View Full Version : Gas Compression
Okay, as no one took me up on the other thread, I'll need to try again.
I am led to understand that air doesn't really compress in a linear way to 300 bar, although it does basically in a normal 232 cylinder - but I don't know why and can't really find any info on this.
I have a 232 and a 300 bar cylinder and can confirm from my experience that this rings true - I don't get the feel of 30% more air in the 300 bar (or extracting my 50 bar reserve - ha ha - 37% more available air).
I guess the answer to this is that there is some other force that at higher pressures repels the molecules or some such. They are surely not so tightly packed they can't go any further otherwise they would become liquid or solid next (although I guess there is some equivalent specific pressure version of the specific heat to overcome requiring further input of energy before the state would actually change).
First point is if someone could point out the mechanism / forces at work here.
Second point is where this mechanism actually kicks in - ie how many bar or is it a range?
Finally is this the same for all gases, or is it only certain gases, maybe just one of the elements in air?
Either feel free to write a full thesis here or simply redirect me to a web page with the explanation, but I couldn't find a complete explanation when I searched the web myself.
PS, no, just knowing that this is how it happens isn't enough. Thanks. :)
nice of you to ask an easy question....
Mr Van de Wall will answer for you:
JOHANNES DIDERIK VAN DER WAALS 1837-1923 Amsterdam University
1910 Nobel Prize for Physics for his work on the equation of state for gases and liquids.
This tends to indicate that he knew his stuff.
OK. The simple rules for gases about pressure, volume and temperature that you learnt in Scuba for beginners are only an approximation. Good enough for some poor lad or lass who has to worry about doing a mask clear without a total sinus washout but now you're grown up and want to breathe fancy stuff it just won't do anymore.
You haven't forgotten but we'll recap anyway.
Do you remember PV=kT?
The ideal gas law? Oh yes. The one that summarised all the others ones that we can't remember the names of. Well let us get rid of that nasty k for an arbitrary constant and turn it into the real one PV=nRT that scientists use. This is much better because we can calculate things with it rather than just do ratios. Let's name the parts in useful units:
P Pressure in bar V Volume in Litres n Quantity of gas in mols R The universal gas constant 0.0831451 if we want to do bar and litres T The temperature in Kelvins (virtually Centigrade+273) mols? Well it's a chemists trick to have a measure of something rather than work in boring units like grams.
A mol is a gram molecule. It is the amount of a substance that weighs X grams where X is the molecular weight of the molecule in question.
So Oxygen has an atomic weight of 16 (well 15.994 if you want to get all isotopic about it) so O2 has a molecular weight of 32 so 32 grams of O2 is one mol and 64 grams is 2 mols etc. Plutonium Oxide has a molecular weight of 536 so it take over half a kilo of that stuff to make a mol but chemists don't care. The neat trick is that 1 mol contains 6.02x1023 molecules. A mol is not so much a quantity as a head count and is great when you are working out how things react.
Great. Real numbers. Let's do an example. The 100% oxygen deco bottle is 3L, it is January at Stoney Cove so it is 4C, that is 277K and we want the whole 300 bar.
So n = PV/RT so n = (fumbles with calculator) n = 39 mols so at 32 grams to the mol we have 1.248 Kilograms of Oxygen.
Then along comes Van der Waals in spoil sport mode and says "well not really".
The trouble is that this thing is the Ideal gas law. That is it only really would work for an ideal gas and all we have are real ones. An ideal gas is about as common as an ideal husband/boy friend or an ideal wife/girl friend. Yup. They don't exist. An ideal gas would be composed of infinitely small molecules that did not attract one another but real gases have real sized molecules taking up the space and they tend to attract and repel one another. Van der Waals was the man who set about solving the problem by working out how to allow for real gases.
What he came up with was not the exact answer but a much better gas equation.
http://www.nigelhewitt.co.uk/diving/maths/vdw1.gifIf you look at it and remember PV=nRT you can see the old ideal gas equation in here but with two extra terms, one applying a fiddle factor to the pressure to allow for the attraction between molecules drawing them inwards and reducing the pressure on the outside world and the other fiddle factor is on the volume where it is effectively reduced to allow for the fact that all these molecules are taking up space. We get two new constants a and b which depend on the gas we are considering.
Back to the example for our tank of O2 and use the Oxygen a value of 1.382 and the b value of 0.03186 and we get a different situation.
Putting our 1.248Kgs ie. our 39 mols of Oxygen into our 3L tank gives 277bar.
OK lets graph that with mols along the bottom and pressure in bar up the left.
http://www.nigelhewitt.co.uk/diving/maths/vdw3.jpg
What's this mean? The nice straight purple line is gas pressure against mols of gas for the Ideal law. The blue line sweeping upwards is Van der Waals' calculation.
Down at 0 to 20 bar, where you did you school physics and your diving it is very good. Up at 100 bar it takes 15 mols of Oxygen to get 100 bar and for 200 bar it takes 30 mols but for 300 bar you do not have the 45 mols you expected but just 41. This is why divers get edgy about mixing Nitrox to 300 bar final pressure.
It gets worse.
We assume for ideal gases that we can work out the partial pressures independently and just add them up (Dalton's Law) and moreover we assume that the ratios don't change with pressure. Now for nitrox it happens that the a and b values for Nitrogen are similar to Oxygen but if (simplistically) we put 100 bar of Oxygen in a tank and then topped it off to 300 bar with pure Nitrogen we do not have 33% Nitrox. It is a bit higher. More like 37%.
We can calculate it but Van der Waals' equation as stated above only applies to the simple monatomic gases and as the molecules of one gas see the others nothing is simple. However we can produce modified a and b constants for the mixed gas formed using the values for each gas combined using:
http://www.nigelhewitt.co.uk/diving/maths/vdw2.gif
What on Earth? Yes. I did university physics and I winced a bit at that one. What it is saying that for a mixed gas made of n gases (1 to n) whose fractions (ratio of mols) are x1, x2, x3... xn and whose a and b values are a1, b1, a2, b2 etc. then you get the global a and b values by taking the formula to the right of the two sigma signs and adding up all the bits. If you have three gases (Oxygen, Nitrogen and Helium for example) then
a = √(a1*a1)*x1*x1 + √(a1*a2)*x1*x2 + √(a1*a3)*x1*x3
+ √(a2*a1)*x2*x1 + √(a2*a2)*x2*x2 + √(a2*a3)*x2*x3
+ √(a3*a1)*x3*x1 + √(a3*a2)*x3*x2 + √(a3*a3)*x3*x3
and naturally b looks much the same. This was probably grief to poor old Van der Waals but we have spread-sheets on our home computers...
Once you have done this you can work out the total pressure but don't think in partial pressures, Dalton style, any more because they don't exist. Definitely don't try to work back from pressure to ratio. It's horrible.
see the complete post at
http://www.nigelhewitt.co.uk/diving/maths/index.html
Dont ya just love good old advancd calculus!
donnyscuba
05-06-08, 08:18
hmmmm........... eh?:confused::confused::confused:
Well done Andy! Take a bow :D
I need to find some pain killers now as my forehead hit the keyboard when I got 2/3 of the way down :rolleyes:
Lizardland
05-06-08, 09:10
Or you can just do what my local shop does, put the cylinders on the scales and start pumping until you hit the right weight of gas in them :D Pressure and temperature become irrelevant because you're dealing in grammes of O2, N2 and He. I've seen them do a trimix fill in a twinset in 10min, cylinders were red hot but give it a couple of hours to cool and the pressure and %ages were spot on.
Yogi Diver
05-06-08, 09:27
Or you can just do what my local shop does, put the cylinders on the scales and start pumping until you hit the right weight of gas in them :D
JOHANNES DIDERIK VAN DER WAALS Eat yer heart out!:D:D:D
Dont ya just love good old advancd calculus!
This was a bit like reading Hawkins, A brief history of time - it started out well and seemed to be helping, until the end when my mind glazed over and I started to wonder if I wanted to know more or even this much, or whether the writer would simply leave me alone.
But thanks , I'll give this another read when I am not at work and see if it gets any better.
woah there Thanks for that Andy, although does it answer the question, I too hit my head on the keyboard about 1/2 way down :(
i could write a simple version for you! like without so many big sums?
this is high school algebra so's it quite easy
http://www.nigelhewitt.co.uk/diving/maths/vdw1.gif
but this is about 3rd year engineering degree level calculus.
http://www.nigelhewitt.co.uk/diving/maths/vdw2.gif
anyone thats ever done proper Fourier Harmonic analysis will manage it, I can highly recommend "Mathematics for Engineers and Scientists by Weltner"
However, the chemistry and physics are again high school "Highers" / 6-form level.
Mmmmmm I just give them my tanks and ask them to be filled, then i empty them when i go for a dive. Did higher physics at School and got a B but never used it again since then, nobody ever asks me the mass coefficent of the vehicle while travelling at 10 m/s anyway.
Yogi Diver
06-06-08, 15:08
Mmmmmm I just give them my tanks and ask them to be filled, then i empty them when i go for a dive. Did higher physics at School and got a B but never used it again since then, nobody ever asks me the mass coefficent of the vehicle while travelling at 10 m/s anyway.
Hi Shog,
You're a car salesman.
What's the mass coefficient of a Mondeo travelling at 10 m/sec?
:D:D
Depends on the surface tension of the road and tyre friction qualities :D :D
Depends on the surface tension of the road and tyre friction qualities :D :D
since they are both acting together, then lets call it an easy 0.79, on a full tank of Gas (thats LPG), and the driver is Dive Granny. On a flat road on a sunny day with no wind.....:cool:
Yogi Diver
29-07-08, 09:44
Just been trying to figure this out again and failing miserably.
(Yes I am at work and bored sh*tless!!:D)
If I manage to do it properly and get 300 bars of EANX40, is it still EANX40 when I breathe it down to 200bar, 100 bar, 50 bar?
You sound about as busy as I am.
(Note: I am normally busy, just working my notice at the moment :D )
Yogi Diver
29-07-08, 09:57
You sound about as busy as I am.
(Note: I am normally busy, just working my notice at the moment :D )
Work is all very well but it's no substitute for reality!:rolleyes:
Just been trying to figure this out again and failing miserably.
(Yes I am at work and bored sh*tless!!:D)
If I manage to do it properly and get 300 bars of EANX40, is it still EANX40 when I breathe it down to 200bar, 100 bar, 50 bar?
Yes it is.
The ratio of each gas doesnt change only the 'amount' of gas you use to produce a specified drop in cylinder pressure due to the non-linear relationship of pressure v volume at the higher end of the graph.
OAIWA ?
JB :O)
Yogi Diver
29-07-08, 10:10
Yes it is.
The ratio of each gas doesnt change only the 'amount' of gas you use to produce a specified drop in cylinder pressure due to the non-linear relationship of pressure v volume at the higher end of the graph.
OAIWA ?
JB :O)
Sounds reasonable. My brain is definitely dead this morning. Probably cos I was up at 5:00am.
Scuba-Doh!
29-07-08, 11:48
Just been trying to figure this out again and failing miserably.
(Yes I am at work and bored sh*tless!!:D)
If I manage to do it properly and get 300 bars of EANX40, is it still EANX40 when I breathe it down to 200bar, 100 bar, 50 bar?
Depends if you've given the gas a good shake up to mix it or not ;-).
Seriously though, when I saw the question I thought "I really should be able to answer this" but came up blank. When I read through tomy's response it made sense but was just out of my curriculum and having not done any Chemistry since 2nd year of secondary school tomy just introduced me to mols (though I'd heard of them before).
Congrats on a good question and excellent response. :D
Depends if you've given the gas a good shake up to mix it or not ;-).
Dunno if you were just kidding there SD , but with some types of gas blending , it can actually take several hours for the differing gases to diffuse together fully within the cylinder.
A 'good shake up' at least metaphorically speaking is a good thing !
Cheers :)
zzzzzzzzzzzzzzzzzz
Oh did someone say something there.....zzzzzzzzzzzzz
Only kidding it is some good questions being asked, beyond my knowledge and interest levels. Its like mobile phones, I know they work but I dont know or care how as long they do work :) Great line in a Joe Rogan stand up sketch about the way we live lifes with loads of gadgets but only a small proportion of the world population actually knows how they work and how to make them. A bit like the Egyptians and their pyramids!
Scuba-Doh!
29-07-08, 12:30
Dunno if you were just kidding there SD , but with some types of gas blending , it can actually take several hours for the differing gases to diffuse together fully within the cylinder.
A 'good shake up' at least metaphorically speaking is a good thing !
Cheers :)
I would hope that by 200bar/100/50 etc it would have been nicely diffused. :)