CPM-3 BENCHMARKING to the DOE/B&W CRITICAL EXPERIMENTS

Transcription

1 CPM-3 BENCHMARKING to the DOE/B&W CRITICAL EXPERIMENTS Kenneth M. Smolinske and Rodney L. Grow Utility Resource Associates Corporation 1901 Research Boulevard, Suite 405 Rockville, Maryland ABSTRACT EPRI-CPM-3 was benchmarked to eight of the DOE/B&W critical experiments described in Urania Gadolinia: Nuclear Model Development and Critical Experiment Benchmark, DOE/ET/ , BAW-1810, April Two types of comparisons were made: K-effective and pin power distribution. Two sets of CPM-3 solutions are presented: 1) CPM-3 in the collision probability matrix (CP) solution is indirectly compared to measurement using MCNP as a bridging calculation; and 2) CPM-3 in the method of characteristics (MOC) solution is directly compared to measurement. 1. INTRODUCTION The EPRI development of CPM-3 1 and the benchmarking of CPM-3 are described in a separate paper for this ANS meeting. This paper describes the extensive effort spent in benchmarking CPM-3 to the DOE/B&W critical experiments 2 and the results obtained from this effort. 2. BENCHMARK PROCESS The eight experiments that were selected to be modeled are: Core ID Short Description Results for benchmark Single enrichment cores I 2.46 w/o fuel with water holes only core k-effective and center assembly power distribution II 2.46 w/o fuel with 16 Ag-In-Cd core k-effective V 2.46 w/o fuel and 28 Gd pins (4 w/o Gd/1.94 w/o U235) core k-effective and center assembly power distribution VI 2.46 w/o fuel and 28 Gd pins with 16 Ag-In-Cd rods core k-effective Dual enrichment cores XII 4.02 in 31x31 inner zone and 2.46 w/o in the outer zone core k-effective and center assembly power distribution XIII 4.02 in 31x31 inner zone with 16 B4C rods and core k-effective 2.46 w/o in the outer zone XIV 4.02 and 28 Gd in 31x31 inner zone and 2.46 w/o in the outer zone core k-effective and center assembly power distribution XV 4.02 and 28 Gd in 31x31 inner zone with 16 B4C rods and 2.46 w/o in the outer zone core k-effective 1

2 These cases were selected to test the capability of EPRI-CPM-3 for a variety of enrichment and absorber combinations. Description of the Experiment The benchmark cases are based on a 3x3 array of 15x15 PWR lattices surrounded by a blanket of pins. This core is submerged in borated water in a 5-foot (ID) aluminum tank. The core contains a total of 4961 pins. The horizontal pin layout of the eight cores are shown in Figures 1 through 8. These figures show the southeast quadrant of the core. The boron concentrations listed in the DOE report are in units of gb NAT /10 6 cc of moderator. These values were converted to true ppm. The largest difference was 3 ppm in core 12. General Modeling Considerations The experimental configurations described in the DOE/B&W report are best modeled in three dimensions for the k-effective comparisons and in two dimensions for the pin power distribution comparisons. EPRI-CPM-3 is a two dimensional, multi-group code, so direct comparisons of predicted k-effective to experiment are not possible. In addition, the full two-dimensional layout in EPRI-CPM-3 is too large for most computers to calculate when CPM-3 is run using the collision probability matrix (CP) solution. So, in order to permit indirect comparisons, MCNP was used as a bridge to check the CP solution of CPM-3 for both reactivity and power distribution comparisons. For the method of characteristics (MOC) solution of CPM-3, the full horizontal layout was modeled and the pin power distribution was compared directly to measurement. The k-effective comparisons required that the CPM-3 include a calculated buckling to account for vertical leakage. Benchmark Cases using the Collision Probability Matrix (CP) Solution The CP solution of EPRI-CPM-3 must be compared as a single assembly to a comparable MCNP because CP solution currently cannot solve a problem as large as the actual experiment. The eight single assembly cases model the center 15x15 assembly of the full critical experiment using both EPRI-CPM-3 and MCNP. The center water hole was modeled without the detector, because the detector was inserted only for the pin power experiments. MCNP Cases Used as a Bridge to the Collision Probability Matrix (CP) Solution For comparison to pin power distribution measurement, the full critical experiments are modeled using horizontally explicit two dimensional MCNP cases for the four cores having pin power measurements. These two dimensional MCNP cases include an approximate model of the central detector, because the detector was included when the cores were burned to produce the power distributions. Only the four cores without Ag-In-Cd (silver, indium, cadmium control rods) or B4C rods have pin power distribution measurements. For comparison to measured reactivity, the two dimensional MCNP cases were changed to three dimensional cases with the active core region 150 cm high with a large volume of water below the core and vacuum above the core. All neutrons reaching the boundary of the problem were 2

3 lost. The center water hole was modeled without the detector, because the detector was inserted only for the pin power experiments. Benchmark Cases using the Method of Characteristics (MOC) Solution The full critical experiments are modeled using horizontally explicit CPM-3 cases for the fuel pin cells in the center of the core. The water outside the core was modeled as lumped blocks to simplify the model setup. For comparison to pin power distribution measurement, these CPM-3 cases include an approximate model of the central detector, because the detector was included when the cores were burned to produce the power distributions. Only the four cores without Ag-In-Cd (silver, indium, cadmium control rods) or B4C rods have pin power distribution measurements. For comparison to measured reactivity, the MOC CPM-3 cases have a central water hole and include a calculated axial buckling term. 3. BENCHMARK RESULTS The results of the comparisons are presented in this paper. Table 1 presents the reactivity comparisons for the CPM-3 CP solution. This table shows: 1. the comparisons between each individual core measurement and its corresponding MCNP three dimensional calculation, and 2. the comparisons between the MCNP and EPRI-CPM-3 assembly calculations. The line labeled 3D core shows the K-effective calculated by MCNP for the experiment and the ρ between the MCNP case and the measurement (assumed to be k=1). ρ = (1-k MCNP ) k MCNP. The line labeled Assembly shows the K-infinite calculated by MCNP and CPM-3 using the CP solution for an assembly representing the central 15x15 array of pins in the experiment. This line also shows the ρ between the MCNP case and CPM-3 case. ρ = (k MCNP -k CPM3 ) (k MCNP.* k CPM3 ). The Average Values sub-table shows the average ρ for the 3D core and Assembly cases. The Assembly results are shown both with and without the AgInCd control rods because the CPM-3 modeling of these control rods is still being investigated. Table 2 presents the reactivity comparisons for the CPM-3 MOC solution. This table shows: 1. the comparisons between each individual core measurement and its corresponding CPM-3 calculation with a calculated buckling. 3

4 The main part of the table shows the K-effective calculated by MCNP and by the MOC CPM-3 for the experiment. It also shows three ρ values: 1. between the MCNP case and the measurement (assumed to be k=1), ρ = (1-k MCNP ) k MCNP ; 2. between the CPM-3 case and the measurement (assumed to be k=1), ρ = (1-k CPM3 ) k CPM3 ; and 3. between the MCNP and CPM-3 cases, ρ = (k MCNP -k CPM3 ) (k MCNP.* k CPM3 ). The Average Values sub-table shows the average ρ for the various cases listed above. The comparisons to CPM-3 are shown both with and without the AgInCd control rods because the CPM-3 modeling of these control rods is still being investigated. Figures 9 through 16 show the pin power distributions for the central 15x15 array of pins and are arranged in pairs (three pages per pair) as follows: The figure labeled MCNP vs. Measurement for CORE nn, Using 2D MCNP shows the comparison of MCNP pin power distribution from the two dimensional case vs. the measured pin power distribution. These pin distributions are normalized to for the full assembly (i.e., the full 15x15 array of pins) so the MCNP Avg and the Meas Avg are not exactly because only an eighth of an assembly is presented. The figure labeled MCNP vs. CPM-3 for CORE nn, Using Single Assembly MCNP shows the comparison of MCNP pin power distribution from the single assembly case vs. the CP CPM-3 single assembly pin power distribution. These pin distributions are normalized to for the full assembly (i.e., the full 15x15 array of pins) so the MCNP Avg and the CPM3 Avg are not exactly because only an eighth of an assembly is presented. The figure labeled CPM-3 vs. Measurement for CORE nn, Using MOC CPM-3 shows the comparison of CPM-3 pin power distribution from the MOC case vs. the measured pin power distribution. These pin distributions are normalized to for the full assembly (i.e., the full 15x15 array of pins) so the MCNP Avg and the Meas Avg are not exactly because only an eighth of an assembly is presented. Benchmark Cases using the Collision Probability Matrix (CP) Solution The most significant observations are: The MCNP vs. measurement comparisons have an average bias of about 260 pcm (MCNP is lower than measurement). The MCNP vs. EPRI-CPM-3 single assembly cases (excluding the Ag-In-Cd control rod cases) have an average bias of about 420 pcm (MCNP is lower than EPRI-CPM-3). These comparisons give an inferred measurement bias for EPRI-CPM-3 of about 160 pcm. The MCNP vs. EPRI-CPM-3 cases for the Ag-In-Cd control rods require more investigation. The MCNP vs. measurement power distributions all have a standard distribution of about 1.4%. 4

5 The MCNP vs. EPRI-CPM-3 single assembly power distributions (excluding the Ag-In-Cd control rod cases) all have a standard distribution of about 0.5%. The MCNP vs. EPRI-CPM-3 single assembly power distributions for the Ag-In-Cd control rod cases have standard distributions of about 1.3%. Benchmark Cases using the Method of Characteristics (MOC) Solution The most significant observations are: The CPM-3 vs. measurement comparisons have an average bias of about 190 pcm. On average, CPM-3 is lower than measurement. The CPM-3 vs. measurement power distributions have standard deviations of 1.2% and 1.4% for fuel without Gd. The CPM-3 vs. measurement power distributions for fuel with Gd are 3.4% and 3.9%. The MOC solutions CPM-3 cases are still being investigated. CONCLUSIONS CPM-3 has been benchmarked to a variety of the critical experiment configurations. These results show good agreement for the central assembly pin power distributions and reactivity. Additional work in progress is an attempt to run the full two dimensional experiments using EPRI-CPM-3 and the full three dimensional experiment using a CPM-3/CORETRAN model. The results from these cases and comparisons to measurement will be provided at the May 7-11, 2000 meeting. ACKNOWLEDGEMENTS The results presented in this paper are a subset of the total benchmarking effort of the CPM-3 benchmarking team. This team led by the authors, consisted of the following individuals and organizations identified below. In addition, the CPM-3 development team consisted of EPRI, the utility sponsors, Utility Resource Associates, TransWare Enterprises and Mark Williams. Steven Baker Public Service Electric & Gas TransWare Enterprises Ronald Furia GPU Nuclear Corp. Keith Dehnbostel Northern States Power Co. David Trace and James Miller Virginia Power Juan Luis Francois Instituto de Investigaciones Electricas Mark Williams Independent Consultant Louisiana State University 5

6 REFERENCES 1 CPM-3 Computer Code Manual, FPR-CPM-001-M-001, Volumes 1 5, July Urania Gadolinia: Nuclear Model Development and Critical Experiment Benchmark, DOE/ET/ , BAW-1810, April

7 The pins that are delineated by the bold line in the figure above represent the center assembly for the power distribution comparisons. Figure 1 Core I Pin Layout 7

8 Figure 2 Core II Pin Layout 8

9 The pins that are delineated by the bold line in the figure above represent the center assembly for the power distribution comparisons. Figure 3 Core V Pin Layout 9

10 Figure 4 Core VI Pin Layout 10

11 The pins that are delineated by the bold line in the figure above represent the center assembly for the power distribution comparisons. Figure 5 Core XII Pin Layout 11

12 Figure 6 Core XIII Pin Layout 12

13 The pins that are delineated by the bold line in the figure above represent the center assembly for the power distribution comparisons. Figure 7 Core XIV Pin Layout 13

14 Figure 8 Core XV Pin Layout 14

15 CORE 1 Problem MCNP CPM3 ρ 3D core ± vs. meas = 1: mcnp vs cpm3 Assembly ± CORE 2 Problem MCNP CPM3 ρ 3D core ± vs. meas = 1: mcnp vs cpm3 Assembly ± CORE 5 Problem MCNP CPM3 ρ 3D core ± vs. meas = 1: mcnp vs cpm3 Assembly ± CORE 6 Problem MCNP CPM3 ρ 3D core ± vs. meas = 1: mcnp vs cpm3 Assembly ± CORE 12 Problem MCNP CPM3 ρ 3D core ± vs. meas = 1: mcnp vs cpm3 Assembly ± CORE 13 Problem MCNP CPM3 ρ 3D core ± vs. meas = 1: mcnp vs cpm3 Assembly ± CORE 14 Problem MCNP CPM3 ρ 3D core ± vs. meas = 1: mcnp vs cpm3 Assembly ± CORE 15 Problem MCNP CPM3 ρ 3D core ± vs. meas = 1: mcnp vs cpm3 Assembly ± Table 1 (1 of 2) Collision Probability Matrix (CP) Reactivity Results 15

16 Average Values ρ 3D core ± MCNP vs measurement (k=1) Assembly ± MCNP vs CPM-3 (all) Assembly ± MCNP vs CPM-3 (no AgInCd) Short Description of Cores: CORE 1: 2.46 w/o fuel with water holes only CORE 2: 2.46 w/o fuel with 16 Ag-In-Cd CORE 5: 2.46 w/o fuel and 28 Gd pins (4 w/o Gd/1.94 w/o U235), with four Gd pins on x- and y-axes CORE 6: 2.46 w/o fuel and 28 Gd pins (matches Core 5) with 16 Ag-In-Cd rods CORE 12: Two enrichments: 4.02 in 31x31 inner zone and 2.46 w/o in the outer zone CORE 13: Two enrichments: 4.02 in 31x31 inner zone and 2.46 w/o in the outer zone with 16 B4C rods CORE 14: Two enrichments: 4.02 and 28 Gd in 31x31 inner zone and 2.46 w/o in the outer zone CORE 15: Two enrichments: 4.02 and 28 Gd in 31x31 inner zone and 2.46 w/o in the outer zone with 16 B4C rods Table 1 (2 of 2) Collision Probability Matrix (CP) Reactivity Results 16

17 Case ID ρ CORE 1 MCNP MOC CPM3 mcnp vs meas cpm3 vs meas mcnp vs cpm ± CORE 2 MCNP MOC CPM3 mcnp vs meas cpm3 vs meas mcnp vs cpm ± CORE 5 MCNP MOC CPM3 mcnp vs meas cpm3 vs meas mcnp vs cpm ± CORE 6 MCNP MOC CPM3 mcnp vs meas cpm3 vs meas mcnp vs cpm ± CORE 12 MCNP MOC CPM3 mcnp vs meas cpm3 vs meas mcnp vs cpm ± CORE 13 MCNP MOC CPM3 mcnp vs meas cpm3 vs meas mcnp vs cpm ± CORE 14 MCNP MOC CPM3 mcnp vs meas cpm3 vs meas mcnp vs cpm ± CORE 15 MCNP MOC CPM3 mcnp vs meas cpm3 vs meas mcnp vs cpm ± Averages ρ ± MCNP vs measurement (k=1) ± CPM-3 vs measurement (k=1) - all ± CPM-3 vs measurement (k=1) - no AgInCd ± MCNP vs CPM-3 (all) ± MCNP vs CPM-3 (no AgInCd) Short Description of Cores: CORE 1: 2.46 w/o fuel with water holes only CORE 2: 2.46 w/o fuel with 16 Ag-In-Cd CORE 5: 2.46 w/o fuel and 28 Gd pins (4 w/o Gd/1.94 w/o U235), with four Gd pins on x- and y-axes CORE 6: 2.46 w/o fuel and 28 Gd pins (matches Core 5) with 16 Ag-In-Cd rods CORE 12: Two enrichments: 4.02 in 31x31 inner zone and 2.46 w/o in the outer zone CORE 13: Two enrichments: 4.02 in 31x31 inner zone and 2.46 w/o in the outer zone with 16 B4C rods CORE 14: Two enrichments: 4.02 and 28 Gd in 31x31 inner zone and 2.46 w/o in the outer zone CORE 15: Two enrichments: 4.02 and 28 Gd in 31x31 inner zone and 2.46 w/o in the outer zone with 16 B4C rods Table 2 Method of Characteristics (MOC) Reactivity Results 17

18 MCNP vs. Measurement for CORE I Using 2D MCNP Detector Water Hole Water Hole Water Hole MCNP (full assembly) Measured MCNP-Measured MCNP Avg MCNP and measured values are Meas Avg from full assembly normalizations Avg Diff Std Dev Min Diff Max Diff The MCNP power distribution above is from the 2D case. The average uncertainty for the MCNP along the horizontal axis is: 1.5% The average uncertainty for the MCNP for the rest of the assembly is: 1.1% Figure 9 (1 of 2) Collision Probability Matrix (CP) Pin Power Distribution Reactivity Results for Core I 18

19 MCNP vs. CPM3 for CORE I Using Single Assembly MCNP Water Hole Water Hole Water Hole Water Hole MCNP (single assy) CPM MCNP-CPM MCNP Avg MCNP values are from a CPM3 Avg full assembly normalization Avg Diff CPM3 values are directly from the Std Dev fission reaction rate distribution edit Min Diff Max Diff The MCNP power distribution above is from the single assembly case. The average uncertainty for the MCNP along the horizontal axis is: 0.4% The average uncertainty for the MCNP for the rest of the assembly is: 0.3% Figure 9 (2 of 2) Collision Probability Matrix (CP) Pin Power Distribution Reactivity Results for Core I 19

20 CPM-3 vs. Measurement for CORE I Using MOC CPM Detector Water Hole Water Hole Water Hole CPM Measured CPM3-Measured CPM3 Avg CPM3 and measured values are Meas Avg from full assembly normalizations Avg Diff Std Dev Min Diff Max Diff Figure 10 Method of Characteristics (MOC) Pin Power Distribution Reactivity Results for Core I 20

21 MCNP vs. Measurement for CORE V Using 2D MCNP Detector Water Hole Water Hole Gd Pin Water Hole MCNP (full assembly) Measured MCNP-Measured MCNP Avg MCNP and measured values are Meas Avg from full assembly normalizations Avg Diff Std Dev Min Diff Max Diff The MCNP power distribution above is from the 2D case. The average uncertainty for the MCNP along the horizontal axis is: 1.8% The average uncertainty for the MCNP for the rest of the assembly is: 1.3% Figure 11 (1 of 2) Collision Probability Matrix (CP) Pin Power Distribution Reactivity Results for Core V 21

22 MCNP vs. CPM3 for CORE V Using Single Assembly MCNP Water Hole Water Hole Water Hole Gd Pin Water Hole MCNP (single assy) CPM MCNP-CPM MCNP Avg MCNP values are from a CPM3 Avg full assembly normalization Avg Diff CPM3 values are directly from the Std Dev fission reaction rate distribution edit Min Diff Max Diff The MCNP power distribution above is from the single assembly case. The average uncertainty for the MCNP along the horizontal axis is: 0.4% The average uncertainty for the MCNP for the rest of the assembly is: 0.3% Figure 11 (2 of 2) Collision Probability Matrix (CP) Pin Power Distribution Reactivity Results for Core V 22

23 CPM-3 vs. Measurement for CORE V Using MOC CPM Detector Water Hole Water Hole Gd Pin Water Hole CPM Measured CPM3-Measured CPM3 Avg CPM3 and measured values are Meas Avg from full assembly normalizations Avg Diff Std Dev Min Diff Max Diff Figure 12 Method of Characteristics (MOC) Pin Power Distribution Reactivity Results for Core V 23

24 MCNP vs. Measurement for CORE XII Using 2D MCNP Detector Water Hole Water Hole Water Hole MCNP (full assembly) Measured MCNP-Measured MCNP Avg MCNP and measured values are Meas Avg from full assembly normalizations Avg Diff Std Dev Min Diff Max Diff The MCNP power distribution above is from the 2D case. The average uncertainty for the MCNP along the horizontal axis is: 1.2% The average uncertainty for the MCNP for the rest of the assembly is: 0.9% Figure 13 (1 of 2) Collision Probability Matrix (CP) Pin Power Distribution Reactivity Results for Core XII 24

25 MCNP vs. CPM3 for CORE XII Using Single Assembly MCNP Water Hole Water Hole Water Hole Water Hole MCNP (single assy) CPM MCNP-CPM MCNP Avg MCNP values are from a CPM3 Avg full assembly normalization Avg Diff CPM3 values are directly from the Std Dev fission reaction rate distribution edit Min Diff Max Diff The MCNP power distribution above is from the single assembly case. The average uncertainty for the MCNP along the horizontal axis is: 0.5% The average uncertainty for the MCNP for the rest of the assembly is: 0.3% Figure 13 (2 of 2) Collision Probability Matrix (CP) Pin Power Distribution Reactivity Results for Core XII 25

26 CPM-3 vs. Measurement for CORE XII Using MOC CPM Detector Water Hole Water Hole Water Hole CPM Measured CPM3-Measured CPM3 Avg CPM3 and measured values are Meas Avg from full assembly normalizations Avg Diff Std Dev Min Diff Max Diff Figure 14 Method of Characteristics (MOC) Pin Power Distribution Reactivity Results for Core XII 26

27 MCNP vs. Measurement for CORE XIV Using 2D MCNP Water Hole Detector Water Hole Water Hole Gd Pin Water Hole MCNP (full assembly) Measured MCNP-Measured MCNP Avg MCNP and measured values are Meas Avg from full assembly normalizations Avg Diff Std Dev Min Diff Max Diff The MCNP power distribution above is from the 2D case. The average uncertainty for the MCNP along the horizontal axis is: 1.4% The average uncertainty for the MCNP for the rest of the assembly is: 1.0% Figure 15 (1 of 2) Collision Probability Matrix (CP) Pin Power Distribution Reactivity Results for Core XIV 27

28 MCNP vs. CPM3 for CORE XIV Using Single Assembly MCNP Water Hole Water Hole Water Hole Gd Pin Water Hole MCNP (single assy) CPM MCNP-CPM MCNP Avg MCNP values are from a CPM3 Avg full assembly normalization Avg Diff CPM3 values are directly from the Std Dev fission reaction rate distribution edit Min Diff Max Diff The MCNP power distribution above is from the single assembly case. The average uncertainty for the MCNP along the horizontal axis is: 0.9% The average uncertainty for the MCNP for the rest of the assembly is: 0.6% Figure 15 (2 of 2) Collision Probability Matrix (CP) Pin Power Distribution Reactivity Results for Core XIV 28

29 CPM-3 vs. Measurement for CORE XIV Using MOC CPM Detector Water Hole Water Hole Gd Pin Water Hole CPM Measured CPM3-Measured CPM3 Avg CPM3 and measured values are Meas Avg from full assembly normalizations Avg Diff Std Dev Min Diff Max Diff Figure 16 Method of Characteristics (MOC) Pin Power Distribution Reactivity Results for Core XIV 29

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