Akademik Veri Yönetim Sistemi
VI International Workshop «Thermal Methods for Enhanced Oil Recovery: Laboratory Testing, Simulation and Oilfields Applications» ThEOR2023, Ankara, Türkiye, 20 - 22 Kasım 2023, ss.48-49
New Definition and Numerical Analysis
of Local Thermal Non-Equilibrium (LTNE)
Conditions in Porous Media: Considering Convection and Conduction Processes for
Darcy Scale Problems
Mehmet Onur Dogan a, *, Yashar Tavakkoli Osgouei a
a Department
of Petroleum and Natural Gas Engineering, Middle East Technical University,
Ankara, Turkey
* Corresponding author: doganon@metu.edu.tr
Keywords: Heat transport, Non-Local Thermal
Equilibrium, Numerical Simulation, Pore Scale Modeling, Interstitial Heat
Transfer Coefficient, Upscaling
ABSTRACT
Heat
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.