KEVOS® MAKEOS · Pneumatics

Gas Cylinder Contents and Duration Check (Peng–Robinson or van der Waals Real Gas)

How much gas is really in a high-pressure cylinder once real-gas behaviour is allowed for, how much of it can be used down to the regulator’s minimum pressure, and will it last the time I need at my usage rate?

Contents of a compressed (non-liquefied) gas cylinder from its water capacity, pressure and temperature, using the compressibility factor Z of a cubic equation of state built from the gas’s critical temperature and pressure: Peng–Robinson (with the acentric factor) or van der Waals (critical constants only), the other shown for comparison, together with the ideal-gas figure. From the contents at the full and lowest usable pressures it gives the usable gas in kilograms and standard litres and how long it lasts at your usage rate, against the time it must last.

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How this tool works

Inputs, units and where to find them

InputUnitTypical source
Equation of statechoicePeng–Robinson is the better general choice for simple gases; van der Waals needs only the critical constants and is mainly for comparison.
Cylinder water capacity (internal volume)LWater capacity stamped on the cylinder (internal volume), for example 50 L for a large industrial cylinder.
Cylinder pressure nowbar gGauge pressure on the cylinder contents gauge now (or the filled pressure on the label).
Lowest usable cylinder pressurebar gLowest cylinder gauge pressure at which the regulator still delivers your outlet pressure and flow, or the residual pressure your supplier asks you to leave.
Gas temperature in the cylinder°CTemperature of the gas in the cylinder, normally the room or outdoor temperature once the cylinder has settled.
Gas properties
Molar mass of the gasg/molMolar mass of the gas, from property data (nitrogen 28.014, argon 39.948, oxygen 31.999).
Critical temperature of the gasKCritical temperature of the gas, from the NIST Chemistry WebBook or a property data book.
Critical pressure of the gasbarCritical pressure of the gas, from the same source as the critical temperature.
Acentric factor of the gas (Peng–Robinson only)Acentric factor of the gas, from the same property data book (nitrogen about 0.037, argon about 0).
Use
Gas use rate at the reference conditionsL/minGas used per minute, measured or set on a flowmeter, expressed at the reference temperature and 101.325 kPa (standard litres per minute).
Reference temperature of the use rate (at 101.325 kPa)°CTemperature that defines your standard litres; 15 °C and 0 °C are both in use, so check the flowmeter or supplier basis.
Time the cylinder must lasthHow long the job, shift or test must run on this cylinder.
Atmospheric pressurekPa absLocal atmospheric pressure, used to turn gauge pressures into absolute (101.325 kPa at sea level).

What each input means

Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.

What this means: Equation of state
Illustration: Equation of stateThe options for Equation of state, with the one currently selected highlighted.Peng–Robinson (critical constants and acent…van der Waals (critical constants only)Example: Peng–Robinson (critical c…Equation of state
What it is
Which cubic equation of state gives the compressibility factor: Peng–Robinson, which also uses the acentric factor, or the simpler van der Waals form from the critical constants alone.
Units and format
Choose one of 2 options from the list: Peng–Robinson (critical constants and acentric factor); van der Waals (critical constants only).
Example
The form opens with “Peng–Robinson (critical constants and acentric factor)” selected as a worked example. Choose the option that matches your case.
Effect on the result
Selects the Z used for the contents; the other equation is still shown beside it.
Get it right
Use Peng–Robinson for the answer and read the van der Waals figure only as a comparison.
What this means: Cylinder water capacity (internal volume)
Illustration: Cylinder water capacity (internal volume)A box drawn in three dimensions; the space it encloses is the volume Cylinder water capacity (internal volume).VExample: 50 LCylinder water capacity (internal volume)
What it is
The internal volume of the cylinder, stamped on its shoulder as the water capacity; the gas fills all of it.
Units and format
Enter a number in L: litres. The form accepts 0.000001 L to 100000 L. Required: the tool does not calculate until every input is valid.
Example
The form opens with 50 L as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Contents and running time scale in direct proportion to the water capacity.
Get it right
Do not confuse it with the gas contents on the label, which is a volume at atmospheric pressure and is far larger.
What this means: Cylinder pressure now
Illustration: Cylinder pressure nowA pressure gauge whose needle moves with Cylinder pressure now; the needle follows the value you type.p₁Example: 200 bar gCylinder pressure now
What it is
The gauge pressure of the gas in the cylinder now, read on the regulator’s contents gauge after the cylinder has settled to room temperature.
Units and format
Enter a number in bar g: bar g. The form accepts 0.01 bar g to 1000 bar g. Required: the tool does not calculate until every input is valid.
Example
The form opens with 200 bar g as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Raises the gas in the cylinder and the usable amount, slightly less than in proportion when Z rises above 1.
Get it right
A cylinder read straight after filling or in the sun reads high; let it reach room temperature first.
What this means: Lowest usable cylinder pressure
Illustration: Lowest usable cylinder pressureA pressure gauge whose needle moves with Lowest usable cylinder pressure; the needle follows the value you type.p₂Example: 10 bar gLowest usable cylinder pressure
What it is
The gauge pressure at which the cylinder stops being useful: the regulator can no longer hold its outlet pressure and flow, or the supplier wants a residual left in it.
Units and format
Enter a number in bar g: bar g. The form accepts 0 bar g to 1000 bar g. Required: the tool does not calculate until every input is valid.
Example
The form opens with 10 bar g as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Gas below this pressure is not counted as usable, so a higher value shortens the running time.
Get it right
Leaving a small residual stops air and moisture getting into the cylinder; many suppliers ask for it.
What this means: Gas temperature in the cylinder
Illustration: Gas temperature in the cylinderA thermometer whose level rises with Gas temperature in the cylinder; the level follows the value you type.TExample: 20 °CGas temperature in the cylinder
What it is
The temperature of the gas inside the cylinder, which together with the pressure fixes how many moles it holds.
Units and format
Enter a number in °C: degrees Celsius. The form accepts -100 °C to 300 °C. Required: the tool does not calculate until every input is valid.
Example
The form opens with 20 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
A colder cylinder at the same gauge reading holds more gas.
Get it right
Use the temperature of the room where the cylinder has stood, not the temperature just after filling.

Gas properties

What this means: Molar mass of the gas
Illustration: Molar mass of the gasA weight resting on a scale; Molar mass of the gas is how much matter it contains, in kilograms or grams.MExample: 28.014 g/molMolar mass of the gas
What it is
The mass of one mole of the gas, used to turn the moles in the cylinder into kilograms.
Units and format
Enter a number in g/mol: g/mol. The form accepts 1 g/mol to 500 g/mol. Required: the tool does not calculate until every input is valid.
Example
The form opens with 28.014 g/mol as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Changes the contents in kilograms in proportion; the standard litres and running time do not depend on it.
Get it right
For a gas mixture use the mole-fraction-weighted average molar mass.
What this means: Critical temperature of the gas
Illustration: Critical temperature of the gasA thermometer whose level rises with Critical temperature of the gas; the level follows the value you type.T꜀Example: 126.2 KCritical temperature of the gas
What it is
The temperature above which the gas cannot be liquefied by pressure alone; with the critical pressure it sets the equation-of-state constants a and b.
Units and format
Enter a number in K: kelvin (a difference of 1 K equals 1 °C). The form accepts 1 K to 2000 K. Required: the tool does not calculate until every input is valid.
Example
The form opens with 126.2 K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Sets how strongly the gas departs from ideal behaviour at the cylinder temperature.
Get it right
Gases with a critical temperature above room temperature, such as CO₂, are liquefied in the cylinder and are refused here.
What this means: Critical pressure of the gas
Illustration: Critical pressure of the gasA pressure gauge whose needle moves with Critical pressure of the gas; the needle follows the value you type.p꜀Example: 33.98 barCritical pressure of the gas
What it is
The pressure of the gas at its critical point, the second constant that scales the equation of state to this gas.
Units and format
Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0.1 bar to 2000 bar. Required: the tool does not calculate until every input is valid.
Example
The form opens with 33.98 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Sets the size of the a and b constants and so the compressibility factor.
Get it right
Check the unit in the data source: critical pressures are often listed in MPa or atm rather than bar.
What this means: Acentric factor of the gas (Peng–Robinson only)
Illustration: Acentric factor of the gas (Peng–Robinson only)A number line with a marker at the value of Acentric factor of the gas (Peng–Robinson only), between its lowest and highest accepted values.-0.51.5ωExample: 0.037Acentric factor of the gas (Peng–Robinson onl…
What it is
A property-data number that describes how far the gas’s vapour pressure departs from that of a simple spherical molecule; Peng–Robinson uses it to adjust the attraction term.
Units and format
Enter a plain number with no unit. The form accepts -0.5 to 1.5. Required: the tool does not calculate until every input is valid.
Example
The form opens with 0.037 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Changes the Peng–Robinson compressibility factor slightly at room temperature.
Get it right
It is a pure number, near zero for argon and small for nitrogen and oxygen; it is ignored by van der Waals.

Use

What this means: Gas use rate at the reference conditions
Illustration: Gas use rate at the reference conditionsA pipe with liquid or gas moving through it; Gas use rate at the reference conditions is the volume that passes per unit of time.QExample: 15 L/minGas use rate at the reference conditions
What it is
How much gas the job draws each minute, expressed as standard litres at the reference temperature and 101.325 kPa rather than at the cylinder pressure.
Units and format
Enter a number in L/min: litres per minute. The form accepts 0.001 L/min to 10000000 L/min. Required: the tool does not calculate until every input is valid.
Example
The form opens with 15 L/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
The running time is inversely proportional to the use rate.
Get it right
Flowmeters for shielding gas read in litres per minute at their own calibration conditions; check them against the reference temperature.
What this means: Reference temperature of the use rate (at 101.3…
Illustration: Reference temperature of the use rate (at 101.325 kPa)A thermometer whose level rises with Reference temperature of the use rate (at 101.325 kPa); the level follows the value you type.T_refExample: 15 °CReference temperature of the use rate (at 101…
What it is
The temperature that defines a standard litre for your use rate; the gas is counted at this temperature and 101.325 kPa.
Units and format
Enter a number in °C: degrees Celsius. The form accepts -50 °C to 50 °C. Required: the tool does not calculate until every input is valid.
Example
The form opens with 15 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
A higher reference temperature gives more standard litres from the same gas, and a longer running time.
Get it right
Gas suppliers and flowmeters use different bases, commonly 15 °C or 0 °C; match the one your use rate is quoted on.
What this means: Time the cylinder must last
Illustration: Time the cylinder must lastA timeline from a start mark to an end mark; Time the cylinder must last is the time between them.startendtExample: 8 hTime the cylinder must last
What it is
How long the cylinder has to supply the job without a change: a shift, a test run or the time to a delivery.
Units and format
Enter a number in h: hours. The form accepts 0.01 h to 100000 h. Required: the tool does not calculate until every input is valid.
Example
The form opens with 8 h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Get it right
Add the time for start-up purges and leaks, which use gas without doing the job.
What this means: Atmospheric pressure
Illustration: Atmospheric pressureA pressure gauge whose needle moves with Atmospheric pressure; the needle follows the value you type.p_atmExample: 101.325 kPa absAtmospheric pressure
What it is
The pressure of the surrounding air, added to the gauge readings to give the absolute pressures the equation of state needs.
Units and format
Enter a number in kPa abs: kPa abs. The form accepts 50 kPa abs to 110 kPa abs. Required: the tool does not calculate until every input is valid.
Example
The form opens with 101.325 kPa abs as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Adds to both absolute pressures; its effect on the contents is small at cylinder pressures.
Get it right
It falls by roughly 1 kPa for every 80 m of altitude near sea level; use the local value at high sites.

Method and formulas

  1. Real gas: pV = Z n R T, with Z the largest root of the cubic equation of state at the absolute pressure and temperature. van der Waals (Greiner eq. 1.33): Z³ − (1 + B)Z² + AZ − AB = 0 with a = 27R²T꜀² ÷ (64p꜀) and b = RT꜀ ÷ (8p꜀) from the critical point (Greiner eqs 3.25–3.27).
  2. Peng–Robinson: a = 0.45724 R²T꜀² ÷ p꜀ × [1 + κ(1 − √(T ÷ T꜀))]², b = 0.07780 RT꜀ ÷ p꜀, κ = 0.37464 + 1.54226ω − 0.26992ω², and Z³ − (1 − B)Z² + (A − 3B² − 2B)Z − (AB − B² − B³) = 0, with A = ap ÷ (RT)² and B = bp ÷ (RT).
  3. Usable moles = n(full) − n(lowest); standard litres = moles × R T_ref ÷ 101.325 kPa; running time = standard litres ÷ use rate.
  4. Example: Z = 1.0228, so the cylinder holds 11.294 kg (ideal gas 11.552 kg); 8,995.9 standard litres are usable, lasting 9.9954 h against 8 h needed.

Limitations

  • Compressed gases above their critical temperature only; liquefied gases (CO₂, LPG, ammonia) are refused, because their contents are set by weight and vapour pressure.
  • Cubic equations of state are approximations: they are least reliable near the critical point and for hydrogen and helium; for custody transfer or safety-critical quantities use the supplier’s contents data or a reference equation of state.
  • The gas is taken at one uniform temperature; fast withdrawal cools the cylinder and lowers the pressure, so the gauge reads low until it warms again.
  • Example values are illustrations. Replace them with values for your actual task.

Typical uses

  • Check how long a nitrogen, argon or oxygen cylinder lasts on a purge, shielding or test duty
  • See how far the ideal gas law misstates the contents at high pressure
  • Decide whether a shift needs a spare cylinder or a manifold

Who it is for

  • Maintenance and process engineers
  • Welding and fabrication supervisors
  • Laboratory and test staff

What you get

  • Compressibility factor and contents now (kg), with the ideal-gas and other-equation figures
  • Usable gas down to the lowest pressure (kg and standard litres)
  • Running time at the use rate against the time needed

Interpreting the result

  • At the same gauge reading, a gas with Z above 1 (nitrogen, hydrogen at room temperature) holds less than the ideal gas law suggests, and one with Z below 1 (argon, oxygen, methane) holds more.
  • When the two equations of state disagree by more than a few per cent, treat the contents as uncertain and confirm them by weighing or with the supplier’s data.

References

  • Greiner W., Neise L. and Stöcker H., Thermodynamics and Statistical Mechanics (Springer-Verlag, New York, 1995), pp. 17–20, 67–70: van der Waals equation of state (eq. 1.33) and its critical constants (eqs 3.23–3.28). Method reference; no text, tables or worked examples are reproduced.
  • Peng D.-Y. and Robinson D. B., A New Two-Constant Equation of State, Industrial & Engineering Chemistry Fundamentals 15 (1976) 59–64.
  • Poling B. E., Prausnitz J. M. and O’Connell J. P., The Properties of Gases and Liquids, 5th edition (McGraw-Hill, 2001): critical constants and acentric factors; no values are reproduced here.
  • NIST Chemistry WebBook, NIST Standard Reference Database 69 (webbook.nist.gov): a source for the property values you enter; no data are reproduced here.

Learn the Concepts Behind This Tool

These KEVOS® Library readings explain the method this tool uses, with worked examples.

KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.

Open the Gas Cylinder Contents and Duration Check (Peng–Robinson or van der Waals Real Gas) calculator

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