Calculation of spectral sets of design parameters for three-section circular arc trajectory
To solve the"cut-and-trial"problem of design parameter input in the wellbore trajectory design,numerical algorithms were developed for the calculation of design parameter spectral sets.Based on the bisection method,this study provides an algo-rithm in the overall allowable range of two design parameters and another in the allowable range of one design parameter when the other is set.These algorithms can effectively calculate the spectrum set boundaries,thus plotting the graphs of above spectral sets.The spectrum set structure theorem is proved as follows:the three-section design parameter spectral set is composed of a 2D bounded connected closed set or the union of several unconnected 2D bounded connected closed sets.Based on the results of nu-merical examples,it is indicated that the proposed algorithms can solve the boundaries of spectrum sets in various cases of being connected and disconnected.Therefore,the computation algorithm for spectral sets is highly valuable in wellbore trajectory de-sign software,which can provide users with the visualized numerical ranges for design parameters,thus improving design effi-ciency.