Improvement and Verification of the START-3 code

Transcription

1 Final Report IAEA Research Contract No.: 12175/R Title of Project: Improvement and Verification of the START-3 code As a constituent of the IAEA CRP Improvement of Models Used for Fuel Behavior Simulation (CRP FUMEX II) Research is carried out in Federal State Unitary Enterprise A.A.Bochvar All-Russia Research Institute of In-organic Materials Chief Scientific Investigator: Grigori Khvostov Time period covered: January 23 September 25

2 Contents Contents Introduction Analyzing the datasets Cases 1 & 2 with Halden IFA 534 rods...5 General remarks on the dataset...5 Comments on the results as presented in Figures 2 through Case 3 (vs. 4) with Halden IFA 597, rod General remarks on the dataset...6 Comments on the results as presented in Figures 1 through Case 4 with rod 8 of Halden IFA General remarks on the dataset...7 Comments on the results as presented in Figures 13 through Case 7 with REGATE experiment...9 General remarks on the dataset...1 Comments on the results as presented in Figures 24 through Cases 14,15 with fuel rods AN3 and AN4 from the RISO III Fission Gas Project...11 General remarks on the dataset...11 Comments on the results as presented in Figures 36 through Cases 16,17,18 with rods BK363, BK365, BK37 of HBEP...13 General remarks on the dataset...13 Comments on the results as presented in Figures 52 through Simplified Cases...14 Simplified Case Simplified Case 27.2(a)...15 Simplified Case 27.2(b)...16 Simplified Case 27.2(c)...16 Simplified Case 27.2(d)...17 Simplified Case 27.3(a,b) Other activities relevant to FUMEX-II Summary and Conclusions...18 References...2 Appendix A: Tables and Figures...21 Appendix B: Development of the Fission Gas Behaviour Model in the START-3 code and its Experimental Support, Paper to International Seminar on Fission Gas Behaviour in Water Reactor Fuels, Cadarache, France, September 2 Appendix C: The dynamic model of grain boundary processes in high burn-up LWR fuel and its application in analysis by the START-3 code, Paper to the International Conference on WWER Fuel Performance, Modeling and Experimental Support, Albena-Varna, Bulgaria, September 29 - October 3, 23 Appendix D: Modelling of Thermal Mechanical Behaviour of High Burn-up VVER Fuel at Power Transients with Especial Emphasis on Impact of Fission Gas Induced Swelling of Fuel Pellets, Paper to International Seminar on Pellet-Clad Interaction in Light Water Reactor Fuels, AIX EN PROVENCE, France, March 9-11, 24 Appendix E: Approaches to Modeling of High Burn-up Structure and Analysis of its Effects on the Behaviour of Light Water Reactor Fuels in the START-3 Fuel Performance Code, WRFPM-25, Kyoto, Japan, October 25 (Accepted for further publication) 2

3 1. Introduction The activity on Improvement and Verification of the START-3 code, as a constituent of the International CRP FUMEX-II carried out under the direction of the IAEA, was conducted in accordance with the original Contract and its two Renewals, by means of analyzing the datasets from the Database for FUMEX-II chosen as the obligatory (preferential) ones for implementation by all the participants. The list of the high priority cases of the Database was defined, to common agreement of the FUMEX-II participants, during the 1-st Research Coordination Meeting of CRP FUMEX-II in Vienna, December 22 and extended further, after the second RCM in Halden, 7-1 September 24. Aside from some spadework, the entire program was implemented in three steps. At the first step, analysis was carried out with respect to - Case 4, aiming at investigation of different aspects of behavior of rod 8 from Halden s IFA-597 and - Cases 14 and 15 upon the bump tests with fuel rods AN3 and AN4 respectively, both from the RISO-III Fission Gas Project. The main objectives of the project, as well as the means of their fulfillment, were more consciously made out on this stage and set forth as follows: - Preliminary analysis of the initial data available in the FUMEX-II Database (precharacterization parameters and irradiation histories) relating to their sufficiency for calculation with the START-3 code; - Analysis of possibility to use the START-3 code as applied to the specified datasets; - Code verification making use of the widest possible range of the experimental data available; - If necessary, improvement of the code and/or refinement of the initial input data. Besides, before launching the work upon analysis of the datasets, an especial routine for converting the data for the irradiation histories represented in the Database into the format available for the START-3 code was developed (Figure 1). Afterwards, at step 2, the focus was on the seven Simplified Cases, as described in the database of FUMEX-II under the common name Case 27. This part of the work pursued numerical analysis of fuel behavior under different irradiation conditions as applied to miscellaneous types and parameters of rod design and fuel structure (Table 1). Most of the simplified cases used notional irradiation histories allowing qualitative validation of the code, although some important generalized experimental evidences were available here too. The 3

4 emphasis was placed on the kinetics of fission gas, specifically fission gas release (FGR), in connection with fuel temperature and burn-up, as the major driving forces of the swelling and release. The acquired benefits were as follows: - Verification of the numerical stability and qualitative adequacy of the results, beyond the currant scope of the code, thereby confirming possibility of its further improvement and verification; - Quantitative verification of the results against the generalized experimental data, such as Halden threshold for fission gas release, and compared to the ranges of measured magnitudes of relative fission gas release in modern PWR fuel rods; - Parametric analysis with a view to finding and ranking the factors affecting fission gas behavior; - Checking different approaches to modeling of processes in order to find out their role in fission gas behavior; - Further comparison with the results of other participants. Anyway, implementation of this stage of the program has allowed dealing with exhaustive ranges of - linear heat generation rate (LHGR) (from 1 to 6 kw/m), - calculated temperature (from about 5 o C to nearly 25 о С) and - burn-up (up to 11 MWd/kgU in a pellet) of the fuel, - parameters of fuel microstructure (grain diameter up to 75 µm). It has made this part of the project very interesting not only from the abstract point of view, but also in the sense of current and, especially, future practical needs. The latest set of calculations is the largest one of all the three steps. It has not been reported yet and is presented here, in this report, for the first time. It spans nearly all the high priority datasets, which remained after the previous two steps, including those defined during the 2-nd RCM on FUMEX-II in Halden, 7-1 September 24, such as - Cases 1 & 2 on Halden IFA 534 rods; - Case 3 with rod 7 of Halden s IFA 597; - Case 7 with the REGATE experiment; - Cases 16,17,18: upon fuel rods BK363, BK365, BK37 from the High Burn-up Effects Program. These datasets touched upon a wide range of modeling issues, specifically - Cladding deformation, that is both the change of cladding diameter and the elongation, at power transients; 4

5 - Transient FGR for standard and large-grained fuels; - Transient fuel swelling due to fission products; - Fission product distribution in a pellet; - Radial profiles of volumetric power density and burn-up; - High-burn-up fuel behavior at a base irradiation, linked tightly to HBS issues. This is the Final Report in the series of our reports to the IAEA upon activity for Improvement and Verification of the START-3 code carried out by the START-3 team in the framework of the CRP FUMEX-II. It comprises all the results of the work conducted during the whole project period, in the order of our getting through the datasets, as outlined above. 2. Analyzing the datasets 2.1 Cases 1 & 2 with Halden IFA 534 rods The main issue of this dataset was transient FGR in large-grained (rod 18) and standard (rod 19) fuels. General remarks on the dataset 1) The revised data has been used. 2) Nevertheless, the specification is sparse. Absent in the datasheets are - Fuel densification; - Open porosity; - O/U-ratio; - Both magnitudes of roughness; - Which type of grain size is given linear intercept or true size? 3) The different numbers of time points in the Halden irradiation histories of the two rods inspired some doubts, even though the same standard procedure of condensation had been used. As the major goal was the comparison, having the same time scale would be better. 4) On this step, a case sensitivity analysis relating to the effect of cladding water-side oxidation on temperature distribution was carried out. It turned out of considerable importance. Comments on the results as presented in Figures 2 through 9 Figure 2: This is calculated and measured fission gas release in both rods. For rod 18 (large-grained fuel), the agreement is very good. For rod 19, the calculated effect of smaller grain is patent, but less pronounced than that according to the data. See analysis below. 5

6 Figures 3,4: This is calculated and measured pressure of gas under the claddings of rods 18 and 19. The agreement is reasonably good. Unlike FGR, the pressure at hot stand-by conditions of rod 19 is not underestimated. Figures 5-7: This is an attempt to find out a reason for underestimating FGR in rod 19. As seen from Figures 5,6, the grain size was not the only difference. The LHGR and calculated temperature in rod 18 are lower than those in rod 19. That competes with the factor of the smaller grain. Figure 7 separates out the effects of grain size and of power. Analysis of Figures 8,9 is optional. These illustrate results of case sensitivity study for the effect of cladding oxide on temperature distribution and FGR. 2.2 Case 3 (vs. 4) with Halden IFA 597, rod 7 Major issues: Cladding elongation. Transient FGR in rod 7 compared with one in rod 8 General remarks on the dataset 1) There is a controversy about cladding oxide thickness in the datasheet (75 microns) and in a Halden report (43 microns); 2) Availability of data on LHGR for more than only 3 axial sections could be better for predicting the elongation; 3) There is no axial slipping with friction taken into consideration in the START-3 code, only sticking after the mechanical contact. However, the relaxation of cladding elongation after the first rise at the beginning of Halden irradiation was obtained through consideration of fuel creep. Comments on the results as presented in Figures 1 through 12 Figure 1: This is the calculated dynamics of cladding elongation against the result of measurement. The calculated curve qualitatively resembles the experimental one. There could be more similarity obtained through adjusting the zero level of calculated elongation. Figure 11: This is FGR in rod 7, against the one in rod 8 of the same IFA 597 (considered before). FGR in rod 7 is overestimated by a factor about 2, while the prediction for rod 8 turned out fine (see the next section in this report). Figure 12: This illustrates why a higher FGR in rod 7 than that in rod 8 is to be calculated in any case. 6

7 2.3 Case 4 with rod 8 of Halden IFA-597 The major issues of this dataset were such as - FGR in base irradiated fuel rod up to a burn-up of around 6 MWd/kgUO2; - Thermal behavior of ultra-high burn-up fuel at power transient in HBWR; - Transient FGR during re-irradiation in HBWR; - Radial profiles of local burn-up and fission products concentration; - Distribution of local fuel porosity across a pellet. General remarks on the dataset Calculation studies implied conducting the following preliminary work. 1) A content of the Database was analyzed in relation to design parameters - of the integral rod, irradiated in BWR Ringhals 1 to the peak section burn-up of 59 MWd/kgUO2 and, - re-fabricated/instrumented rod 8 IFA-597, submitted to re-irradiation in HBWR from a burn-up of 59 to about 62 MWd/kgUO2. The main conclusion drown therefrom was that the database, in general, sustains requirements to the input parameters of the START-3 code enabling - Enough precise assessment of fuel state at the end of base irradiation and, - Further comprehensive analysis of behavior of rod 8 in IFA-597. Only few items could be noticed here as omissions in the current database. For instance, cladding surface roughness (as-fabricated) was found. In this connection, the standard value of.5 microns was assumed for calculation. Besides, it would be interesting to have additional information regarding size distribution, or contribution into total as-fabricated porosity, caused by the fine intra granular pores (less than about.5 microns in size). From point of view of our models, these pores undergo relatively fast resolution under influence of irradiation (irradiation-induced densification, which is more relevant to this particular case) and/or increased temperature (thermal sintering) during early stage of base irradiation. This process leads to a certain increase of fuel-clad gap and reduction of residual as-fabricated porosity, playing a role in calculation of gap heat conductance and fuel thermal conductivity. 2) The content and format of the data on irradiation histories for the peak burn-up section of the integral rod and the whole active part of re-fabricated rod 8 IFA-597 were analyzed. It was found that the database provides enough amount information enabling comprehensive analysis by the START-3 code, although a couple of time steps in the appropriate file seems useless because of their zero duration. 7

8 Comments on the results as presented in Figures 13 through 23 The results of calculation were verified against the widest possible range of the experimental data available, although only the results for fuel temperature during the first four benign power ramps (Wl<2kW/m) of load 2 IFA-597 had been prescribed as obligatory for presentation to the Agency. One possible direction for further code improvement was proposed and justified on the basis of verification. Figures 13 and 14 illustrate conditions of base irradiation of the integral rod in BWR Ringhals1, which had been carried out previously to re-irradiation at Halden. It is seen from figure 13 that linear power was held on a relatively low level throughout base irradiation, not exceeding 22 kw/m. The calculated temperature does not exceed empiric Halden threshold of thermal-diffusion fission gas release. Thus, according to calculation, the mechanisms arising from the features of fuel structural behavior in a high burn-up pellet rim (HBS-effects) predominantly contribute to fission gas release in the integral rod, detected by puncture method at the end of base irradiation (figure 15). The calculated percentage of fission gas released from the peak burn-up section of the integral rod with a section burn-up of 59 MWd/kgUO2 is 3.67%. This result corresponds reasonably with integral value of relative fission gas release measured by puncture methods ( %) at a rod average burn-up of 52 MWd/kgUO2. Figure 16 represents the power history for experimental re-irradiation of rod 8 during loads 2 and 3 IFA-597 in HBWR. Figure 17a testifies a good agreement of calculated fuel temperature with the results of measurement as applied to the first four moderate power ramps in load 2. In the case of load 3 with a higher level of linear power, the preliminary assessment gives a marginal, but systematic, over-prediction in comparison with temperature measured (figure 17b). As analysis shows, the onset of this over-prediction immediately follows the predicted event of fast and significant release of fission gas at the beginning of load 3 (figures 18a and 19). In this connection, additional analysis has been undertaken in relation to fuel-cladding heat conductance, under assumption of decrease in the apparent magnitude of fuel surface roughness, used by calculation of a contact component of the heat-conductance coefficient. As it seen from figures 17b and 18b, such an approach allows essential alleviation of the discrepancy. Analyzing sensitivity of our model for fuel-cladding heat conductance along with the advantages arising from the improved model for fission gas behavior and fuel structure evolution, we have strong incentives to associate this finding with the process of grain sub-division, which is most pronounced in a high burn-up pellet rim. Indeed, this hypothesis seems to be reasonable since, 8

9 under conditions of intensive PCI, decreasing in sub-grain (diffusion domain) size to very low magnitude of about.1 microns can lead to gradual change in fuel surface morphology, compelling it to repeat morphology of cladding inner surface. Thus, the apparent fuel surface roughness should tend to the roughness of cladding, being probably a function of at least one variable of the model, i.e. of the effective sub-grain size at the very edge of a pellet, or more precisely of the fractional volume of emergent structure subjected to microscopic polygonization. The results of calculation and experimental data upon characteristics of fission gas release in rod 8 IFA-597 are presented on figure 19. It is seen from the figure, that calculation corresponds well with experimental value of relative fission gas release at the end of re-irradiation, measured by puncture method. Besides, calculation is in good agreement with pressure transducer measurement in relation to the event of steep increase in gas internal pressure due to fast and significant release of fission gas at the early stage of load 3, after which a credibility of appropriate measurement is lost, as the bellows had reached its pressure limit. Afterwards, attention was paid to verification of the specific models, particularly of those enabling a thorough analysis of interrelated local phenomena coupling fission gas behavior with fuel structure evolution. To this end, the PIE results of the EPMA and optical ceramography were used. As it seen from figure 2, in this particular case, the calculated radial profile of local burnup of the fuel agrees with the experimental data, providing a credible basis for model analysis with respect to the primary source term of the kinetic processes. The calculated profiles (smoothed) for the different fractions of fission gas retained by the fuel with the pertinent results of EPMA are presented on figure 21. One can see, that the calculated matrix gas retention lies in the limits of scatter of experimental points (micro-area measurement) (figure 22). Besides, it seen from figure 23, the calculated distribution of fuel porosity (excluding porosity caused by fine intra-granular bubbles) across a pellet radius corresponds agrees with appropriate experimental data. 2.4 Case 7 with REGATE experiment The major issues of this dataset were such as - Steady-state and transient FGR; - Transient cladding deformation residual change of gladding diameter; - Fission product distribution after power transient. 9

10 General remarks on the dataset 1) Very informative and transparent case, just academic. 2) As the fuel rod was of standard PWR FA 17X17 design, some parameters omitted in the datasheet, such as Length/Mass-ratio for the fuel stack, were imported from other cases. 3) There is no information on fast neutron flux in SILOE. It was calculated through the same correlation as that for PWR. But it seems to be of secondary importance. 4) The agreement with the experimental data turned out very, even surprisingly good. Comments on the results as presented in Figures 24 through 35 Figures 24,25: These show the moderate LHGR and relatively low fission gas release during the base irradiation, typical of commercial LWR Figures 26,27: These illustrate the severe power impulse in SILOE that entails a patent feedback in the calculated temperature after the power dip, caused by the effects of gaseous porosity and FGR Figures 28,29: This is the dynamics of calculated FGR during test irradiation in SILOE. As seen from Figure 17, for the impulse phase, it is typical of diffusion-controlled processes. The agreement with the measurement by puncture is very good. Figures 3,31: These illustrate deformative behavior of the fuel rod components during test irradiation in SILOE. As seen from Figure 3, the cladding is subject to significant elastic and residual strain, which is essentially enforced by transient fuel swelling due to fission products (Figure 31). Figures 32: This is another evidence of transient fuel swelling due to the grain boundary pores in the pellet center, following the intragranular swelling. Figures 33: The agreement for axial distribution of cladding permanent strain is also very satisfactory. Figures 34: This verifies credibility of the GRSWEL-A model, with respect to intragranular Xe concentration. Figures 35: This is worthy of especial notice. Verification like this is always one of the earliest steps in analysis of the datasets where any experimental evidences about radial distribution of local burn-up, such as distribution of neodymium, are available (see, for instance the comments to Figure 2 in this report). This is to make sure whether or not the DISRQV subroutine, which is used in the START-3 code for calculation of radial profile of volumetric power density in pellets, sustains a particular case of interest. In a sense, it is imposed by the fact that this routine was first developed for VVER s 1

11 neutron conditions, although it was fitted with a well developed set of input parameters allowing its application for ordinary UO2, Gd-doped fuel, since recently MOX fuel with WG-Pu etc. On the other side, through the several exercises of the FUMEX II, this one included, it was found that the agreement of the pursuant results with the experimental data are fairly reasonable for other types of LWR conditions (PWR, BWR) aside from VVER ones, unless there are some outstanding parameters, say, enrichment by U235 higher than about 5%. Might we suppose cautiously, that the appropriate features are of secondary importance? 2.5 Cases 14,15 with fuel rods AN3 and AN4 from the RISO III Fission Gas Project The major issues of this dataset were similar to those of above-presented Case 4, although with some more emphasis on distribution of gaseous fission products in the pellets after thermal transient. General remarks on the dataset The experimental rods AN3 and AN4 were re-fabricated/instrumented from the adjacent segments CB8 and CB7 of an integral ANF segmented fuel rod, irradiated in PWR BIBLIS A during four cycles to a burn-up of 4.4 % FIMA. The data files and reports available in the FUMEX-II Database give an exhaustive set of information for through analysis by the START-3 code and pertinent verification and improvement with respect to the two bump tests conducted at Riso, referred to as AN3 and AN4. As in many other cases, the only exclusion is constituted by absent data on technological roughness of the fuel and cladding, so that the standard values of.5 and 2. microns were accepted in calculation for the clad and fuel respectively. Besides, one time interval of the base irradiation history for the segment CB7 (file: basehist.an4, elapsed time: h), is characterized by the incredibly outstanding level of fast neutron flux ( n/cm2/s). Probably, this means n/cm2/s. Comments on the results as presented in Figures 36 through 51 Base irradiation in PWR BIBLIS A An analysis of fuel behavior in the course of base irradiation provides initial conditions for further numerical investigation of the bump tests, regarding state of the fuel and cladding at the beginning of bump. Thus, availability of the data on fission gas release and fission products distribution at the end base irradiation is not only beneficial for code verification, but also enables adequate analysis of the bump tests. 11

12 As it is seen from figure 36,37, the segments were irradiated under relatively moderate conditions. The calculated fission gas release in the segment CB7 is.9%. The appropriate experimental value is.2% as measured by puncture method. Therefore, calculation and experiment are in reasonable agreement in relation to the fact that more than 99% of generated fission gas, was trapped by the fuel at the end of base irradiation. As figures 38,39 show, the most of gas retained by the fuel is distributed in the grains, constituting intragranular gas concentration, with the exception of weak release into the intergranular region in the pellet center (as calculated) and remarkable depression of this concentration on the very edge of pellets, i.e. in the rim-zone (see figures 4,41). Analysis of the bump-test with the fuel rods AN3 and AN4 The bump-test with the fuel rods AN3 and AN4 was aimed at transient behavior of high burn-up LWR fuel. The impotent feature of this particular case is investigation of the influence of filling gas on thermal physical behavior of a fuel rod at power transient, as far as the rod AN3 was initially filled by bar ( о С) helium and, the rod AN4, by almost pure xenon at atmospheric pressure. The power histories of the conducted bumps are presented on figures 42,43. As figures 44(a,b) and 45(a,b) show, the code has demonstrated rather good prediction capability as applied to - fuel centerline temperature versus local linear power at the thermocouple positions of the both rods during the first ramp up to the maximum power and - the overall dynamics of this temperature throughout the bumps. However, the real cause of splashes in the dynamics of measured temperature, after some of power gains, still remains unexplained. Our speculative attempts to justify this effect on the basis of assumed unsteady-state swelling due to fast formation of intragranular gaseous porosity, which temporary decreases fuel thermal conductivity, have not led to the expected explanation. Besides, these peculiarities hardly arise from the local degradation of fuel-cladding heat conductance due to temporary trapping of the released fission gas at the fixed axial position, since the splashes take place in the rod filled by almost pure xenon, equally to that in the rod with helium as initial filling gas. Probably, the real history of local linear power had the same splashes on the edges of active fuel stack, where the thermocouples were situated. It is understood, that we should proceed with elucidation of this interesting phenomenon. Nevertheless, the calculated fission gas release agrees reasonably with the appropriate experimental values as measured by puncture method and inferred from pressure measurement (see figures 46,47) in the course of the tests. 12

13 As usual, the maximum benefit has been derived from the results of EPMA and XRF analysis upon the distribution of fission gas retained by pellets of the two experimental fuel rods after the bump-test. Figures testify evident adequacy in modeling of the fission gas kinetics in the different temperature zones across fuel pellets. 2.6 Cases 16,17,18 with rods BK363, BK365, BK37 of HBEP Major issues: Steady-state FGR at high burn-up, fission product distribution after base irradiation General remarks on the dataset 1) Units of measurement MWd/kgUO2 given in some of the data-files for burn-up are likely wrong. Through reports and calculation this is to be MWd/kgU. 2) The major features of these rods seem to be the relatively high enrichment by U235 and anomalous initial structure of the fuel (high total and open porosity). 3) On this step, a modification was made in the interface of the START-3 code with the DISTRQV routine. It allows adjusting the calculated radial distributions of volumetric power density and burn-up to the experimental data, for example those based on Nd content measured by EPMA, when enrichment by U235 is outstandingly beyond the scope of the routine. The developed procedure applies a smoothing factor to the appropriate profiles, reducing the peripheral upswing, systematically along the whole fuel stack and throughout irradiation history. It allows circumventing the encountered uncertainty in calculated radial distributions for further credible use of the available data for verification of the other models of the code. Comments on the results as presented in Figures 52 through 6 Figures 52,53: These evidences the credible starting position for further analysis, after abovementioned modification in the DISTRQV routine. The agreement seems to be reasonable simultaneously for both sections with essentially different burn-up. Figures 54,55,56: These represent the calculated FGR compared with the data. By and large, the results may be found satisfactory in consideration of complexity of the cases, even though FGR in rod BK365 is overestimated approximately by a factor 2. Vague evidences about densification and cladding oxidation could affect the HBS-assisted FGR through the effect on peripheral fuel temperature. Figures 57-6: These are the results of GRSWEL-A model coupled with the START-3 code against the data obtained from the destructive PIE. On the whole, all that seems fairly reasonable. 13

14 In Figures 59,6, there is an evidence of low-temperature release, to say the least of it, from the outermost radial position where the data on XRF is available. With substitution of Figure 6 by Figure 59 the total concentration of xenon measured by XRF remains on a meta-stable level there, while the local burn-up grows considerably. 2.7 Simplified Cases Simplified Case 27.1 Simplified Cases 27.1,27.2(a-d) focus the kinetics of fission gas, which, according to the general belief, is the functional of fuel temperature and essentially affected by fuel burn-up. Case 27.1 requires definition of the sufficient conditions for the onset of fission gas release in the pellet. 1% FGR is conventionally assumed as the criterion of the onset. These events can be presumably specified by their unique pares of the numbers centerline temperature and burn-up of the pellet. The dependence drawn by these points can be considered as - either the threshold temperature depending on the burn-up, - or the threshold burn-up (incubation period) depending on the irradiation temperature for the initialization of fission gas release in the pellet. At the suggestion of A. Turnbull, in order to obtain the desired solution, we run the code for several time-constant powers, with the determination of the pellet burn-up at which 1% FGR is reached. However, the algorithm implies some uncertainty with respect to determination of appropriate irradiation temperature. Namely, despite the constant LHGR and large gas plenum, avoiding effects of thermal feedback, there are some other processes leading to change of the predicted centerline temperature and temperature profile in the course of irradiation, including - the dynamics of pellet-cladding gap size, - degradation of fuel thermal conductivity, - evolution in radial profile of volumetric heat generation rate etc. In this connection, in order to circumvent the uncertainty, we have taken the decision to use the time-average values of centerline temperature over the periods from the beginning of irradiation till the moment of 1% FGR, although the use of current temperature at the moment of 1% FGR can, in a certain sense, be reasonable alternative to this decision. The dependences obtained for the input parameters, as specified in Table 1, are given on Figure 1. The calculations are carried out for the set of the assumptions (Table 2), regarding - the type of radial profile of volumetric heat release and fission product generation and - the effects of high burn-up structure (HBS) on total fission gas release from the pellet, accounted by the analysis. 14

15 It is noteworthy, that dependences of Models 1 and 3 deal with the total fission gas release, both from the center and HBS-zone of the pellet, whereas those of Models 2 and 4 only take into consideration the conventional, HBS-free, mechanisms of release, mainly from the central part of the pellet. As seen from the results of calculation on Figure 61 - the analytical dependencies agree reasonably with the Halden empiric threshold in the range of burn-up from about 15 to 45 MWd/kgU; - the possibility of the suppression of total gas release by the decrease of temperature is inevitably limited by low-temperature release in the HBS zone, for the burn-up higher than MW/kgU, depending on the type of the radial profile, fuel properties and some other conditions. As for the burn-ups below about 15 MWd/kgU, the predicted thresholds are quite insensitive to a chosen modelling approaches and lie markedly under the empiric curve. However, in this range of burn-up, the resistively of pellet to fission gas release, turned out much more sensitive to the parameters of fuel microstructure, namely to the open porosity and grain size (see Figure 62-64). Thus, as it seen from Figure 64, the assumed modification in these parameters leads to the increase of the incubation burn-up for fission gas release by as march as some 15 MWd/kgU, as well as to the better correspondence with the results of Halden correlation. Simplified Case 27.2(a) Here, we consider the dynamics of total fission gas release from the pellet during the notional irradiation with a constant power of 15 kw/m to a burn-up of 1 MWd/kgU. Both the flat and non-uniform (as-calculated) radial profiles of heat generation are taken into consideration. The results of calculation for fuel temperature and relative fission gas release are given on Figures 65,66 respectively. Figure 67 illustrates how the origin of fission gas release is distributed across a pellet at the end of notional irradiation, by presenting the predicted radial profiles of intragranular and total retention against the curve of cumulative generation. As it seen from Figure 67, in both cases, HBS-related mechanisms in the outer region of the pellet predominantly contribute the value of EOL release. At that, the estimated depth of propagation of HBS evidences turned out impressively large. However, this result, as well as that the EOL values of relative fission gas release are inconsistent with the relationship between fuel temperatures for the two modelling assumptions (see Figure 66 against Figure 65), are well understood in consideration of ultra-high burn-up and very low linear power density during irradiation. 15

16 Simplified Case 27.2(b) This case is just like the previous one, except that notional irradiation implies linear decrease of the power from 2 to 1 kw/m at the EOL, with a target burn-up of 1 MWd/kgU. The results of calculations are illustrated by Figures The important results of calculation for Simplified Cases 27.2(a,b) are summarized in Table 3. The analysis of the last two cases testifies numerical stability, robustness and qualitative adequacy of the code as applied to extremely high level of fuel burn-up, that confirms a possibility to use the code under the similar conditions, subject to appropriate quantitative verification. Simplified Case 27.2(c) This case deals with the preliminary estimation of the advanced PWR fuel behavior during notional irradiation in the perspective cycle of ultra-high target burn-up (14 MWd/kgU in a rod), as proposed by BNFL. The important feature of the case is the assumption of - high resistively to fission gas release due to the use of large-grained fuel pellets (75 µm grain diameter); - and the use of a low-corrosion clad material. The results of calculation for the two approaches to modeling of radial profile of power and fission product generation are given on Figures It is noteworthy, that the assumption of the flat radial profile is quite relevant to this case, as well to the three previous ones, in consideration of the high enrichment of the fuel (Table 1). The calculated distribution of the retained fission gas across the pellet taken from the central portion of the fuel stack, as applied to the end of notional irradiation, is given on Figure 74. As it seen from Figure 74, when the flat profile is assumed, the thermal diffusion in the pellet center and low-temperature release from the HBS zone on the pellet periphery contribute almost equally the total EOL release. In contrast to this, the release from the HBS zone is the predominant mode for the case of the non-uniform radial power profile, that turned out very adverse from the point of view of the predicted total gas release and pressure in the rod (Figure 73). Another noticeable result, seen from Figure 74, is the reduced storage capacity of grain boundaries in the large-grained fuel, as far as the distance between the curves of intra- and total gas retention, representing the amount of fission gas on grain boundaries (mainly in pores), is quite small. The important results of calculation for this case are summarized in Table 4. It is easy to see, that despite the assumption of large grains, the calculated gas pressure in the rod exceeds significantly the coolant pressure. Thus, among other problems, the possible clad lift-off should 16

17 be a subject of attention in the justification of fuel reliability, as applied to fuel cycles with such an ultra-high target burn-up. Simplified Case 27.2(d) Here, we investigate behavior of modern PWR fuels at irradiation to a high (from the presentday point of view) level of burn-up. The specification of the fuel rod, as well as the simplified but real irradiation history have been provided by Dr. F. Sonteimer of FANP. The important advantage of this case is the availability of the experimental data upon the ranges of measured FGR in modern PWR fuel rods, which are very useful for the code verification. The results of calculation are presented on Figures and summarized in Table 5. As it seen from Figure 77, the calculated fission gas release agrees well with the experimental data, in consideration of the generalized character of the input parameters and irradiation history. Simplified Case 27.3(a,b) The results of calculative estimates for some characteristics of CANDU-fuel under the miscellaneous operating conditions are given on Figures These results are certainly of approximately illustrative quality, as far as - this case is definitely far from the statutory scope of the START-3 code, - and also due to some omissions in the case specification (see Table 1), regarding type and properties of cladding and fuel materials, fast neutron flux and so on. 3. Other activities relevant to FUMEX-II The serious work on improvement of the START-3 code was launched in the middle of 9-th, during and after implementing the former CRP FUMEX-I. Specifically, considerable developments were acquired with regard to modeling - the degradation of material properties, such as fuel thermal conductivity, with burn-up; - the evolution in redial distribution of volumetric power density and burn-up in LWR fuel pellets; - the high burn-up fission gas release. Many of achievements resulting from this spide-work were reported to the IAEA Workshop on Implementation of the WWER version of the TRANSURANUS code and its application to the Safety Criteria [1], as well as in our paper [2]. The last one is attached here, to this report, in 17

18 Appendix B. Mentioning the paper [2] is important since it made the bridge between the two successive stages in the developing the model for fission gas behavior and evolution of fuel microstructure, in particular the semi-correlative (GRSWEL) and the more mechanistic (GRSWEL-A) lines. The advanced model GRSWEL-A for analysis of fission gas behavior and micro-structural processes in uranium dioxide fuels had been finally developed and integrated with the START-3 code just before the CRP FUMEX-II started in early 23. The model was extensively verified and validated largely thanks to FUMEX-II. Aside from the last chapter of Ref. [2] (Appendix B), the concept and important results of the advanced modelling were reported recently [3-5] in the papers to International Scientific Meetings partly or completely organized by the IAEA, in the course of implementing our project relevant for FUMEX-II. These papers are attached to the present report in Appendixes C,D,E. 4. Summary and Conclusions The reported activity aimed at a comprehensive analysis with respect to - Cases 1 & 2 with Halden IFA 534 rods; - Case 3 (vs. 4) with Halden IFA 597, rod 7; - Case 4 with rod 8 of Halden IFA-597; - Case 7 with REGATE experiment; - Cases 14,15 with fuel rods AN3 and AN4 from the RISO III Fission Gas Project; - Cases 16,17,18 with rods BK363, BK365, BK37 of HBEP; - Simplified Case 27 In all the cases where experimental data are available, a very satisfactory agreement of the calculation with the measurement was found for the important issues of analysis, such as - Fuel rod mechanical behavior at power transients, specifically cladding deformation; - Thermal behavior of high burn-up fuel at power transients; - Transient FGR for standard and large-grained fuels; - Transient fuel swelling due to fission products; - Fission product distribution in a pellet after base irradiation and thermal transients; - Radial profiles of volumetric power density and burn-up; - High-burn-up fuel behavior at a base irradiation, linked tightly to HBS issues. The improvements made are such as 18

19 - The modified consideration of the effective roughness of the fuel pellet outer surface in the calculation of the contact component of the pellet-cladding heat conductance co-efficient at the presence of HBS, which may be construed as one of the apparent evidences of bonding. - The effect of cladding oxide on temperature distribution in the pellet; - The option of adjusting the calculation for radial profiles of volumetric power density and burn-up to the data, if available. Besides, the analysis of the datasets turned out immensely useful for verification and validation of the GRSWEL-A advanced model of stable fission gas behavior and micro-structural evolutions it the uranium dioxide fuels in a wide range of thermal and irradiation conditions. At last, analyzing the seven Simplified Cases from the FUMEX-II database - Confirmed numerical stability and qualitative adequacy of the results, beyond the currant limits of verification and the confirmed area of application of the START-3 code, thereby testifying to possibility of its further improvement and verification with a view to analysis of the perspective high burn-up cycles using the advanced fuel rod design; - Testified to a reasonably good agreement with the generalized experimental data, such as Halden threshold of fission gas release and the ranges of measured values for fission gas release in modern PWR fuel rods; - Indicated high sensitivity of fission gas behavior to the initial microstructure of the fuel, which outlines possible ways for further improvement of the fuel; - Quantified importance of the HBS-related phenomena in overall behavior of fuel rods at the extended burn-up, along with the conventional HBS-free processes in the central regions of the pellets Attitude of the START-3 team to the plans upon FUMEX-3 is very positive. 19

20 References [1] G. Khvostov, Thermal physical Aspects of Fuel Rod Behavior Modelling Using START-3 Code, IAEA International Workshop on Many of achievements resulting from this spide-work were reported to the IAEA Workshop on Implementation of the WWER version of the TRANSURANUS code and its application to the Safety Criteria, Sofia, Bulgaria, December 7-9, 1998 [2] Yu. Bibilashvili, A. Medvedev, G. Khvostov, et al., Development of the Fission Gas Behaviour Model in the START-3 code and its Experimental Support, International Seminar on Fission Gas Behaviour in Water Reactor Fuels, Cadarache, France, September 2 [3] G. Khvostov, A. Medvedev, S. Bogatyr, The dynamic model of grain boundary processes in high burn-up LWR fuel and its application in analysis by the START-3 code, Paper to the International Conference on WWER Fuel Performance, Modeling and Experimental Support, Albena-Varna, Bulgaria, September 29 - October 3, 23 [4] V. Novikov, A. Medvedev, G. Khvostov, et al., Modelling of Thermal Mechanical Behaviour of High Burn-up VVER Fuel at Power Transients with Especial Emphasis on Impact of Fission Gas Induced Swelling of Fuel Pellets, International Seminar on Pellet-Clad Interaction in Light Water Reactor Fuels, AIX EN PROVENCE, France, March 9-11, 24 [5] (Accepted for further publication) G. Khvostov, V. Novikov, A. Medvedev, et al., Approaches to Modeling of High Burn-up Structure and Analysis of its Effects on the Behaviour of Light Water Rector Fuels in the START-3 Fuel Performance Code, WRFPM- 25, Kyoto, Japan, October 25 2

21 Appendix A: Tables and Figures Table 1- Simplified Case 27.1,2(a-d),3(a,b): Summary table on input parameters of Simplified Cases in FUMEX II database Parameter Simplified Case 27. Fuel rod: Fuel type 1 2(a) 2(b) 2(c) 2(d) 3(a) 3(b) BWR rod design for cross-sectional geometry 17X17 PWR FA design 15X15 PWR FA design CANDU fuel design Fuel stack length, mm Free volume, cm ) ) Length of plenum, mm - 1) Initial filling gas.5 MPa He 2.5 MPa He 2.2 MPa He 8%He+2%Ar at atm. pressure Mean gap size (diametral), µm Pellet: End geometry Flat ended Two dishes No chamfers - Two dishes Two chamfers Outer diameter, mm Inner diameter, mm (solid) (solid) (solid) 2) (solid) Enrichment by U235, wt. % Fuel density, %TD Grain diameter, µm ) 1 6) Open porosity (relative 1 2) 1 2) 1 2) 1 2) contribution to total porosity), % Densification, vol. % ) Stehiometry (O/U or O/M) 2. 2) ) Surface roughness, µm 1 2) 1 2) 1 2) 1 Cladding: Clad material Zr-2 Zr-4 Zr-4 Zr-4 2) Outer diameter, mm Inner diameter, mm Surface roughness.5 2).5 2).5 2).5 Irradiation conditions Place of operation Halden Reactor PWR PWR CANDU Reactor Target/discharge burn-up (rod ) average), MWd/kgU Maximum pellet burn-up, MWd/kgU ) ) Coolant inlet temperature, o C Boiling heavy water at Coolant outlet temperature, o C 24 o C Coolant pressure, MPa Fast neutron flux n/cm 2 /s per kw/m n/cm 2 /s per kw/m n/cm 2 /s per kw/m - 7) 1) Single axial zone with no axial form factor and large plenum is assumed 2) Assumed value 3) Gas plenum volume (excluding the volume of the spring). This value should be added by the volumes of the gap and pellet voids 4) Calculated value 5) Linear intercept 6) Method of measurement is not specified 7) The value is not specified. Low value of fast neutron flux is assumed 21

22 Table 2- Simplified Cases 27.1,2(a-d): Description of approaches to modeling of radial power non-uniformity and HBS effects used in solution of Simplified Cases Designation of approach Description Model 1 - Flat radial profile of volumetric heat rate - HBS analysis is switched ON Model 2 - Flat radial profile of volumetric heat generation rate - HBS analysis switched OFF Model 3 - Non-uniform (as-calculated) radial profile of volumetric heat generation rate *) - HBS analysis is switched ON Model 4 - Non-uniform (as-calculated) radial profile of volumetric heat generation rate *) - HBS analysis switched OFF *) This is made by assuming of the standard VVER-type profile (4.4 wt.% of U235), as a function of pellet average burn-up and dimensionless radial co-ordinates Table 3- Simplified Cases 27.2(a,b): Results of calculation estimates for important fuel characteristics during notional irradiations to a burn-up of 1 MWd/kgU Parameter Case 27.2(a) Time-constant Wl=15kW/m Case 27.2(b) Linear decreasing Wl from 2 to 1 kw/m Model 1 Model 3 Model 1 Model 3 FGR at 1 MWd/kgU, % Maximum fuel temperature during operation, o C Table 4- Simplified Cases 27.2(c): Results of calculation estimates for important fuel characteristics during irradiation in notional fuel cycle provided by BNFL Parameter Model 1 Model 3 Target burn-up, MWd/kgU 14. Maximum pellet burn-up at EOL, MWd/kgU 11. Maximum fuel temperature during operation, o C FGR at EOL, % Maximum gas pressure in the rod during operation, MPa Coolant pressure, MPa 15.5 Table 5- Simplified Cases 27.2(d): Calculated fuel characteristics for simplified, but real, irradiation history as provided by Dr. F. Sonteimer of FANP Parameter Calculation Discharge burn-up, MWd/kgU 71. Maximum pellet burn-up at EOL, MWd/kgU 77.7 Maximum fuel temperature during operation, o C FGR at EOL, % Maximum gas pressure in the rod during operation, MPa Coolant pressure, MPa

23 Irradiation parameter Time original history, which has a time derivative going to infinity at transients smoothed history Figure 1: Illustrating some spade-work Linear smoothing of original irradiation histories for START-3 analysis 12 1 Calculation: rod 18 (LG) rod 19 (SG) PIE Fission gas release, % Time, days Figure 2: Cases 1 & 2 - Halden IFA 534 rods Relative fission gas release in fuel rods 18 and 19 23

24 9 8 Gas pressure, MPa Calculated pressure at working conditions 4 Measured pressure reduced to T=232 o C Burn-up, MWd/kg Figure 3: Cases 1 & 2 - Halden IFA 534 rods Calculated and measured pressure of gas under cladding of rod Calculated pressure at working conditions Gas pressure, MPa Measured pressure reduced to T=232 o C Burn-up, MWd/kg Figure 4: Cases 1 & 2 - Halden IFA 534 rods Calculated and measured pressure of gas under cladding of rod 19 24

25 3 25 rod 18 (LG) rod 19 (SG) Linear power density, kw/m Time, days Figure 5: Cases 1 & 2 - Halden IFA 534 rods LHGR histories for rods 18 and 19 in HBWR Competitive effect of power on FGR Calculation: rod 18 (LG) rod 19 (SG) Temperature, o C Time, days Figure 6: Cases 1 & 2 - Halden IFA 534 rods Maximum fuel temperature calculated for rods 18 and 19 during irradiation in HBWR 25

26 12 Fission gas release, % rod 18 by assuming of smaller grain, just like in rod 19 rod 19 (SG) rod 18 (LG) Eff. of Grain Size Eff. of power PIE Time, days Figure 7: Cases 1 & 2 - Halden IFA 534 rods Case sensitivity analysis for effects of grain size and power on FGR in rods 18 and Effect of clad oxide layer (75 µm thick) 125 Center Temperature, o C Clad inner surface Time, days Figure 8 (optional): Cases 1 & 2 - Halden IFA 534 rods Case sensitivity analysis for effect of cladding oxide on temperature distribution in rod 19 26

27 1 8 Fission gas release, % 6 4 rod 19 (SG) with oxide in a clad rod 19 (SG) without oxide in a clad Eff. of oxide Time, days Figure 9 (optional): Cases 1 & 2 - Halden IFA 534 rods Case sensitivity analysis for effect of cladding oxide on FGR in rod 19.8 mesurement calculation Cladding elongation, mm.4 NO SLIP accounted Burn-up, MWd/kgUO 2 Figure 1: Case 3 - Halden IFA 597 rod 7 Cladding elongation for rod 7 of IFA 597 during irradiation in HBWR 27

28 3 Fission gas release, % Calculation for rod 7 Calculation for rod 8 Overprediction PIE for rod 8 PIE for rod Burn-up, MWd/kgUO 2 Figure 11: Cases 3 vs. 4 - Halden IFA 597 rods FGR in rods of IFA 597 during irradiation in HBWR 4 load 2 load 3 3 Rod 7? FGR in rod 7 = 12.6 % FGR in rod 8 = 15.8 % Max. LHGR, kw/m 2 Rod 8 Rod Cumulative time, h Figure 12: Cases 3 vs. 4 - Halden IFA 597 rods LHGR histories in rods of IFA 597 during irradiation in HBWR 28

29 25 2 LHGR, kw/m Burn-up, MWd/kgUO2 Figure 13: Case 4 - Halden IFA 597 rod 8 Linear heat generation rate vs. section average burn-up for the peak burn-up section of BWR integral rod during base irradiation in Ringhals 1 Temperature, o C Halden FGR threshold Burn-up, MWd/kgUO2 Figure 14: Cases 4 - Halden IFA 597 rod 8 Calculated fuel temperature vs. section average burn-up for the peak burn-up section of BWR integral rod during base irradiation in Ringhals

30 Fission Gas Release, % MEASUREMENT: After base irradiation in Rinhals 1: Total FGR in the full-scale rod % (mesurement) CALCULATION: Section FGR: 3.67 % (calculation) Burn-u p, MWd/kgUO2 Figure 15: Case 4 - Halden IFA 597 rod 8 Calculated section fission gas release vs. section average burn-up for the peak burn-up section of BWR integral rod during base irradiation in Ringhals 1 3 load 2 load LHGR, kw/m Burn-up, MWd/kgUO2 Figure 16: Cases 4 - Halden IFA 597 rod 8 Linear heat generation rate vs. rod average burn-up for T/C position of rod 8 IFA 597 throughout reirradiation in Halden research reactor 3

31 9 8 7 calculation mesurement Temperature, o C LHGR, kw/m (a) 9 8 calculation mesurement Temperature, o C as-fabricated roughness of the fuel surface 4 reduced roughness of the fuel surface LHGR, kw/m (b) Figure 17: Cases 4 - Halden IFA 597 rod 8 Calculated and measured temperature vs. linear heat generation rate in T/C position of rod 8 IFA 597 for (a) - the first four ramps of load 2 and (b) - at the end of load 3 31

32 Temperature, o C Burn-up, MWd/kgUO2 (a) Temperature, o C Burn-up, MWd/kgUO2 (b) Figure 18: Cases 4 - Halden IFA 597 rod 8 Calculated and measured temperature vs. rod average burn-up in T/C position of rod 8 IFA 597 during reirradiation in HBWR with (b) and without (a) an assumption regarding reduction of effective fuel surface roughness in the model of fuel-cladding heat conductance 32

33 2 Puncture mesurement - FGR=15.8% Calculated FGR % 15 FGR, % 1 5 Infered from pressure mesurement Burn-up, MWd/kgUO2 Figure 19: Case 4 - Halden IFA 597 rod 8 Results of calculation and measurement for fission gas release in rod 8 IFA 597 Burn-up, MWd/kgU Distance from pellet outer edge, mm Figure 2: Cases 4 - Halden IFA 597 rod 8 Bar-chart for calculated local burn-up and appropriate measurement by EPMA across fuel pellet in the hottest section of rod 8 IFA 597 after reirradiation in HBWR 6 33

34 1 total retention.9.8 total intragran ular retention Xenon concentration, wt.% matrix fine bubbles.2.1 pores Measurement: Distance from pellet outer edge, mm micro-area concentraition + point concentration Figure 21: Case 4 - Halden IFA 597 rod 8 Calculated and measured distribution for different fractions of fission gas retained by fuel across fuel pellet in the hottest section of rod 8 IFA 597 after reirradiation in HBWR Xenon concentration, wt.% Distance from pellet outer edge, mm Figure 22: Cases 4 - Halden IFA 597 rod 8 Calculated distribution of matrix fission gas retention and micro-area concentration of Xe measured by EPMA in the hottest section of rod 8 IFA 597 after reirradiation in HBWR 6 34

35 25 2 Porosity, % Distance from pellet outer edge, mm Figure 23: Cases 4 - Halden IFA 597 rod 8 Calculated and measured fuel porosity vs. radial position in the hottest section of rod 8 IFA 597 after reirradiation in HBWR 6 35

36 3 Linear power density, kw/m Burn-up, MWd/kgU Figure 24: Case 7 REGATE experiment Maximum linear power density during base irradiation in PWR 5 3 Fission gas release, % Measured by Kr85 activity in the field of plenum Burn-up, MWd/kgU Figure 25: Case 7 REGATE experiment Calculated FGR during base irradiation compared with measurement by Kr85 activity in plenum at EOL 5 36

37 5 Linear power density, kw/m Time, h Figure 26: Case 7 REGATE experiment Maximum linear power density during test irradiation in SILOE Temperature, o C Thermal eff. of porosity and FGR Time, h Figure 27: Case 7 REGATE experiment Calculated maximum fuel temperature during test irradiation in SILOE 37

38 15 Fission gas release, % After puncturing Time, h Figure 28: Case 7 REGATE experiment The overall dynamics of calculated FGR during test irradiation in SILOE 15 Fission gas release, % After puncturing Time, h Figure 29: Case 7 REGATE experiment The dynamics of calculated FGR in the course of power impulse 38

39 9.6 Cladding diameter, mm Residual strain Time, h Figure 3: Case 7 REGATE experiment Calculated outer diameter of cladding in axial section No.5 during test irradiation in SILOE Figure 31: Case 7 REGATE experiment Calculated pellet averaged swelling of fuel in axial section No.5 during test irradiation in SILOE 39

40 1 Porosity, vol.% Calculated emergent porosity (as-fabricated one excluded): intergranular pores intragranular bubbles 2 RIM Center Distance from pellet edge, mm Figure 32: Case 7 REGATE experiment Calculated radial distribution of fuel porosity in a pellet after test irradiation in SILOE After Cladding diameter, mm Befor Axial level, mm measured calculated Figure 33: Case 7 REGATE experiment Calculated axial distribution of cladding outer diameter before and after test irradiation in SILOE 4

41 1.2 1 Xe concentration, wt.% Distance from pellet edge, mm Experimental: Xe concentraition after EPMA, relevant to intragranular Xe Figure 34: Case 7 REGATE experiment Radial distribution of xenon in a pellet after test irradiation in SILOE Calculation: intragranular Xe Xe generated total retention Burn-up, arbitrary units Distance from pellet edge, mm Experimental: infered from Nd content, after EPMA weight everaged for experimental points according to calculation Figure 35: Case 7 REGATE experiment Radial distribution of local burn-up in a pellet after test irradiation in SILOE 41

42 Figure 36 Cases 14,15 with fuel rods AN3 and AN4 from the RISO III Fission Gas Project Average linear heat generation rate in the segment CB7 during base irradiation in PWR BIBLIS A Figure 37: Cases 14,15 with fuel rods AN3 and AN4 from the RISO III Fission Gas Project Fuel centerline temperature for power history of figure 13 as calculated by the START-3 code 42

43 Figure 38: Cases 14,15 with fuel rods AN3 and AN4 from the RISO III Fission Gas Project Radial distribution of intragranular Xe concentration across a pellet of the segment CB7 after base irradiation as calculated by the START-3 code and measured by EPMA Figure 39: Cases 14,15 with fuel rods AN3 and AN4 from the RISO III Fission Gas Project Radial distribution of total Xe concentration across a pellet of the segment CB7 as calculated by the START-3 code and measured by XRF 43

44 Figure 4: Cases 14,15 with fuel rods AN3 and AN4 from the RISO III Fission Gas Project Matrix Xe concentration in the pellet rim for the segment CB7 after base irradiation as calculated by the START-3 code and measured by EPMA Figure 41: Cases 14,15 with fuel rods AN3 and AN4 from the RISO III Fission Gas Project Total Xe concentration in the pellet rim for the segment CB7 after base irradiation as calculated by the START-3 code and measured by XRF 44

45 Figure 42: Cases 14,15 with fuel rods AN3 and AN4 from the RISO III Fission Gas Project Bump power history for the solid pellets of the fuel rods AN3 and AN4 Figure 43: Cases 14,15 with fuel rods AN3 and AN4 from the RISO III Fission Gas Project Bump power history for the bored pellets of the fuel rods AN3 and AN4 (at the thermocouple position) 45

46 (a) (b) calculation measurement Figure 44: Cases 14,15 with fuel rods AN3 and AN4 from the RISO III Fission Gas Project Fuel centerline temperature vs. local linear power at the thermocouple position of the rods AN3 (a) and AN4 (b) 46

47 (a) (b) calculation measurement Figure 45: Cases 14,15 with fuel rods AN3 and AN4 from the RISO III Fission Gas Project The overall dynamics of fuel centerline temperature at the thermocouple position of the rods AN3 (a) and AN4 (b) 47

48 CALCULATION the predicted dynamics Calculated FGR at the end of bump: 28.47% EXPERIMENTAL inferred from pressure measurement FGR as measured by puncture method: 35.5% _ our rough reconstruction of the experimental data for presumably actual release Figure 46: Cases 14,15 with fuel rods AN3 and AN4 from the RISO III Fission Gas Project Fission gas release in the rod AN3 during the bump test CALCULATION the predicted dynamics Calculated FGR at the end of bump: 37.34% EXPERIMENTAL inferred from pressure measurement FGR as measured by puncture method: 4.9% _ our rough reconstruction of the experimental data for presumably actual release Figure 47: Cases 14,15 with fuel rods AN3 and AN4 from the RISO III Fission Gas Project Fission gas release in the rod AN4 during the bump test 48

49 Figure 48: Cases 14,15 with fuel rods AN3 and AN4 from the RISO III Fission Gas Project Distribution of intragranular Xe concentration across a solid pellet of the rod AN3 after bump test as predicted by the START-3 code and measured by EPMA Figure 49: Cases 14,15 with fuel rods AN3 and AN4 from the RISO III Fission Gas Project Distribution of total Xe concentration across a solid pellet of the rod AN3 after bump test as predicted by the START-3 code and measured by XRF 49

50 Figure 5: Cases 14,15 with fuel rods AN3 and AN4 from the RISO III Fission Gas Project Distribution of intragranular Xe concentration across a solid pellet of the rod AN4 after bump test as predicted by the START-3 code and measured by EPMA Figure 51: Cases 14,15 with fuel rods AN3 and AN4 from the RISO III Fission Gas Project Distribution of total Xe concentration across a solid pellet of the rod AN4 after bump test as predicted by the START-3 code and measured by XRF 5

51 Relative burn-up BU(R p -r)/bu aver Axial level: 46. cm; Calculated pellet BU: MWd/kgU estimated from Nd content, after EPMA calculation after fitting the input parameters of DISTRQV routine Distance from pellet edge, µm Figure 52: Case 17 Rod BK365 of HBEP Radial distribution of local burn-up in a peak burn-up pellet at EOL Axial level: 14.5 cm; Calculated pellet BU: MWd/kgU estimated from Nd content, after EPMA calculation after fitting the input paremeters of DISTRQV routine Relative burn-up B(r)/Baver Distance from pellet edge, µm Figure 53: Case 17 Rod BK365 of HBEP Radial distribution of local burn-up in a lower burn-up pellet at EOL 51

52 Fission gas release, % BK Burn-up, MWd/kgU Figure 54: Case 16 Rod BK363 of HBEP FGR vs. rod averaged burn-up 7 Fission gas release, % BK Burn-up, MWd/kgU Figure 55: Case 17 Rod BK365 of HBEP FGR vs. rod averaged burn-up 7 Fission gas release, % BK Burn-up, MWd/kgU Figure 56: Case 18 Rod BK37 of HBEP FGR vs. rod averaged burn-up 7 52

53 2 Axial level: 46. cm; Calculated pellet BU: MWd/kgU Experimental: EPMA data Calculation: intragranular-total intragranular-monoatomic generated total retention Xe concentration, wt.% Distance from pellet edge, µm Figure 57: Case 17 Rod BK365 of HBEP Radial distribution of xenon across a peak burn-up pellet at EOL 2 Axial level: 14.5 cm; Calculated pellet BU: MWd/kgU Experimental: EPMA data Calculation: intragranular-total intragranular-monoatomic generated total retention Xe concentration, wt.% Distance from pellet edge, µm Figure 58: Case 17 Rod BK365 of HBEP Radial distribution of xenon across a lower burn-up pellet at EOL 53

54 3.5 Axial level: 46. cm; Calculated pellet BU: MWd/kgU 3 Relative Xe concentration, %IMA Relative radial co-ordinate R/R Experimental: EPMA data XRF data Calculation: intragranular-total intragranular-monoatomic generated total retention Figure 59: Case 17 Rod BK365 of HBEP Distribution of xenon in rim-layer of peak burn-up pellet at EOL 54

55 3.5 Axial level: 85. cm; Calculated pellet BU: MWd/kgU 3 Relative Xe concentration, %IMA Relative radial co-ordinate R/R Experimental: EPMA data XRF data Calculation: intragranular-total intragranular-monoatomic generated total retention Figure 6: Case 17 Rod BK365 of HBEP Distribution of xenon in rim-layer of a lower burn-up pellet at EOL 55

56 2 Temperature, o C empiric threshold: b=.5exp(98/t) model 1 model 2 model 3 model 4 Low-temperature release from HBS zone Burn-up, MWd/kgU NOTE: The different approaches to modelling of radial power nonuniformity and HBS effects, as described in Table 2, are used Figure 61- Case 27.1: Calculation estimates of critical conditions (centerline temperature vs. pellet burn-up) for the onset fission gas release, according to 1% FGR criterion empiric threshold: b=.5exp(98/t) open pores contribute 1 % into total porosity low open porosity Temperature, o C Burn-up, MWd/kgU NOTE: Calculation by Model 1 (see Table 2) Figure 62- Case 27.1: Calculated conditions for 1% FGR (centerline temperature vs. pellet burn-up) by assuming standard and reduced open porosity of fuel (P open -> ) 56

57 15 14 empiric threshold: b=.5exp(98/t) grain size = 15 µm grain size = 25 µm Temperature, o C Burn-up, MWd/kgU NOTE: Calculation by Model 1 (see Table 2) Figure 63- Case 27.1: Calculated conditions for 1% FGR (centerline temperature vs. pellet burn-up) by assuming standard and increased grain diameter (d g = 25 m) Temperature, o C empiric threshold: b=.5exp(98/t) Standard fuel: grain size = 15 µm open porosity = 1% of tottal value Advanced fuel: grain size = 25 µm low open porosity Burn-up, MWd/kgU NOTE: Calculation by Model 1 (see Table 2) Figure 64- Case 27.1: Calculated conditions for 1% FGR (centerline temperature vs. pellet burn-up) by assuming standard and modified initial parameters of fuel microstructure (P open -> ; d g = 25 m) 57

58 Temperature, o C center mean-volume model 3 model 1 surface Burn-up, MWd/kgU Figure 65- Case 27.2(a): The calculated dynamics of fuel temperature during notional irradiation with a constant power of 15 kw/m to a burn-up of 1 MWd/kgU 5 4 Fission gas release, % model 3 model Burn-up, MWd/kgU Figure 66- Case 27.2(a): Pellet fission gas release during notional irradiation with a constant power of burn-up of 1 MWd/kgU 15 kw/m to a 58

59 3 2.5 Xe concentration, wt.% Generation Total cont. Intragranular cont. Release G.Bound. Cont Distance from the pellet outer surface, µm a) Model 1 (flat radial profile of generation) Xe concentration, wt.% Generation Total cont. Intragranular cont. Release G.Bound. Cont Distance from the pellet outer surface, µm b) Model 3 (non-uniform radial profile of generation) Figure 67- Case 27.2(a): Calculated distribution of the retained fission gas across a pellet at the end of notional irradiation with a constant power of 15 kw/m to a burn-up of 1 MWd/kgU 59

60 Temperature, o C center mean-volume model 1 model 3 25 surface Burn-up, MWd/kgU Figure 68- Case 27.2(b): The calculated dynamics of fuel temperature during notional irradiation with a power, linearly decreasing from 2 to 1 kw/m at a target burn-up of 1 MWd/kgU 5 4 Fission gas release, % model 3 model Burn-up, MWd/kgU Figure 69- Case 27.2(b): Pellet fission gas release during notional irradiation with a power, linearly decreasing from 2 to 1 kw/m at a target burn-up of 1 MWd/kgU 6

61 3 2.5 Xe concentration, wt.% Generation Total cont. Intragranular cont. Release G.Bound. Cont Distance from the pellet outer surface, µm a) Model 1 (flat radial profile of generation) Xe concentration, wt.% Generation Total cont. Intragranular cont. Release G.Bound. Cont Distance from the pellet outer surface, µm b) Model 3 (non-uniform radial profile of generation) Figure 7- Case 27.2(b): Calculated distribution of the retained fission gas across a pellet at the end of notional irradiation with a power, linearly decreasing from 2 to 1 kw/m at a target burn-up of 1 MWd/kgU 61

62 4 Linear Heat Generation Rate, kw/m Max. LHGR Rod average LHGR Burn-up, MWd/kgU Figure 71- Case 27.2(c): Notional history of LHGR for perspective ultra-high burn-up cycle as proposed by BNFL (14 MWd/kgU rod average burn-up at EOL) Temperature, o C model 1 model Burn-up, MWd/kgU Figure 72- Case 27.2(с): Calculated maximum fuel temperature during notional irradiation with a history proposed by BNFL 3 25 Fission gas release, % model 1 5 model Burn-up, MWd/kgU Figure 73- Case 27.2(с): Calculated fission gas release in a fuel rod during notional irradiation with a history proposed by BNFL 62

63 3 Xe concentration, wt.% total content intragranular content generation Distance from the pellet outer surface, µm a) Model 1 (flat radial profile of generation) 3 Xe concentration, wt.% total content intragranular content generation Distance from the pellet outer surface, µm b) Model 3 (non-uniform radial profile of generation) Figure 74- Case 27.2(с): Calculated distribution of retained fission gas across a pellet from central portion of fuel stack, after notional irradiation with a history proposed by BNFL (17.3 MWd/kgU pellet burn-up) 63

64 5 Linear Heat Generation Rate, kw/m Max. LHGR Rod average LHGR Burn-up, MWd/kgU Figure 75- Case 27.2(d): Idealized history of LHGR for real high burn-up fuel cycle as provided by FANP Temperature, o C Burn-up, MWd/kgU NOTE: Calculation is carried out by Model 3 (Table 2), with the parameters according to this real case (Table 1) Figure 76- Case 27.2(d): Calculated maximum fuel temperature in fuel rod during irradiation with simplified real history provided by FANP 64

65 3 25 Fission gas release, % Burn-up, MWd/kgU NOTE: Calculation is carried out by Model 3 (Table 2), with the parameters according to this real case (Table 1) Figure 77- Case 27.2(d): Fission gas release in fuel rod at irradiation with a generalized real history provided by FANF, against available experimental data 2.5 Xe concentration, wt.% total content intragranular content generation Distance from the pellet outer surface, µm NOTE: Calculation is carried out by Model 3 (Table 2), with the parameters according to this real case (Table 1) Figure 78- Case 27.2(d): Calculated distribution of retained fission gas across a pellet from central portion of fuel stack, after irradiation with a generalized real history provided by FANF (76 MWd/kgU pellet burn-up) 65

66 25 6 clad lift-off Temperature, o C Burn-up, MWd/kgU NOTE: Clad lift-off is identified before the target burn-up for the powers from 4 to 6 Figure 79- Case 27.3(a): Estimated centerline temperature in CANDU fuel for series of constant powers in the range from 1 to 6 kw/m 5 6 Relative Fission Gas Release, % ,15,2, Burn-up, MWd/kgU Figure 8- Case 27.3(a): Estimated fission gas release from CANDU fuel for series of constant powers in the range from 1 to 6 kw/m 15 Total volume of gas under clad, cm 3 at STP ,15,2, Burn-up, MWd/kgU Figure 81- Case 27.3(a): Estimated total volume of gas under clad of CANDU rod for series of constant powers in the range from 1 to 6 kw/m 66

67 clad lift-off Gas Pressure, MPa 15 1 Coolant pressure ,15,2, Burn-up, MWd/kgU Figure 82- Case 27.3(a): Estimated gas pressure in CANDU rod for series of constant powers in the range from 1 to 6 kw/m 5 4 Contact pressure, MPa Clad lift-off Burn-up, MWd/kgU NOTE: This illustrates the predicted clad lift-off for the powers from 4 to 6, as a declination of contact pressure, when the pellet remains behind the clad, during their swelling and creep respectively Figure 83- Case 27.3(a): Estimated dynamics of pellet-clad contact pressure in CANDU rod for series of constant powers in the range from 1 to 6 kw/m 67

68 6 Linear Heat Generation Rate, kw/m Figure 84- Case 27.3(b): Proposed irradiation history for CANDU fuel Burn-up, MWd/kgU Pellet center 15 Temperature, o C 1 5 Pellet-average temp. Pellet surface Burn-up, MWd/kgU Figure 85- Case 27.3(b): Calculated temperature of CANDU fuel during notional irradiation 5 Relative Fission Gas Release, % Burn-up, MWd/kgU Figure 86- Case 27.3(b): Calculated fission gas release from CANDU fuel during notional irradiation 68

69 1 Total volume of gas under clad, cm 3 at STP Burn-up, MWd/kgU Figure 87- Case 27.3(b): Calculated total volume of gas under clad of CANDU rod during notional irradiation 25 2 Gas pressure, MPa 15 1 Coolant Pressure Burn-up, MWd/kgU Figure 88- Case 27.3(b): Calculated pressure of gas in CANDU rod during notional irradiation 69

70 1.5 Diametral deformation, % Burn-up, MWd/kgU (a) total linear strain of the clad Pellet swelling, vol. % Conventional empiric estimate: 1 vol.% per 1 MWd/kgU -.5 Gas-induced swelling due to increase of power -1 Eerly-of-life densification Burn-up, MWd/kgU (b) volumetric irradiation-induced swelling and densification of the pellet Gap size, µm Burn-up, MWd/kgU (c) fuel-clad gap size Figure 89- Case 27.3(b): Parameters of deformative behavior of clad and pellet in CANDU rod during notional irradiation 7

71 DEVELOPEMENT OF THE FISSION GAS BEHAVIOUR MODEL IN THE START-3 CODE AND ITS EXPERIMENTAL SUPPORT Yu.K. Bibilashvili, A.V. Medvedev, G.A. Khvostov, S.M. Bogatyr, L.V. Korystine SSC VNIINM, Moscow, Russian Federation Abstract This paper is devoted to the description of the recent developments of the fission gas behaviour model integrated with the START-3 fuel rod calculation code. The main enhancements of the classic model two-stage diffusion + "knock-out and re-coil" providing the extension of its applicability are: the model for low-temperature gas release and fuel structure evolution at ultra high burn up; the correlative model of high temperature and transient gas release due to "ductile" and "brittle" development of the fuel surface-to-volume ratio. Some lines of further development are also presented. In particular, a new model of the intragratular FG behaviour both under steady state and transient conditions is outlined. Paper to be presented to the International Seminar on Fission Gas Behaviour in Water Reactor Fuels, Cadarache, France, September 2

72 Introduction The module GRSWEL for fission gas (FG) behaviour prediction is a part of the full-scale fuel rod (FR) calculation code START-3 which incorporates the interrelated treatments of the FR mechanical and thermal physical behaviour with a view of investigation, justification and licensing of VVER type fuel under normal steady state and transient (moderate) operation conditions. The code flow chart for one-time-step numerical solution with brief description of main structural units and input-output parameters is presented on Fig.1. Input Data: - design parameters (fuel stack and cladding geometry, initial filling gas pressure and composition, fuel loading mass, cladding material properties etc.); - fuel structure properties (initial density, average grain size, densification, volumetric open porosity etc.); - time dependent histories of the average linear heat rate, fast neutron flux, cladding surface temperature, given for the set of axial segments along the fuel stack Iterative Procedure Temperature Field Calculation Fuel Re-structuring Calculation Mechanical Calculation Fission Gas Release and Gas Induced Swelling Time < EndOfStep Output Results: - fuel and cladding strain-stress condition; - cladding damage level as accumulated depth of a crack; - fuel rod elongation; - fuel temperature distribution; - internal gas pressure and composition Figure 1: Flow chart of one-time-step numerical solution The START-3 code deals with FR accident-free performance and so, incorporates a treatment of stable fission gas, neglecting the presence of unstable gases. The following factors of the fission gas influence on the FR behaviour are taken into account: Deterioration of fuel rod mechanical characteristics because of additional fuel stack volumetric instability (Fission Gas Swelling) and fuel rod internal pressure increase (Fission Gas Release); Deterioration of fuel rod thermal-physical characteristics because of fuel porosity development and dilution of initial filling gas (He, as a rule) by FG Products (Xe and Kr). The original FG behaviour model used by the START-3 code is based on solution of a "two-stage diffusion" problem for fission gas in UO 2 polycrystal fuel [1,3]. In this case, the fission gas release kinetics is determined by: 2

73 - diffusive flow of FG monoatoms to grain boundaries; - subsequent "quasi-diffusive" percolation of the intergranular gas to fuel free surface. According to the classic views [2] the model also takes into account the possibility of gas release by the a-thermal "direct recoil" and "knock-out" mechanisms. The calculation of fuel strain induced by fission products takes into account: - accumulation of solid products in fuel matrix; - content of gas monoatoms in fuel matrix; - presence of gas-filled intra- and inter- granular bubbles in fuel, under the assumption that the intragranular bubble is a small solid sphere of volume corresponding to the number of gas atoms inside (more adequate approach is presented below). Some developments of the model made in order to improve its predictionability for the extended range of FR operation conditions The outlined above approach to FG behaviour modelling is commonly known and widely used by well-developed codes. The original version of the model was integrated into the START-3 code in the middle of 8s and demonstrated a good agreement with the experimental observations as applied to quasi- steady state conditions with relatively low operational power and temperature up to a medium (from a present-day point of view) burn up. However, the further filling of the verification matrix by data for a wider range of operational conditions dealing with increase of FR target burn up, higher power generation, transient modes, etc. revealed a series of the facts of FGR underprediction in comparison with experimental data. Thereupon, this original model has been supplemented with a few sub-models providing its adequacy for the enlarged range of application. Low-temperature effects of ultrahigh burn up The PIE of high burn up LWR fuel have shown that one of the main consequences of the burn up extension is the increase of FGR (Fig.3) even under relatively moderate operational conditions (W l < 2 W/cm at EOL). The analysis has allowed to emphasize several possible reasons for this increase: Polygonization of original grains with formation of very small (around,1µm of size) sub-grains, resulting in the matrix gas depletion at the ultrahigh burn up surface of a fuel pellet; Formation of a high-porous layer on a fuel pellet periphery, resulting in additional fuel surface thermal resistance; Fuel thermal conductivity degradation in a pellet's bulk. The former two are caused by radial redistribution of local power density and burn up in a fuel pellet which leads to local ultrahigh burn up of a pellet surface (about 1 MWd/kgU and higher). The START-3 code enables to account for the above-named effects by means of addition of some new sub-models and upgrade of the existing fuel property descriptions, conventionally named a "rim-effect". 3

74 Power density and burn up redistribution To calculate dynamics of the power density and burn up radial profiles, the START-3 code uses an interpolating treatment of the results of neutron calculations, made with the GETERA code. The carried out heterogeneous calculations took into account the effects of the preferential 239 Pu accumulation at a fuel pellet surface due to the epithermal neutrons resonant capture by 238 U and also the "blockage" of 235 U and 239 Pu fission sections in a pellet central part by the presence of Gd absorbers. A number of input parameters such as initial fuel enrichment, density, section average burn up, fuel rod and fuel assembly coordinates etc., are taken into account in calculation. Grain polygonization As a physical basis of the polygonization model we have taken a qualitative consideration that ultrahigh burn up at low-temperature conditions results in the redundant irradiation damages accumulation. The increase of these point defects concentration, in one's turn, could cause their clusterization, forming some spatial, hypothetically twodimensional defects, which can behave as the sub-grain's boundaries. They are assumed to be highly packed intragranular diffusive sinks, efficiently conducting fission gas to the original grain boundary. Taking into account the saturation-limited ability of the original grain boundaries to accumulate the fission gas [3,4], these propositions could explain the fact of FGR increase at high burn up and low-temperature conditions, particularly from a pellet surface. The analysis of the FGR dependency on the FR average burn up and investigations of high burn up structure spatial distribution [5] testify that the polygonization process is a threshold function of fuel burn up and temperature. The temperature threshold of the process is caused by annealing of the irradiating damages and estimated to be around 12 o C. The empirical burn up threshold lies in the range of MWd/kgU of FR-average burn up for VVER type fuel (Fig.3). Summing all aforesaid, the sub-grain diameter d sx chosen as a polygonization parameter is calculated from the empirical rate equation:, T > T annealing n n d 1 =, T sx bu ( )n exp x bux bux d d < s bu bu bu with the initial condition d sx (t=)=d, where d sx - its current value; d s - its asymptotic value (,1 µm); d - original grain diameter; bu x - current local burn up; bu - burn up threshold (9 % h.а.); T annealing temperature threshold (12 o C); n- model's parameter determining the process rate (n=3.). While Т < T annealing the analytical solution of the given equation is: n d d bu sx = 1 exp x d ds bu The presented equation is integrated jointly with the solution of a gas diffusion problem in a sub-grain interior, solved by means of the finite-difference scheme in the corrective equivolumetric network. The presence of the a-thermal irradiation induced diffusivity D irr = k F provides the considerable gas atom flux to a sub-grain boundary: T annealing 4

75 Φ s -π d 2 sx D irr grad(c g ) r=dsx/2 on the condition that d sx d s.1µm. Considering the sub-grains as the ideal gas conductors we can express the rate of gas atoms loss into an original grain boundary as: 3 d. Φbound = Φs d sx Thus, it is clear that the proposed model can explain the experimentally observed matrix xenon depletion at the surface regions of high bun up LWR fuel. The parametric analysis of the model is illustrated by Fig.2. 1 Model Parameters: Curve No. n bu, %h.a. Intragranular Gas Release, % , 7, 2 4, 7, 3 5, 7, 4 3, 11, 5 3, 9, 6 3, 5, Local Burn Up, % h.a. Figure 2: The parametrical analysis of the grain polygonization model 16 Estimation of rim-layer's intergranular fission gas retention and porosity Since the possibility of the low-temperature matrix gas depletion has been demonstrated both by the experimental observations and by the previous modelling analysis, the further step is addressed to a grain boundary fission gas treatment. Let's estimate the relative intergranular fission gas retention q and the porosity P rim in a low-temperature fuel region of burn up bu x. Assume that the intergranular fission gas is contained by the grain face bubbles '' which population has reached the saturation limit [3,4,7] f = πc b r 2 x sin 2 '' θ, where C b bubbles' surface concentration; r x bubble's surface curvature radius. The volumetric concentration of the intergranular atomic gas is: C ''' = n x C ''' '' b = n x C b A g C ''' g /2, '' where n x number of gas atoms in a bubble; C b ''' '' and C b = C b A g C ''' g /2 - bubbles' ' surface and volumetric concentrations; C g grains' concentration; A g grain surface area. Combining the ideal gas law for the fission gas inside a bubble and the static equilibrium condition for an unrestrained bubble's size p g =2γ/r x, it can be written 5

76 2 8 / 3πγf f ( θ )rx n x =, kt where f f (θ) the factor of the accepted bubbles geometry (.186 for the lens with θ =5 о and 1. for the sphere θ=9 о ) By definition of f : C '' b = f /[πr 2 x sin 2 (θ)]. Accepting for simplicity that the specific grain boundary area A g C g '''/2 is equal to the area of highly packed system of spheres with diameter d, it can be written: 8γf ( θ ) f C ''' = 2 kt sin ( θ )d Then, for the relative intergranular retention we have the following expression: ''' C 8γf f ( θ ) f q = =, 2 24 Y ( F t ) kt sin ( θ )d o( 6, 72 1 bu x ) Xe+ Kr where bu x given in MWd/kgU. For the appropriate porosity P rim it can be written: 4 f 4 3 f ( θ ) f r ''' x Prim = Cb π r f ( ) 3 x f θ = 2 sin ( θ )d Substituting in the derived equations the surface energy γ=,6 J/m 2 and using the commonly observed rim-layer's parameters bu x = 1 MWd/kgU, T=675 K, d =1. µm, 2r x = 1. µm, we have obtained the values q and P rim for two types of the bubble geometry and for the limits of fraction coverage area f =.5 (as a prevalent magnitude) and f =.97 (as a theoretical limitation) (Table 1). Table 1:The calculated values of the rim-layer's intergranular FG retention and porosity f Lenticular bubble (θ=5 ) Spherical bubble P rim,% q,% P rim,% q,%,5 2,8 1,1 1, 3,8,97 5,2 2, 18, 7, The presented above assessments, especially the higher values on the right part of the table, are well agreed with the experimental data [7] and testify that - local gas release in low-temperature rim-layers can reach a large value (dozens of percent) and noticeably contribute to integral FGR; - rim-effect induced porosity can significantly exceed its initial value P (3-5)% and influence a thermal state of a fuel stack. Fuel thermal conductivity An ordinary expression for the VVER type fuel is modified with account for porosity increase beyond the domain of applicability of the factor (1-2.5P) [1,6]. 6

77 Discussion of the modelling results The developments presented above have noticeably improved the START-3 code predictionability, as applied to FGR calculations for the high burn up VVER fuel (Fig.6). Accounting for the effects mentioned above result in the significant increase of the predicted FGR. The generalised reasons of this increase: The thermal-physical factor associated with the additional rim-layer thermal resistance resulting in the fuel volume-average temperature increase ("squaring"-effect [6]); The structure evolution associated with the polygonization of fuel grains and the saturation of grain boundaries leading to the low-temperature gas release from a pellet periphery. The previous analysis gives rise to the conclusion that the low-temperature surface FGR can be high enough to contribute the FGR integral value. Moreover, the full-scale calculations and the experimental research show that the usual VVER fuel working conditions are, as a rule, too "smooth" to provide a significant diffusive loss of fission gas from a pellet's central part [7] (see Fig.5). In this case, the a-thermal surface gas release becomes a dominant mechanism. There is another opportunity to check the validity of this conclusion [17]. It uses the known fact that a Xe/Kr fission yield ratio is about twice higher for the Pu fission acts than for the U. Indeed, the increased content of Pu in the fuel pellet periphery makes inevitable some synchronism between dynamics of gas release and change of FR-filling gas Xe/Kr-ratio, if the fission gas is released from the surface. Figures 3 and 4 combine the appropriate available data on VVER fuel rods. The simple analysis using the polynomial approximations of the experimental dependencies reveals that the onset of the more intensive increase of the Xe/Kr-ratio takes place about at the same burn up as the FGR intensification. This fact seems to be a qualitative confirmation of the presence of surface FGR, but needs further clarification. 7

78 5 4 Gas Release, % FR-average Burn Up, MWd/kgU Figure 3: FGR vs. FR-average burn-up for VVER fuel rods Xe/Kr-raitio FR-average Burn Up, MWd/kgU Figure 4: Xe/Kr-ratio for FR-filling gas vs. FR-average burn-up for VVER fuel rods 8

79 15 Section Peak Power, W/cm Local Burn Up, h.at.% 1 5 Standart WWER condition Local Burn Up (calculation) Higher condition Local gas (Xe) retention, wt.% rim center Distance from fuel pellet surface, µm Figure 5: The experimental (Ο, ) and calculated ( ) radial profiles of the matrix Xe content in a VVER type fuel pellet (Pellet BU 5 MWd/kgU) after stepwise power increase Prediction Relative Error δ=(gcalc-gexp)/gexp, (/) FR-average Burn Up, MWd/kgU Figure 6: The relative FGR prediction error for the VVER fuel rods 9

80 The correlative model of surface-to-volume ratio increase The "equivalent spheres" sub-model used by the START-3 code in order to describe the quasi-diffusive intergranular fission gas percolation considers such a fuel inherent parameter as a fuel surface-to-volume ratio (below S/V or s) [1,3]. The following "cumulative" treatment is accepted for the calculation: s = s init + s 1 + s 2, (cm -1 ) The initial value s init is a characteristic of the specific type of as-fabricated fuel. This parameter is determined by the special correlation, accounting for the fresh fuel structure properties (density, grain size, internal free volume). s 1 and s 2 are time-dependent variables. They relate to the proposed possibility of the S/V-ratio development by means of two mechanisms: Thermal mechanism of slow development of the S/V-ratio dependent on fuel temperature and burn-up and formally associated with the "ductile" micro- cracking of fuel [8]; Transient mechanism of fast temperature-independent S/V-ratio development formally associated with the "brittle" micro- cracking of fuel [8,9]. In both cases, the following correlative rate equation is used in order to describe the S/V-ratio dynamics: d s db 1, 2 6 eff. 1, 2 = α λ1, 2 exp( λ1, 2 Beff. 1, 2 ), with zero initial conditions. dt d dt where α - model's parameter (.4); d grain size (cm); λ 1,2 rate coefficients (λ 1 =.225, λ 2 = ). B eff.1,2 are the effective burn up functions (MWd/kgU). The following empirical schemes are used to calculate the effective burn up functions. 1) In case of "ductile" growth the rate equation of the following form is integrated: 3 98., if B < 51 exp, T 273. B eff. 1 = BifB, > 51 exp T where Т- temperature (K); B- actual burn up (MWd/kgU). Thus, the process initialisation is associated with the Halden FGR threshold [12] 2) In case of the "brittle" growth the problem is: B, if σr > σlimit = 15 MPa, ( UPTransient) in pellet field r > r, where r such that σr ( r) = σθ ( r) OR if σ MPa DOWN Transient B z > σ it = eff = lim 15,( ). 2 in pellet field r < r, wherer such that σz( r) = σr( r), in all other cases where σ r,θ,z stress components in a fuel fragment. Thus, this mechanism is realised in the presence of the high enough tensile stress which are typical for thermal transient modes. Almost instant intergranular fission gas release follows the extra free surface formation. The specific rate of that release is determined from the following expression: 1

81 '' d C d ( gr ) = ( s1 + s2 ) (atoms/cm 3 /s), dt 2 dt where C '' intergranular surface concentration of fission gas atoms (atoms/cm 2 ). On the other hand, the model formally predicts the further intensification of FGR because of down-sizing of the effective intergranular diffusion cell A=3/s although some eventual inverse effects of the S/V recovery was experimentally observed [18]. Some modelling results The sub-models presented above have noticeably improved the code's predictionability as applied to FGR in fuel subjected to high temperature and transient conditions. The model's verification was carried out with the use of the results of special experiments obtained in MIR and MR research reactors [7]. In order to illustrate the efficiency of made developments, Figures 7 and 8 present the comparisons of the calculated and experimental FGR, in the fuel rods subjected to the high temperature long-term irradiation (Fig.7 - MR experiment) and to the stepwise-power reirradiation (Fig.8 MIR experiment). At present, a complete set of the START-3 code verification data consists of 92 PIE results, for FGR in standard VVER fuel and fuel subjected to special conditions. The verification has demonstrated a good enough FGR predictionability, as applied to the wide range of FR operation conditions (Fig. 9). 6 5 Max. Linear Power 4 Linear Heat Rate, kw/m 4 2 Gas Release (START-3 Calculation) Experiment Gas Release,% Max. Local Burn Up, MWd/kgU Figure 7: High-temperature FGR in the experimental FR 1 of FA 13 irradiated in the MR Research Reactor 11

82 5 Experiment 5 Linear Heat Rate, kw/m Max. Linear Power Gas Release (START-3 Calculation) Gas Release,% Time, h Figure 8: FGR in the experimental FR 41 re-irradiated in the MIR research reactor 1 92 Standard and Experimental Fuel Rods WWER-44 type standard Fuel Rods WWER-1 type standard Fuel Rods FUMEX experiment MR experiment MIR Experimens: (RAMP, FGR, LongTerm Re-Irradiation) Measurement, % Code Prediction, % Figure 9: All FGR verification data 12

83 Models under development The START-3 code development is realised within the framework of the United Research and Development Program supported by SSC VNIINM RF. In particular, at present time, an improved model for the transient analysis of fuel thermal-physical and structural behaviour with account for the Fission Products state, is under development. The modelling conception lies in the parallel solution of two independent problems: Development of a physical model and an appropriate subprogram providing calculations of the right-hand side of rate equations for time-dependent fuel characteristics; Development and parametric optimization of mathematical methods which ensure numerical stability, precision and running speed, sufficient for model's applicability. Here, we present the sub-model which is a part of the model mentioned above dealing with the intragranular fission gas behaviour. Outline of model Gas monoatoms treatment In order to calculate the mono-atomic matrix gas profile C 1 (ρ) the model solves the following diffusion equation, under assumption that a grain is spherical: C1 1 2 C1 = ρ Dg + G eff, ρ d sx /2, 2 t ρ ρ ρ with zero boundary condition С 1 (ρ=d sx /2)=, accounting for the grain sub-division parameter d sx (see above). The effective source term G eff in the above equation relates to the process of gas atoms generation, small bubble nucleation, gas atoms trapping and resolution. Multigroup analysis of non-equilibrium gas bubbles The analysis of transient behaviour of intragranular gas bubbles population is based on the approach presented in [1]. The instantaneous state of the intragranular bubbles population is determined by three numerical sequences {N i }, {B i }, {M i }, of length N b, according to a number of concerned groups. N i invariant number of gas atoms in a bubble is determined in accordance with the discretization order: ( i + 1), i = 1,...( s 1) N i =, where m and s the model's parameters. mn i 1, i = s,...n b B i time-dependent gas bubbles' volumetric concentration for the i-th group. Bi M = = r dr - time dependent r-moment of gas bubbles' size-distribution for the i-th i Ni const r group. A rate equation for B i takes into account bubbles nucleation, monoatoms absorption, bubble-bubble coalescence, resolution effects, bubble-grain (sub-grain) boundary interactions. 13

84 A rate equation for M i accounts for evolutions both of the bubbles' concentration and their grope effective size R i = M i / B i : M i Ri prediction Bi = Bi + R, i t t t B j = 1...N = const R j = 1...N = const Here R prediction i is a proposed 'new' bubble size after its formation, as a result of some process. To calculate R prediction i a number of hypothesises is used, depending on a process type (coalescence, irradiation induced resolution, etc.). The rate of the non-equilibrium size of a bubble ( P i = P i - 2γ/R i - P ext ) is calculated as: 1 i [ D C D C ] R =, where V V I i Ri D V,I - vacancy and interstitial diffusivity; C V,I difference between the point defect concentrations (dimensionless) in fuel matrix and on a bubble surface. The internal gas pressure P i is calculated from the Van der Waals equation. The total rates of B i and M i are calculated by means of the numerical technique of rate increments or decrements derived from the consecutive calculations of the process rates, accounting for their influence on B i and M i. Analysis of point defects In order to describe the non-equilibrium behaviour of gas filled bubbles and initial intragranular pores, the model incorporates the calculation of thermal-induced concentrations of point defects in the uranium and oxygen sub-lattices (C VU,C IU,C VO, C IO ) [1]. The model also contains two rate equations for the irradiation-induced concentrations of metallic point defects C V and C I. These rate equations take into account production of Frenkel pairs, point defects absorption by different types of traps (gas bubbles, initial pores, grain boundaries, dislocations), vacancy-interstitial recombination. Analysis of the as-fabricated intragranular porosity The model incorporates the multigroup rate analysis of the initial as-fabricated intragranular porosity (initially under-pressurised as a rule). The appropriate rate equations take into account vacancies irradiation injection, backward flow of injected vacancies, absorption of injected vacancies by grain boundaries, high-temperature dynamical disbalance of point defect flows, fission gas atoms absorption and resolution. The analysis of the process mentioned here enables to predict dynamics of the macro process such as fuel irradiation densification and high temperature sintering. Intragranular gas loss The model considers three mechanisms of the intragranular gas loss into the grain boundaries: - the first mechanism is caused by the diffusion flow of FG monoatoms from a grain to a grain boundary; - the other two are stipulated by the bubbles-boundary interactions due to the random and biased motion of bubbles. 14

85 FP induced volumetric strain The current value of the fuel volumetric strain associated with the intragranular process is calculated from the following expression: s N V 4π b 3 = α solid BU + v g ( C1 + N i Bi ) + Ri Bi. V int ra 1 3 s+ 1 The first term of the right-hand side is responsible for strains stipulated by solid FP in the matrix (α solid =,32 vol.% per 1% h.a. of burn up). The second term accounts for the volumetric strain due to the matrix FG monoatoms and the small gas bubbles nucleus considered as solid spheres (ν g = 85 Å 3 ). The last term is the temperature-dependent component of fission gas induced strain associated with formation and development of the intragranular bubble population and evolution of its size-distribution function. The presented above equation for the volumetric strain could easily be transformed into the rate equation form in order to be associated with the full-scale analysis of the fuel stack and cladding mechanical and thermal states. Time integration method The developed set of ordinary rate equations is integrated by means of the implicit method realised in the LSODES subprogram [13]. The parameters of the solver are optimised in order to ensure stability, precision and running speed of calculations within a stand-alone research program module. Some modelling results The improved model presented above enables the interrelated mechanistic analysis of the FG behaviour and structure evolution within a fuel grain both for in-pile and out-pile environments for steady state and fast transient (including RIA-type) conditions. Several calculational exercises demonstrating model scope and adequacy are presented below. We also suppose the analysis similar to that given below could be benefit to further models benchmarking. Steady state analysis Exercise 1: Figure 1 shows the result of calculation of intragranular fuel volumetric strains V/V against a local burn up under steady state low-temperature conditions avoiding the considerable intragranular gas loss. The calculational test demonstrates the trivial linear dependency with the constant of proportionality k=.915 vol.% per 1% h.a. of burn up. The experimental magnitude of this coefficient lies in a range of.8-1. vol.% per 1% h.a. of burn up [11,14,15]. Thus, the calculation is well agreed with the experimental data. The calculated distribution of the integral fuel swelling at EOL is presented in Table 2. The calculation shows that the swelling components have comparable values. Table 2: Intragranular Fuel Swelling Components Local Burn Up, Swelling Contributions, vol.% % h.a. Σ Solid FP Gas Mono atoms Small Bubbles ( 1 Å in size)

86 Intragranular vol. strain V/V, % Test parameters: F= fission/cm 3 /s BU EOL = 5, % h.a. d g = 2 µm T IRR = 173 K T EOL = 293 K P EXT =.1 MPa Fuel Densification "Cold" unrestrained swelling: k=,915 vol.% per 1% h.a. of burn up Burn Up, % h.a. Figure1: Intragranular fuel strain vs. local burn up at low-temperature irradiation Exercise 2: The HEDL (Hanford Engineering Development Laboratory) data [1] are used to verify the intragranular FGR calculation. The intragranular gas retention was measured for various fuel samples subjected to steady state irradiation up to burn up of 4% h.a., in different temperature conditions (from 19 to 195 K). Comparative analysis shows Intragranular Gas Release, % Main fabrication data and irr. conditions: Grain size - 23, µm Fission rate - 3, fissions/cm 3 /s Burn Up - 4,4 % h.a. Experiment Model Prediction Irradiating Temperature, K the model adequacy (Fig.11). Figure11: HEDL Data and Calculation Results for Steady-state Intragranular Gas Release Exercise 3: The next stage of the model's qualitative and quantitative validation deals with the analytical interpretation of the empirical FGR threshold (Halden FGR threshold or Vitanza curve) [12] (Fig. 12). Note that this analysis incorporates a treatment of the intragranular gas only. Thus, the calculations account for neither boundary related incubation process nor temperature and burn up non-uniformity and, so, enables the tendency assessment only. The points of the calculated dependencies T(BU) are obtained as the burn up at which the gas release-to-birth ratio (R/B-ratio) becomes a unit versus the fuel 16

87 irradiation temperature. As it is obvious from Fig.12, the model predicts the values of the temperature threshold and its burn up dependent decrease rate close to the experimental data, especially for the extended burn up when the grain boundary process are negligible from a point of view of their influence on the integral FGR rate under steady state conditions Halden FGR Threshold Temperature, o C 12 8 Calculation for Grain Size 2 µm Calculation for Grain Size 1 µm 4 Grain Boundary Saturation Zone Burn Up, MWd/kgU Figure 12: Model Verification by Halden FGR Threshold Temperature Transient analysis As applied to the transient operation conditions, at present, the model validation consists of qualitative estimation of modelling results, model's parametrical analysis, and a series of analytical tests ensuring stability, precision, and running speed of the numerical solution. Some results of the analytical tests are presented below. Exercise 4: A considerable number of the analytical tests devoted to the control of the numerical solution efficiency were carried out. Fig.13 illustrates one of the tests. The tests dealing with "saw-shaped" histories of the external variables have demonstrated excellent numerical stability and high precision of the calculations, as applied to a wide range and different rates of deviation of the external variables. The external variables for the stand-alone program module are fuel temperature, temperature gradient, fission rate, and external pressure. Exercise 5: The next analytical test (Fig.14) demonstrates the calculated response of the intragranular fission gas state on the fast, "saw-shaped" temperature cycling followed by the fuel cooling down. The dynamics of the FP induced volumetric strain inside a fuel grain is analysed both under the suggestion that a bubble submits the static equilibrium condition (doted line) and that it is a non-equilibrium sphere (solid line). The analysis shows that the account for the bubbles' non-equilibrium is considerable even at the ordinary transient times (hundreds seconds). The strain vs. time analytical dependency demonstrates such effects as a "damping" of strain pulsation during thermal cycling and "freezing" after cooling dawn. Exercise 6: The following test (Fig.15, 16) analyses the intragranular fuel strain response on the very fast, RIA-type, thermal impulse. Besides the shown above effects of "damping" and "freezing", the plots on Fig.15 demonstrate the dependency of strain dynamics from the fuel oxygen-to-metal ratio (O/U-ratio). In order to illustrate the model scope Fig.16 presents 17

88 the calculated instantaneous bubble-size distribution functions at the different stages of the temperature impulse. The upper plot shows that the calculation predicts the presence of a large number of small bubbles, around 1 Å of size, in fuel, after the base low-temperature irradiation, which is in a good agreement with the experimental observations. The bubble size-distribution functions on Fig.16 show the typical exponential tales, which also were experimentally observed in fuel SEM analysis mentioned in Ref. [16]. The analysis of the change of distribution function during the intensive temperature impulse reveals the two factors noticeably influencing on the intragranular fuel strain dynamics: - temperature induced bubble growth due to the internal gas pressure increase; - bubble-size distribution evolution due to the bubble-bubble and bubble-atom interactions which cause a shift of the function extremum to a larger size region. Conclusion In conclusion to the paper it is worth to emphasize some evident advantages of the accepted modelling conception and the model developing within its framework. The model enables the interrelated analysis of the different level physical process in the fuel, from micro- structural behaviour to macro- process, as applied to the wide range of fuel condition. The physical part of the model has a flexible arrangement, so giving capability of parametrical research and comparative analysis of different physical approaches. The structural arrangement of the model allows for further modelling development and facilitates its integration with the full-scale code. The structural isolation of the mathematical part of the model has allowed for experimental providing and parametrical optimisation of the ODE solver enough efficient to the applications within the stand-alone research program module. At present, the model gives the application capability, particularly for more adequate analysis of the FG behaviour under transient conditions, including RIA-type. 18

89 Temperature, K External Input Temperature 2 Cycles Test parameters: F= fission/cm 3 /s BU: up to 7,2 % h.a. d g = 15 µm t CYCLE /2= 1 h T MAX = 1573 K T MIN = 293 K P EXT = 1. MPa Burn Up, % h.a. 1 Gas Release Response Intragranular Gas Release, % Cycles Burn Up, % h.a. FP Induced vol. strain V/V, % Response of FP Induced vol. Strain V/V 2 Cycles Figure13: Burn Up, % h.a. A test of the efficiency of the numerical solution 19

90 25 External Input Temperature Test parameters: Temperature, K F= fiisions/cm 3 /s BU= 7.2 % h.a. d g = 15 µm O/U= 2.5 t CYCLE /2= 1 s T MAX = 273 K T MIN = 1373 K P EXT = 1. MPa Time, h 7 Intragranular Gas Release, % Gas Release Response Time, h 15 Response of FP Indused vol. Strain V/V FP Induced vol. Strain, % nonequilibrium bubbles - equilibrium bubbles Time, h Figure14: The analytical response of the intragranular FG state on the fast temperature cycling followed by the fuel cooling down 2

91 Temperature, K External Input Temperature Test parameters: F= fiisions/cm 3 /s BU= 7.2 % h.a. d g = 15 µm t IMPULS /2= 15 ms T MAX = 28 K T MIN = 1273 K P EXT = 1. MPa Time, ms 25 Response of FP Indused vol. Strain V/V FP Induced vol. Strain, % O/U=2.1 O/U= nonequilibrium bubbles - equilibrium bubbles Time, ms Figure15: The analytical response of the fuel intragranular vol. strain on the very fast, RIAtype temperature impulse 21

92 Bubbles Concentration, 1/cm 3 4e+18 3e+18 2e+18 1e+18 Initial distribution after Base Irradiating up to a burn up of 7.2 % h.a. at T= 1273 K and F= fission/sm 3 /s 2e Bubble Radius, Å t=1 ms Bubbles Concentration, 1/cm 3 1.6e e+16 8e+15 4e+15 t=15 ms t=2 ms Bubble Radius, Å Figure16: The calculated dynamics of the bubble-size distribution function during the very fast, RIA-type temperature impulse (O/U=2.1) 22

93 REFERENCES 1. G. Khvostov, Thermal physical Aspects of Fuel Rod Behavior Modelling Using START-3 Code, IAEA International Seminar, Sofia, Bulgaria, December 7-9, D.R. Olander, "Fundamental aspects of the nuclear fuel reactor elements", US Energy Research and Development Administration, R.J.White, M.O.Tucker, J.Nucl.Mat., 118(1983) "FASTGRASS: A Mechanistic Model for the Prediction of Xe Release from Nuclear Fuel Under Normal and Sever Accident Condition", NUREG/CR-584, ANL-92/3 5. M. Kinoshita et.al., J. Nucl. Mat., 252(1998) N. Kjaer-Pederson, "RIM Effect Observations from the Third RIS Fission Gas Project", IAEA, Ontario, Canada, Medvedev A.V., Khvostov G.A. et.al., " Fission Gas Products Behavior Modelling in the START-3 Code for the VVER Fuel at High Burn Up and Transient Conditions ", IAEA International Seminar, Pamporovo, Bulgaria, 4-8 October, R.J. DiMelfi, L.J. Deitrich, J. Nucl. Technology, Vol.43, May 1979, pp M. Charles, J. Simmons, C. Lemaignan, "Analysis of Mechanisms Involved in Fission Gas Release During Power Transients at High Burn Up", IAEA TCM, Preston, England, September, J.M. Griesmeyer, N.M. Ghoniem, D. Okrent, Nuc. Energy and Des., 55 (1979) A. Smirnov et al, "Behaviour of VVER-44 and VVER-1 Fuel in a Burnup Range of 2-48 MWd/kgU", International Seminar, Sandanski, Bulgaria, April, C. Vitanza et. al., "Fission gas release from in-pile pressure mesurements", Enlarged HPG Meeting on Water Reactor Fuel Performance and Application of Process Computers in Reactor Operation, Loen, Norway, Alan C. Hindmarsh, Andrew H. Sherman, "LSODES: Livermore Solver for Ordinary Differential Equations with General Sparse Jacobian Matrices", march 3, 1987 Version 14. Scientific Issues in Fuel Behaviour", OECD Documents, A Report by an NEA Nuclear Science Committee Task Force, January V.N. Golovanov et al, "Structural Changes in the VVER-1 Oxide Fuel After Irradiation", IAEA TCM, Tokyo, Japan, 28 October- 1 November, J. White, "The growth of Intragranular Bubbles in Post-Irradiation Annealed Fuel", IAEA TCM, Windermere, UK, June, K. Lassmann et al, "Recent development of the TRANSURANUS code with emphasise on high burn up phenomena", IAEA TCM, Windermere, UK, June, G. Gates, "Gas Flow Measurements on SBR MOX Fuel", IAEA TCM, Windermere, UK, June, 2 23

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95 Abstract The Dynamic Model of Grain Boundary Processes in High Burn-up LWR Fuel and its Application in Analysis by the START-3 Code G. Khvostov, A. Medvedev, S. Bogatyr FSUE VNIINM, Moscow, Russian Federation This paper reports a current status of activity upon development and validation of the advanced model of fission gas behavior and pertinent evolution of fuel structure. A special attention is paid to description and validation of the dynamic model aimed at the processes taking place on grain boundaries of polycrystalline LWR fuel based on the use of UO 2, which has been recently developed for the START-3 code. The work is carried out under support of JSC «TVEL». Introduction Modelling of stable fission gas behavior and related evolution of fuel structure is always in the foreground of activities upon development, improvement and verification of the START-3 code. This interest emanates from the remarkable effects in thermal and mechanical state of fuel rods, resulting from generation of gas atoms, mainly in process of fission, and their mobility during further irradiation. Today, it is well known that the fission gas retained by the fuel affects its swelling due to formation of intra- and inter-granular porosity, resulting in additional mechanical loading of the cladding under conditions of pellet-cladding mechanical interaction (PCMI) and, causing additional degradation of fuel thermal conductivity. Alternatively, the fission gas released into the gas plenum affects behavior of the fuel rod owing to decrease of fuel-cladding heat conductance and increase of gas internal pressure. A special attention is paid to modelling of the features in pertinent fuel behavior at an ultra-high burn-up taking place in a pellet rim (higher than about 65 MWd/kgM), as well as to the effects of elevated temperature (more about 13 o C), power transients and maneuvering modes. This paper submits the recently developed model dealing with behavior of the fission gas, after its release from the grain interior, which embraces such processes as formation of fine surface nucleuses and larger inter-granular pores, equi-axial grain growth, direct release and percolation of fission gas to the open surfaces. This model is closely linked to intra-granular behavior of fission gas and essentially overlaps modelling of high burn-up structure (HBS), as well as high temperature- and power transientassisted processes. The several examples of model validation, illustrating credibility of pertinent results as applied to a wide enough range of application, are also presented in the paper. International Conference on WWER Fuel Performance, Modeling and Experimental Support, Albena- Varna, Bulgaria, September 29 - October 3, 23

96 1. The basic elements and scope of the advanced model describing overall behavior of stable fission gas and evolution of fuel structure The dynamic model GRSWEL-A addresses the overall behavior of stable fission gas and pertinent evolution of fuel microstructure. This is the advanced version of the former one referred to as GRSWEL, earlier developed for the START-3 code [1,2]. This new model is being developed with a view to analysis of fuel behavior under in-pile and out-of-pile conditions; at extended rod- and pelletaverage burn-ups (up to about 8 MWd/kgM), as well as at an ultra-high local burn-up in a pellet rim (up to about 2 MWd/kgM); in the exhaustive range of temperature, from the magnitudes, which are typical for the coolant, to the melting point of the fuel; in the long-term modes with slow or absent variation of the parameters of fuel thermal state, as well as at fast power transients including accidents with reactivity insertion. The numerical analysis of fuel behavior is reduced to integration with respect to time, of the set of rate equations for the array of dependent variables, which describes the current state of the fuel as comprehensively as possible. The model variables are logically divided into the gropes, which take into consideration the intra- and inter-granular processes, high burn-up structure features, high-temperature assisted re-crystallization, as well as the dynamics of as-fabricated intra-granular porosity leading to early-of-life fuel densification or thermal sintering. The calculation is carried out as applied to the set of zones in a fuel pellet, characterized by approximately uniform distribution of the external variables supplied by the mechanical and thermal physical modules of the code. The external variables of the model are the local magnitudes of temperature; temperature gradient; fission rate; hydrostatic pressure, which takes into account gas pressure in the plenum and PCMI intensity. The model output provides the integral calculation with the current local and pellet average magnitudes of different components of gas retention and porosity to calculate fuel thermal conductivity, mechanical properties and pellet strain; absolute and relative fission gas release to calculate gas pressure in the plenum and fuel-cladding heat conductance; average grain size, which affects mechanical properties of the fuel (an equi-axial character of grains is assumed). In the next part of the paper we are drawing the most attention to details and validation of the model, which deals with the processes taking place on grain boundaries. This model is coupled with the model of intra-granular processes (see Ref.[3] and the second part of [2]) and, they both, provide advanced numerical analysis of fuel behavior in the integral calculation by the START-3 code. 2. The model of grain boundary processes This model embodies some of the state-of-the-art approaches to numerical description of the processes taking place on grain boundaries in irradiated uranium dioxide fuel [4]. The model is based on the considerations of diffusion theory [5] with respect to analysis of the dynamics of grain boundary pore growth/shrinkage caused by self-diffusion of the fuel material around them. Besides, this widely uses the elements of probability theory thereby accounting for stochastic nature of the analyzed phenomena. The model provides the two-dimensional analyses of grain boundary processes in terms of macrocross-sections (probabilities) and rates of their variation. It spans different types of surface interaction between fine atomic clusters, closed and vented pores, grain edges and technologically open surfaces. The currant state of grain boundaries is described by the sub-array composed of the seven dependent variables, which are as follows: C surface concentration of atomic clusters (B ); C nv surface concentration of closed pores (B nv ); F nv relative surface area covered by closed pores (F nv(b) ); C vn surface concentration of vented pores (B vn ); 2

97 F vn relative surface area covered by vented pores (F vn(b) ); N a.nv the mean number of gas atoms in a closed pore; L 2 specific absolute release of fission gas into the free volume. Note, that the appropriate dependent variables of the overall three-dimensional model, numerically integrated with respect to time, are herein enclosed in brackets. 2.1 The background structure for 2-d modelling of grain boundary processes The background structure of the model is predetermined by the use of the rationalized TKDgeometry [6], as far as the tetrakaidecahedron represents the ideal building block for compacting a close-packed array of equi-axial grains in polycrystalline uranium dioxide fuel. We should briefly remind that in this case, a grain is considered to be composed of fourteen identical right circular cones. The base of such a cone is a circle, which is hereinafter referred to as a grain face. The circumference around such a face is now referred to as a grain edge. From the equivalency between grain volumes in this and spherical geometry, the current mean radius of the grain face can be found in the following way: 1/3 4 R ( t) = tg(arccos( 1 2/ M )) R ( t) =.5558R ( t) (1) gf M g M = 14 g where M - the accepted number of faces per one grain (M=14); R g (t) - mean grain radius in the spherical geometry. Note, that the dependent variable R g (t) (see section 2.3.3) should not be mistaken for another one of the overall model, which implies the mean size of the diffusion domain used for the solution of intragranular problem and is essentially affected by the process of grain sub-division at the initial stage of HBS formation [2,3]. Since the model circumvents an explicit consideration of the capacity of grain edges to accumulate fission gas (see below), the face totality can thereby be considered as the ideal plane, composed of the close-packed array of identical circular cells of the current radius R gf. The set of interfaces between the cells constitutes the network of grain edges. The surface concentration of these cells (grain faces) can be expressed in the following way: C F 1 = πr 2 gf Thus, we have determined the background structure for further two-dimensional modelling of grain boundary processes. At that, any volumetric variable B of the overall three-dimensional model can be associated with the appropriate two-dimensional one C, which is distributed on the surface with the specific area S F /V, by the relationship S B = C V F (3) The total specific surface area of grain faces (cm 2 /cm 3 ) can be found from the equation S 14 3 (4) F V tot = πr 2 2 gf 4πR 3 g and, at the same time, is considered as the sum of open and closed surfaces S S S (5) F V tot F = V open F + V closed The open surface presumably consists of the surface of as-fabricated open pores plus a certain gain due to the early-of-life fragmentation of fuel pellets. This value is assumed to be a homogeneous, invariant characteristic of the fuel and calculated with the use of the special correlations. The initially closed surface of fuel grains represents the working area for the different types of interactions resulting, first, from primary generation of the atomic clusters and closed pores, and then, from growth of the established closed pores. The model analyzes these interactions by assuming that the (2) 3

98 appropriate events are randomly assigned, statistically independent and distributed homogeneously throughout the imaginary plane of grain faces. 2.2 Other objects of modelling Atomic clusters The starting position of the model is that all the fission gases arriving at the surface of fuel grains immediately contribute to the dynamically equilibrium population of atomic clusters, except for cases when they are instantly trapped by either technological open surface, or edges, established pores, etc. The cluster is considered as the solid sphere composed of n gas atoms. The number n is the empiric parameter of the model, which is accepted to be equal to The mean radius r xno of the cluster is calculated from the equation: 4 3 r = n ν (6) 3 π xno g where ν g the volume occupied by one generalized atom of fission gas. The dependent variable of the model characterizing a current state of the atomic clusters is their surface concentration С (t). The initial condition for this variable is always zero: С () >, with the exception of cases when we use the option of re-start of calculation. In this way, the surface concentration of atomic clusters rather quickly goes to the saturation limit, which corresponds to a fractional cover of 25%. At that, the probabilities of instant interactions between the clusters grow rapidly. These interactions are treated as the cause of primary formation of closed pores on grain boundaries. Closed pores In case of non re-crystallized fuel structure, the lenticular shape is attributed to all the pores formed on the grain boundaries (Figure 1.a). The pore parameters taken into consideration by the model are as follows: - Semi-dihedral angle θ, such that γ gb (7) θ = arccos 2γ f where γ f, γ gb - fuel-gas and fuel-fuel surface energies respectively; - Radius of pore surface curvature r f ; - Mixed value r x =r f sinθ, which means projected pore radius. If one of, or both mechanisms of fuel re-crystallization (HBS formation and high-temperature grain growth) taken into consideration by the model, takes place, the spherical configuration is attributed to the certain fraction of the total number of grain boundary pores (Figure 1.b,c). In case of high-temperature assisted grain growth (Figure 1.b), the above-mentioned assumption is justified on the basis of the considerations, which are as follows. The increase of the mean grain radius leads to the evident decreasing in their specific surface area and, most likely, takes place at the expense of the closed surface of fuel grains (see Eqs.4,5,31). At that, all the fission gases, previously accumulated on this surface, including those contained in the closed pores, are assumed extracted from the disappearing area to the free volume of the fuel rod (see the last Eq.32 in Sec.2.3.3). Meanwhile, the remaining pores, which are less affected by the process of grain growth, are presumably situated in the points of four grain meeting, that is in the corners [6] of fuel grains. Their shape broadly approximates the sphere. 4

99 Pores on original grain faces Pores in garin Corners Pores in HBS - zone r x θ r x r x r f r f r f Incipient islands of sub - divided fuel (a) (b) ( с ) (а)- lenticular-shaped pores in non re-crystallized fuel; (b)- high-temperature induced re-crystallization leads to increase of the relative number of the pores in the grain corners, which are approximated by the spherical geometry; (c)- pores, partly or completely encompassed within islands of HBS, can actually possess the irregular configuration, resulting from the randomly assigned process of grain subdivision. However, for the sake of simplicity, they are considered as sphere-shaped NOTE: In all cases, the pore projection is assumed confined to the surface of the original grains Figure 1: The accepted pore geometry in original and re-crystallized fuel In case of HBS, the qualitative model of the morphological evolution of grain boundary pores is illustrated by Figure 1.(c). The most impotent assumption here is that all pertinent processes including pore formation, change of their size and effective geometry, different types of tangential interaction, are confined to the certain vicinity of the original grain boundaries. The thickness of the appropriate layer is limited either by the doubled depth of propagating of the fuel sub-division process from the surface up to the center of the grain, or by the normal dimensions of the largest pores. It is especially important, that in all cases, the pore projection is assumed confined to the surface of the original grains, that is to the places of their origination, throughout irradiation period. It is worthwhile mentioning, that the predominant role of the original grain boundaries in origination of HBS is confirmed by state-of-the-art experimental data, especially by those relating to the characteristics of high burn-up structure in the large-grained fuel, where the in-homogeneous distribution of fuel porosity across original grains is absolutely evident (see for instance figure 11 in [15]). Note, that in both above-mentioned cases, the transition to the spherical geometry of pores is the natural response to the decreasing in fuel anisotropy accompanying these two types of fuel restructuring. The mean volume of the pore is thereby calculated in the following way rx V = r k = k (8) nv 3 π f v π 3 3 sin θ k = k v (1 ε ) + ε ; v where v [ ] ε - overall measure of fuel re-crystallization (see Eq.35); k v =1-3cos(θ)/2+cos 3 (θ)/2=.186 at θ=5 о geometric factor relating volume of lenticular pore to sphere. Van der Waals equation of state is used for the gas in closed pores Pg. nv 2 ν + a Vnv + νb = νrt V ( ) 2 nv where N A,R, a, b - constants; ν=n a.nv /N A ; N a.nv the mean number of gas atoms in pore; T temperature, P g.nv gas pressure. (9) 5

100 In order to describe the current state of closed pores the model uses the set of dependent variables, which is as follows: N a.nv the mean number of gas atoms in a closed pore; C nv surface concentration 2 of closed pores; F nv = π r x C nv relative surface area covered by closed pores. The initial conditions are herein as follows: N a.nv ()= 2n ; C nv (). The initial magnitude of pore projected radius r x () is determined from the condition of static equilibrium 2γ f sinθ (1) P g. nv = + Ph r x where P h effective hydrostatic pressure. Vented pores The model treats any mechanical contact of the established closed pore with the grain edge, which can take place in the course of pore growth, as origination of the vented pore. At that, all the fission gas collected in this pore is assumed immediately released into the free volume of the fuel rod. The further interactions of the growing closed pores with the already established vented those lead to increase of the relative surface area covered by vented pores. The model analyzes behavior of vented pores by assuming that they are always effectively lenticular (k v =k vo ); gas pressure in the vented pores is equal to zero, so that they always shrink under the influence of capillarity and hydrostatic pressure; their interactions with the other objects are randomly assigned, statistically independent and distributed homogeneously throughout the imaginary plane of grain faces. The dependent variables used by the model to describe the current state of vented pores are as follows: C vn surface concentration of vented pores; F vn = π r x(vn) 2 C vn relative surface area covered by vented pores. The initial conditions are determined as C vn () ; r x(vn) ()= r x (). 2.3 The rate equations of the model The current total rates of the dependent variables are calculated by summarizing of the contributions resulting from the processes considered below The instant processes controlled by the flux of inra-granular gas arrival The flux of intra-granular gas arrival at the grain boundary, in the accepted two-dimensional treatment, is 1 SF (11) J g = L1 V tot dl 1 dt where L - volumetric rate of intra-granular gas loss (atoms/cm 3 /s) [2]. 1 Hence, for the volumetric rate of fission gas release due to direct arrival at the open surface one can write S (12) L 2 direct F = J g V open For the primary event of gas cluster formation the model considers possibility of instant interactions of the cluster, which is being generated - with another one earlier generated on the closed surface, attributing to this event a macro-crosssection (probability) S n =C π(2r xno ) 2 ; - with other i clusters by assuming that these events are statistically independent, incompatible and attributing to them macro-cross-sections S n i, where i= 2, n max = N a.nv /n 1; - with a closed pore, characterizing this event by macro-cross-section S 1 =C nv π(r x +r xn ) 2 ; 6

101 - with a grain edge, attributing to this event a probability S 2 =C F π(r 2 gf -(R gf -r xn ) 2 ); - with a vented pore, attributing to this event a macro-cross-section S 3 =C vn π(r x(vn) +r xn ) 2. The resulting surface rate of cluster generation R n and the primary estimate for the surface rate of closed pore formation R b could be expressed in the following way nmax n J max g i i = + +, (13) Rn (1 S1 S2 S3) 1 ( i 1) Sn wn ( i) Sn n i= 1 i= 1 J nmax g i (14) R b = (1 S 1 S 2 S 3 ) wb( i) S n n i= 1 where the weighting factors w n(i) и w b(i) are determined as suggested in [7] wn ( i) n + wb( i) N a. nv = n ( i + 1) (15) w n + w 2 n( i) b( i) N 2 a. nv = n 2 ( i + 1) for i=1, n max Finally, for R n and R b one can write J g (1 S1 S Rb = N ( N R S ) n 2 2Sn (1 Sn ) nmax Sn (1 S 2 ) (1 Sn ) 2n + (1 S + 1) max + nmax ( n 3 2 max a. nv a. nv n ) n n ) J g N. R a nv b (17) n = n The terms of rate equations responding to the generation of gas clusters on the closed surface of the fuel grains can be written in the following way: C = Rn n C nv = R F n nv n b b (18) = R πr N = a. nv n 2 x J S g C nv 1 SF L 2 = J g ( S2 + S3) n V closed In relation to the primary generation of closed pores with the rate R b, the model considers the set of compatible and incompatible events (see Figure 2), accounting for interactions with already established closed pores (index 1); grain edges (index 2); vented pores (index 3). (16) Using the accepted nomenclature, for the macrocross-sections of appropriate interactions one can write S 123 =S 1 * S 2 * S 3 *, S 12 =S 1 * S 2 * -S 123, S 13 =S 1 * S 3 * -S 123, S 23 =S 2 * S 3 * -S 123, (19) S 1 =S 1 * -S 12 -S 13 -S 123, S 2 =S 2 * -S 12 -S 23 -S 123, S 3 =S 3 * -S 13 -S 23 -S 123, Where the prior probabilities are as follows S 1 * =C nv π(2r x ) 2, S 2 * =C F π(r gf 2 -(R gf -r x ) 2 ) (2) S 3 * =C vn π(r x +r x(vn) ) 2 7

102 S total set of events Area 1 - interaction with closed pore; Area 2 - interaction with grain edge; Area 3 - interaction with vented pore Areas 12,23,13,123 - appropriate compatible interactions S - (1 * 2 * 3 * ) generation of new pore Figure 2: Diagram for geometric probabilities of instant interactions at primary generation of closed pore on grain boundary In terms of the above determined macro-cross-sections, the contribution of instant interactions accompanying the primary generation of the closed pores, can be expressed in the following way: = R ( S + S + S + S + S + S ) 23 C nv b S b 2 F ( ) nv = Rbπ rx S1 + S2 + S3 + S123 + S12 + S13 + S23 b Rb Na. nvs1 (21) Na. nv = b Cnv SF L 2 = Rb Na. nv( S2 + S3 + S123 + S12 + S13 + S23) b V closed The processes controlled by pore growth/shrinkage The governing value of the appropriate equations is the rate of pore projected radius r x, which takes into account the mixed surface-volume self-diffusion of the fuel material around pores, as well as the consequences of fuel re-structuring. Its relation to the rate of pore volume can be established by implicit derivation of Eq.8: dv 4 dr = π 2 x k 3r (22) dt 3 v x dt In case of closed pores, the general form of rate equation for pore volume used by the model is as follows: dv dv dv (23) dt nv = (1 ε ) + dt ε dt lens sphere where dv (23.а) dt dv dt lens sphere ( πr sin θ ) [ D C D C ] = 2 f v v i i + 2πwF Ds C r = f 2 1 ( rf ) [ Dv( HBS ) Cv Di Ci In Eqs.23.а and 23.b C C v, i vu, iu = Ω C v, i = ΩC vu r f vu F( λ) 4π ] (23.b) pω + Cvu, i u 1 exp m kt pω, iu 1 exp m kt ; (24) ; (25)

103 p=p g.nv -2γ f /r f -P h ; C v,i - irradiation-induced concentration of point defects; C vu,iu - thermodynamic equilibrium concentration of point defects; w F = 2r f (1-cosθ) - accepted effective width of grain boundary; F(λ) - function of boundary conditions for surface self-diffusion; D v,i - volumetric diffusivity of point defects; D s - surface self-diffusivity (for flat surface); D v(hbs) =f(d s,d v,ε s ) - effective volumetric self-diffusivity enhanced in HBS ε s - specific volume of HBS [8]; Ω - atomic volume for UO 2. In case of vented pores the model uses a simplified version of Eq.23: ( πr sin θ ) [ D C D C ] dvvn dv 1 = 2 2πw D C dt = f v v i i + F s vu dt lens rf F( λ) The rates of the considered macro-cross-sections due to growth of closed pores can be found by means of derivation of Eqs.19: ds 123 /dt=(ds * 1 /dt)s * 2 S * 3 +S * 1 (ds * 2 /dt)s 3 +S * 1 S * 2 (ds * 3 /dt), ds 12 /dt=(ds * 1 /dt)s * 2 + S * 1 (ds * 2 /dt)-ds 123 /dt, ds 13 /dt=(ds * 1 /dt)s * 3 + S * 1 (ds * 3 /dt)-ds 123 /dt, ds 23 /dt=(ds * 2 /dt)s * 3 + S * 2 (ds * 3 /dt)-ds 123 /dt, (27) ds 1 /dt=ds * 1 /dt-ds 12 /dt-ds 13 /dt-ds 123 /dt, ds 2 /dt=ds * 2 /dt-ds 12 /dt-ds 23 /dt-ds 123 /dt, ds 3 /dt=ds * 3 /dt-ds 13 /dt-ds 23 /dt-ds 123 /dt. where (26) ds 1 * /dt=c nv 8πr x (dr x /dt), ds 2 * /dt=c F 2π(R gf -r x ) (dr x /dt), (28) ds 3 * /dt=c vn 2π(r x +r x(vn) ) (dr x /dt). In order to account for sweeping of gas clusters, it is introduced additionally: ds 1 /dt=c nv 2π(r x +r xn )(dr x /dt). (29) Now, for the terms of rate equations, responding to the growth/shrinkage of closed and vented pores, one can write: C = b. growth ds1 C dt 1 ds1 ds12 ds13 ds123 ds2 ds3 ds Cnv = Cnv b. growth 2 dt dt dt dt dt dt dt F nv b. growth 4 * 1 ds 1 2 = + πrx C dt ds2 1 ds Cvn = Cnv + dt dt F b. growth 2 nv b. growth 12 dr x( vn) ds13 1 ds = Cvn 2πrx ( vn) + πrx ( vn) Cvn + Cnvπrx + dt b. growth 2 dt dt ds12 ds13 ds123 ds2 ds3 ds SF = CnvNa. nv dt dt dt dt dt dt V vn b. growth 2 L2 23 b. growth N a. nv b. growth nc = C nv ds dt 1 L Equi-axial grain growth b. growth + N a. nv Cnv b. growth C nv The dynamics of equi-axial grain growth is analyzed on the basis of considerations presented in Ref. [9,1]. The modified formula, currently accepted by the model, disregards explicit effects of burnup, at that, accounting for the blockage of the process on the open surface of the fuel: dr g Eg. growth 1 1 S S (31) dt k exp Rg R F V F V 1 = 1 kt g.max open tot 23 closed 123 (3) 9

104 where k = 2 R g. max k1 exp T k,k,k 1,k 2,E g.growth constants. As applied to the volumetric variables of the overall three-dimensional model, the rates resulting from this process can be written in the following way: d S S dr B F F 1 g = C = C g. growth dt V closed V tot Rg dt d S S dr B F F 1 g nv = Cnv = Cnv g. growth dt V closed V tot Rg dt d S S dr F F 1 g Fnv( B) = Fnv = Fnv g. growth dt V closed V tot Rg dt d S S dr B F F 1 g (32) vn = Cvn = Cvn g. growth dt V closed V tot Rg dt d S S dr F F 1 g Fvn( B) = Fnv = Fnv g. growth dt V closed V tot Rg dt d S S dr L F F 1 g 2 = ( Cn + CnvNa. nv) = ( Cn + CnvNa. nv) g. growth dt V V R dt closed Here, we have formally taken into consideration the condition of total gas amount conservation as applied to the fission gas on the grain boundaries and in the free volume of the fuel rod The total set of rate equations of the model Summarizing all above-mentioned considerations, for the current gross rates of the threedimensional dependent variables responsible for grain boundary behavior, one can write: db S F = C + C + B dt n b. growth V closed g. growth db nv S F = Cnv + Cnv + Cnv + Bnv dt n b b. growth V closed g. growth dfnv( B) S F = Fnv + Fnv + Fnv + Fnv( B) dt n b b. growth V closed g. growth dn a. nv = Na. nv + Na. nv + Na. nv dt n b b. growth db dt df vn = C vn( B) dt vn b. growth SF V closed + B (33) = F dl 2 = L2 dt vn b. growth direct + L2 SF V n vn g. growth + Fvn( B) closed + L2 b + L2 g. growth b. growth + L2 g. growth Here, the above accepted nomenclature is used, that s to say index n means processes resulting from cluster generation; index b spans consequences of pore formation; index b.growth deals with processes arising from pore growth or shrinkage; index g.growth relates to equi-axial grain growth; index direct implies direct release of fission gas through open surface. 3. Gas-induced porosity, fuel swelling and fission gas release Making use of above introduced nomenclature, for the fuel porosity confined within original grain boundaries, one can write: PF = Bnv π rf [ kv(1 ε) + ε ] + Bvn πrf ( vn) kv + P (34) F. as fabricated 3 3 tot g 1

105 On the right-hand side of Eq.34, the first term corresponds to the porosity due to closed pores; the second term represents the contribution of the vented pores; the third one is the as-fabricated intergranular porosity. The overall measure of fuel re-crystallization is calculated as suggested in Ref. [8] 1 ε = (1 ε (35) i i ) where i identifies the type of fuel re-structuring, so that i=1 when this is HBS; i=2 for equi-axial grain growth. The expression used for calculation of the fission-product-induced swelling of the fuel is as follows: V (36) = Ε fuel ( PF PF. as fabricated ) + Bnν g + Ε int ra V where the first term corresponds to the swelling due to grain boundary pores; the second term represents the gas clusters on the boundaries; the third one is the intra-granular swelling [2]. The relative fission gas release is calculated via the dependent variable L 2, as a ratio of release to cumulative generation: f ( t) = fr V fuel V fuel t L r d 2(, ) τ dv t G fg r d (, τ ) τ dv τ (37) where G fg (r,τ) is the gas generation density, and integration is carried out with respect to the total volume of the fuel stack V fuel and irradiation time t. 4. Discussion of modelling results As evident from the previous section, the grain boundary porosity indicates rather explicitly the overall result of modelling with respect to the inter-granular state of the fuel. In this connection, the results of Post Irradiation Examinations (PIE) incorporating Quantitative Image Analysis (QIA) of fuel grain boundary porosity, as well as pore size- and spatial distribution are a priory considered as a basis for validation of the model presented above. Besides, since the processes on grain boundaries are closely linked to those, which take place inside grains, whereas these two modes essentially affect integral behavior of fuel rods, additional experimental data on characteristics of gas retention and release, fuel swelling, etc., are encouraged. 4.1 Out-of-pile annealing of irradiated PWR fuel samples at high-temperature The experiment of I.Zacharie and co-workers was aimed at investigation of out-of-pile structural behavior and fission gas release in the fuel samples, extracted from the pellets after their irradiation in PWR, during two cycles [11,12]. The results of this investigation are of great interest for validation of the model used as a stand-alone unit, as far as they fulfill almost all of the desires mentioned above. The main characteristics of the fuel used in the experiment, as published in [11,12], are given in Table 1. Table 1: Main characteristics of fuel used in experiment of I.Zacharie at al. Characteristic Meaning Type of fuel UO2 O/U ratio 2.5 (assumed) Average grain size (µm) 9.3 Density (%TD) Open porosity (% of total as-fabricated porosity) 1 (assumed) Burn-up (MWd/kgU) 25 Fission gas release Almost all the fission gas generated is presumably distributed uniformly in the matrix 11

106 Figure 3 represents the calculated dynamics of un-restrained inter-granular swelling (a), mean projected radius of pores (b) and fission gas release (c) against the appropriate experimental data, for the samples exposed to temperature varying in the range from 1545 to 1715 o C. As comparison shows, the calculation agrees reasonably with the experimental data. This testifies an adequacy of our modelling as applied to these important characteristics of grain boundary behavior at the absence of irradiation. Besides, one can suppose, that the successful prediction of grain boundary parameters has become possible only on the basis of broadly credible analysis of intra-granular processes, accounting for the known difficulties in modelling of out-of-pile release [13]. Regarding the dynamics of fission gas release at the highest level of temperature (1715 о С), the following is noteworthy. The calculation, carried out by assuming of zero temperature gradient throughout the exposure, corresponds well to the lower border of the field of experimental values, which is, however, characterized by rather large scatter of points. In Ref. [11], this scatter is assumed to be a result of the uncertainty in temperature controlling (±2 о С). On the basis of sensitivity analysis (see Figure 4), we would offer one more possible cause, that s the unforeseen non-uniformity of temperature distribution (temperature gradient), especially at the initial heating of the samples. For this, relatively high, level of temperature, the temperature gradient could remarkably affect release of the intra-granular fission gas owing to the biased motion of the gas inflated bubbles. (a) (b) Experimental points: о С; о С; о С (c) Figure 3: The calculated dynamics of unrestrained inter-granular swelling (a), mean projected radius of pores (b) and fission gas release (c) against appropriate experimental data for samples exposed to temperature varying in the range from 1545 to 1715 o C 12

107 Figure 4: Sensitivity of fission gas release to temperature gradient at annealing temperature 1715 о С, as calculated by the model 4.2 Analysis of High Burn-up Structure features Numerical analysis of the set of features in LWR fuel behavior, conventionally referred to as rimeffect, or more preferably, High Burn-up Structure (HBS) effect, is the tremendously important element of overall justification of high burn-up fuel reliability. Therefore, any model of fuel behavior, integrated with a fuel performance code, must pay especial attention to analysis of this behavior at ultra-high burnup (higher about 65 MWd/kgM) and relatively low temperature (less about 1 o C). Figures 5,6 briefly illustrate an adequacy of our modelling with respect to the matrix effects taking place in HBS zones [3], in spite of the fact, that this is somewhat out of the scope of this paper. However, this constitutes a credible starting position for further analysis of the processes caused by significant depression of intra-granular gas concentration. The important results of model validation relating to analysis of the processes resulting mainly from the lost of fission gases, previously accumulated by the matrix (development of fuel porosity and fission gas release), are presented on Figures Note, that analytical dependencies given on Figures 8,1-12 were obtained by assuming of the standard WWER fuel parameters and fuel temperature, which is low enough to prevent any annealing of the irradiation-induced damages considered by the model as a primary cause of HBS formation [2,3]. That is to say, the X-values of the appropriate plots are in general the effective local burn-ups in the HBS zone. Figure 7 represents the calculated gain of fuel pellet rim porosity versus pellet average burn-up, for the typical WWER irradiation conditions. The result of calculation is presented against the appropriate experimental points [3]. As comparison shows, there is a reasonable agreement between the analytical dependency and experimental data. Besides, the result of calculation seems credible enough with respect to the predicted range of the projected radius of pores formed in a pellet rim (Figure 8), making mention that the appropriate experimental estimates vary in the range from.25 to.5 microns, as published in [16]. As evident from Figures 9,1, according to both experiment researches [16,17] and modelling, the significant increase of fuel porosity is eventually accompanied by the remarkable release of fission gas into the free volume, when the local burn-up at the pellet rim exceeds a value of about 75 MWd/kgU. At that, the calculation agrees well with the experimental data of Ref. [16,17] estimating the threshold burn-up of fission gas release at about 75 MWd/kgU [17], and relative local gas release for a burn-up of 92 MWd/kgU at 2% [16], as applied to PWR pellet rim conditions. As analysis shows, the release of fission gas from a LWR fuel pellet rim can presumably arise from the formation of the set of vented pores (see above) distributed in the nearest vicinity of the original grain boundaries (Figure 11). This maintains the well-developed network of the channels to transport the gas, previously lost by the matrix [2,3], into the edge area, which, in our model is assumed to be equivalent to fission gas release. We suppose, that such a network can be constituted at the early 13

108 stage of HBS formation, when diffusion domains are being formed, thereby somehow transporting the fission gas from the grain interior to the original grain boundaries. Figure 12 illustrates the scenario proposed by the model in relation to fission gas behavior in a HBS zone, representing probabilities of instant interactions, which accompany the generation of the closed pore, as applied to conditions typical for LWR pellet rim. Figure 13 represents the results of calculation and experimental data [18] upon the fuel porosity distribution across the pellet after long-term irradiation in WWER-1 to a pellet average burn-up of 57.1 MWd/kgU. As comparison shows, the calculation agrees well with the experimental data regarding the approximated width of high porous layer, as well as the peak porosity on the very edge of pellets. It is understood, that in addition to the above mentioned features in local micro-structural behavior of LWR fuel at a pellet rim, the integral analysis by the START-3 code incorporates such aspects as the dynamics of the radial profiles of local power and burn-up; degradation of fuel thermal conductivity; decrease of fuel-cladding heat conductance, as well as a plenty of factors affecting thermo-induced release of fission gas and gas-induced swelling. Thus, for example, Figure 14 represents the calculated dynamics of fission gas release in the WWER fuel rods, which are characterized by essentially different relationship between the contributions of thermal-induced release and low-temperature mechanisms into the integral percentage of fission gas release at the end of irradiation. Figure 5: Calculated concentration of intragranular fission gas as a function of local burnup at different irradiation temperatures against experimental data of ITU [14] for matrix xenon concentration in rim-layers of LWR fuel pellets Figure 6: Results of calculation and experimental data [15] upon low-temperature depression of intra-granular xenon concentration in normal and large-grained fuels 14

109 experimental data for WWER fuel model estimate Figure 7: Gain of fuel porosity in a WWER fuel pellet rim as a function of pellet average burn-up vented pores; closed pores Figure 8: Pore projected radius versus local burn-up at low-temperature irradiation, as calculated by model intra-granular release (mainly into pores); gas release into free volume Figure 9: Model estimate and experimental data for fission gas release from LWR pellet rim Figure 1: Calculated fuel porosity and release rate- to -birth rate ratio for fission gas, versus local burn-up at low-temperature irradiation vented pores closed pores Figure 11: Relative grain boundary area covered by pores versus local burn-up at low-temperature irradiation, as calculated by model 15

110 {1} - -interaction with closed pore increase of pressure in closed pores pore growth {12} - compatible interaction with (closed pore + grain edge) origination of vented porosity fission gas release {13} - compatible interaction with (closed pore + vented pore) development of vented porosity fission gas release {123} - compatible interaction with (closed pore + grain edge + vented pore) fission gas release Figure 12: Calculated macro-cross-sections (probabilities) of statistically significant instant interactions accompanying generation of closed pore, at low temperature irradiation typical for LWR pellet rim Figure 13: Calculated profile of fuel porosity in long-term irradiated WWER-1 fuel pellet against experimental data Figure 14: The calculated dynamics of fission gas release in WWER fuel rods with essentially different contributions of thermal-induced release and low-temperature mechanisms in integral percentage of fission gas release at the end of irradiation 16

111 4.3 Analysis of fuel micro-structural behavior at power transients by example of the experiments RAMP and FGR The experiments RAMP and FGR were aimed at investigation of WWER high burn-up fuel behavior at power transients, that is at the fast power ramps (RAMP experimental series) and stepwise increase of linear power (FGR experimental series), carried out in the MIR research reactor (Figure 15.a,b). The details of this experimental work are rather comprehensively described in the earlier publications [19,2]. Here, we are using the results of PIE with optical ceramography of the fuel pellets, discharged from the rods RAMP33 and FGR41, which are characterized by the approximately same level of pellet average burn-up of 5 MWd/kgU. As evident from Figures 16,17, the calculation corresponds well with the measurement, with respect to microscopic porosity distribution across the fuel pellets, as well as the mean grain size in the pellet center of the rod RAMP33. In both cases, moving around from the periphery to the center of the pellets, one can note the sequence of, at least, three pronounced zones, regarding a level of fuel porosity therein (see Figure 16.a,b). They are as follows: HBS-zone - This ultra-high burn-up region of low-temperature irradiation is characterized by high level of porosity. This is most likely formed before the tests, in the course of base irradiation in a power reactor (see Figure 13). A-zone - This represents the microstructure, which is similar to that in fresh fuel. However, some in-depth experimental investigations (see for instance [17]), as well as the modelling, testify incipient evidence of HBS propagation deep into this region. B-zone - This region is characterized by the increased level of gas-induced porosity, caused by thermal-induced diffusion of fission gas from grains to grain boundaries. The existence of C-zone in the central part of fuel pellets (Figure 16.b), which is characterized by the reduced level of fuel porosity, is an attribute of longer-term irradiation at elevated temperature, taking place, for instance, in the FGR experiments. According to our modelling (see Eqs.32), this is due to the extraction of fission gases from grain boundaries, in the course of high-temperature grain growth. Note, that this stage is presumably following the meta-stable increase of fuel porosity caused by intensification of release of the intra-granular fission gas to the grain boundaries (B-zone). At that, the incipient evince of equi-axial grain growth can also be identified even in the pellets, submitted to the relatively short-term power ramps, in the RAMP experiment (Figure 17). Thus, we have presented the three examples of model validation, dealing with essentially different conditions of fuel treatment. It is clear, that verification of the START-3 code is based upon the significantly wider set of experimental data (more than 1 items in all), including PIE of high-burn-up WWER fuel rods, extended sets of RAMP and FGR experiments, databases of the programs FUMEX-I and FUMEX-II etc. Besides, the high-priority lines of the ongoing improvement and verification of our models, including one presented in this paper, address - Modelling of advanced fuel behavior, with especial emphasis on large-grained fuel, as well as the fuel with modified open porosity and O/U-ratio, etc.; - HBS effects in the advanced fuel, as well as for the extended range of fuel burn-up; - Advantages arising from participation in Coordinated Research Program Improvement of Models Used for Fuel Behavior Simulation (CRP FUMEX II), which is currently carried out by the International Atomic Energy Agency *** 17

112 (a) (b) Note: Fuel burn-up in active part of both experimental fuel rods is 5 MWd/kgU (a) fuel rod 33 in RAMP experiment (b) fuel rod 41 in FGR experiment Figure 15: Linear power histories (а) (b) (a) fuel rod 33 in RAMP experiment (b) fuel rod 41 in FGR experiment Figure 16: Fuel porosity distribution across fuel pellets as calculated by the START-3 code and measured by optical ceramography 18

113 Figure 17: Distribution of mean grain size across fuel pellet in fuel rod RAMP33 Conclusion This paper is focused on description and validation of the new dynamic model aimed at the processes taking place on grain boundaries in polycrystalline Light Water Reactor fuel based on the use of UO 2, which has been recently developed for the START-3 code. The analysis embraces such processes as formation of fine surface clusters and larger inter-granular pores, equi-axial grain growth, direct release and percolation of fission gas to the open surfaces. This model is also closely linked to intra-granular behavior of fission gas and essentially overlaps modelling of High Burn-up Structure, as well as high temperature- and power transient-assisted processes. The model embodies some of the state-of-the-art approaches to numerical description of the processes taking place on grain boundaries, incorporating considerations of diffusion theory with respect to analysis of the dynamics of grain boundary pore growth/shrinkage caused by self-diffusion of the fuel material around them. Besides, this widely uses the elements of probability theory thereby accounting for stochastic nature of the analyzed phenomena. The several examples of model validation, illustrating credibility of pertinent results as applied to a wide enough range of application, including high-temperature out-of-pile annealing, High Burn-up Structure Effects and transient behavior of Light Water Reactor fuel, are also presented. As validation shows, the developed model can be accepted as an important element of overall dynamic modelling with a view to justification of reliability of high burn-up Light Water Reactor fuel, and safety analysis, as well. Acknowledgements We wish to thank all pertinent staff of the International Atomic Energy Agency (IAEA) for their assistance in implementation of the project Improvement and Verification of the START-3 code in frames of the IAEA CRP Improvement of Models Used for Fuel Behavior Simulation (CRP FUMEX II) 19

114 REFERENCES 1. G. Khvostov, Thermal physical Aspects of Fuel Rod Behaviour Modelling Using START-3 Code, IAEA International Seminar, Sofia, Bulgaria, December 7-9, Bibilashvili Yu.K., Medvedev A.V.,.Khvostov G.A at al., "Development of the Fission Gas Behaviour Model in the START-3 Code and its Experimental Support", International Seminar, Cadarache, France, September,2 3. G. Khvostov at al., Modelling of rim-layer features in frames of START-3 code development, International Conference on WWER Fuel Performance, Modelling and Experimental Support, Albena, Bulgaria, 1-5 October, R. White, The Development of Grain Face Porosity in Irradiated Oxide Fuel, International Seminar, Cadarache, France, September, 2 5. D.R. Olander, "Fundamental aspects of the nuclear fuel reactor elements", pp ,US Energy Research and Development Administration, R.J.White, M.O.Tucker, J.Nucl.Mat., 118(1983) J.M. Griesmeyer, N.M. Ghoniem, D. Okrent, Nuc. Energy and Des., 55 (1979) M. Kinoshita, Mesoscopic approach to describe high burn-up fuel behavior EHPGM, Loen, Norway, May D.R. Olander, "Fundamental aspects of the nuclear fuel reactor elements", pp ,US Energy Research and Development Administration, J.B. Ainscough, B.W. Oldfield, J.O. Ware, Isothermal grain growth kinetics in sintered UO 2 pellets, JNM 49(1974/1974) I. Zacharie at al., Thermal treatment of uranium oxide irradiated in pressurized water reactor: Swelling and release of fission gases, JNM, 255(1998) I. Zacharie at al., Microstructural analysis and modeling of intergranular swelling of an irradiated UO2 fuel at high temperature, JNM, 255(1998) J.H. Evans, Modelling of Fission Gas bubble Migration to Grain Boundaries During Post- Irradiation Annealing in High Burn-up UO2, International Seminar, Cadarache, France, September,2 14. K. Lassmann at al., "Recent development of the TRANSURANUS code with emphasise on high burn up phenomena", IAEA TCM, Windermere, UK, June, 2M. 15. K. Une at al., Rim structure formation of large-grained UO2 fuel irradiated in the Halden Heavy Water Reactor, EHPGM, Loen, Norway, May D. Baron, J. Spino, D. Papaioannou, Rim Formation and Fission Gas Behaviour: Some Structure Remarks, International Seminar, Cadarache, France, September,2 17. M. Mogensen, J.H. Pearce, C.T. Walker, Behavior of fission gas in the rim region of high burn-up UO2 fuel pellets with particular reference to results from an XRF investigation JNM 264 (1999) A. Smirnov at al., Results of Post-Irradiation Examination to Validate WWER-44 and WWER-1 Fuel Efficiency at High Burnups, International Conference on WWER Fuel Performance, Modelling and Experimental Support, Albena, Bulgaria, 1-5 October, Yu. Bibilashvili at al., " Fission Gas Products Behavior Modelling in the START-3 Code for the VVER Fuel at High Burn Up and Transient Conditions ", IAEA International Seminar, Pamporovo, Bulgaria, 4-8 October, A. Smirnov at al., Fission Gas Release from High Burn-up VVER-44 Fuel Under Steadystate and Transient Operation, International Seminar, Cadarache, France, September,2 2

115 Modelling of Thermal Mechanical Behaviour of High Burn-up VVER Fuel at Power Transients with Especial Emphasis on Impact of Fission Gas Induced Swelling of Fuel Pellets V. Novikov, A. Medvedev, G. Khvostov, S. Bogatyr, V. Kuznetsov, L. Korystin Federal State Unitary Enterprise VNIINM, Moscow, Russian Federation Abstract This paper is devoted to modelling of unsteady state mechanical and thermo-physical behavior of high burn-up VVER fuel at a power ramp. Contribution of the processes related to the kinetics of fission gas to the consequences of pellet-clad mechanical interaction is analyzed by the example of integral VVER-44 rod 9 from the R7 experimental series, with a pellet burn-up in the active part of around 6 MWd/kgU. This fuel rod incurred ramp testing with a ramp value W l 25 W/cm in the MIR research reactor. The experimentally revealed residual deformation of the clad by 3-4 microns in the hottest portion of the rod, with a maximum reached linear power up to 43 W/cm, is numerically justified on the basis of accounting for the unsteady state swelling and additional degradation of fuel thermal conductivity due to temperature-induced formation and development of gaseous porosity within the grains and on the grain boundaries. A good prediction capability of the START-3 code, coupled with the advanced model of fission gas related processes, with regard to the important mechanical (residual deformation of clad, pellet-clad gap size, central hole filling), thermal physical (fission gas release) and micro-structural (profiles of intra-granular concentration of the retained fission gas and fuel porosity across a pellet) consequences of the R7 test is shown. International Seminar on Pellet-Clad Interaction in Light Water Reactor Fuels, AIX EN PROVENCE, France, March 9-11, 24

116 Introduction Of many results obtained from Post Irradiation Examination (PIE) of high burn-up fuel rods after enough intensive power transients in research reactors [1,2], those based on Quantitative Image Analysis (QA), Electron Probe Micro Analysis (EPMA) and X-Ray Fluorescence (XRF), testify significant changes in macro- and micro- structural state of fuel pellets. These changes appear to be - a partial or complete filling of the internal voids in fuel pellets (central hole, dishes etc.); - depression in intra-granular and total concentration of the retained fission gas in the high-temperature areas of fuel pellets; - formation and enhanced development of fuel porosity, about in the same areas of the fuel. By common agreement, the main inducement for these developments is constituted by the intensified diffusive mobility of the fission gases accumulated in the pellet bulk during the base irradiation previous to power ramps. From the point of view of rod reliability, the most unfavorable outcomes of the appropriate kinetic processes are either the unsteady state swelling of the fuel and additional degradation of its thermal conductivity due to formation and development of gas-inflated pores and bubbles. This is evidently able to enlarge the pellet growth and, thereby, to strengthen Pellet-Clad Mechanical Interaction (PCMI), which eventually can lead to clad damage and rod failure. The secondary effect of the fission gas kinetics implies its release into the free volume of the fuel rod, which worsens the conditions of pellet-to-clad heat conductance and increases gas pressure on the clad. That is, in particular, why the development of the advanced model, which embraces the wide set of the kinetic processes related to fission gas and fuel micro-structure in the widest possible range of irradiation conditions, is assumed as a foreground task of the activity upon improvement and verification of the START-3 code for some years. One of the advantages arising from the model application is a possibility to analyze numerically the contribution of above-mentioned effects to thermal-mechanical behavior of fuel rods at power transients under the condition of PCMI. 1. The basic elements and scope of the advanced model describing overall behavior of stable fission gas and evolution of fuel structure The dynamic model GRSWEL-A [3,4] addresses the overall behavior of stable fission gas and pertinent evolution of fuel microstructure. This is the advanced version of the former one referred to as GRSWEL, earlier developed for the START-3 code [4,5]. This new model is being developed with a view to analysis of fuel behavior under in-pile and out-ofpile conditions; at extended rod- and pellet-average burn-ups (up to about 8 MWd/kgM), as well as at an ultra-high local burn-up in a pellet rim (up to about 2 MWd/kgM); in the exhaustive range of temperature, from the magnitudes, which are typical for the coolant, to the melting point of the fuel; in the long-term modes with slow or absent variation of the parameters of fuel thermal state, as well as at fast power transients including accidents with reactivity insertion. The numerical analysis of fuel behavior is reduced to integration with respect to time, of the set of rate equations for the array of dependent variables, which describes the current state of the fuel as comprehensively as possible. The model variables are logically divided into the gropes, which take into consideration the intra- and inter-granular processes, high burn-up structure features, high-temperature assisted re-crystallization, as well as the 2

117 dynamics of as-fabricated intra-granular porosity leading to early-of-life fuel densification or thermal sintering. The calculation is carried out as applied to the set of zones in a fuel pellet, characterized by approximately uniform distribution of the external variables supplied by the mechanical and thermal physical modules of the code. The external variables of the model are the local magnitudes of temperature; temperature gradient; fission rate; hydrostatic pressure, which takes into account gas pressure in the plenum and PCMI intensity. Figure 1 represents the flowchart for the integral analysis of fuel performance at power ramps as realized in the START-3 code coupled with the advanced model GRSWEL-A. The flowchart shows schematically the analyzed processes affecting transient behavior of fuel and cladding, as well as the effects of base irradiation, which are essentially imposed on this behavior. As seen from Figure 1 the GRSWEL-A model provides the integral calculation with the current local and pellet average magnitudes of different components of gas retention and porosity to calculate fuel thermal conductivity, mechanical properties and pellet strain; absolute and relative fission gas release to calculate gas pressure in the plenum and fuel-cladding heat conductance; average grain size, which affects mechanical properties of the fuel (an equi-axial character of grains is assumed). It is noteworthy that despite the complex set of feed-backs and feed-forwards between thermo-mechanical behavior of the fuel rod and micro-processes in the pellet analyzed by the GRSWEL-A model, the resulting output of this model is enough transparent from the point of view of rod reliability due to contribution into possibility of - clad damage either by the mechanism of Stress Corrosion Cracking (SCC) or due to reaching the ultimate strain via the strengthened PCMI; - clad lift-off via the increase of gas pressure in the plenum; - fuel melting via the increase of temperature. The theoretical approaches to modelling of intra- and inter- granular processes as well as their linking to the effects of High Burn-up Structure (HBS) and high-temperature recrystallization, incorporated in the GRSWEL-A model, are rather comprehensively described in [3,4]. Here, it is worthwhile representing the final view of the relationships used for calculation of local fuel porosity in relation to fuel thermal conductivity λ(p tot ) = f(p tot ) λ(p tot =) and volumetric swelling due to the fission products by assuming of its isotropy V/V=3 L/L. The total value of fuel porosity is calculated as the sum of intra- and inter- granular components: P tot =P G +P F The intra-granular component is calculated as [4]: Nb 4π 3 PG = ri Bi + P, G. as fabricated 3 s+ 1 Here, the first term summarizes results of modelling for size distribution of intragranular bubbles with the radii r i and concentrations B i ; the second term takes responsibility for the dynamics of as-fabricated intra-granular porosity during early-life densification (or high-temperature sintering). The equation for the sum inter-granular porosity is as follows [3]: PF = Bnv π rf [ kv(1 ε ) + ε ] + Bvn πrf ( vn) kv + PF. as fabricated 3 3 On the right-hand side of this equation, the first term corresponds to the porosity due to closed pores with the current radius of surface curvature r f and volumetric concentration B nv ; the second term represents the contribution of the vented pores; the third one is the time-constant as-fabricated inter-granular porosity. The time-dependent variable ε and 3

118 coefficient k v account for the current relationship between the numbers of lenticular and spherical pores confined to grain boundaries [4], thereby defining their mean-effective shape in the re-crystallized fuel. The overall measure of re-crystallization is calculated as suggested in Ref. [6] 1 ε = (1 ε i i ) where i identifies the type of fuel re-structuring, so that i=1 when this is HBS; i=2 for equi-axial grain growth. The geometric factor relating volume of lenticular pore to sphere is expressed as: k v =1-3cos(θ)/2+cos 3 (θ)/2=.186 by assuming of θ=5 о pellet fragmentation irradiation-induced densification of fuel high-temperature sintering of fuel (occasional) steady-state swelling of fuel degradation of properties of clad and fuel Base Irradiation thermal pellet-clad contact pellet defragmentation mechanical pellet-clad contact formation of High Burn-up Structure accumulation of fission products and fission gas release thermal expansion of fuel mechanical stress in fuel (hydrostatic pressure) fuel creep pellet growth central hole filling elastic straining of clad plastic straining of clad clad growth by creep data communication mechanical treatment heat generation thermal conductivity pellet-clad heat conductance Power Ramp data communication thermal treatment fission fission product generation point deffect generation in fuel lattice diffusion of gas monoatoms diffusion of point deffects formation of intragranular bubbles trapping of gas monoatoms bubble growth bubble migration bubble coalescence fission gas release through open surface of fuel fission gas release into free volume unsteady state swelling of fuel fuel porosity data communication GRSWEL-A: Behavior of fission gas and fuel micro-structure gas resolution fission gas arrival at closed boundaries of grains formation of intergranular pores intergranular pore growth intergranular interactions fission gas percolation equi-axial grain growth data communication - tensile hoop stress in clad - plastic deformation of clad - clad SCC - ultimate strain of clad Criteorial characteristics of fuel rod: fuel temperature Pertinent Acceptance Critioria: Fuel melting gas pressure on clad Clad 'lift-off' Figure 1: Flowchart for integral analysis of fuel performance at power ramp as realized in the START-3 code coupled with the advanced model GRSWEL-A 4

119 The final equation for irradiation-induced swelling of the fuel is as follows: V = Ε fuel ( PF PF. as fabricated ) + Bnν g + Ε int ra V Here, the first term corresponds to swelling due to grain boundary pores; the second term represents gas clusters on the boundaries of grains; the third one is the intra-granular swelling. The component of fuel swelling relating to the intra-granular processes is calculated from the expression, which is as follows: s N 4π b 3 Εint ra = α solidb + vg ( C1 + NiBi ) + ri B. i 1 3 s+ 1 Here, the first term is responsible for strains due to solid fission products (α solid =.32 vol.% per 1% h.a. of burn-up b); the second term accounts for the volumetric strain due to mono-atoms of fission gas in fuel matrix as well as small nucleuses of gaseous bubbles, which are assumed as solid spheres (N i - the number of gas atoms in the bubble;ν g = 85 Å 3 - the volume occupied by one generalized atom of fission gas); the last term accounts for size distribution of intra-granular bubbles. At last, the relative fission gas release is calculated via the rate of the specific absolute gas loss L 2 (atoms/cm 3 /s), as a ratio of release to cumulative generation: t L r d 2(, τ ) τ dv V fuel f fr ( t) = t G fg r d (, τ ) τ dv V fuel where G fg (r,τ) is the gas generation density, and integration is carried out with respect to the total volume of the fuel stack V fuel and irradiation time t. 2. Design parameters and results of PIE after base irradiation for integral rod 9 in R7 experiment Of six fuel rods re-irradiated at RIAR in the course of the R7 test [1], carried out in1995, integral rod 9 was characterized by the highest level of fuel burn-up in the active part of total fuel stack (6 MWd/kgU) subjected to power transient in the MIR research reactor. Probably, this is the prime cause owing to which the effects of gas-induced swelling were especially pronounced in this case. That (as well as available results of PIE) is why this rod has been chosen here as a referent example for the detailed numerical investigations. 2.1 Fuel rod design and base irradiation conditions Rod 9 was extracted from Fuel Assembly (FA) No.222 after five-year irradiation in Unit 3 of Kola NPP with VVER-44 to a rod average burn-up of 52 MWd/kgU. The main characteristics of rod design and base irradiation, assumed as the input data for the numerical analysis by the START-3 code, are given in Table 1 and shown on Figure 2 [7]. As seen from Figure 2 the base irradiation was carried out under rather moderate conditions, so that the calculated fuel temperature is much less than the empiric threshold for thermal fission gas release throughout operation. Thus, according to the calculation, the most of generated fission gas was accumulated in the fuel matrix at the end of base irradiation, except for the HBS-zone at the pellet rim (see Figures 12,13 with regard to the 5

120 pellet rim). As analysis shows, the HBS effects take prime responsibility for fission gas release of 2.8%, as measured by puncture method in the sibling rod 14 of FA 222. Regarding the mechanical state of the fuel rod after base irradiation, the important evidence arising from the PIE is the absence of any considerable gap (mechanical) between pellets and clad. This testifies the onset of PCMI in the fuel rod before the end of operation in the power reactor. No change in pellet macro-structure in comparison to that of fresh fuel was found by optical ceramography (see the pellet state before the test on Figure 8), with the exception of pellet fragmentation. Table 1: Parameters of rod design and base irradiation conditions Parameter Value Fuel rod: FA type VVER-44 FA No. 222 Fuel stack length, mm 242 Length of plenum, mm 85 Fuel loading mass, g 187 Initial filling gas.6 MPa He Mean gap size (diametral), µm 2 Pellet: Outer diameter, mm 7.56 Inner diameter, mm 1.6 Enrichment by U235, wt. % 4.4 Fuel density, %TD 95 Grain size (Mean linear intercept), µm 6.5 Open porosity (relative contribution to total porosity), % 1 (assumed) Densification, vol. % 1.2 (assumed) Stehiometry (O/U) 2.5 (assumed) Cladding: Clad material Zr+1%Nb Outer diameter, mm 9.1 Inner diameter, мм 7.76 Characteristics of base irradiation: Place of operation Kola NPP Unit-3 Rod average burn-up, MWd/kgU 52 Maximum pellet burn-up, MWd/kgU 6 Fission gas release (in sibling rod),% 2.8 6

121 Linear heat generation rate, W/cm Temperature, o C Calculated temperature LHGR Burn-up, MWd/rgU Figure 2: Maximum linear power and calculated fuel temperature in the leading rod of FA Fuel rod re-irradiation in the MIR research reactor Table 2 represents the important test conditions for rod 9. Table 2: Parameters of rod 9 re-irradiation during the R7 test in the MIR research reactor Parameter Value Length of fuel active part (estimated), mm 75 Fuel burn-up in active part, MWd/kgU 6 Axial form factor for linear power in active part (estimate for time-average value), 1/ Maximum linear heat generation rate during low-power holding, W/cm 178 Linear heat generation rate at the ramp terminal level, W/cm 43 Coolant pressure, MPa 16 Temperature of cladding outer surface in the hottest section for the low-power holding, о С 24 Temperature of cladding outer surface in the hottest section at the ramp terminal level, о С 32 Figures 3,4 illustrate conditions of the test with respect to linear heat generation rate (LHGR) and fuel temperature. As seen from Figure 3, the test irradiation submits the sequence of power modes, which are as follows: - low power holding with the maximum local LHGR of 178 W/cm, which implies a certain rise of the local linear power in comparison to that at the end of base irradiation (about 12 W/cm accordingly to our estimate); - power ramp by W l 25 W/cm during the relatively short period of time (less than about 2 min):; - high power holding with the tendency of gradual increase of the LHGR 7

122 Linear heat generation rate, W/cm re-loading to research reactor low-power holding power ramp local LHGR at the end of base irradiation ( 12 W/cm) Temperature, o C Pellet center Volume average Time, h Figure 3: Maximum linear power (LHGR) history for rod 9 of the R7 test Time, h Figure 4: Calculated fuel temperature in the hottest section of rod 9 during the R7 test 3. Fuel rod behavior at power transient. Results of modelling against experimental data 3.1 Thermo-mechanical behavior The main mechanical consequences of the R7 test with fuel rod 9, as calculated by the START-3 code coupled with the GRSWEL-A model, and according to the PIE, are quantified in Table 3 (see Model A in the Table). As comparison shows, the results of advanced modelling (Model A) agrees reasonably with the experimental data for - residual deformation of the clad as a result of the strong PCMI during the ramp mode (Figures 5-7); - central hole filling by the fuel (Figure 8,9) as a result of fuel creep towards the pellet center under the conditions of elevated temperature (Figure 4) and compressive stress in the pellets; - rise of the pellet-clad gap size resulting from the combination of the two above mentioned conditions. In order to find out the role of fission gas related processes in thermo-physical and mechanical behavior of this particular fuel rod, an additional calculation has been carried out by the assumption that - neither additional degradation of fuel thermal conductivity - nor unsteady state swelling of the fuel due to fission products take place (Model B). The comparative analysis has evidently testified, that the formation of gaseous porosity enlarges significantly pellet growth due to thermal expansion of the fuel with the reduced thermal conductivity, as well as because of the unsteady fuel swelling by itself (Figure 1). At that, the consideration of pellet growth solely on account of thermal expansion is incapable of explanation of deformative behavior of this particular fuel rod (Results of Model B in Table 3). It is noteworthy that accounting for the development of gas porosity has also led to the increase of the predicted temperature of fuel by about 25 o C, which illustrates very well the two-fold character of gas-related effects, affecting both thermal and mechanical behavior of fuel rods at power ramps. The pronounced phases of clad plastic straining within the short period of power ramp, arising from the strengthened PCMI, are predicted with the use of Model A, whereas 8

123 nothing of the sort is found from the calculation with the use of Model B. As seen from Figures 6,7, the calculation shows that namely these developments take prime responsibility for the large residual deformation of the clad, as revealed by the PIE (Figure 5). At that, the short duration of the mode with elevated hoop stress in the clad (from the beginning of ramp to the relatively small dip of the LHGR after ramp) is, probably, why there was no clad damage either by the mechanism of SCC or due to reaching the ultimate strain. Besides, the creep of fuel towards the pellet center, resulting in that more than a half of the initial volume of the central hole in fuel pellets has become filled by the fuel after the test (Figures 8,9), alleviates considerably the strength of the PCMI. Table 3: Results of calculation and experimental data for deformative and thermal characteristics of rod 9 in R7 test Parameter Calculation Measurement Model A Model B Residual deformation of clad (as a result of test), µm Diametral gap size(mainly due to test), µm Relative decrease of central hole volume (total filling) A/A, % Maximum fuel temperature reached during test, о С NOTE: Model A: calculation by the START-3 code coupled with the GRSWEL-A model (see Figure 1) Model В: calculation by the START-3 code partly decoupled from the GRSWEL-A model. Neither additional degradation of fuel thermal conductivity (as-fabricated value of fuel porosity assumed), nor unsteady state swelling of the fuel due to fission products (engineering model 1%swelling per 1% burn-up assumed) are taken into consideration After Outer diameter, mm out of core out of core 9.7 Before Axial co-ordinate, mm Figure 5: Axial profiles of clad outer diameter for active part of integral rod 9, as measured before and after R7 test 9

124 5 4 Hoop stress, MPa Time, h Figure 6: The calculated dynamics of hoop stress in clad of rod 9 during R7 test (with emphasis on the ramp mode) Clad deformation, µm residual deformation Time, h Figure 7: The calculated dynamics of clad deformation for rod 9 during the R7 test (with emphasis on the ramp mode) Before After Figure 8: Fuel pellet macro-structure (cross-sectional view) for rod 9, as examined before and after R7 test 1