KEVOS® MAKEOS · Pneumatics
Gas Throttling Temperature Check (Joule–Thomson Cooling, Regulator Outlet, Preheat)
When this gas is throttled through a regulator or valve from a high to a low pressure, how cold does it come out, and how much preheat keeps the outlet above my lowest allowed temperature?
Temperature change of a gas throttled at constant enthalpy: the Joule–Thomson coefficient from the van der Waals second virial coefficient (2a ÷ RT − b) ÷ Cp, integrated exactly over the pressure drop, or from a known coefficient, giving the outlet temperature, the inversion temperature of the model, the inlet temperature that keeps the outlet at the lowest allowed temperature, and the preheat power for the gas flow, against the lowest acceptable outlet temperature.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Joule–Thomson model | choice | Calculate the coefficient from van der Waals constants, or enter a known coefficient. |
| van der Waals constant a | Pa·m⁶/mol² | van der Waals attraction constant of the gas, from property data. |
| van der Waals constant b | cm³/mol | van der Waals co-volume of the gas, from property data. |
| Joule–Thomson coefficient (known model) | K/bar | Joule–Thomson coefficient measured or tabulated for the gas over the range (used by the known-coefficient model). |
| Molar heat capacity at constant pressure | J/(mol·K) | Molar heat capacity of the gas at constant pressure in the low-pressure (perfect gas) limit. |
| Throttling | ||
| Inlet pressure | bar abs | Absolute pressure before the regulator or valve. |
| Outlet pressure | bar abs | Absolute pressure after it. |
| Inlet temperature | °C | Gas temperature before the regulator. |
| Lowest acceptable outlet temperature | °C | Lowest outlet temperature allowed by the pipe material, seals, freezing or hydrate formation. |
| Gas flow at 15 °C and 101.325 kPa | Sm³/h | Gas flow in standard cubic metres per hour at 15 °C and 101.325 kPa. |
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: Joule–Thomson model
- What it is
- How the Joule–Thomson coefficient is found: from the gas’s van der Waals constants, or from a known coefficient measured or tabulated for the gas.
- Units and format
- Choose one of 2 options from the list: van der Waals constants a and b; Known Joule–Thomson coefficient.
- Example
- The form opens with “van der Waals constants a and b” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Selects which inputs are used for the temperature change.
- Get it right
- Use a known coefficient when you have data for your gas at similar pressures; it is usually more accurate.
What this means: van der Waals constant a
- What it is
- The van der Waals constant measuring the attraction between gas molecules, which makes the gas cool when it expands.
- Units and format
- Enter a number in Pa·m⁶/mol²: Pa·m⁶/mol². The form accepts 0.000001 Pa·m⁶/mol² to 10 Pa·m⁶/mol². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.2303 Pa·m⁶/mol² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger value increases cooling and raises the inversion temperature.
- Get it right
- Tables often give it in L²·bar/mol²: divide by 10 for Pa·m⁶/mol².
What this means: van der Waals constant b
- What it is
- The van der Waals co-volume: the volume per mole taken up by the gas molecules themselves, which makes the gas warm when it expands.
- Units and format
- Enter a number in cm³/mol: cm³/mol. The form accepts 0.001 cm³/mol to 1000 cm³/mol. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 43.1 cm³/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 value reduces cooling and lowers the inversion temperature.
- Get it right
- Tables often give it in L/mol: multiply by 1000 for cm³/mol.
What this means: Joule–Thomson coefficient (known model)
- What it is
- The temperature change per bar of pressure drop when the gas is throttled at constant enthalpy, used directly by the known-coefficient model.
- Units and format
- Enter a number in K/bar: K/bar. The form accepts -5 K/bar to 5 K/bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.45 K/bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The temperature change is directly proportional to it in the known-coefficient model.
- Get it right
- Use a value for your gas near the average temperature and pressure of the drop; positive means it cools.
What this means: Molar heat capacity at constant pressure
- What it is
- The heat needed to warm one mole of the gas by one kelvin at constant pressure, at low pressure where it behaves as a perfect gas.
- Units and format
- Enter a number in J/(mol·K): J/(mol·K). The form accepts 10 J/(mol·K) to 500 J/(mol·K). Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 35.7 J/(mol·K) as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger value reduces the temperature change but raises the preheat power for a given temperature lift.
- Get it right
- Use the value at the inlet temperature from gas property data, in J/(mol·K), not kJ/(kg·K).
Throttling
What this means: Inlet pressure
- What it is
- The absolute pressure of the gas just upstream of the regulator, valve or orifice.
- Units and format
- Enter a number in bar abs: bar abs. The form accepts 0.01 bar abs to 1000 bar abs. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 70 bar abs as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher inlet pressure gives a larger drop and more cooling.
- Get it right
- Add atmospheric pressure to a gauge reading to get absolute pressure.
What this means: Outlet pressure
- What it is
- The absolute pressure of the gas just downstream of the regulator, valve or orifice.
- Units and format
- Enter a number in bar abs: bar abs. The form accepts 0.01 bar abs to 1000 bar abs. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7 bar abs as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A lower outlet pressure gives a larger drop and more cooling.
- Get it right
- Use the regulator’s set point plus atmospheric pressure; it must be below the inlet pressure.
What this means: Inlet temperature
- What it is
- The temperature of the gas as it reaches the regulator, before any cooling from the pressure drop.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -150 °C to 1000 °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
- The outlet temperature follows it nearly degree for degree.
- Get it right
- Use the coldest inlet temperature expected, such as a winter supply or gas from a cold cylinder bank.
What this means: Lowest acceptable outlet temperature
- What it is
- The coldest gas temperature allowed after the regulator, set by pipe and seal materials, freezing of moisture or hydrate formation.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -200 °C to 1000 °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
- Moves the pass line and the preheat needed; the outlet temperature does not change.
- Get it right
- Take the lowest of the pipe material’s minimum design temperature, seal ratings and the gas’s hydrate or dew point.
What this means: Gas flow at 15 °C and 101.325 kPa
- What it is
- The gas flow through the regulator as a volume at 15 °C and one standard atmosphere, used to turn the temperature lift into heater power.
- Units and format
- Enter a number in Sm³/h: Sm³/h. The form accepts 0 Sm³/h to 10000000 Sm³/h. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 Sm³/h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Preheat power rises in proportion to it; the temperatures do not change.
- Get it right
- Use the peak flow, since preheat is needed most when the flow is highest.
Method and formulas
- Throttling keeps enthalpy constant, and for a slightly imperfect gas the Joule–Thomson coefficient is μ = (T dB/dT − B) ÷ C_p (Guggenheim §3.11, §3.20).
- With the van der Waals second virial coefficient B = b − a ÷ RT, μ = (2a ÷ RT − b) ÷ C_p, which changes sign at the inversion temperature 2a ÷ R b (§3.21–3.22).
- dT ÷ dp depends only on T, so the drop integrates exactly: Δp = C_p ∫ T ÷ (2a/R − bT) dT, solved for the outlet temperature; with a known coefficient, ΔT = μ Δp.
- Preheat = molar flow × C_p × (inlet temperature needed − actual inlet temperature).
- Example: methane at 15 °C let down from 70 to 7 bar abs cools to −13.048 °C; keeping the outlet at 0 °C needs 26.52 °C at the inlet, 4.8315 kW for 1000 Sm³/h.
Limitations
- Guggenheim notes that no two-constant formula such as van der Waals fits the second virial coefficient quantitatively; treat the result as an estimate and compare with measured data.
- The second virial (slightly imperfect gas) form is a low-to-moderate pressure approximation; at high pressure use an equation of state or measured enthalpy data.
- Constant heat capacity; no heat gained from the surroundings; kinetic energy changes neglected.
- This is a screening aid: gas pressure reduction stations are designed and approved by qualified gas engineers to the applicable codes.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a gas pressure regulator or let-down valve for freezing at the outlet
- Size the preheater for a gas pressure reduction station
- See whether a gas cools or warms when throttled
Who it is for
- Gas and process engineers
- Mechanical engineers
- Instrument and maintenance technicians
What you get
- Joule–Thomson coefficient and inversion temperature
- Outlet temperature and temperature change
- Inlet temperature and preheat power needed
Interpreting the result
- Most gases cool on throttling at ordinary temperatures; hydrogen and helium warm because they are above their inversion temperatures.
- Frost on a regulator body is a sign the outlet is below 0 °C; moisture and hydrates can block it.
Before relying on the result
- Compare the outlet temperature with a measured Joule–Thomson coefficient or enthalpy data for the gas at the actual pressures.
References
- E. A. Guggenheim, Thermodynamics: An Advanced Treatment for Chemists and Physicists, 5th revised edition (North-Holland, 1967), §3.11 (throttling), §3.20 (Joule–Thomson coefficient), §3.21 (temperature dependence of the second virial coefficient), §3.22 (Boyle and inversion temperatures). 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
Throttling: the Joule–Thomson effect at the regulator
What it covers: Why gas cools through a regulator, LN-1's drop from 15 °C to −20 °C on a full pack, the inversion temperature, why hydrogen warms, CO₂ regulators that freeze, and a cold-gas alarm.
Useful alongside · KEVOS® original book
Throttling, mixing and friction
What it covers: Three losses with no heat and no visible waste: pressure regulators, tempering valves and friction in pipes and filters, their entropy generation, their cost in kilowatts and how to reduce them.
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.