Estimating Drill String Friction with Model-Based and Data-Driven Methods

Abstract

Estimation of the behavior of long dynamic systems with limited sensing remains an open question. In this paper, we consider the rotational motion of a deep drilling system and compare three algorithms to estimate the friction factors along the drillstring and thus provide an estimate of bottomhole rotational velocity. These friction terms characterize the interaction between the drill pipe and the wellbore walls (Coulomb source terms) within the curving wellbore. This information is essential to design the next generation of stick-slip mitigation controllers, to develop real-time wellbore monitoring tools, and to enable effective toolface control for directional drilling. We propose two model-based algorithms (an adaptive observer and a recursive dynamics framework) and a machine learning-based algorithm to estimate friction parameters, all of them presenting advantages and drawbacks. The performances of the two model-based estimators are finally compared with the data-driven neural network.

An Analytical–Numerical Model for Determining “Drill String–Wellbore” Frictional Interaction Forces

“…The author of [9] carried out a thorough analysis of dynamic processes in nonlinear oscillatory mechanical systems and obtained analytical dependencies for the study of nonlinear mechanical systems of a discrete structure, the analogue of which is a drill string. In [69], the drill string is modeled as a flexible rod with discs at both ends, and one of the discs rotates in a cylinder with fluid. The authors considered different curvatures of the rods to investigate the regularities of the "sticking-sliding" interaction of the drill string with the wellbore.…”

“…Therefore, the advantages of the model developed by us over the well-known ones [9,13,15,20,69,82] lie in the possibility of estimating the parameters of stability and dynamic load, taking into account the frictional forces of parts of the drill string against the walls of vertical, curved, and inclined sections of the well. The information about the use of pipes made of various materials, aluminum and titanium alloys and steel, in the layouts of active drill strings gives special importance to this work.…”

“…Study [67] presents a numerical and analytical approach to the contact interaction of thin structures of drill pipes. Papers [68][69][70] analyze factors affecting the "drill strings-well bore" friction during drilling and access the friction force effect on drilling. Publications [71,72] consider the unsteady dynamics of elastic rods with inelastic external resistance, which models the behavior of a pipe drill string.…”

Recursive dynamics interconnection framework applied to angular velocity control of drilling systems

“…Consider the PDE system ( 6)- (7). We assume that the friction coefficients µ k , µ s are known (see [8]). When |ω(t)| > ω c , the disturbance terms are constant.…”

“…Next, we consider the real deviated Well A, where the side forces cannot be neglected anymore. They are assumed to be known without bias (using the estimation procedures given in [8] for instance). For sake of simplicity, we assume they are constant along the drill string (µ s , µ k ) = (0.45, 0.28).…”