API 520 Back Pressure

Calculate gas PRV back pressure and pressure drop through a constant diameter vent (API 520 Section 5.3).

The vent flow is assumed to be isothermal (constant temperature). Minor losses should include bends etc. The vent entry and exit are not included in the minor losses (the fluid dynamic pressure is included in the calculation). The Darcy friction factor is calculated from the pipe roughness using the Von Karman fully turbulent flow equation (valid for high Reynolds numbers). Phase changes and changes in elevation are ignored. The discharge coefficient can be used to factor the mass flow rate.

Tool Input

• schdtype : Vent Schedule Type
• diamtype : Vent Diameter Type
  • ODu : User Defined Vent Outside Diameter
  • IDu : User Defined Vent Inside Diameter
• wtntype : Wall Thickness Type
  • tnu : User Defined Vent Wall Thickness
• rfactype : Vent Internal Roughness Type
  • ru : User Defined Surface Roughness
  • rru : User Defined Relative Roughness
• fdtype : Darcy Friction Factor Type
  • fdu : User Defined Darcy Friction Factor
• leqtype : Minor Pressure Loss Type
  • ku : User Defined Minor Loss K Factor
  • lu : User Defined Minor Loss Length
  • lodu : User Defined Minor Loss Diameters (L/ID)
  • Leu : User Defined Equivalent Length
  • fL/Du : User Defined Pressure Loss Factor
• fluidtype : Fluid Type
  • γu : User Defined Specific Heat Ratio
  • SGu : User Defined Gas Specific Gravity
• dfactype : Discharge Coefficient Type
  • Kdu : User Defined Discharge Coefficient
• voltype : Fluid Flow Rate Type
  • mfu : User Defined Gas Mass Flow Rate
  • ngu : User Defined Gas Mole Flow Rate
• Pa : Ambient Pressure (At Exit)
• To : Fluid Temperature
• Z : Compressibility Factor
• L : Vent Length

Tool Output

• γ : Specific Heat Ratio
• ρe : Exit Density
• ρi : Inlet Density
• Ax : Nominal Cross Section Area
• C : Fluid Speed Of Sound
• Fr : Reaction Force At Exit
• ID : Vent Inside Diameter
• Kd : Discharge Coefficient
• Le : Vent Eqivalent Length
• Mce : Critical Exit Mach Number
• Me : Exit Mach Number
• Mi : Inlet Mach Number
• Pce : Critical Exit Pressure
• Pe : Exit Pressure
• Pi : Inlet Pressure or PRV Back Pressure
• R : Gas Constant
• SG : Gas Specific Gravity Relative To Air
• cvg : Convergence Factor (≅ 1)
• fL/D : Pressure Loss Factor Including Minor Losses
• fd : Darcy Friction Factor
• mf : Mass Flowrate
• mmg : Gas Molar Mass
• ng : Mole Flow Rate
• rr : Surface Roughness Ratio

Calculate liquid PRV back pressure and pressure drop through a constant diameter vent (API 520 Section 5.3).

The vent flow is calculated using Bernoulli's equation. Minor losses should include bends etc. The vent entry and vent exit are not included (the fluid dynamic pressure is included in the calculation). The discharge coefficient can be used to factor the mass flow rate. Phase changes are ignored.

Tool Input

• schdtype : Vent Schedule Type
• diamtype : Vent Diameter Type
  • ODu : User Defined Vent Outside Diameter
  • IDu : User Defined Vent Inside Diameter
• wtntype : Wall Thickness Type
  • tnu : User Defined Vent Wall Thickness
• visctype : Viscosity Type
  • μu : User Defined Dynamic Viscosity
  • νu : User Defined Kinematic Viscosity
• rfactype : Pipe Internal Roughness Type
  • ru : User Defined Surface Roughness
  • rru : User Defined Relative Roughness
• leqtype : Minor Pressure Loss Type
  • ku : User Defined Minor Loss K Factor
  • lu : User Defined Minor Loss Length
  • lodu : User Defined Minor Loss Diameters LoD
  • Leu : User Defined Equivalent Length
  • fL/Du : User Defined Pressure Loss Factor
• fdtype : Darcy Friction Factor Type
  • fdu : User Defined Darcy Friction Factor
• dfactype : Discharge Coefficient Type
  • Kdu : User Defined Discharge Coefficient
• voltype : Fluid Flow Rate Type
  • Qu : User Defined Volume Flow Rate
  • Mu : User Defined Mass Flow Rate
• ρ : Fluid Density
• L : Vent Length
• zi : Vent Inlet Elevation
• ze : Vent Outlet Elevation
• Pe : Outlet Pressure

Tool Output

• μ : Dynamic Viscosity
• Ax : Nominal Cross Section Area
• Fr : Reaction Force At Exit
• ID : Inside Diameter
• Kd : Discharge Coefficient
• Le : Vent Eqivalent Length
• M : Mass Flowrate
• Pi : Inlet Pressure or PRV Back Pressure
• Q : Volume Flowrate
• Re : Design Reynolds Number (Including Discharge Coefficient)
• V : Design Velocity (Including Discharge Coefficient)
• cvg : Convergence Factor (≅ 1)
• fL/D : Pressure Loss Factor Including Minor Losses
• fd : Darcy Friction Factor
• rr : Surface Roughness Ratio

Calculate API 520 gas duct, vent or header critical flow ratios (or Fanno lines) for adiabatic (constant enthalpy) and isothermal (constant temperature) flow using ideal gas compressible flow equations.

Critical flow conditions occur when the exit Mach number equals the critical Mach number and the critical exit pressure is greater than or equal to ambient pressure. For adiabatic flow the critical exit Mach number = 1 (eg sonic flow conditions). For isothermal flow the critical exit Mach number = √γ.

Use the Result Plot option to plot critical pressure loss factor versus inlet Mach number and either flow type or specific heat ratio; or pressure ratio, temperature ratio, density ratio, speed of sound ratio, and velocity ratio, versus either Mach number or pressure loss factor, and versus either flow type or specific heat ratio (Fanno lines). The plot range is set from the calculated value of either the inlet Mach number, or the pressure loss factor in the main calculation. Change the main calculation values to change the plot range.

Tool Input

• fluidtype : Fluid Type
  • γu : User Defined Specific Heat Ratio
• fldtype : Pressure Loss Factor Type
  • Mciu : User Defined Inlet Mach Number
  • fL/Du : User Defined Pressure Loss Factor
• flowtype : Fluid Flow Type

Tool Output

• γ : Specific Heat Ratio
• ρi/ρ* : Inlet Density Over Critical Exit Density Ratio
• Ci/C* : Inlet Speed Of Sound Over Critical Exit Speed Of Sound Ratio
• M* : Critical Exit Mach Number
• Mi : Inlet Mach Number
• Pi/P* : Inlet Pressure Over Critical Exit Pressure Ratio
• Ti/T* : Inlet Temperature Over Critical Exit Temperature Ratio
• Vi/V* : Inlet Velocity Over Critical Velocity Ratio
• cvg : Convergence Factor (≅ 1)
• fL/D* : Critical Duct Pressure Loss factor

Calculate API 520 mass flow rate through a gas pressure relief header for adiabatic and isothermal flow using ideal gas compressible flow equations.

The pressure relief header is assumed to be part of a pressure relief system, and connected to the outlet of a pressure relief valve, relief vent, or a smaller diameter relief header. The header inlet pressure should be set equal to exit pressure of the upstream relief valve, relief vent, or relief header. The header should be sized so that the calculated header mass flowrate is greater than or equal to the valve, or vent mass flowrate. For headers with more than one inlet, the header mass flowrate is divided by the number of inlets. The calculated header flowrate is the maximum possible value. The actual mass flowrate will always be equal to the upstream flowrate and the actual header inlet pressure will be less than or equal to the upstream exit pressure.

For adiabatic flow, the inlet temperature is calculated from the upstream stagnation temperature (the inlet temperature varies with the inlet Mach number). For isothermal flow the inlet temperature should be set equal to the estimated isothermal temperature (eg ambient temperature). The stagnation temperature is constant for adiabatic flow, and varies with Mach number for isothermal flow. Phase changes are ignored.

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 or an equivalent length, 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 exit 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 exit pressure, the header exit flow is sub critical (M < Mc). The header entry flow is assumed to be sub critical for all flow conditions.

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.

Tool Input

• schdtype : Header Schedule Type
• diamtype : Header Diameter Type
  • ODu : User Defined Header Outside Diameter
  • IDu : User Defined Header Inside Diameter
• wtntype : Wall Thickness Type
  • tnu : User Defined Header Wall Thickness
• rfactype : Header Internal Roughness Type
  • ru : User Defined Surface Roughness
  • rru : User Defined Relative Roughness
• fdtype : Darcy Friction Factor Type
  • fdu : User Defined Darcy Friction Factor
• leqtype : Minor Pressure Loss Type
  • ku : User Defined Minor Loss K Factor
  • lu : User Defined Minor Loss Length
  • lodu : User Defined Minor Loss Diameters (L/ID)
  • fL/Du : User Defined Pressure Loss Factor
• numtype : Number Of Inlets Type
  • Nu : User Defined Number Of Inlets
• fluidtype : Fluid Type
  • γu : User Defined Specific Heat Ratio
  • SGu : User Defined Gas Specific Gravity
• zfactype : Compressibility Factor Type
  • Zu : User Defined Compressibility Factor
• cdtype : Discharge Coefficient Type
  • Cdu : User Defined Discharge Coefficient
• flowtype : Flow Type
  • Tou : User Defined Adiabatic Stagnation Temperature
  • Tiu : User Defined Isothermal Inlet Temperature
• Pi : Header Inlet Pressure
• Pa : Ambient Pressure (At Exit)
• L : Header Length

Tool Output

• γ : Specific Heat Ratio
• ρe : Header Exit Density
• ρi : Header Inlet Density
• Cd : Discharge Coefficient
• Ce : Header Exit Speed Of Sound
• Ci : Header Inlet Speed Of Sound
• Fe : Combined Exit Reaction Force (All PRVs)
• Ge : Header Exit Mass Flux
• Gi : Header Inlet Mass Flux
• ID : Header Inside Diameter
• Le : Header Eqivalent Length
• Mce : Header Critical Exit Mach Number
• Mci : Header Critical Inlet Mach Number
• Me : Header Exit Mach Number
• Mi : Header Inlet Mach Number
• N : Number Of PRV's Sharing The Header
• Pe : Header Exit Pressure
• Rg : Specific Gas Constant
• SG : Gas Specific Gravity Relative To Air
• Te : Header Exit Temperature
• Ti : Header Inlet Temperature
• Toe : Exit Stagnation Temperature
• Ve : Header Exit Velocity
• Vi : Header Inlet Velocity
• Z : Compressibility Factor
• cvg : Convergence Factor (≅ 1)
• fL/D : Pressure Loss Factor Including Minor Losses
• fL/Da : Added Friction Loss Factor
• fL/De : Effective Friction Loss Factor
• fd : Darcy Friction Factor
• mf : Mass Flowrate Per PRV
• mmg : Gas Molar Mass
• nf : Mole Flow Rate Per PRV
• rr : Surface Roughness Ratio

Calculate API 520 critical mass flow rate through a pressure relief header for adiabatic and isothermal flow using ideal gas compressible flow equations.

The pressure relief header is assumed to be part of a pressure relief system, and connected to the outlet of a pressure relief valve, relief vent, or a smaller diameter relief header. The header inlet pressure should be set equal to exit pressure of the upstream relief valve, relief vent, or relief header. The header should be sized so that the calculated header mass flowrate is greater than or equal to the valve, or vent mass flowrate. For headers with more than one inlet, the header mass flowrate is divided by the number of inlets. The calculated header flowrate is the maximum possible value. The actual mass flowrate will always be equal to the upstream flowrate and the actual header inlet pressure will be less than or equal to the upstream exit pressure.

For adiabatic flow, the inlet temperature is calculated from the upstream stagnation temperature (the inlet temperature varies with the inlet Mach number). For isothermal flow the inlet temperature should be set equal to the estimated isothermal temperature (eg ambient temperature). The stagnation temperature is constant for adiabatic flow, and varies with Mach number for isothermal flow. Phase changes are ignored.

Header pressure losses are calculated from the pressure loss factor (fld = fL/D + K). The header is assumed to be constant diameter. Minor losses can be accounted for by either the pressure loss factor, or the discharge coefficient. Minor losses 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 header exit flow is assumed to be critical (Mc = 1 for isentropic flow and Mc = √(1/γ) for isothermal flow). The header entry flow is sub critical. Check that the exit pressure is greater than or equal to the ambient pressure. If the ambient pressure is greater than the critical nozzle pressure, the flow is sub critical (M < Mc).

Tool Input

• flowtype : Flow Type
  • Tou : User Defined Adiabatic Stagnation Temperature
  • Tiu : User Defined Isothermal Inlet Temperature
• Pi : Header Inlet Pressure
• γ : Spefic Heat Ratio
• SG : Specific Gravity
• Z : Compressibility Factor
• Cd : Discharge Coefficient
• ID : Header Internal Diameter
• fL/ID : Pressure Loss factor

Tool Output

• Me : Header Exit Mach Number
• Mi : Header Inlet Mach Number
• Pe : Header Exit Pressure
• Rg : Specific Gas Constant
• Te : Header Exit Temperature
• Ti : Header Inlet Temperature
• mf : Header Mass Flowrate
• nf : Header Mole Flow Rate