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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T(oC)

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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calc-0.01

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d(m

/mo)/

dt

exp

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exp

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/mo)/

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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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calc

Step 2nd. Addition of partial reactions, in order to reconstruct the experimental DSC curve

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calc

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d(S

i/Sfi)/

dt

exp

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6

calc-0.01

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d(S

i/Sfi)/

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exp

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i/Sfi)/

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exp

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d(S

i/Sfi)/

dt

exp

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2

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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




3 DIFFERENT MODELS

Type f(S)=Sn (Nightingale)5 Reactions

Type f(S)=S (Simmons)

6 Reactions


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Sf)/

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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


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


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


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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f)/dt

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f)/dt

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f)/dt

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f)/dt

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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


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 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 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

Method based on Linear Increase of Temperature T=at

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