恒工具面角三维水平井轨道设计模型及求解算法

3D horizontal well wellpath model based on constant tool face angle and its algorithm

基于恒工具面角模型的水平井轨道设计缺乏完整性和适用性,且求解过程相当复杂。文中提出一种基于恒工具面角的轨道设计模型及求解算法。通过坐标旋转,将水平井轨道类型转换为2种基本类型,针对"直—增—扭—稳—增—平"六段制典型轨道,从其基本公式和A靶点约束方程出发,建立了初始方位角模型。大量数据计算结果显示,其函数是求解区间上的一元非线性单调函数,可用二分法、黄金分割法及Fibonacci法等一维搜索法计算,并给出了求解算法,具有直观简明、数值计算稳定可靠、无需设初始值等优点。根据初始方位角得到造斜率和工具面角,进而计算出其他全部轨道参数,从而完成三维水平井轨道设计。钻井实例表明,轨道模型、设计方法及算法是正确、合理和可行的,同时也验证了恒工具面角设计模型的优越性。

At present, the planning of horizontal well wellpath based on constant tool face is lack of integrity and applicability, and the solving process is quite complicated. A wellpath planning model and algorithm are proposed based on constant tool face. Horizontal well wellpath types are converted to two basic types by coordinate rotation. Aiming at the "straight-increase-twist-stabilize-increase-flat" six-stage wellpath, initial azimuth angle model was established based on the basic equations and the constraint equations of the A target. The large amount data test results show that the function is a nonlinear monotone function in the search interval, which can be solved with one-dimensional search method such as dichotomy, the golden section and Fibonacci method. This algorithm has such advantages as intuitive, concise, stable and reliable, no need to set initial values. According to the initial azimuth angle, the borehole curvature and the tool face angle are obtained, and then all the wellpath parameters are calculated to complete the 3 D horizontal well wellpath planning. The application of this method to the planning of horizontal well wellpath is applied to the drilling practice. The drilling examples show that the wellpath model, design method and algorithm are correct, reasonable and feasible, and verified the superiority of the constant face model.