1 Introduction:
Multi-group cross-section library is commonly used in solving the neutron transport and photon transport problems for codes adopting deterministic method [7]. The continuous energy cross-section library [8] is used in the codes adopting Monte Carlo method [9]. The deterministic lattice code, SONG (the name of one of the Chinese ancient dynasty), being developed aims at next generation reactors. So it’s necessary to build the multi-group cross-section library SONGLIB correspondingly. Of course, it should be specially designed to meet the requirement of next generation reactors.
As we know, the fuel, coolant, and structure material of next generation reactors may be different compared with traditional reactors. To achieve the sustainable utilization of nuclear energy, Th-U fuel cycle [10], [11] should be one of the options, besides the U-Pu fuel cycle [12]. And for the breeding reactors, the discharge burnup is large in common, which makes the accumulation of minor actinides with high mass numbers not be neglected at the end of their lifetime. Therefore, it’s necessary to consider many more isotopes. Then, the burnup chain and energy group structure should be adjusted to be fit for requirement of the Th-U fuel cycle and deep burnup.
The spectrum of next proliferation reactors is much harder than that of traditional PWR (the special case is that the spectrum of breeding molten salt reactor [13]-[15] can be designed as thermal or epithermal). Thus, neutron resonance absorption and resonance fission effect in the fast energy region and threshold reaction such as n-2n and n-3n reaction might have some influence on the results. The energy group structure should be carefully designed with the fast and thermal spectrum both taken into account, and reaction path should be specially considered.
With these specialties, a large quantity of original work should be carried out to develop an appropriate library for SONG. The SONGLIB is being redesigned. There are 310 nuclides in all. The energy boundary is 0~20MeV which has been divided into 293 groups. Anisotropic scattering is considered with scattering Legendre order set as one according to present calculation requirement of code SONG, which means the scattering matrix is expanded with P0 and P1 polynomials. Main features of SONGLIB are presented and compared with WIMS-D library [16] in Table.1. The design, processing, and test work will be discussed in detail in this paper. Finally, the conclusions are given.
| SONG | WIMS-D | |||
|---|---|---|---|---|
| Energy range (MeV) | 0~20 | 0~10 | ||
| Energy groups | 293 | 69 | ||
| Group structure | ||||
| Thermal | 71 | 42 | ||
| Resonance | 163 | 13 | ||
| Fast | 59 | 14 | ||
| Total isotopes | 310 | 173 | ||
| Burnup related isotopes | ||||
| Actinide | 40 | 25 | ||
| FPs | 122 | 58 | ||
| Other burnable | 71 | 20 | ||
| Resonance related isotopes | ||||
| Actinide | 40 | 11 | ||
| FPs | 56 | 8 | ||
| Burnable-absorber | 46 | 7 | ||
| Control-absorber | 29 | 8 | ||
| Isotope with P1 scatter | 17 | 4 | ||
| Isotope with (n,2n) | 5 | 2 | ||
| Isotope with (n,3n) | 2 | 0 | ||
| Isotope with delayed neutron | 18 | 0 | ||
| Isotope with DPA cross section | 21 | 2 | ||
2 The Design of SONGLIB:
2.1 Nuclide table
The nuclide table is the summary of listed nuclides which the lattice code might use in solving kinds of problems. The isotopes can be divided into two classes, those unburnable and those burnable.
2.1.1 Unburnable isotopes
Unburnable isotopes are those isotopes whose absorption cross-section is very small and whose nuclide density changes slowly during the depletion. Unburnable isotopes include coolant, moderator, structure and cladding material, control rod and detector material, etc, as is listed in Table 2. And for the nature elements, the string ’Nat’ is added to the isotope name.
| Moderator | Coolant | Structure and cladding material | Control rod anddetector material | Others | |
|---|---|---|---|---|---|
| HinH2O | FNat | CNat | NiNat | AgNat | NNat |
| ONat | Li6 | MgNat | CuNat | InNat | N14 |
| SB10 | Li7 | AlNat | ZnNat | CdNat | N15 |
| SB11 | BeNat | SiNat | YNat | BNat | OinUO2 |
| HinPOL | ClNat | PNat | ZrNat | EuNat | KrNat |
| HinZrH | Cl35 | SNat | NbNat | AuNat | ArNat |
| ZrinZrH | Cl37 | KNat | MoNat | PtNat | T3 |
| DinD2O | NaNat | CaNat | SnNat | WNat | |
| BeinBeO | PbNat | TiNat | SbNat | RuNat | |
| OinBeO | BiNat | CrNat | RhNat | ||
| CinGra | He4 | MnNat | CoNat | ||
| HgNat | FeNat | VNat | |||
Moderators like H2O, D2O, polyethylene, BeO, ZrH and graphite are considered. Coolants like Li, Be, F, and Cl used in molten salt reactor, Na, Pb, and Bi used in fast reactor, and He used in high temperature gas cooled reactor are selected as unburnable isotopes. Structure and cladding materials include those elements used in iron-based and nickel-based alloy. Materials used as control rods and detectors include Ag, In, Cd, B, Eu, Au, Pt, W, Ru, Rh, Co, V, etc.
2.1.2 Burnable isotopes
Burnable isotopes are those isotopes whose nuclide density and whose daughter nuclide density changes obviously during the depletion, which can be divided into actinides, fission products, and burnable absorbers. In order to determine the burnable isotopes, it’s necessary to get the burnup chain first.
The discharge burnup of next generation reactors is so large that in the one hand, actinides are more likely to transform into transuranium isotopes such as Am, Cm, Bk and Cf, and in another, daughters of fission products are more easily to accumulate making the burnup chain longer. Besides, for the Th-U fuel cycle reactor as molten salt reactor, the burnup process is different from U-Pu fuel cycle. In view of the above reasons, we should make further efforts to analysis and optimize the burnup chain of actinides, fission products, and burnable absorbers.
The point burnup code ORIGEN-2.1 [17] is adopted to optimize the burnup chain. The isotopes with short decay half-life or with small neutron reaction rate are removed from the original ORIGEN burnup chain. Actinides chain is optimized with Th-U fuel cycle and U-Pu fuel cycle analyzed individually. A similar method is used in the fission product chain optimization. Burnable absorbers include isotopes used in control rod materials such as Ag-In-Cd, Hf and W, burnable poisons such as Sm, Gd, B, and Er, and detector material V and Co. As a result of optimization, there are 233 burnable isotopes which include 40 actinides, 122 fission products, and 71 burnable absorbers.
2.2 Energy group structure
Energy group structure is one of the most important parameters during the processing of multi-group library. Usually, the finer the energy group boundary will be divided, the higher calculation precision will be achieved.
The lattice code SONG aims at solving broad-spectrum problems, which means the spectrum can be thermal, epithermal, or fast. So, it is necessary to divide the energy with a fine mesh throughout the whole range, which will inevitably increase the overall energy groups. Besides, resonance effect should be considered while determining the energy structure. In the first place, the important resonance peaks of absorber, actinides, structure, and coolant should be picked up separately. In the second, resonance peaks of different isotopes should be divided into different groups to the utmost in order to avoid interference of resonance.
The division of energy structure of SONGLIB with isotopes of Th-U fuel cycle involved in such as Th232, U233, Pa233, etc., isotopes of U-Pu fuel cycle involved in such as U235, U238, Pu239, Pu241, etc., and isotopes used in molten salt reactor considered such as F, Li, and Be. The SHEM-361 [6] is referred to, which is the energy structure with 361 neutron groups of open source code Dragon. The group widths of SHEM-361 in the resolved energy domain are small and the self-shielding effect can be described fairly well. However, the resonances are considered much more carefully for SONGLIB in the whole energy range. For example, the resonance effect of Th232 in 630 eV~850 eV energy range is better described for SONGLIB compared with SHEM-361 in the ways that the major resonance peaks are picked up, the major peaks are separated from others, and the peak itself isn’t cut by the energy boundary, as is shown in Fig.1. Besides, many more isotopes are involved during the division of energy groups. The group number of SONGLIB is 293, which is mainly reduced in the thermal range.
2.3 Reaction path
Reaction path is the type of neutron or photon reaction. It must be designed according to the requirment of lattice code, which can actually influence the accuracy and velocity of calculation and functions to be realized. However, some kinds of special reaction paths can’t be directly obtained. It should be processed beforehand. The source of data and the method of processing should be reliable. For SONGLIB, there are 27 reaction paths in all, and some reaction paths are specially handled, as is discussed in details below.
The lattice code SONG adopts the equivalence theory for resonance calculation. Thus the resonance parameters, especially the integral table [18] of resonance cross-section [19], should be provided. The data in the resonance integral table varied with energy group, background cross-section, and temperatures [20] because of the energy self-shielding. Usually, libraries always adopt the uniform resonance energy range for convenience, but the actual resonance energy range of different nuclides is not the same. SONGLIB adopts the non-fixed resonance energy range for every single resonance isotope, which can reduce the overall data amount and better describe the resonance effect especially in the fast energy, such the isotopes of Fe.
The thermal cross-section of moderators such as H2O, D2O, polyethylene, BeO, graphite, ZrH, and UO2 is specially treated whose scattering atom bound in materials affect the incoherent inelastic scattering. Both the P0 and P1 scattering vector and matrix are given in the library. And free gas model is adopted for other isotopes, whose P0 scattering vector and matrix are P1 adjusted. The data of scattering vector and matrix is originated from elastic scattering, inelastic scattering, and n-2n/n-3n. Thus, the cross-section of scattering vector is adjusted to achieve the overall balance of total cross-section.
The reactions such as n-γ, n-f, n-p, n-d, n-t, and n-α are considered when the final absorption cross-section is obtained.
The fission cross-section is the total fission cross-section which includes the first chance fission, second chance fission, etc. And the number of fission neutrons with steady state is calculated with transient neutrons and delayed neutrons both considered.
For those materials whose radiation damage effect should be considered such as C, Al, Fe, Zr, and so on, DPA cross-section is provided.
Burnup related reaction path includes reactions such as fission, capture, n-2n, and n-3n. Besides, SONGLIB also provides the delayed neutron spectrum and delayed neutron fraction divided into six groups, which will be used by the core code [21] later on.
3 Processing of SONGLIB
To obtain the SONGLIB as the requirement of design, there is much work to be done. The flow diagram of SONGLIB processing is shown in Fig.2. There are several kinds of libraries being used or produced during the processing and several tools being developed to realize each process.
3.1 Libraries
As we can see, The ENDF file is indispensable as an input to begin the processing of library. America, Europe, Japan, Russia, and China own different ENDF libraries respectively. There are many differences between these libraries. In this paper, ENDF-B [22] is adopted.
Base library (BASELIB for short) is the intermediate product before processing the multi-group library SONGLIB, which can be built with the standard processing tool and the corresponding ENDF. MATXS format is adopted as the format of BASELIB, which has advantages over other available format in expandability, comprehensiveness, universality, completeness, compactness, and efficiency.
The multi-group library SONGLIB is obtained as the library to be used for the lattice code. There are three kinds of work to be done. Firstly, the data structure should be adjusted for the convenience of lattice code to acquire the data from the library. Secondly, the contents of data should be handled carefully by removing large amount of redundant data and changing the intermediate reaction paths into designed ones. Thirdly, the data should be compressed by removing unnecessary zeros in the library and the output format of library should be binary in order to save the storage space and increase the efficiency of reading.
3.2 Tools
The nuclear data auxiliary processing code NJOYBAT is developed to transform the ENDF library into the BASELIB, which can automatically prepare the input file, produce the multi-group cross-section in MATXS format, and process isotopes in the isotope table batch one by one.
The library management code MANLIB, whose flow chart is shown in Fig.3, is developed to build the SONGLIB from BASELIB with several other functions including the revision, derivation, and data accessing of library. The actual function to be achieved should be pointed out explicitly in the user input file.
5 Test of SONGLIB
In order to carry on the verification work of SONGLIB, the Monte Carlo and depletion code MCNP-ORIGEN is adopted. MCNP-ORIGEN is developed to couple MCNP4C with ORIGEN2.1 and provides update information with burnup about isotope density, cross-section and power distribution. Although, the calculation of Monte Carlo and depletion code is much more time-consuming, the flexibility in the geometric modeling, continuous point cross-section, and the exact description of burnup chain make it much more suitable for comparison of results. The deterministic code SONG has shown better performance in computational efficiency in contrast with MCNP-ORIGEN.
To testify cross-sections of nuclides alone, the simple case of PWR cell is chosen. The calculation is processed under given burnup depth of 40GWD/tHM, and the input isotopes and their nuclear density are the same for two codes. The reaction rate of absorption, fission, capture, and scattering is calculated. The fission rate is only given for actinide isotopes, while the scattering rate is given for others. This is shown from the relative error in Fig.4, the cross-sections of most isotopes fit well with those of MCNP-ORIGEN.
The verification of SONGLIB with depletion is necessary. When depletion is considered, the process is much more complex with different burnup chains introduced, and error can be accumulated with depletion. The case is PWR square lattice with discharged burnup reaching 60GWD/tHM. Fig.5 shows the burnup curve of infinite multiplication factor kinf for PWR. kinf decreases with the burnup owning to the decrease of fission rate of isotope U235. The result fits well with that of MCNP-ORIGEN; The maximum difference is not larger than 350pcm. To state from a more microscopic angle, the nuclear density of several major isotopes under 60GWD/tHM is calculated, as is given in Table.3. For MCNP-ORIGEN, more actinide isotopes with n-2n reaction and α decay are considered, which may influence the accumulation of their daughter isotopes especially for nuclides with small nuclide density, and the maximum relative error reaches 8%. However, better accuracy is acquired for important isotopes such as U235, U238, Pu239, Pu240, Pu241, and Pu242. The difference for fission product is mainly originated from the fission yields and branch ratios, which are related to the spectrum for SONGLIB. The pin power distribution for 1/8 lattice is shown in Fig.6, and the maximum error is not larger than 1%.
| Nuclide | SONG | MCNP-ORIGEN | Relative error(%) |
|---|---|---|---|
| U235 | 5.303E-05 | 5.296E-05 | 0.119 |
| U238 | 2.114E-02 | 2.116E-02 | -0.069 |
| Np237 | 1.743E-05 | 1.604E-05 | 8.667 |
| Np239 | 2.818E-06 | 2.756E-06 | 2.227 |
| Pu238 | 1.087E-05 | 1.026E-05 | 5.963 |
| Pu239 | 1.368E-04 | 1.342E-04 | 1.883 |
| Pu240 | 7.581E-05 | 7.492E-05 | 1.186 |
| Pu241 | 4.560E-05 | 4.519E-05 | 0.914 |
| Pu242 | 3.236E-05 | 3.206E-05 | 0.953 |
| Am241 | 1.356E-06 | 1.365E-06 | -0.672 |
| I135 | 2.419E-08 | 2.386E-08 | 1.384 |
| Xe135 | 7.050E-09 | 7.005E-09 | 0.651 |
| Pm147 | 7.154E-06 | 7.478E-06 | -4.326 |
| Pm148m | 6.350E-08 | 6.078E-08 | 4.465 |
| Pm148 | 4.551E-08 | 4.452E-08 | 2.213 |
| Pm149 | 6.645E-08 | 6.553E-08 | 1.412 |
| Sm147 | 3.624E-06 | 3.876E-06 | -6.495 |
| Sm148 | 1.025E-05 | 1.026E-05 | -0.125 |
| Sm149 | 8.879E-08 | 8.545E-08 | 3.901 |
To verify the adaptability of SONGLIB for different spectrum, case of fast reactor hexagonal lattice with UPuZr fuel is chosen, whose spectrum is harder than PWR, and the discharged burnup reaches 300GWD/tHM. As presented in Fig.7, although the difference is larger than that of PWR, the result is acceptable under 300GWD/tHM burnup depth. More analysis work should be carried out to find the exact reason why the difference is produced.
4 Conclusion
The development of multi-functional lattice code SONG is finished. The corresponding SONGLIB has been designed with new features of the material, spectrum, and burnup depth being considered. In order to achieve the build, management, and maintenance of library, the codes NJOYBAT and MANLIB are self-developed, whose main functions have been achieved. The preliminary test results indicate that the SONGLIB is reliable to some extent, but there is still much more work to be carried out.
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