Standpipes in Fluidized Bed Flow

If the relative upward velocity of the gas (LTf ITp) is greater than the relative velocity at incipient fluidization (LTf LTp)jjj, then fluidized bed flow will result. In fluidized bed flow the pressure gradient is indejjendent of relative gas velocity. Assuming that in fluidized bed flow the entire apparent weight of the particles is supported by the gas flow, then the pressure gradient is given by (see Chapter 7)  

The starting point is Equation (8.13), the equation derived from the continuity equations for gas and solids flow in a pipe. For fine Group A solids in question the relative velocity between gas and particles will be very small in comparison 

Using subscripts 1 and 2 to refer to the upper (low pressure) and lower (high pressure) level in the standpipe, since Mp, Mf and pp are constant  

Let us assume that the voidage 2 is the lowest voidage acceptable for maintaining fluidized standpipe flow. Equation (8.29) allows calculation of the equivalent maximum pressure ratio, and hence the pressure drop between levels 1 and 2. Assuming the solids are fully supported, this pressure difference will be equal to the apparent weight per unit cross-sectional area of the standpipe [Equation (8.26)]. 

If 1 and 2 are known and gas density is regarded as negligible compared to particle density, H may be calculated from Equation (8.30). 

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