A probability model for predicting the bubble size distribution in slug flow in vertical pipes

Abstract

In deep-sea mineral exploitation, slug flow shows promise for efficient mineral air-lifting but also poses risks of serious production safety accidents. Accurate prediction of the two-phase distribution in the liquid slug is crucial for efficient mineral lifting and accident prevention. This study develops a probability model for predicting the bubble size distribution of slug flow in vertical pipes. The liquid slug is divided into the near wake and far wake regions based on Taylor bubble wake influence. In the near wake, the vortex tears the liquid film at the tail of the Taylor bubble and generates new bubbles, while pushing the old bubbles to move towards the Taylor bubble, facilitating gas exchange between the Taylor bubble and the liquid slug. In the far wake region, vortices and random collisions enable dispersed bubbles to exchange gas with each other. These gas exchange processes occur continuously and maintain dynamic equilibrium in stable slug flow. Calculating the probability of the generation and death of a single bubble, along with the analysis of the bubble behavior, yields a probability model for predicting the bubble size distribution. The model is validated using experimental data and shows good consistency. The study investigated factors affecting the distribution of bubble size in slug flow, including gas phase velocity, liquid phase velocity, liquid density, liquid viscosity, and surface tension.