Uncertainties in drill dynamics: the role of the random weight-on-hook

International audienceA drill-string is a slender structure that turns and drills into the rock in search of oil. This paper aims to investigate uncertainties on the weight-on-hook, which is the supporting force exerted by the hook at the top. In a drilling operation there are three parameters that can be continuously controlled: (1) the weight-on-hook, (2) the drilling fluid inlet velocity and (3) the rotational speed of the rotary table. The idea is to understand how the performance of the system (which is measured by the rate-of-penetration) if affected when the weight-on-hook is considered uncertain. A numerical model is developed using the Timoshenko beam theory and discretized by means of the Finite Element Method. The nonlinear dynamics presented includes bit-rock interaction, fluid-structure interaction and impacts. The probability theory is used to model the uncertainties. To construct the probability density function of the random variable, the Maximum Entropy Principle is employed, so that the probability distribution is derived from the mechanical properties of the weight-on-hook