TSUNAMI Analyses of the Similarity and Applicability of Zero Energy Deuterium 2 Critical Experiments for Reactor Physics Code Benchmarking for a Pressurized Water Reactor Small Modular Reactor Design Concept

If new, advanced, and unconventional fuels and fuel cycles are to be implemented in future design variants of different small modular reactor (SMR) technologies [1], it will be necessary to ensure that computational reactor physics codes used in the design and safety analyses of such systems are properly and adequately validated. Proper validation will require adequate and relevant reactor physics measurement data. Previous measurement data may be suitable, provided that there is sufficient similarity to the design application, and also provided that the expected sensitivity and uncertainties can be quantified, and the biases in reactor physics data can be extended from measurement conditions to the reactor design application and operating conditions.

This paper investigates the potential feasibility of the zero energy deuterium 2 (ZED-2) critical facility (see Fig. 1) at Chalk River, Canadian Nuclear Laboratories (CNL), to provide suitable and relevant experimental data to support reactor physics code validation for SMR designs. This feasibility assessment is performed by using the TSUNAMI (Tools for Sensitivity and Uncertainty Analysis Methodology) code package of the SCALE 6.1.2 code suite [4–8]. This assessment was accomplished by developing KENO-VI/KENO-V.a three-dimensional reactor core physics models of the selected SMR design concepts and selected ZED-2 experiments, which were then embedded in TSUNAMI models to perform a sensitivity analysis. The results of this sensitivity analysis were further used to evaluate the similarity between the ZED-2 experiments and the SMR design application. The SMR design concept selected for the study was a pressurized water reactor small modular reactor (PWR-SMR) design similar to that of the NuScale VOYGR iPWR [9,10].

The investigation was performed in three successive stages. In the first stage, an earlier ZED-2 experiment was used in the TSUNAMI assessment. Most of the previous critical experiments in the ZED-2 facility involved the use of natural or slightly enriched uranium oxide (0.711 wt. % ²³⁵U/U to 0.96 wt. % ²³⁵U/U) in CANDU-type (28-elements or 37-element) or CANFLEX-type (43-element) (CANdu FLEXible fuelling) fuel bundles, with heavy water coolant and a surrounding heavy water moderator (see Refs. [11–16]). In the period of 2003 to 2018, additional experiments were performed in the ZED-2 facility with higher uranium enrichments, along with fuels containing plutonium and/or thorium, and use of light water coolant [17–19]. All previous ZED-2 experiments have potential relevance and applicability to SMR applications.

Building on the similarity and sensitivity results of this initial assessment, in the second stage of this study, hypothetical ZED-2 experiments enhancing the capability of the previous experiment were devised by adding gadolinium in the fuel and boron in the water coolant/moderator. Three-dimensional KENO-VI neutron transport models of these experiments were used in the analysis to help identify modifications to the experiments to improve the similarities with the SMR designs. With the knowledge learned in the first two stages, further hypothetical ZED-2 experiments were proposed in a third stage by incorporating a small number of SMR-type test fuel assemblies inserted into a reference core of CANFLEX fuel bundles made of low enriched uranium or recovered uranium (CANFLEX-LEU/CANFLEX-RU) (∼0.95 wt. % ²³⁵U/U to 0.96 wt. % ²³⁵U/U) (see Fig. 2) fuel in a mixed-lattice substitution ZED-2 experiment to align more with the SMR design, and used for even more improvement in similarity. The hypothetical experiments developed in this study can be used to guide the design of future ZED-2 experiments at CNL to support SMR designs development. More details of the proposed hypothetical ZED-2 critical experiments with PWR-SMR test fuels have been discussed previously in Ref. [20], in which critical experiments were simulated using MCNP, and which were used as the basis for KENO-VI/TSUNAMI modeling.

As will be discussed again later, this work found that the PWR-SMR had high similarities, with coefficients of c_k = 0.81±0.01, relative to past ZED-2 CANFLEX-LEU/CANFLEX-RU experiments. With modifications, this similarity coefficient could be improved to 0.88±0.01 in the second stage of hypothetical experiments, and then improved further to a similarity coefficient of 0.95±0.01 in the third stage of hypothetical experiments, when fresh fuel was used in the analysis.

For all KENO-VI and TSUNAMI-3D calculations, a 238-energy-group nuclear cross section data library based on ENDF/B-VI.8 was used by the KENO-VI solver for the forward and adjoint neutron flux calculations [6,8]. It is anticipated that future studies will make use of later versions of the ENDF/B libraries. For the forward neutron flux calculations, the KENO-VI multigroup Monte Carlo calculations of k_eff were performed with 5000 neutrons per generation, 4000 generations, and 100 skipped generations. For the adjoint neutron flux calculations, the KENO-VI calculations were performed with 15,000 neutrons per generation, 4000 generations, and 500 skipped generations. These specifications for the neutron histories resulted in statistical uncertainties in k_eff of less than ±0.001 (±1 mk, ±100 pcm).

One target reactor type was considered in this work: a small pressurized water reactor (PWR-SMR), similar to the NuScale VOYGR iPWR reactor [9,10]. The PWR-SMR was modeled using the KENO-VI three-dimensional Monte Carlo neutron transport code in the SCALE 6.1.2 code suite [4–8]. These models were used in the TSUNAMI nuclear data sensitivity study for comparison to ZED-2 experiments.

For this target reactor type, a PWR-SMR core is modeled, based primarily on information found in Ref. [9] for the NuScale VOYGR iPWR, a 160-MW_th/50-MW_el design. The fuel region consists of fuel pins in a 17 × 17 assembly of elements that are approximately 200 cm long. This design is similar to existing PWR fuel assemblies in larger reactors. Most of the fuel elements are made of pure UO₂ (made of low enriched uranium, LEU), while other fuel elements are made of UO₂ mixed with a small amount of Gd₂O₃ (a burnable neutron absorber). The LEU enrichment varies from 4.05 wt. % ²³⁵U/U (for fuel assemblies with no rods containing Gd₂O₃) to 4.55 wt. % ²³⁵U/U (for fuel assemblies with selected fuel elements containing ∼10 wt. % Gd/(Gd + U) burnable neutron absorber).

The reactor vessel outside the fuel region is modeled as a simple steel cylinder, ignoring any details or attachments. The end regions are also not modeled. This simplified model would not be suitable for a complete and detailed design safety analysis study, but it is considered acceptable for comparing nuclear data sensitivities of the fuel/core for ZED-2 experiments relative to the design application.

The geometry was created with 2-meter-long fuel elements made of UO₂ with a Zircaloy-4 cladding. The elements are placed in a 2D array with empty guide tubes (filled with coolant) in 25 locations. An X–Y cross section view of a fuel assembly is shown in Fig. 3. The assemblies are placed in a cylindrical core in a specific pattern discussed in Ref. [9]. An X–Y cross section view of the core is shown in Fig. 4.

Information found in Ref. [9] provided details of the loading of the equilibrium core with three-batch refueling: fresh, once-burned, and twice-burned fuel assemblies at beginning of cycle. Fuel compositions for the once-burned and twice-burned fuel have been developed and used in other reactor physics studies at CNL using the Serpent code [21]. For this study, several versions of the model with different fuel loadings were created. These model versions are the following:

• “Burned Fuel”: This model uses the complete fuel compositions computed from a previous Serpent physics model. The burned fuel contains many fission products of different elements and isotopes, which are likely to reduce similarity with ZED-2 experiments, since all ZED-2 experiments use fresh, unburned fuel with no fission products.

• “Simple Fuel”: This model removes all isotopes in the burned fuel that have only very trace concentrations present, less than 1.0 × 10⁻¹⁰ atom fraction.

• “Fresh Fuel”: This model uses only the fresh fuel compositions for the whole core and increases the boron concentration in the water moderator/cool to suppress the increased reactivity.

In the first stage of the study, a selection of past ZED-2 experiments was performed from a wide variety of fuel types, and critical experiments involving the use of CANFLEX-LEU fuel were chosen for the analysis. More discussion of the design and details of CANFLEX-LEU fuel bundles and ZED-2 experiments are found in previous publications Refs. [3,11–15], and [20]. A full-core ZED-2 critical experiment with CANFLEX-LEU fuel was selected as the base KENO-VI model for the present analysis.

Based on results obtained with these ZED-2 experiments, additional KENO-VI models were prepared in the second stage of the study for hypothetical ZED-2 experiments that extended the capability of the ZED-2 experiments analyzed in the first stage, by artificially adding gadolinium to the fuel and boron to the coolant.

In the third stage of the study, building on the results of the first two stages, additional ZED-2 hypothetical experiments were devised and modeled in KENO-VI in a mixed-lattice substitution configuration, with PWR fuel assemblies replacing existing CANFLEX-LEU channels. These models are discussed in more detail in Secs. 3.1 and 3.2, and are also discussed previously in MCNP modeling studies by Watts et al. [20].

A full-core ZED-2 critical experiment with CANFLEX-LEU/CANFLEX-RU fuel, light-water coolant, and heavy water moderator at a temperature of 21 °C was selected as the base model for the present analysis, from a suite of moderator temperature experiments.

The KENO-VI modeling of the ZED-2 experiments is a detailed representation of the ZED-2 lattice comprising 52 fuel channels (with each fuel channel containing five CANFLEX-LEU fuel bundles) arranged in an open-centered lattice (no fuel channels at the center) at a 24-cm square pitch lattice spacing, as shown in Fig. 5. The fuel channel assemblies are comprised of aluminum CANDU-type channels (a pressure tube sitting inside a calandria tubes), with each channel containing five CANFLEX bundles, as shown in Fig. 2. The gap between the pressure tube and calandria tube contains air at atmospheric pressure. The ZED-2 experiments are heavy water moderated and light water cooled.

There were two slightly different assembly types in the 52-channel ZED-2 core:

• 48 channels contained five CANFLEX-LEU bundles,

• four channel contained five CANFLEX-RU bundles.

The CANFLEX-RU bundles are very similar to the CANFLEX-LEU bundles, but are made of recovered uranium (RU), which contains a slightly higher content of ²³⁴U, and some ²³⁶U. The CANFLEX-RU fuel is very similar to the CANFLEX-LEU in terms of lattice reactivity, and has the same geometry, as shown previously in Fig. 2.

The hypothetical ZED-2 test configurations use one or more central channels of a PWR type assembly surrounded by channels of CANFLEX-LEU/CANFLEX-RU. The modeling of each component is described below.

The KENO-VI ZED-2 PWR assembly was taken from the initial KENO-VI SMR model based mainly on information described in Ref. [9]. The main assembly KENO-VI model was based on a model previously developed at CNL. The fuel region consists of fuel pins in a 17 × 17 assembly of elements that are approximately 2 m long. Most of the fuel elements are made of pure UO₂ with 4.55 wt. % ²³⁵U/U enrichment, while other fuel elements are made of UO₂ mixed with a small amount of Gd₂O₃ (a burnable neutron absorber). The geometry was created with 2-meter-long fuel elements with a Zircaloy-4 cladding. The elements are placed in a 2D array with empty guide tubes (filled with coolant) in 25 locations.

The KENO-VI model for the fuel channels filled CANFLEX-LEU/CANFLEX-RU bundles were adapted from an earlier KENO-VI ZED-2 model. For these channels, the coolant in the channel is light water. The main difference between the KENO-VI and MCNP models [20] are that the KENO-VI model does not include the end plugs to the channel, as a simplifying approximation. This approximation in the KENO-VI model has been demonstrated in previous analyses to have an insignificant impact on the neutronics behavior of the core.

Two models were created for the KENO-VI study, each with 16 fuel channels. One model has four PWR fuel assemblies and 12 CANFLEX-LEU/CANFLEX-RU fuel channels, while the other model has 12-PWR fuel assemblies and four CANFLEX-LEU/CANFLEX-RU fuel channels. The critical heights for the two ZED-2 configurations are 210.2 cm for the case with four-PWR assemblies and 150.6 cm for the case with 12-PWR assemblies, as reported previously in Ref. [20]. For the KENO-VI models, the only changes that were made between the two cases were to the critical height (which also impacts which bundle in the CANFLEX-LEU channel is only partially submerged) and the number of PWR/CANFLEX channels. Cross-sectional views of the two cores are shown in Fig. 6.

The two cases were run as simple k_eff calculations using KENO-VI with continuous energy nuclear data under the SCALE 6.2.2 code package [6,8] using a continuous energy neutron data library based on ENDF/B-VII.0. The KENO-VI cases were run using 10,000 neutron histories per cycle, and 8000 cycles. The statistical uncertainty in the calculation of k_eff was less than ±0.0001 (±0.1 mk, ±10 pcm). Note that TSUNAMI calculations were performed with multigroup data under SCALE 6.1.2 [4].

These KENO-VI simulations did not include calculation of any nuclear data sensitivities at this stage. The results are mixed, with the k_eff of the four-PWR assembly case approximately 0.27 mk above critical (k_eff ∼ 1.00027±0.00010). This difference (0.27 mk) is considered an acceptable difference from the k_eff = 1.00006±0.00007 obtained with MCNP [20]. As discussed in the previous study [20], the MCNP simulation models of the ZED-2 critical facility with proposed mixed-lattice substitution experiments with PWR-SMR test fuels used MCNP5 v.1.40, with a continuous nuclear data library based on ENDF/B-VII.0. The MCNP simulations were run with 100,000 neutron histories per cycle, 1100 cycles, and 100 dropped cycles, giving a total of 100 × 10⁶ neutron histories, and a statistical uncertainty in the calculation of k_eff of less than ±0.07 mk (±0.00007 Δk/k). The KENO-VI results are thus considered to be consistent with the previous MCNP model [20] and give good results for the subsequent sensitivity study.

The case with 12-PWR assemblies resulted in a KENO-VI calculation of k_eff of 1.00315±0.00010, which is approximately 3 mk above the k_eff value of 1.00004±0.00007 obtained with MCNP [20]. This difference relative to the MCNP results is considered relatively small, although nontrivial. However, even this nonunity result for k_eff in the KENO-VI model is not expected to introduce a large impact on the nuclear data sensitivity. It is anticipated that additional investigations will be carried out in the future to better understand the reason for the 3.1-mk difference between the MCNP and the KENO-VI models for the 12-PWR-FA model.

The channels filled with CANFLEX-LEU/CANFLEX-RU fuel bundles were adapted from an earlier KENO-VI ZED-2 model. For these channels, the coolant in the channel is light water. The main difference between the KENO-VI and MCNP models is that the KENO-VI model does not include the end plugs to the channel. As mentioned before, this approximation in the KENO-VI model has been demonstrated in previous analyses at CNL to have an insignificant impact on the neutronics behavior of the core.

The PWR-SMR system was modeled in KENO-VI, while the ZED-2 reactor experiments were modeled in KENO-V.a. The choice for KENO-VI for the SMR designs was motivated by the irregular geometry of these reactors, which made it difficult for modeling in KENO-V.a geometry specifications. Irrespective of the solver used by TSUNAMI, the main results of these calculations, which are the sensitivity data files, serve the same purpose for the analysis. The choice of the solver used in the TSUNAMI calculations is therefore of no significance for the analysis.

For all TSUNAMI-3D runs, the 238-energy-group nuclear cross section data library ENDF/B-VI.8 was used by the KENO-VI/KENO-V.a solver during the forward and adjoint calculations, in conjunction with SCALE 6.1.2 code suite. For the SAMS sensitivity calculations, which are part of the TSUNAMI-3D sequence, the covariance data library, “44groupcov,” was used.

The original KENO-VI model for PWR-SMR with burned fuel included the ²³⁹U, ²⁴⁴Am, ²⁴⁹Cm, and ²⁵⁰Bk isotopes. However, these isotopes were not present in the data library. For this reason, these isotopes were removed from the KENO-VI model.

The sensitivity data files obtained from the TSUNAMI-3D calculations for the ZED-2 experiments and the SMR design applications were further used by the TSUNAMI-IP module of SCALE 6.1.2 for the calculation of overall similarity coefficients and integrated coverage coefficients for top individual nuclide-reactions. The sensitivity profiles across the neutron energy spectrum for these nuclide-reactions were plotted directly from the sensitivity data files computed by TSUNAMI-3D, and the results are discussed in the next section.

The TSUNAMI similarity and sensitivity analyses involve the comparison of a series of ZED-2 experiments (either existing or hypothetical ones) with the design applications of a PWR-SMR, based on various parameters and sensitivity profiles of relevant nuclide-reactions calculated with TSUNAMI.

The analysis follows a series of generic steps. The process begins with TSUNAMI-3D calculations for each system configuration (ZED-2 experiment or SMR design), employing the KENO-VI/KENO-V.a and SAMS modules. The KENO solver performs the forward and adjoint neutron flux calculations. Once the KENO calculations are completed, the SAMS module is executed to generate the sensitivity data. The TSUNAMI-3D output includes a k_eff value and detailed sensitivity profiles ((dk_eff/dσ)/(k_eff/σ)) per unit lethargy versus neutron energy) for each nuclide-reaction across the neutron energy spectrum. These profiles indicate the sensitivity in k_eff results to changes in nuclide-reactions cross section data. The analysis then proceeds with TSUNAMI-IP calculations, assessing similarities between reactors based on these sensitivity profiles, with a focus on comparing ZED-2 experiments (both previous and hypothetical ones) with a PWR-SMR. Results include similarity integral indices between system pairs (e.g., ZED-2 and SMR), sensitivity data/profiles, and coverage parameters for key nuclide-reactions, alongside sensitivity plots for selected system pairs.

Using TSUNAMI-3D data and the TSUNAMI-IP module, in the first stage of the study, the similarity between the ZED-2 CANFLEX-LEU/CANFLEX-RU experiment and a PWR-SMR was evaluated. The values of similarity coefficients, “c_k,” in Table 1 show varying degrees of similarity. For example, the PWR-SMR design with fresh fuel shares a high similarity (c_k = 0.81±0.01) with ZED-2, suggesting that a further optimized ZED-2 experiment could yield useful data for code validation for PWR-SMRs. In actuality, the similarity coefficients (c_k) are usually computed to three or four decimal places, with an uncertainty that is usually less than ±0.001. However, from a practical standpoint, it is only necessary to know the value of c_k to two decimal places/two significant digits. Specifying the value of c_k to three or four decimal places with the associated uncertainties adds no significant or practical value. Therefore, all values of similarity coefficients herein are specified to two decimal places, with a conservative uncertainty of ±0.01.

The PWR-SMR model with burned fuel and with simple fuel both displayed a significantly lower similarity with ZED-2 (c_k = 0.61±0.01) than the model with fresh fuel. This result demonstrates that isotopes with very low concentrations do not have an impact on the similarities. However, it also demonstrates that burned fuel (with lower concentrations of ²³⁵U, higher concentrations of various actinides (such as isotopes of Np, Pu, Am, Cm, and others), and higher concentrations of neutron-absorbing fission products) contributes to a significant decrease in similarity with ZED-2 when modeled in the PWR-SMR reactor. Similar types of results were found in previously TSUNAMI assessment studies for the applicability of ZED-2 experiments to supercritical water-cooled reactors [22,23]. These results suggest the need for additional ZED-2 experiments with test fuel that simulates or approximates burned fuel to account for the effects of various actinides and neutron-absorbing fission products.

Further insight into the similarity between PWR-SMR and the ZED-2 experiment is obtained by evaluating the sensitivity of the k_eff result in the application (SMR design) to the individual nuclide-reactions, together with the value of the “g-parameter,” which is related to the individual nuclide sensitivities in the experiment (ZED-2). These results are presented in Tables 2 and 3. The PWR-SMR fresh fuel design shows higher similarity, except where boron and gadolinium are not matched in ZED-2 (g-parameter values of zero in Table 2), suggesting possible improvements in similarity if these nuclides were included in either the coolant or fuel in the ZED-2 experiments. In contrast, the burned fuel design for the PWR-SMR introduces additional nuclide-reactions such as Xe-capture and Pu-fission/capture, as seen in Table 3, not present in ZED-2, which, along with lower sensitivities for common reactions like ²³⁵U-fission, results in a reduced similarity coefficient (c_k = 0.61±0.01) compared to fresh fuel (c_k = 0.81±0.01).

The results obtained in the first stage of this study suggested that adding boron and gadolinium to the ZED-2 experiments with CANFLEX-LEU/CANFLEX-RU fuels may increase their c_k similarity to PWR-SMR fresh fuel design, which already shows a c_k value of 0.81±0.01. Starting from the ZED-2 experiment that was used in the first stage of the study, a revised version of the model was produced in the second stage by replacing the individual CANFLEX-LEU elements in the 43-element bundle with PWR fuel elements, compatible in size with the CANFLEX-LEU elements. Therefore, the same 43-element CANFLEX-LEU fuel bundle arrangement is used, but the 43 CANFLEX-LEU fuel elements are replaced with 43 slightly smaller fuel elements that are all the same diameter (0.95-cm outside diameter) and fuel composition as the NuScale-type iPWR fuel, with 4.55 wt. % ²³⁵U/U, and ∼10 wt. % Gd₂O₃/(Gd₂O₃ + UO₂), as illustrated in Fig. 7. The TSUNAMI analysis was repeated for this hypothetical ZED-2 experiment with the modified 43-element fuel bundle design and the PWR-SMR design. This simple replacement of fuel elements resulted in a very low k_eff value of 0.28974±0.00028, which perhaps was not surprising given the relatively high fraction of Gd, with all 43 fuel elements containing 10 wt. % Gd₂O₃/(Gd₂O₃ + UO₂). By comparison, in the NuScale iPWR, the fuel assemblies with Gd poison only have G₂O₃ in 32 out of 264 fuel elements, and approximately 1/3 of all the fuel assemblies in the NuScale iPWR (12 out of 37) contain fuel assemblies with 32 fuel elements containing Gd₂O₃. Thus, the fuel-assembly average concentration is, to a first approximation, 10 wt. % × 32/264 ∼ 1.21 wt. % Gd₂O₃/(Gd₂O₃ + UO₂), while the core-average Gd₂O₃ content in the fuel is ∼1/3 × 1.21 ∼ 0.404 wt. % Gd₂O₃/(Gd₂O₃ + UO₂). Thus, the low k_eff is attributed to the relatively high fraction of gadolinium in the PWR-type fuel elements in the hypothetical 43-element fuel bundles in the ZED-2 experiment, far in excess of the relative fraction in a PWR fuel assembly or the NuScale-type PWR-SMR core. Hence, the TSUNAMI analyses led to a notable and nonsurprising dissimilarity from the PWR-SMR model, with a similarity coefficient of c_k = 0.55±0.01. To enhance similarity, the ZED-2 model was recalibrated by adjusting gadolinium and boron levels to approach a state closer to criticality. Details of these adjustments are explored in Secs. 5.2.1 and 5.2.2.

In refining the ZED-2 hypothetical experiment with 43-element bundles with PWR-type fuel elements to emulate a PWR-SMR reactor, gadolinium levels in the fuel composition were artificially reduced to 1.6 wt. % Gd₂O₃/(Gd₂O₃ + UO₂), from the initial value of 10 wt. %, while no boron was present in the coolant. This value is more realistic, since the PWR-SMR design includes gadolinium in only 32 out of 264 fuel elements, averaging less than 1.2 wt. % Gd₂O₃/(Gd₂O₃ + UO₂) in total. This optimization raised the k_eff value to 0.99648±0.00098, which also increased the similarity coefficient from c_k = 0.55±0.01 to c_k = 0.85±0.01, surpassing the original similarity of c_k = 0.81±0.01 with PWR-SMR fresh fuel obtained in the first stage of the study. These results, as shown in Table 4, indicate that using a fuel composition in ZED-2 closer to PWR-SMR significantly improves the ZED-2 experiment's similarity with the reactor design.

Analyzing the nuclide-reaction sensitivity and coverage in the hypothetical ZED-2 experiment with PWR-SMR fuel element design in 43-element fuel bundles, as shown in Tables 5 and 6, reveals that using 1.6 wt. % Gd₂O₃/(Gd₂O₃ + UO₂) in ZED-2 fuel raises the g-parameter coverage coefficient from 0 to 0.44 for ¹⁵⁷Gd capture, boosting the similarity coefficient (c_k) from 0.81±0.01 to 0.85±0.01 compared to ZED-2 with CANFLEX-LEU fuel without gadolinium. However, full gadolinium concentration from PWR-SMR fuel yields a g-parameter coverage of 1.00 (Table 6), suggesting that increasing the gadolinium content in ZED-2 experiments could further improve the c_k coefficient, especially if the heavy water moderator can be adjusted to achieve near-criticality.

The nuclear data sensitivity plots in Figs. 8–12 provide further insight into the similarities between the PWR-SMR reactor and the ZED-2 hypothetical experiment with PWR-type fuel elements in 43-element bundles containing no boron, but varying amounts of Gd. The similarities are examined through spectral sensitivity plots for key nuclide-reactions, supplementing the data in previous tables. Generally, the sensitivity profiles indicate a decent match. A thermal spectrum shift, where the PWR-SMR profile edges to higher energies due to ZED-2's more thermalized spectrum, can be observed on all figures. Specifically, ¹H elastic scattering shown in Fig. 8 displays a significant profile deviation, resulting in a lower g-parameter coverage coefficient of 0.32, as seen in Table 5. The spectral sensitivity plots in Figs. 11 and 12 highlight the ¹⁵⁷Gd capture sensitivities, where the ZED-2 experiment fully covers the PWR-SMR spectrum with high gadolinium concentration, but not with low concentration, reflected by g-parameter coverage coefficients of 1.00 (in Table 6) and 0.44 (in Table 5).

In a second modification of the hypothetical ZED-2 experiment with PWR-type fuel elements, the boron content in the coolant was varied in search of a value that brings the experiment close to criticality, while gadolinium was not present in the fuel composition. The base configuration of boron in coolant at the concentration found in the PWR-SMR critical configuration and no gadolinium in the fuel composition gave a k_eff value of 1.24390±0.00100, in the ZED-2 hypothetical experiment. Starting from this configuration, the boron concentration in the coolant was increased in order to decrease the reactivity of the experiment, and a boron concentration of 3.2 times larger than the base concentration was found to give a k_eff value of 0.99410±0.00100, close to criticality. The higher boron concentration in the coolant required for fresh PWR-SMR-type fuel is not surprising, given that the PWR-SMR core is a three-batch core, with fresh, once-burned, and twice-burned fuel. The reduced reactivity of the once-burned and twice-burned fuel reduces the amount of boron required to achieve criticality (k_eff = 1.000).

This almost-critical configuration increased the similarity coefficient from a value of c_k = 0.81±0.01 in the case of the actual ZED-2 CANFLEX-LEU experiment versus the PWR-SMR design application with fresh fuel (Table 1), to a value of c_k = 0.88±0.01 for the case analyzed in this section where boron was present in the coolant of the ZED-2 experiment (Table 7). It can also be observed from Table 7 that increasing the boron concentration in the coolant to achieve a close-to-critical state increases the similarity coefficient only by a small amount.

For more insight into the similarities, the nuclide-reaction values for sensitivity and coverage between the hypothetical ZED-2 experiment with PWR-type fuel elements in 43-element bundles and the PWR-SMR application were further analyzed, with results presented in Tables 8 and 9. In particular, the presence of the boron in the coolant of the PWR-SMR design provides a relatively high sensitivity value, as seen in Table 8.

Modeling the hypothetical ZED-2 experiment at the same boron concentration of 1470 ppm boron in water as in the original PWR-SMR coolant provides a g-parameter coverage coefficient value of 0.57 for the ¹⁰B neutron capture reaction, for example, although there is not very much coverage for boron, it is still sufficient to increase the similarity coefficient c_k from 0.81±0.01 to 0.88±0.01 when compared with the case of the hypothetical ZED-2 experiment with CANFLEX-LEU fuel missing the boron in the coolant, as discussed in the previous paragraph.

When analyzing the sensitivity values for the case of the hypothetical ZED-2 experiment with boron at a concentration that is 3.2 times larger than the concentration of the original PWR-SMR H₂O moderator/coolant, corresponding to a concentration of 4700 ppm boron in water, a considerably higher g-parameter coverage coefficient value of 0.88 is obtained (Table 9), by comparison with the 0.57 value in Table 8.

More details into the similarities are provided in Figs. 13–20, again by way of individual nuclide-reaction spectral plots of sensitivities, for the top sensitivity nuclide-reactions presented in the tables above.

For most of the top sensitivities in Table 8, the sensitivity profiles in the plots show relatively good similarity between the hypothetical ZED-2 experiment and the PWR-SMR reactor. The profiles, however, show a shift at the thermal part of the spectrum, with the PWR-SMR profile shifted slightly to higher energies than the ZED-2 experiments, as was the case when gadolinium concentration was varied. This shift seems to be inherent to the specific reactor design and operating conditions and is unrelated to the variation of gadolinium or boron concentration. The result may also be expected due to the large volume of external D₂O moderator in the fuel-channel design for using 43-element CANFLEX-type bundles in the ZED-2 critical facility. It is expected that the ZED-2 heavy water moderated lattices will be much more thermalized than a PWR-SMR fuel assembly lattice.

Since the interpretation of the sensitivity plots in Figs. 13–20 is very similar to the case where the gadolinium variation in fuel was analyzed, the explanation for Figs. 8–12 for that case can be used for more information on the interpretation of these profiles.

The third stage of the study extends the previous two stages, to examine further hypothetical experiments in ZED-2, by incorporating the use of a small number of test fuel assemblies of the small pressurized water reactor (PWR-SMR) inserted into a reference core of CANFLEX-LEU fuel in hypothetical mixed-lattice substitution experiments in the ZED-2 critical facility. Two such experiments were simulated in previous MCNP modeling studies [20]: one with four PWR assemblies, and another with 12 PWR assemblies, surrounded by the CANFLEX-LEU fuel channels.

The values for the global integral similarity index (c_k), presented in Table 10, give a first-glance high-level indication about the level of similarities between the ZED-2 experiments and the PWR-SMR design applications. A few observations can be made by looking at the similarity data in the table. Most importantly, the high c_k value of 0.95±0.01 was calculated between the ZED-2 experiment with 12 PWR fuel-type channels and the PWR-SMR design with fresh fuel. This result is a first indication of very good similarity to highlight the potential for using this hypothetical ZED-2 experiment to provide experimental data to support the reactor physics code validation for the PWR-SMR design. Another important observation is that the similarity between the ZED-2 substitution experiments with PWR test fuel, and the PWR-SMR design decreases notably when the number of PWR channels in the ZED-2 experiments is reduced to 4, for which a c_k value of 0.87±0.01 was calculated. This result, although expected, emphasizes the importance of using more PWR assemblies in the ZED-2 channels to replicate the neutron energy spectrum.

For the case of the burned/spent fuel in the PWR-SMR application, it is clear, as expected, that the ZED-2 experiments with fresh PWR fuel are not as good, with similarity c_k values of 0.63±0.01 and 0.64±0.01. These results suggest that substitution experiments should also be designed with PWR test fuel that approximates/simulates burned PWR-SMR fuel, with a high content level of actinides (such as isotopes of Pu), and other elements (such as Gd and perhaps dysprosium) to represent the neutron absorbing effects of certain fission products.

Further insight into the similarities and the source of departures from the similarity between a pair of systems can be obtained from the evaluation of the sensitivity of the k_eff result in the application (SMR design) to the individual nuclide-reactions, together with the value of the g-parameter, which is related to the extent of the presence (coverage) of this nuclide-reaction in the experiment (ZED-2).

The data in Table 11 show the top sensitivities by nuclide-reaction for the PWR-SMR fresh fuel design, and g-parameter coverage values for the two ZED-2 experiments. The third column gives the values of the sensitivity coefficients, which quantify how sensitive the k_eff result is to that particular nuclide-reaction in the PWR-SMR application; this number is the same for both experiments. The last two columns give the g-parameter coverage coefficient for each of the ZED-2 experiment designs.

It can be observed from these results that the nuclides that contribute to most of the improvements of 12-FA-PWR over 4-FA-PWR are, of course, the nuclides that are present in the PWR assemblies, in particular ¹⁰B and ²³⁵U, with better coverage coefficients between the experiment and the SMR design application in the case of 12-FA-PWR. This better coverage drives the similarity improvement with a coefficient of 0.95±0.01 for 12-FA-PWR versus 0.87±0.01 for 4-FA-PWR, as seen in the results presented in Table 10. Other nuclides, such as ¹H and ²³⁸U, which are also present in the CANFLEX-LEU assemblies of the ZED-2 experiments, do not contribute to this improvement of 12 versus four PWR assemblies. However they do contribute to the overall similarity between the ZED-2 experiments and the PWR SMR design.

More information about how well the SMR design application is represented by the ZED-2 experiments can be inferred from the sensitivity plots. The data in Figs. 21–24 show the sensitivity plots for the top nuclide-reactions for the PWR-SMR design with fresh fuel and the ZED-2 experiments with PWR-type fuel. These plots support the coverage data presented in Table 11, but give more insight into how and why the coverage is provided to the extent calculated by the integral g coefficient of coverage, by showing how the sensitivity profiles between the experiment and application align along the neutron energy spectrum.

In particular, the ¹H scattering reaction, shown in Fig. 21, is notoriously difficult to be covered by sensitivity profiles, due to the large narrow spikes in the resonance region of the spectrum. Large dissimilarities are, however, also seen in the thermal region. It is also true that, among all nuclide-reactions of interest, the hydrogen scattering presents the highest uncertainties, which also contribute to the differences in the sensitivity profiles. These uncertainties are inherent and due to the uncertainty associated with this particular nuclide-reaction in the covariance data libraries.

The profiles for ¹⁰B shown in Fig. 22 look similar in shape between the PWR-SMR design and the two ZED-2 experiments. However, the profiles show differences in magnitude, with smallest magnitude for the 4-FA-PWR, followed by 12-FA-PWR and then the largest PWR-SMR design, suggesting that there might be insufficient boron in the ZED-2 experiments. Relatively speaking, this difference in magnitudes explain the better coverage for the 12-FA-PWR than the 4-FA-PWR, as expected. These profiles also support well the coverage integral coefficient g-parameter from Table 11, with values of 0.20 for the ZED-2 4-FA-PWR experiment and a value of 0.54 for the 12-FA-PWR experiment. The similitude in profile shapes, however, may be an indication that a larger amount of boron in the experiments could make for a better coverage and therefore higher similarity.

The ²³⁵U fission reaction sensitivity profiles presented in Fig. 23 show a better magnitude coverage between the experiments and design application than it was observed for the ¹⁰B profiles, and even more so with magnitudes for the experiments larger than for the PWR-SMR design application, which should provide more coverage. However, it can be observed that the profiles are slightly shifted in the spectrum, with the PWR-SMR design application profile more toward the higher neutron energy than the ZED-2 experiments, as it was discussed and explained before. These results are not surprising, as it was noted before, since the ZED-2 experiment with CANFLEX-LEU has a much more thermalized spectrum, with the bulk of the moderation occurring in the external heavy water moderator region in the lattice cell. This characteristic is therefore a feature of experiments in the ZED-2 critical facility, which can only be improved by reducing the number of the CANFLEX-LEU channels, or by reducing the lattice pitch of the CANFLEX-LEU fuel channels to harden the neutron energy spectrum. These differences in sensitivities account for the integral coverage values of 0.64 and 0.79 for the ZED-2 with 4-FA-PWR and ZED-2 with 12-FA-PWR assembly experiments, respectively. This result again suggests that the ²³⁵U fission reaction has an important role in similarities and therefore supports the argument for designing a more suitable experiment.

The data in Table 12 show the top sensitivities by nuclide-reaction for the four PWR assemblies (4-FA-PWR) and 12 PWR assemblies (12-FA-PWR) burned fuel SMR design, and g-parameter coverage values for the ZED-2 Experiments.

It is of interest to analyze the results for the burned fuel PWR-SMR design by comparison with the results for the fresh fuel design discussed in Sec. 5.3.1 describing the ZED-2 experiments versus fresh fuel PWR-SMR design. In part, when looking at the integral coverage coefficients (g-parameter) in Tables 11 and 12, similar trends with the fresh fuel application case can still be seen for ¹⁰B capture and ²³⁵U fission, for which the 12-FA-PWR experiment fares better than the 4-FA-PWR experiment. In contrast, other nuclides, such as ¹H and ²³⁸U, which are also present in the CANFLEX-LEU assemblies of the ZED-2 experiments, do not contribute to this improvement of 12 versus four PWR assemblies. However, they still contribute to the overall similarity between the hypothetical ZED-2 experiments and the PWR-SMR design.

It is worthy to note that for both the ¹⁰B capture and ²³⁵U fission nuclide-reactions, coverage is actually better for the PWR-SMR design with spent fuel than for the PWR-SMR design with fresh fuel, even though the experiments use fresh PWR-type fuel. For boron capture, for which the 12-FA-PWR experiment has a coverage g-parameter value of 0.53 for the PWR-SMR fresh fuel design and a value of 0.79 for the PWR-SMR burned fuel design (see Tables 11 and 12), this result happens because for the burned fuel, the boron amount is decreased to values that are closer to the ZED-2 PWR experiments. This result can also be observed by analyzing the sensitivity spectrum profiles in Figs. 22 and 25. For ²³⁵U fission, however, the reason for the better coverage of the PWR-SMR spent fuel design (for which a g-parameter value of 0.99 was obtained versus a g-parameter value of 0.79 in the case of PWR-SMR fresh design application) is of a different nature. The sensitivity profiles in Figs. 23 and 26 for the ²³⁵U fission show that, even though the magnitude of this profile is reduced for the burned fuel, at the same time this profile is less shifted to the higher energies as it was for the case of the fresh fuel coverage, which leads to a better coverage for the sensitivity profiles.

The two increases in coverage discussed above are not actually due to a better similarity, which may be somewhat misleading. Analysis of the sensitivity plots, as discussed above, gives more insight into the interpretation of the results and suggests that the integral values of the similarity coefficients c_k in Table 10 and the g-parameter coverage coefficients in Tables 11 and 12 need to be taken only as an overall look into the similarities, while analysis of the sensitivity plots can confirm, totally or partly, these results.

Nevertheless, the dissimilarities between the case of fresh and burned PWR-SMR fuel cases are still present due to the absence in the fresh fuel of nuclides such as ¹³⁵Xe and ²³⁹Pu, which are present in the burned fuel, for which the reactions of neutron capture and fission, respectively, have large associated sensitivities, but zero coverage coefficients, as can be seen in the data from Table 12. The lack of coverage for these nuclides accounts for the significant decrease in overall similarity from the case of fresh PWR-SMR design application, with the similarity coefficient reduced from a very high value of 0.95±0.01 to only 0.64±0.01 for the 12-FA-PWR experiment, as seen in Table 10.

For a better understanding of the differences between the fresh PWR-SMR fuel and burned PWR-SMR fuel, the data in Figs. 27 and 28, which show the sensitivity plots for two of the top nuclide-reactions (¹⁰B capture and ²³⁵U fission) for the PWR-SMR design with fresh fuel and the PWR-SMR design with spent fuel, can be analyzed. A decrease in the magnitude of the sensitivity can be observed for the burned fuel, which is due to the reduce quantities of these nuclides in the burned fuel.

The data in Figs. 25, 26, and 29 show the sensitivity plots for the top nuclide-reactions for the PWR-SMR design with burned fuel and the ZED-2 experiments with PWR-type fuel.

Results for the first stage of the study for sensitivity/similarity between ZED-2 experiments and SMR design applications revealed that the PWR-SMR with fresh fuel had higher similarities (c_k ≥ 0.81±0.01) to past ZED-2 experiments with CANFLEX-LEU/CANFLEX-RU fuel. Dissimilarities of ZED-2 experiments with the PWR-SMR design arose in part from the presence of gadolinium in the PWR-SMR fuel composition and boron in the PWR-SMR coolant, which were absent in the ZED-2 experiment. It was therefore expected that the presence of boron and gadolinium in modified ZED-2 experiments would help improve the similarity. When the PWR-SMR with burned fuel was analyzed, a significantly lower c_k value of 0.61±0.01 with the ZED-2 experiment was obtained. This lower value for c_k is likely due to lack of neutron-absorbing actinides (isotopes Pu, Np, Am, and Cm) and fission products in the fresh fuel used in the ZED-2 experiments.

In the second stage of the study, when the fuel elements in the 43-element CANFLEX-LEU fuel bundle in a hypothetical ZED-2 experiment were replaced with PWR-type fuel elements, with added gadolinium content, but no boron, the similarity coefficient was increased from 0.81±0.01 to 0.85±0.01. When boron was instead added to the H₂O coolant in another configuration of the hypothetical ZED-2 experiment (but no gadolinium in the fuel), the similarity between the hypothetical ZED-2 experiment and the PWR-SMR design was further increased to a similarity coefficient of c_k = 0.88±0.01. It was therefore expected that a combination of the presence of gadolinium in the fuel and boron in the coolant in ZED-2 should raise the similarity coefficient even more. However, because the nuclear data uncertainty for boron is low, the calculated high sensitivity to boron does not have a large impact on the code accuracy in the calculation of k_eff.

In the third stage of the study, the analysis focused on hypothetical mixed-lattice substitution experiments in ZED-2, using CANFLEX-LEU driver fuel, and PWR-type test fuel assemblies. The analysis demonstrated that ZED-2 experiments can be designed to closely simulate the reactor physics conditions of the PWR-SMR design application. TSUNAMI analysis of the hypothetical ZED-2 experiments of the PWR fresh fuel in 12 of the 16 channels provided a relatively high similarity coefficient of c_k = 0.95±0.01. This high similarity was further confirmed by the nuclide-reaction coverage and sensitivity profile analyses. The analysis of the ZED-2 mixed-lattice substitution experiments with four PWR-type fuel assemblies showed a somewhat reduced similarity with a coefficient of c_k = 0.87±0.01. This result emphasizes the importance of the number of representative channels in the ZED-2 experiments.

It was also observed from the study of the sensitivity plots that another source of departure from similarity between the ZED-2 experiments and the PWR-SMR design is the sensitivity profile shift in the spectrum for some of the top nuclide-reactions, such as boron capture and ²³⁵U-fission, with the PWR-SMR design application profiles shifting toward the higher neutron energy relative to those of the ZED-2 experiments. These results can be explained by the fact that the ZED-2 experiment with CANFLEX-LEU has a much more thermalized spectrum, with the bulk of the moderation occurring in the external moderator region in the lattice cell. However, it is anticipated that a redesign of the hypothetical ZED-2 experiments, such as a reduced lattice pitch, could achieve a neutron energy spectrum that is less thermalized, and more representative of the PWR-SMR, and thus could achieve improve similarity coefficients, and better reaction rate sensitivity coverage.

The analysis for the burned fuel for the PWR-SMR design showed significantly reduced similarity, with similarity coefficients of c_k = 0.64±0.01 and c_k = 0.63±0.01 for the 12-assembly and 4-assembly PWR channels, respectively. The small difference in results between the two ZED-2 experiments confirms that the PWR assemblies in the experiments do not play a significant role in representing the PWR-SMR design in this case. If ZED-2 experiments are to be used to support validation for the PWR-SMR design with spent fuel, then a more representative fuel must be used in the experiments, such as fuels containing trace amounts of plutonium [18,19]. However, it is also anticipated that redesigning ZED-2 experiments with PWR-SMR fuel to include boric acid in the H₂O moderator/coolant should also improve the similarity and sensitivity coverage.

Thus, the similarity and sensitivity studies carried out to date give confidence that critical experiments in the ZED-2 facility can be designed to provide suitable data for reactor physics code validation for application to PWR-SMR design applications, such as the NuScale VOYGR iPWR [9,10].

This study provided valuable insights into the applicability of past and hypothetical ZED-2 experiments to support SMR design applications, and it also revealed possibilities for further improvements of the analysis, for the purpose of designing ZED-2 experiments with higher similarity to the SMR design applications. The following are potential options for improvements:

• One example of improvement was highlighted in Sec. 5.3.1, investigating the ZED-2 experiments versus the PWR-SMR design, where the similarity in sensitivity spectrum profile shapes for boron neutron capture indicated that a larger amount of boron in the experiments could provide a better coverage and therefore higher similarity between these two systems.

• Another improvement could be made by a more thorough use of the analysis of the spectral profiles for neutron flux for the ZED-2 experiments and the SMR design applications. In particular, future investigations can focus on comparisons between ZED-2 experiments with four PWR fuel assemblies and experiments with 12 PWR fuel assemblies to show how the thermal flux distribution is affected by the boron absorptions.

• Future studies with SCALE, KENO, and TSUNAMI could use updated code versions and nuclear data libraries, based on ENDF/B-VII.1 or ENDF/B-VIII.0.

The authors recognize the oversight, help, and assistance provided by the following staff at CNL: Ali Siddiqui, Ram Paul, Megan Moore, Nicholas Chornoboy, Aiesha Smith, Sam Kelly, Fred Adams (emeritus), Jimmy Chow, Peter Pfeiffer, and Jonathan McKay. The use and value of the High Performance Computing (HPC) facilities at CNL to support these studies is also recognized.

• Atomic Energy of Canada Limited (AECL), under the auspices of the Federal Nuclear Science and Technology (FST) (Program No. FST-51120.0.A049; Funder ID: 10.13039/501100004953).

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

c_k =

similarity coefficient

keff =

effective neutron multiplication factor (neutrons produced/neutrons lost)

wt. % =

% composition by weight

Greek Symbols

σ =

microscopic cross section

Subscripts or Superscripts

el =

electrical

th =

thermal

Acronyms and Abbreviations

CANDU =

Canada deuterium uranium

CANFLEX-LEU =

CANdu FLEXible Low Enriched Uranium

CANFLEX-RU =

CANdu FLEXible recovered uranium

CNL =

Canadian Nuclear Laboratories

EOC =

end of cycle

FA =

fuel assembly

iPWR =

integral pressurized water reactor

KENO =

a neutronics analysis code in the SCALE code suite

LEU =

low enriched uranium

MCNP =

Monte Carlo N-particle

mk =

milli-k (1 mk = 100 pcm = 0.001 Δk/k), a unit of k_eff

pcm =

per cent mille (1 pcm = 0.01 mk = 0.00001 Δk/k)

PWR =

pressurized water reactor

PWR-SMR =

pressurized water reactor-small modular reactor

RU =

recovered uranium

SCALE =

standardized computer analysis for licensing evaluation: a system of codes developed at Oak Ridge National Laboratory

SMR =

small modular reactor

TRISO =

tristructural isotropic

TSUNAMI =

tools for sensitivity and uncertainty analysis methodology (a sensitivity/uncertainty analysis code in the SCALE 6.1.2 code suite)

ZED-2 =

zero energy deuterium 2

2D =

two-dimensional