Microstructural Heterogeneity Drives Tracer-Specific Systematic Bias in Darcy-Scale Flux Estimation

Abstract. Complex microstructures are commonly simplified to a single continuum for interpreting Darcy-scale heat and solute transport, and tracers are often treated as interchangeable proxies for flux estimation. However, the specific impacts of microstructural heterogeneity on tracer-specific bias regimes remain poorly understood. We conducted controlled laboratory solute and heat tracer experiments using four sands with distinct grain size distributions, combined with micro-CT imaging and topological analysis of a controlled endmember pair. Although Darcy-scale analytical models reproduced observed breakthrough curves with excellent fidelity (mean R² > 0.99, NRMSE < 0.037), tracer-derived fluxes systematically underestimated independently measured Darcy fluxes in a tracer-specific manner. Solute fluxes were linearly underestimated by ~25 % in the more heterogeneous sands, correlating with right-skewed pore-size distributions (skewness = 0.781) and non-Gaussian breakthrough behavior. In contrast, heat fluxes were nonlinearly and velocity-dependently underestimated, reaching up to 45 % (including 19 % spatial variability in volumetric heat capacity) in the most heterogeneous medium, with the solute-to-heat divergence ratio increasing with flow velocity. Micro-CT analysis revealed that the sand mixture possessed a more negative Euler number (−9,210 vs. −6,288) and exhibited representative elementary volume instability, indicating that tortuous pore connectivity amplifies local thermal non-equilibrium under fast flow. Conventional geostatistical metrics (e.g., Matérn smoothness) failed to distinguish these structural differences. These findings demonstrate that microstructural heterogeneity imposes physics-dependent, systematic biases that are invisible to standard continuum models and geostatistical descriptors, and that heat tracers become less reliable than solute tracers under high-velocity heterogeneous conditions. Process-aware metrics linking pore-network topology to transport behavior are needed to resolve these upscaling failures.