Attenuation law of MWD pulses in aerated drilling

A mathematical model for predicting the attenuation of measurement while drilling (MWD) pressure pulses in aerated drilling was proposed using the two-phase flow model and considering the momentum and energy exchange at the phase interface, gravity of each phase, viscous pipe shear and other closing conditions. The small perturbation theory was used to solve the mathematical model; then, a model was established to compute the velocity and attenuation coefficient of mud pulse signal, and the simulated result of the model is in line with the measured attenuation in field test. With the mathematical model, the influencing factors for mud pulse attenuation were simulated and analyzed. The results reveal that the gas holdup, system pressure and pulse frequency are the major influencing factors. In case of low gas holdup (0–5%), as the gas holdup increases, the pulse velocity decreases drastically, and as it further increases, the pulse velocity tends to be flattened; whereas the attenuation coefficient increases gradually with the increase of gas holdup and begins to decline when it reaches maximum. At the same gas holdup, the mud pulse signal shows higher velocity under a high system pressure, and the attenuation coefficient increases faster with increase of the gas holdup under a low system pressure. Both pulse velocity and attenuation coefficient increase gradually with the increase of pulse frequency, and tend to be a stable high value when the frequency exceeds 100 Hz.