Dynamic drill-string modeling for acoustic telemetry

Directional drilling techniques require real-time sensing of the drill bit direction and the downhole environment from the measurement-while-drilling (MWD) sensor module. Traditional telemetry methods such as the mud pulse telemetry are limited to low transmission rates. Acoustic telemetry is a method used for transmitting downhole sensor data and it is orders of magnitude faster than conventional telemetry techniques. However, the selection of appropriate carrier frequencies is critically important to transmit measured data. This study proposes a finite element (FE) model based on the Timoshenko beam theory that predicts dynamics of a drill-string over a wide frequency range and boundary condition. Additionally, a modulated acoustic transmission is developed and performed using the determined carrier frequencies. The signal is modulated using differential binary phase shift keying (DBPSK) and is up-converted to the carrier frequency used for the excitation of the drill-string. Packets of bits are first generated as the telemetry data and then convolutionally encoded to reduce errors at the receiver. The receiver at the surface demodulates and decodes the received acceleration signals to recover the transmitted bits through a digitally implemented lock-in amplifier (LIA). Finally, the transmitted and received bits are compared to calculate the bit-error rate (BER) for each signal-to-noise ratio (SNR) condition. By using the LIA, the receiver can extract severely attenuated acoustic signals, but the dynamics of the drill-string and the additional borehole interactions can degrade the performance of the acoustic telemetry system.