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Pressure Relief System Modules

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CALCULATOR MODULE : ASME B31.1 Power Piping Steam Pressure Relief   ±

Calculate ASME B31.1 power piping steam mass flow rate for pressure relief valves, headers and vents.

For pressure relief valves the mass flow rate can be calculated for isentropic or isothermal flow. The pressure relief valve is assumed to exit directly to ambient pressure. If the ambient pressure is less than the critical pressure the flow is critical (Mc = 1 for isentropic flow and Mc = √(1/γ) for isothermal flow). If exit pressure is greater than the critical nozzle pressure, the flow is sub critical (M < Mc). For isothermal flow a suitable isothermal temperature should be determined. The valve nozzle orifice diameter and cross section area can be calculated from API letter designation (API 526 type D to T), or user defined.

For a combined pressure relief valve and pressure relief header, the mass flow rate can be calculated for

  • Isentropic nozzle and adiabatic header
  • Isentropic nozzle and isothermal header
  • Isothermal nozzle and isothermal header

The pressure relief valve is assumed to exit directly into the header. If the header inlet pressure is less than or equal to the nozzle critical pressure the nozzle flow is critical, and the mass flow rate is restricted by the nozzle. The header inlet pressure is calculated so that the header mass flow rate equals the nozzle mass flow rate. If the header inlet pressure is greater than the critical nozzle pressure, the nozzle flow is sub critical (M < Mc), and the mass flow rate is restricted by the header. The mass flow rate is calculated so that the header inlet pressure is equal to the nozzle pressure. The mass flow rate through the nozzle is always equal to the mass flow rate through the header.

Pressure relief headers are normally part of a pressure relief system, and are usually attached to an upstream device such as a pressure relief valve, a pressure relief vent, or another pressure relief header. The inlet pressure of the header is less than or equal to exit pressure from the upstream device. The header should be sized so that the calculated header mass flowrate is greater than or equal to the mass flowrate of the upstream device. For headers attached to multiple upstream devices, the header mass flowrate is divided by the number of devices. If the header is oversized, the header inlet pressure will reduce so that the actual header mass flowrate is equal to the upstream mass flowrate (there is a pressure drop between the upstream exit and the header inlet).

Pressure relief vents are constant diameter piping, usually with either a valve or a burst disk. Vents usually exit either to atmosphere, or into a header. If the ambient pressure is less than the critical exit pressure exit flow is critical. If the ambient pressure is greater than the critical exit pressure, exit flow is sub critical (M < Mc). The header or vent inlet flow is assumed to be sub critical for all flow conditions. Header and vent pressure losses are calculated from the pressure loss factor (fld = fL/D + K). The Darcy friction factor f is calculated for fully turbulent flow using the rough pipe equation. Minor losses can be included by the minor loss K factor, and should include valves and bends etc. The discharge coefficient can also be used for minor losses, and as a safety factor.

Reference : ANSI/ASME B31.1 : Power Piping (2014)

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CALCULATOR MODULE : Compressible Flow Pressure Relief Valve   ±

Calculate compressible flow pressure relief valve capacity for isentropic, isothermal, and adiabatic conditions.

For pressure relief valves with no header, the mass flow rate can be calculated for isentropic or isothermal flow. The pressure relief valve is assumed to exit directly to ambient pressure. If the ambient pressure is less than the critical pressure the flow is critical (Mc = 1 for isentropic flow and Mc = √(1/γ) for isothermal flow). If the ambient pressure is greater than the critical nozzle pressure, the flow is sub critical (M < Mc). For isothermal flow the stagnation temperature should be close to or equal to the ambient temperature (for example a gas transmission pipeline). Phase changes are ignored.

For a combined pressure relief valve and pressure relief header, the mass flow rate can be calculated for

  • Isentropic nozzle and adiabatic header
  • Isentropic nozzle and isothermal header
  • Isothermal nozzle and isothermal header

The pressure relief valve is assumed to exit directly into the header. If the header inlet pressure is less than or equal to the nozzle critical pressure the nozzle flow is critical (Mc = 1 for isentropic flow and Mc = √(1/γ) for isothermal flow), and the mass flow rate is restricted by the nozzle. The header inlet pressure is calculated so that the header mass flow rate equals the nozzle mass flow rate. If the header inlet pressure is greater than the critical nozzle pressure, the nozzle flow is sub critical (M < Mc), and the mass flow rate is restricted by the header. The mass flow rate is calculated so that the header inlet pressure is equal to the nozzle pressure. The mass flow rate through the nozzle is always equal to the mass flow rate through the header.

For a pressure relief header, the mass flow rate can be calculated for adiabatic or isothermal flow. If the header is attached directly to the outlet of a pressure relief valve (PRV), the header inlet pressure should be set equal to the PRV nozzle outlet pressure. The header should be sized so that the calculated header mass flowrate is greater than or equal to the PRV mass flowrate. For headers with more than one PRV, the header mass flowrate is divided by the number of PRV's. If the header is oversized, the header inlet pressure will reduce so that the actual header mass flowrate is equal to the nozzle mass flowrate (there is a pressure drop between the PRV outlet and the header inlet).

Note : If the PRV is attached to a small diameter header which feeds into a larger diameter header (possibly with multiple PRVs), the large diameter header should be sized first. The inlet pressure for the large diameter header is used as the ambient pressure for the smaller diameter header (and PRV).

Header pressure losses are calculated from the pressure loss factor (fld = fL/D + K). The Darcy friction factor f is calculated for fully turbulent flow using the rough pipe equation. The header is assumed to be constant diameter. Minor losses can be included by the minor loss K factor, and should include valves and bends etc. The header entry and exit losses should not be included (the fluid dynamic pressure loss is included in the calculation). The discharge coefficient can also be used for minor losses, and as a safety factor. If the ambient pressure is less than the critical header pressure the header exit flow is critical (Mc = 1 for isentropic flow and Mc = √(1/γ) for isothermal flow). If the ambient pressure is greater than the critical header pressure, the header exit flow is sub critical (M < Mc). The header entry flow is assumed to be sub critical for all flow conditions.

The effective PRV valve nozzle orifice diameter and cross section area can be calculated from API letter designation (API 526 type D to T). API effective orifice sizing is used to compensate for the friction pressure losses in the relief valve. The combination of valve and nozzle orifice must be tested with the operating fluid at the design conditions, and certified as having a flow rate greater than or equal to the calculated flow rate for the equivalent size. The API 526 orifice sizing assumes isentropic flow. For certified API 526 valves, the isentropic nozzle calculation option should be used.

Note : The pressure relief header calculation is not suitable for pressure relief vents. Headers are assumed to be part of a PRV system. Vents are constant diameter piping attached to a pipeline or pressure vessel.

Use the Result Plot option to plot pressure, mach number and mass flow rate.

Reference : Fluid Mechanics, Frank M White, McGraw Hill

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CALCULATOR MODULE : Compressible Flow Blowdown Time   ±

Calculate compressible flow pipeline or vessel blow down time through a constant diameter vent for adiabatic and isothermal flow using either the integration method, or the simplified method.

The integration method uses numerical integration to calculate the elapsed time between the initial pressure, and the final blow down pressure. At high pressure the vent exit flow is critical (Mc = 1 for adiabatic flow and 1/√γ for isothermal flow). At lower pressures the vent exit flow is sub critical (M < Mc). The vent entry is subsonic at all conditions. Increase the number of steps to improve the accuracy. Use the minimum number of steps required (the method is reasonably accurate with 16 steps). Using a large number of steps may slow down the calculation, especially on older computers. The accuracy of the integration method decreases at pressure less than 1.1 x ambient pressure (ie 110 kPa or 16.2 psi for atmospheric pressure discharge). The blow down time tends to infinity as the final pressure approaches ambient pressure.

The simplified method calculates the blow down time from the initial pipeline gas moles, and the initial vent mole flow rate. The flow is assumed to be always critical, and the pipeline pressure is assumed to decrease exponentially. The simplified method is reasonably accurate for final pressure ≥ 2 x ambient pressure. At low pressures flow is sub critical and the simplified method underestimates the elapsed time relative to the integration method (both methods are less accurate at very low pressure). The simplified method is not recommended for final pressure less than 1.2 x ambient pressure. The blow down time tends to infinity as the final pressure approaches absolute zero.

Minor losses should include the vent entry valves and bends etc. The vent exit should not be included as the fluid dynamic pressure is included in the calculation. Minor losses can be accounted for by using the minor loss factor K, or the discharge coefficient Cd. The discharge coefficient is used to factor the mole flow rate. The gas in the pipeline is assumed to be stationary (stagnation conditions), ie the pipeline diameter >> the vent diameter. Phase changes are ignored. The Darcy friction factor is calculated from pipe roughness assuming fully turbulent flow.

Note : The final blow down pressure should be above ambient pressure (final blow down pressure ≤ ambient pressure causes a divide by zero error).

Reference : Fluid Mechanics, Frank M White, McGraw Hill

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CALCULATOR MODULE : Compressible Flow Pressure Relief Vent   ±

Calculate compressible flow pressure relief vent flow rate and pressure drop for either adiabatic or isothermal flow.

The vent is modelled as a frictionless entry, combined with a frictional constant diameter duct. For adiabatic flow the vent entry is assumed to be isentropic. For isothermal flow, the vent entry is assumed to be isothermal. The vent entry is assumed to be subsonic at all conditions. The pipeline is assumed to be at stagnation conditions (M = 0). At high pressure the vent exit flow is critical flow (Mc = 1 for adiabatic low and `Mc = 1 / (√γ)` for isothermal flow : γ = the gas specific heat ratio). At lower pressures the vent exit flow is sub critical (M < Mc).

Vent flow rate is calculated from the vent pressure loss factor (fld).

`fld = fd L/D + K `

where :

fld = vent pressure loss factor
fd = Darcy friction factor
L = vent length
D = vent inside diameter
K = minor loss K factor

The Darcy friction factor is calculated assuming fully turbulent flow. Minor losses should include the vent entry, and valves, bends etc.. The vent exit should not be included (the fluid dynamic pressure is included in the calculation). The discharge coefficient can be used as a safety factor.

Note : The vent calculation is not suitable for pressure relief headers which are part of a pressure relief valve (PRV) system.

Use the Result Plot option to plot inlet and exit pressure versus stagnation pressure, inlet and exit mach number versus stagnation pressure, or mass flow rate versus stagnation pressure and flow type.

Reference : Fluid Mechanics, Frank M White, McGraw Hill

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CALCULATOR MODULE : Compressible Flow Nozzle Flow Rate   ±

Calculate compressible flow mass flow rate and mole flow rate through a nozzle for isentropic and isothermal flow.

At high pressure the nozzle flow is critical (the critical exit pressure is ≥ the ambient pressure). The critical Mach number Mc = 1 for adiabatic low and Mc = 1 / √γ for isothermal flow (γ = the gas specific heat ratio). At lower pressures the nozzle flow is sub critical (M < Mc) (the critical exit pressure is < the ambient pressure). For isothermal flow the stagnation temperature should be close to or equal to the ambient temperature (eg gas transmission pipeline). The discharge coefficient can be used to account for friction losses, and as a design factor.

Reference : Fluid Mechanics, Frank M White, McGraw Hill

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CALCULATOR MODULE : API 520 Pressure Relief Device   ±
CALCULATOR MODULE : API 520 Gas Pressure Relief Valve   ±

Calculate API 520 gas pressure relief valve (PRV) and rupture disk size.

The flow through the relief valve nozzle is assumed to be sonic (M = 1), adiabatic, and isentropic. If the back pressure is greater than the critical (sonic) pressure the flow is subsonic (M < 1).

Friction losses are accounted for using the discharge coefficient Kd. For initial sizing of PRV's the effective nozzle diameter should be used with the discharge coefficient Kd = 0.975. The actual nozzle diameter and the rated coefficient of discharge should be used to verify that the selected PRV is suitable for the required flow rate. The PRV effective diameter is taken from API 526 (letter designation D to T). Changes in phase are not accounted for.

The calculation can also be used for rupture disks. The rupture disk diameter should be substituted for the nozzle diameter, with a discharge coefficient Kd = 0.62. Rupture disks can also be analysed as part of a relief vent system using the flow resistance method.

Note : The ideal gas calculators use the ideal gas compressible flow equations. The API 520 gas and steam calculations use an approximation of the ideal gas compressible flow equations. Use the ideal gas calculators for a comparison with the API 520 calculators.

Reference : API 520 Sizing, Selection And Installation Of Pressure Relieving Devices (2014)

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CALCULATOR MODULE : API 520 Steam Pressure Relief Valve   ±

Calculate API 520 steam pressure relief valve (PRV) and rupture disk size.

The flow through the relief valve nozzle is analysed using the Napier equation. For temperatures above 1200 F (922 K), the gas PRV calculation should be used. If the back pressure is greater than the critical (sonic) pressure the flow is sub sonic (M < 1).

Friction losses are accounted for using the discharge coefficient Kd. For initial sizing of PRV's the effective nozzle diameter should be used with the discharge coefficient Kd = 0.975. The actual nozzle diameter and rated coefficient of discharge should be used to verify that the selected PRV is suitable for the required flow rate. The PRV effective diameter is taken from API 526 (letter designation D to T). Changes in phase are not accounted for.

The calculation can also be used for rupture disks. The rupture disk diameter should be substituted for the nozzle diameter, with a discharge coefficient Kd = 0.62. Rupture disks can also be analysed as part of a relief vent system using the flow resistance method.

Note : The ideal gas calculators use the ideal gas compressible flow equations. The API 520 gas and steam calculations use an approximation of the ideal gas compressible flow equations. Use the ideal gas calculators for a comparison with the API 520 calculators.

Reference : API 520 Sizing, Selection And Installation Of Pressure Relieving Devices (2014)

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CALCULATOR MODULE : API 520 Liquid Pressure Relief Valve   ±

Calculate API 520 liquid pressure relief valve (PRV) and rupture disk size (certified and non certifed devices).

The flow through the relief valve nozzle is analysed using the Bernoulli equation. Friction losses are accounted for using the discharge coefficient Kd. For initial sizing of PRV's the effective nozzle diameter should be used with the discharge coefficient Kd = 0.65 for certified PRV's and Kd = 0.62 for non certified PRV's. The actual nozzle diameter and rated coefficient of discharge should be used to verify that the selected PRV is suitable for the required flow rate. The PRV effective diameter is taken from API 526 (letter designation D to T). Changes in phase are not accounted for.

The PRV calculation can also be used for rupture disks. The rupture disk diameter should be substituted for the nozzle diameter, with a discharge coefficient Kd = 0.62. Rupture disks can also be analysed as part of a relief vent system using the flow resistance method.

Reference : API 520 Sizing, Selection And Installation Of Pressure Relieving Devices (2014)

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CALCULATOR MODULE : API 520 Pressure Relief Vent   ±

Calculate API 520 flow rate through a constant diameter pressure relief vent.

The vent entry is assumed to be a pressure vessel or piping at stagnation pressure (valid when the pipe or vessel diameter is much greater than the vent diameter). The calculated vent exit pressure is flowing pressure (stagnation pressure minus dynamic pressure).

Vent pressure losses are calculated from the vent pressure loss factor (fld = fL/D + K). Minor losses should include the vent entry, valves and bends etc. The vent exit should not be included. The discharge coefficient can be used to factor the flow rate, depending on the design requirements.

For rupture disks, the flow resistance factor of the rupture Kr should be included in the minor losses (the resistance factor should be factored for the vent diameter). A discharge coefficient of 0.9 or less should be used for rupture disks. Alternatively, the PRV calculators can be used for rupture disk calculations.

Note : The ideal gas calculators use the ideal gas compressible flow equations. The API 520 gas and steam calculations use an approximation of the ideal gas compressible flow equations. Use the ideal gas calculators for a comparison with the API 520 calculators.

Reference : API 520 Sizing, Selection And Installation Of Pressure Relieving Devices (2014)

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CALCULATOR MODULE : API 520 Back Pressure   ±

Calculate API 520 back pressure from mass flow rate through a constant diameter vent.

The calculated vent entry and exit pressures are flowing pressure (stagnation pressure minus dynamic pressure). Minor losses should include bends and valves etc. The vent entry and exit should not be included in the minor losses. The discharge coefficient can be used to factor the mass flow rate, depending on design requirements.

Where multiple pressure relieving devices share a common vent, the back pressure should be calculated for the total mass flow rate.

For relief vents with sections of increasing diameter, the back pressure should be calculated for each constant diameter section, going backwards from exit. The (flowing) exit pressure for each section equals the (flowing) inlet pressure for the previous section.

For pressure relief valves or rupture disks, the (flowing) inlet pressure for the vent is used as the (flowing) back pressure for the pressure relief device. This is valid provided that the vent diameter is greater than the diamter of the PRV nozzle or rupture disk.

Note : The ideal gas calculators use the ideal gas compressible flow equations. The API 520 gas and steam calculations use an approximation of the ideal gas compressible flow equations. Use the ideal gas calculators for a comparison with the API 520 calculators.

Reference : API 520 Sizing, Selection And Installation Of Pressure Relieving Devices (2014)

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