GAP.8.0.1.1.A
June 2, 2003
VAPOR CLOUD EXPLOSION, SAMPLE CALCULATION
INTRODUCTION
Sample calculations of vapor cloud explosion loss estimates are given using English input units only.
In some cases, units from both English and the SI system are used in the same equation. This is due
to the availability of data from the sources indicated. Both probable maximum loss and catastrophic
loss estimates are illustrated.
SELECTION OF MAXIMUM CREDIBLE SPILL
A review of the various processes in a plant may reveal a number of possible large spill sources. The
spill chosen for the probable maximum loss prediction may be different from the choice for the
catastrophic loss potential prediction. Materials used as fuels and the failure of a major storage tank
must be considered in estimating the catastrophic loss potential.
Probable Maximum Loss
Assume that a plant has four reactors in series, each contain 10,000 gal of cyclohexane at 250°F
(121°C) and 250 psig (264.7 psia). The source of the cyclohexane is a 10,000 gal day tank at
essentially atmospheric pressure and temperature.
Instrumentation has been provided to shut down the reactor feed pump upon abnormal low pressure
in the reactor train. Therefore the maximum credible spill for the probable maximum loss is
4 × 10,000 = 40,000 gal. The loss prevention person must decide if the pre-reaction and
post-reaction process storage should be considered in determining the maximum credible spill.
Catastrophic Loss Potential
A 250,000 gal sphere is located in the tank farm and is used to store liquefied petroleum gas (assume
propane) to be used as fuel. The maximum credible spill for the catastrophic loss potential is
250,000 gal of propane.
CALCULATION OF WEIGHT OF MATERIAL IN SYSTEM
Probable Maximum Loss
Since the material in question exists in the system as a liquid, equation 4 will be used to calculate the
weight of the material spilled:
W L = ρVL
From Gallant,1 Volume 2, page 157, Figure 41-5 the liquid density ρ of cyclohexane at 250°F
(121.1°C) is 0.675 g/mL. The volume of the liquid spilled VL is 40,000 gal.
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GAP.8.0.1.1.A
June 2, 2003
Therefore,
W L =8.35×0.675×40,000
WL =225,450lb
Catastrophic Loss Potential
Since the material in the sphere exists as a liquid, equation 4E will be used to calculate the weight of
the material spilled:
From Gallant, Volume 1, page 6, Figure 1-6, the liquid density ρ of propane at 70°F (21°C) is
0.50 g/mL. The volume of the liquid spill VL is 250,000 gal.
Therefore:
W L =8.35×0.50× 250,000
W L =1,043,750lb
CALCULATION OF QUANTITY VAPORIZED
Probable Maximum Loss
Since, from Gallant, Volume 2, page 154, Table 41-1, the atmospheric boiling point of cyclohexane is
80.8°C (177.4°F), Equation 5 will be used to calculate the weight of vapor WV formed following the
spill:
WV =
W L C pm (T1 −T2 )
∆Η υ
From Gallant, Volume 2, page 157, Figure 41-1, the liquid heat capacities C p at various points
between 80.8°C (177.4°F) and 121.1°C (250°F) are as follows:
T
Cp
°C
(cal/g-°C)
080
0.502
085
0.508
090
0.514
095
0.521
100
0.527
105
0.534
110
0.541
115
0.547
120
0.553
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GAP.8.0.1.1.A
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C pm is calculated as a geometric mean and is 0.527 cal/g°C.
From Gallant, Volume 2, page 146, Figure 41-2, the heat of vaporization ∆Η υ at boiling temperature
T2 (177.4°F) (80.8°C) = 85 cal/g.
Therefore:
WV =
225,450×0.527×(121.0 − 80.8)(o C )
85
WV =W =56,191lb
Catastrophic Loss Potential
From Gallant, Volume 1, page 10, Table 1-1, the normal boiling point of propane is -44°F (-42.1°C).
Since this is less than 70°F (21°C), assume that 100% of the spill will vaporize.
Therefore:
WV =W L =W =1,043,750lb
CALCULATION OF ENERGY RELEASED
Probable Maximum Loss
The equivalent energy W e (short ton TNT) of the vapor cloud explosion will be calculated from
equation 6E:
We =
W ∆H c f
4 × 106
Values of ∆H c are found in Perry,2 Page 3-156, Table 3-207. For cyclohexane ∆Η c = 18,846 Btu/lb.
In NFPA Handbook,3 Section 5, Chapter 11, ∆H c = 43,450 kJ/kg (net) = 18,692 Btu/lb. The explosive
yield factor f is 0.02.
Therefore:
We =
56,191 × 18,846 × 0.02
4 × 10 6
W e =5.3 tons TNT
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Catastrophic Loss Potential
The equivalent energy W e (short tons TNT) of the vapor cloud explosion will be calculated from
equation 6E:
We =
W∆H c f
4×10 6
From Perry, Page 3-155, Table 3-207, H c for propane is 19,929 Btu/lb. In NFPA Handbook,
Section 5, Chapter 11, H c = 46,360 kJ/kg (net) = 19,944 Btu/lb. The explosive field factor is 0.02.
Therefore:
We =
1,043,750 × 19,929 × 0.02
4 × 10 6
W e = 104 tons TNT
OVERPRESSURE CIRCLES
From Figure 1, the following overpressure circle diameters are obtained for the probable maximum
loss where W e = 5.3 tons TNT:
1 psi = 1400 ft
2 psi = 860 ft
3 psi = 700 ft
5 psi = 520 ft
From Figure 1, the following overpressure circle diameters are obtained for the catastrophic loss
potential where W e = 104 tons TNT:
01 psi = 3700 ft
02 psi = 2400 ft
03 psi = 1800 ft
05 psi = 1400 ft
07 psi = 1200 ft
10 psi = 1000 ft
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GAP.8.0.1.1.A
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CALCULATION OF CLOUD SIZE
Probable Maximum Loss
The diameter of the vapor cloud formed W L (lb) from spilling of cyclohexane with WV (lb) vaporizing
will be calculated from equation 13E since a 10 ft high cloud is assumed:
Dc = 7.017
W
Mυ
From NFPA 325M,4 the flammable limits (% volume) of cyclohexane are 1.3% to 8%. Therefore υ ,
the fraction of the cloud volume at the midpoint of the explosive range, is calculated from equation 11:
υ=
1.3 + 8
= 0.0465
2 × 100
The molecular weight Μ of cyclohexane from Gallant, Volume 2, Page 154, Table 41-1 or from the
NFPA Handbook, Section 5, Chapter 11 is 84.16.
Therefore:
Dc = 7.017
56,191
= 841 ft
84.16×0.0465
Catastrophic Loss Potential
The diameter of the vapor cloud from a spill of W pounds of propane will be calculated from equation
13E since a 10 ft high cloud is assumed:
Dc = 7.017
W
Mυ
From NFPA 325M, the flammable limits (% volume) of propane are 2.2% to 9.5%. Therefore, the
fraction of the cloud volume represented by vapor when the entire cloud volume is at the midpoint of
the explosive range υ is calculated from equation 11:
υ=
2.2 + 9.5
2 × 100
= 0.0585
The molecular weight M of propane from Gallant, Volume 1, Page 10, Table 1-1, or NFPA Handbook
is 44.094.
Therefore:
Dc = 7.017
1,043,750
= 4464 ft
44.094 × 0.0585
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June 2, 2003
DETERMINATION OF DAMAGE
Appropriate overpressure circles and cloud diameter are drawn on a plan of the plant. See Figures 1,
2 and 3 of this appendix for an illustration of these circles. As indicated in GAP.8.0.1.1, minimum
damage within the various overpressure circles are as follows:
•
•
•
•
Within the 5 psi circle - 100%
Outside the 5 psi but inside the 3 psi circle - 70%
Outside the 3 psi but inside the 1 psi circle - 40%
Tables I and II are used considering the equipment and structures involved to arrive at a more
precise estimate if one or more particular pieces of high value equipment may change the rough
estimates given above.
A d m in
W a re h o u s e
C o m p o u n d in g
M a in t
U tilitie s
W o rs t C a s e
L o s s P o te n tia l
C lo u d
S h o p
W o rs t C a s e
L o s s P o te n tia l
C e n te r
P ro c e s s
P ro c e s s
T a n k F a rm
P r o b a b le M a x im u m
L o s s A n d M a x im u m F o r s e e a b le
L o s s P o te n tia l C e n te r A n d C lo u d
Figure 1. Cloud Size
Approx. Size: 1 in. = 450 ft
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GAP.8.0.1.1.A
June 2, 2003
A d m in
W a re h o u s e
C o m p o u n d in g
M a in t
U tilitie s
S h o p
1
P ro c e s s
2
P ro c e s s
3
5
T a n k F a rm
Figure 2. Estimated Probable Loss Overpressure Circles
Approx. Size: 1 in. = 450 ft
A d m in
W a re h o u s e
C o m p o u n d in g
M a in t
U tilitie s
1
S h o p
2
1 0
7
P ro c e s s
3
5
P ro c e s s
T a n k F a rm
Figure 3. Catastrophic Loss Potential Overpressure Circles Approx. Size: 1 in. = 450 ft
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GAP.8.0.1.1.A
June 2, 2003
REFERENCES
1.
R. W. Gallant, Physical Properties Of Hydrocarbons, Volumes 1 & 2, Gulf Publishing Company, Houston, TX.
2.
R. H. Perry, D. Green, Perry’s Chemical Engineers’ Handbook, 6 edition, McGraw-Hill Book Company, New York, NY.
3.
NFPA Handbook, 16th edition, National Fire Protection Association, Quincy, MA.
4.
NFPA 325M-1984, Fire Hazard Properties Of Flammable Liquids, Gases, And Volatile Solids, National Fire Protection
Association, Quincy, MA.
th
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