Drill-string horizontal dynamics with uncertainty on the frictional force

This paper analyzes the dynamics of a horizontal drill-string. In this dynamics, the frictional forces between the column and the borehole are relevant and uncertain. A stochastic model is proposed for the frictional coefficient: a random field with exponential autocorrelation function. In the numerical analysis, the drill-string is modeled using the bar model (tension/compression), and is discretized by means of the finite element method. An oscillatory force (due to mud motor) is imposed on the system and there is a bit–rock interaction as the column moves forward. We propose a new way to measure the efficiency of the process: an output/input power ratio. The resultant random ratio is analyzed, and it turns out that it presents a bimodal characteristic, an unexpected result.