4.1. Code Comparison for Model Validation
A first verification/validation of the quality of the SCALE/POLARIS application for a molten salt fast reactor is based on a comparison to the SERPENT Monte-Carlo code for one specific case (see
Figure 5) based on using identical modelling approaches as given above.
A first comparison of the SCALE/POLARIS results and the Monte-Carlo results show a steady state offset of ~2400 pcm for the ENDF/B 7.1 library and an offset of ~1500 pcm for the ENDF/B 7.0 library. These numbers seems very high when compared to LWR modelling quality, but we have to consider here, that the system is a fast reactor system and fast reactor systems tend to be much more sensitive, thus there the calculation accuracy is lower. In addition, we have to keep in mind that the used libraries are not identical and that a part of the core composition is made up of chlorine, which isn’t a standard nuclear reactor material (e.g., problems of 35Cl(n,p) XS). In addition, the code in the current state uses a multi-group approach with a group structure developed for LWR analysis and the model is based on flat flux approximation within the, for a lattice code, very large calculation regions. The strong influence of the library in the two Monte Carlo simulations (more than 800 pcm) shows that the uncertainty is still high for the given combination of materials and neutron spectrum, which identified a demand for improving the cross section basis before going into deeper calculations. Taking all these factors into account and remembering that the calculations aim to demonstrate the feasibility of a breeding system, the application of SCALE/POLARIS seems appropriate. Over all, besides the initial offset, the burnup curve shows only a relatively robust bias over the whole burnup of ~2400 ± 200 pcm. Thus the results for the breeding evaluation will be rather robust, since both codes deliver comparable results.
A first justification of the bias and how large the influence of the bias is, is given in
Figure 6. To compensate the bias an increase of ~1% in the
235U enrichment would be required, which relates to ~5% error in the enrichment determination or the system size would have to be increased by ~8 cm in radius which relates to a change of ~7% in the estimated diameter. In a real breeder design, the preferred approach would be to increase the core size, since increasing the fissile loading tends to decrease the breeding efficiency [
16]. Both results indicate that the accuracy of the simulation is acceptable for the envisaged feasibility study.
However, when considering the change from a 2D system to a spherical 3D system, the leakage will significantly change and this would finally result in a very sharp drop in the criticality of the test system to keff = 0.911. Thus, in a future case when considering the 3D realistic core a significant correction has to be envisaged or the development of a more reliable and sufficiently efficient 3D tool.
4.2. Results and Discussion for the Two Component System
Natural chlorine consists of two isotopes,
35Cl and
37Cl, with a composition of 76% to 24%. Currently, most of the chlorine based molten salt reactor systems aim to use enriched
37Cl. This has two reasons, the significantly higher neutron absorption cross section of
35Cl and the possibility of the formation of
36Cl by activation processes, a radioactive isotope with long half-life [
22]. However, for a system with a very high content of uranium and a comparably low content of NaCl it could be interesting from economic point of view, to test the effect of natural NaCl (76%
35Cl and 24%
37Cl), while enriched
375Cl is still used for the production of the UCl
3.8 where the Cl content is significantly higher. When natural NaCl is applied for the investigation UCl
3.8 this leads to a final composition to a
35Cl content of ~18%. Thus, the decision should finally be made on the influence of the
35Cl content on criticality, on the cost (and the safety case) of producing NaCl with enriched
37Cl, and on the cost of the formed
36Cl to be forwarded to the final disposal at the end of operation. Whereupon the formation of
36Cl has to be seen and evaluated in recognition of all other long lived fission products, which will be formed in the reactor. The investigation of the effect on criticality is given in
Figure 7. There appears a clear criticality reduction (~2200 pcm, compare the red line against the blue line) over the whole observed burnup period due to the
35Cl in the NaCl component of the fuel. This loss in criticality has either to be compensated by a slight increase of the core size leading to a reduced leakage or by an increase of the content of fissile material. Or to look at it the other way round, the higher criticality achieved by using enriched
37Cl in the sodium chloride can be used to reduce the initial enrichment of fissile material. To match both criticality curves the case with natural NaCl requires a
235U enrichment of 19.21% to achieve a slightly positive Δk
eff integral over the considered burnup, which is required to compensate for the neutron leakage in the third dimension and to create a reasonable modelling of the breeding without a significant disturbance caused by the normalization of the fission source. The system with enriched
37Cl in the NaCl achieves almost the same initial k
eff and the almost identical Δk
eff integral with only 18.32%. The detailed comparison of the k
eff over burnup in
Figure 7 indicates a slightly improved breeding (less steep decrease of k
eff over burnup, see grey curve) caused by the reduced initial enrichment. The influence seems negligible in comparison with the expected accuracy of the calculations (comparison to the Monte-Carlo result). However, it is relevant, since it confirms the expectation that a core with lower fissile content tends to deliver improved breeding performance [
16], and here we approach the level of a sensitivity evaluation since both results are produced with an identical code setting besides the enrichment of fissile material.
In general, an economic analysis will be required to identify the preferred solution, which will be influenced by the cost of the 37Cl enrichment, the production of the specific NaCl, and the core size determining the amount of salt required as well as the follow up cost of the larger system and the cost of disposal of an additional radioactive material, the bred 36Cl, the salt activation and the Sulphur production. However, there is an additional argument, as using natural NaCl is inherently safer as it requires a smaller quantity of chlorine at all and fewer unit operations to prepare the salt. We have to keep in mind, even without the nuclear part dealing with the chlorine will require special safety procedures. This gives evidence for the feasibility from a reactor physics point of view for future discussions on economy, chemistry, and nuclear waste management.
The dimension search is started with a uranium based core composition using a two component system with 53% NaCl and 47% UCl
3.8. The first system size, which achieves with a low enriched uranium loading, a sufficiently positive Δk
eff integral that is compensated for the leakage in the third dimension over the considered burnup period of 80 GWd/t
HM has a radius of 120 cm in the model and required an initial
235Uenrichment of 19.68%. The burnup specified here is a requirement for the simulation of the system to be kept in a reasonable balance over the whole period considered in order to get a reliable breeding estimation. The steep k
eff curve over burnup requires a significant excess reactivity at the beginning of the calculation, which would not be the case in an actual molten salt reactor. However, it indicates that the criticality of the system reduces significantly due to the consumption of the fissile material and a concomitant accumulation of fission products, this therefore indicates that there is insufficient breeding. The initial excess reactivity is needed to get the mentioned slightly positive integral of Δk integrated over burnup. This integration is essential to achieve a realistic model for the breeding under the approximations of a lattice code with normalization of the fission source in the k
eff calculation – in the case of a positive integral (0 to 40 GWd/t
HM) breeding is underestimated due to the normalization reducing the fission source, while in the negative integral (40 to 80 GWd/t
HM), breeding is overestimated due to the artificial increase of the neutron source by normalization. In a real molten salt reactor with online processing, the strong criticality decrease would be compensated by the feeding of additional fissile material, while the fission product accumulation would partly be reduced by the foreseen online salt clean-up – both online processes are not considered here, since the aim is just to investigate the breeding and the dependence on the system dimension based on a model with reduced complexity. The dimension search in
Figure 8 shows the reduced loss in k
eff over burnup with an increased system size and a reduced initial enrichment requirement (16.53% for radius 145 cm and 14.73% for 170 cm).
In general, the results for the increase of the system size indicate that a system with sufficient breeding can be found based on the studies sizes, but the size of the POLARIS model would have to be increased to move to larger core sizes. To avoid this change the next step will be performed by changing the nature of the fissile material from
235U to plutonium. The use of plutonium as fissile material improves the breeding potential of the system significantly, see
Figure 9. The k
eff over burnup curve is clearly flattened for each of the considered cases when plutonium is used as fissile material instead of
235U, when comparing the dotted lines with circles and the solid lines with squares. The most interesting case is the 170 cm radius with plutonium as fissile material. This case delivers an almost flat k
eff over burnup curve over the whole burnup period of 80 GWd/t
HM considered, even for the applied reduced modelling conditions, which omit the effect of the salt clean-up.
The results given in
Figure 9 confirm that it will be possible to achieve sufficient breeding in a molten salt system based on the investigated NaCl-UCl
4 with 47% UCl
4 system under the given modelling conditions (UCl
3.8, 1050K average fuel temperature, 3.2 g/cm
3 salt density, 1239 MWth power), but for the current results only if Pu is used as fissile material. However, the results can only be seen as a preliminary outcome, since to achieve a really robust modelling and simulation result, the input database will have to be improved by applying a more appropriate reactor design and a robust modelling approach for a molten salt reactor with online processes for feeding and clean-up, as well as by improved experiments to determine the thermo- physical data of the salt composition in more detail. However, these first results indicate that despite the uncertainties described above, the proposed salt configuration can be used for the design of a breeding based molten salt reactor system with a reasonable reactor size of ~3.5 m diameter in a spherical configuration. A more precise modelling and simulation approach would be required to achieve a realistic design including the effects of the external loops required for cooling. However, it becomes obvious that the Pu driven core is more efficient since plutonium produces a higher number of neutrons per fission in the fast neutron spectrum than
235U. Thus more neutrons are available for capture reactions leading to breeding.
A more detailed analysis of breeding in the case with Pu as a fissile material and with a wider varying model size is given in
Figure 10. It is clearly visible that the breeding improves with increasing system size and the correlated lower initial content of Pu as fissile material, see
Table 2. After the breakthrough is almost reached with a radius of 1.7 m, the two larger systems show a clear increase of k
eff during the operation, which clearly indicates that efficient breeding is taking place, there is even enough breeding to compensate the accumulation of fission products. However, it has to be kept in mind that these two cases start with a k
eff lower than one, thus on the one hand the start-up of the system wouldn’t be possible, while on the other hand the result is slightly adulterated due to the normalization of the initial fission source creating a slightly higher fission source than in a realistic case. This will lead to a slight improvement of the initial breeding process, even if the integral of Δk over burnup is observed to be slightly positive. In addition, the results do not tell the complete truth since the Pu content is only given in absolute atom% of Pu, but the real absolute amount of Pu depends on the volume of salt in the core, while this volume depends on the radius and the burnup is normalized to the ton of heavy metal which also changes.
To reflect the above described issue, the curves of
Figure 11 have been renormalized taking into account the absolute amount of Pu in the core as well as the change in the absolute heavy metal content, while keeping the core power constant for all cases. In this figure it becomes clear that a larger core, with the identical power, thus consequently with a lower power density will operate for a much longer time period based on the initial loading and an improved breeding performance. Therefore, the inclusion of more Pu seems to be a very attractive alternative, at least as long as the fuel cost is low enough and as long as the plutonium doesn’t degrade in the core, as it was observed in the CAPRA simulations. This brings us back to the initial study and why it would be important to be able to use natural NaCl. When this is combined with the operation of the reactor on spent nuclear fuel from light water reactors as proposed in [
9,
10], the larger core alternative could be of high interest which is in very strong contrast to typical fast reactor designs and they are typically designed around a very high power density mainly due to the high fuel cost related to the production of MOX fuel [
23].
However, since the core is based on Pu, which is in the case of UK is available from the reprocessing and the related stockpile, it will be worth to put an additional glance on the Pu utilisation in the different investigated core dimensions. The aim has to be to increase the Pu utilisation with increased core dimension and the required increased Pu loading in the core, only when this condition is fulfilled will the increase of the core dimension be efficient. This mentioned Pu utilisation in equivalent full power days per inserted ton of Pu is investigated in
Figure 12.
There is a clear increase in the number of full power days per inserted amount of Pu visible, which confirms that the number of full power days increases with increasing core radius faster than the amount of Pu that is required to operate the system. The result confirms the expectations that breeding is traditionally more efficient with reduced initial Pu loading per unit volume [
16] as well as coinciding with the opposite observation that the breeding performance and the Pu fissile quality tend to degrade with very high Pu content in cores. This effect has been observed in the modelling and simulation investigations of the CAPRA project, which investigated plutonium burning [
24]. Based on this final test, it seems from a reactor physics point of view a really attractive approach to accept a lower power density, based on the comparable low fuel cost for the proposed NaCl-UCl system (compared to MOX fuelled fast reactors) and the significantly better breeding performance. This could be of particular interest when considering the operation of a reactor on spent nuclear fuel from LWRs creating the link between power production [
9,
13] and waste management [
10,
12]. However, for a final decision it would be better to have a full economic analysis, which evaluates not only the reactor physics, but also the cost of construction and operation.
4.3. Results and Discussion for the Three Component System
Following the approach given in the introduction the detailed analysis of the two component system will be compared in the section with the three component system [
18] with it’s clearly higher UCl content (59.5% instead of 47 % in the two component system) in the salt composition.
Figure 13 shows the dimension search for the 2-D system indicating an almost identical breeding behaviour than in the two-component system (cf.
Figure 10). The results indicate that a system with a radius of 170 cm or more is required to achieve sufficient breeding in a self-sustainable mode over an acceptable operational burnup of at least 60 GWd/t
HM.
A more detailed comparison of the behaviour of the two and the three-component system is given in
Figure 14 showing a very tiny improvement of the breeding in the three-component system. A more detailed look into the modelling of the different systems indicates why we see an almost identical behaviour. The two-component system was configured by adding plutonium to a given salt composition (47% UCl in 53% NaCl) since Pu typically forms PuCl
3. Thus, when adding about 6% PuCl to the leading salt composition, the overall heavy metal salt content in the mixture increases to 50%. This approach has been used due to the lack of information about the achievable composition and it is not investigated regarding the solubility issues of the composition. In contrast to this adding approach, a replacing approach has been used in the three-component system. The addition of the PuCl
3 has been compensated by reducing the UCl
3 component in the mixture to ensure that in this approach the solubility issues are considered. It seems most likely that the Pu component will replace a part of the U component with the identical oxidation state. Thus, this approach is from chemical and solubility point of view the more correct one. The detailed information on all the compositions calculated is given in
Table A1 for comparison. A detailed comparison of the two 1.7 m cases (row 7 and row 12) shows that for the exactly identical Pu content, the fissile content, normalized on the overall heavy content, is lower in the three component case.
The three component system is only slightly better in breeding, but there is still the question of the quality of the density data and the mentioned solubility issue for the two-component system. In general, it should be expected that the three-component system delivers a higher density due to the higher uranium content, 47% in the 2-component system versus 59.5% in the three-component system (compare again row 7 and 12 of
Table A1 for the HM content). However, the current database does not give sufficiently detailed data on the density to make a final conclusion to study all details. This leads to the conclusion, that improved basic thermo-physical knowledge is essential for more detailed and reliable studies on molten salt systems based NaCl-UCl systems and the composition related breeding performance.
This leaves just one final question open, how could this system work for countries which do not possess a stockpile of separated Pu as is the case in the UK. Would it be possible to achieve a reasonable breeding in a system operated on enriched uranium? In general, it should be possible, since the Russian BN reactors are traditionally mainly operated on enriched uranium [
25]. This final investigation is based on the three-component system, since improved breeding performance is expected due to the higher uranium loading for this salt composition.
Figure 15 indicates that breeding in a uranium based system is possible, however only on the cost of a significantly larger system with a significantly higher amount of heavy metal in the core (see
Table A1). The result confirms the expectation that it is possible to operate a fast reactor on
235U as fissile material, but it is much less efficient than the operation on plutonium. The main reason is the significantly lower amount of neutrons created per fission event in uranium than with plutonium. At an incident neutron energy of 100 keV it is more than 0.5 neutrons more (+40% neutrons per fission) in
239Pu and
241Pu, than for
235U and about the same at 1 MeV neutron energy (~+25% neutrons per fission). A detailed list of the results and input values like fissile enrichment is given in
Appendix A,
Table A1.