Propagation of extensional and torsional waves in a real drill string

The waves propagating along the drill string are used as a pilot signal in seismic while-drilling. To evaluate phase and group velocities, we calculate the propagation of extensional and torsional stress waves along a typical drill string of oil-well drilling. The algorithm simulates a regular and not-periodic geometry of drill pipe, and attenuation effects. The shots are located at the bit, at the end of the bottom hole assembly, at the top drive and at the middle of the drill pipe with the aim to simulate noise. The propagation model includes the gravity effects, the temperature dilatation, the variable thickness of pipes, the formation, and the dispersion caused by geometrical properties. The irregular grid is adapted to the structure and the geometry of the real drill string. The real drill-bit data of extensional waves are compared to the simulated seismograms.