In order to understand the thermal recovery Behavior of an engineered geothermal system (EGS), this paper develops a model in which fluid circulates in a single, planar hydraulic fracture with a constant hydraulic aperture via multiple recharging and discharging wells. The coupled equations for heat convection in the fracture plane and heat transfer into the rock are provided for steady and irrotational fluid flow conditions. By using velocity potentials and streamline functions, the temperature along a streamline is found to be only a function of the potential. By utilizing the Laplace transformation, the analytical solutions in the Laplace space for the temperature field are found, which are numerically inverted for time-domain results. Several examples with different arrangements of injection and production wells are investigated and the comparison with other published results is provided. The semi-analytical results demonstrate that the proposed model provides an efficient and accurate approach for predicting the temperatures of a multi-well reservoir system.

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