Design of an experimental breeder reactor run 138B reactor physics benchmark evaluation management application

ABSTRACT

Reactor Monte Carlo simulations present numerous challenges including input file generation and processing output files for relevant results. Creating an input file for a heterogeneous core is further complicated when using depleted fuel. Performing perturbations to geometry and material characteristics exacerbates the challenge due to human errors if the input files are manually generated. The difficulty of generating input files is often encountered during the process of performing a reactor physics benchmark evaluation. These challenges were encountered when performing a reactor physics benchmark evaluation for the Experimental Breeder Reactor II (EBR-II), a sodium cooled fast reactor. The EBR-II Monte Carlo input file uses more than 1,000 unique material specifications and ~8,000 regions. To address the input file generation challenge, a computer application was designed to automate the input file generation process. The application utilizes user input from a graphical user interface in conjunction with spreadsheets containing material and geometric data to generate Monte Carlo input files. The application, called MICKA, was used to generate input files to support the reactor physics benchmark evaluation for EBR-II. This paper describes the reactor configuration and provides information about the application design and capabilities for addressing challenges often encountered in reactor physics benchmark evaluations.

KEYWORDS:

• Benchmark
• computer code
• MCNP
• reactor physics
• sodium cooled fast reactor

1. Introduction

The Experimental Breeder Reactor II (EBR-II) was a sodium-cooled, metal-uranium-fueled fast reactor designed and operated by Argonne National Laboratory (ANL). EBR-II first went critical in 1964, and in 1969 achieved its full power level of 62.5 MW_th [1,2]. During the 1960’s, EBR-II’s main goal was to provide groundwork in developing a liquid-metal cooled fast reactor with on-site fuel reprocessing. The 1970’s brought a close to the reprocessing research phase and EBR-II then focused on irradiation capabilities and providing information for fast reactor materials. The 1980’s brought about another major change for the EBR-II facility when it became a test subject for safety analysis in liquid metal cooled reactors. A landmark reactor safety experiment program tested EBR-II’s ability to respond to severe accident conditions such as station blackout without a scram. The most severe tests were conducted during Run 138B and were designed to test a liquid metal cooled reactor’s ability to cope with catastrophic failures in the heat removal systems [3].

EBR-II contained 637 assemblies in a hexagonal lattice, which contained a driver, reflector, and outer blanket region. The reactor used seven assembly types; driver, half-worth driver, dummy, experimental, control, reflector, and blanket assemblies. The central core region contained 83 fueled assemblies, along with 10 control assemblies. Each assembly contained five distinct axial regions; lower adapter, lower extension, core region, upper extension, and upper pole piece. The lower adapter fixed the assembly into the core grid plate, while the upper pole piece was used for assembly handling. The upper/lower extension regions contained stainless-steel shield blocks with holes for coolant flow. For driver assemblies, the core region contained the fuel. Driver assemblies contained 91 fuel pins arranged in a hexagonal lattice. Similarly, half-worth driver assemblies contained 45 fuel pins along with 46 stainless-steel pins and were typically placed near the center of the core to reduce the flux in this area. EBR-II contained fueled control assemblies, which consisted of concentric hexagonal ducts, where the inner hexagonal duct contained the fuel region of the assembly. The inner duct was able to move into the core to control the power. The control rods were slightly smaller than a typical driver assembly and contained 61 fuel pins. There were three types of control assemblies that EBR-II used; safety, control, and high-worth control. The high-worth assemblies contained seven boron-carbide poison pins in the upper extension region, in addition to the 61 fuel pins in the fuel region. The safety and control assemblies only contained the fuel region and did not have the additional poison pins. The other assemblies followed a similar axial configuration but had a lower importance for the reactor physics benchmark and are described in detail in the benchmark report [4].

Fuel pins consisted of a 34.29 cm long fuel slug with a diameter of 0.33 cm using metallic uranium-fissium fuel, initially enriched to ~67 wt%. Fissium was a collection of alloying metals (Mo, Ru, Rh, Pd, Zr, and Nb totaling 5 wt%) that simulated the dominant mid-cycle fission products. A sodium metal bond was placed between the fuel pin and cladding; above the sodium bond, the plenum was filled with an inert gas. The cladding was 316 stainless-steel with a thickness of 0.03 cm, which gave the fuel pin an outer diameter of 0.442 cm. To prevent pin-to-pin contact, each pin had a 0.12 cm wire wrap which ran toroidally up the cladding. Each driver assembly contained approximately 2.5 kg of ²³⁵U, with the entire core containing ~250 kg. The core lattice had a hexagonal pitch of 5.89 cm, with an effective core height and diameter of 34.29 cm and 69.67 cm.

To preserve important information related to EBR-II, a reactor physics benchmark evaluation was performed in accordance with the Reactor Physics Experiment Evaluation Project Handbook (IRPhEP) [4,5]. The IRPhEP is organized under the auspices of the Organization of Economic Cooperation and Development (OECD) Nuclear Energy Agency (NEA) Nuclear Science Committee through the Working Party on Reactor Systems (WPRS). This multi-national effort to consolidate and preserve past reactor physics experiments has seven main goals; (1) to consolidate and preserve the information that already exists worldwide; (2) make lost data available; (3) identify areas where more data is required; (4) draw upon the international reactor physics communities resources to fill the needs; (5) identify discrepancies between calculations and experiments due to lack of reported experimental data, cross-section data, cross-section processing codes, and neutronic codes; (6) eliminate redundant research and processing of reactor physics experiment data; and (7) improve the future experimental planning, execution, and reporting. The IRPhEP handbook is designed to allow users to gain a better understanding of reactor technologies through models. These models are based upon known experiments, with known reactor constants such as criticality, control rod worth, etc. A benchmark model must incorporate as much detail as possible to allow appropriate conclusions to be drawn.

Idaho State University was awarded a grant from the US Department of Energy – Nuclear Energy University Program to develop an EBR-II benchmark evaluation suitable for inclusion in the IRPhEP handbook. The benchmark evaluation process fundamentally focused on uncertainty quantification. To quantify the uncertainties, a detailed model of the reactor was prepared, and numerous model perturbations were performed to assess the reactivity change associated with the uncertainty in various parameters. For this work, MCNP6 was selected to perform the neutronics calculations [6]. Some of the most important parameters evaluated included manufacturing dimensional and material composition uncertainties.

It was quickly concluded that hand creation of MCNP input files was infeasible and provided a significant pathway for error. The EBR-II core at the time of Run 138B was composed of irradiated fuel, which was dependent on core location and length of time in the core. Data for the depleted fuel and many material compositions was obtained from ANL, but still provided a challenge due to the multitude of materials present. In the EBR-II core model, there were 1,400 unique material compositions, mainly in the form of depleted fuel. The atom density compositions from ANL were produced by a proprietary ANL depletion code where the assemblies were homogenized. To prepare the MCNP input files, the atom densities had to be translated to the associated volumes derived from engineering drawings of the assemblies. The detail necessary in the reactor model resulted in input files approaching 40,000 lines without comments. To automate the input file generation process, a computer application called MCNP Input and Kcode Architect (MICKA) was prepared. As MICKA was developed, additional enhancements were added to allow automated execution of MCNP, extraction of desired results, and generation of plots to ensure the desired outcome. The challenges and solutions associated with designing the application are discussed in the following section and are intended to guide others facing similar challenges.

2. MICKA

This section is presented in four major units; MICKA interface and data processing, data manipulation, perturbations, and additional functionality. The interface section provides a description for MICKA’s framework and a general algorithm for loading, manipulating, and processing reactor data. The data manipulation section discusses how MICKA takes given EBR-II data and incorporates known physics to create a realistic model. The perturbation sections provided an overview of how perturbations are performed using MICKA. The presentation from microscopic to macroscopic detail allows for a greater understanding of how to approach perturbations for materials, dimensions, and a full assembly/core. This is followed by a discussion on the additional functionality which was built into MICKA; homogenization, duct bowing, and post processing.

2.1. Interface/data processing

The application was written using MATLAB [7]. A sample of the GUI interface can be seen in Figure 1 and allows the user to rapidly edit, build, and execute an MCNP input file for the desired EBR-II configuration. MICKA has three main sections; (1) load user inputs and benchmark data spreadsheets, (2) create the MCNP input file for the user specified core, and (3) execute MCNP. The detailed process can be seen in Figure 2.

Figure 1. MICKA GUI interface

Figure 2. MICKA flow chart

MICKA allows the user to alter nearly every aspect of the EBR-II core model from the material composition to control rod positions. The ability to manipulate each aspect of the core was vital for MICKA to be useful to allow altering specific aspects of the EBR-II core, while keeping the bulk of the information constant.

Reading and manipulating large amounts of data was where MICKA provided eloquence, speed, and accuracy over manual input file creation. Data pertinent to EBR-II was stored in 17 spreadsheets, which contain material and geometry information including uncertainties and tolerances for the given data. MICKA organized the data and then applied multiple conversions to obtain the correct MCNP format for dimensions or materials. These data manipulations were performed by two major functions, DimMapper and MatMapper.

DimMapper read in the dimension spreadsheets and stored the data in a 723 by 179 array. The columns were broken into triplets containing the dimension, uncertainty, and tolerance for an assembly component. Each row of the array represented one assembly position which has markers to denote a MICKA ID number, EBR-II position, assembly type, and assembly name. DimMapper created an initial framework for the geometric dimensions which were perturbed, if necessary, before being written into the MCNP input file. Along with this, DimMapper converted the dimensions in the spreadsheets from imperial to SI units to be compatible with MCNP input file requirements.

MatMapper read in the material spreadsheets and performed processing on the material data. The fuel composition data obtained from ANL for each assembly was homogenized and contained the atom densities for the cladding, sodium, uranium, minor actinides, and lumped fission products. To create a heterogeneous MCNP model, fuel composition data was separated from structural material, and a volume correction was performed to obtain the correct atom density. The fuel consisted of three separate axial regions (upper, middle, and lower), each with unique isotopic distributions. Once the volume correction was obtained, MICKA converted the lumped fission product values from the ANL provided composition to a specific set of fission product isotopes. These were derived from independent depletion calculations correlated to ANL reported ²³⁵U, ²³⁹Pu, ¹³⁹La, and ¹⁴⁸Nd values [8]. Once the composition of each axial fuel section was determined, the information was used to calculate the average burnup for the assembly. A feature was added to MICKA to produce a plot depicting the driver section of the core with the calculated assembly burnup provided for each assembly; see Figure 3.

Figure 3. Burnup map for Run 138B

MICKA also read a spreadsheet containing isotopic information from the chart of the nuclides; this included the atomic mass, natural abundance, and density of all relevant isotopes. This allowed MICKA to calculate atom percent from a given weight percent. This process was important when considering materials, like stainless-steel, which are rarely given in atom density, due to the multitude of elements present. MICKA used total atom density with an isotopic atom composition for fuel, and weight composition for non-fuel materials to allow for verification and internal consistency checking.

2.2. Data manipulation

MatMapper also performed cross-section and physical dimension updates. For cross-section updates, MICKA built temperature adjusted cross-section sets to correspond to the temperature present in the system. MatMapper performed two types of physical swelling corrections to specific assemblies within the core; burnup (irradiation) swelling and thermal swelling.

The first type of swelling was irradiation swelling, which was based on the burnup of driver assemblies and only performed on the driver fuel, blanket fuel, and boron carbide poison slugs. MICKA read the ¹⁴⁸Nd, ¹³⁹La, and minor actinide data and used this information to determine the burnup for each fuel section. The burnup for each fuel section was then used to perform the swelling calculations. Once the burnup map was calculated, the average burnup for an assembly was determined, and the dimensions and materials were sent through a series of functions to perform swelling calculations. The fuel slugs were expanded in radial and axial directions based on previously published EBR-II burnup induced swelling observations [9]. A self-check was set to determine if the slug diameter exceeded the cladding diameter. If this was true, the fuel slug diameter was changed to a value just slightly smaller than the cladding inner diameter. After the height and radius were adjusted, a new volume was calculated for density, which ensures the mass of fuel was preserved. As noted, the burnup calculations were done on each fuel section and then averaged for an assembly burnup. This means all fuel pins in an assembly were expanded to the same value despite differences which may have occurred due to spatial positioning in the assembly. The burnup calculations were also performed on the high worth control rods which contained boron carbide as a neutron poison. The boron carbide went through a similar burnup calculation to determine a burnup percent for the poison and to calculate a new atom density for the boron carbide, which was unique to each high worth control rod assembly.

The second type of swelling was thermal swelling and was performed on all stainless-steel and sodium components. Thermal swelling was performed using an average temperature in the core to adjust the atom density of each material based on the linear expansion coefficients. Each unique stainless-steel and sodium homogenization had an expansion coefficient calculated based on the ratio of the two materials. The swelling calculations were first performed on the cladding. This was performed using data obtained from regression plots, where each type of stainless-steel has a unique plot [9]. Each pin in an assembly is swelled both axially and radially, a new volume was calculated, and a shift in the pin was calculated to ensure the swelling does not produce geometric interference in MCNP. MICKA also set a limit on the maximum swelling amount to eliminate geometric interference. The new volume was then used to calculate a new atom density for the cladding material to conserve the mass. It is important to note that although driver fuel, blanket fuel, and poison slugs all underwent thermal expansion, only irradiation swelling was modeled due to its greater impact.

After the swelling calculations were performed throughout the entire core, duplicate material composition information stored in MICKA was eliminated. A cleaner function was implemented to remove excess data to prevent cluttering the MCNP input file. The function determines if cells have an identical material, and if so, replaces them both with a generic version. For example, sodium gets created ~700 times but was replaced with one generic definition used throughout the input file.

Once the MCNP input file surface, cell, and data cards were created, MICKA analyzed all the elements within the model and created a new file to perform cross-section Doppler broadening. Doppler broadening for EBR-II was performed on 89 cross sections within the benchmark model. To perform these adjustments, a new cross section library was created based on the user selected temperature. MICKA did this by creating a separate MAKXSF input file. MAKXSF was a code which could manipulate cross-section libraries for MCNP to create a set of temperature dependent libraries and provide Doppler broadening for resolved data at higher temperatures [10]. MICKA created the input file based on a user defined temperature profile and found the two closest and most current cross-section libraries to be used for interpolation. When MAKXSF was complete, MICKA took the directory and library, and copied the files into the same folder where the input file was created.

2.3. Geometric and material perturbations

The overarching goal of MICKA was to allow perturbations to be made to the model while avoiding the arduous task of manually altering the input files. MICKA allowed the perturbation of nearly all dimensions and materials within the EBR-II model. Due to the complexity of the EBR-II core model, each assembly was created separately to account for differences in burnup or assembly type. This approach created a plethora of surfaces, which challenged character limits imposed by MCNP. To overcome the MCNP character limits, MCNP lattices were used for the fuel pins in an assembly to consolidate the number of surfaces required. The drawback of this approach was that any perturbation would be applied to all pins within a specified assembly. Although this limits individuality in pins, it was determined that individual pin perturbations were not necessary for the benchmark evaluation and greatly reduces the input file size.

Multiple types of material perturbations were performed: (1) isotope, (2) composition, (3) smear, and (4) density. Isotope perturbations required entering the nuclide identification number, choosing an atom percentage to perturb, and applying an appropriate scaling factor (used for the benchmark uncertainty quantification evaluation). Composition perturbations involved perturbing an element which perturbed all subsequent isotopes. For example, in stainless-steel if iron were perturbed, all five isotopes were perturbed, while the remaining elements of stainless-steel were adjusted to maintain the total atom density. Smear perturbations required adjusting the weight percent of sodium in the smeared material and adjusting the stainless-steel weight percent accordingly. Density perturbations adjusted the mass density of material, which could include a smeared material.

Along with material perturbations, MICKA was also capable of handling a multitude of dimensional perturbations. Retaining the integrity of the model required multiple sub-functions whose purpose was to read perturbations and all the surrounding dimensions. It then performed checks to ensure the perturbed dimension did not exceed the surrounding dimensions. If those dimensions were exceeded, MICKA not only informed the user where the model was violated, but suggested a new scaling factor for the perturbation. For example, if a fuel slug were to be perturbed and the radius exceeded the inner cladding radius, it would be flagged. The perturbations for a fuel pin included fuel slug height/radius, sodium level height, fuel cladding height/thickness/radius, and wire wrap height/radius. Similarly, poison pins had perturbations for the poison slug height/radius, poison cladding height/thickness/radius, and wire wrap height/radius. On an assembly level, the perturbations included hex duct width, inner hex duct width (only applicable to the control rods), upper extension, lower extension, and lower adapter. Each perturbation could be done individually, or multiple perturbations could be run concurrently.

2.4. Full core perturbations

In addition to performing material and dimensional perturbations, the benchmark evaluation required the perturbation of unique features within the core. Some features, like temperature, were applied across the entire core in a uniform manner. The temperature adjustment played a factor in multiple component’s materials, namely the density and cross-section sets used. MICKA also had the ability to incorporate unique cross-section treatments such as S(α,β) to areas which incorporate carbon. This was achieved by creating a new cross-section set for each run, and determining which areas needed S(α,β) treatment.

It was the goal of MICKA to allow the EBR-II core model to be dynamic in the sense that each run could be different from the last, and additional information could be gained from the changes. One aspect was to allow the control rods to vary in position based on user input. The benchmark analysis required the control rods to be stationary, unless their position was the perturbation in question. In general, the user can define the control rod position for each individual assembly and can thus infer quantities such as control rod worth.

2.5. Homogenization

Due to the number of assemblies and the details attributed to each assembly, it was determined MICKA would be used to create individual input files for multiple types of simplifications and homogenizations. To allow for this, multiple new assembly maker functions were created in parallel with the original functions. The new functions used all the dimensional and material information from the heterogeneous model, and applied a homogenization algorithm to create a simplified assembly. These simplifications took two different forms; the removal of components, and the homogenization of components. The removal of components was straight forward and required removing and altering minor sections of the original assembly maker. The more in-depth process was homogenizing the multiple types of assemblies.

To create a homogenized assembly, the first step was to read the original dimensions, materials, and positional origin for the assembly type. The dimension, material, and origin information was then passed to multiple sub-functions. The sub-functions calculated the volumes and volume percents for each component of the assembly for the homogenization process. They then converted material data in both weight percent and atom percent to an atom density, which was used to create one material for the entire homogenized region. Finally, data for the material composition and density was passed to the main assembly creation function, which would print out the new material being used, along with cell and surface cards. This information was then fed back into the main program of MICKA to write the MCNP input file. The homogenization process was not extended to every type of assembly in the EBR-II core; the control rods and experimental assemblies were not homogenized. The control rods were not homogenized due to the inability to retain movement with the homogenized assembly. The experimental assemblies were not homogenized due to the lack of knowledge of each assembly, thus homogenization would provide no additional information about the core.

2.6. Axial bowing

After the creation of the geometry and material perturbation code, a new feature was added to MICKA. Given the discretization of geometry inside of MICKA, it was apparent that a unique simulation could capture the negative reactivity effects due to core flowering [11]. Core flowering was performed by bowing each assembly duct individually with horizontal slices. Each slice of the duct was translated in space according to a finite element analysis simulation of the temperature induced structural deformation. Figure 4 shows how the finite element analysis node positions were translated to the slices of the MCNP model built by MICKA.

Figure 4. Assembly bowing transformation

To represent the core flowering, each duct had the mechanical stresses and subsequent deformation resolved. MICKA took the deformation information and calculated a net average displacement for each duct and core slice.

2.7. Pre/post processing

To aid in verification and input file creation, MICKA ran multiple pre and post processing functions. On the pre-processing side, MICKA used an input file comparator which took the benchmark model as-is and compared it to an input file created for a perturbation. MICKA returns information about what changed between the two files to determine if a perturbation was performed correctly. Along with this, MICKA read a SCALE output file from a depletion analysis and converted the materials to an excel spreadsheet. The SCALE 6.1 TRITON output was associated with a bridging depletion calculation performed on a single fuel assembly to obtain the fission product distribution since the composition data from ANL contained only a lumped fission product value. The bridging depletion calculation was performed by matching the ANL ²³⁵U ²³⁹Pu, ¹³⁹La, and ¹⁴⁸Nd reported values and then using the fission product distribution results. These materials are then read to create the fission product details for the fuel material composition while removing materials with concentrations of less than 10⁻¹⁵ atoms/b-cm. Finally, MICKA also created a separate numbering scheme for keeping track of the assemblies within the core. The number scheme is used throughout the input file and provided an intuitive nomenclature. The number scheme started from the central assembly and spiraled outward. For example, the central position 01A01 would be MICKA ID#1, the next position 02A01 would be MICKA ID#2.

For post-processing, MICKA read the output file created by MCNP and determined if each cell in the model was adequately sampled and reported any deficiencies. Once all the perturbations are run, MICKA read each output file and created an excel spreadsheet. This spreadsheet contained the multiplication factor, its associated uncertainty, the perturbation performed, the perturbation quantity, and the scaling factor associated with the perturbation. Finally, MICKA has built-in capabilities for plotting the flux from a mesh tally. The mesh tally was read by MICKA which plotted the flux values over a core representation.

3. Verification

The mass of ²³⁵U was of high importance in the MCNP model, and it was imperative that the mass stayed consistent throughout MICKA while various calculations and manipulations were performed. This was ensured by calculating the total fuel mass before and after each function, which maintained model understanding and mass conservation during processing. Along with this check, each material’s atom or weight percent is normalized to one. This allowed MICKA to check the normalization anytime a material was passed through a new function. The normalization gave MICKA the ability to quickly determine if any function had either failed to renormalize or caused an unknown change in the material composition. Figure 5 shows an output plot from MICKA with the fuel mass of a single pin per assembly. The fuel mass in each assembly in Figure 5 was stored and checked throughout MICKA to ensure mass conservation.

Figure 5. Fuel mass of a single pin per assembly

It is important to note that throughout the entire process, MICKA retained 15 significant figures for materials and dimensions and only rounds when creating the MCNP input file. This prevented unnecessary truncation errors, especially since many of the material compositions are extremely small. Despite this, there were still slight changes in the material composition between initial inputs from excel spreadsheets and the final output. These differences were expected due to the arduous process of translating the materials multiple times before the final output.

For a given dimension perturbation which involved fuel, the mass of fuel remained constant. This means the density would decrease in a perturbation which expanded the fuel or increase in a perturbation which shrunk the fuel in some way. The same was true for material composition perturbations; if the atom density of the fuel was altered, the overall atom density would increase. The same procedures were followed for the homogenization process. The initial ²³⁵U mass was stored before the homogenization process took place. The homogenization functions then performed the volume correction for the atom densities and smeared the fuel across the entire fuel region. Once the homogenization took place, the mass of ²³⁵U was again calculated and compared to the initial ²³⁵U mass.

4. Results

4.1. Benchmark simplifications

Maintaining a benchmark model which was easily perturbed and retained the most accurate representation of EBR-II, was important to the validity of the calculation. This meant that two separate iterations of models were created. The detailed model encompassed as much information from the physical reactor as possible. The model used to calculate perturbations introduced several simplifications to reduce the model’s complexity and increase its robustness for perturbations. These simplifications were introduced as biases to the reported value of k_eff for Run 138B. The difference in the multiplication factor of the detailed model versus the simplified model are shown in Table 1 along with the benchmark reported value. The detailed model and simplified model had a multiplication factor ~1000 pcm higher than expected drawing heavily from the fact that neither model incorporated thermal expansion, and there were thermal gradients in the core which lead to various mechanical stresses that were not modeled.

Table 1. EBR-II multiplication factors

Model Type	keff
Detailed	1.01169 ± 0.00005
Simplified	1.01396 ± 0.00005
Benchmark	1.00927 ± 0.00618

The first bias introduced was the homogenization and removal of various components in EBR-II. In a parametric study, it was determined that materials outside of the core liner were negligible and that the homogenization of blanket rows 13–16 reduced the model input file by a factor of two. Similarly, the lower adapters of all the assemblies were removed and replaced with sodium, as their distance from the core made them neutronically insignificant, and there was a large uncertainty in the sodium to stainless-steel ratio. Since MICKA had a built-in routine for homogenization, it was simple to create a model which only homogenized a portion of the core and removed specific assembly components. This meant that the blanket assemblies in rows 13–16 were converted to a homogenized representation without the use of manual calculations.

Along with homogenizations for the benchmark, the fuel element and fuel slug were not swelled in the benchmark model. MICKA had the ability to perform fuel element and fuel slug swelling, however the swelling was disabled to allow beginning of life fuel element and fuel slug perturbations. Similarly, the burnup of ¹⁰B was not included in the benchmark model. This meant that each poison assembly was modeled with beginning of life boron content. These biases were unquantifiable without MICKA’s ability to perform the swelling calculations and ¹⁰B burnup.

The final biases introduced to the benchmark model were due to the thermal expansion of multiple materials in the core. The thermal expansion of the sodium bond above the fuel slug was found to have a bias due to the exchange of plenum gas with sodium. Along with this, complex structural expansion effects could not easily be modeled with MCNP and were taken from a list of reported values. Similar to the irradiation swelling of components, MICKA had the capability to introduce thermal expansion for individual components, like the sodium bond in the fuel. This enabled the benchmark to quantify the impact of thermal expansion for sodium. Although this could not be easily extended to the remainder of thermal expansion, it provided valuable insight into thermal expansion in regions that were adjacent to the fuel.

The total bias in the benchmark model was 0.00927. When this is added to the reported value of k_eff of the experiment (1.0000), it was found that the multiplication factor of the experiment was 1.00927. The multiplication value shows that the benchmark model did not capture all of the necessary physics and adjusting the critical value of the experiment with the biases accounts for the deviations of the models to the experiment.

Along with the biases that were calculated, a number of additional simplifications were made. These simplifications were assumed to be negligible, or a modeling choice that was deemed appropriate. This included modeling the wire wrap as a cylinder with the appropriate diameter, but with an increased density to account for the excess material associated with a toroidal wrap. Another viable method was to smear the stainless-steel into the surrounding sodium. Similarly, at the top and bottom of fuel/poison pins, there was a small spade and welding plug that were not explicitly modeled. For these small components, an equivalent amount of stainless-steel was modeled above and below the fuel/poison element. It was determined that maintaining the material content was more important than retaining small geometry changes in the core. This same reasoning also led the grid plate to be homogenized into the lower extension to reduce model complexity but retain material mass. Another important simplification was the inclusion of a single temperature (617 K) for the entire model. This approach was taken due to a lack of information about the temperature distribution throughout the core. MICKA did have a capability to introduce a temperature profile where body temperatures could mimic an approximate distribution. The decision was made that a uniform temperature would lead to an understood result whereas an approximate distribution had more unknowns. Capturing what was known about the experiment was the primary goal of the benchmark, not to approximate the unknown. One of the results of the benchmark perturbations was that the effect of temperature was directly coupled to the sodium density, which was the primary driver in the change of multiplication. Any temperature distribution applied to the benchmark model was overshadowed by the change in temperature of the sodium.

MICKA allowed for the quantification of several simplifications, which helped reduce the burden of running multiple perturbations for the benchmark model. These simplifications allowed MICKA to perform over 150 perturbations and determine the sensitivity of various reactor components.

4.2. Benchmark results

The MICKA application was designed to aid in the development of the EBR-II reactor physics benchmark evaluation; namely in creating the various models that were required for simulating and perturbing the Run 138B core configuration. Each model represented a perturbation on a single component; this included material and geometry perturbations. The models were all run independently to determine the resulting change in the multiplication factor. It was this change in the multiplication factor which was sought after to understand the sensitivity of minute changes in the core. These sensitivities give future reactor designers and code developers a better understanding of components needing strict limits during manufacturing, and components where more leniency is appropriate. For example, it was found that perturbing the lumped fission products had no effect on the multiplication factor. This implied that the exact composition of the lumped fission products is of lesser importance. Over 150 perturbed models were created, and a majority of them resulted in little or no change in the multiplication factor, indicating that the core was not sensitive to those perturbations. Some of these included the blanket slug diameter, the fuel slug diameter, and the fissium/fission product concentrations. Others had a more profound impact such as the ²³⁵U composition, ¹⁰B concentration in boron carbide, and the metal constituents of 316 stainless-steel. Each of these perturbations contributed to the uncertainty measurement for the EBR-II benchmark, where an overview of the top five contributors and the total uncertainty can be seen in Table 2. Table 2 also shows the results of the temperature perturbation due to the uncertainty in the thermocouple measurements.

Table 2. Overview of evaluated uncertainty for the EBR-II benchmark [12]

Perturbation	Uncertainty (±Δkeff)
^235U Composition	0.00535
Driver Mass	0.00523
Assembly Pitch	0.00098
SS316 Nickel Content	0.00074
Density 304L	0.00068
Temperature ± 7 K	0.00021
Total Benchmark Uncertainty	0.00618

The total evaluated uncertainty represents the effect of geometric, material, and other physical uncertainties on the multiplication factor for EBR-II. These uncertainties stem from manufacturing tolerances on components, uncertainty of material compositions, and physical readouts from various instruments.

5. Conclusions

MICKA was created to help generate the EBR-II Run 138B benchmark and to be easily transferable to other reactor designs. Data used in the benchmark model was contained in a series of excel files which were specific to EBR-II, however the format can be used to incorporate additional reactor designs. Adapting MICKA to a different liquid metal reactor would require updating these design specifications. Each specification uses a triplet system to describe the dimension, where the first value is the design value, which is followed by the uncertainty and the tolerance. MICKA will check dimensions relative to each other to ensure the model does not violate a physical geometry. Along with this, if the uncertainty or tolerance is not known, it will not cause repercussions in the design and it will only prevent the application of perturbations to the dimension. Materials are also contained in excel spreadsheets, which are easy to update for different fuel, cladding, or coolant types. The materials are contained in two major forms, standard materials and fuel specific materials. The standard materials consist of non-unique materials in the core such as stainless-steel, sodium, or plenum gas, where additional materials could be added with relative ease. The fuel materials are specific to each assembly in the core and would require the user to input the isotopic concentrations of each fuel assembly, which would be tedious but could easily be automated.

Despite the burden of adding each fuel assembly, it provides a level of detail that is instrumental to performing a benchmark. Once the new assembly dimensions and materials have been created, the last major obstacle will be creating a new core map to describe where the assemblies should be placed in the core. This type of work has already been done with the advent of core homogenization, which required creating new core maps for each type of homogenized assembly. The core spreadsheet has the built-in positions required for creating a hexagonal lattice, where the user would need to declare an assembly for each position to create a unique core. To utilize MICKA to perform additional benchmark calculations, there would be a learning curve, similar to utilizing and new code suite. However, the power of being able to generate hundreds of detailed MCNP models without manually adjusting an MCNP input file would far outweigh the initial time spent to understand, update, and implement MICKA. To this end, updating MICKA would require little work for a similar geometry core and would be useful for modeling additional EBR-II runs, or benchmark modeling for other fast reactors.

The EBR-II reactor physics benchmark evaluation model required extreme detail to properly quantify associated uncertainties. To attain the required level of detail and perform the number of perturbations required for a benchmark model, it was unrealistic to create separate models by hand. MICKA was created to automate the MCNP input file creation process and allow for ease of user manipulation. MICKA was able to read data from multiple excel spreadsheets, which describe both geometric and material features of EBR-II, and created unique MCNP input files based on user preference. These preferences can include perturbations to materials or dimensions, control rod height, homogenization structures, and temperature. With these abilities, a user can run multiple simulations in parallel to optimize characteristics of a similar EBR-II core without rebuilding an MCNP input file from scratch. Most importantly, MICKA allowed for the creation of over 150 perturbations to be made to EBR-II; each perturbation with its own unique input file. Leveraging these abilities, MICKA created and ran each perturbation to determine the effect initial uncertainties and tolerances had in manufacturing the EBR-II core. Due to these abilities, a list of evaluated uncertainties was created, which contributed to the creation of an IRPhEP benchmark evaluation for EBR-II Run 138B. The corresponding author may be contacted for inquiries related to obtaining a copy of the application.

Disclosure statement

No potential conflict of interest was reported by the authors.