Validation of a Continuous-Energy Monte Carlo Burn-up Code MVP-BURN and Its Application to Analysis of Post Irradiation Experiment

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1 Journal of Nuclear Science and Technology ISSN: (Print) (Online) Journal homepage: Validation of a Continuous-Energy Monte Carlo Burn-up Code MVP-BURN and Its Application to Analysis of Post Irradiation Experiment Keisuke OKUMURA, Takamasa MORI, Masayuki NAKAGAWA & Kunio KANEKO To cite this article: Keisuke OKUMURA, Takamasa MORI, Masayuki NAKAGAWA & Kunio KANEKO (2000) Validation of a Continuous-Energy Monte Carlo Burn-up Code MVP-BURN and Its Application to Analysis of Post Irradiation Experiment, Journal of Nuclear Science and Technology, 37:2, , DOI: / To link to this article: Published online: 07 Feb Submit your article to this journal Article views: 429 View related articles Citing articles: 65 View citing articles Full Terms & Conditions of access and use can be found at Download by: [ ] Date: 08 January 2018, At: 13:17

2 Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 37, No. 2, p (February 2000) Validation of a Continuous-Energy Monte Carlo Burn-up Code MVP-BURN and Its Application to Analysis of Post Irradiation Experiment Keisuke OKUMURA*,t, Takamasa MORI*, Masayuki NAKAGAWA* and Kunio KANEKO** * Department of Nuclear Energy System, Japan Atomic Energy Research Institute ** Integrated Technical Information Research Organization (Received April 8, 1999), (Revised September 9, 1999) In order to confirm the reliability of a continuous-energy Monte Carlo burn-up calculation code MVP BURN, it was applied to the burn-up benchmark problems for a high conversion LWR lattice and a BWR lattice with burnable poison rods. The results of MVP-BURN have shown good agreements with those of a deterministic code SRAC95 for burn-up changes of infinite neutron multiplication factor, conversion ratio, power distribution, and number densities of major fuel nuclides. Serious propagation of statistical errors along burn-up was not observed even in a highly heterogeneous lattice. MVP-BURN was applied to the analysis of a post irradiation experiment for a sample fuel irradiated up to 34.1 GWd/t, together with SRAC95 and SWAT. It was confirmed that the effect of statistical errors of MVP-BURN on a burned fuel composition was sufficiently small, and it could give a reference solution for other codes. In the analysis, the results of the three codes with JENDL-3.2 agreed with measured values within an error of 10% for most nuclides. However, large underestimation by about 20% was obse.rved for 238 Pu, 242 m Am and 244 Cm. It is probable that these discrepancies are a common problem for most current nuclear data files. KEYWORDS: MVP-BURN, Monte Carlo burn-up calculation, continuous energy, depletion equation, benchmark calculation, post irradiation experiment, JENDL-3.2, computer calculation, errors, comparative evaluations, burnup, reliability I. Introduction The continuous-energy Monte Carlo method is the most reliable method in the field of neutron transport problems because of its precise geometrical modeling and continuous-energy treatment. Recent progress of supercomputers has made it possible to apply the method to some burn-up problems(1)-( 3). In spite of still expensive computation costs, the Monte Carlo method is very useful in solving special burn-up problems for which we have few calculation experiences or difficult problems to treat with conventional deterministic neutron transport codes. They are, for example, investigations of rim burn-up effectsc1), plutonium spot effectsc3) in a fuel pellet, developments of new burnable poisoned fuel, analyses of irradiated materials in a three-dimensional heterogeneous capsule in a research reactor, and so on. The continuous-energy Monte Carlo code MVP(4 )( 5) employs a fast computation algorithm suitable for recent vector and/or parallel computers; it realizes a speed-up factor of ten or more on such super-computers(6). Therefore, MVP can reduce the large computation time required for the repeated use of a Monte Carlo code at * Takai-mum, Naka-gun, Ibaraki-ken ** Nishi-Shinbashi, Minato-ku, Tokyo t Corresponding author, Tel , Fax , okumura@mike.tokai.jaeri.go.jp many burn-up time-steps. In order to apply it to various burn-up calculation problems, we have developed the MVP-BURN code(7l by implementing an auxiliary modular code BURN which calculates the buildup and decay of nuclides in irradiated materials (here we simply refer to it as depletion calculation). Careful verifications and investigations are necessary especially for the reliability of calculated burn-up parameters, before applying it to problems with no reference solutions, because there remain such problems as propagation of statistical errors in Monte Carlo burn-up calculations. II. Burn-up Calculation Method An execution of the continuous-energy Monte Carlo code is possible if geometry and material compositions are given. As a result of the Monte Carlo calculation, microscopic reaction rates of every nuclide are calculated. On the other hand, depletion calculation is possible if the microscopic reaction rates are given. Therefore, the coupling of a Monte Carlo code and a depletion calculation code can be directly realized only by implementing an interface program between them. The BURN code has the functions of depletion calculation, file management and interface with MVP. Alternate executions of MVP and BURN constitute a whole burn-up calculation. As the continuous-energy Monte Carlo method is timeconsuming, two kinds of time-step units are adopted in 128

3 Validation of a Continuous-Energy Monte Carlo Burn-up Code MVP-BURN 129 MVP-BURN. One is the burn-up step unit with a relatively broad time interval, and the other is the sub-step unit in each burn-up step. At each burn-up step, MVP is executed for an eigenvalue problem and relative microscopic reaction rates are obtained for capture, fission and ( n, 2n) reactions by the track length estimator or collision estimator. The value of neutron multiplication factor is calculated in MVP on the basis of the principle of maximum likelihood using the values obtained by several correlated estimators. The total power level is assumed to be constant in each burn-up step interval. The interval is further divided into several sub-steps for the depletion calculation by BURN. The depletion equation for the interval of the n-th burn-up step [tn-l, tn] can be expressed by Eq. (1), under the assumption that the relative distribution of the microscopic reaction rates does not change during the time interval of the burn-up step although their absolute values may change to keep the total power level constant: dnf(t) L f. \ NZ( ) - J--tiAJ i dt ' #i + L Fact(t){gk--+ick + "'/k--+ifk + hk--+i wnn:(t) k-=f.i - [>.; + Fact(t){A; + Wt}]Nt(t), where i, j, k: Depleting nuclide number z: Depleting zone number N: Atomic number density >., f: Decay constant and branching ratio g, "'/, h: Yield fraction of each transmutation C: Relative microscopic capture reaction rate calculated with MVP at t=tn-l F: Relative microscopic fission reaction rate calculated with MVP at t=tn-1 W: Relative microscopic (n, 2n) reaction rate calculated with MVP at t=tn-1 A: Relative microscopic absorption reaction rate (=C+F) with MVP at t=tn-1 Fact(t): Normalization factor to convert relative reaction rates to absolute ones. The normalization factor Fact(t) for the interval of the m-th sub-step [tm-1, tm] E [tn-1, tn] is given by Fact(tm-1 :S t :S tm) = P(tn-1 :St :S tn) ILL K:;F/ Nt(tm_i)VZ, where P: Constant power level in [tn-1, tn] given by input data K:;: Energy release per fission of the i-th nuclide. Then, Eq. (1) can be solved analytically by the method of the DCHAIN code(8) for each sub-step. The method of DCHAIN is based on Bateman's method(9 ) with a mod- z ' (1) (2) ification for more accurate treatment of cyclic burn-up chain caused by a-decay or ( n, 2n) reaction. The statistical errors of the microscopic reaction rates obtained with MVP are not reflected in the depletion calculation. That is to say, the propagation of the statistical errors along burn-up steps is not taken into account. Though methods to treat the propagation< 10 > are being investigated by many researchers, it seems to take more time to put them to practical use in MVP-BURN. The effect of statistical errors in a burn-up calculation will be discussed based on our experiences in Sec. V-1. III. Library Data and Burn-up Chain To apply a continuous-energy Monte Carlo code to realistic burn-up problems, a lot of nuclide-wise neutron cross section libraries are necessary for actinides, fission products (FPs) and burnable poisons. In addition, they have to be prepared at actual temperatures depending on a problem to be solved. So far, cross section libraries have been prepared for about 160 nuclides at a room temperature. They were produced, within an interpolation error of 0.1%, from the JENDL-3.2 file< 11 ) with a library production code system LICEM< 12>. The cross section data in the unresolved resonance region is expressed by probability tables, which are necessary for accurate analysis of reactors with hard neutron spectra, although the computation cost is very high to produce the probability tables. This practical problem was overcome by a utility code ART(6), which has the functions of Doppler broadening calculation of the resolved resonance cross sections and temperature interpolation of the probability tables in the unresolved resonance region. ART can immediately prepare libraries at arbitrary temperatures from those produced with LICEM at a room temperature. The burn-up chain model for MVP-BURN can be easily changed according to fuel or reactor types under consideration. Figure 1 shows the chain model used for the MVP-BURN calculations in this study. It treats 19 heavy nuclides from 235 U to 245 Cm, and 34 FPs including 4 pseudo ones. The chain model for FPs is simpler compared with other codes; SRAC95< 13), for instance, employs a more detailed chain model that treats 66 FPsC 7 )C 16). The simple chain model was constructed so that major burn-up characteristics would agree well with those obtained with the detailed chain model in the lattice burn-up calculations for various reactorsc 7). The point-wise cross section libraries occupy a lot of memory capacity, and the required memory size increases with the numbers of treated nuclides and temperatures. The simple chain model is necessary to avoid computer memory shortage; otherwise problems to be solved or available computers would be limited. The MVP libraries for the pseudo FPs were produced from the group constants of the corresponding FPs in the SRAC95 library. The constants with a 107-energy group structure was first converted into point-wise cross section data in the ENDF-B format, by assuming that elastic scattering is isotropic in the center-of-mass system VOL. 37, NO. 2, FEBRUARY 2000

4 130 K. OKUMURA et al. u" I< >, Pu23;1---+o EC I ! "---- _...i7ili -- "' ::.::.:: Am 42 -,:-- -- (n,_2n) (n,'y) 1,, :: _::--.. Am lt!g_ --- decay IT j " J C'm242++Cm243++Cm244++Cm245-+ (a) fission Tc e \s ,. Rh Cdll S56 (pseudo from 0235) ---+ '\utol \& PdlOS---+ / dl S86 (pseudo from 0238) ---+ \e '7\Pm148 1>r143d S96 (pseudo from Pu239)---+ l \16 (pseudofrompu241)---+ Sm Sm SmlSO---+ Sml Sm152 / Eu153 /Eu154 7 Eu155 7 Eu Fig. 1 Gdl Gd Gd Gd Gdl (b) Burn-up chain model of MVP-BURN for (a) heavy nuclides, (b) fission products and burnable poisons and that continuum inelastic and ( n, 2n) reactions are isotropic in the laboratory system. After that, the MVP libraries were produced in a conventional way. IV. SRAC95 Calculation Although there are several numerical benchmark problems for lattice burn-up calculations, reliable reference solutions are rare and most solutions greatly differ from each other, because there are many uncertainties resulting from nuclear data, burn-up chain models, resonance treatments, computation methods to solve transport and depletion equations, and so on. SRAC95 was used for comparison with MVP-BURN, because some of the uncertainties can be eliminated. In this chapter, the data and methods of SRAC95 are briefly described. SRAC95 is a system including several elementary transport and diffusion codes<13l( 14l. A collision probability option in SRAC95 was commonly used for all the problems in this study with a 107-group library based on JENDL-3.2. Other libraries are also available. Effective microscopic cross sections of all resonant nuclides were obtained by the table-look-up method<14l of resonance self-shielding factors by assuming the narrow resonance approximation. For major resonant nuclides, the effective cross sections were modified by a super-fine group (16,000 groups) collision probability calculation by the PEAC0<14l routine in the energy range from thermalcut-off energy to 130 e V. The cut-off energy is 2.38 e V for all problems in this study. No geometrical simplification like a cylindrical cell modeling was employed. The method of SRAC95 to solve a depletion equation is the same as that ofmvp-burn. The detailed burn-up chain model was used for SRAC95, while the equivalent simple one was used for MVP-BURN to avoid a shortage of memory capacity. Therefore, the essential differences between the following MVP-BURN and SRAC95 calculations are the resonance treatments and the transport calculation methods. V. Numerical Benchmarks 1. High Conversion Light Water Reactor Lattice (1) Benchmark Problem MVP-BURN was first applied to a numerical benchmark problem< 15l on the cell burn-up calculation for a High Conversion Light Water Reactor (HCLWR) lattice. The lattice geometry is shown in Fig. 2. It is characterized by a hexagonal Pu02-U02 fuel lattice with a tight rod-to-rod pitch. The moderator-to-fuel volume ratio is about half those of current PWRs. As neutron absorption is dominant in the resonance energy region, accurate data and methods are required for the calculation of effective resonance absorptions. In the international JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

5 Validation of a Continuous-Energy Monte Carlo Burn-up Code MVP-BURN 131 Fig. 2 t V.,/V i=l.1 Lattice geometry of HCLWR benchmark usr-r-... :,rr;::i:::i======= easel J i o Case2 1.lO \;;:: : mean(casel,case2) ;...,.._ =reference 1i y. i= 1.os :.. o,_.. :... :... :... _ 1 : rt-. ; : :, 1 o.9sof-'-._...':'10!:-'-'.....,,..20,..._,.... 3='=o,..._...,_4,1, _.SO. benchmark comparison in 1988, large differences were observed among submitted solutions< 15) for the burn-up changes of infinite neutron multiplication factor k 00 and conversion ratio. That is the reason why we have chosen this problem as a first trial of MVP-BURN. (2) Effect of Statistical Error In order to judge the reliability of calculated results of MVP-BURN, statistical uncertainty was investigated by carrying out burn-up calculations under the following six conditions: Case 1: The number of neutron histories=300,000= 5,000 particlesx60 batches (plus initial 10 batches skipped from tally), Case 2: The number of neutron histories is the same as in Case 1, but a different initial random number is used, Case 3: The number of neutron histories=45,000= 1,000 particlesx45 batches (plus 5 initial batches skipped from tally), Case 4: The number of neutron histories is the same as in Case 3, but a different initial random number is used, Case 5: The number-of neutron histories=2,000=100 particles x 20 batches (plus 5 initial batches skipped from tally), Case 6: The number of neutron histories is the same as in Case 5, but a different initial random number is used. Here, the mean value of k 00s and its uncertainty are defined from the results of several executions of MVP BURN in the following manner: and _ k(tn) { a;ttn)} koo(tn) = l (3) z=-2 i CTi (tn) 1 1 / z=-2-, CTi (tn) i where i: Case identification of several MVP-BURN executions tn: n-th burn-up step a 2 : Variance obtained with MVP at each burnup step point without consideration for propagation of statistical errors. The calculated k 00s for the above six cases are shown VOL. 37, NO. 2, FEBRUARY 2000 (4) Fig. 3 k=s in HCLWR benchmark calculated with MVP BURN for Cases 1 and 2 using different initial random numbers (300,000 neutron histories) Mean value is based on Eq. (3). in Figs. 3 and 4(a), (b). In Cases 1 and 2, the statistical errors of k 00s at every burn-up step point are sufficiently small (a<0.1%) and the effect of different initial random numbers is hardly observed. Therefore, the mean value of k 00s obtained from Cases 1 and 2 can be regarded as a good reference value for other cases. Figure 4(c) shows the ratio of the mean value of k 00s from Cases 3 and 4 to the reference value. The ratio of individual k 00 to the reference value is also shown in the same figure. The same kinds of ratios for Cases 5 and 6 are shown in Fig. 4(d). From these figures, it is observed that the mean values k 00(tn) agree with the reference value within the mean uncertainties u(tn), even when the number of neutron histories is very small as in Cases 5 and 6. Thus reliable burn-up calculation results and their uncertainties can be obtained from two or more executions of MVP BURN with a small number of histories. This procedure is more practical than the trial-and-error one of changing the number of neutron histories until expected calculation accuracy is obtained. An inverse of the number of neutron histories can be used instead of af (tn) in Eq. (3) in averaging the parameters such as the atomic number densities of depleting nuclides whose standard deviations are not calculated. (3) Comparison with SRAC95 The burn-up changes of the k 00s and instantaneous conversion ratios obtained with MVP-BURN and SRAC95 are compared in Fig. 5, where they are plotted only at the burn-up step points requested by the benchmark specification. The conversion ratio is defined as the ratio of the total capture rate of fertile nuclides ( 238U, 240 Pu) to the total absorption rate of fissile ones ( 235 U, 239 Pu, 241 Pu). The values of MVP-BURN are the above-mentioned mean ones from Cases 1 and 2. The maximum differences between the SRAC95 and MVP-BURN results are 0.27%.dk for k 00 at 25 GWd/t and 0.53% for conversion ratio at 30 GWd/t. Such small differences have been often observed in our comparisons between MVP and SRAC95 results for statistic problems. In the present case, for instance, the differences in k 00 and conversion ratio at zero burn-up state are

6 132 K. OKUMURA et al.,e ,...,.., _,-_... _--... _... _"':..,... _,--... _--... _":J J 1.05 = ] 1.00 Case3 o Case reference --mean(case3,case4) ,e-1.10 a 'i "';' 1.05.::ii= 1.00 Cases o Case6 --mean(case5,case6) reference --., (a) (b) ' , , i 1.01ooi:: ::::::;1 _._ -r4=:==;f.::::::::::=::=l=:::::,,,"'"c-t -= C :. : -----! 'S ' '.Sl Case3 / reference o Case4 / reference --mean(case3,case4) / reference Fig (c) Cases / reference o Case6 / reference --mean(case5,case6) / reference I I l I '... 0 : : : , Effects of initial random numbers and neutron histories on k= in HCLWR benchmark In Cases 3 and 4, the number of histories is 45,000 but different initial random numbers are used. In Cases 5 and 6, the number of histories is 2,000 but different initial random numbers are used. Reference is mean value of Cases 1 and 2 in Fig. 3_ Error bar is based on Eq_ (4) \,.,... L O-SRAC i...,..mvp-burn -..._:. 't other solutions ,,_.,,_.,,_ os I 0.82 C =.e Sl f i "' (d) --O-SRAC95...,..MVP-BURN =---'""""'-::-".10;:--'-'-2='=0.L...<.,::3'--:-040=--'-'"----'---'---='50 (a) (b) Fig. 5 Comparison of (a) koc,s and (b) instantaneous conversion ratios in HCLWR benchmark Result of MVP-BURN is mean value of Cases 1 and 2 (See Fig_ 3). JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

7 Validation of a Continuous-Energy Monte Carlo Burn-up Code MVP-BURN 133 (0.23±0.06)%Llk and (0.34±0.16)%, respectively. The atomic number densities of plutonium isotopes calculated with both codes agree well within 1 % except for 238Pu (3%) at the end of burn-up (50GWd/t). Thus, satisfactory agreements were obtained between the results of both codes for major burn-up parameters of the HCLWR lattice. In Fig. 5, large spreads of k 00s and conversion ratios are observed among 17 other solutions. These differences include the effect of different nuclear data files employed by benchmark participants. To estimate it, burn-up calculations were carried out with SRAC95 by using several libraries generated from different nuclear data files. As shown in Table 1, this effect is relatively small through burn-up duration. It seems that the large differences are mainly caused by insufficient treatments of resonance shielding and by use of burn-up chain models inappropriate for the HCLWRC15l-C18l. Even well validated codes for current reactors do not always give a sufficient accuracy for new types of reactors like the HCLWR, because most of the codes are optimized to reduce computation time and required memory for their applications. For example, the resonance shielding is often neglected for the nuclides whose contributions are small in conventional reactors. As MVP-BURN always considers the resonance shielding effect of any nuclide in any resonance energy, it is an effective means especially for burn-up analyses of new types of reactors. 2. BWR Lattice with Adjacent Gadolinium Pins (1) Benchmark Problem A benchmark comparisonc19 l was proposed in 1981 to investigate the calculation accuracy of burn-up characteristics for the BWR fuel assembly with poisoned fuel rods. The simplified BWR lattice geometry for the problem is shown in Fig. 6. This problem is appropriate to verify the applicability of MVP-BURN to fuel assemblies with high heterogeneities and fuel rods with burnable poison nuclides. Details of benchmark specifications and ten provided solutions are summarized in Ref. (19). In both of the calculations with MVP-BURN and SRAC95, a poisoned fuel pellet was divided into eight annual depleting zones to consider the change of spa- Fig. 6 Lattice geometry of BWR benchmark tial shielding effect of Gd20 3 during burn-up time, while unpoisoned fuel pellets were not divided, for the burnup changes of microscopic absorption rates of gadolinium nuclides are so rapid that small intervals of burn-up step are required. The intervals were 0.25 GWd/t up to 8.0 GW d/t and 0.5 GW d/t thereafter for both codes. In the MVP-BURN calculation, a large number of neutron histories (670,000) was used to get a sufficiently accurate k 00 (a<0.1%) at each burn-up step point. (2) Comparison with SRAC95 Major calculated results are shown in Figs. 7 and 8. The maximum [and average] differences, along burnup, between the SRAC95 and MVP-BURN are 0.85 [0.24]%Llk in k 00, 1.2 [0.56]% in power density of an unpoisoned fuel rod (No. 4 pin in Fig. 6), and 3.2 [2.4]% in that of the poisoned rod. As the maximum differences are almost comparable to those at the zero burn-up state (e.g. 0.81%Llk in k 00 ), they are considered to be caused mainly by an inaccuracy of the SRAC95 calculation. However, general burn-up characteristics are similar between both codes, in comparison with the other solutions. (3) Effect of Statistical Error Figure 9 shows the burn-up change of k 00 for the case of poor neutron histories ( =2,000), together with that predicted with sufficient histories. The solid line in the figure is a fitted curve by the 3rd-order polyno- Table 1 Effects of different nuclear data files on HCLWR benchmark results with SRAC95 Nuclear data for SRAC95 JENDL-2t JENDL-3.2 JEF-2.2 ENDF-B/IV ENDF-B/V1tt BOL (OGWd/t) k-infinity EOL (50GWd/t) Instantaneous conversion ratio BOL EOL (0 GWd/t) (50GWd/t) t With old version of SRAC in 1988 tt Release-5 VOL. 37, NO. 2, FEBRUARY 2000

8 ' 134 K. OKUMURA et al. mial expression based on the least squares method. It is surprising that general behavior of k 00s is well predicted within about 2cr with only 2,000 neutron histories even in the highly heterogeneous lattice. The Monte Carlo burn-up calculation is more stable than it was expected. VI. Analysis of Spent Fuel Composition 1. Irradiated Fuel Sample and Calculation Method In order to evaluate the calculation accuracy for realistic spent fuel compositions, a post irradiation experiment<20> (PIE) was analyzed with MVP-BURN and other deterministic codes for a sample fuel irradiated in a PWR (Mihama-3). Destructive analysis for nuclides of uranium, transuranium and FPs was performed for 9 samples of spent fuels at Japan Atomic Energy Research Institute (JAERI). Details of the experimental procedure and results are reported in Ref. (20). The following 6 burn-up calculations were carried out for the most irradiated sample whose exposure is 34.1 GWd/t. Two calculations with MVP-BURN were performed by changing random numbers with the JENDL-3.2 library. The number of 340,000 neutron histories was traced with 34 batches and the last 300,000 histories were tallied at each burn-up step point. The SRAC95 calculations were performed with the libraries generated from three different nuclear data files, namely, JENDL- 3.2, JEF-2.2<21> and ENDF /B-VI<22> (Release-5). The SWAT<23) code, which is a combined code of SRAC95 and ORIGEN2. 1 <24)( 25), was also used to confirm effects of different depletion calculation methods and burn-up chain models. It treats 1,227 nuclides in the depletion calculation by the method of ORIGEN2.l. The cross section library of SWAT consists of multi-group infinite dilution cross sections based on JENDL-3.2 for 247 nu- Fig. 7 i IC.e -'"I MVP-BURN --0- SRAC95-10 other solutions 0 95 o,_._ ,_..._,6c-'--=-s.10 Comparison of koc,s in BWR lattice benchmark The 10 solutions (Ref. (15)) are plotted only at 11 burn-up points (0, 1, 2, 10 GWd/t) a3,e! "Cl! &l 1.1 = c. = 1.10 z._, c. a = 1.00 : :c = Fig. 8...,._.MVP-BURN --O-SRAC other solutions j I i --r c= Bum-up (GWd/t) (a) Fig i 1.10.e -'"I koc, in BWR benchmark with very poor neutron histories Solid line means 3rd-order polynominal fitting by least squares method. Comparison of pin powers for (a) unpoisoned fuel rod and (b) poisoned fuel rod iri BWR benchmark ' r i (b) JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

9 Validation of a Continuous-Energy Monte Carlo Burn-up Code MVP-BURN 135 clidesc 23l and one-group cross sections of the ORIGEN library for other nuclides. A spectrum calculation is carried out with SRAC95 at each burn-up step point. The spectrum is used for energy condensation of the infinite dilution cross sections. In addition, capture and fission cross sections of major resonant nuclides are replaced by those obtained with SRAC95. The irradiation history of the sample fuel is given in a literaturec20l, which is shown in Fig. 10. Therefore, an infinite unit cell model was employed for the burn-up calculations with an effective rod-to-rod pitch. The effective pitch was determined so that a spectrum index ( <Pfast/ <Ptherma!) in the sample fuel might agree with that obtained by a heterogeneous assembly calculation with SRAC95 as shown in Fig. 11, because the sample was located next to a guide tube in the fuel assembly. It was assumed that temperatures of fuel, cladding and moderator and a concentration of boric acid were constant during burn-up duration. They were 1,150K, 608K, 588K and 500 ppm, respectively. The temperatures were estimated from the burn-up averaged liner heat rating of the sample fuel (see Fig. 10) and a vertical position where the sample was irradiated in the PWR. The boric acid concentration is a conventional value at the middle of a cycle. In order to estimate uncertainties due to these assumptions, sensitivity studies were carried out with SRAC95 and JENDL-3.2 by changing assumed parameters, efi30 i.. oi 10...:::., GWd/t ] annual inspection 19.4 Wd/t (9da s) 34.lGWd/t Time (days) Fig. 10 Irradiation history of a sample fuel in analysis of spent fuel composition fective pitch, temperatures and boron concentration, in proper ranges. From this study, it was concluded that about 4% should be considered as an uncertainty of the calculated results, especially for the sensitive nuclides 23sPu, 239Pu, 241 Pu, 241 Am, 242m Am, 243Cm, 244Cm and 154Eu. 2. Results and Discussions (1) Comparison among Calculated Results with JENDL- 3.2 All of the calculated results are summarized in Table 2. Before comparing with experimental data, it is useful to compare the calculated results of MVP BURN, SRAC95 and SWAT. They use their own libraries but are based on the same JENDL-3.2. The depletion calculation method of MVP-BURN is the same as that of SRAC95, although MVP-BURN uses the simplified chain model equivalent to the detailed one used in SRAC95. On the other hand, the calculation method of the effective cross sections is the same between SRAC95 and SWAT for all nuclides treated in the detailed chain model of SRAC95. We can obtain peculiar features of each code and an uncertainty due to the different burnup calculation methods. From the comparison between the two MVP-BURN results, the propagation effect of statistical errors is estimated to be less than 1.0% for the atomic number densities of measured nuclides. The average for nuclides is only 0.2%, which is surprising if we consider that 20 times of MVP execution were done in the burn-up calculation. Since the difference for 237Np is prominent, the production path of 237Np by (n, 2n) reaction of 238 U may be contributing. The statistical errors for the ( n, 2n) reaction rates are about 2.0% in each burn-up step, while those for the microscopic capture or fission reaction rates are about 0.2%. The final result of MVP-BURN is taken as the averaged value of the two results. Thus the effect of the statistical errors is supposed to be less than 0.5%. It is a sufficient accuracy for PIE analysis. From the comparison between the SRAC95 and SWAT u i:q... ;;,. ;l "... i..... ti i White reflective B.C. 5.2 ::I Q 5.0 -; 4.8 s c: "' 4.0 ::I 4.2 Q fa;, "" ' Effective cell pitch(cm) Guide tube Sample fuel._... [t] Fig. 11 Calculation model for a 107-group collision probability calculation with SRAC95 to determine an effective cell pitch applied to PIE analysis VOL. 37, NO. 2, FEBRUARY 2000

10 136 K. OKUMURA et al. Table 2 Results of an analysis for a post irradiation experiment with MVP-BURN, SRAC95 and SWAT JENDL-3.2 JEF-2.2 ENDF/ B-VI Calculation/ Calculation Calculation/Experiment Measured nuclides Exp. error (%) MVPti; SRAC/ SRAC/ SWAT/ Mvpt3 / SWAT/ SRAC/ SRAC/ SRAC/ MVPt2 SWAT Mvpt3 MVPt3 E E E E E 235u u su Np pu pu Pu Pu pu Am mAm Am cm cm cm Nd Nd l48nd 2.0 No datat No data No data No data Cs 2.8 No datat No data No data No data I54Eu t5 0.89t t5 o.89t5 1.53t5 1.05t5 tl, t2 Ratio of two MVP-BURN results obtained with different random numbers. t3 Average of two MVP-BURN results: (MVPtl+MVPt2)/2 t 4 Treated as lumped fisson products in MVP-BURN t 5 Underestimated (about 10%) by insufficient resonance treatments of SRAC95 and SWAT for 152 Sm results, the effects of different depletion calculation methods and chain models are estimated to be less than 4.0%. The maximum differences are observed for 237Np and 242 m Am. In SWAT, fission and capture cross sections are replaced by those obtained with SRAC95; however, (n, 2n) cross sections are not replaced. Furthermore, the values of branching ratio from 241 Am to 242m Am (see Fig. 1) are different. Since the branching ratio is not evaluated in JENDL-3.2, SRAC95 and MVP BURN employ the value (=11.6%) taken from ENDF /B VI (Release-2) by using a 107-group capture rate of 241 Am in a typical PWR as an energy weighting function. On the other hand, SWAT employs a 5% smaller value taken from the ORIGEN library. The differences between the SRAC95 and SWAT results are mainly caused by the above situations, rather than by the differences of the depletion calculation methods and the chain models. From the comparison between the MVP-BURN and SRAC95 results, a large difference over 10% is observed only for 154 Eu. It is the same in the comparison between the MVP-BURN and SWAT results. In order to find the cause of this discrepancy, the effective microscopic cross sections of Eu isotopes and Sm isotopes (see Fig. 1) obtained with MVP-BURN and SRAC95 were compared. As a result, it was found that the effective capture cross section of 152 Sm with SRAC95 was smaller by about 25%, which is caused by the NR approximation with no mutual shielding considerations for the 152 Sm giant resonance in 8.0 ev. This will be improved by preparing the super-fine group cross section data for PEACO. The library for PEACO is not prepared for all available nuelides in SRAC95. In the PIE analyses for FPs, a special attention is necessary because the resonance shielding of FPs is often roughly treated in nuclear calculation codes for the reason that they are not sensitive to criticality, power distributions and so on. (2) Comparison with Experimental Data The discrepancies beyond experimental errors are observed for several nuclides. However, we discuss here only 154Eu 238Pu 242mAm and 244Cm whose C/E values de- ' ' ' viate by more than 10% from unity, because careful and more PIE analyses seem to be necessary for the other nuclides. As for 154 Eu, the result with JEF-2.2 shows a considerably large overestimation, while MVP-BURN with JENDL-3.2 predicts the experimental result within its JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

11 Validation of a Continuous-Energy Monte Carlo Burn-up Code MVP-BURN 137 experimental error. This large overestimation with JEF- 2.2 is attributed to the smaller capture cross section of 154E in JEF-2.2. The capture cross section is 1/5-1/10 those of the other evaluations, in the energy range from 0.leV to 0.4eV. On the other hand, the results of SRAC95 and SWAT with JENDL-3.2 for 154E, which have about 10% discrepancies, are expected to approach to the MVP-BURN result by the improvement of the resonance treatment for 152Sm, while the discrepancy of the result with ENDF/B-VI will become larger. As for 238Pu, 242m Am and 244Cm, serious underestimations are observed for the results with any code and any library employed in this study. In addition, similar results were obtained from the PIE analysis with SRAC95 for the other sample fuels. If we believe the experimental values for these nuclides, the discrepancies are attributed to the following possibilities: (1) The smaller productions of 238Pu are due to underestimation of the capture cross section of 236 U and/or 237Np. Other possibilities are underestimation of the (n, 2n) cross section of 238U and overestimation of the absorption cross section of 238Pu. (2) The smaller production of 242m Am is due to underestimation of the capture cross section of 241 Am and/or underestimation of the branching ratio from 241 Am to 242m Am. (3) The smaller production of 244Cm is due to underestimation of the capture cross section of 243 Am and/or overestimation of the absorption cross section of 244Cm. It is probable that the large underestimation by about 20% or more of the productions of 238Pu, 242mAm and 244Cm is a common problem for most current nuclear data files. In spite of the large discrepancies for the atomic number densities of these nuclides, they usually do not affect the integrated burn-up parameters such as neutron multiplication factor, conversion ratio and power distribution. That is because the fractional absorption rate of all the discrepant nuclides is negligibly small (less than 10-4% in this study) even at the end of burn-up. However, if the above possibilities are true, it is difficult to obtain accurate burn-up parameters even with MVP BURN for the system where the discrepant nuclides are concentrated or lumped. Such situations will appear in nuclear design studies of transmutation reactors for minor actinides, inert-matrix fuel reactors, irradiation of actinides in a capsule, and so on. Further investigations are necessary for calculations, post irradiation experiments and nuclear data files related to productions of 238pu, 243 Am and 244Cm. VII. Conclusions A continuous-energy Monte Carlo burn-up code MVP BURN was developed to make burn-up analyses for which we have few experiences or difficult problems to treat with deterministic codes. MVP-BURN was verified by numerical benchmarks for an HCLWR lattice with a hard neutron spectrum and for a BWR lattice VOL. 37, NO. 2, FEBRUARY 2000 with burnable poison rods. The analysis results showed that MVP-BURN could well predict major burn-up parameters, such as neutron multiplication factor, conversion ratio and pin power distribution. Serious effects of propagation of statistical errors were not observed in this study even when the number of neutron histories was considerably reduced. MVP-BURN was applied to a post irradiation experiment analysis. It was confirmed that the effect of statistical errors on a burned fuel composition was sufficiently small, and it could give a reference solution for other codes by using an appropriate burn-up chain model. The three different burn-up calculation codes including MVP BURN predicted the measured fuel composition within an error of 10% for most nuclides. However, underestimation by about 20% or more was observed for 238Pu, 242mAm and 244Cm. It is probable that the underestimation is a common problem for most current nuclear data files. Further investigations are necessary on calculations, experiments and nuclear data files by paying attention to the production and transmutation paths of 23sPu, 242m Am and 244Cm. ACKNOWLEDGMENT The authors wish to express their gratitude to Mr. K. Suyama for his valuable information on post irradiation experiment analyses and for his instruction to make use of the SWAT code. -REFERENCES- ( 1) Kameyama, T., Matsumura, T., Kinoshita, M.: Trans. Am. Nucl. Sci., 66, 197 (1992). ( 2) Kelly, D. J.: Proc. Int. Conf. on Mathematics and Computations, Reactor Physics, and Environmental Analyses, Portland, Vol. 2, p (1995). 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