The Canadian pressure-tube super critical water-cooled reactor (PT-SCWR) is an advanced generation IV reactor concept which is considered as an evolution of the conventional Canada Deuterium Uranium (CANDU) reactor that includes both pressure tubes and a low temperature and pressure heavy water moderator. The Canadian PT-SCWR fuel assembly utilizes a plutonium and thorium fuel mixture with supercritical light water coolant flowing through the high-efficiency re-entrance channel (HERC). In this work, the impact of fuel depletion on the evolution of lattice physics phenomena was investigated starting from fresh fuel to burnup conditions (25 MW d kg−1 [HM]) through sensitivity and uncertainty analyses using the lattice physics modules in standardized computer analysis for licensing evaluation (SCALE). Given the evolution of key phenomena such as void reactivity in traditional CANDU reactors with burnup, this study focuses on the impact of fission products, 233U breeding, and minor actinides on fuel performance. The work shows that the most significant change in fuel properties with burnup is the depletion of fission isotopes of Pu and the buildup of high-neutron cross section fission products, resulting in a decrease in cell k with burnup as expected. Other impacts such as the presence of protactinium and uranium-233 are also discussed. When the feedback coefficients are assessed in terms of reactivity, there is considerable variation as a function of fuel depletion; however, when assessed as Δk (without normalization to the reference reactivity which changes with burnup), the net changes are almost invariant with depletion.

## Introduction

The Canadian pressure tube super-critical water-cooled reactor (PT-SCWR) is a generation IV reactor concept utilizing a pressure tube design with supercritical light water as coolant. It is considered as an evolution of the Canada Deuterium Uranium (CANDU) reactor maintaining key features such as separation of the high-pressure coolant and the low-temperature and pressure heavy water moderator [1].

The PT-SCWR fuel channel design utilizes a re-entrant coolant flow path which is termed the high-efficiency re-entrant channel (HERC). As shown in Fig. 1 [2], the coolant flows from the inlet plenum at 350  °C and 25.8 MPa downward through the center flow tube in each fuel assembly. The coolant at the bottom of the channel is redirected upward around the fuel elements to the outlet plenum where it exits the fuel channel at 625  °C and 25.0 MPa. The Canadian PT-SCWR reference design includes a 64-element fuel assembly arranged in two concentric rings with 15% and 12% PuO2 in ThO2 in the inner and outer rings, respectively [3]. The PT-SCWR core is vertically oriented and batched fueled, where the fuel assembly has a 5 m active length and zirconium modified stainless steel cladding [3] with isotopic atomistic densities, material temperatures, and geometry specifications given by Hummel [2].

Owing to the significant differences in HERC fuel design relative to the standard CANDU reactor lattice, a benchmark analysis was performed comparing the two-dimensional (2D) lattice level neutronic behavior for the different lattice physics code applications [4]. Moreover, a recent sensitivity and uncertainty study for the PT-SCWR lattice cell with fresh fuel concluded that although the changes in net reactivity from lattice level perturbations were small (e.g., coolant density and fuel temperature feedbacks), these results were in fact driven by large and opposing changes in key lattice physics phenomena [5]. Given the considerable differences in fuel composition with burnup, the evolution of these offsetting reactivity differences must be considered. In this work, sensitivity and uncertainty analyses were performed using the standardized computer analysis for licensing evaluation (SCALE) code to assess the changes in these phenomena expected throughout a fueling cycle (25 MW d kg−1 [HM]).

## Modeling and Calculation Methods

Simulations and lattice cell calculations were performed using the 238 energy group ENDF/VII.0 library distributed in SCALE version 6.3.1 [6,7]. Fuel burnup simulations were performed with the transport rigor implemented with time-dependent operation for neutronic depletion [8] module that employs new extended step characteristics-based weighting transport code (NEWT) [9] as multigroup transport solver. NEWT is a deterministic code that solves the neutron transport equation using the discrete ordinates method utilizing both the extended step characteristics approximation and the method of characteristics within the mesh. This makes it highly sensitive to the cell mesh, and therefore, a mesh-size sensitivity study was performed to determine the mesh quality necessary such that the code outputs' sensitivity to further mesh refinement was minimal [5]. NEWT was used to examine the reaction rates, the homogenized cross sections, flux spectrum, the components of the four-factor formula, and the neutron multiplication factor for the infinite lattice cell.

In addition to the geometrical input, NEWT requires information for self-shielding since the PT-SCWR lattice cell is characterized by concentric fuel rings which is different from the regular square lattice of light water reactors. Consequently, Dancoff factors (DFs), which are used by NEWT to perform accurate self-shielding calculations for fuels with nonsquare lattice pitch, were calculated a priori for all the study cases using Monte Carlo DANCOFF [10]. Ideally, DFs vary with the fuel pin positions; however, fuel pins located within the same ring have very similar DFs. A sensitivity study shows that the small changes in DFs have a minor effect on the transport calculations, and therefore, an average value was calculated for each fuel ring to be consistent with the previous study [5] and the SCALE manual recommendation [7]. NEWT performs the self-shielding calculation using the dan2pitch card that relies on the precalculated DFs to determine the equivalent lattice pitch. This approach has a limitation due to many constraints and factors, especially the coolant density [11]. As a result, an altered coolant density of 0.4 g/cm3 was used in the self-shielding calculation when the coolant density in the fuel region drops below 0.4 g/cm3 since this methodology proved to be the most consistent when compared to continuous energy results [11].

The nuclear data sensitivity and uncertainty analysis presented in this work was performed using tools for sensitivity and uncertainty analysis methodology implementation (TSUNAMI)-2D code [68,12,13]. TSUNAMI-2D executes the NEWT module in SCALE to calculate the forward and the adjoint flux solutions that are used by sensitivity analysis module for SCALE (SAMS) [6,14,15] to generate the sensitivity coefficients for k with respect to each cross section. SAMS determines the sensitivity coefficients for each energy group and reaction as nondimensional quantity defined as percentage effect on the system's neutron multiplication factor, k, to a percentage change in the nuclear reaction cross sections. For the cross section nuclear $Σx,gi$ with the process x of nuclide i in energy group g, the sensitivity coefficient as a function of the neutron multiplication factor can be expressed as [15]
$sensitivity=dkkΣx,gidΣx,gi$
(1)
In SCALE 6.3.1, SAMS modules calculate the total sensitivity (complete sensitivity) of the neutron multiplication factor as a combination of two factors: the implicit and the explicit terms. The total sensitivity is given by [15]
$(Sk,Σx,gi)total=(Sk,Σx,gi)explicit+(Sk,Σx,gi)implicit=Σx,gik∂k∂Σx,gi+∑j∑hΣy,hjk∂k∂Σy,hj×Σx,giΣy,hj∂Σy,hj∂Σx,gi$
(2)

where $Σy,hj$ represents the cross section nuclear data component for the process y of nuclide j in energy group h. The explicit sensitivity component relates to the sensitivity of the neutron multiplication factor to a direct perturbation in the cross section data, while the implicit sensitivity component determines the sensitivity resulting from self-shielding phenomena [15]. It is noteworthy that in both terms of sensitivity, 1/k is present, and hence, the sensitivities reported by NEWT are normalized to a reference multiplication constant, which itself is a function of burnup.

The scenario selection, geometry, and lattice meshing in this work are consistent with the methodology proposed by Moghrabi and Novog [5] used for fresh fuel, so a comparison between fresh and burnup fuels can be achieved. Based on this previous work, simulations were performed at two axial positions: 25 cm and 475 cm from the bottom of the channel to access the lattice cell characteristics at the bottom (channel inlet) and top (channel outlet) of the channel, respectively. The temperatures and properties of the different lattice cell components at 25 cm and 475 cm were taken from Sharpe et al. [4], and the DFs used are given in Moghrabi and Novog [5]. In this work, the effect of fuel irradiation (25 MW d kg−1 [HM]) on lattice cell physics phenomena was investigated through sensitivity and uncertainty analysis of the nuclear data library for the normal operating condition (NOC) and a set of perturbed cases as listed in Table 1.

## Results

### Normal Operating Conditions.

To investigate the effects of fuel burnup, the components of the four-factor formula were examined and a comparison between fresh and burnup cases was performed at the bottom and top of the fuel channel as outlined below.

#### Effect of Depletion on the Four-Factor Formula.

The value of each of the four factors was calculated for fresh and irradiated fuels at the bottom of the channel (at 25 cm from the bottom of the channel) as shown in Table 2. Figure 2 shows a comparison of the multiplication constants and each of the four factors fresh and irradiated SCWR fuels as well as those for a typical CANDU reactor lattice. The main contributor to the decrease in neutron multiplication factor with burnup is the change in reproduction factor (η) as expected. The PT-SCWR is characterized by batch fueling giving rise to excess reactivity (at the beginning of cycle) compared to a conventional CANDU reactor which utilizes online refueling, and hence, has less excess reactivity at zero burnup. A direct comparison of all the factors of the four-factor formula shows that

1. The reproduction factor in the PT-SCWR decreases sharply from 1.736 to 1.565 with depletion. The decrease in reproduction factor with burnup results from the depletion of fissile isotopes which directly reduces the reproduction factor. The enrichment of the SCWR fuel results in much higher reproduction factor than that of the natural uranium utilized in CANDU reactor.

2. In the PT-SCWR, the thermal utilization factor decreases from 0.861 for fresh fuel to 0.853 at midburnup conditions. The decrease in the thermal utilization factor with fuel burnup is driven by the high absorption of fission products such as 135Xe. Such changes are consistent with the sensitivity results from TSUNAMI that also demonstrate significant negative sensitivities to these isotopes in irradiated fuel. The PT-SCWR has a lower thermal utilization factor than the CANDU reactor due to the high thermal neutron absorption taking place in 1H which was discussed thoroughly in Moghrabi and Novog [5].

3. The resonance escape probability decreases slightly with fuel burnup from 0.675 to 0.670 in the PT-SCWR, mainly due to small increases in minor actinides and protactinium (which is bred from thorium). The TSUNAMI analysis discussed later shows that the sensitivities to these isotopes increase in magnitude with burnup, albeit these sensitivities are still small relative to other contributors. A comparison between the PT-SCWR and the CANDU reactor shows that the differences in the lattice pitch and fuel geometry play a significant role; the PT-SCWR is characterized by a tight lattice pitch compared to the CANDU reactor. Consequently, it possesses a harder neutron spectrum. This explains the significantly lower resonance escape probability in the PT-SCWR compared to a typical CANDU reactor.

4. As shown in Table 2, the fast fission factor decreases from 1.276 for fresh fuel to 1.262 at midburnup conditions. It is also worthwhile to note that the fast fission is a misnomer in this regard. SCALE computes the fast fission factor in the four-factor formula as the ratio of all fission neutrons to thermal fission neutron with a thermal cut-off set at 0.625 eV. Therefore, the decrease in fissions within the epithermal regions appears as a decrease in fast fissions reported by the code. While SCALE's limitations in this regard show changes in fast-fission within the four-factor formula, a comparison between fission reaction rate spectra shows that high energy fissions, in fact, do not change appreciably with burnup. Given the harder spectrum in the SCWR compared to traditional CANDU reactor designs, the proportions of fissions above 0.625 eV are higher in the SCWR, and hence, SCALE reports this as a larger fast fission factor relative to the CANDU reactor value.

#### Sensitivity and Uncertainty Analysis.

The most significant sensitivities calculated by TSUNAMI-2D for the reference case of the PT-SCWR at the bottom of the channel are presented in Table 3. These sensitivities are integrated over all energy levels and are broken down per reaction for each isotope. A comparison between fresh and irradiated fuels shows that the k isotopic sensitivities are almost identical. 2H appears in the highest sensitivity list due to its essential role in the neutron moderation process. The most significant change with irradiation is that the system becomes highly sensitive to fission in 233U and absorption in 135Xe which is expected since (i) 232Th is transmuted into 233U with burn-up and (ii) Xenon effects increase with burnup until its concentration is saturated. Other isotopes such as higher order actinides and protactinium also are present in the irradiated case; however, their sensitivity magnitudes are less than those reported in Table 3. It is noteworthy that k is still highly sensitive to the absorption in 1H at midburnup even though it does not appear on the list of most sensitive isotopes. The 1H overall sensitivity becomes small compared to the more sensitivity isotopes in the TSUNAMI analysis since the negative absorption sensitivity cancels the positive scattering contribution, yielding a relatively small total sensitivity compared to these other isotopes. In reality, the individual sensitivities of these reactions are high.

The sensitivities presented in Table 3 can be used to support the description of the physical phenomena in Secs. 2 and 3.1.1. The decrease in the reproduction factor is driven by the reduction in number density of the fissile isotopes relative to all other materials in the lattice. Overall, the sensitivities of the fissile isotopes become more positive, while the sensitivity to nonfissile fuel materials becomes more negative with burnup. This is expected since the number density of fissile components (except 233U) decreases with time hence making the calculation of k more sensitive to the remaining material, while for nonfissile actinides their increasing absorption relative to fission isotopes drives the sensitivity to be more negative. The increase of the negative sensitivities of 232Th and nonfissile Pu materials relative to the fissile materials supports the relative large reductions in the reproduction factor.

Absorption sensitivities of all fuel isotopes and the main structural materials increase except for 239Pu which explains the slight decrease in resonance escape probability and thermal utilization factor through competing phenomena as described earlier. TSUNAMI results have shown less neutron thermal absorption in 1H with burnup which has a positive impact on the thermal utilization factor that will be counterbalanced with the strong absorption (and high sensitivity) of Xe.

The uncertainty in k due to uncertainties in the nuclear date library for irradiated fuel was found to be 7.13 mk which is marginally higher than the case for fresh fuel (6.96 mk) [5]. Nuclides with uncertainty contribution higher than 0.5 mk are listed in Table 4. The uncertainties in k for 239Pu($υ$), which is the main contributor to the uncertainty, and [239Pu(fission), 239Pu(n, γ)] reactions decrease while there is a slight increase in all other uncertainties per isotope and reaction. The primary difference between fresh and burnup fuel cases is that 135Xe (n, γ) uncertainty contributions increase with the increasing irradiation. The small increase in total uncertainty due to fuel burnup is consistent with the conventional behavior of CANDU reactor lattice cell uncertainty analysis. In conventional CANDU reactor, the uncertainty in k decreases initially due to the 239Pu peak and then increases thereafter [16]. The negative uncertainty contributions of 2H shown in Table 4 are not truly negative; however, it is actually canceling the impacts of other (positive) uncertainty contributions by accounting for shared sources of uncertainty.

#### Effect of Elevation on Reactivity.

Since the thermal-hydraulic conditions and moderating behavior change significantly from the bottom to the top of the core, the impact on reactivity as a function of elevation was investigated and discussed later. As shown in Table 2, the changes in multiplication and each of the four factors are consistent between the bottom and top of the channel albeit with slightly different magnitudes. The difference in reactivity between the inlet and outlet of the channel is 0.28 mk for fresh fuel and 2.05 mk for depleted fuel as shown in Table 5. Also shown in Table 5 is the contribution of each of the four-factors to the change in reactivity and shows that

1. The resonance escape probability (p) is the dominant contributor to the reactivity change between the top and the bottom of the channel with a value of −22.28 mk and −23.17 mk in the case of fresh and burnup fuels, respectively. After investigating each reaction with and without the isotopes present with irradiation, we found no significant changes in physics phenomena with relatively insignificant changes in the escape probability. This is particularly evident when one considers that under irradiated conditions, the value of k is smaller, and hence, given k is used in both of the normalizations when calculating the reactivity and in the denominator of the sensitivity coefficients, all contributions are magnified slightly as burnup increases. Hence when we examine Δk, rather than ρ, while we see a large change in resonance escape on a reactivity basis (normalized to the depleted fuel's total reactivity) between the top and bottom of the core, there is almost no change in Δk (not normalized) over this height with burnup.

2. The fast fission factor increases by 17.93 mk from the bottom to the top of the core which is slightly higher than the case of fresh fuel (15.96 mk). Since there is a large change in epithermal fission (due to the harder spectra at the top of the channel) between the bottom and top of the core and SCALE reports this as a change in fast fissions. However, these differences are not sensitive to fuel depletion, and again when one considers that the irradiated case has a smaller reference k (which acts to multiply the observed differences), the phenomena remain relatively unchanged. This is supported by examining Δk without normalization, which shows negligible change between the irradiated and a fresh fuel conditions.

3. The thermal utilization factor increases with elevation by 7.18 mk for irradiated fuel as compared to 5.41 mk in the fresh fuel case. While the irradiated case shows lower values for both the lower and upper elevation, the absolute differences in k between the bottom and top of the core are very similar, again the reactivity changes reflecting that the absolute values of the reference k are lower in the depleted case.

4. The reproduction factor is the largest contributor to k of the four factors and decreases strongly with burnup; however, the differences between the top and bottom of the core are negligible relative to the magnitude of their contribution (on the order of 1 mk or less).

### Coolant Density Reactivity.

Several studies have identified interesting lattice physics phenomena for the Canadian PT-SCWR [2,5,16] for cases where nonequilibrium voiding conditions occur. Although the concept of coolant void is not relevant to supercritical coolants, it is nevertheless used here for consistency with the existing CANDU reactor literature and should be interpreted as the coolant density reactivity. These interesting lattice physics phenomena may occur during transient events where the inner flow channel coolant density remains relatively unperturbed while the outer coolant density decreases (outer coolant void (OCV)), or when the inner flow channel coolant density drops the outer channel coolant density remains relatively unchanged (inner coolant void (ICV)). The term “total coolant void” (TCV) corresponds to the lattice case where the coolant density in the whole fuel assembly drops uniformly within both regions: inner and outer, and is often referred to as equilibrium voiding conditions. The reactivity behavior and the four factors have been investigated using sensitivity and uncertainty analyses for each of the voided cases (ICV, OCV, and TCV). Examination shows that fuel burnup effects at the top and bottom of the channel positions are characterized by the same behavior with a slight change in the degree of magnitude, and consequently, the discussion outlined below considers effects only at the bottom of the channel.

#### Inner Coolant Void Reactivity.

The reactivity decreases in the ICV case at the bottom of the channel are −20.00 and −31.06 mk for fresh fuel and depleted fuel, respectively, as shown in Table 6. The sensitivities presented in Table 7 confirm such negative reactivity responses. These negative reactivity changes are due to large and offsetting physics phenomena. First of all, in the ICV case, neutron moderation through scattering with the 1H in the central tube is eliminated, and consequently, neutrons would have to travel further to reach the heavy water moderator and thus the probability of resonance capture phenomena is increased [5], or alternatively the escape probability decreases (approximately −110 to −120 mk).

With the large reduction in moderation with inner coolant voiding, the neutron flux spectrum becomes harder, and given that SCALE reports any increase in epithermal fissions above 0.625 eV as a contributor to fast fissions, the reported fast fissions increase with voiding. Thus, the fast fission factor increases by 72.28 and 81.12 mk for fresh and depleted fuels although there is no discernable difference in the actual 1 MeV fission rate in either case. In examining the absolute values of the fast fission factor changes with ICV in Fig. 3, the effects are almost identical with the larger reactivity reported in the depleted case resulting from the normalization which has a lower denominator (i.e., k decreases with burnup).

The thermal utilization factor increases due to voiding as expected since the absorption in 1H is reduced and this contributes approximately 18 mk toward the void reactivity. The contribution again increases with burnup due to the lower reference k in the depleted case, although the absolute changes in utilization are approximately identical in both the depleted and fresh fuel cases.

The uncertainty from the nuclear data library in ICV reactivity for the burnup case is slightly higher than the case of fresh fuel as shown in Table 4. The dominant contributor to uncertainty in k is 239Pu($υ¯$) reaction consistent with the fresh fuel results. The slight increase in the total uncertainty in k can be explained based on the physics of the CANDU reactor found in the literature independent of the codes normalization process. The uncertainty in some of the 239Pu reactions and particularly 239Pu($υ¯$) decreases to counterbalance the increase in the uncertainties from the other reactions causing a slight increase in the total void uncertainty in the case of fuel burnup.

#### Outer Coolant Void Reactivity.

The OCV case possesses a positive reactivity response which must be considered in the safety analysis during loss-of-coolant accident cases with nonequilibrium voiding in the channel. In outer coolant voiding conditions, the reactivity increases by 10.10 mk for fresh fuel and by 9.02 mk for burnup fuel as shown in Table 6. Mainly, the positive contributions of fast fission factor and thermal utilization factor are partially offset by the reduction in negative contribution of the resonance escape probability and the reproduction factor. It is interesting that in the OCV case, the reactivity associated with the lower density coolant in the outer region of the fuel decreases with burnup. The sensitivities presented in Table 8 confirm such positive reactivity variation at the channel inlet (at 25 cm from bottom of the channel).

Examination of the previous ICV case and top to bottom reactivity changes showed that phenomena were largely consistent in the depleted and fresh fuel cases, with the reactivity effects of these changes being larger in the depleted cases due to the lower reference k value used in the normalization. The same phenomenological behavior was observed for the OCV case. This was confirmed by comparing the change in each of the four factors for both types of fuel as shown in Fig. 4. While examining the changes in reactivity, one sees a significant change in some phenomena and the changes are driven by the denominator (i.e., k) in the normalization process. The relative contribution of the four factors to the OCV reactivity is larger for the irradiated fuel compared to the fresh fuel; however, the absolute change in their values is the almost unchanged with depletion, except for the reproduction factor. The reproduction factor in the OCV case increases by 1.78 mk for fresh fuel, while it decreases by 1.83 mk for depleted fuel, mainly due to less production in 239Pu and 241Pu. This was confirmed through the sensitivity analysis results that show a larger decrease in nubar in 239Pu and 241Pu for depleted fuel compared to fresh fuel. Similar to Secs. 3.1 and 3.2.1, SCALE normalizes the sensitivities to the k at each burnup step, and hence, reported sensitivities will tend to increase with burnup.

The uncertainty due to the nuclear data library for the OCV case with burnup fuel was found to be 6.91 mk which is slightly higher than the case of fresh fuel (6.71 mk) as shown in Table 4. As discussed previously, the decrease in the uncertainty of some of 239Pu reactions and particularly the 239Pu($υ¯$) reaction counterbalances the increase of the uncertainty in the other isotopes and reactions causing the small positive increase in the total uncertainty in k.

#### Total Coolant Void Case.

The reactivity decreases in the total coolant void case, as per the fundamental design requirements in case of loss-of-coolant accident. Consequently, neutron moderation is taking place only in the low-pressure heavy water moderator with negative reactivity changes of −11.31 mk and −22.33 mk for fresh and depleted fuels, respectively, as presented in Table 6. These reactivity effects are similar to those of the ICV case albeit lower in magnitude since the negative contribution from inner coolant void is partially offset from the effects of outer coolant that exists within the fuel region. As per Table 6, the negative contribution of resonance escape probability and reproduction factor counterbalances the positive contribution of the fast fission factor and thermal utilization factor. Examining the absolute values of the four factors shows that they possess the same change in both types of fuel in TCV case. However, the depleted fuel has a lower reference value of k, and thus, the relative contribution to the total coolant void reactivity in both types of fuel is different. Based on the relative changes in reactivity, the resonance escape probability decreases by 152.64 mk and 167.22 mk for fresh and burnup fuels, respectively. On the other hand, the thermal utilization factor increases by 28.36 mk and 33.96 mk for fresh and burnup fuels, respectively. Due to the total loss of coolant, the neutron spectrum becomes harder compared to the reference case causing an increase in the epithermal fissions (above 0.625 eV) which was reported by SCALE as an increase of fast fissions. Thus, the fast fission increases by 109.13 mk for fresh fuel and by 121.57 mk for burnup fuel at the channel inlet. The most significant change in the case of fuel burnup is the larger negative contribution of the reproduction factor to the change in void reactivity due to the decrease of neutron reproduction in 239Pu with burnup which is expected.

Similar to the previous discussion on the effects of fuel depletion on uncertainty, the total uncertainty in k due to the nuclear data for the TCV decreases slightly for depleted fuel as shown in Table 4. For the irradiated fuel, the total uncertainty found to be 7.24 mk compared to 7.06 mk for fresh fuel. The increase in the uncertainty of the different isotopes and reactions is counterbalanced by the decrease in the uncertainty of some of Pu reactions; in particular, 239Pu($υ¯$) is the dominant contributor to the total uncertainty to cause a slight increase of uncertainty with burnup.

#### Comparison of SCWR and CANDU Reactor Voiding Phenomena.

The Canadian PT-SCWR is an advanced nuclear energy system that has interesting and important lattice physics phenomena which are different from the conventional CANDU reactor. A comparison between the Canadian PT-SCWR and the typical CANDU reactor in case of coolant voiding is demonstrated in Fig. 5, where the net coolant void reactivity is shown along with the contributions of each factor of the four-factor formula as per the nuclear reactor design for fresh fuel. As shown in Fig. 5, CANDU reactors have a positive coolant void reactivity, while the PT-SCWR has a positive OCV and negative void reactivity response in both of the ICV and TCV conditions. The main difference between the two nuclear reactor designs is the lattice cell pitch size, multiple coolant flow paths, enrichment, and the subsequent effects on the neutron spectrum. The tight lattice pitch and enrichment in the PT-SCWR cause a harder neutron spectrum as compared to a typical CANDU reactor. In the PT-SCWR, the coolant has an important role in the neutron moderation process and losing the coolant has three major impacts on the lattice cell. First, a large decrease in the resonance escape probability occurs which contribute a large negative feedback. Second, an increase in the epithermal fissions which in SCALE is reported as an increase in fast fissions. Finally, the thermal utilization factor increases with less thermal neutron absorptions in 1H causing a positive contribution to the reactivity. For ICV and TCV cases, the large changes in escape probability dominate, whereas in the OCV case the positive contributions overcome the escape phenomena and dominate. As shown in Fig. 5, the conventional CANDU reactor lattice cell experiences a small increase (compared to the PT-SCWR lattice cell) in the fast fission factor and the thermal utilization factor when the coolant density drops to a very low value. This increase causes a relatively small positive reactivity change (compared to the PT-SCWR) from phenomena similar to those discussed earlier. The CANDU reactor lattice cell is well moderated and the neutron spectrum dominated by thermal neutrons from the moderator. Under normal operating conditions, the thermal neutrons returning back from the moderator collide with the hot coolant and some fractions are up-scattered to energies within the resonance range. In the coolant voiding case, up-scattering with the coolant nuclides does not occur and a larger fraction of returning thermal neutrons will be absorbed directly within the fuel causing more fissions. In addition, there are small positive contributions resulting from the lack of coolant which allows fast neutrons to avoid scattering down to resonance energies during their travel from the fuel to the external moderator. In the PT-SCWR, the neutron spectrum returning from the moderator has a large fraction in the epithermal energy range, and under normal operating conditions, some of these neutrons become thermalized by the thin layer of coolant in the outer region of the bundle. For outer coolant voiding in the PT-SCWR, the phenomena are similar to that in a CANDU reactor with the exception that the contribution from resonance escape phenomena is smaller in magnitude.

### Fuel Temperature Coefficient.

The effects of fuel depletion on fuel temperature coefficient (FTC) were investigated at the top and the bottom of the channel. When the fuel temperature is increased by 100 K, the reactivity decreases by 1.20 mk and 1.03 mk corresponding to −0.012 mk/K and −0.0103 mk/K at the bottom and top of the channel, respectively. A comparison between fresh and burnt fuels at both positions along the channel shows that the difference in the total reactivity change due to fuel temperature perturbations is relatively small. The fuel temperature coefficient is negative for fresh and burnup fuels at both positions due to the Doppler broadening effect.

Examining the effects of the four factors shows that the Canadian PT-SCWR lattice cell experiences differing behavior to that of the typical CANDU reactor. In CANDU reactor, the low-lying 239Pu peak plays an important role in the fuel temperature reactivity behavior with depletion. The CANDU reactor fresh fuel lattice cell has a small and negative fuel temperature coefficient which becomes much less negative as 239Pu builds up with burnup. Given the increase in absorption in this low-lying fission peak with temperature, the accumulation of 239Pu will tend to make the fuel slightly more reactive with the increasing temperature, although the net FTC remains negative. On the other hand, the PT-SCWR fuel initially contains high Pu loading, and hence, the fuel feedback for fresh fuel is lower in magnitude than CANDU reactor fuel. With fuel depletion, there is a reduction in 239Pu concentration which would tend to make the fuel temperature coefficient more negative, which is consistent with the observed results.

The feedbacks are similar at the top and bottom of the core and throughout the depletion phase as shown in Tables 9 and 10. With the increasing fuel temperature, the dominant phenomenon is the resonance escape probability which decreases by 1.30 mk and 1.38 mk for fresh and depleted fuels, respectively. Such changes arise from Doppler broadening and are consistent with expectations. The effect is slightly higher for depleted fuel due to the relative dependence of the parameters on the reference k which is lower in case of depleted fuel as well as from changing isotopics (i.e., increases in nonfission absorptions). The increase in the absorption sensitivities in Table 11 in most of the fuel isotopes is consistent with the changes in resonance escape probability discussed earlier. The low-lying absorption resonances in 239Pu fission resonance cause a small positive contribution in the thermal utilization factor for both fresh and depleted fuels. The behavior of the reproduction factor changes for depleted fuel compared to fresh fuel although the value of the reproduction factor is very small compared to the net reactivity change. Of note is that the changes in reproduction factor with temperature have different signs when comparing midburnup fuel to fresh fuel conditions. With burnup, the contribution of 233U increases which has a lower capture to fission ratio as compared to the fresh fuel fission isotopes. Hence, when perturbing the fuel temperature, the low-lying 233U fission resonances broaden and thus increase the proportion of fissions coming from 233U which has a higher reproduction factor in general. Sensitivity results shown in Table 11 show the strong sensitivity to 233U fission reaction in the depleted case and the sensitivity tends to increase in the perturbed fuel temperature cases, which is consistent with the rationale provided earlier.

### Coolant Temperature Coefficient.

The coolant temperature coefficient (CTC) was investigated at the channel inlet and outlet in case of fuel burnup, and a 100 K increase in the coolant temperature causes the reactivity to increase by 4.71 mk and 3.86 mk for fresh and depleted fuels, respectively, corresponding to a coolant temperature coefficient of 0.0471 mk/K and 0.0386 mk/K.

As shown in Tables 9 and 10, the increase in the thermal utilization factor for fresh and depleted fuels at both positions is the most significant phenomenon related to coolant temperature perturbations. Again, the low-lying Pu fission resonances at approximately 0.3 eV are important contributors. The neutron up-scattering from hot coolant nuclides tends to shift thermal neutrons toward the low-lying Pu resonances. At the bottom of the channel, the thermal utilization factor increases by 4.21 mk and 5.11 mk for fresh and depleted fuels, respectively. The contribution to the relative reactivity change is slightly magnified due to its dependence on the value of k which is lower for irradiated fuel.

Interestingly, the behavior of the reproduction factor changes for burnup fuel compared to fresh due to coolant temperature perturbation. At the bottom of the channel, the reproduction factor decreases by 1.6 mk for fresh fuel, while it increases by 1.38 mk for depleted fuel. Such changes are consistent with the phenomena described in the fuel temperature coefficient results in that the importance of 233U becomes more significant with burnup, and therefore, any changes that increase the proportion of fissions in uranium will tend to increase the overall reproduction factor (since the capture to fission ratio in 233U is lower than that of Pu fuels). Given that higher coolant temperatures will tend to up-scatter neutrons to energies corresponding to the low-lying fission resonances of 233U, the reproduction factor increases with the increasing temperature in depleted fuels where 233U is present. The changes in fast-fission and resonance escape reported by SCALE were small with respect to coolant temperature changes.

The sensitivities of the highest contributing isotopes to the nuclear data sensitivity at the bottom of the channel are listed in Table 12 and confirm the discussion earlier. For fresh fuel, the sensitivity of Pu fissions increases with the increasing coolant temperature which is consistent with the increases in thermal utilization reported earlier. In depleted fuel, the increase in sensitivity in 233U with fuel temperature indicated its increasing importance due to up-scattering within the coolant. As expected, when the coolant temperature is increased, the absorption sensitivity of 1H increases so that it appears in the list of the isotopes with highest contribution to the nuclear data library sensitivities.

### Moderator Temperature Coefficient.

The moderator temperature coefficient (MTC) was calculated for depleted fuel by increasing the moderator temperature by 20 K, which causes the reactivity to increase by 0.98 mk and 0.83 mk corresponding to a MTC of 0.049 mk/K and 0.0415 mk/K at the channel inlet and outlet, respectively. Similar to fresh fuel, the outlet is slightly less sensitive to moderator temperature since the coolant temperature is higher in this region which affects the up-scattering and the increase in the thermal utilization factor. The physical phenomena affecting the MTC are identical to those affecting the coolant temperature coefficient.

## Conclusion

The lattice physics phenomena of the Canadian PT-SCWR 64-element with fuel burnup were investigated. Sensitivity and uncertainty analysis was performed identifying the isotopes, reactions, and nuclides with highest contribution to uncertainty or sensitivity of k for the reference case and perturbed scenarios. The main conclusion of this work:

1. (1)

The reactivity change and the four factor behavior in case of fuel burnup is quite similar to the fresh fuel case with some differences mainly due to the presence of Xenon and 233U, and changes in the concentration of Pu isotopes.

2. (2)

The tight lattice pitch of the PT-SCWR causes a harder neutron spectrum which increases the importance of the coolant in the neutron moderation process in both fresh and burnup fuel lattices as compared to traditional CANDU reactor designs.

3. (3)

The decrease in neutron reproduction rate is considered as the main contributor to the decrease in reactivity with fuel burnup and results from the overall decrease in fissile content in the fuel with burnup. The system also becomes highly sensitive to 233U and 135Xe with fuel burnup as a consequence of the Th–Pu fuel mixture and fission product behavior.

4. (4)

Overall, the feedback coefficients are consistent between fresh and depleted fuels with only minor changes occurring due to fission product, 233U, and minor actinides build-up as well as Pu depletion. The most significant difference in fuel phenomena in depleted fuel is related to the reproduction factor which may differ significantly under moderator, coolant, or fuel temperature perturbations. These changes are driven by the increasing importance of 233U with fuel burnup since 233U possess a lower capture to fission ratio than that of the Pu fissile isotopes present in fresh fuel. Knowing that the concentration of produced 233U is much smaller compared to the depletion of Pu, the Canadian SCWR is a thermal reactor with a total conversion ratio less than 1.

5. (5)

The Canadian PT-SCWR design has interesting lattice physics phenomena that are different from the conventional CANDU reactor. The Canadian PT-SCWR is characterized by strong negative void reactivity which is important in case of safety analysis and some accident scenarios such as loss of turbine in boiling water reactor or rod ejection in pressurized water reactor; however, small positive void reactivities are possible under nonequilibrium voiding scenarios. These effects do not change significantly with fuel depletion.

## Funding Data

• Natural Science and Engineering Research Council.

• Chalk River Nuclear Laboratories.

• The Canadian generation IV program.

## Nomenclature

### Greek Symbols

Greek Symbols

• ρ =

reactivity (mk)

•
• Σ =

neutron macroscopic cross section (cm−1)

### Nondimensional Numbers

Nondimensional Numbers

• f =

thermal utilization factor

•
• k =

neuron multiplication factor

•
• k =

infinite neuron multiplication factor

•
• n =

neutron

•
• p =

resonance escape probability

•
• γ =

gamma

•
• ε =

fast fission factor

•
• η =

reproduction factor

### Acronyms

Acronyms

• CANDU =

•
• CTC =

coolant temperature coefficient

•
• DF =

Dancoff factor

•
• ENDF =

evaluated nuclear data file

•
• FTC =

fuel temperature coefficient

•
• HERC =

high-efficiency re-entrant channel

•
• HM =

heavy metal

•
• ICV =

inner coolant void

•
• MTC =

moderator temperature coefficient

•
• NEWT =

new extended step characteristics-based weighting transport code

•
• NOC =

normal operating condition

•
• OCV =

outer coolant void

•
• PT-SCWR =

pressure tube super critical water-cooled reactor

•
• SAMS =

sensitivity analysis module for SCALE

•
• SCALE =

standardized computer analysis for licensing evaluation

•
• TCV =

total coolant void

•
• TSUNAMI =

tools for sensitivity and uncertainty analysis methodology implementation

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