Influence of solid-phase settlement on two-phase wave velocity along offshore wellbore

Based on the experimental data of solid-phase settling of drilling fluid, taking into account factors such as drilling fluid density, gas compressibility, frequency, interphase resistance, and virtual mass force after solid-phase settling, A mathematical model for pressure wave velocity in the offshore annular air-liquid two-phase system was developed using the dual-fluid conservation equations. The pressure wave determinant was obtained through small disturbance changes, and the model was solved through computational programming. The results show that as the fluid density increases or the compressibility decreases, the annular pressure wave velocity increases. As the fluctuation frequency diminishes, the momentum exchange between phases becomes more adequate, resulting in a decline in pressure wave velocity. Temperature exerts little influence on the single-phase pressure wave velocity in gas, drilling fluid, and cement slurry. As the system pressure rises, the velocity of the pressure wave increases. In comparison with the gas phase, the system pressure exerts a more significant influence on the pressure wave velocity within cement slurry. When the system pressure is 50 MPa, considering the significant impact of solid phase settlement on pressure waves, the pressure wave velocity of annular drilling fluid increases from 777.36 m/s to 1266.87 m/s, an increase of 62.97%. When the system pressure is 0.3 MPa, the effect of solid phase settlement on drilling fluid pressure wave velocity is not significant, and the effect of solid phase settlement on pressure wave velocity is only 0.75%. This article not only provides wave velocity parameters for transient flow calculation, but also provides theoretical basis for the design of throttle valve action time for offshore drilling and completion.