Simulation of stress waves in attenuating drill strings, including piezoelectric sources and sensors

A key element in drill steering and prediction of lithology ahead-of-the-bit is the transmission of while-drilling information from the bottom of the well to the rig operator and the geophysicists. Mud-pulse telemetry, based on pressure pulses along the drilling mud and extensional waves through the drill string, is the most used technique. The last method, properly designed, could transmit data rates up to 100 bits per second, against the 1 or 2 bits per second achieved with pressure pulses. In this work, a time-domain algorithm is developed for the propagation of one-dimensional axial, torsional, and flexural stress waves, including transducer sources and sensors. In addition, the equations include relaxation mechanisms simulating the viscoelastic behavior of the steel, dielectric losses, and any other losses, such as those produced by the presence of the drilling mud, the casing, and the formation. Moreover, the algorithm simulates the passbands and stopbands due to the presence of the coupling joints and pulse distortion and delay due to nonuniform cross-section areas. Acoustic and electric pulses, generated at one location in the string, can be propagated and detected at any other location by piezoelectric and acoustic sensors, such as PCB accelerometers, clamp-on ammeters, force, and strain transducers.