The Use of a Convection Boundary Condition in the Simulation of a Heat Tracer Experiment Conducted in Bedrock

Heat transfer experiments conducted in the subsurface are usually interpreted using either analytical or numerical models, which incorporate first-type boundary conditions (specified temperature) to introduce the heat into the solution domain. An alternative approach is to use a third-type boundary condition, often refereed to as a convection bc in the heat transfer literature, which includes a heat transfer coefficient to accommodate the exchange of heat between fluid flowing outside the domain to that inside the domain under potential. To explore the impact of this boundary condition, a semi-analytical model was developed for a linear flow system in a discrete rock fracture with advective heat transfer in the fracture and conductive heat transfer in the matrix. To illustrate the influence of the heat transfer coefficient, the model is applied to the results of a heat tracer experiment conducted in a discrete fracture connecting two boreholes in a crystalline rock, with warm fluid injection in one borehole and passive temperature measurement in the other.  The experimental results were also simulated using a similar model having a first-type condition at the injection borehole for comparison. The simulations show that the heat transfer coefficient has a significant influence on the shape of the breakthrough curve and allows for an excellent match with the field data, whereas the model with the first-type condition cannot obtain a match of similar quality.