Consequence

Analysis:
Explosion
Modelling
OBJECTIVES

Able to understand fundamentals of

industrial explosion

Able to perform modeling and

consequence assessment on industrial
explosion
 What types of
explosion are you
familiar with
 Condensed
Explosion Phase
Explosion
Military

Controlled:
Mining Explosion
Chemical &
Physical Uncontrolled:
Explosion Typical Industrial
Industrial Explosion
Remember: Vapor Cloud
Explosion
Cloud
Expansion

Chemical energy is
transformed into mechanical
energy via shock wave (40%
transformation).
Fire Models
EMPIRICAL ANALYTIC MODELS

TNT Method
Multi-Energy Method
Baker-Strehlow Method

NUMERICAL 3D CFD MODELS

Turbulent analysis
Empirical relations
TNT Method
Calculation Procedures:

According to this method,

Equivalent TNT Mass
the power of the vapor
cloud explosion equates
to an equivalent mass Scaled Distance
of TNT (tri-nitrotoluene)
that would produce the
Explosion Blast Strength
same explosive power. (Overpressure)
TNT Method

Equivalent TNT Mass 𝑀 𝑓𝐸 ∆𝐻𝑐 𝑀𝐺

𝑇𝑁𝑇=
∆𝐻𝑇𝑁𝑇
Scaled Distance Where
MG (kg) denotes the mass of the flammable gas
that takes part in the explosion,
∆Hc (kJ/kg) is the heat combustion
Explosion Blast Strength ∆HTNT (kJ/kg) = 4,760 kJ/kg.
(Overpressure)
fE (-), denotes the fraction of the energy released
as shock wave (usually value between 0.01 and
0.1).
TNT Method

Equivalent TNT Mass 𝑥

𝑍= 1/3
𝑀𝑇𝑁𝑇
Scaled Distance
Where
x (m) is the distance from the center of explosion
Explosion Blast Strength MTNT (kg) denotes the equivalent TNT Mass
(Overpressure)
 The overpressure is estimated through the
diagram of overpressure as a function of the
TNT Method scaling distance (Brasie & Simpson 1968).

Equivalent TNT Mass

Scaled Distance

Explosion Blast Strength

(Overpressure)
TNT Method
Alternatively, overpressure, Ps (kPa), can be
Equivalent TNT Mass estimated using

2
𝑍
Scaled Distance 80,800 1 +
4.5
𝑃𝑠 =
2 2 2
Explosion Blast Strength
𝑍 𝑍 𝑍
1+ 1+ 1+
(Overpressure) 0.048 0.32 1.35
TNT Method Output:

Equivalent TNT Mass

Scaled Distance

Explosion Blast Strength

(Overpressure)
TNT Method
Pros:
TNT Method is very simple and easy to use. It is then widely employed
in the calculation of the overpressure of an explosion.

Cons:
TNT Method does not consider the space configuration where the
explosion takes place.

Parameter fE in most cases is unknown but greatly influences the

prediction
Exercise
Example 1. The PEMEX LPG (Liquefied Propane Gas) Terminal, of 16,000 m3 capacity, in San Juan
Ixhuatepec in the outskirt of Mexico City, was regularly supplied by 3 refineries. At 5:35 am of November
19, 1984, the control room noticed a pressure drop in the pumping station, without however being able to
find its cause. An 8-inch diameter pipeline between a spherical storage tank and a group of cylindrical
vessels was leaking. The leak lasted beween 5-10 min, while a 0.4 m/s wind was in the area. A large
vapor cloud was formed, followed by a VCE. The resulting causalities included 550 deaths and more than
6,400 wounded. Material damages were estimated at $34,000,000 (in 2005 prices). The facilities dated
from 1961-1962 and thus had already been in operation fro 20 years. During this time, the area surrounding
the terminal was inhabited, and there were houses within a distance of 130 m. the terminal’s capacity was
16,000 m3 (29,760 kg), and it is estimated that about 4,750 kg of propane leaked and evaporated into the
atmosphere. In Figures 1 and 2, the area layout as well as photographs before and after the explosion, are
shown. Local observations showed that in a distance of 25 m, 75, 125 and 200 m, and draw the
overpressure curve as a function of the distance from the center of the explosion. The following data are
available:

•Heat of combustion of propane, ∆Hc: 46,010 kJ/kg

•Heat of combustion of TNT, ∆HTNT: 4,760 kJ/kg
•Assume 𝑓𝐸 is 0.05
Baker-Strehlow
Method
The Baker-Strehlow considers the Calculation Procedures:
presence of obstacles in the
expansion of the flame causes
vapor cloud explosions of higher Cloud Dimensions
intensity.

Flame Speed

Explosion Blast Strength

(Overpressure)

Non-obstructed region Obstructed region

Baker-Strehlow
Method
The volume, V (m3), of the resulting vapor cloud
(composed of flammable gas and air) is calculated
Cloud Dimensions from the reaction’s stoichiometry, from which the
volume of the required oxygen is obtained and
therefore the volume of the required air.

Flame Speed The radius of the resulting cloud, R (m), is

derived from the volume, V (m3), of the cloud,
considered as a hemisphere, as
Explosion Blast
Strength 1/3
(Overpressure) 3𝑉
𝑅=
2𝜋
Baker-Strehlow
Method The parameters which influence the flame speed according
to the Baker-Strehlow method, are the way the flame
expands, the density of the fuel and the obstacle density
Cloud Dimensions

Flame Speed

Explosion Blast
Strength
(Overpressure)
Baker-Strehlow
Method 3-D: when a flame is free to expand in three dimensions (spherically or
hemispheric ally), the total surface area of the flame is increased
analogous to the square of the distance from the center of the explosion.
The flame flow field can weaken freely in the three dimensions. For
Cloud Dimensions this reason field velocities are low, and thus the disturbances to the field
because of obstacles are small. Furthermore, the effects of these
disturbances to the flame speed is small, as they effect only a small part
of the initial surface of the flame.

Flame Speed 2-D: in a two dimension expansion (e.g., expansion of cylindrical

flame under a concrete floor or deck) the total surface of the flame is
analogous to the distance from the center of the explosion. Hence
disturbances of the flame surface will have a greater effect than in a
Explosion Blast three-dimensional expansion, and disturbances in the flow field will
Strength also be stronger.
(Overpressure)
1-D: during a one-dimensional expansion (e.g., expansion of a flame
inside a cylinder), the flame surface is stable, there is almost no
weakening of the field, and there is no deviation from the existing flow
field. Thus, a very powerful feedback mechanism is created for the
increase of the flame acceleration.
Baker-Strehlow
Method
Fuel Reactivity: is also seperated in three categories.
Cloud Dimensions Low reactivity
is shown by gases like methane and carbon monoxide.
High reactivity
is exhibited only by hydrogen, acetylene, ethylene oxide, propylene
oxide and ethylene (the flame speed in laminar flow of these fuels
Flame Speed
exceeds the value of 0.8 m/s).
All remaining fuels are considered a fuels of middle reactivity.

The obstacle density: is the most difficult parameter to be quantified

Explosion Blast (there have been many attempts to quantify this parameter, which are
Strength well outside the scope of this course). Hence the correct use of this
(Overpressure) parameter relies on the logic and judgment of the reader.
Baker-Strehlow
Method
Cloud Dimensions Energy of explosion, E (MJ)

𝐸 = 𝑉 ∆𝐻𝑐 × 𝜌 × (𝑟𝑎𝑡𝑖𝑜 𝑜𝑓 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 ∶ 𝑎𝑖𝑟)

Flame Speed
Where,
∆𝐻𝑐 is the heat of combustion, (MJ/kg),
Explosion Blast 𝑉 is the volume of the cloud (𝑚3 )
Strength
(Overpressure)
𝜌 is the density (kg/m3)
Baker-Strehlow
Method A scaled pressure, 𝑃′𝑠 , and a scaled distance, 𝑟′ , are
calculated

Cloud Dimensions −1/3

𝑃𝑠 𝐸
𝑃′𝑠 = ′
𝑟 =𝑥
𝑃𝑎 𝑃𝑎
Flame Speed
Where Ps (MPa) denotes the overpressure caused by the explosion, Pa (MPa) the
ambient pressure (= 0.1 MPa), x (m), the distance from the center of the explosion and
E (MJ), the total energy released by the explosion.
Explosion Blast The calculation procedure is carried out in the following steps:
Strength 1) For every region the flame sped is selected (from Table 1)
(Overpressure)
2) The energy, E, released by the explosion in this region is then calculated.
3) Following that, for a specific distance, x, the scaled distance r’, is calculated.
4) From the n e x t Figure, the scaled overpressure corresponding to this scaled
distance is obtained, and from this the overpressure, Ps (MPa), of the explosion.
Baker-Strehlow
Method
Cloud Dimensions

Flame Speed

Explosion Blast
Strength
(Overpressure)

Figure. Scaled overpressure as a function of the

scaled distance (Baker-Strehlow method)
Exercise
Example 1. The PEMEX LPG (Liquefied Propane Gas) Terminal, of 16,000 m3 capacity, in San Juan
Ixhuatepec in the outskirt of Mexico City, was regularly supplied by 3 refineries. At 5:35 am of November
19, 1984, the control room noticed a pressure drop in the pumping station, without however being able to
find its cause. An 8-inch diameter pipeline between a spherical storage tank and a group of cylindrical
vessels was leaking. The leak lasted beween 5-10 min, while a 0.4 m/s wind was in the area. A large
vapor cloud was formed, followed by a VCE. The resulting causalities included 550 deaths and more than
6,400 wounded. Material damages were estimated at $34,000,000 (in 2005 prices). The facilities dated
from 1961-1962 and thus had already been in operation fro 20 years. During this time, the area surrounding
the terminal was inhabited, and there were houses within a distance of 130 m. the terminal’s capacity was
16,000 m3 (29,760 kg), and it is estimated that about 4,750 kg of propane leaked and evaporated into the
atmosphere. In Figures 1 and 2, the area layout as well as photographs before and after the explosion are
shown. Local observations showed that in a distance of 25 m, 75, 125 and 200 m, and draw the
overpressure curve as a function of the distance from the center of the xplosion. The following data are
available:

•Heat of combustion of propane, ∆Hc: 46,010 kJ/kg

•Heat of combustion of TNT, ∆HTNT: 4,760 kJ/kg
•Density of propane : 1.86 kg/m3
Effects of
Explosion
Probit
𝑃𝑟 = 𝑘1 + 𝑘2 ln 𝑉

Causative Probit Parameters

Type of Injury
factor
or damage k1 k2
(V)
Deaths from Overpressure
-77.1 6.91
lung hemorrhage (N/m2)
Eardrum Overpressure
-15.6 1.93
ruptures (N/m2)
Structural Overpressure
-23.8 2.92
damage (N/m2)
Overpressure
Glass breakage -18.1 2.79
(N/m2)