Mendil, ChafiaaKidouche, MadjidDoghmane, Mohamed Zinelabidine2021-01-252021-01-252020https://doi.org/10.1007/978-3-030-63846-7_24https://link.springer.com/chapter/10.1007/978-3-030-63846-7_24https://dspace.univ-boumerdes.dz/handle/123456789/6216Modeling of vibrations dynamic during drilling hydrocarbons wells is one of the main challenge facing drillers. Indeed, in order to design controllers that can eliminate or at least minimize such phenomenon, it is mandatory to know with some degrees of certain how the bit faces these vibrations. In literature, there are many models that have been designed to represent the drill string behaviour under torsional vibrations since they are the most harmful ones. It has been proven that stick-slip phase generated by the torsional vibrations is the generator of other types of phenomena (i.e. Bit bounce and whirling). The main objective of this study is to review all the models and compare them in order to set the advantages and drawback of each of them. Moreover, this comparison has allowed us to determine which model to use for designing robust controllers for mitigating the torsional vibrations, thus, diminish all of its effects and the other type of vibrations. The obtained results have supported and demonstrated the conclusive comparative studyenModelingTorsional vibrationsStick-Slip phenomenonComparative studyOther