Measuring the efficiency of vertical drill-strings: A vibration perspective

Abstract A drill-string is a slender structure with nonlinear dynamics; it is an equipment used in the oil industry to drill the rock in the search of oil and gas. The aim of this paper is to investigate the efficiency of the drilling process in terms of input/output power. The continuum system is linearized about a prestressed configuration, the finite element method is applied to discretize the linear system, then a reduced-order model is constructed using the normal modes of the linear system; only torsional and axial vibrations are considered in the analysis. Uncertainties related to the speed imposed at the top are also included in the analysis. The rotational top speed is modeled using two different stochastic processes and the Monte Carlo Method is employed to approximate the statistics of the response of the resulting stochastic differential equations.

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