Drillstring vibration analysis using differential quadrature method
Drillstring vibration analysis using differential quadrature method
复制标题
DOI：
10.1016/j.petrol.2009.11.016
复制
发表时间：
2010-02
影响因子：
--
通讯作者：
H. Hakimi;S. Moradi
中科院分区：
文献类型：
--
作者：
H. Hakimi;S. Moradi
在这项研究中，应用微分求积法(DQM)分析了近直井中钻柱的振动。首先，进行非线性静力分析，找出管柱在井壁上的有效长度。光束曲率的精确形式被用来表示弦。为了模拟钻柱不同部分与井壁之间的接触，通过在其长度上放置一系列弹簧来模拟地层。然后将DQM方法应用于钻柱段的非线性微分方程组以及确定边界和界面边界条件的微分方程组。非线性方程组的求解采用牛顿-拉夫森算法。然后对钻柱进行自由振动分析，确定钻柱的固有频率。利用静力分析得到的有效长度，对钻柱进行自由振动分析，得到钻柱的横向固有频率，而用钻柱的全长计算其轴向和扭转固有频率。一系列算例的数值结果证实了该方法在处理钻柱振动问题上的有效性和准确性。
In this study, the differential quadrature method (DQM) is applied to analyze the drillstring vibrations in a near vertical hole. First, a nonlinear static analysis is performed to find the effective length of the string where it rests on the borehole wall. The exact form of the beam curvature is used to formulate the string. To model the contact between different parts of the drillstring and the borehole wall, the formation is modeled by a series of springs placed through its length. Then the DQM is applied to the nonlinear differential equations of drillstring sections and those defining the edge and interface boundary conditions. The Newton–Raphson algorithm is used to solve the system of nonlinear equations. Next a free vibration analysis is carried out to determine the natural frequencies of the drillstring. Using effective length derived from static analysis, free vibration analysis is performed to find the lateral natural frequencies of the drillstring, while the full length of the string is used to compute its axial and torsional natural frequencies. The numerical results obtained from a series of case studies confirm the efficiency and accuracy of the method in dealing with drillstring vibration problems.