RUSSIAN RESEARCH CENTER "KURCHATOV INSTITUTE" NUCLEAR REACTOR INSTITUTE DEPARTMENT OF PHYSICAL AND TECHICAL RESEARCHES OF ADVANCED REACTORS
9th AER SYMPOSIUM SK00ST13O ON VVER REACTOR PHYSICS AND REACTOR SAFETY SESSION 8: Spent Fuel Transmutations
P.NALEKSEEV, RA.FOMICHENKO, AA.DUDNIKOV
PROJECT OF MOLTEN SALT REACTOR FOR SPENT FUEL TRANSMUTATIONS
NEUTRON-PHYSICAL CHARACTERISTICS: MODELS AND CALCULATIONS
TECHNICAL PROPOSALS ON THE SOFTWARE
MOSCOW 1999
C:\TEMrvhuinitov-pres nf '"' Abstract A brief review of the codes available for the neutron-physical calculations of the heterogeneous nuclear reactors and critical assemblies is presented. These programs can be used for simulation of the reactor part in the Accelerator Driven Transmutations Technology (ADTT) for Molten Salt Reactor Project. Present review describes the programs that do not use empirical coefficients typical for the existing engineering program complexes intended for the calculation of thermal reactors. This is particularly important for the calculation of the non-standard situations in reactor as well as for designing the new reactor concepts.
762 C:\TEMPVJDdniltov-pre.vnf Statement of work
The problem of convenient software selection for MSR calculations is closely connected with the main goals and design of Molten Salt Reactor Unit for Spent Fuel Transmutation and its nuclear fuel cycle. Generally there are five groups of codes depending on their assignment: • codes and databases for neutron physics calculations; • codes and databases for thermal-hydraulics calculations; • codes and databases for structural mechanics calculations; • codes and databases for nuclide transformation calculations and nuclear fuel cycle optimization; • codes and databases for modeling of chemical processes in the molten salt and its interaction with construction materials.
In neutron physics calculations for MSR project software includes both well-known and widely used codes such as: • WIMS - for modeling of the neutron-physical processes in considered installations on the base of the Surface Harmonic Method (SHM); • MCNP - for neutron, photon, electron or coupled neutron/photon/electron transport, including the capability to calculate eigenvalues for critical systems; • NJOY - for producing pointwise and multigroup nuclear cross sections and related quantities from evaluated nuclear data in the ENDF format; and engineering codes designed in RRC KI: • JAR - for the calculations in theoretical neutron-physical studies of the different reactor types with rather moderate calculational time expenses; • CONSUL - for the calculations of nuclear reactor characteristics on the basis of correlated neutron, temperature and isotope distributions; • ISTAR - for nuclide transformation calculations and fuel cycle optimization; and some others. Also nuclear databases are used such as evaluated data files of ENDF type (libraries ENDF/B-VI, JENDL-3.2, JEF-2.2, and BROND-2.2).
The abstracts of codes are represented in Appendix A.
C:\TUMPVIwlnikov-prcs.rtf Appendix A. Software for MSR project neutron physics calculations
A.l. WIMS-D4, WIMS-SH It is proposed to carry out the modeling of the neutron-physical processes in considered installations on the base of the Surface Harmonic Method (SHM) [1-3]. Surface Harmonic Method is a mathematical nuclear reactor model, which allows for steady-state calculations to reduce the methodical part of the inaccuracy to the level connected with the uncertainty of knowledge in microconstants only (in the absence of other uncertainties). Main advantages of the SHM are shown by the account for the different heterogeneities (just in the places of the heterogeneities the main improvement occurs) that is particularly essential in the objects considered. For such calculations we use the WIMS-SH program complex [4,5]. The WIMS-SH program complex unites the English program WIMS-D4 [6] with a series of cell programs (RACIA [7], KLARA [8], and RADIC [9]) specific for the SHM. These programs solve the neutron transport equation in cylindrical and cluster cells by the Surface Pseudo-Sources Method [10] with different boundary conditions. The main new adjustments taken into account in the SHM in contrast to the Traditional Homogenization Method are: 1. Correction for the large step size. 2. Account for cell surroundings by the calculation of its characteristics. 3. Improvement of the group Fick's law. 4. Account for higher spatial harmonics. 5. Transport correction at cell boundaries. Preserving all possibilities of the~WIMS-D4 program, the WIMS-SH complex allows to calculate group cell characteristics both for the traditional equations of the homogenization method and for the more precise SHM equations. The WIMS-SH complex has its own micro cross-section library. The micro cross-section library of the WIMS-SH is prepared on the basis of the UKNDL data. The library contains 90 nuclides, 33 isotopes of them are the fission products, and the rest of fission products are included into pseudonuclide. For 235U, 238U nuclides the recent evaluations are available: for B8U - from ENDF/B-V files, for ^U - from BROND files. The WIMS-SH library has demonstrated a good quality for the research reactors and power reactors with uranium fuel (VVER, RBMK). Recently, for the solution of the problems concerning the transmutation of minor actinides a new library prepared in IPPE (Obninsk) was included in WIMS-SH. New library contains the necessary transuranium elements and 33 fission products. There is the possibility to increase the number of fission products and long-life nuclides to 200. A.2. JAR, JAR-SH The JAR program complex [11] provides wide possibilities for the calculation theoretical neutron-physical studies of the different reactors types with rather moderate calculation time expenses. In this complex the efficient algorithms are suggested for the consequent increase of the spatial approximation in the diffusion approach. The finite-difference mesh in plane can consist of the triangular, square or hexagonal cells. A calculation model can be presented in 30, 45, 60,90, 120, 180 and 360-degree symmetry sectors for corresponding calculation geometries. The possibility to make the calculations in the transport approximation by the discrete ordinates method is provided by the JAR-SN version [12]. The diffusion calculation results can be used as an initial approximation. The JAR program complex contains the modules for the calculation of the adjoint function, effective delayed neutron fraction, prompt neutron lifetime as well as sensitivity coefficients of the Keff and reactivity effects to the changes of the technological
C:\TEMP\dudnikov-pres.rtf 764 parameters and reactor sizes. In the modified type these modules are used for the solution of the spatial kinetics problems. The JAR (JAR-SN) program complex has been verified by calculations of several international benchmark models in all geometries and different approximations [12,13]. By means of the JAR complex the calculations both for the traditional homogenization method and for the SHM can be carried out. For the realization of SHM equations in JAR (JAR-SH version) several changes and additions were made which are connected mainly to the following particularities of the SHM: • Full matrix of the diffusion coefficients and the full matrix of the scattering cross-section. • Dependency of the all cross-sections on the unknown Keff of the reactor (it is necessary to organize an additional layer of iterations); • Unknown value in SHM equations is not the average cell flux, but the neutron level in the cell, so the calculation algorithm for the necessary cell functionals (reaction rates) is slightly changed. It has been shown that the calculation of the heterogeneous reactor cores by the JAR-SH version based on the SHM finite-difference equations with the efficient cell characteristics allows to describe the stationary states with the sufficient accuracy. For the solution of spatial kinetics problems the JAR-IQS program [14] realizing different modifications of the improved quasi-static method (IQS) has been developed on the basis of the JAR program complex. This program is a part of the software package for the core dynamics calculations. The main differences of modifications in methods based on conditional variable separation (which the IQS-method belongs to) from so-called 'direct' methods are the presentation of the solution in terms of values having physical sense (for instance, system reactivity), and possibility to carry out component analysis of errors in time integration. This allows to speak of special perspective of their use in the calculation of transients in ADS systems. The source of inaccuracy in calculations can be directly interpreted in terms of integral and local reactor parameters. The direct comparison can be carried out between results of nonstationary calculations by the JAR-IQS program and calculations by the JAR complex with the use of perturbation theory methods. A.3. CONSUL The CONSUL program complex [15] is intended for the calculations of nuclear reactor characteristics on the basis of correlated neutron, temperature and isotope distributions. The CONSUL complex ensures the calculation of practically important characteristics for power reactors. The structure of the reactor calculation has the following form: • calculation of elementary reactor cells for the preparation of cell neutron-physical constants; • solution of the neutron transport problem in a reactor fuel assembly (or physical zone) and reactor itself in a few-group approximation; • evaluation of thermal-physical core parameters; • solution of the fuel burn-up problem, and, if required, calculation of fuel rod behavior under base irradiation conditions. These calculation stages are coupled through the small number of parameters, for instance, average fuel or coolant temperature, burn-up etc. The approach, realized in the CONSUL complex, consists in the mutual coordination of all calculation stages. All typical feedback characteristic can be taken into account. The balance method for the
CATRMINJudnikov-prcs.rtf calculation of coolant characteristics and heat transfer in fuel is used. The bum-up equations are solved for the main fuel cycles analytically that allows within the framework of one algorithm to consider the fuel burn-up process and xenon transients. The coordination of neutron spectrums, isotope and temperature fields is achieved by iterative process at each burn-up step. The cell programs included in the CONSUL complex provide homogenized macroparameters for physical zones as well as microconstants for the burn-up calculations. The calculation of the space-energy neutron distribution in the GETERA program [16] is based on the 22-group description of neutron spectrum in the moderation range (above 2.15 eV) and detailed description of neutron spectrum in the thermalization range. The microconstant library in the moderation range is based on the ARAMAKO system (ABBN). In the thermalization range the 100-group library of thermal constants derived from ENDF/B-IV is used. Spatial calculations within the cell are carried out by the first collision probability method. Spectrum calculations with a given neutron leakage from the considered area are possible, if the value of respective buckling is provided. The calculation of a fuel assembly (or physical zone) is carried out taking into account the neutron spectrum of its surroundings. The albedo conditions at the its boundaries are accepted as characteristics of surrounding spectrum. They can be determined from the full-core calculations. The solution of equations for neutron currents is carried out in 2D geometry in diffusion or PSn- approximation [17] by the PANORAMA program module [18]. At the stage of reactor calculation for the solution of neutron transport equations in the three- dimensional geometry the PANORAMA-3 program module is used. For the reactor calculations in (x-y) plane the PSn-method for transport calculation allowing to increase the calculation accuracy at the presence of strong absorbers and at the boundary of reactor is used along with the diffusion approximation. Reactor calculations can be performed also in (r-z) geometry by NKRZ module both in diffusion and PSn-approximations. Recently, efforts for modification of CONSUL module NKRZ ((r-z) geometry) for the solution of spatial kinetics have been undertaken. These module, along with the LOOP code for calculations of transients in MSR and LMR reactor installations (this code describes the dynamics of circulation circuits) forms a part of the software package for the core dynamics calculations. A.4. ISTAR The features of MSR concept require paying more attention to codes and databases for nuclide transformation and fuel cycle optimization. Namely: • the placement of considerably large amounts of minor actinides and fission products in core has an effect on neutron spectrum and so on neutron cross-sections; thus one should use over again prepared cross-sections for nuclide transformation calculations; • • uncertainties and insufficient information in decay parameters, fission product yields and other nuclear data for many nuclides suppose one to have an easy and sure instrument to control, correct and update data in databases; • the on-line reprocessing of the irradiated salt composition circulated in MSR radically differs from the procedures of convenient reactors reloading, so new algorithms and codes must be designed for nuclear fuel cycle calculations; • -using MSR as an element necessary for closing nuclear fuel cycle in a three-component nuclear power scheme requires codes to solve the problem of several systems and nuclide streams between them; • in addition a progress in hard- and software for personal computers allows not lesser progress in codes and databases design.
C:\TEMPVludnikov-prcx.rtf 766 various codes and usage of standard electronic tables for entire problem information and development of set of codes operating with these tables. Thus the transparency of information is achieved, and standard software offers easy and sure data maintaining. Generally there are four groups of electronic tables: decay parameters and nuclear data not depending from neutron flux formed table DECAYS, data for this table are extracted from ENDF/B libraries and Japan JNDC FP Decay Data File Version 2; fission product yields formed table YIELDS, data for this table are extracted from ENDF/B libraries and Japan JNDC FP Decay Data File Version 2; nuclear data depending on neutron flux formed tables XSECTIONS; there are one-group cross sections obtained from neutron-physics calculations of given system using codes MCNP4A [20], NJOY [21] and databases ENDF [22]; another data and results are also stored in VECTORS tables; the arrival/withdrawal of nuclides in the system may be specified as a rate and/or in quasi-lambda form. Using standard software one can manage an information to obtain the tables most suited to the problem. Code ISTAR can solve among others problems of the type:
dt for given time t > to , where nj(t) - i-th nuclide amount in given system, nucl; njo - initial amount of i-th nuclide in system, nucl; Ajj - constant of transformation of nuclide i to nuclide j, I/sec; qi - rate of i-th nuclide arrival/withdrawal in system, nucl/sec. Code ISTAR solves the problem and sets results to respective VECTORS table. For any table it is possible to print the report in ASCII codes. An option exists to gather several XSECTIONS and VECTORS table to solve the problem of several systems and nuclide streams between them. We used in our calculations nuclear data for 125 heavy nuclides from Fr to Fm (among them 65 nuclides have neutron cross-sections) and for 1227 nuclides of fission products from V to Lu (among them 166 nuclides have neutron cross-sections).
A.5. MCNP
MCNP [20] is a general-purpose Monte Carlo N-Particle code that can be used for neutron, photon, electron or coupled neutron/photon/electron transport, including the capability to calculate eigenvalues for critical systems. The code treats an arbitrary three-dimensional configuration of materials in geometric cells bounded by first- and second-degree surfaces and fourth-degree elliptical tori. Pointwise cross-section data are used. For neutrons, all reactions given in a particular cross- section evaluation (such as ENDF/B-VI) are accounted for. Thermal neutrons are described by both the free gas and S(a,$) models. For photons, the code takes account of incoherent and coherent scattering, the possibility of fluorescent emission after photoelectric absorption, absorption in pair production with local emission of annihilation radiation, and bremsstrahlung. A continuous slowing down model is used for electron transport that includes positrons, k x-rays, and bremsstrahlung but does not include external or self-induced fields. Important standard features that make MCNP very versatile and easy to use include a powerful
CATLMPVludnikov-prcs.rtf '«' general source, criticality source, and surface source; both geometry and output tally plotters; a rich collection of variance reduction techniques; a flexible tally structure; and an extensive collection of cross-section data.
A.6.NJOY
The NJOY [21] nuclear data processing system is a comprehensive computer code package for producing pointwise and multigroup nuclear cross sections and related quantities from evaluated nuclear data in the ENDF format. The U.S. Evaluated Nuclear Data Files (ENDF) have progressed through a number of versions, notably ENDF/B-IH, ENDF/B-IV, and ENDF/B-V. The latest version, ENDF/B-VI, has recently become available. The ENDF format is also being used in other modern libraries such as JEF-I and JEF-II libraries produced in Europe. These libraries represent the underlying nuclear data from a physics viewpoint, but practical calculations usually require special libraries for particle transport codes or reactor core physics codes. This is the mission of NJOY - to take the basic data from the nuclear data library and convert it into the forms needed for applications.
C:\TEMl^dudnikov-|Kex.rtf 1. Laletin N.I. On the Equations of Heterogeneous Reactor (review). VANT., Ser. FTYaR, M NIOET, 1981, 5(18), p. 31-46. 2. Laletin N.I. Basic Principles for Developing Equations for Heterogeneous Reactors. - Nucl. Sci. Eng., 1983, vol. 83, p. 133. 3. Laletin N.I., Sultanov N.V., Boyarinov V.F. Surface Harmonic and Surface Pseudo-Sources Methods. SF/ANS, ENS International Conference on the Physics of Reactors. April 23-27, 1990, Marseille, France, vol. 2, pp. XII-39 - XII-48. 4. Laletin N.I., Sultanov N.V., Boyarinov V.F., Voitovetsky S.V. Annotation of the WIMS-SU program. VANT., Ser. FTYaR, 1991, 1, pp. 26-33. 5. Laletin N.I., Sultanov N.V., Boyarinov V.F., et. al. WIMS-SU complex codes and SPEKTR code. SF/ANS, ENS. International Conference on the Physics of Reactors. April 23-27, 1990, Marseille, France, vol. 4, p. PV148-I57. 6. Askew J.R., Fayers F.J., Kamsell P.B. A General Description of the Lattice Code WIMS- JBNES, 1966, p. 564. 7. Sultanov N.V. Annotation of the RACIA program. VANT., Ser. FTYaR, 1989, 2. 8. Sultanov N.V. Annotation of the KLARA-1 program. Ibid., 1989,2. 9. Boyarinov V.F. Annotation of the RADIKF and RADIKF-ES programs. Ibid., 1988, 2, p. 71. 10. Laletin N.I. Surface Harmonics Method for the Solution of Neutron Transport Equations (Gn-approximations). - In : Methods for the Calculation of the Neutron Fields in Thermal Reactors. M., Atomizdat, 1974, p. 187. 11. Yaroslavtseva L.N. The JARB program complex for the Calculation of Neutron-physical Characteristics of Nuclear Reactors. VANT, Ser. FTYaR, 1983, .8 (37), pp. 41-43. 12. Yaroslavtseva L.N. et al. The Multidimensional Code JARSN for Next Generation Reactors and Benchmark 3-D Neutron Transport Calculations. Proc. of OECD-NEA Top. Meeting, Saclay, France, Oct. 22-23, 1990. 13. Yaroslavtseva L.N., Fomichenko P.A., Alekseev P.N. Verification of the Stationary and Nonstationary Algorithms in the JAR complex. In Proc. of the 'Neutronics-92' Conference, Obninsk, 1994. 14. Fomichenko P.A., Yaroslavtseva L.N., Alekseev P.N. Analysis of the Efficiency for Various Modifications of the Improved Quasi-Static Method for Spatial Kinetics in the JAR-IQS Code. // Proc. of 8th Top. Meet, on Reactor Physics Problems, Sept 1993, M.: MEPhI, 1993, v. 1, pp. 50-52. 15. V.F. Tsibulsky, A.V. Tchibiniaev. The CONSUL Program for the Complex Calculations of Nuclear Reactors. VANT, Ser. FTYaR, 1995. 16. Belousov N., Bichkov S., Marchuk Yu. et al. The Code GETERA for Cell and Polycell Calculation. Modes and Capabilities. Proc. of ANS Top. Mtg. on Advances in Reactor Physics, March 8-11, 1992, Charleston USA, Vol. 2, p. 516-518. 17. V.F. Tsibulsky, A.V. Tchibiniaev. The Balance Method for the Solution of the Neutron Transport Problem Taking into Account the Discrete Angular Flux Dependence (PSn- Method). Preprint IAE-4988/4, M., 1989. 18. A.V. Tchibiniaev. The Solution of the Neutron Transport Equation in the Hexagonal Geometry in Diffusion Approximation and by the PSn-Method. Preprint IAE-5392/4, M., 1991. 19. Nevinitsa V.A., Polismakov A.A., Fomichenko P.A., Gagin V.L., Dudnikov A.A. Some of Tasks in Modeling of Local Power Distribution and Fuel Irradiation in Molten Salt Reactor Unit. RRC Kl report, Hz 35/1-266-97 (October 1997). 20. J.F.Briesmeister (Editor), MCNP - A General Monte Carlo N-Particle Transport Code, Version 4B, User's Manual, Los Alamos National Laboratory Report LA-12625-M, (March 1997).
C:\TEMIMuUnifcov-pccs.rtf 21. R.E.MacFarlane and D.W.Muir, The NJOYNuclear Data Processing System, Version 91, User's Manual, Los Alamos National Laboratory Report LA-9303-M, (May 1982). 22. P.F.Rose and C.L.Dunford, Eds., ENDF-102. Data Formats and Procedures for the Evaluated Nuclear Data File,ENDF-6, Brookhaven National Laboratory Report BNL-NCS- 44945 (July 1990). 23. A.C.Hindmarsh, ODEPACK, a Systematized Collection of ODE Solvers, in Scientific Computing, R.S.Stepleman et al. (eds.), North-Holland, Amsterdam, 1983, pp. 55-64. 24. S.C.Eisenstat, M.C.Gursky, M.H.Schultz, and A.H.Sherman, Yale Sparse Matrix Package. I. The Symmetric Codes, Int. J. Num. Math. Eng., 18 (1982), pp. 1145-1151. 25. S.C.Eisenstat, M.C.Gursky, M.H.Schultz, and A.H.Sherman, Yale Sparse Matrix Package. II. The NonSymmetric Codes, Research Report No. 114, Dept. of Computer Sciences, Yale University, 1977.
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