抛物线型井眼轨道的数学模型及其设计方法

Mathematical model and design methods of parabola well paths.

井眼轨道设计是实现定向钻井的首要环节。下部钻柱比较符合抛物线的力学模型,所钻出的井眼轨迹更接近于抛物线,因此将井眼轨道设计成抛物线具有理论依据。抛物线剖面设计的实质是确定抛物线井段的形状和位置,抛物线的特征参数P决定了其形状,而抛物线井段的起至井斜角或后续稳斜井段的段长等参数决定了抛物线井段在井身剖面中的位置。系统地阐述了抛物线轨道的力学模型和数学模型,分析了抛物线剖面的特征参数和设计条件,提出了2种抛物线剖面的设计方法———迭代法和直接法。在相同的条件下,这2种方法的设计结果是相同的,可以相互验证。但是,直接法不需要进行迭代计算,设计条件具有较好的可操作性,便于推广应用。通过对抛物线剖面的优化设计可以降低摩擦阻力和摩阻力矩,有利于减少钻柱和套管的磨损;可以改善钻柱的受力状况,减轻钻柱的疲劳破坏、减少产生键槽的几率;可以施加高钻压连续钻进,有利于提高机械钻速。

Well-path planning is the prerequisite for operators to drill directional or horizontal wells successfully.The deformation of a bottom drilling string accords with the mechanics model of parabola,and the drilled wellbore trajectory almost approximates to parabola,thus it is reasonable to plan well paths using parabola model in theory.The essential of planning a parabola well path was to determine the shape and position of the parabola section.The characteristic parameter of a parabola,P,describes its shape,and the parameters,such as starting inclination,ending inclination,length of the succeeding hold-up section,locate the position of the parabola section in the well path profile.The author systematically discussed the mechanical and mathematical models of a parabola well path,analyzed the characteristic parameters and known data of a parabola profile,and presented two methods for planning the parabola profile(iterative calculation and explicit solution).With the same requirements,the two methods educed the same planned results and certify each other.The method of explicit solution,avoiding a trial-and-error procedure and iterative calculations,provided excellent maneuverability of planning requirements,and it was convenient for oil field application.Optimally planning parabola profiles could reduce the drag and torque of a pipe string in favor of decreasing the wear and tear quantity of drilling string and casing,improve the status of the forces applied on them,lighten their fatigue failure and reduce the probability of creating key ways.Accordingly,operators could apply higher WOB and drill continuously,which was propitious to increasing penetration rate.