PLUTONIUM RECYCLING IN PRESSURIZED WATER REACTORS: INFLUENCE OF THE MODERATOR-TO-FUEL RATIO

Transcription

1 PLUTONIUM RECYCLING IN PRESSURIZED WATER REACTORS: INFLUENCE OF THE MODERATOR-TO-FUEL RATIO FISSION REACTORS KEYWORDS: plutonium recycling, moderator-to-fuel ratio, PWR JAN LEEN KLOOSTERMAN* Delft University of Technology Interfaculty Reactor Institute, Mekelweg 15, NL-2629 JB Delft, The Netherlands EVERT E. BENDE NRG, P.O. Box 25, NL-1755 ZG Petten, The Netherlands Received February 8, 1999 Accepted for Publication December 15, 1999 The reactor physics trends that can be observed when the moderator-to-fuel (MF) ratio of a mixed-oxide (MOX) fuel lattice increases from two (the standard value) to four are investigated. The influence of the MF ratio on the moderator void coefficient, the fuel temperature coefficient, the moderator temperature coefficient, the boron reactivity worth, the critical boron concentration, the mean neutron generation time, and the effective delayed neutron fraction has been investigated. Increasing the MF ratio to values larger than three gives a moderator void coefficient sufficiently large to recycle the plutonium at least four times. Also, the values of other parameters like the boron reactivity worth, the fuel temperature coefficient, the moderator temperature coefficient, and the mean neutron generation time improve with increasing MF ratio. The effective delayed neutron fraction is almost independent of the MF ratio. According to a point-kinetics model, the response of a MOX-fueled reactor with an MF ratio of four to a moderator temperature decrease is similar to that of a UO 2 -fueled reactor with an MF ratio of two. Scenario studies show that recycling plutonium four times in pressurized water reactors reduces the plutonium production by a factor of three compared with a reference once-through scenario, but the americium and curium production triples. If the plutonium remaining after recycling four times is disposed of, the radiotoxicity reduces by only a factor of two. This factor increases to a maximum of five if the plutonium can be eliminated in special burner reactors. Recycling of americium and curium is needed to reduce the radiotoxicity of the spent fuel to lower values. In general, the plutonium mass reduction increases and the minor actinide production decreases with increasing MF ratio of the MOX fuel. Enlarging the MF ratio can be achieved by increasing the rod pitch or by reducing the fuel pin diameter. In both cases, the economic penalty is about the same and is quite large. I. INTRODUCTION * J.L.Kloosterman@iri.tudelft.nl The slowdown of fast reactor development argues for another solution to the plutonium produced in light water reactors ~LWRs!. One option is to recycle this reactorgrade plutonium in current LWRs before disposition or further use in fast reactors. In present-day pressurized water reactors ~PWRs!, the amount of mixed-oxide ~MOX! fuel in the core is limited to 30 to 50% ~Refs. 1 and 2! by licensing requirements, constraints on the reactivity worth of the control rods, and the fast neutron fluence on the reactor vessel. The latter two effects are mainly due to the high neutron absorption cross sections of the plutonium isotopes, the large number of fission neutrons released by fissioning plutonium ~see Fig. 1!, and the slightly harder fission spectrum of 239 Pu compared with 235 U. The MOX fuel fraction in the core may increase when special measures are taken to improve the controllability of the reactor. Even full-mox cores are feasible. 3 8 In such cases, increasing the moderator-to-fuel ~MF! ratio leads to a better thermalization of the neutron spectrum NUCLEAR TECHNOLOGY VOL. 130 JUNE

2 ν(e) Pu241 Pu239 Pu240 Pu242 U E (MeV) Fig. 1. The number of neutrons released per fission as a function of the incoming neutron energy for several uranium and plutonium isotopes. The isotope 235 U has the lowest neutron production per fission event. and a correspondingly higher boron reactivity worth. Furthermore, enhancing the moderation increases the net plutonium consumption, which implies that fewer PWRs are needed to recycle a certain amount of plutonium and leads to a more homogeneous core composition and a flatter power profile. Multiple recycling of plutonium in present-day PWRs is limited. Each recycling increases the plutonium density to compensate for the ever-decreasing fraction of fissile plutonium isotopes. After two recyclings, the plutonium density in the fuel becomes so high that the moderator void coefficient becomes weakly negative or even positive. Clearly, this is not allowed under any circumstances. Increasing the MF ratio reduces the resonance absorption rate and increases the reactivity worth of the fissile plutonium isotopes. This translates into a lower required plutonium density and, together with the lower fuel volume, a strongly negative moderator void coefficient ~MVC!. Therefore, multiple recycling of plutonium becomes feasible in a PWR with enhanced moderation. The number of times plutonium can be recycled depends on the MF ratio, the target burnup, and the blending ratio at the reprocessing plant ~present-day technology requires that spent MOX fuel be mixed with a three times larger amount of spent UO 2 fuel to limit the alpha emission rate and the heat generation during the reprocessing!. This work describes the reactor physics impact of MOX fuel in PWRs. To this end, the following parameters have been calculated as a function of burnup: the fuel temperature coefficient ~FTC!, the moderator temperature coefficient ~MTC!, the boron reactivity worth ~BRW!, the critical boron concentration ~CBC!, the MVC, the neutron generation time L, and the effective delayed neutron fraction b eff. This has been done for standard UO 2 fuel as a reference and for MOX fuel with an MF ratio between two and four, varied by either reducing the fuel pin diameter or by widening the lattice. As shown in this paper, increasing the MF ratio improves some reactor physics characteristics of MOX fuel. Other solutions to achieve this, like mixing enriched uranium through the MOX fuel 9 or designing a heterogeneous fuel assembly, 10 are not considered. The reference reactor used in all calculations is a French N4 PWR operated with five batches of UO 2 fuel with an initial enrichment of 4% and an exit burnup of 47.5 GWd0 tonne HM. The plutonium in the spent fuel has been recycled four times. In this paper, attention focuses on reactor physics trends. More results are given in Ref. 11. Parts of this paper dealing with reactor physics trends were published in Ref. 12, while the scenario studies were published in Ref. 13. This paper is organized as follows: The calculation procedures are described in Sec. II. Section III discusses reactor physics differences between UO 2 fuel and MOX. Section IV describes reactor physics trends resulting from increasing the MF ratio. Section V describes reactor physics trends resulting from multiple recycling of plutonium. Section VI discusses trends in moderator cooling accidents. Section VII presents results on scenario studies and radiotoxicity reduction. II. CALCULATIONAL PROCEDURE For the calculations, the OCTOPUS burnup and criticality code system 14 was used, applying the BONAMI- NITAWL-XSDRNPM codes for resonance shielding and one-dimensional spectrum calculations and the ORIGEN-S code for burnup calculations. All nuclear data used are based on the JEF2.2, EAF3, and EAF4 libraries. 15,16 Reactivity coefficients and kinetic parameters have been calculated at a number of branchings during burnup. The FTC has been calculated by increasing the fuel temperature by 100 K, the MTC by increasing the moderator temperature by 10 K, the BRW by increasing the boron density by 100 ppm, and the MVC by decreasing the moderator density to 1% of its nominal value. All reactivity coefficients have been calculated by Dk0~kDP! where DP is the change of parameter ~fuel temperature, boron density, etc!. At each branching, an adjoint calculation has been performed and the contributions of the individual nuclides to the FTC, the mean neutron generation time L, and the effective delayed neutron fraction b eff have been calculated by the VAREX code. 17 Furthermore, VAREX calculates the fast ~nonthermal! fission factor e, the resonance escape probability p, the fraction of thermal neutrons absorbed in the fuel f, and the number of neutrons released per thermal absorption in the fuel h ~Ref. 18!. 228 NUCLEAR TECHNOLOGY VOL. 130 JUNE 2000

3 The product of these four factors equals k`. The energy boundary between the fast and thermal energy groups was chosen at ev, which implies that the thermal group includes the lowest resonance of 239 Pu at 0.3 ev. To calculate the plutonium density in the fuel and the CBC in the moderator, it has been assumed that the fuel reactivity decreases linearly as a function of burnup and that the core contains the same number of assemblies in each of the five fuel batches. In that case, the linear reactivity model 19 can be applied, which implies that the reactivity at the end of the third fuel batch equals the reactivity at the end of the equilibrium batch. Core calculations show that the N4 reactor with fuel enrichment of 4% running in a five-batch mode is able to achieve a burnup of 47.5 GWd0tonne HM. From this, it can be deduced that the plutonium density must be high enough that the k` at the end of the third fuel batch equals that of standard 4% enriched 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 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. Figure 2 shows the scheme for plutonium recycling. The isotopic composition of the plutonium in the spent UO 2 fuel is used for fabrication of the fresh MOX fuel. For the second, third, and fourth recycling, the spent MOX fuel is 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. As mentioned before, all recycling calculations have been done for MF ratios from two ~the standard value for UO 2 fuel! to four. This has been accomplished in two different ways: by reducing the fuel pin diameter or by increasing the fuel pitch. UO2 MOX1 MOX2 MOX3 MOX4 2 years 2 years ADVANCED 5 years PWR 2 years 2 years 2 years STANDARD PWR ADVANCED PWR ADVANCED PWR ADVANCED PWR 5 years 5 years 5 years 5 years PLUT1 PLUT2 PLUT3 PLUT4 PLUT5 Fig. 2. The scheme for multirecycling plutonium in PWRs. The Pu in the UO 2 spent fuel is recovered and recycled in an advanced PWR with enhanced moderation. The spent MOX fuel is blended with a three times larger amount of spent UO 2 fuel before reprocessing. When a mixture of plutonium isotopes is used as fuel instead of fissile 235 U, the resonance integral increases considerably. Table I shows the neutron capture and fission resonance integrals at infinite dilution 20 for the relevant uranium and plutonium isotopes. Clearly, the resonance integrals for the plutonium isotopes are much higher than those for 235 U. To achieve similar burnups, the atomic density of fissile plutonium isotopes in fresh MOX fuel should be equal to the 235 U density in fresh UO 2 fuel. In fact, it should be larger to compensate for the increased neutron capture by the even nonfissile plutonium isotopes. As a consequence, the resonance absorption rate ~both capture and fission reactions! is much larger in MOX fuel than in UO 2 fuel with the same MF ratio. This has a large impact on the various reactor physics parameters. III. RESULTS: CHANGING FROM UO 2 TO MOX FUEL ~WITH CONSTANT MF RATIO! TABLE I The Neutron Capture and Fission Resonance Integrals of Uranium and Plutonium Isotopes at Infinite Dilution ~Ref. 20! Isotope I g ~b! I f ~b! 235 U Pu Pu Pu Pu RGPu a a RGPu stands for reactor grade plutonium with the PLUT1 composition indicated in Fig. 2. NUCLEAR TECHNOLOGY VOL. 130 JUNE

4 The burnup reactivity loss is lower for MOX fuel than for UO 2 due to conversion of even nonfissile plutonium isotopes to odd fissile ones, besides the conversion of 238 Uto 239 Pu. Figure 3 shows k` as a function of burnup for UO 2 fuel and for MOX with MF 2 and MF 4. The higher resonance absorption rate in MOX fuel changes the fast fission factor e and the resonance escape probability p. Figures 4 and 5 show the four factors e, p, f, and h for UO 2 and MOX fuel, respectively, as a function of burnup. Clearly, the fast fission factor e is larger for MOX fuel and the resonance escape probability p is smaller. Also, h is slightly smaller for MOX fuel due to neutron capture by even plutonium isotopes. At the end of each fuel batch, f tends to unity due to the linearly decreasing boron concentration in the moderator, which diminishes the neutron absorption by the moderator. Consequently, all thermal neutrons are absorbed by the nuclides in the fuel. For MOX fuel, the FTC changes slightly due to negative contributions of the even plutonium isotopes, a smaller negative contribution of 238 U, and small positive Four factors UO2 MF=2 k inf η f p ε UO2 MF=2 MOX MF=2 MOX MF= Burnup (GWd/tHM) Fig. 4. The four factors as a function of burnup for UO 2 fuel with MF 2. The product of the four factors equals k`. During each fuel burnup cycle of 9.5 GWd0tonne HM, the boron concentration decreases linearly from the CBC to zero. K inf Burnup (GWd/tHM) Fig. 3. The k` as a function of burnup for UO 2 fuel and for MOX fuel with MF values of 2 and 4. The burnup reactivity loss is the largest for UO 2 fuel and the lowest for MOX fuel with MF 2 due to conversion of even Pu isotopes to fissile ones. During each fuel burnup cycle of 9.5 GWd0tonne HM, the boron concentration decreases linearly from the CBC to zero. contributions of the odd plutonium isotopes. Table II gives the contributions of the isotopes that dominate the FTC at beginning of life ~BOL! and end of life ~EOL!. The contribution of 238 U is smaller in MOX fuel, but this is ~over!compensated by the larger contributions of 240 Pu and 242 Pu. Two effects with opposite sign determine the MTC. 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.!. Second, the moderator density decreases, which gives less moderation and, if the fuel is properly undermoderated, a lower reactivity. Simultaneously, the density of the dissolved boron decreases, which gives a positive reactivity insertion. Clearly, this effect may not exceed the reactivity decrease due to reduced moderation. The burnup-averaged MTC equals 46 pcm0k for UO 2 fuel and 54 pcm0k for MOX fuel. To limit the consequences of moderator cooling accidents, the MTC may not be too strongly negative. The BRW is much lower for MOX fuel than for UO 2 because of the harder neutron spectrum and the 230 NUCLEAR TECHNOLOGY VOL. 130 JUNE 2000

5 MOX MF=2 k inf η f p ε UO2 MF=2 MOX MF=2 Four factors Neutron spectrum (au) Burnup (GWd/tHM) Fig. 5. The four factors as a function of burnup for MOX fuel with MF 2. During each fuel burnup cycle of 9.5 GWd0tonne HM, the boron concentration decreases linearly from the CBC to zero. TABLE II The Contributions of the Dominant Isotopes to the FTC FTC ~pcm0k! a Isotope Fuel Type BOL EOL 238 U UO Pu UO U MOX Pu MOX Pu MOX Pu MOX a pcm percent of milli Energy (ev) Fig. 6. The neutron spectrum in arbitrary units ~au! at BOL for UO 2 and MOX fuel with MF 2. The MOX spectrum is much harder. correspondingly smaller spectrum-averaged absorption cross section of 10 B. Figure 6 shows the neutron spectrum at BOL for the two fuel types. The burnup-averaged BRW equals 7.7 pcm0ppm for UO 2 and only 2.4 pcm0ppm for MOX. Due to this low reactivity worth, the CBC equals almost 1200 ppm for MOX fuel, compared with 875 ppm for UO 2, despite the lower reactivity loss during burnup. Usually, the magnitude of the MVC is much smaller for MOX fuel than for UO 2, which makes it a critical parameter for multiple recycling of plutonium. Upon voiding, the capture-to-fission ratio of the even plutonium isotopes decreases by a factor of 20 to 30, while for 235 U this ratio increases. Together with the large density of plutonium in MOX fuel ~'10%! compared with the low density of 235 UinUO 2 ~'4%!, this may lead to weakly negative or even positive MVC values. For UO 2, this coefficient equals 527 pcm0%, while for MOX it is no larger than 210 pcm0%. The much harder neutron spectrum in MOX fuel gives a value for L that is three to four times smaller than in UO 2 fuel. For MOX fuel, L is as low as 5{10 6 s. Finally, b eff was examined. For UO 2 fuel, this parameter decreases from 0.7% at BOL to 0.5% at EOL because of depletion of 235 U and buildup of 239 Pu that has a smaller delayed neutron fraction. The burnup-averaged value equals 0.56%. In MOX fuel, 239 Pu dominates the fission process and b eff equals only 0.39%. The isotopic contributions to b eff for both UO 2 and MOX fuel are shown in Figs. 7 and 8. Because of the large delayed neutron fraction of 238 U, the contribution of this nuclide is quite large ~20 to 30%!. NUCLEAR TECHNOLOGY VOL. 130 JUNE

6 UO2 MF=2 U235 U238 Pu239 Pu240 Pu MOX MF=2 U235 U238 Pu239 Pu240 Pu Contribution to B eff (%) Contribution to B eff (%) Burnup (GWd/tHM) Burnup (GWd/tHM) Fig. 7. The isotopic contributions to b eff of UO 2 fuel with MF 2 as a function of burnup. During each fuel burnup cycle of 9.5 GWd0tonne HM, the boron concentration decreases linearly from the CBC to zero. Fig. 8. The isotopic contributions to b eff of MOX fuel with MF 2 as a function of burnup. During each fuel burnup cycle of 9.5 GWd0tonne HM, the boron concentration decreases linearly from the CBC to zero. In conclusion, both the fuel and moderator temperature coefficients are more strongly negative for MOX fuel than for UO 2, which is undesirable from the viewpoint of the larger temperature and power reactivity defects and the larger impact in case of moderator cooling accidents. Compared with UO 2 fuel, MOX fuel 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 The disadvantages described in Sec. III can be reduced by increasing the MF ratio of the fuel lattice. This enhances the moderation and reduces the neutron absorption rate in the resonance region. Due to the more thermalized neutron spectrum ~see Fig. 9!, the reactivity worth of the fissile plutonium isotopes increases, and the needed plutonium density in the fuel decreases. For example, the plutonium weight fraction in MOX fuel with MF 2 equals 10%, while this is,6% for MOX with MF 4. The resonance absorption rate decreases with increasing MF ratio, which reduces the conversion rate of even plutonium isotopes to odd ones and of 238 Uto 239 Pu. Consequently, the burnup reactivity loss increases. For MOX fuel with an MF ratio of four, the burnup reactivity loss compares with that of standard UO 2 fuel ~MF 2!. The MF ratio can be increased either by increasing the rod pitch or by reducing the fuel pin diameter. In both cases, thermal-hydraulic considerations have to be taken into account. In the first case, the linear power is kept constant at its nominal value of W0cm to limit the fuel centerline temperature, which is first-order proportional to the linear power. 18 This implies that the core power density decreases in proportion to the squared value of the pitch. In this case, the fuel cycle length does not change. In the second case, the diameter of the fuel pin is reduced. If the linear power is kept constant, the heat flux through the rod outer surface increases. This might be unacceptable from the viewpoint of departure from nucleate boiling accidents. For the linear power, P lin holds: P lin F H 2pR. ~1! 232 NUCLEAR TECHNOLOGY VOL. 130 JUNE 2000

7 1.00 MOX MF=4 2.2 MOX MF=4 BOL EOL k inf η f p ε Neutron spectrum (a.u.) Four factors Energy (ev) Fig. 9. Neutron spectra in arbitrary units at BOL and at EOL for MOX fuel with MF 4. These neutron spectra are much more thermalized than the neutron spectrum of MOX fuel with MF 2 ~see Fig. 6! Burnup (GWd/tHM) Fig. 10. The four factors for MOX fuel with MF 4 as a function of burnup. These values compare well with those of UO 2 fuel ~see Fig. 4!. During each fuel burnup cycle of 9.5 GWd0tonne HM, the boron concentration decreases linearly from the CBC to zero. Here, F H is the heat flux at the rod outer surface and R is the fuel radius. Reducing the fuel radius with constant heat flux implies that the linear power reduces in proportion to the fuel radius. In addition, this reduces the fuel centerline temperature, because this temperature is firstorder proportional to the linear power. For the specific power, P spec holds: P spec P lin pr 2 1 r HM F H 2 R 1 r HM. ~2! Here, r HM is the heavy metal density of the fuel. Clearly, when the fuel radius reduces with constant heat flux, the specific power increases. This implies that the target burnup of 47.5 MWd0kg will be reached with shorter cycle length proportional to the fuel pin radius. Because refueling costs are first-order inversely proportional to the fuel cycle length, and because the linear power reduces in proportion to the radius, the economic impact is inversely proportional to the squared value of the fuel pin radius. Figure 10 shows the four factors for MOX fuel with MF 4. The nonthermal fission factor is much lower than that of MOX fuel with MF 2 ~see Fig. 5! and even slightly lower than that of standard UO 2 fuel ~see Fig. 4!. However, the resonance escape probability p is larger, which compensates for the lower e. In general, the four factors of MOX fuel with MF 4 compare with those of UO 2 fuel with MF 2. The FTC is shown in Fig. 11 as a function of burnup. Two differences are apparent. First, the values here are 20 to 30% lower than for standard MOX fuel due to the lower resonance absorption rate. Second, the values for the case with increased rod pitch are smaller than for the case with reduced pin diameter. With reduced pin diameter, the fuel is distributed more homogeneously, which increases the resonance absorption rate and the FTC. The MTC for MOX fuel during the first recycling with enhanced moderation ~MF 4! is lower than for MOX fuel with MF 2. Averaged over burnup, the MTC equals only 23 pcm0k for the case with increased pitch and 32 pcm0k for the case with reduced pin diameter, while it is 54 pcm0k for MOX fuel with MF 2. Because of the softening of the neutron spectrum with increasing MF ratio, the BRW for MOX fuel with MF 4 compares with that of standard UO 2 fuel ~ 7.7 pcm0 NUCLEAR TECHNOLOGY VOL. 130 JUNE

8 MOX MF=4 pin pitch the BRW, the MVC, and the neutron generation time are comparable with that of standard UO 2 fuel. Third, 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) Burnup (GWd/tHM) Fig. 11. The FTC of MOX fuel with MF 4 as a function of burnup. The irregular behavior is due to the boron concentration in the moderator, which decreases linearly during each fuel burnup cycle from the CBC to zero. In the case where the pin diameter is reduced ~solid line!, spatial self-shielding decreases. This causes lower resonance integrals, which leads to a stronger negative reactivity coefficient. ppm!. Furthermore, due to the low conversion rate and the corresponding large net depletion rate of the fissile isotopes, the neutron spectrum softens considerably as a function of burnup. This gives values about twice as large for the BRW at EOL. Despite the large burnup reactivity loss of MOX fuel with MF 4, the BRW is so large that the CBC equals only 625 ppm, while it is 1200 ppm for the MOX fuel with MF 2. Enhancing the moderation increases the magnitude of the MVC. The MVC of MOX fuel with MF 4 compares with that of standard UO 2 fuel ~about 500 pcm0 %!, which is an important safety aspect. Other parameters like the L also improve. Increasing the MF ratio from two to four increases L from 5{10 6 to 2{10 5 s. The b eff depends on the contributions of the fissile isotopes to the fission power, which are not very sensitive to the MF ratio. For MOX fuel with MF 4, b eff equals 0.39%. In conclusion, increasing the MF ratio improves the safety characteristics of MOX fuel. First, the temperature coefficients are negative but not too large. Second, V. RESULTS: RECYCLING PLUTONIUM Recycling plutonium in MOX fuel according to Fig. 2 reduces the fraction of fissile isotopes in plutonium. Consequently, the plutonium density in the fuel increases at each recycling to meet the reactivity requirements. Table III shows the plutonium weight fractions in the fuel as a function of the MF ratio and of the recycling number. The plutonium density increases with recycling number but decreases with the MF ratio. The burnup reactivity loss reduces with recycling number due to the increasing plutonium density and the corresponding higher conversion rate of even plutonium isotopes to odd ones. The FTC depends only slightly on the recycling number. Although the plutonium density in the fuel and the resonance absorption rate increase with recycling number, the higher contributions due to the even plutonium isotopes are compensated by a lower contribution due to 238 U. The resultant values are shown in Table IV, which confirms that the FTC reduces with increasing MF ratio but depends very little on the recycling number. The MTC shows an interesting dependence on the MF ratio and on the recycling number, as shown in Table V. For low MF ratios ~MF 2!, the MTC decreases with increasing recycling number, while for high MF ratios ~MF 4!, it increases. To understand this behavior, one has to realize that the moderator-to-plutonium atomic ratio ~hereafter referred to as the MPu ratio! increases with the MF ratio but decreases with recycling number because of the increasing plutonium density. Basic TABLE III The Plutonium Density in the Fuel Plutonium Density ~wt%! MF Ratio NUCLEAR TECHNOLOGY VOL. 130 JUNE 2000

9 TABLE IV The FTC* TABLE VI The MVC* FTC ~pcm0k! MF Ratio Fuel Type UO MOX MOX MOX *Results are for reduced pin diameter. MVC ~pcm0%! MF Ratio Fuel Type UO MOX MOX MOX *Results are for reduced pin diameter. TABLE V The MTC* MTC ~pcm0k! MF Ratio Fuel Type UO MOX MOX MOX *Results are for reduced pin diameter. reactor physics tells us that the curve of k` versus the MPu ratio shows an inflection point. Apparently, this point occurs at an MPu ratio corresponding with the second recycling of the MF 3 case. For that case, the MTC is most strongly negative. For lower MF ratios, the MPu ratio is smaller, while for larger MF ratios, the MPu is larger. 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 VI shows the values obtained. One should realize that the uncertainties in these values are quite large, partly because the increased radial leakage upon voiding is 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 21 showed that the uncertainty due to the latter reason may range up to 50 pcm0%. Taking a safety margin of two times this value, plutonium recycling in PWRs is limited to two times for a standard fuel lattice. For MF ratios of three and larger, the plutonium can be recycled at least four times. Because the plutonium density in the fuel increases with recycling number, the neutron spectrum hardens and the BRW decreases. Table VII shows the BRW as a function of the MF ratio and the recycling number. At first order, the CBC is given by CBC Dr BRW, ~3! where Dr is the burnup reactivity loss during the third fuel batch ~pcm! and BRW is the boron reactivity worth ~pcm0ppm!. For UO 2 fuel, the CBC equals 875 ppm. For the first recycling, the CBC equals 1190 ppm for MOX fuel with MF 2 and 625 ppm for the MOX with MF 4. As shown in Table VIII, the CBC does not strongly vary with recycling number because both the BRW and the burnup reactivity loss decrease with increasing recycling number. For MF, 3, the CBC increases slightly with increasing recycling number, while for MF. 3, it decreases. The neutron generation time L decreases with recycling number because of the increasing plutonium TABLE VII The BRW* BRW ~pcm0ppm! MF Ratio Fuel Type UO MOX MOX MOX *Results are for reduced pin diameter. A low value indicates a relatively hard neutron spectrum. NUCLEAR TECHNOLOGY VOL. 130 JUNE

10 TABLE VIII The CBC* TABLE X The Effective Delayed Neutron Fraction b eff * CBC ~ppm! MF Ratio Fuel Type UO MOX MOX MOX *Results are for reduced pin diameter. b eff ~%! MF Ratio Fuel Type UO MOX MOX MOX *Results are for reduced pin diameter. density and the correspondingly harder neutron spectrum. The results are given in Table IX. As mentioned in Secs. III and IV, b eff depends mainly on the contributions of the fissile isotopes to the fission power, and it is therefore not very sensitive to the recycling number. The resultant values are given in Table X. In conclusion, multiple recycling of plutonium gives an ever-increasing plutonium density in the fuel with a corresponding increase of the resonance absorption rate and a hardening of the neutron spectrum. This generally decreases the BRW, the MVC, and the neutron generation time. The FTC is affected only slightly by the multiple recycling. For low MF ratios, the MTC 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. RESULTS: MODERATOR COOLING ACCIDENTS As mentioned before, MOX fuel has stronger negative FTC and MTC values compared with UO 2 fuel. The TABLE IX The Mean Neutron Generation Time L* L~ms! MF Ratio Fuel Type UO MOX MOX MOX *Results are for reduced pin diameter. A low value indicates a relatively hard neutron spectrum. first can be a disadvantage because of the larger temperature and power reactivity defects, while the second may worsen the consequences of moderator cooling accidents. In fact, the latter type of accident is the most penalizing scenario for PWRs using MOX fuel. 8 In this section, such a scenario is investigated by means of a point-kinetics reactor model with both fuel and moderator temperature feedback. In the model, all reactivity coefficients, kinetic parameters, heat capacities, and heat transfer coefficients are assumed constant during the transient and independent of the actual fuel and moderator temperatures. It is emphasized that the results of this simple analysis are only comparative rather than absolute and that a more advanced safety analysis is necessary to provide a basis for licensing. The equations for the power density P and the concentration of the delayed neutron precursors D i are given by the well-known point-kinetics equations using six groups of delayed neutrons. 18 The fuel and moderator temperatures ~T f and T m! are described by the following two equations using Newton s law of cooling 22 : dt f dt and dt m dt where 1 C f r f P~t! h s A f C f r f ~T f T m! ~4! h s A m C m r m ~T f T m! h m ~T out T in!, ~5! C f,c m heat capacities of fuel and moderator, respectively ~J{g 1 {K 1! A f contact surface between fuel and moderator per unit fuel volume ~cm 1! A m contact surface between fuel and moderator per unit moderator volume ~cm 1! r f,r m fuel and moderator densities, respectively ~g{cm 3! 236 NUCLEAR TECHNOLOGY VOL. 130 JUNE 2000

11 h s heat transfer coefficient from the coolant to the moderator ~W{K 1 {cm 2! h m power removal inverse time constant ~s 1!. The transient is initiated by an instantaneous moderator temperature decrease of 20 K at the inlet. The resultant reactivity, moderator and fuel temperatures, and relative power are shown in Figs. 12 through 15. Because the moderator temperature is calculated as the arithmetic mean of the inlet and outlet temperatures, it decreases only 10 K at the beginning of the transient ~see Fig. 13!. However, it continues to decrease for a few tenths of a second, after which it increases ~this is especially the case for UO 2 fuel!. This effect is due to the heat removed by the moderator, which is proportional to the difference of the outlet and inlet moderator temperatures. At nominal conditions, this difference equals ;30 K, but at the beginning of the transient it increases considerably. This means that much more heat is removed from the system, while the heat transferred from the fuel to the moderator remains almost constant ~because the difference between the fuel and moderator temperatures is much larger!. Therefore, an imbalance exists, and the moderator temperature decreases during the first tenths of a second. Only after the fuel temperature increases substantially ~see Fig. 14! does the heat Reactivity MF=2 MF=3 MF=4 UO2 Moderator temperature (K) MF=2 MF=3 MF=4 UOX Time (s) Fig. 13. Moderator temperature as a function of time. At t 1 s, the moderator temperature at the inlet decreases by 20 K. transfer from the fuel to the moderator become so large that the moderator temperature increases again. A new equilibrium state is formed when the heat transfer from fuel to moderator matches the heat removed by the moderator. Figure 15 shows the relative power as a function of time. In this case, all fuels but the UO 2 and the MOX fuel with MF 4 become prompt critical because of the fact that the MTC has larger negative values for MOX fuel with a low MF ratio. This leads to a large power spike at the beginning of the transient. Although the differences are rather small, the results of MOX fuel with a high MF ratio are closer to those of UO 2 fuel than the results of MOX fuel with a low MF ratio. This seems to justify the conclusion that for this type of accident, a larger MF ratio is beneficial for the first one or two recyclings, while a ratio of two is beneficial for the third and fourth recyclings ~see Table V!. VII. RESULTS: SCENARIO STUDIES Time (s) Fig. 12. Reactivity as a function of time. At t 1 s, the moderator temperature at the inlet decreases by 20 K. If the plutonium in the spent fuel of a reactor is completely recycled in another reactor, the reactor park operates at equilibrium. Such a park contains reactors loaded with fresh UO 2 fuel and reactors loaded with MOX fuel NUCLEAR TECHNOLOGY VOL. 130 JUNE

12 1200 MF=2 MF=3 MF=4 UO2 100 MF=2 MF=3 MF=4 UO Fuel temperature (K) Relative power Time (s) Fig. 14. Fuel temperature as a function of time. At t 1 s,the moderator temperature at the inlet decreases by 20 K. made of recycled plutonium. Table XI shows the composition of such a reactor park ~the fraction of reactors containing fresh UO 2 fuel, the fraction containing MOX fuel of the first recycle, the fraction containing MOX fuel of the second recycle, etc.!. About 80% of the reactors are loaded with UO 2 fuel. This fraction decreases slightly with increasing MF ratio, which is due to two opposite effects. On the one hand, the needed plutonium fraction in the MOX fuel decreases with increasing MF ratio, which means that fewer UO 2 reactors are needed to fuel the MOX reactors. On the other hand, the plutonium consumption in the MOX reactors increases slightly with increasing MF ratio, which means that more UO 2 -fueled reactors are needed. For an annual electricity production of 100 GW, about 102 reactors are needed of 1450 MW~electric! each with an availability factor of nearly 70%. The actinide masses produced yearly are shown in Table XII for the equilibrium reactor parks and for a once-through reactor park containing solely UO 2 -fueled reactors as a reference. In Table XII, it is assumed that all actinides are completely sent to the waste repository ~see Losses column!, except for the plutonium, which is recovered with a loss fraction of 0.12% ~the minimum achievable nowadays!. The fourth column shows the plutonium mass recycled each time. After four recyclings, the remaining unloaded plutonium can be sent to the waste repository or stored for Time (s) Fig. 15. Normalized power as a function of time. At t 1s, the moderator temperature at the inlet decreases by 20 K. TABLE XI The Composition of the Reactor Park ~Fraction of Each Type of Reactor! in Equilibrium Fuel Type UO 2 MOX MOX MOX MOX Cycle Number REFR MF MF MF further use. The sixth column in Table XII shows the ratio of the actinide masses produced by the advanced reactor park and by the UO 2 -fueled once-through park ~REFR scenario!. Clearly, plutonium recycling reduces considerably the plutonium production ~factors of 0.42, 0.36, and 0.31! at the expense of americium and curium production that is two to four times higher. 238 NUCLEAR TECHNOLOGY VOL. 130 JUNE 2000

13 TABLE XII The Actinide Production in a 100-GW~electric! Reactor Park Scenario Actinide Losses ~kg0yr! Recycled Mass ~kg0yr! Total Mass ~kg0yr! Mass Ratio a ~MF0REFR! Once-through mode ~UO 2 fuel! REFR Np Pu Am Cm Total Plutonium recycled four times in MOX-fueled reactors MF 2 Np Pu Am Cm Total MF 3 Np Pu Am Cm Total MF 4 Np Pu Am Cm Total a Actinide production relative to that of the once-through scenario. Figure 16 shows the radiotoxicity curve of the reference once-through scenario and those of the recycling scenarios. After recycling four times, the plutonium is sent to the waste repository ~dotted line! or stored for further use ~dashed line!. Clearly, the plutonium remaining after recycling four times contributes significantly to the radiotoxicity produced by the park. Therefore, we recommend continuing the recycling of this plutonium in thermal or fast reactors. However, even in the case of complete elimination of this plutonium, the reduction of the radiotoxicity does not exceed a factor of 5 due to the accumulation of americium and curium. These reduction numbers agree well with those of other scenario studies found in the literature. 23 Recycling of minor actinides is necessary to further reduce the radiotoxicity of the spent fuel. VIII. CONCLUSIONS The conversion from UO 2 to MOX fuel without changing the MF ratio has a considerable impact on the reactivity coefficients and kinetic parameters of the fuel, which are important for a safe control of the reactor. Because of the stronger resonance absorption rate in MOX fuel, the fast fission factor increases while the resonance escape probability and the neutron generation time decrease. Furthermore, because of the large thermal absorption cross sections of plutonium isotopes, the BRW decreases. All these disadvantages can be overcome by enhancing the MF ratio. From a reactor physics standpoint, MOX fuel with MF 4 is similar to UO 2 fuel with MF 2, except for the delayed neutron fraction, which depends mainly on the contributions of the individual isotopes to the fission rate. This fraction ranges from 0.56% in UO 2 fuel to 0.39% in MOX fuel. Multiple recycling of plutonium in MOX fuel in a PWR 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 values higher than three. In an equilibrium reactor park with four-time recycling of plutonium in PWRs with an MF ratio of four, the production of plutonium is reduced by a factor of three at the expense of a tripled production of americium and curium. The resulting reduction of the radiotoxicity NUCLEAR TECHNOLOGY VOL. 130 JUNE

14 10 12 MOX MF=4 OnceThrough Losses+Inventory Losses the Delft University of Technology. The authors acknowledge the European Commission for co-funding this work under the contract Evaluation of Possible P&T Strategies and of Associated Means to Perform Them ~EC contract FI4I-CT !. Radiotoxicity (Sv per 100 GWea) REFERENCES 1. G. J. SCHLOSSER, W. D. KREBS, and P. URBAN, Experience in PWR and BWR Mixed-Oxide Fuel Management, Nucl. Technol., 102, 54~1993!. 2. F. BURTAK, L. HETZELT, and W. STACH, Advanced Mixed Oxide Fuel Assemblies with Higher Plutonium Contents for Pressurized Water Reactors, Nucl. Eng. Des., 162, 159 ~1996!. 3. J. BERGERON, R. LENAIN, and S. LOUBIERRE, 100% Plutonium Recycling Feasibility in a 900 Mwe PWR Core, Proc. Int. Conf. Physics of Reactor Operation, Design, and Computation (PHYSOR 90), Marseille, France, April 23 26, 1990, p. VI-1 ~1990! Storage time (a) Fig. 16. The radiotoxicity of the reactor park consisting of UO 2 - fueled reactors in once-through mode ~curve labeled Once-Through!, and of the reactor park with plutonium recycling in MOX-fueled reactors with MF 4. After recycling four times, the plutonium is assumed to be disposed of ~curve labeled Losses Inventory! or to be stored for further use ~curve labeled Losses!. reaches a factor of two when the plutonium remaining after recycling four times is disposed of, and a factor of five when the remaining plutonium is eliminated in special burner reactors. The radiotoxicity can be reduced further by recycling the remaining americium and curium. Whatever method one chooses to increase the MF ratio, increasing the fuel rod pitch or reducing the fuel pin diameter, the economic penalty is considerable. Compared with the standard fuel lattice ~MF 2!, this penalty equals 25% for MF 3 and almost 40% for MF 4. To reduce these penalties, optimization from the thermalhydraulic point of view might be considered, but this is outside the scope of this study. Here, we aimed at a comparative study of the influence of the MF ratio rather than to design an optimal fuel lattice for MOX fuel in PWRs. ACKNOWLEDGMENTS This study was performed at the Netherlands Energy Research Foundation and at the Interfaculty Reactor Institute of 4. P. BARBRAULT, A Plutonium-Fueled High-Moderated Pressurized Water Reactor for the Next Century, Nucl. Sci. Eng., 122, 240 ~1996!. 5. U. KASEMEYER, J.-M. PARATTE, P. GRIMM, and R. CHAWLA, Comparison of Pressurized Water Reactor Core Characteristics for 100% Plutonium-Containing Loadings, Nucl. Technol., 122, 52~1998!. 6. R. GIREUD, B. GUIGON, R. LENAIN, N. BARBET, and E. ROYER, A 100% MOX Core Design Using a Highly Moderated Concept, Proc. Int. Conf. Future Nuclear Systems (GLOBAL 97), Yokohama, Japan, October 5 10, 1997, p. 848 ~1997!. 7. G. ROUVIERE, G. B. BRUNA, J. L. GUILLET, and J. PELET, 1300 Mwe PWR, A New Step in Full MOX Core Design, Proc. Int. Conf. Future Nuclear Systems (GLOBAL 99), Jackson Hole, Wyoming, August 29 September 3, 1999, American Nuclear Society ~1999!. 8. S. ANIEL-BUCHHEIT, A. PUILL, R. SANCHEZ, and M. COSTE, Plutonium Recycling in a Full-MOX 900- MW~electric! PWR: Physical Analysis of Accident Behaviors, Nucl. Technol., 128, 245 ~1999!. 9. G. YOUINOU, M. DELPECH, J. L. GUILLET, A. PUILL, and S. ANIEL, Plutonium Management and Multirecycling in LWRs Using an Enriched Uranium Support, Proc. Int. Conf. Future Nuclear Systems (GLOBAL 99), Jackson Hole, Wyoming, August 29 September 3, 1999, American Nuclear Society ~1999!. 10. A. PUILL and J. BERGERON, Advanced Plutonium Fuel Assembly: An Advanced Concept for Using Plutonium in Pressurized Water Reactors, Nucl. Technol., 119, 123 ~1997!. 11. J. L. KLOOSTERMAN, Multi-Recycling of Plutonium in Advanced PWRs, ECN-R , Netherlands Energy Research Foundation ~1998!. 240 NUCLEAR TECHNOLOGY VOL. 130 JUNE 2000

15 12. J. L. KLOOSTERMAN, Reactor Physics Aspects of Plutonium Recycling in PWRs, Proc. Int. Conf. Physics of Nuclear Science and Technology, Islandia, New York, October 5 8, 1998, p. 127, American Nuclear Society ~1998!. 13. J. L. KLOOSTERMAN, Multiple Recycling of Plutonium in Advanced PWRs, Proc. 5th Int. Conf. Recycling, Conditioning and Disposal (RECOD 1998), Nice, France, October 25 28, 1998, p. 266 ~1998!. 14. J. L. KLOOSTERMAN, J. C. KUIJPER, and P. F. A. DE LEEGE, The Octopus Burnup and Criticality Code System, Proc. Int. Conf. Physics of Reactors (PHYSOR 96), Mito, Japan, September 16 20, 1996, p. B-63 ~1996!. 15. J. E. HOOGENBOOM and J. L. KLOOSTERMAN, Generation and Validation of ORIGEN-S Libraries for Depletion and Transmutation Calculations Based on JEF2.2 and EAF3 Basic Data, Nucl. Eng. Des., 170, 107 ~1997!. 16. J. KOPECKEY and D. NIEROP, The European Activation File EAF4, Summary Documentation, ECN-C , Netherlands Energy Research Foundation ~1995!. 17. J. L. KLOOSTERMAN, Program VAREX, A Tool for Variational Analysis of Reactivity Effects with XSDRNPM, Report ECN-I , Netherlands Energy Research Foundation ~1996!; updates in notes JB0ak ~1996! and NUC0EB0mh09500 ~1997!. 18. J. J. DUDERSTADT and L. J. HAMILTON, Nuclear Reactor Analysis, John Wiley & Sons, New York ~1976!. 19. M. J. DRISCOLL, T. J. DOWNAR, and E. E. PILAT, The Linear Reactivity Model for Nuclear Fuel Management, American Nuclear Society, LaGrange Park, Illinois ~1990!. 20. Neutron Cross Sections, Vol. I, Part B, S. F. MUGHAB- GHAB et al., Eds. Academic Press, New York ~1984!. 21. Physics of Plutonium Recycling, Vol. VI, Organization for Economic Cooperation and Development, Paris ~2000!. 22. D. L. HETRICK, Dynamics of Nuclear Reactors, American Nuclear Society, LaGrange Park, Illinois ~1993!. 23. J. P. GROUILLER, J. L. GUILLET, H. BOUSSIER, and J. L. GIROTTO, Nuclear Materials Recycling in Conventional or Advanced Reactors: A Scenario Study, Proc. Int. Conf. Future Nuclear Systems (GLOBAL 99), Jackson Hole, Wyoming, August 29 September 3, 1999, American Nuclear Society ~1999!. Jan Leen Kloosterman ~PhD, applied physics, Delft University of Technology, The Netherlands, 1992! is a reactor physicist at the Interfaculty Reactor Institute of the Delft University of Technology. His background includes gammaray shielding and neutron streaming through ducts and transmutation of plutonium, minor actinides, and long-lived fission products. His current interests include reactor dynamics and physics of innovative reactor systems. Evert E. Bende ~MS, theoretical physics, University of Utrecht, The Netherlands, 1993; PhD, reactor physics, Delft University of Technology, The Netherlands, 2000! is employed by NRG. His background includes reactor physics, transmutation of actinides, core design, and transient analysis. NUCLEAR TECHNOLOGY VOL. 130 JUNE