A Sensing and Computational Framework for Estimating the Seismic Velocities of Rocks Interacting With the Drill Bit

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 modeled as functions of the force-on-bit and rock velocities. The rock velocity independent formulation of the force-on-bit, along with the modeling of the seismic waves generated by drill bit-rock interaction as a function of force-on-bit and rock velocities, allows us to estimate seismic velocities of rocks interacting with the drill bit. We use the alternating minimization algorithm to estimate the velocities. Numerical examples of simulated data are indicators of the validity of the approach. The proposed methodology is the first step toward a subsurface-aware drilling system.