An integral equation solution for three-dimensional heat extraction from planar fracture in hot dry rock

In the numerical simulation of heat extraction by circulating water in a fracture embedded in geothermal reservoir, the heat conduction in the reservoir is typically assumed to be one-dimensional and perpendicular to the fracture in order to avoid the discretization of the three-dimensional reservoir geometry. In this paper we demonstrate that by utilizing the integral equation formulation with a Green's function, the three-dimensional heat flow in the reservoir can be modelled without the need of discretizing the reservoir. Numerical results show that the three-dimensional heat conduction effect can significantly alter the prediction of heat extraction temperature and the reservoir life as compared to its one-dimensional simplification.