2.1 Core geometry and material description

As shown in Fig. 1, a cylinder core (2.1 m radius and 4.6 m height) comprising of a lattice of 10 cm pitch hexagonal elements with hollow cylindrical channels to allow fuel salt circulation is chosen. The radius of these fuel channels is 2.03 cm, corresponding to a salt fraction of about 15%. The total volume of the fuel salt in the reactor is about 20 m³, which contains three parts: the salt in the graphite channels in the core (9 m³), the plenum salt above and below the core (4.5 m³), and the salt in the heat exchangers that are external to the core (6.5 m³). A 50-cm-thick radial thorium blanket is arranged to improve the breeding capacity and it also consists of the same graphite hexagonal elements but with a larger channel radius of about 4 cm. This geometry is based on the optimization by L. Mathieu et al. [22], but the core height to diameter ratio is adjusted to about 1.095 instead of 1.0 in order to improve the temperature reactivity coefficients in such a thermal MSR.

Figure 1:Full-screen View

(Color online) Geometrical description for the quarter of the reactor core.

In order to enhance the solubility of PuF₃ to convert ²³²Th to ²³³U in such a Pu-started MSR, a fuel salt with 78 mol% LiF-22 mol% (ThF₄+PuF₃), rather than the LiF/BeF₂ salt used in MSBR [17], is chosen. Its density at the mean operation temperature (973K) is about 4.125 g/cm³ with a dilatation coefficient of 8.82×10^-4 g/cm³/K [23]. ⁷Li is enriched to 99.995% to lower the neutron capture in ⁶Li. The salt used in the blanket is the same as the fuel salt except for the absence of plutonium. The nuclear grade graphite used as the moderator and reflector has a density of 1.843 g/cm³.

2.2 Calculation tool descriptions

In this work, an in-house developed tool, named MSR reprocessing sequence (MSR-RS) [24, 25], is employed, which can be used to simulate on-line processing and refueling by coupling with various functional modules in SCALE6.1 [26]. Fig. 2 presents the detailed flowchart of MSR-RS. The criticality calculation performed by KENO-VI, a three-dimensional monte carlo criticality computer code, is based on a whole core. The Couple calculation is used to produce the binary nuclear data libraries for Origen-s code by combining problem-dependent, one-group cross sections with state-of-the-art ENDF/B-VII nuclear decay data and energy-dependent fission product yields. The one-group cross sections are generated by using a multigroup cross-section library and the problem-dependent multigroup fluxes which are prepared in a KENO-VI sequence with a 238-group ENDF/B-VII nuclear base. The Origen-s calculation is performed with on-line refueling and reprocessing. Afterwards, the effective multiplication factor (k_eff) is obtained based on the KENO-VI module to determine whether the feed rate is appropriate for critical operation. If k_eff is within the range, the next step calculation will be performed similarly until all burn-up steps are accomplished. It should be noted that the core power (2250 MWth) is maintained constant in each step of depletion calculation.

Figure 2:Full-screen View

Flowchart of MSR-RS.

2.3 Feeding modes and processing options

Considering the depletion of the initial plutonium and thorium, and the accumulation of the fission products (FPs), the fissile and fertile materials should be fed into the core to ensure the reactor steady-state operation. In both of the B&B scenario and the PB&B scenario, the amount of ²³²Th is kept constant while the concentration of fissile fuel is adjusted as required to maintain the criticality of the core. ²³³Pa is extracted continuously and placed outside the core to decay into ²³³U. However, the feeding of the fissile materials is different from each other for the two scenarios. In the B&B scenario, if the produced ²³³U is enough to maintain the reactor criticality, no additional plutonium is needed to be fed and the excess ²³³U is stored. Otherwise, extra plutonium would have to be added into the core to compensate for the lack of ²³³U. While in the PB&B scenario, all the ²³³U produced from the decay of the extracted ²³³Pa will be accumulated outside the core until it reaches the required startup mass for a new reactor. Thus the criticality of the core is maintained by refueling plutonium.

The salt processing, mainly associated with the protactinium extraction and the FPs removal, is complicated but essential to obtain a high breeding performance. In this work, the fuel processing scheme used in the MSBR project [27] is chosen and the influence of the reprocessing period (RP) on the fuel transition is analyzed by increasing the reference period (10 days) to 2 months and 6 months (the extraction efficiencies are assumed constant). The processing of the fertile salt in the blanket is similar to that in the core, but the ²³³U produced in the blanket is also extracted by effective fluorination.

3.1 Evolution of uranium and plutonium isotopes

The initial plutonium obtained from LWR (burn-up of 60 GWd/t) spent fuel consists of about 4% ²³⁸Pu, 51% ²³⁹Pu, 25% ²⁴⁰Pu, 12% ²⁴¹Pu, and 8% ²⁴²Pu [28]. At the initial time, about 6.85 t plutonium and 41.5 t ²³²Th dissolved in the fuel salt are required to reach criticality. Figures 3 and 4 give the evolutions of the inventories of main plutonium isotopes and uranium isotopes in the fuel salt for all the three RP options respectively. It should be noted that the initial load of Pu between the three RP cases is equal, and the slight difference shown in Fig. 3 is mainly caused by the additional Pu within a relatively short time after startup. For both of the 10-day and the 60-day RP cases, a relatively small amount of additional plutonium (RP=10 days: 268 kg; RP=60 days: 533 kg) is required before the reactor becomes self-sustaining. Thereafter, the concentrations of ²³⁹Pu, ²⁴⁰Pu, and ²⁴¹Pu decrease rather sharply (see Fig. 3 (a) and Fig. 3 (b)), while those of ²³⁸Pu and ²⁴²Pu decrease slowly before 10 years due to the key reactions from ²³⁹Pu and ²⁴¹Pu, which are shown as follows:

Figure 3:Full-screen View

(Color online) Evolution of plutonium isotopes in the core for different RP options.

Figure 4:Full-screen View

(Color online) Evolution of uranium isotopes in the core for different RP options.

${}^{239}Pu{\stackrel{(\text{n,}\gamma )}{\to }}^{240}Pu{\stackrel{(\text{n,}\gamma )}{\to }}^{241}Pu{\stackrel{(\text{n,}\gamma )}{\to }}^{242}Pu$

${}^{241}Pu{\stackrel{\beta }{\to }}^{241}Am{\stackrel{(\text{n,}\gamma )}{\to }}^{242}Am$

${}^{242}Am(83.1\%){\stackrel{\beta }{\to }}^{242}Cm{\stackrel{\alpha }{\to }}^{238}Pu$

After 20 years, the inventories of all plutonium isotopes approach their equilibrium. Meanwhile, one can find from Fig. 4 (a) and Fig. 4 (b) that the inventory of ²³³U in both the RP cases first increases quickly from the startup to gradually replace the fissile plutonium isotopes (²³⁹Pu and ²⁴¹Pu) to maintain the reactor criticality and then decreases owing to the depletion of the other three Pu isotopes (²³⁸Pu, ²⁴⁰Pu, ²⁴²Pu) and the accumulated Minor Actinides (MAs), mainly ²⁴¹Am, ²⁴³Am, and ²⁴⁴Cm, which have a much higher capture cross section than their fission cross section. An equilibrium inventory of ²³³U is reached at about 30 years. The equilibrium value for ²³³U is about 790 kg for the 10-day case and about 850 kg for the 60-day case, both of which are a little more than the required critical mass (about 753 kg) to start a new reactor with ²³³U.

As a result of the above fuel transition, fission rate of the main fissile materials (²³³U, ²³⁵U, ²³⁹Pu, and ²⁴¹Pu) in the core has also changed. In order to illustrate this, the 10-day RP case is taken as an example to present the detailed evolution of the fraction of total fission rate, as shown in Fig. 5. The fraction of ²³⁹Pu decreases rather quickly from about 72.4% at initial time to about 3.7% at 10 years, while ²⁴¹Pu’s contribution to fission rate rises to 32.5% at about 5 years due to the captures in ²⁴⁰Pu, which extends the fission of Pu beyond 10 years after startup. Meanwhile, ²³³U plays a more and more important role in maintaining the criticality of the core and its fraction exceeds that of the ²³⁹Pu and ²⁴¹Pu after about 3.8 years. At equilibrium state, ²³³U contributes about 87.4% of the total fission rate, and ²³⁵U is about 10%.

Figure 5:Full-screen View

(Color online) Fission rate fraction of ²³³U, ²³⁵U, ²³⁹Pu, and ²⁴¹Pu for the 10-day RP case.

Compared with the other two RP cases, the system with the 180-day RP is complicated regarding to the evolutions of the inventories of Pu isotopes and U isotopes, as shown in Fig. 3 (c) and Fig. 4 (c). After an almost similar evolution to above two RP cases for about 45 years, the inventories of plutonium isotopes increase sharply. In order to explain this, the fractions of fission rate for the fissile nuclides are also given, as presented in Fig. 6. It can be found that the contribution of ²³³U to the total fission rate increases continuously and exceeds 80% at about 28 years, thus resulting in an increase of the added ²³³U and therefore, a decrease of the accumulated ²³³U that is stored outside the core. At about 45 years, the accumulated ²³³U has been almost burnt off and the external plutonium would have to be refueled into the core to maintain the criticality of the core, which accounts for the sharp increase of the inventories of plutonium isotopes. Influenced by the refueled plutonium, the fission fraction of ²³³U decreases drastically and then increases with the inventory of ²³³U in the core. This process is very similar to that of startup and such complicated transition behaviors involved with the increase and decrease of plutonium and ²³³U will repeat periodically in the following years, as indicated in Fig. 3 (c) and Fig. 4 (c). Therefore, for the 180-day RP case, the fuel transition can only be accomplished by refueling external fissile material successively during the operation, which is significantly different from the other two RP cases. More details on the accumulated ²³³U storied outside the core will be discussed in the next subsection in order to better understand these transition behaviors.

Figure 6:Full-screen View

(Color online) Fission rate fraction of ²³³U, ²³⁵U, ²³⁹Pu, and ²⁴¹Pu for the 180-day RP case.

3.2 Net ²³³U production and conversion ratio

Two main parameters of interest to evaluate the transition performance, the net ²³³U production, and the conversion ratio, are discussed in this section. After startup with the plutonium, the reactor can sustain a critical operation on both the additional supplied plutonium and its self-produced ²³³U. When the reactor operates solely on its self-produced ²³³U and the reactivity for the core is beyond the allowable level (k_eff=1), some excess ²³³U as a net production should be stored outside the core to control the reactivity. It is obvious that the stable increase of net ²³³U production can only be achieved in a breeder reactor. Fig. 7 and Fig. 8 give the evolutions of net ²³³U production and associated conversion ratio for various RP options. It is found that the net ²³³U can be produced even before the conversion ratio actually exceeds unity, which is due to the fact that ²³³U is more reactive than ²³⁹Pu in such a thermal neutron reactor. One can also find that the net ²³³U production is strongly dependent on the processing rate, and this will be discussed below.

Figure 7:Full-screen View

(Color online) Net ²³³U production for different RP options in B&B scenario.

Figure 8:Full-screen View

(Color online) Conversion ratio for different RP options.

The net ²³³U production can be analyzed from the aspects of ²³³U breeding and depletion. The transition case with a 10-day RP is chosen to discuss the evolution of the net ²³³U production. During the first 7 years of this case, the ²³³U inventory increases relatively quickly to its peak value in order to supply the reactivity loss caused by two factors: the produced MAs and the depleted initial fissile plutonium isotopes. As shown in Fig. 5, ²³³U’s contribution to the total fission rate has increased to about 50% at 7 years. Meanwhile, the conversion ratio increases quickly during this stage. A combined result of the ²³³U production and depletion is a slow increasing of the net ²³³U production. While in the following 5 years (7∼12 years), the conversion ratio increases continuously and more quickly than the ²³³U depletion rate (²³³U’s fraction of the total fission rate at 12 years is about 73%), thus leading to a higher net ²³³U production rate than that in the first 7 years. The third stage (12∼28 years) is similar to the second stage but with an even higher conversion ratio. The last stage is the equilibrium stage, which corresponds a constant annual yield of about 42 kg. For the 60-day RP transition case, the behavior of the net ²³³U production before 28 years is almost similar to that of the 10-day RP case but with a much lower net ²³³U production. The conversion ratio at the equilibrium state is very close to 1.0 (about 0.996), resulting in a very slow decrease of net ²³³U production.

As discussed in the previous subsection, the transition behaviors are complicated for the 180-day RP case, which is determined by the degraded breeding capacity stemming from the slow fuel reprocessing. It can be found from Fig. 7 that the net ²³³U production decreases when ²³³U contributes about 80% of the total fission rate (see Fig. 6) and slightly increases when external Pu is refueled into the core, which can greatly reduce the consumption of ²³³U. Meanwhile, the corresponding conversion ratio, shown in Fig. 8, first increases, then decreases, and then fluctuates periodically. Consequently, the fuel transition from the initial plutonium to thorium fuel cycle can not be accomplished, and the reactor operates as a converter with such a limited processing option.

3.3 Neutron spectrum shift

During the fuel transition, the neutron spectra in both the fuel zone and the fertile blanket are shifted downward (toward softer) from the initial time to the equilibrium state (T=100 years), as illustrated in Fig. 9, which gives the spectrum shift for the 10-day RP case. The sufficiently strong thermal neutron captures in plutonium isotopes, including the resonance captures in ²⁴⁰Pu at about 1.06 eV (The capture cross section is about 1.15×10⁵ barns) and ²⁴²Pu at about 2.67 eV (The cross section is about 3.21×10⁴ barns), are the primary contributors to the harder spectrum at the initial time (see Fig. 9 (a)). While at the equilibrium state for the Th/²³³U fuel cycle, the plutonium isotopes are almost burnt off and simultaneously, the moderator-to-fuel ratio becomes higher due to decrease of the heavy mental inventories, both of which result in softening the neutron spectrum. Such a distinct spectrum shift can certainly affect the core behaviors, one of which is the temperature reactivity coefficients that will be discussed in the next section.

Figure 9:Full-screen View

(Color online) Initial and equilibrium normalized neutron spectra of the fuel zone and fertile blanket for the 10-day RP case.

The neutron spectra for the 60-day RP case are almost similar to those for the 10-day case, but a little harder at the equilibrium state due to more FPs accumulation. As to the neutron spectra shift for the 180-day RP case, it is more complicated owning to the re-supplied plutonium at about 45 years, 72 years and 99 years. In order to illustrate this, a new parameter, energy of the average lethargy causing fission (EALF) is introduced to evaluate how fast or thermal the reactor spectrum is [29], which is shown in Fig. 10. It can be found from the comparison that the EALF for the 180-day RP case fluctuates periodically, which is caused by the refueling of Pu fuel as discussed in Sect. 3 3.1.

Figure 10:Full-screen View

(Color online) Energy of the average lethargy causing fission (EALF) for different RP options.

3.4 Temperature reactivity coefficients

The temperature reactivity coefficients (TRC) is an important parameter to evaluate the safety performance during the transition. It is responsible to the reactivity transient and can be calculated based on reasonable approximation that the core behaves isothermally. Actually, due to the most nuclear fissions taking place in the core active region, the fuel salt temperature changes much faster and stronger than the moderator temperature and the fertile salt temperature. Accordingly, the TRC of the three components at the mean operation temperature (973K) are calculated separately and their combined effects are also given.

The fuel salt TRC is a combined effect of the Doppler effect and the fuel dilatation effect, and therefore it can be calculated by changing the fuel salt temperature (corresponds to the Doppler effect) and density (corresponds to the dilatation effect caused by temperature change) simultaneously (the parameters of the moderator and the fertile salt are kept constant). In this calculation, the effective multiplication factor (k_eff) at three points (893, 973, and 1053 K) is calculated and the fuel salt TRC can be obtained from a linear fit to the data plotted as reactivity versus 1/T (δρ/δT, T is the fuel salt temperature). At 973 K, the reactivity is about zero in order to simulate the transient response of a critical system. Similar calculations for the fertile salt TRC are conducted. The TRC of the moderator in the core active region and fertile zone (the reflector graphite is not included) corresponds to the effect of increasing of the moderator temperature (Similarly, the parameters of the fuel salt and fertile salt are kept constant), and it can also be calculated by using linear fitting method. The graphite density coefficient is usually small and can be essentially negligible [30]. The total TRC combines above three effects together assuming that all the three components undergo equal temperature changes. It should be noted that the selected temperatures (893K and 1053 K) are based on the consideration of the mean operation temperature (973K) and the range of validity of the formula for salt density given by Ignatiev V. et al [23].

Figure 11 presents the fuel salt TRC, fertile salt TRC, moderator TRC, and the total TRC for the 10-day RP case respectively. One can firstly find that the total TRC is always negative during the operation, but varies from -8.17 pcm/K at initial time to about -1.75 pcm/K at about 100 years. This remarkable change is mainly due to the graphite TRC which appears to be quite sensitive to the fuel composition and the neutron spectrum in the core. When the temperature of the graphite increases, the spectrum shifts upwards, and further results in relative cross-section changes between fissions in fissile nuclides and captures in fertile nuclides, which is the primary source of the moderator reactivity effect. The calculation shows that the captures in fertile nuclides increase, especially for ²⁴⁰Pu, while the fissions in ²³⁹Pu and ²⁴¹Pu decrease if the graphite temperature increases at the initial time. With respect to the positive graphite TRC after the transition, it is also caused by the spectrum shift, which has been discussed in detail [8, 30]. As to the fuel, the TRC increases from -4.37 pcm/K at the initial time to about -3.0 pcm/K at the equilibrium state owning to both of the increase of the fuel doppler effect and density effect.

Figure 11:Full-screen View

(Color online) Temperature reactivity coefficients for the 10-day RP case.

The TRC for the 60-day RP case is similar to that for the 10-day RP case and the total TRC at 100 years is about -1.68 pcm/K. As to the 180-day RP case, the total TRC fluctuates between a sufficiently negative value (about -7 pcm/K) and a relatively small value (about -1.51 pcm/K), which is also caused by the re-supplied plutonium.