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 is based on calculation methods as given in API 520 part 1 (7th ed., , 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 i k k i b k P Pwhere:P bMaximum back pressurekPa a P Upstream 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,ig Ideal 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 iIdeal gas heat capacity ratio-C p,ig Ideal gas heat capacity at constant pressure kJ/kg.KMW 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 K K P K C W A cb d ⋅⋅⋅⋅⋅⋅=160,13where:A Required discharge area (for standard types see table 1) mm 2 W Required mass flow through the device. kg/hr CCoefficient determined from an expression of the ratio of the specific heats (k = C p /C v ) of the gas or vapor at inlet relieving conditions. This can be obtained from figure 32in API 520 or with the following formulae:1112520-+⎪⎭⎫⎝⎛+⋅⋅=k k k k Chr lb R lb 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()b c d P P P MW TZ K K F W A -⋅⋅⋅⋅⋅⋅=29.17where:A Required discharge area (for standard types see table 1) mm 2 W 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 k k k111122- 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 RELIEFSHN c b d K K K K K P WA ⋅⋅⋅⋅⋅⋅=4.190where:A Required discharge area (for standard types see table 1) mm 2 W Required mass flow through the device.kg/hr P Upstream 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 kPaa106103324.0100002764.0-⋅-⋅=P P K N-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 RELIEFblv c w d P P G K K K K Q A -⋅⋅⋅⋅=78.11where:A Required discharge area (for standard types see table 1) mm 2 Q 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-RnReynolds 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.。