Gas discharge rate calculator for pressurised releases
A gas discharge calculation gives the source term for almost every consequence study: jet fire, dispersion, indoor build-up and explosion overpressure all begin with a mass release rate. This module integrates the discharge from the stagnation condition inside the vessel down to atmospheric pressure, switching automatically between choked (sonic) and subsonic flow as the upstream pressure falls.
Open the Gas Discharge moduleWhat this calculator returns
- Initial and time-varying mass release rate
- Flow regime (choked or subsonic) at each time step
- Exit velocity, exit temperature and exit density
- Total released inventory and time to depressurise
Required inputs
- Stagnation pressure and temperature inside the equipment
- Hole diameter or equivalent leak area
- Discharge coefficient
- Gas composition or a selected library component
Calculation method
The upstream state is evaluated with the Peng-Robinson equation of state so that the compressibility factor Z reflects the real gas, with a fallback to ideal-gas behaviour for user-defined components without binary data.
The critical pressure ratio is tested at every step. While the ambient pressure is below the critical value the flow is choked and the exit Mach number is unity; below that threshold the isentropic subsonic expression is used.
The vessel inventory is depleted by numerical integration, so the release rate decays as the vessel pressure falls, rather than being frozen at the initial value.
Governing equations
m = Cd A P0 sqrt( k M / (Z R T0) ) ( 2 / (k + 1) ) ^ ((k + 1) / (2 (k - 1)))Choked (sonic) mass release rate through the leak path.
m = Cd A P0 sqrt( 2 M k / (Z R T0 (k - 1)) [ (Pa/P0)^(2/k) - (Pa/P0)^((k+1)/k) ] )Subsonic mass release rate once the pressure ratio is above critical.
Pcrit / P0 = ( 2 / (k + 1) ) ^ (k / (k - 1))Critical pressure ratio that separates the two flow regimes.
Nomenclature
- m
- mass release rate, kg/s
- Cd
- discharge coefficient, dimensionless
- A
- hole area, m2
- P0, T0
- stagnation pressure (Pa) and temperature (K)
- Pa
- ambient (downstream) pressure, Pa
- k
- ratio of specific heats, Cp/Cv
- M
- molar mass, kg/mol
- Z
- compressibility factor, dimensionless
- R
- universal gas constant, 8.314 J/(mol K)
Assumptions and limitations
- Isentropic expansion through the leak path with a constant discharge coefficient.
- Single-phase gas at the orifice; two-phase flashing releases are handled by the blowdown module.
- Uniform stagnation conditions in the equipment at each time step.
Reference practice
- Consistent with the discharge treatment in API 521 and the CCPS Guidelines for Consequence Analysis of Chemical Releases.
Worked example
Methane at 50 bara and 15 degC leaking through a 10 mm hole with a discharge coefficient of 0.62 and a compressibility factor of 0.90.
| Step | Value | Basis |
|---|---|---|
| Hole area A | 7.85e-5 m2 | A = pi d^2 / 4 with d = 0.010 m |
| Critical pressure | 27.2 bara | Pcrit = P0 (2/(k+1))^(k/(k-1)) with k = 1.31, so the flow starts choked |
| Initial release rate | 0.44 kg/s | Choked expression with M = 0.016 kg/mol, T0 = 288 K, Z = 0.90 |
| Regime change | below about 27 bara | The integration switches to the subsonic expression as the vessel depressurises |
0.44 kg/s is the source term that feeds the dispersion, jet fire or indoor build-up study; because the module integrates the inventory, the rate falls continuously rather than staying at the initial value.
Illustrative numbers only — rerun the module with the project basis of design before using any result.
Common questions
When is a gas release choked?
Whenever the ambient pressure is below the critical pressure P0 (2/(k+1))^(k/(k-1)) — roughly 0.53 P0 for most hydrocarbons. Above that ratio the release becomes subsonic and the rate falls faster.
Which discharge coefficient should be used?
0.61 to 0.62 is the usual value for a sharp-edged hole, and 0.8 to 1.0 for a rounded nozzle or a full-bore pipe break. The rate scales linearly with Cd.
Does the hole size matter more than the pressure?
Yes. Rate scales with the square of the hole diameter but only linearly with stagnation pressure, so doubling the hole quadruples the source term.
Related calculators
- Two-Phase Blowdown — Two-phase blowdown and depressurisation calculator
- Gas Dispersion — Atmospheric gas dispersion calculator
- Indoor Release — Indoor release concentration and ventilation calculator