Time-Variant Burst Strength of Casing with Geometrical Eccentricity Considering Mechano-Electrochemical Interaction
Authors: Wang Jieli , Dong Xuelin , Gao Deli 
Published: September 2023

ABSTRACT
The casing is one of the main barriers to ensuring the well integrity. Casing integrity damage due to eccentricity and corrosion is a severe failure mode. This study aims to evaluate the time-variant burst strength of casing with geometric eccentricity in a corrosion environment. Based on a complex stress function in bipolar coordinates, the analytical solution of casing stress distribution is obtained. The prediction model of burst strength is established, in which the mechano-electrochemical (M-E) interaction is considered. Next, the accuracy of this model is validated by comparing the results with numerical simulations. Finally, the effects of eccentricity, initial corrosion rate, and internal pressure on the casing burst strength are investigated. Results indicate that the casing eccentricity is critical for casing burst strength. The casing eccentricity results in a local stress concentration at the thinnest wall thickness and enhances the M-E interaction. The enhanced M-E interaction accelerates the corrosion rate, resulting in the rapid strength degradation of the casing. The service time of the casing decreases with the increase of internal pressure and initial corrosion rate, and the eccentricity aggravates this trend. The work provides guidelines for casing integrity evaluation in a corrosive environment.

INTRODUCTION
In the process of oil and gas well development, the casing is often corroded because of acid gas. Corrosion will lead to the thinning of casing wall thickness and the degradation of casing burst strength. (Lin et al., 2016). On the other hand, casing internal eccentricity is typical in manufacturing and difficult to avoid altogether (Tan et al., 2018). Therefore, it is important to predict the burst strength of corroded casing with internal eccentricity in the casing integrity assessment; burst strength is the minimum internal pressure that can cause casing burst failure.
The types of casing corrosion include uniform corrosion, pitting corrosion, and stress corrosion, which not only cause the wall thickness of the casing to be thinned but also cause local corrosion perforation and cracking. So far, the influence of different types of corrosion behavior on casing strength has been widely studied. Sun et al. (2004) studied the influence of different corrosion pit shapes on the stress concentration degree of the casing and established a calculation model to predict the strength degradation of the casing. The results show that the corrosion depth is the most sensitive parameter affecting the stress concentration factor. Xu et al. (2014) used ANSYS finite element software to study the influence of different shapes of corrosion defects on the strength of casing and obtained the strength change law of corroded casing. Zhang et al. (2018) used a high-temperature and high-pressure reactor to simulate downhole production conditions, predicted the corrosion rate of the casing, and then calculated the residual strength of the corroded casing according to the API specification 5CT. The above research mainly starts from the electrochemical theory of casing corrosion, which fully considers the influence of different types of corrosion defects on the strength degradation of the casing, but ignores the influence of mechanical factors on the casing corrosion process. Many studies have shown that stress can accelerate the corrosion evolution process, resulting in the early failure of engineering structures. Gutman (1994) proposed the original mechanical-electrochemical model to study the corrosion process of metals under stress. According to this theory, the applied stress will cause the equilibrium potential to move in the negative direction. The local current density will increase, eventually leading to the aggravation of the anodic metal corrosion dissolution process (Xu et al., 2012). Cheng et al. (2009; 2010;2016) based on the theoretical relationship between corrosion current density and mechanical stress, a large number of numerical and experimental analyses of metal corrosion were carried out. The results show that the synergistic effect of the stress field and electrochemical field at adjacent corrosion defects is significant. Specifically, M-E interaction leads to higher stress concentration, larger current density, and faster corrosion growth. Gao et al. (2008) combined with the theory of chemical mechanical effect, established the calculation model of the influence of external stress on casing corrosion rate and concluded that the greater the stress of the corroded casing, the more the service life of the casing is reduced. Yang et al. (2016) analyzed the effect of load on the corrosion behavior of steel in an acid solution by electrochemical experiments and verified the synergistic effect of elastic stress and corrosion. Then, a finite element analysis (FEA) simulation program considering the coupling process of corrosion and stress is proposed to analyze the fatigue damage of the joint. Based on the mechanical-electrochemical interaction mechanism, Zhang et al. (2017) established an analytical formula for the influence of stress on the life attenuation of the casing. Sun et al. (2020) used finite element software to analyze the mechanochemical interaction at the overlapping corrosion defects on the steel pipe. The results show that the presence of corrosion defects will cause local stress concentration in the pipeline and enhance the influence of M-E interaction on pipeline corrosion. Yan et al. (2014) established a string strength attenuation model under uniform corrosion conditions. The results show that the life of the casing is prolonged by 46.7% without considering the promoting effect of stress on corrosion. The above results show that coupling corrosion and stress will lead to accelerated corrosion and mass loss, resulting in material strength degradation. However, the casing integrity defects due to eccentricity and corrosion should be studied more systematically.