Nonlinear Analysis Of Tubing Buckling In Directional Wells

Flexible drilling-tubing has been frequently used in advanced directional petroleum wells, and the stability of the tubing is one of the key factors to be success in drilling engineering. It is required for us to understand the detailed buckling behavior of tubing in order to optimize the design of drilling assembles and to reduce the cost. Nowadays, theories and numerical methods are, however, far more perfect for the analysis of tubing buckling in both straight and curved wells. Therefore, there is an urgent need for more comprehensive researches in this field. Firstly, the governing differential equilibrium equations and their corresponding functional for tubing buckling in arbitrary straight wells are established. And equilibrium equations considering effects of tangent frictions are also presented. In the analysis, effects of gravity, torque and deviation angle are included. A finite element (FE) incremental weighted iteration method, which can speed up the convergence process, is proposed to solve the nonlinear eigenvalue problem of tubing buckling in straight wells. The method is different from existing ones adopting pre-assumed displacements. It is found that the high order terms in governing differential equilibrium equations must be retained in order to obtain the helical buckling behaviors. The influence of different boundary conditions on the buckling of tubing is also investigated. A method to determine critical loads of both lateral buckling and helical buckling by solving nonlinear eigenvalue problems is presented. The nonlinear quasi-static loading problem is solved by FE method together with Newton-Raphson method to obtain the entire buckling process of tubing in straight wells. The contact force per unit length and the bending-moment of the tubing are calculated. The influence of different boundary conditions on the buckling of tubing is studied. Similarly, a method to compute critical loads of both lateral buckling and helical buckling by soling quasi-static loading problem is also given. Thus, the definition of lateral buckling and helical buckling of tubing in straight wells is presented. Secondly, the governing differential equilibrium equations and their corresponding functional for tubing buckling in constant-curvature plane wells are derived, and the effect of gravity, well curvatures and the deviation angles at the top end of tubing is included in the analysis. Similar to the straight wells, the finite element incremental weighted iteration method is also utilized to solve the nonlinear eigenvalue problems of tubing buckling in curved wells, and the FE method together with Newton-Raphson method are utilized to solve the quasi-static loading problems of tubing in curved wells. The influences of gravity, well curvatures, deviation angles at the top end of the tubing and different boundary conditions on the buckling of tubing in curved wells are investigated. The entire buckling process of tubing is presented. A method to determine critical loads of lateral buckling and helical buckling by solving nonlinear eigenvalue problems as well as nonlinear quasi-static loading problems is proposed. Thus, the definition of lateral buckling and helical buckling of tubing in curved wells is also presented. A linearly variable curvature well is then analyzed by FE method with constant curvature beam element. The influence of the variable curvature to the buckling behavior of tubing is given. Finally, the newly developed differential quadrature (DQ) method is utilized to directly solve the governing differential equilibrium equations for obtaining tubing buckling behaviors in straight wells without and with tangential friction forces. The DQ results are compared well with the FE results for the cases without friction forces thus the program and the applicability of the DQ method are verified. The influence of tangent frictions to the buckling of tubing is given.