Numerical analysis of local thermal non-equilibrium experiments reveals conceptual regimes of grain-scale heat transport

Abstract

Modeling heat transport in saturated porous media typically assumes local thermal equilibrium (LTE) conditions, though this assumption lacks justification. Recent work has revealed local thermal nonequilibrium (LTNE) effects for groundwater flow conditions, which standard one‐dimensional analytical and numerical models fail to capture accurately. In this study, we develop and validate a 2D numerical model for two‐phase heat transport at the granular scale to describe experimental LTNE effects previously observed, by coupling heat fluxes in both phases with a heat transfer term. Our results show that LTNE and non‐uniform flow effects are superimposed and challenging to disentangle. However, the experimental results, expressed as temperature difference between solid and fluid phase (ΔT(t)), best match the case where the heat transfer coefficient hsf → ∞(maximal efficiency), showing that hsf is insensitive for flow rates of 3–23m d􀀀 1 and grain sizes of 5–30 mm. The model further confirms that different and negative ΔT(t) for same grain sizes are caused by non‐uniform flow where arrival of the thermal front varies at the grain scale. Overall, our findings reveal multiple different heat transport concepts: (a) LTE, which is widely used; (b) Baseline LTNE, arises from different thermal properties between phases; (c) Phase transfer LTNE, which involves a limited heat transfer rate between phases; (d) Non‐uniform flow LTNE, which is caused by pore‐scale flow variations. This detailed concept of LTNE effects suggests that interphase heat transfer plays a negligible role toward LTNE effects at the granular scale under conditions relevant for hydrogeology.