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

Abstract

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.