cpm-3 benchmarking to the doe/b&w critical ...cpm-3 in the method of characteristics (moc)...

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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 20850

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/3421-41, BAW-1810, April 1984. 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-31 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 experiments2 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

2.46 w/o in the outer zone core k-effective

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

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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 gBNAT/106 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

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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-kMCNP) ÷ kMCNP. 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.

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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-kMCNP) ÷ kMCNP; 2. between the CPM-3 case and the measurement (assumed to be k=1), ∆ρ = (1-kCPM3) ÷ kCPM3; 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 1.000 for the “full assembly” (i.e., the full 15x15 array of pins) so the “MCNP Avg” and the “Meas Avg” are not exactly 1.000 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 1.000 for the “full assembly” (i.e., the full 15x15 array of pins) so the “MCNP Avg” and the “CPM3 Avg” are not exactly 1.000 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 1.000 for the “full assembly” (i.e., the full 15x15 array of pins) so the “MCNP Avg” and the “Meas Avg” are not exactly 1.000 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%.

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• 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

Keith Dehnbostel Northern States Power Co.

Juan Luis Francois Instituto de Investigaciones Electricas

Ronald Furia GPU Nuclear Corp.

David Trace and James Miller Virginia Power

Mark Williams Independent Consultant Louisiana State University

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REFERENCES

1 CPM-3 Computer Code Manual, FPR-CPM-001-M-001, Volumes 1 – 5, July 1999. 2 “Urania Gadolinia: Nuclear Model Development and Critical Experiment Benchmark,”

DOE/ET/3421-41, BAW-1810, April 1984.

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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

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Figure 2

Core II – Pin Layout

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Figure 3

Core V – Pin Layout

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Figure 4

Core VI – Pin Layout

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Figure 5

Core XII – Pin Layout

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Figure 6

Core XIII – Pin Layout

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Figure 7

Core XIV – Pin Layout

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Figure 8

Core XV – Pin Layout

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CORE 1 Problem MCNP CPM3 ∆ρ3D core 0.99680 ± 0.00067 vs. meas = 1: 0.0032

mcnp vs cpm3Assembly 1.05082 ± 0.00031 1.057260 -0.0058


mcnp vs cpm3Assembly 0.88715 ± 0.00064 0.872011 0.0196




mcnp vs cpm3Assembly 0.81716 ± 0.00063 0.802780 0.0219









Table 1 (1 of 2) Collision Probability Matrix (CP) Reactivity Results

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Average Values

∆ρ3D core 0.0026 ± 0.0009 MCNP vs measurement (k=1)Assembly 0.0008 ± 0.0115 MCNP vs CPM-3 (all)Assembly -0.0058 ± 0.0010 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

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Case ID ∆ρCORE 1 MCNP MOC CPM3 mcnp vs meas cpm3 vs meas mcnp vs cpm3

0.99680 ± 0.00067 0.996651 0.0032 0.0034 0.0001CORE 2 MCNP MOC CPM3 mcnp vs meas cpm3 vs meas mcnp vs cpm3




0.99821 ± 0.00070 1.006369 0.0018 -0.0063 -0.0081CORE 13 MCNP MOC CPM3 mcnp vs meas cpm3 vs meas mcnp vs cpm3



0.99798 ± 0.00066 1.000162 0.0020 -0.0002 -0.0022Averages

∆ρ0.0026 ± 0.0009 MCNP vs measurement (k=1)0.0019 ± 0.0054 CPM-3 vs measurement (k=1) - all-0.0001 ± 0.0046 CPM-3 vs measurement (k=1) - no AgInCd-0.0006 ± 0.0047 MCNP vs CPM-3 (all)-0.0026 ± 0.0038 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

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MCNP vs. Measurement for CORE IUsing 2D MCNP

1.038 1.023 1.004 1.001 0.990 0.955 0.951Detector 1.018 1.011 0.987 0.981 0.997 0.966 0.945

0.020 0.012 0.017 0.020 -0.007 -0.011 0.0061.040 1.070 1.017 1.008 1.055 0.984 0.9431.019 1.067 1.012 1.009 1.058 0.999 0.9450.021 0.003 0.005 -0.001 -0.003 -0.015 -0.002

1.079 1.096 1.058 0.942Water Hole 1.081 1.090 Water Hole 1.032 0.953

-0.002 0.006 0.026 -0.0111.066 1.105 1.075 0.993 0.9301.054 1.104 1.086 0.989 0.9450.012 0.001 -0.011 0.004 -0.015

1.068 0.966 0.931Water Hole 1.059 0.965 0.934

0.009 0.001 -0.0030.974 0.933 0.913

MCNP (full assembly) 0.988 0.938 0.923Measured -0.014 -0.005 -0.010MCNP-Measured 0.918 0.905

0.925 0.914MCNP Avg 0.998 MCNP and measured values are -0.007 -0.009Meas Avg 0.997 from full assembly normalizations. 0.894Avg Diff 0.001 0.903Std Dev 0.011 -0.009Min Diff -0.015Max Diff 0.026

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

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MCNP vs. CPM3 for CORE IUsing Single Assembly MCNP

1.056 0.997 0.975 0.973 0.976 0.957 0.945Water Hole 1.054 0.997 0.973 0.969 0.978 0.960 0.947

0.002 0.000 0.002 0.004 -0.002 -0.003 -0.0021.024 1.054 0.998 1.000 1.040 0.984 0.9521.028 1.049 1.001 1.000 1.038 0.986 0.953-0.004 0.005 -0.003 0.000 0.002 -0.002 -0.001


0.007 0.007 0.001 -0.0031.048 1.093 1.077 0.990 0.9551.050 1.093 1.077 0.995 0.955-0.002 0.000 0.000 -0.005 0.000

1.056 0.973 0.949Water Hole 1.055 0.971 0.948

0.001 0.002 0.0010.988 0.953 0.943

MCNP (single assy) 0.992 0.954 0.943CPM3 -0.004 -0.001 0.000MCNP-CPM3 0.945 0.935

0.943 0.937MCNP Avg 0.997 MCNP values are from a 0.002 -0.002CPM3 Avg 0.997 full assembly normalization. 0.932Avg Diff 0.000 CPM3 values are directly from the 0.937Std Dev 0.003 fission reaction rate distribution edit. -0.005Min Diff -0.005Max Diff 0.007

The MCNP power distribution above is from the single assembly case.


Figure 9 (2 of 2)

Collision Probability Matrix (CP) Pin Power Distribution Reactivity Results for Core I

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CPM-3 vs. Measurement for CORE IUsing MOC CPM-3

1.037 1.025 1.005 1.004 1.000 0.978 0.955Detector 1.018 1.011 0.987 0.981 0.997 0.966 0.945

0.019 0.014 0.018 0.023 0.003 0.012 0.0101.031 1.057 1.026 1.020 1.036 0.989 0.9601.019 1.067 1.012 1.009 1.058 0.999 0.9450.012 -0.010 0.014 0.011 -0.022 -0.010 0.015


-0.010 -0.019 -0.011 0.0111.055 1.076 1.057 0.992 0.9541.054 1.104 1.086 0.989 0.9450.001 -0.028 -0.029 0.003 0.009

1.039 0.972 0.944Water Hole 1.059 0.965 0.934

-0.020 0.007 0.0100.984 0.951 0.929

CPM-3 0.988 0.938 0.923Measured -0.004 0.013 0.006CPM3-Measured 0.930 0.917

0.925 0.914CPM3 Avg 0.999 CPM3 and measured values are 0.005 0.003

Meas Avg 0.997 from full assembly normalizations. 0.903Avg Diff 0.002 0.903Std Dev 0.014 0.000Min Diff -0.029Max Diff 0.023

Figure 10

Method of Characteristics (MOC) Pin Power Distribution Reactivity Results for Core I

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MCNP vs. Measurement for CORE VUsing 2D MCNP

1.057 0.928 0.180 0.931 1.053 1.067 1.071Detector 1.005 0.913 0.170 0.932 1.036 1.063 1.072

0.052 0.015 0.010 -0.001 0.017 0.004 -0.0011.031 1.018 0.942 0.999 1.127 1.099 1.0740.999 1.017 0.931 1.007 1.125 1.094 1.0890.032 0.001 0.011 -0.008 0.002 0.005 -0.015


-0.002 -0.002 -0.007 -0.0130.184 1.065 1.137 1.083 1.0720.181 1.050 1.131 1.088 1.0860.003 0.015 0.006 -0.005 -0.014

1.035 1.029 1.065Gd Pin Water Hole 1.048 1.035 1.070

-0.013 -0.006 -0.0050.190 0.959 1.041

MCNP (full assembly) 0.187 0.963 1.054Measured 0.003 -0.004 -0.013MCNP-Measured 1.008 1.062

1.018 1.060MCNP Avg 0.965 MCNP and measured values are -0.010 0.002Meas Avg 0.963 from full assembly normalizations. 1.068Avg Diff 0.002 1.070Std Dev 0.014 -0.002Min Diff -0.015Max Diff 0.052



Figure 11 (1 of 2)

Collision Probability Matrix (CP) Pin Power Distribution Reactivity Results for Core V

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MCNP vs. CPM3 for CORE VUsing Single Assembly MCNP

1.108 0.957 0.182 0.944 1.053 1.060 1.060Water Hole 1.103 0.961 0.184 0.946 1.054 1.066 1.061

0.005 -0.004 -0.002 -0.002 -0.001 -0.006 -0.0011.071 1.068 0.950 1.025 1.128 1.086 1.0651.071 1.055 0.952 1.026 1.126 1.094 1.0680.000 0.013 -0.002 -0.001 0.002 -0.008 -0.003


0.000 0.009 0.004 0.0040.184 1.061 1.142 1.081 1.0520.187 1.059 1.136 1.084 1.058-0.003 0.002 0.006 -0.003 -0.006

1.040 1.021 1.033Gd Pin Water Hole 1.035 1.020 1.037

0.005 0.001 -0.0040.188 0.937 1.019

MCNP (single assy) 0.189 0.946 1.021CPM3 -0.001 -0.009 -0.002MCNP-CPM3 0.995 1.029

0.997 1.028MCNP Avg 0.966 MCNP values are from a -0.002 0.001CPM3 Avg 0.967 full assembly normalization. 1.035

Avg Diff 0.000 CPM3 values are directly from the 1.039Std Dev 0.005 fission reaction rate distribution edit. -0.004Min Diff -0.009Max Diff 0.013



Figure 11 (2 of 2)

Collision Probability Matrix (CP) Pin Power Distribution Reactivity Results for Core V

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CPM-3 vs. Measurement for CORE VUsing MOC CPM-3

1.048 1.016 0.244 0.937 0.987 1.054 1.079Detector 1.005 0.913 0.170 0.932 1.036 1.063 1.072

0.043 0.103 0.074 0.005 -0.049 -0.009 0.0071.038 1.050 0.989 0.969 1.063 1.073 1.0870.999 1.017 0.931 1.007 1.125 1.094 1.0890.039 0.033 0.058 -0.038 -0.062 -0.021 -0.002


0.015 -0.032 -0.045 -0.0070.256 1.032 1.090 1.078 1.0810.181 1.050 1.131 1.088 1.0860.075 -0.018 -0.041 -0.010 -0.005

1.032 1.038 1.067Gd Pin Water Hole 1.048 1.035 1.070

-0.016 0.003 -0.0030.263 0.986 1.048

CPM-3 0.187 0.963 1.054Measured 0.076 0.023 -0.006CPM3-Measured 1.022 1.053

1.018 1.060CPM3 Avg 0.969 CPM3 and measured values are 0.004 -0.007

Meas Avg 0.963 from full assembly normalizations. 1.057Avg Diff 0.005 1.070Std Dev 0.039 -0.013Min Diff -0.062Max Diff 0.103

Figure 12

Method of Characteristics (MOC) Pin Power Distribution Reactivity Results for Core V

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MCNP vs. Measurement for CORE XIIUsing 2D MCNP

1.104 1.044 1.007 0.992 0.994 0.958 0.921Detector 1.075 1.041 1.006 1.019 1.000 0.960 0.923

0.029 0.003 0.001 -0.027 -0.006 -0.002 -0.0021.099 1.124 1.035 1.023 1.081 0.985 0.9201.067 1.125 1.044 1.034 1.075 0.987 0.9270.032 -0.001 -0.009 -0.011 0.006 -0.002 -0.007


0.034 0.001 0.022 -0.0171.085 1.149 1.095 0.969 0.9121.083 1.137 1.102 0.979 0.9080.002 0.012 -0.007 -0.010 0.004

1.068 0.933 0.879Water Hole 1.071 0.939 0.895

-0.003 -0.006 -0.0160.957 0.912 0.881

MCNP (full assembly) 0.958 0.900 0.883Measured -0.001 0.012 -0.002MCNP-Measured 0.884 0.850

0.884 0.856MCNP Avg 0.998 MCNP and measured values are 0.000 -0.006Meas Avg 0.998 from full assembly normalizations. 0.825Avg Diff 0.000 0.845Std Dev 0.014 -0.020Min Diff -0.027Max Diff 0.034



Figure 13 (1 of 2)

Collision Probability Matrix (CP) Pin Power Distribution Reactivity Results for Core XII

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MCNP vs. CPM3 for CORE XIIUsing Single Assembly MCNP

1.070 0.989 0.963 0.961 0.966 0.954 0.938Water Hole 1.066 0.986 0.963 0.960 0.968 0.951 0.937

0.004 0.003 0.000 0.001 -0.002 0.003 0.0011.022 1.062 0.993 0.990 1.054 0.979 0.9391.028 1.060 0.996 0.998 1.051 0.981 0.943-0.006 0.002 -0.003 -0.008 0.003 -0.002 -0.004


0.003 0.010 0.002 -0.0031.047 1.113 1.102 0.989 0.9441.052 1.110 1.096 0.994 0.947-0.005 0.003 0.006 -0.005 -0.003

1.071 0.959 0.941Water Hole 1.069 0.964 0.939

0.002 -0.005 0.0020.986 0.942 0.936

MCNP (single assy) 0.991 0.945 0.934CPM3 -0.005 -0.003 0.002MCNP-CPM3 0.934 0.934

0.935 0.930MCNP Avg 0.996 MCNP values are from a -0.001 0.004CPM3 Avg 0.996 full assembly normalization. 0.929

Avg Diff 0.000 CPM3 values are directly from the 0.931Std Dev 0.004 fission reaction rate distribution edit. -0.002Min Diff -0.008Max Diff 0.010



Figure 13 (2 of 2)

Collision Probability Matrix (CP) Pin Power Distribution Reactivity Results for Core XII

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CPM-3 vs. Measurement for CORE XIIUsing MOC CPM-3

1.087 1.057 1.029 1.014 1.008 0.965 0.929Detector 1.075 1.041 1.006 1.019 1.000 0.960 0.923

0.012 0.016 0.023 -0.005 0.008 0.005 0.0061.076 1.105 1.051 1.040 1.057 0.985 0.9351.067 1.125 1.044 1.034 1.075 0.987 0.9270.009 -0.020 0.007 0.006 -0.018 -0.002 0.008


0.000 -0.014 -0.005 -0.0031.084 1.111 1.080 0.981 0.9261.083 1.137 1.102 0.979 0.9080.001 -0.026 -0.022 0.002 0.018

1.050 0.952 0.905Water Hole 1.071 0.939 0.895

-0.021 0.013 0.0100.970 0.918 0.885

CPM-3 0.958 0.900 0.883Measured 0.012 0.018 0.002CPM3-Measured 0.888 0.862

0.884 0.856CPM3 Avg 0.999 CPM3 and measured values are 0.004 0.006


Figure 14

Method of Characteristics (MOC) Pin Power Distribution Reactivity Results for Core XII

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MCNP vs. Measurement for CORE XIVUsing 2D MCNPWater Hole

1.110 0.984 0.180 0.974 1.056 1.017 1.019Detector 1.091 0.992 0.162 0.976 1.057 1.038 1.028

0.019 -0.008 0.018 -0.002 -0.001 -0.021 -0.0091.079 1.116 0.991 1.048 1.143 1.072 1.0281.080 1.118 1.000 1.054 1.158 1.091 1.028-0.001 -0.002 -0.009 -0.006 -0.015 -0.019 0.000


0.017 0.008 0.011 -0.0180.185 1.110 1.175 1.066 1.0140.164 1.114 1.151 1.059 1.0130.021 -0.004 0.024 0.007 0.001

1.090 1.002 0.990Gd Pin Water Hole 1.080 1.011 1.003

0.010 -0.009 -0.0130.179 0.940 0.972

MCNP (full assembly) 0.162 0.942 0.976Measured 0.017 -0.002 -0.004MCNP-Measured 0.987 0.971

0.965 0.978MCNP Avg 0.965 MCNP and measured values are 0.022 -0.007Meas Avg 0.964 from full assembly normalizations. 0.965Avg Diff 0.001 0.959Std Dev 0.013 0.006Min Diff -0.021Max Diff 0.024



Figure 15 (1 of 2)

Collision Probability Matrix (CP) Pin Power Distribution Reactivity Results for Core XIV

28

MCNP vs. CPM3 for CORE XIVUsing Single Assembly MCNP

1.115 0.974 0.177 0.960 1.045 1.034 1.010Water Hole 1.110 0.971 0.184 0.951 1.026 1.024 1.015

0.005 0.003 -0.007 0.009 0.019 0.010 -0.0051.072 1.093 0.969 1.027 1.129 1.067 1.0261.067 1.077 0.973 1.026 1.120 1.058 1.0220.005 0.016 -0.004 0.001 0.009 0.009 0.004


0.007 0.006 0.012 0.0080.179 1.108 1.161 1.069 1.0280.187 1.100 1.151 1.061 1.020-0.008 0.008 0.010 0.008 0.008

1.087 1.019 1.011Gd Pin Water Hole 1.067 1.004 1.005

0.020 0.015 0.0060.182 0.957 1.008

MCNP (single assy) 0.188 0.946 0.993CPM3 -0.006 0.011 0.015MCNP-CPM3 0.991 1.009

0.977 0.995MCNP Avg 0.965 MCNP values are from a 0.014 0.014CPM3 Avg 0.958 full assembly normalization. 1.013

Avg Diff 0.007 CPM3 values are directly from the 1.003Std Dev 0.007 fission reaction rate distribution edit. 0.010Min Diff -0.008Max Diff 0.020



Figure 15 (2 of 2)

Collision Probability Matrix (CP) Pin Power Distribution Reactivity Results for Core XIV

29

CPM-3 vs. Measurement for CORE XIVUsing MOC CPM-3

1.112 1.070 0.241 0.998 1.013 1.031 1.025Detector 1.091 0.992 0.162 0.976 1.057 1.038 1.028

0.021 0.078 0.079 0.022 -0.044 -0.007 -0.0031.099 1.120 1.045 1.021 1.094 1.058 1.0341.080 1.118 1.000 1.054 1.158 1.091 1.0280.019 0.002 0.045 -0.033 -0.064 -0.033 0.006


0.013 -0.023 -0.030 0.0020.241 1.100 1.126 1.057 1.0260.164 1.114 1.151 1.059 1.0130.077 -0.014 -0.025 -0.002 0.013

1.068 1.014 1.001Gd Pin Water Hole 1.080 1.011 1.003

-0.012 0.003 -0.0020.237 0.953 0.977

CPM-3 0.162 0.942 0.976Measured 0.075 0.011 0.001CPM3-Measured 0.962 0.966

0.965 0.978CPM3 Avg 0.968 CPM3 and measured values are -0.003 -0.012


Figure 16

Method of Characteristics (MOC) Pin Power Distribution Reactivity Results for Core XIV

cpm-3 benchmarking to the doe/b&w critical ...cpm-3 in the method of characteristics (moc)...

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