CBB2093 (4) Source Models

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CHAPTER 4

Source Models

AP Dr Azmi Mohd Shariff CAB2093 Process Safety and Loss Prevention2

Chapter Outline

Introduction

Liquid Discharge

Vapor Discharge

Flashing Liquids

Liquid Pool Evaporation or Boiling


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Instructional Learning Objectives

After completing this chapter, students should be able todo the following:

Understand the requirements for consequencemodeling procedure

To describe the possible options of how materialscould be released from any process due to an accident

To apply suitable source model in order to estimate theamount of released materials


IntroductionConsequences Analysis Procedure

Selection of a Release Incident

Selection of a Source Model

Selection of a Dispersion Model

Flammable/Toxic

Selection ofEffect Model

Selection of Fire& Explosion Model

Mitigation Factors

Consequence Model

Loss of containmentRupture or break in pipelineHole in a tank or pipelineRunaway reactionFire external to vesselTo describe release accident

Total quantity releasedRelease durationRelease rate Neutrally buoyant models

Results from the modelsDownwind concentrationArea affectedDuration

Response vs dose

Probit modelToxic responseNo. of individuals affectedProperty damage

ModelsTNT EquivalencyMulti-Energy ExplosionFireballResultsBlast overpressureRadiant heat flux Escape

Emergency ResponseContainment dikesPPE


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IntroductionRelease Mechanisms

Release mechanisms are classified into wide and limitedaperture releases.

Wide aperture large hole develops and substantialamount of material released in a short time. Eg.overpressure and explosion of a storage tank.

Limited aperture material is released at a slow rate thatupstream conditions are not immediately affected

Several basic source models frequently used; Flow of liquid through a hole Flow of liquid through a hole in a tank Flow of liquids through pipes Flow of vapor through holes

Flow of gases through pipes Flashing liquids Liquid pool evaporating or boiling


Various types of limited aperture releases


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Released of vapor or/and liquid


Liquid DischargeFlow of Liquid through a Hole

P = 1 a tm

U2 = U

External SurroundingsLiquid Pressurized w ithinProcess Unit

Pg

To

U1= 0

z = 0

W s = 0

Liquid escaping thr ough a hole in a process unit.


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Equation for velocity of fluid exiting the leak through asmall hole:

Mass flow rate Qm resulting from a hole of area A:

The total mass of liquid spilled depends on the totaltime that the leak is active.

g

o

2 cg Pu C

m o c g2Q uA AC g P



The discharge coefficient Co is a functionof the Reynolds number of the fluidescaping the leak and the diameter of thehole

As a guideline; For sharp-edge orifices and Re > 30,000, Co ~

0.61. The exit velocity is independent of thehole size.

For well rounded-nozzle, Co = 1 For short pipe attached to vessel with length todiameter ratio < 3, Co = 0.81.

When Co is unknown, use Co = 1 to maximisethe computed flows.


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Liquid DischargeFlow of Liquid through a Hole in a Tank



Equation for instantaneous velocity of fluid exiting theleak :

The instantaneous mass flow rate Qm resulting from ahole of area A:

L

gc

ogh

PgCu

2

L

gc

om ghPg

ACAuQ

2


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The liquid level height in the tank at any time t;

The mass discharge rate at any time t;

2

22

2

t

A

ACgtgh

Pg

A

AChh

t

oo

L

gc

t

oo

LL

tA

AgCghPgACAuQt

ooL

gcom

22

2



The time te for the vessel to empty to the level of theleak is found;

If the vessel is at atmospheric pressure, Pg = 0;

gco

L

gct

o

e

Pggh

Pg

A

A

gCt

22

1

o

Lt

o

e ghA

A

gCt 2

1


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Vapor DischargeFlow of Vapor through a Hole

At Throat:

P

U < Sonic Velocity

External SurroundingsGas Pressurized w ithinProcess Unit

Po

To

U0= 0

z = 0

W s = 0

A free e xpansion gas leak. The gas expan ds isentropi-cally through the hole. The gas properties (P,T) andvelocity change during t he expa nsion



The mass flow rate at any point during theisentropic expansion;

The maximum flow;

1

0

/2

00

001

2

P

P

P

P

TR

MgAPCQ

g

cM

)1(

1

2

o

choked

P

PWhere =Cp/Cv is the ratio of heat capacityPchoked is the maximum downstreampressure


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The choked pressure Pchoked is the maximumdownstream pressure resulting in maximum flowthrough the hole or pipe.

For downstream pressure < Pchoked The velocity of the fluid at the throat of the leak is the

velocity of sound at the prevailing conditions

The velocity and mass flow rate cannot be increasedfurther by reducing the downstream pressure; they areindependent of the downstream conditions.

This type of flow is called choked, critical, orsonic flow.

For ideal gases the choked pressure is a functiononly of the heat capacity ratio, .



For an air leak to atmosphere (Pchoked = 14. 7psia)

If the upstream pressure is greater than

14.7/0.528 = 27.8 psia, or 13.1 psig, the flowwill be choked and maximised through theleak

Conditions leading to choked flow arecommon in the process industries.

Gas Gamma Pchoked

Monotonic 1.67 0.487Po

Diatomic and air 1.40 0.528Po

Triatomic 1.32 0.542Po


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P < P choked

At Throat:

P = Pchoked

U= Sonic Velocity

External SurroundingsGas Pressurized w ithinProcess Unit

Po

To

U0= 0

Choked flow of gas through a hole. The gas velocity issonic at the throat. The m ass flow rate is independent ofthe dow nstream pressure.


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For choked flow, the maximum flow is;

For sharp-edged orifices, Re > 30,000 (and notchoked), Co = 0.61.

For choked flows, Co increases as the downstreampressure decreases. For these flows and for situations

where Co is uncertain, a conservative value of 1.0 isrecommended.

Values for the heat capacity ratio for a variety ofgases are provided in Table 4-3.

1

1

0

001

2

TR

MgAPCQ

g

c

chokedM


Flashing Liquid

Liquids stored under pressure above their normalboiling point temperature present substantialproblems because of flashing.

If leak, the liquid will partially flash into vapor,sometimes explosively.

Flashing occurs so rapidly that the process isassumed to be adiabatic.

The fraction of the liquid vaporized is;

v

bpvv

H

TTC

m

mf

)( 0


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Flashing Liquid

The fraction of the liquid vaporized can also bedetermined using mean heat capacity andmean latent heat of vaporization over thetemperature range To to Tb ;

The fraction of the vaporized water can beobtained from Steam Table;

v

bpvv

H

TTC

m

mf

)(exp1

0

liquidvaporvliquidfinal HHfHH


Flashing Liquid

Two-phase flow conditions may be present forflashing liquids escaping through holes andpipes.

If the fluid path length of the release is short(through a hole in a thin wall container), non-equilibrium conditions exist, and the liquid doesnot have time to flash within the hole; the fluidflashes external to the hole. The fluid (liquid)

flow through hole applies;

m o c g2Q uA AC g P


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Flashing Liquid

If the fluid path length through the release isgreater than 10 cm (through a pipe or thick-walled container), equilibrium flashing conditionsare achieved and the flow is choked. A goodapproximation is to assume a choked pressureequal to the saturation vapor pressure of theflashing liquid. This condition valid for liquidsstored at a pressure higher than the saturationvapor pressure (P > Psat). The followingequations apply;

satcfom PPgACQ 2


Flashing Liquid

For liquids stored at their saturation pressure P= Psat, the mass flow rate is determined by;

p

c

fg

vm

TC

g

v

AHQ


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Liquid Pool Evaporating or Boiling

Liquids with high Psat evaporate faster; theevaporation rate (Qm) is a function of P

sat.

A generalized expression for the vaporizationrate;

For many situations, Psat >> P such as for anopen vessel or from a spill of liquid;

Lg

sat

mTR

PPMKAQ

Lg

sat

mTR

MKAPQ



The concentration (in ppm) of a volatile in anenclosure resulting from evaporation of a liquid;

For most situations T = TL;

The gas mass transfer coefficient is estimatedusing;

Ko = 0.83 cm/s for water

610

PkQ

KAPC

v

sat

ppm

3/1

M

MKK oo

610

Lv

sat

ppmPTkQ

KATPC


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The rate of boiling is determined by assumingthat all the heat from the surroundings is usedto boil the liquid in the pool ;

The heat transfer from the surroundings can befrom the followings ;

From the ground by conduction

From the air by conduction and convection

By radiation from the sun/adjacent sources such as fire

The heat transfer from the ground is given by;

v

g

mH

AqQ

2/1t

TTkq

s

gs

g

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CBB2093 (4) Source Models

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