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.

Incident Flux 
sufficient to cause damage to process equipment
minimum energy required for piloted ignition of wood, melting plastic
will cause no discomfort for long exposure


    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.

 Point-Source 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

mf  = mass of fuel in the fireball(kg)
Ta = atmospheric transmissivity(-)
Hc = 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/m2)
R = assumed to be 0.4.

 Solid Frame Model

    The Solid flame model is more realistic than the point-source 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

Dc = final fireball diameter(m)
Tc = fireball duration(s)
mf = 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

q = radiation received by the receptor(kW/m2)
E = surface emissive power(kW/m2)
F = view factor(-)
ta = 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


zc = the height of the fireball above the ground(zc>= Dc/2)
Dc = 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.


    A flash fire is the non-explosive 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 air-fuel mass ratio(r) from the stoichiometric mixture composition fst, 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 fst and the expansion ratio for stoichiometric combustion a has to be calculated and is described below.

    for f>fst

                for f<= fst

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:

H = visible flame height(m)
S = 2.3 * Uw  = flame speed (m/s)
Uw = wind speed (m/s)
D = cloud depth (m)
g = gravitational acceleration(m/s2)
po = fuel-air mixture density(kg/m3)
pa = density of air(kg/m3)
r = stoichiometric air-fuel mass ratio
a = expansion ratio for the stoichiometric combustion under constant
       pressure (usually 8 for hydrocarbons)
f = fuel-air mixture composition(fuel volume ratio)
fst = stoichiometric mixture composition(fuel volume ratio)

The final steps for calculating the radiation heat flux include the following:

  1.  Assume a flame shape.
  2.  Determine the distance between the flame and the object(X).
  3.  Determine  the view factor (F).
  4.  Determine the atmospheric transmissivity (assumed as one in the software for conservative results).
It is assumed that the flash fire forms a vertical plane surface and hence the view factor for a vertical plane surface is used in the calculations.  Determination of radiation heat flux can be done by using the following equation:


 E = 173 kW/m2 (Reported by Blackmore (1982).
 ta = 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.


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 well-determined pattern.

There are basically four features which must be present for an effective vapor cloud explosion to occur with an effective blast.  These are:

        There are basically two major processes involved with vapor cloud explosions; deflagration or detonation.  Deflagration can be defined as a combustion mode in which the propagation rate is dominated by both molecular and turbulent transport processes.  Deflagration occurs when the burning velocity is relatively slow, usually at approximately 1 m/s.  Research has shown that turbulence is always present in vapor cloud explosions.  The gas explosion, as in deflagration, occurs mainly due to the interaction between turbulence and combustion.  In an incipient gas explosion, flame propagation is laminar immediately following ignition which generates expansion and produces a flow field.  The combustion rate is increased by turbulence.  This leads to a chain reaction and a self-feeding chain in which more fuel is converted into combustion products per unit volume and time while expansion flow becomes stronger.

        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:

These mechanisms are responsible for causing very high flame speeds and as a result, strong blast pressures.There are basically two approaches followed in the calculation of radiation effects of vapor cloud explosions.  Conventional TNT-Equivalency method and the Multienerg method.

 Conventional TNT-Equivalency 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 TNT-Equivalency used for blast modeling is directly related to the damage patterns observed in major vapor cloud explosion incidents, the TNT-blast 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.


Fl = Flash fraction (-)
Cp = Mean specific heat (J/kg/K)
DT = temperature difference between vessel temperature and boiling
  temperature at ambient pressure (K).
LH = 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.




Wf = weight of the fuel in the cloud

Fl = Flash fraction

Q = quantity of fuel released

The equivalent-charge weight of TNT can now be calculated as shown below:


WTNT = equivalent weight of TNT (kg)
Wf  = weight of fuel in the solid (kg)
Hf = heat of combustion fuel (J/kg)
HTNT  = Blast energy TNT   =  4.68 MJ/kg
ae = TNT-equivalency/yield factor  =0.03

The blast effects can then be determined as below:

The side-on blast wave peak overpressure produced by the detonation of a TNT charge is graphically represented as dependent on the Hopkinson-scaled distance from the charge.

RH = Hopkinson-scaled distance (m/kg1/3)
WTNT = charge weight of TNT (kg)
RH = real distance from charge (m)
Thus, the side-on overpressure due to vapor cloud explosion can be obtained from the Hopkinson-scaled 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 sub-explosions 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:

It is important to consider each blast separately, then assume that the full quantities of fuel-air mixture present within the partially confined areas and jets contribute to the blast. Then  the volumes of fuel-air mixture present in the individual areas are estimated and identified as blast sources. For a safe and conservative estimate of the strength for the sources of strong blast, an initial strength of 10 should be chosen, but normally a source strength of 7 seems to more likely represent the actual data.  Once the quantities of E and the initial blast strengths of the individual equivalent fuel-air charges are estimated, the Sachs-scaled blast side-on overpressure can be found from the graph.

The Sachs-scaled distance is calculated by the following formula:

 RS = Sachs-scaled distance from charge center(-)
 R = Real distance from the charge center(m)

The real blast side-on overpressure and positive-phase duration can be calculated from the Sachs-scaled quantities as given below:


 DPs = Side-on blast overpressure(Pa)
 DPs = Sachs-scaled side-on blast overpressure
 Po = Ambient pressure


The following procedure is based on a World Bank report.




    XE: Fraction of heat produced as radiation (Range : 0.13 - 0.35)
       Step 3: INCIDENT HEAT
    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.


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