Vertical pneumatic moving bed

Knowlton has cautioned on the difference between small diameter and large diameter systems for pressure losses. The difference between these systems is especially apparent for dense phase flow where recirculation occurs and wall friction differs considerably. Li and Kwauk (1989, 1989) have also studied the dense phase vertical transport in their analysis and approach to recirculating fluid beds. Li and Kwauk s analysis included the dynamics of a vertical pneumatic moving bed upward transport using the basic solid mechanics formulation. Some noncircular geometries were treated including experimental verification. The flows have been characterized into packed and transition flows. Accurate prediction of the discharge rates from these systems has been obtained. 

Li, H., and Kwauk, M., Vertical Pneumatic Moving-Bed Transport -1. Analysis of Flow Dynamics, Chem. Engr. Sci., 44 249-259 (1989)... 

The basic character of non-fluidized gas-particle flow is the existence of contact pressure (or stress) among particles and between particles and the pipe wall. Both theoretical analyses and experimental results (Terzaghi, 1954 Johanson and Jenike, 1972 Li and Kwauk, 1989) showed that the pressure of the interstitial fluid in particulate material neither compresses nor increases the shear resistance of the particulate material. After Walker (1966) and Walters (1973), Li and Kwauk (1989) analyzed the stresses in a vertical pneumatic moving-bed transport tube by using the stress theory of particulate media mechanics and Mohr circles, shown in Figs. 19 and 20, and gave the following stress ratios at any point in the flow field ... 

For stable moving-bed uptransport of particles in a tapered spout, the drag force of the flowing gas on the particles is used to overcome gravity, acceleration, and wall friction. Vertical force balance on a horizontal element of solid particles in a trapezoidal pneumatic moving bed, shown in Fig. 7, gives... 

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