A Sensing and Computational Framework for Estimating the Seismic Velocities of Rocks Interacting With the Drill Bit
Résumé
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 top-drive 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.
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