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Thursday, September 11, 2008

Two Useful Equations For Flow Conversion between Air - Vapor & Actual - Standard

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Hydrocarbon condensate generated from fractionation unit and condensate stabilization unit will be stored in condensate tank before it is loaded into ship for export. The condensate storage tank is blanketed with inert gas i.e. Nitrogen to avoid moisture ingress and contaminated the condensate. Condensate storage tank in normally fixed roof tank and protected by Pressure Vacuum Relief Valve (PVRV) from overpressure and vacuum hazard. Concerning vacuum hazard and causes, read more in "Vacuum Hazard - Another Catastrophic Factor..." and some recommendations to minimize /avoid vacuum hazard in "4-steps Approach to Combat Vacuum Hazard".

In sizing a PVRV for tank, API Std 2000 Venting Atmospheric and Low Pressure Storage Tanks is used. In the standard, inbreathing rate due to thermal and pump-out and outbreathing due to pump-in, thermal and fire can be referred. Nevertheless, the Outflow and Inflow rate are presented in air equivalent flow at Standard condition (14.7 psia & 60 degF) for English unit and Normal condition (1.014 bara & 0 degC) for SI unit. There are some level of conversion required between actual vapor flow, standard vapor flow and air standard flow. Sometime it creates some confusion to engineer.

Following are some equations for the conversion and pretty useful for young engineer for verification purpose.

(A) Convert Air Volumetric Flow (@ Std) to Vapor Volumetric Flow (@ Std)
Vapor Volumetric Flow @ STD = Air Volumetric Flow @ STD × Vapor Temperature Correction Factor / Vapor Specific Gravity Correction Factor

[Eq.1]

QStd,Vap = QStd,Air × √[(TStd,Vap+460) ⁄ (TActual,Vap+460)] / √[MWVap / MWAir]

where
QStd,Vap = Vapor Volumetric Flow @ STD (SCFH)
QStd,Air = Air Volumetric Flow @ STD (SCFH)
TStd,Vap = Vapor Temperature @ STD = 60 degF
TActual,Vap = Actual Vapor Temperature (degF)
MWVap = Vapor Molecular Weight
MWAir = Air Molecular Weight (28.96)


(B) Convert Vapor Volumetric Flow (@ Std) to Vapor Volumetric Flow (@ Actual)

Vapor Volumetric Flow @ PT = Vapor Volumetric Flow @ STD × [Actual Temperature / Standard Temperature] × [Std Pressure / Actual Pressure ]

[Eq.2]
QActual,Vap = QStd,Vap × [(TActual,Vap+460) ⁄ (TStd,Vap+460)] × [PStd,Vap/PActual,Vap]

where
QActual,Vap = Actual Vapor Flow (SCF)
PStd,Vap = Vapor Pressure @ STD (14.7 psia)
PActual,Vap = Actual Vapor Pressure (psia)


Example 1 :
Nitrogen (MW=28) blanketing a tank. The calculated air flow @ std is 50,000 SCFH. The tank is at 1 psig and 68 degF when venting via PVRV occurred. Calculate the equivalent Nitrogen relief load at actual flow condition.

From [Eq.1]
QStd,N2 = QStd,Air × √[(TStd,N2+460) ⁄ (TActual,N2+460)] / √[MWN2 / MWAir]

QStd,N2 = 50000 × √[(60+460) ⁄ (68+460)] / √[28 / 28.96]

QStd,N2 = 50463.22 SCFH


From [Eq.2]
QActual,N2 = QStd,N2 × [(TActual,N2+460) ⁄ (TStd,N2+460)] × [PStd,N2/PActual,N2]

QActual,N2 = 50463.22 × [(68+460) ⁄ (60+460)] × [14.7/(14.7+1)]

QActual,N2 = 47975.91 CFH


Example 2 :
A tank feed from condensate stablizer. In case of gas blowby, flash vapor generated plus displaced vapor (MW = 35) is 60,000 CFH and tank is at 1.5 psig and 122 degF when venting via PVRV occurred. Calculate the equivalent Air flow at STD condition.

From [Eq.2]
QAct,Vap = QStd,Vap × [(TAct,Vap+460) ⁄ (TStd,Vap+460)] × [PStd,Vap/PAct,Vap]

QStd,Vap = QAct,Vap × [(TStd,Vap+460) ⁄ (TAct,Vap+460)] × [PAct,Vap/PStd,Vap]

QStd,Vap = 60000 × [(60+460) ⁄ (122+460)] × [(1.5+14.7)/14.7]

QStd,Vap = 59078.48 SCFH


From [Eq.1]

QStd,Vap = QStd,Air × √[(TStd,Vap+460) ⁄ (TActual,Vap+460)] / √[MWVap / MWAir]

QStd,Air = QStd,Vap × √[(TActual,Vap+460) ⁄ (TStd,Vap+460)] / √[MWAir / MWVap]

QStd,Air = 59078.48 × √[(122+460) ⁄ (60+460)] / √[28.96 / 35]

QStd,Air = 68710.62 SCFH

Concluding Remark
Above equations are pretty useful for conversion of air - vapor and actual-standard condition especially when you are dealing with tank relief sizing and PVRV verification.

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