KEVOS® MAKEOS · Pneumatics
Gas Separation Energy Check (Ideal Mixing, Least Work, Nitrogen Generator Efficiency)
What is the least energy any machine could use to separate this product purity from air, how does my nitrogen generator’s actual energy compare, and is it within my target?
Second-law benchmark of a gas separator such as a nitrogen generator: the waste-stream composition from a balance on the wanted gas, the recovery, the least separation work from the Gibbs energy of ideal mixing RT Σ x ln x of the product and waste less that of the feed, the least work for the same purity at a very large feed ratio, the second-law efficiency of the actual specific energy, and the yearly energy and cost (excluding GST), against the target specific energy.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Wanted gas in the feed | % | Share of the wanted gas in the feed (nitrogen with argon is about 79 % of dry air). |
| Product purity | % | Purity of the product gas. |
| Feed per unit of product (air factor) | mol/mol | Moles (or normal cubic metres) of feed per unit of product, from the generator data. |
| Ambient temperature | °C | Ambient temperature at which the separation takes place. |
| Plant and energy | ||
| Product flow | Nm³/h | Product flow in normal cubic metres per hour (0 °C, 101.325 kPa). |
| Actual specific energy | kWh/Nm³ | Measured or quoted energy per normal cubic metre of product. |
| Target specific energy | kWh/Nm³ | Specific energy you are aiming for or were promised. |
| Running hours per year | h | Hours a year the generator runs at this flow. |
| Electricity price (excluding GST) | AUD/kWh | Electricity price excluding GST (registered businesses claim the GST back). |
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: Wanted gas in the feed
- What it is
- The mole fraction of the wanted gas in the feed, counting any gases that may stay in the product as part of 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 79% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A richer feed lowers the least work for the same purity.
- Get it right
- For nitrogen generators count argon with nitrogen: together about 79 % of dry air.
What this means: Product purity
- What it is
- The mole fraction of the wanted gas in the product, as set on the generator or required by the process.
- 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 99.9999%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 99% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Higher purity raises the least work, and in real generators the air factor too.
- Get it right
- Use the purity actually delivered, not the best the generator can make; it must exceed the feed share.
What this means: Feed per unit of product (air factor)
- What it is
- The amount of feed gas taken in for each unit of product, in moles or normal cubic metres; the rest leaves as waste.
- Units and format
- Enter a number in mol/mol: mol/mol. The form accepts 1.0001 mol/mol to 1000 mol/mol. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 mol/mol as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger feed ratio changes the waste composition and lowers the least work towards its floor.
- Get it right
- Take it from the generator data at your purity; it must be large enough to supply the wanted gas in the product.
What this means: Ambient temperature
- What it is
- The temperature at which the gases are mixed and separated, which sets the scale of the least separation work.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -50 °C to 100 °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 least work rises in proportion to absolute temperature.
- Get it right
- Use the ambient or air intake temperature.
Plant and energy
What this means: Product flow
- What it is
- The product gas delivered per hour, measured as volume at 0 °C and one standard atmosphere (normal cubic metres).
- Units and format
- Enter a number in Nm³/h: Nm³/h. The form accepts 0.001 Nm³/h to 1000000 Nm³/h. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 Nm³/h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Yearly energy and cost rise in proportion; the efficiency does not change.
- Get it right
- Convert standard cubic metres at 15 °C by multiplying by 273.15 ÷ 288.15.
What this means: Actual specific energy
- What it is
- The electrical energy the separator actually uses for each normal cubic metre of product, including its air compressor.
- Units and format
- Enter a number in kWh/Nm³: kWh/Nm³. The form accepts 0.0001 kWh/Nm³ to 100 kWh/Nm³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.25 kWh/Nm³ 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 falls in inverse proportion; yearly energy and cost rise in proportion.
- Get it right
- Divide the measured average input power in kW by the product flow in Nm³/h.
What this means: Target specific energy
- What it is
- The specific energy you are aiming for, were promised by a supplier or use as a benchmark for this purity.
- Units and format
- Enter a number in kWh/Nm³: kWh/Nm³. The form accepts 0.0001 kWh/Nm³ to 100 kWh/Nm³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.3 kWh/Nm³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Moves the pass line only.
- Get it right
- Make sure it counts the same equipment and reference conditions as the actual figure.
What this means: Running hours per year
- What it is
- The number of hours in a year the separator runs at this product flow.
- Units and format
- Enter a number in h: hours. The form accepts 0 h to 8784 h. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4000 h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Yearly energy and cost rise in proportion.
- Get it right
- Use metered running hours, or shifts per week times hours times weeks a year.
What this means: Electricity price (excluding GST)
- What it is
- What the site pays per kilowatt-hour of electricity, excluding GST, including energy and usage-based network charges.
- Units and format
- Enter a number in AUD/kWh: Australian dollars per kilowatt-hour. The form accepts 0 AUD/kWh to 10 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
- Yearly costs rise in proportion.
- Get it right
- Take it from a recent bill; demand charges are left out of a per-kWh price.
Method and formulas
- Waste composition from the balance x_W = (AF x_F − x_P) ÷ (AF − 1); recovery = x_P ÷ (AF x_F).
- For ideal gas mixtures the Gibbs energy of mixing is RT Σ x ln x per mole (Guggenheim §4.18–4.20); the least separation work per mole of product = 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 very large this falls to RT [g(x_P) − g(x_F) − (x_P − x_F) ln(x_F ÷ (1 − x_F))], the least for that purity; one normal cubic metre is 101 325 ÷ (R × 273.15) mol.
- Second-law efficiency = least specific energy ÷ actual specific energy; yearly energy = flow × hours × specific energy.
- Example: 99 % nitrogen from air at an air factor of 3 needs at least 603.66 J/mol, 0.0074812 kWh/Nm³; at 0.25 kWh/Nm³ the generator is 2.9925 % efficient.
Limitations
- Two components (wanted gas and the rest) and ideal gases at ambient temperature; real air has several components.
- The least work is a thermodynamic floor that no real separator approaches; low second-law efficiency is normal for small generators.
- The actual and target energies must use the same boundary (compressor input, dryers, boosters) and the same reference conditions.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Benchmark a nitrogen generator’s energy against the thermodynamic least
- Show what a higher purity set point costs
- Compare a generator’s energy with a supplier’s target
Who it is for
- Energy and utilities engineers
- Plant engineers
- Business owners comparing gas supply options
What you get
- Waste composition and recovery
- Least work and least specific energy
- Second-law efficiency and yearly energy and cost
Interpreting the result
- Use the result to compare options and set points, not to expect the minimum: the compressor’s own losses dominate the real energy.
- Raising purity raises the air factor, so energy rises faster than the least work suggests.
References
- E. A. Guggenheim, Thermodynamics: An Advanced Treatment for Chemists and Physicists, 5th revised edition (North-Holland, 1967), §4.18–4.20 (ideal mixtures and their thermodynamic functions). Method reference; no text, tables or examples are reproduced.
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
What entropy counts
What it covers: Entropy at the molecular scale: counting arrangements, S = k ln W, why spontaneous change is near certain, what mixing does, and why a cool room lowers entropy without breaking the second law.
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