1

A comparison study of pool fire modeling Muhammad Masum Jujuly

Table of Contents

A comparison study of pool fire modeling ..................................................................................... 1

1. Introduction: ........................................................................................................................ 2

2. Burning Rate Calculation: .................................................................................................... 3

2.1 Theoretical Models ............................................................................................................ 3

2.2 Experimental Studies on Mass Burning Rate: ................................................................... 7

2.3 Comparison with Different Models ................................................................................. 10

3. Flame Geometry ................................................................................................................ 12

3.1 Models of Flame Geometry ........................................................................................ 15

3.2 Experimental Results and New Model ....................................................................... 17

3.3 Dimensionless Numbers Effecting Flame Geometry .................................................. 19

4. Thermal Radiation Model .................................................................................................. 20

4.1 Point Source Model (Large distance) ......................................................................... 20

4.2 Solid Flame Radiation Model ...................................................................................... 22

2

1. Introduction:

Fire and explosions are one of the most dangerous accidents in process facilities; especially pool

fire is the most frequent. Several catastrophic accidents occurred in past few years e.g.

Buncefield, UK (2005), Puerto Rico, USA (2009) and Sitapura, India (2009) caused by pool fire. In

order to avoid such calamity a detail study on pool fire is required to save human lives and

protect the destruction of the facility. This report aims to study the different pool fire models

and validate the study with experimental data. In order to quantify the risk involve in pool fire

catastrophe it is imperative to understand the characteristics of the pool fire. In this study the

various methods of determining the fuel burning rate, emissive power of the pool fire in

existing literatures will be discussed.

We can describe our process of the solution step in a nutshell below:

Pool fire characteristics largely depend upon the fuel type and pool diameter. The fuel burning

rate is a function of the fuel properties and pool diameter as mentioned before. There are

several methods of calculating mass burning rates. Most famous methods are:

a. Zabetakis-Burgess method

b. Burgess-Strasser-Grumer method

c. Mudan method

d. Fays method

e. Hottel method

f. Babrauskas method

Fuel type and pool diameter

Mass burning

rate

Flame geometry

Environmental parameters

effect

Thermal radiation

model

Radiation to

receiver

3

2. Burning Rate Calculation:

In order to calculate the mass burning rate, the type of fuel is considered in here is gasoline

and various pool diameter is chosen as D = 2, 8, 16 and 25 meters. The different methods of

calculating the burning rate is discussed below:

2.1 Theoretical Models

2.1.1 Zabetakis-Burgess Method:

This method is based on the radiation, convective term is not included. The analytical

expression of the method is:

=

4 1

+

Tf is the flame temperature, which is an unknown parameter, since the Tf is unknown so an

empirical model has been proposed as:

= (1 )

The value of for gasoline is 0.055kg/m2s and is 2.1 for the same fuel. The ambient

temperature is 298K and for this temperature the mass burning rate is calculated:

Pool diameter (m) 2 8 16 25

Mass burning rate (kg/m2s)

0.0541 0.0549 0.055 0.055

2.1.2 Burgess-Strasser-Grumer Method:

This method is experimental result and they found that the burning rate of the fuel is

proportional to the ratio of heat of combustion and total heat required to vaporize the fuel. The

expression can be given as:

=1

[ + ( )]

Here, the value of c1 is 1.27x10-6m/s.

Hc (Kj/kg) 43700 Hv (Kj/kg) 330

(kg/m3) 740 Cp (Kj/Kg K) 2.21

Tb(K) 340 Ta (K) 298

For ambient environment the value of m is = 0.097 kg/m2s.

4

2.1.3 Mudan Method

This methid is similar to the Burgess-Strasser-Grumer but the method covered the lpg fire along

with higher hydrocarbons. The uncertainty of Mudan method is high then Burgess-Strasser

method due to the lack of a parameter.

=1

[ + ( )]

The calculated value of m= 0.103 kg/m2s at ambient condition and c1 is given 0.001 kg/m2s.

The parameters are shown in a tubular format for calculating mass burning rate [Babrauskas,

Estimating large pool fire burning rates]:

5

2.1.4 Fays Model

Fays pool fire modeling is one of the most widely used to determine the burning rate and

thermal flux. Fay has used gray gas sub model and in this model the soot concentration is

assumed to be the proportional to the local concentration of products. When the parameters

like fuel properties, pool diameters are known then burning rate can be evaluated. If the

thermal radiation is small compared to heat convection then the burning rate of circular shaped

pool according to Fays model would be:

= 1 0.19 1.30 103(

(1 + ))

Where hc, hv and f are the heat of evaporation, heating value and mass ratio (product/fuel) of

the fuel and shows the uncertainty of the equation.

Pool Dia (m)

Mass burning rate (Fay)

kg/m2s

Fay 19% max kg/m2s

Fay 19% min kg/m2s

2 0.064 0.076 0.052

8 0.129 0.153 0.104

16 0.182 0.217 0.148

25 0.228 0.272 0.185

Here, f = fuel/mass ratio. For CaHbOc fuel:

f = 137.9+

4

2

12++16 ; and for gasoline the value is 15.5.

2.1.5 Hottel Method:

Hottel gives the correlation for optically thick and thin flame regimes is:

=103

Here, the factor 10-3 derived from the Tf is the maximum adiabatic flame temperature of the

fuel (for gasoline its 1450 K), is the beam length correction factor and is the Stephan-

Boltzmann constant.

The calculated value of m= 0.132 kg/m2s.

6

2.1.6 Babrauskas Method:

Babrauskas suggested in his paper Estimating Large Pool Fire Burning Rates a set of pool fire

data for gasoline and LNG with different diameters. The gasoline data is below:

Pool diameter (m) 2 8 16 25

Mass burning rate (kg/m2s)

0.05 0.06 0.055 0.055

7

2.2 Experimental Studies on Mass Burning Rate:

There are several experimental studies e.g. Koseki et. al. (2000) with crude oil and (D=5, 10,

20m), Chatris et. al (2001) with gasoline and diesel and (D = 1.5, 3, 4m), Blanchat et. al. using

JP8 with (D=8m) and Mishra (2008) with (D=1m) etc. The experimental results are shown

below:

2.2.1 Kosekis Experiment

Table: Experimental results of burning data from Koseki et. al. (2000)

Koseki et. al. conducted experiment with Arabian light crude oil (API density 0.84 at 15oC) in 5,

10 and 20m diameter pans and H/D was 1.9.

Pool diameter (m) 5 10 20

Mass burning rate 0.0365 0.0416 0.0491

The pool diameter vs. mass burning rate has been drawn from the experimental data of Koseki

showing the linear relationship. The extrapolation of data will provide the burning rate at 2, 8,

16 and 25m.

Pool diameter (m) 2 8 16 25

Mass burning rate (kg/m2s) 0.032 0.04 0.048 0.055

0

0.02

0.04

0.06

0 5 10 15 20 25 30

mas

s b

urn

ing

rate

(kg

m2 s

)

pool dia (m)

Koseki et. al. burning rate data extrapolation

8

2.2.2 Chatris Experiment

Figure: Mass burning rate of Chatris et. al. (2001) (a) as a function of pool dia, (b) comparing

with other different models for gasoline.

Chatris et. al. proposed the m value as 0.077kg/m2s and mean beam length correction factor

as 1.35m-1 for gasoline. According to their model the mass burning rate of gasoline following

the equation would be:

= (1 )

Pool diameter (m) 2 8 16 25

Mass burning rate (kg/m2s)

0.071 0.076 0.077 0.077

2.2.3 Blanchat Experimental Results:

Thomas Blanchat et. al. conducted their experiment with JP8 fuel. They have used 8m dia pan

and four different experiments had been performed varying the wind speed.

9

For Test-1 the wind speed was the minimum, and this result is considered in this study as:

m = 0.058kg/m2s (D=8m)

2.2.4 Mishra Experiment

Mishra et. al. conducted experiment on burning of organic substances (kerosene and

peroxides). They have used pool diameter 1m. The experiment shows that the burning rate of

organic materials slightly changed with diameter. They have also attached the maximum

burning rate of different fuels with pool diameter of 1m.

For gasoline, the burning rate is selected as: m = 0.085 kg/m2s

10

2.3 Comparison with Different Models

Figure: Comparison among the different theoretical models of mass burning rate

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 5 10 15 20 25 30

ma

ss b

urn

ing

ra

te (

kg

m2s)

Pool dia (m)

Mass Burning Rate Comparison with Different Models

ZabetakisBurgess

Burg-Strasser-Grum

Mudan

Fay

Hottel

Babrauskas

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 5 10 15 20 25 30

mas

s b

urn

ing

rate

(kg

m2 s

)

Pool dia (m)

Experimental Data Comparison of Mass Burning Rate

Koseki exp

Chatris exp

Blanchat exp

Mishra exp

11

Figure: Comparison of the experimental data of Mass burning rate

Figure: Experimental value and theoretical model of the mass burning rate with pool diameter.

From the above result, Chatris et.al. experimental data is the most reliable source for gasoline

burning . Blanchat et.al. conducted experiment with jet fuel (JP8) and Koseki et.al. with JP4.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 5 10 15 20 25 30

ma

ss b

urn

ing

ra

te (

kg

m2s)

Pool dia (m)

Mass Burning Rate: Theretical and Experimental Model

ZabetakisBurgess

Burg-Strasser-Grum

Mudan

Fay

Hottel

Babrauskas

Koseki exp

Chatris exp

Blanchat exp

Mishra exp

12

3. Flame Geometry

The geometry of the flame depends upon the length of the flame, pool diameter (= flame

diameter), mass burning rate, temperature of the flame and radiative properties of the flame.

The flame of a pool often assumed as cylindrical shape. The ratio of the length of flame and

diameter (L/D) gives the idea of flame geometry, proposed by Blinov and Khudiakov, and

extended by Hottel.

Figure: Liquid burning rate and flame height as a function of fire regime (Hottel)

The time average flame length (or flame height) L is defined as the height of plume zone Lp (or

Hp in the figure) and the combustion zone (or clear flame zone) Lc. Some different models

defined it as the height of the plume zone (Lp) and the height of clear zone (combustion zone)

Lcl (Hcl in figure) and pulsation zone Lpl (Hpl).

However, the flame geometry depends on the ratio of buoyancy to momentum force, which is

Froude number (Fr). Froude number is a function of mass burning rate and the diameter of the

pool.

=

()

Here, m is the mass burning rate of the fuel, is the density of the flame and D is the pool

diameter.

13

For different mass burning rate and the pool diameter the Froude number i.e. the flame

geometry would be different. A correlation of Froude number and diameter is drawn:

Figure: The correlation of Froude number with pool diameter at different mass burning rate.

Figure: The correlation of Froude number with pool diameter at mass burning rate 0.071, 0.076,

0.077 respectively (Chatris et. al.)

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0 5 10 15 20 25 30

Fr

Pool dia (D)

Fr and D correlation with different burning rate

(m'=0.055)

(m'=0.065)

(m'=0.075)

(m'=0.085)

(m'=0.095)

(m'=0.105)

Power ((m'=0.055))

Power ((m'=0.065))

Power ((m'=0.075))

Power ((m'=0.085))

Power ((m'=0.095))

Power ((m'=0.105))

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0 5 10 15 20 25 30

Fr

D (m)

Pool Dia Vs. Froude Number

14

Flame length and shape is a function of Froude number (Fr) and non-dimensional wind velocity

(u*). This can be estimated as the following correlation:

=

Here, a,b,c are experimental/modeling parameters. There are many correlations to determine

the value of these parameters, e.g. Thomas, Moorehouse, Munoz, Pritchard-binding, Fay etc.

The correlations of these parameters are presented in a chart.

Figure: Pool fire flame geometry

Table: Empirical correlations for estimation of L/D

Method a b c Comment

Thomas (u=0) 42 0.61 0 wood (no wind)

Thomas (u=u*) 55 0.67 -0.21 wood (wind)

Moorehouse 6.2 0.254 -0.044 LNG

Munoz 1 8.44 0.298 -0.126 gasoline, diesel(H/D max)

Munoz2 7.74 0.375 -0.096 gas. diesel

Pritchard-Binding

10.615 0.305 -0.03

Fay1 11.1 2/3 0 Gasoline clear flame zone

Fay2 14 2/5 0 Visible flame zone

15

3.1 Models of Flame Geometry

3.1.1 Thomas Method:

Thomas had used wood cribs to determine the length of the flame. According to his model:

= 42 0.61

3.1.2 Moorehouse Method:

Moorehouse measured the L/D for large LNG fire. Accrding to Moorehouse the model is:

= 6.2 0.2540.044

3.1.3 Munoz Method

Munoz measured L/D for several types of fuels. For diesel and gasoline his proposed models

are:

= 7.74 0.3750.096 (Nominal L/D)

= 8.44 0.2980.126 (L/D maximum)

3.1.4 Pritchard-Binding Method:

Pritchard-Binding proposed (1992) an improved method for calculating mean length of the

flame. According to this method, the mean length of the flame:

= 10.615 0.3050.03

3.1.5 Fays Method:

Fays method (2006) is used to calculate the L/D ratio, the flame length of Fay is divided by 2

parts, combustion length (Lc) and plume zone visible flame length (Lv). In this study, however,

the flame length of combustion zone has been considered ans the mean flame length.

According to Fays model the L/D ratios are:

=

922

32

1

3

= 14

2

5

16

The graphs are generated to show the correlation between the pool diameter and flame length

in different methods:

0

0.5

1

1.5

2

2.5

3

0 10 20 30

L/D

Pool dia (m)

Thomas L/D

0

0.5

1

1.5

2

2.5

0 10 20 30

L/D

Pool dia (m)

Moorehouse L/D

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 10 20 30

L/D

Pool dia (m)

Munoz L/D

0

0.5

1

1.5

2

2.5

3

0 10 20 30

L/D

Pool dia (m)

Pritchard-Binding L/D

0

0.1

0.2

0.3

0.4

0.5

0.6

0 10 20 30

Lc/D

pool dia (m)

Fay Lc/D

0

0.5

1

1.5

2

2.5

0 10 20 30

Lv/D

Pool dia (m)

Fay Lv/D

17

3.2 Experimental Results and New Model

With m= 0.077 kg/m2s for a gasoline fire with = 1.4 kg/m3 and the parameters a, b, c from the

table gives the L/D of a 3m, 20m and 23m pool fire:

Pool dia (m)

m' (Chatri

s et. al.)

Fr Thomas Moorehouse

Munoz Pritchard-Binding

Fay (combustio

n zone)

Fay (Visibl

e flame zone)

3 0.071 0.0093 2.42 1.89 1.34 2.55 0.49 2.15

20 0.077 0.0039 1.43 1.51 0.97 1.96 0.27 1.52

23 0.077 0.0036 1.37 1.49 0.94 1.91 0.26 1.48

According to Munoz et.al. the experimental result for a 3m pool fire, the L/D was

1.3

18

The experimental result shows the L/D of pool fire is: 1.6 < (L/D)exp < 2.2. For a relatively large

gasoline tank (D = 23m) the experimental result was: (H/D)exp=1.7. None of the correlation

mentioned in above table can give better result for the experimental data.

However, a new method has been proposed to calculate the L/D which match the experimental

result with a=3.33 and b=0.12 and c=0 (no wind condition). According to this method the

(L/D)3m=1.9, (L/D)20m = 1.712 and (L/D)23m=1.7. New method for gasoline with no wind

condition and cylindrical shaped flame:

= 3.33 0.12

The result shows the close match to the experimental data, summarized in the table below:

Pool dia (m) Experimental data Result from the proposed method

3 1.3

19

3.3 Dimensionless Numbers Effecting Flame Geometry

Heat release from the pool fire acts to decrease the density of the surrounded gas. The action

on gravitational force (g) on the resulting density differences between the flame and

surrounded gas helps the gas to accelerate upward. Some non-dimensional parameters can

characterize the flow of fire: Fr (Froude number), Re (Reynolds number), Ri (Richardson

number), Pr (Prandlt number) and Le (Lewis number). The Strouhal number (St) is appropriate

for the unsteady flow and periodic phenomena which is common for pool fire, especially in the

presence of wind. These parameters are defined as:

=

=

()

=

=

2

=

=

Cp

=

=

Cp

=

1

= fL

=

Strouhal number (St) is a function of Richardson number (Ri), and Ri = constant*(Fr)-1

According to Gilchrist et.al., Strouhal number, = , where a = 0.52 and b = 0.505.

This relationship is similar to the L/D ratio with the Froude number. So, the Strouhal number also has an effect to the flame geometry depending on the length and diameter of the pool.

0

0.01

0.02

0.03

0.04

0.05

0.06

0 0.005 0.01 0.015

Stro

uh

al N

um

be

r (S

t)

Froude Number (Fr)

Correlation between Strouhal number and Froude number

0

0.01

0.02

0.03

0.04

0.05

0.06

0 10 20 30

Stro

uh

al N

um

be

r (S

t)

Pool Diameter (m)

Change of Strouhal number with diameter

20

4. Thermal Radiation Model

In order to describe thermal radiation from a large pool fire, different semi-empirical models

has been developed such as: zone model, field model, integral model etc. Zone models are

based on the differential equations for mass and energy balance. Field models are stationary

model, based on solving the time average Navier-Stokes PDE with some empirical sub models.

These models are also known as cold models and used for predicting non reacting flows.

Integral models comprise between semi-empirical and field models. These are based on

differential equations of zone model but included sub-models for turbulence, reaction, heat

transfer etc. Until now a very few integral models are able to predict the consequences of

accidental fire.

4.1 Point Source Model (Large distance)

The point source thermal radiation models based on the assumptions: the flame represents as a

point (single source) of thermal energy, energy radiated from the flame is a specified fraction of

energy released during the combustion and the thermal radiation intensity varies inversely

proportional with the square of the distance.

Figure: A point source radiation model

Moorehouse and Pritchard calculated the maximum surface emitting power (SEP) from a point

source model is:

=

1 + 4()

21

Here, Fs is radiation fraction (radiated heat loss fraction), depending on the type of fuel and

pool diameter. According to Yang et.al. (1993), for gasoline with large pool dia (D >2m) the

radiation fraction is 0.2.

Figure: Radiation fraction with pool diameter (Yang et.al.)

Fays model has employed Gray gas model which is mentioned earlier. The radiation fraction at

the gray gas model is expressed as,

{}

4 =

Where or the SEPz is the emissive power and its value is maximum when kz=1. is a

dimensionless constant and at the combustion zone 1, so the maximum emissive power at

the combustion where kz=1, the radiation fraction would be,

4 1

= 0.3678

However, in this study the radiation fraction is considered 0.2 as shown by Koseki et. al.

The correlation of SEPmax with the pool diameter is shown at the figure below:

22

Figure: Maximum surface emitting power with the pool diameter.

The point source model can predict radiation in from the flame but since it underestimates the

thermal radiation so its useless in closer distance. In closer distance the irradiance mostly

depends upon the length, shape and its orientation to the radiation.

4.2 Solid Flame Radiation Model

Solid flame model (radiation model without black soot) is calculated:

= (4

4)

is the grey gas emitter ( = 0.95), T is the ambient flame temperature.

The solid flame radiation method has certain limitation on determining the grey gas emission

value and this method gives very conservative values. Solid flame model can be modified to get

better result.

4.2.1 Modified Solid Flame Radiation Model

In modified solid flame model (MSFM) two zones has been considered: clear zone and soot

zone. Maximum surface emitting power (SEPmax)of MSFM can be calculated as (Vela et. al.):

=

4()

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30

SEP

max

Pool dia (m)

SEPmax with pool diameter

Thomas

Moorehouse

Munoz

Pritchard-Binding

Fay(Vis)

New Method

23

Table: SEPmax for MSFM with various pool diameter

Pool dia (m)

Thomas Moorehouse Munoz Pritchard-Binding

Fay Proposed Method

2 56.44 77.87 107.13 57.12 66.23 79.65

8 88.46 97.70 144.97 74 91.03 91.90

16 109.84 107.73 166.44 83 105.39 96.91

25 125.86 114.02 180.97 88.84 115.23 99.54

SEP for lower clear zone, = (1 ) , for gasoline k = 2

SEP for upper soot zone, = + 1

Figure: MSFM with lower clear zone and upper sooty zone

Haggland and Person (1976) has shown that for oil products 80% are covered by soot and

surface emitting power of soot SEPSZ=20kW/m2. There are some other methods of calculating

SEPact and one of the famous methods is TNO (2005) method.

Table: Actual surface emitting power according to TNO method

Surface emitting power for both lower clear zone and upper sooty zone has been calculated for

(D=3,8,16,25m) with different flame structures. The final result has been shown:

24

Figure: Lower clear zone surface emitting power (SEPCL)

Figure: Upper sooty zone surface emitting power (SEPu)

0

20

40

60

80

100

120

140

160

180

200

0 5 10 15 20 25 30

SEP

CL

Pool dia (m)

Lower clear zone SEP with pool diameter

Thomas

Moorehouse

Munoz

Pritchard-Binding

Fay(Vis)

New Method

0

10

20

30

40

50

60

0 5 10 15 20 25 30

SEP

u

Pool dia (m)

Upper sooty zone SEP

Thomas

Moorehouse

Munoz

Pritchard-Binding

Fay(Vis)

New Method

25

Next update: Two zone radiation model, Environmental factors

(transmissivity), Total heat flux calculation, Risk calculation