Numerical simulation study on critical liquid and sand carrying velocities of gas-liquid-sand multiphase flow in vertical and horizontal wellbore sections

A segmented simulation is used to examine flow behaviors in vertical and horizontal shale-oil wellbores. Built with Poly-Hexcore meshing, the model couples Euler-Euler and KTGF approaches, and incorporates the Dranchuk-Abu-Kassim equation for real-gas compressibility along with a liquid-film shielding correction for interphase drag. In vertical sections, falling below the 6.5 m/s critical liquid-carrying velocity changes the regime from annular to slug flow, increasing liquid holdup by 372%. For the horizontal sections, the critical sand-carrying velocity is 7.5–8.0 m/s; below 8.0 m/s, the sand volume fraction surges from 0.0092 to 0.1864, forming a stationary bed. Theoretical evaluations reveal that classical steady-state models severely underpredict the liquid loading threshold (yielding only 0.78 m/s), demonstrating the limitations of traditional droplet theories under extreme pressures. The key contribution of this work is combining the real-gas EOS with film shielding to accurately resolve these transient multiphase instabilities. These results provide practical guidelines for deep-well deliquification.