Laboratory heat transport experiments reveal grain-size- and flow-velocity-dependent local thermal non-equilibrium effects

Abstract

Heat transport in porous media is crucial for gaining Earth science process understanding and for engineering applications such as geothermal system design. While heat transport models are commonly simplified by assuming local thermal equilibrium (LTE; solid and fluid phases are averaged) or local thermal non-equilibrium (LTNE; solid and fluid phases are considered separately), heat transport has long been hypothesized, and reports have emerged. However, experiments with realistic grain sizes and flow conditions are still lacking in the literature. To detect LTNE effects, we conducted comprehensive laboratory heat transport experiments at Darcy velocities ranging from 3 to 23 m d−1 and measured the temperatures of fluid and solid phases separately for glass spheres with diameters of 5, 10, 15, 20, 25, and 30 mm. Four replicas of each size were embedded at discrete distances along the flow path in small glass beads to stabilize the flow field. Our sensors were meticulously calibrated, and measurements were post-processed to reveal LTNE, expressed as the difference between solid and fluid temperature during the passing of a thermal step input. To gain insight into the heat transport properties and processes, we simulated our experimental results in 1D using commonly accepted analytical solutions for LTE equations and a numerical solution for LTNE equations. Our results demonstrate significant LTNE effects with increasing grain size and water flow velocity. Surprisingly, the temperature differences between fluid and solid phases at the same depth were inconsistent, indicating non-uniform heat propagation likely caused by spatial variations in the flow field. The fluid temperature simulated by the LTE and LTNE models for small grain sizes (5–15 mm) showed similar fits to the experimental data, with the RMSE values differing by less than 0.01. However, for larger grain sizes (20–30 mm), the temperature difference between fluid and solid phases exceeded 5 % of the system's temperature gradient at flow velocities ≥17 m d−1, which falls outside the criteria for the LTE assumption. Additionally, for larger grain sizes (≥20 mm), the LTNE model failed to predict the magnitude of LTNE (i.e., temperature difference between fluid and solid phase in time series) for all tested flow velocities due to experimental conditions being inadequately represented by the 1D model with ideal step input. Future studies should employ more sophisticated numerical models to examine the heat transport processes and accurately analyze LTNE effects, considering non-uniform flow effects and multi-dimensional solutions. This is essential to determine the validity limits of LTE conditions for heat transport in natural systems such as gravel aquifers with grain sizes larger than 20 mm.