Theoretical analysis of gas–liquid–solid three-phase flow in air-lift pipelines for mineral particles

The air-lift system has attracted considerable attention in the field of deep-sea mineral particle transport due to its simple structural design and low maintenance costs. This system operates by injecting compressed air into a long, vertical pipeline, reducing the average density of the fluid mixture and facilitating the upward transport of liquid and solid particles. In this study, a theoretical model based on the multi-fluid method is developed to simulate the flow characteristics within an air-lift system. The pipeline flow is assumed to be steady, with separate sets of governing equations applied to the liquid–solid two-phase flow section below the air injection point and the gas–liquid–solid three-phase flow section above it. These equations are solved using the fourth-order Runge–Kutta method. During the iterative process, the liquid superficial velocity at the inlet is continuously adjusted to ensure that the outlet pressure converges to atmospheric pressure. The influences of key parameters—such as pipe diameter, solid density, particle diameter, submergence ratio, and the length ratio of two-phase to three-phase flow—on system performance are systematically investigated. The model is further applied to a long-distance pipeline scenario, and the variations in flow parameters along the pipeline are analyzed, offering valuable insights for optimizing air-lift systems in deep-sea mineral transport applications.