Open AccessResearch on Well Trajectory Deduction Method Based on Pythagorean-Hodograph Quintic Space Curves
Author(s) -
Yufei Li,
Yinping Cao,
Yuxue Liu,
Mingfei Li,
Yihua Dou,
Jiantao Zhang,
Lin Zhang
Publication year - 2019
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/688/3/033068
Subject(s) - azimuth , spline interpolation , curvature , interpolation (computer graphics) , tangent , trajectory , mathematics , mathematical analysis , geometry , point (geometry) , quintic function , curve fitting , hodograph , computer science , physics , nonlinear system , astronomy , quantum mechanics , animation , statistics , computer graphics (images) , bilinear interpolation
Considering the influence of key parameters such as bore angle, azimuth and sounding of wellbore, based on the spatial five-time PH curve with continuous unit tangent and directional curvature, no need for iteration, using Bessel polynomial interpolation method, optimization the spatial model and the curve description can accurately deduct the spatial parameters of the fifth point according to the determined four points of the space, and then establish the wellbore trajectory analytical equation to generate the well trajectory curve. Taking a directional well as an example, the wellbore trajectories of the wells from 403.9 meters to 976 meters were fitted by PH, cubic spline and linear interpolation method respectively, and compared with the real measuring points. The results show that the wells fitted by PH method, the differences of the bevel angle and the measured point, the azimuth angle and the measured point are 0.910° and 5.7°. The differences of the cubic spline and the measured point, the straight line method and the measured point are 4.240°, 5.86° and 6.54°, 9.09°. For the PH method, the trajectory inclination and azimuth differences are the smallest, which are 3.51% and 3.17%.