Numerical Simulation Study of Thermoelastic Stress Field Around the Wellbore
Authors: Wang Haiyang , Zhou Desheng , Jie YeNan , Gao Qian , Ma XianLin 
Published: September 2022

ABSTRACT:
Analysis of the stress field around the wellbore is a prerequisite for predicting the formation breakdown pressure. With the development of hot dry rock and deep oil and gas reservoirs, thermoelastic stress has become one of the significant factors in the analysis of the stress field around the wellbore. Based on linear elastic theory and heat transfer theory, this paper analyzed the effect mechanism of thermoelastic stress around the wellbore by establishing a two-dimensional wellbore physical model. Through the finite difference method, this paper simulated the thermoelastic stress field around the wellbore under quasi-static and transient conditions. Numerical simulation results show that the calculation results of the finite difference scheme established in this paper are consistent with the analytical solutions under quasi-static conditions. The finite difference scheme established in this paper can accurately calculate the thermoelastic stress field around the wellbore. When the cold liquid injected from the wellbore acts on the hot rock, the circumferential tensile stress is generated around the wellbore. With the increase of Young’s modulus, Poisson’s ratio, and the linear expansion coefficient of the rock, the thermoelastic circumferential stress value around the wellbore increases significantly. The faster the cooling rate of the wellbore, the greater the thermoelastic circumferential stress generated around the wellbore. The finite difference solution of the thermoelastic stress field established in this paper can provide theoretical guidance for the design of hot dry rock hydraulic fracturing and drilling fluids.

INTRODUCTION
Hydraulic fracturing is a significant development technology for unconventional reservoir exploitation (Wang et al., 2021). With the increase of reservoir mining depth and the development of hot dry rock, the influence of thermal stress during hydraulic fracturing becomes more and more important (Zhou et al., 2020).
The heat exchange between the fracturing fluid and the reservoir causes the rock temperature to change, which in turn generates thermal stress. Thermal stress will directly change the effective stress field of the reservoir and affect the failure of the wellbore and the propagation of fractures (Wang and Papamichos, 1994). Chen and Ewy (2005) found that heating the wellbore increases collapse and fracturing mud weight, destabilizing the near-wellbore area. Ghassemi et al. (2009) established a coupled thermoelastic model of a chemically-active rock, which showed that cooling high-salinity mud would increase the possibility of tensile failure. Zhou et al. studied the stress field formed by the seepage force around the wellbore and analyzed the effect of poroelastic stress on the initiation of fractures (Zhou et al., 2021; Wang et al., 2021). Zhou and Ghassemi (2009) developed a finite element model that couples linear and nonlinear chemistry-pore-thermoelasticity, which can be used to analyze the wellbore stability of shale reservoirs. Roy et al. (2018) studied the effect of thermal stress on the integrity of the wellbore during the CO2 injection process, and the results show that the existence of effective in-situ horizontal stress reduces the negative impact of the thermal stress around the wellbore. Wang et al. (2019) developed a new non-isothermal wellbore strengthening model, which showed that mud loss aggravated the redistribution of thermal stress near the wellbore. The above studies have shown that during fluid injection, thermal stress has a significant impact on wellbore stability. It is necessary to study the thermoelastic stress generated by the cooling effect of the fracturing fluid during the hydraulic fracturing process to analyze the initiation of the hydraulic fracturing fracture.