Analytical Model for Thermal Response in a Fracture Due to a Change in Flow Rate

Abstract

This paper describes an analytical model for thermal transport through a single fracture with a change in flow rate at a given point in time. The model can be used to assess the effects that a change in injection rate might have on thermal recovery in a fractured geothermal system. The model is also a useful benchmarking tool for hydrothermal reservoir simulators. Finally, the model may act as a stepping stone for the development of an analytical model for thermal transport with fully variable flow rate. The paper describes the solution to the governing differential equation in detail. The final solution to the problem is provided in two-dimensional Laplace space. Although this solution could have been converted to real space, we chose to solve it using a numerical inversion code. The result was verified by comparison to results from the groundwater simulator FEFLOW. The two responses match with a small discrepancy that is likely due to numerical error.