Thorium-containing HPLWR fuel assemblies

As it was discussed in the previous section, the fuel assembly of HPLWR contains 40 fuel rods. In this section five different thorium-containing cases were inves-tigated and the results were compared to the reference (design) case. In these models, 4 or 8 ThO₂-fuelled fuel rods are placed in different positions. The cases are shown in Fig. 3.5. 4 thorium-containing fuel rods mean that 10% of the fuel as-sembly is changed while the 8 thorium rods containing models have 20% thorium.

About 14 MWd/kgHM burnup is achieved at the end of the 500 EFPD.

In the investigated models the thorium-containing fuel rods did not contain any fissile isotope at BOC. Fig. 3.6 shows the normalized infinite multiplication factor changes during the examined period. The normalization means that the initial values are shifted to 1.0. In this way the trends of the lines can be compared without biasing them. In all cases a drastic drop in the multiplication factor can be seen in the first two days. This is caused by the reactor poisons, the effect of which was mentioned in the previous section.

Comparing the different cases, the first consequence is that all the thorium-containing calculations have slightly less decreasing multiplication factor than the reference case has. The multiplication factor change is about 10.5% in the reference case. However, when four thorium rods are in the models, this change becomes

Figure 3.5: The investigated cases in case of HPLWR (blue circles: UO₂ pins, red circles: ThO₂ pins)

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0

0 . 8 8 0 . 9 0 0 . 9 2 0 . 9 4 0 . 9 6 0 . 9 8 1 . 0 0

Normalized infinite multiplication factor (-)

E f f e c t i v e f u l l p o w e r d a y ( d a y )

R e f e r e n c e c a s e 1 s t c a s e ( 4 T h r o d s ) 2 n d c a s e ( 4 T h r o d s ) 3 r d c a s e ( 4 T h r o d s ) 4 t h c a s e ( 8 T h r o d s ) 5 t h c a s e ( 8 T h r o d s )

Figure 3.6: The change of the shifted infinite multiplication factors for the HPLWR reactor

51 CHAPTER 3. CALCULATIONS WITH INFINITE LATTICE MODELS

about 10%. There is only a slight difference in the 1st, 2nd and 3rd cases in terms of this parameter, so the position hardly influences the infinite multiplication factor changes. When the number of thorium-containing fuel rods are increased to eight, the results are different from each other depending on the positions. In the fourth case, four of the thorium rods are placed next to the moderator channel while in the fifth case these are placed in the corners of the moderator channel. The other four thorium-containing rods have only UO₂ neighbours. These results suggest that the moderator of the central channel helps the production of fissile ²³³U.

The initial multiplication factor results can be seen in Fig. 3.7. The 1st, 2nd and 3rd cases contain 4 thorium-based fuel rods. The results show that in these cases the deviation ofk_inf values is less than 0.5%. On the other hand, the average of the above values is about 4% less than the multiplication factor of the reference case. This is caused by the smaller amount of fissile isotope content of the fuel assembly. In the cases in which the fuel assembly contains eight thorium rods (4th and 5th cases), the results are significantly separated. When the thorium rods are immediate neighbours of the moderation channel (4th case), the initial infinite multiplication factor decrease is 9.5% compared to the reference case, while in the 5th case it is only 8.6%. This is most probably caused by the spectrum. In the fourth case the thorium rods are in a more thermalized spectrum than the rods in the fifth case. In this way the thorium rods are decreasing the thermal spectrum of the UO₂-containing fuel rods which causes less fission at the beginning.

0 2 4 6 8

1 . 0 6 1 . 0 8 1 . 1 0 1 . 1 2 1 . 1 4 1 . 1 6 1 . 1 8

k ^{i n i t}

i n f[ - ] = ( - 0 . 0 1 3 4 ±0 . 0 0 0 6 )⋅N

T h - p i n s[ - ] + ( 1 . 1 7 8 6 ±0 . 0 0 3 4 ) C a l c u l a t e d r e s u l t s F i t t e d l i n e a r

Initial infinite multiplication factor (-)

N u m b e r o f t h o r i u m - c o n t a i n i n g f u e l r o d s ( - )

Figure 3.7: The change of the initial multiplication factors in the HPLWR reactor

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 0 . 0 %

0 . 1 % 0 . 2 % 0 . 3 % 0 . 4 % 0 . 5 % 0 . 6 % 0 . 7 % 0 . 8 % 0 . 9 % 1 . 0 %

Normalized233 U amount in the Th pins (-)

E f f e c t i v e d a y s ( d a y s ) 1 s t c a s e ( 4 T h r o d s )

2 n d c a s e ( 4 T h r o d s ) 3 r d c a s e ( 4 T h r o d s ) 4 t h c a s e ( 8 T h r o d s ) 5 t h c a s e ( 8 T h r o d s )

Figure 3.8: The normalized amount of fissile isotopes in the thorium rods in case of HPLWR (m_fissile/m_ThO2)

Table 3.3: The produced²³³U ratio in thorium-containing HPLWR after 500 EFPD (m_fissile/m_ThO2)

Case Mass percentage First case 0.8468%

Second case 0.8214%

Third case 0.8086%

Fourth case 0.8829%

Fifth case 0.8433%

The normalized mass of ²³³U produced is shown in Fig. 3.8. The produced fissile isotope amounts were normalized with the mass of the thorium-containing fuel rods in the initial state. The results correspond to the previously seen ones.

With 4 thorium rods present in the models, the production is very similar (the cases are within 0.4%). In the case of 8 thorium rods, in the 4th investigated model the ²³³U production was about 5 g more than in the 5th case (which means 0.4%

at the end of the investigated cycle). The mass percentage of the produced ²³³U is summarized in Tab. 3.3. In the best case, 0.88%²³³U content could be achieved until the end of the investigated 500 effective days with the originally designed fuel assembly of the HPLWR (fourth case).

53 CHAPTER 3. CALCULATIONS WITH INFINITE LATTICE MODELS

1 E - 9 1 E - 8 1 E - 7 1 E - 6 1 E - 5 1 E - 4 1 E - 3 0 . 0 1 0 . 1 1 1 0

0 . 0 0 E + 0 0 0 2 . 0 0 E + 0 1 2 4 . 0 0 E + 0 1 2 6 . 0 0 E + 0 1 2 8 . 0 0 E + 0 1 2 1 . 0 0 E + 0 1 3 1 . 2 0 E + 0 1 3 1 . 4 0 E + 0 1 3 1 . 6 0 E + 0 1 3

1 E - 9 1 E - 8 1 E - 7 1 E - 6 1 E - 5 1 E - 4 1 E - 3 0 . 0 1 0 . 1 1 1 0

0 . 0 0 E + 0 0 0 2 . 0 0 E + 0 1 2 4 . 0 0 E + 0 1 2 6 . 0 0 E + 0 1 2 8 . 0 0 E + 0 1 2 1 . 0 0 E + 0 1 3 1 . 2 0 E + 0 1 3 1 . 4 0 E + 0 1 3 1 . 6 0 E + 0 1 3 Φ (1/(cm2 ⋅s))

E n e r g y ( M e V ) R e f e r e n c e c a s e ( B O C )

4 . c a s e ( B O C )

- 1 0 0 - 8 0 - 6 0 - 4 0 - 2 0

0

2 0 4 0 6 0 8 0 1 0 0

Difference (%) Difference (%) D i f f e r e n c e

Φ (1/(cm2 ⋅s))

E n e r g y ( M e V ) R e f e r e n c e c a s e ( E O C )

4 . c a s e ( E O C )

- 1 0 0 - 8 0 - 6 0 - 4 0 - 2 0

0

2 0 4 0 6 0 8 0 1 0 0

D i f f e r e n c e

Figure 3.9: The neutron spectrum in the HPLWR at BOC (upper) and EOC (lower)

In Fig. 3.9, the spectra (group fluxes) of the reference and the fourth cases can be seen for BOC and EOC. Similarly to the previous investigations, the values are averaged for the fuel pins. The differences are highlighted to better understanding how the spectrum changes. As it was discussed in Sec. 2.2, the difference bar indicates in a given energy group which case has more neutrons. If the difference is negative, the flux of the thorium-containing case is higher, otherwise the flux of the reference case. The 100 energy groups have equal lethargy width.

For BOC, the differences highlight that the spectrum of the thorium-containing case is more thermalized than that of the reference case in the infinite reactor model. For the higher energy region (2·10⁻⁵ MeV and above) there are more neutrons in the reference case. This tendency remains the same for EOC as well.

Tab. 3.4 shows the effective delayed neutron fraction values for BOC and EOC for the different cases. The change is within 4% for every case at BOC. At EOC, the effective delayed neutron fraction decreases due to the higher amount of plutonium and ²³³U. The value is the least in the fourth case when it is about 8% less than in the reference case. However, it is very probable that the differences are caused by the significant variances.

Table 3.4: The effective delayed neutron fraction in HPLWR for BOC and EOC

BOC EOC

Reference case 0.00673±0.00020 0.00578±0.00018 First case 0.00709±0.00020 0.00584±0.00018 Second case 0.00648±0.00019 0.00552±0.00017 Third case 0.00694±0.00019 0.00574±0.00018 Fourth case 0.00666±0.00019 0.00529±0.00017 Fifth case 0.00673±0.00019 0.00576±0.00018

Since HPLWR is the first investigated reactor type with thermal spectrum, it was also examined whether the chosen time steps are appropriate and do not bias the results. In the additionally performed simulations the time steps were set in every 25 EFPD similarly to the ones which could have been seen in Sec. 2.2. In accordance with the sensitivity analysis of ALLEGRO, the two investigated cases are the reference one and the one with the highest amount of thorium (fourth case).

Fig. 3.10 shows that with the originally chosen time steps almost exactly the same results can be achieved (within statistical errors) in both cases (the difference is less than 0.2%). Based on this result, the originally chosen time steps are considered as an adequate choice for the analysis of thermal reactors.

55 CHAPTER 3. CALCULATIONS WITH INFINITE LATTICE MODELS

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0

1 . 0 4 1 . 0 6 1 . 0 8 1 . 1 0 1 . 1 2 1 . 1 4 1 . 1 6 1 . 1 8

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0

0 . 9 6 0 . 9 8 1 . 0 0 1 . 0 2 1 . 0 4 1 . 0 6 1 . 0 8 1 . 1 0

Infinite multiplication factor (-)

E f f e c t i v e f u l l p o w e r d a y ( d a y )

R e f e r e n c e c a s e ( I ) R e f e r e n c e c a s e ( I I )

Infinite multiplication factor (-)

E f f e c t i v e f u l l p o w e r d a y ( d a y )

4 t h c a s e ( I ) 4 t h c a s e ( I I )

Figure 3.10: The neutron spectrum in the HPLWR at BOC (upper) and EOC (lower)

In document Generation IV Reactors (Pldal 50-57)