2010-084_hal
TRANSCRIPT
-
8/9/2019 2010-084_hal
1/11
-
8/9/2019 2010-084_hal
2/11
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
i n e r i s - 0 0 9 7 6 2 2 4 , v e r s i o n
1
- 9 A p r 2 0 1 4
-
8/9/2019 2010-084_hal
3/11
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.
i n e r i s - 0 0 9 7 6 2 2 4 , v e r s i o n
1
- 9 A p r 2 0 1 4
-
8/9/2019 2010-084_hal
4/11
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
-
8/9/2019 2010-084_hal
5/11
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)
i n e r i s - 0 0 9 7 6 2 2 4 , v e r s i o n
1
- 9 A p r 2 0 1 4
-
8/9/2019 2010-084_hal
6/11
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:
i n e r i s - 0 0 9 7 6 2 2 4 , v e r s i o n
1
- 9 A p r 2 0 1 4
-
8/9/2019 2010-084_hal
7/11
(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.
i n e r i s - 0 0 9 7 6 2 2 4 , v e r s i o n
1
- 9 A p r 2 0 1 4
-
8/9/2019 2010-084_hal
8/11
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
i n e r i s - 0 0 9 7 6 2 2 4 , v e r s i o n
1
- 9 A p r 2 0 1 4
-
8/9/2019 2010-084_hal
9/11
-
8/9/2019 2010-084_hal
10/11
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
i n e r i s - 0 0 9 7 6 2 2 4 , v e r s i o n
1
- 9 A p r 2 0 1 4
-
8/9/2019 2010-084_hal
11/11
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
1.
Johnson, A .D. , Br ightwe l l , H .M . , and Cars ley A . J ., A M o d e l for Predic t ing the T h e r m a l
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) .
2 . Ch a m b e r l a in ,
G.A.,
D e v e lo p m e n t s
in
D e s ign M e th o d s
for
Predic t ing Thermal Radia t ion
from Flares,
Chem
Eng Res Des. 65 : 29 9 - 309 ( 19 87 ) .
3 .
C o o k , J., Ba h a r a m i , Z., and W h i t e h o u se , R.J., A Co m p r e h e n s iv e P r o g r a m for
Calcula t ion of F lame Radia t ion Leve ls , J. Loss Prev.Process In., 3: 150-155 (1990) .
4 . H éb r a r d , J., and L a c o m e , J.M., Eva lua t ion of T w o - P h a se F lo w M o d e l s for A c c id e n t a l
Re lease and Com par ison wi th Exper imen ta l Da ta , Proceedings of the 11
th
International
Conference Multiphase Flow in Industrial Plants 7 47 - 7 59 , 2008 .
5 . G ó m e z - M a r e s ,
M.,
M u ñ o z ,
M., and
Casa l ,
J.,
Axia l Tem pera ture Dis t r ibut ion
in
Ver t ica l
Jet Fires, Journal of Hazardous Material 172: 54-60 (200 9) .
6 . Hann,
D., and
M u n g a l ,
M.G.,
D i r e c t M e a su r e m e n t
of
E n t r a in m e n t
in
Reac t ing /Nonreac t ing Turbulent J e ts ,
Combustion
and
Flame
124 : 37 0 - 389 ( 2001 ) .
7 .
Becker ,
H.A., and
Y a m a z a k i ,
S.,
E n t r a in m e n t , M o m e n tu m F lu x
and
Tempera ture
in
Ver t ica l F ree Turbulent Diffus ion F lam es , Combustion and Flame 53 : 123 - 149 ( 19 7 8 ) .
8 . R icou, F.P., and Spa ld ing , D.B., M e a su r e m e n t s of E n t r a in m e n t by A x i sy m m e t r i c a l
Turbulent J e ts ,
J.
FluidMech. 11 : 21 - 32 ( 19 61 ) .
9 . Am er ican Pe t ro leu m Ins t i tu te , Gu ide for Pressure Re l iev ing and Depress ing Sys tem s ,
API Recomm ended Practice 52 1 , A p p e n d ix
A,
1 9 7 3 .
10 . Ber t rand ,
J.P., and
Durusse l ,
T.,
Compte-rendu des Essa is Réalisés à l'Institut
TOTALGAZ. R e sso n s - su r - M a tz ,
2 0 0 5 .
1 1 . De l icha ts ios ,
M.A.,
Smoke Yie lds f rom Turbulent Buoyant
Jet
F l a m e s , Fire Safety
Journal
20:
29 9 - 311 ( 19 9 3 ) .
12 .
Cleaver ,
R.P.,
Cu m b e r ,
P.S., and
Fa i rwea the r ,
M.,
Predic t ions
of
Free
Jet
Fires from
High Pressure , Sonic Re lease , Combustion and Flame 132 : 463 - 47 4 ( 2003 ) .
13 . JFSH (Jet Fire) Theory Document, DNV Software, 14-2 0, 2 0 0 5 .
i n e r i s - 0 0 9 7 6 2 2 4 , v e r s i o n
1
- 9 A p r 2 0 1 4