Abstract:

The problem of multidirectional contact of drill string with borehole wall is usually studied by using penalty function method, gap-element method, formal stiffness method and loosing constraint method. But these methods have slow calculation speed and are difficult to meet the requirements of engineering application. A new solution for nonlinear finite element equations of multidirectional contact of drill string with wall of borehole was proposed by establishing three-dimensional finite element model of drill string in the curved well bore and definite condition of the contact between drill string and borehole wall on the basis of cellular automata. This solution method is suitable for solving the nonlinear contact problem of drill string in the three-dimensional curved well bore and has the advantages of simple programming and convergence speed. It can be used to solve the complex boundary conditions of collision in three-dimensional curved borehole.

Key words: three-dimensional curved well bore, nonlinear problem, cellular automata, nonlinear equation, drill string mechanics, finite element method, solution method

摘要：

目前研究钻柱与井壁多向接触问题普遍采用罚函数法、间隙元法、形式刚度法和放松约束法等,其计算速度慢,难以满足工程应用要求。通过建立三维弯曲井眼钻柱有限元模型和钻柱与井壁接触碰撞的定解条件,利用元胞自动机的基本理论,提出了一种基于元胞自动机的钻柱多向接触非线性有限元方程的求解方法。该方法具有编程简单、收敛速度快等优点,能够较好地解决钻柱在三维弯曲井眼中与井壁接触碰撞的复杂边界条件问题,适用于三维弯曲井眼钻柱接触非线性问题的求解。

关键词: 三维弯曲井眼, 非线性问题, 元胞自动机, 非线性方程, 钻柱力学, 有限元法, 求解方法