Understanding the math behind partial pressure blending

[jwalko]

Hi all:

Not sure if this post belongs here...but wasn't sure where else to post it.

Back story...taking my tanks to my dive shop for a nitrox fill. They are currently filled with air. I am going on a dive trip in a couple of weeks and want 32%. I asked them if they can do a partial pressure fill and they said yes...they'll bleed off the tanks and then top off to get to 32%.

This got me thinking about the math involved in figuring out how much to bleed off and then how much to add to get to the right %.

I know there are software tools available, but I really want to understand the math. Not that I don't trust the tools...but I'm the kind of person who wants to understand how things work. Can someone either point me in the right direction for reading materials, or give me the formula for figuring out a couple of different scenarios...

Scenario 1, I have tanks full...want to bleed off part and add 50% or 100% 02 to get to a certain percentage (say 32% or 36%). As an example, I have an 85 cu ft LP steel tank (2600 PSI) with 2600 lbs currently in it. How much do I bleed off and then add 02 to get to 32%?

Scenario 2, tanks are empty (I know this used to be standard for PP blending...but I'm curious if it still is...my shop indicated that it wasn't necessary), how much 02 to add, and then top off with air to get to a certain percentage.

This is for my knowledge only...I'm not going to try to do my own blending...I just want to understand it.

Thanks;

John

 

[USMC]

I wrote a spreadsheet to figure it out. It's just too much math to do on a calculator.



It comes down to how much 100% to add to get 32% of total tank volume, I start with 400 - 1000 Lbs in the tank to limit the increased pressure needed.

 

[dfx]

Let's see... I really have no idea about this myself, but I'm gonna try doing it with regular math and physics just to see if it adds up... I hope somebody else can confirm or refute this.

With a 85 cuft tank at 2600 psi filled with air you have 85*21% = 17.85 cuft of O2 in there. The remaining 85-17.85 = 67.15 cuft are N2.

You want it filled with 2600 psi at 32% O2. You want 85*32% = 27.2 cuft of O2. The remaining 85-27.2 = 57.8 cuft would be N2.

So you need to bleed off the tank until you have only 57.8 cuft of N2 in there and then top it off with 100% O2.

At 21% O2, you'd have 57.8 cuft N2 in the tank when you have 57.8/79% = 73.165 cuft of air in the tank.

With the given tank, you'd have that much air in the tank when the pressure is 2600*(73.165/85) = 2238 psi.

So you bleed off the tank until it reads 2238 psi and then top it off with 100% O2 to give you 85 cuft of gas at 2600 psi with 32% O2.

Am I right? Of course this doesn't take adiabatic heating/cooling into account, which will influence pressure, so YMMV. Or maybe I'm totally off.

---------- Post added April 26th, 2013 at 12:21 PM ----------

Another (easier) way to do it...

At 2600 psi with air, you have 2600*21% = 546 psi of O2 in the tank and 2600*79% = 2054 psi of N2.

You want to have 2600*32% = 832 psi of O2 in the tank and 2600*68% = 1768 psi of N2.

So you bleed off the tank until you have 1768 psi of N2 in the tank, with the current 21% O2 mix. You have that at 2600*(1768/2054) = 2238 psi.

Then you top it off with 100% O2 until 2600 psi.

 

[steveharriss]

2600psi is 179Bar. Most O2 comes in cylinders at 200Bar. You don't want to be putting pure O2 into another cylinder at those pressures. PP blending works better (safer) when the O2 is put in first as you're then dealing with it at much safer pressures. Better to dump the air you have and start afresh.

We put O2 into cylinders with 50Bar or so of gas remaining from another dive and blend from there.

 

[JohnN]

Then you top it off with 100% O2 until 2600 psi.

Ahhhh, but what if you don't have a booster pump that will handle O2 and you're filling from a bank and the pressure is down (a little). Or you want EAN32 in a HP tank. . .


If you have the booster pump, then an O2 stick is almost trivial to build and you can do a continuous fill.



John N

 

[dfx]

Ahhhh, but what if you don't have a booster pump that will handle O2 and you're filling from a bank and the pressure is down (a little). Or you want EAN32 in a HP tank. . .

Yes, like I said, purely mathematical and theoretical writeup...

 

[miked]

While I doubt that this is the easiest way, it is one way: use a system of equations.

Where "A" is the amount of air (21 % oxygen), in psi, and X is the psi of pure oxygen (100% oxygen ).


The system would look like:

A + X = total tank pressure
.21A + X = (percent of your target mix) x (total tank pressure)

(Top equation:in words: psi of air + psi of oxygen = total psi in tank)
(Bottom equation in words: psi of oxygen in "A" psi of air + psi of oxygen in "X"psi of O2 = total psi of O2 in tank)


(note: if you had 50% O2 available, the second equation would look like
.21A +.50X= (percent of your target mix) x (total tank pressure)

Applying it your scenario 1:for a 32% mix

A + X = 2600
.21A + X = 832 (note:.32x2600 = 832)

Solving the system (in this case, subtract the bottom equation from the top) gives
.79A= 1768...or A= 2238 (approx)

and, since A + X = 2600 → X= 2600 -2238 =362.

Which means: bleed off 362 psi of air, then fill the tank with 362 psi of pure O2.


Scenario 2 would use the same 2 equations, yielding: 2238 psi of air, 362 psi of pure o2

Hope that this is clear, and helps. (I was a bit light on details-slow typist!!)

Edit: reinforcing "slow typist": when I started to answer, there were NO replies!!!

 

[USMC]

This ^ math is why I wrote the spreadsheet, it even gives the ability to use less than 100% O2 that I get from my OxyGen.

 

[miked]

This ^ math is why I wrote the spreadsheet, it even gives the ability to use less than 100% O2 that I get from my OxyGen.

Nice spreadsheet. If I'm reading it correctly, it can be used for tanks having a starting fO2 other than .21.


I agree that the math is not for everybody. However, it can be used by modifying the system- especially the second equation- to be:
A + X = the "goal" psi in your tank ( 2600 in the OP's example)

.21A +( percent of O2 in your added gas)X= (percent of your target mix) x (total tank pressure);

For your table's 95% ,
you'd have:
A + X = final tank pressure
.21A + .95X = (desired % blend) x (final tank pressure)

 

[USMC]

Nice spreadsheet. If I'm reading it correctly, it can be used for tanks having a starting fO2 other than .21.


I agree that the math is not for everybody. However, it can be used by modifying the system- especially the second equation- to be:
A + X = the "goal" psi in your tank ( 2600 in the OP's example)

.21A +( percent of O2 in your added gas)X= (percent of your target mix) x (total tank pressure);

For your table's 95% ,
you'd have:
A + X = final tank pressure
.21A + .95X = (desired % blend) x (final tank pressure)

Thanks
Yes it can start with any mixture and finish with any of your choosing.
Took some time to get the formulas correct, but it works well. This is a starting point and the final mixture still gets verified after each fill.
I offered it in another trend for anyone to use, (send your email in a PM) the only thing I ask is if you request a copy please help out a Veteran or Veteran group in your area.