Conference Paper COMPARISONS BETWEEN WIMS-AECL, RFSP, AND MCNP FOR PREDICTION OF REACTIVITY IN BARE CORES OF VARIOUS SIZES COMPANY WIDE CW-119190-CONF-011 Revision 0
Prepared by Rédigé par
Bromley Blair - Reactor Physicist
Reviewed by Vérifié par
Adams Fred P - Senior Reactor Physicist Approved by Approuvé par
Radford Darren D. - Manager, Computational Reactor Physics 2011/08/11 2011/08/11 UNRESTRICTED ILLIMITÉ
Atomic Energy of Énergie Atomique du Canada Limited Canada Limitée
2251 Speakman Drive 2251 rue Speakman Mississauga, Ontario Mississauga (Ontario) Canada L5K 1B2 Canada L5K 1B2 American Nuclear Society (ANS) Annual Winter Meeting. UNRESTRICTED October 30 – November 3, 2011, Omni Shoreham Hotel, Washington, DC, U.S.A. CW-119190-CONF-011
Comparisons Between WIMS-AECL, RFSP, and MCNP for Prediction of Reactivity in Bare Cores of Various Sizes
Blair P. Bromley, John Vandersleen**
AECL – Chalk River Laboratories, Chalk River, Ontario, ON, Canada K0J 1P0, [email protected] ** Queen’s University, Department of Chemical Engineering, Kingston, Ontario, Canada
wt% U-235/U) uranium dioxide fuel clad in Zircaloy-4, INTRODUCTION along with a central burnable neutron absorber (BNA) pin containing zirconia/dysprosia/gadolinia/yttria. See Fig. 1. It has been observed in a number of recent physics code (e.g., WIMS-AECL, RFSP, MCNP) comparisons [1, 2, 3] with ZED-2 heavy water critical experiment measurements for ACR1-type lattices [4], that there can be differences in the prediction of keff, and differences in the bias for the prediction of the coolant void reactivity (CVR). Such differences relative to measurements and between codes may change in scaling up from small ZED-2 critical experiments to much larger reactor cores, such as the ACR-1000 [5, 6]. To better understand potential causes for these differences, and scaling trends with reactor size, code-to-code comparisons were performed for the simpler problem of a bare cylindrical core filled with a repeating lattice and constant properties. Pressure Tube Calandria Tube DESCRIPTION OF ACTUAL WORK Zirconium Wire Clip
The objective was to perform comparisons between Fig. 1. Cross Section View of ACR-LEU in an WIMS-AECL [7], RFSP [8, 9], and MCNP5 [10] in the Aluminum PT/CT Channel prediction of keff and coolant void reactivity worth (CVR = (kvoid-kcool)/(kvoid×kcool)) for bare core reactor models of TABLE I. ACR-LEU Bare Core Operating Conditions a repeating lattice of 43-element ACR-LEU fuel in aluminum pressure tube / calandria tube channels at 24- Temperature 300 K cm square pitch, at varying height and radius, with and Coolant H2O without H O coolant. The code models for the ACR-LEU Density of Coolant - Cooled 0.99661 g/cm3 2 3 fuel are based on earlier studies [1, 2]. These Density of Coolant - Voided 9.9661E-04 g/cm Moderator Heavy water comparisons would provide insight into the limitations Weight Percent D2O in Moderator 99.750 wt% and applicability for deterministic codes (e.g., WIMS- Weight Percent H2O in Moderator 0.250 wt% AECL, RFSP) and their associated approximations, and Density of Moderator 1.10385 g/cm3 areas for improvement. The results might also suggest the applicability of small-scale, higher leakage experimental Approximations and simplifying assumptions were made results to large-scale applications, and could complement for the analyses. All of the reactors modeled were sensitivity/uncertainty methods for estimating the cylindrical bare cores at a uniform 300 K, with other extension of code validation results. operating conditions held constant, as shown in Table I. Since the key value of interest was coolant void reactivity ACR-LEU Bare Core Lattice (CVR), cases were run both with light water (H2O) coolant, and with void (void = 0.001H2O). Bare cores The lattice modeled was based on that developed for ranged in size from 3 to 12 bundles high; each bundle is the 43-element ACR-LEU fuel bundle in aluminum ACR- ~50 cm long. Radial dimensions were determined using a 2 2 type channels at a 24-cm square lattice pitch, as described buckling ratio similar to the ACR-1000 (B z/B r 0.45, in previous analyses [1, 2]. The ACR-LEU fuel bundle is H/2R 0.97). All cores were essentially right cylinders, composed of 42 pins of low enriched uranium oxide (1.7 filled with a uniform, repeating lattice. In both the MCNP and RFSP code models, the cylindrical boundary cuts 1 ACR (Advanced CANDU Reactor) and ACR-1000 are through a lattice cell, with vacuum boundary conditions Registered Trademarks of Atomic Energy of Canada beyond the core radius. The maximum diameter (612.6 Limited (AECL) cm) is over 25 lattice pitches. American Nuclear Society (ANS) Annual Winter Meeting. UNRESTRICTED October 30 – November 3, 2011, Omni Shoreham Hotel, Washington, DC, U.S.A. CW-119190-CONF-011
Computer Codes and Libraries 0.1 mk) and also in the fast and thermal flux tallies (F4:n) for the axial and radial neutron flux distributions WIMS-AECL and WIMS Utilities (less than 1%). The neutron flux tally data was curve- fitted to obtain buckling data for use in stand-alone WIMS-AECL Version 3.1.2 [7] was used in conjunction WIMS-AECL calculations of keff. with an 89-group library based on ENDF/B-VI.5 and ENDF/B-VI.7. WIMS-AECL is a 2-D (x-y) lattice RESULTS physics code employing collision probability methods to solve the multi-group integral neutron transport equations, Buckling and is well suited for bundle geometries. The discretization and modeling options and approximations The bare core dimensions for each test case are used for WIMS-AECL were similar to those in other shown in Table II, along with the radial and axial studies for ACR-type lattices [1, 5]. There are several bucklings derived from the cosine-Bessel curve fits types of leakage models that allow WIMS-AECL to use ((r,z)=A cos((z-z ))J (r), B2 = 2, B2 =2) of the 2 2 0 max 0 z r input bucklings (B r, B z) to calculate keff, or to do a neutron flux distributions (fast and thermal) computed in critical buckling search. The B0B0 leakage option in the MCNP5 simulations, both cooled and voided cases. WIMS-AECL uses the diffusion approximation with isotropic transport diffusion coefficients, while the B1B1 TABLE II. Bucklings Derived for Bare Lattices of ACR- leakage option uses the B1 transport approximation in LEU Based on Curve Fits of Flux Distributions from combination with the Benoist anisotropy formalism to MCNP5 Simulations correct for direction-dependent leakage. WIMS Utilities Version 2.0.1 [8] was used to extract 89- Cooled ACR-LEU Bare Lattices (24-cm pitch) 2 2 2 2 group macroscopic cross-sections and neutron fluxes from Br Br Bz Bz the TAPE16 binary output data file of WIMS-AECL, and H (cm) R (cm) (m-2) (m-2) (m-2) (m-2) to condense and homogenize that data into two-group, 148.590 76.901 9.078 0.018 4.032 0.045 cell-averaged cross-sections, which then can be used in 198.120 102.391 5.205 0.001 2.325 -- core calculations by RFSP. 247.650 127.881 3.382 0.001 1.507 -- 297.180 153.371 2.363 -- 1.062 -- RFSP 396.240 204.350 1.339 -- 0.606 -- 495.300 255.330 0.861 -- 0.388 -- RFSP is a three-dimensional (x-y-z), two-group diffusion, 594.360 306.309 0.608 -- 0.271 -- finite difference code, which computes three dimensional Voided ACR-LEU Bare Lattices (24-cm pitch) 2 2 2 2 neutron flux and power density distributions in a reactor Br Br Bz Bz -2 -2 -2 -2 core, and also core reactivity, =(k-1)/k. RFSP Version H (cm) R (cm) (m ) (m ) (m ) (m ) 3.5.1 [9] was used in conjunction with two-group, 148.590 76.901 9.013 0.010 3.991 0.033 homogenized lattice-cell cross sections generated by 198.120 102.391 5.137 0.002 2.300 0.003 WIMS-AECL with the B1B1 leakage option, using a 247.650 127.881 3.341 -- 1.496 -- 297.180 153.371 2.343 -- 1.052 -- default critical spectrum. Although WIMS-AECL(B1B1) 396.240 204.350 1.335 -- 0.598 -- uses the Benoist formalism, the resulting transport cross 495.300 255.330 0.861 -- 0.386 -- sections are converted by WIMS Utilities into isotropic 594.360 306.309 0.604 -- 0.272 -- values (D= (2Dr+Dz)/3), since RFSP 3.5.1 does not make use of direction-dependent diffusion coefficients. Mesh Only flux data in the asymptotic region, where the sizes of dx=dy=8 cm, and dz=6.2 cm were used; smaller fast/thermal flux ratio remains relatively constant (usually mesh sizes had a negligible impact on keff results, even for a lattice-pitch distance from the vacuum boundary), were the smallest cores (<0.5 mk; 1 mk = 100 pcm = 0.001 used in the curve fits. The uncertainty was based on k/k). spread between the fast and thermal results, and was largest for the smallest core, and negligible, “--”, for MCNP larger cores. The voided cores had slightly smaller bucklings (differences ranging from 0.003 m-2 to 0.1 m-2), MCNP5 Version 1.30 [10] was used in conjunction with a owing to the larger transport mean free path and continuous energy library based on ENDF/B-VI.8 [11] to extrapolation distances. Based on one-group diffusion model the ACR-LEU lattices in detail with fewer theory for bare cores, and the buckling components approximations in spatial, energy or angular resolution. determined from the MCNP5 calculations, the average Simulations were typically run with 100 million histories radial extrapolation distance was approximately 3 cm for (50,000 histories/cycle, 2200 cycles, 200 cycles dropped) the cooled cases, and 3.6 cm for the voided cases, while to ensure that low statistical uncertainties in keff (less than American Nuclear Society (ANS) Annual Winter Meeting. UNRESTRICTED October 30 – November 3, 2011, Omni Shoreham Hotel, Washington, DC, U.S.A. CW-119190-CONF-011 the average axial extrapolation distance was 4.1 cm for in going from small leaky cores to large cores. It is the cooled cases, and 4.6 cm for the voided case. recognized that these cores are essentially right cylinders, Anisotropy in neutron leakage is indicated by the 2RH, where the impacts of anisotropy in the diffusion differences in the radial and axial extrapolation distances. coefficients (e.g., Dx, Dy, Dr, Dz) will be minimized, and where the lateral components and axial component of 2 2 2 keff and CVR Calculations leakage are comparable (DxB x DyB y DrB r/2 2 DzB z). Such comparable results in CVR between B1B1 The calculations of keff for each test case using and B0B0 leakage models may not hold in very high MCNP5, RFSP, and WIMS-AECL with the B1B1 and 2R/H (“pancake”) or very low 2R/H (“pencil”) cores. B0B0 leakage models are shown below in Table III. RFSP calculations show slightly larger differences Uncertainties in keff for MCNP are less than 0.1 mk, and relative to MCNP for larger cores, but then diverge not shown. Discrepancies in keff relative to MCNP significantly as the core size is reduced below 250 cm, as increase as the size of the core is reduced and leakage shown in Fig. 2. effects become significant, particularly with cores less The use of 2-group homogenized diffusion cross than 250 cm in height and diameter. WIMS-AECL sections in RFSP based on the WIMS-AECL(B1B1) (B1B1) calculations tend to under-predict keff relative to instead of WIMS-AECL(B0B0) calculations leads to MCNP, ranging from -0.1 mk to -12 mk, whereas the use lower discrepancies in keff relative to MCNP. Aside from of the B0B0 leakage model gives positive discrepancies the known limitations of using two-group diffusion theory ranging from +2 mk to +34 mk. RFSP calculations fall in to model neutron transport in compact cores, the between the B1B1 and B0B0 results, ranging from -2.6 divergence of the RFSP CVR results for smaller, heavy- mk to +22.7 mk. water-moderated cores is likely attributed to the fact that From this data, one can also infer the CVR worth, RFSP 3.5.1 does not make use of direction-dependent and it ranges from -170 mk to -12 mk. The differences in diffusion coefficients. It is expected that minor CVR worth calculations for RFSP and WIMS-AECL improvements to both WIMS Utilities and RFSP could (B1B1, B0B0) relative to MCNP5 are plotted against core enable improvements in predictions for smaller cores. height in Fig. 2. The uncertainties in the WIMS-AECL results due to the uncertainties in the bucklings are CONCLUSIONS propagated through, but are only significant for the smallest core (~1.3 mk). The analyses presented constitute code-to-code comparisons between WIMS-AECL 3.1.2, RFSP 3.5.1, and MCNP5 Version 1.30 calculations of k and CVR Difference in CVR Worth eff (Relative to MCNP) worth for bare core reactor models of an ACR-type 4.0 lattice, with variations in reactor size, with and without 3.0 RFSP-MCNP H2O coolant. The analyses examine the reactor scaling effects on the code-to-code differences. 2.0 WIMS-AECL(B1B1)-MCNP The larger keff discrepancies for WIMS-AECL with WIMS-AECL(B0B0)-MCNP 1.0 the B0B0 leakage model relative to the B1B1 demonstrate 0.0 that the use of higher-order transport models, and a correction for direction dependence are needed to better -1.0 represent the anisotropy that occurs in such lattices, -2.0 particularly in small cores. However, the larger -3.0 discrepancies in keff for the B1B1 leakage model in
Difference in CVR Worth CVR(mk)Worth in Difference -4.0 compact cores indicate that there is still further room for 0 100 200 300 400 500 600 700 improvement in the leakage model used in the 2-D Bare Reactor Height (cm) WIMS-AECL lattice physics calculation. The differences in CVR worth are fairly constant with respect to reactor size, except for very small core Fig. 2. Difference in CVR Worth Calculations for sizes, where RFSP results diverge significantly. The Various Bare Cores with ACR-LEU apparent -1.6 mk to -2.9 mk discrepancy between the various deterministic codes and MCNP5 for the Although comparison to MCNP shows the B0B0 evaluation of CVR worth at large core sizes is attributed leakage model to be less accurate than the B1B1 leakage to the differences in the nuclear data libraries used, the model for predicting keff, most of the discrepancies cancel geometric and discretization approximations made in in prediction of CVR worth, and both B1B1 and B0B0 modeling the fuel bundles, and the use of multi-group leakage models show differences relative to MCNP transport theory (or two-group diffusion theory) vs. the ranging from -3 mk to -1.5 mk, not changing significantly direct simulation approach used with MCNP5. American Nuclear Society (ANS) Annual Winter Meeting. UNRESTRICTED October 30 – November 3, 2011, Omni Shoreham Hotel, Washington, DC, U.S.A. CW-119190-CONF-011
The bare cores simulated in this study range in size Proceedings of PHYSOR 2010, Pittsburgh, PA, from (R, H) ~ (76 cm, 149 cm) to (306 cm, 594 cm). By U.S.A., May 9-14 (2010). comparison, ZED-2 experiments with ACR-type fuels and 3. B. P. BROMLEY et al., “Comparison of MCNP lattices [1, 2, 3, 4] can have cores that are as small as 150 and WIMS-AECL/RFSP Calculations Against cm in height, or 165 cm in diameter. However, these Critical Heavy Water Experiments in ZED-2 with cores are surrounded by large radial and axial reflectors, CANFLEX-LVRF and CANFLEX-LEU Fuels,” such that the reactor size, as defined by the extent of the Proceedings of M&C 2009, Saratoga Springs, New vacuum boundaries, will be on the order of at least 255 York, May 3-7, (2009). cm in height, and 456 cm in diameter. Thus, one might 4. M.B. ZELLER, “Physics Experiments in the ZED- expect that the equivalent bare core results would be 2 Reactor in Support of the Advanced CANDU comparable to those shown for the 5-bundle and larger Reactor,” Proceedings of 25th CNS Annual cores. Code-to-code differences in CVR worth do not Conference, Toronto, June 6-9 (2004). vary by more than 1 mk in going from a 250-cm-high to a 5. W. SHEN, et al., “Benchmarking of WIMS- 600-cm-high core. This suggests that code validation AECL/RFSP Multi-cell Methodology with MCNP results for CVR using ZED-2 experiments may be directly for ACR-1000 Full-Core Calculations,” applicable for larger-scale applications (e.g., ACR-1000), Proceedings of PHYSOR 2008, Interlaken, provided that an appropriate uncertainty is applied to Switzerland, September 14-19 (2008). cover scaling effects. 6. J. HOPWOOD, “The AECL ACR-1000 Reactor”, Proceedings of PHYSOR-2006, Vancouver, British ACKNOWLEDGMENTS Columbia, Canada, September 10-14 (2006). 7. D.V. ALTIPARMAKOV, “New Capabilities of the This study was completed as part of a summer student Lattice Code WIMS-AECL,” Proceedings of research project. Thanks are extended to Alex Trottier, PHYSOR 2008, Interlaken, Switzerland, September Jeremy Pencer, Boris Shukhman, David Watts, and Fred 14-19 (2008). Adams (AECL, Chalk River Laboratories), for their 8. T. LIANG et al., “Improvement and Qualification insights and assistance with this work. of WIMS Utilities,” Proceedings of 29th CNS Annual Conference, Toronto, June 1-4 (2008). REFERENCES 9. W. SHEN, et al. “Evolution of Computer Codes for CANDU Analysis”, Proceedings of PHYSOR 1. J. PENCER, et al., “Comparison of WIMS-AECL / 2010, Pittsburgh, PA, U.S.A., May 9-14 (2010). DRAGON / RFSP and MCNP Results with ZED-2 10. X-5 MONTE CARLO TEAM, “MCNP – A Measurements for Control Device Worth And General Monte Carlo N-Particle Transport Code, Reactor Kinetics”, Proceedings of PHYSOR 2010, Version 5”, LA-UR-03-1987, (April 2003). Pittsburgh, PA, U.S.A., May 9-14 (2010). 11. D.V. ALTIPARMAKOV, “ENDF/B-VII.0 versus 2. F.C. WONG, et al., “Reactivity and Flux ENDF/B-VI.8 in CANDU Calculations”, Calculations Using MCNP for Heavy-Water Proceedings of PHYSOR 2010, Pittsburgh, PA, Experiments in the ZED-2 Critical Facility Using May 9-14 (2010). Low-Enriched Uranium Fuel Bundles”,
TABLE III. keff Calculations and Differences for Various Bare Core Lattices
# H (cm) R (cm) MCNP RFSP-MCNP WIMS-AECL WIMS-AECL Bundles (mk) (B1B1) – MCNP (B0B0) –MCNP High (mk) (mk)
kcool kvoid kcool kvoid kcool kvoid kcool kvoid 3 148.590 76.901 0.83457 0.73252 13.7 22.7 -12.2 -10.8 34.4 25.6 4 198.120 102.391 0.94401 0.87396 8.9 9.5 -6.0 -6.8 25.9 20.0 5 247.650 127.881 1.00372 0.95296 6.1 4.3 -3.4 -5.1 19.2 14.5 6 297.180 153.371 1.03936 1.00079 4.2 1.6 -2.1 -4.1 14.5 10.7 8 396.240 204.350 1.07722 1.05242 2.1 -0.9 -0.8 -2.8 9.1 6.2 10 495.300 255.330 1.09571 1.07800 1.1 -2.1 -0.1 -2.4 6.4 3.6 12 594.360 306.309 1.10626 1.09231 0.2 -2.6 -0.3 -2.3 4.3 2.0