A dynamic heat transfer coefficient between fractured rock and flowing fluid

Abstract

Estimation of heat production remains a major challenge for geothermal industry. In continuum mechanics two main approaches need to be separated to model heat transfer between fluid and rock: local thermal equilibrium (LTE) and local thermal non-equilibrium (LTNE). While LTNE does not require the strong assumption of instantaneous local thermal equilibrium, the parameters for explicit heat transfer between rock and fluid are only loosely defined. This work focuses on the heat transfer coefficient between rock walls and flowing fluid. Based on an experimental setup with simple geometry and a steady state scenario, we derive a dynamic heat transfer coefficient dependent on fracture aperture, flow velocity and thermal parameters. We compare our model to experimental data and achieve a good agreement for most temperatures. In comparison to a static heat transfer coefficient, a dynamic coefficient changes the fluid and rock temperature distribution in the fractured system. We then show possible extensions of our dynamic approach with a simulation on reservoir scale. In opposite to existing models and empiric approaches our model intrinsically adjusts to spatial heterogeneity and temporal changes in flow and temperature field. The model is based on well-defined physical parameters which can be easily obtained from standard laboratory tests and dependent on characteristic variables like velocity and rock temperature. Our model can be extended by including more constitutive relationships linking permeability, fracture aperture, fluid pressure and heat transfer.