REACTOR PHYSICS ASPECTS OF PLUTONIUM RECYCLING IN PWRs

REACTOR PHYSICS ASPECTS OF PLUTONIUM RECYCLING IN s Present address: J.L. Kloosterman Interfaculty Reactor Institute Delft University of Technology Mekelweg 15, NL-2629 JB Delft, the Netherlands Fax: ++31 15-2786422, E-mail: klooster@iri.tudelft.nl Former address: J.L. Kloosterman Netherlands Energy Research Foundation (ECN) P.O. Box 1, NL 1755 ZG Petten, the Netherlands ABSTRACT Burnup calculations have been performed to calculate reactor physics parameters like reactivity coefficients and kinetic parameters as a function of burnup for MOX fuel with different moderator-to-fuel ratios. From the reactor physics point of view, MOX fuel in a with a moderator-to-fuel ratio of 4 is very similar to UO 2 fuel with a ratio of 2, except for the delayed neutron fraction which is reduced by 50%. I. INTRODUCTION The slow down of fast reactor development urges for another solution to get rid of the plutonium generated in light water reactors. One possibility is to recycle this plutonium in Mixed-OXide (MOX) fuel assemblies in s before disposition or further use. When the fissile 235 U in standard UO 2 fuel is replaced by a mixture of plutonium isotopes, the reactor physics parameters of the fuel change considerably with associated impact on the controllability of the reactor. This paper describes the reactor physics impact of MOX fuel in s. The fuel temperature coefficient (FTC), the moderator temperature coefficient (MTC), the boron reactivity worth (BRW), the critical boron concentration (CBC), the moderator void coefficient (MVC), the neutron generation time (Λ), and the effective delayed neutron fraction (β eff ) have been calculated as a function of burnup for standard UO 2 fuel and for MOX fuel. The reference reactor used in the calculations is a French N4 operated with five batches of UO 2 fuel with an initial enrichment of 4% and an exit burnup of 47.5 GWd/tHM. The calculations on the MOX fuel have been done for several moderator-to-fuel volume (MF) ratios ranging from 2 to 4. The plutonium in the spent fuel has been recycled four times. II CALCULATIONAL PROCEDURES The calculations have been performed with the OCTOPUS burnup and criticality code system 1, applying the BONAMI-NITAWL-XSDRNPM codes for the resonance shielding and 1-D neutron spectrum calculations, and the ORIGEN-S code for the burnup calculations. Nuclear data used are based on the JEF2.2 and EAF4.1 libraries. The reactivity coefficients and kinetic parameters have been calculated at a number of branchings during the burnup. The FTC has been calculated by increasing the fuel temperature with 100 K, the MTC by increasing the moderator temperature with 10 K, the BRW by increasing the boron density with 100 ppm and the MVC by decreasing the moderator density to 1% of its nominal value. All reactivity coefficients have been calculated by δk/k. At each branching, an adjoint calculation has been performed to calculate the contributions of the individual nuclides to the FTC by means of first-order perturbation theory 2 and to calculate Λ and β eff. The plutonium density in the MOX fuel and the CBC in the moderator have been determined by assuming that the fuel reactivity decreases linearly as a function of burnup, and that the core contains the same number of assemblies of each of the five fuel batches. Then the reactivity curve of the third fuel batch resembles that of the equilibrium core, and the plutonium density should be such that the k during the third fuel batch equals that of standard UO 2 fuel (1.057), while the CBC should be such that the reactivity loss during the third fuel batch is zero. Then the boron concentration, which is assumed to decrease linearly as a function of burnup, compensates for the reactivity loss due to depletion of fissile material and buildup of fission products. The result is a constant k with value of 1.057 during the third fuel batch. Because the plutonium density and the boron concentration depend on each other, these two parameters had to be determined iteratively. The scheme for the plutonium recycling calculations is shown in figure 1. For the first recycling, the isotopic composition of the plutonium in the spent UO 2 fuel is used for the manufacturing of the MOX fuel. For the second, third and fourth recycling, the spent MOX fuel is assumed to be blended with a three times larger amount of spent UO 2 fuel before reprocessing. The sensitivity of the results to this blending ratio has not been investigated. All recycling calculations have been done for MF ratios varied

between 2 (the standard value for UO 2 fuel) and 4. This has been accomplished in two different ways: by reducing the fuel pin radius or by increasing the fuel rod pitch. In the first case, the heat flux at the rod outer surface has been preserved to keep the DNB margin. This means that both the linear power and the fuel cycle length have to be reduced proportional to the fuel radius. In the second case, the linear power has been preserved to limit the fuel centerline temperature in the rod. This means that the core power density is reduced proportional to the square of the fuel rod pitch. The economic impact of increasing the MF ratio is numerically about the same for both methods. UO2 MOX1 MOX2 MOX3 MOX4 2 years STANDARD 5 years 2 years ADVANCED 5 years 2 years ADVANCED 5 years 2 years ADVANCED 5 years 2 years ADVANCED 5 years PLUT1 PLUT2 PLUT3 PLUT4 PLUT5 Figure 1: The scheme for the multi-recycling of plutonium in s. should be larger to compensate for the extra neutron absorption by the even non-fissile plutonium isotopes. This means that the neutron resonance absorption rate (both capture and fission reactions) in MOX fuel is much larger than in UO 2 fuel with the same MF ratio. The larger resonance absorption rate in MOX fuel causes many differences in reactor physics parameters compared with standard UO 2 fuel, which will be explained in this section. The burnup reactivity loss is lower for MOX fuel due to the conversion of the even non-fissile plutonium isotopes to odd fissile ones. This is seen in figure 2, which shows the k curves for UO 2 and MOX fuels with MF=2 and for MOX fuel with MF=4. The increased resonance absorption rate can be clearly seen from the four factors of the four factor formula: the fast fission factor ε, the resonance escape probability p, the thermal utilization f, and the number of fission neutrons produced per thermal neutron absorbed in the fuel η. Figures 3 and 4 show these four factors as a function of burnup for UO 2 and MOX fuel, respectively. Clearly, the fast fission factor ε (better named the non-thermal fission factor) is much larger and the resonance escape probability much smaller for MOX fuel than for UO 2 due to the much higher resonance absorption rate. The η for MOX fuel is slightly smaller, while the f does not differ very much between the two fuels. At the end of each fuel batch, f tends to unity due to the linearly decreasing boron concentration in the moderator. At the end of each fuel batch when the boron concentration is zero, the neutron absorption rates by the moderator and the structural materials are negligible and all thermal neutrons are absorbed by the nuclides in the fuel. Table 1: The neutron capture and fission resonance integrals (barn) for uranium and plutonium isotopes at infinite dilution. RGPu stands for reactor grade plutonium with the PLUT1 composition in figure 1. Isotope I γ I f 235 U 144 275 239 Pu 200 301 240 Pu 8100 9 III RESULTS: CHANGING FROM UO 2 TO MOX FUEL When a mixture of plutonium isotopes is used as a fuel instead of the fissile 235 U, the neutron resonance integral increases considerably. Table 1 shows the neutron capture and fission resonance integrals for the relevant uranium and plutonium isotopes at infinite dilution. Clearly the resonance integrals of the plutonium isotopes are much larger than that of the 235 U. In practice the number of fissile plutonium isotopes in the fresh MOX fuel should be as large as the 235 U number density in UO 2 fuel. In fact it 241 Pu 162 570 242 Pu 1115 5 RGPu 2126 234

K inf 1.3 1.2 1.1 1.0 UO2 MF=2 MOX MF=2 MOX MF=4 contribution of the 238 U is smaller in MOX, but this is compensated by the larger contributions of 240 Pu and 242 Pu. Table 2: The contributions of the individual isotopes to the fuel temperature coefficient (pcm/k). Isotope Fuel type BOL EOL 238 U UO 2-2.5-2.5 240 Pu UO 2 0-0.70 238 U MOX -2.2-2.2 240 Pu MOX -0.75-0.75 0.9 242 Pu MOX -0.30-0.35 Figure 2: The k as a function of burnup for UO 2 and MOX fuel with MF=2 and for MOX with MF=4. 2.2 UO2 MF=2 2.2 MOX MF=2 2.0 1.8 k inf η f p ε 2.0 1.8 k inf η f p ε 1.6 1.6 1.4 1.4 Four factors 1.2 Four factors 1.2 1.0 1.0 0.8 0.8 0.6 0.6 0.4 The FTC is larger for MOX fuel than for UO 2 due to 0.2 0.4 0.2 Figure the extra 3: The contributions four factors of as the a even function plutonium of burnup isotopes. for UO 2 fuel with MF=2. The FTC is larger for MOX fuel than for UO 2 due to the extra contributions of the even plutonium isotopes. Table 2 gives the contributions of the most important isotopes to the FTC at BOL and at EOL of the fuel. The Figure 4: The four factors as a function of burnup for MOX fuel with MF=2. The MTC is due to two effects with opposite sign. First a temperature increase shifts the Maxwell spectrum to higher energies, which reduces the neutron absorption by the parasitic absorbers in the fuel (fission products etc.). Secondly, the moderator density decreases which gives less moderation and, if the fuel is properly undermoderated, a

lower reactivity. If boron is present in the moderator, its density also decreases which gives a positive reactivity insertion. Clearly the boron concentration may never be that high that the reactivity effect due to the reduced boron concentration is larger than that due to the reduced moderation. For UO 2 fuel, the burnup averaged MTC equals -46 pcm/ppm, while this is -54 pcm/ppm for MOX. An increase of the MTC amplifies the consequences of moderator cooling accidents and should therefore be limited. The BRW is much lower for MOX fuel than for UO 2 due to the much harder neutron spectrum and the correspondingly smaller spectrum averaged absorption cross section of the 10 B. Figure 5 shows the neutron spectrum at BOL for the two fuel types. The burnup averaged BRW equals -7.7 pcm/ppm for the UO 2 and only -2.4 pcm/ppm for the MOX. Due to this low reactivity worth, the CBC equals almost 1200 ppm for the MOX, while this is only 875 ppm for the UO 2 fuel, despite the lower burnup reactivity loss for the MOX. Neutron spectrum (au) 10.00 1.00 0.10 0.01 UO2 MF=2 MOX MF=2 0.00 10 2 10 1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 Energy (ev) Figure 5: The neutron spectrum at BOL for UO 2 and for MOX fuel with MF=2. The MVC is one of the most critical parameters for the recycling of plutonium in LWRs. Due to the relatively large plutonium density in the MOX ( 10%) compared with the 235 U density in UO 2 fuel ( 4%), and due to the fact that the capture-to-fission ratio of the even plutonium isotopes decreases with a factor of 20 to 30 upon voiding while that ratio of 235 U increases, the MVC is much smaller for MOX fuel than for UO 2. For UO 2, this coefficient equals -527 pcm/%, while it is only -210 pcm/% for the MOX fuel. The much harder neutron spectrum in the MOX fuel gives a value for Λ which is three to four times smaller than in UO 2 fuel. For MOX fuel Λ equals only 5 10-6 s. Finally the β eff was examined. For UO 2 fuel, this parameter reduces from 0.7% at BOL to 0.5% at EOL, mainly due to the depletion of 235 U and the buildup of 239 Pu, which has a very small delayed neutron fraction. In MOX fuel, the fission process is dominated by this latter isotope, and the β eff equals only 0.4%. The contributions to the β eff for both UO 2 and MOX fuel are shown in figures 6 and 7. Notice the quite large contribution of 238 U to the β eff (20 to 30%) due to the large delayed neutron fraction of this isotope. In conclusion, the temperature coefficients for both the fuel and the moderator are larger negative for MOX fuel than for UO 2, which is undesirable from the viewpoint of fuel and/or moderator cooling accidents. Compared with UO 2 fuel, a MOX fueled reactor has a shorter neutron generation time and a smaller delayed neutron fraction. This makes it necessary to improve the controllability of a full MOX reactor by special measures. IV RESULTS: INCREASING THE MF RATIO Much of the disadvantages described in the previous section can be reduced by increasing the MF ratio of the fuel lattice, which enhances the moderation and reduces the neutron absorption rate in the resonance region. Due to the more thermalized neutron spectrum, the reactivity worths of the fissile plutonium isotopes are higher and the needed initial plutonium density in the fuel lower. With a MF ratio of 2, the plutonium weight fraction in the fuel equals 10%, while this is only 5.9% for MOX with MF=4. Due to the lower resonance absorption rate, the conversion rate of even plutonium isotopes to odd ones and of 238 U to 239 Pu is lower, which gives a burnup reactivity loss comparable with that of standard UO 2 fuel.

100 90 80 UO2 MF=2 92235 92238 94239 94240 94241 100 90 80 MOX MF=2 92235 92238 94239 94240 94241 70 70 Contribution to B eff (%) 60 50 40 Contribution to B eff (%) 60 50 40 30 30 20 20 10 10 0 0 Figure 6: The isotopic contributions to the β eff of UO 2 fuel with MF=2 as a function of burnup. Figure 7: The isotopic contributions to the β eff of MOX fuel with MF=2 as a function of burnup. Figure 8 shows the four factors for the MOX fuel with MF=4. Clearly, the fast or non-thermal fission factor is much lower than for standard MOX fuel with MF=2 (see figure 4), and even slightly lower than for standard UO 2 fuel (see figure 3). The lower ε is compensated by a larger resonance escape probability p. In general, the four factors of the MOX fuel with MF=4 compare very good with those of the UO 2 fuel with MF=2. The FTC is shown in figure 9 as a function of burnup. Two differences are apparent. First, the values for the FTC are 20 to 30% lower than for standard MOX fuel due to the lower neutron resonance absorption rate. Secondly, the values for the case with an increased pitch are lower than for the case with a reduced pin diameter. The latter effect is due to the more homogeneous distribution of the fuel in the moderator in case the pin diameter is reduced, which gives a larger resonance absorption rate and a correspondingly larger value for the FTC. The MTC for MOX fuel with enhanced moderation Four factors 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 MOX MF=4 k inf η f p ε 0.2 Figure 8: The four factors for MOX fuel with MF=4 as a function of burnup.

contributions of the fissile isotopes to the fission power. For MOX with MF=4, β eff equals 0.4%. In conclusion, enhancing the MF ratio improves the safety characteristics of MOX fuel. Firstly, the temperature coefficients are negative, but not too large. Secondly, the boron reactivity worth, the moderator void coefficient, and the neutron generation time are comparable with that of standard UO 2 fuel. Thirdly, the plutonium density in the fuel and the boron concentration in the moderator are less than in standard MOX fuel. Only the delayed neutron fraction does not improve, as this parameter mainly depends on the contributions of the individual plutonium isotopes to the fission power rather than on the MF ratio. Fuel temp coef (pcm/k) 1.8 1.9 2.0 2.1 2.2 2.3 MOX MF=4 pin pitch 2.4 2.5 2.6 Figure 9: The fuel temperature coefficient of MOX fuel with MF=4 as a function of burnup. The MTC for MOX fuel with enhanced moderation (MF=4) is lower than for standard MOX fuel. Its burnup averaged value equals only -23 pcm/k for the case with increased pitch and -32 pcm/k for the case with reduced pin diameter, while it is -54 pcm/k for the standard MOX with MF=2. The thermalized neutron spectrum in the MOX fuel with MF=4 gives a large value for the BRW comparable with that of standard UO 2 fuel (-8 pcm/k). Furthermore, due to the low conversion rate and the correspondingly large depletion rate of the fissile plutonium isotopes, the neutron spectrum softens considerably as a function of burnup, which gives about twice as large values for the BRW at EOL. Despite the large burnup reactivity loss of the MOX fuel with MF=4, the BRW is that large that the CBC equals only 625 ppm, while this is 1200 ppm for the MOX fuel with MF=2. Increasing the MF ratio to 4 gives a much larger moderator void coefficient (MVC) equal to that of standard UO 2 fuel (about -500 pcm/%). This is an important safety aspect of MOX fuel with enhanced moderation. Other parameters like the Λ also improve. Increasing the MF ratio from 2 to 4 increases the Λ from 5 10-6 to 2 10-5 s. The β eff does not depend on the MF ratio, but on the V RESULTS: MULTIRECYCLING OF PLUTONIUM Recycling plutonium in MOX fuel according to the scheme presented in figure 1 reduces the fraction of fissile isotopes in plutonium. Consequently, the plutonium density in the fuel has to increase each recycling to meet the reactivity requirements. Table 3 shows the plutonium weight fractions in the fuel as a function of the MF ratio and the recycling number. Table 3: The plutonium density ( w %) in the fuel. MF Recycling number Ratio 1 2 3 4 2 10.0 13.0 15.0 16.6 3 6.5 10.1 12.8 15.1 4 5.9 8.7 11.1 13.5 The burnup reactivity loss reduces with increasing recycling number due to the increasing plutonium density and the corresponding higher conversion rate of even plutonium isotopes to odd ones. The FTC does hardly depend on the recycling number. Although the plutonium density in the fuel and the resonance absorption rate increase with the recycling number, the increase of the contributions due to the even plutonium isotopes is compensated by a decrease of the 238 U contribution. The MTC shows an interesting dependence on the MF ratio and on the recycling number, as shown in table 4. For low MF ratios, the MTC decreases with increasing recycling number, while for high MF ratios it increases. To understand this behaviour, one has to realize that the moderator-to-plutonium number density ratio (in the remainder referred to as the MPu ratio) increases with the MF ratio, but decreases with recycling number due to the increasing plutonium density. From basic reactor physics

one knows that the curve of the k versus the MPu ratio shows an inflection point. Apparantly, this point occurs at an MPu ratio corresponding with the second recycling of the MF=3 case. For that case the MTC is largest negative. For lower MF ratios, the MPu ratio is smaller, while for larger MF ratios the MPu is larger. Table 4: The moderator temperature coefficient (pcm/k). Results for reduced pin diameter. MF Fuel Recycling number Ratio type 1 2 3 4 2 UO 2-46 2 MOX -54-43 -37-32 3 MOX -54-57 -54-51 4 MOX -32-45 -49-50 As mentioned before, the MVC is one of the most critical parameters, which limits in many cases the number of times plutonium can be recycled. Table 5 shows the values obtained. One should realize that the uncertainties in these values are quite large. Not only because the increased radial leakage upon voiding was not accounted for, which underestimates the MVC, but also because of cross-section uncertainties and approximations in the codes used. Results from international benchmark calculations 3 show that due to the latter reason, the uncertainty may range up to 50 pcm/%. Taking a realistic (but arbitrary) safety margin of two times this value, plutonium recycling in s is limited to two times for a standard fuel lattice. For MF ratios larger than three, the plutonium can be recycled at least four times. Table 5: The moderator void coefficient (pcm/%). Results for reduced pin diameter. MF Fuel Recycling number Ratio type 1 2 3 4 2 UO 2-527 2 MOX -210-113 -58-21 3 MOX -443-320 -239-180 4 MOX -519-432 -365-307 Due to the increasing plutonium density in the fuel with increasing recycling number, the neutron spectrum hardens and the BRW decreases. Table 6 shows the BRW as a function of the MF ratio and the recycling number. Table 6: The boron reactivity worth (pcm/ppm). Results for reduced pin diameter. MF Fuel Recycling number Ratio Type 1 2 3 4 2 UO 2-7.7 2 MOX -2.4-2.0-1.8-1.7 3 MOX -6.1-4.2-3.9-3.5 4 MOX -9.6-7.5-6.4-5.7 The CBC is at first order equal to the ratio of the burnup reactivity loss (pcm) and the BRW (pcm/ppm). For the UO 2 fuel the CBC equals 875 ppm. For the first recycling, the CBC equals about 1200 ppm for the MOX with MF=2 and 625 ppm for the MOX with MF=4. The CBC does not depend much on the recycling number due to the facts that both the BRW and the burnup reactivity loss decrease with increasing recycling number. For the fourth recycling, the CBC equals 1360 and 510 ppm for the MOX fuels with MF=2 and MF=4, respectively. The neutron generation time Λ decreases with increasing recycling number due to the higher plutonium density and the correspondingly harder neutron spectrum. The results are given in table 7. For the same reason why the β eff does not depend on the MF ratio, it is also not dependent on the recycling number. Table 7: The neutron generation time Λ (µs). Results for reduced pin diameter. MF Fuel Recycling number Ratio Type 1 2 3 4 2 UO 2 18 2 MOX 5.3 4.3 3.9 3.6 3 MOX 14 10 8.5 7.6 4 MOX 21 16 14 13 In conclusion, multiple recycling of plutonium gives an ever increasing plutonium density in the fuel with a corresponding increase of the neutron resonance absorption rate and a hardening of the neutron spectrum. This generally decreases the boron reactivity worth, the moderator void coefficient, and the neutron generation time. The fuel temperature coefficient is hardly affected by the multiple recycling. For low MF ratios, the moderator temperature coefficient decreases with increasing recycling number, while the reverse is true for high MF ratios. The number of times plutonium can be recycled is limited in a standard fuel lattice with a MF ratio of 2.

VI CONCLUSIONS The conversion from UO 2 fuel to MOX fuel without changing the moderator-to-fuel volume (MF) ratio changes considerably the reactivity coefficients and kinetic parameters of the fuel which are important for a safe control of the reactor. Due to the stronger resonance absorption rate in the MOX fuel, the fast fission factor increases, while the resonance escape probability and the neutron generation time decrease. Furthermore, due to the large thermal absorption cross sections of plutonium isotopes, the boron reactivity worth decreases. All these disadvantages of using MOX fuel can be overcome by enhancing the MF ratio. From a reactor physics point of view, MOX fuel with a MF ratio of 4 is very similar to UO 2 fuel with MF=2, except for the delayed neutron fraction, which does not depend on the MF ratio but on the contributions of the individual isotopes to the fission rate. This parameter has a value of 0.6% in UO 2 fuel and of 0.4% in MOX fuel. Multi-recycling of plutonium in MOX fuel in a with a standard fuel lattice (MF=2) is limited to two times at the maximum. This number can be increased to at least four by increasing the MF ratio to three or higher. The equilibrium reactor park composition and the actinide mass balances in the park as well as the radiotoxicity reduction which can be achieved in such a park are presented elsewhere in literature 4,5. VII ACKNOWLEDGEMENTS This study has been performed at the Netherlands Energy Research Foundation (ECN, Petten, the Netherlands). The author acknowledges the European Union for co-funding this work under the contract entitled Evaluation of Possible P&T Strategies and of Associated Means to Perform Them (EU contract FI4I-CT95-0006, ECN project 7.1038). REFERENCES 1. J.L. Kloosterman et al, The Octopus Burnup and Criticality Code System, In Proc. PHYSOR 96, Mito, Japan, 16-20 Sep 1996. 2. J.L. Kloosterman, VAREX, A Tool for Variational Analysis of Reactivity Effects with XSDRNPM, Report ECN-I-95-037, Netherlands Energy Research Foundation (ECN), Petten, Netherlands, Oct 1995. 3. OECD Physics of Plutonium Recycling, Vol VI, To be published 1998. 4. J.L. Kloosterman, Multiple Recycling of Plutonium in Advanced s, In Proc. 5 th Int. Conf. on Recycling, Conditioning and Disposal (RECOD 1998), 25-28 Oct 1998, Nice, France. 5. J.L. Kloosterman, Multi-recycling of Plutonium in Advanced s, Report ECN-R-98-007, Netherlands Energy Research Foundation (ECN), Petten, Netherlands, Jun 1998.