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Application of Bayesian networks to hydrogen hazards in
nuclear
chemical plants
Fayaz Ahmed, MSc BEng C Eng MIChemE
[email protected]
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Presentation structure
• Introduction
• Hydrogen generation mechanisms in nuclear chemical plants
• Hydrogen hazard management
• Bayesian methodology
• Case Study 1- Hydrogen hold-up and sudden release
• Case Study 2- Assessment of equipment reliability
• Conclusions
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Introduction (1)
• Hydrogen generation in nuclear chemical plants presents a
considerable challenge.
• Corrosion of metal fuel cladding waste and radiolysis are the
main mechanisms.
• Consequences from hydrogen explosions can be significant.
• The Fukushima Daichaii event illustrates potential effects of
hydrogen explosions (Figure 1).
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Introduction (2)
• Duty Holder is legally required to demonstrate risk is
ALARP.
• Demonstration of ALARP requires accurate risk analysis.
• Bayesian Belief Networks (BBNs) provide an improved means of
risk quantification.
• Two case studies on application of BBNs to hydrogen safety are
explored.
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Figure 1: Damage caused by the Fukushima Daiichai H2 Explosions
[1]
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Hydrogen generation mechanisms in nuclear chemical plants
(1)
• Corrosion of magnesium metal (Magnox) fuel
cladding waste in storage vessels
• Magnesium hydroxide sludge formed as a bi-
product of corrosion
• Hydrogen hold-up occurs within Magnox sludge
waste
• Sudden release of hydrogen into vessel ullage
space
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Hydrogen generation mechanisms in nuclear chemical plants
(2)
• Alpha, Beta Gamma radiation in radioactive liquors results in
radiolysis.
• Water dissociates to form hydrogen and the hydroxyl
radical:
H + e- +H2O →H2 + OH-
• Radiolytic hydrogen generation rate is primarily affected by
the ‘G-value’.
• G- value is number of H2 molecules evolved per 100eV of energy
absorbed by the medium
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Chronic hydrogen hazard management (1)
• Waste storage vessel lids feature filtered outlets.
• Filtered vents designed to keep chronic H2concentration in
ullage to
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Chronic hydrogen hazard management (2)
• Gas hold-up leads to waste expansion and reduction in ullage
volume.
• Ullage volume is maximised to allow for waste expansion.
• Adverse waste disturbance could lead to a sudden release of H2
in vessel ullage.
• Hazard management strategy is to reduce the risk of adverse
disturbance of vessel.
• Figure 2 illustrates the key variables and effects.
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Figure 2: Key variables affectingH2 hold-up and sudden
release
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Radiolytic hydrogen hazard management (1)
• Vessel ullage space purged with compressed air via
pneumercators (Figure 3).
• Use ventilation extract fans as the driving force for hydrogen
removal.
• For increased reliability, backup compressed air systems are
introduced.
• Aim is to keep hydrogen concentration at 25% of the Lower
Flammability Limit, i.e. 1%v/v.
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Figure 3: Equipment for management of radiolytic H2 in process
vessels
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Bayesian methodology (1)
• A statistical technique for modelling cause and effect
relationships.
• Method relies on the concept of Bayes Theorem [2]:
P(A|B) = (P(A) x P(B|A))/P(B)
• P(A) and P(B) are the probabilities of events A and B
occurring.
• P(A) is probability of the hypothesis before any evidence is
available.
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Bayesian methodology (2)
• P(A|B) is a conditional probability of observing hypothesis A
if B is true.
• P(B|A) is the probability of event B occurring if A is
true.
• The equation in previous slide represents only two
variables.
• Complex models with multiple variables require use of software
, e.g. Netica [3].
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Bayesian Network Process
• Bayesian software sets causal variables and effects in a
graphical network (BBN).
• Each cause (Parent) is connected to the effect (Child) by an
arc.
• Nodes can be Discrete or Continuous.
• Conditional Probability Tables (CPTs) are generated.
• CPTs can be based on expert judgement or mathematical
functions.
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Case Study 1: H2 hold-up and sudden release - Objectives
1) Apply BBN technique to:
• Determine the key sensitivities affecting sudden release of
hydrogen from sludgy waste forms.
• Assess the impact of sudden release on the vessel ullage H2
concentration.
2) Use the results to determine the benefits of the BBN
technique.
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Case Study 1: H2 hold-up and sudden release- BBN analysis
The following data was input into the BBN:
• 99% probability of waste expansion fraction being in the range
15-20 %v/v.
• 85% probability of a low corrosion hydrogen generation rate of
0.1 l/hr.
• 85% probability of the equilibrium hydrogen concentration
being in the range 0 to 0.25%v/v.
BBN (Figure 4) constructed by replicating Figure 2 and using
above input data.
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Figure 4: BBN analysis for case study 1-H2 hold-up and sudden
release
13-Sudden release occurs
TrueFalse
6.8393.2
5-Vessel internal vol (l)
4-Sludge waste volume (l)
9- Sudden hydrogen release volume (l)
0 to 13.313.3 to 26.726.7 to 40
93.24.112.67
7.91 ± 6.3
10-Total hydrogen volume in ullage (l)
0 to 16.716.7 to 33.333.3 to 50
93.94.521.57
9.62 ± 7.2
1- Equilibrium hydrogen volume (l)
0 to 22 to 44 to 6
94.15.640.25
1.12 ± 0.76
15-Hydrogen concn in ullage (%v/v)
0 to 44 to 88 to 31.231.2 to 41.641.6 to 54.7
36.935.427.40.41.023
8.38 ± 8.33-Equilibrium H2 concn (%v/v)
0 to 0.250.25 to 2
85.015.0
0.275 ± 0.41
2-Ullage volume (l)
111 to 174174 to 237237 to 300
68.031.40.54
163 ± 35
6- Vessel contents volume (l)
14-Fraction of held-up H2 released
zeroUp to twenty percent
93.26.83
0.0137 ± 0.05
8-Hydrogen hold-up volume (l)
0 to 100100 to 150150 to 180
1.090.09.00
128 ± 2012- Zoning system fails
TrueFalse
6.7093.3
7-Waste swelling fraction
No expansionUp to 15 percentUp to 20 percent
1.090.09.00
0.153 ± 0.021
11-Crane PLC fails
TrueFalse
0.1499.9
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Case Study 1: H2 hold-up and sudden release- BBN results
• The probability of hydrogen hold-up volume being in the range
100-150 litres is 90%.
• Adverse waste disturbance leads to sudden release of hydrogen
gas.
• The probability of sudden hydrogen release volume being in the
range 0 to 13.3 litres is 93.2%.
• The probability of ullage hydrogen concentration being in the
range 0-4%v/v is 36.9%.
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Case Study 1: H2 hold-up and sudden release- Updating of BBN
• BBN updating capability enables a ‘reverse analysis’ to
predict key sensitivities.
• The probability of ullage hydrogen concentration, Node 15, in
the 0-4%v/v range is updated to 100% (Figure 5).
• Main sensitivities are crane PLC and vessel transfer zoning
system failures.
• Both failures lead to adverse waste disturbance.
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Figure 5: Updated BBN for case study 1- H2hold-up and sudden
release
13-Sudden release occurs
TrueFalse
0.9199.1
5-Vessel internal vol (l)
4-Sludge waste volume (l)
9- Sudden hydrogen release volume (l)
0 to 13.313.3 to 26.726.7 to 40
99.20.84
0
6.76 ± 4
10-Total hydrogen volume in ullage (l)
0 to 16.716.7 to 33.333.3 to 50
100 0 0
8.35 ± 4.8
1- Equilibrium hydrogen volume (l)
0 to 22 to 44 to 6
93.95.790.27
1.13 ± 0.77
15-Hydrogen concn in ullage (%v/v)
0 to 44 to 88 to 31.231.2 to 41.641.6 to 54.7
100 0 0 0 0
2 ± 1.23-Equilibrium H2 concn (%v/v)
0 to 0.250.25 to 2
85.114.9
0.274 ± 0.41
2-Ullage volume (l)
111 to 174174 to 237237 to 300
60.738.40.90
168 ± 37
6- Vessel contents volume (l)
14-Fraction of held-up H2 released
zeroUp to twenty percent
99.10.91
0.00181 ± 0.019
8-Hydrogen hold-up volume (l)
0 to 100100 to 150150 to 180
1.4990.67.96
127 ± 2012- Zoning system fails
TrueFalse
0.8999.1
7-Waste swelling fraction
No expansionUp to 15 percentUp to 20 percent
1.4990.67.96
0.152 ± 0.023
11-Crane PLC fails
TrueFalse
.019 100
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Case study 2: Reliability of purge air supply for radiolytic H2
management
• Variables are represented by purge air equipment (Figure 3)
and associated failure modes.
• Key failure modes included, normal air supply, back-up air
compressors, site power supply and emergency diesel generator.
• Each variable modelled as a Discrete Node with a failure being
in True or False state.
• Based on the Prior failure probabilities of the primary nodes,
the BBN is given in Figure 6.
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Figure 6: BBN for case study 2-unavailability of the purge air
system
HE1
True
False
1.0
99.0
OPFAIL1
True
False
1.75
98.3
PRINST
True
False
0.75
99.3
COMPA
True
False
24.5
75.5
BACKUP
True
False
7.65
92.4
FACTAIR
True
False
0.80
99.2
TOP EVENT
True
False
0 +
100
POWER
True
False
0.43
99.6
BACKUP COMPRESSORS FAIL
True
False
6.00
94.0
EMERGF
True
False
0.16
99.8
HE2
True
False
1.0
99.0
COMPB
True
False
24.5
75.5
OPFAIL2
True
False
36.8
63.2
DCOMP
True
False
35.7
64.3
HPLV
True
False
0.01
100
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Case study 2: Reliability of purge air supply for radiolytic H2
management
• The results show that the unavailability of the purge air
system is low, i.e. 1x10-6 (Top Event probability shown as
‘0+’).
• Back- up compressor and emergency diesel compressor system
failures are accountable for the Top Event probability of
1x10-6.
• Factory air and power supply failures present the key
sensitivities for Top Event to occur indefinitely (Figure 7).
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Figure 7: Updated BBN for case study 2-unavailability of the
purge air system
HE1
True
False
11.3
88.7
OPFAIL1
True
False
34.3
65.7
PRINST
True
False
22.9
77.1
FACTAIR
True
False
100
0
TOP EVENT
True
False
100
0
BACKUP COMPRESSORS FAIL
True
False
67.8
32.2
BACKUP
True
False
100
0
POWER
True
False
100
0
EMERGF
True
False
100
0
OPFAIL2
True
False
100
0
COMPA
True
False
74.1
25.9
HPLV
True
False
0.31
99.7
DCOMP
True
False
83.7
16.3
HE2
True
False
2.35
97.7
COMPB
True
False
74.1
25.9
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Conclusions
• Hydrogen generation in nuclear chemical plants is a complex
process.
• The H2 explosion scenarios are affected by multiple dependent
variables.
• Bayesian networks are demonstrated to provide an improved
means of modelling dependency and uncertainty.
• The Bayesian updating feature has enabled a reverse analysis,
hence sensitivity prediction.
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References
[1] Fuchigami, M., Kasahara, N., The 2011 Fukushima nuclear
power plant accident, 2015, Elsevier Ltd, ISBN
978-0-08-100118-9.
[2] Bolstad, W. M., 2007, Introduction to Bayesian Statistics,
Second Edition, ISBN-0-470-14115-1.
[3] Netica, Norsys, Available at www.norsys.com.
