# A Study on the Stress Field Around an Elliptical Wellbore with an Eccentric Casing in Deep Wells
###### Abstract  
Casing stress distribution is one of the most relevant topics in the study of the wellbore stress field. Due to factors such as uneven geostress, the wellbore is often elliptical, and the casing may not necessarily be in the center of the wellbore. This article adopts the theory of elasticity and uses the finite element method for calculation. The main research focuses on the effects of ovality and eccentricity on the overall stress distribution of the casing and the stress distribution at the interface between the casing and cement sheath (i.e., the outer wall of the casing). The research results indicated that when the casing is centered, higher ellipticity is beneficial for improving the casing's response to non-uniform stress. However, when the casing is eccentric, higher ellipticity significantly increases the non-uniformity of the stress distribution and the risk of stress concentration in the casing. The risk of casing failure increases with increasing non-uniform stress. Additionally, a lower elastic modulus and higher Poisson ratio of the cement can improve the casing's response to stress. This research result has a certain reference value for implementing high-quality cementing construction and ensuring the normal production of oil and gas wells. elliptical wellbore; casing stress; non-uniform geostress 2024202411888. 2024202411888.  
the influence of non-uniform stress and irregular wellbore shapes on the stress distribution in the casing. Early scholars both domestically and internationally have made idealized assumptions on the mechanical model of the casing-cement-formation system. They assumed that the wellbore shape is relatively regular and the casing is centered, while there is complete bonding between the casing, cement annulus, and formation. In relevant studies, [PERSON] et al. [6] proposed a numerical model based on the finite element method for this situation, and [PERSON] et al. [7] established a two-dimensional model of the composite system. [PERSON] [8] conducted numerical simulations using the Monte Carlo method, and [PERSON] [9] conducted research using ABAQUS finite element software, investigating the influence of the elastic modulus and Poisson ratio of the cement sheath, formation characteristics, and internal pressure of the casing on the initial failure pressure of the cement forming interface. Additionally, [PERSON] [10] proposed an elastic solution, and [PERSON] [11] proposed a closed-form solution. When studying wellbore problems, the assumption that the casing is located at the center of the wellbore is often not fully satisfied. In practice, the casing is prone to eccentricity due to geological factors, wellbore inclination, and uneven formation stresses [12]. [PERSON] [13] conducted numerical simulations of casings in eccentric states, and [PERSON] [14] found that with an increase in pipeline eccentricity, the pressure drop decreases significantly. [PERSON] et al. [12] discovered that eccentricity has a significant impact on the size of the interface micro-annulus. [PERSON] [15] found that when the initial tensile (shrinkage) is combined asymmetrically with the casing, casing eccentricity does not have a significant influence on stress distribution. Under the influence of non-uniform formation stresses, the wellbore does not always maintain a circular shape but may gradually form an elliptical wellbore. In response to this issue, [PERSON] et al. [16] studied the stress distribution characteristics of the wellbore surrounding rock in collapsible formations and proposed that under non-uniform stress conditions, the wellbore in collapsible formations will exhibit an elliptical shape. [PERSON] [17] proposed a rapid and accurate method for evaluating casing ellipticity deformation. [PERSON] et al. [18] successfully obtained semi-analytical solutions for stress distribution at various interfaces of the composite system using the method of complex variable functions. [PERSON] [19] studied the initiation characteristics of cracks in elliptical wellbores. [PERSON] et al.