Numerical Integral Calculation in Borehole Trajectory Model

In order to improve calculation speed of the definite integrals in the drilling design software, the basic formula of the borehole trajectory model and the integral parameter conversion were adopted. The calculation of seven trigonometric and one logarithmic functions was reduced to that of three trigonometric and one logarithmic functions required by the integrand of the definite integral in the north and east coordinates by the constant tool face method. The trigonometric functions in the integrand of the definite integral with a horizontal projection length by the space arc method were simplified, so as to improve the calculation speed of the definite integral. Using the variable step size Simpson numerical integration formula to calculate the above two kinds of definite integrals, the calculation accuracy can be controlled to arbitrary precision. The calculation shows that the new algorithm in this paper not only improves the calculation speed but also has the same calculation accuracy as the public data. The algorithm given in this paper is further improves and refines of the borehole trajectory calculation and can be applied in the software development of drilling.