KEVOS® MAKEOS · Pneumatics
Compressed Gas Stored Energy Check (Isothermal Exergy, Isentropic and Brode Burst Energy, pV Product)
How much energy is stored in a compressed-air receiver or gas vessel, how much of it could do useful work, how much could a sudden rupture release, and is its pressure × volume above the limit my classification uses?
Energy stored in an ideal gas compressed in a rigid vessel and settled at the ambient temperature: the isothermal expansion work pV ln(p ÷ p₀), the useful work (exergy) after the work of pushing back the atmosphere is taken away, the isentropic expansion energy and the Brode upper bound that hazard assessments use for a sudden rupture, the atmospheric air needed to fill the vessel and the compressor energy at your specific power, the share of that energy kept as exergy, and the gauge pressure × volume product against the limit you enter.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Vessel internal volume | L | Internal (water) volume of the receiver or vessel from its nameplate or drawing. |
| Gas pressure | bar g | Gauge pressure of the gas: the working pressure, or the test pressure if the test is pneumatic. |
| Atmospheric pressure | kPa abs | Local atmospheric pressure (101.325 kPa at sea level). |
| Ratio of specific heats γ of the gas | Ratio of specific heats of the gas (air and nitrogen about 1.4, argon and helium about 1.67). | |
| Filling and classification | ||
| Compressor specific power (per m³/min of inlet air) | kW/(m³/min) | Compressor input power per cubic metre per minute of air delivered, measured at inlet conditions, from the compressor data sheet (for example a CAGI sheet) or an audit. |
| Pressure × volume limit you apply | MPa·L | The gauge pressure × volume above which your classification, standard or site rule treats the vessel differently; take it from that rule. |
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: Vessel internal volume
- What it is
- The volume inside the vessel that the compressed gas fills, from its nameplate, data report or drawing.
- Units and format
- Enter a number in L: litres. The form accepts 0.000001 L to 10000000 L. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 500 L as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- All stored energies and the pV product are proportional to the volume.
- Get it right
- Include connected pipework and other receivers that cannot be isolated from it.
What this means: Gas pressure
- What it is
- The gauge pressure of the gas in the vessel: the working pressure, or the test pressure for a pneumatic test.
- Units and format
- Enter a number in bar g: bar g. The form accepts 0.001 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
- Raises every stored energy and the pV product; exergy rises faster than in proportion because of the logarithm.
- Get it right
- For a pneumatic test use the test pressure; it is higher than the working pressure.
What this means: Atmospheric pressure
- What it is
- The pressure of the surrounding air, which the gas would expand down to and against which it must push.
- 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
- Sets the absolute pressure and the expansion ratio; its effect is small at high pressures.
- Get it right
- It falls with altitude; use the local value at a high site.
What this means: Ratio of specific heats γ of the gas
- What it is
- The ratio of the gas’s specific heat at constant pressure to that at constant volume, which sets how much it cools as it expands suddenly.
- Units and format
- Enter a plain number with no unit. The form accepts 1.01 to 1.67. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.4 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger ratio lowers the isentropic and Brode energies.
- Get it right
- Diatomic gases such as air and nitrogen are about 1.4; monatomic argon and helium about 1.67.
Filling and classification
What this means: Compressor specific power (per m³/min of inlet…
- What it is
- The electrical input of the compressor for each cubic metre per minute of air it delivers, counted at inlet conditions: a measure of how efficiently it compresses.
- Units and format
- Enter a number in kW/(m³/min): kW/(m³/min). The form accepts 0.01 kW/(m³/min) to 100 kW/(m³/min). Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6.5 kW/(m³/min) as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The fill energy is proportional to it, so a higher value lowers the share kept as exergy.
- Get it right
- Take it at the pressure you fill to; data sheets give it at the rated pressure and full load.
What this means: Pressure × volume limit you apply
- What it is
- The gauge pressure × internal volume above which the rule you work to puts the vessel into a higher category, written in megapascal-litres.
- Units and format
- Enter a number in MPa·L: MPa·L. The form accepts 0.001 MPa·L or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 MPa·L as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The decision fails when the vessel’s pV product is above this value.
- Get it right
- Take the limit from the classification rule that applies to your vessel and contents; it is not a design allowance.
Method and formulas
- At constant temperature the reversible work equals the change in free energy (Greiner eq. 4.45); for an ideal gas expanding from p to p₀ this is W = pV ln(p ÷ p₀). Pushing back the atmosphere takes (p − p₀)V of it, leaving the exergy X = pV ln(p ÷ p₀) − (p − p₀)V.
- A sudden release is closer to adiabatic: isentropic expansion energy E = pV ÷ (γ − 1) × [1 − (p₀ ÷ p)^((γ − 1) ÷ γ)], and the Brode upper bound E_B = (p − p₀)V ÷ (γ − 1).
- Air to fill from atmospheric = (p − p₀)V ÷ p₀; fill energy = specific power × air volume ÷ 60 (kWh); pV product = gauge pressure (MPa) × volume (L).
- Example: 813.85 kJ of exergy (0.22607 kWh), 680.4 kJ isentropic and 1,250 kJ by Brode; pV = 500 MPa·L against a limit of 1000.
Limitations
- Ideal gas in a rigid vessel at ambient temperature; at high pressures real-gas behaviour changes the amount of gas stored (see the gas cylinder contents tool).
- Burst energies are upper-bound estimates of the energy released; how much becomes blast, fragment or thermal energy depends on the failure and is not modelled.
- Screening aid only: pressure equipment design, testing and classification follow the applicable standards (for example AS 4343 hazard levels and AS 1210) and a qualified engineer.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Show how much energy a receiver or test vessel holds before a pressure test or a change of size
- Compare the useful energy stored with the electricity used to fill it
- Check the pressure × volume product against the limit your classification or site rule uses
Who it is for
- Mechanical and pressure-equipment engineers
- Maintenance and safety staff
- Compressed-air system auditors
What you get
- Isothermal expansion work and exergy (useful work)
- Isentropic and Brode burst energies
- Air and compressor energy to fill, and the share kept as exergy
- pV product against your limit
Interpreting the result
- The Brode figure is the largest of the three and is the cautious one for hazard screening; the exergy is the most a perfect air motor could ever recover.
- A pneumatic test stores far more energy than a hydrostatic test at the same pressure, because a liquid stores almost none; this is why hydrostatic testing is preferred.
References
- Greiner W., Neise L. and Stöcker H., Thermodynamics and Statistical Mechanics (Springer-Verlag, New York, 1995), pp. 52–53, 91–95: reversible and irreversible expansion work (eq. 2.50) and the free energy as the reversible work at constant temperature (eqs 4.45 and 4.53). Method reference; no text, tables or worked examples are reproduced.
- Crowl D. A. and Louvar J. F., Chemical Process Safety: Fundamentals with Applications (Prentice Hall): energy of a compressed gas release by the Brode, isothermal, isentropic and thermodynamic-availability expressions.
- AS 4343, Pressure equipment — Hazard levels: hazard level depends on the pressure, volume and contents; levels are not reproduced here.
- Compressed Air and Gas Institute (CAGI) performance data sheets: compressor specific power.
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