Analytical Solutions for a Wellbore Subjected to a Non-isothermal Fluid Flux: Implications for Optimizing Injection Rates, Fracture Reactivation, and EGS Hydraulic Stimulation

Hydraulic stimulation in enhanced geothermal systems (EGS) involves massive injection of cold fluid into target hot geothermal reservoir through a long open hole section to trigger slip on preexisting fractures and enhance permeability. Fluid injection is typically conducted at a specified rate in a step-increasing manner until the pore pressure exceeds the minimum principal stress. During each step, the injection rate is kept constant. This paper presents analytical solutions for a wellbore subjected to cooling and a constant fluid flux on borehole wall and far field in situ stress in a thermoporoelastic medium with applications to hydraulic stimulations in EGS. The temporal- spatial distribution of temperature, pore pressure and stress are obtained by means of Laplace transform and load decomposition. The results show that for granite and a typical fluid injection scenario, thermal effect is pronounced in the vicinity of the wellbore. At early time, cooling-induced pore pressure/ hoop stress counteract the injection induced pore pressure/hoop stress. With increasing time, the induced pore pressure and hoop stress result predominantly from fluid injection, and cooling plays a marginal role.