Modelling of drill string nonlinear dynamics with a drilling fluid flow

Abstract

In this work the development of mathematical models of drill string dynamics under the influence
of internal drilling fluid flow, which is of great importance for ensuring fast, cost-effective and safe
process of oil and gas well drilling, is conducted. It is a reason for in-depth research of the drilling
fluid influence on the motion of drill strings. The modelling is complicated by consideration of geometric
nonlinearity, rotation of the drill string and the effect of external force factors. Relations
of Novozhilov’s nonlinear theory of elasticity form the model framework. Ostrogradsky-Hamilton’s
variation principle is applied for derivation of the drill string governing equations. It is assumed
that the drilling fluid flow moves at constant speed. The obtained nonlinear mathematical models,
describing lateral vibrations of the drill string as a compressed rod, generalize well-known linear
models taking into account the effect of the drilling fluid. These models will enable to solve a wide
range of problems concerning the drilling equipment nonlinear dynamics on a qualitatively new
and mathematically valid level.