KEVOS® MAKEOS · Pneumatics
Nitrogen or Oxygen Generator Energy Check (Minimum Separation Work, Second-Law Efficiency, Running Cost)
What is the least energy physics allows for making nitrogen or oxygen of my purity from air at this air factor, how does the generator’s actual specific energy compare, and what does the gas cost to make each year?
Second-law check of an on-site gas generator (PSA, membrane or other) treating air as a two-part oxygen–nitrogen mixture of ideal gases: the oxygen content of the waste stream from the oxygen balance, the minimum (reversible, isothermal) work of separation from the entropy of mixing, RT[Σ n x ln x] of the products less that of the feed, per cubic metre of product at your reference temperature, the lowest minimum with complete recovery, the recovery of the wanted gas, the second-law efficiency of the generator’s actual specific energy, and the yearly energy and cost at your flow, hours and tariff.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Oxygen content of the feed air | % | Oxygen content of the air drawn in; dry air is 20.95 % by volume, and argon is counted with the nitrogen here. |
| Oxygen content of the product | % | Oxygen content of the product: the residual oxygen for a nitrogen generator (1 % for 99 % nitrogen) or the purity for an oxygen generator. |
| Air factor (feed air ÷ product, by volume) | × | Volume of air the generator takes in for each volume of product, from the supplier’s data at your purity (it rises steeply for higher purity). |
| Separation temperature | °C | Temperature at which the separation takes place, normally near ambient for PSA and membrane units. |
| Plant | ||
| Product flow | m³/h | Product flow at the reference conditions. |
| Reference temperature of the flows (at 101.325 kPa) | °C | Temperature that defines the cubic metres of the flow and specific energy (0 °C for normal cubic metres, 15 or 20 °C in some data sheets). |
| Actual specific energy (including the air compressor) | kWh/m³ | Electrical energy per cubic metre of product, including the air compressor and dryer, from the supplier’s data or your own meter readings. |
| Running hours per year | h/year | Hours a year the generator runs at this flow. |
| Electricity price (ex GST for a GST-registered business) | AUD/kWh | Electricity price per kilowatt-hour on one GST basis. |
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: Oxygen content of the feed air
- What it is
- The share of oxygen by volume in the air the generator draws in; the rest is treated as nitrogen, with argon counted in it.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0.01% to 99.99%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20.95% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the composition of the feed and so the mixing entropy to be undone.
- Get it right
- Dry air is 20.95 %; leave it unless the feed is enriched or comes from another process.
What this means: Oxygen content of the product
- What it is
- The share of oxygen in the gas the generator delivers: the residual oxygen for a nitrogen generator, or the purity for an oxygen generator.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0.001% to 99.999%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Purer product needs more separation work and usually a much higher air factor.
- Get it right
- Nitrogen purity of 99 % means 1 % oxygen here; 99.9 % means 0.1 %.
What this means: Air factor (feed air ÷ product, by volume)
- What it is
- How many volumes of air the generator takes in for each volume of product it delivers; the rest leaves as waste enriched in the other gas.
- Units and format
- Enter a number in ×: a multiplier (type 1.5 for 1.5 times). The form accepts 1.001 × to 1000 ×. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 × as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher air factor lowers the minimum separation work towards the complete-recovery value but wastes more compressed air in practice.
- Get it right
- Take it from the supplier’s performance table at your purity and temperature; it rises steeply at high purity.
What this means: Separation temperature
- What it is
- The temperature at which air is separated; the minimum work is proportional to this absolute temperature.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -200 °C to 200 °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
- The minimum work rises in proportion to the absolute temperature.
- Get it right
- Use the adsorber or membrane temperature, normally close to the room temperature for on-site generators.
Plant
What this means: Product flow
- What it is
- How much product gas the generator delivers per hour, counted at the reference temperature and 101.325 kPa.
- Units and format
- Enter a number in m³/h: cubic metres per hour. The form accepts 0.000001 m³/h to 10000000 m³/h. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 m³/h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The yearly energy and cost scale in direct proportion.
- Get it right
- Use the average demand, not the generator’s rated maximum, for the yearly energy.
What this means: Reference temperature of the flows (at 101.325…
- What it is
- The temperature that defines the cubic metres used for the flow and specific energy: 0 °C for normal cubic metres, 15 or 20 °C on some data sheets.
- 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 0 °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 means fewer moles in each cubic metre, so the minimum work per cubic metre falls.
- Get it right
- The flow, specific energy and air factor must all use the same reference temperature.
What this means: Actual specific energy (including the air compr…
- What it is
- The electricity the whole generator uses for each cubic metre of product, including its air compressor and dryer.
- Units and format
- Enter a number in kWh/m³: kWh/m³. The form accepts 0.000001 kWh/m³ to 100 kWh/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.3 kWh/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The second-law efficiency is inversely proportional to it; the yearly energy and cost are proportional.
- Get it right
- Data sheets sometimes quote the generator alone without the compressor; add the compressor’s share.
What this means: Running hours per year
- What it is
- The number of hours a year the generator runs at the flow entered, used for the yearly energy and cost.
- Units and format
- Enter a number in h/year: h/year. The form accepts 0 h/year to 8784 h/year. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4000 h/year as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The yearly energy and cost scale in direct proportion.
- Get it right
- Count the hours at this average flow; standby with the compressor unloaded uses less energy.
What this means: Electricity price (ex GST for a GST-registered…
- What it is
- What one kilowatt-hour of electricity costs the plant, used for the yearly running cost of the generator.
- Units and format
- Enter a number in AUD/kWh: Australian dollars per kilowatt-hour. The form accepts 0 AUD/kWh to 100 AUD/kWh. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.25 AUD/kWh as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The yearly cost scales in direct proportion.
- Get it right
- Use the average tariff including demand charges, ex GST for a GST-registered business.
Method and formulas
- Mixing different ideal gases at the same temperature and pressure raises the entropy by ΔS = −nR Σ xᵢ ln xᵢ (Greiner eq. 5.40); at constant temperature the reversible work to undo it is the rise in free energy, T ΔS (Greiner eq. 4.45).
- Per mole of product with air factor AF: waste oxygen x_W = (AF x_F − x_P) ÷ (AF − 1); W_min = RT[g(x_P) + (AF − 1) g(x_W) − AF g(x_F)], with g(x) = x ln x + (1 − x) ln(1 − x). As AF grows without limit the minimum falls to RT[g(x_P) − g(x_F) − (x_P − x_F) ln(x_F ÷ (1 − x_F))].
- Per cubic metre of product: W_min × 101.325 kPa ÷ (R T_ref); second-law efficiency = W_min ÷ actual specific energy; yearly energy = flow × hours × specific energy.
- Example: the minimum is 0.0074574 kWh/m³ against 0.3 kWh/m³ actual, a second-law efficiency of 2.4858 %; 60,000 kWh a year costs A$15,000.
Limitations
- Air is treated as a two-part ideal mixture of oxygen and nitrogen, with argon counted as nitrogen; real nitrogen generators pass most of the argon into the product, and oxygen generators pass part of it.
- The minimum work assumes products and waste leave at the feed temperature and pressure; product delivered at pressure needs further compression work that is not included.
- The actual specific energy must include the air compressor, since that is where nearly all the energy goes.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a supplier’s specific energy claim for a nitrogen or oxygen generator
- Compare generators of different purity and air factor on the same basis
- Estimate the yearly electricity cost of on-site gas
Who it is for
- Process and utilities engineers
- Energy managers
- Buyers comparing generator quotations
What you get
- Oxygen content of the waste stream and recovery of the wanted gas
- Minimum separation work at this air factor and with complete recovery
- Second-law efficiency of the actual specific energy
- Yearly energy and cost
Interpreting the result
- Practical generators use many times the minimum work, because the air is compressed and then most of it is vented; a low second-law efficiency is normal, but comparing generators on it at the same purity shows which wastes least.
- Raising the purity raises the air factor steeply, so specifying higher purity than the process needs is the most common avoidable cost.
References
- Greiner W., Neise L. and Stöcker H., Thermodynamics and Statistical Mechanics (Springer-Verlag, New York, 1995), pp. 132–134, 91–93: entropy of mixing of different ideal gases (Gibbs’ paradox, eq. 5.40) and the free energy as the reversible work at constant temperature (eq. 4.45). Method reference; no text, tables or worked examples are reproduced.
- Çengel Y. A. and Boles M. A., Thermodynamics: An Engineering Approach (McGraw-Hill): exergy and the minimum work of separating a mixture.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Explains the concept · KEVOS® original book
Making oxygen
In Industrial Gases by the Numbers
What it covers: Compare the ways oxygen has been made, from chemicals and electrolysis to distilling liquid air, and calculate the energy and yields that decided which method won.
Method explained here · KEVOS® original book
Assist gases: oxygen, nitrogen and air
In Laser Processing by the Numbers
What it covers: What oxygen, nitrogen and compressed air each do in a laser cut, the heat from burning iron, nozzle gas flow, and supplying nitrogen from cylinders, bulk liquid or a generator.
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.