三维悬链线轨道设计的数值算法  

Numerical Algorithm for 3D Catenary Wellpath Design

作　　者：杨音 马睿思 

机构地区：[1]中国石油长城钻探工程有限公司钻井二公司,辽宁凌海121207 [2]长江大学石油工程学院,湖北荆州434023

出　　处：《中外能源》2014年第11期56-60,共5页Sino-Global Energy

摘　　要：有学者提出了考虑方位漂移的三维悬链线轨道设计问题,并建立了数学模型和数值求解的基本思路,为方位漂移轨道设计技术的应用提供了理论框架,但对求解数学模型的实际算法描述不甚清晰,有可能影响其在大位移井工程设计实践中的广泛应用。考虑方位漂移因素的设计约束方程组是一个具有3个独立未知数、多个隐含未知数的非线性方程组,需要使用数值迭代法才能求出其数值解。给出解析形式的垂深增量公式,利用约束方程组中的垂深方程,将3个独立未知数中的一个表示为其他未知数的函数,从而使设计约束方程组可以降维为二元非线性方程组,降低了数值求解的规模和难度。结合隐含未知数的递推计算策略,采用缩半网格法能可靠地求出降维后的设计约束方程组的数值解,特别适用于计算机编程实现。Some scholars have proposed design problem of 3D catennary wellpath considering azimuthal drift, and built basis thinking of mathematic model and numerical algorithm ,which may provide theoretical frame- work for the technology application of wellpath design with azimuthal drift.But the description on actual algorithm for solving mathematic model is not clear,which will have an impact on the wide application of it during the practice of engineering design on the extended reach wells.Design constraint equation set considering the azimuthal drift is a nonlinear one with three independent unknowns and several implicit unknowns ,whose numerical solution may be solved using numerical iteration method.Analytical formula of increment of true vertical depth is given ,and one of the three independent unknowns may represent a function of other unknowns using the true vertical depth equation in the constraint equation set.And then the design constraint equation set reduced to a nonlinear equation set with only two unknowns,which can make numerical solving simpler and easier.Together with recursive calculation of the implicit unknowns,numerical solution of the equation set with dimensionality reduction may he solved using zoom-half grid method,and it is especially available to computer programming realization.

关 键 词：三维悬链线 轨道设计 方位漂移 大位移井 设计约束方程组 数值求解 

分 类 号：TE22[石油与天然气工程—油气井工程]