Flammable gas and liquids have given rise to accidents involving fire in industries. The effect of fires are radiation heat. As a result of heat objects may be ignited and living organisms may be burned. Accidents and casualties result in loss of life and property in industries. The likelihood of occurrances of fire accidents can be reduced by process design and reliability. Mathematical models and computer models are employed for calculating the consequences of such events which helps in the research for mitigation of their consequences.
The most common scenarios of fire and
explosions are Boiling Liquid Expanding Vapor Explosion (BLEVE), flash
fires, vapor cloud explosions and pool fires. The following sections deal
with these four scenarios and their estimation. The assessment approach
is based on the calculation of dose radiation (energy per unit area). The
following table will give you an idea on the damage as a result of fire.



sufficient to cause damage to process equipment 

minimum energy required for piloted ignition of wood, melting plastic 

will cause no discomfort for long exposure 
BOILING LIQUID EXPANDING VAPOR EXPLOSION (BLEVE)
It is widely referred to as fireball and is an explosion resulting from the failure of a vessel containing a liquid at a temperature significantly above its boiling point at normal atmospheric pressure. In case of container failure, instantaneous boiling occurs depending on the boiling point of the liquid. This leads to vaporization of a large fraction of liquid. If the temperature of the liquid is higher than the homogeneous nucleation temperature or superheat limit temperature then, instantaneous boiling occurs. If the temperature is below the superheat limit temperature, the energy for the blast and fragment generation is released mainly from expansion of vapor in the space above the liquid. In both cases, when a container is engulfed in fire, its metal is heated and loses mechanical strength. At wetted surfaces, supplied heat is transmitted to its liquid contents, thus raising liquid temperature but keeping the wetted portion of the vessel relatively cool.
The calculations done for BLEVE are the fireball diameter and fireball duration. There are two general methods used for BLEVE calculation.
PointSource model
A point source model is used to calculate the radiation effects of the fireball. According to this approach the peak thermal input at a distance L is given by
where,
m_{f} = mass of fuel in the fireball(kg)
Ta = atmospheric transmissivity()
H_{c} = net heat of combustion per unit mass(J/kg)
R = radiative fraction of heat of combustion()
L = distance from fireball center to receptor(m)
q = radiation received by the receptor(W/m^{2})
R = assumed to be 0.4.
Solid Frame Model
The Solid flame model is more realistic
than the pointsource model because the fireball's dimensions, its surface
emissive power, atmospheric attenuation and view factor(which includes
the object's orientation relative to the fireball and its distance from
the fireball's center) are all addressed in this model. In most cases
the BLEVE fireball is assumed to touch the ground since that gives a conservative
prediction of the radiation.
The following equations are used to
calculate the average values of fireball diameter and fireball duration:
for mf < 30,000 kg
for mf >= 30,000 kg
where,
D_{c }= final fireball diameter(m)
T_{c} = fireball duration(s)
m_{f} = mass of fuel in fireball (kg)
Radiation received, for a receptor not normal to the fireball, can be calculated using the solid flame model as follows
where,
q = radiation received by the receptor(kW/m^{2})
E = surface emissive power(kW/m^{2})
F = view factor()
t_{a} = atmospheric
transmissivity()
For a point on the plane surface located at a distance L from the center of a sphere that can view the entire fireball, the view factor (F) for a vertical surface is given by
where,
z_{c} = the height of the fireball above the ground(z_{c}>=
D_{c}/2)
D_{c} = diameter of the fireball.
The calculation of the view factor is useful in the calculations of the radiation effects. The value of atmospheric transmissivity is taken as one for conservative results. The height of the fireball is also assumed to be equal to half of the diameter for conservative results. The view factor is also calculated assuming the receptor at the vertical surface.
FLASH FIRES
A flash fire is the nonexplosive combustion of a vapor cloud resulting from a release of flammable material into the open air, which after mixing with air, ignites. A flash fire results from the ignition of a released flammable cloud in which there is essentially no increase in combustion rate. The ignition source could be an electric spark, a hot surface, friction between moving parts of a machine or an open fire.
Part of the reason for flash fires is that, flammable fuels have a vapor temperature which is less than the ambient temperature. Hence, as a result of a spill, they are dispersed initially by the negative buoyancy of cold vapors and subsequently by the atmospheric turbulence. After the release and dispersion of the flammable fuel the resulting vapor cloud is ignited and when the fuel vapor is not mixed with sufficient air prior to ignition, it results in diffusion fire burning. Therefore, the rate at which the fuel vapor and air are mixed together during combustion determines the rate of burning in the flash fire.
The main dangers of flash fires are radiation and direct flame contact. The size of the flammable cloud determines the area of possible direct flame contact effects. Radiation effects on a target depend on several factors including its distance from the flames, flame height, flame emissive power, local atmospheric transmissivity, and cloud size. Most of the time, flash combustion of a flash fire lasts no more than few seconds.
Flash fire dynamics are determined as below:
The flame speed on the basis of wind speed is calculated using the following equation.
To calculate the square of the ratio of fuel density and the density of air from molecular weights, the equation described below is used.
The next step is to calculate the stoichiometric airfuel mass ratio(r) from the stoichiometric mixture composition f_{st}, and air and fuel molecular weights which is done below:
Then the calculation of w from the actual mixture composition f, the stoichiometric mixture composition f_{st} and the expansion ratio for stoichiometric combustion a has to be calculated and is described below.
for f>f_{st}
for f<= f_{st}
One of the most important steps is the calculation of the flame height from the cloud depth d, and gravitational acceleration g which is given below:
where,
H = visible flame height(m)
S = 2.3 * U_{w} = flame speed (m/s)
U_{w} = wind speed (m/s)
D = cloud depth (m)
g = gravitational acceleration(m/s^{2})
p_{o} = fuelair mixture density(kg/m^{3})
p_{a} = density of air(kg/m^{3})
r = stoichiometric airfuel mass ratio
a = expansion ratio for the
stoichiometric combustion under constant
pressure (usually
8 for hydrocarbons)
f = fuelair mixture composition(fuel
volume ratio)
f_{st} = stoichiometric
mixture composition(fuel volume ratio)
The final steps for calculating the radiation heat flux
include the following:
where,
E = 173 kW/m^{2} (Reported by Blackmore
(1982).
t_{a} = Atmospheric
transmissivity and is taken equal to 1 for conservative results for LMG
and propane flash fires.
Flame height and flame speed can now be computed , but flame position and shape as a function of time must be specified.
VAPOR CLOUD EXPLOSIONS
The Vapor Cloud Explosions begin with a release of a large quantity of flammable vaporizing liquid or gas from a storage tank, transport vessel or pipeline producing a dangerous overpressure. These explosions follow a welldetermined pattern.
There are basically four features which must be present for an effective vapor cloud explosion to occur with an effective blast. These are:
The second process known as Detonation occurs when the flame speed is very high at approximately 2500 m/s. Because of the flame speed detonation is more dangerous than deflagration. Vapor cloud detonations are unlikely because for a detonation to propagate, the flammable part of the cloud must be homogeneously mixed and such homogeneity rarely occurs. Once detonation does occur, turbulence is no longer required to maintain the speed of propagation. In the detonation type of combustion, a strong shock wave propagates the reaction front which compresses the mixture beyond its autoignition temperature while the shock is maintained by the heat released from the combustion reaction.
Turbulence is always present in vapor cloud explosions and significantly enhances the combustion rate in deflagration. Therefore, it is important to understand how turbulence occurs. Turbulence in a vapor cloud explosion can arise in any of three ways:
Conventional TNTEquivalency Method
In the first approach called the conventional TNT equivalency method, a vapor cloud's explosive power is proportionally related to the total quantity of fuel present in the cloud. And the explosive power of a vapor cloud is expressed as an energetically equivalent charge of TNT located in cloud's center. The value of the proportionality factor, that is, TNT equivalency, is deduced from damage patterns observed in a large number of vapor cloud incidents. Since the value of TNTEquivalency used for blast modeling is directly related to the damage patterns observed in major vapor cloud explosion incidents, the TNTblast model gives very accurate results if overall damage potential of a vapor cloud is the only concern.
The flash fraction of fuel is determined on the basis of actual thermodynamic data.
where,
Fl = Flash fraction ()
C_{p} = Mean specific heat (J/kg/K)
DT = temperature difference
between vessel temperature and boiling
temperature at ambient pressure (K).
L_{H} = Latent heat of vaporization (J/kg)
Exp = base of natural logarithm
The weight of the fuel Wf in the cloud is equal to the flash fraction times the quantity of fuel released. To allow for spray and aerosol formation, the cloud inventory should be multiplied by 2.
where,
W_{f }= weight of the fuel in the cloud
Fl = Flash fraction
Q = quantity of fuel released
The equivalentcharge weight of TNT can now be calculated as shown below:
where,
W_{TNT} = equivalent weight of TNT (kg)
W_{f} = weight of fuel in the solid (kg)
H_{f} = heat of combustion fuel (J/kg)
H_{TNT} = Blast energy TNT
= 4.68 MJ/kg
a_{e} = TNTequivalency/yield
factor =0.03
The blast effects can then be determined as below:
The sideon blast wave peak overpressure produced by the detonation of a TNT charge is graphically represented as dependent on the Hopkinsonscaled distance from the charge.
where,
R_{H} = Hopkinsonscaled distance (m/kg1/3)
W_{TNT} = charge weight of TNT (kg)
R_{H} = real distance from charge (m)
Thus, the sideon overpressure due to vapor cloud explosion
can be obtained from the Hopkinsonscaled TNT charge blast.
Multienergy method
In this method
turbulence is assumed to be the major cause of explosive.It is based on
the concept that explosive can develop only in an intensely turbulent mixture
or in obstructed and partially confined areas of the cloud. Hence, a vapor
cloud explosion is modeled as a number of subexplosions corresponding
to the number of areas within the cloud which burn under intensely turbulent
conditions.
Normally, the practical examples of potential centers
of strong blast in vapor cloud explosions are:
The Sachsscaled distance is calculated by the following formula:
where,
R_{S} = Sachsscaled distance from charge
center()
R = Real distance from the charge center(m)
The real blast sideon overpressure and positivephase duration can be calculated from the Sachsscaled quantities as given below:
where,
DP_{s} = Sideon
blast overpressure(Pa)
DP_{s} = Sachsscaled
sideon blast overpressure
P_{o} = Ambient pressure
POOL FIRES
EXAMPLE: FIRE FROM A POOL OF FUEL SPREADS OVER THE GROUNDThe following procedure is based on a World Bank report.
Step 1: BURNING RATES:
BOILING POINT > AMBIENT TEMPERATURE
BOILING POINT < AMBIENT TEMPERATURE
Step 3: INCIDENT HEATX_{E}: Fraction of heat produced as radiation (Range : 0.13  0.35)
T: Transmissivity of the air path to a receiver (conservative estimate T=1)r: Distance of the object from the pool
Paper on related topic:
Development of a Numerical Model for Studying Flash Fire Dynamics
by Ashok Kumar, Raminder Saluja and Pavankumar Pakala.



