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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.

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We have developed a sensing and computational framework to estimate seismic velocities of rocks interacting with the drill-bit during the drilling process. The performance of drilling depends on our knowledge of the subsurface. The interaction between the drill-bit and rock can introduce severe vibrations in the drill-string and result in safety and performance issues. However, we can use seismic waves radiated from drill-bit-rock interactions to determine seismic velocities of the rocks interacting with the drill-bit. Our approach consists of a distributed (wave equation) representation of the dynamics of the drill-string for which we show (using Riemann's invariants and a backstepping approach) that it is possible to express the force-on-bit as a function of the top-drive force and the topdrive velocity, without requiring explicit information about the subsurface properties. We also show that seismic waves generated by drill-bit-rock interaction can be modelled as functions of the force-on-bit and of rock velocities. The rock velocity independent formulation of the force-on-bit, along with modelling of the seismic waves generated by drill-bit-rock interaction as a function of force-on-bit and rock velocities allow us to estimate seismic velocities of rocks interacting with the drill-bit. We use the alternating minimization algorithm to estimate the velocities. Numerical examples on simulated data are indicators of the validity of the approach. The proposed methodology is the first step towards a subsurface-aware drilling system.