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.     

The response of fission gas bubbles to the dynamic behavior of point defects

A model has been developed to investigate the response of fission gas bubbles to the dynamic behavior of uranium point defects in uranium oxide. Simple thermodynamics is used to calculate the thermal equilibrium concentrations of both anion and cation point defects in UO_2±x and fully dynamic rate theory has been extended to estimate the dynamic concentrations of uranium vacancies and interstitials and the enhanced self-diffusion of uranium during constant temperature and thermal transient irradiations.During low temperature irradiations, fission production of uranium Frenkel pairs is dominant and the slow migration rate of the vacancies leads to long start-up transients (~10⁶ s in stoichiometric UO₂ at 1000 K) as the vacancies reach a quasisteady state with the microstructure. Thermal ramp behavior of the point defects and fission gas cavities depends primarily upon the initial concentration of point defects, and the temperature at which the thermal production of point defects becomes dominant. Our results indicate that non-equilibrium fission gas behavior is important for both constant temperature and thermal transient irradiations and that fission gas bubble behavior models must consider fuel stoichiometry. Below about 2200 K the dynamic behavior of the point defects should be incorporated as well.     

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.     

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 ( ).     

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.     

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.     

The mechanistic prediction of transient fission-gas release from LWR fuel

The steady-state and transient gas release and swelling subroutine (GRASS-SST) is a mechanistic computer code for the prediction of fission-gas behavior in UO₂-base fuels. GRASS-SST treats fission-gas release and fuel swelling on an equal basis and simultaneously treats all major mechanisms that influence fission-gas behavior. The GRASS-SST transient analysis has evolved through comparisons of code predictions with the fission-gas release and physical phenomena that occur during reactor operation and transient direct-electrical heating (DEH) testing of irradiated light-water reactor fuel. The GRASS-SST steady-state analysis has undergone verification for end-of-life fission-gas release and intragranular bubble-size distributions. The results of GRASS-SST predictions for transient fission-gas release during DEH tests are in good agreement with experimental data. Comparisons of GRASS-SST predictions of gas release and bubble-size distributions with the results of DEH transient tests indicate that (1) coalescing bubbles do not have sufficient time to grow to equilibrium size during most transient conditions, (2) mobilities of fission-gas bubbles in UO₂ are enhanced during nonequilibrium conditions if the excess pressure in the bubble is sufficient to generate an equivalent stress greater or equal to the yield stress of the surrounding matrix, and (3) channel formation on grain surfaces and coalescence of the channels with each other and with the tunnels of gas along the grain edges can contribute to grain-boundary separation and/or the rapid, long-range interconnection of porosity. The phenomena of grain-boundary separation and/or long-range interconnection of porosity provides an important release mechanism for fission gas that has moved out of the grains of irradiated fuel.     

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.     

MARGARET: A comprehensive code for the description of fission gas behavior

The relevant phenomena concerning stable-fission gas behavior in nuclear fuels are combined in a single model: MARGARET. This same tool can be used for base irradiations up to high burnup, ramp tests and annealing tests. The representation of intragranular or intergranular bubbles and fabrication pores is highly mechanistic. The partition of fission gas between these cavities and dissolved in the solid permits determination of swelling of the fuel. The released gas is obtained by difference between the created and retained gas in the fuel. The model has been validated against base irradiations, ramps and annealing tests of UO₂ fuel. The article presents the complete equations of the model in the base irradiation condition (Part I), followed by a detailed analysis of the behavior of a fuel irradiated up to 61 GWd/tU, extensively examined after irradiation (Part II). Part III presents the specific additional terms used for the calculation of transient and annealing conditions.     

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 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.     

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.     

A new code for predicting the thermo-mechanical and irradiation behavior of metallic fuels in sodium fast reactors

An engineering code to predict the irradiation behavior of U–Zr and U–Pu–Zr metallic alloy fuel pins and UO₂–PuO₂ mixed oxide fuel pins in sodium-cooled fast reactors was developed. The code was named Fuel Engineering and Structural analysis Tool (FEAST). FEAST has several modules working in coupled form with an explicit numerical algorithm. These modules describe fission gas release and fuel swelling, fuel chemistry and restructuring, temperature distribution, fuel–clad chemical interaction, and fuel and clad mechanical analysis including transient creep-fracture for the clad. Given the fuel pin geometry, composition and irradiation history, FEAST can analyze fuel and clad thermo-mechanical behavior at both steady-state and design-basis (non-disruptive) transient scenarios.FEAST was written in FORTRAN-90 and has a simple input file similar to that of the LWR fuel code FRAPCON. The metal–fuel version is called FEAST-METAL, and is described in this paper. The oxide–fuel version, FEAST-OXIDE is described in a companion paper. With respect to the old Argonne National Laboratory code LIFE-METAL and other same-generation codes, FEAST-METAL emphasizes more mechanistic, less empirical models, whenever available. Specifically, fission gas release and swelling are modeled with the GRSIS algorithm, which is based on detailed tracking of fission gas bubbles within the metal fuel. Migration of the fuel constituents is modeled by means of thermo-transport theory. Fuel–clad chemical interaction models based on precipitation kinetics were developed for steady-state operation and transients. Finally, a transient intergranular creep-fracture model for the clad, which tracks the nucleation and growth of the cavities at the grain boundaries, was developed for and implemented in the code. Reducing the empiricism in the constitutive models should make it more acceptable to extrapolate FEAST-METAL to new fuel compositions and higher burnup, as envisioned in advanced sodium reactors.FEAST-METAL was benchmarked against the open-literature EBR-II database for steady state and furnace tests (transients). The results show that the code is able to predict important phenomena such as clad strain, fission gas release, clad wastage, clad failure time, axial fuel slug deformation and fuel constituent redistribution, satisfactorily.     

The development of a mechanistic code on fission product behavior in the polycrystalline UO2 fuel

The current status of a mechanistic code (RTOP) on fission product behavior in the polycrystalline UO₂ fuel is described. Outline of the code and implemented physical models is presented. The general approach to the code validation is discussed. It is exemplified by the results of validation of the models of oxidation and grain growth. The different models of intragranular and intergranular gas bubbles behavior have been tested and the sensitivity of the code in the framework of these models has been analyzed. An analysis of available models of the resolution of grain face bubbles is also presented.     

The response of carbide fuel elements to fast thermal transients using the UNCLE-T-BUBE code

The response of fuel elements to fast thermal transients have great implications to the safety of LMFBR's. In this article, fission gas swelling and release, and clad stress and strain are computed for a carbide fuel element during several fast thermal transients as a function of steady stae power and percent burnup. The computations are made with the UNCLE-T-BUBE code which allows for equilibrium and nonequilibrium fission gas bubbles. In some of the transients, the code UNCLE-T-BUBE predicts fuel-clad gap closure, attended with a high clad hoop stress, whereas UNCLE-T does not. It is also found that allowing for nonequilibrium fission gas bubbles strongly affects fuel swelling and clad strain but has negligible effect on gas release.