Re-solution effects and fission gas swelling in UO2

A fission gas swelling model is proposed which enables one to calculate swelling in the vicinity of grain boundary networks and in imperfection-free regions. The grain boundary swelling requires a knowledge of the gas accumulation and the reaction-rate at the boundary. The gas accumulation was calculated by deriving a modified form of Fick's second law wherein it was assumed that because of re-solution effects the in-pile diffusion coefficient can be described as a function of the gas concentration but is independent of the actual operating time. Reaction-rates for bubbles at grain boundaries were derived in the manner discussed by de Jong and Koehler in their treatment of vacancy clustering. The results indicate that there is a grain size of about 10⁻⁴ cm for which the swelling is a maximum, which increases somewhat with irradiation temperature and with depletion at a constant temperature. The results enable one to predict the swelling and the mean radii of both intergranular and intragranular bubbles. Mean bubble radii predicted using the re-solution swelling model are in reasonable agreement with radii obtained from electron micrographs of irradiated UO₂ fuel samples. It is argued that gas bubble migration is the predominant means by which gas atoms arrive at grain boundaries at irradiation temperatures above about 900°C.     

Modeling of fission gas swelling in LWR UO2 fuel under irradiation

An understanding of the behavior of fission gas in uranium dioxide (UO₂) fuel is necessary for the prediction of the performance of fuel rods under irradiation. A mechanistic model for matrix swelling by the fission gas in LWR UO₂ fuel is presented. The model takes into account intragranular and intergranular fission gas bubbles behavior as a function of irradiation time, temperature, fission rate and burn-up. The intragranular bubbles are assumed to be nucleated along the track of fission fragments, which play the dual role of creator and destroyer of intragranular bubbles. The intergranular bubble nuclei is produced until such time that a gas atom is more likely to be captured by an existing nucleus than to meet another gas atom and form a new nucleus. The capability of this model was validated by a comparison with the measured data of fission gas behavior such as intragranular bubble size, bubble density and total fuel swelling. It was found that the calculated intragranular bubble size and density are in reasonable agreement with the measured results in a broad range of average fuel burn-ups 6–83 GW d/tU. Especially, the model correctly predicts the fuel swelling up to a burn-up of about 70 GW d/tU.     

The fission gas bubble distribution in a mixed oxide fast reactor fuel pin

The fission gas bubble distribution has been studied in a mixed oxide fast reactor fuel pin irradiated in DIDO MTR to 2.8% burn-up at centre and surface temperatures of 2000 and 1000°C. The intragranular fission gas bubbles are very small (<6 nm diameter) and this is a consequence of the high re-solution rate at fast reactor ratings. The bubbles nucleate heterogeneously and linear arrays of bubbles, due to nucleation on fission tracks, are observed up to irradiation temperatures of 1900°C. At 1980°C ~4% of the fission gas produced is present in intragranular bubbles. There is no definite evidence for gas bubble mobility or coalescence. Apart from any effects of columnar grain growth fission gas release in fast reactor fuel pins seems to occur predominantly by the diffusion of single gas atoms, at least up to irradiation temperatures of 2000°C.     

弥散型燃料的裂变气体行为研究

探讨了弥散型燃料中对辐照肿胀有重要影响的裂变气体的行为机理。裂变气体原子聚集成气泡引起燃料相肿胀，气泡的尺寸分布是影响辐照肿胀的重要因素。决定气泡生长的裂变气体的行为机理主要有：裂变气体原子的产生和热扩散迁移，气泡的成核和聚合长大，气泡内气体原子的重溶，燃料相的辐照亚晶化等过程。燃料中各种尺寸的气泡浓度随时间的变化率可用气泡生长的动力学速率方程组来描述。当裂变密度较高时，辐照产生的缺陷引起燃料相的     

Modelling intragranular fission gas release in irradiation of sintered LWR UO2 fuel

A model for the release of stable fission gases by diffusion from sintered LWR UO₂ fuel grains is presented. The model takes into account intragranular gas bubble behaviour as a function of grain radius. The bubbles are assumed to be immobile and the gas migrates to grain boundaries by diffusion of single gas atoms. The intragranular bubble population in the model at low burn-ups or temperatures consists of numerous small bubbles. The presence of the bubbles attenuates the effective gas atom diffusion coefficient. Rapid coarsening of the bubble population in increased burn-up at elevated temperatures weakens significantly the attenuation of the effective diffusion coefficient. The solution method introduced in earlier papers, locally accurate method, is enhanced to allow accurate calculation of the intragranular gas behaviour in time varying conditions without excessive computing time. Qualitatively the detailed model can predict the gas retention in the grain better than a more simple model.     

On the rate theory model for fission-gas behaviour in nuclear fuels

The rate theory model of the homogeneous nucleation and subsequent growth of intragranular fission gas bubbles has been extended to allow for the inclusion of very much larger bubbles. A simple treatment of the behaviour of grain-boundary gas is included in the present model, which allows for the re-solution of gas from intergranular bubbles. The effect of varying the model parameters and of including bubble mobility in the theory have been considered and it is concluded that the dominant parameters for gas release are temperature, grain size, re-solution rate and bubble migration and coalescence.     

Effect of non-equilibrium fission gas and fuel creep on swelling and release in irradiated carbide fuels

The code UCSWELL was developed to simulate fission gas behavior in carbide fuels. In the present work, one of the limiting assumptions in UCSWELL - that matrix gas bubbles are in equilibrium with gas atom concentration - is removed and non-equilibrium matrix fission gas bubbles are allowed, but with relaxation to equilibrium by means of vacancy diffusion and thermal and radiation-induced creep of the fuel. For a given grain size, the difference in swelling between equilibrium and non-equilibrium with relaxation bubble fission gas treatment increases with decreasing irradiation temperature. At a given temperature, the non-equilibrium effect is more pronounced for larger grain fuel. This is to be expected because the creep rate (and hence the rate at which bubbles grow to an equilibrium size) decreases as temperature decreases and/or as grain size increases. At temperatures, where the creep rate is grain size insensitive, grain size remains important to the equilibrium process in so far as the grain boundary is a source of vacancies to the non-equilibrium bubbles. While the difference in these quantities is at the most on the order of 20% for the steady operating conditions considered, it is anticipated that the non-equilibrium effects become more pronounced during reactor overpower and undercooling transients.     

A comparison between fission gas release data and FEMAXI-IV code calculations

The FEMAXI-IV code is an extension of the earlier version FEMAXI-III. The primary improvement in the new version is the provision for treating the fuel rod behavior during an operational transient. For this purpose, the time-dependent models are used for heat conduction, fission gas release, and mixing of the released gas with the plenum gas.In FEMAXI-IV, the fission gas release model was thoroughly revised from the previous version. It is based on the fission gas release model presented by White and Tucker. The model takes into account the following mechanisms:

&#x02022; - diffusion of gas atoms to the grain boundary;

&#x02022; - sweeping of gas atoms by grain growth;

&#x02022; - precipitation of gas atoms into intragranular gas bubbles;

&#x02022; - resolution of gas atoms from intragranular and grain boundary gas bubbles;

&#x02022; - fission gas release due to bubble interconnection.

The model was incorporated into FEMAXI-IV and code calculations were compared with the fission gas release data obtained in the Inter-Ramp and Over-Ramp experiments.This paper describes the fission gas release model involved and results of calculations.     

A dynamic intragranular fission gas behavior model

A model for the non-equilibrium behavior of intragranular fission gas in uranium oxide fuel is developed to study the fundamental phenomena that determine fission gas effects. The dynamic behavior of point defects and the variations in stoichiometry are explicitly represented in the model. The principle of distribution moment invariance is used to allow approximations that significantly reduce computational expense without sacrificing accuracy. A dynamic intragranular gas release and swelling (DIGRAS) computer code, that is based on the non-equilibrium model, was developed for both steady-state and transient applications. The code utilizes implicit multistep numerical integration methods, and is designed to give detailed information on all the physical processes that contribute to fission gas behavior.Simulations of steady-state irradiations indicate that the gas bubble re-solution process is very significant and results in very few large bubbles. The assumptions of equilibrium bubble sizes for normal steady-state irradiations in fast reactors appears to be adequate. On the contrary, a fully dynamic fission gas and point defect treatment was found necessary for transient simulations. The fuel stoichiometry was found to play an important role in determining bubble kinetics. This is mainly due to the strong dependence of point defect populations on stoichiometry. In fast transients, bubbles were found to be highly overpressurized, which suggests that a mechanistic plastic growth model is also needed.     

Reply to: “Comments on studies on diversion cross-Flow between two parallel communicating channels by a lateral slot — Part I” by J. Weisman

A model for the non-equilibrium behavior of intragranular fission gas in uranium oxide fuel is developed to study the fundamental phenomena that determine fission gas effects. The dynamic behavior of point defects and the variations in stoichiometry are explicitly represented in the model. The principle of distribution moment invariance is used to allow approximations that significantly reduce computational expense without sacrificing accuracy. A dynamic intragranular gas release and swelling (DIGRAS) computer code, that is based on the non-equilibrium model, was developed for both steady-state and transient applications. The code utilizes implicit multistep numerical integration methods, and is designed to give detailed information on all the physical processes that contribute to fission gas behavior.Simulations of steady-state irradiations indicate that the gas bubble re-solution process is very significant and results in very few large bubbles. The assumptions of equilibrium bubble sizes for normal steady-state irradiations in fast reactors appears to be adequate. On the contrary, a fully dynamic fission gas and point defect treatment was found necessary for transient simulations. The fuel stoichiometry was found to play an important role in determining bubble kinetics. This is mainly due to the strong dependence of point defect populations on stoichiometry. In fast transients, bubbles were found to be highly overpressurized, which suggests that a mechanistic plastic growth model is also needed.     

A hexagonal percolation model for zone-dependent pore interlinkage fraction and its application to the prediction of fission gas release

A percolation model is proposed to determine the interlinkage fraction of intergranular pores in the restructured and cracked fuel. A fuel rod is simulated as a large hexagon which consists of many small hexagonal grains. The fuel rod is divided into four zones of which boundaries are determined depending on their morphological and thermal properties. Grain size grown during irradiation is calculated using the FASTGRASS code and is used to calculate the number of hexagonal rings in zones. It is assumed that there is a circumferential crack at each zone boundary and radial cracks dividing zones radially. The algorithm for calculation of the pore interlinkage fraction (PIF) includes several steps; checking the site-occupancy, labeling the occupied sites, checking the site's connectivity to the nearest occupied sites, and counting the number of sites in the cluster connected to the free space. The Monte Carlo method is used for checking site-occupancy and the Hoshen-Kopelman method is applied to labeling. The site occupation probability is assumed to be the ratio of the current swelling to the maximum fractional swelling of pores in the grain edge, which is approximately 8.7%. The proposed model provides zone-dependent PIFs as a function of the site occupation probability. Comparisons of the calculated results with experimental data including the AECL-2230,CBX fuel rod of fractional gas release are done by replacing the PIF function in the FASTGRASS code with the calculated zone-dependent PIFs. Restructuring with cracks is found to affect fission gas release significantly. The calculated fission gas release as a function of linear heat rate shows better fitting to the experimental data than the simple model in the FASTGRASS code. The fission gas release is also sensitive to the maximum fractional volume swelling. The main advantage of this model is to treat the interlinkage phenomena in the grain boundaries more realistically than the single PIF correlation and to take into account of grain growth and cracks parametrically.     

A microstructure-dependent model for fission product gas release and swelling in UO2 fuel

A model for the release of fission gas from irradiated UO₂ fuel is presented. It incorporates the relevant physical processes: fission gas diffusion, bubble and grain boundary movement, intergranular bubble formation and interlinkage. In addition, the model allows estimates of the extent of structural change and fuel swelling. In the latter, contributions of thermal expansion, densification, solid fission products, and gas bubbles are considered. When included in the ELESIM fuel performance code, the model yields predictions which are in good agreement with data from UO₂ fuel elements irradiated over a range of water-cooled reactor conditions: linear power outputs between 40 and 120 kW m⁻¹, burnups between 10 and 300 MW h(kg U)⁻¹, and power histories including constant, high-to-low and low-to-high power periods.The predictions of the model are shown to be most sensitive to fuel power (temperature), the choice of diffusion coefficient for fission gas in UO₂, and burnup. The predictions are less sensitive to variables such as fuel restraint, initial grain size and the rate of grain growth.     

Molecular dynamics simulation of intragranular Xe bubble re-solution in UO2

The homogeneous re-solution of Xe fission gas bubbles in UO₂ is investigated by combined Monte Carlo and molecular dynamics simulations. Using a binary collision model, based on the Ziegler-Littmark-Biersack potential [J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, Stopping and Ranges of Ions in Matter, vol. 1, Pergamon Press, New York, 1984], the recoil energy distribution of fission gas atoms is obtained. An extensive library of fission gas atom displacement cascades is then compiled using molecular dynamic simulations. It used for calculating recoil spectrum averaged quantities. The calculations yield a re-solution parameter for homogeneous re-solution and a displacement distribution of fission gas atoms around the fission gas bubbles. The results disagree considerably from past estimates. The importance of channeling and threshold energy for fission gas escape are discussed.     

Fission gas disposition in decay heat environment

A computer code is developed to model fission gas disposition in UO₂ fuel during nearly isothermal heating, as would result from decay heat. The intragranular analysis, random diffusion model, uses a spatial solution for random migration and bubble coalescence. Nonequilibrium bubble growth and interactions between bubbles as well as nonequilibrium bubblegrain boundary interactions are considered. In the intergranular analysis, grain growth is allowed until tunnels have formed; this is set at 6% grain edge swelling. Grain face bubbles are assumed uniform in size and distribution. Grain edge tunnels are approximated in toroidal geometry. The model (a system of two grains, one shrinking and one growing but with total volume conserved; each grain originally contained 50% of the total fission gas) is applied to a “postulated” LMFBR accident condition involving a slow “nearly isothermal” heating of the fuel. The intragranular release is computed at 3.4% without grain growth, but at 14% with grain growth. Intragranular release is found to be dominated by grain growth.The analysis was applied also to the FGR-34 transient of HEDL. It is pointed out, however, that in the FGR-34 experiment thermal gradients were present whereas in the present code, only isothermal heating is considered. In spite of this significant difference between the modeled and the observed thermal state of the fuel, the comparison was carried out with a purpose to examine the existence of nonequilibrium attractive forces, between bubbles and grain boundaries, which were suggested by HEDL as perhaps responsible for the bubble denuding observed on both sides of the grain boundary. The computations did demonstrate the existence of nonequilibrium conditions, but the computed intragranular bubble radii, with only random diffusion as the operative mechanism, were well below the reported values. It is likely that this descrepancy between computed and observed bubble radii is due to (1) the presence in FGR-34 tests of thermal gradients, which would make bubble biased migration operative, and/or (2) the possibility of very strong enhancement, significantly more than two orders of magnitude, of the diffusion coefficient due to the prevailing nonequilibrium bubble conditions. The present code treats nonequilibrium conditions, but contains no physical mechanism for diffusion enhancement.     

The release of fission gas from nuclear fuels during temperature transients

The fractional release of rare gas atoms from a spherical grain of uranium dioxide containing a uniform concentration of gas atoms and intragranular bubbles is calculated for short-duration temperature transients and post-irradiation annealing. The released fraction is shown to reach a small maximum value which is dependent only on the grain size, gas atom concentration and intragranular bubble distribution. The analysis therefore may be applied to any fuel material providing these parameters are known. The conclusion therefore is that during a brief temperature transient, only a very small fraction of gas will be released from grain interiors to grain boundaries. Consequently the majority of gas released into the free volume of a pin will come from gas already residing on grain boundaries and released by mechanical cracking; the fractional gas release is small and should not cause undue concern. The calculations do not cover the case of fuel melting.     

An advanced model for grain face diffusion transport in irradiated UO2 fuel. Part 1: Model formulation

An advanced model for the grain face transport of gas atoms, self-consistently taking into consideration the effects of atom diffusion over the grain surface, their trapping by and irradiation induced resolution from intergranular bubbles is presented. The model allows prediction of a noticeable gas release from UO₂ fuel without visible interlinkage of grain face bubbles, i.e. at very low grain face coverage, below the critical value manifested by formation of bubble channels on grain faces interconnected with open porosity, in accordance with experimental observations of UO₂ and MOX fuel behaviour under various irradiation conditions.     

On the role of grain boundary diffusion in fission gas release

It is generally believed that thermal fission gas release from LWR fuel occurs mainly via interconnected grain boundary bubbles. Grain boundary diffusion is not considered to be a significant mechanism. We investigated this supposition by two methods; first, by assessing the distance a gas atom can migrate in a grain boundary containing perfectly absorbing traps. For areal number densities and fractional coverages by the traps observed in fuel irradiated to burnups exceeding ∼20 MWd/kg, gas atoms will be trapped after a migration distance equal to the size of a grain or less. This supports the supposition for medium-to-high burnups. However, the above-mentioned model is inapplicable for trace-irradiated specimens. In our second analysis, we examined Xe release from trace-irradiated UO₂. The measurements indicated that the liberation involves more than only lattice diffusion at the specimen surface, and that the data are consistent with sequential lattice and grain boundary diffusion unimpeded by intergranular traps. The analysis also provided rough estimates of the grain boundary diffusion coefficient in UO₂.