Testing the EPRI Reactivity Depletion Decrement Uncertainty Methods

Transcription

1 Testing the EPRI Reactivity Depletion Decrement Uncertainty Methods by Elliot M. Sykora B.S. Physics, Massachusetts Institute of Technology (0) Submitted to the Department of Nuclear Science and Engineering in partial fulfillment of the requirements for the degree of Master of Science in Nuclear Science and Engineering at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY September 05 c Massachusetts Institute of Technology 05. All rights reserved. Author... Department of Nuclear Science and Engineering August, 05 Certified by... Kord Smith KEPCO Professor of the Practice of Nuclear Science and Engineering Thesis Supervisor Certified by... Benoit Forget Professor of Nuclear Science and Engineering Thesis Reader Accepted by... Chair, Department Committee on Graduate Students

2

3 Testing the EPRI Reactivity Depletion Decrement Uncertainty Methods by Elliot M. Sykora Submitted to the Department of Nuclear Science and Engineering on August, 05, in partial fulfillment of the requirements for the degree of Master of Science in Nuclear Science and Engineering. Abstract An EPRI study[], published in 0, used measured flux map data (taken over operational cycles of the Catawba and McGuire nuclear power plants) to determine fuel assembly reactivity decrements versus burnup. The analytical techniques used to infer measured assembly reactivities required perturbation calculations using D nodal diffusion core models. Subsequently, questions have arisen within the Nuclear Regulatory Commission (NRC) as to potential uncertainties in measured assembly reactivity decrements that might have arisen from approximations of the -group nodal methods and perturbation techniques employed. Subsequently, Gunow[] used full-core, multi-group, neutron transport models to replace the nodal diffusion core models, and he demonstrated that measured reactivity decrements were independent of the core model. In this thesis, two cycles of the BEAVRS PWR reactor benchmark are used to test the EPRI methodology, now including testing of not only the nodal core diffusion model, but also the perturbation technique itself. By changing the perturbation technique from assembly reactivity to assembly-average fuel temperature, it is demonstrated that measured reactivity decrements are almost independent of the perturbation technique - with a level of precision greater then the 50 pcm reactivity decrement uncertainty assigned in the EPRI study. These new results demonstrate that the reactivity decrements and uncertainties derived by nodal diffusion and burnup perturbation in the original EPRI study hold up to further scrutiny, and they remain credible for licensing application of burnup credit in Spent Fuel Pool (SFP) criticality analysis. Thesis Supervisor: Kord Smith Title: KEPCO Professor of the Practice of Nuclear Science and Engineering Thesis Reader: Benoit Forget Title: Professor of Nuclear Science and Engineering

4 Acknowledgments I would like to express my gratitude to my research advisor Professor Kord Smith for the useful comments, remarks and engagement through the learning process of this master s thesis. Furthermore, I would like to thank Professor Benoit Forget for his support throughout this project and for introducing me to the topic. Also, I would like to thank Geoff Gunow for providing assistance in building the SIMULATE- and CASMO-5 models. This work was supported by the Electric Power Research Institute.

5 Contents Introduction 6 Background 8. Description of Method of Characteristics Description of Nodal Methods Methods and Measurement Data. Descriptions of Full Core Modeling BEAVRS Benchmark Cycle Cycle Generating Tilt Corrected Data Setup of the Gap Test Standard Model Considerations HFP Approximations & Influence on Results CASMO-5 MxN Considerations Methods to Infer Reactivity Decrement Uncertainties Tilt Correction, Gap Test, and Early Cycle Results. Results of Tilt Corrected Data Gap Test Results Magnitude of Simulated Tilt HZP Comparisons to Calculations HFP Results Standard Model HFP Results HFP results Cycle HFP results Cycle

6 6 Inferring Reactivity Decrements Results Reporting Results in Reactivity Perturbing Sub-batch Burnup in SIMULATE- and CASMO-5 MxN Cycle Results Cycle Results Perturbing Burnup vs Fuel Temperatures in CASMO-5 MxN Cycle Results Cycle Results Summary of Calculated Reactivity Decrements Summary Conclusions Future Work References 88 8 Appendix Detailed Maps of the Full Cycle Depletion Points CASMO-5 MxN Cycle CASMO-5 MxN Cycle SIMULATE- D Cycle SIMULATE- D Cycle

7 List of Figures. The picture on the left shows the unique material regions in an assembly such as fuel, cladding, and coolant. The picture on the right shows how these regions are discretized into source regions. [] SIMULATE- radial discretization for the quarter core model. There are four nodes per assembly. [] BEAVRS Cycle layout of fuel assemblies showing the assembly enrichment distribution by color and the burnable poison locations by number. [] Scale view of burnable poison pins in cycle. [] BEAVRS Cycle fresh fuel enrichment locations shown in color, burnable poison positions in the fresh fuel are labeled by number, and the once burned shuffled assemblies are labeled by their cycle locations. [] 8. CASMO-5 MxN HZP minus BEAVRS Data. RMS is Full power points (above 80% power) used in cycle depletion. The List of full power points here (in GWd/T) are 0.88,.0,.5,.6,.0,.6, 6.9, 7.5, 8.70, 9.80,.08,.,.9. We do not use the 9.80 GWd/T data because the measurement occurred when the reactor was at full power for a very brief period Full power points used in cycle depletion. The list of full power points here (in GWd/T) are.,.,.,.0,.0, 5., 6.5, 7.7, 8.7, 9.6, Reactivity of an assembly with.% enriched fuel and burnable poisons as a function of burnup exposure reactivity coefficient of an assembly with.% enriched fuel and burnable poisons as a function of burnup The temperature reactivity coefficient of an assembly with.% enriched fuel and burnable poisons as a function of temperature at a beginning, middle, and end of cycle statepoint

8 . Planar peripheral assembly fractional tilt of measured fission rates for cycle. Positive tilt in the x direction means that the measurements were higher on the east side of the core. Positive tilt in the y direction means that the measurements were higher on the south side of the core.. Planar peripheral assembly fractional tilt of measured fission rates for cycle. Positive tilt in the x direction means that the measurements were higher on the east side of the core. Positive tilt in the y direction means that the measurements were higher on the south side of the core. Cycle has a very small tilt at BOC and it too goes away with depletion. Early Cycle displays the only truly significant tilts..... HZP CASMO-5 MxN with a 0.5 cm southeast gap minus no gap shows the distribution of tilt. The top number shows the fission rates of the gap case. The next line shows the fractional difference of the gap minus no gap case CASMO-5 MxN HZP minus BEAVRS Data. RMS is CASMO-5 MxN HZP minus tilt corrected data. RMS is CASMO-5 MxN HZP Manual Baffle with a 0.5cm Gap minus BEAVRS Data. RMS is CASMO-5 MxN HFP.0 GWd/T Manual Baffle with No Gap minus BEAVRS Data. RMS is CASMO-5 MxN HFP.0 GWd/T with a 0.5 cm southeast gap minus no gap shows the distribution of tilt. The top number shows the fission rates of the gap case. The next line shows the fractional difference of the gap minus no gap case CASMO-5 MxN HFP.0 GWd/T Manual Baffle with 0.5 cm gap minus BEAVRS Data. RMS is CASMO-5 MxN HFP.6 GWd/T Manual Baffle with No Gap minus BEAVRS Data. RMS is

9 . CASMO-5 MxN HFP.6 GWd/T with a 0.5 cm southeast gap minus no gap shows the distribution of tilt. The top number shows the fission rates of the gap case. The next line shows the fractional difference of the gap minus no gap case CASMO-5 MxN HFP.6 GWd/T Manual Baffle with 0.5 cm gap minus BEAVRS Data. RMS is CASMO-5 MxN HFP. GWd/T Manual Baffle with No Gap minus BEAVRS Data. RMS is CASMO-5 MxN HFP. GWd/T with a 0.5 cm southeast gap minus no gap shows the distribution of tilt. The top number shows the fission rates of the gap case. The next line shows the fractional difference of the gap minus no gap case CASMO-5 MxN HFP. GWd/T Manual Baffle with 0.5 cm gap minus BEAVRS Data. RMS is Normalized fission rate RMS error of CASMO-5 MxN and SIMULATE- D vs BEAVRS data and tilt corrected data in cycle. Data is folded into an octant Normalized fission rate RMS error of SIMULATE- D and SIMULATE- D vs BEAVRS data and tilt corrected data in cycle. Data is folded into an octant Normalized fission rate RMS error of CASMO-5 MxN and SIMULATE- D vs BEAVRS data and tilt corrected data in cycle. Data is folded to quarter core Normalized fission rate RMS error of SIMULATE- D and SIMULATE- D vs BEAVRS data and tilt corrected data in cycle. Data is folded to quarter core

10 6. RMS difference of CASMO-5 MxN compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle. The sub-batch reactivity was perturbed via changing the sub-batch exposure as shown on the x-axis. The circle represents the initial unperturbed point RMS difference of CASMO-5 MxN compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle. The sub-batch reactivity was perturbed via changing the sub-batch fuel temperature as shown on the x-axis RMS difference of CASMO-5 MxN compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle. The sub-batch reactivity (represented in pcm) was perturbed via changing the sub-batch fuel temperature in three cases and via changing the sub-batch exposure in three cases RMS difference of CASMO-5 MxN and SIMULATE- compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle. The sub-batch reactivity (represented in pcm) was perturbed via changing the sub-batch exposure RMS difference of CASMO-5 MxN and SIMULATE- compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle. The sub-batch reactivity (represented in pcm) was perturbed via changing the sub-batch exposure RMS difference of CASMO-5 MxN and SIMULATE- compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle while starting from the optimal perturbation point of the.% enriched subbatch. The sub-batch reactivity (represented in pcm) was perturbed via changing the sub-batch exposure

11 6.7 RMS difference of CASMO-5 MxN and SIMULATE- compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle. The sub-batch reactivity (represented in pcm) was perturbed via changing the sub-batch exposure RMS difference of CASMO-5 MxN and SIMULATE- compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle. The sub-batch reactivity (represented in pcm) was perturbed via changing the sub-batch exposure RMS difference of CASMO-5 MxN and SIMULATE- compared to BEAVRS data for the fresh,.% and.% enriched, fuel sub-batch in Cycle. The sub-batch reactivity (represented in pcm) was perturbed via changing the sub-batch exposure RMS difference of CASMO-5 MxN compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle. The sub-batch reactivity (represented in pcm) was perturbed via changing the sub-batch fuel temperature in three cases and via changing the sub-batch exposure in three cases RMS difference of CASMO-5 MxN compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle. The sub-batch reactivity (represented in pcm) was perturbed via changing the sub-batch fuel temperature in three cases and via changing the sub-batch exposure in three cases RMS difference of CASMO-5 MxN compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle while starting from the optimal perturbation point of the.% enriched sub-batch. The subbatch reactivity (represented in pcm) was perturbed via changing the sub-batch fuel temperature in three cases and via changing the subbatch exposure in three cases

12 6. RMS difference of CASMO-5 MxN compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle. The sub-batch reactivity (represented in pcm) was perturbed via changing the sub-batch fuel temperature in three cases and via changing the sub-batch exposure in three cases RMS difference of CASMO-5 MxN compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle. The sub-batch reactivity (represented in pcm) was perturbed via changing the sub-batch fuel temperature in three cases and via changing the sub-batch exposure in three cases RMS difference of CASMO-5 MxN compared to BEAVRS data for the fresh,.% and.% enriched, fuel sub-batch in Cycle. The subbatch reactivity (represented in pcm) was perturbed via changing the sub-batch fuel temperature in three cases and via changing the subbatch exposure in three cases The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at.0 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at.5 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at.6 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at.0 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at.6 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at 6.9 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at 7.5 GWd/T exposure in Cycle. The RMS difference is

13 8.8 The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at 8.70 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at.08 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at. GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at. GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at. GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at.0 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at.0 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at 5. GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at 6.5 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at 7.7 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at 8.7 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at 9.6 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at 0. GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of SIMULATE- D compared to BEAVRS data at.0 GWd/T exposure in Cycle. The RMS difference is

14 8. The difference in fission rates of SIMULATE- D compared to BEAVRS data at.5 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of SIMULATE- D compared to BEAVRS data at.6 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of SIMULATE- D compared to BEAVRS data at.0 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of SIMULATE- D compared to BEAVRS data at.6 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of SIMULATE- D compared to BEAVRS data at 6.9 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of SIMULATE- D compared to BEAVRS data at 7.5 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of SIMULATE- D compared to BEAVRS data at 8.70 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of SIMULATE- D compared to BEAVRS data at.08 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of SIMULATE- D compared to BEAVRS data at. GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of SIMULATE- D compared to BEAVRS data at. GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of SIMULATE- D compared to BEAVRS data at. GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of SIMULATE- D compared to BEAVRS data at.0 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of SIMULATE- D compared to BEAVRS data at.0 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of SIMULATE- D compared to BEAVRS data at 5. GWd/T exposure in Cycle. The RMS difference is 0.08.

15 8.6 The difference in fission rates of SIMULATE- D compared to BEAVRS data at 6.5 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of SIMULATE- D compared to BEAVRS data at 7.7 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of SIMULATE- D compared to BEAVRS data at 8.7 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of SIMULATE- D compared to BEAVRS data at 9.6 GWd/T exposure in Cycle. The RMS difference is The difference in fission rates of SIMULATE- D compared to BEAVRS data at 0. GWd/T exposure in Cycle. The RMS difference is 0.0.8

16 List of Tables. Variables in the neutron transport equation CASMO-5 MxN Simulation Parameters Summary Table of exposure reactivity coefficients and temperature reactivity coefficients Inferred Fuel Batch Reactivity Bias by perturbing sub-batch burnup in SIMULATE- and sub-batch burnup and fuel temperature in CASMO- 5 MxN. The differences in the biases inferred by the two methods is shown in the far right columns

17 Introduction The storage of spent nuclear fuel is an important issue in the nuclear industry. Since no long term storage solution has been approved in the United States, the utilities must continue to safely use spent fuel pools (SFP) and dry casks for storage. Criticality analyses of these storage methods rely on lattice physics codes to accurately predict nuclide inventories in each spent fuel assembly. Current procedures for defining the uncertainty in these calculations follow the NRC Kopp Memo which directs analysts to add 5% of the calculated reactivity decrement to compensate for depletion uncertainties.[] The technical basis for the Kopp Memo was simply engineering judgment of the SFP criticality analyses. Given the improvements in methods used in SFP criticality analysis, a firm technical basis for the Kopp Memo criteria is desired by the NRC. Doing so will help maintain the desired safety margin while not being unnecessarily conservative. An unnecessarily conservative safety margin will increase spent fuel storage costs, making nuclear power less competitive without improving safety. In 0, EPRI sponsored a study focused on experimental quantification of PWR fuel reactivity burnup decrement uncertainties. The reactivity decrement is defined as the difference between the fuel assembly k-infinity at zero burnup and the k-infinity at the calculated exposure point. The study used the Studsvik Core Management System (CMS) suite to simulate core behavior, and used measured data from PWR operating cycles from Catawba and McGuire nuclear power plants.[] The EPRI study used nodal methods (SIMULATE-) to analyze the reactivity decrement biases, but inherent assumptions in nodal methods may introduce biases and uncertainties. Gunow s thesis [] quantified the bias introduced by nodal methods by comparing reactivity decrements derived with nodal methods to multi-group transport methods, which have far fewer assumptions. Specifically, he used a method of characteristics (MOC) solver to solve the neutron transport equation. He approximated reactivity decrement biases by perturbing fuel sub-batch reactivities by changing the exposure of all assemblies in a sub-batch. [] Gunow s study modeled the BEAVRS PWR 6

18 and used in-core flux map data to compare the reactivity decrements inferred with different core simulation tools. To strengthen the confidence in these results, Gunow suggested three follow-on tasks: ) Improving thermal hydraulic modeling is needed in a full core MOC solver. ) Comparing D nodal and transport methods. ) Investigating different methods for perturbing sub-batch reactivity. The Studsvik MOC solver does not have thermal hydraulic feedback and D transport methods are still too computationally cumbersome. The main goal of this study is to approximate reactivity decrement biases by perturbing fuel sub-batch reactivities using fuel temperature. This method of approximating reactivity decrement biases would provide evidence that biases are independent of the perturbation method. This study will supplement the EPRI work by using different methods to test results and assumptions. The relationship between fuel temperature and reactivity is found to be even more stable than that of fuel burnup and reactivity particularly at the beginning of the cycle because burnable poison depletion competes with fuel depletion when burnup perturbation was employed. Additionally, this study will investigate the tilt observed in the measured data in order to better understand its cause and improve comparison to simulations. The BEAVRS data is not symmetric which is probably caused by some asymmetry in reactor fabrication or loading of the fuel assemblies. The asymmetry in the data cannot be explained by neutron detector uncertainties alone. A new mechanism will be proposed which simulates one potential cause of the tilt in the theoretically symmetric reactor. The preliminary work in this thesis is needed to independently verify Gunow s reactivity decrement biases that were based on perturbing the exposure of sub-batches. 7

19 Background As in the EPRI study, the Studsvik CMS codes were used for simulation.[] In order to understand how the core simulations are performed, we need to understand the various methods used in the Studsvik CMS codes used in this study. The Studsvik CMS codes used were SIMULATE-, CMSLINK, CASMO-5 and its extension to full core D modeling, CASMO-5 MxN. CASMO-5 is a lattice depletion code based on MOC, SIMULATE- is a nodal code, and CMSLINK is a linking code that takes CASMO-5 data and constructs a cross section library for SIMULATE-. Section. contains a brief description of the method of characteristics (MOC) while Section. describes nodal diffusion methods. A more detailed explanation of MOC and nodal methods can be found in Gunow s thesis.[]. Description of Method of Characteristics The method of characteristics is a method of solving partial differential equations. Specifically we want to apply it to the neutron transport equation which is described in Eq... ~ r (~r, ~,E)+ T (~r, E ) (~r, ~,E)= Z 0 de 0 Z =+ (~r, E ) k eff d ~ 0 S (~r, ~ 0! ~,E 0! E) (~r, ~ 0,E 0 ) Z 0 Z de 0 F (~r, E 0 ) d ~ 0 (~r, ~ 0,E 0 ) (.) 8

20 Variable Description ~r Spatial position vector ~ Angular direction vector E Neutron Energy Angular neutron flux k eff Effective neutron multiplication factor T Neutron total cross section S Neutron scattering cross section F Neutron fission cross section Energy spectrum of neutrons from fission Number of neutrons per fission Table.: Variables in the neutron transport equation. This equation assumes that there is an isotropic distribution of emitted fission neutrons and that there are no neutron-neutron collisions. The equation is stated for continuous cross section, however, for the MOC calculation used in CASMO-5, one needs to use discrete multi-group cross sections. To collapse continuous energy cross sections to group cross sections, one must specify the energy interval for each neutron energy group. Then we can calculate the average cross section over each energy interval weighted by the neutron scalar flux in order to preserve reaction rates. MOC is an iterative method that tracks angular flux in discrete directions over the entire domain. These tracks cover the entire geometry that is sub-divided into source regions. The neutron source, composed of in-scattering and fission, is assumed to have a certain shape in a source region, such as a flat spatial distribution. Each track segment contained in a source region contributes to that region s scalar flux. MOC needs very fine spacing and a large number of angles to cover the geometry with adenseangulardistributionandafineenoughmeshofneutronsourcestoaccount for the flux gradients. Figure. shows how the unique materials in an assembly are finely discretized into source regions. 9

21 Figure.: The picture on the left shows the unique material regions in an assembly such as fuel, cladding, and coolant. The picture on the right shows how these regions are discretized into source regions. []. Description of Nodal Methods Nodal diffusion methods are a significant simplification of the neutron transport methods. However, they can have high accuracy and computational efficiency when consistently formulated. Nodal methods avoid the explicit modeling of heterogeneous regions by treating large nodes, such as a radial plane of an assembly, as a homogeneous region. These methods assume that the angular distribution of neutrons are at most linearly anisotropic, which may not accurately describe angular distributions that are near high absorbing or scattering regions. However, an equivalent diffusion theory parameter, such as an assembly discontinuity factor (ADF), can be computed for each homogeneous region that approximately captures the effect of the truly heterogeneous geometry. Nodal methods solve the D diffusion equation by transverse integrating over two directions, thus leaving a set of coupled D diffusion equations. Higher-order or even 0

22 analytical spatial solutions are then used to solve each D diffusion equation. With approximations to capture the effects of xenon, fuel temperature, and cross sections between nodes, the coupled D equations can be solved accurately. Nodal methods reduce the runtimes of a full core depletion by orders of magnitudes, but this method also introduces new assumptions. The nodal method relies on -group cross section data which may not describe neutronic behavior as accurately as a full-core multi-group MOC calculation and must be generated by numerous D lattice calculations using an MOC code. The nodal method also uses a coarse radial discretization, with one node per quarter assembly shown in Figure.. This study evaluates the uncertainty on fuel assembly reactivity introduced by nodal methods as compared to the full-core multi-group MOC transport method calculations.

23 Figure.: SIMULATE- radial discretization for the quarter core model. There are four nodes per assembly. []

24 Methods and Measurement Data. Descriptions of Full Core Modeling Two models are used to calculate full core depletions: the nodal method and the D MOC transport method. In this study, SIMULATE- is used as the nodal diffusion code, and CASMO5 MxN as the full core MOC code. Each code can produce simulated fission rates that can be compared to measured data. The root-mean-square (RMS) error of the fractional difference of simulated fission rates to measured fission rates is used to summarize the accuracy of the model at a given statepoint. This is needed to infer reactivity decrement bias by searching for assembly reactivity changes that produce best agreement between measured and computed fission rates. First, a standard library of a multi-group cross sections needs to be computed. Nuclear data for use in CASMO-5 is collected from ENDF-B/VII data and contains microscopic cross sections in 586 energy groups that are functions of material temperature and background cross sections. CASMO-5 calculations condense the cross sections to a few groups. Next, the neutron transport problem is solved for each unique assembly using the few group cross sections using the D method of characteristics (MOC). In this case, the group structure has 9 energy groups ranging from 0 5 ev to 0 MeV. This range covers a few groups for fast neutrons, and a significant number of groups in the resonance region and thermal region. Each unique assembly is simulated at various reactor conditions by varying fuel temperature, moderator temperature, and boron concentration. Unique assemblies are also modeled with a baffle and barrel present to produce radial and axial reflector data. This yields accurate two-group cross sections with assembly discontinuity factors (ADFs) that are used by SIMULATE- to solve the full-core simulation. CASMO-5 MxN takes orders of magnitude longer to solve the problem, but does so with many fewer assumptions than the nodal method. This MOC solver eliminates the diffusion approximation and it has increased spatial resolution and increased energy resolution. The spatial resolution is increased by or orders of magnitude from

25 SIMULATE- and the energy resolution is increased from groups to 5 groups. Since CASMO-5 MxN does not have thermal hydraulic feedback, the thermal hydraulic behavior is extracted from nodal results and input into CASMO-5 MxN cases for a more realistic comparison. These steps were followed to produce SIMULATE- D results: Run CASMO-5 with the SC edit for each unique assembly in order to create two group cross sections and ADFs. Use the library created from CASMO-5 for a SIMULATE- D calculation. For cycle, use the core axial buckling terms produced in the D calculation for a SIMULATE- D calculation. For cycle, the average core axial buckling term (as a function of core-averaged burnup) from cycle is mapped onto individual assembly burnups to produce local assembly bucklings for a SIMULATE- D calculation. These steps were followed to produce CASMO-5 MxN results: Extract axially collapsed fuel and moderator temperature maps at every statepoint produced by the SIMULATE- D calculation and place them into the CASMO-5 MxN input file. The D results produce the most accurate temperature maps. For cycle, compute the average core axial buckling term produced in the SIMULATE- D calculation and place this into the CASMO MxN input file. For cycle, the average core axial buckling term (as a function of core-averaged burnup) from cycle is mapped onto individual assembly burnups to produce local assembly bucklings for a CASMO-5 MxN calculation.

26 . BEAVRS Benchmark Any full core model needs to be compared to a detailed and relevant benchmark to validate its methods. The results of various CASMO-5 MxN and SIMULATE- simulations are compared against the BEAVRS benchmark to evaluate errors caused by underlying assumptions in each program/method. This benchmark specifies the radial geometry of each pin type used throughout the core. It also specifies the configuration of these pin within an assembly, including various configurations of burnable absorbers. On an assembly level, the benchmark describes the locations of the various enriched assemblies, the locations of the instrument tubes and control rod banks. Finally, the dimensions of the baffle, core barrel, and neutron shield pads, as well as, all the material properties are specified in the benchmark. Parameters that can change from cycle to cycle are discussed in this section. The benchmark has measured fission rates from 5 U fission chambers from two operating cycles of a PWR. The axial distribution of computed fission rates is axially integrated into a D radial fission rate map to compare with the measured data in each cycle. Since the measured fission rates are only known at the assemblies with an instrument tube (58 locations), the simulated fission rates are renormalized to match the sum of the 58 measured signals at these locations... Cycle Cycle of the BEAVRS benchmark begins with all fresh fuel with enrichments of.6%,.%, and.% 5 U fuel (by weight). The initial isotopic distribution is known with high confidence because it is specified in the manufacturing of the fuel. Notice in Figure. that the sub-batches of enriched assemblies are octant symmetric. Other than the instrument tubes, the core is octant symmetric. These few instrument tubes will not change the fission rate distribution significantly.[] Since the core is loaded octant symmetric, cycle can be calculated in quarter core with either rotation or reflected boundary conditions. 5

27 The burnable poisons are made of borosilicate glass (pyrex).5% B O and are inserted into octant symmetric guide tube locations. Fig.. shows the enrichment distribution and the number of burnable poisons in each assembly. Fig.. shows the scale view of the burnable poison rods. This figure shows how the assemblies are rotated to be octant symmetric with respect to the burnable poisons. Figure.: BEAVRS Cycle layout of fuel assemblies showing the assembly enrichment distribution by color and the burnable poison locations by number. [] 6

28 Figure.: Scale view of burnable poison pins in cycle. [].. Cycle The.% and.% enriched fuel from cycle one (once burned) is shuffled in different positions as shown in Fig... Only one.6% enriched assembly from cycle is kept and placed at the core center. The poison pins are removed from the once-burned fuel from cycle feed fuel. The.% and.% enriched fresh fuel are placed throughout the core, also shown in Fig... All of the sub-batches of enriched assemblies in the cycle map are quarter core symmetric. However, it is not fully quarter core 7

29 symmetric because the center assembly came from an outside location which will give it an unsymmetrical burnup distribution. More importantly, the cycle core is no longer octant symmetric. If octant symmetric, one could use reflective boundary conditions to simulate in quarter core. Given this lack of octant symmetry, one must run cycle depletions in full core. Figure.: BEAVRS Cycle fresh fuel enrichment locations shown in color, burnable poison positions in the fresh fuel are labeled by number, and the once burned shuffled assemblies are labeled by their cycle locations. [] 8

30 . Generating Tilt Corrected Data The BEAVRS measured data is not symmetric as shown in the HZP case in Figure.. The simulated fission rates are much higher than the measured fission rates in the NW corner and are much lower in the SE corner. These data are expected to be nearly symmetric since the core is constructed as such. There may be some asymmetry in the real reactor or uncertainties in the detector measurements. The simulated measurements on the other hand will always be symmetric since the model is symmetric. Some of the differences between calculated and measured fission rates can be removed by averaging, or folding rotationally symmetric assemblies. While this method produces symmetric data, it ignores the cause of errors. This section discusses what the asymmetry looks like and the following section discusses possible reasons why the asymmetry exists. 9

31 Detector Fission Rate Fractional Difference # Symmetry Positions Figure.: CASMO-5 MxN HZP minus BEAVRS Data. RMS is A tilt in the data is observed leading to high RMS errors. Since we are not sure what phenomenon in the reactor is causing the tilt, we want to remove it from the data so that we can compare how accurate our simulations are to a theoretically symmetric reactor. In order to better evaluate the performance of the simulations, any errors introduced by this asymmetry or tilt should be eliminated. We correct the measured fission rates assuming deviations that take the form of a pure linear tilt. We need 0

32 to find a linear tilt such that the x-y tilt coefficients minimize the measured fission rate deviations from a pure linear tilt. This corresponds to fitting a best fit plane adjustment of the measured data. We use detector signals at symmetric locations to deduce the orientation of the plane of tilt that minimizes deviations (RMS error) of the symmetric detector fission rates relative to the plane. Then we create a new data set called tilt corrected data that is the measured data made symmetric by removing the tilt of the best fit plane. This new set of measured data will have been filtered by a planar linear tilt and produce a much more symmetric distribution. We want to compare all of our simulations with this new symmetric data set. This is a systematic means to interpret what the fission rate map would look like without any tilt in the data. This shows that much of the uncertainties are not coming from the simulations. Some uncertainty might be coming from the fact the the reactor has slightly different conditions than specified in the reactor plans.. Setup of the Gap Test The tilt in the data from a real world reactor could be coming from a variety of sources when building a real reactor. To test a possible core configuration that could be causing a tilt in the measured data, a 0.5cm water gap is modeled in between the fuel assemblies and the baffle in the southeast corner of the core. This is a possible situation that may occur when loading the fuel from the northwest corner into the southeast corner. The assemblies may not sit flush on the baffle and there will be extra space somewhere between the assemblies or between the assemblies and the baffle to allow for thermal expansion and swelling of the assemblies. We might expect that the tilt will be the highest at the beginning of the cycle and it decreases as the assemblies swell and fill in the gap between the baffle wall. The test was performed using CASMO-5 MxN. This code will not allow the user to place a gap between the assembly and the automatically-generated baffle. So, a manual baffle was created by adding the extra water gap to the baffle model. With the correct density adjustments, these regions replicate a steel baffle with a specified

33 amount of water gap. CASMO-5 MxN had to be run in full core because this added gap eliminated the model symmetry..5 Standard Model Considerations.5. HFP Approximations & Influence on Results There are a number of approximations made in the HFP model for both SIMULATE- and CASMO-5 MxN. Each approximation contributes to a small increase in the RMS error versus the measured data. We are forced to make most of these approximations because of the limitations of the code or computational power and the assumptions are discussed below. All of the influences of these assumptions, with the exception of the thermal expansion approximation used in SIMULATE-, are discussed in Gunow s thesis. The assumptions are stated here for completeness. Thermal Hydraulic Feedback Thermal hydraulic feedback is important, but it is not implemented in full core CASMO-5 MxN. However, SIMULATE- has a thermal hydraulic feedback model. A full cycle depletion in SIMULATE- is used to obtain the thermal hydraulic feedback behavior. These results are input into CASMO-5 MxN as described in section.. Using data from SIMULATE- as an input to CASMO-5 MxN is not ideal because full cycle depletion results from CASMO-5 MxN are not completely independent of full cycle depletion results obtained using SIMULATE-. D Modeling We need to model in D since D transport methods are too computationally cumbersome. The D model requires an axial buckling parameter generated by D SIMULATE- cycle depletion to capture the axial leakage effect. The D SIMULATE- model can take buckling terms at each depletion step but the CASMO- 5 MxN D model only allows one cycle-averaged buckling term for all burnup points. Since partial rod insertions cannot be accurately modeled in two dimensions, we are forced to neglect rod insertions. At full power there is only one bank slightly inserted. Some errors are introduced at the point of insertion. Overall, this effect

34 only increases the total RMS errors by a small amount, since only five assemblies out of 9 assemblies are significantly affected. Baffle Thickness CASMO-5 MxN can only model an integer number of pin pitches for the baffle. We must model the. cm thick baffle with the correct properties under these restrictions. A good approximation is to preserve the product of baffle thickness and material density. Two scenarios were used to test this. The first case was limited to an integer number of.7 cm pin pitches. The second case was limited to an integer number of.9 cm pin pitches. The baffle density was changed to accommodate these restrictions. There was little difference in these cases, which suggests that either approximation is valid. SIMULATE- Geometry The assembly pitch was changed in the SIMULATE- modelinordertoeliminatea0.cmwatergapbetweenthebaffleandtheouter assembly around the entire core since it was included in the baffle/reflector nodes. Since the volume of the assemblies would change in this situation, the power density of the fuel rods is also changed in order to preserve the total core power. Full power points Depletion steps are compared near full power to be consistent with the original EPRI study. CASMO-5 MxN is run at full power for the full cycle depletion. Flux map points that have a power above 80% are used. The chosen measurement points for cycle are shown in Figure.5 and for cycle are shown by green dots in Figure.6.

35 Figure.5: Full power points (above 80% power) used in cycle depletion. The List of full power points here (in GWd/T) are 0.88,.0,.5,.6,.0,.6, 6.9, 7.5, 8.70, 9.80,.08,.,.9. We do not use the 9.80 GWd/T data because the measurement occurred when the reactor was at full power for a very brief period. Figure.6: Full power points used in cycle depletion. The list of full power points here (in GWd/T) are.,.,.,.0,.0, 5., 6.5, 7.7, 8.7, 9.6, 0..

36 .5. CASMO-5 MxN Considerations CASMO-5 MxN is structured such that reflected boundary conditions can be used. Given that cycle is octant symmetric, it can be run with quarter core symmetry. Cycle is run in full core geometry and takes much longer to run than cycle. Table. states the simulation parameters for a very detailed transport calculation. Sensitivity analysis of each of these parameters was tested to determine the proper balance between accuracy and computation time. The optimal parameters selected are shown in Table.. Azimuthal Angles Ray Spacing Polar Angles Energy Groups Geometry Cycle quarter core Cycle full core Table.: CASMO-5 MxN Simulation Parameters..6 Methods to Infer Reactivity Decrement Uncertainties The reactivity decrement is defined as the difference between the assembly k-infinity at zero burnup and the k-infinity at the calculated exposure point. If the full cycle depletion models were perfectly accurate, one would know the reactivity decrement of all the fuel assemblies in the core with certainty. One would find the assembly reactivity decrement from the depletion model and find the k-infinity vs exposure curve for the specific type of assembly, as calculated by CASMO-5. A.% enriched assembly with burnable poisons is shown as an example in Figure.7. However, since the full cycle depletion models do not predict core behavior perfectly, we need to infer the true reactivity of an assembly. To determine the inferred reactivity of the fuel, a series of perturbations are applied to a sub-batch of fuel. These perturbations change the reactivity of the sub-batch of 5

37 fuel via changing the exposure or temperature of an assembly. The fuel assembly subbatch is chosen by a common characteristic, such as having the same fuel enrichment. When the fuel reactivity of a sub-batch is perturbed at a specified depletion point, the RMS error of the new simulated point will change. The minimum RMS point, along with its corresponding reactivity perturbation, is considered the most accurate representation of the core behavior. The magnitude of the reactivity perturbation at the minimum RMS point is used to infer the bias of the CASMO-5 predicted reactivity decrement. This study perturbed the fuel sub-batch exposures from + GWd/T to - GWd/T in steps of 0. GWd/T. The sub-batch fuel temperatures were perturbed from -50K to +50K in steps of 5K. In order to convert the exposure values or temperature values to reactivity, the exposure reactivity coefficient or fuel temperature coefficient of reactivity of the assemblies in the sub-batch is needed. The exposure reactivity coefficient is the derivative of the k-infinity vs burnup of an assembly at a given burnup point. An example of a exposure reactivity coefficient curve derived from Figure.7 is shown in Figure.8. There are multiple unique assembly types within a sub-batch. The exposure reactivity coefficient is computed for each unique assembly by using the k-infinity vs exposure curve and the central difference approximation. The exposure reactivity coefficient for the sub-batch is approximated as the weighted average coefficient of the unique assemblies within the sub-batch. This average exposure reactivity coefficient and the difference between the average exposure of the sub-batch at the base point and at the minimum RMS point is used to determine the reactivity decrement error. The sub-batch reactivity decrement error is described in Eq.. kbias lattice (Ebias lattice )= (Emin lattice Ebase lattice ) dk de lattice E lattice base (.) where k is the lattice critical eigenvalue at the measured boron concentration, E is exposure, E lattice base point, and E lattice min is the average exposure of the fuel batch of interest at the base is the average exposure of the sub-batch after optimal perturbations (smallest RMS error). The fuel temperature coefficient of reactivity is determined by 6

38 taking the derivative of k-infinity versus temperature at the given exposure point. Then, the average fuel temperature coefficient for the sub-batch is approximated as the weighted average coefficient of the unique assemblies within the sub-batch. The average temperature reactivity coefficient and the average temperature of the subbatch at the base point and at the minimum RMS point is used to determine the reactivity decrement error. The reactivity decrement error is described in Eq... kbias lattice (Tbias lattice )= (Tmin lattice Tbase lattice ) dk dt lattice T lattice base (.) where k is the lattice critical eigenvalue at the measured boron concentration, T is the fuel temperature, T lattice base the base point, and T lattice min is the average temperature of the fuel batch of interest at is the average temperature of the sub-batch after optimal perturbations (smallest RMS error). Figure.9 shows that the temperature reactivity coefficient is around -.5 pcm/k at three different cycle points. The relationship between fuel temperature and reactivity is more stable than fuel exposure and reactivity at the beginning of the cycle because burnable poison depletion competes with fuel depletion. 7

39 ..05 BP inserted BP pulled 0.95 k inf Burnup (GWd/T) Figure.7: Reactivity of an assembly with.% enriched fuel and burnable poisons as a function of burnup. 8

40 Exposure Reactivity Coefficient (pcm/gwd/t) BP inserted BP pulled Burnup (GWd/T) Figure.8: exposure reactivity coefficient of an assembly with.% enriched fuel and burnable poisons as a function of burnup. 9

41 Temperature Reactivity Coefficient (pcm/k) Fuel Temperature (K) Figure.9: The temperature reactivity coefficient of an assembly with.% enriched fuel and burnable poisons as a function of temperature at a beginning, middle, and end of cycle statepoint. 0

42 TiltCorrection, GapTest, andearlycycleresults This section will discuss the results of tilt correcting the BEAVRS data and how the baffle gap model can explain the tilt in the data. The models are tested against the HZP and early HFP points.. Results of Tilt Corrected Data Figure. and Figure. show the planar tilt coefficients found in cycle and cycle, respectively. The tilt coefficients describe the magnitude of linear peripheral assembly fractional tilt of the best fit plane to the measured data in the x and y directions at a given statepoint. The fractional tilt is defined as simulated reference reference and the magnitude of the tilt is quoted as the tilt at the most peripheral assemblies. The method used to determine the tilt coefficients was described in section.. The planar tilt is large at HZP and decreases quickly with burnup. As depletion increases, the assemblies that have higher fission rates will deplete more quickly, resulting in a reduced tilt over time. The cause of the tilt is not known, and it is difficult to determine what causes the tilt to change over time. Geometrical changes occurring throughout the cycle depletion (e.g. reduction in inter-assembly gaps through swelling) could help restore symmetry, explaining the reduction in measured tilt..

43 8 7 X Direction Y Direction Planar Tilt of Measured Fission Rate Cycle burnup (GWd/T) Figure.: Planar peripheral assembly fractional tilt of measured fission rates for cycle. Positive tilt in the x direction means that the measurements were higher on the east side of the core. Positive tilt in the y direction means that the measurements were higher on the south side of the core.

44 8 7 X Direction Y Direction Planar Tilt of Measured Fission Rate Cycle burnup (GWd/T) Figure.: Planar peripheral assembly fractional tilt of measured fission rates for cycle. Positive tilt in the x direction means that the measurements were higher on the east side of the core. Positive tilt in the y direction means that the measurements were higher on the south side of the core. Cycle has a very small tilt at BOC and it too goes away with depletion. Early Cycle displays the only truly significant tilts.. Gap Test Results.. Magnitude of Simulated Tilt Figure. shows a comparison of fission rates at HZP from the manually-created baffle with no water gap versus the manually created baffle with a 0.5cm water gap in the southeast corner. A manually created baffle with no gap is used for a direct comparison rather than the CASMO-5 MxN generated baffle. The fission rates increase by about 9% near the gap and continually decrease towards the opposite side of the core. In the northwest corner the fission rates have dropped to about % below

45 the no gap reference. This test does not produce a purely linear tilt, but it shows that a smooth and significant tilt can be introduced with only a 0.5cm water gap on one edge of the baffle. The magnitude of the introduced tilt is comparable to the approximately 6% planar tilt calculated at HZP in cycle. The 6% tilt means that the overall difference between opposite sides of the core is %. The simulated gap has the same net difference in tilt as observed in the measurement. Detector Fission Rate Fractional Difference # Symmetry Positions Figure.: HZP CASMO-5 MxN with a 0.5 cm southeast gap minus no gap shows the distribution of tilt. The top number shows the fission rates of the gap case. The next line shows the fractional difference of the gap minus no gap case.

46 .. HZP Comparisons to Calculations The BEAVRS benchmark specifies the hot zero power (HZP) configuration. The HZP simulation shown in Figure. shows a relatively high RMS difference vs the measured data. Figure.5 is a comparison of CASMO-5 MxN HZP to tilt corrected data. Correcting for the tilt is a systematic means to interpret what the fission map would look like without any tilt. A comparison of Figure. and Figure.5 shows that the radial tilt in the measured fission rates causes a large portion of the difference. There is still an in-out tilt present in Figure.5, but it is less significant. A comparison of Figure.5 and Figure.6 shows that the correction of measured tilt and the simulation of the gap yields much reduced measurement errors relative to the uncorrected case. The comparison to the tilt corrected data was the most accurate at a.9% RMS difference compared to the gap test simulation with an RMS of.8%. However, a large portion of the tilt was corrected by simulating the gap at the baffle, suggesting that the test is a plausible explanation for the tilt seen in the measured data. If it was feasible to simulate smaller inter-assembly gaps throughout the SE region of the core, it is expected that the induced tilt would be closer to linear and show results even closer to the tilt corrected case. Since the tilt exists in the data, especially at HZP, future comparisons will be made to the tilt corrected data in addition to the uncorrected data to test if the interpretation of the results would be any different if the tilt was corrected. Fission rate tilts are most pronounced at HZP because there is no feedback. 5

47 Detector Fission Rate Fractional Difference # Symmetry Positions Figure.: CASMO-5 MxN HZP minus BEAVRS Data. RMS is

48 Detector Fission Rate Fractional Difference # Symmetry Positions Figure.5: CASMO-5 MxN HZP minus tilt corrected data. RMS is

49 Detector Fission Rate Fractional Difference # Symmetry Positions Figure.6: CASMO-5 MxN HZP Manual Baffle with a 0.5cm Gap minus BEAVRS Data. RMS is HFP Results The linear tilt in the HFP data is rapidly diminished with depletion as shown in Figure.. The sensitivity to baffle gap also decreases with cycle depletion shown in Figure.8,., and.. Figure.8 shows a 5% increase in fission rate in the SW corner and a.% decrease in fission rate in the NE corner. The calculated tilt is 8

50 about %, or a net of % from the SW corner to the NE corner. The simulated baffle gap is over-correcting the real tilt by about.% at this point. Figure. shows a.6%increaseinfissionrateintheswcorneranda0.8%decreaseinfissionrate in the NE corner. The calculated tilt is about.5%, or a net of % from the SW corner to the NE corner. The simulated baffle gap is over-correcting the real tilt by about.% at this point. Figure. shows a.6% increase in fission rate in the SW corner and a 0.% decrease in fission rate in the NE corner. The calculated tilt is about %, or a net of % from the SW corner to the NE corner. The simulated baffle gap is over-correcting the real tilt by about 0.8% at this point. The sensitivity to the baffle gap does not decrease as fast as the real tilt. However, by the. GWd/T point the real tilt is small and the simulated tilt from the baffle gap has decreased to the approximately correct level. The simulations with and without tilt at three early cycle points are compared to the measured data in Figure.7,.9,.0,.,., and.5. At the.0 GWd/T and.6 GWd/T points, the simulated baffle gap results have similar total errors to the no gap case because the assemblies near the baffle gap were over corrected. If the gap was reduced in size at these points, it would follow the more rapid reduction in tilt that is in the measured data. At the.gwd/t point, the baffle gap tilt is now closely following the calculated tilt in the data. The comparison of Figure., and.5 shows a reduction in the total RMS error. Overall, the gap does not fix the tilt perfectly because the magnitude of the induced tilt is reduced more slowly than the measured tilt as burnup increases. The assemblies that had higher than estimated fission rates will deplete faster and, likewise, assemblies that have lower than estimated fission rates will deplete slower. This feedback will reduce errors in the calculated vs measured fission rates as depletion increases. 9

51 Detector Fission Rate Fractional Difference # Symmetry Positions Figure.7: CASMO-5 MxN HFP.0 GWd/T Manual Baffle with No Gap minus BEAVRS Data. RMS is

52 Detector Fission Rate Fractional Difference # Symmetry Positions Figure.8: CASMO-5 MxN HFP.0 GWd/T with a 0.5 cm southeast gap minus no gap shows the distribution of tilt. The top number shows the fission rates of the gap case. The next line shows the fractional difference of the gap minus no gap case. 5

53 Detector Fission Rate Fractional Difference # Symmetry Positions Figure.9: CASMO-5 MxN HFP.0 GWd/T Manual Baffle with 0.5 cm gap minus BEAVRS Data. RMS is

54 Detector Fission Rate Fractional Difference # Symmetry Positions Figure.0: CASMO-5 MxN HFP.6 GWd/T Manual Baffle with No Gap minus BEAVRS Data. RMS is

55 Detector Fission Rate Fractional Difference # Symmetry Positions Figure.: CASMO-5 MxN HFP.6 GWd/T with a 0.5 cm southeast gap minus no gap shows the distribution of tilt. The top number shows the fission rates of the gap case. The next line shows the fractional difference of the gap minus no gap case. 5

56 Detector Fission Rate Fractional Difference # Symmetry Positions Figure.: CASMO-5 MxN HFP.6 GWd/T Manual Baffle with 0.5 cm gap minus BEAVRS Data. RMS is

57 Detector Fission Rate Fractional Difference # Symmetry Positions Figure.: CASMO-5 MxN HFP. GWd/T Manual Baffle with No Gap minus BEAVRS Data. RMS is

58 Detector Fission Rate Fractional Difference # Symmetry Positions Figure.: CASMO-5 MxN HFP. GWd/T with a 0.5 cm southeast gap minus no gap shows the distribution of tilt. The top number shows the fission rates of the gap case. The next line shows the fractional difference of the gap minus no gap case. 57

59 Detector Fission Rate Fractional Difference # Symmetry Positions Figure.5: CASMO-5 MxN HFP. GWd/T Manual Baffle with 0.5 cm gap minus BEAVRS Data. RMS is Overall, it is important to show that this tilt is real and not just a measurement error or uncertainty in order for the BEAVRS benchmark to be accepted. This tilt helps justify eliminating early cycle depletion points in the original EPRI study.[] It shows that the RMS errors in the early cycle do not hinder interpretation of reactivity decrement data. 58

60 The source of the tilt is not just a simple fuel assembly/baffle gap. The HFP results show that the tilt in the measured data is reduced much faster than the tilt modeled by the simple gap and the source of the tilt is still unknown. However, since the tilt in the measured data is reduced to negligible levels with depletion it does not affect the results of this study. 59

61 5 Standard Model HFP Results 5. HFP results Cycle The HFP results show the baseline accuracy of simulations. A fission rate error distribution plot similar to the plots provided for the the HZP point are made at every HFP statepoint and shown in the Appendix, section 8.. Figure 5. displays the RMS error at each statepoint as a summary of the results. This plot shows how well the model predicts core behavior throughout a full cycle depletion. The results show that the RMS errors with respect to BEAVRS data and tilt corrected data decrease as depletion increases. The errors burn out because regions that were predicted to have higher than actual reactivity will be depleted more quickly. The data in Figure 5. was folded to an octant because the calculated core model is octant symmetric. This reduces the RMS errors because some of the errors introduced by the tilt are cancelled out between quadrants. The figure also shows a comparison to tilt corrected data. The tilt corrected data gives better results than just folding in the early cycle points. However, as the cycle depletion increases, the amount of tilt is reduced so there is no longer a significant error reduction by using the tilt corrected data. Figure 5. compares CASMO-5 MxN to the SIMULATE D model. The SIMULATE- D model performs better than CASMO-5 MxN at the early cycle point, but by the middle of the cycle the results are comparable. The SIMULATE- D model is compared to the CASMO-5 MxN model because CASMO-5 MxN is also a D model, and the reactivity decrement bias studies are based on these two models. Figure 5. shows the RMS error of the SIMULATE- D model in comparison to the D model. The SIMULATE- D model has a higher RMS than the D model as expected. Notice that the D model benefits greatly from comparing to tilt corrected data in the early cycle but by the end of the cycle the difference is negligible. 60

62 5.5 Cycle SIMULATE D vs BEAVRS SIMULATE D vs tilt corrected CASMO 5 MxN vs BEAVRS CASMO 5 MxN vs tilt corrected.5 RMS Difference (%) Cycle burnup (MWd/kg) Figure 5.: Normalized fission rate RMS error of CASMO-5 MxN and SIMULATE- D vs BEAVRS data and tilt corrected data in cycle. Data is folded into an octant. 6

63 5.5 Cycle SIMULATE D vs BEAVRS SIMULATE D vs tilt corrected SIMULATE D vs BEAVRS SIMULATE D vs tilt corrected.5 RMS Difference (%) Cycle burnup (MWd/kg) Figure 5.: Normalized fission rate RMS error of SIMULATE- D and SIMULATE- D vs BEAVRS data and tilt corrected data in cycle. Data is folded into an octant. 5. HFP results Cycle Figure 5. and 5. show the same RMS error graphs displayed in the previous section, but for cycle data. Notice that at the beginning of the cycle, RMS errors are comparable between SIMULATE- D and CASMO-5 MxN. The data are folded to quarter core in this case, and we see that comparing to the tilt corrected data gives alargeerrorreductioninthebeginningofthecycleandamoderateerrorreduction towards the end of the cycle. There is a tilt in the data at the beginning of the cycle that is reduced to negligible levels by mid cycle. The CASMO 5-MxN and 6

64 SIMULATE- D cases compare well to each other and are both somewhat higher than the SIMULATE- D case throughout the depletion as expected. 5.5 Cycle SIMULATE D vs BEAVRS SIMULATE D vs tilt corrected CASMO 5 MxN vs BEAVRS CASMO 5 MxN vs tilt corrected.5 RMS Difference (%) Cycle burnup (MWd/kg) Figure 5.: Normalized fission rate RMS error of CASMO-5 MxN and SIMULATE- D vs BEAVRS data and tilt corrected data in cycle. Data is folded to quarter core. 6

65 5.5 Cycle SIMULATE D vs BEAVRS SIMULATE D vs tilt corrected SIMULATE D vs BEAVRS SIMULATE D vs tilt corrected.5 RMS Difference (%) Cycle burnup (MWd/kg) Figure 5.: Normalized fission rate RMS error of SIMULATE- D and SIMULATE- D vs BEAVRS data and tilt corrected data in cycle. Data is folded to quarter core. 6

66 6 Inferring Reactivity Decrements Results As discussed in section.6, the exposure and fuel temperature of a sub-batch of fuel was perturbed in order to infer the reactivity decrement. A sub-batch of fuel is chosen by its enrichment. Assemblies with similar enrichment have similar properties. Asimulationmayhaveerrorsduetounder-predictingtheabsorptionofthefuel depletion isotopics or some other physical behavior. By perturbing the sub-batch reactivity we can change the properties of the set of fuel assemblies. There will be an optimal perturbation in these parameters that will produce the best fit to the measured data. This amount of perturbation is the reactivity decrement bias of the simulation. That is, how far off the simulation was from predicting the correct reactivity of the fuel. All of the results in chapter 6 are compared to BEAVRS data without the tilt correction. The investigation of the tilt in the data showed that it is reduced quickly and will not affect the overall accuracy of the model substantially. Also, the sub-batches used in this study are symmetric so perturbing to find a best fit to the data could not remove the tilt. The results would be the same so we choose to perform the reactivity decrement measurements on the original set of data to be consistent with prior studies. 6. Reporting Results in Reactivity This section explains the methods used to construct the graphs in the next sections in terms of reactivity. Increasing burnup usually means that a sub-batch of fuel will decrease in reactivity. This is not always true as shown in Figure 6. in the case of the.% enriched sub-batch at the early cycle point. Increasing temperature always results in decreasing reactivity. So, if all the comparisons were observed only in burnup space and temperature space, one may think that the perturbation of subbatch burnup and sub-batch temperature gave different results. Figure 6. shows the.% enriched sub-batch burnup perturbations in burnup space and Figure 6. shows the.% enriched sub-batch temperature perturbation in temperature space. 65

67 Figure 6. shows both of these figures displayed with respect to reactivity in pcm, defined as k eff k eff.reactivityisthemorerelevantvalueandisusedgoingforwardfor comparisons of all the results. 7 6 CASMO 5.6 GWd/T CASMO GWd/T CASMO 5.08 GWd/T 5 RMS Difference (%) Sub batch Burnup Average (GWd/T) Figure 6.: RMS difference of CASMO-5 MxN compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle. The sub-batch reactivity was perturbed via changing the sub-batch exposure as shown on the x-axis. The circle represents the initial unperturbed point. 66

68 7 6 Cycle :.% sub batch perturbations CASMO 5.6 GWd/T CASMO GWd/T CASMO 5.08 GWd/T 5 RMS Difference (%) Fuel Temperature Perturbation (K) Figure 6.: RMS difference of CASMO-5 MxN compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle. The sub-batch reactivity was perturbed via changing the sub-batch fuel temperature as shown on the x-axis. 67

69 7 6 5 CASMO 5.6 GWd/T exposure perturbation CASMO GWd/T exposure perturbation CASMO 5.08 GWd/T exposure perturbation CASMO 5.6 GWd/T temperature perturbation CASMO GWd/T temperature perturbation CASMO 5.08 GWd/T temperature perturbation RMS Difference (%) pcm Figure 6.: RMS difference of CASMO-5 MxN compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle. The sub-batch reactivity (represented in pcm) was perturbed via changing the sub-batch fuel temperature in three cases and via changing the sub-batch exposure in three cases. 6. Perturbing Sub-batch Burnup in SIMULATE- and CASMO- 5 MxN This section compares the reactivity decrement bias of the SIMULATE- model and the CASMO-5 MxN model. The reactivity was perturbed by changing the exposure of a given sub-batch of fuel. 68

70 6.. Cycle Results In cycle, perturbations of exposure were performed using both SIMULATE- and CASMO-5 MxN at three statepoints representing the beginning, middle, and end of cycle. The perturbation was done by replacing each assembly in the sub-batch with the same assembly from a previous or future statepoint from a fine time-step depletion. This changes the exposure of the sub-batch of fuel. In the first case, the.% enriched fuel sub-batch exposure was perturbed. Figure 6. shows that the optimal reactivity perturbations were roughly the same whether they were done in the SIMULATE- model or the CASMO-5 MxN model. The middle of cycle point covers amuchsmallerrangeofpcmbecausethereactivityderivativeoftheseassemblies is small at this point since this sub-batch has a large number of burnable poisons. However, the inferred reactivity can be determined as long as the minimum point is found. Figure 6.5 shows the results of the.% enriched fuel sub-batch perturbation. The reactivity change of the.6 GWd/T point is somewhat larger in CASMO-5 MxN than in SIMULATE-, but they are in the same direction. Lastly, Figure 6.6 shows a perturbation of the.% enriched fuel sub-batch while using the optimal perturbation for the.% assembly as a starting point. There is not a large change in reactivity because the.% assembly was already at the optimal conditions, so there was less room to improve the fit to the measured data. Similar reactivity errors are calculated irrespective of which fuel batch is selected and which code is used. 69

71 7 6 5 CASMO 5.6 GWd/T CASMO GWd/T CASMO 5.08 GWd/T SIMULATE.6 GWd/T SIMULATE 6.9 GWd/T SIMULATE.08 GWd/T RMS Difference (%) pcm Figure 6.: RMS difference of CASMO-5 MxN and SIMULATE- compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle. The sub-batch reactivity (represented in pcm) was perturbed via changing the sub-batch exposure. 70

72 RMS Difference (%) CASMO 5.6 GWd/T CASMO GWd/T CASMO 5.08 GWd/T SIMULATE.6 GWd/T SIMULATE 6.9 GWd/T SIMULATE.08 GWd/T pcm Figure 6.5: RMS difference of CASMO-5 MxN and SIMULATE- compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle. The sub-batch reactivity (represented in pcm) was perturbed via changing the sub-batch exposure. 7

73 7 6 5 CASMO 5.6 GWd/T CASMO GWd/T CASMO 5.08 GWd/T SIMULATE.6 GWd/T SIMULATE 6.9 GWd/T SIMULATE.08 GWd/T RMS Difference (%) pcm Figure 6.6: RMS difference of CASMO-5 MxN and SIMULATE- compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle while starting from the optimal perturbation point of the.% enriched sub-batch. The sub-batch reactivity (represented in pcm) was perturbed via changing the sub-batch exposure. 6.. Cycle Results In cycle, there are also three perturbations of exposure performed with both SIMULATE- and CASMO-5 MxN. The first case is the.% enriched assemblies shown in Figure 6.7. These are the same.% enriched assemblies from cycle located in different positions due to the core shuffling. The curves are very flat and wide here, indicating that the sub-batch now has a smaller reactivity slope and the reactor is less sensitive to reactivity change for this sub-batch in cycle. The optimal perturbations are similar when computed by CASMO-5 MxN vs SIMULATE-. It is important that the curves look approximately the same, but in this case we do not want to 7

74 credit the minimum value as a good indication of the true reactivity because it is highly sensitive. The original EPRI study calculates a sensitive parameter which is the RMS peak to the minimum. If this value is too small, the data point would not be used. Figure 6.8 shows the.% assembly perturbation results. SIMULATE- shows alargerreactivitydecrementbiasattheearlycyclepoint,butitisstillinthesame direction as the CASMO-5 MxN bias. The other points match up closely. Lastly, the fresh fuel containing.% and.% enriched bundles are perturbed as shown in Figure 6.9. Again, SIMULATE- shows a larger bias at the early cycle point, but it is in the same direction as CASMO-5 MxN. Overall, similar reactivity errors are calculated irrespective of which fuel batch is selected and which core model was used. RMS Difference (%) CASMO 5.0 GWd/T CASMO GWd/T CASMO GWd/T SIMULATE.0 GWd/T SIMULATE 6.5 GWd/T SIMULATE 9.6 GWd/T pcm Figure 6.7: RMS difference of CASMO-5 MxN and SIMULATE- compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle. The sub-batch reactivity (represented in pcm) was perturbed via changing the sub-batch exposure. 7

75 7 6 CASMO 5.0 GWd/T CASMO GWd/T CASMO GWd/T SIMULATE.0 GWd/T SIMULATE 6.5 GWd/T SIMULATE 9.6 GWd/T 5 RMS Difference (%) pcm Figure 6.8: RMS difference of CASMO-5 MxN and SIMULATE- compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle. The sub-batch reactivity (represented in pcm) was perturbed via changing the sub-batch exposure. 7

76 7 6 CASMO 5.0 GWd/T CASMO GWd/T CASMO GWd/T SIMULATE.0 GWd/T SIMULATE 6.5 GWd/T SIMULATE 9.6 GWd/T 5 RMS Difference (%) pcm Figure 6.9: RMS difference of CASMO-5 MxN and SIMULATE- compared to BEAVRS data for the fresh,.% and.% enriched, fuel sub-batch in Cycle. The sub-batch reactivity (represented in pcm) was perturbed via changing the sub-batch exposure. 6. Perturbing Burnup vs Fuel Temperatures in CASMO-5 MxN This section compares the reactivity decrement bias of the CASMO-5 MxN model perturbing exposure and perturbing fuel temperature. Both methods change the sub- 75

77 batch reactivity, and therefore, change the core fission rate distributions. We want to investigate if the method of perturbation affects the inferred reactivity decrement errors. Table 6. shows that the exposure reactivity coefficient of the heavy burnable poison sub-batches changes dramatically from the beginning of the cycle to the end of the cycle. The burnable poisons create a positive reactivity coefficient in the beginning of the cycle. As they burn out, the relationship becomes constant. The exposure reactivity coefficient also changes depending on the enrichment of the fuel. Finally, the exposure reactivity coefficient increases with burnup, regardless of burnable poisons. The temperature reactivity coefficient is nearly constant throughout the cycle for each sub-batch. It is much easier to perform reactivity perturbation with these properties. This section will test if the reactivity decrement results are independent of the method of perturbation. Reactivity"Derivatives"Used"to"Convert"Exposure"and"Temperature"Perturbations"to"Reactivity Cycle Enrichment- Cycle- Burnup- Fuel-- Burnup- kinf dk/de dk/dt % "GWd/T GWd/T pcm/gwd/t pcm/k "/" "/" "/" "@". min "@". min "@". min Table 6.: Summary Table of exposure reactivity coefficients and temperature reactivity coefficients. 76

78 6.. Cycle Results In cycle, three perturbations of temperature and exposure were performed using CASMO-5 MxN. The exposure perturbation results for CASMO-5 MxN are the same as the CASMO-5 MxN results in the previous section. They are displayed again to compare to the temperature perturbation method. The temperature perturbation was done by changing the assembly fuel temperature at each of the sub-batch locations in a range from -50K to +50K. Figure 6.0 shows the perturbation of the.% sub-batch. Notice that the 0 pcm point is the same for the exposure perturbation and the temperature perturbation at a given cycle point. The yellow curve has a much narrower range than all the other curves because the.% enriched sub-batch as a small exposure reactivity coefficient at this cycle point. All the points show a similar reactivity decrement bias. Figure 6. shows the results of the.% enriched sub-batch perturbations. All three cycle points show a similar reactivity decrement bias. Lastly, Figure 6. shows the results of the.% perturbation given a starting point of the.% minimum point. There is not a large change in reactivity here because the.% assembly was already at the optimal conditions, so there was less room to improve the fit to the measured data. Similar reactivity errors are calculated irrespective of which fuel batch is selected and which perturbation method is used. 77

79 7 6 CASMO 5.6 GWd/T exposure perturbation CASMO GWd/T exposure perturbation CASMO 5.08 GWd/T exposure perturbation CASMO 5.6 GWd/T temperature perturbation CASMO GWd/T temperature perturbation CASMO 5.08 GWd/T temperature perturbation 5 RMS Difference (%) pcm Figure 6.0: RMS difference of CASMO-5 MxN compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle. The sub-batch reactivity (represented in pcm) was perturbed via changing the sub-batch fuel temperature in three cases and via changing the sub-batch exposure in three cases. 78

80 7 6 CASMO 5.6 GWd/T exposure perturbation CASMO GWd/T exposure perturbation CASMO 5.08 GWd/T exposure perturbation CASMO 5.6 GWd/T temperature perturbation CASMO GWd/T temperature perturbation CASMO 5.08 GWd/T temperature perturbation 5 RMS Difference (%) pcm Figure 6.: RMS difference of CASMO-5 MxN compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle. The sub-batch reactivity (represented in pcm) was perturbed via changing the sub-batch fuel temperature in three cases and via changing the sub-batch exposure in three cases. 79

81 7 6 CASMO 5.6 GWd/T exposure perturbation CASMO GWd/T exposure perturbation CASMO 5.08 GWd/T exposure perturbation CASMO 5.6 GWd/T temperature perturbation CASMO GWd/T temperature perturbation CASMO 5.08 GWd/T temperature perturbation 5 RMS Difference (%) pcm Figure 6.: RMS difference of CASMO-5 MxN compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle while starting from the optimal perturbation point of the.% enriched sub-batch. The sub-batch reactivity (represented in pcm) was perturbed via changing the sub-batch fuel temperature in three cases and via changing the sub-batch exposure in three cases. 6.. Cycle Results In cycle, three sub-batches were perturbed at the beginning, middle, and end of cycle. Figure 6. shows the results of the.% enriched (once burned) sub-batch perturbation. The sub-batch is very insensitive to changes in reactivity by both changing the exposure, and changing the fuel temperature. It is difficult to find a 80

82 minimum RMS point in these circumstances, but the shape of the graphs show good agreement between both perturbation methods. Again, the sensitivity parameter in the original EPRI study would exclude this data point because the slope of the curve is so shallow. Figure 6. shows the results of the.% enriched (once burned) subbatch. The curves at all burnup points look very similar because the perturbation in exposure is more constant at these higher burnup points. The measured reactivity bias is similar using either perturbation method. Figure 6.5 shows the.% and.% (fresh fuel) sub-batch results. Again, the perturbation in exposure is stable in this sub-batch so all of the curve are similar to the temperature perturbation curves. The measured reactivity bias is similar using either perturbation method. 8

83 7 6 CASMO 5.0 GWd/T exposure perturbation CASMO GWd/T exposure perturbation CASMO GWd/T exposure perturbation CASMO 5.0 GWd/T temperature perturbation CASMO GWd/T temperature perturbation CASMO GWd/T temperature perturbation 5 RMS Difference (%) pcm Figure 6.: RMS difference of CASMO-5 MxN compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle. The sub-batch reactivity (represented in pcm) was perturbed via changing the sub-batch fuel temperature in three cases and via changing the sub-batch exposure in three cases. 8

84 7 6 5 CASMO 5.0 GWd/T exposure perturbation CASMO GWd/T exposure perturbation CASMO GWd/T exposure perturbation CASMO 5.0 GWd/T temperature perturbation CASMO GWd/T temperature perturbation CASMO GWd/T temperature perturbation RMS Difference (%) pcm Figure 6.: RMS difference of CASMO-5 MxN compared to BEAVRS data for the.% enriched fuel sub-batch in Cycle. The sub-batch reactivity (represented in pcm) was perturbed via changing the sub-batch fuel temperature in three cases and via changing the sub-batch exposure in three cases. 8

85 7 6 5 CASMO 5.0 GWd/T exposure perturbation CASMO GWd/T exposure perturbation CASMO GWd/T exposure perturbation CASMO 5.0 GWd/T temperature perturbation CASMO GWd/T temperature perturbation CASMO GWd/T temperature perturbation RMS Difference (%) pcm Figure 6.5: RMS difference of CASMO-5 MxN compared to BEAVRS data for the fresh,.% and.% enriched, fuel sub-batch in Cycle. The sub-batch reactivity (represented in pcm) was perturbed via changing the sub-batch fuel temperature in three cases and via changing the sub-batch exposure in three cases. 6. Summary of Calculated Reactivity Decrements Changing the method of simulation or the method of perturbation does not change the measured reactivity bias. The results of the previous sections are summarized in Table 6.. It shows the SIMULATE- reactivity decrement biases determined from exposure perturbations as well as the CASMO-5 MxN biases determined from both exposure and temperature perturbations. Overall, similar reactivity errors are 8

86 calculated irrespective of which fuel batch is selected and how it is perturbed. It is important to look at the summary statistics of the differences in these methods rather than the nominal value of the biases in each case. This set of points is a small set of possible points that could have been found in the EPRI study. We only want the differences in the methods to evaluate possible uncertainty of the SIMULATE- EPRI biases. Overall, the calculated bias does not change significantly from either code or method. The EPRI study uses a 50 pcm uncertainty of the bias regression curves. The standard deviation of the differences of biases shown here are much lower than the assigned uncertainty. The EPRI study was produced using SIMULATE- with exposure perturbations to find the reactivity decrement biases. Fuel"Assembly"Reactivity"Decrement"Biases"for"BEAVRS"Cycle""and"Cycle""(CASMO05""with"ENDF0B/VII) SIMULATE-Bias- CASMO-Bias- CASMO-Bias- SIMULATE-A- Bias-Difference- Cycle- Fuel-- (burnup-pert.)-- (burnup-pert.)- (temp.-pert.)-- CASMO-Bias- (burnup-pert.-a- Cycle Enrichment- Burnup- Burnup- Δk Δk Δk- (burnup-pert.)- temp.-pert.)- % "GWd/T GWd/T pcm pcm pcm pcm pcm "/" "/" "/" "@". min "@". min "@". min S.D."of"Bias Mean"Bias Table 6.: Inferred Fuel Batch Reactivity Bias by perturbing sub-batch burnup in SIMULATE- and sub-batch burnup and fuel temperature in CASMO-5 MxN. The differences in the biases inferred by the two methods is shown in the far right columns. 85

87 7 Summary 7. Conclusions This study investigated using SIMULATE- with exposure perturbations and CASMO- 5 MxN with exposure and temperature perturbations to calculate reactivity decrement biases. The results of this study show that similar reactivity decrement biases are calculated irrespective of how it is perturbed. Overall, this is important because it confirms that the EPRI study was valid in only using SIMULATE- with exposure perturbations to calculate reactivity decrement biases. An NRC information notice in 0 stated that Regarding the depletion uncertainty, the Kopp letter states the following: A reactivity uncertainty due to uncertainty in the fuel depletion calculations should be developed and combined with other calculational uncertainties. In the absence of any other determination of the depletion uncertainty, an uncertainty equal to 5 percent of the reactivity decrement to the burnup of interest is an acceptable assumption. [5] Perturbations in temperature and burnup found reactivity decrement uncertainties that were well under the 50 pcm mark set in the EPRI study. Therefore, the conclusions of the EPRI study are valid and show that the Kopp memo is conservative, but given the uncertainty calculations performed, the 5% decrement could possibly be lowered while maintaining the same safety standards. 7. Future Work Improved Thermal Hydraulic Modeling in an MOC Solver Currently CASMO- 5 MxN does not have a thermal hydraulic feedback model. To improve the accuracy of the calculation, temperature maps were extracted from the SIMULATE- results since it has a built in thermal hydraulic feedback model. However, this introduces some dependency on SIMULATE-, a nodal method. The main purpose of using a MOC solver was to verify the reactivity decrements independently of the nodal model. 86

88 In order to show fully independent results, a thermal hydraulic feedback model should be implemented into a MOC solver. D Transport Method The original EPRI study used D nodal methods to calculate reactivity decrement uncertainties. Ideally, this study would use D MOC methods in order to independently determine the reactivity decrement uncertainties. However, since the D MOC model is computationally cumbersome, this study compared the results of the D nodal method versus the D MOC method. The D models are less accurate, but can be solved in a reasonable amount of time. A D transport method would need to solve approximately 00 full core statepoints in a reasonable timeframe in order to compare results to nodal methods using the BEAVRS benchmark. 87

89 References [] K. Smith, et al., Benchmarks for Quantifying Fuel Reactivity Depletion Uncertainty, Electric Power Research Institute (EPRI), Palo Alto, CA, Technical Report Number 0909, (0). [] G. Gunow, "LWR Fuel Reactivity Depletion Verification Using D Full Core MOC and Flux Map Data," Master s thesis, Massachusetts Institute of Technology, (05). [] J. Rhodes, et al., CASMO5 Overview USNRC Pre-Submittal Meeting, (05). [] N. Horelik, B. Herman, B. Forget, and K. Smith. "Benchmark for Evaluation and Validation of Reactor Simulations (BEAVRS), v..," (0). [5] United States Nuclear Regulatory Commission Office of Nuclear Reactor Regulation Office of New Reactors, "Nonconservative Criticality Safety Analyses for Fuel Storage," (0). [6] J. Cronin, et al., SIMULATE- Methodology Manual, STUDSVIK/SOA-95/8, Studsvik of America, Inc., (995). [7] J. Rhodes, et al., CASMO-5 A Fuel Assembly Burnup Program User s Manual, SSP-07/ Rev 8, (0). [8] T. Bahadir, et al., CMSLINK User s Manual, STUDSVIK/SOA-97/0, Studsvik of America, Inc. (997). [9] L. Kopp, NRC memorandum from L. Kopp to T. Collins, "Guidance on the Regulatory Requirements for Criticality Analysis of Fuel Storage at Light-Water Reactor Power Plants," dated August 9, 998 (ADAMS Accession No. ML007800). 88

90 8 Appendix 8. Detailed Maps of the Full Cycle Depletion Points 8.. CASMO-5 MxN Cycle H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions P.0 MWD/kg S.6cm assembly version D vs beavrs RMS=0. Figure 8.: The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at.0 GWd/T exposure in Cycle. The RMS difference is

91 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.: The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at.5 GWd/T exposure in Cycle. The RMS difference is

92 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.: The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at.6 GWd/T exposure in Cycle. The RMS difference is

93 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.: The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at.0 GWd/T exposure in Cycle. The RMS difference is

94 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions P.6 MWD/kg S.6cm assembly version D vs beavrs RMS=0 Figure 8.5: The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at.6 GWd/T exposure in Cycle. The RMS difference is

95 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.6: The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at 6.9 GWd/T exposure in Cycle. The RMS difference is

96 H G F E D C B A File Data Detector Fission Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.7: The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at 7.5 GWd/T exposure in Cycle. The RMS difference is

97 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.8: The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at 8.70 GWd/T exposure in Cycle. The RMS difference is

98 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.9: The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at.08 GWd/T exposure in Cycle. The RMS difference is

99 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.0: The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at. GWd/T exposure in Cycle. The RMS difference is

100 8.. CASMO-5 MxN Cycle H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.: The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at. GWd/T exposure in Cycle. The RMS difference is

101 H G F E D C B A File Data Detector Fission Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.: The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at. GWd/T exposure in Cycle. The RMS difference is

102 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions P. MWD/kg S.6cm assembly version D vs beavrs RMS=0.0 Figure 8.: The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at.0 GWd/T exposure in Cycle. The RMS difference is

103 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.: The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at.0 GWd/T exposure in Cycle. The RMS difference is

104 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.5: The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at 5. GWd/T exposure in Cycle. The RMS difference is

105 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.6: The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at 6.5 GWd/T exposure in Cycle. The RMS difference is

106 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.7: The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at 7.7 GWd/T exposure in Cycle. The RMS difference is

107 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.8: The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at 8.7 GWd/T exposure in Cycle. The RMS difference is

108 H G F E D C B A File Data Detector Fission Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.9: The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at 9.6 GWd/T exposure in Cycle. The RMS difference is

109 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions P 0. MWD/kg S.6cm assembly version D vs beavrs RMS=0 Figure 8.0: The difference in fission rates of CASMO-5 MxN compared to BEAVRS data at 0. GWd/T exposure in Cycle. The RMS difference is

110 8.. SIMULATE- D Cycle H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.: The difference in fission rates of SIMULATE- D compared to BEAVRS data at.0 GWd/T exposure in Cycle. The RMS difference is

111 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.: The difference in fission rates of SIMULATE- D compared to BEAVRS data at.5 GWd/T exposure in Cycle. The RMS difference is

112 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.: The difference in fission rates of SIMULATE- D compared to BEAVRS data at.6 GWd/T exposure in Cycle. The RMS difference is 0.0.

113 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.: The difference in fission rates of SIMULATE- D compared to BEAVRS data at.0 GWd/T exposure in Cycle. The RMS difference is

114 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.5: The difference in fission rates of SIMULATE- D compared to BEAVRS data at.6 GWd/T exposure in Cycle. The RMS difference is

115 H G F E D C B A File Data Detector Fission Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions P 6.9 MWD/kg S.6cm assembly version D vs beavrs RMS=0. Figure 8.6: The difference in fission rates of SIMULATE- D compared to BEAVRS data at 6.9 GWd/T exposure in Cycle. The RMS difference is

116 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.7: The difference in fission rates of SIMULATE- D compared to BEAVRS data at 7.5 GWd/T exposure in Cycle. The RMS difference is

117 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.8: The difference in fission rates of SIMULATE- D compared to BEAVRS data at 8.70 GWd/T exposure in Cycle. The RMS difference is

118 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions.08 MWD/kg S.6cm assembly version D vs beavrs RMS=0 Figure 8.9: The difference in fission rates of SIMULATE- D compared to BEAVRS data at.08 GWd/T exposure in Cycle. The RMS difference is

119 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.0: The difference in fission rates of SIMULATE- D compared to BEAVRS data at. GWd/T exposure in Cycle. The RMS difference is

120 8.. SIMULATE- D Cycle H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions P. MWD/kg S.6cm assembly version D vs beavrs RMS=0 Figure 8.: The difference in fission rates of SIMULATE- D compared to BEAVRS data at. GWd/T exposure in Cycle. The RMS difference is

121 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.: The difference in fission rates of SIMULATE- D compared to BEAVRS data at. GWd/T exposure in Cycle. The RMS difference is

122 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.: The difference in fission rates of SIMULATE- D compared to BEAVRS data at.0 GWd/T exposure in Cycle. The RMS difference is 0.05.

123 H G F E D C B A File Data Detector Fission Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.: The difference in fission rates of SIMULATE- D compared to BEAVRS data at.0 GWd/T exposure in Cycle. The RMS difference is 0.06.

124 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.5: The difference in fission rates of SIMULATE- D compared to BEAVRS data at 5. GWd/T exposure in Cycle. The RMS difference is 0.08.

125 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.6: The difference in fission rates of SIMULATE- D compared to BEAVRS data at 6.5 GWd/T exposure in Cycle. The RMS difference is 0.09.

126 H G F E D C B A File Data Detector Fission Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions P 7.7 MWD/kg S.6cm assembly version D vs beavrs RMS=0.0 Figure 8.7: The difference in fission rates of SIMULATE- D compared to BEAVRS data at 7.7 GWd/T exposure in Cycle. The RMS difference is

127 H G F E D C B A Detector File Fission Data Rate % Difference Fractional to Reference Difference # Symmetry # of Folds Positions Figure 8.8: The difference in fission rates of SIMULATE- D compared to BEAVRS data at 8.7 GWd/T exposure in Cycle. The RMS difference is