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/S f )/dt T( o C) Michael Lasithiotakis Barry Marsden James Marrow Andrew Willets 1-Materials Performance Centre, School of Materials, The University of Manchester 2-Nuclear Graphite Research Group School of Mechanical, Aerospace and Civil Engineering, The University of Manchester Assessments from DSC measurements

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 temperature Destruction of container Contamination (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 ton intermediate level waste Why Waste Where does Wigner Energy come from?

Nature of Problem….. Formation of defects Cascade Interstitial 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 general Arrhenius Equation Via Logarithm S=fraction of energy released T=temperature f(s)=mathematic interrelation to the S, k=factor of speed of reaction A=factor of Arrhenius or pre-exponential factor E a =Activation Energy R=Universal Gas Constant =8,314 J/(mol. o K) 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 = -E a / R AEaEa

EaEa ΔHΔH H1H1 H2H2 H 12 Activation Energy

Previous researchers…….  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 Type f(S)=S Nightingale: Simmons: 3 Models Type f(S)=S γ  γ (or n)=6-8

Historical Data Windscale piles Various Heating rates Various Irradiation doses JAERI JRR-2 experimental reactor

Extraction of A and E a from Simmons-Nightingale models taking logarithms Y =a +bx a=lnA, b=-E a /R Extraction of a and b by the Least Squares Method A EaEa Y =a +bx SimmonsNightingale 6<γ<8

Type f (S) =S (Simmons) Very poor results Effort to reproduce the experimental curve

Type f (S) =S n (Nightingale) Better results, but still not acceptable Effort to reproduce the experimental curve

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) Total production of energy and rate of energy production for N overall reactions i=1,2,3, N Individual Components are supposed to react separately following the Arrhenius Equation For n=1 Simmons For n<>1 Nightingale c i =percentage of contribution of reaction i to the overall energy production s i =energy produced by the reaction i (Iwata’s Idea)

Step 1st. Examining the DSC curve and isolating of peaks and shoulders

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=-E a /R

Step 2nd. Addition of partial reactions, in order to reconstruct the experimental DSC curve Application of Linear Regression model on values A i, E i, c i, n i Problem Solved Poor results

3 DIFFERENT MODELS Type f(S)=S n (Nightingale) 5 Reactions Type f(S)=S (Simmons) 6 Reactions Type f(S)=S n (Nightingale) 6 Reactions A i (1/min) E ai (J/mol )c i (%)n A i (1/min) E ai (J/mol )c i (%)n A i (1/min) E ai (J/mol )c i (%)n A i (1/min) E ai (J/mol )c i (%)n

IWATA 5 Rate of heating : 5 o C/min Simmons model with 6 pseudo-reactions

B2-2L Nirex. Rate of heating : 10 o C/min Simmons with 6 pseudo-reactions.

IWATA 1 Rate of heating : 5 o C/min f(S)=S n (Nightingale) 6 Reactions.

NIREX B12-2L Rate of heating :10 o C/min f(S)=S n (Nightingale) 5 Reactions

IWATA 5. Rate of heating : 5 o C/min. f(S)=S n (Nightingale) 5 Reactions.

Lexa f. Rate of heating : 10 o C/min. f(S)=S n (Nightingale) 5 Reactions.

Type f(S)=S n (Nightingale) 5 Reactions Results for Dev1 for all the experiments

Type f (S) =S n (Nightingale) 5 Reactions Variation of values for all DSC experiments analyzed 1 st reaction Stability of A and E a are similar in all cases n and c vary A and E 2 nd Reaction More variation that first reaction Activation energies are of the same order around 73 kJ/mol A in the 3 rd reaction Variation between 5.34x x10 6 reaching 3,18x10 7 (some of high rates) - Iwata series, E a around 75 kJ/mol between th reaction Not required when modelling the Iwata series A, value of 1.88x10 6 in most cases A mainly around 5.07x10 5 for the LEXA f and LEXA g specimens. 5 th reaction Absent in the Iwata series A value for A between 2.47x10 5 or 2.88x10 5 E a around 75 kJ/mol ranging between 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.

Optimization of parameters dev(1) and dev(2) Divergence between the experimental and calculated values of S f Divergence between calculated and experimental derivatives expressed in percentage, associating the biggest rate of reaction that is observed in experimental DSC curve Dev 1 Dev 2 Z= total number of measurements N= number of parameters used, i.e. A, c and possibly n