Stochastic drill-string dynamics - random weight-on-hook (WOH)

International audienceA drill-string is a slender structure that turns and drills into the rock in search of oil. There are many sources of uncertainties in this problem, but in this article only the weight-on-hook, which is the support force exerted by the hook at the top, is considered random. In a drilling operation there are three parameters that can be continuously controlled: (1) the weight- on-hook, (2) the drilling fluid flow, and (3) the speed of the rotary table. A numerical model is developed using the Timoshenko beam theory and discretized by means of the Finite Element Method. The main efforts that the column is subjected to are considered: rotation at the top, hanging force at the top, bit-rock interaction, fluid-structure interaction that takes into account the drilling fluid that flows downwards the column then goes upwards in the annulus, shock and rubbing between the column and the borehole, and the own weight of the column. To derive the probability density function of the random variable WOH, the Maximum Entropy Principle is used, so that the probability distribution is coherent with the physics