This paper is concerned with the theoretical analysis to obtain the flow characteristics of multiphase mixtures in a vertically fixed air-lifting pipe. In this present investigation, the case is treated where a transition process from a solid-liquid two-phase mixture flow to a solid-gas-liquid three-phase mixture by injecting gas-phase into the upriser through a gas injector is present. The system of equations governing the liquid-solid two-phase mixture flow consists of two mass conservation equations, two momentum conservation equations and a requirement for two phase volumetric fractions. Again, the gas-liquid-solid three-phase how field after the position of gas injection is solved by three mass conservation equations, three momentum equations, a gas equation of state and a requirement for the individual phase volumetric fractions. The transitions of the flow pattern of gas phase from bubbly to slug flows and from slug to churn hows are taken into account in the system of equations governing the three-phase flows. In order to verify the validity of the system of governing equations accounting for the how patterns transitions of gas-phase, the flow characteristics calculated on the basis of the present theoretical model have been compared with experimental data measured by the other investigators. As a result, we have found that the present theoretical model built up in this study gives a good fit to the experimental data obtained by several investigators. Furthermore, we have demonstrated that the present model is capable of predicting the maximum solid/liquid volumetric flux.