Source Models1

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SOURCEMODELS

Source Models 1

Mr.RogerDeo

Source Models 2

Source Models 3


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Source

Model

Dispersion

Model

Release

Incident

Source Models 4

Fire and

Explosion

Model

Effect

Model

Mitigation

Risk

Background

Mosthazardousincidentsstartwithsomeformofdischargeof

flammableortoxicmaterialoutofitsnormalcontainment.

Dischargescanbeofliquid,gasesortwophasedischarge.

Modelsareavailablethatprovideanestimationofthetotal

quantityreleased,thedischargerate andthetimetakenfor

discharge.

Thisinformationisusedasessentialinputsintoothermodels.

Source Models5

Dispersion

Model

Discharge

Rate Model

Dispersion

Model

Source Models 6

Flash and

EvaporationFlash and

Evaporation

Discharge

Rate Model


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Description Thefirststageistheidentificationofconceivable

dischargescenarios withtheresultingeffectsonthematerialreleasephase.

Severalimportantissueshastobeconsideredare

theholesize,leakduration,releasephase,end

point,thermodynamicpath etc.

Source Models 7

Topics

Dischargeofaliquidoutofavessel/pipe

Dischargeofagasoutofavessel/pipe

Dischargeoccurringin2phases

Dr. H. FarabiSource Models 8

Source Models 9


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Scenarios

Liquiddischarge

Holeinatmosphericstoragetankat

atmosphericpressure fromvesselorpipe

underliquidhead

Holeinvesselorpipecontaining

pressurizedliquidbelowitsboilingpoint

Source Models 10

Scenarios

Gasdischarges

Holeinequipmentpipe/vesselcontaining

gasunderpressure

Reliefvalvedischargeofvaporonly

o ngo evapora ono qu poo

Reliefvalvedischargefromtopofpressurizedstoragetank

Generationoftoxiccombustionproducts

asaresultoffire

Source Models 11

Scenarios

Twophasedischarges

Holeinpressurizedstoragetank/pipe

containingliquidaboveitsnormalboilingpoint

Reliefvalvedischarge(e.g.,dueto

foamingliquidorrunawayreaction)

Source Models 12


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Source Models 13

Thermodynamicpathandendpoint Thespecificationofathermodynamicpathand

endpointisimportanttothedevelopmentofthe

sourcemodel.

T especi icationo w et ert epat is

isenthalpic,isentropic,isothermalandadiabatic

areimportantintheselectionofanappropriate

modelandthecalculationofthatmodel.

Source Models14

Thermodynamicpath Forisentropicreleasestheequilibriumflashmodel

canbeusedtodeterminethefinaltemperature,

composition andphasesplitsatambient

temperature.Ifaphasechangeisencounteredthen

.

willflashatitsboilingpointandamixturewillflash

continuously.

Forreleasesofgaseseitheradiabaticorisothermal

modelsareavailable.

Source Models 15


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LeakdurationandholesizesThereisnogeneralconsensusonthesize

andlengthsofeitherofthese.Studies has

expressedaleakdurationof3to10minutes

andaholesizeofbetween 2inchesandthe

sizeofthepipe(fullbreakage)

Source Models 16

FundamentalequationsFundamentalequationdischargescanbemodeledbythemechanicalenergyequation

Where

P ressure(force/area)

( ) ( ) 0m

Wevv

g2

1zz

g

gdP sf

21

22

c

12

c

P

P

1

1

=++++ &

(Equation 1)

density(mass/volume)g accelerationduetogravity(length/time2)

gc gravitationalconstant(force/massaccelaeration)

z verticalheightfromsomedatum(length)

v finalvelocity(length/time)

Ws istheshaftwork(energy/time)m massflowrate(mass/time)Source Models 17

EquationsThefrictionallosstermisgivenas

=

c

2

ffg2

vKe

fL4

Equation 2

Wheref fanningfrictionfactor

L length

d diameter

Kf istheexcessheadlossduetopipeandfittings

Source Models 18

df = Equat on 3


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LiquiddischargesThenormaldrivingforcefordischargeisnormally

pressure,withthepressureenergybeingconvertedto

kineticenergyduringthedischarge.Sincethedensity

remainsconstantduringthedischargethenthe

pressureintegralinthemechanicalenergybalancecan

beintegratedtogivethefollowingsimplifiedformula

(equation10)

Source Models 22

( ) ( ) 0m

Wevv

g2

1zz

g

gPP sf

21

22

c

12

c

12 =++++

(Equation 10)

Liquiddischargefromapipe

P1 P2

Source Models 23

A

v1

PipeflowThemassfluxthroughthepipeisconstantand,for

pipesofconstantcrosssectionalarea,theliquid

velocityisconstantalongthepipe.

Thefrictionlossesoccurduetotheliquidflow.If

shaftwork:

( ) ( ) 0vvg2

1zz

g

gPP 21

22

c

12

c

12 =++

Source Models 24

(Equation 11)

(Bernoulli equation)


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Dischargeofpurenonflashingliquidthroughasharporifice

Themodelisdevelopedfromthemechanicalenergy

balancebyassumingthatthefrictionallossisrepresentedbyadischargecoefficientCD

(Equation12)

Where

Aisthearea(length2)

P1 istheupstreampressure

P2 isthedownstreampressure

Source Models 25

21cD PPg2ACm =&

ThefollowingaresuggestedforthedischargecoefficientCD:

ForsharpedgedorificesandReynoldsnumberin

excessof30,000CD approaches0.61.

ForawellroundedorificetheCD approachesunity

notgreaterthan3,theCDapproaches0.81

Wherethedischargecoefficientisunknownor

uncertainaCD=1shouldbeusedtomaximize

computedflowstoobtainaconservativevalue

Source Models 26

DischargecoefficientFromthe2KMethodthedischargecoefficientcan

becalculatedasfollows

Equation13

Source Models 27

+=

f

D

K1

1C


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Generalprocedurefordeterminingthemassdischargefromapipingsystem

1.Given:length,diameter,typeofpipe,elevations changesandpressures;work

inputoroutputtothefluidduetopumps

turbinesetc.Numberoffittingsandthe

propertiesofthefluid,includingdensity

andviscosity.Source Models 28

2. Specifytheinitialandfinalpoint,this

mustbedonecarefullysincethe

individualtermsintheequation(10)are

highlydependentonthisspecification

3. Determinethepressuresandelevation

attheinitialpointanddeterminethe

initialfluidvelocityatpoint1Source Models 29

4. Guessavalueforthevelocityatpoint2.Ifafully

developedturbulentflowisexpectedthenthis

stepisnotrequired

5. Determinethefrictionfactorofthepipeusing

eitherequationsorthechart.

Source Models 30


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6. Determinetheexcessheadlossinthepipeusing

equation(3)andthefittings,usingequation4.Sumthe

headlosstermsandcomputethenetfrictionlossterm

usingequation(2). Usethevelocityatpoint2

=c

2

ffg2

vKe Equation 2

7. Computethevaluesofallthetermsinequation(10).If

itisnotequaltozerothengobacktothe4th step.

8. DeterminethemassflowratevAm =&

Source Models 31

d

fL4K f = Equation 3

Dischargeofliquidfromatank

Initial level V1

Dr. H. FarabiSource Models 32

hL

AV2

LiquidoutflowoutofatankForholesintanksthedischargeofmaterial

throughaholeresultsinthelossofliquidand

theloweringoftheliquidlevel.Forthiscase,

equation(12)iscoupledwithamassbalanceontheliquidinthetanktoobtainthe

followingexpressionforthetankdrainage

time.

Source Models 33

=1

2

V

VD h

)h(dV

g2AC

1t (Equation 14)


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Where tisthetimetodrainthetankfrom

=1

2

V

VD h

)h(dV

g2AC

1t (Equation 14)

volumeV2 tovolumeV1 (time)

Vistheliquidvolumeinthetankabove

theleak(length3)

histheheightoftheliquidabovetheleak

(length)

Source Models 34

LiquidoutflowofatankThemassdischargerateisdeterminedbythe

followingequation.Thefrictionisrepresentedbythe

dischargecoefficientCDandaccountsforthe

pressureduetotheliquidheadabovethehole

Source Models 35

+

== L

gc

D ghPg

2ACvAm&

(Equation 15)

Where

visthefluidvelocity(length/time)

Aistheareaofthehole(length2)

CD

isthemassdischargecoefficient(dimensionless)

+

== L

gc

D hgPg

2ACvAm& (Equation 15)

gc isthegravitationalconstant(force/massacceleration)

Pg isthegaugepressure

istheliquiddensity(mass/volume)

gistheaccelerationduetogravity(length/time2)

hL istheheightofliquidabovethehole

Source Models 36


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GasdischargesGasdischargeoccursbyavarietyofmeans

fromaholein avesseltoleaksonpipelines

andtheopeningofreliefvalves.Thereare

differentprocedurestodealwithallofthese.

Themajorityofcasesthedischargeisinitially

eithersonicorchoked.

Source Models 37

Gasdischarge Asthepressuredropsthegasexpands.The

pressureintegralinthemechanicalenergybalance

(equation1)wouldrequireanequationofstate

an a ermo ynam cpa spec ca on o

completetheintegration.

Source Models 38

( ) ( ) 0m

Wevv

g2

1zz

g

gdP sf

21

22

c

12

c

P

P

1

1

=++++ &

(Equation 1)

ForgasdischargethroughholesEquation(1)is

integratedalonganisentropicpath

Theequationassumesthatthegasis

ideal,thereisnoshaftworkandthatthere

isnoheattransfer.

Thedischargerateisgivenbelow

Source Models 39

( )

=

k

1k

1

2k

2

1

2

1g

c1D

P

P

P

P

1k

k

TR

Mg2APCm&

(Equation 16)


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GasdischargeWhere

m - mass flow rate of gas through the hole (mass/time)

CD - mass discharge coefficient (dimensionless)

A - area of the hole (length2)

P1 - pressure upstream of the hole (force/area)

Source Models 40

gc - grav tat ona constant ( orce mass-acce erat on)

M - molecular weight of the gas (mass/mole)

k - heat capacity ratio, Cp/Cv (unitless)

Rg - ideal gas constant (pressure-volume/mol-deg)

T1 initial upstream temperature of the gas (deg)

P2 downstream pressure (force/area)

GasdischargeTheequationrepresentingthesonicorchockedflowis

( )( )1k

1k

1g

c1D

1k

2

TR

MkgAPCm

+

+

=& (Equation 17)

Source Models 41

The condition for a choked flow

(i.e. the pressure ratio required to achieve choking)

)1k(k

1

choked

1k

2

P

P

+

= (Equation 18)

GasDischargeForgasreleasedthroughpipestheissueofwhether

thereleaseisadiabaticorisothermalisimportant.

Forbothcasesthevelocitywillincreaseduetothe

dropinpressureofthegas.Foradiabaticflowsthe

temperaturemayincreaseordecreasedependingon

thetemperatureandthefrictionalforcesactingon

it.

Source Models 42


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Foradiabaticflowsthechokingpressureis

lessthantheisothermalchokingpressure

Forrealflows,theactualflowratewillbeless

thantheadiabatic redictionbut reater

thantheisothermalprediction.Thereisvery

littledifferencebetweentheadiabaticand

isothermalflows

Source Models 43

Whencompressiblefluidsdischargefromtheendofareasonablyshortpipe ofuniformcrosssectionareaintoanareaoflargercrosssectiontheflowisusuallyconsideredtobeadiabatic.Thisstatementissupportedby

130and220pipediametersdischargingairintotheatmosphere.Therefore,theadiabaticflowmodel isusedforcompressiblegasdischargedthroughpipes.

Source Models 44

GasdischargeForidealgasflowthemassflowforboth

sonicandsubsonicdischargeisgivenby

theDarcyequation

(Equation19)

Source Models 45

( )

=f

2111

K

PPg2YAm&


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Where

mmassflowrateofgasthroughthehole(mass/time)

Y gasexpansionfactor(unitless)

A areaofthedischarge(length2

)gc gravitationalconstant(force/massacceleration)

1 upstreamgasdensity

P1 pressureupstreamofthehole(force/area)

P2 downstreampressure(force/area)

kf Theexcessheadlossusing2Kmethod

Source Models 46

Thegasexpansionfactorisdependent

onlyontheheatcapacityratioofthegas,

k,andonthefrictionalelementsonthe

flow ath, k .Itisdeterminedusin onl

acompleteadiabaticflowmodel.

Thefollowingprocedureisusedto

determinethegasexpansionfactor:Source Models 47

TheupstreamMachnumber,Ma,isdetermined and

thensubstitutedintothelatterequationthe

procedureinvolvesthedeterminationoftheupstream

Manumber bytrialanderrorandifitmeetsthe

conditionsbelow.Useaspreadsheet.

(Equation20)

Source Models 48

( ) =+

+

+01

1

1

2ln

2

122

1

fKMaMak

Yk


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Thenextstepistodeterminethesonicpressure

ratio

(Equation21)

Iftheactualratiois reaterthanthisthentheflowis

1

2

11

1

21

+=

k

Y

MaP

PP

sonicorchokedandthepressuredroppredictedby

(21)isused.Ifless,thentheflowisnotsonic,and

theactualpressuredropratioisused

Source Models 49

Gasdischarge FinallytheexpressionYiscalculatedfrom

(Equation22)

Source Models 50

=21

1

2 PPMaY

f

Gas discharge

Source Models 51


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2Phasedischarge Whenanypressurizedliquidaboveitsnormal

boilingpointisreleasedtoatmosphericpressure

itwillbegintoflashandthe2phaseflowwill

occur

Themodelsthatwillbepresentedwillpredict

minimummassfluxesandmaximumpressure

drops

Source Models 55

2PhasedischargeThenonreactive(reactivecasenotconsideredyet)case

involvesflashingoftheliquidsastheyaredischargedfrom

containment.

Twos ecialconsiderationsaretakenintoaccount

1. Iftheliquidissubcooled,thedischargeflowwillchokeatits

saturationvaporpressureatambienttemperature

2. Iftheliquidisstoredunderitsownvaporpressure,amore

detailedanalysisisrequired

Source Models 56

Bothsituations areaccountedforbythefollowing

expression

(Equation23)

Where

misthetwophasemassdischargerate

N

GGAm

2

ERM2

sub +=&

Aistheareaofthedischarge(length2)

Gsub isthesubcooledmassflux(mass/areatime)

GERM istheequilibriummassflux(mass/areatime)

Nthenon equilibriumparameter(dimensionless)

Source Models 57


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Thesubcooledmassfluxisgivenby

(Equation24)

Where

[ ]satDsub PPgCG = 112

Psat isthesaturatedvaporpressure

Pisthestoragepressure

1 istheliquiddensity

CD isdischargeCoefficient

Source Models 58

Forsaturatedliquidsifthedischargelengthisgreaterthan0.1m(approximatelygreaterthan10diameters)theequilibriummassfluxisgivenby;

(Equation25)

Where P

c

fg

fg

ERMTC

g

v

hG =

Hfg istheenthalpychangeinvaporization

Vfg isthechangebetweenspecificvolumebetweenliquidandvapor

Tisthestoragetemperature

CpisthespecificheatcapacitySource Models 59

TherelationshipforNthenonequilibriumparameter

isgivenbelow

(Equation26)

Where

CPfgD

fg

L

L

TCvCP

hN +

=

22

1

2

2

Pisthetotalavailablepressuredrop

Lpipelengthtoopening

Lc isthedistancetoequilibriumconditions

(usually0.1m)

Source Models 60

Source Models1

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