(4) Source Model_2013

CHAPTER 4

Source Models

Chapter Outline

• Introduction• Liquid Discharge• Vapor Discharge• Flashing Liquids• Liquid Pool Evaporation or Boiling

After completing this chapter, students should be able to do the following: Understand the requirements for

consequence modeling procedure To describe the possible options of

how materials could be released from any process due to an accident

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

Instructional Learning

Objectives

Outline & Learning Objectives

2

Consequences Analysis Procedure

Selection of a Release Incident

Selection of a Source Model

Selection of a Dispersion Model

Flammable/Toxic

Selection of Effect Model

Selection of Fire & Explosion Model

Mitigation Factors

Consequence Model

Loss of containment• Rupture or break in pipeline• Hole in a tank or pipeline• Runaway reaction• Fire external to vesselTo describe release accident

• Total quantity released• Release duration• Release rate Neutrally buoyant models

Results from the models• Downwind concentration• Area affected• Duration

• Response vs dose• Probit model• Toxic response• No. of individuals affected• Property damage

Models• TNT Equivalency• Multi-Energy Explosion• FireballResults• Blast overpressure• Radiant heat flux • Escape

• Emergency Response• Containment dikes• PPE

3

Spills of materials can lead to disaster • toxic exposure • fire • explosion

Materials are released from holes, cracks in various plant components • tanks, pipes, pumps • flanges, valves

Source models represent the material release process – provision of useful information for determining the consequences of an accident• rate of material release• total quantity released

Introduction

4

Source Models

• 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 vapour through holes

– Flow of gases through pipes

– Flashing liquids

– Liquid pool evaporating or boiling

5

Release Mechanisms

• Classified into wide and limited aperture releases.

• Wide aperture – large hole develops and substantial amount of material released in a short time.

• E.g. overpressure and explosion of a storage tank.

• Limited aperture – material is released at a slow rate that upstream conditions are not immediately affected.

• E.g. Release from cracks, leaks etc

• Relief system is designed to prevent over-pressure 6

7

Figure 1 Various types of limited aperture releases.

Release Mechanisms – Limited Aperture

Released of vapour8

Release Mechanisms – Influence of physical state

For gases or vapours stored in a tank, a leak results in a jet of gas or vapour

Released of vapour or two phase liquid9

Release Mechanisms – Influence of physical state

Stream of liquid flashing partially into vapour (stored under pressure above boiling point

Stream of escaping liquid

10

A mechanical energy balance describes the various energy forms associated with flowing fluids:

whereP is the pressure (force/area)r is the fluid density (mass/volume)ū is the avg. instantaneous velocity of the fluid (length/time)gc is the gravitational constant (length mass/force time²)a is the unitless velocity profile correction factor with the

following values: (0.5 for laminar flow), (1.0 for plug flow), (>1.0 for turbulent flow)

z is the height above datum (length)F is the net frictional loss term (length force/mass)Ws is the shaft work (force length)m is the mass flow rate (mass/time)

m

WFz

g

g

g2

²udP s

cc

Liquid DischargeFlow of Liquid through a Hole

11

Typical simplification on the mechanical energy balance Incompressible Fluid - Density is constant No elevation difference (∆z = 0)

No shaft work, Ws = 0

Negligible velocity change (small aperture), ∆u = 0

PdP


Liquid escaping through a hole in a process unit.

12

• Equation for velocity of fluid exiting the leak through a small hole:

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

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

go

2 cg Pu C

m o c g2Q uA AC g P


• The discharge coefficient Co is a function of the Reynolds number of the fluid escaping the leak and the diameter of the hole

• As a guideline;

– For sharp-edge orifices and Re > 30,000, Co ~ 0.61. The exit velocity is independent of the hole size.

– For well rounded-nozzle, Co = 1

– For short pipe attached to vessel with length to diameter ratio < 3, Co = 0.81.

– When Co is unknown, use Co = 1 to maximise the computed flows.

13


At 1 p.m. the plant operator notices a drop in pressure

in a pipeline transporting benzene. The pressure is

immediately restored to 100 psig. At 2.30 p.m. a ¼-inch

diameter leak is found in the pipeline and immediately

repaired. Estimate the total amount of benzene spilled.

The specific gravity of benzene is 0.8794.

Flow of Liquid through a HoleExample

The drop in pressure observed at 1 p.m. is indicative of a leak in the pipeline. The leak is assumed to be active between 1 p.m. and 2.30 p.m., a total of 90 minutes. The area of the hole is

The density of the benzene is,

ft1041.3

4

²in144²ft1²in25.014.3

4

²

4

d

A

3m

3m ft/lb9.54ft/lb4.628794.0

Flow of Liquid through a HoleExample Solution

Using the leak mass flow rate equation given (slide 12) and a discharge coefficient of 0.61 is assumed for this orifice-type leak, the mass flow rate is

The total quantity of benzene spilled is

slb

ft²

in²

in²

lb

s² lb

lb ft

ft

lb

m

f

f

m3m

48.1

14410017.329.54)2(

61.0²ft1041.3

Pg2ACQ

4

gcom

mm lb7990min)60min)(90(s

lb48.1

s

gallons 1090

Flow of Liquid through a HoleExample Solution

Liquid DischargeFlow of Liquid through a Hole in a Tank

17

An orifice-type leak in a process vessel. The energy due to the pressure of the fluid height above the leak is converted to kinetic energy as the fluid exits through the hole. Some energy is lost due to frictional fluid flow.


18

Equation for instantaneous velocity of fluid exiting the leak :

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

Lgc

o ghPg

Cu

2

Lgc

om ghPg

ACAuQ

2

19

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

• The mass discharge rate at any time t;

tA

AgCgh

PgACAuQ

t

ooL

gcom

22

2

2

22

2

t

A

ACgtgh

Pg

A

AChh

t

ooL

gc

t

ooLL


20

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

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

gco

Lgct

oe

Pggh

Pg

A

A

gCt

22

1

oL

t

oe gh

A

A

gCt 2

1


A cylindrical tank 20-feet high and 8-feet in diameter is used to store benzene. The tank is padded with nitrogen to a constant, regulated pressure of 1 atm gauge to prevent explosion. The liquid level within the tank is presently at 17 feet. A 1-inch puncture occurs in the tank 5 feet off the ground due to the careless driving of a fork lift truck. Estimate

a. the gallons of benzene spilled,

b. the time required for the benzene to leak out, and

c. the maximum mass flow rate of benzene through the leak.

The specific gravity of benzene at there conditions is 0.8794.

Flow of Liquid through a Hole in a TankExample

The density of the benzene is

The area of the tank is

The area of the leak is

The gauge pressure is

3m

3m

ftlb9.54

)ftbl4.62)(8794.0(

²ft1045.54

)²in144f1)²(in1)(14.3( 3t

A

²ft2.504

)²f8)(14.3(

4

²

tdAt

ft²lb1012.2²)ft²in144²)(inlb7.14)(atm1( f3

f gP

Flow of Liquid through a Hole in a TankSolution

a. The volume of benzene above the leak is

This is the total benzene that will leak out.

b. The length of time for the benzene to leak out is:

gallonsftgalffft²) 3 506,4)48.7)(t5t17(2.50(hAV oLt

minutesss²ft²fts²s²ft²

fts²

ft

ft

lb

ft²

lb

lb

ft.lb

ft²

f

s²)ft

3m

f

f

m

4.563386)22.7(4692484

1217.3229.54

1012.2²s.

17.322

1045.5

²t2.50

17.32)(61.0(

1

Pg2gh

Pg2

A

A

gC

1t

21

3

3

gcoL

gct

oe


This appears to be more than adequate time to stop the leak or to invoke an emergency procedure to reduce the impact of the leak. However, the maximum discharge occurs when the hole is first opened.

c. The maximum discharge occurs at t = 0 at a liquid level of 17.0 feet. The mass flow rate is:

s²ft²1026.3)61.0)(ft²1045.5)(ftlb9.54(

2

333m

oL

gcom gh

PgACQ

slb4.10 mmQ


25

Gas and vapour discharges are classified into throttling and free expansion releases. For throttling releases, the gas issues through a

small crack with large frictional losses; very little of energy inherent with the gas pressure is converted to kinetic energy.

For free expansion releases, most of the pressure energy is converted to kinetic energy; the assumption of isentropic behaviour is usually valid.

Source models for throttling releases require detailed information on the physical structure of the leak; they will not be considered here. Free expansion release source models require only the diameter of the leak.

Vapour DischargeFlow of Vapour through a Hole


26

A free expansion gas leak. The gas expands isentropically through the hole. The gas properties (P,T) and velocity change

during the expansion

• The mass flow rate is given by the following expression:

where g is the ratio of the heat capacities

• The above expression describes the mass flow rate at any point during the isentropic expansion

1

0

/2

0000 1

2

P

P

P

P

TR

MgAPCQ

g

cM

27


VP CC

• For safety studies, the maximum flow rate of vapour through the hole is required

• Pressure ratio resulting in the maximum flow through the hole or pipe is given by the

• Pchoked is the maximum downstream pressure (choked pressure).

• For downstream pressure < Pchoked

– Fluid velocity at the throat of the leak is the velocity of sound at the prevailing conditions

– Velocity and mass flow rate are independent of the downstream conditions.

)1(

o

choked

1

2

P

P

28


P < P choked

At Throat:

P = Pchoked

U = Sonic Velocity

External SurroundingsGas Pressurized withinProcess Unit

Po

To

U0=0

Choked flow of gas through a hole. The gas velocity is sonic at the throat. The mass flow rate is independent of the downstream pressure.

29


• For an air leak to atmosphere (Pchoked = 14.7 psia),

if the upstream pressure is greater than 14.7/0.528 = 27.8 psia, or 13.1 psig, the flow will be choked and maximised through the leak

• Conditions leading to choked flow are common in the process industries.

Gas Gamma P choked

Monotonic 1.67 0.487 P o

Diatomic and air 1.40 0.528 P o

Triatomic 1.32 0.542 P o

30


• At the choked condition, the flow is maximum:

• For sharp-edged orifices, Re > 30,000 (and not choked), Co = 0.61.

• For choked flows, Co increases as the downstream

pressure decreases. For these flows and for situations where Co is uncertain, a conservative

value of 1.0 is recommended.

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

11

0g

c00chokedM 1

2

TR

MgAPCQ

31


32

A 0.1 inch hole forms in a tank containing

nitrogen at 200 psig and 80°F. Determine the

mass flow rate through this leak.

Flow of Vapour through a HoleExample

For the diatomic gas nitrogen, g = 1.4. Thus,

An external pressure less than 113.4 psia will result in choked flow through the leak. Since the external pressure is atmospheric in this case, choked flow is expected and Equation 40 applies. The area of the hole is

psia psia choked 4.1137.14200528.0P

A d 2

4

3.14 0.1in 21ft2 144in2

45.4510 5ft2

The discharge coefficient, Co, is assumed to be 1.0. Also,

335.0833.04.2

2

1

2

R54046080

psia7.2147.14200

00.64.04.211

o0

T

Po

Flow of Vapour through a HoleSolution

Then, using the maximum flow rate equation:

slb

.slblblb

RRlb.moleft.lb1545

lb.molelbs²lbft.lb

ft²in²in²lbft²

mchoked

22f

2mf

oof

mfm

f

choked

2m

4

5

11

og

coom

1079.3Q

10064.5685.1

335.0540

28.17.324.1

1447.2141045.50.1

1

2

TR

MgAPCQ

Flow of Vapour through a HoleSolution

Flashing Liquid

• Liquids stored under pressure above their normal boiling point temperature present substantial problems because of flashing.

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

• Flashing occurs so rapidly that the process is assumed to be adiabatic.

• The fraction of the liquid vaporized is;

v

bpvv H

TTC

m

mf

)( 0

36

37

• The fraction of the liquid vaporized can also be determined using mean heat capacity and mean latent heat of vaporization over the temperature range To to Tb;

• The fraction of the vaporized water can be obtained from Steam Table;

v

bpvv

H

TTC

m

mf

)(exp1 0

liquidvaporvliquidfinal HHfHH

Flashing Liquid

38

• Two-phase flow conditions may be present for flashing liquids escaping through holes and pipes.

• 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 does not have time to flash within the hole; the fluid flashes external to the hole. The fluid (liquid) flow through hole applies;

m o c g2Q uA AC g P

Flashing Liquid

39

• If the fluid path length through the release is greater than 10 cm (through a pipe or thick-walled container), equilibrium flashing conditions are achieved and the flow is choked. A good approximation is to assume a choked pressure equal to the saturation vapor pressure of the flashing liquid. This condition valid for liquids stored at a pressure higher than the saturation vapor pressure (P > P sat). The following equations apply;

satcfom PPg2ACQ

Flashing Liquid

40

p

c

fg

vm TC

g

v

AHQ

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

Flashing Liquid

41

• Liquids with high Psat evaporate faster; the evaporation rate (Qm) is a function of Psat.

• A generalized expression for the vaporization rate;

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

Lg

sat

m TR

MKAPQ

Liquid Pool Evaporating or Boiling

Lg

sat

m TR

PPMKAQ

42

• The concentration (in ppm) of a volatile in an enclosure resulting from evaporation of a liquid;

• For most situations T = TL;

• The gas mass transfer coefficient is estimated using;

• Ko = 0.83 cm/s for water

3/1

M

MKK o

o


610PkQ

KAPC

v

sat

ppm

610Lv

sat

ppm PTkQ

KATPC

43

• The rate of boiling is determined by assuming that all the heat from the surroundings is used to boil the liquid in the pool ;

• The heat transfer from the surroundings can be from 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;

2/1t

TTkq

s

gsg


v

gm H

AqQ

Conclusion

44

Source models represent the material release process - information for determining the consequences of an accident

The purpose of the source model is to determine:

• The form of material released, solid, liquid or vapour;

• The total quantity of material released; and• The rate at which it is released. These information is required for any quantitative dispersion model study.

Two types of release mechanisms: wide aperture release & limited aperture release – influence the nature of release of materials.

45

Thank you for your attention.

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(4) Source Model_2013