[1] Analysis of abnormal transients and design based accidents

In the safety analysis of nuclear power plants, safety system models and scenarios of abnormalities are implemented into the plant dynamics calculation code. Abnormal events are classified into abnormal transients and design basis accidents depending on the initial event frequency, namely, high and low frequencies respectively.

For examples, Fig. 2.45 describes the plant system of a SCWR with the safety system and Fig. 2.46 shows the calculation model of its safety analysis code [27, 29].

The SCWR is a direct steam cycle system and its safety system is similar to that of BWRs. Safety relief valves (SRVs) and an automatic depressurization system (ADS) are installed into the main steam lines. Turbine bypass valves are used to dump the main steam to the condenser at a sudden closure of the main steam control valves. This is made in a manner to prevent damage to the turbine from over-rotation by a turbine load loss due to a breakdown of the electric transmission system. The high-pressure auxiliary feedwater system (AFS, high — pressure coolant injection system) is equipped to maintain coolant supply at an abnormal event of the main feedwater system. The low pressure coolant injection (LPCI) system is prepared to flood and cool the core after reactor depressurization at a loss of coolant accident (LOCA). The water is fed from the suppression chamber or condensate water storage tank. The LPCI system also

Bottom

Dome

< 9 Meshes)

Fig. 2.46 Calculation model for abnormal transient and accident analysis

has the function of residual heat removal (RHR) after reactor shutdown. The boric acid injection system (standby liquid control system, SLC system) is provided for backup shutdown.

Figure 2.46 models main steam control valves (turbine control valves), SRVs, turbine bypass valves, AFS, reactor coolant pump (RCP), and so on. The core is modeled by average and hot channels. Since abnormal events for safety analysis are often relatively short-term ones, heat removal models including the turbine system are not always necessary. The calculation model in the figure does not comprise safety systems for LOCA analysis such as the LPCI. General-purpose safety analysis codes have models to handle those systems.

Reactor power uprates are intended to raise the reactor electric power by about several to 20 % as thermal power rise without compromising reactor safety in existing nuclear power plants. For example, a reactor power uprate by 5 % in 20 power plants has the same effect as the construction of a new power plant. European and USA regulatory authorities have given about 160 approvals for these uprates and extensive experience has been gained since the 1970s. Classifications of reactor power uprates are described below.

(1) Measurement-Uncertainty-Recapture type

MUR types of power uprates are based on improved measurement of feedwater flow rate through use of ultrasonic flow metering to significantly reduce the uncertainty in thermal power calculations for safety analysis. Reduction of the uncertainty can result in uprates of up to 1.5 % in reactor thermal power (steam flow rate) within the allowable range of safety analysis.

A malfunction of the chemical and volume control system or an operator’s error can cause an unplanned abnormal dilution or boration in the primary coolant. In the automatic control mode of control rods, reactor power is kept constant and control rods are withdrawn or inserted depending on the boration or dilution, and the power distribution is varied.

Such an abnormal transient arising from normal operation such as load following operation can be analyzed and evaluated as the maximum linear power density by a core nuclear calculation. Fq x relative power, namely, maximum linear power density is evaluated for abnormal withdrawal of control rods at power in Fig. 3.55 and for abnormal dilution or boration in the primary coolant in Fig. 3.56.

It is seen that both maximum linear power densities are lower than the design limit of 59.1 kW/m for the 17 x 17 fuel assembly. In the case of abnormal dilution or boration in the primary coolant, the linear power density can be maintained below 59.1 kW/m, even for the large (absolute value) Axial Flux Difference for the following two reasons.

• Corrective action of operator can be expected, since the transient is relatively slow

• Even if the corrective action of operator is not taken, the power is reduced or the reactor is tripped by the over-temperature A T or over­power AT with large absolute value of AI.

The spent fuel of LWRs contains minor actinides (MAs) i. e. Np, Am, Cm etc. as well as plutonium. In the conventional nuclear fuel cycle with high — decontamination reprocessing, those MAs are disposed in a deep geological repository as high-level radioactive waste and they will be supervised and stored long term. To reduce the environmental load, it is desirable to reduce the inventory of the high-level radioactive waste and to shorten the period for supervising it. The future fuel cycle is being researched in several countries toward reducing the MA inventory in the waste and hence reducing the environmental load by reloading the MAs to a reactor without separation from U and Pu. In such a fuel cycle, the decay time of the radioactive waste, defined as the period in which the radioactive toxicity decays to that of the amount of natural uranium needed for the equivalent electric power generation resulting in the production of the waste, may be shortened from several hundred thousand years to hundreds of years. The principle of transmuting the MAs in the reactor core is as follows. The value of (oc/of), i. e.the ratio of the capture cross section of a heavy nuclide oc to its fission cross section of is generally small for a fast neutron spectrum, and MAs, i. e. Np and Am having even number of neutrons, have a threshold energy of fission at several hundred keV. Thus, (oc/of) quickly decreases for the energy above the threshold.

For this reason, the fraction of fission is high while that of build-up to heavier nuclei by successive neutron captures is small when MAs are transmuted by fast reactors. In other words, MAs can be utilized as the nuclear fuel. Even if the MA recycle is repeated in fast reactors, production of heavier nuclei is small compared to thermal reactors. This also implies that useless consumption of neutrons is smaller in fast reactors. In the case of thermal reactors, the MA nuclei with even numbers of neutrons which are not fissile are transmuted by capturing neutrons, thus the consumption of neutrons tends to be larger. In summary, MA transmutation by fast reactors has advantages from viewpoints of suppressing the production of heavier nuclei and neutron economy. The burnup chain including MA nuclei is shown in Fig. 4.14.

When MAs are utilized as fuel, two methods are considered. One is using driver fuel containing homogeneously distributed MAs (homogeneous loading). The other is separately fabricating MA fuel assemblies containing higher MA fraction and loading them into the core (heterogeneous loading). The core characteristics for each method are being researched. The influence of the homogeneous loading on the core characteristics is small. However, heat and neutron generations of the fresh fuel are large and the number of fuel assemblies needing special treatments is huge because all the fuel assemblies contain MAs. On the other hand, in the heterogeneous loading the number of such assemblies is limited. However, the influence on the core characteristics is relatively large. The loading position of the MA fuel assemblies must be suitably selected.

From the viewpoint of reducing the inventory of radioactive waste, trans­mutation of long-lived fission products (LLFPs) is desired as well as MA

reaction

jj Fissile nude

Fig. 4.14 Burnup chain [4]

nuclei. 129I (half-life: 16 million years, 99Tc (half-life: 210 thousand years) and 135Cs(half-life: 2.3 million years), which are recognized to have potentially high environmental loads from viewpoint of inventory, half-life and mobility, are the targets of transmutation. The LLFP nuclei in the spent fuel are to be included in LLFP-containing fuel assemblies and reloaded to the reactor. As for 135Cs, under the assumption of element separation (not isotope separation), reduction of its inventory by transmutation is difficult due to the new produc­tion from Cs. Thus, I and Tc are the major targets. Since the principle of

LLFP transmutation is neutron capture, lower neutron energy provides higher transmutation efficiency. When LLFPs are transmuted by fast reactors, moder­ator pins will be provided in the LLFP assemblies for improving the transmu­tation efficiency. The loading positions of the LLFP assemblies must be carefully chosen considering the influence on the core characteristics.

In the same way as for 135Xe, the production-destruction equations of 149Sm are solved and some features of its negative reactivity from reactor startup to after shutdown can be discussed. 135Xe has a significantly large thermal absorption cross section and undergoes decay with a half-life of about 9 h as well. On the other hand, 149Sm is a stable nuclide with a large thermal absorption cross section and this is the major difference between the both poisons.

Fig. 1.7 eactivity

insertion due to 135Xe burnout at re-startup [7]

Shutdown

0.1

Equilibrium 1,5Xe

—[min]—>

In the production processes of 149Sm described in Fig. 1.5, 149La, 149Ce, 149Pr, and 149Nd are the main relevant FPs. They decay comparatively rapidly to 149Pm due to their short half-lives. The production-destruction equations are set up with due attention paid to 149Pm and 149Sm. The nuclide concentrations of 149Pm and 149Sm are denoted by P(t) and S(t), the decay constant of 149Pm is XPm, the thermal absorption cross section of 149Sm is WSm, and the fission yield of 149Nd is уNd. Thus the production-destruction equations of 149Pm and 149Sm can be written as below.

(1.37)

[1] Solution at initial startup

Here, a reactor is considered that is starting up from a clean condition in which there are no FPs. Solving Eqs. (1.36) and (1.37) with the initial conditions of P

(0) = S(0) = 0 gives the next solutions.

APm

(1.39)

<Уа O’а Ф Apm

The equilibrium concentrations, Peq and Seq, are found to be Eqs. (1.40) and (1.41).

(1.40)

(1.41)

The reactivity change due to the equilibrium 149Sm is then expressed as Eq. (1.42).

It should be particularly noted that this reactivity change is independent of the neutron flux in contrast to 135Xe. In a 235U-fueled thermal reactor, this reactiv­ity change is

In comparison with 135Xe, this is a secondary reactivity effect which is about —0.69 dollars for the delayed neutron fraction.

[2] Solution after shutdown

After shutdown, 149Sm builds up as the accumulated 149Pm decays. However, unlike 135Xe, which undergoes decay, 149Sm is stable and remains in the reactor.

The production-destruction equations of the 149Pm and 149Sm concentrations after shutdown are given below.

(1.43)

(1.44)

With the concentrations at shutdown denoted by P0 and S0, respectively, the concentrations at the later time t become Eqs. (1.45) and (1.46).

P(t)=P0e Xpmt

Stt^So+PoCL-e-^O

Fig. 1.8 Negative reactivity due to 149Sm after shutdown [7]

If 149Pm and 149Sm are at their equilibrium concentrations at shutdown, P0 and S0 are given by Eqs. (1.40) and (1.41). Equation (1.46) can then be rewritten as the following.

ЛРт

The post-shutdown reactivity change due to 149Sm at the later time t is obtained as Eq. (1.48).

(1.48)

The reactivity change of Eq. (1.48) is shown in Fig. 1.8 for a 235U-fueled thermal reactor after shutdown. It is observed that, like 135Xe, the post­shutdown buildup of 149Sm increases with increasing the neutron flux before shutdown. The buildup is, however, saturated to an asymptotic value dependent on the flux because 149Sm does not decay. The 149Sm poisoning is small compared with 135Xe poisoning and does not have a large effect on the reactor

dead time. In addition, 149Pm has a relatively long half-life of 2.21 days so that the 149Sm buildup proceeds comparatively slowly.

When a reactor is restarted after shutdown, the burnout of the accumulated 149Sm gives a positive reactivity to the system toward the equilibrium value at operation. This effect occurs regardless of how long after shutdown the re-startup occurs.

Nuclear design codes do not use all the massive information contained in the evaluated nuclear data file and also cannot always effectively read out neces­sary data because of the data format putting weight on the compact storage. Therefore, nuclear design codes do not directly read out the evaluated nuclear data file, but (i) extract necessary data and (ii) prepare a preprocessed data set (reactor constant library) which is one processed suitably for each code. A series of tasks is done in order, for example, to select nuclides and cross section data required for nuclear design, to prepare their infinite dilution cross sections and self-shielding factor tables for a specified energy group structure of a nuclear design code, and to store the data in a quickly accessible form. As nuclear data processing code systems to perform such work, NJOY [9] of LANL and PREPRO [10] of IAEA have been used all over the world.

There are two different forms of the reactor constant library; a continuous — energy form and a multi-group energy form. The former is used in continuous — energy Monte Carlo codes such as MCNP [11] and MVP [12] and the latter in nuclear design codes.

Since most nuclear design codes are provided as a set with a multi-group reactor constant library, it is usually unnecessary to process the evaluated nuclear data file in the nuclear design. However, when introducing the latest evaluated nuclear data file or changing the energy group structure to meet advances in fuel and design specification of nuclear reactors, a new reactor constant library is prepared using the nuclear data processing code system. The reactor constant library, with which a nuclear design calculation begins, might be regarded as a general-purpose library. However, it should be noted that a weighting spectrum specified in part for a reactor type and resonance approx­imations are employed in preparing a multi-group form library.

Nuclear characteristic calculation methods depend on the type of reactor being targeted. The following discussions center on LWR (especially BWR) calculation methods which need the most considerations such as heterogeneity of the fuel assembly, effects of the nuclear and thermal-hydraulic coupled core calculation, and so on.

From the viewpoint of fuel integrity during reactor operation, the following two mechanisms are considered in fuel rod design as a mechanism of fuel failure and the design criteria and limit values are set for each.

(i) Cladding damage due to overheating resulting from insufficient cooling

For fuel failure prevention, BWRs are designed to assure that at least 99.9 % of the fuel rods in the core would not be expected to experience boiling transition during normal operation and abnormal transients. As a performance indicator of the design criterion, critical power ratio (CPR) is defined as the ratio between the critical power at a boiling transition in the thermally severest location of a fuel assembly, and the assembly power at normal operation. Fuel rods are designed to have a larger CPR than the minimum critical power ratio (MCPR) even at abnormal transients causing a change in coolant flow rate and reactor power (e. g., MCPR > 1.07). In normal operation, MCPR is restricted to a higher value (e. g., 1.2—1.3), so that it does not reach the limit in abnormal transients considering that MCPR falls in the abnormal transients. Since MCPR strongly depends on the radial power peaking of core, the radial power distribution should be flattened to place MCPR beyond the restriction.

(ii) Cladding damage due to deformation resulting from a relative expan­sion between pellet and cladding

Gaseous FPs are released into the gap between pellet and cladding with fuel burnup, and then accumulated in the gas plenum, which causes an internal pressure rise of the cladding. Pellet swelling causes pellet­cladding contact, and stress to the cladding. In abnormal transients, the stress will increase with a temperature rise since the thermal expansion rate of zircaloy in cladding is smaller than that of UO2 pellets.

Based on these phenomena, BWRs are designed to assure that the plastic circumferential deformation of cladding due to pellet-clad interaction (PCI) will not be expected to exceed 1 % at abnormal transients. In normal operation, there is a restriction on maximum linear heat generation rate (e. g., 44 kW/m) to restrain PCI.

In addition, an allowable maximum burnup of fuel assemblies is set based on operating experiences and irradiation tests. The core and fuel rod design and the core management are done so that the burnup limit is not exceeded.

The spent fuel storage pool is connected to the reactor well through the pool gate installed on the top floor in the reactor building and fuel is stored in spent fuel storage racks which are fixed to the bottom of the pool. The spent fuel storage pool is designed with a capacity that all fuel assemblies in the core can be moved to the pool even after spent fuel is stored as planned. The spent fuel storage pool of ABWRs, as shown in Table 3.10, can accommo­date a fuel amount to as much as about 430 % of the whole core.

Spent fuel storage racks are designed to assure that the effective multi­plication factor is maintained at less than 0.95 in any cases to be expected for water temperature in the pool and fuel location in the racks under the maximum fuel storage, by holding a proper fuel assembly spacing to prevent criticality of storage fuel. In the analysis of subcriticality in spent fuel storage, the infinite multiplication factor of stored fuel to be loaded into the core is assumed to be 1.30, the same as for the fresh fuel storage. Recently, stainless steel containing boron as a neutron absorber is used in spent fuel storage racks to increase storage density.

The wall and bottom of the spent fuel storage pool and cask pit are shielded by a concrete wall and the top of spent fuel is secured by a water depth to ensure a sufficient shielding effect. The internal surface of the pool and cask pit is lined with stainless steel to prevent leaks. In addition, the spent fuel storage pool and cask pit are designed to have no drains and check valves are established in pipes connected to the pool, to prevent outflow from the pool by siphon effect even if the pipes break.

Fuel handling facilities are designed to have a structure in which fuel assemblies can be handled independently to prevent criticality of fuel, and in which the transportation (from core to the spent fuel storage pool) and storage (to cask) of spent fuel can be performed under water.

The spent fuel pit, established in the fuel handling building, uses reinforced concrete facilities. The wall and bottom of the spent fuel pit are shielded by a sufficiently thick concrete wall and the top of the spent fuel is secured by a water depth to ensure a sufficient shielding effect. The internal surface of the spent fuel pit is lined with stainless steel to prevent water leakage from the spent fuel pit even if a fuel assemby is dropped. In addition, spent fuel is stored under borated water in the spent fuel pit which is designed to remove decay heat by the spent fuel cooling system.

Spent fuel racks to vertically store fuel assemblies are arranged in the spent fuel pit. The spent fuel racks have a structure in which fuel assemblies are inserted one by one in each rack. In a recent design, spent fuel racks are designed which use boron-added stainless steel, and to assure that the effective multiplication factor of less than 0.98 is maintained even in a severe condition such as unborated water flooding under the maximum storage amount of fresh fuel, a proper fuel assembly spacing is held to prevent criticality of storage fuel. Table 3.14 shows that the storage capability reaches about 920 % of the whole core fuel in this example.

Fresh fuel assemblies as well as spent rod cluster control assemblies and burnable poison assemblies are temporarily stored in the spent fuel racks.

A cask pit is also established near the spent fuel pit to accommodate spent fuel into a spent fuel transport cask.

The excess reactivity and the power distribution, etc. are described below as examples of nuclear design results [28].

(1) Excess reactivity

The excess reactivity is compensated by the control rods and the burnable poison. The power distribution is adjusted to keep the maximum fuel temperature below the limit. If the control rod insertion depth changes significantly with burnup, the power distribution changes, and hence there is a concern that the fuel temperature cannot be kept below the limit. Thus, the control rods are used for mainly the power level control and reactor shutdown. The reactivity change with burnup is compensated by the burn­able poison. In this way, shallow insertion of the control rods is kept throughout the burnup period.

кeff without burnable poison

Reactivity compensated

by burnable poison

diameter

Begin of life

100 200 300 400 500 600 660

Burnup day

Fig. 4.34 Change of effective multiplication factor with burnup

In the nuclear design results, the effective multiplication factor changes with burnup (bold solid line) in Fig. 4.34. This line is the effective multipli­cation factor change that is calculated for full power operation with all the control rods fully withdrawn. If the burnable poison is not used, the effective multiplication factor is over 1.25 at the beginning of the burnup period and it rapidly decreases with burnup. It is difficult to compensate for such a change using only the control rods. If the compensation is made only by the control rods, it becomes difficult to keep the maximum fuel temperature below the limit at the beginning of the burnup period due to deep insertion of the control rods. With the burnable poison, the change of the effective multiplication factor is made small after accumulation of Xe at the beginning of the burnup period. The control rod insertion is kept almost constant throughout the burnup period. The control rods are slightly inserted in core and gradually withdrawn with burnup. Such a small change in the effective multiplication factor is owing to the adequate adjustment of the diameter and boron concentration of the burnable poison rods. With too large a diameter and too low a boron concentration, boron burns out rapidly and hence the excess reactivity recovers, which requires deep insertion of the control rods in the middle of burnup period. With too small a diameter and too high a boron concentration, on the other hand, the burnup of boron is too slow and hence

the excess reactivity decreases too fast, which makes it impossible to achieve the designed burnup days. In the HTTR core design, the diameter and boron concentration were suitably adjusted so that the changes in the control rod insertion depth and power distribution were kept small.

(2) Reactor shutdown margin

It is necessary to ensure sufficient shutdown margin even if the pair of control rods having the maximum reactivity worth is fully withdrawn(one rod stuck condition). In the assessment of the reactor shutdown margin, the total control rod worth with one rod stuck minus the calculation error is used as the available control rod worth. That available worth minus the maximum excess reactivity was confirmed to be more than 1 %4k/k so that the reactor shutdown margin is sufficient.

(3) Temperature reactivity coefficient

A reactor core must have negative feedback characteristics to damp a change in the power level. The reactivity change against the change in the fuel temperature by 1 °C i. e. the Doppler coefficient was confirmed to be negative for the entire operating region. The reactivity change against the change in the graphite temperature by 1 °C i. e. the moderator temper­ature coefficient was also confirmed to be negative throughout the burnup period. However, it possibly becomes positive at the end of burnup cycle due to accumulation of 239Pu. This is because the neutron spectrum shifts to higher energy by the elevation of graphite temperature and fission reaction rate due to resonance of 239Pu increases as shown in Fig. 4.35. Shifting of the neutron spectrum decreases neutron absorption by Xe, which also

possibly leads to a positive moderator temperature coefficient. Even if the moderator temperature coefficient is positive, the combined reactivity coefficient (combination of Doppler and moderator temperature coeffi­cients) is kept negative for the entire operating region. Thus, inherent safety is ensured.

(4) Power distribution

The calculated axial power distribution is shown in Fig. 4.36. At the beginning of the burnup period, the power is relatively high in the core upper region having higher uranium enrichment and it is relatively low at the core lower region. The power density at the upper region gradually decreases with burnup. The control rods are gradually withdrawn from about 440 days and then the power density at the upper region increases again. Since such top peak distribution is achieved throughout the burnup period, the maximum fuel temperature is kept below the limit.

(5) Burnup

In order to achieve high burnup of spent fuel, it is better to increase the number of refueling batches. In the FSV reactor where the refueling method with multiple batches was adopted, the radial peaking factor was high because the fresh fuel columns were adjustment to the burnt fuel columns. The HTTR, which was aimed at achieving a high outlet gas temperature of 950 ° C could not adopt the same multiple batch refueling method as of the FSV because such a method causes high fuel temperature in fresh fuel column. In the HTTR, all the fuel blocks are replaced at the same time (one batch method). As a result, the maximum burnup of spent fuel is 33G Wd/t which is lower than those of other types of HTGRs. For the commercial deployment of the block type HTGRs, the burnup of spent fuel should be increased by the axial fuel shuffling method [46]. In this method, an axially exponential power distribution can be achieved by loading the fresh fuel in the core upper region and the burnt fuel in the lower region.