Propagation velocity and time laws of backpressure wave in the wellbore during managed pressure drilling

When gas invasion, especially overflow, occurs at the bottom hole in the process of managed pressure drilling (MPD), it is common to apply backpressure on the wellbore by adjusting the backpressure pump and throttle valve, so as to rebuild bottom hole pressure balance. If it is still thought that the wellhead backpressure is loaded to the bottom hole instantaneously, there will be larger errors between the calculated wellbore parameters and the actual wellbore flow parameters, which will result in well control failure and even well blowout. In this paper, a pressure wave propagation equation suitable for the gas-liquid two-phase flow in the annulus was established based on the global averaged gas-liquid two-phase flow model to investigate the propagation velocity and time of backpressure wave in the wellbore. Then, gas-liquid interaction was introduced to carry out coupling solution on the equation set. It is shown that pressure wave velocity increases with the increase of drilling mud density, but decreases with the increase of void fraction and virtual mass force coefficient. It changes drastically at first, and then slows down. What's more, when the void fraction is greater than 0.1 or the virtual mass force coefficient exceeds 0.2, the momentum between gas phase and liquid phase is fully exchanged, and the pressure wave velocity decreases slowly, approaching a stable value. In Well Penglai 9 in the Sichuan Basin, for example, the average time of single pressure wave propagation is about 50 s, and the total propagation time of 4 rounds is about 200 s, which accounts for more than 67% of the total time of system control response. It is indicated that the propagation velocity and time of the pressure wave in the annulus calculated by this method can greatly improve the accuracy of managed pressure response time of MPD drilling system and the control precision of adaptive throttle valve.