A note on the multiphase balance equations

Abstract

The formulation and use of the momentum equations for multiphase systems are not always consistent in the literature. The objective of this note is to clarify an issue, which long has hounded the literature on the multiphase flow equations. The standard book by Gidaspow, which historically has formed the basis of at least two of the major CFD software packages in common use today, describes three formulations of the momentum equations for fluid (continuous phase)-solids (dispersed phase) flows that are often not clearly distinguished, as this note will demonstrate.

This note focuses on Models “A” and “B”, which are more widely used than model “C”. Their form and significance are discussed, as are the most common flaws in their interpretation and use.

The equations are listed in their differential form, the form in which they are normally used, although in their nature, and when derived, the equations are not differential.