The drilling operations use a rotary slender structure introduced inside the drill well. The nonlinear dynamics with bit-bouncing, stick-slip phenomena, and pulsating mud flow may yield the premature wear and damage of drilling equipment and should be investigated to improve the reliability of drilling operations. This work presents the beam element formulation to model the drilling nonlinear dynamics. The well-pipe contacts are modeled by the radial elastic stops. The fluid–structure interactions are considered. The first step consists in computing the static position of structure to determine the contact points and calculate the preloaded state. These results are then considered to calculate the Campbell diagram. The potentially unstable speeds of rotation are identified. The results show that the modal coupling phenomena strongly occur for the three-dimensional well. The well-pipe contacts modify the modes in rotation, and the rotating fluid induces a strong deviation of the flexural mode curves.

In rotary drilling, a drillstring is an assembly of slender pipes. It is used to transmit the driving torque of a motor at the drilling surface to the drill bit at the bottom hole of a 3D well. Numerous vibratory phenomena are induced during the drilling: whirling, stick-slip, bit-bouncing, lateral instability, inducing in particular reduction of the rate of penetration and mean time between failures. For the rotordynamics prediction of such a structure, the drillpipes are modelled with Timoshenko beam elements, containing 12 degrees of freedom, equipped with distributed radial stop-ends. The rotary motion is assumed to have a constant speed of rotation imposed at the top of the drillstring. The drilling mud is taken into account by using a fluid-structure interaction model. The numerical simulations concern a real 3D-borehole and a parametric analysis is carried out for determining the role of the mud density and of the flows rate on the drillstring dynamics. It is shown that increasing the flow rate and densifying the drilling fluid reduce the fluid damping effect that increases drillstring lateral vibrations.

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