A Novel Dynamic Model for Predicting Pressure Wave Velocity in Four-Phase Fluid Flowing along the Drilling Annulus

A dynamic pressure wave velocity model is presented based on momentum equation, mass-balance equation, equation of state, and small perturbation theory. Simultaneously, the drift model was used to analyze the flow characteristics of oil, gas, water, and drilling fluid multiphase flow. In addition, the dynamic model considers the gas dissolution, virtual mass force, drag force, and relative motion of the interphase as well. Finite difference and Newton-Raphson iterative are introduced to the numerical simulation of the dynamic model. The calculation results indicate that the wave velocity is more sensitive to the increase of gas influx rate than the increase of oil/water influx rate. Wave velocity decreases significantly with the increase of gas influx. Influenced by the pressure drop of four-phase fluid flowing along the annulus, wave velocity tends to increase with respect to well depth, contrary to the gradual reduction of gas void fraction at different depths with the increase of backpressure (BP). Analysis also found that the growth of angular frequency will lead to an increase of wave velocity at low range. Comparison with the calculation results without considering virtual mass force demonstrates that the calculated wave velocity is relatively bigger by using the presented model.