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.

Starting gauge pressure

bar

Ending gauge pressure

bar

Internal cylinder water volume

L water volume

Analyzed oxygen

% O₂

Starting cylinder-gas temperature

°C

Ending cylinder-gas temperature

°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.

\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

$n_i$: gas amount in state i: 1 at the start, 2 at the end (the gas constant cancels, so it is left out)
$V_{\text{w}}$: internal water volume (L)
$P_i$: absolute pressure: gauge reading + 1.01325 bar
$T_i$: cylinder-gas temperature in kelvin
$Z_i$: compressibility of the O₂/N₂ mix at that pressure and temperature
$V_{\text{ref}}$: 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

Endpoint real-gas estimate at 20 °C and 1 atm; not a planning capacity.

Linear P × V: 2,100 L
Modeled difference: -8.3%

Frequently Asked Questions

Is this the true amount of gas used?

No. It is a bounded equation-of-state estimate. Its usefulness depends on internal cylinder water volume, two representative cylinder-gas temperatures, pressure readings, gas analysis, and the stated reference condition. Sensor and timing uncertainty can exceed the interpolation error.

Why does this result differ from pressure drop times cylinder size?

The linear rule ignores temperature and pressure-dependent compressibility. This model estimates the inventory at each endpoint using absolute pressure, temperature, and a Z factor, then expresses the difference at 20 °C and one standard atmosphere.

Can I enter an AL80 as 80 cubic feet?

No. The input is the cylinder's internal water volume. An imperial 80 cu ft rating is already a nominal free-gas capacity at rated service conditions; treating it as internal volume would count the capacity conversion again.

Does water temperature equal cylinder-gas temperature?

Only when the cylinder and gas have genuinely reached thermal equilibrium with the water. A recently filled, transported, breathed, or rapidly cooled cylinder may not be at that state. Measure each endpoint with its pressure rather than silently reusing one water temperature.

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