NUMERICAL METHODS OF CALCULATION MINIMUM-CURVATURE
Lu Gang
Abstract
Lu Gang
Abstract
The minimum-curvature method is one of the most basic methods in the inclinometry calculation and the wellpath design, it has been widely used in the trajectory calculation. In this paper, the computer numerical calculation using minimum-curvature method has been researched, the azimuth definition and its ambiguity were elaborated when the deviation angle was zero. Secondly, the process of coordinate incremental calculation and the method to reduce the number of trigonometric calculation were analyzed. In the situation of small bending angle, the coordinate computation using high accuracy approximate formula replaced the direct calculation which was easily lead to division overflow, which enhanced the stability and the computational accuracy of computational process. Thirdly, in terms of the calculation to the length of horizontal projection, the Gauss numerical integration method has been used. Besides, the proposed methods can be used to the computer software development in the trajectory calculation using minimum-curvature method.
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The minimum-curvature method is one of the most basic methods in the inclinometry calculation and the wellpath design, it has been widely used in the trajectory calculation. In this paper, the computer numerical calculation using minimum-curvature method has been researched, the azimuth definition and its ambiguity were elaborated when the deviation angle was zero. Secondly, the process of coordinate incremental calculation and the method to reduce the number of trigonometric calculation were analyzed. In the situation of small bending angle, the coordinate computation using high accuracy approximate formula replaced the direct calculation which was easily lead to division overflow, which enhanced the stability and the computational accuracy of computational process. Thirdly, in terms of the calculation to the length of horizontal projection, the Gauss numerical integration method has been used. Besides, the proposed methods can be used to the computer software development in the trajectory calculation using minimum-curvature method.
Key concepts: Curvature, Computation, Trigonometric functions, Azimuth, Mathematics, Process (computing), Algorithm, Trigonometry