Method based on Linear Increase of Temperature T=at
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Transcript of Method based on Linear Increase of Temperature T=at
Method based on Linear Increase of Temperature T=at
Application of Independent Parallel Reactions Model on the Annealing Kinetics of Irradiated Graphite Waste.
(Simulation of Wigner Energy Release)
d(S
/Sf)/
dt
T(oC)
Michael LasithiotakisBarry MarsdenJames MarrowAndrew Willets
1-Materials Performance Centre, School of Materials, The University of Manchester
2-Nuclear Graphite Research GroupSchool of Mechanical, Aerospace and Civil Engineering, The University of Manchester
Assessments from DSC measurements
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Problem…
Early UK graphite moderated research and production reactors operated at low temperatures, below 150°C.
Significant amounts of stored (Wigner) energy that may be relatively easily released
Exothermic behavior Rapid increase of temperatureDestruction of containerContamination (ground water)Oxidation of graphite
Decommissioning issues
characterization of graphite samples
long term "safe-storage"
reactor core dismantling graphite waste packaging
final disposal of this irradiated graphite waste.
Future= Decommissioning-Production of 85000 ton intermediate level waste
Why Waste
Where does
Wigner
Energy c
ome from?
Nature of Problem…..
Formation of defects
CascadeInterstitial defects
Interstitial loops
Vacancy defects
Chemical Kinetic Analysis and Thermal Characterization=Assessments on Speed of Reactions
Description of the behavior of the samples over a wide range of experimental conditions
Prediction of the behavior outside the domain of investigation
Characterization of samples and establishment of a deeper insight into the processes involved
Aim of Kinetic Analysis of Wigner Energy Release
Better understanding of radiation damage in graphite crystals
Robust prediction of stored energy release particularly for new conditions such as decommissioning
Gaining an understanding of the characteristics of the annealing procedures-reactions
Correlation with microstructural analysis using techniques such as TEM and Raman
Proposed to test these various kinetic models against experimental data
Basic Relation of kinetics in generalArrhenius Equation
RT
EAk aexp
TR
EAk a 1
lnln TR
EAk a 1
303.2loglog
Via Logarithm
)(Skfdt
dS
S=fraction of energy releasedT=temperaturef(s)=mathematic interrelation to the S, k=factor of speed of reactionA=factor of Arrhenius or pre-exponential factorEa=Activation EnergyR=Universal Gas Constant =8,314 J/(mol.oK) The mathematic function f(S) that until today has been more frequently used, is f(S)=S.
Y =a +b x
or
Y =a +b x
Extraction of a and b by the Least Squares Method
a = lnA, b = -Ea / R
A Ea
Ea
ΔH
H1
H2
H
1 2
Activation Energy
Previous researchers…….
SkT
EA
dt
dS
exp
Constant Activation Energy Model
Activation energy remains constant over the temperature
range of the release
General Model
Activation Energy is a function of temperature
Constant Frequency / Variable Energy Model
1)(
exp0
dt
tkT
EtaType f(S)=S
Nightingale:
kT
EAS
dt
dSexp
Simmons:
3 Models
Type f(S)=Sγ
γ (or n)=6-8
Historical Data
Windscale piles
Various Heating rates
Various Irradiation doses
JAERI JRR-2 experimental reactor
Extraction of A and Ea from Simmons-Nightingale models
RT
ESA
dt
dSexp
RT
EA
SdtdS
aexp
RT
EA
SdtdS
a
lnln
taking logarithms
Y =a +bx
a=lnA, b=-Ea/R
Extraction of a and b by the Least Squares Method
A Ea
RT
EA
SdtdS
aexp^
RT
EAS
dt
dSexp
RT
EA
SdtdS
a
ln
^ln
Y =a +bx
Simmons Nightingale
6<γ<8
Type f (S) =S (Simmons)
•Very poor results
Effort to reproduce the experimental curve
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d(S/
Sf)/
dt
Type f (S) =Sn (Nightingale)
•Better results, but still not acceptable
Effort to reproduce the experimental curve
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d(S/
Sf)/
dt
Initial Conclusions
• One reaction is not enough to reproduce the experimental curve.
• More than one reactions are needed.
Possible Reasons:
•Territories with different properties
•Possibly, more than one components
1. Amorphous territories, 2. Crystalline territories, 3. Dislocations, different types of
dislocations etc.).
Composite material (The term “Graphite” is
misleading.) => Different behaviour of each part.
1. Impurities
2. Contamination by other elements, due to construction, and usage in the reactor core).
Independent parallel reactions taking place without interactions with each other
Model of Independent Parallel Reactions (Pseudo-reactions)
i
isS
i
ii dt
dsc
dt
dS
Total production of energy and rate of energy production for N overall reactions
i=1,2,3, N
Individual Components are supposed to react separatelyfollowing the Arrhenius Equation
ni
ii
i sRT
EaA
dt
ds
exp
For n=1 Simmons For n<>1 Nightingale
ci=percentage of contribution of reaction i to the overall energy production
si=energy produced by the reaction i
(Iwata’s Idea)
Step 1st. Examining the DSC curve and isolating of peaks and shoulders
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RT
EAs
dt
dsc
dt
dSii
ii exp
RT
EA
dt
dsc
SdtdS
ai
ii
iexp
RT
EA
SdtdSi
a
ii
lnln
taking logarithms
Assumption of the Dominant Reaction: •The only reaction taking place in this territory is one
particular reaction without any contribution of the others.
Solving for a particular territory(Least squares etc.) Y = a + b x
a=lnA, b=-Ea/R
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d(m
/mo)/
dt
exp
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d(m
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exp
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d(m
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exp
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d(m
/mo)/
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exp
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calc0
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d(m
/mo)/
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exp
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calc
Step 2nd. Addition of partial reactions, in order to reconstruct the experimental DSC curve
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exp
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d(S
i/Sfi)/
dt
exp
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i/Sfi)/
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exp
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d(S
i/Sfi)/
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exp
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T(oC)
d(S
i/Sfi)/
dt
exp
1
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5
6
calc
Application of Linear Regression model on values Ai, Ei, ci, ni
Problem Solved
Poor results
Ai (1/min) Eai(J/mol) ci(%) n1 13413969 68127 0.40 12 5830216 70505 0.23 13 2481650 72804 0.22 14 558297 77470 0.11 15 180650 79241 0.04 16 106406 82310 0.05 1
Ai (1/min) Eai(J/mol) ci(%) n1 13413969 68915 0.42 12 5830216 70420 0.23 13 2481648 72800 0.18 14 558296 77520 0.11 15 180650 79233 0.06 16 106405 82320 0.05 1
Ai (1/min) Eai(J/mol) ci(%) n1 13413969 68915 0.47 12 5830216 70420 0.33 13 2481648 72800 0.17 14 558296 77520 0.03 15 180650 79233 0.00 16 106405 82320 0.00 1
Ai (1/min) Eai(J/mol) ci(%) n1 13413969 68915 0.59 12 5830216 70420 0.46 13 2481648 72800 0.30 14 558296 77520 0.15 15 180650 79233 0.12 16 106405 82320 0.09 1
3 DIFFERENT MODELS
Type f(S)=Sn (Nightingale)5 Reactions
Type f(S)=S (Simmons)
6 Reactions
Type f(S)=Sn (Nightingale)6 Reactions
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d(S/
Sf)/
dt
Ai (1/min) Eai(J/mol) ci(%) n
1 13413971 68060 0.40 1
2 5830216 70497 0.25 1
3 2481649 73216 0.19 1
4 558317 75181 0.11 1
5 180605 80626 0.10 1
6 106446 81638 0.00 1
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d(S/
Sf)/
dt
Ai (1/min) Eai(J/mol) ci(%) n
1 13413971 68060 0.40 0.9742197
2 5830216 70497 0.25 0.99802
3 2481649 73216 0.19 1.0020313
4 558317 75181 0.11 1.0029613
5 180605 80626 0.10 0.9991581
6 106446 81638 0.00 1
Ai (1/min) Eai(J/mol) ci(%) n
1 13413971 68060 0.38 0.9594927
2 5830216 70497 0.27 0.9906821
3 2481649 73216 0.18 1.0052211
4 558317 75181 0.11 1.0057841
5 180605 80626 0.10 0.9985629
6 106446 81638 0.00 1.0000484
Ai (1/min) Eai(J/mol) ci(%) n
1 13413971 67541 0.25 0.6775962
2 5830217 68801 0.37 1.0363428
3 2481650 73001 0.22 1.0470488
4 558318 75081 0.12 1.2131955
5 180598 80823 0.09 0.9728748
6 106446 81638 0.00 1.0000484
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d(S/S
f)/dt
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f)/dt
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f)/dt
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d(S/S
f)/dt
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T(oC)
d(S/S
f)/dt
IWATA 5Rate of heating : 5oC/minSimmons model with 6 pseudo-reactions
B2-2L Nirex. Rate of heating : 10 oC/minSimmons with 6 pseudo-reactions.
IWATA 1Rate of heating : 5oC/minf(S)=Sn (Nightingale) 6 Reactions.
NIREX B12-2LRate of heating :10oC/minf(S)=Sn (Nightingale) 5 Reactions
IWATA 5. Rate of heating : 5oC/min. f(S)=Sn (Nightingale) 5 Reactions.
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T(oC)
d(m
/mo)/d
texp
1
2
3
4
5
calc
Lexa f. Rate of heating : 10oC/min. f(S)=Sn (Nightingale) 5 Reactions.
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T(oC)
d(S
/Sf)/
dt
exp
1
2
3
4
5
calc
Type f(S)=Sn (Nightingale)5 Reactions
Results for Dev1 for all the experiments
DSC f(S)=S f(S)= Sn f(S)= Sn
DATA (Simmons) (Nightingale (Nightingale(DEV1) 6 Reactions 6 Reactions 5 Reactions
IWATA 1 3.99 2.09 1.08IWATA 2 6.01 4.07 1.80IWATA 5 6.75 4.69 2.67
IWATA 10 5.53 3.90 1.85IWATA 20 6.31 4.98 2.66IWATA 50 5.77 4.45 2.67
IWATA 100 6.57 5.86 2.80LEXA a 2.46 1.68 1.20LEXA b 3.18 2.25 1.03LEXA c 2.60 1.79 0.61LEXA d 1.69 1.54 0.48LEXA d 1.11 1.00 1.57LEXA e 8.02 1.43 1.64LEXA g 1.91 1.32 0.75
B2-2L Nirex 1.78 1.48 1.42B2-12L Nirex 2.29 1.94 0.64
TMS 2 33-57-15 BR 2.90 2.04 1.23W/Scale 2,5 2.31 2.01 1.31
W/Scale 2,5 II 2.34 2.01 1.55W/Scale 25 3.12 2.57 1.16
W/Scale 25 II 3.29 2.67 1.23W/Scale 50 3.47 2.91 1.42
DSC f(S)=S f(S)= Sn f(S)= Sn
DATA (Simmons) (Nightingale (Nightingale(DEV1) 6 Reactions 6 Reactions 5 Reactions
IWATA 1 3.99 2.09 1.08IWATA 2 6.01 4.07 1.80IWATA 5 6.75 4.69 2.67
IWATA 10 5.53 3.90 1.85IWATA 20 6.31 4.98 2.66IWATA 50 5.77 4.45 2.67
IWATA 100 6.57 5.86 2.80LEXA a 2.46 1.68 1.20LEXA b 3.18 2.25 1.03LEXA c 2.60 1.79 0.61LEXA d 1.69 1.54 0.48LEXA d 1.11 1.00 1.57LEXA e 8.02 1.43 1.64LEXA g 1.91 1.32 0.75
B2-2L Nirex 1.78 1.48 1.42B2-12L Nirex 2.29 1.94 0.64
TMS 2 33-57-15 BR 2.90 2.04 1.23W/Scale 2,5 2.31 2.01 1.31
W/Scale 2,5 II 2.34 2.01 1.55W/Scale 25 3.12 2.57 1.16
W/Scale 25 II 3.29 2.67 1.23W/Scale 50 3.47 2.91 1.42
Type f (S) =Sn (Nightingale)5 Reactions
Variation of values for all DSC experiments analyzed
A (1/min) E (kJ/mol) n c(%)
Min 7.04x1010 95 0.85 6.2
1st Reaction Max 7.04x1010 103 3.59 71.3Mean 7.04x1010 100 1.57 30
Min 8.86x105 64 0.46 4.5
2nd Reaction Max 6.63x107 77 2.54 53.1Mean 1.99x107 73 1.08 26.13
Min 8.39x104 66 0.68 18.8
3rd Reaction Max 3.18x 107 84 2.3 41Mean 7.80x106 76 1.5 28.87
Min 5.07 x105 83 0.38 6.1
4th Reaction Max 1.88 x106 113 1.58 22.4Mean 1.69 x106 93 0.98 12.21
Min 2.47 x105 70 0.18 2.5
5th Reaction Max 2.88 x105 93 1.61 21.6Mean 2.82 x105 85 0.9 13.59
1st reaction•Stability of A and Ea are similar in all cases •n and c vary
A and E 2nd Reaction •More variation that first reaction •Activation energies are of the same order around 73 kJ/mol
A in the 3rd reaction•Variation between 5.34x106 -8.39x106 reaching 3,18x107 (some of high rates) - Iwata series, Ea around 75 kJ/mol between 65 - 85
4th reaction •Not required when modelling the Iwata series•A, value of 1.88x106 in most cases•A mainly around 5.07x105 for the LEXA f and LEXA g specimens.
5th reaction•Absent in the Iwata series•A value for A between 2.47x105 or 2.88x105
• Ea around 75 kJ/mol ranging between 70-90
n and c for the different DSC runs - more variation.
•n generally increasing for the first two reactions and decreasing
for the other three reactions, with
increased irradiation fluence, as assessed from the LEXA model
results.
•c does not indicate the percentage of different types of defects on the overall defect population •c= part of their contribution to energy released •Some types of defects may not contribute their full capacity -Different values of fluence - Change of Heating rate
Conclusions
Independent parallel reactions model
•Good predictions of the kinetics
•Variation of values within appropriate limits
•Relative stability of assessed values has been achieved
Acknowledgements.
• Greek State Scholarships Foundation
• Materials Performance Centre
• Dr Steve Preston – (Former Nirex)
Appendix
RULES and PARAMETERS for ACHIEVING REALISTIC INTERPRETATIONS
1-Satisfactory results. Dev1<3%.
2-Application of one calculated model to other experimental data, for verification.
3-Choice of the simplest model.
4-Results between different experiments may vary slightly.
5-Conditions of experiment, play a vital role in the variation of values.
6-The shape of the calculated curve must follow the experimental.
7-Experience in choosing peaks and shoulders.
])(
)()([.100(%)2
exp
0exp
f
calcf
S
SSabsdev
Optimization of parameters dev(1) and dev(2)
Divergence between the experimental and calculated values of Sf
Divergence between calculated and experimentalderivatives expressed in percentage, associating the biggest
rate of reaction that is observed in experimental DSC curve
])/max[(
)/(100(%)1
expdtdS
NZSUMdev DSC
Dev 1
Dev 2
Z= total number of measurements
N= number of parameters used, i.e. A, c and possibly n
2
1
exp
N
i
calc
iiDSC dt
dS
dt
dSSUM