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The densities and isotopic compositions of actual MOX fuel to be considered in future applications will be different from these simple sample models. Accordingly, for consistency, a series of HELIOS cases was performed with standardized LEU, WG, and RG compositions. All the fuel was assumed to be 10.4 g/cm 3 , and for MOX fuel Pu-content was defined as total Pu wt% in total heavy element inventory (U+Pu). The vector for reactor grade Pu (RG) is assumed to be: 1% 238 Pu, 59% 239 Pu, 24% 240 Pu, 11% 241 Pu, and 5% 242 Pu. The vector for weapons grade Pu (WG) is assumed to be 0.05% 238 Pu, 94.3% 239 Pu, 5.0% 240 Pu, 0.6% 241 Pu, and 0.05% 242 Pu. For the following series of calculations, MOX loadings of 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20 wt% Pu were modelled, LEU enrichments of 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20 wt% 235 U were considered. The level of natural boron in the coolant is assumed to be 600 ppm. The calculations were performed for void levels ranging from 0 - 100% in intervals of 10%. The attached Figures 6-8 show curves of calculated void reactivities as functions of void for LEU, WG, and RG fuel, for fresh and the midburnup (equilibrium) burnup levels. For each fuel type, the curves are shown for a large number of MOX loadings or enrichment levels. From the large set of data gathered in these studies, three representative examples are tabulated for the void reactivity and void reactivity coefficients for LEU, WG, and RG fuel. The results are summarized in Tables VI and VII. Table VI. Void Reactivity Effects (%) for Fresh and Midburnup Fuel Fuel 10% void 50% void 100% void ¨© § ¢¡£¤§¦ ¨© ¢¡¢£¤§¦ ¨© § ¡£¤§¦ ¨© ¢¡¢£¥¤§¦ ¨© § ¢¡£¤§¦ ¨© ¢¡¢£¥¤§¦ LEU 4 wt% -1.104 -1.761 -9.765 -14.088 -69.820 -73.835 WG MOX 6 wt% -1.286 -1.628 -9.021 -10.691 -33.146 -32.939 RG MOX 8 wt% -1.332 -1.441 -7.549 -8.039 -18.898 -17.870 For 10% voiding, the void reactivity for WG and RG are similar, and more negative than LEU, for fresh fuel. For midburnup fuel, LEU is more negative while RG is least negative. For 100% voiding in fresh fuel, LEU has a much more negative void reactivity effect than MOX, and RG has the least negative. For midburnup fuel, the voiding reactivity effect for 100% voiding becomes more negative in LEU but becomes somewhat less negative in WG and RG. As seen in the curves in the Figures 6-8, the reactivity behavior of the different types of MOX and LEU fuel changes as the enrichment or MOX Pu content changes. An interesting threshold figure-of-merit (FOM) to consider is the calculated minimum enrichment or MOX loading at which the reactivity effect becomes positive upon voiding for the three fuel types. This FOM is tabulated in Table VII for LEU, WG MOX and RG MOX. Table VII. Minimum Fuel Enrich. or Pu Loading at Which Voiding Reactivity Becomes Positive. Fuel Type MOX loading or enrichment (wt%) LEU 20.0 WG MOX 12.8 RG MOX 12.4 8
The thresholds are evident in Figures 6-8 where the lowest-enrichment curve first crosses the reactivity=0.00 line. The void reactivity becomes positive for midburnup fuel (20 MWd/kgHE) at the enrichment or MOX loading values tabulated in Table VII. The midburnup state is a good average representation of the equilibrium operating PWR. The enrichment or Pu-content thresholds for fresh fuel (solid curves) to have a positive reactivity feedback effect would be slightly higher than the corresponding midburnup thresholds (dashed curves), for all three fuel types. The results presented in Table VII are consistent with the findings of the OECD/NEA benchmark study of void reactivity effects in PWRs, as discussed in reference 8, which says that “the inherent void reactivity of MOX assemblies becomes positive somewhere between 10 and 14 w/o total Pu content.” It is important to note that the Pu-content levels being considered for MOX fuel for Pu disposition are considerably less than the values presented in Table VII. 5. CONCLUSIONS From the independent assessments of the Island and the full MOX LTA designs by ORNL (United States) and RRC-KI (Russian Federation), some of the conclusions include: • there is good general consistency between the results of LTA design assessments by HELIOS-1.4 (ORNL) and TVS-M (RRC-KI). • good agreement between HELIOS-1.4 and TVS-M results for the zero-power calculations. • the temperature reactivity effect (with boron in the coolant) is smaller (less positive, or negative) for MOX than the reference LEU case. • furthermore, the temperature reactivity effect is smaller (less positive, or negative) for the full MOX LTA designs than for the Island LTA designs. • when the temperature reactivity effect is positive for boronated coolant cases, it is mainly because of the expansion of the coolant and the resulting reduction in the 10 B concentration. From the study of void reactivity effects in PWRs for nominal LEU, RG, and WG fuels, some of the observations include: • for 10% voiding, the void reactivities for WG and RG are similar, and more negative than LEU, for fresh fuel. • for midburnup fuel, for 10% voiding, LEU voiding reactivity is most negative while RG voiding reactivity is least negative. • for 100% voiding in fresh fuel, LEU has a much more negative void reactivity effect than MOX, and RG has the least negative. • for midburnup fuel, the 100% voiding reactivity effect becomes even more negative in LEU but becomes somewhat less negative in WG and RG. From PWR scoping studies for a wide range of LEU enrichments or MOX Pu-content levels, it is observed that: • the minimum LEU 235 U enrichment for a positive void reactivity is 20.0 wt%. • the minimum Pu-content at which RG MOX has a positive void reactivity is 12.4 wt%. • the minimum Pu-content level for which WG MOX has a positive void reactivity (under these very unusual conditions) is 12.8 wt%. 9
Page 1 and 2: PU DISPOSITION IN RUSSIAN VVERS: PH
Page 3 and 4: The calculations for the VVER LTA s
Page 5 and 6: The agreement for the boron reactiv
Page 7: Results shown in Tables III and IV
Page 11 and 12: Figure 1: Representation of a VVER
Page 13 and 14: Peak Relative Pin Power 1.20 1.15 1
Page 15 and 16: Peak Pin Power Ratio 1.50 1.45 1.40
Page 17 and 18: Reactivity [1/k_inf,unvoid - 1/k_in

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