Integral equation solution of heat extraction from a fracture in hot dry rock

In the study 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 this paper, we demonstrate that by an integral equation formulation utilizing Green's function, the multi-dimensional heat flow in the reservoir can be modelled. In the resulting numerical solution system, the discretization of reservoir geometry is entirely eliminated, leading to a much more efficient scheme. The multi-dimensional heat conduction effect as compared to its one-dimensional simplification is studied.