Drilling is one of the costliest and risky activities in oil and gas industry due to complexity of interactions with downhole formation. Under such conditions, the uncertainty of drillstring behavior increases, and hence, it becomes difficult to predict the causes, occurrences, and types of failures. Lateral and torsional vibrations often cause failure of bottom hole assembly (BHA), drillstring failure, drill bit, and wall borehole damages. In this work, a model is presented to determine the impact of lateral and torsional vibrations on a drillstring during the drilling operation. The model aims to mimic real drillstring behavior inside a wellbore with regards to its dynamic movements due to multiple real situations such as eccentricity of collars, drill pipe sections, and stick-slip phenomena occurring due to the interaction of the bit and the drillstring with the well formation. The work aims to develop a basis for determining critical operating speeds and design parameters to provide safe drilling procedures and reduce drillstring fatigue failure. Lagrangian approach is used in this study to attain drillstring lateral and torsional vibration coupling equations. The nonlinear equations are solved numerically to obtain the response of the system. In this work, we also present a brief description of an in-house constructed experimental setup. The setup has the capability to imitate the downhole lateral and torsional vibration modes. Parameters from the experimental investigations are incorporated for validation of the mathematical models and for prediction of the drillstring fatigue life. Such investigations are essential for oil/gas industries as they provide solutions as well as recommendations about operating speed, lateral and torsional amplitudes measurements and corrections, and the conditions for avoiding occurrence of natural frequency(ies) of the system.

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