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INTRODUCTION

Jet fires occur as a result of ignition and combustion of flammable release (natural

gas,

  LPG and others) usually from a pipe or tank. They emit high radiative flux

creating a risk for hum ans and plants . A safety en gineer ne eds to dete rm ine the flam e

trajectory, flame length and radiative fluxes to the surrounding plant and personnel.

Typical critical radiative fluxes for humans are 3, 5, 8 kW/m

2

  which represents

respectively threshold for injured, 1% lethality and 5% lethality in French legislation.

In order to predict jet fires effects and especially radiative fluxes generated by flame,

several models have been developed. The current software uses semi-empirical

mo dels to com pute the distances of therm al effects a ssociated w ith jet fires. This

software is based on models which calculate geometry of the frustum based on input

data (mass flow rate, orifice diameter, pressure in the pipe or tank, wind speed and

others) and flame characteristics are obtained from experimental data  [1-3] .  The semi-

empirical models are less expensive to implement because they are usually based on

simple equations, and these models are easier to formulate , modify and implement in

computer programs. Furthermore, they require low computational resources.

However, such an approach is highly dependent on experimental data , and therefore i t

is limited to the types of fires investigated during the experiments. Moreover, this

approach is rarely applicable to very large scales (flame length greater than 100 m)

because experiments at this scale are scarce. Finally, in the case of horizontal or

inclined released jet fires, semi-empirical models do not take into account the

buoyancy effect which significantly changes the shape of the flame (bent shape). As

an example, the semi-empirical model by Johnson [1] takes into account buoyant

forces but, being based on natural gas experiment; it cannot be used for LPG releases

for which it was not validated.

Computational Fluid Dynamics, CFD, is a lso used to predict je t f ire effects . However

CFD models are highly CPU time consuming and are not a lways suitable to produce

quick results .

As a com prom ise, a 1D model based on simplif ied f luid mech anic equations is

presented in this paper for predicting the flame shape and radiation field for large-

scale gas or liquid released jet fires. In the following section, the mathematical basis

used in this computational model is presented. In the next section, predicted values

obtained with the je t f ire model are com pared w ith semi-em pirical mo del results and

with experimental data .

PHYSICAL BASIS  OF THE   MODEL

Jet f ire is one highly directional phenomenon due to high source momentum close to

the release point, which means that the 3D fluid mechanic equations can be reduced to

a 1D axisymm etric model. The present model uses a pheno men ological approach

based on global balances for the characteristics of a steady-state jet fire. The model

uses the following input data: pipe or tank pressure, orifice diameter, ambient wind

speed and temperature. F igure 1 presents s tep-by-step m ethodolog y of the mod el. In

each control volume represented by a frustum located by a downwind curvil inear

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coord ina te ,  s,  physic al quanti t ies including ma ss, mo me ntum , temperatu re, density ,

v o lu me are calculated seq uential ly using the physic al laws. F inally , the flame shape is

represen ted

 by

 lateral surface

 of

 the whole control volum e ( i .e .

 the

 s um

 of

 each cell) .

Horizontal jet fi re

Wind direction

Release poi

'

  ^ \

i

 =

 1

t

——

i= 2

—

_ - —

Vol

n

i = n

. - -

s

i=n +

 1

Buoyancy

forces  U

Figure 1. Step-by-step methodo logy of the model.

T he

 jet

  fire methodology

  is

 presen ted

 and

 demons t ra ted

  for

 natural

 gas,

 p ro p a n e

 and

butane, a l though  its  extension  to  oth er fuels  or  fuels m ixtur es  is  straightforward.

Following paragraphs describe different sub-models incorporated

  in

  this

  jet

  fire

mo d e l .

Source Term Calculation

In order

  to

  est imate

  jet

 fire effects from

  a

  l ine rupture

  or a

  leak,

  it is

  required

 to

calculate  the  release characteris t ics  in te rms of ma ss f low rate , velocity , tem perature

and l iquid mass fract ion. Depending

  on the

 release ph ase (gaseous, l iquid,

 or two

phase f low)

 and the

 nature

 of

 the breach ( l ine rupture, leak

 or

 others) , d ifferent mo dels

are used [4 ] . De script ions of these m odels are out of the top ic of the present s tudy.

The Fundamental Conservation Equations

In a  steady flow, the fluid m echan ics equations set can be reduced to:

1) Conservation of mass

dm

(1)

ds

T he

 air

 mass p roduction rate

  fn

a

 depends

 on

 the

 entrainm ent rate mo del, described

 in

the fol lowing paragraph.  The  vaporised mass prod uction rate  is  calculated with the

vaporisat ion Eq.

 4.

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2) Conserva tion of mom entum

For the s teady state , the momentum balance can be expressed as:

7  b

ds

where  F

b

  is the buoyant vert ical force acting on the control volume,  F

a

  is the drag

force due to wind which is supposed to act in the direction perpendicular to the je t

axis for the comp uted control volum e, shift ing the reaction zone of the je t .

The third term in Eq. 2 is related to the air entrainment. Its contribution rises with

curvil inear coordinate in relat ion to air entrainment model as described below.

3) Conserva tion of energy

The f irs t pr inciple of thermodynamics leads to the energy conservation equation that

can be expressed using several quanti t ies . The present model uses the total enthalpy

equation that can be expressed for the steady state as follows:

— = Qc-Qv- m

f

h

f

  - m

g

h

g

  -

  m

Uq

h

Uq

  (

3

)

The first term on the right is the source term related to fuel nominal heat release and

mass of reacting gas:

Qc=Xc

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Figure 2

IR picture of

 the

 jet fire (INER IS experim ents).

The r ight of Eq. 3 also represents energy consumption for heating non-reacting

products , burned gas from the previous control volume, unburnt gas and l iquid fuel ,

respectively. Lateral boundaries of the control volume are considered adiabatic .

4) Perfect gas law

To close the equations sets, an equation of state is required. The perfect gas law was

cons idered :

P =

(5)

RT

  ombustion Model

The mixture composit ion is defined by the equivalent ra t io:

m

(6)

where the nominator is the fuel to air mass rat io in the mixture and the denominator is

the s toichiometric fuel to air mass rat io corresponding to complete combustion. I t can

be assumed that no combustion occurs in the lift-off zone, and that the reaction is

infinitely fast be yo nd the lift-off heig ht; the com bus tion proces s is then m ixin g-

controlled .

Irreversible one-step reaction of hydrocarbon fuel and oxygen is considered, in which

if

  è <

 1  (lean mixture) then:

(7)

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else (rich mixture):

C.H. \x + y

4

Air entrainment Model

(8)

T he  air  en t ra inment  in  reacting turbulent  jet is a  fundam ental param eter that

de te rmines

  the jet

  fire develop me nt s ince

  it

  controls

  the

  mixing rate

  and,

consequen t ly , the fuel burning rate . The air entrainm ent rate can be writ ten as:

dm

a

  =

  m

0

C

d

ds ,

d*

(9)

where

  d is

 th e

 jet

 mo me n tu m d ia me te r

 (d*  = d

o

{p

o

/p

a

f

12

)-

Accord ing  to [6], the  local en trainmen t rate coeff ic ient ,  C

e

l, depends  on  b u o y a n c y ,

axial posit ion

  and

  tempera tu re .

  To

  describe

  the

  effect

  of

  buoyancy , B ecker

  and

Y a m a z a k i  [7] introduced a  parameter that can be expressed as:

4 = RP—

  (

10

)

where  R

i

  =

  gd*/u

0

2

  is the  Richarson num ber . Paramete r  £  contains  the  integrated

effect

  of

  buoyancy a long

 the

  jet .

 Han and

 M u n g a l

  [6]

 related

 the

 buoyancy paramete r

F

  with

 the air

 entrainm ent coeff ic ient:

  e

l

  11)

As shown in Fig. 3, according to the Ricou and Spalding approach [8], the air

entrainment coefficient is constant. Alternatively, according to Han and Mungal [6],

buoyancy increases the air entrainment coefficient along the jet axis.

0,9   -

0,8   -

0,7

  -

0,6

3 0,5  -

  0 4 -

0,3   -

0,2   -

0 1 -

Local air entrainement

0.32  Ricou and Spalding)

0.090P'

2

0  100 200 300 400

x /d*

F i g u r e  3

L o c a l

 air

 e n t r a i n m e n t .

Thermal Radiation Intensity

Accord ing to the  solid f lame model,  the  Surface Emissive P ower  (SEP,  k W / m

2

) can

be related to the fraction  of  heat radiated from  the  surface  of the  flame  &, fuel m ass

flow rate

  m,

  total heat re leased

 AH

C

 by the

 following equation:

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(12)

where

  th e

  flame surface area

  A is

  given

  by the sum of

  lateral area

  of all the

  control

volumes.

  The

 fraction

  of

 heat radiated from

  th e

 surface

  of

  the flame &

 is

 given

 by [3] :

  •

[ 0 . 2 1 e - ° - ° °

3 2 3 i

  + 0 . 1 1 l ^ | 2 1 < M   < 6 0

2 1

1.69.(0.21e-

000323

  °+0.1l)  M

w

  > 60

In

  Eq. 13,

 u

0

 is the jet

  inlet velocity

  and

 M

w

  is the

  molecular weight

  of the

  fuel. This

model assumes that

  the

  flame emits homogeneous surface radiative flux

  and

 does

 no t

take into account

  th e

  fact that

  th e

  radiative emissions depend

  on

  temperature

  and

chemical compo sition

  of the

  flame zone which vary along

  th e

  flame axis. Moreover,

the thermal radiation

  is

 also dependent

  on

  soot concentration.

Finally,

  th e

 radiative flux rece ived

 b y a

  target outside the

 je t

 fire

  is

 expressed

 a s:

q=VFxSEPXT,

  (14)

where  VF

 is the

  view factor.

  It

  depends

  on

 location

  of the

  flame

  in

  space relative

  to

the target position.

  The

  view factor between

  an

  elementary receiver surface

  C and an

elementary emitter area

  dA

 from

  th e

 control volume surface

  is

 given

 b y:

ldA

,

  (15)

Ttr

where  6j

 is the

  angle between local normal

  to

  surface element  dA

 and the

 line joining

elements

  dA

 and

 target,

  and

 8

2

 is the

 angle between normal

  of

 the target

 an d the

 same

line.  The

  atmospheric transmisivity 

is

  obtained

  by the

  Brzustowski

  and

  Sommer 's

empirical

  law [9] .

RESULTS AND DISCUSSION

Comparison Between Predicted and Measured Values

A safety engineer

  is

  mainly interested

  in

  predicting

  th e

  worst case scenarios

  for the

accidental phenomena. That

  is the

  reason

  why, in

  case

  of

  released

  je t

  fire,

  th e

downwind effects

  of

  horizontal

  je t

  fire

  are

  most thoroughly investigated

  and the

critical thresholds

  of

 3,

 5, and 8

 kW/m

2

  are examined.

Large-scale experiments data

  are

  scarce

  in the

  literature. Moreover,

  in the jet

  fire

experiments,

  th e

 radiometers

  are not

  normally located downwind,

  in the

  flame axis;

instead, they

  are

  usually located

  on the

  flame side, which

  is out of the

  topic

  of the

present paper.

Experimental data used

  in

  this work

  are

 listed

  in

 Table

  1. It

  includes data

  fo r

  natural

gas,

 propane

  and

 butane

 j e t

  fires releases.

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Table 1 Experimental overview.

Reference

Test

Fuel

Release

Phase

M a s s

flow Rate

(kg/s)

Release

direction

Johnson [1]

Tes t 1083 ,

T y p e C

Natural Gas

Gaseous

8,4

Horizon ta l

Cook and

al .

  [3 ]

3 ,2 GW

Natura l

G as

Gaseous

65.1

Vertical

INERIS [10]

Test 1

Test 2

Propane

Liquid

1,5

Vertical

4,1

Vertical

Test 3 T est 4

Butane

Liquid

1,5

Vertical

3

Vertical

Figure 4 and Table 2 show a comparison of computed incident radiat ive f lux and

flame length with experimental results .

At small and medium scale , the level of agreement between the model predict ions and

experimental measurements is good for far field. All predicted jet fire radiative flux

and flame leng th are within 10% of the me asure d value , 15 % for flame length.

However, i t can be observed that the model tends to underest imate the results which

can be problematic in safety department. It is essential to ensure that the discrepancy

between prediction and measured values does not increase at large scale and in case of

horizontal L PG released je t f ires.

Two parameters could be reviewed in order to make results more conservative: the

radiativ e fraction of the flame and the air entra inm ent param eter of the jet. A radiative

fraction predict ion model based on Stefan-Boltzmann law which gives the radiat ion

of a black body in relation to its temperature, coupled with a simplified soot formation

model, for example, the model in [11] would distribute radiative heat on the flame

surface. This model will be integrated in the near future, with the contribution of

medium-scale experiments , in order to compute more accurately the surface emissive

power .

Soot concentration peaks at the fuel-rich side of the flame. in region I, see Fig. 1. At

the same time, the peak temperature is located in the region II, as mentioned in the

combustion model section. As a result, in any jet fire regions I and II emit the largest

radiative flux. However, in the present model, the radiative flux is assumed to be

uniformly distributed over the flame surface. More experiments will also be necessary

to improve the air entrainment model.

Comparison

 of

 INERIS

 and

 Semi-empirical Models

Two representat ive medium scale scenarios of accidental l iquid je t f ire were computed

in this work using two models. The first one is the new model presented in this paper

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Table 3 Scenario assumptions.

Scenar io

1

2

Mass flow rate [kg/s]

15

50

14

.̂12

10

 

8 -

| e

ce

 

4

 

£

  o -

PROPANE 15 kg/s

\

  2

  Horizontal

V e r t i c a l - 2 0 - 1

6

 

^ - S h e l l M o d e l

 ||

  INERIS

  I

*•

50 100 150 200

PROPANE 50 kg/s

14 :

12 -

10 -

8 -

6 -

4 -

2 -

50 100 150 200

14

ï o

I

 8

 

I 6 -

i

4

 

? 2 -

BUTANE 15 kg/s

14 -

12 -

10 -

8 -

6 -

4 -

2 -

BUTANE 50 kg/s

0 50 100 150

Distance from the jet exit (m)

200

0 50 100 150 200

Distancefrom the jet exit

  m )

D

Figure 5 Comparison of incident radiative flux between INERIS and Phast prediction.

The new model s ignif icant ly reduces

  the

 incide nt radia tive flux re lated

  to

  horizonta l

je t f i re when comparing with  the values ob ta ined us ing Phast v6.5 . The d if ference  is

be tween  -25% and -15% for the 8  k W / m

2

  threshold  and  reaches  -30% for the

15 k W / m

2

  flux. This

 is

 due

 to

 the fact that the mod el flame s hape takes prop er accoun t

of  the balance betwe en  the initial jet m o m e n t um  and the buoy ant forces , g iven bent

shape to the f lame, increas ing  the dis tance b etwee n  the flame  and the target  and so

that decreasing the incident radiative flux. On the other hand, the radiative flux related

to vertical jet  fire  and compu ted  by both models  are re la t ive ly c lose  (no more than

+ 15 % of  discrepancy) .

CONCLUSIONS

The ca lcula t ion  of jet  fires effects  is  essent ia l when assess ing  the  safety  of  h igh -

pressure process ing of f lamm able mater ia ls . A new m odel has been developed for the

jet fires occurring

 in

 large-sca le industr ia l acc idents .

Un l ike more complex mode l ing app roaches

  as

  CF D m odel , th is mode l provides

 the

capabi l i ty to yield satisfactory predi ctions of the radiativ e flux from the jet fire w ith a

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little computer run time. Both at small and large scale, the predictions are in good

agreement with the measurements for far field. Furthermore, the results computed

with this model have been compared with those computed with semi-empirical

approach based on the Cook's model [3]. This highlights a smaller incident radiative

flux from the horizontal jet fire. A discrepancy up to 25% can be noticed. If this

model is validated at large-scale, it can then be used to assess safe separating distances

in industrial sites.

Further work remains to be performed to validate this model, and to assess the ability

of the model to predict a wider range of fires types, especially for horizontal and

inclined jet fires. Large scale experiments with the horizontal and inclined releases

will be carried out in the near future to validate this new model.

REFERENCES

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Radia t ion Hazards f rom L arge-Sca le Hor izonta l ly Re leased Na tura l Gas

 Jet

 Fires,

 

Trans

IChemE

  94

 Par t B: 157 -168 (19 94) .

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from Flares,

Chem

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