A united dynamic pressure wave velocity model in four-phase flow during managed pressure drilling operations

A predictive model was established to assess the velocity of dynamic pressure waves in four-phase flow during Managed Pressure Drilling (MPD) operations. The model takes into account a variety of factors such as pressure, temperature, gas dissolution, the volume factor of the oil phase, virtual mass force, drag force, the void fraction of gas/oil/drilling mud/water phases, and angular frequency. The approach is predicated upon momentum and mass conservation equations, the equation of state (EOS), and small perturbation theory. The investigation further encompasses finite-difference techniques, the Newton-Raphson iteration, and cubic spline methods. The findings reveal that the speed of pressure waves is considerably influenced by fluctuations in gas influx rate, while showing less susceptibility to increments in oil/water influx rates. Furthermore, heightened backpressure (BP) reduces the gas void fraction at diverse annulus depths and has a tendency to increase the velocity of pressure waves in four-phase flow. Moreover, an increase in angular frequency leads to a proportionate rise in the velocity of pressure waves. Irrespective of the presence or absence of virtual mass force, it has been observed that the velocity of pressure waves remains at a relatively low level.