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Relief Valve & Discharge Line Sizing

Size the pressure relief valve and its inlet and discharge lines to EN 13136 for CO2 and other refrigerants: required capacity, valve area, back pressure, inlet pressure drop, dry-ice risk and outlet noise.
R744 · 60.0 bar · DN15

Refrigerant and system

All at once: the design case for fire, when every valve can relieve. One at a time: when the valves protect parts that cannot relieve together. Each valve's back pressure is checked against its own limit.
Refrigeration copper (EN 12735-1) and steel are the most common for relief lines. Plumbing copper and press systems are fine if the pipe and fittings withstand the back pressure and are approved for the refrigerant – press fittings for water often have EPDM seals that do not withstand refrigerants and oil. Copper must not be used with ammonia.

Relief valves

Paste the valve data sheet
One row per position, as in the valve data sheet. The lines are sized for the valve capacity Qm × quantity (safe side); Qmd is checked against it. To calculate like the manufacturer, enter the adjusted capacity Qmd' instead of Qm. The gas temperature is only needed when the pressure is above the critical pressure (CO2: 73.8 bar), e.g. the high-pressure side. Temperature unknown? Use the hot-gas temperature – a higher temperature gives a larger line (safe side).

Common discharge line: last tee → outlet

0 for an outlet to atmosphere; enter the pressure if the line discharges into a system under pressure. Size Auto = the smallest that keeps every valve's back pressure (and the noise requirement). No line may be smaller than the valve outlet.

Noise at the outlet

Estimate after API 521 / ISO 23251 of the jet at the outlet. With a noise requirement, the smallest size that meets both the back pressure and the noise requirement is chosen. Buildings, reflections and silencers change the real level.

Project

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Units

Flow diagram

The diagram is drawn from the data on the left. Click a valve to edit it, or a pipe to change its size and length; a red line = the limit is exceeded.
V1DN1060.0 bar500 kg/hDN10 · 0.3 m9.6 %outlet91 dB(A) @ 10 mDN15 · 10.0 m · 4 bends500 kg/h · 5.50 bar

Valves – back pressure

ValveSet pressure (bar)Flow (kg/h) BranchPressure at tee (bar)Back pressure (bar)% of set Segment after teeKbInletStatus
V160.00 500.0DN10 5.505.76 9.6 %DN151.000 0.02 %OK

Common discharge line – all sizes

The last segment (last tee → outlet) in every size; the segments before it are chosen automatically for each row. Pressure at tee = the pressure at the last tee; worst % = the highest back pressure in percent of set pressure among the valves. * = choked flow at the outlet.

Calculation basis

Show calculation

Per pipe

PipeMass flow [kg/s]Density [kg/m³]Inner Ø [mm]Velocity [m/s]RefLength (+ equivalent) [m]Δp [bar]Δp/m [Pa/m]Note
Inlet V10.1389269.313.63.55623,0000.02710.1 (+0.251)0.011911,9000.02 % / 3.0 %
Branch V10.138911.4913.683.2623,0000.02710.30.26488,1009.6 % / 10 %
Common line V1 → outlet0.13892.48217.3238490,0000.025510 (+1.8)5.555,000choked · 5.50 bar

Basis of calculation

Method
EN 13136 (as referred to by EN 378-2): required capacity and valve capacity at set pressure plus overpressure; discharge lines as isothermal compressible flow with choking, solved from the outlet back to each valve at the gas temperature of the relieving state; inlet line as incompressible flow at the relieving density.
Equations
  • Qm = 0.2883 · C · Kb · A · Kdr · √(p0/v0)
  • C = 3.948 · √(κ · (2/(κ+1))^((κ+1)/(κ−1)))
  • p1² − p2² = G² · R·T · (f·L/D + ΣK + 2·ln(p1/p2))
  • p* = G · √(R·T) (choked end)
  • Δp_inlet = (f·L/D + ΣK) · ρ·v²/2
  • K_bend = 21.3 · fT (Crane TP-410)
  • L_eq = ΣK · D / f
Friction
Darcy–Weisbach · Colebrook–White (64/Re < 2300)
Fluid data
CoolProp 8.0.0
Standards
EN 13136:2013+A1:2018 · EN 378-2 · EN ISO 4126-1 · API 521 / ISO 23251 · Crane TP-410
Notes
  • Gas lines: density and velocity at the downstream end of the pipe; Δp includes the drop at a choked end. The note gives the inlet drop and the back pressure as % of the set pressure against the limit. The outlet section shows the pressure at its start (above atmospheric).

Relief valve and discharge line FAQ

How do you size a relief valve to EN 13136?

First the required discharge capacity: for fire 10 kW/m² times the vessel's outer surface divided by the latent heat, otherwise the compressor flow or the heat input. EN 13136 then gives the valve area from Qm = 0.2883·C·Kb·A·Kdr·√(p0/v0) at the set pressure plus 10 %.

Calculate it in the tool above

How much back pressure can a safety valve take?

Conventional safety valves usually allow at most 10 % of the set pressure; balanced valves allow more, as the maker states. The inlet line may lose at most 3 %. The calculator finds the discharge line back pressure with compressible flow and choking.

Calculate it in the tool above

How do you size a common discharge header for several relief valves?

Each valve's back pressure is checked with all valves relieving at once (fire) or one at a time. The segments between the tees carry the flow of the valves upstream and may differ in size; a common rule of thumb is a header area at least the sum of the branch areas.

Calculate it in the tool above

What is special about CO2 (R744) relief valves?

The pressures are high and on the high-pressure side CO2 is often supercritical, so the valve is sized for gas at a temperature. When CO2 expands below 5.2 bar dry ice forms, so the discharge line must be short and self-draining with no low points.

Calculate it in the tool above

Can copper pipe be used for the relief line?

Yes for HFC/HFO and CO2 if the pipe withstands the back pressure: refrigeration copper to EN 12735-1, or plumbing copper EN 1057 and press systems with fittings approved for the refrigerant. Copper is not allowed with ammonia; use steel or stainless.

Calculate it in the tool above

How loud is a relief valve when it blows?

Often above 100 dB(A) near the outlet. The calculator estimates the noise to API 521 and picks a bigger line when a noise requirement is set; if that is not enough, move the outlet or fit a silencer.

Calculate it in the tool above

Assumptions: Discharge capacity and valve flow to EN 13136:2013+A1, as referred to by EN 378-2 (EN ISO 24664:2024 not yet checked) (Qm = 0.2883·C·Kb·A·Kdr·√(p0/v0)); discharge line with isothermal compressible flow and choking, gas temperature = relieving temperature (conservative); inlet line as incompressible flow. Refrigerant data from CoolProp reference equations. Noise estimated after API 521 / ISO 23251.

Disclaimer: This tool does not guarantee correct results. Safety devices must be selected and approved by a competent person; always check against EN 378, EN 13136, the valve maker's data and local rules.

Help – relief valve and discharge line

The calculator follows EN 13136: first the required discharge capacity, then the valve's flow area or capacity, then the pressure drop in the inlet line and the back pressure in the discharge line.

1. Refrigerant and pressure

  • Choose the refrigerant and the set pressure (gauge). The valve relieves at the set pressure plus the overpressure (normally 10 %).
  • Most cases relieve saturated vapour. Above the critical pressure (e.g. CO2 on the high-pressure side, above 73.8 bar) or for superheated gas, e.g. on the hot-gas line, choose gas at a temperature. It works for every refrigerant in the list.
  • Refrigerants not in the list can be calculated with “Other refrigerant” and the maker's data.

2. Required capacity

  • Fire: EN 13136 uses a heat flux of 10 kW/m² on the vessel's outer surface; the capacity is that heat divided by the latent heat.
  • Compressor: swept volume × suction gas density × volumetric efficiency. Heat source: the heat input divided by the latent heat.

3. Valve

  • With Kdr and the flow area from the data sheet, the valve's capacity is compared with the required capacity. With the area at 0, the area needed is shown.
  • The discharge line is sized for what the valve can discharge, not only for what is required.
  • Choose how the valve data is given: flow area and Kdr, API 526 orifice, capacity at your conditions or capacity at the data sheet's conditions (converted). Only one way is used at a time; the other fields are hidden. The capacity can be given in kg/h, kg/s, lb/h or Nm³/h.

4. Lines

  • The inlet line may lose at most 3 % of the set pressure. The discharge line is checked for each size; the smallest size that keeps the back pressure within the limit is chosen.
  • For ammonia, copper is not allowed. For CO2, watch the dry-ice warning.
  • Several valves: add valves in the Valves panel. Each valve has its own capacity, inlet line and branch line to the common discharge line. The diagram shows the whole system; click a valve to edit it.
  • The common line is cut at every tee: each segment carries the flow of the valves before it and gets its own size. The sizes keep every valve's back pressure within the valve's limit, with all valves at once or one at a time, and can also be chosen by hand.

5. Noise, save and print

  • Enter the distance to the nearest listener and a noise requirement to get a warning when the estimate is above it.
  • With a noise requirement, the smallest size that meets both the back pressure and the noise is chosen. A bigger line gives a lower outlet velocity and so less noise. If no size meets it, the distance where it is met is shown.
  • A silencer is optional: choose a type for typical values or enter the maker's insertion loss and loss coefficient. The silencer's pressure drop is included in the back pressure.
  • “Save” downloads the project as a file, “Open” opens it again, “Print” prints the results.