Analysis of the Instantaneous Local Thermal Equilibrium Assumption for Heat Exchange between Rock Matrix and Fracture Water

For theoretical modeling of water flow and heat transfer processes in fractured rocks, one of the most commonly employed assumptions is that instantaneous local thermodynamic equilibrium exists between the water, the fills in the fractures, and the surfaces of the neighboring rock matrix blocks. An analysis of the effects of such assumption is conducted through semi-analytical calculations of heat transfer in a single fracture impermeable rock. It is observed that, for the heat exchange between water and fill, the ratio of the convective coefficient and the grain size acts as the major influencing factor to the validity of the instantaneous local thermal equilibrium between water and fill, that the discrepancies caused by using the thermal equilibrium for heat exchange between rock matrix and water can be significant at locations close to the heat source and at early times of the process, but reduce rather quickly to negligible levels as the distance to the heat source and the time increase, and that the influence of the thermal equilibrium assumption also becomes less significant if the water velocity is small, if the heat capacity and conductivity of rock matrix is small and the convection coefficient is large.