[Bored chemist]

In the case of everest top, the molecular weight of nitrogen is similar to air, hence the separating factor is very small compared to mixing factors which come from diffusion and agitation by wind.

People think it's the wind that keeps the atmosphere mixed; it's not.
Wind speeds are typically a few metres per second.
Thermal speeds are about 100 times higher.

[Bored chemist]

How much g-force is required to get 75% SO2 in the bottom half of the pipe?

Very roughly, enough that, if you dropped something, the kinetic energy it picked up as it fell would be enough to double its thermodynamic energy.
Most people don't even know that dropping something warms it up.
You would need a gravitational field such that dropping an apple off a chair would cook it when it landed.

[hamdani yusuf (OP)]

Most people don't even know that dropping something warms it up.
You would need a gravitational field such that dropping an apple off a chair would cook it when it landed.

Is the warming caused by air friction or is it by impact with the floor?

[hamdani yusuf (OP)]

In the case of everest top, the molecular weight of nitrogen is similar to air, hence the separating factor is very small compared to mixing factors which come from diffusion and agitation by wind.

People think it's the wind that keeps the atmosphere mixed; it's not.
Wind speeds are typically a few metres per second.
Thermal speeds are about 100 times higher.

I think I've already included the thermal speed factor when I mentioned diffusion.

[hamdani yusuf (OP)]

Even in  a sealed container with no temperature gradient, you won't get a useful degree of separation.

What do you think will happen if I put a mixture of Helium, Nitrogen, and SO2 with equal volume and pressure inside a 10 meters vertical pipe. Will we get the same composition between top and bottom part?

Very Very nearly.

Fundamentally, we need to consider two terms.
How much energy does a mole of SO2 release by sinking to the bottom (and letting the air rise).
How much thermal energy does that same SO2 have.

Say the pipe is a metre high and initially full of 50:50 SO2 in air.
If all the SO2 "settled" then it would (at the same pressure)  move down from (on average) 0.5 metres to (again, on average) 0.25 metres
a Mole of SO2 has a bass of about 64 grams.
And it falls (on average) by 0.25 metres.
In doing so it releases  potential energy equal to Mgh
0.064 *9.81*0.25
That's 0.157 J
And, in doing so it lifts the air- which takes (by a similar calculation)
0.029 *9.81*0.025
That's 0.071 J
So the net energy released by letting it settle is
0.157-0.071 =0.085 J/ mole

And the (thermal) kinetic energy of a mole of SO2 is 3/2 RT
where R is the gas constant- about 8.31 J/mol/K

So, with a temperature of about 300K, the energy is about 2500 J/ mole
So the thermal energy is roughly 2500/ 0.085 i.e. about 30,000 times bigger than the gravitational energy. We can see there's not going to be much separation.

We can now use the Boltzmann distribution to see what the proportions of the material will be in the upper and lower energy states (corresponding to the upper and lower halves of the tube).

The Botzman factor is given here
https://en.wikipedia.org/wiki/Boltzmann_distribution

Boltz.png (2.68 kB . 157x92 - viewed 14963 times)

e_j and  e_i are the gravitational energies in the upper and lower states.
And the difference between them is 0.085 J/mole

KT is 2500

So the Boltzmann factor is exp(0.085/2500) which is 1.000034
For every molecule in the upper half of the tube, there will be 1.000034 in the bottom half.

It's slightly less bad with a 10 metre pipe. Exp((0.85/2500) roughly 1: 1.00034
So, 50.0085% of the SO2 would be in the lower half of the tube and 49.9915 % in the top.

Speaking as an analytical chemist, there's no way you could measure that difference.

Typical gas centrifuge rotors are of the order of 50 millimetres in radius and spin at something like 60,000 revolutions per minute.
The calculation here
https://en.wikipedia.org/wiki/Centrifuge
gives the "acceleration" as
1.1118 * r/1000000 * n^2
where r is the radius and n is the number of revolutions per minute.
In the case of a gas centrifuge that gives something like
1.118 * (50 /1000000) * 60000^2
About 200,000 g

It's tricky to build stuff that will survive forces  200,000 times its weight.

Even with those sorts of figures, the gas centrifuges used for isotope enrichment  are not good enough.
You need cascades of them in series.
But, as you say, the SO2/ air case is much easier than U₂₃₅F6 vs U₂₃₈F6

If we had one of those centrifuges then the energy difference between "top" and "bottom" would be 20 times less- because of the difference in "height"- 50mm vs 1 metre)  But 200,000 times more because of the increased acceleration.
So that's a 10,000 fold improvement overall.
So the exponential factor is improved from about 30,000 to about 3
exp(0.333) is about 1.4
So your gas stream containing 0.2%  would be split into a rich stream containing about 0.28% and a "clean" stream containing about  0.14%.


I don't know what the pollution control limits are where you are, but I will guess that they might let you vent a waste stream with 100 ppm v/v
And your current effluent is 0.2% which is 2000 ppm
So you need a 20 fold reduction.
You can get that by cascading centrifuges. each one gives a reduction  of SO2 by  a factor of about 1.4 So, about 9 stages should do it.

Then we need to look at running costs.
In order to work, the gas gas to get spun up to high speed. and then slowed down again when it leaves as either  the enriched or depleted stream.The tangential speed of a centrifuge like this is about mach 2

I really appreciate your time and effort you've spent to write this post. Thank you very much. I hope you are fine there especially during this pandemic.

So, you need to figure the cost of raising all your effluent gas to mach 2 (then slowing it down again) 9 times.
Each tonne of gas will need to be whizzed up to 700 m/s- which takes 1/2 *1000*700^2 Joules of energy
That's 245 MJ per tonne.
Nine times
2.2 GJ per tonne.
So one tonne per second would take 2.2 GW
Or 1 tonne per day would need 25.5 KW
24 Hrs at that rate, if it was on my electricity bill would cost about £100

Is your product worth £100 per tonne?



Almost anything is a better option than a gas centrifuge

We can save energy using regenerative design. Our utility air dryer condenses water vapor by cooling it and then heat the dry air back after the water condensate is drained. So the only energy lost is for cooling the water vapor into condensate. The energy for cooling and reheating the air is significantly reduced.
In principle, the energy used to speed up the gas can be reclaimed back when it is slowed down.

[Bored chemist]

Most people don't even know that dropping something warms it up.
You would need a gravitational field such that dropping an apple off a chair would cook it when it landed.

Is the warming caused by air friction or is it by impact with the floor?

Whichever.
The point is that this would be a world where it took as much energy to lift a pan of water onto the cooker as it would to boil it.

[Bored chemist]

I think I've already included the thermal speed factor when I mentioned diffusion.

And that diffusion is why, at equilibrium, 49.9915 %of the SO2 is in the "wrong" half of the tube.

In principle, the energy used to speed up the gas can be reclaimed back when it is slowed down.

If you are lucky, you might recover enough energy to power the pumps etc you would need to get the product through the plant.

[hamdani yusuf (OP)]

In this video, the gas don't seem to diffuse much. Jump to 2:30 to see what I mean.

[Bored chemist]

The essential point of that video is that they use a gas with one of the slowest diffusion rates available.