Dahoe AE — Blast Scaling
Opening of the document
Blast Scaling
Explosion Effects on Equipment,
Structures, People and the Environment Dr Arief Dahoe Explosion, Hydrogen Safety and Combustion Scientist ACKNOWLEDGEMENTS Dutch Armed Forces Knowledge Center for Explosion and Hydrogen Safety http://www.explosionsolutions.org/kcehs/
METHODS FOR THE EVALUATION OF BLAST EFFECTS
Source: Hydrohub Innovation Program.
Safety aspects of green hydrogen production on industrial scale. Public Report, Institute for Sustainable Process Technology, The Netherlands, November 2023. [10].
Explosion Effects on Equipment,
Structures, People and the Environment Dr Arief Dahoe Explosion, Hydrogen Safety and Combustion Scientist ACKNOWLEDGEMENTS Dutch Armed Forces Knowledge Center for Explosion and Hydrogen Safety http://www.explosionsolutions.org/kcehs/
METHODS FOR THE EVALUATION OF BLAST EFFECTS
Source: Hydrohub Innovation Program.
Safety aspects of green hydrogen production on industrial scale. Public Report, Institute for Sustainable Process Technology, The Netherlands, November 2023. [10].
Full text, so the search can find this document · 20 kB of text
• Methods and models:
TNT Equivalency Method [2, 7], Multi Energy Method [11], Baker-Strehlow-Tang Method [8, 12], SCOPEmodel [13] and the Congestion Assessment Method [14].
• Methods and models are incorporated into commercial software:
PHAST, SAFETI, SHELL FRED, SCOPE [13], EFFECTS, FLACS, KFX, and EXIM.
• The latest version of SHELL FRED deploys the model in Ref. [15].
2
charge weight
mb in 1995 has
nd off of 4.5m
cks may range gigantic truck City, the mend their effects
may be subjected to impact by debris that may cause additional damage.
ir blast waves
ical properties
hows a typical
rival time tA, t that position e of overpresPo. The prest time td, then Pso- (creating a turning to amquantity Pso is e-on overpresr merely peak
Over-pressure
(side-on)
Over-pressure
Reflected
Pressure
Blast wave
Stand-off distance
Unconfined
interaction [1].
Figureexplosion:
3: BlastBlast-structure loads on a building
If the exterior building walls are capable of
resisting the blast load, the shock front penetrates through window and door3 openings, subjecting the floors, ceilings, walls, contents, and people to
Plume rise due to momentum and buoyancy. Concentration distribution from a vented plume [2].
4
Jet fire formation during large scale hydrogen releases [3].
Vessel with a volume of 16.2 m3 ; pressure: 24 bar.
Orifice/nozzle diameter: 42 mm.
Outflow: 27 kg H2 released in 30 seconds.
5
Blast wave formation.
6
Figure 4-4
Blast pressure
on a structure
Blast effects
pressure effects on a structure [4].
SOURCE: NAVAL FACILITIES ENGINEERING SERVICE CENTER, USER’S GUIDE ON PROTECTION AGAINST TERRORIST VEHICLE BOMBS, MAY 1998
7
of the timing of events, the building is engulfed by the shock wave
Cellular cross-section
Injury due to blast effects [2, 5, 6].
8
9
Entry
1
Overpressure
(kPa)
190
2
69–76
3
70
4
5
60
55
6
7
8
9
10
11
50–55
50
40–45
35–40
20–40
35
12
13
14
15
30–35
30
20–28
24
16
17
15–20
20
18
19
18
16
20
15
Damage/injury
Occupants of unstrengthened building will be killed by direct action of blast, by being struck by building debris, or by impact against hard surfaces [7].
Occupants of unstrengthened building are expected to suffer severe injuries or death from direct blast, building collapse, or translation [7].
Probable total destruction of buildings; heavy machine tools moved and badly damaged [2].
Loaded train boxcars completely demolished [2].
Occupants of unstrengthened building will be killed or incur serious injuries by blast to eardrums and lungs, by being blown down or struck by fragments and building debris [7].
Unreinforced brick panels, 25–35 cm thick, fail by shearing or flexure [2].
Loaded tank cars/train wagons overturned; brick walls, 20–30 cm thick, collapse [2].
Collapse of pipe bridge [2].
Displacement of pipe bridge, failure of piping [2].
Large trees fall down [2].
Breakage of wooden telephone poles; most buildings destroyed, except for concrete reinforced shear wall buildings; platting of cars and trucks pressed inwards [2].
Near-complete destruction of houses [2].
Cladding of light industrial buildings ruptured. Panelling torn-off [2].
Frameless, self-framing steel panel building demolished; rupture of oil storage tanks [2].
Personnel injuries of a serious nature or possible death are likely from fragments, debris, firebrands or other objects. There is a 10% chance of eardrum rupture [7].
Unreinforced concrete or cinderblock walls shattered [2].
Heavy machines in industrial buildings suffer little damage; steel frame building distorted and pulled away from foundations [2].
Lower limit of serious structural damage; 50% destruction of brickwork of houses [2].
Personnel may suffer temporary hearing loss or injury from secondary blast effects such as building debris and the tertiary effect of displacement. No fatalities or serious injuries from direct blast are expected [7].
Partial collapse of walls and roofs of houses [2].
10
Table 1: Continued.
21
7–15
22
23
10
5.9–8.3
24
25
26
27
28
29
8
7
3.5–7
5
3
2
30
31
32
33
34
1
0.7
0.3
0.2
0.15
Corrugated asbestos shattered. Corrugated steel or aluminum panels fastenings fail, followed by buckling; wood panel fastenings fail, panels blown in [2].
Steel frame of clad buildings slightly distorted [2].
Personnel are provided a high degree of protection from death or serious injury with injuries that do occur being principally caused by glass breakage and building debris [1].
Partial demolition of houses, made uninhabitable [2].
Collapse of roof of a tank [2].
Windows usually shattered; occasional damage to window frames [2].
Minor damage to house structures [2].
Limited minor structural damage [2].
Probability of 0.95 of no serious damage beyond this value; some damage to house ceilings;
50% of window glass broken [2].
Typical threshold for glass breakage [2].
Breakage of small windows under strain [2].
Loud noise similar to sonic boom; occasional glass failure [2].
No structural damage; occasional breaking of large window panes already under strain [2].
Annoying noise [2].
11
plosie en brand bij een Noors waterstoftankstation:
dracht en leerstof kswaterstaat
kswaterstaat
NUARI 2020
CEMBER 2019
GASEOUS HYDROGEN STORAGE – EXPLOSION HAZARDS
Kjorbo, Norway
Monday 10 June 2019 at 17:30 h
Hydrogen Explosion (3.0 – 3.5 kg H2 ) Glass damage at 60 – 70 m distance Office at 60 m distance LESSEN VAN HET KJØRBO-INCIDENT Houses at > 225 m distance
Figuur 15: Impressie schade intern.
De bovenstaande foto toont de eindtoestand. In het volgende hoofdstuk gaan we in op de toedracht en op de processen direct na de lekkage tot aan de eindtoestand.
3.2
Repressie
12 door de brandweer
Door de commandant, de heer Sverre Junker van de lokale brandweer, is een uitgebreide terugkoppeling gegeven tijdens de persconferentie op 28 juni 2019 in Oslo [zie referentielijst]. Wij beschikken over de videoopname, maar de spreker heeft zijn verhaal in het Noors verteld. Uit de sheets van hem zijn diverse zaken
DELFT UNIVERSITY OF TECHNOLOGY – GREEN VILLAGE Explosion involving 3.5 kg hydrogen Blast calculation according to Ref. [8].
70
>7
6
5
35
4.5
70
52.5
35
17.5
-17.5
-35
-52.5
-70
17.5
Distance [m]
-17.5
Overpressure [kPa]
Distance [m]
52.5
4
3.5
3
2.5
2
-35
1.5
-52.5
<1
Deflagration
-70
70
> 250
200
150
35
100
Distance [m]
-17.5
70
52.5
35
17.5
-17.5
-35
-52.5
-70
17.5
Overpressure [kPa]
Distance [m]
52.5
70
50
40
30
-35
20
15
-52.5
< 10
Detonation
-70
13
PRESSURE WAVEFORM – BLAST DOMAIN AND ACOUSTIC DOMAIN P
P
i
+
i+
∆P +
i−
i−
∆P +
P0
P0
t
∆P −
∆ta
∆t
+
∆t
−
t
∆P −
∆ta
Blast Domain
∆P + :
∆P − :
i+ :
i− :
Peak overpressure
Peak under pressure
Positive phase impulse R ∆t+ |P (t) − P0 | dt Negative phase impulse R ∆t− |P (t) − P0 | dt
∆t
+
Acoustic Domain
∆ta : Arrival time
∆t+ : Positive phase duration ∆t− : Negative phase duration
14
∆t
−
PRESSURE WAVEFORM – PARAMETRIZATION
Friedlander Equation [9]:
h
i
h
i
∆t
∆t
+
∆P = ∆P 1 − + exp − + ∆t ∆t
Air blast at 1.3 m from a free-field 1 kg TNT explosion [9].
15
Modified Friedlander Equation [9]:
h
i
h
i
∆t
∆t + ∆P = ∆P 1 − + exp −α + ∆t ∆t
Figure 4-1. The negative phase is usually less important in a design than the positive phase.
When the incident pressure wave impinges on a structure that is not parallel to the direction of the wave’s travel, it is reflected and reinforced, producing what is known as reflected pressure. The
Figure 4-1
❍ Explosive properties (type of material, energy output, and quantity of explosive)
Typical pressure-time history
Pressure waveform, P (t), and impulse waveform, 4-2
typical explosive detonation. The magnitude and distribution of blast loads on a structure vary greatly with several factors:
T = time (ms)
EXPLOSIVE BLAST
R
Figure
waveform by a detonation [4].
|P
(t)4-3− P0Typical | dt,impulse generated
EXPLOSIVE BLAST
4-4
EXPLOSIVE BLAST
Pressure waveform = P (t)
Impulse waveform =
R
|P (t) − P0 | dt
=⇒
i+ =
16
R
∆t+ |P (t) − P0 | dt
i− =
R
∆t− |P (t) − P0 | dt
Schardin destruction curves
Pressure impulse diagram
17
flected pressure to the peak incident pressure (Cr = Pr / Pi). This figure shows that reflected pressures for explosive detonations
Figure 4-2
Reflected
pressure
coefficient
versus
angle of incidence [4].
Reflected pressure coefficient vs. angle of incidence
z −z
Acoustic impedance: z = ρc. Reflection coefficient: Γ = zs + zg .
s
EXPLOSIVE BLAST
18
g
4-3
BLAST SCALING
E ∝ d3
E ∝ k 3 d3
R
← d →
kR
← kd →
P
P
i+
∆P
ki+
+
∆P
i
P0
Blast scaling:
i+ =
+
i a0
1/3
EP02
−
ki−
P0
t
∆P −
∆ta
∆t+
R
(E/P0 )1/3
−
i− = i a01/3
EP02
R=
+
t
∆P −
∆t−
k∆ta
k∆t−
k∆t+
+
∆P + = P P− P0
−
∆P − = P P− P0
+
−
0
∆t+ =
∆t a0
(E/P0 )1/3
19
0
∆t− =
∆t a0
(E/P0 )1/3
∆ta =
∆ta a0
(E/P0 )1/3
HOPKINSON – CRANZ SCALING
√
∆P + = βM 1/3 = β 3 M 1 kg
2 kg
E ∝ M =⇒ ∆P + = β̃E 1/3
5 kg
10 kg
=⇒
20 kg
+
+
β = ∆P1/3 and β̃ = ∆P
M
E 1/3
Condensed phase explosives
RDX
HMX
Pressure, P [bar]
TNT
Energy
Bis-oxadiazole
Substance
TNT
RDX
HMX
Energy release [MJ kg91 ]:
Detonation pressure [bar]:
Detonation velocity [km s91 ]:
TNT-equivalency [-]:
4.68
2.05·105
6.95
1.1
5.15
3.30·105
8.75
1.2
5.85
4.00·105
9.10
1.4
Bisoxadiazole
7.02
2.94·105
8.180
1.68
20
H2
142
14.5
1.968
34
Distance, R [m]
SACH SCALING
Condensed phase explosives
Condensed phase explosives
Energy
h i
Scaled overpressure, ln PP
0
Pressure, P [bar]
Vapor cloud explosions
Mach number
"
R
Scaled distance, ln
1/3
(E/P0 )
Distance, R [m]
Sach variables:
R=
R
(E/P0 )1/3
Parametrization scaled blast curve:
ia0
1/3
0
EP02
h
i
h
i2
h
i3
1
1
1
ln P = α1
+ α2 + α3 + ...
ln P ln P ln P P P =P
21
i =
#
TNT EQUIVALENCY METHOD
For vapor cloud explosions, the equivalent mass of TNT is calculated using the following expression:
MTNT = η
M ∆Hc
∆HTNT
or MTNT = η
M ∆Hd
∆HTNT
(1)
where:
M is the mass (kg) of fuel in the cloud or a quantity of condensed phase explosives ∆Hc is the lower heat of combustion of the fuel (kJ kg−1 ) ∆Hd is the decomposition energy release by a condensed phase explosive (kJ kg−1 ) η is the explosion yield factor (-) ∆HTNT is the decomposition energy of TNT (4680 kJ kg−1 ) MTNT the mass of TNT that would produce the same degree of damage (kg) Although the value of η is influenced by the reactivity of the fuel involved and the eventual partial confinement of the cloud, the currently accepted value is 3% (η = 0.03) for hydrocarbons. Whereas a value of 10% (η = 0.1) is being applied for hydrogen.
Definition of a TNT∗ -equivalent:
1 kT TNT∗ = 1012 cal = 4.18·1012 J
or, equally
1 kg TNT∗ = 106 cal = 4.18·106 J
Notice that the chemical substance TNT has a TNT∗ -equivalency of (4.68 MJ kg−1 /4.18 MJ kg−1 ) = 1.12 22
MULTI ENERGY METHOD – NOMOGRAMS
• Van den Berg A.C. The multi-energy method - a framework for vapor cloud explosion blast prediction.
Journal of Hazardous Materials, 12:1–10, 1985 [11].
• Van den Berg A.C. A 1-D variable flame speed blast simulation code using a flux-corrected transport algorithm. Report PML 1980-162, TNO Prins Maurits Laboratory, The Netherlands, 1980 [16].
• Wiekema B.J. Vapour cloud explosion model. Journal of Hazardous Materials, 3:221–232, 1971 [17].
23
MULTI ENERGY METHOD – BLAST STRENGTH INDEX
Selection of the Blast Strength Index Ignition energy Level of obstruction
Weak
Strong
X
X
X
Weak
X
X
X
X
X
X
X
Strong
Not Established
Established
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Blast
strength
Not Established
X
X
X
X
X
X
Degree of confinement
X
X
7 – 10
7 – 10
5–7
5–7
4–6
4–6
4–5
4–5
3–5
2–3
1–2 1
Source:
• Kinsella K.G. A rapid assessment methodology for the prediction of vapour cloud explosions. Research Report 357, Technical Research Centre of Finland, 1993 [18].
24
MULTI ENERGY METHOD – SAFETY DISTANCES
Hoeveelheid waterstof in drukhouder
Source: Van der Linden M. and Wolting A.G. Effecten van waterstofexplosies. Public report 20240032, National Institute for Public Health and the Environment (RIVM), The Netherlands, 2024 [19].
Results obtained with:
Blast Strength Index = 10
25
BAKER-STREHLOW-TANG METHOD – NOMOGRAMS
• Tang M.J. and Baker Q.A. A new set of blast curves from vapor cloud explosion. Process Safety Progress, 18:235–240, 1999 [8].
• Baker Q.A., Tang M.J., Scheier E.A. and Silva G.J. Vapor cloud explosion analysis. Process Safety Progress, 15:106–109, 1996 [20].
26
SCOPE & CONGESTION ASSESSMENT METHOD
Source: Refs. [13, 14].
27
SHELL FRED CODE & DOROFEEV MODEL
Source: Dorofeev S.B. Evaluation of safety distances related to unconfined hydrogen explosions. International Journal of Hydrogen Energy, 32:2118–2124, 2007 [15].
4 σy Rα Sf = σSuT 1 + (2) 3 x (σx)2 , 1/2 1/6 SuT v ℓt = a rms (3) SuL SuT δL , vrms = b Sf
σ−1
σ
(4)
Combination of (2), (3) and (4):
Sf = a2 σ(σ − 1)SuL
4 σy Rα
1+
3 x (σx)2
28
2
ℓt
δL
1/3
(5)
FORMATION OF A BLAST WAVE BY A VERY INTENSE EXPLOSION
Source: Taylor G.I. The air wave surrounding an expanding sphere. Proceedings of the Royal Society of London, Series A:
mMathematical and Physical Sciences, 186:273–292, 1946 [21].
Source: Taylor G.I. The formation of a blast wave by a very intense explosion. I. Theoretical discussion. Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, 201:159–174, 1950 [22].
Source: Taylor G.I. The formation of a blast wave by a very intense explosion. II. The atomic explosion of 1945. Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, 201:175–186, 1950 [23].
29
FORMATION OF A BLAST WAVE BY A VERY INTENSE EXPLOSION −1/5 2/5
R = C(γ)E 1/5 ρ0
t
where
C(γ) =
γ − 1 + (γ + 1)y1 γ − 1
γ + 1 + (γ − 1)y1 γ + 1
30
and
γ = CP /CV
PLUTONIUM
Formation:
1
238
239
0n + 92U −−→ 92U 23 239 Np + β − −→ 239 93 92U − mins 2.36 239 239 −→ Pu + β − 93Np − days 94
Natural decay:
24100 235
239
−−→ 92U + 42He
94Pu − years
Chain reaction:
1
239
240
0n + 94Pu −−→ [ 94Pu]
73 % 134
103
1 [ 240 94Pu] −−→ 54Xe + 40Zr + 3 0n 27 % 240 [ 240 94Pu] −−→ 94Pu + γ
31
RADIOACTIVE DECAY CASCADE: PLUTONIUM AND URANIUM
32
PHASE DIAGRAM: PLUTONIUM AND PLUTONIUM – GALLIUM ALLOY
Plutonium
Plutonium – Gallium Alloy
33
FORMATION OF A BLAST WAVE BY A VERY INTENSE EXPLOSION
DIMENSIONAL ANALYSIS
Express the shock wave radius R as a power-law function of energy, E, the ambient density, ρ0 , and time t:
R = f (E, ρ0 , t) = CE a ρb0 tc Substitute the units of the physical quantities involved, a b [m] = kg m2 s−2 kg m−3 [s]c to obtain a system of algebraic equations, m: 1 = 2a − 3b kg: 0 = a + b s: 0 = −2a + c that can be solved to yield:
a = 1/5 Hence
b = −1/5
−1/5 2/5
R = CE 1/5 ρ0
t
c = 2/5
=⇒
R
=C
−1/5
E 1/5 ρ0 t2/5
34
Bibliography
[1] Ngo T., Mendis P., Gupta A., and Ramsay J. Blast loading and blast effects on structures – An overview.
Electronic Journal of Structural Engineering, 7:76–91, 2007. Special Issue: Loading on Structures.
[2] Casal J. Evaluation of the effects and consequences of major accidents in industrial plants. Industrial Safety Series. Elsevier, Amsterdam, 2008.
[3] Groethe M., Merilo E., Colton J., Chiba S., Sato Y., and Iwabuchi H. Large-scale hydrogen deflagrations and detonations. International Journal of Hydrogen Energy, 32:2125–2133, 2007.
[4] Federal Emergency Management Agency (FEMA). Reference manual to mitigate potential terrorist attacks against buildings. Number FEMA 426 in Risk Management Series. McGraw-Hill, Washington D.C, December 2003.
[5] Gupta R.K. and Przekwas A. Mathematical models of blast-induced TBI: current status, challenges, and prospects. Frontiers in Neurology, 4: Article 59, 2013.
[6] Przekwas A., Somayaji M.R., and Gupta R.K. Synaptic mechanisms of blast-induced brain injury. Frontiers in Neurology, 7: Article 2, 2016.
[7] Baker W.E., Cox P.A., Westine P.S., Kulesz J.J., and Strehlow R.A. Explosion Hazards and Evaluation, volume 5 of Fundamental studies in engineering. Elsevier Scientific Publishing Company, New York, 1983.
[8] Tang M.J. and Baker Q.A. A new set of blast curves from vapor cloud explosion. Process Safety Progress, 18:235–240, 1999.
35
[9] Dewey J.M. Blast Effects: Physical Properties of Shock Waves, chapter The Friedlander Equations, pages 37–55. Shock Wave and High Pressure Phenomena. Springer, New York, 2018.
[10] Hydrohub Innovation Program. Safety aspects of green hydrogen production on industrial scale. Public report, Institute for Sustainable Process Technology, The Netherlands, November 2023.
[11] Van den Berg A.C. The multi-energy method - a framework for vapor cloud explosion blast prediction. Journal of Hazardous Materials, 12:1–10, 1985.
[12] Tang M.J. and Baker Q.A. Comparison of blast curves from vapor cloud explosions. Journal of Loss Prevention in the Processes Industries, 13:433–438, 2000.
[13] Puttock J.S., Yardley M.R., and Cresswell T.M. Prediction of vapour cloud explosions using the SCOPE model. Journal of Loss Prevention in the Processes Industries, 13:419–431, 2000.
[14] Puttock J.S. Developments in the Congestion Assessment Method for the prediction of vapour-cloud explosions.
In Pasman H.J., Fredholm O., and Jacobsson A., editors, Loss Prevention and Safety Promotion in the Process Industries, Proceedings of the 10th International Symposium, pages 1107–1133, Stockholm, Sweden, June 2001.
Elsevier.
[15] Dorofeev S.B. Evaluation of safety distances related to unconfined hydrogen explosions. International Journal of Hydrogen Energy, 32:2118–2124, 2007.
[16] Van den Berg A.C. A 1-D variable flame speed blast simulation code using a flux-corrected transport algorithm.
Report PML 1980-162, TNO Prins Maurits Laboratory, The Netherlands, 1980.
[17] Wiekema B.J. Vapour cloud explosion model. Journal of Hazardous Materials, 3:221–232, 1971.
[18] Kinsella K.G. A rapid assessment methodology for the prediction of vapour cloud explosions. Research Report 357, Technical Research Centre of Finland, 1993.
36
[19] Van der Linden M. and Wolting A.G. Effecten van waterstofexplosies. Public report 2024-0032, National Institute for Public Health and the Environment (RIVM), The Netherlands, 2024.
[20] Baker Q.A., Tang M.J., Scheier E.A., and Silva G.J. Vapor cloud explosion analysis. Process Safety Progress, 15:106–109, 1996.
[21] Taylor G.I. The air wave surrounding an expanding sphere. Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, 186:273–292, 1946.
[22] Taylor G.I. The formation of a blast wave by a very intense explosion. I. Theoretical discussion. Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, 201:159–174, 1950.
[23] Taylor G.I. The formation of a blast wave by a very intense explosion. II. The atomic explosion of 1945.
Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, 201:175–186, 1950.
37
TNT Equivalency Method [2, 7], Multi Energy Method [11], Baker-Strehlow-Tang Method [8, 12], SCOPEmodel [13] and the Congestion Assessment Method [14].
• Methods and models are incorporated into commercial software:
PHAST, SAFETI, SHELL FRED, SCOPE [13], EFFECTS, FLACS, KFX, and EXIM.
• The latest version of SHELL FRED deploys the model in Ref. [15].
2
charge weight
mb in 1995 has
nd off of 4.5m
cks may range gigantic truck City, the mend their effects
may be subjected to impact by debris that may cause additional damage.
ir blast waves
ical properties
hows a typical
rival time tA, t that position e of overpresPo. The prest time td, then Pso- (creating a turning to amquantity Pso is e-on overpresr merely peak
Over-pressure
(side-on)
Over-pressure
Reflected
Pressure
Blast wave
Stand-off distance
Unconfined
interaction [1].
Figureexplosion:
3: BlastBlast-structure loads on a building
If the exterior building walls are capable of
resisting the blast load, the shock front penetrates through window and door3 openings, subjecting the floors, ceilings, walls, contents, and people to
Plume rise due to momentum and buoyancy. Concentration distribution from a vented plume [2].
4
Jet fire formation during large scale hydrogen releases [3].
Vessel with a volume of 16.2 m3 ; pressure: 24 bar.
Orifice/nozzle diameter: 42 mm.
Outflow: 27 kg H2 released in 30 seconds.
5
Blast wave formation.
6
Figure 4-4
Blast pressure
on a structure
Blast effects
pressure effects on a structure [4].
SOURCE: NAVAL FACILITIES ENGINEERING SERVICE CENTER, USER’S GUIDE ON PROTECTION AGAINST TERRORIST VEHICLE BOMBS, MAY 1998
7
of the timing of events, the building is engulfed by the shock wave
Cellular cross-section
Injury due to blast effects [2, 5, 6].
8
9
Entry
1
Overpressure
(kPa)
190
2
69–76
3
70
4
5
60
55
6
7
8
9
10
11
50–55
50
40–45
35–40
20–40
35
12
13
14
15
30–35
30
20–28
24
16
17
15–20
20
18
19
18
16
20
15
Damage/injury
Occupants of unstrengthened building will be killed by direct action of blast, by being struck by building debris, or by impact against hard surfaces [7].
Occupants of unstrengthened building are expected to suffer severe injuries or death from direct blast, building collapse, or translation [7].
Probable total destruction of buildings; heavy machine tools moved and badly damaged [2].
Loaded train boxcars completely demolished [2].
Occupants of unstrengthened building will be killed or incur serious injuries by blast to eardrums and lungs, by being blown down or struck by fragments and building debris [7].
Unreinforced brick panels, 25–35 cm thick, fail by shearing or flexure [2].
Loaded tank cars/train wagons overturned; brick walls, 20–30 cm thick, collapse [2].
Collapse of pipe bridge [2].
Displacement of pipe bridge, failure of piping [2].
Large trees fall down [2].
Breakage of wooden telephone poles; most buildings destroyed, except for concrete reinforced shear wall buildings; platting of cars and trucks pressed inwards [2].
Near-complete destruction of houses [2].
Cladding of light industrial buildings ruptured. Panelling torn-off [2].
Frameless, self-framing steel panel building demolished; rupture of oil storage tanks [2].
Personnel injuries of a serious nature or possible death are likely from fragments, debris, firebrands or other objects. There is a 10% chance of eardrum rupture [7].
Unreinforced concrete or cinderblock walls shattered [2].
Heavy machines in industrial buildings suffer little damage; steel frame building distorted and pulled away from foundations [2].
Lower limit of serious structural damage; 50% destruction of brickwork of houses [2].
Personnel may suffer temporary hearing loss or injury from secondary blast effects such as building debris and the tertiary effect of displacement. No fatalities or serious injuries from direct blast are expected [7].
Partial collapse of walls and roofs of houses [2].
10
Table 1: Continued.
21
7–15
22
23
10
5.9–8.3
24
25
26
27
28
29
8
7
3.5–7
5
3
2
30
31
32
33
34
1
0.7
0.3
0.2
0.15
Corrugated asbestos shattered. Corrugated steel or aluminum panels fastenings fail, followed by buckling; wood panel fastenings fail, panels blown in [2].
Steel frame of clad buildings slightly distorted [2].
Personnel are provided a high degree of protection from death or serious injury with injuries that do occur being principally caused by glass breakage and building debris [1].
Partial demolition of houses, made uninhabitable [2].
Collapse of roof of a tank [2].
Windows usually shattered; occasional damage to window frames [2].
Minor damage to house structures [2].
Limited minor structural damage [2].
Probability of 0.95 of no serious damage beyond this value; some damage to house ceilings;
50% of window glass broken [2].
Typical threshold for glass breakage [2].
Breakage of small windows under strain [2].
Loud noise similar to sonic boom; occasional glass failure [2].
No structural damage; occasional breaking of large window panes already under strain [2].
Annoying noise [2].
11
plosie en brand bij een Noors waterstoftankstation:
dracht en leerstof kswaterstaat
kswaterstaat
NUARI 2020
CEMBER 2019
GASEOUS HYDROGEN STORAGE – EXPLOSION HAZARDS
Kjorbo, Norway
Monday 10 June 2019 at 17:30 h
Hydrogen Explosion (3.0 – 3.5 kg H2 ) Glass damage at 60 – 70 m distance Office at 60 m distance LESSEN VAN HET KJØRBO-INCIDENT Houses at > 225 m distance
Figuur 15: Impressie schade intern.
De bovenstaande foto toont de eindtoestand. In het volgende hoofdstuk gaan we in op de toedracht en op de processen direct na de lekkage tot aan de eindtoestand.
3.2
Repressie
12 door de brandweer
Door de commandant, de heer Sverre Junker van de lokale brandweer, is een uitgebreide terugkoppeling gegeven tijdens de persconferentie op 28 juni 2019 in Oslo [zie referentielijst]. Wij beschikken over de videoopname, maar de spreker heeft zijn verhaal in het Noors verteld. Uit de sheets van hem zijn diverse zaken
DELFT UNIVERSITY OF TECHNOLOGY – GREEN VILLAGE Explosion involving 3.5 kg hydrogen Blast calculation according to Ref. [8].
70
>7
6
5
35
4.5
70
52.5
35
17.5
-17.5
-35
-52.5
-70
17.5
Distance [m]
-17.5
Overpressure [kPa]
Distance [m]
52.5
4
3.5
3
2.5
2
-35
1.5
-52.5
<1
Deflagration
-70
70
> 250
200
150
35
100
Distance [m]
-17.5
70
52.5
35
17.5
-17.5
-35
-52.5
-70
17.5
Overpressure [kPa]
Distance [m]
52.5
70
50
40
30
-35
20
15
-52.5
< 10
Detonation
-70
13
PRESSURE WAVEFORM – BLAST DOMAIN AND ACOUSTIC DOMAIN P
P
i
+
i+
∆P +
i−
i−
∆P +
P0
P0
t
∆P −
∆ta
∆t
+
∆t
−
t
∆P −
∆ta
Blast Domain
∆P + :
∆P − :
i+ :
i− :
Peak overpressure
Peak under pressure
Positive phase impulse R ∆t+ |P (t) − P0 | dt Negative phase impulse R ∆t− |P (t) − P0 | dt
∆t
+
Acoustic Domain
∆ta : Arrival time
∆t+ : Positive phase duration ∆t− : Negative phase duration
14
∆t
−
PRESSURE WAVEFORM – PARAMETRIZATION
Friedlander Equation [9]:
h
i
h
i
∆t
∆t
+
∆P = ∆P 1 − + exp − + ∆t ∆t
Air blast at 1.3 m from a free-field 1 kg TNT explosion [9].
15
Modified Friedlander Equation [9]:
h
i
h
i
∆t
∆t + ∆P = ∆P 1 − + exp −α + ∆t ∆t
Figure 4-1. The negative phase is usually less important in a design than the positive phase.
When the incident pressure wave impinges on a structure that is not parallel to the direction of the wave’s travel, it is reflected and reinforced, producing what is known as reflected pressure. The
Figure 4-1
❍ Explosive properties (type of material, energy output, and quantity of explosive)
Typical pressure-time history
Pressure waveform, P (t), and impulse waveform, 4-2
typical explosive detonation. The magnitude and distribution of blast loads on a structure vary greatly with several factors:
T = time (ms)
EXPLOSIVE BLAST
R
Figure
waveform by a detonation [4].
|P
(t)4-3− P0Typical | dt,impulse generated
EXPLOSIVE BLAST
4-4
EXPLOSIVE BLAST
Pressure waveform = P (t)
Impulse waveform =
R
|P (t) − P0 | dt
=⇒
i+ =
16
R
∆t+ |P (t) − P0 | dt
i− =
R
∆t− |P (t) − P0 | dt
Schardin destruction curves
Pressure impulse diagram
17
flected pressure to the peak incident pressure (Cr = Pr / Pi). This figure shows that reflected pressures for explosive detonations
Figure 4-2
Reflected
pressure
coefficient
versus
angle of incidence [4].
Reflected pressure coefficient vs. angle of incidence
z −z
Acoustic impedance: z = ρc. Reflection coefficient: Γ = zs + zg .
s
EXPLOSIVE BLAST
18
g
4-3
BLAST SCALING
E ∝ d3
E ∝ k 3 d3
R
← d →
kR
← kd →
P
P
i+
∆P
ki+
+
∆P
i
P0
Blast scaling:
i+ =
+
i a0
1/3
EP02
−
ki−
P0
t
∆P −
∆ta
∆t+
R
(E/P0 )1/3
−
i− = i a01/3
EP02
R=
+
t
∆P −
∆t−
k∆ta
k∆t−
k∆t+
+
∆P + = P P− P0
−
∆P − = P P− P0
+
−
0
∆t+ =
∆t a0
(E/P0 )1/3
19
0
∆t− =
∆t a0
(E/P0 )1/3
∆ta =
∆ta a0
(E/P0 )1/3
HOPKINSON – CRANZ SCALING
√
∆P + = βM 1/3 = β 3 M 1 kg
2 kg
E ∝ M =⇒ ∆P + = β̃E 1/3
5 kg
10 kg
=⇒
20 kg
+
+
β = ∆P1/3 and β̃ = ∆P
M
E 1/3
Condensed phase explosives
RDX
HMX
Pressure, P [bar]
TNT
Energy
Bis-oxadiazole
Substance
TNT
RDX
HMX
Energy release [MJ kg91 ]:
Detonation pressure [bar]:
Detonation velocity [km s91 ]:
TNT-equivalency [-]:
4.68
2.05·105
6.95
1.1
5.15
3.30·105
8.75
1.2
5.85
4.00·105
9.10
1.4
Bisoxadiazole
7.02
2.94·105
8.180
1.68
20
H2
142
14.5
1.968
34
Distance, R [m]
SACH SCALING
Condensed phase explosives
Condensed phase explosives
Energy
h i
Scaled overpressure, ln PP
0
Pressure, P [bar]
Vapor cloud explosions
Mach number
"
R
Scaled distance, ln
1/3
(E/P0 )
Distance, R [m]
Sach variables:
R=
R
(E/P0 )1/3
Parametrization scaled blast curve:
ia0
1/3
0
EP02
h
i
h
i2
h
i3
1
1
1
ln P = α1
+ α2 + α3 + ...
ln P ln P ln P P P =P
21
i =
#
TNT EQUIVALENCY METHOD
For vapor cloud explosions, the equivalent mass of TNT is calculated using the following expression:
MTNT = η
M ∆Hc
∆HTNT
or MTNT = η
M ∆Hd
∆HTNT
(1)
where:
M is the mass (kg) of fuel in the cloud or a quantity of condensed phase explosives ∆Hc is the lower heat of combustion of the fuel (kJ kg−1 ) ∆Hd is the decomposition energy release by a condensed phase explosive (kJ kg−1 ) η is the explosion yield factor (-) ∆HTNT is the decomposition energy of TNT (4680 kJ kg−1 ) MTNT the mass of TNT that would produce the same degree of damage (kg) Although the value of η is influenced by the reactivity of the fuel involved and the eventual partial confinement of the cloud, the currently accepted value is 3% (η = 0.03) for hydrocarbons. Whereas a value of 10% (η = 0.1) is being applied for hydrogen.
Definition of a TNT∗ -equivalent:
1 kT TNT∗ = 1012 cal = 4.18·1012 J
or, equally
1 kg TNT∗ = 106 cal = 4.18·106 J
Notice that the chemical substance TNT has a TNT∗ -equivalency of (4.68 MJ kg−1 /4.18 MJ kg−1 ) = 1.12 22
MULTI ENERGY METHOD – NOMOGRAMS
• Van den Berg A.C. The multi-energy method - a framework for vapor cloud explosion blast prediction.
Journal of Hazardous Materials, 12:1–10, 1985 [11].
• Van den Berg A.C. A 1-D variable flame speed blast simulation code using a flux-corrected transport algorithm. Report PML 1980-162, TNO Prins Maurits Laboratory, The Netherlands, 1980 [16].
• Wiekema B.J. Vapour cloud explosion model. Journal of Hazardous Materials, 3:221–232, 1971 [17].
23
MULTI ENERGY METHOD – BLAST STRENGTH INDEX
Selection of the Blast Strength Index Ignition energy Level of obstruction
Weak
Strong
X
X
X
Weak
X
X
X
X
X
X
X
Strong
Not Established
Established
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Blast
strength
Not Established
X
X
X
X
X
X
Degree of confinement
X
X
7 – 10
7 – 10
5–7
5–7
4–6
4–6
4–5
4–5
3–5
2–3
1–2 1
Source:
• Kinsella K.G. A rapid assessment methodology for the prediction of vapour cloud explosions. Research Report 357, Technical Research Centre of Finland, 1993 [18].
24
MULTI ENERGY METHOD – SAFETY DISTANCES
Hoeveelheid waterstof in drukhouder
Source: Van der Linden M. and Wolting A.G. Effecten van waterstofexplosies. Public report 20240032, National Institute for Public Health and the Environment (RIVM), The Netherlands, 2024 [19].
Results obtained with:
Blast Strength Index = 10
25
BAKER-STREHLOW-TANG METHOD – NOMOGRAMS
• Tang M.J. and Baker Q.A. A new set of blast curves from vapor cloud explosion. Process Safety Progress, 18:235–240, 1999 [8].
• Baker Q.A., Tang M.J., Scheier E.A. and Silva G.J. Vapor cloud explosion analysis. Process Safety Progress, 15:106–109, 1996 [20].
26
SCOPE & CONGESTION ASSESSMENT METHOD
Source: Refs. [13, 14].
27
SHELL FRED CODE & DOROFEEV MODEL
Source: Dorofeev S.B. Evaluation of safety distances related to unconfined hydrogen explosions. International Journal of Hydrogen Energy, 32:2118–2124, 2007 [15].
4 σy Rα Sf = σSuT 1 + (2) 3 x (σx)2 , 1/2 1/6 SuT v ℓt = a rms (3) SuL SuT δL , vrms = b Sf
σ−1
σ
(4)
Combination of (2), (3) and (4):
Sf = a2 σ(σ − 1)SuL
4 σy Rα
1+
3 x (σx)2
28
2
ℓt
δL
1/3
(5)
FORMATION OF A BLAST WAVE BY A VERY INTENSE EXPLOSION
Source: Taylor G.I. The air wave surrounding an expanding sphere. Proceedings of the Royal Society of London, Series A:
mMathematical and Physical Sciences, 186:273–292, 1946 [21].
Source: Taylor G.I. The formation of a blast wave by a very intense explosion. I. Theoretical discussion. Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, 201:159–174, 1950 [22].
Source: Taylor G.I. The formation of a blast wave by a very intense explosion. II. The atomic explosion of 1945. Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, 201:175–186, 1950 [23].
29
FORMATION OF A BLAST WAVE BY A VERY INTENSE EXPLOSION −1/5 2/5
R = C(γ)E 1/5 ρ0
t
where
C(γ) =
γ − 1 + (γ + 1)y1 γ − 1
γ + 1 + (γ − 1)y1 γ + 1
30
and
γ = CP /CV
PLUTONIUM
Formation:
1
238
239
0n + 92U −−→ 92U 23 239 Np + β − −→ 239 93 92U − mins 2.36 239 239 −→ Pu + β − 93Np − days 94
Natural decay:
24100 235
239
−−→ 92U + 42He
94Pu − years
Chain reaction:
1
239
240
0n + 94Pu −−→ [ 94Pu]
73 % 134
103
1 [ 240 94Pu] −−→ 54Xe + 40Zr + 3 0n 27 % 240 [ 240 94Pu] −−→ 94Pu + γ
31
RADIOACTIVE DECAY CASCADE: PLUTONIUM AND URANIUM
32
PHASE DIAGRAM: PLUTONIUM AND PLUTONIUM – GALLIUM ALLOY
Plutonium
Plutonium – Gallium Alloy
33
FORMATION OF A BLAST WAVE BY A VERY INTENSE EXPLOSION
DIMENSIONAL ANALYSIS
Express the shock wave radius R as a power-law function of energy, E, the ambient density, ρ0 , and time t:
R = f (E, ρ0 , t) = CE a ρb0 tc Substitute the units of the physical quantities involved, a b [m] = kg m2 s−2 kg m−3 [s]c to obtain a system of algebraic equations, m: 1 = 2a − 3b kg: 0 = a + b s: 0 = −2a + c that can be solved to yield:
a = 1/5 Hence
b = −1/5
−1/5 2/5
R = CE 1/5 ρ0
t
c = 2/5
=⇒
R
=C
−1/5
E 1/5 ρ0 t2/5
34
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[2] Casal J. Evaluation of the effects and consequences of major accidents in industrial plants. Industrial Safety Series. Elsevier, Amsterdam, 2008.
[3] Groethe M., Merilo E., Colton J., Chiba S., Sato Y., and Iwabuchi H. Large-scale hydrogen deflagrations and detonations. International Journal of Hydrogen Energy, 32:2125–2133, 2007.
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[6] Przekwas A., Somayaji M.R., and Gupta R.K. Synaptic mechanisms of blast-induced brain injury. Frontiers in Neurology, 7: Article 2, 2016.
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[8] Tang M.J. and Baker Q.A. A new set of blast curves from vapor cloud explosion. Process Safety Progress, 18:235–240, 1999.
35
[9] Dewey J.M. Blast Effects: Physical Properties of Shock Waves, chapter The Friedlander Equations, pages 37–55. Shock Wave and High Pressure Phenomena. Springer, New York, 2018.
[10] Hydrohub Innovation Program. Safety aspects of green hydrogen production on industrial scale. Public report, Institute for Sustainable Process Technology, The Netherlands, November 2023.
[11] Van den Berg A.C. The multi-energy method - a framework for vapor cloud explosion blast prediction. Journal of Hazardous Materials, 12:1–10, 1985.
[12] Tang M.J. and Baker Q.A. Comparison of blast curves from vapor cloud explosions. Journal of Loss Prevention in the Processes Industries, 13:433–438, 2000.
[13] Puttock J.S., Yardley M.R., and Cresswell T.M. Prediction of vapour cloud explosions using the SCOPE model. Journal of Loss Prevention in the Processes Industries, 13:419–431, 2000.
[14] Puttock J.S. Developments in the Congestion Assessment Method for the prediction of vapour-cloud explosions.
In Pasman H.J., Fredholm O., and Jacobsson A., editors, Loss Prevention and Safety Promotion in the Process Industries, Proceedings of the 10th International Symposium, pages 1107–1133, Stockholm, Sweden, June 2001.
Elsevier.
[15] Dorofeev S.B. Evaluation of safety distances related to unconfined hydrogen explosions. International Journal of Hydrogen Energy, 32:2118–2124, 2007.
[16] Van den Berg A.C. A 1-D variable flame speed blast simulation code using a flux-corrected transport algorithm.
Report PML 1980-162, TNO Prins Maurits Laboratory, The Netherlands, 1980.
[17] Wiekema B.J. Vapour cloud explosion model. Journal of Hazardous Materials, 3:221–232, 1971.
[18] Kinsella K.G. A rapid assessment methodology for the prediction of vapour cloud explosions. Research Report 357, Technical Research Centre of Finland, 1993.
36
[19] Van der Linden M. and Wolting A.G. Effecten van waterstofexplosies. Public report 2024-0032, National Institute for Public Health and the Environment (RIVM), The Netherlands, 2024.
[20] Baker Q.A., Tang M.J., Scheier E.A., and Silva G.J. Vapor cloud explosion analysis. Process Safety Progress, 15:106–109, 1996.
[21] Taylor G.I. The air wave surrounding an expanding sphere. Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, 186:273–292, 1946.
[22] Taylor G.I. The formation of a blast wave by a very intense explosion. I. Theoretical discussion. Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, 201:159–174, 1950.
[23] Taylor G.I. The formation of a blast wave by a very intense explosion. II. The atomic explosion of 1945.
Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, 201:175–186, 1950.
37