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Mixing Time and Residence Time

Q: I'm going to calculate residence time in a static mixer, but I don't know what the exact difference is between mixing time and residence time. Are the baffles shape and their numbers and the Re number of the mixed fluid the only parameters that affect the residence time? What about the entrance distance of the mixer? Is that up to me, or it has a specified amount? If the mixed flow regime is laminar at the beginning, it must be Turbulent after passing the inserts? Should I consider this change of Re number through mixer for my calculation? About the mixer specification, I am going to use a helical static mixer for just mixing two different fluids (there is no suspension or bubble in the mixed flow.)

A:

The residence time in a static mixer is just the length of the mixer divided by the flow velocity.  Flow velocity is just volumetric flow rate divided by the cross-sectional area of the pipe.  You need to decide on those values.  Typical flow velocities are 4 to 10 feet/second, the lower end of that range is probably more typical of laminar flow applications, you can do the units conversion to whatever units you want to use.
 
Baffle shape and number will affect the mixing.  The Re number can be calculated and used to decide how many baffles (elements) are needed for good mixing.  If the flow entering the mixer is laminar, it will remain laminar throughout the mixer.  The Re number does not change.
 
I am not sure what you mean by entrance distance to the mixer.  The point where your two fluids should be only about a pipe length upstream from the mixer.  For best flow, the upstream and downstream pipe should be straight for at least 10 pipe diameters.  Static mixers are like a pipe section with some additional pressure drop that provides the energy for mixing to take place.

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What is the best way to approach gas-gas mixing?
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Q = 1Nm³/hr
He= 0.99
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Temp= 25 degrees C

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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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