This paper treats theoretical analyses to predict the steady flow characteristics of multiphase mixture in an air lifting pipe. When slurries containing solid particles such as manganese nodules are lifted from the deep-sea bed to the sea surface by an air lift pump, gas phase is injected halfway into a lifting pipe with a very large length ranging from the sea floor of about 5, 000 m in depth to the sea surface. Therefore, liquid-solid two-phase flow is formed in a deeper part of the lifting pipe, but changes into gasliquid-solid three-phase flow just after the position of the gas injection.
Here, the case is treated where slurries are the solid particles-sea water two-phase mixture before the position of the gas injection and the air-solid particles-sea water three-phase mixture after that. The equations governing the liquid-solid two-phase slurry flow consist of two continuity equations, two momentum equations and an equation for two-phase volume fractions. However, the gas-liquid-solid threephase flow field after the position of the gas injection is governed by three continuity equations, three momentum equations, a gas equation of state and an equation for three-phase volume fractions. In the two-phase region, the individual volume fractions and lifting velocities of the solid and liquid phases remain self-evidently unchangeable. The abrupt drop of the volume fractions as well as the abrupt jump of the lifting velocities occur at the transitional position from the two-phase to the three-phase flow. In the three-phase region, the three momentum equations for the individual phases are solved as the perturbation from the solutions to the equilibrium/homogeneous flow and then the remaining five flow properties are determined.
Some numerical experiments are performed using a set of five equations in the two-phase region and a set of eight equations in the three-phase region for determining the flow properties. By comparing the non-equilibrium solutions with the numerical results of the case where the three-phase flow is assumed to be in velocity equilibrium, it is numerically shown that the equilibrium solution gives a threshold of the highest possible solid-phase mass flux on condition that bath the gas-phase and liquid-phase mass fluxes are kept constant. With increasing solid particle size the non-equilibrium solution obtained directly as the perturbation from the equilibrium one is found to have a tendency to deviate from the original equilibrium one. Such important problems are described in detail.
