Stability Analysis of Drill Strings with Initial Curvature in a Fluid Flow under Environmental Uncertainty

The paper explores the nonlinear dynamics of drill strings under stochastic factors and external influences by providing its comprehensive analysis. These studies are motivated by the need to improve the safety and efficiency of drilling operations in complicated conditions. The authors model the dynamics of drill strings from the perspective of the randomness of the processes involved, enabling a broader range of operational modes for drilling equipment to be considered, as well as enhancing the accuracy and efficiency of optimal decision-making. The nonlinear dynamics of the drill string are examined under the influence of random factors and environmental conditions. The mathematical model of the drill string describes its planar vibrations accounting for the initial curvature of the string, external loads, fluid flow around the string, and frictional forces against the wellbore walls. The randomness of the effects is taken into account through the friction coefficient. Stochastic terms derived using the prior probability distribution, which allows the application of Shannon’s maximum entropy principle, are employed in the study. A numerical experiment is conducted to identify instability zones of the drill string motion. The study relies on the Galerkin method and partial discretization method. The influence of random factors on the drill string stability is revealed.