Hydrodynamic modeling

Experimental studies of risers have shown that these systems are often characterized by complex flow phenomena such as non-uniform spatial distribution of particles, large slip velocities between the phases, and the existence of several possible pressure gradients and solids holdups for specified values of gas and solid flow rates (see Chapter 2 — Hydrodynamics). The particle concentration profile influences the distribution of residence times of particles and may lead to recirculation of particles against the direction of their net motion. These effects are critically important in predicting the conversion in systems in which the particles react chemically with the gas or catalyse a gaseous reaction. Hence, an accurate understanding of the mechanism responsible for the cross sectional distribution of solids is necessary to predict the performance of these systems. Empirical correlations have generally proven unsuccessful as they are typically limited to the database used to develop them and ignore the effect of radial non-uniformity of the basic variables. However, fundamentally based models have made some progress in this direction. These models can be used to predict how various parameters vary as system conditions change. This is very important, especially to determine the effects of scale-up, design and optimization. A review of these models is the subject of this chapter.