# Multi-Objective Optimization of Drilling Trajectory Considering Buckling Risk
## 6 Conclusions  
In directional drilling, unlike vertical drilling, curved and horizontal sections exist in the drilling trajectory, and this requires further consideration when designing the drilling trajectory. Typically, buckling is caused by drag and torque induced on the drilling pipe. A lock-up phenomenon can occur as a result of such buckling, which can cause accidents that impede drilling. In this study, multi-objective optimization was performed to reduce the risk of buckling in the drilling trajectory and its length. The main conclusions of this study are as follows:  
* To calculate the load on the drilling pipe, the torque generated from the drill bit and the drag generated between the borehole wall and drilling pipe were considered during tripping of the drilling pipe.
* The objective function used for optimization was defined in terms of the length and load of the drilling trajectory, and to consider the risk of buckling, optimization was performed by calculating the load of the drilling pipe.
* The risk of buckling was determined using the critical buckling load and helical buckling load values in each section.
* There was a possibility of buckling when designing with the existing method, but this was avoided when designing a drilling orbit with the method presented here.
* This method is economical because it reduces the length of drilling trajectory compared to the existing method and the time and cost of drilling.
* By adjusting the weight in the objective function, the designer can design the drilling trajectory by giving more weight to the length of the drilling trajectory or load on the drilling pipe.
* Although the drilling trajectory is often designed using the empirical method, a more effective drilling trajectory can be designed using this method.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Application B (Theoretical Well)** & & \\  & **Existing** & **New** & **New/Existing Ratio** \\ \hline Total measured depth (ft) & 12,829 & 11,739 & 0.915 \\ Drag force (lbf) & 53,501 & 52,093 & 0.974 \\ Torque (lbf.ft) & 10,498 & 9395 & 0.895 \\ Horizontal section & No buckling & No buckling & - \\ Second build-up section & No buckling & No buckling & - \\ Second hold section & No buckling & No buckling & - \\ First drop off section & No buckling & No buckling & - \\ First hold section & Sinusoidal buckling & No buckling & - \\ First build-up section & No buckling & No buckling & - \\ \hline \hline \end{tabular}
\end{table}
Table 14: Comparison of existing design and new design for application B.  
* However, for the method presented in this paper, only the soil character was used to generate coefficient of friction. Further research is needed, as it is not free to set avoidance sections such as groundwater.  
Conceptualization, J.J. and S.-c.S.; methodology, J.J. and J.B.; data curation and software, C.L.; formal analysis, J.J. and B.-C.P.; supervision, S.-c.S. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Korea Institute for Advancement of Technology (KIAT) grant funded by the Korea Government (MOTIE) (no. P0001968, Competency Development Program for Industry Specialists).  
Not applicable.  
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.  
The authors declare no conflict of interest.