三维定向井轨道设计新方法─恒装置角法

A new approach to 3D direction well track design---the constant tool surface angle method

王立波 鲁港

WANG Libo LU Gang

中国石油长城钻探工程公司第二钻井分公司，辽宁盘锦　124010 辽河油田公司勘探开发研究院，辽宁盘锦　124010

Drilling Company under CNPC Greatwall Drilling Company, Panjin 124010, China Research Institute of Petroleum Exploration and Development, Liaohe Oilfield Company, Panjin 124010, China

由于在恒装置角曲线井眼轨道的坐标增量计算中使用了定积分，致使相应的井眼轨道设计问题的求解非常困难，不仅计算时间长，且算法收敛性差。在假设弯曲井段为恒装置角曲线条件下，建立了新的三维定向井和侧钻井井眼轨道设计数学模型；使用幂级数展开方法计算井段坐标增量公式中的定积分，将井眼轨道设计模型中的多元非线性方程组求解问题降维转化为二元非线性优化问题，极大地降低了数值计算的复杂度。使用数值优化算法对恒装置角井眼轨道设计问题进行求解，不仅减少了计算时间，增强了算法稳定性，而且具有全局收敛性质。实际算例表明，新方法能够快速、有效地求解恒装置角型井眼轨道设计问题，所使用的幂级数展开方法适用于解决恒装置角井眼轨道计算的一系列问题，是一种有效的数学简化方法。

As definite integral is used for coordinate increment calculation of well track with constant tool face angle, it gets more difficult to find the solution to the problem of corresponding well track design. For example, the calculation takes long time and the convergence of the calculation method gets poor. Supposing the curved portion is a constant tool face angle curve, new mathematical models of well track design of 3D directional wells and sidetracked holes are established. By using the power series expanding method to calculate the definite integral, the solution to multivariate nonlinear equations is dimensionally transformed into binary nonlinear optimization. As a result, the numerical calculation gets less complicated remarkably. By using the numerical optimization method, the calculation saves more time, the stability of the method gets more stabilized, and the convergence is improved as a whole. A great number of examples show that the new calculating method can be used to find the solution to the design problem of well track with constant tool surface angle more rapidly and effectively. The power series expanding method, a very effective mathematical simplification method, is proved to be applicable to a series of calculating problems of well track with constant tool face angle.