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     

The migration of intragranular fission gas bubbles in irradiated uranium dioxide

The mobility of intragranular fission gas bubbles in uranium dioxide, irradiated at 1600–1800°C, has been studied following isothermal annealing at temperatures below 1600°C. The intragranular fission gas bubbles, average diameter approximately 2 nm, are virtually immobile at temperatures below 1500°C. The bubbles have clean surfaces with no solid fission product contamination and are faceted to the highest observed irradiation temperature of 1800°C. This bubble faceting is believed to be a major cause of bubble immobility. In fuel operating below 1500°C the predominant mechanism allowing the growth of intergranular bubbles and the subsequent gas release must be the diffusion of dissolved gas atoms rather than the movement of entire intragranular bubbles.     

Computer modeling of steady state fission gas behavior in carbide fuels

A model for the simulation of long-term, steady-state fission gas behavior in carbide fuels is formulated. It is assumed that fission gas release occurs entirely through gas atom diffusion to grain boundaries and cracks. Fission gas bubbles are assumed to remain stationary and to grow as the net result of gas atom precipitation into the bubbles from the matrix solid and gas atom re-solution from the bubbles into the matrix. Furthermore, assuming that local gas atom redistribution process in the immediate neighborhood of a bubble is very rapid, the bubble size is assumed to correspond to the equilibrium size that maintains exact balance between the rate of gas atom re-solution and that of gas atom precipitation.The model also treats the effect of attachment between bubbles and second-phase precipitates; the experimentally observed faster growth rate of precipitate bubbles is simulated using a reduced re-solution parameter for precipitate bubbles. With the grain matrix assumed to be spherical, the model allows the computation of the radial distribution of the intragranular bubbles and the gas atom concentration in the matrix.The flux of gas atoms arriving at the grain boundary is computed. The continual growth of grain boundary bubbles, resulting from the accumulation of gas atoms on the grain boundary, leads to grain boundary interlinkage and all gas atoms that subsequently reach the grain boundary are assumed to be released. Similarly, all gas atoms generated following the interlinkage of intragranular bubbles are also assumed to be immediately released.Application of the model indicates that fission gas swelling is largely due to intragranular bubbles. Grain boundary bubbles, although very large in size, contribute little to fission gas swelling and the contribution from gas atoms in solid solution in the matrix is even less significant.Physical parameters entering the model were assigned numerical values that closely represent the physical characteristics of the irradiation samples. Careful comparisons between the results of sensitivity studies and the experimental data readily identify the re-solution parameter to have the strongest influence on the results predicted by the code and that the grain size, and not the temperature, is the dominant factor affecting gas release.When allowance is made for the uncertainties of the experimental data, the predicted fission gas swelling also correlates well with experiment. The spread in the fuel swelling data, however, indicates that fuel cracking, and not fission gas swelling alone, very often contributes significantly to the fuel external dimensional changes. The linear fission gas swelling rate prediceted by the model exhibits almost a linear variation with temperature. This result correlates well with the linear swelling rate obtained from experimental swelling data if immersion density data alone are used, in order to eliminate the sources of uncertainties associated with fuel cracking.     

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.     

Simulation of non-equilibrium fission gas behaviour during fast thermal transients

A code for predicting the behavior of non-equilibrium fission gas in oxide fuel elements undergoing fast thermal transients is developed. A new variable, the equilibrium variable (EV), is introduced which, together with bubble radius r, completely specifies a fission gas bubble with respect to its size and equilibrium condition. The code is used to simulate the measurements in two TREAT transients with peak temperatures of 2477 and 2000 K. The computations are in fair agreement with the observations for bubbles smaller than 964 Å in diameter, but not for the larger bubbles. In all simulations, bubbles that grew during the heat-up phase of the transient were found to be “frozen” at a larger than equilibrium size during the cooldown phase of the transient. This phenomenon can significantly affect posttransient swelling and gas release. It is also found that the assumption of equilibrium can introduce considerable error in the computed bubble distribution, swelling and gas release at the end of as well as at post fast thermal transients; for example, the non-equilibrium model releases more gas. The code is also used to simulate the H3 TREAT transient as analyzed by Stahl and Patrician (initial temperature equal to 785 K with a maximum of 2393 K attained in 4.2 seconds, maximum thermal gradient of 10 000 K/cm and grain diameter of 4 to 10 μm) using the ideal gas as well as the Van der Waal's equations of states. The gas inventory at the start of the transient is assumed to be at equilibrium in the smallest radius group (6.2 Å), and the initial bubble concentration is assumed to be 1.2 × 10¹⁹/cc. Release rate is found to be strongly dependent upon grain size and initial bubble concentration; a 4 micron diameter grain releases about 95% of the gas retained at the start of the transient, while 6 and 10 micron grains release 68% and 20% respectively. When the initial bubble concentration is reduced by a factor of 16 for the 10 micron grain, fractional release increases to 62%. Gas release is found to result primarily from small bubbles ( ).     

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 development of grain-face porosity in irradiated oxide fuel

The predominant mode of fission gas release occurs through atomic diffusion to the grain boundaries. In oxide fuels the fission gases initially precipitate as an array of small lenticular bubbles of circular projection. The arrival of additional gas and vacancies causes these bubbles to grow and coalesce into fewer, larger bubbles. Depending on the irradiation conditions and temperatures, these bubbles may develop either as circular lenticular pores or as extended multi-lobed pores. Eventually the pores may intersect the grain edges where pathways may be formed which enable the gas to migrate to the outer geometry of the fuel and hence to the gap and the pin free volume. Recent extensive PIE campaigns on irradiated fuels have provided a large database of inter-granular porosity development and, from these, models of bubble growth, coalescence, morphological relaxation and venting have been developed.     

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.     

Behaviour of fission gas products in single crystal UO2 during intermediate temperature irradiation

A new mathematical interpretation is presented of fission gas release from monocrystalline uranium dioxide fuel during intermediate temperature irradiation in terms of a defect trap model, knock-out process and diffusion of bubbles. In the present model it is assumed that gas in an intermediate state exists side by side with the dissolved fission gas and that trapped in bubbles. It is assumed also that the isolated gas atoms, being re-dissolved, are immobile.The present model gives a satisfactory interpretation of the relative proportions of isotopes in the steady state fission gas release at diffrent temperatures. The dependence of fractional fission gas release on fission rate is also interpreted; regimes either proportional to fission rate or inversely proportional to fission rate are predicted depending on the fission rate interval considered. Both temperature dependent and temperature independent fission gas release can arise.The presented dynamic method of studying the release of fission gases during irradiadion provides a further test beside the static method of the veracity of the assumed mechanisms. Calculations show that fission gas behaviour becomes more complex for oscillated fission rate in the regime where the fractional release is inversely proportional to the fission rate for the steady state.     

Swelling and gas release in oxide fuels during fast temperature transients

A previously reported intergranular swelling and gas release model for oxide fuels has been modified to predict fission gas behavior during fast temperature transients. Under steady state or slowly varying conditions it has been assumed in the previous model that the pressure caused by the fission gas within the gas bubbles is in equilibrium with the surface tension of the bubbles. During a fast transient, however, net vacancy migration to the bubbles may be insufficient to maintain this equilibrium. In order to ascertain the net vacancy flow, it is necessary to model the point defect behavior in the fuel. Knowing the net flow of vacancies to the bubble and the bubble size, the bubble diffusivity can be determined and the long range migration of the gas out of the fuel can be calculated. The model has also been modified to allow release of all the gas on the grain boundaries during a fast temperature transient.The gas release predicted by the revised model shows good agreement to fast transient gas release data from an EBR-II TREAT H-3 (Transient Reactor Test Facility) test. Agreement has also been obtained between predictions using the model and gas release data obtained by Argonne National Laboratory from out-of-reactor transient heating experiments on irradiated UO₂. It was found necessary to increase the gas bubble diffusivity used in the model by a factor of thirty during the transient to provide agreement between calculations and measurements. Other workers have also found that such an increase is necessary for agreement and attribute the increased diffusivity to yielding at the bubble surface due to the increased pressure.     

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.     

The D-COM blind problem on fission gas release: The predictions of the TRANSURANUS and future codes

The concentration of retained xenon, the percentage of porosity and the UO₂ grain size have been measured as a function of radial position in the base irradiated rod AG11-8 and the transient tested rod AG11-10. In the base irradiation, densification of the fuel took place and slight grain growth occurred at the pellet centre. Gas release was not detected. During the transient test, 15–20% of the xenon inventory was released from the fuel grains. Gas release was accompanied in the central region of the fuel by an increase in the porosity from 4.7 to 6–8%. These findings are compared with the predictions made by the fuel performance code TRANSURANUS. The code predictions are in good agreement with the experimental observations. FUTURE was used to investigate the development of gas bubbles and the mechanisms controlling gas release in the rods during the base irradiation and the transient test. According to FUTURE fission gas will have accumulated on the grain boundaries during the base irradiation. The code indicates that variations in the fuel microstructure resulting from the base irradiation will have caused the level of gas release to vary along the fuel stack in rods AG11-9 and AG11-10 during the transient test. FUTURE also suggests that fission induced bubble re-solution became increasingly important for release during the latter stages of the transient test. Moreover, the code calculations imply that bubble migration could have played a significant role in the release process.     

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.     

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.     

An improved equation of state for inert gases at high pressures

A hard sphere equation of state is developed in order to describe inert gas behaviour at high temperatures and/or pressures. In the low density limit it is shown to simplify to the reduced van der Waals equation of state. At high pressure the reduced van der Waals EOS is shown to be seriously in error with the limited experimental data whilst the hard sphere is in good agreement with this data. Further the use of the reduced van der Waals EOS to estimate the number of atoms in a bubble is shown to lead to an under estimate of that number, especially for small bubbles. This represents an important correction in fuel swelling and gas release calculations. Finally, the use of the hard sphere EOS in modelling fission gas behaviour during a thermal transient is shown to be a more robust estimator of the fission gas pressure in bubbles than the reduced van der Waals EOS.     

UO2燃料裂变气体渗流模型研究

为分析UO₂燃料晶界气泡连通导致裂变气体间歇性释放的动力学过程,从而解决目前扩散模型预测的沿芯块径向释放份额与实验测量不符的问题,采用二维渗流模型模拟UO₂燃料晶界气泡网络的演化及与燃料棒内自由空间连通的释放过程。研究结果表明,渗流模型预测沿芯块径向的裂变气体释放份额在芯块中间部分出现局部峰值,并随着时间向芯块外侧推进,与辐照试验观察到不同燃耗下径向裂变气体分布现象定性符合。因此,本研究建立的渗流模型能够从机理上解释此前扩散模型未能预测的UO₂燃料裂变气体释放份额沿径向非单调分布现象。      

Phase-field modeling of gas bubbles and thermal conductivity evolution in nuclear fuels

A phase-field model was developed to simulate the accumulation and transport of fission products and the evolution of gas bubble microstructures in nuclear fuels. The model takes into account the generation of gas atoms and vacancies, and the elastic interaction between diffusive species and defects as well as the inhomogeneity of elasticity and diffusivity. The simulations show that gas bubble nucleation is much easier at grain boundaries than inside grains due to the trapping of gas atoms and the high mobility of vacancies and gas atoms in grain boundaries. Helium bubble formation at unstable vacancy clusters generated by irradiation depends on the mobilities of the vacancies and He, and the continuing supply of vacancies and He. The formation volume of the vacancy and He has a strong effect on the gas bubble nucleation at dislocations. The effective thermal conductivity strongly depends on the bubble volume fraction, but weakly on the morphology of the bubbles.