A novel stochastic process to model the variation of rock strength in bit-rock interaction for the analysis of drill-string vibration

A common issue faced in the oil and gas industry is the vibration of drill-strings, which are detrimental to operational efficiency and can incur in great financial losses. Because of this, a great effort has been devoted in the literature to the analysis of these vibrations. In addition, the modeling uncertainties and variations in environmental factors, like lithology, corroborates the use of stochastic models instead of deterministic ones. Therefore, the three main objectives of this work are: (i) to propose a novel stochastic model to describe the uncertainties on the rock strength by means of stochastic processes; (ii) to propose a novel coupled stochastic process, which considers the bit dynamics, and; (iii) to analyze the effect of such uncertainties on torsional vibration severity. The drill-string is described by a continuous axial-torsional model discretized by means of the finite element method. A coupled nonlinear bit-rock interaction model is considered, in which the cutting component of torque is modeled as a stochastic process in order to consider the variations on rock strength while drilling. Ito stochastic differential equations are used to generate two different stochastic processes: Ornstein-Uhlenbeck process and a novel coupled process. The second one considers the bit dynamics in order to describe better the physics when severe torsional vibration happens. The statistics of the response show that the uncertainties on rock strength may lead to predictive scenarios where the amplitude of vibrations at the bit are significantly larger than the ones provided by the deterministic model. Also, the differences between the processes are small when the vibration at the bit is small, but the novel process presents the worst case when severer vibrations are present. (C) 2019 Elsevier Ltd. All rights reserved.