DESCRIPTIONThis document briefly describes the one phase relief valve calculation spreadsheet, which will be the standard relief valve calculation tool of LGN. The calculation method used in this spreadsheet isbased on calculation methods as given in API 520 part 1 (7thed., 2000, page 41-56). It is strongly recommended to read these pages before one starts with the calculations. All calculations are done in SI units.FORMULASGAS AND VAPOR FLOW∙ Flow through the relief valve is called critical if112-⎪⎪⎭⎫⎝⎛+≤i ik k i bk P Pwhere:P b Maximum back pressurekPa a PUpstream relieving pressure. This is the set pressure plus the allowable overpressure plus atmospheric pressure.kPa a k i Ideal gas heat capacity ratio or C p,ig / C v,ig -C p,ig Ideal gas heat capacity at constant pressure kJ/kg.K C v,igIdeal gas heat capacity at constant volumekJ/kg.KAlthough this equation is only valid for ideal gases, it may be used to calculate critical pressure ratio. k i can be obtained from table 7 in API 520 part 1. Otherwise, the following formula can be used:RMW c MW c k ig p ig p i -⋅⋅=,,where:k i Ideal gas heat capacity ratio-C p,ig Ideal gas heat capacity at constant pressure kJ/kg.K MW Molecular weight -R Gas constant KJ/kmol.KIf the ideal gas heat capacity is not known, use the actual heat capacity in the same equation. Errors are found to be only small.∙ Critical Flow (Gas or Vapor): The following equation can be used to size a pressure relief device in gas or vapor service that operates at critical flow conditions.MWZT KKP KC W A cbd⋅⋅⋅⋅⋅⋅=160,13where:A Required discharge area (for standard types see table 1) mm 2W Required mass flow through the device. kg/hr CCoefficient determined from an expression of the ratio ofthe specific heats (k = C p /C v ) of the gas or vapor at inlet relieving conditions. This can be obtained from figure 32 in API 520 or with the following formulae:1112520-+⎪⎭⎫ ⎝⎛+⋅⋅=k k k k C hr lb Rlb lb f mole m ⋅⋅⋅ C p Heat capacity at constant pressure at relieving conditionskJ/kg.K C vHeat capacity at constant volume at relieving conditions kJ/kg.K K dEffective coefficient of discharge. For preliminary sizing, use the following values:∙ For relief valve with or without rupture disk: 0.975 ∙ For installation of rupture disk only: 0.62-P Upstream relieving pressure. This is the set pressure plus the allowable overpressure plus atmospheric pressure.kPa a K bCapacity correction factor due to back pressure, to be applied for balanced type relief valves only; Forpreliminary sizing, this can be estimated from figure 30 in API 520 (see also table 2).For conventional and piloted operated valves K b =1 -K cCombination correction factor for installations with a rupture disk upstream of the PSV.∙ K c = 1.0 when a rupture disk is not installed∙ K c = 0.9 when a rupture disk is installed upstreamthe PSV and does not have a published value -T Relieving temperature at inlet of the relief valve. K Z Compressibility factor at inlet relieving conditions -MWMolecular weightKg/kmolThe above equation should also to be used to size balanced pressure relief valves in subcritical flow (in this case K b should be obtained from the manufacturer).∙ Subcritical Flow: Required relief valve area for conventional and pilot operated relief valves()bcdP P P MW TZ KKF W A -⋅⋅⋅⋅⋅⋅=29.17where:A Required discharge area (for standard types see table 1) mm 2W Required mass flow through the device. kg/hr F 2Coefficient of subcritical flow, see figure 34 in API 520 or use the following equation:()()⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡--⋅⋅⎪⎭⎫ ⎝⎛-=-r r r k k F kk k 111122- kRatio of specific heats, C p / C v- r Ratio of back pressure to upstream relieving pressure, P b / P- C p Heat capacity at constantkJ/kg.K C v Heat capacity at constant volumekJ/kg.K KdEffective coefficient of discharge. For preliminary sizing, use the following values:∙ For relief valve with or without rupture: 0.975 ∙ For installation of rupture disk only: 0.62-K cCombination correction factor for installations with a rupture disk upstream of the PSV.∙ K c = 1.0 when a rupture disk is not installed∙ K c = 0.9 when a rupture disk is installed upstreamthe PSV and does not have a published value -Z Compressibility factor at inlet relieving conditions - T Relieving temperature at inlet of the relief valve KMW Molecular weightKg/kmol P Upstream relieving pressure. This is the set pressure plus the allowable overpressure plus atmospheric pressure.kPa a P bMaximum back pressurekPa aSTEAM RELIEFSHNcbdKKKKKP WA ⋅⋅⋅⋅⋅⋅=4.190where:A Required discharge area (for standard types see table 1) mm 2W Required mass flow through the device.kg/hr PUpstream relieving pressure. This is the set pressure plus the allowable overpressure plus atmospheric pressure.kPa a K dEffective coefficient of discharge. For preliminary sizing, use the following values:∙ For relief valve with or without rupture: 0.975 ∙ For installation of rupture disk only: 0.62-K bCapacity correction factor due to back pressure. This can be obtained from the manufacturer’s literature or estimated from figure 30 of API 520 (see also table 2). The back pressure correction factor applies to balanced bellows valves only.For conventional and piloted operated valves K b =1 -K cCombination correction factor for installations with a rupture disk upstream of the PSV.∙ K c = 1.0 when a rupture disk is not installed∙ K c = 0.9 when a rupture disk is installed upstreamthe PSV and does not have a published value -K NCorrection factor for Napier equation.For P ≤ 10,339 kPaaK N = 1For P > 10,339 and P ≤ 22,057 kPaa106103324.010*******.0-⋅-⋅=P P KN-K SHSuperheat steam correction factor. This can be obtained from table 3 (equivalent to table 9 of API 520). For saturated steam at any pressure K SH = 1.0-LIQUID RELIEFblvcwdP P G KKKKQ A -⋅⋅⋅⋅=78.11where:A Required discharge area (for standard types see table 1) mm2Q Volume flow rateL/min K dEffective coefficient of discharge that should be obtained from the valve manufacturer. For a preliminary sizing, an effective discharge coefficient can be used as follows: ∙ For relief valve with or without rupture disk in liquidservice: 0.65∙ For installation of rupture disk only: 0.62-K W Correction factor due to back pressure. If the back pressure is atmospheric, use a value for K w of 1.0. Balanced bellows valves in back pressure servicerequire the correction factor to be determined from table 2 (equivalent to figure 31 of API 520). Conventional and pilot operated valves require no special correction. -K cCombination correction factor for installations with a rupture disk upstream of the PSV.∙ K c = 1.0 when a rupture disk is not installed∙ K c = 0.9 when a rupture disk is installed upstreamthe PSV and does not have a published value -G l Liquid gravity at flowing conditions referred to water at standard conditions- P Upstream relieving pressure. This is the set pressure plus the allowable overpressure plus atmospheric pressure.kPa a P b Maximum back pressurekPa a K VCorrection factor due to viscosity. Factor can be determined from figure 36 in API 520 or from the following equation:.15.175.342878.29935.0-⎪⎭⎫ ⎝⎛++=Rn Rn K v-Rn Reynolds number.AG Q Rn l ⋅⋅⋅=μ18800-μLiquid viscositycPTo make an estimate for the area, initially K v = 1 is taken and an initial area can be calculated. From there the Reynolds number can be calculated. With this Reynolds number K v can be calculated and from there the correct estimate for the relief valve area.RUPTURE DISK SIZING ONLYThe sizing of a rupture disk is done by using the appropriate equation as listed above. When using these equations, a coefficient of discharge, K d of 0.62, should be used.VALVE SELECTIONWhen the required size has been calculated, the valve is selected based on API 526 (see table 1). The valve types are standard types. For high-pressure systems a different valve number from the ones given may be required. This must be checked by the user.If the required area is greater than that of a 8 T 10 size multiple valves will be specified. All data concerning selected area and maximum flow through selected relief valve will then be based on one valve.TEMPERATURE ESTIMATESThe spreadsheet estimates a device outlet temperature under chapter “Device Output Data”.The outlet temperature of the valve in steam service has been estimated by100100⋅=b sat P Twhere:P b Back pressurekPa a T satSteam saturation temperature°CAbove pressures of 1 bar this is accurate to about 2 %.The outlet temperature for vapors and gasses, under the assumption of adiabatic expansion, is determined by:kk b inout P P T T 1-⎪⎭⎫ ⎝⎛⋅=where:T out Relieving temperature at outlet of the relief valve K T in Relieving temperature at inlet of the relief valve K P b Maximum back pressurekPa a P Upstream relieving pressure. This is the set pressure plus the allowable overpressure plus atmospheric pressure.kPa a kRatio of specific heats at relieving conditions, C p / C v-TABLESTable 1Orifice Areas and TypesTable 2Gauge Pressure Ratio in %Correction Factors, K b and K wTable is based on figures 30 and 31 in API 520 PT 1 (p. 37+38)Where:P b Back Pressure kPa g P s Relief device set pressure KPa gTable 3Superheat Correction Factors, KSH (=Table 9 in API 520(p. 51))HISTORYChanges from V 1.0 to V 1.1∙Added the legal statement∙J17: conversion factor 2.20462 in stead of 2.2046∙J18/19: corrected formulas and gave correct values for 1 atm in kPa and psi.∙J21: conversion factor 4.1868 in stead of 4.186.∙J23: corrected conversion error (factor 1000) for lb/ft3.∙J25/26: Removed saturated steam temperature and superheat temperature.∙F27: removed specific gravity from input, as density is already an input.∙F31 (new): Corrected formula to be used for gas or steam and lookup to start at zero value∙F34 (new): lookup to start at zero value.∙J35 (new): rounded the temperature off to full decades.∙Removed Cv value of valve.∙Added note that if multiple valves are specified, the data is per valve.∙On sheet values:∙Removed orifice Cv value∙Corrected conversion from psig to kPaa (superheat correction factors-table) and corrected one value∙Rounded off the gauge pressure ratio and corrected it for value used (not bar).∙Changed Pb/P for Kw in that table to start at 0, not 1.∙Removed the factor 100 used for critical flow area calculation∙Changed text part of area and flow calculation.∙Changed pressure to work in kPa, not bar, for X49.∙Put specific gravity on this sheet for use in formulas.∙Added references to Word-file∙Added valve selection and temperature estimates paragraphs∙Added symbols∙Changed order of tables and corrected∙in table 1 the area of an H orifice is 0.785 in2, not 1.00 in2∙in table 2 set the bottom limit for Pb/P at 0, not 1.∙In table 3 800°F, 1500 psig K sh=0.86, not 0.85.∙In case k or ki is 1, value is changed to 1.+1.e-10∙In case of Liquid Relief with multiple relief valves, the actual valve area was calculated as zero.Corrected by calculating the number of relief valves correctly.Changes from V 1.1 to V 1.2∙Removed units of measurement for ki (Cell K23)∙Changed unit of measurements of Superimposed Backpressure from delta pressures to absolute pressures. The formula that calculates the Maximum Backpressure has been correctedaccordingly.Changes from V 1.2 to V 1.3∙Layout changes to the spreadsheet, manual and TQM registration.∙Modified Kb calculation that was based on Pb/Pset and is now based on the ratio Pb/Prel∙Added warning to the spreadsheet that in case RV = Rupture Disk, the user also must select Yes in box “Rupture Disk combined with RV”.∙Added warning that in case of subcritical balanced relief valves, the Kb factor has to be obtained from the manufacturer.∙Adjusted the formula that calculates factor Kn, required factor for steam relief valves.∙Modified the lookup that determined factor Ksh. Old method could give a wrong value.∙Adjusted the orifice size description in table 1.Changes from V 1.3 to V 1.4∙Modified calculation of liquid specific gravity∙Comments for back pressure, built-up back pressure and superimposed back pressure aligned with API。
