## 2 Numerical Simulation  
The simulator used in this study is called Wellscan v3.8 and it gives a physics-based representation of drill string vibrations. This shows how the drill bit and formation work together in a nonlinear way, including damping effects, and allows for real-time simulation of torque and rotational speed variations. The calibration of model parameters was based on empirical data from previous experimental works [48] and field data [49] so as to accurately represent down-hole conditions. The downscale model was based on the laboratory small-scale setup introduced by [48], which had a total length of 15 m. By applying a geometrical scaling factor of 1:30 for the total length and bit diameter [49], the simulation produced an upscaled well with a length of 450 m. Table 1 presents a detailed comparison of the key parameters used for both the upscale and downscale drill strings. This scaling allows for a realistic replication of the drill string's dynamics on a larger scale, while maintaining the proportional relationships between the components and forces involved. The bit diameter was equally scaled, with the upscale bit measuring 5.625 inches in diameter, while the downscale bit diameter was proportionally reduced to 0.20 inches. While geometric scaling principles for length and diameter were adhered to, certain operational parameters like RPM, torque, density, and static and dynamic friction did not strictly follow the 1:30 scaling factor. This slight deviation was quite necessary due to the inevitable physical limitations and practical constraints of the downscale setup. It was impossible to scale down these parameters in a linear manner because doing so would have resulted in certain values that would be beyond the realistic operational range of the downscale system and would, therefore, render it and the model inaccurate. The precise values for the RPM, torque, density, and friction coefficients were thus chosen independently for both setups so that the dynamic response of the upscale drill string under torsional loads could be accurately'modeled' by the downscale setup. Both strings were subjected to the same top RPM. The upscale string was subjected to torques of 500 kgfm, 1500 kgfm, and 4500 kgfm at distinct phases, reflecting the forces typically experienced during actual drilling operations. The downscale string, however, experienced significantly lower torques, scaled down to 0.01 kgfm, 0.03 kgfm and 0.09 kgfm.  
To carry out the comparison, the drilling dynamics module within the simulator was utilized to evaluate the torsional vibration signatures for both the upscale and downscale drill strings. The simulator operates using two primary torque and drag models: the soft-string model and the stiff-string model. The soft-string model, as the name suggests, assumes continuous contact with the wellbore, simplifying the analysis by neglecting the stiffness and bending moment effects. However, the stiff-string model (Abis) provides a more accurate representation of the drill string behavior accounting for stiffness and is particularly useful in wells with complex trajectories. The model applied the Abis stiff string model due to its capability to deliver a more realistic assessment of downhole configurations, making it ideal for examining the torsional dynamics in tortuous well paths.