三维井孔轴线的几何描述与套管摩阻的数值模拟

GEOMETRIC DESCRIPTION OF BOREHOLE CENTERLINE IN THREE-DIMENSIONAL DIGITAL SIMULATION OF DRAG IN CASING RUNNING

为了用测斜数据描述井孔轴线的几何特性,以便于对下套管作业中的摩擦阻力进行预测,以微分几何理论为基础,建立了井孔轴线上的井斜角、方位角与自然坐标系各单位矢量的几何关系,得到了用井斜角和方位角的变化率表示的曲率和扭率,并提出了对测斜数据进行插值和光顺化处理的方法。另一方面,考察了井孔内具有抗弯刚度套管微元的平衡状态,建立了套管微元所应满足的控制微分方程及其差分格式。通过对控制方程的求解可以得到套管上各点的约束反力和摩擦阻力。

In order to describe the geometric characteristics of the centerline of borehole with directional survey data and predict the drag of casing in running, the relations among the unit base vectors in natural curvilinear coordinates and the deviation and azimuth angles along the borehole centerline are established. Then the total flexural curvature and the natural tortuosity of the centerline can be expressed with the change rates of deviation and azimuth angles. Some technical treatments are put forward to smoothen and interpolate the directional survey data along the centerline. On the other hand, the equilibrium state of a free-isolated stiff casing element is examined. The governing differential equations of the casing in running are formulated and solved using finite difference method. The constrained reactions and drag along the casing are obtained.