Application of the lumped-parameter method for modeling nonlinear vibrations of drill strings with stabilizers in a supersonic gas flow

Abstract

In this paper, we study the nonlinear dynamics of a drill string under the effect of external loads in a supersonic gas flow, taking into account supporting stabilizers. The case of the drill string spatial lateral vibrations, which are the main cause of the drilling equipment failures, is considered. To account for nonlinear effects, a mathematical model based on the general relations of Novozhilov's nonlinear theory of elasticity is developed. The discretization of the model is conducted using the lumped-parameter method. The explicit fourth order Runge-Kutta method is utilized for obtaining a numerical solution for the studied system. The effect of damping elements (supporting stabilizers) on the drill string lateral vibrations is analyzed. Numerical illustrations are presented, and the corresponding recommendations for deep and shallow drilling are given.