Numerical method for analyzing the nonlinear dynamic response of tubing running in a cased borehole

Abstract

With the development of deeper and longer wells, the environment of the borehole becomes much more complex, leading to a higher risk of tubing failure. To accurately describe the contact force between the tubing and the borehole, a new method is developed to analyze the non-linear dynamic response of the tubing under complex loading condition. Based on the finite element method, the equilibrium equation of tubing segment is established, where the tubing is simulated by three-dimensional elastic beam elements and the contact between the tubing and borehole is represented by two no-linear springs. The element stiffness matrix was assembled under nodal coordinate system, and the modified square root algorithm was adopted to solve the large-scale banded systems of linear equations. Then, the contact force and position were solved by multi-step iterative method, and thus a new numerical method for analyzing the non-linear dynamic response of tubing was developed. Results show that, the new method could greatly improve the counting rate for analyzing the large deformation of tubing, and also could accelerate the convergence of the non-linear contact problem. This makes it describe well the no-linear dynamic behavior of the tubing, which is helpful for the optimization design and security evaluation of the tubular assembled in complex conditions. This method has been widely applied on the high angle deviated wells in the Shengli oilfields.