Modeling of critical sand-carrying flow rate of gas-liquid-solid three-phase flow in an inclined pipe

• Agitated-annular transition emerges at critical sand-carrying • Quantifies particle shape effect on critical velocity, revealing gas-liquid slip phenomenon • Proposes a critical velocity model for irregularly-shaped particles The critical sand-carrying velocity of gas-liquid-solid three-phase flow is widely applied in natural gas extraction, such as coalbed methane wells and tight gas wells. A common issue encountered when applying critical sand-carrying flow velocity models is that they are only applicable to spherical solid particles and have suboptimal computational accuracy. This study combined indoor experiments with theoretical derivations to investigate the flow patterns of gas-liquid-solid three-phase flow at critical states, revealing the mechanisms by which particle shape and gas-liquid velocities influence critical sand-carrying flow velocity. Based on this, a theoretical model for critical sand-carrying flow velocity was established. The results indicate that under critical conditions, the gas-liquid-solid three-phase flow exhibits a flow pattern transitioning from turbulent flow to annular flow. The critical sand-carrying flow velocities for ellipsoidal, octahedral, hexagonal, and tetrahedral particles are 5.18%, 8.83%, 16.73%, and 23.86% higher than those of spherical particles, respectively. The liquid phase exhibits dual effects during sand transport: under low flow velocity conditions (<2 m/s), it serves as a transport medium while also providing a lubricating effect. when the flow velocity exceeds 2 m/s, a threshold effect occurs. Based on this, a critical sand-carrying flow velocity model applicable to solid particles of different shapes was established. Compared with models proposed by previous scholars, the new model significantly improves computational accuracy (error within 9%) and expands the applicability range by introducing the particle specific surface area and slip factor to quantify the morphological characteristics of non-spherical particles and the slip effects between multiphase fluids, respectively.