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IndustrialValves

CalculationsforDesign,Manufacturing, Operation,andSafetyDecisions

FirstEdition

KaranSotoodeh

UniversityofStavanger

Oslo,Norway

PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey. PublishedsimultaneouslyinCanada.

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LibraryofCongressCataloging-in-PublicationData

Names:Sotoodeh,Karan,author.

Title:Industrialvalves:calculationsfordesign,manufacturing, operation,andsafetydecisions/KaranSotoodeh.

Description:Firstedition.|Hoboken,NewJersey:Wiley,[2023]| Includesbibliographicalreferencesandindex.

Identifiers:LCCN2023002088(print)|LCCN2023002089(ebook)|ISBN 9781394185023(cloth)|ISBN9781394185030(adobepdf)|ISBN 9781394185054(epub)

Subjects:LCSH:Valves–Designandconstruction–Mathematics.|Fluid dynamics–Mathematics.|Engineeringmathematics–Formulae.

Classification:LCCTS277.S682023(print)|LCCTS277(ebook)|DDC 621.8/40151–dc23/eng/20230302

LCrecordavailableathttps://lccn.loc.gov/2023002088

LCebookrecordavailableathttps://lccn.loc.gov/2023002089

CoverImage(s):Rawf8/AdobeStockPhotos;WhoisDanny/AdobeStockPhotos CoverDesign:Wiley

Setin9.5/12.5ptSTIXTwoTextbyStraive,Pondicherry,India

1FlowCapacity 1

1.1Introduction 1

1.2FlowCoefficientChartandFlowCurve 8

1.3RangeabilityandTurndown 12

1.4ValveAuthority 14

1.5ValveGain 15 QuestionsandAnswers 16 FurtherReading 20

2ValveSizing 22

2.1Introduction 22

2.2IsolationValveSizing 22

2.3Nonreturn(Check)ValveSizing 26

2.4ControlValveSizing 34

2.4.1ControlValveSizingforLiquids 34

2.4.1.1SpecifytheVariablesRequiredtoSizetheValve 35

2.4.1.2DeterminetheEquationConstant(N) 37

2.4.1.3DeterminePipingGeometryFactor(FP) 37

2.4.1.4DeterminetheMaximumFlowRate(qmax)andMaximumPressure Drop(ΔPmax) 39

2.4.1.5SolveforFlowCoefficient 44

2.4.1.6SelecttheCorrectValveSize 44

2.4.2ControlValveSizingforGasandSteam 47

2.4.2.1SpecifytheVariablesRequiredtoSizetheValve 47

2.4.2.2DeterminetheEquationConstant(N) 48

2.4.2.3DeterminePipingGeometryFactor(FP) 48

2.4.2.4DeterminetheExpansionFactor(Y) 48

2.4.2.5SolvefortheRequiredFlowCoefficient(Cv) 50

2.5SafetyReliefValveSizing 56

2.5.1SizingforGasorVaporRelief 59

2.5.1.1CriticalFlow 59

2.5.1.2SubcriticalFlow 73

2.5.2SizingforSteamRelief 75

2.5.3SizingforLiquidRelief 79

2.5.3.1SizingforLiquidReliefwithCapacityCertification 79

2.5.3.2SizingforLiquidReliefWithoutCapacityCertification 84

2.5.4SizingforTwo-PhaseLiquid/VaporRelief 85

2.5.4.1SizingforSaturatedLiquidandSaturatedVapor,LiquidFlashes 88

2.5.4.2SizingforSubcooledatthePressureReliefValveInlet 91

2.5.5SizingforFireCaseandHydraulicExpansion 93

2.5.5.1HydraulicExpansion(ThermalExpansion) 95

2.5.5.2SizingSafetyValvefortheFireCase 96

QuestionsandAnswers 103 FurtherReading 110

3CavitationandFlashing 112

3.1Introduction 112

3.2Cavitation 112

3.2.1WhatisCavitation? 112

3.2.2CavitationEssentialParameters 113

3.2.3CavitationAnalysis 115

3.3Flashing 116

QuestionsandAnswers 118 FurtherReading 123

4WallThickness 125

4.1Introduction 125

4.2ASMEB16.34MinimumWallThicknessCalculation 125

4.2.1ConservationApproach(MandatoryAppendixA) 125

4.2.2NonconservationMethod 129

4.2.3ASMESec.VIIIDiv.02WallThicknessCalculation 134

4.3WaferDesignThicknessValidation 136

QuestionsandAnswers 142 FurtherReading 147

5MaterialandCorrosion 149

5.1Introduction 149

5.2CarbonDioxideCorrosion 150

5.2.1CorrosionMechanism 150

5.2.2CorrosionMitigation 151

5.2.3CorrosionRateCalculation 152

5.2.3.1BasicCO2 CorrosionRate 152

5.2.3.2CorrectiveCO2 CorrosionRate 154

5.2.3.3FinalCO2 CorrosionRate 161

5.3PittingCorrosion 162

5.4CarbonEquivalent 165

5.5Hydrogen-InducedStressCracking(HISC)Corrosion 167

5.5.1HISCandVulnerableMaterials 168

5.5.2HISCandStress 168

5.5.3HISCandCathodicProtection 168

5.5.4HISCandDNVStandard 169

QuestionsandAnswers 177

FurtherReading 184

6Noise 185

6.1IntroductiontoSound 185

6.2IntroductiontoNoise 186

6.3NoiseinIndustrialValves 189

6.3.1MechanicalNoiseandVibration 190

6.3.2FluidNoise 190

6.3.2.1AerodynamicNoise 191

6.3.2.2HydrodynamicNoise 191

6.3.3NoiseControlStrategies 191

6.4NoiseCalculationsforPipesandValves 192

6.4.1AcousticFatigueAnalysis 192

6.4.1.1SoundPowerLevelCalculations 193

6.4.1.2MachNumber 198

6.4.2NoiseinControlValves 203

6.4.2.1AerodynamicNoiseinControlValves 203

6.4.2.2HydrodynamicNoiseinControlValves 208

6.4.3NoiseinPressureSafetyorReliefValves 215

6.4.3.1CalculationofNoiseEmissionAccordingtoISO4126-9 216

6.4.3.2CalculationofNoiseEmissionAccordingtoAPI521 218

6.4.3.3CalculationofNoiseEmissionAccordingtoVDI2713 221 QuestionsandAnswers 222

FurtherReading 231

7WaterHammering 233

7.1Introduction 233

7.2WaterHammeringandPressureLossinCheckValves 233

7.3WaterHammeringCalculations 243 QuestionsandAnswers 249

FurtherReading 256

8SafetyValves 258

8.1Introduction 258

8.2SafetyValveParts 259

8.3SafetyValveDesignandOperation 259

8.3.1DesignandOperationParameters 259

8.3.1.1OverpressureCriteria 277

8.3.2PrincipleofOperation 278

8.3.3SafetyValveReactionForces 282

8.3.4SafetyValveCapacityConversion 294

QuestionsandAnswers 296 FurtherReading 302

9SafetyandReliability 304

9.1Introduction 304

9.2SafetyStandards 305

9.3RiskAnalysis 308

9.4BasicSafetyandReliabilityConcepts 312

9.4.1SystemIncidentsandFailures 312

9.4.1.1FailureRate 313

9.4.1.2RepairRate 317

9.4.1.3MeanTimetoFailure(MTTF) 317

9.4.1.4MeanTimeBetweenFailure(MTBF) 318

9.4.1.5MeanTimetoRepairandRecovery(MTTR) 319

9.4.1.6MeanTimetoDetection(MTTD) 319

9.4.2ReliabilityandUnreliability 319

9.4.3AvailabilityandUnavailability 331

9.5SafetyIntegrityLevel(SIL)Calculations 336

9.5.1SIL 336

9.5.2ProbabilityofFailureonDemand(PFD) 338

9.5.3MeanDowntime 339

9.5.4DiagnosticCoverage 342

9.5.5SafeFailureFraction(SFF) 342

9.6ConditionMonitoring(ValveWatch) 347 QuestionsandAnswers 348 FurtherReading 354

10ValveOperation 357

10.1Introduction 357

10.2ValveTorque 358

10.3StemDesign 363

10.3.1MASTCalculations 363

FlowCapacity

1.1Introduction

Valveflowcapacity,alsocalledflowcoefficientorcapacityindex,isdefinedasthe valve’scapacityforaliquidorgastoflowthroughit.TheflowcoefficientistechnicallydefinedastheflowrateofwaterinUSgallonsperminuteatthetemperatureof60 Fwithapressuredropof1psiacrossthevalve.Flowcoefficient,as shownwithparameter Cv,increasesbyopeningthevalvetothemaximumvalue whenthevalveis100%open.Pressuredrop,alsocalleddifferentialpressure,is definedasthedifferencebetweentheinletandoutletofthevalve;foravalvewith aspecificsize,thegreaterthedifferentialpressure,thegreatertheflowrate.These twoparameters,flowrateanddifferentialpressure,arebroughttogetherbyaflow coefficient,whichallowstheperformancesofdifferentvalvesregardingflowrates tobecompared.Thedifferentialpressureacrossthevalvesiscalculatedbyknowingtheflowrates,andfinally,theflowratesaredeterminedforgivendifferential pressurevalues.Furthermore,theflowcoefficientisanessentialparameterfor sizingvalves.Theflowcoefficient(Cv)forliquidsiscalculatedfromEq.(1.1).

FlowCoefficient(Cv)CalculationforLiquids

where:

Cv:Flowcoefficient(USgalperminute[gpm]/psi); Q:Flowrate(USgpm);

SG:Fluid-specificgravity(dimensionless)calculatedbyEq.(1.2); ΔP:Differentialpressureacrossthevalve(poundpersquareinch[psi]).

Note:Water-specificgravityisequaltoone.

IndustrialValves:CalculationsforDesign,Manufacturing,Operation,andSafetyDecisions, FirstEdition.KaranSotoodeh.

SpecificGravity(SG)Calculation

where:

ρfluid:Densityofthefluidpassingthroughthevalve;

ρwater:Waterdensityequalto1g/cm3 or1000kg/m3

Tosummarize,theflowcoefficientcalculatedbyEq.(1.1)isaparameter obtainedbyexperimentsthatindicatetheflowcapacityofincompressiblefluid (liquid)duringnonchokedandnonflashingflowconditionswithaunitofdifferentialpressureacrossthevalve.Chokedflowisfluidwithalimitedmassflowrate duetorestrictionslikenozzles,orifices,andreducers.Flashingflowreferstothe significantevaporationofliquidduetoadramaticpressuredrop.

Example1.1 Calculatetheflowcoefficientofacontrolvalvethatpasses20US gpmofwaterwitha4psipressuredropinafullyopenposition.

Answer

Twoflowcoefficientsarecommonlyusedintheoryandpractice:oneAmerican flowcoefficient(Cv)andtheothermetric(Kv)alsocalledtheflowfactor.Themetricversionoftheflowcoefficientorflowfactoroffersthemeasurementintermsof cubicmetersperhour(m3/h)offlowinatemperaturerangeof5–30 Cforadifferentialpressureof1bar.Theflowfactor(Kv)forliquidsiscalculatedbyEq.(1.3).

FlowFactor(Kv)CalculationforLiquids

where:

Kv:Flowcoefficient(m3/h bar);

Q:Flowrate(m3/h);

SG:Fluid-specificgravity(dimensionless)calculatedthroughtheuseofEq.(1.2);

ΔP:Differentialpressureacrossthevalve(bar).

1.1Introduction 3

Theflowcoefficient(Cv)forairandgasesiscalculatedbasedoneitherEq.(1.4) orEq.(1.5),dependingonthecriticalityofthepressuredrop.Acriticalpressure dropindicatesanoutletpressure(PO)thatislessthanorequalto50%oftheinlet pressure(Pi).Anoncriticalorsubcriticalpressuredropiswheretheoutletpressure ishigherthan50%oftheinletpressure.

FlowCoefficientCalculationforAirandGases(CriticalPressureDrop)

where:

Cv:Flowcoefficient(Standardcubicfeetperminute[SCFM]/psi);

Q:Gasflowrate(Standardcubicfeetperminute[SCFM]);

SG:Specificgravityofflowinggasrelativetoairat14.7psiand60 F(Note1);

T:Flowingairorgastemperature( F);and Pi:Inletgasabsolutepressure(psia)(Note2).

Note1

ThespecificgravityofsomecommongasescanbefoundinTable1.1.SGofair isequaltoone.

Table1.1 Specificgravityofsomecommongases.

Table1.1 (Continued)

Note2

Absolutepressuremeasurementconsiderszeroasthereferencepoint,anditis thetotalpressureofgaugeandatmosphericpressurevalues.Atmospheric pressurerepresentsthepressurewithintheearth’satmosphere.

FlowCoefficientCalculationforAirandGases(Noncritical PressureDrop)

where:

PO:Outletgasabsolutepressure(psia); ΔP:Differentialpressurebetweentheinletandoutlet(psia)equalto Pi PO; T:Fluidtemperature( F).

Example1.2 Airwithapressureof1000psiaisflowingthroughaglobevalve thatreducesthepressureto400psia.Consideringtheflowofairthroughthevalve is400SCFM,anditstemperatureis30 C,whatisthevalve’sflowcoefficientin SCFM/psi?

Answer

Figure1.1isaschematicofthevalve,inlet,andoutletairincludingvaluesof pressure,flowrate,andspecificgravity.

Figure1.1 Aglobevalveschematicincludinginletandoutletairservice,valuesof pressure,andflowrate.

Theserviceisair,andtheoutletpressureislessthanhalfoftheinletpressure indicatingacriticalpressuredrop,sotheflowcoefficientiscalculatedusing Eq.(1.4).Theairtemperatureis30 C,whichequalsto86 F.

Example1.3 Methane(CH4)withaflowrateof100SCFMandapressureof140 psiaispassingthroughacontrolvalve,whichreducesthepressureto110psia. Assumingthegastemperatureisequalto60 F,calculatetheflowcoefficient Cv.

Answer

Theoutletpressureis78.5%oftheinletpressure,soEq.(1.5)forgaseswithnoncriticalpressuredropshouldbeused.Thespecificgravityofmethaneis0.565,per Table1.1.

Theflowfactor(Kv)forairandgasesiscalculatedbasedoneitherEq.(1.6) orEq.(1.7),dependingonthecriticalityoftheflowandpressuredrop. Asupercriticalfloworpressuredropindicatesanoutletpressure(PO)thatisless thanorequalto50%oftheinletpressure(Pi).Anoncriticalpressuredropiswhere theoutletpressureishigherthan50%oftheinletpressure.

Conversionsbetweentheflowcoefficientandflowfactorarecalculatedfrom Eqs.(1.8)and(1.9).

RelationshipBetweenFlowCoefficientandFactor

Example1.5 Calculatetheflowcoefficient(Cv)forthecontrolvalvein Example1.4.

Answer

1.2FlowCoefficientChartandFlowCurve

Aflowcoefficientchartorflowcurveshowstherelationshipbetweentheopening percentageandtheamountorpercentageof Cv orflowrate.Figure1.2isaflow characteristicschartorcurveshowingtherelationshipbetweentheopeningratio ofvalvesandthepercentageofmaximumfloworflowcoefficient.Threeflow

C v95 =700×0 95=665

Therefore,theflowcoefficientsofthevalveat5%and95%openingpercentages are35and665,respectively.

Example1.7 Acontrolvalvewithanequalpercentageflowcharacteristichasa flowcoefficientof640atafullyopenposition.Calculatethe Cv valueofthevalveat 10%and90%openingpercentages,respectively.

Answer

Flowratesand Cv valuesarenotincreasedlinearlybyincreasingthevalveopening percentageforanequalpercentagecharacteristic.Thus,valuesofflowrateand flowcoefficientatanyvalveopeningpercentageforanequalpercentageflowcharacteristicarecalculatedaccordingtoEqs.(1.12)and(1.13),respectively.

ValveFlowRateCalculationBasedonValveOpeningPercentageforan

Therefore,theflowcoefficientsofthevalveat10%and90%openingpercentages are18.93and432.80,respectively.

Valvesaredividedintotwomajorcategoriesbasedontheclosuremember motion:linearandquarter-turn.Linearmotionvalvessetoffhaveaclosurememberthatmovesupanddownwithalinearmotiontochangetheflowratethrough

1.2FlowCoefficientChartandFlowCurve 11

thevalve.Quarter-turnlikeballandbutterflyvalvesinwhichaclosuremember andthestemrotate90 betweentheopenandclosedpositions.Thevalveflow coefficientchartorflowcharacteristicforaquarter-turnvalvecouldbeprovided asarelationshipbetweentheflowrateor Cv andtheangleofthestemorclosure member.Itshouldbenotedthattheangleofstemandclosurememberforquarterturnvalvesisequal.Forexample,Figure1.3illustratesacoupleofflowcoefficient chartsorcurvesfora38 CL1500(equivalentto250barnominalpressure)ball valve.Thecharthereshowstherelationshipbetweentheangleofstemandflow coefficient,whereasthelowerchartillustratestheconnectionbetweentheopening percentageandtheflowcoefficientofthevalve.Evenwhenthestemangleis33 , noflowispassingthroughthevalve,meaningthatthevalvehasanequalpercentageflowcharacteristic.Inlightofthefactthat90 rotationofthestemandclosure membercorrespondsto100%orfullvalveopening,usinginterpolation,a33 stem anglecorrespondsto36.6%opening.Thefullopen Cv ofthevalveistheonetypicallyprovidedbyvalvemanufacturersongeneralarrangement(GA)valvedrawings,whichis118,179gpminthiscase.GAvalvedrawingsdeliverthedimensions

Tables of estimated Cv values

1.3RangeabilityandTurndown 13

rangeabilityenablescontroloftheflowoverthewiderflowrange.Acontrolvalve isanactuatedglobevalveusedtocontrolthefluidbyalteringthesizeofthefluid passage.Directflowratecontrolleadstochangesinmajorprocessquantitiessuch aspressure,temperature,andliquidlevel.Anactuatorisamechanicalorelectrical deviceinstalledontopofindustrialvalvestooperate(openandclose)thevalves automaticallywithoutanyneedforanoperator.Rangeabilityisdefinedastheratio ofmaximumflowtoaminimumcontrollableflowofavalveinstalledinapiping system,whichiscalculatedbyEq.(1.14).Thus,iftheminimumcontrollable flowis10%ofthemaximumcontrollableflow,therangeabilityofthevalveis 100/10=10.Itisimportanttonotethattheminimumcontrollableflowisnot theflowleakagethroughthevalvewhenitisclosed.

Valvesareoftennotrequiredtohandlethemaximumcontrollableflow;asan alternative,themaximumoperationflowpassesthroughthevalve.Thus,theterm turndownisequaltoorsmallerthanrangeabilityandiscalculatedaccordingto Eq.(1.15).Forexample,thevalveforwhichtherangeabilityiscalculatedmayneed tohaveamaximumnormaloperationflowequaltoonly70%ofthemaximum controllableflow,sotheturndownis70/10=7.

RangeabilityCalculation

R= Maximumcontrollableflow Minimumcontrollableflow

TurndownCalculation

1 14

T= Maximumnormaloperatingflow Minimumcontrollableflow 1 15

Example1.8 Themaximumandminimumcontrollableflowsbyacontrolvalve areat95%and5%oftheirfullopeningpositions,respectively.Calculatethevalve rangeabilityintwocasesofthelinearandequalpercentageflowcharacteristics.

Answer

R = Maximumcontrollableflow Minimumcontrollableflow = Flowat95 valveposition Flowat5 valveposition

R =Linearflowcharacteristic= 95 qmax 5 qmax = 95 5 =19

R =Equalpercentageflowcharacteristic= qmax × α0 95 1 qmax × α0 05 1 = 500 95 1 500 05 1 = 0 8223 0 0243 =33 84

Industrial valves: calculations for design, manufacturing, operation, and safety decisions karan sot

IndustrialValves

LimitofLiability/DisclaimerofWarranty

Contents

FlowCapacity

1.1Introduction

SpecificGravity(SG)Calculation

FlowFactor(Kv)CalculationforLiquids

1.2FlowCoefficientChartandFlowCurve