Heat transfer in a fracture embedded in a finite matrix: On the role of geometries and thermal dispersivity in the fracture

Abstract

Understanding heat transfer in the discrete fracture embedded in a finite rock matrix is critical to the investigation of thermal energy transfer in the fracture network and the assessment of geothermal energy recovery in the enhanced geothermal system (EGS). In this study, an analytical model is proposed for transient and steady-state thermal energy transfer in a discrete fracture embedded in a finite rock matrix. The heat transfer model accounts for thermal convection, velocity-dependent thermal dispersion and longitudinal thermal conduction in the fracture, and thermal conduction in the rock matrix. The influence of the outer boundaries of the finite rock matrix will also be considered along with thermal exchange between the fracture and rock matrix. The thermal transfer processes in those two domains are coupled by assuming the continuity of temperatures and thermal fluxes along the fracture-rock matrix interfaces. The solutions are validated with the existing analytical solution and numerical model, and proved to be robust and accurate. The study implies that: 1) the geometries, such as the fracture aperture and thickness of the rock matrix, have an important influence on the temperature distribution. The fracture temperature will change in a greater range in the wider fracture and thicker rock matrix; 2) longitudinal thermal conduction in the fracture does not have a major influence on the temperature distribution in the system, and thus can be ignored; 3) thermal dispersivity in the fracture is an important mechanism to include. Ignoring thermal dispersion in the fracture will misestimate the temperature significantly. Also, thermal conductivity in the rock matrix is a key parameter for the thermal exchange between the rock matrix, surrounding environment and fracture. When the rock matrix has a greater thermal conductivity, the temperature in the fracture is observed to change less. The analytical model proposed in this study is implemented to analyze the thermal flow-through experiments in fractured core samples by Zhao (1987) and estimate the thermal dispersivity values in the fracture. The Morris global sensitivity analysis is conducted to identify the most influential input variables and estimate the interaction effects. The global sensitivity analysis is consistent with thermal breakthrough curve analysis and indicates that the temperature in the fracture is sensitive to fracture aperture, rock matrix radius, thermal dispersivity in the fracture and thermal conductivity in the rock matrix, and insensitive to longitudinal thermal conductivity in the fracture.