During the recovery of enhanced geothermal system (EGS) reservoirs, water is cycled between engineered hydraulic well doublets. When cooled water is re-injected into the fracture system underground, the temperature in the matrix decreases, resulting in the shrinkage of matrix rock and enhancement of the permeability of fractures. Such a phenomenon is known as the thermal unloading process, the accurate modeling of which requires coupled thermal-hydraulic-mechanical simulation approaches. In this work, we brought out a novel derivation of the thermal-hydraulic-mechanical model of the matrix-fracture interaction, in order to capture the transient behavior of the fracture system in the thermal unloading process. We analytically solve the temperature field inside a matrix rock that is surrounded by fractures, using Fourier series and separation of variables. The temperature field is used to calculate the stress as well as the displacement field in the matrix rock during the thermal unloading process. Based on the analytical solution of the displacement field, we are able to obtain the deformation of the matrix rock, and therefore obtain the change in the aperture/permeability of the fracture system. Our analytical model has been successfully implemented in an in-house simulator. The simulation results show that when injection temperature is lowed by 10 Celsius degree, the fracture permeability near the cold injector is enhanced by about eight times, which matches well with field observations. The proposed model can also be used to fast estimate the permeability variation during real-time injection monitoring in real practices.

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