Modeling lateral vibration of bottom hole assembly using Cosserat theory and laboratory experiment verification

Lateral vibrations are a complex form of vibrations that may occur while drilling. The understanding of their motion has been relatively comprehensive; however, further studies on their internal mechanisms are required. Existing dynamics models of the drill string are difficult to apply owing to the large number of assumptions and simplifications. The curved elastic rod described by the Cosserat theory can be used as an ideal model to study the motion and mechanical characteristics of drill string because of its large deformation and extreme slender-ness. On the basis of existing research, this study proposes a comprehensive drill string dynamics model based on the Cosserat theory. The model is applied to study the lateral vibrations of a bottom hole assembly (BHA), considering factors such as the mass eccentricity, material viscosity, and weight-on-bit (WOB). The established model and experimental device were used to conduct simulations of specific schemes and examine the lateral vibrations of the BHA under the influence of the deviation angle, rotational speed, WOB, and friction coefficient. The accuracy of the established model and its generality were verified by comparing the data from theoretical calculations and experimental simulations. The results demonstrate that the lateral vibrations of the BHA in a nonvertical well indicate the reciprocating oscillation located at the lower right side of the wellbore. The amplitude of the lateral vibration can be increased by reducing the deviation angle or increasing the rotational speed and the friction coefficient. In a vertical well, the BHA exhibits forward whirl, irregular motion, and backward whirl as the rotational speed and friction coefficient increase. Increasing the WOB has insignificant effect on the lateral vibrations of the BHA at the maximum WOB value achieved by the experimental device. However, further increasing the WOB in the theoretical calculation could cause the buckling and backward whirl of the BHA in a vertical well.