Estimating friction factors while drilling

Abstract

We design and test an algorithm for estimating the bit angular velocity and side forces on a drill string using only topside measurements fed into an adaptive observer. To derive the algorithm gains the drill string is modeled as a distributed wave equation coupled with Ordinary Differential Equations (ODEs) at the boundaries which represent the lumped dynamics of the top-drive and BHA, respectively. Here, the algorithm uses only measurements from the top-drive, while the non-linear side-forces are lumped at the BHA. The obtained observer gains are then implemented on a previously validated torsional drill string model with a distributed BHA model and distributed Coulomb side forces implemented as an inclusion. This design approach combines a high fidelity model with recent theoretical developments on estimation of PDEs to find appropriate feedback gains to ensure a fast and robust tuning. The feasibility of the approach is illustrated by showing convergence in estimated friction factors to the true values when testing on simulated data. When testing on full scale field data, friction factors converge to the same value for different initial values which indicates both good estimates and a robustness of the approach. The estimates produced by the algorithm can be displayed to a driller in real time in an advisory system, and the result can be built on to help optimize the drilling operation, detect faults and unwanted incidents, aid on-site decision making, and improve control of directional drilling.

Closed-loop tool face control with the bit off-bottom

“…The model referenced in the previous section has been used to estimate downhole and along-string angular velocity and torque and has been validated with field data [14]. In this section, we extend this work to estimate in real time the tool face orientation.…”

“…where φ 0 corresponds to the initial tool face orientation. More precisely, the observer designed in [14] combines the proposed model of the system dynamics with measurements from physical sensors. This observer relies on the measured top-drive angular velocity ω 0 .…”

“…The estimation of the tool face orientation is obtained improving the soft-sensor introduced in [14] and based on the backstepping methodology [16]. This adaptive observer algorithm provides reliable estimates of the states (torque and angular velocity) of the system, of the friction coefficients related to the side forces (µ s and µ k ) using the measurement of ω 0 .…”

“…In this section we recall the observer equations given in [14] as a copy of the plant equation plus some correction terms and then use them to derive an estimate of the tool face,φ b (t), as given in equation (24).…”

“…Let us denote with the• superscript the estimated states and e =ω 0 − ω 0 the measured estimation error of the topdrive angular velocity. The observer equations given in [14] in terms of Riemann invariants read as followṡ…”