conduction Processes for Darcy Scale ProblemsMehmet Onur Dogan a, *, Yashar Tavakkoli Osgouei aa Department of Petroleum and Natural Gas Engineering, Middle East Technical University, Ankara, Turkey* Corresponding author: doganon@metu.edu.trKeywords: Heat transport, Non-Local Thermal Equilibrium, Numerical Simulation, Pore Scale Modeling, Interstitial Heat Transfer Coefficient, UpscalingABSTRACTHeat transport processes in porous media can be encountered in a wide range of applications, e.g., exploitation of geothermal reservoirs, steam injection for Enhanced Oil Recovery, waste disposal of heat-generating materials, porous fire insulators for building insulation, micro-cooling devices, and food processing. Conducting numerical pore scale analysis for these problems can indeed be impossible, particularly when the structure of the pore space is unknown. Even if we were to know the exact structure of the pore space, the computational cost of performing pore scale analysis for the entire system would be enormous. This highlights the importance and utility of using averaged Darcy scale models and making simplifying assumptions like Local Thermal Equilibrium (LTE) where appropriate. The basic conceptual model approach assumes that the fluid and solid phases within a Representative Elementary Volume (REV) are at LTE, having the same temperature. While this assumption simplifies the analysis, it’s crucial to bear in mind that it may not be valid under all conditions. Depending on the fluid and solid thermal properties and fast flow conditions (e.g., in fractured porous media), the LTE assumption might be breached. Under Local Thermal Non-Equilibrium (LTNE) conditions, the temperatures of the fluid and solid phases differ, which necessitates considering two energy balance equations for fluid and solid phases separately. The energy balance equations for these phases are linked with heat source terms, which are defined by the interstitial heat transfer coefficient. Numerical analyses have shown that the primary determinant at the Darcy scale is this interstitial heat transfer coefficient between the solid and fluid phases. The validity of LTE assumption must be checked before using it for Darcy scale applications. If LTE assumption fails, then interstitial heat transfer coefficient can be calculated from pore scale analysis. W.J. Minkowycz et al., (1999) explored how sudden changes in the heat source impact Non-Local Thermal Equilibrium (NLTE) conditions through analytical solutions at the Darcy scale, where they focused on Sparrow (Sp) number and Pechlet number (Pe). Wang et al., (2017) examined NLTE conditions in porous media within a system comprising a trapped fluid-solid matrix, where they focused on Sp number only. Kim et al., (2000) analyzed local thermal equilibrium in microchannel heat sinks, where they focused on conductive dominant problems considering temperature difference between solid and fluid phases in microscale versus the temperature difference between the outer boundaries of the domain. Their theory of LTE condition is based on the studies of Quintard and Whitaker, (1995). In this study, this theory for LTE condition is further developed including conductive only, convective only, and both conductive and convective dominant processes. New LTE conditions are formulated with the help of dimensionless Sp and Pe numbers. The theory is tested for LTE conditions considering pore scale analysis as a reference solution to extract the interstitial heat transfer coefficient and average the Darcy scale properties.

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https://hdl.handle.net/11511/106084

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Department of Petroleum and Natural Gas Engineering, Conference / Seminar