L 36- Fluidized bed Reactor Design

Modeling of Fluidized Bed Reactors Basic two-phase model for fluidized bed. Simple plug flow and complete mixing models are inadequate for predicting conversion in fluidized beds. Neither of these models can explain experimental conversion, x versus W/F, curves below those for complete mixing. Such an observation can only be explained by assuming that a fraction of the gas bypasses the catalyst.

Hydrodynamic Flow Models. The behavior of rising gas bubbles is important, since they probably cause much of the difficulty. Two developments : The first is Davidson's (Two Phase model) remarkable theoretical development and experimental verification of the flow in the vicinity of a single rising bubble in a fluidized bed which is otherwise at minimum fluidizing conditions. K-L Model :The bed contains bubbles surrounded by thin clouds rising through an emulsion. Shape of bubble is distorted hemisphere or dome of a Mushroom.

Extremes of gas flow in the vicinity of rising gas bubbles in BFBs.

The rise velocity of the bubble u b, depends only on the bubble size, and that the gas behavior in the vicinity of the bubble depends only on the relative velocity of rising bubble and of gas rising in the emulsion u e. For the fine particle bed, gas circulates within the bubble plus a thin cloud surrounding the bubble. Thus the bubble gas forms a vortex ring and stays segregated from the rest of the gas in the bed.

Modeling of Fluidized Bed Reactors

Basic two-phase model for fluidized bed.

Two-phase model to represent the bubbling fluidized bed, with its six adjustable parameters, v l, V 1, (D/uL) 1, (D/uL) 2, m, K.

10 We ignore the flow of gas through the cloud since the cloud volume is very small for fast bubbles. K BC, K CE  infinite We ignore the flow of gas, either up or down, through the emulsion since this flow is much smaller than the flow through the bubbles. First order Reaction Application to Catalytic Reactions Neglecting gas flow in cloud nad emulsion

TWO PHASE REACTOR MODEL Solid balance : πR² L = π R² L0 + π R² L (NV) Or L= L 0 /1-NV L= height of fluid bed, L 0 =height of the unexpanded bed N= Number of bubbles per unit volume of bed V=average volume per bubble R= radius of the bed. For mass transfer between bubbles and emulsion phase define a mass exchange coefficient as the sum of individual coefficients relating to diffusional transport and cross flow

Mass exchange coefficient: Q (or K bc )= q+ kd S Q: Overall coefficient (vol./time) q= cross flow coefficient (vol./time) Kd= normal mass transfer coefficient, S= interface area NO REACTION IN BUBBLE PHASE => Cocn. Changes of position are possible only via interphase transport and mass balance in the reactor.

Material Balance for Gas and for Solids Material balance for the bed materials yields: U br = 0.711(gd b ) 1/2, (acceleration of gravity = 9.8m/s 2 ) m/s rise velocity of a single bubble in a Bed otherwise at u mf. Rise velocity of bubbles in a bubbling bed

f b = , vol. of solid /vol. of bubbles] in bubble phase f c in cloud phase and fe in emulsion phase f or ϒ. f b +f c +f e = f total = 1- ἐ f

Solid balance