The understanding of helium behaviour in nuclear fuel is fundamental for assessing the performance of the fuel itself, both in-pile and in storage conditions. After the production (by ternary fissions, (n,α)-reactions and α-decay) helium can be (i) released from the fuel, increasing the pressure inside the fuel element, or (ii) retained in the fuel dissolving in the lattice, or precipitating as bubbles in the fuel matrix. Both of these processes activate several coupled mechanisms (e.g., increase of stresses in the cladding, degradation of the fuel thermal conductivity, volumetric swelling of the fuel) affecting the fuel rod performance with important consequences for the safety. In view of the important influence of helium on the fuel performance and considering its peculiar characteristics (i.e., higher solubility in the fuel matrix in comparison with the other inert gases produced during the fission event), the accurate modelling of helium behaviour is crucial. In order to determine the diffusivity and solubility of helium in nuclear fuel (basic parameters required for modelling its behaviour), a considerable number of separate effects experiments have been performed in the last fifty years. The experimental results are highly spread, implying that correlations derived with no previous careful data analysis are going to be affected by high uncertainties. In this thesis work, I made a critical review of the helium diffusion coefficients and the helium solubility (i.e., Henry’s constant) as determined from experiments. This review covers all the experimental results available. I categorized the measured diffusion coefficients and Henry’s constants depending on the technique used to introduce the helium in the samples (either infusion, implantation and doping) and the characteristics of the sample itself (single crystal, poly-crystal or powder). This categorization strategy allowed showing a high degree of clustering in the available data. I derived different correlations for both the diffusion coefficient and the Henry’s constant depending on the combination of helium introduction technique and sample crystalline structure. Since each of the new proposed correlations describes a specific combination/cluster, the uncertainty associated with a specific correlation is less compared to the previously available correlations. Recommendations are given for each new proposed correlation for both application scope in terms of conditions (e.g., in-pile, storage) and in terms of modelling-scale (e.g., meso-scale models dealing with single fuel grains, integral models considering the fuel pellet-scale). To exploit the new set of proposed correlations in fuel performance codes (i.e., TRANSURANUS), I developed a new modal algorithm to efficiently solve the helium diffusion problem, applying it to the helium behaviour model proposed by Talip et al. (2014a). The adopted modal algorithm shows computational requirements in line with the needs of state-of-art fuel performance codes. I verified the modal algorithm by comparing its results with those obtained by means of the reference finite element tool COMSOL Multiphysics on several typical temperature histories. The verification is made using the diffusion coefficients fitted by Talip et al. (2014a) on their own experimental data. Then, I validated the model against the experimental data coming from two measurements deeply different in terms of helium introduction technique used and characteristics of the samples measured, using the new correlations for the helium diffusion coefficient. Lastly, in order to investigate how the initial different percentage of bubbles could affect the helium release, I made a sensitivity analysis on the initial concentration of helium both as single gas and bubbles and on their spatial distribution in the fuel grain. The sensitivity analysis pointed out that the fraction of helium precipitated in bubbles has a limited importance compared to the spatial distribution of the bubbles and the single gas atoms (uniform or not).
Comprendere il comportamento dell’elio nel combustibile nucleare è fondamentale per valutare la performance del combustibile stesso, sia nelle condizioni di funzionamento in reattore sia durante lo stoccaggio. Dopo essere stato prodotto (per mezzo di fissioni ternarie, reazioni (n,α) e decadimenti α) l’elio può essere (i) rilasciato dal combustibile, aumentando la pressione all’interno della barretta, oppure (ii) trattenuto nel combustibile, dissolvendo nel reticolo, o precipitando in bolle nella matrice di combustibile. Entrambi questi processi attivano alcuni meccanismi accoppiati (come l’aumento degli sforzi sulla guaina, la degradazione della conducibilità termica del combustibile e il suo rigonfiamento volumetrico) che influenzano la performance del combustibile e potrebbero avere importanti conseguenze ai fini della sicurezza. Pertanto, vista l’importante influenza dell’elio sulla performance del combustibile e considerate le sue peculiarità (tra le quali una solubilità nella matrice del combustibile più alta rispetto a quella degli altri gas inerti prodotti durante un evento di fissione), diventa cruciale modellizzare in modo accurato il comportamento dell’elio. A partire dagli anni ’60 sono stati fatti molti esperimenti per determinare la diffusività e la solubilità dell’elio nel combustibile nucleare (parametri richiesti per modellizzarne il comportamento). Tuttavia i risultati sperimentali risultano sparpagliati e le correlazioni da essi derivati sono affette da grande incertezza. In questa tesi, ho fatto una revisione critica dei coefficienti di diffusione dell’elio e della sua solubilità (in termini di costante di Henry) prendendo in considerazione tutti i risultati sperimentali disponibili in letteratura. In dettaglio, ho catalogato i coefficienti di diffusione e le costanti di Henry in base alla tecnica usata per introdurre l’elio nei campioni (infusione, impiantazione ionica e dopaggio) e alle caratteristiche del campione stesso (monocristallino, policristallino o polvere). Questa classificazione ha messo in evidenza la presenza di forti raggruppamenti nei dati sperimentali disponibili. Così ho derivato delle nuove correlazioni sia per il coefficiente di diffusione che per la costante di Henry in base alle diverse combinazioni di tecnica di introduzione usata e struttura cristallina del campione. Poiché ciascuna delle nuove correlazioni proposte descrive una specifica combinazione/raggruppamento, l’incertezza associata a una specifica correlazione è più bassa rispetto a quella associata alle correlazioni precedentemente utilizzate. Pertanto, per ciascuna delle nuove correlazioni proposte vengono fornite delle raccomandazioni di utilizzo in base alle specifiche condizioni (in reattore o in deposito) e al modelling-scale (modelli in meso-scala nel caso di singoli grani di combustibile oppure macro-scala nel caso di pastiglie intere). Per sfruttare il nuovo set di correlazioni proposte nei codici di performance del combustibile (per esempio TRANSURANUS), ho sviluppato un nuovo algoritmo modale in grado di risolvere il problema della diffusione in modo efficiente e con requisiti computazionali in linea con le esigenze dei codici di performance e l’ho applicato al modello proposto da Talip et al. (2014a) per il trasporto intra-granulare dei gas. Ho poi verificato l’algoritmo modale confrontando i suoi risultati con quelli ottenuti con COMSOL Multiphysics (programma agli elementi finiti) per diverse storie di temperatura. La verifica è stata fatta utilizzando i coefficienti di diffusione fittati da Talip et al. (2014a) sui suoi stessi dati sperimentali. In seguito, ho validato il modello mediante i dati sperimentali provenienti da due misure profondamente diverse in termini sia di tecnica di introduzione dell’elio usata sia di struttura cristallina dei campioni misurati, usando per il coefficiente di diffusione dell’elio le nuove correlazioni. Successivamente, al fine di investigare come la diversa percentuale iniziale di bolle potrebbe influenzare il rilascio di elio, ho fatto un’analisi di sensitività sulla concentrazione iniziale di elio in forma sia di singoli atomi che di bolle. L’analisi di sensitività ha messo in evidenza che la frazione di elio precipitato nelle bolle ha un’importanza limitata rispetto alla distribuzione spaziale delle bolle e dei singoli atomi (uniforme oppure no).
Assessment of helium intra-granular behaviour in nuclear oxide fuels
COGNINI, LUANA
2015/2016
Abstract
The understanding of helium behaviour in nuclear fuel is fundamental for assessing the performance of the fuel itself, both in-pile and in storage conditions. After the production (by ternary fissions, (n,α)-reactions and α-decay) helium can be (i) released from the fuel, increasing the pressure inside the fuel element, or (ii) retained in the fuel dissolving in the lattice, or precipitating as bubbles in the fuel matrix. Both of these processes activate several coupled mechanisms (e.g., increase of stresses in the cladding, degradation of the fuel thermal conductivity, volumetric swelling of the fuel) affecting the fuel rod performance with important consequences for the safety. In view of the important influence of helium on the fuel performance and considering its peculiar characteristics (i.e., higher solubility in the fuel matrix in comparison with the other inert gases produced during the fission event), the accurate modelling of helium behaviour is crucial. In order to determine the diffusivity and solubility of helium in nuclear fuel (basic parameters required for modelling its behaviour), a considerable number of separate effects experiments have been performed in the last fifty years. The experimental results are highly spread, implying that correlations derived with no previous careful data analysis are going to be affected by high uncertainties. In this thesis work, I made a critical review of the helium diffusion coefficients and the helium solubility (i.e., Henry’s constant) as determined from experiments. This review covers all the experimental results available. I categorized the measured diffusion coefficients and Henry’s constants depending on the technique used to introduce the helium in the samples (either infusion, implantation and doping) and the characteristics of the sample itself (single crystal, poly-crystal or powder). This categorization strategy allowed showing a high degree of clustering in the available data. I derived different correlations for both the diffusion coefficient and the Henry’s constant depending on the combination of helium introduction technique and sample crystalline structure. Since each of the new proposed correlations describes a specific combination/cluster, the uncertainty associated with a specific correlation is less compared to the previously available correlations. Recommendations are given for each new proposed correlation for both application scope in terms of conditions (e.g., in-pile, storage) and in terms of modelling-scale (e.g., meso-scale models dealing with single fuel grains, integral models considering the fuel pellet-scale). To exploit the new set of proposed correlations in fuel performance codes (i.e., TRANSURANUS), I developed a new modal algorithm to efficiently solve the helium diffusion problem, applying it to the helium behaviour model proposed by Talip et al. (2014a). The adopted modal algorithm shows computational requirements in line with the needs of state-of-art fuel performance codes. I verified the modal algorithm by comparing its results with those obtained by means of the reference finite element tool COMSOL Multiphysics on several typical temperature histories. The verification is made using the diffusion coefficients fitted by Talip et al. (2014a) on their own experimental data. Then, I validated the model against the experimental data coming from two measurements deeply different in terms of helium introduction technique used and characteristics of the samples measured, using the new correlations for the helium diffusion coefficient. Lastly, in order to investigate how the initial different percentage of bubbles could affect the helium release, I made a sensitivity analysis on the initial concentration of helium both as single gas and bubbles and on their spatial distribution in the fuel grain. The sensitivity analysis pointed out that the fraction of helium precipitated in bubbles has a limited importance compared to the spatial distribution of the bubbles and the single gas atoms (uniform or not).| File | Dimensione | Formato | |
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https://hdl.handle.net/10589/131903