Three-phase gas-liquid-solid flow phenomena in pipes are observed in air-lift pumps for transporting solid materials, coal liquefaction plants, and so forth. In analyzing or numerically simulating three-phase flow phenomena, one needs a set of basic equations which describe the conservations of mass, momentum and energy for three-phase media.
The purpose of this paper is a formulation of the basic equations in three-phase flow for practical applications. The derivation of the equations was carried out for the mixture model in neglecting the interfacial force and energy. First, using a characteristic function of each phase in the mean of distribution, the physical parameters of three-phase flow were defined as field quantities, and then the local instantaneous and averaged conservation equations of mass, momentum and energy were derived. Secondly, taking radial distribution of the physical parameters into account, one-dimensional basic equations were represented by means of the drift flux model on the basis of the local averaged equations.