Thought experiment: Diffusion between tanks

[tridacna]

Assume the following:

Three gas cylinders each filled to half working pressure.

Tank 1 has EAN25.
Tank 2 has EAN50
Tank 3 has EAN75

All three are connected together with a standard whips. Assume ID of 1/8".

Whips are turned on simultaneously.

How long before the gas diffuses between all three tanks until EAN50 is achieved in all three? Obviously the diameter and length of the whips are the most important variables here. If the ID of the whip is the same as the ID of the tank, equilibrium will be established almost immediately. But we're trying to contemplate a real life working situation.

I'm a mathematician and my buddy is an engineer. We've struggled unsuccessfully trying to establish some kind of formula to establish diffusion patterns. Anyone out there in "Fluid Dynamic land " have any ideas?

 

[RyanT]

Test it empirically. My guess is that it would take quite a while.

 

[2airishuman]

Can't give you a formula, but I would be very surprised if you could measure a change in composition with a standard handheld analyzer after, say, a week.

 

[KeithG]

some light reading

Oxygen Diffusion/Air - Cornell Composting

and

http://lss.fnal.gov/archive/2005/conf/fermilab-conf-05-635-ad.pdf

 

[tbone1004]

the dip tubes are VERY small so are the passages in the tank valve itself. I would guess a long long time before you'd see anything meaningful. @victorzamora is a fluid dynamicist and may be able to answer though

 

[lowviz]

...//... How long before the gas diffuses between all three tanks until EAN50 is achieved in all three? ...

Wow.

If I had to model it I would use the mean free path for each gas and random walk theory (http://ocw.mit.edu/courses/mathemat...d-diffusion-fall-2006/lecture-notes/lec01.pdf). Figure out what percent of the wall was the exit port, and go to it. I'd make the whips zero length and see what I got wrt a few quick experiments. I'm guessing that you would get pretty close under ideal conditions.

Problem is, IMHO, other forces are overwhelming. Like convection and physical motion. I base this on the fact that jetting O2 on top of a tank of air won't give you a good reading for quite a while. Exact same diameter. On the few rare occasions that I was in a hurry, my LDS would analyze, roll the tank for 15 minutes, then re-analyze. Try it, really surprising.

 

[victorzamora]

Diffusion of different gases between cylinders of the same pressure gets REALLY wonky and hard to model. LowViz had a good recommendation, and you can start plugging in variables using experimental data to get a decent model. Doing it via purely theoretical model isn't healthy to think about because of how many factors are at play. It's a weird dynamic because no P difference means no gas movement but pp differences will induce a tension. There's no surface tension, but there are elements of friction between layers.

 

[tridacna]

Wow.

If I had to model it I would use the mean free path for each gas and random walk theory (http://ocw.mit.edu/courses/mathemat...d-diffusion-fall-2006/lecture-notes/lec01.pdf). Figure out what percent of the wall was the exit port, and go to it. I'd make the whips zero length and see what I got wrt a few quick experiments. I'm guessing that you would get pretty close under ideal conditions.

Problem is, IMHO, other forces are overwhelming. Like convection and physical motion. I base this on the fact that jetting O2 on top of a tank of air won't give you a good reading for quite a while. Exact same diameter. On the few rare occasions that I was in a hurry, my LDS would analyze, roll the tank for 15 minutes, then re-analyze. Try it, really surprising.

Wait. Assume two magical tanks with tops cut off. One tank is placed on top of the other separated from the other by a magical plate. One half EAN25 the other EAN75 - both at pressure. Plate is removed joining tanks forming one tank. How long before EAN50 is achieved? Intuitively one assumes the gasses would equalise fairly quickly. Am I wrong?

 

[lowviz]

...//... Intuitively one assumes the gasses would equalise fairly quickly. Am I wrong?

Real world experience says: Yes. (I was just as surprised as you are)

Take a tank full of air (below working pressure) and add O2, N2, He, your pick. All you need is an oxygen analyzer and a clock. My LDS folded, have another in my gunsights. I may re-do exactly that test when I try them out. It would be a great test to see if they release the non-blended tank...

 

[victorzamora]

Wait. Assume two magical tanks with tops cut off. One tank is placed on top of the other separated from the other by a magical plate. One half EAN25 the other EAN75 - both at pressure. Plate is removed joining tanks forming one tank. How long before EAN50 is achieved? Intuitively one assumes the gasses would equalise fairly quickly. Am I wrong?

Yeah, you're actually pretty wrong there. It's VERY counter-intuitive. This scenario isn't AS perfect as what you're discussing, but take a set of doubles. Isolate them. Pump pure O2 into one and air into the other, both at equal pressures. You'd expect a mix of EAN60.5 when you open the isolator....and it WILL eventually get there, but it takes a while. SOP in many shops that do partial pressure fills is to roll the tanks around before analyzing.

Heck, I witnessed FIRST HAND a shop pump O2 into a tank, then air into that, and then analyze only EAN23. After some rolling of the tank, it analyzed at EAN30. The different gas mixtures almost act like fluids of different densities...which they shouldn't do. It's very counter-intuitive.