Standpipes in Packed Bed Flow

If the relative upward velocity of the gas Uf- Up) is less than the relative velocity at incipient fluidization (Llf - Up), then packed bed flow results and the relationship between gas velocity and pressure gradient is in general determined by the Ergun equation [see Chapter 6, Equation (6.11)]. 

The Ergun equation is usually expressed in terms of the superficial gas velocity through the packed bed. However, for the purposes of standpipe calculations it is useful to write the Ergun equation in terms of the magnitude of the velocity of the gas relative to the velocity of the solids Lfrei (= Uf — Up ). (Refer to Section 8.1.4 for clarification of relationships between superficial and actual velocities.) 

Superficial gas velocity, U = 8 LTrei And so in terms of LJrei the Ergun equation becomes  

The equation allows us to calculate the value of LTrei required to give a particular pressure gradient. We now adopt a sign convention for velocities. For standpipes it is convenient to take downward velocities as positive. In order to create the pressure gradient in the required direction (higher pressure at the lower end of the standpipe), the gas must flow upwards relative to the solids. Hence, LTrei should always be negative in normal operation. Solids flow is downwards, so Up, the actual velocity of the solids (relative to the pipe wall), is always positive. 

Knowing the magnitude and direction of Up and LTrei, the magnitude and direction of the actual gas velocity (relative to the pipe wall) may be found from IJrei = Hf — Up. In this way the quantity of gas passing up or down the standpipe may be estimated. 

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