4.3.1 Setting the enrichment of the fissile material

The first stage in the nuclear design of an iPWR (or any reactor, large or small) is to determine the enrichment requirements for the fuel to provide the energy output over the time period requested by the utility. (As for large PWRs, the current design limit, primarily on fuel manufacturing and transportation (both from a criticality control perspective) is 5 wt% U-235.) Once a reactor is at equilibrium conditions (for example, after several cycles/years of operation), the cycle length and operations are more constant, e. g., how many assemblies in a reload of fuel or target burnup. At these conditions, the enrichment is unlikely to change a great deal. However, in the early cycles of operation, and as equilibrium operations are approached, the enrichment will need to vary to reflect these changes. Similarly if the utility changes cycle length, such as going from 12 to 18 months between outages, again the enrichment requirements will change. Even though eventually the enrichments may not need to be changed to achieve the required cycle length, the nuclear design, including the development of the loading pattern (see Section 4.3.3), and assessment of the key safety and performance criteria still have to be completed.

Clearly the designer has to define the enrichment to obtain the required cycle length. But equally important is that the fuel needs to have sufficient enrichment to ensure sufficient reactivity not just for the next cycle, but for its design lifetime, which is typically anywhere between one and four cycles of operation depending on the iPWR, and the fuel design (as described later in this section). For the initial estimate, and prior to completing the detailed nuclear design using reactor analysis
tools (such as CASMO-SIMULATE or PARAGON-ANC), the designer usually relies on either rules of thumb, or an experience base that they can call upon for a specific reactor to provide the initial estimate. Linear reactivity models can also be used to assist in the estimation.

The nuclear designer has to work closely with the utility at this point because they will have analyzed the optimum cycle length of operation for their reactor, from an electricity demand perspective, duration of outage and for planning, e. g., if there are several iPWR units on the same site, there will be a master schedule for maintenance and refueling outages throughout the year. The utility will have forecast the practical and economic optimum for operations, including the potential for early shutdown or stretch out in operations.

Since the enrichment of the fuel is governed by the desired cycle length of operation and the burnup of the discharged fuel, the fraction of the core replenished each cycle has to also be considered. Generally in iPWRs (as in all large PWRs), a fraction of the core (referred to as a ‘batch’) is replaced after each cycle of operation. The remainder of the fuel is then reloaded back into the core, albeit in different locations to their previous location — the locations within the core of the fresh and previously irradiated fuels are known as the ‘core loading pattern’ which is described in Section 4.3.3. However, in at least some iPWR designs, there is a plan to discharge all of the fuel after each cycle. The proportion of the core replaced and the frequency in which is replaced is known as the ‘fuel management’ scheme. Here are some examples to illustrate:

• 4 X 12 month fuel management scheme: lA of the fuel assemblies are replaced months;

• 3 X 18 month fuel management scheme: Vs of the fuel assemblies are replaced months;

• 2 X 24 month fuel management scheme: й of the fuel assemblies are replaced months;

• 1 X 48 month fuel management scheme: all of the fuel assemblies are replaced months.

It should be noted that the cycle length is the time interval between one cycle beginning and the start of the next subsequent cycle. This means that the durations quoted above include the time required for the maintenance and refueling outage. As such they are not the length of time that the core is operating at full power. Therefore, in calculating the actual energy produced in that time, capacity factors have to be taken into account.

The capacity (or load) factor is the percentage of electrical power that a reactor actually produced in a given period compared with the electrical power that could be produced if the unit were operated continuously at full power in the same period. For example, if a reactor’s name-plate capacity was 1 000 MW hours of electrical power, but in a given year it produced 800 MW hours, then the capacity factor would be quoted as 80%.

In the above examples, the first number not only indicates the proportion of the core replaced, but it also refers to the number of cycles of irradiation that the fuel
will be in the core for; 4, 3, 2 and 1 respectively. Therefore, to calculate the discharge burnup of the fuel batch on average, one simply needs to multiply the cycle length (in MWd/MTHM) by the number of cycles.

Therefore, at equilibrium, the discharge burnup of a batch of fuel assemblies is:

BDischarge = N x S x L x C [4.2]

where : N = number of batches,

: S = specific power of the iPWR (MWth/tonne)

: L = length of cycle (in days)

: C = capacity factor (%)

For example, assume an iPWR has a thermal power of 500 MW, 12 MTHM of fuel, a capacity factor of 90% and a cycle length of 15 months (~450 days), for a three batch scheme, the discharge burnup would be:

BDischarge = 3 x (500/12) x 450 x 0.90 [4.3]

= 50 625 MWd/MTHM

It should be noted that this is the batch average burnup, and not all of the fuel assemblies discharged at the end of that cycle of operation will have achieved the same burnup because the fuel in that batch is positioned in different locations in the core and will be irradiated at slightly different powers, may have had control rods inserted into them during operation, etc. Similarly, because of their location in the core, in the assembly, next to guide thimbles, BPs, etc., each fuel rod will have a different burnup, as will the pellets in the fuel rods. As explained above, the assemblies, rods, and pellets will have limits that the designer has to check are not violated.

For example, for a quoted ‘batch average’ burnup of 45 GW d/MTHM, a typical peak assembly burnup within that batch would be 50 GW d/MTHM, a peak pin burnup would be typically 55 GW d/MTHM, and a peak pellet, of the order of 60 GW d/ MTHM. This illustrates very clearly why it is important for the designer to minimize the variation of the burnup of pins within the assembly, and of assemblies within the batch, because large variations will lead to violations of the limits/warrantees potentially, and therefore limit the utilization of the entire batch unnecessarily.

An increase in the number of batches results in an increase in discharged burnup achievable, while requiring lower enrichments, and therefore results in a lower fuel cost overall. This is most easily represented by the equation:

2n

^Discharge = "—— B1 [4.4]

(n + 1)

where n = number of batches and B1 = burnup of single batch core (which is equivalent to the cycle length).

For example, a two-batch core design will have an equilibrium discharge burnup ~33% greater than a single batch, and a three-batch core design will be 50% greater than the single batch. The theoretical limit in the improvement is 100% over the single batch. However, increasing the number of batches decreases the cycle length, and results in more frequent refueling, which decreases the capacity factor of the iPWR. Even with a small number of assemblies in the core that need refueling and/ or reloading, this can have a notable impact on the economics, and so generally a compromise of two to four batches is used.