KEVOS® MAKEOS · Pneumatics
Gas Pressure Reduction Cooling Check (Joule–Thomson Temperature Drop, Outlet Temperature, Preheat)
How much does a gas cool when its pressure is reduced through a regulator or valve, does the outlet stay above the lowest temperature allowed, and how much preheat is needed if it does not?
Temperature change of a gas throttled at constant enthalpy through a regulator, valve or orifice: the Joule–Thomson coefficient either entered or estimated from van der Waals constants and integrated over the pressure drop, the outlet temperature and drop, the inversion temperature of the van der Waals gas, and the inlet temperature and preheat power needed to keep the outlet at the lowest temperature you allow.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Coefficient | choice | Whether the Joule–Thomson coefficient is estimated from the gas’s van der Waals constants or entered directly from measured data. |
| Inlet gas temperature | °C | Temperature of the gas just upstream of the regulator or valve. |
| Inlet pressure (absolute) | bar | Absolute pressure upstream (gauge pressure plus the atmospheric pressure). |
| Outlet pressure (absolute) | bar | Absolute pressure downstream. |
| Gas properties | ||
| van der Waals constant a | L²·bar/mol² | The van der Waals attraction constant of the gas, from a property table (convert L²·atm/mol² by × 1.01325). |
| van der Waals constant b | L/mol | The van der Waals excluded-volume constant of the gas, from the same table. |
| Molar heat capacity at constant pressure | J/(mol·K) | Molar heat capacity of the gas at constant pressure, from a property table, at about the working temperature. |
| Joule–Thomson coefficient (entered) | K/bar | The Joule–Thomson coefficient from measured data for the gas over the working pressures and temperatures (used only when the coefficient is entered). |
| Flow and limit | ||
| Gas mass flow | kg/h | Mass flow of gas through the regulator, used for the preheat power. |
| Molar mass of the gas | g/mol | Molar mass of the gas, to turn the mass flow into a molar flow. |
| Lowest acceptable outlet temperature | °C | The lowest outlet temperature you accept, from frost, hydrate, dew point, material or downstream equipment limits. |
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: Coefficient
- What it is
- How the Joule–Thomson coefficient, the temperature change per bar of pressure drop at constant enthalpy, is obtained: estimated from the van der Waals constants of the gas, or entered from measured data.
- Units and format
- Choose one of 2 options from the list: Estimate from van der Waals constants; Enter a Joule–Thomson coefficient.
- Example
- The form opens with “Estimate from van der Waals constants” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Selects which inputs are used: the constants a, b and Cp, or the entered coefficient.
- Get it right
- Use entered measured data when you have it; the van der Waals estimate is rough at high pressure.
What this means: Inlet gas temperature
- What it is
- The temperature of the gas as it reaches the regulator, valve or orifice, before any cooling from the pressure drop.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -150 °C to 500 °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 warmer inlet gives a warmer outlet and, for the van der Waals estimate, a slightly smaller coefficient.
- Get it right
- Measure it at the regulator inlet; gas from a buried main or a cold cylinder can be well below air temperature.
What this means: Inlet pressure (absolute)
- What it is
- The absolute pressure of the gas upstream of the pressure reduction, which is the gauge reading plus the atmospheric pressure.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0.000001 bar to 1000 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 70 bar 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 pressure drop and so a larger temperature drop.
- Get it right
- Add about 1 bar to a gauge reading to get absolute pressure.
What this means: Outlet pressure (absolute)
- What it is
- The absolute pressure of the gas downstream of the regulator or valve, after the pressure reduction.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0.000001 bar to 1000 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7 bar 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 temperature drop.
- Get it right
- It must be lower than the inlet pressure; use the set pressure of the regulator plus atmospheric pressure.
Gas properties
What this means: van der Waals constant a
- What it is
- The van der Waals constant that represents the attraction between the gas molecules; the attraction is what makes most gases cool when they expand at constant enthalpy.
- Units and format
- Enter a number in L²·bar/mol²: L²·bar/mol². The form accepts 0 L²·bar/mol² to 100 L²·bar/mol². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.408 L²·bar/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 gives a larger cooling coefficient and a higher inversion temperature.
- Get it right
- Tables often give it in L²·atm/mol²; multiply by 1.01325 to get L²·bar/mol².
What this means: van der Waals constant b
- What it is
- The van der Waals constant that represents the volume taken up by the gas molecules themselves; on its own it makes a gas warm on throttling.
- Units and format
- Enter a number in L/mol: L/mol. The form accepts 0 L/mol to 1 L/mol. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.03913 L/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 the cooling coefficient and lowers the inversion temperature.
- Get it right
- Take it from the same table as a so the pair belongs together; it is in litres per mole.
What this means: Molar heat capacity at constant pressure
- What it is
- The heat needed to raise one mole of the gas by one kelvin at constant pressure, which converts the enthalpy change into a temperature change and sets the preheat power.
- Units and format
- Enter a number in J/(mol·K): J/(mol·K). The form accepts 1 J/(mol·K) to 1000 J/(mol·K). Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 29.1 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
- With the estimated coefficient a larger heat capacity reduces the temperature drop; it always raises the preheat power for each kelvin.
- Get it right
- Use the molar value in J/(mol·K), not a specific heat in kJ/(kg·K); multiply a specific heat by the molar mass to convert.
What this means: Joule–Thomson coefficient (entered)
- What it is
- The measured change in gas temperature per bar of pressure drop when the gas expands at constant enthalpy, used directly when the coefficient is entered.
- 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 0.25 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 drop rises in proportion to it when the coefficient is entered.
- Get it right
- A positive value means cooling; use a value averaged over the actual pressure and temperature range.
Flow and limit
What this means: Gas mass flow
- What it is
- The mass of gas passing through the pressure reduction each hour, used only to find the preheat power.
- Units and format
- Enter a number in kg/h: kg/h. The form accepts 0 kg/h to 10000000 kg/h. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 kg/h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The preheat power rises in proportion; the temperatures do not change.
- Get it right
- Use the peak flow for the preheater size; a volume flow in standard cubic metres needs the gas density to convert.
What this means: Molar mass of the gas
- What it is
- The mass of one mole of the gas, which turns the mass flow into a molar flow for the preheat power.
- Units and format
- Enter a number in g/mol: g/mol. The form accepts 1 g/mol to 1000 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
- A larger molar mass means fewer moles per kilogram and a smaller preheat power.
- Get it right
- Use the average molar mass for a gas mixture such as natural gas, from its composition.
What this means: Lowest acceptable outlet temperature
- What it is
- The lowest gas temperature you accept downstream of the pressure reduction, set by frost, hydrate or dew point limits, seal and material limits, or downstream equipment.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -200 °C to 500 °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 limit makes a preheat more likely and raises the inlet temperature and power needed.
- Get it right
- Allow a margin above the hydrate or dew point of the actual gas; wet gas can block a regulator at temperatures above 0 °C.
Method and formulas
- Throttling keeps enthalpy constant (H1 = H2), so the temperature follows dT/dP = μ_JT along the pressure drop.
- van der Waals estimate at low pressure: (∂H/∂P)_T = b − 2a ÷ RT, so μ_JT = (2a ÷ RT − b) ÷ Cp; it is integrated from P1 to P2 by fourth-order Runge–Kutta. The inversion temperature, where μ_JT = 0, is 2a ÷ Rb. An entered coefficient is used as a constant.
- Preheat: the inlet temperature that gives the lowest allowed outlet temperature is found by bisection; preheat power = molar flow × Cp × the temperature rise.
- Example: nitrogen-like constants, 70 to 7 bar from 15 °C: μ_JT = 0.26944 K/bar at the inlet, a 17.781 K drop to −2.781 °C; preheating to 17.534 °C (0.073106 kW for 100 kg/h) keeps the outlet at 0 °C.
Limitations
- The van der Waals coefficient is a low-pressure estimate and is only approximate at high inlet pressures; use measured data or a real-gas property program for design.
- No heat gain from the surroundings, no liquid drop-out and no change in kinetic energy.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check whether a pressure regulator will frost or freeze
- Size a gas preheater ahead of a pressure reduction station
- Estimate the cooling across a let-down valve or orifice
Who it is for
- Gas and process engineers
- Instrument and maintenance technicians
- Plant designers
What you get
- Joule–Thomson coefficient, temperature drop and outlet temperature
- Inversion temperature of the van der Waals gas
- Inlet temperature and preheat power needed
Interpreting the result
- Above its inversion temperature a gas warms on throttling; hydrogen and helium do this at room temperature.
- A positive temperature drop means the outlet is colder; moisture in the gas can then freeze or form hydrates in the regulator.
Before relying on the result
- Compare the coefficient with measured Joule–Thomson data for the actual gas composition.
- Follow the regulator maker’s and the gas network operator’s requirements for preheating and freezing protection.
References
- Linder, B., Thermodynamics and Introductory Statistical Mechanics (Wiley-Interscience, 2004), section 3.7.4, printed pp. 29–31: the Joule–Thomson coefficient, constant enthalpy throttling and (∂H/∂P)_T = b − 2a ÷ RT for a van der Waals gas. Method reference; no source 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.