Analytical method of design of three-dimensional double-target-point wellbore trajectory

Five sections design of three-dimensional double-target-point wellbore trajectory is complex and need a numerical iterative method for solving nonlinear simultaneous equations, and the method has the disadvantages of dependence on initial conditions,a lower convergence rate and diverging easily, and has a approximate solution. A new method can transform nonlinear simultaneous equations into two characteristic polynomial of degree 4 by elimination, which solution is a analytical solution of the nonlinear simultaneous equations. The solution algorithm is given in this paper, and the characteristic polynomial is solvable depends on whether there are less than 1 positive real root. In the case of solvability, the solution can be directly obtained by positive real root of characteristic polynomial and analytical formula of the known design parameters. The method is faster than the numerical iterative calculation method, the computational results accurate. Elimination skill has important significance for other wellbore trajectory design.