FIRE ACCIDENTS IN PROCESS PLANTS:
MATHEMATICAL MODELING AND RESEARCH NEEDS
Eulàlia Planas and Joaquim Casal
Centre for Studies on Technological Risks (CERTEC)
Department of Chemical Engineering. Universitat Politècnica de Catalunya
Barcelona. Catalonia, Spain. www.certec.upc.es
Summary
Fire accidents play an important role, not only because they are more frequent than
explosions and toxic releases but also because of their effects. Although thermal effects
usually reach shorter distances than blast or toxic clouds, they often affect other
equipment, thus originating a dangerous domino effect. Their mathematical modeling is
therefore essential in risk analysis. However, this modeling is not yet correctly solved:
some variables are poorly known, there are a number of uncertainties and some of the
equations widely applied should be improved. In this chapter this situation is analyzed
and recommendations are suggested concerning the research needs.
Introduction
Major accidents have been defined as “an occurrence such as a major emission, fire or
explosion resulting from uncontrolled developments in the course of the operation of
any establishment... and leading to serious danger to human health and/or the
environment, immediate or delayed, inside or outside the establishment, and involving
one or more dangerous substances” (CCPS, 1999). Major accidents involve essentially
explosions, toxic releases and fires, and an accidental scenario can involve more than
one of these basic accidents; thus, typical sequences are constituted by an explosion
followed by a fire, a fire followed by an explosion, or a fire originating a toxic cloud.
A major accident is always originated by a loss of containment. This can be due to the
collapse or the explosion of a tank, the failure of a pipe, a leak trough a hole, etc. After
the initial release, the incident can follow different ways and diverse accidental
scenarios can be reached depending on the circumstances and on the physical state of
the released substance. If it is a liquid, a pool can be formed. If the substance is
flammable and is ignited, there will be a pool fire; if it is not immediately ignited, the
evaporation can give rise to a toxic or a flammable cloud which, if ignited, will lead to a
flash fire and possibly to an explosion. If a two phase mixture is released, a cloud can
occur (depending on the meteorological conditions). If a gas is released, a cloud can
exist in low speed releases; at high (usually sonic) speed, the substance will probably be
quickly dispersed, but a jet fire is possible. In any case, the final scenario will be a fire,
an explosion, a toxic cloud or no outcome (i.e. quick dispersion into the atmosphere).
To perform a risk analysis, the effects of such major accidents must be estimated: blast
and missiles ejection in the case of explosion, thermal radiation intensity in the case of
fire and toxic dose in the event of a toxic cloud. They can be estimated by using
mathematical models of the involved phenomena. Diverse models have been proposed
for these accidents, with different degrees of complexity. Simple models are easy to use,
but can give significant errors; complex models should provide more accurate
predictions, but usually require detailed information which often is not available.
The mathematical modeling of major accidents is a field in which there are still many
gaps and which requires a significant effort to improve our knowledge. An essential
aspect is the need to check the models, and this is only possible through the comparison
of the model predictions with real data. Data from real accidents are very important but,
unfortunately, they are scarce. Another source of data is the experimental work.
However, to increase its significance, it should be performed at a large scale and this is
difficult and expensive, so the data available are as well relatively scarce.
Fire accidents
Fire accidents are the most frequent major accident. Gómez-Mares et al. (2008) found
that 59% of these events were fires, 35% were explosions and 6% were gas clouds.
There are several types of fire accidents, depending on the circumstances and on the
substances involved. Figure 1 is a simplified scheme of the diverse possibilities.
Loss of containment
of a flammable substance
Liquid
Fireball
Running liquid fire
Tank fire
Gas
Pool fire
Flash fire
Fire on ground
Jet fire
Fire on water
Fig. 1. Types of fire accidents (modified from Casal, 2008).
A pool fire occurs when a spill of liquid fuel is ignited. The size of the pool will be
determined by the ground features, by the eventual existence of a confining bund or by
the balance between the release rate and the evaporation rate. After a first step, the
flames size and shape remain approximately constant, with large fluctuations. The
combustion is rather bad and large amounts of smoke are produced. A significant part of
the flames surface is covered by non-luminous black smoke. The thermal intensity
decreases quickly as the distance from the flames increases. A similar scenario can
occur when there is a fire in a tank storing a flammable liquid; in this case, large
inventories can imply large fires, very difficult to be extinguished (BMIIB, 2008).
Jet fires occur when there is a release and ignition of a flammable gas or two-phase flow
trough a hole, a flange, etc., at a relatively high speed. The combustion is much better
than in pool fires; thermal effects can be locally very intense, especially if there is flame
impingement, but their size is usually relatively reduced as compared to pool fires.
When a flammable cloud –usually due to a liquid spill or a two-phase release– is
ignited, the flames propagate through the flammable mixture and a flash fire occurs: a
quick and short phenomenon which can be accompanied by mechanical effects (blast).
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Finally, the fireball is usually associated to the sudden loss of containment of a
pressurized liquefied fuel, typically LPG. The two-phase cloud can burn only on its
outer surface as inside there is no oxygen. This phenomenon has a short duration, but
the thermal radiation intensity is very strong.
Generally, the effects of a fire are limited to relatively short distances as compared to
explosions or toxic clouds. However, in process or storage plants fires can affect other
equipments, especially if there is flame impingement, thus increasing the scale of the
accidental scenario through the domino effect. Therefore, in risk analysis the estimation
of fire effects and consequences as a function of distance can be very important.
Mathematical modeling of accidental fires
Different models have been proposed to predict the thermal radiation intensity received
by a given target located a certain distance from the flames. The so-called solid flame
model is probably the most widely used as, although it is rather simple, it gives
relatively good estimations of fire effects. It will be used here to analyze the gaps and
uncertainties associated to this mathematical modeling. According to it, the thermal
radiation intensity reaching a given surface can be expressed as:
I=FE
(1)
where  is the atmospheric transmissivity (-), F is the view factor (-) and E is the
average emissive power of the flames (kW m-2).  accounts for the absorption of
thermal radiation by the atmosphere layer located between the flames and the target, due
essentially to carbon dioxide and humidity.  can be estimated as a function of the
atmospheric humidity and the distance between the flames and the target. F is the ratio
between the amount of thermal radiation emitted by a flame and the amount of thermal
radiation received by a given target not in contact with the flame. F depends on the size
and shape of the flame, on the distance between the flame and the target and on the
relative position of the flame and the target. Its values are tabulated for the most
common situations (cylindrical fire, rectangular fire, etc.). Finally, E is the average
radiant heat emitted per unit surface of the flame and per unit time (kW m-2).
Pool/tank fires
Pool surface and fire shape
Pool or tank fires are the most frequent of the accidents involving fire. They reach a
steady state and last a significant time. The shape and size will depend on the area and
shape of the pool. If there is a bund and the amount of spilled liquid is enough to cover
the whole bounded surface, the area of the pool surface is well established. If the
amount is smaller, the surface of the pool fire will be smaller than the bounded surface.
If there is no limiting barrier, the pool diameter will increase up to the moment in which
the evaporation equals the release rate (maximum pool size); maximum values
proposed: 44 m for pools on land and 113 m for pools on water. For the pool thickness,
a minimum value of 5 mm is usually assumed. For tank fire, the maximum pool size is
the tank diameter (additional pool surface can be due to the eventual spill on the dike).
A square or rectangular pool will imply an approximately parallelepipedic flames body,
while a circular pool will originate a cylindrical fire. However, these are only
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approximate shapes; due to the turbulence of the phenomenon, the flames undergo a
significant fluctuation and fireballs are formed in the top.
Flames height
The fluctuation of flames implies a statistical approach to define an average height. The
usual criterion is that of intermittency proposed by Zukoski et al. (1984): the fraction of
time during which the length of the flame is at least greater than L; the average length is
defined as the length at which the intermittency reaches a value of 0.5 (Fig. 2).
1.0
Intermittency
0.8
0.6
(L/D)av
0.4
0.2
(L/D)max
0.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
L/D
Fig.2. Intermittency for a pool fire.
In practice, the height of flames in a pool fire is estimated by applying a semi-empirical
expression. The most widely used is that proposed by Thomas (1963):
 m 
H
 42 

D
  a gD 
0.61
(2)
where H is the average flames height (m), D is the pool diameter (m), m is the burning
rate (kg m-2 s-1), a is the air density (kg m-3) and g is the acceleration of gravity (m s-2).
However, even though this expression is often applied to hydrocarbon pool fires, it was
obtained from experimental data from wood cribs fire. Therefore, probably it gives a
significant error and a correction should be introduced.
Surface emissive power
E the radiant heat emitted from the flame per unit surface and per unit time. It is a
function of the substance burned and of the type of fire. It can be expressed as a
function of emissivity and of flame temperature; however, an average value of E is
usually taken from tables for the different fuels. A better estimation can be made by
applying the following expression:
Eav  xlum Elum  1  xlum Esoot
(3)
where xlum is the fraction of the fire surface covered by the luminous flame.
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Jet fire
Among fire accidents, jet fire direct effects are the least severe, due to their relatively
reduced size. However, jet fires can severely affect equipment, especially if there is
flame impingement: in 50% of fire accidents registered in the data bases there was a
domino effect (Gómez-Mares et al., 2008). Nevertheless, the current knowledge of the
main features and behavior of jet fires is still rather poor.
Flame shape and size
The shape of a jet fire depends on the type of jet (low velocity or high (often sonic)
velocity) and on its direction: horizontal, inclined. The frustum of a cone can describe
fairly well low velocity flares or even an inclined jet fire, while a spindle or a cylinder
represent vertical jet fires. The cylindrical shape is simply described and the view factor
can be calculated in a relatively simple way. Diverse expressions have been suggested
for calculating both the flame length of jet fires. Although these expressions have been
usually obtained from experimental data, most of these data were obtained with small
jet fires, and some of them with subsonic jets. Thus, again some uncertainty exists when
calculating the effects of a jet fire.
Fig. 3. Suggested shapes for a jet fire.
The lift-off is the distance from the fuel release point to the start of the flame. Together
with flame length, it determines the position of the flame and the distance over which
there can be flame impingement on nearby equipment. The situation with lift-off is
similar to that found with flame length. There are diverse expressions available to
estimate it, usually as a function of Froude or Reynolds number (Re):
S  c Re e
(4)
Fireball
Fireballs, usually associated to the explosion (often a BLEVE) of a vessel, release large
amounts of thermal energy in a short time, originating very strong thermal radiation
intensities with severe potential effects. The thermal effects of a fireball can be
estimated by applying the solid flame model. To do this, the size, position and duration
of the fireball are required and can be calculated with rather simple expressions:
D  mM n
diameter:
5
(5)
height at which the centre of the fireball is located:
H  pD
(6)
and duration time:
t  qM r
(7)
The problem is that at least twenty expressions have been proposed by diverse authors,
with different values for the constants m, n, p, q and r. Another variable which is still
subjected to uncertainty is the fraction of the energy released which is emitted as
thermal radiation. All these values require a validation from experimental work, which
in this case is rather complex, expensive and difficult to perform.
Flash fire
This is the type of fire accident which has been less studied and, from the point of view
of mathematical modeling, it is practically unknown. There is only a semi-empirical
model proposed by Raj and Emmons (1994) to estimate the height of the flames.
Although usually a simplifying assumption is applied in risk analysis (people inside the
flash fire die, those outside do not undergo any damage), some experimental work
would be quite interesting, although it seems rather complex to perform it.
Experimental work: general considerations
A set of variables have an influence on the thermal intensity reaching a target. Amongst
them, the following ones are the most significant:
-
fuel mass flow rate, fuel mass involved, pool surface
burning velocity
flames size and shape
flames temperature
surface emissive power
radiant heat fraction
atmospheric transmissivity.
These variables depend on the type of fire, substance involved and meteorological
conditions. For example, E has not the same value for a pool fire than for a jet fire, the
fire shape depend on the direction in the case of a jet, on the existence of wind and, etc.
Large scale experimental data are essential in order to determine them.
There is a considerable literature describing experimental studies on thermal radiation
from flames. However, a number of these studies have focused on small-scale pool fires
or jet fires, which differ significantly from large turbulent fires. Pool fires of less than 1
m in diameter or jet fires with a length less than approximately 0.5 m can not be
considered representative of real full-scale fires occurring in industrial plants. In the
following paragraphs, only a few of them are commented.
Experimental work on pool fires
Diverse authors have performed experimental research with large pool fires; only a few
of them are commented here. Experimental data obtained with different fuels (crude oil,
kerosene, heptane, JP4, etc.) have been published by Koseki (2000). Hayasaka et al
(1992) measured the emissivity for heptane pools with a diameter of 3 m. Planas et al
(2003) measured also the emissivity from hydrocarbon pool fires by using infrared
thermography. The main features of gasoline and diesel oil pool fires of up to 6 m
diameter have been studied by Chatris et al. (2001) and Muñoz et al. (2004).
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Experimental work on jet fires
Hawthorne et al. (1949) worked with vertical flames up to 1 m in length; the expression
proposed by these authors to calculate the flames length is still used. Classical studies
concerning flares under the action of wind were published by Kalghatgi (1983) and
Chamberlain 1987). Sonju and Hustad (1986) worked with methane and propane
subsonic jet fires up to 8 m in length. Johnson et al. (1994) obtained experimental
results with large horizontal natural gas jet fires. Vertical sonic and subsonic propane
jet fires have been studied by Sugawa and Sakai (1997) (7-8 m length) and Palacios et
al (2009) (up to 10 m length). Hydrogen sonic flames up to 1.4 m in length have been
studied by Mogi and Horiguchi (2009).
Experimental work on fireballs
Experimental work has been restricted to few experiments performed at rather small
scale. No experimental work has been performed with large scale fireballs. However,
some accidents have been analyzed and expressions allowing the estimation of fireball
size, elevation and duration have been obtained (for example, see Satyanarayana et al.
(1991) for a review and Martinsen and Marx (1999) for the estimation of E).
Experimental work on flash fires
As far as we know, no experimental data are available on flash fire –probably the most
difficult to be obtained– except for those published by Raj and Emmons (1975).
Research needs
Diverse aspects must be improved concerning our knowledge of accidental fires. The
value of emissive power as a function of the type of fire and fuel is still poorly known
for all types of fire. The same happens with the radiant heat fraction. In the case of pool
fires, the expressions to predict the burning rate should also be improved. And, for all
types of fire, the size and shape of flames is still modeled in a rather unaccurate way.
The influence of cross wind (inclination and shape of the flames) on large jet fires
should also be studied, as well as the behavior of horizontal and inclined sonic jet fires.
The expressions used to estimate the main features of fireball (Eqs. 5, 6 and 7) should
be improved and, furthermore, the evolution and dynamics of fireball from its first step
are still poorly known; to solve these aspects, the analysis of accidents is essential.
Finally, some research on (large) flash fires would be quite interesting, although this
type of experimental research is significantly difficult.
Taking all this into account, it is evident that more data obtained from large scale fires
are required to improve mathematical modeling and that, once more, the interest of fully
analyzing the accidents that occur should be emphasized.
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