Probabilistic analysis of drill string under uncertain conditions for flow velocity and axial compressive load

Abstract

In this paper, the probabilistic stability of drill string under stochastic parameters in time domain is investigated. The collar part of the drill string is modeled as a nonlinear elastic isotropic rotating rod exposed to internal and external fluid flow, axial compressive load, and torque. The stochastic parameters are the internal flow velocity and axial compressive load, which are assumed as stationary random processes with Gaussian distribution. The governing equations are derived by means of Novozhilov's nonlinear theory of elasticity with the implementation of Hamilton's principle. Afterward, the stochastic averaging method and linearization theory are used to examine the system stability. As a result, the effects of power spectral density of random functions, the angular velocity of rotating rod, flow velocity, axial compressive load magnitude and damping coefficients on the stability regions of the system are studied. The results show that increasing the power spectral density and angular velocity decrease the critical mean flow velocities. Moreover, the damping coefficient of the external drilling fluid has a significant effect on the stability region, and the stochastic compressive load and stochastic flow velocity change the stable zone.