Uncertainty analysis method for the output force vector control on the rib of the orienter in coiled tubing drilling

This work addresses the uncertainty associated with downhole parameters in coiled tubing drilling and proposes a new method for controlling the output force vector on the ribs of the orienter, enabling more precise control of the actual wellbore trajectory. Based on the principles of longitudinal and transverse bending beams, we construct a 3D mechanical model of the Bottom Hole Assembly (BHA) used in coiled tubing drilling. We then analyze the spatial geometry relating the force direction on the orienter's rib and the tool face angle, establishing a comprehensive steering resultant force vector model. Applying the principle of minimum energy, we explore traditional control schemes for the output force on each rib and reveal its intricate variation patterns. We conduct a statistical analysis to investigate the randomness distribution state and sensitivity of the experimental parameters, allowing us to derive the probability density and cumulative probability functions for the twodimensional random variables linked to the output force on the ribs. Confidence interval models are constructed to predict the output forces with a predetermined level of certainty. Finally, we experimentally verify the proposed uncertainty control method in real-world coiled tubing drilling. Our results show that the randomness of weight on bit (WOB) and the tool face angle of rib 1# are the main factors influencing the uncertainty of the output force control. When the output forces vector on the ribs exceeds the uncertainty confidence interval, the actual wellbore trajectory significantly deviates from the designed one. Conversely, when the output forces vector falls within the confidence interval, the error between the actual and designed wellbore trajectories is significantly smaller. This validates the rationality and effectiveness of the proposed uncertainty analysis method, providing valuable guidance for implementing wellbore trajectory control in coiled tubing drilling.