Improvement of friction estimation along wellbores using multi-scale smoothing of trajectories

Drilling monitoring aims at anticipating and detecting any drill string failures during well construction. A key element for the monitoring activity is the estimation of friction along the wellbore trajectory. Friction models require the evaluation of the actual wellbore trajectory. This evaluation is performed applying any of various reconstruction methods available in the industry to discrete deviation measurements. Although all these methods lead to nearly identical bit location, friction estimations are highly dependent on reconstruction methods due to huge dierences in the trajectory derivatives. To control this instability, a new reliable estimation of wellbore friction using a nonlinear trajectory smoothing process is introduced. This process uses a multi-scale approach and a specic nonlinear smoothing through subdivision schemes and their related decimation schemes. Two smoothing processes are compared: one using an interpolatory subdivision operator, and the other, a non-interpolatory subdivision operator. Validation has been performed on a synthetic plane noisy trajectory. The non-interpolatory process provides trajectory derivatives estimate much closer to those of the initial trajectory. Both processes have been applied to a real three-dimensional wellbore trajectory, improving signicantly the friction estimates.