The Spectral Theory for Parameters Design of Directional Well Trajectory

In order to solve the difficulty in designing 3D well trajectory with given parameters,a reliable method to get solution by trajectory design equation was studied.Based on the fact that there exists a definite set mapping between known design parameters and the solutions of trajectory design equations,the article proposed a new concept of known design parameters spectra set,the spectra set and new concept of drawing by computer graphics theory were put forward.When the trajectory design equations have analytic solution,the inequality expression of the spectra set can be directly obtained by using the constraint condition of analytic solution;when there isn’t an analytic solution,the approximation of the spectra set is given by pseudo-analytic solution based on characteristic real root of polynomial.A complete visualized spectrogram can be constructed with less than 3 spectra dimensions.When there are more than 3 spectra dimensions,high dimensional data visualization approach is required to construct spectrogram.Software implementation and practical application indicated that spectra theory can eliminate the blindness of known design parameters and thus greatly enhance designing efficiency.