A force balance model of a spouted bed for Darcy and non-Darcy flow in the annulus

A mathematical model based on Mamuro and Hattori's force model including the drag force effect on the particles in the annulus of a spouted bed was constructed. The results from this model were compared with previous work, including Mamuro and Hattori's model for Darcy's law and Epstein and Levine's model and that proposed by Hattori et al. for non-Darcy flow in the annulus, none of which included the effect of drag force on particles. Results presented in the paper showed that when drag force was included in the force balance model, a lower value of U_a/U_mf, the ratio of superficial fluid velocity in the annulus to minimum fluidization velocity, was obtained. Z/H_m, the ratio of axial distance from fluid inlet to the maximum spoutable bed depth, increased compared with models where the effect of drag was absent. Our results also showed an increase in radial cross flow from the spout to the annulus, especially in the lower part of the bed compared to those obtained by Mamuro and Hattori. The proposed model was found to be sensitive to Janssen's factor, J, and also displayed a qualitative agreement with the Hattori et al. model which was proposed for non-Darcy conditions.