Preamble

Enhanced Quantitative Analysis of Beryllium Shim Worth in NIRR-1 Post-HEU to LEU Conversion Using WIMS-ANL and REBUS-ANL

Dennis Solomon Balami (First Author), Department of Physics, University of Maiduguri, Borno State, Nigeria

John Simon, National Open University Nigeria, Abuja, Nigeria

Abdulsamad Asuku, Centre for Energy Research and Training (CERT), Ahmadu Bello University Zaria, Kaduna State, Nigeria

Yakubu Ibrahim Viva, Centre for Energy Research and Training (CERT), Ahmadu Bello University Zaria, Kaduna State, Nigeria

Rabiu Nasiru, Department of Physics, Ahmadu Bello University Zaria, Kaduna State, Nigeria

ABSTRACT

This work presents a detailed, benchmarked evaluation of the reactivity worth of top beryllium shim plates in the Nigerian Research Reactor-1 (NIRR-1) following conversion from high-enriched uranium (HEU) to low-enriched uranium (LEU) fuel. Multigroup cross sections were generated with WIMS-ANL and coupled full-core reactivity and shim-insertion studies performed with REBUS-ANL; deterministic results were validated against MCNP benchmarks and experimental measurements reported in the NIRR-1 Safety Analysis Report. For a full shim stack (120 mm total) we obtain total top-shim worths of 19.5 mk (1950 pcm) for the HEU configuration and 18.3 mk (1830 pcm) for the LEU configuration. Saturation-fit analysis using an asymptotic exponential model yields asymptotic worths δk∞ ≈ 19.2 mk (HEU) and 18.1 mk (LEU), with 95% of δk∞ reached at 10.2 ± 0.5 cm (HEU) and 10.0 ± 0.4 cm (LEU)—quantitatively confirming the practical 10–12 cm saturation window. REBUS-ANL underpredicts measured differential worth by ≈5–6% (≈1 mk), while MCNP shows closer agreement. Dose/activation assessments indicate inner-shim gamma heating (0.042–0.048 W/cm³) and post-shutdown dose rates (≈45 mR/hr HEU, 52 mR/hr LEU after 1000 h) remain within operational limits. The analysis demonstrates that conversion to LEU produces only modest reduction in top-shim effectiveness (≈4% deviation). Dominant model uncertainties arise from group-collapse approximations and 2-D geometric effects. The study provides operationally useful guidance for uncertainty budgeting, shim management, and potential design optimizations for extended core lifetime.

Keywords: NIRR-1; beryllium shim plates; WIMS-ANL; REBUS-ANL; reactivity worth; saturation analysis; Monte Carlo validation; thermal-hydraulics; activation

Introduction

The Nigerian Research Reactor-1 (NIRR-1) is a Miniature Neutron Source Reactor (MNSR) that has been pivotal in supporting nuclear research and education in Nigeria since its first commissioning in 2004 [1, 2, 3, 4]. Because of their compact nature and the need for substantial thermal neutron flux, MNSRs were initially designed and commercially deployed with High Enriched Uranium (HEU) fuel. However, due to proliferation concerns that bear on global nuclear security, the joint effort of the International Atomic Energy Agency (IAEA) and the Reduced Enrichment for Research and Test Reactors (RERTR) program has recorded significant success in the conversion of research reactors from HEU to Low Enriched Uranium (LEU) [3, 4].

Driven by the same momentum, NIRR-1 has recently undergone conversion from its initial HEU fuel to LEU fuel in support of the global effort toward reduction of proliferation risks associated with HEU [2]. Generally, MNSRs are characterized by a small window of excess reactivity that is available for operation—about 4 mk (or 0.57%)—estimated to sustain the reactor operation cycle for 12 years at a regime of 2.5 hours per day, 4 days per week, and 48 weeks per year, equivalent to 216 Full Power Effective Days (FPED) [4, 5]. To compensate for reactivity loss due primarily to fuel burnup and buildup of poisons such as xenon and samarium, the reactor was designed with a provision for a shim tray at the top of the reactor core to allow addition of a good neutron reflector [3, 6]. The addition of the top reflector increases the population of fast neutrons in the core which are expected to collapse to thermal energies after moderation and enhances recovery of lost reactivity [6]. In all commercially deployed MNSRs including NIRR-1, the top shims are made of beryllium, just like those located at the bottom and annular regions of the reactor core. The beryllium shims therefore serve to compensate for loss in core excess reactivity upon addition in the top tray [6]. These beryllium shim plates can be stacked to varying thicknesses to achieve a desired reactivity gain, thereby extending the reactor's operational cycles and longevity.

As already demonstrated by [3, 4], the conversion process impacted several neutronic parameters of the NIRR-1 'as-built' LEU core due to changes in reactor core configuration. However, the extent to which beryllium shim worth was impacted after converting NIRR-1 from HEU to LEU is yet to be delineated, highlighting a gap in literature that needs to be filled to provide comprehensive understanding of the advantages of converting MNSRs from HEU to LEU, which will further spur support for the global research reactor conversion program. Understanding shim effectiveness is particularly crucial for the NIRR-1 'as-built' LEU core since its neutron spectrum differs from that of the former HEU core and significantly affects core lifetime longevity.

This study addresses this gap by conducting a comprehensive comparative analysis of beryllium shim worth in both HEU and LEU cores using advanced computational tools such as WIMS-ANL and REBUS-ANL. The primary objective is to calculate the worths of beryllium shim plates for both HEU and 'as-built' LEU cores and compare them with measured data to provide a reliable estimate of the impact of conversion on shim worth. By benchmarking calculated results against established data in the Safety Analysis Report (SAR), this research provides valuable insights into retention of initial overall characteristics of NIRR-1 before conversion and offers impetus to other MNSR operators yet to convert.

To enhance the novelty of this analysis, additional reactor physics parameters affected by HEU-to-LEU conversion are incorporated, including control rod worth, neutron flux distributions, temperature reactivity coefficients, and void coefficients, drawing from comparative studies in similar MNSR conversions [7, 8, 9]. Furthermore, thermal hydraulics considerations are integrated to evaluate how changes in shim worth influence coolant flow, fuel temperature peaking, and overall safety margins, which are critical for low-power reactors like MNSRs operating under natural convection [10, 11]. Predictions for extended shim thicknesses beyond 120 mm are proposed, suggesting diminishing returns in reactivity gain due to neutron leakage and spectrum hardening, potentially extending core lifetime by 5-10% in LEU configurations [12].

Materials and Methods

2.1 Materials

The materials utilized for this study are the Nigerian Research Reactor-1, the Winfrith Improved Multigroup Scheme-Argonne National Lab (WIMS-ANL), and the REactor BUrnup System-Argonne National Lab (REBUS-ANL) computer codes.

2.1.1 Description of NIRR-1

The Nigeria Research Reactor-1 (NIRR-1) is a Miniature Neutron Source Reactor (MNSR) located at the Centre for Energy Research and Training (CERT), Ahmadu Bello University, Zaria [7, 8]. NIRR-1 is a low-power, tank-in-pool, light water reactor designed and deployed by the China Institute of Atomic Energy (CIAE) [9, 10]. The reactor achieved first criticality on February 3, 2004 [2, 8] and operated continuously for 10 years using HEU fuel. The NIRR-1 HEU core was operated at a nominal thermal power of 31 kW until it was permanently shut down for conversion. Structurally, the core consists of upper and lower grid plates held in position by four tie rods 600 mm long. The two grid plates contain 347 lattice positions distributed in 10 concentric circles of different radial pitch, with the central position holding the control rod guide tube while the remaining lattice positions are occupied by tie rods, active fuel rods, and dummy fuel rods [4]. The core is surrounded by annular beryllium reflectors which form a narrow orifice with the bottom beryllium plates to allow inflow of light water that serves as both moderator and coolant. The topmost part of the core is covered by the top beryllium shim tray which also forms the upper orifice where coolant exits. The core is surrounded by 10 irradiation channels, 4 reactivity regulator guide tubes, fission chambers, and a reactivity startup guide tube also known as the slant tube. The ten irradiation channels are positioned such that 5 are in the annular beryllium while the other 5 are located outside the core. All reactor core components are encapsulated in a cylindrical aluminum vessel with volume 1.5 m³, which is immersed in a water-filled pool with volume 27 m³, as shown in Figures 1, 2, 3 and 4 [8, 3, 4]. Technical specifications of the HEU and 'as-built' LEU cores are presented in Table 1 [TABLE:1], indicating the technical differences between the two configurations.

Figure 1 [FIGURE:1]: NIRR-1 reactor core in operation [5]

Figure 2 [FIGURE:2]: MCNP Model for the radial core configuration of NIRR-1 [8]

Figure 3 [FIGURE:3]: MCNP Model for the axial cross section of NIRR-1 [8]

Figure 4 [FIGURE:4]: REBUS-ANL model of NIRR-1 [8]

Table 1: Technical Design Parameters for NIRR-1 HEU and LEU Cores [8, 4, 3, 10, 11]

Design Parameter HEU Core LEU Core Rated Thermal Power 31 kW 31 kW Fuel Type UAl₄ UAl₄ Fuel Enrichment 90.2% <20% Loading of U-235 in the core ~1.0 kg ~1.0 kg Fuel Diameter 4.3 mm 4.3 mm Length of active fuel region 230 mm 230 mm Cladding material Zircaloy-4 Zircaloy-4 Cladding Thickness 0.6 mm 0.6 mm Number of Active fuel Pins 347 335 Number of Dummies 0 12 Grid plates/dummy/tie rods material Zircaloy-4 Zircaloy-4 Control rod guide tube Cadmium Cadmium Clean Core Excess Reactivity ~4 mk ~4 mk Control rod worth -7 mk -7 mk Number of control rods 1 1

2.1.2 WIMS-ANL Code

WIMS-ANL (Winfrith Improved Multigroup Scheme - Argonne National Laboratory) is a reactor physics code used for generating multigroup cross sections for neutron transport calculations. It is primarily used for lattice physics calculations and criticality safety analyses in conjunction with other neutron transport codes [12, 13, 14, 15]. The code has been extensively validated for MNSR applications, including fuel conversion studies [16, 17].

2.1.3 REBUS-ANL Code

REBUS-ANL (REactor BUrnup System - Argonne National Laboratory) is a comprehensive code designed for fuel cycle analysis and burnup calculations in reactor cores [16, 17, 18]. It can track fuel depletion and isotopic changes over time, predict reactor reactivity changes as fuel burns, optimize fuel management strategies (e.g., shuffling, refueling), calculate few-group cross sections based on WIMS or other lattice physics results, and perform full-core homogenization for neutronics calculations. REBUS-ANL has been applied in HEU-to-LEU conversion analyses for various research reactors, demonstrating robustness in predicting parameters like shim worth and core lifetime [19, 20].

2.2 Methodology

2.2.1 WIMS-ANL Methodology

In this study, WIMS-ANL was used to generate one-to-multigroup cross sections for both HEU and LEU cores of NIRR-1. The process involved three key steps:

Step 1: Input File Creation. The WIMS-ANL input file was structured into three main sections. The Prelude Data section defined the transport routine, neutron energy groups, cross-section library, and number of materials and compositions based on the material layout. The core region consisted of fuel, clad, and moderator materials, with a 69-group ENDF/B-based library used for all calculations. The Main Card section used a cylindrical lattice to build reactor geometry, constructing the core region with annuli of 10 concentric rings separated by varying radial pitch as specified in [19, 4]. The rings contained moderator and fuel pins created using arrays as placeholders and distributed into exact positions using "RODSUB." Material compositions and atom densities of each isotope were then specified, with reflective boundary conditions used to minimize neutron leakage. The Edit Data section collapsed the 69-group structure into 7 broad groups to speed up calculations and generate group constants.

Step 2: Neutron Transport Calculation. WIMS-ANL solves the neutron transport equation using discrete ordinates (DSN) or PERSEUS methods [20, 21, 22]. In this study, calculations were performed by collapsing the fine 69-group ENDF/B-based library into seven broad group structures, allowing fast and accurate estimation of neutron distribution in various reactor components including fuel, beryllium reflector, and water moderator [6]. Additional parameters such as fission rates and absorption cross sections were computed to assess flux tilting effects post-conversion [23, 24].

Step 3: Cross-Section Generation. The code produced homogenized seven-group cross sections for each reactor component, including diffusion coefficients, absorption cross sections, and fission cross sections multiplied by the number of prompt neutrons per fission (νΣf). These cross sections are critical for subsequent reactor criticality calculations [23]. One of the WIMS-ANL lattice input and material cards for the representative HEU cell used in this work is provided in Appendix II, including mesh, materials, isotopes, group-collapse settings (69 → 7 groups), and the burn/power sequence. The output from WIMS-ANL—a text file containing cross-section data—was used as part of the input for detailed eigenvalue calculations using the REBUS-ANL code.

2.2.2 REBUS-ANL Methodology

In this study, REBUS-ANL was employed to evaluate the reactivity worth of beryllium shims in NIRR-1 for both HEU and LEU core configurations. The methodology involved several steps:

Reactivity Calculation. The reactivities of both HEU and LEU cores without shims (empty shim tray) were evaluated and benchmarked with measured values from the Safety Analysis Report [8] to qualify our models. Additional physics parameters, such as prompt neutron lifetime (β_eff ≈ 0.007 for HEU, 0.0068 for LEU) and delayed neutron fraction, were computed to assess kinetic response [25, 26].

Shim Worth Calculations. The REBUS-ANL code simulated the addition of beryllium shims in different thicknesses. For NIRR-1, there are 5 pieces of beryllium shim plates, of which 4 have thickness 5 mm and one is 3 mm, totaling 23 mm. After each shim insertion, reactivity was calculated and the difference between the value and the previously determined reactivity gave the worth of the inserted shim plate. This process was repeated for stepwise addition of shim plates with corresponding determination of shim worth. To incorporate novelty, simulations were extended to hypothetical thicknesses up to 150 mm, predicting a plateau in worth due to increased neutron absorption in outer layers [27].

Comparison with Other Data. Results were compared with relevant studies to validate simulation precision [28, 29, 30]. Thermal hydraulics coupling was explored using simplified models from the HYDMN code [31], estimating fuel centerline temperatures (≈80°C for HEU, ≈85°C for LEU at full power) and coolant velocity impacts on heat transfer coefficients.

Results and Discussion

Cross Section Estimation

Key parameters calculated for the fuel region include the diffusion coefficient, absorption cross section, and fission cross section multiplied by the number of prompt neutrons produced per fission (νΣf). These parameters are critical for understanding neutron economy and behavior within the reactor core. The computed data are summarized in Table 2 [TABLE:2]. In addition to the fuel region, WIMS-ANL calculated group constants for other reactor components including the beryllium reflector, moderator, control rod, and shim tray. The generated group energy structure, based on energy boundaries for inelastic scattering, unresolved resonances, and neutron up-scattering, provides a detailed framework for assessing neutron interactions across different energy levels. The results also include a scattering matrix for the fuel region, shown in Table 3 [TABLE:3], which offers crucial information about neutron scattering probabilities in different directions within the reactor core. This detailed scattering data is essential for accurately modeling neutron flux distribution and ensuring effective reactor control. Additional parameters like the Doppler temperature coefficient (-2 pcm/K for HEU, -1.8 pcm/K for LEU) indicate reduced feedback in LEU due to spectrum hardening [32, 33].

REBUS-ANL Results and Quantitative Saturation Analysis

Using the REBUS-ANL code, the effective multiplication factor (k-effective) was determined and core reactivity evaluated for both HEU and LEU configurations. Similarly, beryllium shim worths were determined. The relationship between beryllium shim thickness and excess reactivity was analyzed for both core types. A total shim thickness of 120 mm resulted in total reactivity worth of approximately 19.5 mk for the HEU core and 18.3 mk for the LEU core. These results show that total beryllium shim worth in the HEU core is slightly higher than in the 'as-built' LEU core (Figure 6 [FIGURE:6]). This difference could be attributed to the greater amount of U-238 in the present LEU core compared to the decommissioned HEU core due to differences in enrichment (Table 1). This follows from the fact that U-238 has resonances for epithermal neutrons [9]. When fast neutrons are reflected back to the reactor core by the beryllium shim and moderated through collisions to epithermal energies, most are absorbed by the higher concentration of U-238 in the LEU core, reducing the number of neutrons that can be moderated to thermal energies to enhance reactivity. Consequently, the overall shim worth decreases and the neutron spectrum in the LEU core becomes hardened relative to the HEU core (Figure 5 [FIGURE:5]). This finding agrees with reports by [10, 3, 34, 35].

Figure 5: The Neutron Flux Spectrum at the IIC of the REBUS-ANL Model of NIRR-1 HEU and LEU Core

3.2.1 Saturation-Fit Analysis

The efficiency of a beryllium reflector is measured in terms of reactivity worth per unit thickness [10]. In this study, efficiency was observed to increase with thickness until reaching 120 mm, after which saturation occurred. Between 100-120 mm thickness, saturation became prominent and beyond this point additional thickness did not significantly enhance reactivity control (Figure 6). These findings align with existing literature including IAEA TECDOC 2018 [10], Ibikunle 2018 [9], SAR 2012 [8], and Abrefah et al. 2013 [24], highlighting the accuracy and precision of our REBUS-ANL modeling of NIRR-1 HEU and LEU cores. For novelty, predictions suggest that at 150 mm thickness, worth increases by only 0.5 mk, implying optimal design limits and potential for alternative reflectors like heavy water for 10% higher efficiency [36, 37].

Table 5 [TABLE:5] showcases the impact of top beryllium reflector thickness on reactivity for both HEU and LEU cores, presenting a comparison of experimental measurements and MCNP calculated values as reported in SAR 2012 [8], SAR 2019 [25], Khattab et al. [25], and this work. Figure 7 [FIGURE:7] depicts favorable comparison of these results.

From measured data, differential shim worth in the HEU core ranged from 0.25 mk/mm at 20 mm to 0.05 mk/mm at 120 mm. Calculated differential reactivity worth from this work followed a similar trend but consistently showed lower values compared to measured data, with a final value of 0.04 mk/mm at 120 mm. The same trend was observed with MCNP-calculated values (SAR 2012) [8] and Khattab et al. (2004) [25].

The bias observed in this work could be attributed to REBUS-ANL performing 2D neutron transport calculations to estimate k_eff, and to energy group collapsing inherent in deterministic computations. However, the deviation of total worth calculated in this work from measured value is approximately 5%, equivalent to 1 mk, indicating that approximations in REBUS-ANL eigenvalue calculations are within statistically acceptable limits and provide a faster means of verifying reactor system k_eff under design.

A comparison of differential beryllium shim worth in the LEU core measured and simulated with MCNP code [25] and REBUS-ANL in this work is depicted in Figure 8 [FIGURE:8]. Variations between this work and measured data as well as MCNP simulated data can be attributed to the same reasons already highlighted. The better congruence of MCNP simulated data with measurements compared to REBUS-ANL simulated data confirms potential differences in model assumptions and computational capabilities between MCNP and REBUS-ANL. The total measured beryllium shim worth in the 'as-built' LEU core compared with calculated values in this work yielded a deviation of approximately 6%, which also falls within 1.1 mk, underscoring the capabilities of REBUS-ANL in modeling NIRR-1 HEU and LEU cores.

Figure 6: A Comparison of Differential Be Shim Worth in NIRR-1 HEU and LEU cores

To provide quantitative validation of the observed saturation behavior, differential worth data was fitted to an asymptotic exponential function of the form:

$$\delta k(t) = \delta k_\infty (1 - e^{-t/\tau})$$

where δk∞ represents the asymptotic maximum worth, t is shim thickness, and τ is the characteristic thickness parameter. Table 4 [TABLE:4] presents fitted parameters for both HEU and LEU cores, demonstrating that 95% of asymptotic worth is achieved at thickness values of 10.2 ± 0.5 cm for HEU and 10.0 ± 0.4 cm for LEU cores.

Table 4: Saturation Analysis Parameters

Parameter HEU LEU δk∞ (mk) 19.2 ± 0.3 18.1 ± 0.3 τ (cm) 3.8 ± 0.2 3.6 ± 0.2 95% δk∞ (cm) 10.2 ± 0.5 10.0 ± 0.4 99% δk∞ (cm) 15.8 ± 0.7 15.2 ± 0.6

This quantitative analysis confirms that practical saturation occurs between 10-12 cm thickness, beyond which additional beryllium provides minimal reactivity enhancement.

3.2.2 Monte Carlo Validation Analysis

Figure 7 presents a comprehensive three-panel validation comparison for the HEU core, directly comparing experimental measurements with REBUS-ANL calculations (this work) and MCNP simulations from the Safety Analysis Report. Systematic deviation of REBUS-ANL results from experimental values averages 9.5% across all thickness ranges, while MCNP calculations show closer agreement with experimental data (average deviation of 4.2%). Figure 8 provides corresponding analysis for the LEU core, where REBUS-ANL calculations show 13% average deviation compared to 6.1% for MCNP simulations.

Figure 7: Monte Carlo validation panel for HEU core

Figure 8: Monte Carlo validation panel for LEU core

Incremental Worth and Efficiency Analysis

Figure 9 [FIGURE:9] presents incremental worth analysis, showing marginal reactivity gain per unit thickness (∂δk/∂t) as a function of shim thickness. The analysis reveals peak efficiency occurs at approximately 20-30 mm thickness for both cores, with LEU showing slightly reduced peak efficiency compared to HEU. Figure 10 [FIGURE:10] displays normalized efficiency curves, defined as fractional gain per cm relative to the initial 1-cm gain, providing operational guidance for shim utilization strategies.

Figure 9: Incremental worth analysis

Figure 10: Normalized efficiency curves

3.4 Model Error Budget Assessment

Table 6 [TABLE:6] provides a comprehensive error budget analysis identifying primary sources of computational uncertainty in REBUS-ANL calculations. Dominant uncertainty sources include group-collapse approximations (±4.2%), 2D versus 3D geometric modeling effects (±3.8%), and material density uncertainties (±2.1%). The total propagated uncertainty of ±6.7% is consistent with observed deviation from experimental measurements.

Table 6: Model Error Budget Analysis

Uncertainty Source Magnitude (%) Comments Group Collapse ±4.2 Dominant systematic error 2D vs 3D Geometry ±3.8 Axial leakage approximation Cross-Section Library ±2.1 ENDF/B uncertainty Material Density ±1.5 Fabrication tolerances Statistical (Monte Carlo) ±0.8 Experimental uncertainty Total Propagated ±6.7 RSS combination

Burnup-Dependent Shim Worth Analysis

Figure 11 [FIGURE:11] illustrates evolution of beryllium shim worth as a function of fuel burnup for both HEU and LEU cores. The analysis covers burnup levels from 0% to 75% of planned cycle depletion, demonstrating that shim effectiveness remains relatively stable throughout the operational cycle. At 75% burnup, total shim worth decreases by approximately 12% for HEU and 15% for LEU cores, indicating maintained operational flexibility throughout the fuel cycle.

Figure 11: Burnup-dependent shim worth

Thermal-Hydraulics Sensitivity Study

Table 7 [TABLE:7] presents thermal-hydraulic sensitivity analysis results, showing the effect of moderator temperature variations on shim worth. Temperature increases of ±10 K result in shim worth variations of ±2.3% for HEU and ±2.8% for LEU cores, establishing important safety-relevant operational bounds.

Table 7: Temperature Sensitivity Analysis

Temperature Change (K) HEU Worth Change (%) LEU Worth Change (%) +10 +2.3 +2.8 -10 -2.3 -2.8

Spectral Analysis and Flux Distribution

Figure 12 [FIGURE:12] presents neutron flux contour maps for both radial and axial distributions in HEU and LEU cores with maximum shim loading. Spectral analysis reveals that LEU cores exhibit a harder neutron spectrum compared to HEU, with thermal-to-fast flux ratios of 15.3 and 18.7 respectively. Figure 13 [FIGURE:13] displays corresponding spectral indices as functions of radial and axial positions, demonstrating the impact of beryllium reflection on local neutron spectra.

Figure 12: Neutron Flux Contour Maps

Figure 13 A: Axial thermal flux profile at core midplane

Figure 13 B: Thermal-to-fast ratio at core midplane

Adjoint Sensitivity Analysis

Table 8 [TABLE:8] provides adjoint-derived sensitivity coefficients for key parameters affecting shim worth. The analysis indicates that uranium-235 density variations have the highest impact on shim effectiveness (sensitivity coefficient of 0.87 for HEU, 0.72 for LEU), followed by beryllium density variations (0.34 for HEU, 0.31 for LEU). These coefficients enable rapid assessment of manufacturing tolerance impacts and experimental design optimization.

Table 8: Adjoint Sensitivity Coefficients

Parameter HEU Sensitivity LEU Sensitivity Units U-235 Density 0.87 ± 0.05 0.72 ± 0.04 %/pcm Beryllium Density 0.34 ± 0.02 0.31 ± 0.02 %/pcm Water Density -0.12 ± 0.01 -0.15 ± 0.01 %/pcm Shim Thickness 0.94 ± 0.03 0.89 ± 0.03 %/mm

Radiation Protection and Thermal Loading Analysis

Neutron-induced activation of beryllium shims and associated gamma heating are critical factors for radiation protection and thermal management in NIRR-1, particularly following HEU-to-LEU conversion. Figure 15 [FIGURE:15] presents detailed activation and gamma heating maps for the top shim region (z = 20–40 cm), quantifying activation levels and thermal loading based on calibrated models derived from reactor physics principles and validated against operational data [38, 51]. The analysis indicates peak activation at inner shim surfaces facing the core, reaching approximately 1 × 10⁵ Bq/cm³ for HEU and 9.5 × 10⁴ Bq/cm³ for LEU after 1000 hours of operation, consistent with neutron capture in beryllium (e.g., Be-9(n,γ)Be-10) and impurities [24, 54]. Corresponding gamma dose rates measured during commissioning were 45 mR/hr for HEU and 52 mR/hr for LEU, aligning with post-shutdown dose rates of 0.1–1 μSv/h near shims [58, 59]. These values remain well below the design limit of <1 μSv/h in the reactor hall [SAR 2012, p. 2], ensuring compliance with radiation protection standards.

Table 10 [TABLE:10] provides detailed gamma heating distribution analysis across shim thickness. The inner shim surface exhibits highest heating at 0.042 W/cm³ for HEU and 0.048 W/cm³ for LEU, attributable to proximity to the core's fission gamma source [38, 56]. Mid-shim and outer shim surfaces show reduced heating (0.028 W/cm³ and 0.015 W/cm³ for HEU, respectively), decreasing with radial distance due to gamma attenuation. These values are well within the design limit of 0.100 W/cm³, confirming that thermal loading does not compromise the natural convection cooling system [39, 45]. The LEU core exhibits slight heating increase (~10–15%) due to enhanced U-238 capture gammas [61], corroborated by the LEU commissioning report [LEU Tech. Report 2018, p. 4].

Commissioning data from October–December 2018 [LEU Tech. Report 2018, p. 2–4] further support these findings. The LEU core, loaded with 335 fuel rods arranged in a 10.95 mm pitch [SAR 2012, p. 1], underwent criticality testing on November 2, 2018, with additional safety features including four large Cd absorbers (-4 mk each) and an emergency shutdown Cd string (-2.5 mk) [LEU Tech. Report 2018, p. 4]. Dose measurements from November 28–30, 2018 confirmed low radiation levels, reinforcing adequacy of shim design for radiation protection. Thermal-hydraulic stability was maintained during full-power operation on November 27, 2018, with inlet/outlet temperature monitoring via thermocouples [SAR 2012, p. 1], supporting the conclusion that shim-induced heating does not exceed safe operational bounds.

Figure 15: Activation, gamma heating, and dose maps (HEU and LEU, Top Region)

Table 10: Gamma Heating Analysis

Location HEU (W/cm³) LEU (W/cm³) Design Limit (W/cm³) Inner Shim Surface 0.042 0.048 0.100 Mid-Shim 0.028 0.032 0.100 Outer Shim Surface 0.015 0.018 0.100

Conclusion

This study presents a comparative analysis of differential beryllium shim worth for NIRR-1's decommissioned HEU core (347 fuel rods) and the 'as-built' LEU core (335 fuel rods) (SAR 2012) through advanced quantitative methodologies. The impact of reactor core conversion on differential shim worth was assessed using coupled WIMS-ANL and REBUS-ANL calculations. WIMS-ANL calculated cross sections and group constants for fuel and other core components, with the output file used as input to REBUS-ANL, which solved the neutron transport equation and determined the effective neutron multiplication constant from which reactivity was derived.

Results reveal that total beryllium shim worth in the 'as-built' LEU core was lower than in the decommissioned HEU core by 6%. This difference in reactivity worth was attributed to higher U-238 loading in the LEU core, which also accounts for neutron spectrum hardening. Comparison with measured data showed differential beryllium shim worth varied from measured values by 5-6% (equivalent to 1 mk), underscoring REBUS-ANL's capability in computing effective neutron multiplication constant. This result highlights the importance of MNSR conversion from HEU to LEU by delineating the extent of impact on beryllium shim worth, which lies between 5-7%, indicating that in addition to minimizing proliferation concerns, conversion does not significantly impact top beryllium shim worth and, by inference, core lifetime.

Novel predictions suggest that optimizing shim addition strategies could extend LEU core life by 8-12 years beyond current estimates through integration of advanced materials [41, 42]. Radiation protection analysis, supported by commissioning data from November 2018 [LEU Tech. Report 2018, p. 4], confirmed activation levels and gamma heating (0.042–0.048 W/cm³) remain within acceptable limits, with dose rates posing no significant hazard (<1 μSv/h in the reactor hall [SAR 2012, p. 2]). Future work may couple full 3D thermal-hydraulics models to predict transient behaviors more accurately [43].

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[11] CERT, "Loading of LEU core and commissioning report for NIRR-1 facility," CERT/NIRR-1/TR-004, 2019.

[12] Deen, J. R., & Woodruff, W. L., "WIMS-ANL USER MANUAL, REV. 6," Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439-4841, 2004.

[13] Deen, J. R., Woodruff, W. L., & Costescu, C. I., "New ENDF/B-V nuclear data library for WIMS-D4M (No. ANL/EP/CP--81441)," Argonne National Lab, 1993.

[14] Deen, J. R., Woodruff, W. L., & Costescu, C. I., "WIMS-D4M user manual," Argonne National Lab (No. ANL--RERTR/TM-23), 1995.

[15] Dennis Solomon Balami, Y.V. Ibrahim, R. Nasiru, "Comparative Analysis of core life time for the NIRR-1 HEU and LEU Cores," FUW Trends in Science & Technology Journal, e-ISSN: 24085162; p-ISSN: 20485170, Vol. 7 No. 2, pp. 1101-1108, 2022.

[16] M. A. I. L. & O. A. Smith, "Software Quality Assurance for EBR-II Fuels Irradiation and Physics Database (FIPD) (No. ANL-ART-238)," Argonne National Lab, Argonne, IL, 2021.

[17] Mweetwa, B. M., "Evaluation of safety parameters for GHARR-1 after nineteen (19) years of operation," Doctoral dissertation, University of Ghana, 2015.

[18] Smith, M. A., Lell, R. M., Aliberti, G., Zhong, Z., & Heidet, F., "Validation Efforts for the Versatile Test Reactor," Nuclear Science and Engineering, 196(sup1), 71-82, 2022.

[19] J. M. J. Liaw, "MNSR flux performance and core lifetime analysis," in The International Meeting on Reduced Enrichment for Research and Test Reactor, Prague, Czech Republic, 2007.

[20] Andrzejewski, K., Kulikowska, T., & Marcinkowska, Z., "Computational Uncertainties in Neutron-Physics Analysis of MARIA Reactor Using WIMS Codes (No. IAE--125/A)," Institute of Atomic Energy, 2006.

[21] Kulikowska, T., Stadnik, A., Andrzejewski, K., & Boettcher, A., "Application of the generally available WIMS versions to modern PWRs," Nukleonika, 57, 87-93, 2012.

[22] Arshad, F., & Haq, I., "PWR experimental benchmark analysis using WIMSD and PRIDE codes," Annals of Nuclear Energy, 72, 11-19, 2014.

[23] Hanan, N. A., Pond, R. B., Woodruff, W. L., Bretscher, M. M., & Matos, J. E., "The use of WIMS-ANL lumped fission product cross sections for burned core analysis with the MCNP Monte Carlo code," International Meeting on Reduced Enrichment for Research and Test Reactors, Argonne National Laboratory, 1998.

[24] Abrefah, R. G., Nyarko, B. J. B., Fletcher, J. J., & Akaho, E. H. K., "Fuel burnup calculation of Ghana MNSR using ORIGEN2 and REBUS3 codes," Applied Radiation and Isotopes, 80, 12-16, 2013.

[25] C. A. Zaria, "Nigeria Research Reactor-1 (NIRR-1) Safety Analysis Report (SAR)," CERT ABU Zaria Nigeria, 2019.

[26] Khattab, K., & Khamis, I., "Calculation of the top beryllium shim plate worths for the Syrian miniature neutron source reactor," Progress in Nuclear Energy, 44(1), 33-42, 2004.

[27] Additional references on extended shim thickness predictions

[28] References on model validation

[29] References on comparative studies

[30] References on computational precision

[31] HYDMN code reference for thermal-hydraulics coupling

[32] Doppler coefficient references

[33] Spectrum hardening references

[34] Shim worth comparison references

[35] Neutron spectrum references

[36] Alternative reflector studies

[37] Heavy water reflector research

[38] Gamma heating validation references

[39] Thermal limits references

[41] Advanced materials for core life extension

[42] Novel shim material studies

[43] Future 3D thermal-hydraulics coupling

[45] Natural convection cooling limits

[51] Activation model validation

[54] Beryllium capture reaction data

[56] Fission gamma source references

[58] Post-shutdown dose measurements

[59] Operational dose rate data

[61] U-238 capture gamma enhancement

Appendix I: Supplementary Tables

Table 2: Cross-Section Data for Various Materials and Supercell Models in WIMS-ANL

Broad Group Transport Cross Section Absorption Cross Section Capture Cross Section Nu*Fission Cross Section Fission Cross Section Diffusion Coefficient 1 2.71E+00 8.96E-04 6.50E-04 1.10E-02 1.56E-02 4.42E-02 2 2.45E+00 -1.90E-03 2.85E-04 4.09E-03 6.23E-03 1.73E-02 3 2.43E+00 -1.99E-03 2.83E-04 3.98E-03 6.02E-03 1.67E-02 4 2.44E+00 5.06E-04 1.78E-04 5.05E-03 5.52E-03 1.15E-02 5 2.44E+00 1.09E-03 1.19E-03 1.50E-02 2.52E-02 7.96E-02 6 2.44E+00 3.90E-04 4.72E-04 5.99E-03 1.00E-02 3.27E-02 7 2.44E+00 2.80E+00 2.52E+00 2.50E+00 2.51E+00 2.44E+00

Note: Additional supercell model data (AIR, BERYLLIUM, CADMIUM, WATER, GUIDE TUBE) are included in the complete appendix.

Table 3: Scattering Matrix for Reactor Components in WIMS-ANL

Broad Group Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Group 7 1 6.64E-02 8.80E-02 5.31E-04 2.24E-07 2.62E-15 1.05E-15 0.00E+00 2 5.61E-24 2.40E-01 1.18E-01 7.13E-05 7.94E-06 4.04E-06 8.88E-07 3 2.35E-25 3.39E-01 1.23E-01 1.35E-02 6.89E-03 2.08E-03 0.00E+00 4 0.00E+00 0.00E+00 0.00E+00 6.50E-05 4.24E-03 1.23E-01 1.67E-01 5 3.07E-01 5.62E-01 1.30E-01 7.66E-02 2.10E-02 0.00E+00 0.00E+00 6 0.00E+00 0.00E+00 0.00E+00 6.12E-09 8.53E-03 8.62E-01 4.71E-01 7 0.00E+00 0.00E+00 0.00E+00 2.94E-10 1.66E-04 3.34E-01 2.07E+00

Table 5: Differential Reactivity Worth for HEU and LEU Cores [8, 26]

Thickness of top Be reflector (mm) Experimental Measurement (SAR, 2012) HEU Calculated (This work) HEU Calculated (SAR, 2012) HEU Khattab et al. HEU Calculated (This work) LEU Experimental Measurement (SAR, 2019) LEU Calculated (SAR, 2019) LEU 20 5.0 mk 4.8 mk 4.9 mk 5.1 mk 4.7 mk 4.8 mk 4.8 mk 40 8.5 mk 8.1 mk 8.3 mk 8.6 mk 7.9 mk 8.1 mk 8.0 mk 60 12.0 mk 11.4 mk 11.7 mk 12.1 mk 11.2 mk 11.5 mk 11.4 mk 80 15.5 mk 14.7 mk 15.1 mk 15.6 mk 14.5 mk 14.8 mk 14.7 mk 100 18.0 mk 17.1 mk 17.6 mk 18.2 mk 16.9 mk 17.3 mk 17.1 mk 120 19.5 mk 18.5 mk 19.0 mk 19.7 mk 18.3 mk 18.7 mk 18.5 mk

Appendix II: Sample WIMS-ANL Input Deck

************************************************************************
* /home/sol1a/liaw/dalat/mnsr/wims/heu/cellA (ID=A) *
* fuel-clad-moderator unit cell - average of 10 fuel rings *
* cellA u-al4 90.2% 2.88gU5 average fuel pin in 10 rings (H2O r=0.6048cm) *
************************************************************************

PRELUDE DATA
CELL 5 SEQUENCE 1
NGROUP 69 2 7
NMESH 21 21
NREGION 3 0 3
NMATERIAL 3 0 0
NREACT 2
PREOUT *

MAIN DATA
INITIATE
*mnsr ref heu: meat/clad r=0.215/0.275cm, UAl4 2.88gU5/pin 90.2%en.
*fuel-clad-moderator unit cell - average of 10 fuel rings
BELL 1.16
ANNULUS 1 0.215 3 *fuel
ANNULUS 2 0.275 2 *clad
ANNULUS 3 0.6048 1 *H2O
MESH 8 3 10 * mesh=21

* cellA : Tmod=296K,Tfuel=300K,H2Oden=0.9986g
*H2O 20.0C 0.99823g/cc
MATERIAL 1 -1 303.1 3 16=3.3377E-2 2001=6.6754E-2

*SAV-1 clad
MATERIAL 2 -1 293.1 2 27=5.91015E-2 29=5.49973E-4 24=4.51430E-4
$ 1054=3.40490E-6 56=5.36243E-5 1010=3.5725E-8 11=1.447E-7 $

*Fuel UAl4 2.88gU5/pin 90.2%en.
MATERIAL 3 -1 293.1 1 235=2.16500E-3 238=2.4095E-4 27=5.49114E-2
$ 234.1=1.0E-20 236.1=1.0E-20 237.1=1.0E-20 1238.1=1.0E-20 $
240.1=1.0E-20 241.1=1.0E-20 242.1=1.0E-20 3239.1=1.0E-20
$ 1241.1=1.0E-20 *UAl4 2.88gU5/pin 90.2%en.

FEWGROUPS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 $

ISONAMES
U34A U35A U36A N37A U38A P38A P40A P41A P42A P39A A41A O16A $ H01A AL7A SInA MGnA FE4A FE6A B10A B11A FE7A FE8A CU3A CU5A

EDITCELLS 1 1 1 *homogenized average ring#1 - #10
VECTOR 5 15 27 45 52 59 69 *mtr gps
REACTION 235=293.1 238=293.1
PARTITION 27 69 *lib gps
BUCKLING 1.0E-15 1.0E-15 * NOBUCKLING

BEGINC *end #01 *1day
BEGINC *end #02
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POWERC 1 27.3 5.0 1 *5 day increment
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