EANx Shaken or Stirred?

[miketsp]

bizzare...

my first rough shot at surfing around the net trying to figure this out gives an RMS velocity of around 500 m/s for N2 and O2 and 1348 m/s for He, but a mean-free path at 300 bar of around 50 A for He. that gives a diffusion coefficient of around 2.5 x 10**-6 m^2/s which means an average delta-T of like 400000 seconds (111 hours) to travel a meter.

There seems to be a consistency here.
According to Bird & Welty (see below) the diffusion coefficient is function of pressure & temperature.
There is a formula which I can't reproduce here which starting at a reference condition lets you generate a modelled condition.
If we assume that the temperature is constant, most of the complicated terms disappear leaving a linear pressure relationship.
So starting with an O2 N2 binary pair at 20C the reference diffusion coefficient is approximately 0.22cm2/s.
At 200bar it will be 200 times less, ie. 0.0011cm2/s.
If x is the rms diffusion radius.
So taking x^2=2 x D x t.
In 60seconds, x^2 = 0.13 or x = 0.36cm
In 400000 seconds x=30cm
Within an order of magnitude of your result.

Diffusion is much slower than I would have imagined intuitively. :11:

The obvious answer of course is that most diffusion takes place while pressures are lower at the beginning of the fill and normally the lower pressure gas enters first to occupy the whole volume available.


Transport Phenomena. Bird, R.B., W.E. Stewart, and E.N. Lightfoot. 1960. John Wiley & Sons. NY. 780 pp

Fundamentals of Momentum, Heat, and Mass Transfer, 3rd Ed. Welty, J.R., C.E. Wicks, and R.E. Wilson. 1984. John Wiley & Sons,NY. 803 pp

 

[Rick Murchison]

There seems to be a consistency here.
According to Bird & Welty (see below) the diffusion coefficient is function of pressure & temperature.
There is a formula which I can't reproduce here which starting at a reference condition lets you generate a modelled condition.
If we assume that the temperature is constant, most of the complicated terms disappear leaving a linear pressure relationship.
So starting with an O2 N2 binary pair at 20C the reference diffusion coefficient is approximately 0.22cm2/s.
At 200bar it will be 200 times less, ie. 0.0011cm2/s.
If x is the rms diffusion radius.
So taking x^2=2 x D x t.
In 60seconds, x^2 = 0.13 or x = 0.36cm
In 400000 seconds x=30cm
Within an order of magnitude of your result.

Diffusion is much slower than I would have imagined intuitively. :11:

The obvious answer of course is that most diffusion takes place while pressures are lower at the beginning of the fill and normally the lower pressure gas enters first to occupy the whole volume available.


Transport Phenomena. Bird, R.B., W.E. Stewart, and E.N. Lightfoot. 1960. John Wiley & Sons. NY. 780 pp

Fundamentals of Momentum, Heat, and Mass Transfer, 3rd Ed. Welty, J.R., C.E. Wicks, and R.E. Wilson. 1984. John Wiley & Sons,NY. 803 pp

I think y'all are missing the major mixing component in a tank fill, which isn't diffusion but rather mechanical. Gas is not gently poured into the container, even on a slow fill, but rather injected a few inches into the tank at the end of the valve tube, creating turbulence and subsequent mixing of the gasses continuously during the fill (hence the efficacy of the "final slam" method). Diffusion finishes off the already "mostly done" process; the final stable mix is achieved much sooner than if the gasses were truly stratified and dependent upon diffusion alone for the final complete mixing.
Rick

 

[lamont]

I think y'all are missing the major mixing component in a tank fill, which isn't diffusion but rather mechanical. Gas is not gently poured into the container, even on a slow fill, but rather injected a few inches into the tank at the end of the valve tube, creating turbulence and subsequent mixing of the gasses continuously during the fill (hence the efficacy of the "final slam" method). Diffusion finishes off the already "mostly done" process; the final stable mix is achieved much sooner than if the gasses were truly stratified and dependent upon diffusion alone for the final complete mixing.
Rick

Right, so lets figure out what scale of 'structure' diffusion will be able to finish off...

Turns out that my statistical and thermal physics book (Reif) has a sample problem for diffusion of N2 across a 1m chamber at 1 atm. The answer is conveniently in the back of the book and is 3 hours. Which agrees with the numbers that I was getting as well.

At 300 bar, the diffusion constant is 300 times smaller and the viscosity of the gases is 300 times higher. That makes for 900 hours to cover 1m which is similar to what I computed for Helium (Helium is faster and smaller though so it diffuses faster -- 100 hours).

So, lets instead ask what scale will be covered by diffusion over 1 hour. That is 900 times less, which will cover 1/sqrt(900) = 1/30 of the distance or about 3 cm.

So, you need to introduce enough bulk flow in your cylinder to remove structure greater than 3 cm in order to have diffusion over the course of an hour remove the rest of it.

And the analogy is probably that gas diffusion at 300 bar becomes less like diffusion of a drop of food coloring in a glass of water, and more like diffusion of something in motor oil or maple syrup. That viscosity may also explain why a slow fill isn't sufficient to produce convection to remove all the structure.

 

[Rick Murchison]

So, lets instead ask what scale will be covered by diffusion over 1 hour. That is 900 times less, which will cover 1/sqrt(900) = 1/30 of the distance or about 3 cm.

So, you need to introduce enough bulk flow in your cylinder to remove structure greater than 3 cm in order to have diffusion over the course of an hour remove the rest of it.

I think I'm going to adopt the method of slam filling that last 50 psi myself...
Rick

 

[MXGratefulDiver]

I think y'all are missing the major mixing component in a tank fill, which isn't diffusion but rather mechanical. Gas is not gently poured into the container, even on a slow fill, but rather injected a few inches into the tank at the end of the valve tube, creating turbulence and subsequent mixing of the gasses continuously during the fill (hence the efficacy of the "final slam" method). Diffusion finishes off the already "mostly done" process; the final stable mix is achieved much sooner than if the gasses were truly stratified and dependent upon diffusion alone for the final complete mixing.
Rick

Exactly ... diffusion models assume that the two gasses are being mixed at the same relative pressure, and under static conditions. That's not how it happens. The turbulance of the air entering the dip tube will do most of the mixing almost immediately.

A better analogy would be mixing gasoline for a two-stroke engine. You pour a bit of oil in the bottom of the container, then finish filling the container at your local gas pump. How much diffusion does it take to mix the two? Not much ... if any. The turbulance of the gas entering the container does the job almost completely (and immediately).

Rather than relying on theoretical mathematical models, why don't y'all do the empirical measuring I mentioned earlier. I'm sure a few of the folks involved in this discussion have access to an O2 analyzer ... and seeing is believing ...

... Bob (Grateful Diver)

 

[miketsp]

Exactly ... diffusion models assume that the two gasses are being mixed at the same relative pressure, and under static conditions. That's not how it happens. The turbulance of the air entering the dip tube will do most of the mixing almost immediately.
..snip..

After playing with some of the equations, I'm not that sure how much turbulence there is during a fill. Lamont's analogy of something nearer motor oil is probably not far wrong. Sure there will be some mixing but more like a fluid than the way we imagine gases blowing around.
This may help to explain why rolling a cylinder does have some effect on the contents. I feel sure that rotating a cylinder containing 1 bar would not cause any mixing effect as the friction between the inner surface and the mass of gas would not be significant. However at 200 bar it's another ball-game.
I'm still meditating on the heat transfer properties of compressed gases - how long does it really take for the cylinder and gas to stabilise at room temperature?

 

[DA Aquamaster]

Exactly ... diffusion models assume that the two gasses are being mixed at the same relative pressure, and under static conditions. That's not how it happens. The turbulance of the air entering the dip tube will do most of the mixing almost immediately.

A better analogy would be mixing gasoline for a two-stroke engine. You pour a bit of oil in the bottom of the container, then finish filling the container at your local gas pump. How much diffusion does it take to mix the two? Not much ... if any. The turbulance of the gas entering the container does the job almost completely (and immediately).

Rather than relying on theoretical mathematical models, why don't y'all do the empirical measuring I mentioned earlier. I'm sure a few of the folks involved in this discussion have access to an O2 analyzer ... and seeing is believing ...

Exactly Bob. When I fill deco bottles I do the 02 pretty slow at 50-60 psi/min to keep things cool, but the last 1900 psi of air on top of the O2 needed for 50% fills in 30's and 40's is put in over the course of only about 5-6 minutes. There is some heating that occurs so I normally overshoot by about 150 psi to account for the cooling that will occur. I can analyse immediately and know within a few 10th of a percent where it will be in 24 hours.

 

[lamont]

i had a minor little eureka moment when i put it all together about why N2/O2 becomes thick to breathe deep (increased viscosity) and why He in the mix deep will help with breathing. obviously its because viscosity is proportional to pressure in a gas, while He is a smaller molecule so its mean-free path is higher, cross section is lower and viscosity is lower.

so, if nitrox starts getting too thick to breathe easily at 7-10 ata, at 200-300 bar it will be much thicker than what we're used to.

 

[Lead_carrier]

Just drop the tanks off to Rick. Pick them up in a couple of days. Plenty of time for complete mixing a-la naturel. No muss, no fuss. Just good diving.