**3.4. Time evolution of the** *K***eff**

carried out within this period and the fuel may decay within this period from the heat built up in the core. The 10-day time step was chosen from examples used in the MCNPX user's

In all, the uranium nuclide inventory shows similar variation with burnup time for all three different fuel grades. There is a rapid decrease of 235U and a slightly lower decrease for 238U in burnup time because these radionuclides are consumed as the fission process progresses. 236U radioisotopes, which are not fissile with thermal neutrons and are generated mainly due to gamma radiation emission of 235U as fission proceeds, are observed to increase with burnup time for each of the three fuel grades. Very little of 238U is consumed in the fission process as this is only fissionable and the main fissile material is 235U, which decreases rapidly. The uranium inventory is found to decrease for MOX fuel, but on a slightly lower scale relative to the other fuel grades due to relatively little uranium composition used in its fabrication. Our study shows that the 240Pu isotope is observed to buildup steadily for each of the three fuel grades. The 240Pu radioisotope, however, rises on a much higher scale in MOX than in CEU and UOX. This is because 240Pu is formed in a nuclear reactor by occasional neutron capture

For 135Xe in **Figure 3**, a similar pattern is observed for all three fuel grades. There is a rapid accumulation of 135Xe after the first burn step, a result which might lead to a drastic drop in *K*eff. This is known as the xenon poisoning. The production of 135Xe isotopes after this burn step gradually decreases, a result which helps to regulate the reactivity of the system. The accumulation of the fission product 135Cs shows a linear variation with the burnup time for

by 239Pu, much of which forms the initial fissile fuel material in MOX fuel.

**Figure 3.** Atom density of 135Xe as a function of burnup time.

all three fuel grades as seen in **Figure 4**.

manual [14].

48 Nuclear Material Performance

The study of the variation of *K*eff with core burnup is of much importance as it describes whether or not the chain reaction in a nuclear reactor is stable or self-sustained. The results also give very important details on the core lifetime, defined as the length of time the reactor effective multiplication factor is above one. There is a large drop in *K*eff during the first burn step as shown in **Figure 5**. This drop can be attributed to a drastic reduction in reactivity due primarily to the buildup of burnable poisons such as 135Xe and the depletion of fresh fuel. The Keff is then gradually seen to decrease.

A similar pattern of the variation of *K*eff with time is observed in all three different fuel grades. MOX fuel, however, might be much more effective in improving the core lifetime of the reactor, as *K*eff is observed to remain critical for a much longer time relative to the other fuels. For UOX and CEU to maintain criticality for longer burn days, an increase in the mass fractions or weight percent (particularly for the fissile isotopes) is required. This is not too desirable due to the extremely high cost involved.

Hermine et al. [15] conducted research on the variation of *K*eff with burnup time using AP1000 and a very high temperature reactor (VHTR) fuel cycle. Transuranic fuel arising from the AP1000 reactor was used as a part of fuel-loading of the VHTR. Transuranic fuels are fuels in which conventional uranium fuels have been mixed with a transuranic element (elements with atomic number greater than 92) in the form of mainly plutonium. A transuranic fuel containing 40% of weapons-grade plutonium (WGPu) was found as the best compromise [15]. A drastic first drop in *K*eff occurred due to the depletion of burnable poisons, which is also observed in this study. The reactor life was extended by at least 36.7% when part of the low enriched uranium (LEU) is replaced by TRU, a result which agrees with the ability of TRU fuel to remain critical for a much longer time.

**Figure 5.** *K*eff of different fuel grades as a function of burnup time.

The atom densities and radioactivities in Bequerel were calculated for each of the three fuel grades at the end of the 220-day burnup. The total radioactivities of both actinides and nonactinides were calculated for each fuel grade as shown in **Table 5**. In the event of a severe reactor core accident, the radiological hazard posed is proportional to the concentrations and radioactivities of these radionuclides. The total atom densities and radioactivities are also very important parameters in estimating which fuel grade performs better, posing a relatively less hazard at the end of the burnup time or core lifetime of the reactor. For the same burnup time, MOX fuel is found to have a relatively less total radioactivity of the reactor core, almost 15% reduction as compared to the other fuel grades.

The results from the burnup simulations were compared with some results obtained from literature to assess the validity. Yan Cao et al. [6] performed burnup simulations using the MCNPX code for a PWR with 3.15% enriched UO2 fuel. The uranium isotope depletion, increase in fissile plutonium isotope and that of 241Pu and 242Pu in that simulation are in good agreement with the results obtained from this study. Also, in assessing the accuracy of a new Monte Carlo based burnup code, burnup simulations were performed for a VVER-1000 assembly using UO2 and UO2GDO3 nuclear fuel types [5]. Again, the plot of atom densities of key radionuclides with burnup time showed good agreement with the results obtained from this study. Khattab et al. calculated the total radioactivity for a 220-day burnup period of a miniature neutron source reactor using the GETERA code. The total radioactivity at the end of the reactor core was calculated based on 19 selected radionuclides, which were considered essential to potential radiological hazard associated with the severe reactor accident in the MNSR core. This value was found to be 9.462 × 1013 Bq [7]. This study calculated the total radioactivities of the reactor core based on all radioactive actinides and non-actinides present at the end of the reactor core life as shown in **Table 5**. Comparison of the values shows reasonable agreement.


**Table 5.** Total activities of actinides and non-actinides after core burnup.

#### **3.5. System Burnup and Neutronics Data**

**Figure 5.** *K*eff of different fuel grades as a function of burnup time.

50 Nuclear Material Performance

reduction as compared to the other fuel grades.

reasonable agreement.

The atom densities and radioactivities in Bequerel were calculated for each of the three fuel grades at the end of the 220-day burnup. The total radioactivities of both actinides and nonactinides were calculated for each fuel grade as shown in **Table 5**. In the event of a severe reactor core accident, the radiological hazard posed is proportional to the concentrations and radioactivities of these radionuclides. The total atom densities and radioactivities are also very important parameters in estimating which fuel grade performs better, posing a relatively less hazard at the end of the burnup time or core lifetime of the reactor. For the same burnup time, MOX fuel is found to have a relatively less total radioactivity of the reactor core, almost 15%

The results from the burnup simulations were compared with some results obtained from literature to assess the validity. Yan Cao et al. [6] performed burnup simulations using the MCNPX code for a PWR with 3.15% enriched UO2 fuel. The uranium isotope depletion, increase in fissile plutonium isotope and that of 241Pu and 242Pu in that simulation are in good agreement with the results obtained from this study. Also, in assessing the accuracy of a new Monte Carlo based burnup code, burnup simulations were performed for a VVER-1000 assembly using UO2 and UO2GDO3 nuclear fuel types [5]. Again, the plot of atom densities of key radionuclides with burnup time showed good agreement with the results obtained from this study. Khattab et al. calculated the total radioactivity for a 220-day burnup period of a miniature neutron source reactor using the GETERA code. The total radioactivity at the end of the reactor core was calculated based on 19 selected radionuclides, which were considered essential to potential radiological hazard associated with the severe reactor accident in the MNSR core. This value was found to be 9.462 × 1013 Bq [7]. This study calculated the total radioactivities of the reactor core based on all radioactive actinides and non-actinides present at the end of the reactor core life as shown in **Table 5**. Comparison of the values shows The burnup is given in units of gigawatt days (GWD) per metric tons of uranium (MTU), where MTU is the sum of the masses of isotopes with protons ≥90. The nuclear fission rate (*f*) is calculated from the product of the macroscopic fission cross-section (∑*f*) and the neutron flux (). The power density (*p*) is determined as the product of the nuclear fission rate and the energy per fission (*w*). The average neutron flux is thus directly proportional to the power level in the reactor. As fuel consumption takes place with time, the neutron flux also increases, since the power is also directly related to the fuel content.

A look at the neutron fluxes of all three fuel grades reveals a general increase with time as seen in **Tables 5**–**7**, with UOX having a slightly higher average flux relative to CEU and MOX. The neutron flux increased by 20% for UOX fuel compared to a 17% increase in MOX fuel. The flux for UOX fuel at the end of burnup exceeds that of CEU by 17.87% and MOX by 22.68% with that of CEU exceeding MOX by 6%. This characteristic of UOX which may be due to its high fissile material density enhances the system power level. Again, these re‐ sults agree with the peak reactivity parameter results in **Table 4** in which UOX and CEU had much higher reactivity relative to MOX. The burnup values indicate the fission energy released per metric ton of uranium. MOX fuel indicates comparable, but slightly higher, val‐ ues of fuel burnup relative to UOX as shown in **Tables 6** and **7**. The burnup value at the end of the burn step for MOX exceeds that of CEU by 44% and UOX by 23%. This is due to the fact that MOX fuel remains much critical for a high part of the burnup period relative to the other two. **Table 8** shows CEU fuel with much lower fuel burnup values relative to the other two fuels, which may be due to its lower fissile material density.



**Table 6.** Neutronics and burnup data for UOX fuel.


**Table 7.** Neutronics and burnup data for MOX fuel.


**Table 8.** Neutronics and burnup data for CEU fuel.
