The multiphase flow models were used to predict pressure drop and segregation of particles flowing in a vertical pipe. To compare calculations with data, it was necessary to assume an effective particle size based on a coefficient of restitution and on inlet void fractions. Different partifle size distributions with equal average particle size generate distinctly different pressure drops and segregations. Contribution of solid interaction force is very important in accounting for the segregation of the particles in a vertical pipe.All models gave a reasonable prediction of the design parameters. The pressure drops predicted by the models agreed well with both high-and low-pressure experiments. For the design of vertical solids pneumatic transport systems, the literature offers several empirical correlations and hydrodynamic models. The former are limited to the particular data base and the latter are generally limited to narrow particle size distributions. To design for the transport of solids of wide distribution requires a proper accounting of both the segregation of particles and its effects on pressure drop and choking limits.
HAMlDA hydrodynamic model of such systems must consider the solids as a component of many phases. If the solids are assumed to consist of a finite number of solid phases, previously developed two-or threephase hydrodynamic models can be extended to the more complex systems. Furthermore, it is apparent that interaction between particles should be considered in the model. The present work is directed along these paths.
CONCLUSIONS AND SIGNIFICANCEIn this work, a multiphase hydrodynamic model was developed for vertical pneumatic transport of solids to account for the effects due to particle size distribution. The model includes terms to account for particle interaction. The potential of predictions of phenomena such as choking, solids segregation, and minimum pressure drop was shown, and the dangers of using a mean particle size in a system of wide distribution were demonstrated. The appropriateness of the model was shown by comparison of calculated and reported pressure drops in systems of widely different operating pressures. The studies indicate the importance of and therefore the need for better estimates of particle interaction forces and voidage to relate segregation and pressure drop to the operating parameters of flow rates, size distribution, and pressure.