EVALUATION OF PWR AND BWR CALCULATIONAL BENCHMARKS FROM NUREG/CR-6115 USING THE TRANSFX NUCLEAR ANALYSIS SOFTWARE

ANS MC2015 - Joint International Conference on Mathematics and Computation (M&C), Supercomputing in Nuclear Applications (SNA) and the Monte Carlo (MC) Method Nashville, Tennessee April 19 23, 2015, on CD-ROM, American Nuclear Society, LaGrange Park, IL (2015) EVALUATION OF PWR AND BWR CALCULATIONAL BENCHMARKS FROM NUREG/CR-6115 USING THE TRANSFX NUCLEAR ANALYSIS SOFTWARE B. P. Richardson TransWare Enterprises Inc. 1565 Mediterranean Dr., Sycamore, IL 60178 brad.richardson@transware.net ABSTRACT Evaluations have been performed for two calculational benchmarks described in NUREG/CR-6115 using the TRANSFX Nuclear Analysis Software. TRANSFX uses a deterministic, three-dimensional, multigroup nuclear particle transport theory code (TRANSRAD) that performs neutron and gamma flux calculations. TRANSFX couples the nuclear transport method with a general geometry modeling capability to provide a flexible and accurate tool for determining fluxes for any light water reactor design. TRANSFX supports the mtehod of characteristics solution technique, a three-dimensional ray-tracing method based on combinatorial geometry, a fixed source iterative solution with anisotropic scattering, thermal-group upscattering treatments, and a nuclear cross-section data library based upon the ENDF/B-VI data file. These benchmarks are identified in U.S. NRC Regulatory Guide 1.190 for the purpose of qualifying a methodology for performing reactor pressure vessel fast fluence calculations. It is noted that the reference results are based on a 3D synthesis method and TRANSFX is a full 3D method, so some differences are expected. The overall comparison to results give a calculated to reference ratio of 1.09 with a standard deviation of ±0.11. This is within the uncertainty associated with the reference values, and within the 20% uncertainty allowed by Reg. Guide 1.190, demonstrating that the TRANSFX Software is capable of performing neutron transport calculations for evaluating RPV neutron fluence. Key Words: neutron fluence, Reg. Guide 1.190, RPV, benchmark 1 INTRODUCTION The benchmarks evaluated in this analysis are identified in U. S. Nuclear Regulatory Commission (NRC) Regulatory Guide (Reg. Guide) 1.190 [1] for use in demonstrating the capability of a methodology to perform acceptable fast neutron fluence calculations to be used as input to material embrittlement calculations in accordance with Reg. Guide 1.99 [2]. The benchmarks evaluated include typical pressurized water reactor (PWR) and typical boiling water reactor (BWR) configurations, for which flux results have been calculated using a synthesis approach based on a two-dimensional discrete ordinates methodology [3]. These benchmarks are evaluated using the 3D TRANSFX Nuclear Analysis Software (TRANSFX) developed by TransWare Enterprises Inc [4]. TRANSFX uses a deterministic, three-dimensional, multi-group nuclear particle transport theory code (TRANSRAD) that performs neutron and gamma flux calculations. TRANSFX couples

B. P. Richardson the nuclear transport method with a general geometry modeling capability to provide a flexible and accurate tool for determining fluxes for any light water reactor design. TRANSFX supports the method of characteristics solution technique, a three-dimensional ray-tracing method based on combinatorial geometry, a fixed source iterative solution with anisotropic scattering, thermal-group up-scattering treatments, and a nuclear cross-section data library based upon the ENDF/B-VI data file. In accordance with the intent of Reg. Guide 1.190, the benchmark evaluations are performed using methods and procedures as close as is reasonable to those that will be used to perform fast neutron fluence evaluations of commercial light water reactor (LWR) reactor pressure vessels (RPV). These methods and procedures include geometry modeling techniques, reactor core (neutron source) treatments, and integration parameters. 2 BENCHMARK EVALUATIONS The referenced benchmark report is examined to determine the necessary information required to construct models for each configuration. The required information includes dimensions for each of the components of the configurations, composition information for those components, and core power distributions. This information is used to construct detailed, accurate, 3-dimensional models of each configuration. Various 2-D and 3-D forms of these models are used to conduct a variety of sensitivity studies. These studies are used to determine the optimum parameters required to achieve an asymptotic solution to the neutron flux distribution. The parameters considered in these studies include material region mesh size, geometry model extent, ray spacing, angular quadrature (number of ray directions), and convergence criteria. 2.1 BWR Calculational Benchmark The BWR Calculational Benchmark is prescribed by the U. S. NRC for use in benchmarking pressure vessel neutron fluence prediction methodologies. A description of the dimensions and material compositions required to perform the BWR Calculational Benchmark is provided in NUREG/6115 [3]. TRANSRAD predicted reaction rates for capsule dosimetry are compared to the values reported in NUREG/6115 [3]. Details of the model and comparison results are provided in the following subsections. 2.1.1 Reactor system geometry The BWR Calculational Benchmark is based on a typical 3833 MW boiling water reactor (BWR) having calculated dosimeter reaction rates in the surveillance capsule location adjacent to the pressure vessel inner wall. There are 24 jet pump assemblies positioned every 15 degrees of Page 2 of 12

Evaluation of NUREG/CR-6115 Benchmarks Using TRANSFX Figure 1. Elevation view of the BWR calculational benchmark reactor circumference in the downcomer region. Figure 1 provides an elevation view of the BWR Numerical Benchmark reactor. The reactor core region is composed of 800 fuel assemblies. Regions outside the core consist of the shroud; downcomer, containing jet pumps and risers; pressure vessel; mirror insulation; and an outer concrete biological shield. A stainless steel surveillance capsule is located on the inside RPV liner wall at 3 azimuth. The active core height is 381 cm. Regions below the active core height include the inlet region and core plate region. Regions above the active core include a top guide region and upper reflector region. Table I provides the material composition for each region of the BWR Numerical Benchmark reactor represented in the TRANSRAD model. Page 3 of 12

B. P. Richardson Figure 2. Planar view of the BWR calculational benchmark reactor 2.1.2 TRANSRAD model For reference purposes, a coordinate system is imposed upon the model. Figure 2 illustrates the coordinate system in relation to the primary components of the BWR Calculational Benchmark reactor. The positive Z axis extends vertically upward. The axial geometry is shown in Figure 1. The TRANSRAD model for the BWR Calculational Benchmark consists of an octant of the core. Axially, the BWR Calculational Benchmark is modeled from 0.0 cm to 485.99 cm (as shown in Figure 1) for a total height of 485.99 cm. The active core region is 381 cm high. The active core region contains 25 axial nodes that are each 15.24 cm in height. The regions above the active core are 13 cm high and contain 5 axial nodes. The regions below the active core are 17 cm high and contain 5 axial nodes. The following regions are modeled axially as one region each: inlet, core plate, top guide and upper reflector region. The inlet region is 12.39 cm high, the core plate region Page 4 of 12

Evaluation of NUREG/CR-6115 Benchmarks Using TRANSFX Table I. Material compositions for regions in BWR calculational benchmark problem Region Material Composition Water Regions Water Fuel Regions 235 U, 238 U, O, Zr, Water Jet Pump Water Water Jet Pump Metal Chromium, Iron, Nickel Jet Pump Riser Water Water Jet Pump Riser Metal Chromium, Iron, Nickel Reflector Water Shroud Stainless Steel SS-304 Downcomer Water Surveillance Capsule Stainless Steel SS-304 RPV Liner Stainless Steel SS-304 RPV Wall Steel Cavity Air (Oxygen) Insulation Liner Stainless Steel SS-304 Insulation Aluminum Biological Shield Concrete Inlet Water, Zr, SS-304 Core Plate Water, SS-304 Top Guide Water, Zr Upper Reflector Water, Zr, SS-304 is 37.04 cm high, the top guide region is 37.04 cm high, and the upper reflector region is 18.52 cm high. Radially, the BWR Calculational Benchmark model extends from the center of the core to the outside surface of the biological shield (477.5 cm) as shown in Figure 2. The fuel assemblies are represented in the X-Y plane of the model as partly homogenized regions in the peripheral assemblies and as fully homogenized regions inside the core. The geometrical regions outside the core region coincide with the ex-core material regions (i.e., water regions, stainless steel regions, and air regions). The three-dimensional model consists of 58,890 regions. There are 2,118 regions per axial plane in the fuel zone and 1,485 regions per plane for the zones outside the active core. The power density is normalized to full core power as specified in NUREG/6115 [3]. 2.1.3 Results Table II presents a comparison of the predicted reaction rates produced by the TRANSRAD and NUREG calculation methods for the BWR Calculational Benchmark evaluation. The average comparison (TRANSRAD/NUREG) for all calculated reaction rates is 1.05 with a comparison Page 5 of 12

B. P. Richardson standard deviation of ±0.02. The average comparison and standard deviation for the capsule location is given for each of the reactions 237 Np(n,p), 238 U(n,f), 58 Ni(n,p) 58 Co, 54 Fe(n,p) 54 Mn, 46 Ti(n,p) 46 Sc, and 63 Cu(n,α) 60 Co. The TRANSRAD calculated reaction rate results are in reasonably good agreement with the NUREG values, which is expected at a core mid-plane elevation. Table II. Reaction rate (in rps/atom) comparison results (TRANSRAD/NUREG) for capsule at 3 Capsule Radial Location Source 237 Np(n,p) 238 U(n,f) 58 Ni(n,p) 58 Co 54 Fe(n,p) 54 Mn 46 Ti(n,p) 46 Sc 63 Cu(n,α) 60 Co 318.348 cm TRANSRAD 2.30 10 15 5.27 10 16 2.42 10 16 1.89 10 16 4.28 10 17 2.90 10 18 NUREG 2.10 10 15 5.05 10 16 2.33 10 16 1.82 10 16 4.20 10 17 2.89 10 18 Calc/Ref 1.09 1.04 1.04 1.04 1.02 1.00 1.04 0.03 319.195 cm TRANSRAD 2.17 10 15 4.84 10 16 2.16 10 16 1.69 10 16 3.80 10 17 2.57 10 18 NUREG 2.04 10 15 4.65 10 16 2.08 10 16 1.62 10 16 3.70 10 17 2.55 10 18 Calc/Ref 1.07 1.04 1.04 1.04 1.03 1.01 1.04 0.02 320.041 cm TRANSRAD 2.03 10 15 4.39 10 16 1.92 10 16 1.49 10 16 3.35 10 17 2.27 10 18 NUREG 1.91 10 15 4.18 10 16 1.82 10 16 1.42 10 16 3.23 10 17 2.23 10 18 Calc/Ref 1.06 1.05 1.05 1.05 1.04 1.02 1.05 0.01 320.887 cm TRANSRAD 1.90 10 15 3.98 10 16 1.71 10 16 1.32 10 16 2.95 10 17 2.01 10 18 NUREG 1.77 10 15 3.71 10 16 1.58 10 16 1.23 10 16 2.79 10 17 1.93 10 18 Calc/Ref 1.08 1.07 1.08 1.08 1.06 1.04 1.07 0.01 Average 1.08 1.05 1.05 1.05 1.04 1.02 1.05 Standard Deviation 0.01 0.01 0.01 0.02 0.01 0.01 0.02 Avg. Std. Dev. 2.2 PWR Calculational Benchmark The PWR Calculational Benchmark is prescribed by the U. S. NRC for use in benchmarking pressure vessel neutron fluence prediction methodologies. A description of the dimensions and material compositions required to perform the PWR Calculational Benchmark is provided in NUREG/6115 [3]. TRANSRAD predicted reaction rates for capsule dosimetry are compared to the values reported in NUREG/6115 [3]. Details of the model and comparison results are provided in the following subsections. 2.2.1 Reactor system geometry The PWR Calculational Benchmark uses a typical 2527.73 MWt pressurized water reactor (PWR) having calculated dosimeter reaction rates in the surveillance capsule locations inside the pressure vessel and other dosimetry in the cavity region outside the vessel. Two reactor problems are evaluated: Standard Core Loading (SCL) and Low Leakage Core Loading (LLCL). Each reactor problem uses the same dimensional information and varies only by the core configuration and power factor. Page 6 of 12

Evaluation of NUREG/CR-6115 Benchmarks Using TRANSFX Figure 3. Elevation view of the PWR calculational benchmark reactor SCL and LLCL configurations The SCL problem is described as a reactor with a standard core loading pattern. The LLCL problem is identical to the SCL problem, with the exception that the core loading pattern is based on a low-leakage core design. The reactor components include the core region, core baffle, core barrel, thermal shield, pressure vessel, vessel insulation and biological shield. Also included are representations of surveillance capsules loaded inside the pressure vessel and other dosimetry mounted in the cavity region outside the vessel. Outside the core beltline, and specifically above and below the reactor core region, components that include the core plates are represented as homogenized material regions. The primary purpose of the material homogenizations is to provide an axial reflector for the transport calculations. The total height of the benchmark problems, however, is sufficient to approximate the scope of what would be described as the RPV beltline region. Page 7 of 12

B. P. Richardson Figure 4. Radial view of the PWR calculational benchmark SCL and LLCL TRANSRAD models Figure 3 and Figure 4 illustrate the axial and radial configurations, respectively, of the SCL and LLCL problems as modeled with TRANSRAD. Note that the surveillance capsules are mounted in their correct positions. For the in-vessel capsules, the front capsule correctly shields the back capsule in the TRANSRAD model, whereas separate capsule models were developed and run in NUREG/6115 [3]. The reactor core and core baffle are modeled with their correct rectangular forms, which also varies from the cylindrical-based geometries documented in NUREG/6115 [3]. As depicted in Figure 3, the total height of the model is 382.115 cm. The core height, or active fuel height, is shown as 335.28 cm. The region below the reactor core is a homogenized lower reflector. The region above the active core height is a homogenized upper reflector. The components outside the reactor core run the full height of the problem, with the exception of the surveillance capsules that match the core height. Page 8 of 12

Evaluation of NUREG/CR-6115 Benchmarks Using TRANSFX Figure 4 provides a radial view of the SCL and LLCL reactor problems at an elevation near the reactor core mid-plane. The core region is composed of 204 fuel assemblies. Regions outside the core consist of the core baffle, core barrel, thermal shield, downcomer, pressure vessel cladding, pressure vessel, vessel insulation, biological shield liner, and biological shield (concrete) wall. The in-vessel surveillance capsules (Capsules 1 and 2) are located on the outer surface of the thermal shield and the inside surface of the vessel liner wall. The in-vessel capsules are each positioned at the 20 azimuth. The ex-vessel capsule (Capsule 3) is mounted in the cavity region near the inside surface of the biological shield at the 9.5 azimuth. 2.2.2 Reactor system material composition Table III provides the material composition for each region of the PWR Calculational Benchmark problems as represented in the TRANSRAD model. Table III. Material compositions for regions in PWR calculational benchmark problem Region Fuel Regions Baffle/Water Gap Bypass Core Barrel Thermal Shield Downcomer Surveillance Capsules RPV Liner RPV Wall Cavity RPV Insulation Biological Shield Liner Biological Shield Lower Reflector Upper Reflector Shield Zone Regions Material Composition 235 U, 238 U, 239 Pu, 240 Pu, O, Zr, Al, Cr, Fe, Ni, Water, 10 B Stainless Steel (SS-304), Water, 10 B Water, 10 B Stainless Steel (SS-304) Stainless Steel (SS-304) Water, 10 B Stainless Steel (SS-304) Stainless Steel (SS-304) Carbon Steel (SA-302B) Air Cr, Mn, Fe, Ni, Al, N, O Carbon Steel (SA-302B) Reinforced Concrete Water, 10 B, Stainless Steel (SS-304) Water, 10 B, Stainless Steel (SS-304) Cr, Mn, Fe, Ni, Water, 10 B 2.2.3 TRANSRAD model For reference purposes, a coordinate system is imposed upon the models. The models assume that the origin of the problem geometry is at (0,0,0), which corresponds to the radial center of the reactor at the lowest elevation in the problem. Figure 3 illustrates the axial coordinates for the PWR Calculational Benchmark problems, while Figure 4 illustrates the radial coordinates. The TRANSRAD models for the two PWR Calculational Benchmark problems consist of an octant of the core. As illustrated in Figure 4, each benchmark model is represented in the octant azimuthal symmetry form as described in NUREG/6115 [3], with a radial dimension ranging from Page 9 of 12

B. P. Richardson 0 cm at the center of the reactor core region to 549.275 cm at the outside surface of the biological shield wall. Each problem uses reflective boundary conditions at the 0 (west face) and 45 (diagonal face) azimuths of the reactor models. Each problem also uses vacuum boundary conditions at the outermost radial surface of the biological shield wall and at the top and bottom surfaces of the reactor problems. The height of the upper reflector region above the reactor core for both problems is 32.865 cm. The upper reflector region is described in NUREG/6115 [3] with homogenized materials and is consequently modeled as two planes of equal height in TRANSRAD. The lower reflector region is specified in NUREG/6115 [3] with homogenized materials and a height of 13.970 cm. It is modeled as a single axial plane in the TRANSRAD models. The fuel assemblies are represented in the X-Y plane of the model as pin-wise regions in the peripheral assemblies and as fully homogenized regions inside the core. The geometrical regions outside the core region coincide with the ex-core material regions (i.e., water regions, stainless steel regions, and air regions). The power density is normalized to full core power as specified in NUREG/6115 [3]. For the two-dimensional sensitivity evaluations, the radial power distribution at the core elevation corresponding to core mid-plane is used. The active core region for has an axial height of 335.28 cm. The active core region contains 25 axial nodes that are each 13.4112 cm in height. The three-dimensional models for the problems each consist of 83,276 mesh regions. 2.2.4 Results Table IV presents a comparison of the predicted reaction rates produced by the TRANSRAD and NUREG calculation methods for the PWR Calculational Benchmark SCL and LLCL evaluations. The highest differences primarily result from the differences between the TRANSFX Nuclear Data Library cross-sections used in TRANSRAD and BUGLE-93 cross-sections used in DORT. One of the primary changes from BUGLE-93 to the TRANSFX Nuclear Data Library was implemented to increase neutron transport through steel to correct observed deficiencies in BUGLE-93 comparisons in cavity dosimetry measurements. Overall the LLCL comparison ratios are lower than the SCL comparisons. This results from the difference in the fission source treatment by TRANSRAD and DORT. The SCL configuration has significantly lower exposures in the peripheral assemblies than the LLCL configuration, thereby resulting in the TRANSRAD source calculations deviating more significantly in the SCL case than the LLCL case. As expected, the Capsule 2 comparisons are depressed relative to the Capsule 1 and Capsule Page 10 of 12

Evaluation of NUREG/CR-6115 Benchmarks Using TRANSFX 3 comparisons as a result of shielding by Capsule 1. The DORT analysis used separate models containing only Capsule 1 or Capsule 2. The NUREG reaction rates for the 65 Cu reaction in the SCL Capsule 2 and the 237 Np reaction in the LLCL Capsule 2 are higher than the equivalent reaction rates in the corresponding Capsule 1 locations. All other reaction rates exhibit a decrease as they move farther from the center of the core, as would be expected. Based on these two reaction rates exhibiting behavior different from all the other reaction rates, they are considered suspect and excluded from the summary statistics of the reaction rate comparisons in Table IV. Taking into consideration the above factors, the TRANSRAD calculated reaction rate results are in acceptable agreement with the NUREG values. Table IV. Reaction rate (in rps/atom) comparison results (TRANSRAD/NUREG) for surveillance capsules in the SCL and LLCL configurations SCL LLCL Reaction Capsule 1 Capsule 2 Capsule 3 Capsule 1 Capsule 2 Capsule 3 27 Al(n,α) 24 Na 1.12 0.96 1.20 1.01 0.86 1.09 32 S(n,p) 32 P 1.12 1.01 1.25 1.04 0.94 1.16 46 Ti(n,p) 46 Sc 1.11 0.97 1.23 1.02 0.89 1.13 54 Fe(n,p) 54 Mn 1.12 1.01 1.25 1.04 0.93 1.16 56 Fe(n,p) 56 Mn 1.12 0.96 1.21 1.01 0.87 1.11 58 Ni(n,p) 58 Co 1.13 1.02 1.26 1.05 0.94 1.17 63 Cu(n,α) 60 Co 1.11 0.96 1.21 1.01 0.87 1.11 65 Cu(n,2n) 64 Cu 1.14 0.10* 1.21 1.01 0.85 1.08 115 In(n,n ) 115m In 1.25 1.18 1.40 1.17 1.10 1.32 237 Np(n,f) 1.25 1.25 1.36 1.18 0.12* 1.28 238 U(n,f) 1.17 1.09 1.28 1.09 1.02 1.20 Average 1.15 1.04 1.26 1.06 0.93 1.16 Standard Deviation 0.05 0.10 0.07 0.06 0.08 0.08 Minimum 1.11 0.96 1.20 1.01 0.85 1.08 Maximum 1.25 1.25 1.40 1.18 1.10 1.32 * Values are suspect based on NUREG reaction rate in Capsule 2 being significantly higher than NUREG reaction rate in Capsule 1. 3 CONCLUSIONS The average comparisons to all of the reaction rates from the calculational benchmarks evaluated are presented in Table V. These results agree within the calculational uncertainty associated with both codes, and are within the allowed 20% uncertainty identified in Reg. Guide 1.190. Page 11 of 12

B. P. Richardson Table V. Calculational benchmark results Benchmark Average C/M Standard Deviation Num. Comparisons BWR 1.05 0.02 24 PWR-SCL 1.15 0.11 32 PWR-LLCL 1.05 0.12 32 Total 1.09 0.11 88 4 REFERENCES [1] Calculational and Dosimetry Methods for Determining Pressure Vessel Neutron Fluence, Nuclear Regulatory Commission, Regulatory Guide 1.190 (2001). [2] Radiation Embrittlement of Reactor Vessel Materials, Nuclear Regulatory Commission, Regulatory Guide 1.99, Revision 2 (1988). [3] J. F. Carew et al., PWR and BWR Pressure Vessel Fluence Calculation Benchmark Problems and Solutions, NUREG/CR-6115 (2001). [4] D. B. Jones et al., TRANSFX Theory Manual, TWE-TFX-001-FM-016-001 (2015). Page 12 of 12