When a cool fluid such as water is injected into a hot reservoir, a growing region of cooled rock is established around the injection well. The rock matrix within the cooled region contracts, and a thermoelastic stress field is induced around the well. For typical waterflooding of a moderately deep reservoir, horizontal earth stresses may be reduced by several hundred psi. If the injection pressure is too high or if suspended solids in the water plug the formation face at the perforations, the formation will be fractured hydraulically. As the fracture grows, the flow system evolves from an essentially circular geometry in the plan view to one characterized more nearly as elliptical.
This paper considers thermoelastic stresses that would result from cooled regions of fixed thickness and of elliptical cross section. The stresses for an infinitely thick reservoir have been deduced from information available in public literature. A numerical method has been developed to calculate thermoelastic stresses induced within elliptically shaped regions of finite thickness. Results of these two approaches were combined, and empirical equations were developed to give an approximate but convenient, explicit method for estimating induced stresses.
An example problem is given that shows how this theory can be applied to calculate the fracture lengths, bottomhole pressures (BHP's), and elliptical shapes of the flood front as the injection process progresses.