A numerical scheme for heat transfer in fluid flowing in three-dimensional fractures

We present a numerical scheme using a finite volume method (FVM) to simulate the heat transfer in fluid flowing in a three-dimensional fracture in a rock mass. Heat conduction in the rock mass and heat exchange between the fluid and the rock mass are considered, but fracture deformation is not. This scheme could approximate the thermal energy extraction process from a geothermal system when the fractures have been established and the fluid pressure and temperature variations are not high enough to cause a significant change of the fracture aperture. The FVM was employed to solve the pressure and temperature of fluid with the same triangular control cells. The heat conduction in the rock mass was simulated with an indirect boundary element method (IBEM), which uses the triangular control cells of the FVM as the discretization boundary elements. The fluid pressure and temperature are coupled in two systems of equations and a sequential coupling iteration procedure was employed to solve the equations. This paper introduces the FVM for the fluid temperature and the sequential iteration procedure for temperature and pressure which was implemented in a code, and the numerical results agree well with an analytical solution for the temperature of fluid flowing through a rectangular fracture. The numerical scheme was then employed to simulate illustration examples of heat transfer between two well holes.