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Gas Management

Real-Gas Cylinder Estimate

Compare the conventional pressure-volume rule with a bounded endpoint model using measured cylinder-gas temperatures and oxygen composition.

Cylinder endpoint measurements
Use internal water volume and gas temperatures measured with the pressure readings. Nominal rated capacity and water temperature are not substitutes.
Measurement examples
bar

Allowed range: 1 to 350 bar.

bar

Allowed range: 0 to 350 bar.

L water volume

Allowed range: 3 to 30 L water volume.

% O₂

Allowed range: 21 to 40 % O₂.

°C

Allowed range: 0 to 40 °C.

°C

Allowed range: 0 to 40 °C.

Estimated gas removed
The model and conventional comparison use different named surface conventions; neither is a measured “true” amount.
Modeled at 20 °C and 1 atm
1,926 L
Endpoint real-gas estimate
Linear pressure × water volume
2,100 L
Conventional 1 bar rule
Modeled difference
-8.3%
Not an accuracy claim

Interpolated compressibility factors

Start Z
1.03399
End Z
0.99040
Reference Z
0.99965

Model output is not planning capacity

Use the cylinder manufacturer's rated capacity and conservative reserves for dive planning. This estimate is for examining a measured pressure-and-temperature interval; it does not improve an unmeasured warm fill or replace gauge, analyzer, and temperature uncertainty.
Endpoint inventory model

A rigid cylinder holds an amount of gas proportional to absolute pressure divided by compressibility and temperature. Gas removed is the difference between the start and end states, expressed as a volume at the reference state.

ni=Pi VwZi TiVref=(n1−n2) Zref TrefPref\begin{aligned} n_i &= \frac{P_i \, V_{\text{w}}}{Z_i \, T_i} \\[0.5em] V_{\text{ref}} &= (n_1 - n_2) \, \frac{Z_{\text{ref}} \, T_{\text{ref}}}{P_{\text{ref}}} \end{aligned}

Where

nin_i
gas amount in state i: 1 at the start, 2 at the end (the gas constant cancels, so it is left out)
VwV_{\text{w}}
internal water volume (L)
PiP_i
absolute pressure: gauge reading + 1.01325 bar
TiT_i
cylinder-gas temperature in kelvin
ZiZ_i
compressibility of the O₂/N₂ mix at that pressure and temperature
VrefV_{\text{ref}}
gas removed, as surface volume at 20 °C and 1 atm
Why two temperatures?

Pressure alone cannot distinguish gas removal from cooling. A water temperature can stand in for cylinder gas only after genuine thermal equilibrium.

The model covers 21–40% O₂, 0–40 °C, and 0–350 gauge bar. It throws outside that domain instead of extrapolating.

What the table represents

Z factors come from CoolProp 7.2.0 HEOS for binary O₂/N₂ mole mixtures, sampled every 5 °C and 10 bar and interpolated at runtime. Atmospheric argon and trace gases are not included.

Result

1,926 L removed