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I am looking for anyone who might be interested in working on the equations
needed to allow real-time mixing of a 3 component gas blend.
For the last 6 months we have been working on a way to predict the exact
mixing sequence needed to obtain a final blend of 3 or more gases.
The goal is to accurately predict both the real-time thermal rise of the
compressed gases as well as the compressability durring the continuous fill
cycle.
Make no mistake, this is no small feat of math.
In the last 6 months I have had 2 professional mathmaticians, a physicist
and a chemist give up.
The final object is to allow the user to specify a
A. specific cylinder, say an OMS-120 (which we have a database of internal
information on)
B. a final fill pressure, say 350 bar
C. and a final mix, say 15%O2, 45% He, 40%N2
and for the equation to come back with the proper fill sequence,
by fill rate and by pressure to obtain a final blend within 2% accuracy.
So the final result might look like this..
1. O2 @ 57 psi/min, from 0 to 14Bar (203psi)
2. He @ 100 psi/min, from 14Bar to 170.8Bar (203 to 2477psi)
3. Air up to final pressure of 350 Bar or 5076PsiA
Interested?
Feel up to a real challange??
If so, let me know.
===============
This is one form of the Beattie-Bridgeman Equation of state for gas that we
have been trying to get working for us.
P=(RT/VV)x[V+Bo(1-b/V)]x(1-c/VTTT)-(Ao/VV)x(1-a/V)
where:
P=Pressure (is ATMs)
V=Specific Volume (is Liters)
R=Gas Constant, (0.08206)x{[(atm)x(litres)]/[(g-mole)x(degrees Kelvin)]}
T=Temperature in degrees Kelvin
a, b, c, Ao, Bo, are gas coefficients.
Constants A0 a Bo b c
Helium 0.0216 0.05984 0.01400 0.0 40
Neon 0.2125 .02196 0.02060 0.0 10
Argon 1.2907 0.02328 .03931 0.0 59900
Hydrogen .1975 -0.00506 .02096 -0.04359 504
Nitrogen 1.3445 .02617 .05046 -0.00691 42000
Oxygen 1.4911 .02562 .04624 .004208 48000
Air 1.3012 0.01931 0.04611 -0.001101 43400
However, since we are adding gases to our mixture one by one, the
mixture and its coefficients will be changing continuously.
This shouldn't be a major problem, we just need to use some calculus, and
attempt
to constantly redefine the values of the coefficients.
We break the problem up into small increments, such as adding enough gas
to raise the pressure by 1 bar. Then we assume that the A and B
constants stay constant throughout the 1 bar interval. When the pressure
has risen by one bar, we recalculate the Coeficients and assume that
they stay constant over the next 1 bar increment. And so on...
If this is too course, try 0.5 bar intervals and if it is too fine try 2
bar, whatever works.
Air is considered a pure gas as it has a known set of coefficients.
A cylinder is considered empty when at 1ATM pressure, and is generally
flushed to have only one gas in it (Air, Oxygen, Helium) as a rule.
Occasionaly we will want to start off with a know miture left over
from a previous dive so as to conserve the valuable Helium or Neon.
The temp of the cylinder rises as gas is compressed into it.
But the equation must be able to allow us to predict the rate of rise in
internal temperature as well to maintain an accurate final prediction.
======an example attempt without thermal consideration======
Filling of SCUBA cylinder to 15% O2, 45%He, 40%N2
Order of compression
1. O2 @ 57 psi/min.
2. He @ 100 psi/min.
3. Air up to final pressure of 350 Bar or 5076PsiA
First cut at fill pressures
Final blend 45%He + 40%N2 +15%O2 = 100% mixture X
Secondary blend 73%N2 +27%O2 = 100% mixture X2
Mix of air 78%N2 +21%O2 = air error mix approx. 1%
% of air needed to give required N2 mix
A(0.78N2 + 0.21O2) + B*O2 = 0.73N2 + 0.27O2
A*0.78N2 - 0.73 = 0 th. A = 0.936
A*0.21O2 + B*O2 -0.27O2 = 0 th. B= 0.073
The air and O2 mix takes up 55% of the final blend th. total filling by
output volume in pressure of 350Bar
Air = 0.512 or 179.2Bar
O2 = 0.040 or 14.0Bar
th. He = 0.448 or 156.8Bar
th initial pressure filling would be
O2 up to 14Bar (203psi)
He from 14Bar to 170.8Bar (203 to 2477psi)
Air from 170.8Bar to 350Bar (2477 to 5076psi)
Since the compressability of the gasses will change the amount of gas
stored in the cylinder
PsiA Bar Z O2% He% N2%
203 14 0.9901 100 0 0
2477 170.8 1.08462 8.5 91.5 0
5076 350 1.23686 15 45 40
from PV = znRT
V = 10L = 10**10-3m3
R = 8.3144J/mol K @350Bar and 68deg. F (35,000kPa, 293.15K)
n= 1160.98mole of blend
To generate output volume of 15%O2, 45%He and 40%N2
PsiA Bar kPa O2-100% He-100% N2-100%
14.70 1 101.325 z=0.9993 z=1.00063 z=0.99977
203 14 1,400 z=1.00879
1. O2 up to 203 PsiA 1399.3kPa V at 101.325 = 0.13938m**3
2. He up to 2,477PsiA 17078.3kPa V at 101.325 = 1.53248m**3
3. Air up 5,076PsiA 35,000kPa V at 101.325 = 1.25962m**3
output O2 = 5% He = 52% [air(21%O2,78%N2)] = 43%
Final percentages O2 = 14% He = 52% N2 = 34%
th. require air to be pumped 5% earlier in pressure
O2 up to 203PSIA
He 203 - 2363PSIA
O2,N2 2363 - 5076PSIA
as long as the pumped gas remains at 68 deg. F
=====================
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
Christopher M. Parrett, President, Abysmal Diving Inc.
6595 Odell Place, Suite G. Boulder Colorado, USA 80301
Ph.303-530-7248, fx 303-530-2808
Makers of ABYSS, Advanced Dive Planning Software.
Available in English, French, German, Portuguese and Swedish.
Abyss, Mixed Gas, Technical Nitrox, Recreational Air.
Abyss, Technical Logbooks featuring 22 integrated databases.
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