摘要
结合定向井井眼轨迹的三维空间特征和超细长杆柱在井眼中的双重非线性(接触非线性和几何非线性)特征,同时考虑Ray-leigh阻尼及液体摩擦影响,建立了抽油杆柱三维动态有限元方程。利用Newmark法对抽油杆柱运动过程进行时间域离散,采用结点迭代的循环求解方法对三维动态有限元方程进行了数值求解,并用直接约束法对杆/管接触问题进行了处理,得到了抽油杆柱每一结点6个自由度方向的变形和载荷。以实测井底泵功图为边界条件,求出了抽油杆柱与油管的动态接触位置,并获得了地面示功图,将预测结果与实测地面示功图进行了对比。结果表明,结点迭代法可以避免大型矩阵的数值计算问题,与Newmark法相结合,能够较准确地求解出井下抽油杆柱的三维受力及运动状态。
Integrated with 3D features of the wellbore trajectory in directional wells and double nonlinear（contact nonlinear and geometric nonlinear） features of super-thin rod strings in wellbores,a 3D dynamic finite element equation of sucker rod strings was established by taking effects of the Rayleigh damping and fluid friction into account.With the time-domain straggling of the kinetic process for sucker rod strings by the Newmark method,this 3D dynamic finite element equation was circularly solved using the crunode iterative method,therefore,the deformation and load of sucker rod strings in six variance orientations for each node could be obtained through treating with the dynamic contact between tube and rod by means of a direct constraint procedure.Dynamic contact positions between tube and rod were located according to boundary conditions of the measured downhole pumping dynamometer card and then the surface dynamometer card of sucker rod strings could be obtained by the crunode iterative method.The comparison between the predicted and the measured results showed that integrated with the Newmark method,this crunode iterative method could avoid the numerical calculation of large-scale matrix,and could more accurately decipher 3D stress and dynamic states of downhole sucker rod strings.
出处
《石油学报》
EI
CAS
CSCD
北大核心
2010年第6期1018-1023,共6页
Acta Petrolei Sinica
基金
国家自然科学基金项目(No.50674065)资助
关键词
定向井
抽油杆柱
有限元
双重非线性
结点迭代法
directional well
sucker rod string
finite element
double nonlinear
crunode iterative method
