# Eccentric Wear Mechanism and Centralizer Layout Design in 3D Curved Wellbores
## 3 Optimisation Design Method for the Arrangement of Centralisers  
The arrangement of centralisers is a critical aspect of sucker rod string design, with the primary objectives of reducing rod-tubing wear, improving system efficiency, and extending the service life of the equipment. Common design methods for sucker rod centralisers in oilfields are as follows: The sucker rod string is simplified as a slender, simply supported beam, with the suspension point and the upper end of the pump serving as two simple supports while ignoring the effects of rod string torsion and the three-dimensional wellbore. Axial loads and lateral forces on the sucker rod string are analysed. Based on the theory of elasticity, a buckling equation for the rod string is established to analyse its buckling behaviour under axial loads and lateral forces, determining the deformation curve of the rod string. Using the solution of the buckling equation, the contact points between the rod string and the tubing are calculated. These contact points typically occur in areas with significant lateral forces (such as curved or horizontal sections of the wellbore). Centralisers are then positioned at the contact points between the rod string and the tubing. The traditional design method for centralisers is simple and practical, making it suitable for vertical wells and some directional wells. However, this traditional method does not account for three-dimensional wellbore trajectories, rod string torque effects, or dynamic behaviour, resulting in limited applicability under complex well conditions. This article addresses the limitations of traditional centraliser design methods under complex well conditions and proposes a centraliser design theory and method based on a three-dimensional mechanical coupling mathematical model. This method comprehensively considers the dynamic behaviour of the sucker rod string, wellbore trajectory, and complex loading conditions, optimising the placement and spacing of centralisers to enhance system efficiency and reduce eccentric wear. The optimised design process for the centraliser proposed in this article is as follows:  
1. Collecting well conditions and design parameters: Inputting data such as wellbore trajectory, rod string parameters, and fluid column characteristics to provide a foundation for model calculations. 2. Establishing a three-dimensional mechanical coupling mathematical model: Taking into account the axial load, lateral forces, torque effects on the sucker rod string, and the three-dimensional curvature of the wellbore trajectory. 3. Calculating the stress state of the rod string: Using the model to calculate the axial load, lateral force distribution, and dynamic stress conditions of the rod string. 4. Analysing the buckling behaviour of the rod string: Studying the buckling forms of the rod string under different load conditions (e.g., two-dimensional buckling, three-dimensional helical buckling). 5. Determining the contact points between the rod string and the tubing: Calculating the positions of contact points between the rod string and the tubing based on the stress and buckling analysis results. 6. Optimising the placement of centralisers: Prioritising placing centralisers in areas with contact points and high lateral forces. 7. Dynamically adjusting the spacing of centraliser placement: Adjusting the spacing of centralisers dynamically based on the wellbore curvature and the stress distribution of the rod string, avoiding the limitations of fixed-spacing designs. 8. Validating the design: Checking whether the centraliser placement effectively reduces wear and buckling, ensuring the design meets the requirements of actual well conditions. (9) Adjusting model parameters and re-optimising: If the design does not meet the requirements, model parameters must be adjusted (e.g., rod string diameter, number of centralisers), and the placement re-optimised.