Steady-state and transient core feasibility analysis for a thorium-fuelled reduced-moderation PWR performing full transuranic recycle

Annals of Nuclear Energy 72 (2014) 320–337 Contents lists available at ScienceDirect Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene Steady-state and transient core feasibility analysis for a thorium-fuelled reduced-moderation PWR performing full transuranic recycle Benjamin A. Lindley a,⇑, Ali Ahmad b, N. Zara Zainuddin a, Fausto Franceschini c, Geoffrey T. Parks a a Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK W. Wilson School of Public and International Affairs, Princeton University, Princeton, NJ, USA c Westinghouse Electric Company LLC, Cranberry Township, PA, USA b a r t i c l e i n f o Article history: Received 28 January 2014 Received in revised form 16 May 2014 Accepted 21 May 2014 Keywords: PWR Transuranic Thorium Mechanical shim Rod-ejection accident Shutdown margin a b s t r a c t It is difficult to perform multiple recycle of transuranic (TRU) isotopes in PWRs as the moderator temperature coefficient (MTC) tends to become positive after a few recycles and the core may have positive reactivity when fully voided. Due to the favourable impact on the MTC fostered by use of thorium (Th), the possibility of performing Th–TRU multiple-recycle in reduced-moderation PWRs (RMPWRs) is under consideration. Heterogeneous fuel design with spatial separation of Th–U and Th–TRU is necessary to improve neutronic performance. This can take the form of a heterogeneous fuel assembly (TPUC), or whole assembly heterogeneity (WATU). Satisfactory discharge burn-up can be maintained while ensuring negative MTC, with the pin diameter of a standard PWR increased from 9.5 to 11 mm. However, the reactivity becomes positive when the coolant density in the core becomes extremely low. This could lead to positive reactivity in some loss of coolant accident (LOCA) scenarios, for example a surge line break, if the reactor does not trip. To protect against this beyond design basis accident, a second redundant set of shutdown rods is added to the reactor, so that either the usual or secondary rods can trip the reactor when there is zero coolant in the core. Even so, this condition is likely to be concerning from a regulatory standpoint. Reactivity control is a key challenge due to the reduced worth of neutron absorbers and their detrimental effect on the void coefficients, especially when diluted, as is the case for soluble boron. Mechanical shim is therefore employed. As a result, it is difficult to maintain adequate core power peaking over the cycle, and careful lattice and core design is required, particularly for the WATU design. An adequate shutdown margin (SDM) can be maintained in both cases, but this requires use of B4C rods with enriched Boron-10 in B. A higher Boron-10 enrichment is required for the TPUC fuel design. The response to a rod ejection accident (REA) is significantly worse than in conventional PWRs due to a lower delayed neutron fraction, but fuel enthalpy deposition limits can be satisfied. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Multiple recycle of transuranic (TRU) isotopes in thermal spectrum reactors results in a degradation of the Pu fissile quality with build-up of higher actinides, some of which (e.g. 241Am) are thermal neutron absorbers. This leads to increasing Pu feed requirements to sustain criticality and accordingly larger TRU content in the multi-recycled fuel inventory, ultimately resulting in a positive moderator temperature coefficient (MTC). Due to the favourable impact on the MTC fostered by use of Th, the possibility of performing Th–TRU multiple-recycle in reduced-moderation PWRs (RMPWRs) is being considered. The objective is to allow ‘complete’ recycle of TRU for waste management purposes, rather ⇑ Corresponding author. Tel.: +44 1223 748569; fax: +44 1223 765932. E-mail address: bal29@cam.ac.uk (B.A. Lindley). http://dx.doi.org/10.1016/j.anucene.2014.05.027 0306-4549/Ó 2014 Elsevier Ltd. All rights reserved. than improved fissile utilisation or improved core performance over conventional PWRs. Increasing the fuel pin diameter improves the trade-off between achievable burn-up and MTC, but is ultimately limited by thermal–hydraulic constraints. A reoptimisation of the core design is necessary to minimise the fuel pin diameter at which the neutronic constraints can be satisfied. An alternative method for designing a hard spectrum PWR core could be to add some fraction of D2O to the coolant. This hardens the spectrum without reducing the core coolant inventory, and this has been the motivation for U (Hiruta and Youinou, 2013) and Th (Takaki and Mardiansah, 2012) PWR breeder reactor concepts, although the former required high leakage design to achieve a negative void coefficient. D2O has also been considered for BWRs (Hibi et al., 2001), but this has the severe disadvantage of the potential for tritium leakage in the steam generators of the primary circuit. (Harris, 2013) found that the neutron spectrum from use of mixes 321 B.A. Lindley et al. / Annals of Nuclear Energy 72 (2014) 320–337 of H2O and D2O coolant in a PWR resulted in an unfavourable spectrum for TRU burning. This was due to increased resonance flux relative to fast and thermal flux, increasing the detrimental resonance capture effects on neutron economy and void reactivity. In addition to the negative MTC requirement around the zero void point, it is also desirable to ensure the core has negative reactivity when fully voided in order to ensure acceptable response to loss of coolant accidents (LOCAs). At low coolant density, the reactivity can increase rapidly with reduced coolant density. Two voiding conditions are considered: zero coolant density and coolant density for a core filled with saturated steam at the operating pressure (15.5 MPa, resulting in a coolant density of 95.5 kg/m3). These are termed the zero coolant reactivity (ZCR) and fully voided reactivity (FVR) respectively.1 When the core is depressurized, the steam density is essentially zero. Hardening the neutron spectrum by increased pin diameter and TRU loading tends to decrease the worth of neutron poisons, which impacts reactivity control. This necessitates the use of control rods with enriched B4C pellets to maintain adequate shutdown margin (SDM) (Fridman and Kliem, 2011). Multi-recycled Th–TRU fuel has a considerably more complex isotopic composition than U–Pu mixed oxide fuel (MOX), or even multi-recycled U–TRU fuel. The fuel is composed of: fertile 232Th; 231 Pa (neutronically insignificant but important for long-term radiotoxicity); U bred from 232Th, which is composed of 233-6U (collectively called U3); Pu and minor actinides (MAs: Np, Am, Cm and higher). These can be recycled homogeneously, or partitioned individually during reprocessing. This partitioning presents additional reprocessing challenges (Franceschini et al., 2013) but may be beneficial for neutronic reasons – specifically, a much more thermalised spectrum in the U3 which improves the MTC, and a harder spectrum in the TRU, which improves the neutron economy, while maintaining roughly the same core average neutron spectrum (Lindley et al., 2013a) – and to limit fabrication costs. Fuel containing U3 and MAs must be fabricated remotely, which is the reason why partitioning of MAs from the Pu is often proposed for U-based heterogeneous recycle schemes (Varaine et al., 2010). Separation of Pu from other TRU isotopes in this manner has been considered for reduced-moderation BWRs (Lindley et al., 2014a). Heterogeneous (‘CORAIL’) assemblies have frequently been considered for partially MOX-fuelled cores (Kim et al., 2002) and variants for Th–Pu fuels in LWRs have also been considered (Sorensen et al., 2006). While the neutronic advantages of this are often demonstrated at an assembly level, once the fuel has been separated into components of different neutronic characteristics, the possibility to manage them separately at the full-core level presents itself, which proves highly advantageous. Typically, PWRs are controlled by a combination of stationary poisons (e.g. burnable absorbers integral to the fuel, burnable poison inserts, etc.), soluble boron and control rods. Both stationary poisons and soluble boron tend to make the MTC worse, and this is particularly so for soluble boron. In contrast, use of control rods for mechanical shim can improve the MTC. Using mechanical shim instead of chemical shim is therefore desirable, although this may not be possible within power peaking constraints. Some LWRs, such as AP1000sÒ2 (Onoue et al., 2003), utilise mechanical shim for load following and to reduce the number of changes in boron concentration. However, rod insertion typically results in a 1 i.e. 100% void fraction. This term is selected for consistency with previously published papers. Depending on the relevant core condition, FVR could reasonably be used to mean reactivity at zero coolant density or 100% void fraction. 2 AP1000 is a trademark or registered trademark of Westinghouse Electric Company LLC, its affiliates and/or its subsidiaries in the United States of America and may be registered in other countries throughout the world. All rights reserved. unauthorised use is strictly prohibited. Other names may be trademarks of their respective owners. depressed local power distribution, with a subsequent power spike when the rods are extracted due to the rod shadowing the fuel. This tends to increase the core form factors (Franceschini and Petrovic, 2009). Partial axial insertion of the rods skews the power towards the bottom of the core, which increases power peaks and triggers Xe transients (Franceschini and Petrovic, 2008). This is mitigated by the low reactivity swing to be controlled by rods of less than 2000 pcm, due to: the high content of MA and even-numbered isotopes of Pu in the fuel; the hard neutron spectrum; and the use of burnable absorbers. The hard neutron spectrum also acts to reduce power variations across the core by increasing the mean neutron path. The RMPWR core considered in this paper does not use soluble boron. In PWRs, the neutronic feasibility of multiple recycle is severely limited by the thermal neutron spectrum. This is exacerbated by the decay of fissile 241Pu into 241Am between recycles. In this study, 5 years are assumed between recycles to permit aqueous reprocessing. For a standard 17  17 Westinghouse fuel assembly with 12.6 mm pin pitch, increasing the pin diameter from the reference value of 9.5–11 mm hardens the neutron spectrum (Table 1), improving neutron economy and reducing the TRU feed necessary at equilibrium to maintain adequate cycle length with a negative MTC and FVR (Lindley et al., 2013b), although the ZCR is substantially positive. An 11 mm pin diameter is approximately the maximum that can be used without violating thermal–hydraulic constraints (Lindley et al., 2014b). The FVR is relevant because in many design basis accidents the maximum core void fraction (VF) is 90% (AREVA/EDF, 2012). Hence, if the FVR is negative, this provides protection against all but the most severe LOCAs. Consideration of the ZCR and FVR in conjunction allows the minimum allowable water density in the core to be interpolated. While it is obviously very desirable to have a negative ZCR, it is found that this is almost certainly unachievable for the RMPWR. It must be stressed that this is an undesirable condition that may make it difficult to license the core, but it is not necessarily unacceptable. Th–TRU and Th–U3 are separated into different assemblies or different regions of the same assembly. Furthermore, the batch strategies of the two fuel types are different: the Th–TRU is left in the core for twice as long as the Th–U3, due to its lower burnup reactivity swing and to maximise the ratio of 241Pu fissions to decays, which improves the neutron economy and reduces the FVR and ZCR. However, several outstanding issues need to be resolved: – Consideration of the reactor’s neutronic response to a large break (LB) LOCA with and without trip, given that the ZCR is positive; – Confirmation of the feasibility of controlling the core using mechanical shim instead of soluble poison; – Confirmation of the feasibility of achieving an adequate SDM; – Confirmation that there is a satisfactory response to reactivity transients, notably a rod ejection accident (REA), due to the low delayed neutron fraction. Table 1 Assembly parameters. Fuel pellet radius Fuel pin diameter Pin pitch (square) Pins/assembly Active height Hydrogen to heavy metal (H/HM) ratio Reference PWR RMPWR 4.095 mm 9.5 mm 12.6 mm 264 (17  17) 366 mm 1.98 4.845 mm 11 mm 12.6 mm 264 (17  17) 366 mm 1.09 322 B.A. Lindley et al. / Annals of Nuclear Energy 72 (2014) 320–337 This paper presents a detailed core analysis in order to address these issues. 2. Method 2.1. Fuel cycle modelling The RMPWR is fuelled by an external supply of TRU mixed with Th as oxide fuel. At the end of the cycle, all actinides are assumed to be reprocessed and returned to the reactor, suitably topped up with feed. A fuel density of 95% of theoretical is desirable for neutronic reasons and has been assumed, although in practice this may be difficult to achieve with remote fabrication. The TRU feed is assumed to be UO2 4.4 wt% enriched PWR discharge, burned to 52 GWd/t and cooled for 10 years. The composition is given in Table 2. The feed to the reactor is 50% TRU and 50% Th. Only the equilibrium cycle is considered. In practice, the approach to steady state is also very important, but the equilibrium cycle gives a good indication of the neutronic feasibility of the fuel cycle and reactor concept, and, for thermal spectrum designs, is often the limiting case. The equilibrium cycle is approached by time-marching to the steady state assuming a constant waste reload fraction, i.e. proportion of feed which is not 232 Th, and a constant discharge burn-up. Therefore, the cycles in the convergence on steady state are not meaningful, and this procedure is simply a method to converge upon the steady state. 2.2. Fuel design A heterogeneous fuel assembly design is considered, which is similar in concept to other heterogeneous assemblies including CORAIL designs with UO2 and MOX pins (Kim et al., 2002), CONFU fuel designs with UO2 and fertile-free pins (Shwageraus, 2003), and LEU–Th seed blanket unit designs (Todosow and Kazimi, 2004). Here, pins with a more thermal spectrum are placed near the guide tubes and pins with a faster spectrum are placed at the assembly edge. This is described as TRU pins at the Periphery of the fuel assembly with U3 pins at the Centre (TPUC) (Fig. 1). Previous papers (Rahman et al., 2012; Lindley et al., 2013a, 2013b, 2014a, 2014b) considered an inverted design, but as it is desirable in this case to have a thermal spectrum in the Th-U3 pins, here they are placed near the guide tubes. This actually makes only a slight difference, as the dominant effect is due to a much larger thermal and resonance capture cross-section in the Th–TRU pins, such that the guide tube effect is secondary. However, the main advantage is an increase in the SDM of around 300 pcm, by increasing the thermal neutron flux in the guide tubes. The neutron flux for the Th– TRU and Th–U3 regions of the TPUC assembly are shown in Fig. 2, with comparison to the flux in an unmodified U-fuelled PWR. The ratio of the fluxes in the Th–TRU and Th–U3 regions (plotted for the inverted design) is shown in Fig. 3. This ratio is virtually the same for TPUC and WATU designs. These fluxes were calculated using a development version of the WIMS 10 (Winfrith Table 2 Waste feed composition. Isotope at.% Isotope at.% Isotope at.% 241 5.77 7.15E-03 1.60 2.99E-07 5.73E-03 0.50 245 0.06 6.46E-03 9.34E-05 7.04E-06 4.94 238 2.74 48.45 21.03 8.45 6.46 Am 242m Am 243 Am 242 Cm 243 Cm 244 Cm Cm 246 Cm 247 Cm 248 Cm 237 Np Pu 239 Pu 240 Pu 241 Pu 242 Pu Fig. 1. TPUC fuel design with 144 Th–TRU pins (blue) and 120 Th–U3 pins (green) per assembly. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Improved Multigroup Scheme, Newton et al., 2008) lattice physics code. An alternative to the heterogeneous assembly concept is whole assembly heterogeneity, here referred to as Whole Assembly TRU U3 (WATU). WATU’s principal advantage is the potential to manage the Th–TRU and Th–U3 on different fuel management schemes. For this fuel type, there is motivation for leaving the Th–TRU pins in the reactor for longer than the Th–U3 pins. It also simplifies the assembly design and quality assurance processes in assembly fabrication. For WATU, a checkerboard array of the fuel assembly types appears sensible, and this renders the scheme amenable to placing the Th-U3 assemblies in the rodded positions. As burnable absorbers are not thought appropriate for this design (Lindley et al., 2014c), the guide tubes in the Th–TRU assemblies are replaced with additional fuel pins. This has the obvious drawback of constraining the fuel management scheme but hardens the neutron spectrum in the Th–TRU pins. The supercell model for this fuel design is shown in Fig. 4. This corresponds to an infinite checkerboard of assemblies. In addition, the guide tubes are an important part of the fuel assembly structure, so replacing them in this manner will require structural changes to the fuel assembly, or it may be necessary to retain at least some of the guide tubes. It is anticipated that wire wraps will be utilised instead of conventional grid spacers (Lindley et al., 2014b). Gd2O3 is used as a burnable poison, and is placed in the more thermal Th–U3 pins, to reduce their high initial reactivity. The spectrum is soft enough for the Gd2O3 to burn out sufficiently rapidly (i.e. with one cycle, about 10 GWd/t). Reactivity varies greatly with burn-up in the Th–U3 pins, initially rising as the Gd burns out then falling as U3 depletes and fission products accumulate (Fig. 5). In contrast, the neutron multiplication factor of the Th–TRU fuel is essentially constant over a high burn-up range due to the conversion of fertile isotopes, such as 232Thu and 240Pu, over the cycle. This motivates leaving Th–TRU assemblies in the reactor for longer than Th–U3 assemblies. In addition, maximising the burn-up of the Th–TRU improves the ratio of 241Pu fissions to decays, which improves the neutron economy and reduces the FVR. This Th–TRU multi-pass methodology is also applicable to the TPUC assembly. The Th-U3 ‘driver’ can be replaced with fresh Th–U3 (held in reserve) after one pass (i.e. after 3 cycles) through 323 Normalised flux per unit lethargy (n/cm2/s) B.A. Lindley et al. / Annals of Nuclear Energy 72 (2014) 320–337 0.6 PWR Enriched U RMPWR TPUC TH-TRU RMPWR TPUC Th-U3 fuel 0.5 0.4 0.3 0.2 0.1 0 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 Neutron Energy (eV) Fig. 2. Neutron flux in unmodified PWR compared to RMPWR (without burnable poisons). 2.0 No Gd in Th-U3 Pins ThTRU flux/ThU3 flux 1.8 Gd in Th-U3 Pins 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 Neutron energy (eV) Fig. 3. The ratio of the neutron fluxes in Th–TRU and Th–U3 pins with and without burnable poisons. the core, and the Th–TRU can remain for an additional pass. Holding Th–U3 pins in reserve in this manner is not anticipated to increase proliferation concerns as any realistic multi-recycle scheme leads to significant out-of-reactor fissile inventories and potentially management of fuel supply of multiple reactors on different outage schedules. Separable assembly designs have been considered for U–Th open cycle ‘seed-blanket unit’ concepts (also known as Radkowsky Thorium Fuel), for example in (Todosow and Kazimi, 2004). These assembly designs consist of a central removable seed subassembly, surrounded by a blanket sub-assembly which can reside in the core for multiple passes. A demonstration assembly of Lightbridge’s VVERT design was successfully fabricated by Westinghouse Electric Company LLC (Todosow and Galperin, 2009), and no practical manufacturing obstacles are anticipated. The TPUC assembly design is conceptually the same as the seed-blanket unit. The disadvantage of increasing the number of Th–TRU passes is a decrease in net 233U breeding and reduced opportunities to load TRU into the core. In this paper, two Th–TRU passes per Th–U3 pass are considered. This allows sensible batch management of the TCUP case. For the WATU case, a pass ratio intermediate between 1:1 and 2:1 may be feasible or preferable. However, a 2:1 pass ratio gives a 1 year equilibrium cycle length and peak discharge burn-up in the Th–TRU fuel of 58 GWd/t, which is similar to the maximum achieved in Generation III+ PWRs. While this is thought reasonable, cycle lengths lower than 1 year are likely to be economically penalizing. The number of Th–TRU pins can easily be varied for TPUC fuel. In WATU, the analogue is to vary the relative number of assemblies, but a 1:1 ratio is used here for simplicity and consistency between the supercell transport calculation and the full-core calculation (see below). In principle, it is possible to thermalise the spectrum in the Th– U3 pins even more by reducing their diameter relative to the Th– TRU pins. Based on calculations performed for BWR designs (Lindley and Parks, in press-a) this may increase the maximum allowable TRU loading in the assembly, but is likely to penalize the neutron economy such that the average discharge burn-up becomes lower which in this case is unlikely to be acceptable. It is also possible to separate the Th–U3 and Th–TRU into a macroheterogeneous ‘2-region core’, e.g. with Th–TRU at the core periphery and Th–U3, towards the centre. This was investigated for an axially heterogeneous design of BWR (Lindley and Parks, in 324 B.A. Lindley et al. / Annals of Nuclear Energy 72 (2014) 320–337 Fig. 4. WATU fuel design and lattice used for supercell calculations. Th–TRU pins are blue and Th–U3 pins green. The model is symmetric about the line X = Y, but this model is easier to specify in WIMS. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) 2.3. Lattice calculations 1.18 ThTRU ThU3 k-inf in fuel channels 1.16 1.14 1.12 1.1 1.08 1.06 1.04 1.02 1 0.98 0 5 10 15 20 25 30 Burn-up (GWd/t) Fig. 5. kinf in Th–TRU and Th–U3 pincells within the WATU supercell model. press-b – an axially heterogeneous design was selected in part for calculation simplicity). In this case, the design was not pursued further due to large power swings between Th–U3 and Th–TRU regions as the fuel was depleted, which also results in a large variation in FVR over the cycle. It is possible that this will be mitigated by designing a multi-batch, radially heterogeneous core, such that this warrants further investigation for the RMPWR. As the thermal neutron diffusion length is of the order of 1 pin pitch and the TPUC and WATU fuel designs have similar neutronic performance, it is not thought that separating theTh–U3 and Th–TRU into bigger regions will have a significant impact on the spectral variation between regions. Lattice calculations were performed using a development version of WIMS 10 (Newton et al., 2008) with the JEF-2.2 data library. A 172-group calculation with geometric approximations was first performed using the collision probability method to generate 11-group cross-sections. A few-group solution in detailed geometry was then performed using the method of characteristics. This 2-step procedure greatly speeds up the calculations but introduces an error of 200 pcm. In future, the number of groups will be increased from 11 to 20. The subgroup method was used to generate 172-group cross-sections for 232Th, 233U, 239Pu and 240 Pu to properly treat resonance interaction. This method is computationally expensive with factorial complexity so only the most important isotopes are considered. Other isotopes are treated using the standard equivalence theory (Powney and Newton, 2004). A core burn-up of 10.17 GWd/t per cycle is specified for the isotopic convergence, single-assembly analysis and full-core analysis. This corresponds to 346 days of full power operation (i.e. a 1 year cycle with downtime). Compared to a Monte Carlo analysis using the same 172 group data library in MONK (Answers, 2001), WIMS generally predicts FVR and ZCR values 600 pcm higher for Th–U3–TRU fuel. Additional errors are introduced by the 172 group structure, in particular due to the limited number of fast energy groups, for example around the 232Th fission thereshold energy. This may be an issue given the hard spectrum of the RMPWR, and also in particular for fully voided calculations. Further analysis and comparison with Monte Carlo cross sections in a large number of groups (or continuous energy representation) is needed. In addition, JEF-2.2 generally predicts FVR and ZCR values 1500 pcm higher than ENDF/B7 (apparently due to a higher 232Th capture cross section B.A. Lindley et al. / Annals of Nuclear Energy 72 (2014) 320–337 Fig. 6. Multi-pass fuel loading scheme. in the 4–48 keV range), which leads to substantial uncertainty in their values (although JEF-2.2 is ‘conservative’) (Lindley et al., 2014c). Given that the core design and equilibrium isotope vector have been derived using WIMS 10, it may be worth rerunning the analysis using a Monte Carlo code with a hyperfine energy group scheme to perform the lattice calculations, although this is computationally expensive. A proportion of the U3 was held back at the start of the first pass. The fuel was burned to 30.5 GWd/t, and then the fission products were removed from the Th–U3 pins. The retained U3 was then loaded, and the Th fraction set to give the correct fuel proportion. The small quantity of TRU produced during the first pass in the Th–U3 pins was stored for subsequent recycle in the Th–TRU pins. At the end of the second pass, all the fission products were removed and, after 5 years decay, the reactor was refuelled with a mix of 232 Th and the reload isotope vector in Table 2, while holding a proportion of the total U3 inventory in reserve. The overall waste reload fraction (fraction of feed which is not 232Th) is calculated based on the average waste reload fraction over both passes through the core. In practice, the residual U3 in the Th–U3 pins is obviously not instantly reprocessed at the end of Pass 1 and instead the Pass 2 U3 comes from an earlier pass after cooling and reprocessing. However, the equilibrium fuel cycle methodology is exactly equivalent in this respect. This methodology is shown in Fig. 6. Only a single depletion history was performed, as is typical for PWR calculations. However, it must be noted that the reactivity is somewhat sensitive to the power history of the fuel assembly, due to 241Pu decay into 241Am, and 233Pa decay into 233U (these effects act somewhat in opposition). The equilibrium isotope vector is somewhat sensitive to the average assembly power, such that it is possible that power history over the equilibrium cycle is also significant. It is worth considering this effect in future calculations. The effective delayed neutron fraction (beff) was calculated using the Monte Carlo code SERPENT (Leppänen, 2007) (for a 2D lattice calculation) due to limitations with WIMS when calculating the kinetic parameters of Th-U3 fuels. A hyperfine energy group calculation was performed.3 2.4. Core calculations A full-core model based on a 3411 MW 193 assembly 4-loop Westinghouse PWR (Watt’s Bar, 2009) was used compare the performance of the different fuel management schemes. The analysis was performed in PANTHER (Hutt et al., 1991). Two-group crosssections for PANTHER were generated by condensing the multigroup cross-sections with the WIMS flux solution – this is a standard procedure in WIMS. Data was taken from the supercell model of Fig. 4 for the WATU fuel. The reflective boundary conditions through the assembly 3 For this fuel, there were problems when calculating an accurate value of beff with JEF-2.2 in SERPENT. Therefore the ENDF/B7 data library was used instead. Use of different data libraries for different parameters in this manner is not ideal, but the JEFF-3.1 and ENDF/B7 data libraries were found to give virtually identical values of beff giving confidence that this is acceptable. 325 midpoints in the supercell model are a good approximation to the conditions in the core and 2-group cross-sections are derived using an appropriate spectrum. Each assembly contained 4 radial nodes in this case. In PANTHER, it is possible to employ assembly discontinuity factors such that the PANTHER fluxes are forced to match the lattice solution, resulting in an exact match in kinf for an identical problem (Knight et al., 2013). It is possible to generate approximate discontinuity factors in PANTHER ‘on the fly’ using an ‘embedded method’ described in (Knight et al., 2013). While practical, this method is currently difficult and time-consuming to set up, so the discontinuity factors were not implemented for the WATU model. It is also possible to derive the discontinuity factors using a supercell calculation in WIMS, and pass the calculated assembly average and assembly edge fluxes to PANTHER – again this is difficult and time-consuming to set up and is not performed here. This results in errors of 0.5% in the fast neutron flux, and 8% in the thermal neutron flux in PANTHER relative to the WIMS solution, which can lead to errors of 5% in interface pin powers. This is deemed acceptable for the purposes of this feasibility analysis but future analysis will use discontinuity factors. The TPUC core accounts for flux variation across the assembly by normalising to the cell edge flux rather than the cell average flux. This is the usual procedure employed in PANTHER, and is acceptable because, as is usual, the reflective boundary condition at the assembly edge is an accurate approximation to core conditions. WIMS contains a specific calculation route to account for reflector effects, by setting fast and thermal cross sections to accurately reproduce the neutron currents at the core/assembly interface. Pin power reconstruction is not employed for the full-core model, due to the unsuitability of the method (no discontinuity factors) for deriving them. A complex fuel design is needed to achieve adequate pin power peaking (discussed in Section 3), and evaluation of an accurate maximum pin power peaking also needs to consider control rod history effects on pin-level power peaking due to the use of mechanical shim. These in-depth calculations are beyond the scope of this feasibility study, and a simpler approach is adopted with pin-level and assembly-level power peaking considered separately, and multiplied together to estimate total power peaking. Given the hard neutron spectrum and heterogeneous fuel, use of 2 energy groups may not be sufficient, and use of more groups will be considered in future. Furthermore, additional uncertainty in the MTC, FVR and ZCR will be introduced in PANTHER, as the averaging of the mesh-by-mesh MTCs in the core may introduce inaccuracies, and for the FVR and ZCR the treatment of leakage becomes extremely important. The fuel conductivity for Th–TRU is estimated using the model for Th–Pu in (Cozzo et al., 2011), with the TRU proportion taken as the Pu proportion. This significant assumption is made due to limited data availability. The conductivity for Th-U3 is taken from (Yang et al., 2004). PANTHER’s simple thermal feedback model represents only a single pin-cell type per node, so the average thermal conductivity was derived to represent the net effect of the two separate pin types. This approach is sufficient to treat neutronic– thermal–hydraulic feedback effects to a reasonable degree of accuracy, as the Doppler Coefficients (DCs) of the two fuel types are very similar (3.5 pcm/K for a single-assembly analysis with 100 K perturbation in fuel temperature). For WATU, different conductivities were implemented in different assemblies. 3. Lattice design The fuel equilibrium isotope vectors derived using the multiple recycle methodology described in Section 2 are given in Table 3. 326 B.A. Lindley et al. / Annals of Nuclear Energy 72 (2014) 320–337 Table 3 Equilibrium fuel isotope vectors at beginning of cycle (BOC). BOC at.% 241 Am 242m Am 243 Am 243 Cm 244 Cm 245 Cm 246 Cm 247 Cm 248 Cm 237 Np 238 Pu 239 Pu 240 Pu 241 Pu 242 Pu 232 Th 233 U 234 U 235 U 236 U TRU U3 Fissile* * 233 U, 235 U, TPUC WATU Average Th–TRU 1.29 0.03 0.74 0.00 0.54 0.22 0.20 0.04 0.02 0.59 2.24 3.65 5.12 1.14 2.68 77.32 2.03 1.54 0.46 0.46 18.50 4.49 7.28 2.37 0.06 1.36 0.00 0.99 0.40 0.37 0.07 0.04 1.08 4.11 6.69 9.39 2.09 4.91 66.08 239 Pu and 33.92 0.00 8.78 241 Th–U3 Average Th–TRU 90.50 4.30 3.26 0.97 0.97 0.00 9.50 5.27 1.31 0.04 0.73 0.00 0.52 0.22 0.19 0.05 0.02 0.59 2.17 3.59 5.25 1.07 2.66 77.56 1.96 1.42 0.42 0.45 18.41 4.25 7.04 2.51 0.08 1.40 0.00 1.00 0.42 0.36 0.10 0.04 1.13 4.16 6.88 10.06 2.05 5.10 64.71 35.29 0.00 8.93 Th–U3 91.11 4.10 2.97 0.88 0.94 0.00 8.89 4.98 Pu are considered fissile. Table 4 Fuel discharge burn-ups (GWd/t). Th-TRU Th-U3 Core average TPUC WATU 60.8 30.1 41.2 57.8 31.8 41.0 These fuel compositions are almost identical, despite slight differences in the region sizes, and relative numbers of Th–TRU and Th–U3 pins. The TRU incineration rate is 172 kg/GWthyr for the WATU design and 192 kg/GWthyr for the TPUC design. Fuel discharge burn-ups are given in Table 4. As the cycle length is fixed, these are also the discharge burn-ups for the core analysis. The discharge burn-up is somewhat lower than the enriched Ufuelled PWR. The heterogeneous fuel design introduces a strong thermal flux gradient at the interface between the Th–TRU and Th–U3 pins. In addition, the Th–U3 reactivity varies rapidly with burn-up: first increasing due to burnable poison depletion, then decreasing with 233 U fission and fission product accumulation. In contrast, the Th– TRU reactivity is roughly constant, as MA isotopes and even isotopes of Pu are depleted. This leads to variations in power swings between regions over the core life, making it difficult to limit pin-level power peaking. Variable fissile loading between pins is necessary to counteract this. In this paper, suitable designs are derived by hand, but computational optimisation will be pursued in future. The TPUC design utilises four fissile loading zones for both the Th–TRU and Th–U3 pins, summarized in Fig. 7. The assembly design and power peaking up to 20.5 GWd/t are shown in Fig. 7. This covers the first 2 cycles of operation within the core. Twice-burned assemblies are assumed not to be the ‘hot’ assembly, such that when the assembly is burned beyond 20.5 GWd/t higher pin-level power peaking is allowable. The power peaking is limited to 1.09 over the cycle, which is slightly higher than UO2 assemblies (1.06) but may still be acceptable in conjunction with low power-peaking core design. The use of enrichment zoning increases Fig. 7. Th–TRU and Th–U3 fissile loadings; assembly design and pin power peaking for TPUC. the complexity of fuel fabrication, as 8 different pin types will need to be accurately loaded into the assembly with remote fuel fabrication. Use of mechanical shim can lead to local assembly hot spots when the rods are withdrawn, as the adjacent fuel pins experience depressed flux and are therefore under-burned. However, rod shadowing was found not to adversely affect pin-level power peaking, leading to 1% increases or decreases in pin-level power peaking. The WATU supercell enrichment zoning (also utilising four compositions for both Th–U3 and Th–TRU) is shown in Fig. 8, with the power peaking over the cycle also given. In this case, the power peaking is normalised relative to the assembly, rather than the supercell, i.e. Th–U3 pin power is normalised relative to average Th–U3 pin power and Th–TRU pin power is normalised relative to average Th–TRU pin power. Assembly-level power variations will be considered at core level in this case. The Th–TRU pin-level power peaking can be limited to 1.07. In addition, the assembly contains 288 pins, compared to the usual 264, reducing the power in the average pin. This is discussed further in Section 6. The Th–U3 design is further complicated by the use of Gd in only some of the pins. This leads to large power swings across this assembly, and a maximum power peaking of 1.12. The above lattice design assumes a perfect checkerboard of Th–TRU and Th–U3 assemblies in the core. However, symmetry B.A. Lindley et al. / Annals of Nuclear Energy 72 (2014) 320–337 327 Fig. 9. Pin-level power peaking for infinite lattice of Th–U3 assemblies with fissile loadings defined as in Fig. 8. conditions necessitate a slight deviation from this pattern, leading to neighbouring assemblies of the same type in some areas of the core. The accurate calculation of local pin-level power peaking requires pin power reconstruction with a core analysis, and the use of several supercell calculations to derive varying discontinuity factors for different core positions, but the effects of identical neighbouring assemblies can be readily approximated by assuming an infinite lattice of one assembly type. An infinite lattice of Th–U3 assemblies with the fissile zoning defined in Fig. 7 would have a BOC power peaking of 1.27 (Fig. 9). The power peaking reduces to 1.11 (comparable to the supercell design) by the end of the first cycle – when the Gd at the centre of the assembly has burned out. The power peaking in Fig. 9 is obviously unacceptable. Changing the fissile zoning for specific assemblies is possible, but leads to problems when shuffling the fuel at end of cycle (EOC). As the problem appears limited to the first pass of fuel, while the Gd burns out, it appears more sensible to change the Gd loading design for the fresh assembly, i.e. utilise different Gd loadings for assemblies in different positions in the core. After the first pass, the Gd has burned out. A rigorous analysis of all fuel loading histories, e.g. where the Th–U3 assembly is initially next to a Th–TRU assembly, then shuffled to be next to a Th–U3 assembly, is needed to confirm this. 4. Core design and mechanical shim Fig. 8. Th–TRU and Th–U3 fissile loadings; assembly design and pin power peaking for WATU. Achieving adequate core power peaking requires derivation of a suitable loading pattern (LP). Here, this is combined with use of mechanical shim, which also necessitates finding a suitable control rod programme (CRP). PANTHER contains optimisation algorithms that can be used to derive suitable LPs, but the process is complicated by the need for a complementary CRP. For the TPUC core, an approximate LP (shown in Fig. 10) is used to repeatedly shuffle and deplete the core, to generate fuel with a characteristic range of burn-ups for an equilibrium cycle. The fuel loading is then optimised for the final ‘equilibrium’ cycle using the genetic algorithm in PANTHER (Parks, 1996) (Fig. 11). This does not represent true equilibrium, but, in reality, a true equilibrium cycle is almost never reached, and cycle-by-cycle LP design is pursued in any case. This process is therefore highly appropriate for determining the feasibility of finding a suitable LP plus CRP which results in acceptable core form factors. Highly enriched B4C rods are used to ensure adequate control rod worth. This is discussed further in the next section. Rod banks are defined as in Fig. 12, and a basic CRP is defined both for the initial cycles and the final equilibrium cycle (i.e. this CRP is fixed during the genetic algorithm search). The full CRP for the final cycle is then derived by hand, and is shown in Fig. 13. The basic CRP 328 B.A. Lindley et al. / Annals of Nuclear Energy 72 (2014) 320–337 Fig. 10. LP used to bring the TPUC core to equilibrium. Fig. 11. LP used for the TPUC equilibrium cycle. utilises banks CV and CD only, with insertions as in Fig. 13, with the additional banks utilised only in the final cycle. A criticality search throughout the cycle is defined using bank OD, such that criticality is maintained at 1.0015 for most of the cycle. The maximum dip in criticality of 70 pcm occurs in the middle of the cycle where bank OD is fully withdrawn; this would, in practice, be compensated for by adjustment of bank MV, but this is cumbersome to perform in PANTHER. The cycle length is 346 days, corresponding to a cycle length of 1 year and the discharge burn-up matching that used in deriving the equilibrium fuel composition. The WATU LP is more difficult to define, as a checkerboard loading scheme for the Th–TRU and Th–U3 assemblies is desired. It was therefore defined by hand, and was identical for the initial cycles and the equilibrium cycle (Fig. 14). A CRP was only defined for the equilibrium cycle and is shown in Fig. 15. The checkerboard condition is violated in positions E12, D12, D13 and C13 due to symmetry constraints, but is satisfied elsewhere. There are 96 Th–TRU assemblies and 97 Th–U3 assemblies, which is close to the 1:1 ratio used in the supercell analysis (which did not consider the 4th batch assembly at the reactor centre). Therefore, the supercell analysis described in Section 2 is deemed valid for deriving equilibrium fuel compositions and 2-group cross-sections. All rod bank positions contain a Th–U3 assembly with guide tubes. The core performance is almost identical with a Th–TRU assembly at the core centre, but a Th–U3 assembly is needed to utilise the central shutdown rod-cluster-control-assembly (RCCA). The cycle length is 346 days, and keff is maintained at 1.0000 by a criticality search on bank OD, except for the final 5 days, where the reactor becomes slightly subcritical. EOC keff is 23 pcm subcritical. A slight increase in TRU loading is therefore necessary to maintain criticality over the cycle. The reactivity coefficients for both designs are given in Table 5. Convergence of the FVR and ZCR in PANTHER is problematic. This is thought to be a result of the almost zero thermal neutron flux. Fig. 12. Rod bank definition for the TPUC and WATU cores. ‘S2’ denotes an independent set of shutdown rods which is not present in Westinghouse 4-loop PWRs but is added in Section 7 for LBLOCA mitigation. ⁄Not present in WATU core as incompatible with LP. 329 Bank insertion (%) B.A. Lindley et al. / Annals of Nuclear Energy 72 (2014) 320–337 100 CV 90 CD 80 MV 70 OV Table 5 Core reactivity coefficients. TPUC BOC BOC BOC EOC BOC BOC BOC EOC OD 60 50 WATU 40 30 20 (rods out) (all rods in) (rods out) (all rods in) MTC (pcm/K) DC (pcm/K) FVR ZCR 12.1 10.1 68.0 19.6 8.8 9.5 58.4 17.4 3.6 3.8 2.7 3.8 3.8 3.8 2.7 3.9 0.020 0.025 0.066 0.035 0.013 0.021 0.126 0.026 0.040 0.039 0.018 0.030 0.040 0.031 0.008 0.035 10 0 0 50 100 150 200 250 300 350 Time (days) 1.14 no Gd 1.13 Fig. 13. CRP used for the TPUC equilibrium cycle. Gd 1.12 1.11 k-inf 1.1 1.09 1.08 1.07 1.06 1.05 1.04 1.03 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Coolant Density (kg/m3) Fig. 16. k-inf with and without burnable poison for fresh fuel over a range of coolant densities. Fig. 14. LP used to bring the WATU core to equilibrium, and for the WATU equilibrium cycle. 1.45 1.4 90 Bank insertion (%) 80 70 Power peaking OD CV MV OV 100 60 50 1.35 1.3 1.25 40 RFF RFF(FdH) (F∆H) 1.2 30 AFF AFF 20 1.15 10 0 0 0 50 100 150 200 Time (days) 250 300 50 100 150 200 250 300 350 Time (days) 350 Fig. 17. RFF and AFF for the TPUC equilibrium cycle. Fig. 15. CRP for the WATU equilibrium cycle. There is substantial margin of subcriticality for the MTC and FVR. However, the ZCR is substantially positive, to such an extent that it appears unlikely to be able to modify the design to make it negative. Increasing the pin diameter will allow the TRU reload fraction to be reduced and hence the ZCR to be made less positive, but this may violate thermal–hydraulic limits (Lindley et al., 2014b). In general, insertion of control rods improves the MTC, FVR and ZCR, so calculation of reactivity coefficients with rods out leads to a conservative calculation. The DC is comparable to or slightly more negative than that of UO2 fuelled reactors (Westinghouse Electric Company LLC, 2010a) due to the high resonance flux in the reactor. The neutronic response to a LBLOCA is a serious concern and is further discussed in Section 7. kinf at different coolant densities is plotted for fresh fuel with and without Gd in Fig. 16. The is a sharp rise in reactivity as the coolant density drops below 0.2 g/cm3, leading in this cases for to a negative FVR and positive ZCR. For the reactor core this is somewhat offset by leakage effects. Note that the MTC is substantially positive with Gd, and is only negative for the full core due to multi-batch effects. 5. Core form factors The maximum radial form factor (RFF) calculated for normalised hot channel rise in enthalpy for the TPUC design is 1.41 (Fig. 17). The axial form factor (AFF) is calculated as the maximum power in an XY plane of the reactor divided by the average power of an XY plane of the reactor. An AFF based on the maximum ratio of peak to average power in an individual channel would be misleading as this ratio is very high in channels with partially inserted rods, due to very low power at the top of the rod. The AFF is 1.42 and the maximum total power peaking is 1.97. The AFF is slightly 330 B.A. Lindley et al. / Annals of Nuclear Energy 72 (2014) 320–337 Fig. 18. Core power distribution for the TPUC equilibrium cycle at (left to right) 0, 26, 33 (top row), 199, 255 and 346 days (bottom row). Spectral colour scale represents channel power: red = hot, blue = cold, normalised to extreme values (highest power shown in Fig. 17, lowest power 0.3–0.35). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) 1.55 1.5 1.45 Power peaking higher than without the use of rod shim, but still less than the chopped cosinusoidal distribution typically used in minimum departure from nuclear boiling ratio (MDNBR) calculations. Multiplying the maximum RFF by the pin power peaking of 1.09 gives an estimate of the maximum pin-level normalised hot channel rise in enthalpy (FDH) of 1.54. Applying an uncertainty factor of 1.05 and an engineering tolerance factor of 1.03 (as in Westinghouse Electric Company LLC, 2010a) gives a total power peaking of 2.32. For comparison, (Watt’s Bar, 2009) allows a total heat flux hot channel factor of 2.40 and a maximum FDH of 1.55, so the TPUC design just satisfies these criteria. The AP1000 allows somewhat higher values of 2.60 for total heat flux hot channel factor and 1.65 for maximum FDH (Westinghouse Electric Company, 2010a). The core power distribution over life is given in Fig. 18. The rod bank switching leads to large changes in the flux profile over the reactor life, with large flux depressions around the inserted banks. However, the bank switching prevents high power peaking due to rod shadowing effects at EOC. The RFF and AFF for the WATU design are given in Fig. 19. The maximum RFF is 1.47 (occurring at BOC) but in the Th–U3 the RFF is at most 1.41. A higher RFF is allowable in the Th–TRU assemblies due to the larger number of pins. The AFF is at most 1.55, which is less than that used for chopped cosine MDNBR calculations but higher than desirable. This is due to partial insertion of a high worth rod bank. Allowing for pin power peaking, the maximum FDH in the Th-U3 is estimated as 1.58, which exceeds the allowable value of 1.55 for Watt’s Bar but is within the AP1000 design value. Due to the restricted core design, it appears advisable to seek improved lattice designs with power peaking of at most 1.10 (compared to 1.12) as this will allow the Watt’s Bar design limit to be satisfied. The maximum FDH in Th–TRU is 1.44 (including pin power peaking but adjusting for the larger number of pins in the assembly, i.e. normalising power for a 264-pin assembly) which is substantially lower than the design value. The total power peaking in the Th–U3 is approximately 2.59 (allowing for uncertainties and engineering tolerances), which exceeds the Watt’s Bar design value but is just within the AP1000 criterion of 2.60. Significant reduction of the AFF over the early part of the cycle is advisable to achieve an acceptable 1.4 1.35 1.3 RFF RFF(FdH) (F∆H) 1.25 AFF AFF 1.2 Maximum FdH F∆H in Maximum inThU3 ThU3 1.15 0 50 100 150 200 250 300 350 Time (days) Fig. 19. RFF and AFF for the TPUC equilibrium cycle. value, which requires use of a lower worth rod bank for partial insertion to bring the reactor to criticality, although this is difficult to achieve with the selected LP without increasing the RFF. The total power peaking in the Th–TRU is 2.42, which is slightly greater than the Watt’s Bar design value. Computational optimisation seems advisable. The WATU rod banks are higher worth than the TPUC rod banks. However, as both satisfy the SDM criterion (Section 6), it may be acceptable to reduce the worth of some of the WATU rod banks, which may improve the AFF. The RFF over life for the WATU design is given in Fig. 19. At EOC, there is a suppressed power distribution in the centre of the core, due to the placement of low reactivity twice-burned Th-U3 assemblies close to the core centre and limited use of inner rod banks (CD and CV) over the cycle. The axial offset of the power peak from the centre of the core is given in Fig. 21. This is generally larger for the WATU design than the TPUC design, consistent with the AFF. As expected, the offset position becomes positive towards EOC as the rod banks are withdrawn, due to rod shadowing effects. 331 B.A. Lindley et al. / Annals of Nuclear Energy 72 (2014) 320–337 100 Time (days) TPUC 0 WATU 50 0 50 100 150 200 250 300 350 -500 TPUC 0 -1000 -50 SDM (pcm) Offset of position of maximum axial power from centreline (cm) Fig. 20. Core power distribution for the WATU equilibrium cycle at (left to right) 0, 47, 227 (top row), 269 and 346 days (bottom row). Spectral colour scale represents channel power: red = hot, blue = cold, normalised to extreme values (highest power shown in Fig. 19, lowest power 0.3–0.35). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) -100 -150 0 50 100 150 200 250 300 WATU -1500 -2000 -2500 350 Time (days) Fig. 21. Axial offset of position of maximum axial power for the TPUC and WATU equilibrium cycles. See Fig. 20. 6. Shutdown margin The SDM is reduced relative to conventional PWRs, a common problem with MOX cores exacerbated in RMPWRs due to the harder neutron spectrum from the reduced H/HM ratio and higher TRU loading. Highly enriched B4C rods can be used to mitigate this issue and control the reactivity, and in this study 95% enrichment of 10B in B is used. Highly enriched B4C rods are also under consideration for reduced-moderation BWRs (Downar et al., 2012). As with MOX cores, use of additional rod bank positions (difficult in retro-fit cores due to fixed RCCA positions) can be used to reduce the enrichment of 10B required, or to increase the overall control rod worth. The 10B in the control rods exposed at the high core neutron flux will deplete. This will require dedicated management of the control rods, including shuffling or replacement when the worth has decreased to unacceptable levels or the rod mechanical performance has degraded. Lattice calculations indicate that the control -3000 -3500 -4000 Fig. 22. SDM over the equilibrium cycle for the TPUC and WATU designs. rods lose 5% of their worth when burned to 20 GWd/t. For cycle-average control using 12% of the available worth (typical), this roughly equates to a 5% loss of rod worth over 16 years of operation (16 cycles). The rods will need to be shuffled and replaced regularly and the reduction in worth needs to be taken into account, but this should not represent a fundamental barrier to feasibility. These effects will be considered in more detail in future work. The SDM was calculated throughout life for a reactor trip from hot full power (HFP) to hot zero power (HZP), with no change in Xe population4, with the highest worth rod remaining out of the core. A 10% reduction is made for modelling uncertainties, and a 10% reduction is also made to account for control rod depletion (i.e. an overall reduction of 20%). The Doppler defect is increased by 20% to account for uncertainty. The value of the Doppler defect is 2000 pcm, lead4 The Xe level increases following trip, but typically no credit is taken for this. Removal of the Xe entirely would make the SDM worse by 600 pcm in this case. 332 B.A. Lindley et al. / Annals of Nuclear Energy 72 (2014) 320–337 Normalised neutron flux in WATU guide relative to normalised flux in TPUC guide tube (n/cm2/s) 1.5 Gd in pins 1.4 No Gd in pins 1.3 1.2 1.1 1 0.9 0.8 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 Neutron energy (eV) Fig. 23. Ratio of the flux in control rod guide tubes in WATU core relative to TPUC core. ible with the pressure vessel, and the feasibility of this needs to be established. Table 6 SDM with zero coolant density (pcm). TPUC WATU Usual rods Added emergency shutdown rods 4313 7242 2261 2650 ing to a reduction in SDM of 400 pcm. For both the TPUC and WATU designs, the highest worth rod throughout life is F10 and its symmetry positions, i.e. the rods of bank CD. In the TPUC design, rod bank CD is inserted for most of life, including at the time of minimum SDM, but no credit is given for this when assuming a stuck rod during a trip, as subcriticality must also be ensured if the highest worth rod is accidentally removed from a shut-down reactor. The variation in the SDM over the equilibrium cycle for both designs is given in Fig. 22. The SDM is always better than the minimum allowable 1300 pcm (Watt’s Bar, 2009). The minimum SDM for the TPUC and WATU designs is 1311 and 2576 pcm respectively, so the SDM requirement for the TPUC design is only just met. The highest worth rod is 1330–1400 pcm for TPUC and 1600–2500 pcm for WATU. The WATU design gives a much higher SDM than the TPUC design, partly due to a higher thermal neutron flux in the guide tube positions (Fig. 23). This is especially pronounced without Gd in the Th–U3 pins (i.e. when the Gd has burned out). Most rod captures are for neutron energies of around 1000 eV, so the increase in rod worth for the WATU design may be partly explained by reduced thermal neutron availability for 233U fissions. The SDM for the WATU design is comparable to conventional PWRs (Fridman and Kliem, 2011) and is high enough that the enrichment of 10B in B in the control rods can be reduced somewhat. As the WATU control rod worth is 35% higher than the TPUC total control rod worth, and the TPUC design meets the SDM criteria, this implies that the 10B enrichment in the WATU rods can be reduced from 95% to roughly 70% (a higher reduction might be possible due to saturation effects). This will reduce control rod cost. A slight further reduction is possible in both cases, as the SDM is slightly greater than the minimum. Alternatively, highly enriched rods can be replaced less often. It may be possible to increase the shutdown worth and reduce rod shadowing effects by utilising control rods which are longer than the fuel assemblies. This would allow different sections of the bank to be utilised for mechanical shim and for shutdown. As a result, it may be possible to employ a lower worth section for shim (towards the bottom of the bank) and a higher worth section for shutdown (towards the top of the bank, which is only inserted during shutdown). Use of longer control rods may not be compat- 7. Neutronic response to LOCA During an LBLOCA, the primary circuit depressurizes over a period of 50 s and the coolant drains out of the reactor core in a period of around 20 s. The core is then reflooded by the emergency core cooling system such that the collapsed liquid level rises substantially above zero after around 50 s (AREVA/EDF, 2012; Westinghouse Electric Company LLC, 2010b). For the design basis accidents considered in (AREVA/EDF, 2012), the mid-core VF is limited to at most 90% for 9 of the 10 considered break sizes, the exception being a surge line break. The top of core is uncovered for smaller breaks. The negative FVR protects against these LOCAs – hence it is considered advantageous to design for a negative FVR even when a negative ZCR is not possible. Even in a surge line break, the VF in the lower core is still substantially less than 1 at all times. A more detailed thermal–hydraulic analysis is necessary to take into account the increased pin size compared to a regular PWR, in conjunction with coupled neutronics to accurately determine whether a criticality accident is possible in this case. In the postulated design basis accident, reactor trip is assumed such that the reactor shuts down rapidly. In any case, for LEUfuelled cores the FVR and ZCR are substantially negative, so a trip is not necessary to shut down the core. For the RMPWR LBLOCA design basis accident, the reactor is shut down provided the reactor trips and the control rod worth is sufficient to shut down the reactor under fully voided conditions. For beyond design basis accidents, where the reactor does not trip, the RMPWR may experience a criticality accident during a LBLOCA if the water level in the core drops to a sufficiently low level following depressurization. This could lead to reactor containment being breached. While it should still be possible to license a plant with a positive ZCR, this is likely to concern a regulator. If it is possible to achieve a negative ZCR with a modified design, then it may be difficult to justify a positive ZCR. If not, then the likelihood of beyond design basis accidents, where the positive VC of the RMPWR becomes a concern, must be assessed, together with a severe accident analysis. This may lead to the requirement of additional safety measures, and a demonstration that the risks are as low as reasonably practical.5 In the UK, the licensing regime allows for a positive VC provided it is controllable and does not lead to unacceptable consequences – hence a limit needs to be placed on the maximum allowable ZCR if 5 Private communication with Dr. Peter Dolan, August 2013; Prof. Mike Weightman, October 2013. 333 B.A. Lindley et al. / Annals of Nuclear Energy 72 (2014) 320–337 (a) 1000 (a) 1400 1E-9 1200 1E-6 1E-9 1000 600 Reactivity (pcm) Reactivity (pcm) 800 1E-6 400 200 0 -200 800 600 400 200 0 -200 -400 0.00 -400 0.05 0.10 0.15 0.20 -600 Time (s) (b) 1000 0 0.01 0.02 0.03 0.04 0.05 Time (s) (b) 1400 800 600 1000 1E-6 1E-9 Max Tf (C) Max Tf (C) 1200 400 200 0 0.00 1E-9 600 400 200 0.05 0.10 0.15 0.20 Time (s) Fig. 24. (a) Reactivity and (b) maximum fuel temperature for TPUC 100 ms rod ejection at 1E-6 and 1E-9 power levels. the condition is plausible in a LBLOCA. It is also required that ‘‘unintended criticality cannot occur unless at least two unlikely, independent concurrent changes’’ in conditions occur. In an LWR, this can correspond to a LBLOCA without trip, i.e. failure of both the coolant and trip systems. Common-mode failures can be problematic, notably due to earthquakes (where lateral movement of the core relative to the reactor roof could jam any control rod actuator).6 Two independent means of shutting down the reactor are also required (UK Office of Nuclear Regulation, 2008). In the extremely unlikely case of a LBLOCA combined with ejection of all the control rods, the core will undergo a severe accident even if the VC at 100% VF is kept negative by using rods. Any reactor which relies on mechanical shim (e.g., any BWR) will experience a more severe accident if a LBLOCA is combined with simultaneous full rod withdrawal from the core. A LBLOCA without trip is presumably a more likely event (in particular, commonmode failures must be rigorously investigated – e.g. an earthquake which laterally displaces the control rods while simultaneously causing a surge line break) but a full understanding of the licensing requirement is necessary to properly assess the design. Here, the requirement for two independent means of shutting down the reactor is interpreted as necessitating a redundant set of shutdown rods with separate actuators, such that either set can shut down the reactor in a LBLOCA. This is similar to the use of two independent sets of shutdown rods in sodium-cooled fast reactors, although in these the void reactivity is often limited to 6$ (<2000 pcm) (Tobita, 2013), about half the value of the ZCR for the RMPWR (up to 4000 pcm or 12$). Some designs of sodium-cooled fast reactor have a higher sodium void reactivity, especially burner designs (Hoffman et al., 2006). 6 1E-6 800 Private communication with Dr. Tony Judd, October 2013. 0 0 0.01 0.02 0.03 0.04 0.05 Time (s) Fig. 25. (a) Reactivity and (b) maximum fuel temperature for TPUC 10 ms rod ejection at 1E-6 and 1E-9 power levels. An alternative is to use a completely separate shutdown system, e.g. a shutdown assembly at the centre of the core – although this would require a substantially modified reactor design. Use of separate redundant shutdown systems is also used in CANDUs, which have a positive ZCR of 500–1500 pcm (much lower than that considered here). This takes the form of a set of shutdown rods and gadolinium salt injection into the calandria (CANDU, 2012). In CANDUs, the shutdown rods have the advantage of operating in a relatively low pressure core, although in a LBLOCA core depressurization has also occurred which may help ensure the reliability of any redundant shutdown system, including a set of redundant shutdown rods as described in this section. The use of an additional set of shutdown rods is likely to disallow a retro-fit core due to the need to place them. The added rods are shown in Fig. 12 labelled ‘S2’. It must be noted that higher prediction of FVR (and ZCR) in JEF-2.2 than ENDF/B7 and the discrepancy relative to a multi-group Monte Carlo calculation could lead to an overestimate of as much as 2000 pcm in the FVR and ZCR (Lindley et al., 2014c). This would not make the ZCR negative, but would make it substantially less positive. The SDM with zero coolant density for the usual and added sets of rods is given in Table 6 (note the total reactivity in Table 6 includes the ZCR and control rod worth). A 10% uncertainty factor in the rod worth is assumed in both cases. 10% rod depletion is considered for the usual rods, but as the added rods are not used for shim, no depletion is assumed. The highest worth rod is assumed to be stuck for both rod banks. There is no Doppler defect as the rods are not required to achieve HZP, there is essentially no heat transfer when the core has zero coolant density, and the DC is in any case very low with zero coolant density ( 0.2 pcm/K). The 334 B.A. Lindley et al. / Annals of Nuclear Energy 72 (2014) 320–337 (a) (a) 1200 2000 1E-6 1E-9 1000 Reactivity (pcm) Reactivity (pcm) 800 600 400 200 0 -200 1200 800 400 0 -400 -800 -400 -600 0.00 -1200 0.05 0.10 0.15 0 0.20 Time (s) (b) 0.01 0.02 (b) 1200 2000 800 600 Max Tf (C) 2400 1E-6 1E-9 0.03 0.04 0.05 Time (s) 1400 1000 Max Tf (C) 1E-6 1E-9 1600 1600 1200 1E-6 1E-9 800 400 400 200 0 0.00 0 0 0.05 0.10 0.15 0.01 0.02 0.20 Time (s) very small DC also prevents Doppler effects from terminating overpower transients before containment is breached in a criticality accident, for this high a ZCR. The SDM is calculated for 52 and 73 days into the cycle for TPUC and WATU respectively, as these are the points of lowest SDM under operating conditions. Results are strongly indicative that a satisfactory SDM can be maintained throughout the cycle and that a reactor trip will still shut down the reactor at zero coolant density. 8. Rod ejection accident analysis The most severe reactivity accident in a PWR is typically a rod ejection accident (REA). The RMPWR operates with beff of 0.00318, significantly lower than that of a typical PWR (Diamond et al., 2002), so the enthalpy deposition in the fuel can be expected to be much higher than with conventional fuel. The enthalpy deposition from a prompt supercritical rod ejection can be predicted by the zero-dimensional adiabatic Nordheim-Fuchs model to be proportional to (reactivity insertion – beff) (Hetric, 1993). For the WATU fuel, this can be as high as 2200 pcm. Fortunately, the enthalpy deposition is typically much less than the maximum permissible, such that a substantial increase in this value is allowable. The Nordheim-Fuchs model generally gives the correct relationship, but not the constant of proportionality determined by the power peaking (Diamond et al., 2002). PANTHER is used here with rod ejection at the point of maximum rod worth. No reactor trip was modelled. Results were checked by comparing with a point kinetics model, with the RFF in the ejected assembly taken from PANTHER. The point kinetics code PTS-ADS (Ahmad et al., 2012) was used, and gave good agreement with PANTHER for maximum fuel temperature rise. 0.04 0.05 Fig. 27. (a) Reactivity and (b) maximum fuel temperature for WATU 10 ms rod ejection at 1E-6 and 1E-9 power levels. 1.2E+06 1E-6 1E-9 1.0E+06 Power (MW) Fig. 26. (a) Reactivity and (b) maximum fuel temperature for WATU 100 ms rod ejection at 1E-6 and 1E-9 power levels. 0.03 Time (s) 8.0E+05 6.0E+05 4.0E+05 2.0E+05 0.0E+00 0.00 0.05 0.10 0.15 0.20 Time (s) Fig. 28. Power for 100 ms REA at 1E_6 and 1E-9 power levels with WATU fuel. Reactivity and power both oscillate leading to secondary power pulses. Using MOX fuel typically results in a lower beff. For MOX cores, this is somewhat mitigated by the lower control rod worth due to the hard neutron spectrum (Fridman and Kliem, 2011). However, in this case the rod worth is similar to or greater than that for typical PWRs due to the use of enriched B4C rods. Higher rod worth is required to achieve the same SDM due to the use of mechanical shim. Increasing the number of control rods would reduce the required individual rod worth. The enthalpy deposition must be limited due to pellet cladding mechanical interaction and fuel melting criteria. The limit depends 335 B.A. Lindley et al. / Annals of Nuclear Energy 72 (2014) 320–337 Table 7 REA analysis results. Ejection time (ms) Zero power level 100 100 10 10 Approx. HZP enthalpy deposition limit: 1E-6 1E-9 1E-6 1E-9 115.7 Maximum fuel enthalpy rise (cal/g) Power pulse width (ms) Peak reactivity (pcm) TPUC WATU TPUC WATU TPUC WATU 42.7 44,7 69.6 69.6 69.5 70.4 111.6 123.5 2.6 2.3 1.2 1.2 1.8 1.6 0.8 0.7 746 816 1317 1322 973 1068 1726 1940 800 Reactivity, 100 ms ejection Reactivity (pcm)/ Fuel temperature rise (K) 600 Reactivity, 100 ms ejection, 10x lifetime 400 Reactivity, 10 ms ejection 200 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Temperature, 100 ms ejection -200 Temperature, 100 ms ejection, 10x lifetime -400 Temperature, 10 ms ejection -600 Time (s) Fig. 29. Reactivity and fuel temperature rise variation for REA test cases of 10 ms ejection, 100 ms ejection and 100 ms ejection with artificially increased neutron lifetime. on burn-up due to effects of hydrogen pickup and oxide wall thickness in the clad. In the UK EPR, the enthalpy deposition limit (cal/g) on clad failure7 up to 69 GWd/t is (AREVA/EDF, 2012):    BU  49 Min 162:26; 141:4  29tanh : 8:5 ð1Þ for linear heat rate = 0 W/cm, and    BU  54:6 Min 123:68; 108:66  35:6tanh 11:1 ð2Þ for linear heat rate = 200–300 W/cm, where BU is the burn-up in GWd/t. Applying these formulae at HFP and HZP for the Th–TRU fuel in the TPUC assembly, with a maximum average discharge burn-up of 61 GWd/t, gives enthalpy deposition limits of 115.7 and 90.1 cal/g respectively. In the WATU case, the hot assembly contains only ThU3, with a maximum discharge burn-up of 32 GWd/t, giving enthalpy deposition limits of 162.3 and 123.7 cal/g respectively. However, the neighbouring assembly to the ejected rod can have a power up to 90% as high as in the ejected assembly, such that the 61 GWd/t limits are adopted throughout. These limits may not be appropriate to the different fuel type considered here, but are indicative of an acceptable fuel enthalpy deposition rate. The reactor was assumed to be held at HZP with all the control rods in. This renders the reactor slightly subcritical but provides a reasonable approximation to the power peaking and rod worth of the worst REA conditions. As rods are withdrawn to bring the reactor to criticality, it is assumed the highest worth rods are withdrawn first, such that the conditions for the postulated REA do not get worse for other HZP states. A beff value of 318 pcm was used in this analysis, but it is possible that it could be even lower 7 Non-SI units of cal/g are used throughout this section in accordance with standard practice. at some point in the cycle, and beff is often reduced in REA analysis to account for uncertainties – this is not performed here. There is also a small amount of data library uncertainty in beff. REA simulations are typically performed for a 100 ms ejection time and a HZP level of 1E-4% of full power (Diamond et al., 2002). This results in complete ejection of the rod before the fuel temperature spike acts to insert negative reactivity. However, the RMPWR has a much reduced neutron lifetime of 3 ls compared to 30 ls in a conventional PWR. This means that Doppler feedback can act to limit the maximum reactivity insertion before the rod is fully ejected, depending on the speed of the ejection and the zero power level. Therefore, simulations are performed for 10 and 100 ms ejection times and 1E-6 and 1E-9 power levels. The reactivity insertion and maximum fuel temperature rise for 100 ms ejections for the TPUC case are given in Fig. 24. The rod worth is 1422 pcm, but the maximum reactivity increase is much less. The reactivity oscillations are a consequence of the temperature rise occurring before the rod has fully ejected. This behaviour has also been predicted using a point kinetics model. If the rod ejection time is reduced to 10 ms, the rod fully ejects for both zero power levels, leading to a higher reactivity insertion and fuel temperature increase (Fig. 25). For the WATU fuel, the rod worth is 2480 pcm, but again for a 100 ms ejection time the maximum reactivity is limited by the fuel temperature rise (Fig. 26). The maximum fuel temperature rise is 400 K higher than for the TPUC case. For a 10 ms ejection time, the rod almost fully ejects, leading to an even larger maximum fuel temperature rise (Fig. 27). The maximum enthalpy rises, peak reactivity insertions and power pulse width (defined as the time during which the power is >50% of the maximum; noting that the reactivity oscillates in some cases leading to secondary power pulses as shown in Fig. 28) are given in Table 7. These only include assembly-level effects, so the hot pin may have a 10% higher enthalpy rise. For the WATU case, the maximum enthalpy rise is almost as much as 336 B.A. Lindley et al. / Annals of Nuclear Energy 72 (2014) 320–337 the limit for a 10 ms ejection. When allowing for uncertainties, or potentially a lower maximum enthalpy rise, this may necessitate a reduced control rod worth, or being able to demonstrate that the rod ejection will not be this rapid. The enthalpy deposition is not particularly sensitive to the zero power level. The rod ejection speed is determined by power level, reactor height, system pressure and the RCCA material. However, it can be difficult to justify the assumptions used for ejection time and zero power level such that it is thought that conservative values should be used. HFP was also considered, both for switch-on and due to the use of mechanical shim. However, the enthalpy deposition in this case was much lower due to rapid fuel and coolant feedback. Finally, the effect of the neutron lifetime on limiting the fuel temperature increase can be effectively demonstrated by artificially reducing the neutron velocity by an order of magnitude – resulting in a similar neutron lifetime to a conventional PWR. This is obviously non-physical. In the test case, shown in Fig. 29, the reactivity insertion when the rod is fully ejected is 700 pcm. A 10 ms ejection, or 100 ms ejection with artificially increased neutron lifetime, result in a fully ejected rod before temperature feedback effects compensate. This leads to a maximum fuel temperature rise of 500 K in both cases. With a 100 ms ejection time with the correct neutron lifetime, the reactivity increase is limited to 500 pcm, leading to a proportionally lower fuel temperature rise. 9. Conclusions The ability of the TPUC and WATU fuel designs to satisfy power peaking, SDM, neutronic conditions related to LOCA and REA conditions has been investigated. Use of these fuel management schemes in the RMPWR allows a negative FVR to be achieved, which improves the response to LOCAs. However, the ZCR is substantially positive, which could lead to positive reactivity in some LOCA scenarios, for example a surge line break, if the reactor does not trip. To properly evaluate the severity of different LOCA scenarios, it is necessary to couple PANTHER to a thermal–hydraulic code such as RELAP5 (Kozlowski et al., 2004). To protect against this beyond design basis accident, a second redundant set of shutdown rods is added to the reactor, so that either the usual or secondary rods can trip the reactor when there is zero coolant in the core. Even so, this condition is likely to be concerning from a regulatory standpoint. The additional control rods are likely to disallow retro-fit of an existing core, due to the need to place additional RCCAs which penetrate the pressure vessel. Alternative shutdown methods such as a central shutdown assembly may also be worth considering, although these would probably also disallow a retrofit core. Further work could consider reducing the core height would increase both the beneficial leakage effect on ZCR, such that a wider, flatter core with a tighter lattice may be advantageous. This would require a larger pressure vessel (which would be expensive) and also result in a non-retrofit core design. However, this would also give scope to redesign the core to better satisfy other criteria, e.g. power peaking and shutdown worth. Despite use of mechanical shim, designs with relatively low RFF values of 1.41 have been identified for both designs (for WATU it is slightly higher in the Th–TRU assemblies, but the larger number of pins mean that this is allowable). However, the relatively high pin-level power peaking makes it difficult to satisfy likely RFF constraints, meaning that a large number of fissile zones are necessary to limit assembly-level power peaking. For the WATU design, this is further complicated by slight deviation from a checkerboard assembly design. The TPUC design satisfies power peaking limits, but the WATU design has a high AFF leading to an unacceptable total hot channel factor. This requires use of a lower reactivity worth partially inserted rod bank in the CRP. The TPUC design can just satisfy the SDM requirement and likely limits on enthalpy deposition in the fuel following an REA. The actual enthalpy deposition is sensitive to the rod ejection speed, although a conservative value can be used for this. The WATU design allows a higher SDM to be achieved, but the increased rod worth leads to a worse REA response. This is readily mitigated by reducing the 10B enrichment in the control rods, such that the SDM requirement is still satisfied but the REA performance is improved. This may also improve the AFF by reducing the worth of the partially inserted control bank. Overall, the TPUC design is preferable for ease of designing a core with acceptable power peaking, meaning that safety criteria can be more readily satisfied, but the WATU design allows a reduction in 10B enrichment in the control rods. Use of control rods which extend beyond the core may allow rod shadowing effects to be reduced and shutdown margin to be increased. The low beff and low neutron lifetime associated with these fuels may also adversely affect the response to other transients and accidents, in particular accidents involving reactivity insertion due to inadvertent rod withdrawal etc. In any case the core control system will require ‘re-tuning’. Detailed analysis of LOCAs and analysis of other transients are the next steps to be pursued in analysing this design. Again, this will require coupling of PANTHER with a thermal–hydraulics code. Due to the limitations of deterministic reactor physics codes for analysis of the unconventional fuel design and neutron spectrum considered here, it may be worth re-analysing the equilibrium core using a Monte Carlo code to produce multi-group cross sections for PANTHER; to utilise both assembly discontinuity factors and a higher number of groups in PANTHER. Acknowledgements We would like to thank Dr Paul Bryce of EDF Energy for his helpful comments on a draft version of this manuscript, and EDF Energy for providing access to PANTHER. We are also grateful to Tony Roulstone, Dr Tony Judd, Dr Peter Dolan, Prof. Mike Weightman and the reviewers for their advice. We gratefully acknowledge the support of Prof. Paul Smith and the rest of the ANSWERS team at AMEC for providing access and guidance on the use of WIMS 10. The first author would like to acknowledge the UK Engineering and Physical Sciences Research Council (EPSRC) and the Institution of Mechanical Engineers for providing funding towards this work. References Ahmad, A., Sheehy, S., Parks, G., 2012. The effect of beam interruptions on the integrity of ADSR fuel pin cladding: a thermo-mechanical analysis. Ann. Nucl. Energy 46, 97–105. Answers, 2001. MONK. A Monte Carlo Program for Nuclear Criticality Safety and Reactor Physics Analyses. User Guide for Version 9, ANSWERS/MONK/REPORT/ 005, SERCO, Winfrith, United Kingdom. AREVA/EDF, 2012. UK EPR Pre-Construction Safety Report. Sub-chapter 14.5 – Analyses of the PCC-4 events. UKEPR-0002-145 Issue 08, AREVA NP SAS, Paris, France; EDF, Montrouge, France. CANDU, 2012. EC6: Enhanced CANDU 6 techincal summary. Available from: http:// www.candu.com/site/media/Parent/EC6%20Technical%20Summary_201204.pdf (Accessed 6/5/14). Cozzo, C., Staicu, D., Somers, J., Fernandez, A., Konings, R.J.M., 2011. Thermal diffusivity and conductivity of thorium-plutonium mixed oxides. J. Nucl. Mater. 416, 135–141. Diamond, D.J., Bromley, B.P., Aronson, A.L., 2002. Studies of the Rod Ejection Accident in a PWR. W-6382 1/22/02, Brookhaven National Laboratory, Upton, New York. Downar, T., Hall, A., Jabaay, D., Ward, A., Greenspan, E., Ganda, F., Bartoloni, F., Bergmann, R., Varela, C., DiSanzo, C., Kazimi, M., Shwageraus, E., Feng, B., Herman, B., 2012. Technical evaluation of the hitachi resource-renewable BWR B.A. Lindley et al. / Annals of Nuclear Energy 72 (2014) 320–337 (RBWR) Design Concept. Report Number 1025086, Electrical Power Research Institute, Palo-Alto, California. Franceschini, F., Lindley, B.A., Fiorina, C., Lahoda, E., Wenner, M., 2013. Promises and challenges of thorium implementation for transuranic transmutation – 13550. In: Proc. Int. Conf. Waste Management 2013, Phoenix, Arizona. Franceschini, F., Petrovic, B., 2008. Advanced operational strategy for the IRIS reactor: load follow through mechanical shim (MSHIM). Nucl. Eng. Des. 12, 3240–3252. Franceschini, F., Petrovic, B., 2009. A soluble boron-free core design for the IRIS-50. Trans. Am. Nucl. Soc. 100, 553–555. Fridman, E., Kliem, S., 2011. Pu recycling in a full Th-MOX PWR core. Part I: steady state analysis. Nucl. Eng. Des. 241, 193–202. Harris, A.D.H., 2013. Heavy water as a thorium breeder reactor coolant. MEng report, University of Cambridge (available on request). Hetric, D.L., 1993. Dynamics of Nuclear Reactors. American Nuclear Society, La Grange Park, Illinois, pp. 164–170 (Chapter 5). Hibi, K., Shimada, S., Okubo, T., Iwamura, T., Wada, S., 2001. Conceptual designing of reduced-moderation water reactor with heavy water coolant. Nucl. Eng. Des. 210, 9–19. Hiruta, H., Youinou, G., 2013. Preliminary neutronic study of D2O-cooled high conversion PWRs. In: Proc. Int. Conf. GLOBAL 2013, Salt Lake City, USA. Hoffman, E.A., Yang, W.S., Hill R.N., 2006. Preliminary core design studies for the advanced burner reactor over a wide range of conversion ratios. Argonne National Laboratory, ANL-AFCI-177. Hutt, P.K., Gaines, N., Halsall, M.J., McEllin, M., White, R.J., 1991. The UK core performance package. Nucl. Energy 30, 291–298. Kim, T.K., Stillman, J.A., Taiwo, T.A., Hill, R.N., Finck, P.J., Salvatores, M., 2002. Assessment of transuranics stabilization in PWRs. In: Proc. Int. Conf. PHYSOR 2002, Seoul, Korea. Knight, M., Bryce, P., Hall, S., 2013. WIMS/PANTHER analysis of UO2/MOX cores using embedded supercells. Nucl. Technol. 183, 398–408. Kozlowski, T., Miller, R.M., Downar, T.J., Barber, D.A., Joo, H.G., 2004. Consistent comparison of the codes RELAP5/PARCS and TRAC-M/PARCS for the OECD MSLB coupled code benchmark. Nucl. Technol. 146, 15. Leppänen, J., 2007. Development of a New Monte Carlo Reactor Physics Code. Helsinki University of Technology DSc thesis, VTT Publications 640. Lindley, B.A., Franceschini, F., Parks, G.T., 2013a. Void reactivity feedback analysis for U-based and Th-based LWR incineration cycles. In: Proc. Global 2013, Salt Lake City, Utah. Lindley, B.A., Zainuddin, N.Z., Franceschini, F., Parks, G.T., 2013b. Analysis of advanced PWR loading schemes for transuranic incineration in thorium. In: Proc. Int. Conf. ICONE21, Chengdu, China. Lindley, B.A., Franceschini, F., Parks, G.T., 2014a. The closed thorium-transuranic fuel cycle in reduced-moderation PWRs and BWRs. Ann. Nucl. Energy 63, 241– 264. Lindley, B.A., Zainuddin, N.Z., Ferroni, P., Hall, A., Franceschini, F., Parks, G.T., 2014b. On the use of reduced-moderation LWRs for transuranic isotope burning in thorium fuel – Part II: Core analysis. Nucl. Technol. 185, 147–173. Lindley, B.A., Zainuddin, N.Z., Ferroni, P., Hall, A., Franceschini, F., Parks, G.T., 2014c. On the use of reduced-moderation LWRs for transuranic isotope burning in thorium fuel – Part I: assembly analysis. Nucl. Technol. 185, 127–146. Lindley, B.A., Parks, G.T., in press-a. Axially homogeneous thorium fuel designs for transuranics burning in reduced-moderation BWRs. PHSYOR 2014, Kyoto, Japan. 337 Lindley, B.A., Parks, G.T., in press-b. Axially heterogeneous thorium fuel designs for transuranics burning in reduced-moderation BWRs. PHSYOR 2014, Kyoto, Japan in press. Newton, T., Hosking, G., Hutton, L., Powney, D., Turland, B., Shuttleworth, E., 2008. Developments within WIMS10. In: Proc. Int. Conf. PHYSOR 2008, Interlaken, Switzerland. Onoue, M., Kawanishi, T., Carlson, W.R., Morita, T., 2003. Application of MSHIM core control strategy for Westinghouse AP1000 nuclear power plant. In: Proc. Int. Conf. GENES4/ANP2003, Kyoto, Japan. Parks, G.T., 1996. Multiobjective pressurized water reactor reload core design by nondominated genetic algorithm search. Nucl. Sci. Eng. 124, 178–187. Powney, D.J., Newton, T.D., 2004. Overview of the WIMS 9 Resonance Treatment. ANSWERS/WIMS/TR.26, Issue 1, SERCO, Winfrith, United Kingdom. Rahman, F.A., Franceschini, F., Wenner, M., Lee., J.C., 2012. Thorium fuel options for sustained transuranic burning in Pressurized Water Reactors – 12381, In: Proc. Int. Conf. Waste Management 2012, Phoenix, Arizona. Shwageraus, E., 2003. Rethinking the Light Water Reactor Fuel Cycle. Massachusetts Institute of Technology PhD thesis. Sorensen, R.T., Davis, J.C., Lee, J.C., 2006. Thorium-based fuels for enhancing plutonium transmutation in light water reactors. Trans. Am. Nucl. Soc. 94, 87– 88. Takaki, N., Mardiansah, D., 2012. Core design and deployment strategy of heavy water cooled sustainable thorium reactor. Sustainability 4, 1933–1945. Tobita, Y., 2013. Safety strategy of JSFR establishing in-vessel retention of core disruptive accident. In: Proc. Int. Conf. on Fast Reactors and Related Fuel Cycles (FR13) Paris, France. Todosow, M., Galperin, A., 2009. Heterogeneous Assembly Design for Utilization of Thorium in VVER Reactors, Proc. Advances in Nuclear Fuel Management IV (ANFM 2009). Todosow, M., Kazimi, M., 2004. Optimization of Heterogeneous Utilization of Thorium in PWRs to Enhance Proliferation Resistance and Reduce Waste. BNL73152-2004 MIT-NFC-065, Brookhaven National Laboratory, Upton, New York. UK Office of Nuclear Regulation, 2008. Safety Assessment Principles – 2006 edition (Revision 1, February 2008). Paragraphs 449, 451 and 474; Engineering Principle for Criticality Safety 2 (ECR.2). Available from: <http:// www.hse.gov.uk/nuclear/saps/saps2006.pdf Accessed 15/10/13>. Varaine, F., Buiron, L., Boucher, L., Verrier, D., 2010. Overview on homogeneous and heterogeneous transmutation in a French new SFR: Reactor and fuel cycle impact. In: Proc. 11th International Exchange Meeting on P&T, San Francisco, California. Watts Bar, 2009. Watts Bar Unit 2 final safety analysis report (FSAR) Amendment 93, Section 4. Accessed through http://adams.nrc.gov/wba/. Accession number ML091400651, 30/4/09. Westinghouse Electric Company LLC, 2010a. AP1000 Pre-Construction Safety Report. Chapter 4 Section 3 – Nuclear Design. UKP-GW-GL-732, Westinghouse Electric Company LLC, Cranberry Township, Pennsylvania. Westinghouse Electric Company LLC, 2010b. AP1000 Pre-Construction Safety Report. Chapter 15 Section 6 – Nuclear Design. UKP-GW-GL-732, Westinghouse Electric Company LLC, Cranberry Township, Pennsylvania. Yang, J.H., Kang, K.W., Song, K.W., Lee, C.B., Jung, Y.H., 2004. Fabrication and thermal conductivity of (Th, U)O2 pellets. Nucl. Technol. 147, 113–119.