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Void reactivity and pin power calculation for a CANDU cell using the SEU-43 fuel bundle
Annals of Nuclear Energy 30 (2003) 301–316 www.elsevier.com/locate/anucene
Void reactivity and pin power calculation for a CANDU cell using the SEU-43 fuel bundle M. Constantin*, D. Gugiu, V. Balaceanu Institute for Nuclear Research, PO Box 78, 0300 Pitesti, Romania Received 22 March 2002; received in revised form 3 May 2002
Abstract The CANDU type reactors have the ability to accommodate a wide variety of fuel types. For all the used fuel types the void coefficient of the reactivity is positive. In our paper a heterogeneous two-stratified coolant model is used for SEU-43 fuel bundle type. This is slightly enriched uranium (near 1%) with 43 fuel rods developed in INR Pitesti. The coolant is treated as a two-phase (liquid and vapour) medium, gravitationally separated. Eigenvalues are computed with the transport code CP_2D at different void fractions and burnup points. For the fresh fuel the MCNP results on the two-startified model a homogeneous model is used to benchmark CP_2D results. # 2002 Elsevier Science Ltd. All rights reserved.
1. Introduction The CANDU (CANada Deuterium Uranium) type reactors have the ability to accommodate a wide variety of fuel types. In order to meet extended burnup and consequently to reduce the total fuel cycle cost some fuel bundle concepts have been developed in different countries. In INR Pitesti the SEU-43 project (Slightly Enriched Uranium-43 fuel elements) was started in early ’90s. A step by step strategy was adopted with every new step based on the complete utilization of the results obtained in the previous one (Horhoianu, 1992). This paper is focused on the calculation of some local parameters for the void problem of a CANDU cell using SEU-43 fuel bundle. A partial or total voided channel, determined by a rupture accident in the coolant system, is considered. The results were obtained by the first flight collision probability (FFCP) code CP_2D3.0 * Corresponding author. Fax: +40-1-312-5896. E-mail addresses: [email protected] or [email protected] (M. Constantin). 0306-4549/03/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0306-4549(02)00056-7
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(Constantin, 2000) for some coolant states corresponding to the void fractions 0, 25, 50, 75, 100% and for four burnup points of 0, 8000, 13,000 and 25,000 MWd/TU. In the case of the fresh fuel the CP_2D results are explicit compared with the results obtained by the Monte Carlo MCNP4C code (Briesmeister, 2000). As it has proved during years, the Monte Carlo method is the most appropriate method to simulate complex 3-D geometries, and to solve the complicated problems involving statistical processes such as the radiation interaction with materials. Because of the limited data available for irradiated fuel at hot operating conditions, it has become a common practice to use the continuous-energy Monte Carlo methods as a major tool to compensate the scarcity of the experimental results. In this paper the results from MCNP are used to benchmark the CP_2D calculations and to assess the accuracy of the void reactivity and pin powers computed with CP_2D. Both codes have used a two stratified coolant model (as it is well known the CANDU channel is placed horizontally and the loss of coolant can produce a separation of the coolant into a liquid and a vapour phase). The model was developed in a previous paper (Constantin and Balaceanu, 2002) for a typical CANDU cell (standard 37-fuel bundle) in order to obtain the void reactivity and the pin powers. The void reactivity was compared with literature results (HELIOS code-F, Rahnema et al., 1998) and has shown a fair agreement. The two stratified model of the coolant in CANDU type reactor offers detailed information about the neutronic behaviour of each fuel rod during the accident. The powers per element for symmetrical rods have values depending on the phase surrounding each rod. In this paper the results for the voided CANDU cell with SEU-43 fuel bundle are compared with the voided typical CANDU cell for the purpose of the fuel performance assesment. The results represent a first estimation of the SEU-43 neutron local parameters during the accident.
2. The SEU-43 fuel bundle and the geometrical model The major feature of SEU-43 bundle is an increase in the number of fuel elements from 37, in the standard CANDU-6 bundle, to 43 elements. On the other hand an enrichment in U235 is present (different variants—nearly 1%—have been analyzed in the SEU-43 project, but in this paper only the 0.96% value was considered). SEU-43 CANDU cell is based on a single cluster, with 43 fuel elements bundle (Fig. 1) and consists of two fuel type element sizes: the 11.46 mm diameter elements in the outer and the intermediate ring, and the 13.65 mm diameter elements in the inner and center rings. The other elements of the cell are the same as those of the standard cell (a pressure tube filled with heavy water coolant, a helium filled gap, and a Calandria tube surrounded by heavy water moderator). The fuel elements are made from UO2 fuel, with a 0.96% enrichment in U235. A fuel gap and a Zircaloy cladding surround each rod. In all cases, the temperatures of the fuel, fuel gap, cladding, coolant, pressure tube, gap, Calandria tube, and moderator are 1209.0, 1209.0, 1209.0, 542.0, 542.0, 542.0, 341.0, and 341.0 K, respectively.
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Fig. 1. The MM model with two coolant phases (liquid and vapour) for a SEU-43 CANDU cell (43 rod cluster geometry).
The coolant density in the hot operation condition (HOC) is 0.804055 g/cc. Other four coolant states corresponding to the void fractions of 25, 50, 75 and 99% are considered. The reference state is the normal coolant operating state (the HOC state). The others are partial loss of coolant accident states (the last can be practically considered as a total loss of coolant accident state). Despite of the standard 37-fuel bundle where the maximum burnup is about of 13,000 MWd/TU (reached only for some fuel bundles of the core) the SEU-43 fuel bundle can reach a maximum burnup of 25,000 MWd/tU (Patrulescu and Dobrea, 2000). The void reactivity results are produced at cell-averaged burnups of 0, 8000, 13,000 and 25,000 MWd/TU. The second point corresponds to the mid-burnup value (the average burnup in the core) of the standard CANDU-6 fuel. The material temperatures and composition (except the fuel) are exactly the same as those used in CANDU-6. The most of the results are obtained on the two-stratified model both for the SEU-43 and standard fuel bundle. Both the homogeneous (HM) and the two-stratified model (TSM) were used in CP_2D and in MCNP only for the fresh fuel and a 50% void fraction in order to reveal the homogeneization effect on the local parameters. For the TSM, the loss of coolant is equivalent (for the cell calculation purpose) with two region (a liquid phase and a vapour phase). For
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the HM the loss of coolant is treated by the decreasing of the coolant density in the whole channel.
3. The CP_2D and MCNP codes CP_2D is a two dimensional transport, first flight collision probability (FFCP) code for detailed fuel assembly hyperfine flux distribution calculation. The flexibility of the geometry allows the treatment of circular or rectangular fuel pin clusters as well as of a relatively large local zone with homogeneous fuel assemblies. A detailed pin structure and individual fuel elements description are permitted. Also the boundary of the assembly can be exactly treated. The first version, CP_2D1.0, was released in 1998. The second, CP_2D2.0, was released in 1999 and uses a multistratified coolant model for CANDU loss of coolant accident analysis. The third version, CP_2D3.0, incorporates a generalized burning scheme. It was released in 2001 and this is the version used in the paper. The main approximations are derived from the FFCP method: (A1)—the (A2)—the (A3)—the (A4)—the
isotropy of the boundary in-coming flux; isotropy of the local sources and scatterings; flat scalar fluxes on each volumetric regions; flat partial currents on each boundary surface subdivision.
For the analyzed problem (see Fig. 1) the boundary is rectangular, and the reflective conditions are used. The material regions are divided into a number of annular and sectorial regions. For example, the fuel pins are subdivided into 10 regions. In the TSM the coolant material region introduces more complicated subdivisions which appear from the superposing of the fuel pins, from the separation line of the two phases, as well as from the annular and sectorial geometry of the coolant. The first flight collision probabilities (FFCPs) are calculated on the actual exact geometry without a subdivision into simple cells, like in the supercell method. This means a direct coupling of the all regions of the problem without interface currents. Obviously the number of the FFCPs and consequently the memory requirements are important, but nowadays this is not a real problem. The simplicity of the FFCPs, the transfer probabilities (TPs) and the escape probabilities (EPs) calculation is realized by the factor geometry-formalism (Weiss and Ball, 1991). At the ray tracing level the geometry of the problem (the target geometry) G(N) is decomposed into a finite number of simple geometries [factor geometries, F(i), i=1,...,N]. Then GðNÞ ¼ Fð1Þ Fð2Þ ::: FðNÞ: The factor geometries used in the paper for a typical voided CANDU cell are: circles, rectangles and line segments. The factorisation is used only for the ray tracing performing not for the iterative solving of the fluxes equation system. For this purpose the Gauss–Seidel method with SOR is used. A burnup module is able to treat the isotopes’ detailed evolution during the operation.
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MCNP code uses the actual geometry of the analyzed problem, but the neutron transport is performed in 3D geometry. The third axis is along the fuel bundle. For simplicity the 3D geometry elements, like the end plate, were homogeneised into the 2D structure in order to have the same geometrical model as in CP_2D. All the external surfaces of the cell were considered as being reflective in order to estimate the eigenvalue k-infinity. In the calculations performed for fresh fuel a Watt spectrum was used as starting source of neutrons with a uniform volume distribution in all the 43 fuel pins. The material temperatures were accounted for in neutron cross-section evaluations using the TEMP card for each material regions in MCNP4C input; the code adjust automatically the elastic and total neutron cross-section involved in free gas thermal treatment of neutron interactions. All the Monte Carlo simulations were performed using the KCODE (criticality calculation) facility of the MCNP code with the following options: a total of 1000 cycles to be done, 80 inactive cycles, and a number of 2500 source histories per keff cycle.
4. Cross-sections generation For CP_2D cross-sections generation the WIMSD-5B library was used (Halsall and Taubman, 1986). For TSM two sets of cross-sections were used: for normal state (HOC) and for perturbed state (coolant region total voided). The temperatures for perturbed state are the same as for HOC, thus no temperature void effect was considered. In the TSM the fuel elements can be total immersed in the coolant, partial immersed or total surrounded by the vapour region (see Fig. 1). The code CP_2D uses the void ratio as an input data and automatically classifies the fuel elements; consequently it puts the type of the cross-sections (as perturbated or HOC) for any fuel regions. The partial immersed fuel elements are treated as total voided or total immersed into liquid phase (by rounding the fraction of immersion). In MCNP4C runs, the neutron cross-sections were selected from those libraries which evaluation dates (years) correspond to WIMS-5B library, in order to perform the best comparison of the results. Thus, the major part of the neutron cross-section libraries involved in MCNP4C calculations has the extension *0.50c (as defined in MCNP) and are represented by kidman, endf5u, rmccs or dre5 libraries; the sources of these libraries are ENDF/B-V nuclear data or LLNL (Lawrence Livermore National Laboratory). The ENDL85 was also used (evaluated nuclear data libraries compiled by Nuclear Data Group at LLNL). For some isotopes, the libraries having the ENDF/B-VI source were used in MCNP runs (in MCNP formalism these libraries have the extension *0.60c). From the point of view of the cross-sections, major differences between MCNP and CP_2D calculations appear: in MCNP the continuos-energy neutron interaction data are used (depending primarily on the number of resolved resonances for each
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isotope, the resulting energy grid may contain as few as 250 points or as many as 22,500 points); in CP_2D the WIMS 69 energy groups library is used. All the CP_2D calculations have been performed on a 7-group energy structure: 10 MeV– 5.53 KeV, 5.53 KeV–3.30 eV, 3.30–0.625 eV, 0.625–0.22 eV, 0.22–0.14 eV, 0.14–0.03 eV, 0.03–0.0 eV.
5. Results and discussions The primary results consist of the K-infinity values and pin powers for some coolant density and different burnup points. 1 In Table 1 the K-inf and reactivity values ¼ K1reff Kvoided obtained by CP_2D cell and MCNP codes are compared for SEU-43 fresh fuel cell at 0, 25, 50, 75, 99% void fractions. A fairly agreement is observed, although two different libraries and numerical methods have been used. An underestimation of the reactivity values of CP_2D related to MCNP reactivity values (up to 7%) is to be noticed. In Fig. 2 the void reactivity versus void fraction (CP_2D and MCNP results) for SEU-43 fresh fuel cell is represented. The linear dependence for both codes is a normal behaviour. In Table 2 the pin powers obtained by CP_2D and MCNP for fresh fuel SEU-43 cell and different void fraction (0, 50, and 99%) are compared. The pin powers are normalized to the mean value and represent linear powers, not power densities. The results show a fair agreement: the maximum relative difference is +4.9% (CP_2D versus MCNP) for the fifth fuel rod in the case of a 50% voided cell. A conclusion of a previous study of the TSM (Constantin and Balaceanu, 2002) was that, from the point of view of the reactivity effect, the homogeneisation of the loss of coolant is a good approximation and the TSM is not a compulsory model. However, other cell parameters (power and flux distributions) need a more detailed treatment. The TSM is able to calculate the asymmetries of the fluxes and power distributions. Table 3 shows the TSM effect obtained both with CP_2D and MCNP. The same behaviour (except for few elements) is observed for comparisons between
Table 1 The void reactivity comparison between CP_2D and MCNP codes for the SEU-43 voided cell (fresh fuel) Void fraction (%)
0 25 50 75 99 a
"¼
CP
2D MCNP 100: MCNP
Epsa (%)
rho (pcm)
K-inf CP_2D
MCNP
CP_2D
MCNP
1.21941 1.22450 1.23043 1.23690 1.24193
1.21841 1.22384 1.23021 1.23681 1.24207
0 341 734 1160 1487
0 364 787 1221 1563
– 6 7 5 5
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Fig. 2. The void reactivity versus void fraction; CP_2D and MCNP results for SEU-43 fresh fuel cells.
TSM result and homogeneous model (HM) results. The HM underestimates the pin powers values for the fuel elements placed into the vapour region and, conversely, it overestimates the values for the immersed (into the coolant) fuel elements. Thus, the fuel elements from the outer ring placed into the vapour are more exposed to a failure then the HM predicts. The comparison of the TSM versus HM relative differences was intended to benchmark CP_2D TSM results by using the MCNP results. The same behaviour of the pin powers can be seen more explicitly in Fig. 3. For the SEU-43 fuel bundle at different burnup points (8000, 13,000 and 25,000 MWd/TU) the paper shows only CP_2D results. The main reason is the strong difference in the definition of the pseudo-fission product for WIMSD-5B and ENDF/ B-V (used by MCNP) libraries. On the other hand, the version MCNP4C have not a burnup module. Thus, we have considered the CP_2D benchmarking process by the MCNP code is relevant, in this stage, only for the fresh fuel. Fig. 4 shows the K-infinity values as a function of void fraction for different burnups burnups (8000, 13,000, 25,000 MWd/TU). Unlike CANDU-6 fuel bundle
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Table 2 CP_2D and MCNP pin powers (normalized to the mean power) comparison for fresh fuel and different void fraction of the SEU-43 cell Fuel elem.
Void fraction 0%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 a
"¼
50%
99%
MCNP
CP_2D
eps (%)
MCNP
CP_2D
eps (%)
MCNP
CP_2D
eps (%)a
0.997 1.063 1.060 1.064 1.062 1.064 1.063 1.066 0.854 0.853 0.850 0.855 0.854 0.854 0.853 0.853 0.856 0.855 0.851 0.857 0.851 0.854 1.077 1.076 1.078 1.074 1.076 1.075 1.076 1.078 1.076 1.078 1.078 1.078 1.075 1.078 1.077 1.075 1.080 1.077 1.078 1.078 1.075
1.022 1.070 1.075 1.083 1.092 1.092 1.083 1.075 0.851 0.850 0.855 0.858 0.860 0.867 0.865 0.871 0.865 0.867 0.860 0.858 0.855 0.850 1.061 1.063 1.067 1.065 1.063 1.067 1.067 1.065 1.066 1.066 1.069 1.069 1.066 1.066 1.065 1.067 1.067 1.063 1.065 1.067 1.063
2.5 0.7 1.4 1.8 2.8 2.6 1.9 0.8 0.5 0.3 0.5 0.4 0.7 1.5 1.4 2.1 1.0 1.4 1.2 0.2 0.4 0.4 1.5 1.2 1.0 0.9 1.2 0.7 0.8 1.1 0.9 1.1 0.8 0.8 0.8 1.1 1.1 0.7 1.2 1.4 1.2 1.0 1.1
1.031 1.090 1.101 1.105 1.101 1.078 1.069 1.070 0.860 0.866 0.871 0.869 0.873 0.874 0.872 0.862 0.851 0.851 0.847 0.849 0.846 0.847 1.061 1.062 1.063 1.065 1.062 1.061 1.062 1.062 1.068 1.070 1.071 1.063 1.059 1.062 1.061 1.064 1.063 1.062 1.058 1.059 1.059
1.050 1.087 1.124 1.140 1.155 1.101 1.078 1.072 0.850 0.864 0.879 0.882 0.891 0.897 0.893 0.887 0.857 0.855 0.845 0.843 0.841 0.841 1.043 1.056 1.063 1.064 1.061 1.064 1.065 1.062 1.060 1.061 1.069 1.049 1.041 1.040 1.038 1.040 1.040 1.035 1.038 1.042 1.038
1.9 0.4 2.0 3.2 4.9 2.1 0.8 0.3 1.1 0.2 0.9 1.5 2.0 2.6 2.4 2.9 0.7 0.4 0.2 0.7 0.6 0.7 1.6 0.5 0.1 0.1 0.1 0.3 0.3 0.0 0.7 0.8 0.2 1.4 1.7 2.1 2.2 2.3 2.2 2.5 1.9 1.6 1.9
1.061 1.113 1.110 1.111 1.115 1.115 1.113 1.112 0.866 0.863 0.868 0.865 0.866 0.866 0.866 0.870 0.867 0.863 0.865 0.863 0.864 0.864 1.050 1.049 1.047 1.049 1.051 1.050 1.049 1.050 1.053 1.049 1.049 1.052 1.051 1.049 1.053 1.045 1.041 1.048 1.050 1.051 1.050
1.084 1.111 1.118 1.131 1.159 1.158 1.130 1.117 0.857 0.855 0.866 0.867 0.875 0.885 0.886 0.892 0.885 0.884 0.872 0.865 0.864 0.854 1.032 1.033 1.041 1.039 1.035 1.039 1.041 1.037 1.037 1.038 1.049 1.049 1.037 1.036 1.035 1.034 1.029 1.032 1.038 1.041 1.033
2.2 0.2 0.7 1.9 4.0 3.9 1.5 0.4 1.1 0.9 0.3 0.3 1.1 2.3 2.3 2.5 2.1 2.4 0.9 0.2 0.1 1.2 1.7 1.4 0.6 0.9 1.5 1.1 0.8 1.3 1.5 1.0 0.0 0.3 1.3 1.2 1.7 1.0 1.1 1.5 1.2 0.9 1.7
PPCP 2D PPMCNP 100: PPMCNP
a
a
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Table 3 CP_2D and MCNP pin powers (normalized to the mean power) comparison for fresh fuel and different void fraction of the SEU-43 cell by using HM and TSM Fuel rod
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
Vf=50%
Vf=50%
MCNP HM
MCNP TSM
eps (%)
CP_2D HM
CP_2D TSM
eps (%)
1.028 1.086 1.085 1.085 1.086 1.085 1.083 1.083 0.859 0.857 0.862 0.859 0.860 0.860 0.858 0.861 0.857 0.860 0.858 0.857 0.861 0.860 1.062 1.061 1.064 1.061 1.064 1.062 1.061 1.064 1.064 1.067 1.064 1.066 1.064 1.065 1.065 1.066 1.064 1.065 1.066 1.068 1.066
1.031 1.090 1.101 1.105 1.101 1.078 1.069 1.070 0.860 0.866 0.871 0.869 0.873 0.874 0.872 0.862 0.851 0.851 0.847 0.849 0.846 0.847 1.061 1.062 1.063 1.065 1.062 1.061 1.062 1.062 1.068 1.070 1.071 1.063 1.059 1.062 1.061 1.064 1.063 1.062 1.058 1.059 1.059
0.3 0.4 1.5 1.8 1.4 0.6 1.3 1.2 0.1 1.0 1.0 1.2 1.5 1.6 1.6 0.1 0.7 1.1 1.3 0.9 1.8 1.5 0.1 0.1 0.1 0.4 0.2 0.1 0.1 0.2 0.4 0.3 0.7 0.3 0.5 0.3 0.4 0.2 0.1 0.3 0.8 0.8 0.7
1.051 1.090 1.095 1.106 1.120 1.120 1.106 1.095 0.854 0.853 0.860 0.863 0.867 0.875 0.874 0.880 0.874 0.875 0.868 0.863 0.860 0.853 1.047 1.049 1.054 1.052 1.049 1.053 1.054 1.051 1.052 1.052 1.058 1.058 1.052 1.052 1.051 1.054 1.053 1.049 1.052 1.054 1.049
1.050 1.087 1.124 1.140 1.155 1.101 1.078 1.072 0.850 0.864 0.879 0.882 0.891 0.897 0.893 0.887 0.857 0.855 0.845 0.843 0.841 0.841 1.043 1.056 1.063 1.064 1.061 1.064 1.065 1.062 1.060 1.061 1.069 1.049 1.041 1.040 1.038 1.040 1.040 1.035 1.038 1.042 1.038
0.1 0.2 2.5 3.0 3.0 1.8 2.6 2.2 0.5 1.3 2.2 2.2 2.6 2.4 2.1 0.8 2.0 2.4 2.7 2.3 2.2 1.4 0.4 0.7 0.8 1.1 1.1 1.0 1.0 1.0 0.8 0.8 1.1 0.8 1.1 1.1 1.3 1.4 1.3 1.4 1.3 1.2 1.0
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Fig. 3. SEU-43 bundle pin powers (normalized to the mean power). Comparison between CP_2D and MCNP for 50% void fraction and fresh fuel.
where the value of 13,000 MWd/TU is the maximum burnup (reached only for some fuel bundles of the core) for SEU-43 fuel bundle this is the average burnup. The maximum burnup for SEU-43 is about 25,000 MWd/TU. The 8000 MWd/TU point was chosen for the reason to compare the void reactivity between SEU-43 and CANDU-6 voided cells (at the average burnup point in CANDU-6 type reactor). For high burnup the reactivity values are smaller than for the average burnup, but for large void fractions (typical in LOCA) the differences are not very important (1437 related to 1539 pcm). The pin powers (normalized to the mean power) for 8000, 13,000 and 25,000 MWd/TU burnups are inter-compared for two state (HOC and 99% void fraction) in Table 4. For simplicity, let’s compare the pin powers for the fuel rods indexed as 1, 4, 13 and 29 (radial placed on center, inner, intermediate and respectively outer ring—see Fig. 1). For the HOC at 8000 MWd/TU (Vf=0%) the radial dependence of the pin powers is 1.089, 1.133, 0.865, 1.042. The dependence is influenced by two
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Fig. 4. K-infinity as a function of void fraction for SEU-43 cell, different burnups.
factors: the radial dependence of the flux and the different areas of the rods. Let’s remind ourselves that we used pin powers as linear powers normalized to the mean value. In the void state (Vf=99%) the radial dependence is 1.160, 1.185, 0.878, 1.015 with an increasing of all the values, except the outer fuel rod. The same behaviour appears for both 13,000 and 25,000 MWd/TU burnups. In the voided cells the pin powers for the center, inner and intermediate rings increase, whereas the pin powers for the outer ring decrease. For the burnup dependence it must be noted that the pin power values increase with the burnup in the outer ring, and decrease in the intermediate ring. For the inner and the center rings the maximum values are obtained at
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Table 4 CP_2D pin powers (normalized to the mean power) for the SEU-43 cell at different burnups- hot operating conditions (Vf=0%) and large void conditions (Vf=99%) Fuel rod
Burnup (MWd/TU) 8000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
13,000
25,000
Vf=0%
Vf=99%
Vf=0%
Vf=99%
Vf=0%
Vf=99%
1.089 1.135 1.133 1.133 1.134 1.134 1.133 1.133 0.865 0.866 0.865 0.866 0.865 0.867 0.864 0.866 0.864 0.867 0.865 0.866 0.865 0.866 1.038 1.040 1.043 1.041 1.040 1.040 1.042 1.042 1.039 1.039 1.042 1.042 1.039 1.039 1.042 1.042 1.040 1.040 1.041 1.043 1.040
1.160 1.197 1.186 1.185 1.193 1.192 1.184 1.185 0.880 0.877 0.878 0.876 0.878 0.878 0.877 0.878 0.877 0.877 0.876 0.874 0.877 0.877 1.009 1.011 1.016 1.013 1.011 1.010 1.015 1.013 1.009 1.011 1.017 1.017 1.010 1.009 1.011 1.009 1.002 1.007 1.012 1.016 1.011
1.115 1.150 1.149 1.149 1.150 1.150 1.149 1.149 0.861 0.863 0.861 0.863 0.862 0.863 0.861 0.863 0.861 0.863 0.862 0.863 0.861 0.863 1.034 1.036 1.039 1.037 1.036 1.036 1.038 1.038 1.035 1.035 1.038 1.038 1.035 1.035 1.038 1.038 1.036 1.036 1.037 1.039 1.036
1.186 1.211 1.201 1.200 1.207 1.207 1.198 1.200 0.876 0.873 0.874 0.872 0.874 0.874 0.873 0.874 0.873 0.873 0.872 0.870 0.873 0.873 1.006 1.008 1.013 1.010 1.007 1.007 1.011 1.009 1.006 1.007 1.013 1.013 1.007 1.005 1.008 1.006 0.999 1.004 1.009 1.012 1.008
1.081 1.118 1.117 1.117 1.117 1.117 1.117 1.117 0.846 0.848 0.847 0.848 0.847 0.848 0.846 0.848 0.846 0.848 0.847 0.848 0.847 0.848 1.057 1.058 1.061 1.059 1.058 1.058 1.060 1.060 1.057 1.057 1.060 1.060 1.057 1.057 1.060 1.060 1.058 1.058 1.059 1.061 1.058
1.149 1.176 1.167 1.166 1.173 1.172 1.164 1.166 0.861 0.859 0.859 0.858 0.859 0.859 0.858 0.859 0.858 0.858 0.857 0.855 0.858 0.858 1.029 1.031 1.036 1.033 1.030 1.030 1.034 1.032 1.029 1.030 1.036 1.036 1.030 1.028 1.031 1.029 1.022 1.027 1.032 1.035 1.030
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average burnup. The maximum values of the pin power occur in the inner ring for all studied burnup points both for HOC and 99% voided cell. The same behaviour appears for the TSM (see Fig. 3) at 0 MWd/TU, but for the rods surrounded by the vapour region (‘void region’). A comparison between SEU-43 and CANDU-6 voided cells is presented in Tables 5–7. The void reactivity values are compared in Table 5, for a 99% void fraction and different burnup points. It can be observed that the void reactivity values for SEU-43 cells are in the same range like the CANDU-6 cells. For the -fresh fuel the void reactivity of SEU-43 is 9.1% related to the CANDU-6 voided cell. For SEU-43 the void reactivity remains nearly constant up to the average burnup and slightly decreases at high burnup. The pin powers normalized to the mean power and averaged per rings, for fresh fuel and HOC, are presented in Table 6. Whereas for CANDU-6 the maximum pin powers is obtained for the outer ring, for SEU-43 fuel bundle the maximum pin power is obtained for the inner ring. A comparison of all pin powers, between CANDU-6 and SEU-43 cells, for fresh fuel and a 50% void fraction, is presented in Table 7. The maximum pin power is 1.128 for CANDU-6 and 1.138 for SEU-43, in the positions (4,4)=(outer ring, fourth rod), respectively (2,3)=(inner ring, third rod). Both the two rods are immersed into the vapour phase.
Table 5 The void reactivity comparison between SEU-43 and standard CANDU cell, for a 99% void fraction Burnup [MWd/tU]
0 8000 13,000 25,000
Reactivity [pcm] CANDU standard
SEU-43 (0.96%)
1635 1551 1205 –
1487 1531 1539 1437
Table 6 The pin powers (normalized to the mean power and averaged per rings): comparison between SEU-43 and standard CANDU cell, for fresh fuel and HOC Ring
CANDU-6
SEU-43
Center Inner Intermediate Outer
0.784 0.820 0.986 1.127
1.022 1.081 0.860 1.066
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Table 7 The pin powers (normalized to the mean power): comparison between SEU-43 and standard CANDU cell, for fresh fuel and a 50% void fraction CANDU standard Fuel rod (ring, position)
SEU-43 Pin powers
Fuel rod (ring, position)
Pin powers
(1,1) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
0.805 0.853 0.871 0.852 0.824 0.824 0.824
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (3,7) (3,8) (3,9) (3,10) (3,11) (3,12)
0.952 0.956 0.937 0.933 0.951 0.951 0.916 0.909 0.897 0.896 0.906 0.918
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (4,7) (4,8) (4,9) (4,10) (4,11) (4,12) (4,13) (4,14) (4,15) (4,16) (4,17) (4,18)
1.113 1.125 1.125 1.128 1.126 1.126 1.127 1.125 1.125 1.122 1.101 1.099 1.097 1.096 1.096 1.097 1.099 1.100
(1,1) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (2,7) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (3,7) (3,8) (3,9) (3,10) (3,11) (3,12) (3,13) (3,14) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (4,7) (4,8) (4,9) (4,10) (4,11) (4,12) (4,13) (4,14) (4,15) (4,16) (4,17) (4,18) (4,19) (4,20) (4,21)
1.050 1.108 1.133 1.138 1.134 1.088 1.075 1.080 0.864 0.881 0.887 0.886 0.890 0.886 0.881 0.872 0.850 0.848 0.844 0.846 0.845 0.851 1.046 1.057 1.064 1.063 1.061 1.062 1.066 1.063 1.059 1.059 1.062 1.047 1.039 1.038 1.039 1.039 1.038 1.037 1.039 1.043 1.043
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6. Conclusions 1. The comparison of the MCNP and CP_2D results, on the two stratified model (TSM), shows a fair agreement, but with a systematic slight underestimation of the void reactivity by CP_2D code. The difference appears mainly from the used libraries. The results have been compared only for the fresh fuel for the reason of the absence of the burnup module in MCNP4C and the different definition of the pseudo-fission product used by the libraries. 2. The model proposed for the loss of coolant accident in CANDU type reactor with a separation into the liquid and vapour phases (the TSM) offer detailed information about the neutronic behaviour of each fuel rod during the accident. The power per element for symmetrical rods has values depending on the phase surrounding each rod. The HM underestimates the values for the fuel elements placed into the vapour region and conversely it overestimates the values for the immersed (into the coolant) fuel elements. The same behaviour is observed both in the MCNP and CP_2D results. 3. The values of void reactivities for cells with SEU-43 fuel bundle are closed to the voided CANDU-6 cells. From this point of view we do not expect major consequences in the safety analysis of the SEU-43 related to the safety analysis of the standard core. 4. The maximum pin power locations are different for the two kind of fuel bundle: the outer ring for the standard fuel and the inner ring for the SEU43. The behaviour is identical for the HOC and the voided cells, with the difference of the placement of the maximum power (fuel rods placed into the vapour phase for the voided cases). 5. The void reactivity shows an approximative linear dependence with the void fraction. For the fresh fuel the relative difference between void reactivity of SEU-43 and CANDU-6 voided cell is about 9%. For SEU-43 the void reactivity remains aproximately constant with the burnup, with a slight decrease at high burnup.
References Briesmeister, J.F. (Ed.), 2000. MCNP—A General Monte Carlo N-Particle Transport Code, Version 4C. LA-13709-M. Constantin, M., Balaceanu, V., 2002. Void reactivity and pin power calculation for a typical CANDU cell using CPs and a two-stratified coolant model. Annals of Nuclear Energy 29 (7), 483–488. Constantin, M., 2000. Neutron transport by collision probability method in complicated geometries. International Conference on Supercomputing in Nuclear Application, 4–7 September, Tokyo, Japan. Halsall, M.J., Taubman, C.J., 1986. The ‘19860 WIMS Nuclear Data Library. AEEW-R 2133. Reactor Phisics Division, AEE, Winfrith, UK. Horhoianu, G., 1992. Improvement of the CANDU fuel element performance in order to increase the ability to operate at high powers and to meet high burnup. Final Report to IAEA research contract 6197/RB. INR Pitesti, Romania.
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Rahnema, F., Mosher, S., Parvaiz, A., Serghiuta, D., 1998. Void reactivity calculations in a typical CANDU cell using MCNP and helios. International Conference on the Physics of Nuclear Science and Technology, 5–8 October, Long Island, USA, pp. 356–361. Patrulescu, I., Dobrea, G., 2000. CANDU Core Calculations for SEU-43 fuel type. Internal Report-5904. INR Pitesti, Romania. Weiss, Z., Ball, G., 1991. Ray Tracing in Complicated Geometries. Annals of Nuclear Energy 18 (8), 483– 488.
Void reactivity and pin power calculation for a CANDU cell using the SEU-43 fuel bundle M. Constantin*, D. Gugiu, V. Balaceanu Institute for Nuclear Research, PO Box 78, 0300 Pitesti, Romania Received 22 March 2002; received in revised form 3 May 2002
Abstract The CANDU type reactors have the ability to accommodate a wide variety of fuel types. For all the used fuel types the void coefficient of the reactivity is positive. In our paper a heterogeneous two-stratified coolant model is used for SEU-43 fuel bundle type. This is slightly enriched uranium (near 1%) with 43 fuel rods developed in INR Pitesti. The coolant is treated as a two-phase (liquid and vapour) medium, gravitationally separated. Eigenvalues are computed with the transport code CP_2D at different void fractions and burnup points. For the fresh fuel the MCNP results on the two-startified model a homogeneous model is used to benchmark CP_2D results. # 2002 Elsevier Science Ltd. All rights reserved.
1. Introduction The CANDU (CANada Deuterium Uranium) type reactors have the ability to accommodate a wide variety of fuel types. In order to meet extended burnup and consequently to reduce the total fuel cycle cost some fuel bundle concepts have been developed in different countries. In INR Pitesti the SEU-43 project (Slightly Enriched Uranium-43 fuel elements) was started in early ’90s. A step by step strategy was adopted with every new step based on the complete utilization of the results obtained in the previous one (Horhoianu, 1992). This paper is focused on the calculation of some local parameters for the void problem of a CANDU cell using SEU-43 fuel bundle. A partial or total voided channel, determined by a rupture accident in the coolant system, is considered. The results were obtained by the first flight collision probability (FFCP) code CP_2D3.0 * Corresponding author. Fax: +40-1-312-5896. E-mail addresses: [email protected] or [email protected] (M. Constantin). 0306-4549/03/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0306-4549(02)00056-7
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(Constantin, 2000) for some coolant states corresponding to the void fractions 0, 25, 50, 75, 100% and for four burnup points of 0, 8000, 13,000 and 25,000 MWd/TU. In the case of the fresh fuel the CP_2D results are explicit compared with the results obtained by the Monte Carlo MCNP4C code (Briesmeister, 2000). As it has proved during years, the Monte Carlo method is the most appropriate method to simulate complex 3-D geometries, and to solve the complicated problems involving statistical processes such as the radiation interaction with materials. Because of the limited data available for irradiated fuel at hot operating conditions, it has become a common practice to use the continuous-energy Monte Carlo methods as a major tool to compensate the scarcity of the experimental results. In this paper the results from MCNP are used to benchmark the CP_2D calculations and to assess the accuracy of the void reactivity and pin powers computed with CP_2D. Both codes have used a two stratified coolant model (as it is well known the CANDU channel is placed horizontally and the loss of coolant can produce a separation of the coolant into a liquid and a vapour phase). The model was developed in a previous paper (Constantin and Balaceanu, 2002) for a typical CANDU cell (standard 37-fuel bundle) in order to obtain the void reactivity and the pin powers. The void reactivity was compared with literature results (HELIOS code-F, Rahnema et al., 1998) and has shown a fair agreement. The two stratified model of the coolant in CANDU type reactor offers detailed information about the neutronic behaviour of each fuel rod during the accident. The powers per element for symmetrical rods have values depending on the phase surrounding each rod. In this paper the results for the voided CANDU cell with SEU-43 fuel bundle are compared with the voided typical CANDU cell for the purpose of the fuel performance assesment. The results represent a first estimation of the SEU-43 neutron local parameters during the accident.
2. The SEU-43 fuel bundle and the geometrical model The major feature of SEU-43 bundle is an increase in the number of fuel elements from 37, in the standard CANDU-6 bundle, to 43 elements. On the other hand an enrichment in U235 is present (different variants—nearly 1%—have been analyzed in the SEU-43 project, but in this paper only the 0.96% value was considered). SEU-43 CANDU cell is based on a single cluster, with 43 fuel elements bundle (Fig. 1) and consists of two fuel type element sizes: the 11.46 mm diameter elements in the outer and the intermediate ring, and the 13.65 mm diameter elements in the inner and center rings. The other elements of the cell are the same as those of the standard cell (a pressure tube filled with heavy water coolant, a helium filled gap, and a Calandria tube surrounded by heavy water moderator). The fuel elements are made from UO2 fuel, with a 0.96% enrichment in U235. A fuel gap and a Zircaloy cladding surround each rod. In all cases, the temperatures of the fuel, fuel gap, cladding, coolant, pressure tube, gap, Calandria tube, and moderator are 1209.0, 1209.0, 1209.0, 542.0, 542.0, 542.0, 341.0, and 341.0 K, respectively.
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Fig. 1. The MM model with two coolant phases (liquid and vapour) for a SEU-43 CANDU cell (43 rod cluster geometry).
The coolant density in the hot operation condition (HOC) is 0.804055 g/cc. Other four coolant states corresponding to the void fractions of 25, 50, 75 and 99% are considered. The reference state is the normal coolant operating state (the HOC state). The others are partial loss of coolant accident states (the last can be practically considered as a total loss of coolant accident state). Despite of the standard 37-fuel bundle where the maximum burnup is about of 13,000 MWd/TU (reached only for some fuel bundles of the core) the SEU-43 fuel bundle can reach a maximum burnup of 25,000 MWd/tU (Patrulescu and Dobrea, 2000). The void reactivity results are produced at cell-averaged burnups of 0, 8000, 13,000 and 25,000 MWd/TU. The second point corresponds to the mid-burnup value (the average burnup in the core) of the standard CANDU-6 fuel. The material temperatures and composition (except the fuel) are exactly the same as those used in CANDU-6. The most of the results are obtained on the two-stratified model both for the SEU-43 and standard fuel bundle. Both the homogeneous (HM) and the two-stratified model (TSM) were used in CP_2D and in MCNP only for the fresh fuel and a 50% void fraction in order to reveal the homogeneization effect on the local parameters. For the TSM, the loss of coolant is equivalent (for the cell calculation purpose) with two region (a liquid phase and a vapour phase). For
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the HM the loss of coolant is treated by the decreasing of the coolant density in the whole channel.
3. The CP_2D and MCNP codes CP_2D is a two dimensional transport, first flight collision probability (FFCP) code for detailed fuel assembly hyperfine flux distribution calculation. The flexibility of the geometry allows the treatment of circular or rectangular fuel pin clusters as well as of a relatively large local zone with homogeneous fuel assemblies. A detailed pin structure and individual fuel elements description are permitted. Also the boundary of the assembly can be exactly treated. The first version, CP_2D1.0, was released in 1998. The second, CP_2D2.0, was released in 1999 and uses a multistratified coolant model for CANDU loss of coolant accident analysis. The third version, CP_2D3.0, incorporates a generalized burning scheme. It was released in 2001 and this is the version used in the paper. The main approximations are derived from the FFCP method: (A1)—the (A2)—the (A3)—the (A4)—the
isotropy of the boundary in-coming flux; isotropy of the local sources and scatterings; flat scalar fluxes on each volumetric regions; flat partial currents on each boundary surface subdivision.
For the analyzed problem (see Fig. 1) the boundary is rectangular, and the reflective conditions are used. The material regions are divided into a number of annular and sectorial regions. For example, the fuel pins are subdivided into 10 regions. In the TSM the coolant material region introduces more complicated subdivisions which appear from the superposing of the fuel pins, from the separation line of the two phases, as well as from the annular and sectorial geometry of the coolant. The first flight collision probabilities (FFCPs) are calculated on the actual exact geometry without a subdivision into simple cells, like in the supercell method. This means a direct coupling of the all regions of the problem without interface currents. Obviously the number of the FFCPs and consequently the memory requirements are important, but nowadays this is not a real problem. The simplicity of the FFCPs, the transfer probabilities (TPs) and the escape probabilities (EPs) calculation is realized by the factor geometry-formalism (Weiss and Ball, 1991). At the ray tracing level the geometry of the problem (the target geometry) G(N) is decomposed into a finite number of simple geometries [factor geometries, F(i), i=1,...,N]. Then GðNÞ ¼ Fð1Þ Fð2Þ ::: FðNÞ: The factor geometries used in the paper for a typical voided CANDU cell are: circles, rectangles and line segments. The factorisation is used only for the ray tracing performing not for the iterative solving of the fluxes equation system. For this purpose the Gauss–Seidel method with SOR is used. A burnup module is able to treat the isotopes’ detailed evolution during the operation.
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MCNP code uses the actual geometry of the analyzed problem, but the neutron transport is performed in 3D geometry. The third axis is along the fuel bundle. For simplicity the 3D geometry elements, like the end plate, were homogeneised into the 2D structure in order to have the same geometrical model as in CP_2D. All the external surfaces of the cell were considered as being reflective in order to estimate the eigenvalue k-infinity. In the calculations performed for fresh fuel a Watt spectrum was used as starting source of neutrons with a uniform volume distribution in all the 43 fuel pins. The material temperatures were accounted for in neutron cross-section evaluations using the TEMP card for each material regions in MCNP4C input; the code adjust automatically the elastic and total neutron cross-section involved in free gas thermal treatment of neutron interactions. All the Monte Carlo simulations were performed using the KCODE (criticality calculation) facility of the MCNP code with the following options: a total of 1000 cycles to be done, 80 inactive cycles, and a number of 2500 source histories per keff cycle.
4. Cross-sections generation For CP_2D cross-sections generation the WIMSD-5B library was used (Halsall and Taubman, 1986). For TSM two sets of cross-sections were used: for normal state (HOC) and for perturbed state (coolant region total voided). The temperatures for perturbed state are the same as for HOC, thus no temperature void effect was considered. In the TSM the fuel elements can be total immersed in the coolant, partial immersed or total surrounded by the vapour region (see Fig. 1). The code CP_2D uses the void ratio as an input data and automatically classifies the fuel elements; consequently it puts the type of the cross-sections (as perturbated or HOC) for any fuel regions. The partial immersed fuel elements are treated as total voided or total immersed into liquid phase (by rounding the fraction of immersion). In MCNP4C runs, the neutron cross-sections were selected from those libraries which evaluation dates (years) correspond to WIMS-5B library, in order to perform the best comparison of the results. Thus, the major part of the neutron cross-section libraries involved in MCNP4C calculations has the extension *0.50c (as defined in MCNP) and are represented by kidman, endf5u, rmccs or dre5 libraries; the sources of these libraries are ENDF/B-V nuclear data or LLNL (Lawrence Livermore National Laboratory). The ENDL85 was also used (evaluated nuclear data libraries compiled by Nuclear Data Group at LLNL). For some isotopes, the libraries having the ENDF/B-VI source were used in MCNP runs (in MCNP formalism these libraries have the extension *0.60c). From the point of view of the cross-sections, major differences between MCNP and CP_2D calculations appear: in MCNP the continuos-energy neutron interaction data are used (depending primarily on the number of resolved resonances for each
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isotope, the resulting energy grid may contain as few as 250 points or as many as 22,500 points); in CP_2D the WIMS 69 energy groups library is used. All the CP_2D calculations have been performed on a 7-group energy structure: 10 MeV– 5.53 KeV, 5.53 KeV–3.30 eV, 3.30–0.625 eV, 0.625–0.22 eV, 0.22–0.14 eV, 0.14–0.03 eV, 0.03–0.0 eV.
5. Results and discussions The primary results consist of the K-infinity values and pin powers for some coolant density and different burnup points. 1 In Table 1 the K-inf and reactivity values ¼ K1reff Kvoided obtained by CP_2D cell and MCNP codes are compared for SEU-43 fresh fuel cell at 0, 25, 50, 75, 99% void fractions. A fairly agreement is observed, although two different libraries and numerical methods have been used. An underestimation of the reactivity values of CP_2D related to MCNP reactivity values (up to 7%) is to be noticed. In Fig. 2 the void reactivity versus void fraction (CP_2D and MCNP results) for SEU-43 fresh fuel cell is represented. The linear dependence for both codes is a normal behaviour. In Table 2 the pin powers obtained by CP_2D and MCNP for fresh fuel SEU-43 cell and different void fraction (0, 50, and 99%) are compared. The pin powers are normalized to the mean value and represent linear powers, not power densities. The results show a fair agreement: the maximum relative difference is +4.9% (CP_2D versus MCNP) for the fifth fuel rod in the case of a 50% voided cell. A conclusion of a previous study of the TSM (Constantin and Balaceanu, 2002) was that, from the point of view of the reactivity effect, the homogeneisation of the loss of coolant is a good approximation and the TSM is not a compulsory model. However, other cell parameters (power and flux distributions) need a more detailed treatment. The TSM is able to calculate the asymmetries of the fluxes and power distributions. Table 3 shows the TSM effect obtained both with CP_2D and MCNP. The same behaviour (except for few elements) is observed for comparisons between
Table 1 The void reactivity comparison between CP_2D and MCNP codes for the SEU-43 voided cell (fresh fuel) Void fraction (%)
0 25 50 75 99 a
"¼
CP
2D MCNP 100: MCNP
Epsa (%)
rho (pcm)
K-inf CP_2D
MCNP
CP_2D
MCNP
1.21941 1.22450 1.23043 1.23690 1.24193
1.21841 1.22384 1.23021 1.23681 1.24207
0 341 734 1160 1487
0 364 787 1221 1563
– 6 7 5 5
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Fig. 2. The void reactivity versus void fraction; CP_2D and MCNP results for SEU-43 fresh fuel cells.
TSM result and homogeneous model (HM) results. The HM underestimates the pin powers values for the fuel elements placed into the vapour region and, conversely, it overestimates the values for the immersed (into the coolant) fuel elements. Thus, the fuel elements from the outer ring placed into the vapour are more exposed to a failure then the HM predicts. The comparison of the TSM versus HM relative differences was intended to benchmark CP_2D TSM results by using the MCNP results. The same behaviour of the pin powers can be seen more explicitly in Fig. 3. For the SEU-43 fuel bundle at different burnup points (8000, 13,000 and 25,000 MWd/TU) the paper shows only CP_2D results. The main reason is the strong difference in the definition of the pseudo-fission product for WIMSD-5B and ENDF/ B-V (used by MCNP) libraries. On the other hand, the version MCNP4C have not a burnup module. Thus, we have considered the CP_2D benchmarking process by the MCNP code is relevant, in this stage, only for the fresh fuel. Fig. 4 shows the K-infinity values as a function of void fraction for different burnups burnups (8000, 13,000, 25,000 MWd/TU). Unlike CANDU-6 fuel bundle
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Table 2 CP_2D and MCNP pin powers (normalized to the mean power) comparison for fresh fuel and different void fraction of the SEU-43 cell Fuel elem.
Void fraction 0%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 a
"¼
50%
99%
MCNP
CP_2D
eps (%)
MCNP
CP_2D
eps (%)
MCNP
CP_2D
eps (%)a
0.997 1.063 1.060 1.064 1.062 1.064 1.063 1.066 0.854 0.853 0.850 0.855 0.854 0.854 0.853 0.853 0.856 0.855 0.851 0.857 0.851 0.854 1.077 1.076 1.078 1.074 1.076 1.075 1.076 1.078 1.076 1.078 1.078 1.078 1.075 1.078 1.077 1.075 1.080 1.077 1.078 1.078 1.075
1.022 1.070 1.075 1.083 1.092 1.092 1.083 1.075 0.851 0.850 0.855 0.858 0.860 0.867 0.865 0.871 0.865 0.867 0.860 0.858 0.855 0.850 1.061 1.063 1.067 1.065 1.063 1.067 1.067 1.065 1.066 1.066 1.069 1.069 1.066 1.066 1.065 1.067 1.067 1.063 1.065 1.067 1.063
2.5 0.7 1.4 1.8 2.8 2.6 1.9 0.8 0.5 0.3 0.5 0.4 0.7 1.5 1.4 2.1 1.0 1.4 1.2 0.2 0.4 0.4 1.5 1.2 1.0 0.9 1.2 0.7 0.8 1.1 0.9 1.1 0.8 0.8 0.8 1.1 1.1 0.7 1.2 1.4 1.2 1.0 1.1
1.031 1.090 1.101 1.105 1.101 1.078 1.069 1.070 0.860 0.866 0.871 0.869 0.873 0.874 0.872 0.862 0.851 0.851 0.847 0.849 0.846 0.847 1.061 1.062 1.063 1.065 1.062 1.061 1.062 1.062 1.068 1.070 1.071 1.063 1.059 1.062 1.061 1.064 1.063 1.062 1.058 1.059 1.059
1.050 1.087 1.124 1.140 1.155 1.101 1.078 1.072 0.850 0.864 0.879 0.882 0.891 0.897 0.893 0.887 0.857 0.855 0.845 0.843 0.841 0.841 1.043 1.056 1.063 1.064 1.061 1.064 1.065 1.062 1.060 1.061 1.069 1.049 1.041 1.040 1.038 1.040 1.040 1.035 1.038 1.042 1.038
1.9 0.4 2.0 3.2 4.9 2.1 0.8 0.3 1.1 0.2 0.9 1.5 2.0 2.6 2.4 2.9 0.7 0.4 0.2 0.7 0.6 0.7 1.6 0.5 0.1 0.1 0.1 0.3 0.3 0.0 0.7 0.8 0.2 1.4 1.7 2.1 2.2 2.3 2.2 2.5 1.9 1.6 1.9
1.061 1.113 1.110 1.111 1.115 1.115 1.113 1.112 0.866 0.863 0.868 0.865 0.866 0.866 0.866 0.870 0.867 0.863 0.865 0.863 0.864 0.864 1.050 1.049 1.047 1.049 1.051 1.050 1.049 1.050 1.053 1.049 1.049 1.052 1.051 1.049 1.053 1.045 1.041 1.048 1.050 1.051 1.050
1.084 1.111 1.118 1.131 1.159 1.158 1.130 1.117 0.857 0.855 0.866 0.867 0.875 0.885 0.886 0.892 0.885 0.884 0.872 0.865 0.864 0.854 1.032 1.033 1.041 1.039 1.035 1.039 1.041 1.037 1.037 1.038 1.049 1.049 1.037 1.036 1.035 1.034 1.029 1.032 1.038 1.041 1.033
2.2 0.2 0.7 1.9 4.0 3.9 1.5 0.4 1.1 0.9 0.3 0.3 1.1 2.3 2.3 2.5 2.1 2.4 0.9 0.2 0.1 1.2 1.7 1.4 0.6 0.9 1.5 1.1 0.8 1.3 1.5 1.0 0.0 0.3 1.3 1.2 1.7 1.0 1.1 1.5 1.2 0.9 1.7
PPCP 2D PPMCNP 100: PPMCNP
a
a
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Table 3 CP_2D and MCNP pin powers (normalized to the mean power) comparison for fresh fuel and different void fraction of the SEU-43 cell by using HM and TSM Fuel rod
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
Vf=50%
Vf=50%
MCNP HM
MCNP TSM
eps (%)
CP_2D HM
CP_2D TSM
eps (%)
1.028 1.086 1.085 1.085 1.086 1.085 1.083 1.083 0.859 0.857 0.862 0.859 0.860 0.860 0.858 0.861 0.857 0.860 0.858 0.857 0.861 0.860 1.062 1.061 1.064 1.061 1.064 1.062 1.061 1.064 1.064 1.067 1.064 1.066 1.064 1.065 1.065 1.066 1.064 1.065 1.066 1.068 1.066
1.031 1.090 1.101 1.105 1.101 1.078 1.069 1.070 0.860 0.866 0.871 0.869 0.873 0.874 0.872 0.862 0.851 0.851 0.847 0.849 0.846 0.847 1.061 1.062 1.063 1.065 1.062 1.061 1.062 1.062 1.068 1.070 1.071 1.063 1.059 1.062 1.061 1.064 1.063 1.062 1.058 1.059 1.059
0.3 0.4 1.5 1.8 1.4 0.6 1.3 1.2 0.1 1.0 1.0 1.2 1.5 1.6 1.6 0.1 0.7 1.1 1.3 0.9 1.8 1.5 0.1 0.1 0.1 0.4 0.2 0.1 0.1 0.2 0.4 0.3 0.7 0.3 0.5 0.3 0.4 0.2 0.1 0.3 0.8 0.8 0.7
1.051 1.090 1.095 1.106 1.120 1.120 1.106 1.095 0.854 0.853 0.860 0.863 0.867 0.875 0.874 0.880 0.874 0.875 0.868 0.863 0.860 0.853 1.047 1.049 1.054 1.052 1.049 1.053 1.054 1.051 1.052 1.052 1.058 1.058 1.052 1.052 1.051 1.054 1.053 1.049 1.052 1.054 1.049
1.050 1.087 1.124 1.140 1.155 1.101 1.078 1.072 0.850 0.864 0.879 0.882 0.891 0.897 0.893 0.887 0.857 0.855 0.845 0.843 0.841 0.841 1.043 1.056 1.063 1.064 1.061 1.064 1.065 1.062 1.060 1.061 1.069 1.049 1.041 1.040 1.038 1.040 1.040 1.035 1.038 1.042 1.038
0.1 0.2 2.5 3.0 3.0 1.8 2.6 2.2 0.5 1.3 2.2 2.2 2.6 2.4 2.1 0.8 2.0 2.4 2.7 2.3 2.2 1.4 0.4 0.7 0.8 1.1 1.1 1.0 1.0 1.0 0.8 0.8 1.1 0.8 1.1 1.1 1.3 1.4 1.3 1.4 1.3 1.2 1.0
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Fig. 3. SEU-43 bundle pin powers (normalized to the mean power). Comparison between CP_2D and MCNP for 50% void fraction and fresh fuel.
where the value of 13,000 MWd/TU is the maximum burnup (reached only for some fuel bundles of the core) for SEU-43 fuel bundle this is the average burnup. The maximum burnup for SEU-43 is about 25,000 MWd/TU. The 8000 MWd/TU point was chosen for the reason to compare the void reactivity between SEU-43 and CANDU-6 voided cells (at the average burnup point in CANDU-6 type reactor). For high burnup the reactivity values are smaller than for the average burnup, but for large void fractions (typical in LOCA) the differences are not very important (1437 related to 1539 pcm). The pin powers (normalized to the mean power) for 8000, 13,000 and 25,000 MWd/TU burnups are inter-compared for two state (HOC and 99% void fraction) in Table 4. For simplicity, let’s compare the pin powers for the fuel rods indexed as 1, 4, 13 and 29 (radial placed on center, inner, intermediate and respectively outer ring—see Fig. 1). For the HOC at 8000 MWd/TU (Vf=0%) the radial dependence of the pin powers is 1.089, 1.133, 0.865, 1.042. The dependence is influenced by two
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Fig. 4. K-infinity as a function of void fraction for SEU-43 cell, different burnups.
factors: the radial dependence of the flux and the different areas of the rods. Let’s remind ourselves that we used pin powers as linear powers normalized to the mean value. In the void state (Vf=99%) the radial dependence is 1.160, 1.185, 0.878, 1.015 with an increasing of all the values, except the outer fuel rod. The same behaviour appears for both 13,000 and 25,000 MWd/TU burnups. In the voided cells the pin powers for the center, inner and intermediate rings increase, whereas the pin powers for the outer ring decrease. For the burnup dependence it must be noted that the pin power values increase with the burnup in the outer ring, and decrease in the intermediate ring. For the inner and the center rings the maximum values are obtained at
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Table 4 CP_2D pin powers (normalized to the mean power) for the SEU-43 cell at different burnups- hot operating conditions (Vf=0%) and large void conditions (Vf=99%) Fuel rod
Burnup (MWd/TU) 8000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
13,000
25,000
Vf=0%
Vf=99%
Vf=0%
Vf=99%
Vf=0%
Vf=99%
1.089 1.135 1.133 1.133 1.134 1.134 1.133 1.133 0.865 0.866 0.865 0.866 0.865 0.867 0.864 0.866 0.864 0.867 0.865 0.866 0.865 0.866 1.038 1.040 1.043 1.041 1.040 1.040 1.042 1.042 1.039 1.039 1.042 1.042 1.039 1.039 1.042 1.042 1.040 1.040 1.041 1.043 1.040
1.160 1.197 1.186 1.185 1.193 1.192 1.184 1.185 0.880 0.877 0.878 0.876 0.878 0.878 0.877 0.878 0.877 0.877 0.876 0.874 0.877 0.877 1.009 1.011 1.016 1.013 1.011 1.010 1.015 1.013 1.009 1.011 1.017 1.017 1.010 1.009 1.011 1.009 1.002 1.007 1.012 1.016 1.011
1.115 1.150 1.149 1.149 1.150 1.150 1.149 1.149 0.861 0.863 0.861 0.863 0.862 0.863 0.861 0.863 0.861 0.863 0.862 0.863 0.861 0.863 1.034 1.036 1.039 1.037 1.036 1.036 1.038 1.038 1.035 1.035 1.038 1.038 1.035 1.035 1.038 1.038 1.036 1.036 1.037 1.039 1.036
1.186 1.211 1.201 1.200 1.207 1.207 1.198 1.200 0.876 0.873 0.874 0.872 0.874 0.874 0.873 0.874 0.873 0.873 0.872 0.870 0.873 0.873 1.006 1.008 1.013 1.010 1.007 1.007 1.011 1.009 1.006 1.007 1.013 1.013 1.007 1.005 1.008 1.006 0.999 1.004 1.009 1.012 1.008
1.081 1.118 1.117 1.117 1.117 1.117 1.117 1.117 0.846 0.848 0.847 0.848 0.847 0.848 0.846 0.848 0.846 0.848 0.847 0.848 0.847 0.848 1.057 1.058 1.061 1.059 1.058 1.058 1.060 1.060 1.057 1.057 1.060 1.060 1.057 1.057 1.060 1.060 1.058 1.058 1.059 1.061 1.058
1.149 1.176 1.167 1.166 1.173 1.172 1.164 1.166 0.861 0.859 0.859 0.858 0.859 0.859 0.858 0.859 0.858 0.858 0.857 0.855 0.858 0.858 1.029 1.031 1.036 1.033 1.030 1.030 1.034 1.032 1.029 1.030 1.036 1.036 1.030 1.028 1.031 1.029 1.022 1.027 1.032 1.035 1.030
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average burnup. The maximum values of the pin power occur in the inner ring for all studied burnup points both for HOC and 99% voided cell. The same behaviour appears for the TSM (see Fig. 3) at 0 MWd/TU, but for the rods surrounded by the vapour region (‘void region’). A comparison between SEU-43 and CANDU-6 voided cells is presented in Tables 5–7. The void reactivity values are compared in Table 5, for a 99% void fraction and different burnup points. It can be observed that the void reactivity values for SEU-43 cells are in the same range like the CANDU-6 cells. For the -fresh fuel the void reactivity of SEU-43 is 9.1% related to the CANDU-6 voided cell. For SEU-43 the void reactivity remains nearly constant up to the average burnup and slightly decreases at high burnup. The pin powers normalized to the mean power and averaged per rings, for fresh fuel and HOC, are presented in Table 6. Whereas for CANDU-6 the maximum pin powers is obtained for the outer ring, for SEU-43 fuel bundle the maximum pin power is obtained for the inner ring. A comparison of all pin powers, between CANDU-6 and SEU-43 cells, for fresh fuel and a 50% void fraction, is presented in Table 7. The maximum pin power is 1.128 for CANDU-6 and 1.138 for SEU-43, in the positions (4,4)=(outer ring, fourth rod), respectively (2,3)=(inner ring, third rod). Both the two rods are immersed into the vapour phase.
Table 5 The void reactivity comparison between SEU-43 and standard CANDU cell, for a 99% void fraction Burnup [MWd/tU]
0 8000 13,000 25,000
Reactivity [pcm] CANDU standard
SEU-43 (0.96%)
1635 1551 1205 –
1487 1531 1539 1437
Table 6 The pin powers (normalized to the mean power and averaged per rings): comparison between SEU-43 and standard CANDU cell, for fresh fuel and HOC Ring
CANDU-6
SEU-43
Center Inner Intermediate Outer
0.784 0.820 0.986 1.127
1.022 1.081 0.860 1.066
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Table 7 The pin powers (normalized to the mean power): comparison between SEU-43 and standard CANDU cell, for fresh fuel and a 50% void fraction CANDU standard Fuel rod (ring, position)
SEU-43 Pin powers
Fuel rod (ring, position)
Pin powers
(1,1) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
0.805 0.853 0.871 0.852 0.824 0.824 0.824
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (3,7) (3,8) (3,9) (3,10) (3,11) (3,12)
0.952 0.956 0.937 0.933 0.951 0.951 0.916 0.909 0.897 0.896 0.906 0.918
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (4,7) (4,8) (4,9) (4,10) (4,11) (4,12) (4,13) (4,14) (4,15) (4,16) (4,17) (4,18)
1.113 1.125 1.125 1.128 1.126 1.126 1.127 1.125 1.125 1.122 1.101 1.099 1.097 1.096 1.096 1.097 1.099 1.100
(1,1) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (2,7) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (3,7) (3,8) (3,9) (3,10) (3,11) (3,12) (3,13) (3,14) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (4,7) (4,8) (4,9) (4,10) (4,11) (4,12) (4,13) (4,14) (4,15) (4,16) (4,17) (4,18) (4,19) (4,20) (4,21)
1.050 1.108 1.133 1.138 1.134 1.088 1.075 1.080 0.864 0.881 0.887 0.886 0.890 0.886 0.881 0.872 0.850 0.848 0.844 0.846 0.845 0.851 1.046 1.057 1.064 1.063 1.061 1.062 1.066 1.063 1.059 1.059 1.062 1.047 1.039 1.038 1.039 1.039 1.038 1.037 1.039 1.043 1.043
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6. Conclusions 1. The comparison of the MCNP and CP_2D results, on the two stratified model (TSM), shows a fair agreement, but with a systematic slight underestimation of the void reactivity by CP_2D code. The difference appears mainly from the used libraries. The results have been compared only for the fresh fuel for the reason of the absence of the burnup module in MCNP4C and the different definition of the pseudo-fission product used by the libraries. 2. The model proposed for the loss of coolant accident in CANDU type reactor with a separation into the liquid and vapour phases (the TSM) offer detailed information about the neutronic behaviour of each fuel rod during the accident. The power per element for symmetrical rods has values depending on the phase surrounding each rod. The HM underestimates the values for the fuel elements placed into the vapour region and conversely it overestimates the values for the immersed (into the coolant) fuel elements. The same behaviour is observed both in the MCNP and CP_2D results. 3. The values of void reactivities for cells with SEU-43 fuel bundle are closed to the voided CANDU-6 cells. From this point of view we do not expect major consequences in the safety analysis of the SEU-43 related to the safety analysis of the standard core. 4. The maximum pin power locations are different for the two kind of fuel bundle: the outer ring for the standard fuel and the inner ring for the SEU43. The behaviour is identical for the HOC and the voided cells, with the difference of the placement of the maximum power (fuel rods placed into the vapour phase for the voided cases). 5. The void reactivity shows an approximative linear dependence with the void fraction. For the fresh fuel the relative difference between void reactivity of SEU-43 and CANDU-6 voided cell is about 9%. For SEU-43 the void reactivity remains aproximately constant with the burnup, with a slight decrease at high burnup.
References Briesmeister, J.F. (Ed.), 2000. MCNP—A General Monte Carlo N-Particle Transport Code, Version 4C. LA-13709-M. Constantin, M., Balaceanu, V., 2002. Void reactivity and pin power calculation for a typical CANDU cell using CPs and a two-stratified coolant model. Annals of Nuclear Energy 29 (7), 483–488. Constantin, M., 2000. Neutron transport by collision probability method in complicated geometries. International Conference on Supercomputing in Nuclear Application, 4–7 September, Tokyo, Japan. Halsall, M.J., Taubman, C.J., 1986. The ‘19860 WIMS Nuclear Data Library. AEEW-R 2133. Reactor Phisics Division, AEE, Winfrith, UK. Horhoianu, G., 1992. Improvement of the CANDU fuel element performance in order to increase the ability to operate at high powers and to meet high burnup. Final Report to IAEA research contract 6197/RB. INR Pitesti, Romania.
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Rahnema, F., Mosher, S., Parvaiz, A., Serghiuta, D., 1998. Void reactivity calculations in a typical CANDU cell using MCNP and helios. International Conference on the Physics of Nuclear Science and Technology, 5–8 October, Long Island, USA, pp. 356–361. Patrulescu, I., Dobrea, G., 2000. CANDU Core Calculations for SEU-43 fuel type. Internal Report-5904. INR Pitesti, Romania. Weiss, Z., Ball, G., 1991. Ray Tracing in Complicated Geometries. Annals of Nuclear Energy 18 (8), 483– 488.