Poroelastic and thermoelastic effects of cold-water injection in an enhanced geothermal system (EGS) are investigated by considering water injection into an infinite fracture in hot, permeable and impermeable rock. Assuming a constant injection rate and one-dimensional Darcy type leak-off, a semi-analytic solution is developed for the pressure in the fracture and reservoir. Solutions for the resulting poroelastic and thermoelastic induced fracture aperture changes are also developed. The application of the solutions shows that as expected, poroelastic effects reduce the fracture aperture due to fluid leak-off into the reservoir and cause the pressure in the fracture to increase. In contrast, the thermoelastic effects increase the fracture aperture. As a result the fracture pressure is significantly lowered in the fracture. Comparison of poroelastic and thermoelastic effects with respect to injection pressure and aperture variations shows the thermoelastic effects are dominant in EGS type environments.
An enhanced geothermal system (EGS) involves injection of cold fluid into existing or man-made fractures in hot dry rock. The fluid extracts heat from the hot dry rock, which is then extracted for energy use. Knowledge of the reservoir response to injection is important for successful enhanced geothermal system (EGS) development. In particular, it is necessary to understand the mechanisms that play a role in phenomena such as variation of injectivity with temperature and occurrence of seismicity. As injected water travels through existing or man-made fractures, it interacts with the reservoir rock giving rise to chemical, thermoelastic, and poroelastic phenomena, which affect the fracture geometry. Some of these mechanisms have been studied using a line fracture injection/extraction model. For example, Kumar and Ghassemi  studied the role of silica precipitation/dissolution, and found that when the initial rock temperature and quartz content are higher in the rock than the fluid, dissolution increases the fracture aperture near the inlet while precipitation decreases fracture aperture near the extraction point. The significance of thermallyinduced stresses in a planar fracture from cold water injection has been addressed also (see e.g., [2, 3]). The influence of poroelastic and thermoelastic processes on fracture aperture has been studied using a fully coupled model of a uniformly pressurized and cooled crack . The thermoelastic and poroelastic changes in the fracture aperture and pressure in a line fracture injection/extraction model were studied in .
In this paper, we study the aperture variation and the resulting pressure change for the problem of cold water injection into a radial fracture (see Fig. 1). A partially coupled formulation allows for analytic solutions of the induced pressure and temperature fields in the fracture and reservoir. These are applied to derive expressions for the fracture aperture change induced by thermoelastic and poroelastic stresses. The resulting variation in fracture pressure due to aperture changes is also studied. We apply an axisymmetric condition to treat a vertical section of a horizontal planar fracture.