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Determining the Agitator Shaft Loading and Power

Q: I am working on the design for a fluid bed reactor. The design includes an agitator that will move the aggregate in the bed. Do you know of equations that I can use to determine the agitator shaft loading and the power required for the agitation?

A: There are no equations to directly determine agitator power for several reasons.  First, the shape of the impeller is important to performance, shape and power characteristics are unique to each mixer type.  Second, the power requirement in a powder application depends on the bulk density and the flow characteristics of the aggregate in the bed.
 
About the only "equation" that does apply is that power will be roughly proportional to the bulk density of the aggregate, the rotational speed of the mixer cubed, and the diameter of the mixer impeller raised to the fifth power.  The base line characteristics must be determined by experimental measurement.  Actual power requirements may also change with the shape, size, and flow characteristics of the aggregate.
 
No simple answer to this question - too many variables and unknowns.

Here are more of the latest questions on: Mixing

How do I select the optimal location for an impeller inside a tank?
I am new to tank mixing and I have a question about selecting the optimal location (and orientation) for an impeller inside a tank. I am dealing with a tank that contains very light materials (0.7 and 0.8 SG). The contents have been sitting in the tank and are stratified. Please let me know if there is some sort of general process for selecting the proper impeller position.

The tank is 120 ft. in diameter, 45 ft. high. It is allowed to only have one mixer. The first layer of material has a specific gravity of 0.75 is 32 ft. high. The second layer of the tank has a specific gravity of 0.67 and is 10 ft. high; making the total contents of the tank 42 ft. high. The purpose of the mixer is to have complete mixing within 6 hours.

Is a UDIF impeller suitable?
We have been using a UDIF agitator for emulsion polymerization mixing for 1cp to 8,000 cp. Is this type of agitator suitable for mixing?

What kind of agitator is suitable for a range of viscosities?
Our process dissolves several types of polymers in appropriate solvents. During the solving process, the viscosity might reach to the value of 8,000 cp. Our vessel dimension is 30 cm in diameter and 70 cm in height. What kind of agitator is suitable for this purpose?

What is the best way to approach gas-gas mixing?
I want to mix two low viscous gas streams in laminar regime. I am planning to mix them by passing through a pipe filled with spherical pebbles or some structured packing. I want to calculate the length required for the mixing expected. My required process stream details are as follows:

Q = 1Nm³/hr
He= 0.99
H₂= 0.01
P= 1.2 bar
Dia of pipe = 1/2 inch
Temp= 25 degrees C

I have gone through the text book "Handbook of Industrial Mixing." But that textbook has procedure for only commercially available static mixers. Please guide me through the design. Is dispersion model helpful in finding the length? If so, how?

We would like to have a general idea of pumping number for our reactors. Can you help us with blend-time calculations?
To characterize one of the reactors at plant scale, we use the discoloration method. The parameters for the mixing time are calculated based according to the following formula:

t_mix= K/(aN(D/T)^b (T/Z)^0.5 )
N = impeller speed
D = diameter stirrer
T = diameter tank
Z = liquid height
The divisor is known as Kmix

Because we don't really know the uniformity (U) reached with this method we don't replace K with

K = -ln (1-U)

But get the best fit for K, a and b by means of the least square method. It is known that the pumping number can be determined by

N_Q= (Vk_mix)/(ND^3 )

We would like to have a general idea of pumping number for our reactors. So if we would like to deviate the pumping number from the above method would it be correct that for T=Z (so at a fixed volume based on the reactor geometry) we use the following formula.

N_Q= (VaN(D/T)^b)/(ND^3 )

Working in a turbulent regime, this result in a constant pumping number related to the tank geometry. Would the above approach be correct to compare pumping and mixing time capabilities of different reactor set ups? I think that not working at a fixed uniformity results in a gap in the above approach.

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