The critical factors that affect bottomhole stick–slip vibrations during vertical drilling operations are thoroughly investigated and analyzed in this research. Influential factors, such as rotation speed, weight on bit (WOB), bottom hole assembly (BHA) configuration, and formation properties, were studied in order to understand their part in the stick–slip phenomena. The analysis is based on a thorough review of previous research conducted on stick–slip drilling vibrations. A mathematical model was created that not only explains axial vibrations but also includes the torsional vibrations present in stick–slip occurrences, which helps with understanding the stick–slip phenomena better. This model can be used as an analytical tool to predict and evaluate the behavior of drilling systems under various operational circumstances. Furthermore, two drilling tests using a WellScan simulator were performed to validate the research findings and assess mitigation techniques’ viability. These test scenarios reflect the stick–slip vibration-producing situations, allowing us to test mitigation strategies. The finding of this study shows the effectiveness of two tactics for reducing stick–slip vibrations. First was the reduction of WOB, which successfully lowered the occurrence of stick–slip vibrations. The second was the increase in the rotation speed, which helped to control the stick–slip problem and increased the drilling speed. This study explains the complex dynamics of stick–slip vibrations during vertical drilling and offers practical, tried-and-true methods for reducing their adverse effects on drilling operations.

Torsional vibrations pose a serious challenge in drilling operations and can lead to effects such as stick-slip phenomena, tool wear, and reduced drilling efficiency. While previous research has been conducted on torsional vibrations, there is a notable gap in comparative studies that assess the scalability of downscale models to real-world drilling conditions. This study fills this gap by systematically comparing torsional vibrations in downscale and upscale drill strings under different torque conditions at three different depths, shedding light on scaling effects in drilling vibrations. Numerical simulation was carried out taking into account non-linear interactions, damping effects, and torque variations. The laboratory set-up was for a well length of 15 m and was geometrically scaled to represent an upscale well of 450 m. Certain operational parameters such as rotation speed, torque, density, and friction coefficients were modified to keep realistic dynamic behavior, and all models were run at an identical speed of rotation to enforce consistency. The results show that both the upscale and downscale models exhibited stick-slip behavior, but differences in vibration intensity and stabilization trends point out how scaling affects torsional dynamics. Notably, the upscale bit first faced higher torsional oscillation than the set rotation speed after overcoming stick-slip before stabilizing, whereas the downscale bit went through prolonged stick-slip instability before synchronization. This study enhances the understanding of scaling effects in torsional drilling vibrations, offering a foundation for optimizing experimental setups and improving predictive modeling in drilling operations.