**3.3. Burnup calculations**

**FUEL CLAD** *K***eff at BOL** *K***eff at EOL** CEU Stainless steel 0.91187 ± 0.00311 0.80920 ± 0.00097

ing the overall *K*eff value in the long term.

when cross-checked.

46 Nuclear Material Performance

and density.

as (Eq. 8):

**3.2. Nuclear fuel reactivity**

Zircaloy 0.97923 ± 0.00210 0.86789 ± 0.00105 Zirconium 0.95529 ± 0.00232 0.84828 ± 0.00054

**Table 3.** *K*eff values for different clad materials at the beginning and end of burnup steps for MOX, UOX and CEU fuel.

Oxidation of zirconium metal reduces the ductility and robustness of zirconium metal, and hence increases the probability for the escape of thermal neutrons from the core of the reactor [12]. This further reduces the effectiveness of zirconium for higher and prolonged fuel burnups. With respect to zirconium alloys, the hydrogen produced by oxidation of zirconium in steam diffuses into the alloy, causing the formation of zirconium hydrides. The hydrides formed are less dense and more brittle than the zirconium alloy and leads to the weakening of the clad material. This is especially the case in zirconium-2 alloy. The zirconium-4 alloy has a reduced composition of iron and no nickel composition; this reduces the hydride effect by reducing the tendency to pick up hydrogen. This characteristic of zircaloy-4 used improves its mechanical properties, reducing the probability of escape of thermal neutrons considerably, thus improv‐

The thermal conductivities listed in **Table 2** reveal a higher value for zirconium and zircaloy, as compared to that of stainless steel. A high value means that heat can be quickly conducted away from the reactor core to the coolant. This prevents very high temperature buildup in the core leading to the melting of the fuel material or clad. The thermal conductivity of zirconium alloys, with thermal expansivity of nearly one-third that of stainless steel, is superior compared to that of stainless steel and other nuclear fuel storage materials. This also gives zirconium alloys superior dimensional stability at elevated temperatures. MCNP offers a number of statistical checks to assess the validity of a criticality calculation, which can be found in the MCNP user's manual [11]. These were found to be in good agreement with the output file

Reactivity is the degree of neutron multiplication in the reactor core. This parameter is directly related to the tendency of the reactor core to change power level. Also, control rods can be used to obtain a desired power level change or keep the power level constant by adjusting the reactivity when raised or lowered into the reactor core. Other factors which affect the reactivity include the density and temperature of the coolant or moderator and also the fuel temperature

The reactivity for the three different fuel grades is calculated as a function of burnup, and the peak reactivity determined for each fuel grade is shown in **Table 4**. The reactivity is evaluated An expected core lifetime of 220 days is used for the reactor core since the *K*eff drops drastically after this period, hence reducing the criticality. Usually, using large time steps of 50 and above leads to encountering large flux shape change and may lead to inaccurate results. Time steps small enough to capture the flux-shape change accurately over time is necessary according to Pelowitz [14]. Again, the time step chosen for a particular reaction depends on the core lifetime of the reactor with larger core lifetimes having larger time steps. Khattab et al. [7] used a 20 day time step for a 200 days expected operating life time of an MNSR. The 10-day period (between 60 and 70 days) was chosen to allow for maintenance operations. No burnup is 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 manual [14].

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 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.

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

**Figure 4.** Atom density of 134Cs as a function of burnup time.
