Engineering task and calculation objective
Safety valves are the last line of defense of any pressure equipment: if the control system fails or an upset occurs — an external fire, loss of cooling — the valve must discharge the resulting mass flow completely before the pressure rises to an unacceptable level. Engineers who need to size a safety valve or calculate the required narrowest flow area will find the governing rules in AD 2000-Merkblatt A2 of the German AD 2000 pressure vessel code, supplemented by the American practice API RP 520.
From the mass flow to be discharged, the set pressure and the fluid properties, module A2 determines the required narrowest flow area of the valve — separately for gases, vapours and liquids. For compressible fluids the outflow function, the pressure ratio to the back pressure, and the molar mass, temperature and real-gas factor enter the calculation; for liquids the pressure difference and the density. The certified discharge coefficient accounts for the real flow behaviour of the specific valve make.
In practice this calculation is needed whenever pressure vessels, steam generators or piping systems are protected against overpressure: for new designs, for changed operating conditions (higher mass flow, different fluid) and for re-rating existing valves. In addition, inlet and discharge lines can be assessed for pressure drop and built-up back pressure — an excessive pressure drop in the inlet line causes the valve to chatter.
Standard and calculation basis: AD 2000 A2: 2020-01 & API RP 520
Calculation workflow
- Define the upset scenario and the mass flow: First, the mass flow to be discharged in the upset case is determined — for example from the maximum heating duty, the maximum feed flow or the fire case. The set pressure of the valve and the allowable back pressure downstream of the valve are also fixed at this stage.
- Record the fluid and its properties: Depending on the state of matter, different fluid properties are required: for gases and vapours the molar mass, isentropic exponent, temperature and real-gas factor at the valve inlet; for liquids the density. The module distinguishes the calculation paths for gases, vapours and liquids via the calculation options.
- Determine the outflow function and pressure ratio: For compressible fluids it is checked whether the flow in the narrowest cross-section is critical (near-sonic) or subcritical. This yields the outflow function which, together with the certified discharge coefficient of the valve, describes the actual flow capacity.
- Calculate the required narrowest flow area: From the mass flow, set pressure, fluid properties and discharge coefficient, the required narrowest flow area A0 is determined to AD 2000 A2 or API RP 520. A valve is then selected whose narrowest flow area is at least equal to this value.
- Verify the inlet and discharge lines: Finally, the inlet line and the discharge line are checked: the pressure drop in the inlet line should not exceed 3 % of the set pressure, and the built-up back pressure in the discharge line must be compatible with the valve design (with or without a balancing bellows).
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Density | ρ | kg/m³ |
| Specific volume | v | m³/kg |
| Molar mass | M | kg/kmol |
| Compressibility factor | Z | – |
| Gas constant | R | J/(kg·K) |
| Specific heat capacity (pressure) | cp | J/(kg·K) |
| Pressure (abs) | p0 | bar |
| Temperature | t | °C |
| Back pressure (abs) | pa | bar |
| Mass flow | qm | kg/h |
| Downstream mass flow | q | kg/s |
| Flow figure | αw | – |
| Actual cross section diameter | do | mm |
| Upstream pressure drop | ΔP | Pa |
| Inside diameter feed pipe | DE | mm |
| Isentropic exponent | k | – |
| Static pressure before PRV (abs) | py | bar |
| Allowable friction factor blow-off pipe | ζz,blow | – |
| End pressure in blow-off pipe (abs) | pn | bar |
| Response pressure PRV | pe | bar |
| For and holds: | a = > 0.14 ζz = > 2 | – |
| Compressibility factor at pipe end | Zn | – |
| Hydrostatic Pressure (abs) | ph | bar |
| Back pressure outside blowoff pipe (abs) | pao | bar |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Flow figure | αw | – |
| Actual cross section diameter | do | mm |
| Required cross section area | Ao | mm² |
| Required cross section diameter | do,req | mm |
| Pressure ratio | Pv | – |
| Discharge function | ψ | – |
| Allowable friction factor feed pipe | ζz,feed | – |
| Allowable friction factor blow-off pipe | ζz,blow | – |
| Inside diameter blowoff pipe | DA | mm |
| Required effective discharge area | A | mm² |
| Upstream relieving pressure | P1 | kPa |
| Reynolds Number | R | – |
| Back pressure with Qa | P2Qa | kPa |
| Actual flow rate | Qa | l/min |
| Actual effective discharge area | Aa | mm² |
| Actual correction factor viscosity | Kva | – |
Calculation options
Calculation Options
Gases and vapours · Liquids · Liquids according API 520
Worked example
A vessel containing water is to be protected against overpressure. In the upset case, 20,000 kg/h of water must be discharged. The set gauge pressure of the safety valve is 10 bar above the back pressure (discharge to atmosphere), and the certified discharge coefficient for liquids is αw = 0.55. Find the required narrowest flow area A0 — a worked example of safety valve sizing to AD 2000 A2.
Given values
| Mass flow qm | 20,000 kg/h |
| Pressure difference Δp (set pressure − back pressure) | 10 bar |
| Density of water ρ | 998 kg/m³ |
| Certified discharge coefficient αw | 0.55 |
Solution
Formula for liquids to AD 2000 A2
For liquids, with qm in kg/h, Δp in bar, ρ in kg/m³ and A0 in mm²:
A0 = 0.6211 · qm / (αw · √(Δp · ρ))
Insert the numerical values
√(Δp · ρ) = √(10 · 998) = 99.9
A0 = 0.6211 · 20,000 / (0.55 · 99.9) = 12,422 / 54.95 = 226 mm²
Corresponding narrowest diameter
d0 = √(4 · A0 / π) = √(4 · 226 / π) ≈ 17.0 mm
A valve is selected whose certified narrowest flow area is at least 226 mm².
Result
| Required narrowest flow area A0 | 226 mm² |
| Corresponding narrowest diameter d0 | ≈ 17.0 mm |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
How does sizing to AD 2000 A2 differ from sizing to API RP 520?
Both codes lead to the required narrowest flow area, but they use different sets of formulas, unit systems and coefficients. AD 2000 A2 works with the certified discharge coefficient from German component type testing, while API RP 520 uses discharge coefficients and correction factors (e.g. for back pressure on balanced-bellows valves). For plants within the scope of the European Pressure Equipment Directive, AD 2000 A2 is normally governing; for international projects or US specifications it is API RP 520.
What does the certified discharge coefficient αw mean and where do I obtain it?
The certified discharge coefficient describes the ratio of the mass flow that can actually be discharged to the theoretical mass flow of an ideal nozzle. It is verified by the valve manufacturer through component type testing and is stated in the component data sheet (VdTÜV data sheet or manufacturer documentation), separately for gases/vapours and for liquids. Without this value no specific valve can be verified — a generic assumption is acceptable for preliminary sizing only.
Why must the pressure drop in the inlet line not exceed 3 % of the set pressure?
When the valve opens, the pressure drop in the inlet line lowers the pressure at the valve inlet. If this loss exceeds the blowdown (reseating pressure difference), the valve closes again, the pressure rises again — the valve chatters. This rapid opening and closing destroys seat and disc and drastically reduces the relieving capacity. That is why AD 2000 A2 and API RP 520 limit the inlet-line pressure loss to about 3 % of the set gauge pressure.
Does the back pressure in the discharge line have to be considered when determining the flow area?
Yes. For liquids, the pressure difference between set pressure and back pressure enters the formula directly. For gases, the pressure ratio decides whether the flow is critical or subcritical; at high back pressure the capacity drops. In addition, the built-up back pressure affects the function of spring-loaded valves — without a metal bellows, depending on the manufacturer, only about 10 to 15 % of the set pressure is usually permissible as built-up back pressure.