Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor

Progress in Nuclear Energy xxx (2014) 1e22

Contents lists available at ScienceDirect

Progress in Nuclear Energy journal homepage: www.elsevier.com/locate/pnucene

Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor
n Perko
a, *, Sandro Pelloni b, Konstantin Mikityuk b, Jiri Krepel b, Ma
te
Szieberth c, Zolta e  
te
Hala
sz c, €tan d, Branislav Vrban e, Jakub Lüley e, Stefan Cerba , Ma Girardin Gae c c , 1 a f
ndor Fehe
r , Tibor Reiss , Jan Leen Kloosterman , Richard Stainsby , Sa Christian Poette g a

Delft University of Technology, Faculty of Applied Sciences, Department of Radiation Science and Technology, Section Nuclear Energy and Radiation Applications, Mekelweg 15, 2629 JB Delft, The Netherlands b Paul Scherrer Institut, 5232 Villingen, PSI, Switzerland c
gtudoma
nyi Egyetem, Nuklea
ris Technikai Int
} szaki
} egyetem Rakpart 9, 1111 Budapest, Hungary Budapesti Mu es Gazdasa ezet, Mu d Ecole Polytechnique F
ed
erale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland e Slovak University of Technology in Bratislava, Institute of Nuclear and Physical Engineering, Ilkovicova 3, 81219 Bratislava, Slovakia f National Nuclear Laboratory, Chadwick House, Warrington Road, Birchwood Park, Warrington WA3 6AE, United Kingdom g


l’Energie DEN/CAD/DER/SESI/LC4G, Centre de Cadarache, Commissariat a Atomique et aux Energies Alternatives, 13108 Saint Paul-Lez-Durance, France

a r t i c l e i n f o

a b s t r a c t

Article history: Received 20 November 2013 Received in revised form 17 March 2014 Accepted 28 September 2014 Available online xxx

The Generation IV initiative was launched with the goal of developing nuclear reactors which surpass current designs in safety, sustainability, economics and non-proliferation. From the six most promising concepts the Gas Cooled Fast Reactor (GFR) represents a challenging and innovative idea that is prominent in the sustainability aspect with the ability to have a closed fuel cycle and the potential to burn minor actinides (MAs). The European FP7 GoFastR project was one of the latest steps in the development and further optimization of GFRs. This paper presents a comprehensive overview of the neutronic performance of GFR2400 which was considered as a conceptual design for a large scale GFR within the collaboration. This reactor is the newest on the evolutionary path of fully ceramic GFRs featuring ceramic fuel and structural materials allowing high temperatures and efficiency using helium coolant. An important innovation of the current design is the application of refractory metallic liners to enhance the fission product retention of the cladding, resulting in a significant neutronic penalty during normal operation, at the same time being advantageous under transient conditions involving spectrum softening. Using the ERANOS and SCALE code systems several parameters were determined for beginning of life (BOL) conditions, including excess reactivity, various reactivity effects such as depressurization, Doppler or thermal expansion effects, as well as kinetic parameters. An extensive sensitivity and uncertainty analysis of these parameters was also done with the 15 group BOLNA and 44 group SCALE covariance libraries. Open and closed fuel cycle operations were investigated and the transmutational capabilities were studied with the GFR connected to traditional light water reactors in a symbiotic system. The presented analysis shows that the GFR2400 design is a major improvement compared to previous concepts. All preliminary constraints are respected resulting in a manageable initial Pu inventory of 10 t/ GWel at 45% plant efficiency, a low MA mass fraction of 1% by self-recycling and a near zero breeding gain without the use of fertile blankets. At the same time the reactor has acceptable safety features precluding super-prompt-criticality in depressurized conditions at BOL and in open cycle equilibrium. Either of the two planned control devices is sufficient to shut down the reactor independently of the other and the

Keywords: Generation IV Gas Cooled Fast Reactor Closed fuel cycle Transmutation Core characterization Neutronic performance

* Corresponding author. Tel.: þ31 15 27 86618; fax: þ31 15 27 86422.
), [email protected] E-mail addresses: [email protected] (Z. Perko (S. Pelloni), [email protected] (K. Mikityuk), [email protected] (J. Krepel), [email protected] (M. Szieberth), Gaetan.Girardin@epfl.ch €tan), [email protected] (B. Vrban), [email protected] (S. Fehe
r), (G. Gae [email protected] (T. Reiss), [email protected] (J. Leen Kloosterman), [email protected] (R. Stainsby), [email protected] (C. Poette). 1 On leave to PSI. http://dx.doi.org/10.1016/j.pnucene.2014.09.016 0149-1970/© 2014 Published by Elsevier Ltd.


, Z., et al., Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor, Progress in Nuclear Please cite this article in press as: Perko Energy (2014), http://dx.doi.org/10.1016/j.pnucene.2014.09.016


et al. / Progress in Nuclear Energy xxx (2014) 1e22 Z. Perko

2

refractory liners introduce significant negative reactivity in case of water ingress. However the occurrence of hot spots when all control rods are inserted needs further analysis. The design also shows promising closed fuel cycle and transmutational performance. However e as is the case in other fast reactors e the fuel cycle closure causes safety related parameters to degrade, most importantly the depressurization reactivity effect to exceed the effective delayed neutron fraction in the current design. To assess the acceptability of this deterioration further analysis is needed. Finally, it can be concluded that current commercial codes are satisfactory for such analysis; however there is a need for better covariance data. Several parameters exceed their target uncertainty value, most notably the k-effective by a factor of 6, the main source of the uncertainty being the inelastic scattering of 238 U. © 2014 Published by Elsevier Ltd.

1. Introduction The Gas Cooled Fast Reactor (GFR) is one of six advanced reactor concepts selected by the Generation-IV International Forum (US DOE, 2002) e a cooperative international endeavor organized to carry out the needed research and development (R&D) for the assessment of the feasibility and performance capabilities of the next generation of nuclear energy systems. The majority of the selected concepts are fast neutron spectrum reactors, including gas, sodium and lead cooled systems, as well as the non-moderated version of the molten salt reactor. They were chosen due to their potential of recycling all actinides and closing the fuel cycle. This would allow fast reactors to substantially improve fuel utilization particularly by making it possible to feed the reactors in equilibrium with only natural or depleted uranium. Furthermore the quantity, the radiotoxicity and the decay heat of radioactive waste could be reduced by only having to dispose of fission products and reprocessing losses in an ideal case. The specific merits of modern GFR designs compared to other fast reactor systems originate from the use of helium as the primary coolant. Since it introduces practically no moderation the GFR's neutron spectrum is one of the hardest among fast reactors, making it ideal for recycling all actinides, including minor actinides (MAs). Helium is inert and transparent, eliminating most problems related to coolant interaction with structural materials and making online visual inspection of the core possible. Due to its low density and neutronic transparency the void reactivity effect is low, which is obviously advantageous for reactor safety. Last but not least, the core outlet temperature is not limited by the coolant characteristics, making it attractive for potential hydrogen production and other process heat applications. The GFR fuel and core concept has been developed during the last decade within the framework of successive European projects (Stainsby et al., 2011). This evolution included designs of coated particle fuel with or without a binding matrix, silicon carbide blocks with dispersed microparticle fuel inside, the idea of silicon carbide plates with fuel pellets arranged in honeycomb structure, finally arriving to the current design of a hexagonal lattice of cylindrical fuel rods consisting of a column of fuel pellets inside the composite silicon carbide cladding (van Rooijen et al., 2005; Bosq et al., 2006; da Cruz et al., 2006; Chauvin et al., 2007; Dumaz
et al., 2012; Zabiego et al., 2013). et al., 2007; Perko This paper summarizes the main results of the neutronic studies performed in the framework of the European FP7 GoFastR project (Stainsby et al., 2011) for the GFR2400 design, a large scale helium cooled fast spectrum reactor with 2400 MWth thermal power. The most essential parameters characterizing the core were determined both for beginning of life conditions as well as during burnup, accompanied by their respective uncertainties originated from deficiencies in the current knowledge of nuclear data and the fuel

manufacturing process. Several safety related quantities have been evaluated and the transmutational capabilities of the design have been assessed. Following the description of the core in Section 2 the computational tools used for our analysis are introduced in Section 3. The most important neutronic parameters for the start-up core e including excess reactivity, power distribution, as well as kinetic parameters e are presented in Section 4 with various reactivity effects being detailed in Section 5. Finally, Section 6 outlines the results of fuel cycle and transmutational studies, whereas in Section 7 the main conclusions of the presented work are drawn. By reporting the current status of the neutronic studies for the GFR core in Europe this paper can be especially useful for follow-up R&D studies related to neutronics and safety analysis of Gas Cooled Fast Reactors. 2. The European 2400 MW Gas Cooled Fast Reactor design The starting point of a new core design in the GoFastR project was the plate-type concept featuring carbide fuel with silicon carbide fiber reinforced silicon carbide (SiCf/SiC) cladding that was studied in the preceding GCFR FP6 STREP project (European Commission, 2006, page 210e225). The goal was to achieve a more realistic and feasible, fully ceramic model which would satisfy all the ambitious GFR requirements. An original optimization study carried out at CEA resulted in such a design, which was called the GFR2400 “academic core” (or shortly GFR2400) and was considered as a reference concept for a commercial size Gas Cooled Fast Reactor (Richard et al., 2010). The remainder of this section is devoted to a detailed description of this reactor focusing on the active core, for more information the reader is referred to the companion paper by Stainsby et al. (2014). 2.1. General design description The most important parameters of GFR2400 are summarized in Table 1. The reactor is a large scale Gas Cooled Fast Reactor with 2400 MWth thermal power and uses helium coolant at a high

Table 1 Basic design parameters of GFR2400. The concept features a large scale He cooled GFR with ceramic fuel and cladding. Parameter

Value

Parameter

Value

Thermal power [MW] Primary pressure [MPa] Mass flow rate [kg/s] Core inlet temp. [ C] Secondary coolant IHX inlet temp. [ C]

2400 7 1213 400 20%He, 80% N2 346

Primary coolant Pressure drop in core [MPa] Bypass flow rate [kg/s] Core outlet temp.a [ C] Secondary pressure [MPa] IHX outlet temp. [ C]

He 0.143 60 780 6.5 750

a

After mixing with bypass flow.


, Z., et al., Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor, Progress in Nuclear Please cite this article in press as: Perko Energy (2014), http://dx.doi.org/10.1016/j.pnucene.2014.09.016


et al. / Progress in Nuclear Energy xxx (2014) 1e22 Z. Perko

3

pressure of 7 MPa to ensure adequate heat transfer. The coolant volume fraction in the core is high in order to have a small pressure drop that allows decay heat removal by natural circulation under pressurized conditions. To deal with depressurized accidents three dedicated decay heat removal loops (each capable of removing 100% of the decay heat) and six gas reservoirs are available. During normal operation the power is transferred to the secondary side via three 800 MW power conversion systems equipped with heat exchangers (IHX) and blowers. The secondary coolant is a helium nitrogen mixture and the overall plant efficiency is expected to be around 45% in an indirect Brayton cycle. According to the original optimization study at closed cycle equilibrium the minor actinide fraction in the fuel remains around 1 at% (atomic percentage) and a near zero breeding gain can be achieved without the use of fertile blankets, thereby eliminating the associated proliferation risks. 2.2. Fuel assembly design To enable the high temperature operation needed for high efficiency GFR2400 is based on ceramic materials. Due to its numerous favorable properties SiCf/SiC is envisaged as cladding material (Zabiego et al., 2013) whereas the choice of fuel is uranium plutonium carbide (UPuC). Carbides are favored to oxides and nitrides since they have higher heavy metal density and make it easier to counterbalance the large coolant volume fraction of roughly 43 V/V%. The details of the fuel are given in Table 2. The isotopic composition of uranium corresponds to natural uranium whereas that of plutonium is characteristic of twice recycled mixed oxide (MOX) fuel expected to be available in France from 2016 (van Rooijen and Kloosterman, 2009). Two types of fuel assemblies (FAs) are used: inner core (IC) assemblies with lower and outer core (OC) assemblies with higher plutonium content in order to flatten the flux distribution and the power profile in the core. The porosity of the fuel is 20%. A schematic view of the pins is depicted in Fig. 1 whereas Table 3 gives the detailed geometrical description. The addition of SiC fiber to the SiC cladding material improves its strength, at the same time makes the porous ceramic less leak tight by enabling gases to diffuse into the coolant through a network of micro-cracks. To limit this process and ensure fission product confinement within the pins thin liners are envisioned on the inner side of the SiCf/SiC tubes. These liners are made up by refractory metals, i.e. metals with high melting temperature. For the current design rhenium (Re) and a tungstenerhenium compound featuring a 14 m/m% Re and 84 m/m% W (W14Re) were chosen. The gap between the pellets and the liners is filled with He at 1 MPa pressure. The full length

Table 2 Fuel composition of GFR2400. Natural uranium and plutonium from twice recycled MOX fuel is used. The outer core (OC) assemblies have higher plutonium content than the inner core (IC) ones in order to flatten the power profile. Pu isotopic composition [m/m%a]

U isotopic composition [m/m%]

Pu-238 Pu-239 Pu-240 Pu-241 Pu-242 Am-241 PuC molar mass [g/mol] PuC densityb [g/cm3] PuC content in IC [V/V%c] PuC content in OC [V/V%]

U-235 U-238

a b c

2.7 56.0 25.9 7.4 7.3 0.7 251.6771 10.88 14.12 17.65

0.72 99.28

Fig. 1. Cross sectional view of the fuel pin of GFR2400. To ensure fission product confinement thin metallic liners are envisioned on the inner side of the ceramic cladding.

of the pins is 3 m including the active height of 165 cm and the fission gas plenums above (85 cm) and below (50 cm). To deal with the expected limitations in the cladding fabrication and the risks of damage during handling and transport the pins are planned to be made up by half pins of 150 cm length. Each fuel assembly (FA) is hexagonal and contains 217 pins in a triangular array surrounded with a SiC wrapper tube (see Fig. 2). The spacer grids keeping the pins in place are also made of silicon carbide, whereas the 1 m high axial reflectors above and below the fission gas plenums consist of Zr3Si2. 2.3. Core layout The core contains 516 fuel assemblies in a hexagonal array and is divided into two zones of almost equal size: an inner core with lower and an outer core with higher plutonium content. 18 places are reserved for control system devices (CSDs or control rods) and 13 for diverse safety devices (DSDs or safety rods). The absorber rods in both groups are made up by boron carbide (B4C, with boron enriched in 10B to 90%) whereas the material of the structural elements is a special steel alloy (AIM1). The axial reflectors and the 480 radial reflectors are made up by Zr3Si2. For these core elements no detailed layout was made, only their expected volumetric composition was determined (for details see in Table 4). The full core layout can be seen in Fig. 3 (note that the fuel pins are not depicted individually).

Table 3 Geometrical properties of the GFR2400 active core at room temperature (20  C). Pin

UC UC UC UC

molar mass [g/mol] densityb [g/cm3] content in IC [V/V%] content in OC [V/V%]

Mass percentage. Values include the 20% porosity of the ceramic fuel. Volume percentage.

250.0399 10.904 85.88 82.35

Fuel assembly

Core

Region

Radius [cm]

Region

Dimension [cm]

Assembly type

Number

Pin Gap W14Re liner Re liner Clad SiC liner

0.3355 0.35 0.354 0.355 0.455 0.458

Wrapper (inside) Wrapper (outside) Coolant (outside FA) Active height Lattice pitch No. of pins in FA

8.5645 8.7645 8.9145 165 1.157 217 (pcs)

FA IC FA OC FA CSD DSD Reflector

516 264 252 18 13 480


, Z., et al., Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor, Progress in Nuclear Please cite this article in press as: Perko Energy (2014), http://dx.doi.org/10.1016/j.pnucene.2014.09.016


et al. / Progress in Nuclear Energy xxx (2014) 1e22 Z. Perko

4

ERANOS calculations the JEFF-3.1 cross section library was used, with 33, 136 and 172 group structures. For the fuel regions these were generated by the ECCO cell code from a 1968 fine group cross section data, while for the non-fuel regions (reflectors, control rods, etc.) the standard 33 and 172 group ERANOS cross section libraries were adopted. Both two- and three-dimensional models of the reactor were built applying homogeneous and heterogeneous fuel assembly models as well. The three-dimensional (hexagonal-z, R-z) transport and diffusion calculations were carried out with the nodal code VARIANT, while the two-dimensional transport calculations were done with the discrete ordinates code BISTRO using P1S8 (and in some cases P1S16) approximation.

Fig. 2. Cross sectional view of the fuel assembly of GFR2400.

3. Computational tools, models and data During the project several different codes and models were used by the different participants for their respective neutronics calculations. Some parameters were determined independently which serves as a verification of the used methods and gives confidence about results that were only computed individually. This section gives an overview of the computational aspects of the research presented in this paper. As the majority of the calculations were done with ERANOS and SCALE, Sections 3.1e3.2 are devoted for the description of the developed models, followed by the details of the MCNP and SERPENT computations in Section 3.3. Finally in Section 3.4 the tools used in the transmutation and fuel cycle studies are introduced. 3.1. ERANOS calculations During the project extensive use was made of the ERANOS code system (Edition 2.2-N) (Rimpault et al., 2002) for determining various neutronic parameters, performing sensitivity and uncertainty analysis as well as burnup and fuel cycle studies. For all Table 4 The composition of additional core elements of GFR2400. Core element

Material

Volume fraction [V/V%]

Upper reflector (UR) Radial reflector (RR) Lower reflector (LR) Control and shutdown rods (CSD and DSD)

Zr3Si2 He (7 MPa) Zr3Si2 He (7 MPa) Zr3Si2 He (7 MPa) B4Ca AIM1 SiC He (7 MPa) AIM1 SiC He (7 MPa)

60 40 80 20 60 40 30.26 11.22 10.85 47.67 1.20 10.85 87.95

Rod follower (RF)

a

Boron enriched in

10

B to 90%.

3.1.1. Model details for beginning of life conditions For three-dimensional simulations 20 cm long axial nodes were used and the individual assemblies made up the nodal discretization in the radial direction. For the two-dimensional calculation the mesh size was 3 cm in both directions. To account for the spacer grid making up 0.8 V/V% of the fuel assembly the 0.2 cm width of the FA wrapper was increased to 0.237 cm, i.e. the heterogeneously distributed grid material in the axial direction was homogeneously smeared into the wrapper zone. To simulate operating conditions the pin sizes, the lattice pitch and the wrapper thickness were expanded using the SiC linear expansion coefficient of 0.47,105  C1 and a characteristic temperature increase of 640  C, while preserving the fuel mass. Furthermore it was assumed that the diagrid keeping the fuel assemblies in place is made of AIM1, therefore the external across size of the FAs was adjusted using an expansion coefficient of 1.81,105  C1 and the 400  C inlet temperature of the coolant. To account for the axial expansion the nonbonded approach was used allowing the fuel and the cladding to expand separately, therefore the height of the active region was determined by the bigger expansion of the fuel. Relevant reactivity effects were both determined with direct calculations and adjoint methods. Standard perturbation techniques were applied to break down reactivity changes into individual contributions allowing for a deeper understanding. In this study the physical components breakdown scheme of ERANOS (Tommasi, 2007) was used identifying the input from the various reactions of the different isotopes, as well as the leakage effect. In diffusion theory the latter comes from the variation of the diffusion coefficients, while in transport theory it is the contribution of the anisotropic terms in the perturbation integrals, i.e. the higher moments of the flux and the adjoint function, and the anisotropic parts of the expansion of the scattering cross sections. This approach is preferred as it offers a consistency between the diffusion and transport breakdowns. For quantifying uncertainties the 15 group BOLNA (Salvatores et al., 2008) covariance library was used. Since this contains no information about rhenium isotopes which proved to be important three different approaches were tested to assess the Re related uncertainties: a, covariance data for Re-185 and Re-187 assumed to be the same as that of Fe-56; b, covariance data for Re-185 and Re-187 assumed to be the same as that of Fe-56, with the relative uncertainty increased to 100%; c, uncertainty kept at 100% and supposing fully anti-correlated, uncorrelated or fully correlated data. 3.2. SCALE calculations Parallel to ERANOS the SCALE 6/6.1 code system (SCALE, 2009) was used to derive the most important neutronic parameters


, Z., et al., Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor, Progress in Nuclear Please cite this article in press as: Perko Energy (2014), http://dx.doi.org/10.1016/j.pnucene.2014.09.016


et al. / Progress in Nuclear Energy xxx (2014) 1e22 Z. Perko

5

Fig. 3. Cross sectional view of the core of GFR2400. The number of inner and outer core assemblies is roughly the same. Fission gas plenums are located both above and below the fuel assemblies. All rods are positioned in their parking place above the core.

independently, to determine control rod worths and to perform fuel cycle and minor actinide burning studies. These calculations were based on the most up-to-date ENDF/B-VII cross section library, both in the standard 238 group structure and in continuous energy. For the multigroup calculations the BONAMI and CENTRM modules were used to perform self-shielding. For the fuel regions the MULTIREGION treatment was applied e featuring concentric rings of different materials describing the precise geometry of the pins e together with the buckled cylinder option and white boundary conditions to take into account axial leakage and lattice effects respectively. For the structural parts the infinite homogeneous medium approximation was used. Three-dimensional models of the reactor were built applying geometrically precise, completely heterogeneous as well as homogeneous fuel assemblies. The homogenized models were used for the computationally expensive control rod worth and burnup calculations, while the heterogeneous model was used for characterizing beginning of life (BOL) conditions. The XSDRN-PM one-dimensional discrete ordinates code was used to homogenize fuel pins and the hexagonal fuel assemblies by approximating them with a cylindrical geometry containing the homogenized fuel region, the SiC wrapper and the He gap between the FAs. All three-dimensional transport calculations were performed with the KENOeVI Monte carlo module, whereas XSDRN-PM and the NEWT two-dimensional method of characteristics codes were used for quantifying the effects of geometrical uncertainties in pin dimensions and pellet positions. For the sensitivity and uncertainty calculations the TSUNAMI module was applied.

account by homogeneously mixing it into the coolant inside the fuel assemblies. Thermal expansion was modeled with a radial and an axial expansion factor (DR ¼ 0.687% and DH ¼ 1.163% respectively) via uniformly inflating the core while decreasing number densities to preserve masses. This is a simpler approach than the one used in the ERANOS calculations, since the elementary cell was also expanded according to the AIM1 properties, however it proved to be satisfactory. For decomposing reactivity effects the k-effective sensitivity coefficients calculated by TSUNAMI were used. Self-shielding calculations were carried out for the reference conditions (i.e. operating temperatures and primary pressure) and a perturbed state (e.g. increased fuel temperature or decreased pressure) using the CSAS-MG sequence, then the resulting group-wise cross sections were read from the AMPX working format cross section libraries for all reactions, isotopes, energy groups and regions of the reactor. Combining the fractional change of the macroscopic cross sections with the sensitivity profiles, i.e. summing up the products of the group-wise k-effective sensitivities with the fractional cross section changes provides a decomposition of reactivity changes into isotopes, reactions and spatial regions. This allows an almost identical decomposition to the one given by ERANOS, the only difference is that here no separation of the transport effect is done. The uncertainty analysis for the k-effective was based on the 44 group SCALE covariance library (Williams et al., 2009) and traditional Monte-Carlo sampling for the geometrical uncertainties.

3.2.1. Model details for beginning of life conditions In the heterogeneous SCALE models the spacer grid between the pins (making up 0.8 V/V% of the fuel assemblies) was taken into

For some of the calculations Monte Carlo transport codes €nen, 2010)) and 2 verSERPENT-1.1.16 (developed at VTT (Leppa sions of MCNP (MCNPX-2.7.0 (Pelowitz, 2011) and MCNP5 (MCNP,

3.3. MCNPX and SERPENT calculations


, Z., et al., Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor, Progress in Nuclear Please cite this article in press as: Perko Energy (2014), http://dx.doi.org/10.1016/j.pnucene.2014.09.016


et al. / Progress in Nuclear Energy xxx (2014) 1e22 Z. Perko

6

2003), both developed at the Los Alamos National Laboratory) were also used. These mainly included reference computations to check multigroup results, correctness of homogenization in case of burnup and control rod worth studies, and the investigation with respect to water/steam ingress into the core. For the latter both the ENDF/B-VII and JEFF-3.1.1 nuclear data libraries were used together with a geometrically precise three-dimensional model of the fuel assemblies with reflective boundary conditions on the sides of the hexagon and void boundaries under and above the axial reflectors. No spacers or control rods were considered and the simulations were performed at room temperature to ease the comparison. Since water significantly changes the neutron spectrum, the usual S(a,b) treatment option was included for the bounded hydrogen in it. 3.4. Fuel cycle simulation tools In order to investigate and quantify the sustainability advantages of the GFR two different fuel cycle simulation tools were developed and used with slightly different purposes. The ERANOS based EQL3D procedure primarily aims at achieving the final equilibrium state, however its main strength is the good fidelity to capture the trend in the cycle-by-cycle transitions. The other procedure is the SCALE based FITXS, which is a flexible burnup model that enables several hundreds or thousands of calculations with a simplified core model to accomplish a parametric study and evaluate the transmutation capabilities. The subsequent two sections provide a brief description of these two tools and their use in our study along with the necessary assumptions and data. 3.4.1. Fuel cycle simulations based on ERANOS and the EQL3D method The ERANOS based EQL3D procedure (Krepel et al., 2009) can be employed to yield the description of two basic situations:  the equilibrium of an open fuel cycle can be calculated, i.e. the periodic operation with fresh fuel without any recycling; and  the equilibrium of a closed fuel cycle can be calculated, where an asymptotic state is reached by operation with a fixed fuel management scheme involving recycling the reactor's own fuel.

In both cases the explicit cycle-by-cycle reactor operation under the specified periodic fuel management is simulated until the equilibrium state is reached. The main assumptions of the EQL3D procedure are constant core power, constant fuel management scheme, and constant total mass of fuel after each reprocessing. Under these assumptions the simulated reactor eventually reaches a meaningful equilibrium state in which the concentrations of the actinides do not vary (or vary negligibly) from one cycle to the other. In this study EQL3D was used to simulate the open and closed cycle operation of GFR2400 by applying 33 group cross sections and VARIANT to perform the necessary transport calculations in a hexagonal-z geometry with 5 axial nodes. The two-zone core of the reactor is designed for a 3 batch cycle operation with total 1443 EFPD (effective full power day) fuel residence in the core. Accordingly, each of the two zones was subdivided into three assembly batches with equal number of fuel assemblies (see Fig. 4) and in each zone the OUT-IN-IN fuel reshuffling scheme was applied, meaning that the fresh fuel was always placed at the periphery and was shuffled batch wise inwards. Such a pattern is unrealistic; however, as shown in (Krepel et al., 2010) for a previous GFR core, the reloading pattern has only limited influence on the integral core parameters, for instance the reactivity or isotope mass evolutions. It can nonetheless strongly influence the local power peaking factor. In this EQL3D model an ideal reprocessing was supposed, hence all actinides were fully recycled with zero losses and only fission products were removed and replaced by natural uranium. For reshuffling and refuelling 30 days were envisaged with a cycle length of 3,(481 þ 30) ¼ 1533 days. The same time period was assumed for the long-term cooling and the reprocessing of the unloaded fuel, i.e. the unloaded batches spent 1533 days outside the core before being instantaneously reprocessed and reloaded. These 1533 days correspond to 4.2 years, which is not in agreement with the 5 years selected for the FITXS method discussed in the next section and it may introduce some discrepancies. Nevertheless, the sensitivity of the results to the cooling time is relatively low in this range (Krepel et al., 2010). 3.4.2. Fuel cycle simulations based on SCALE and the FITXS method For all SCALE based fuel cycle calculations the FITXS procedure was used. FITXS is a quick and flexible burnup method developed at

Fig. 4. Layout of the two-zone GFR core and its subdivision into three batches with equal number of assemblies (88 and 84 per batch in the inner and outer zones respectively). 18 positions (in light gray) are reserved for control rods and 13 (in dark gray) for safety rods.


, Z., et al., Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor, Progress in Nuclear Please cite this article in press as: Perko Energy (2014), http://dx.doi.org/10.1016/j.pnucene.2014.09.016


et al. / Progress in Nuclear Energy xxx (2014) 1e22 Z. Perko


sz et al., BME (Szieberth et al., 2012; Szieberth and Reiss, 2013; Hala 2013), which is based on fitted cross sections. The method copes with the two main challenges concerning fuel cycle studies with transmutation options:  The first challenge is that the evaluation of the different transmutation options can only be performed if the detailed composition of the final waste is known, which requires the tracking of a wide range of isotopes in the fuel cycle and the determination of the accurate make-up of the spent fuel.  The other challenge is that minor actinide recycling in transmutation fuel cycles results in a wide range of possible isotopic compositions in the core, influencing the neutron spectrum and therefore the burnup process as well. Unfortunately most scenario codes contain cross section sets only at a few burnup steps, which is not flexible enough for such analysis (Boucher et al., 2010). Furthermore the detailed burnup calculations are too time consuming to be inserted in the simulation of the complete fuel cycle. The FITXS procedure offers an attractive solution to these issues by approximating the cross sections as a 2nd order multidimensional polynomial function of the isotopic composition. This means that each cross section depends on the Ni amount of all n isotopes as

sðNÞ ¼ a0 þ

n X j¼1

aj Nj þ

n X n X

aj;k Nj Nk :

j¼1 k¼1

The 16 most important actinide isotopes (234236,238U, Np, 238242Pu, 241,242m,243Am, 244,245Cm) and the total quantity of fission products (calculated from the number of fissions) are considered for the description of the isotopic composition, i.e. they make up the N vector (with a length of n ¼ 17). The a0,aj and aj,k coefficients of the cross sections are obtained by fitting to the results of numerous core calculations. In order to perform this least-square-fit the one group cross sections have to be calculated for various different compositions. Due to the large number of fitted parameters practically a few thousand core calculations have to be performed, therefore a simplified core model is necessary, which can provide the homogenized one group cross sections. Once the least-square-fit is done the computationally expensive neutronics calculations can be spared and the cross sections needed for the burnup calculations can quickly be determined using the isotope inventory of the reactor together with the fitted coefficients. In this study the simplified core model was a three-dimensional model with homogenized fuel assemblies and other core components. The full core calculations necessary for the least-square-fit were performed with SCALE's KENOeVI module in 238 groups and in some selected cases the correctness of the applied homogenization techniques was checked against detailed Monte Carlo results with MCNP for a fuel assembly in an infinite lattice. Approximately 2000 simplified full core calculations were performed and for each of them a different isotopic composition was assumed for the fuel. These were obtained by randomly sampling the actinide composition taking into account the following constraints: 237239

 Pu number density in the fuel was varied between 10 and 25% of the total actinide number density.  The ratio of the Pu content of the inner and outer core was kept at 0.8 which is also the case for the initial loading.  MA number density in the fuel was varied between 0 and 10% of the total actinide number density.

7

 The rest of the actinide content of the fuel was U.  The isotopic composition of the heavy metal elements was also randomly distributed, but limits were set to every isotope considering the isotopic composition of the initial charged fuel and the equilibrium composition estimated by preliminary calculations (Szieberth et al., 2012; Szieberth and Reiss, 2013;
sz et al., 2013). Hala  Fission products were considered with a general fission yield vector. Their quantity is directly related to the burnup level of the fuel which was varied between 0 and approximately 10%. Results show that the fitted functions can reproduce the calculated cross sections with a few percent maximum deviation but it is very important to ensure that the isotopic composition does not depart from the fitting domain during the simulations. The full core calculations also determine the k-effective for the different compositions. This makes it possible to fit the k-effective as a function of the isotope inventory as well, which provides the great advantage that the fissile loading for the required excess reactivity can be determined in the fuel cycle model. In this study the above described burnup model was used to build a simplified fuel cycle model shown in Fig. 5. The model was developed in MATLAB environment. It contains the GFR burnup model and is capable of following the material flows between reactors and storages. The fuel cycle contains two types of reactors: the GFR and conventional light-water reactors (LWRs). LWRs were operated in onceethrough cycle: they were fed by 3.6% enriched U and the fuel was discharged after 33 MWd/kgU burnup. The spent fuel was considered with the composition shown in Table 5. No recycling into LWRs was considered, instead the spent fuel was moved to partitioning and the Pu and MA fractions were recycled into the GFR. As fertile material the GFR was fed with natural U, furthermore Pu and MAs from the reprocessed LWR fuel. The GFR was operated in three-batch cycle, one third of the core was discharged and replaced with fresh fuel in every cycle (481 EFPD) and each fuel element spent 3 cycles in the core. The Pu content of the charged fuel was calculated with iteration in order to set the excess reactivity at the beginning of cycle (BOC) for the coming cycle as 0

EOC kBOC ¼ kBOC eff eff  keff þ 1:005:

(1)

The above approach is based on the expectation that the multiplication factor at the end of the next cycle is 1.005 and that

Fig. 5. The considered fuel cycle model. Pu and MA from LWR is fed to GFR only when the required amount is not present in the corresponding storage.


, Z., et al., Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor, Progress in Nuclear Please cite this article in press as: Perko Energy (2014), http://dx.doi.org/10.1016/j.pnucene.2014.09.016


et al. / Progress in Nuclear Energy xxx (2014) 1e22 Z. Perko

8

Table 5 Considered LWR spent fuel composition after 33 MWd/kgU burnup and 5 years of cooling. MA isotope

Ratio

Pu isotope

Ratio

Np-237 Am-241 Am-242m Am-243 Cm-243 Cm-244 Cm-245 Cm-246 Cm-247

0.4953 0.3156 0.00103 0.1476 0.00044 0.03695 0.00262 0.00047 0.00001

Pu-238 Pu-239 Pu-240 Pu-241 Pu-242

0.0268 0.5640 0.2402 0.0991 0.0697

Component Total Pu Total MA

Ratio 0.00905 0.00067

the change of the k-effective is the same for the next cycle as the current one. MAs were considered to be loaded homogenously into the core and different options were investigated concerning the MA content of the charged fuel. The discharged fuel from the GFR was partitioned after 5 years of cooling and was sent to the corresponding storage (U, Pu or MA). The U, Pu and MA need of the GFR was taken from the storage, and natural U or Pu and MAs from LWR spent fuel were only used when the amount in the storage was not enough. The developed FITXS tool is capable of following the above fuel cycles for a long term (hundreds of cycles) in a reasonable CPU time (few minutes). This is important for reaching the equilibrium in the system and all simulations were continued till then. Although the time needed to get to the equilibrium was too long to be realistic in a fuel cycle simulation (i.e. several hundreds of years), it is useful for the investigation of the equilibrium state, which is important for its evaluation. 4. Basic neutronic parameters and related uncertainties at BOL To gain a detailed neutronic characterization of the reference design several important parameters were determined for beginning of life operating conditions, most of them by multiple participants which served as a verification of the used models. Corresponding uncertainty studies were also performed revealing that numerous target values are violated. This section gives an overview of these results. 4.1. Excess reactivity Table 6 shows the effective multiplication factor at the beginning of life with the different models and codes. In general there is good agreement between the results with some notable differences. The most significant deviation (up to 600 pcm) is found in the k-effective values obtained by using diffusion theory, this is due to the low density of the rod follower material (filling the space

Fig. 6. k-effective sensitivity profile of

238

U calculated by SCALE and ERANOS.

below all control and safety rods, which are supposed to be in their parking position above the active core, see Fig. 3). The homogenization of the fuel assemblies and the number of neutron energy groups have smaller effects (100e150 pcm). The final difference between the codes is 400 pcm, which is acceptable considering the different cross section libraries (ENDF/B-VII vs. JEFF3.1), programs and ways of accounting for thermal expansion. 4.1.1. Sensitivitiy and uncertainty analysis of the excess reactivity The sensitivities and the sensitivity profiles (i.e. the group-wise sensitivities) of the k-effective were also determined. In SCALE these were calculated using the fully detailed three-dimensional model of the reactor and the TSUNAMI module, whereas in ERANOS diffusion theory was applied with a three-dimensional heterogeneous model in the VARIANT module. In the latter case the 238 group structure of SCALE was approximated by mocking up the 1968 fine group structure available in ERANOS to a SCALE-like structure, which can be done relatively well above 10 eV. Fig. 6 and Fig. 7 show the comparison of the explicit sensitivity profiles of 238U and 239Pu. The agreement between the two codes is excellent, only slight differences are experienced in a few of the energy groups. As expected both profiles show regular behavior. In case of 238U, a typical (thermal) absorber actinide the sensitivity is negative at most energies as slower neutrons are mainly captured, it only becomes slightly positive above 1 MeV when the energy of the neutrons exceeds the threshold of fast fission. In case of 239Pu, a (thermally) fissile isotope the total sensitivity is positive in all energy groups, as it is dominated by the fission sensitivity being bigger than the absolute value of the radiative capture sensitivity.

Table 6 The effective multiplication factor with different codes, models and cross section data.

Model details

ERANOS

SCALE

k-effective

Model details

Homogenized

33 group 172 group Diffusion, 33 group Diffusion, 172 group

Heterogeneous

2D

3D

2D

3D

1.01558 e e e

1.01674 e 1.01060 e

1.01706 1.01834 e e

1.01827 1.01957 1.01216 1.01325

k-effective Value

Std.

At 20  C, 238 group

1.02613

2.6,104

Expanded, 238 group

1.02357

3.7,104


, Z., et al., Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor, Progress in Nuclear Please cite this article in press as: Perko Energy (2014), http://dx.doi.org/10.1016/j.pnucene.2014.09.016


et al. / Progress in Nuclear Energy xxx (2014) 1e22 Z. Perko

Fig. 7. k-effective sensitivity profile of Pu-239 calculated by SCALE and ERANOS.

Capture is solely due to radiative capture, while scattering due to inelastic scattering only becomes noticeable at high energies. Some of the most important sensitivities obtained by TSUNAMI are summarized in Table 7, together with the results of threedimensional ERANOS diffusion calculations (in 33 groups using heterogeneous fuel-assemblies). The explicit sensitivities are the traditional k-effective sensitivity coefficients, whereas the implicit ones calculated by SCALE show the implicit effects due to selfshielding, for the exact definitions and more details see (SCALE, 2009; Rearden et al., 2011). The k-effective is most sensitive to 239 Pu and 241Pu (the main fissile isotopes), to 238U (the main absorber) and to the vast amounts of natural carbon in the core (denoted by C-000 in Table 7 and in the rest of the paper). The sensitivities to all other isotopes are an order of magnitude smaller

Table 7 The sensitivity of the k-effective (Dk/k%) to the individual isotopes and reactions calculated by SCALE and ERANOS. Isotope Reaction ERANOS

Pu-239 Pu-239 U-238 U-238 U-238 U-238 U-238 Pu-241 Pu-241 Si-28 Si-028 Si-028 U-235 Re-187 Re-185 W-184 W-184 C-000c He-004

Total Fission Total Nubar Fission Capture Inelastic Total Fission Total n,p Capture Total Capture Capture Total Elastic Elastic Elastic

SCALE a

Explicit

Explicit

Implicit

Total

þ3.961e01 þ4.437e01 2.189e01 þ1.479e01 þ8.866e02 2.189e01 8.650e02 þ8.095e02 þ8.680e02 4.070e02 e 4.363e03b þ2.336e02 1.639e02 1.072e02 4.848e03 5.659e05 9.600e02 3.700e03

þ3.9768e01 þ4.4602e01 2.1519e01 þ1.4795e01 þ8.6768e02 2.1612e01 8.7828e02 þ8.0061e02 þ8.5860e02 2.8811e02 2.2831e03 1.6445e03 þ2.3016e02 1.6246e02 1.0807e02 5.0409e03 þ1.3319e04 8.6072e02 3.3188e03

2.1150e03 5.9614e04 þ6.2981e03 þ0.0000eþ00 3.9836e06 þ6.1604e04 3.9247e05 1.5506e04 6.5054e05 þ4.1647e04 þ2.4852e08 þ1.0673e06 7.4708e05 þ2.4084e04 þ6.4441e05 þ4.9077e04 þ4.5414e04 2.9582e03 2.5469e06

þ3.9557e01 þ4.4542e01 2.0889e01 þ1.4795e01 þ8.6764e02 2.1550e01 8.7867e02 þ7.9906e02 þ8.5795e02 2.8395e02 2.2831e03 1.6435e03 þ2.2941e02 1.6005e02 1.0743e02 4.5502e03 þ5.8733e04 8.9030e02 3.3213e03

a The total sensitivities calculated by SCALE are the sum of the explicit and implicit sensitivities, not to be confused with the sensitivity to the total “reaction” of an isotope, which signals the sensitivity to its number density. b Contains the lumped (n,p) reaction sensitivity as well. c C-000 stands for natural carbon.

9

than to 239Pu, including the traditionally important 235U. The fast spectrum of the system is well signaled by the fact that the fission cross section and the n values of 238U are equally important as its capture cross section. Though the liners are very thin the large density of the metals results in high nuclide densities and substantial amounts of rhenium (and tungsten) in the core, there are approximately 489 kg of 185Re and 827 kg of 187Re excluding the fission plenums. This, together with the fact that the capture cross section of both isotopes is significant at higher energies as well (up to around 1 MeV) results in sensitivities close to that of some of the fuel isotopes. TSUNAMI even provides insight into such unusual reactions as the n,p reaction of 28Si, which makes up a significant portion of its total reaction in the reactor. Furthermore it seems that some of the tungsten isotopes have a more significant implicit effect through self-shielding than direct contribution to the change of the k-effective. Comparing the explicit sensitivity coefficients of SCALE with the ERANOS results the agreement is excellent for most isotopes, however some noticeable differences are found for natural carbon, 4He (up to 12%) as well as for some of the smaller sensitivities such as the elastic scattering of 184W. The uncertainty of the effective multiplication factor and its isotopic decomposition can be seen in Table 8, where both the SCALE results based on the 44 group SCALE covariance library and the ERANOS results based on three-dimensional 33 group diffusion calculations and the 15 group BOLNA covariance library are summarized. The overall agreement between the codes and data libraries is satisfactory (1.78% vs. 1.7%), but there are some deviations in the isotopic decomposition. 238U is clearly the dominant source of uncertainty, particularly due to its inelastic scattering. The other significant contributors are the plutonium isotopes, most importantly 241Pu and 239Pu. For the latter two isotopes the discrepancy between SCALE and ERANOS is quite significant, while SCALE assigns the higher contribution to 239Pu (in agreement with the slightly higher sensitivity of the k-effective) ERANOS does so to 241 Pu. Since the sensitivity graphs obtained with the two codes are almost identical when using a similar group structure (see Fig. 7), this discrepancy can be explained by the sensitivity to the group structure and the differences in the covariance data, most notably the missing fission spectrum uncertainties in the BOLNA library which account for an 0.33% k-effective uncertainty in case of 239Pu. There are also differences in the carbon, 28Si and 4He uncertainties, which can partly be explained by the higher sensitivity coefficients of ERANOS. In the ERANOS results the structural materials also induce significant uncertainties. The negative squared uncertainty values due to the elastic scattering of certain isotopes are indicative of significant cross-correlations between reactions and some numerical inaccuracies in the BOLNA covariance matrix, namely suspected problems with its positive definiteness. The SCALE results well show that the Re and W uncertainties are not to be neglected, they are even higher than 235U values. The Re covariances are however not part of BOLNA, hence their effect was assessed by considering the uncertainty associated with its two isotopes similar to that of 56Fe with the three different options presented in Section 3.1.1. The uncertainties obtained in this way are summarized in Table 9 and e except for option a e show significant increases in the uncertainty of the neutronic parameters (especially considering the Doppler and depressurization effects, see later in Section 5). However looking at the uncertainty decomposition of the k-effective based on the SCALE covariance data and considering the roughly 0.1% and 0.065% uncertainties due to 185Re and 187Re respectively it can be suspected that the values in Table 9 are somewhat overpredictive for options b and c. The uncertainty results for the k-effective show rather good correspondence with an earlier study on the uncertainties and sensitivities of advanced nuclear systems (Aliberti et al., 2006).


, Z., et al., Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor, Progress in Nuclear Please cite this article in press as: Perko Energy (2014), http://dx.doi.org/10.1016/j.pnucene.2014.09.016


et al. / Progress in Nuclear Energy xxx (2014) 1e22 Z. Perko

10

Table 8 Isotopic decomposition of the k-effective uncertainty obtained with ERANOS (ER) and SCALE (SC) calculations. The inelastic scattering of 238U is clearly the dominant source, but significant contributions can be assigned to the plutonium isotopes as well. Capture [%]

Fission and productiona [%]

Elastic scat. [%]

Inelastic scat. [%]

Total isotopic uncertainty [%]

ER

SC

ER

SC

ER

SC

ER

SC

ER

SCb

U-235 C-000 U-238 Pu-238 Pu-239 Pu-240 Pu-241 Pu-242 Am-241 He-004 Si-028 Zr-090 B-010 Re-187 W-183

0.09 0.01 0.47 0.02 0.27 0.15 0.04 0.12 0.01 e 0.12 e 0.03 e e

0.076 0.000 0.301 0.020 0.245 0.034 0.017 0.025 0.009 e 0.013 0.007 0.000 0.097 0.081

0.03 e 0.17 0.19 0.21 0.24 0.75 0.15 0.01 e e e e e e

0.021 e 0.195 0.151 0.698 0.181 0.120 0.032 0.002 e e e e e e

e 0.30 0.11 e 0.01 e e e e 0.02 0.03 e e e e

0.000 0.051 0.008 0.000 0.001 0.000 0.000 0.000 0.000 0.003 0.016 0.056 0.000 0.005 0.005

e 0.05 1.40 e 0.07 0.01 0.01 0.01 e e 0.16 0.01 e e e

0.004 0.047 1.443 0.004 0.098 0.023 0.010 0.011 0.004 0.000 0.039 0.000 0.000 e 0.029

0.08 0.31 1.48 0.19 0.35 0.28 0.75 0.19 0.01 0.02 0.20 0.01 0.03 e e

0.079 0.065 1.489 0.153 0.745 0.193 0.129 0.042 0.010 0.003 0.054 0.059 0.001 0.097 0.086

Total

0.60

0.418

0.87

0.772

0.28

0.078

1.41

1.448

1.78

1.702

Nuclide

a

For the SCALE results these are the square roots of the sums of the squared uncertainties due to the fission cross section, average number of fission neutrons and the fission spectrum. b These values are the square roots of the sums of all squared uncertainties associated with an isotope, including the cross correlations between isotopes.

There a 1.9% overall uncertainty was reported for a GFR using partial energy correlation approach for a 17 group covariance data. The isotopic decomposition was also found to be similar, 238U (1.22%) and 239Pu (1.03%) being the main contributors while having smaller contributions (and bigger differences from this research) from 241Pu (0.57%), 241Am (0.43%) and 28Si (0.42%). Considering the 0.3% target value for the k-effective uncertainty (Salvatores et al., 2008) it can be concluded that the current design greatly violates it, from several different sources, the 238U and 239Pu alone have a higher contribution regardless of the used covariance data. Hence there is definitely a need for better nuclear data, in particular to the aforementioned isotopes and reactions. 4.1.2. The effects of geometrical uncertainties on the excess reactivity Since the fuel pin and assembly designs, as well as the used ceramic materials are very innovative their manufacturing process is expected to be less precise than current standards. Therefore an assessment of the effects of geometrical uncertainties on the keffective was also done using SCALE (Hartman, 2012). Two actions were taken: simulating an infinite array of fuel pins where the geometrical sizes (i.e. the radii of the individual material regions) were assumed to have Gaussian distributions and simulating an infinite array of fuel assemblies where the pellets were uniformly positioned inside the pins and all 217 pin positions were perturbed with a Gaussian distribution around their reference place.

Table 9 Uncertainties including the effects of Re based on three-dimensional diffusion calculations (ERANOS). Parameter

k-effective

Doppler

Depressurization

Reference value

1.01206

1064 pcm

302 pcm

Re uncertainty option

1s-uncertainties [%]

BOLNA Option a Option b Option c, fully anti-correlated Option c, uncorrelated Option c, fully correlated

1.78 1.78 2.04 1.78 1.91 2.12

Target accuracy [%]

0.3

5.11 5.24 11.67 8.53 8.92 13.32 7

8.87 8.89 10.48 9.2 9.67 11.08 7

Table 10 shows the effect of the uncertainties present in the individual material regions of the pin on the effective multiplication factor of the infinite array. The standard deviation of the fuel and the cladding corresponds to a geometrical accuracy of 10 mm, while that of the liners to 1 mm. The liners were envisioned to be manufactured with a fixed thickness on the inside of the cladding, hence whenever the boundary of a layer was modified the preceding layers were shifted inwards keeping their width fixed, which results in a decreased material quantity. Since an infinite array of pins was modelled these uncertainties should be considered overpredictive as they correspond to changing the geometry of all pins in the lattice in the same way. Not surprisingly the uncertainty in the fuel pellet radius has the biggest effect on the effective multiplication factor, as it introduces an uncertainty of 0.17%. This effect is solely due to uncertainty in the fuel mass, with the density assumed constant the increased pellet radius simply introduces more fissile material increasing the k-effective. When the size of the pellet is perturbed assuming a constant mass and uncertain density, the uncertainty and the sensitivity of the k-effective are negligible. Increasing the width of any other material region decreases the k-effective, as the overall absorption is increased due to the increased amount of absorbers. The rhenium liner also has a significant effect on the uncertainty, being responsible for 0.15%. The contribution of the tungstenerhenium liner and the cladding is less important. When all material boundaries are simultaneously perturbed the final uncertainty estimate is 0.25%, which is significantly smaller than the cross section uncertainty. Moreover the major part of this comes from the changing amount of fissile material in the modelled infinite pin lattice, hence in a real reactor the overall uncertainty is

Table 10 Effects of perturbing individual material boundaries (1D transport). Material region

1s-uncertainty of region boundary [%]

1s-uncertainty of k-effective [%]

Fuel pellet W14Re-liner Re-liner Cladding inward Cladding outward

0.3 2.5 10 0.97 0.97

0.17642 0.05889 0.15098 0.03865 0.06738


, Z., et al., Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor, Progress in Nuclear Please cite this article in press as: Perko Energy (2014), http://dx.doi.org/10.1016/j.pnucene.2014.09.016


et al. / Progress in Nuclear Energy xxx (2014) 1e22 Z. Perko

11

expected to be smaller due to the counterbalancing effect of the different pins. However locally these uncertainties are definitely not negligible, especially considering the 0.3% target value for the keffective uncertainty (see in Table 9). The effects of pellet and pin positioning were investigated using NEWT to model a fuel assembly in an infinite array of assemblies with the liners and the cladding homogenized and the cross sections collapsed to a 20 group structure to reduce computational costs. All pin positions were perturbed independently with a standard deviation of s ¼ 400 mm and only physically possible lattices were taken into account, without overlaps. The pellet positions inside the pins were also perturbed independently with a uniform distribution. The obtained 1s-uncertainty of the k-effective is small, only s ¼ 0.039%. This result confirms that from the keffective point of view the exact geometry of the reactor is much less important than the material composition in case of a fast reactor. 4.2. Flux distribution, power peaking and fundamental adjoint with related uncertainties The neutron spectra in the inner and outer cores are depicted in Fig. 8. For most of the energy range good agreement is found between the 172 group ERANOS (two-dimensional transport with heterogeneous fuel assemblies) and the 238 group SCALE calculations, however differences are found below 10 eV. This is not surprising considering that the Monte-Carlo results become increasingly noisy the lower the energy gets, all groups had relative errors higher than 10% below 10 eV, several groups having zero tallies or tallies with 100% relative error (especially in the inner core having a harder spectrum). In the most important energy groups however the errors of the flux are small (below 1%). Moreover ERANOS calculations showed that there is a significant group effect for the thermal and epithermal energy regions, causing the flux to be underpredicted when using less groups (33 groups vs 172 groups). As can be expected, the spectrum is harder in the inner regions than in the outer ones, as in the center we experience slightly bigger group fluxes above 100 eV and lower ones below 100 eV. The most important resonances are also clearly seen (238U resonances at 6.67 eV, 20.87 eV and 36.68 eV, 240Pu resonance at 1.05 eV, or 242Pu resonance at 2.67 eV). Fig. 9 shows the change of the total flux as a function of the distance from the center of the core at the active core mid plane (based on 172 group ERANOS

Fig. 9. The radial flux distribution along the core calculated by two different ERANOS models.

calculations with three-dimensional diffusion and twodimensional transport methods, using heterogeneous and homogeneous fuel assembly models respectively). As can be seen the flux peak does not occur in the middle of the core, rather at the border of the two fuel zones, naturally leading to a similar power distribution. The power peaking factor and the power lower depression factor were also determined by ERANOS calculations. The obtained values show only very little method dependence (much smaller than the k-effective), the results of two-dimensional 33 group transport calculations with heterogeneous fuel assemblies are summarized in Table 11 together with the associated uncertainties. Just like in case of the effective multiplication factor, the main contributors to the uncertainty are 238U (due to inelastic scattering) and 241Pu (due to fission and production), with smaller contributions from 239Pu, carbon and 240Pu. The obtained uncertainty of 2.11% is somewhat higher than the 1.8% reported in (Aliberti et al., 2006) and also exceeds the target accuracy of 2%. Finally, Fig. 10 shows the adjoint function in the inner and the outer zones. Neutron importance is high in the thermal range and in the energy range of fast fissions. Here the resonances are even easier to see, the significant decrease of the adjoint function can almost always be associated with the resonance capture of an isotope in the fuel. 4.3. Kinetic parameters and related uncertainties

Fig. 8. The neutron spectrum in the inner and outer core. For energies below 10 eV the Monte Carlo results (SC) have increasingly high errors and become less reliable.

For transients and accidental conditions the kinetic parameters of the reactor are of fundamental importance. Hence the effective delayed neutron fraction and the neutron generation time were calculated both with ERANOS and with SCALE. The parameters are summarized in Table 12, showing good agreement and no significant model dependency. Table 13 gives further insight into the effective delayed neutron fraction by decomposing it to the individual isotopes and delayed neutron groups (based on SCALE results and ENDF/B-VII data). A surprisingly high fraction of the delayed neutrons, roughly 50% is produced by 238U, the main fissile isotopes of 239Pu and 241Pu being responsible for another 40% and all other fissionable nuclides producing the rest. Moreover the inner core is responsible for a relatively higher amount of the delayed neutrons (compared to its volume fraction) in correspondence with the harder neutron spectrum and the importance of 238U to beff. The uncertainty of the effective delayed neutron fraction obtained by ERANOS together with its isotopic decomposition can be


, Z., et al., Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor, Progress in Nuclear Please cite this article in press as: Perko Energy (2014), http://dx.doi.org/10.1016/j.pnucene.2014.09.016


et al. / Progress in Nuclear Energy xxx (2014) 1e22 Z. Perko

12

Table 11 The uncertainty of the power peaking factor, the power lower depression factor and the effective delayed neutron fraction obtained by 2D transport calculations (ERANOS). Parameter

Power peaking factor

Power lower depression factor

Effective delayed neutron fractiona

Value

1.559

0.317

401 pcm

1s uncertainty [%]

2.11

2.13

2.16

U-235 U-238 Pu-238 Pu-239 Pu-240 Pu-241 Pu-242 Am-241 C-000 Si-028

0.10 1.88 0.16 0.35 0.24 0.70 0.15 0.01 0.38 0.24

0.10 1.76 0.24 0.38 0.30 0.97 0.24 0.01 0.33 0.22

0.08 1.58 0.61 0.92 0.54 0.73 0.12 0.03 0.25 0.20

Target accuracy

2

2

5

Table 12 The kinetic parameters with different codes, models and cross section data. ERANOS Model details

2D 33 group 172 group a

a Uncertainty values do not contain the direct effect, i.e. the uncertainty due to the number of prompt and delayed neutrons. Supposing a 5% uncertainty for these results in a 5.4% final uncertainty for beff.

seen in Table 11. As expected, the main isotopic contributors are 238 U, 239Pu, 241Pu, 238Pu and 240Pu. As the delayed neutron data is not part of the BOLNA covariance matrices, the presented uncertainties do not contain the direct term coming from the delayed neutron fractions themselves. An assessment of this direct term was obtained by assuming that the effective delayed neutron fraction equals the fundamental delayed neutron fraction and that the number of prompt and delayed neutrons is energy independent and uncorrelated. By supposing a 5% 1s-uncertainty for the number of delayed neutrons for all isotopes the final estimate of the effective delayed neutron fraction uncertainty is 5.4%, showing a significant increase. This value exceeds the 5% target, however it should be noted that the majority of the uncertainty comes from the direct term for which only an assumption could be made. Nevertheless, the 5% uncertainty of the delayed neutron data can be considered realistic considering the high fraction of Pu isotopes in

Fig. 10. The adjoint function in the fuel calculated by SCALE. The most important resonances are clearly seen, like the 240Pu resonance at 1.05 eV or the 238U resonance at 6.67 eV.

b c

SCALE

beff [pcm] a

405 401

3D

L [ms] b

405 401

2D

a

0.59 0.63

Model details 3D

b

0.61 0.66

At 20  Cc Expandedc

beff [pcm]

L [ms]

3D

3D

414 415

0.67 0.69

Transport calculations. Diffusion calculations. With 238 group cross sections.

the fuel and the available measurement data (Keepin et al., 1957; Piksaikin et al., 2002). 5. Relevant reactivity effects and related uncertainties Any change that causes a shift in the reactivity of a reactor leads to transient behavior. Since for GFRs accidents present especially challenging situations, the accurate determination of such reactivity effects is of critical importance. This section summarizes the most important effects with their related uncertainties including Doppler temperature feedback, voiding and depressurization, expansion and water ingress effects. 5.1. Doppler effect The most important feedback in nuclear reactors is the Doppler effect caused by the broadening resonances of nuclides with increasing temperature. This results in higher fission and capture resonance integrals, the net effect on reactivity usually being negative. The strength of the Doppler effect can be characterized by the Doppler constant defined as Dr/ln(Tper/Tref), where Dr is a certain reactivity change corresponding to variation of the fuel temperature from a reference value of Tref to a perturbed value of Tper. With direct calculations these parameters are easily determined, however more insight is gained by decomposing them to the individual isotopic contributions using perturbation methods. The estimated Doppler constants are summarized in Table 14. For the ERANOS calculations Tref ¼ 1263.16 K and Tper ¼ 453.16 K (corresponding to full power and decay heat conditions) were chosen, whereas the SCALE results were calculated using increased temperatures of 1313.16 K and 1363.16 K, i.e. an increase of 50 K and 100 K. Only small differences can be observed between the methods and the codes (less than 3%) and a very similar value is obtained as in (Aliberti et al., 2006) (1077). Table 15 gives the isotopic decomposition of the Doppler constant for the 33 group heterogeneous ERANOS model and the non-expanded SCALE model, both obtained with transport theory. As can be seen there is good qualitative agreement between the codes, the dominant role of the 238U capture is obvious, and the partly compensating effects of 239Pu capture and fission are also highlighted. Though the net effect of 239Pu is positive it is highly suppressed by 238U, since the increase of the 239Pu fission cross section starts at lower neutron energy than that of the 238U capture cross section (in correspondence with their respective resonance structures), which combined with the flux change results capture to prevail (Krepel et al., 2011). The quantitative agreement between the codes is less precise, the most significant difference is that SCALE calculates a higher capture contribution from 238U which is partly counterbalanced by its elastic scattering. These differences are mainly caused by the different cross sections and more importantly the different decomposition methods: in ERANOS only the scalar fluxes are used for calculating the capture and elastic contributions and all


, Z., et al., Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor, Progress in Nuclear Please cite this article in press as: Perko Energy (2014), http://dx.doi.org/10.1016/j.pnucene.2014.09.016


et al. / Progress in Nuclear Energy xxx (2014) 1e22 Z. Perko

13

Table 13 Decomposition of effective delayed neutron fraction of 415 pcm to isotopes, regions and delayed neutron groups (SCALE). Isotope

Region

Am-241 Am-241 Pu-238 Pu-238 Pu-239 Pu-239 Pu-240 Pu-240 Pu-241 Pu-241 Pu-242 Pu-242 U-235 U-235 U-238 U-238 Total Total

Effective delayed neutron fractions [pcm]

OC IC OC IC OC IC OC IC OC IC OC IC OC IC OC IC OC IC

beff,1

beff,2

beff,3

beff,4

beff,5

beff,6

beff

0.0025 0.0026 0.0392 0.0417 1.8427 1.9821 0.2368 0.2422 0.4455 0.4855 0.0642 0.0649 0.2965 0.4213 1.1430 1.4847 4.0706 4.7250

0.0188 0.0190 0.2573 0.2740 12.428 13.399 1.9345 1.9827 5.6605 6.1774 0.7715 0.7804 1.5587 2.2173 9.4134 12.242 32.043 37.091

0.0112 0.0113 0.1654 0.1758 9.0863 9.7739 1.1120 1.1371 3.4444 3.7488 0.4020 0.4056 1.4820 2.1068 10.707 13.904 26.411 31.263

0.0246 0.0248 0.3816 0.4064 17.023 18.346 2.4921 2.5529 8.6489 9.4315 1.0704 1.0821 3.4158 4.8673 32.431 42.216 65.487 78.927

0.0125 0.0126 0.1689 0.1798 8.7866 9.4655 1.3455 1.3778 4.8618 5.2997 0.7365 0.7444 1.3852 1.9726 21.145 27.506 38.442 46.559

0.0047 0.0048 0.0792 0.0862 3.8905 4.2795 0.6071 0.6351 2.5238 2.8125 0.3410 0.3518 0.8534 1.2409 13.824 18.434 22.123 27.845

0.0743 0.0750 1.0916 1.1639 53.057 57.246 7.7280 7.9278 25.585 27.955 3.3856 3.4294 8.9915 12.826 88.663 115.79 188.58 226.41

anisotropy is lumped in a transport effect, hence the missing capture (negative) and elastic (positive) contributions partly cancel each other and the remainder of the anisotropy is manifested in the transport/leakage term. The different group structure is also responsible for the discrepancy to a certain extent. The uncertainty of the Doppler reactivity effect (when decreasing the fuel temperature from nominal conditions to decay heat conditions) together with its isotopic decomposition is presented in Table 16 and in Table 17 respectively, all based on ERANOS calculations. As expected very good agreement is found between the transport and diffusion results, and the dominance of 238U (4.04%) and 241Pu (1.96%) is prevailing. Further significant contribution comes from natural carbon (1.92% due to elastic scattering), 239 Pu (1.11%) and 28Si (0.55%). The overall uncertainty of 5.1% is in satisfactory agreement with the 5.5% value presented in (Aliberti et al., 2006) and the isotopic contributions are also similar, with a slightly lower value for 238U (3.2%) and higher for 239Pu (2.6%). However when the Re isotopes are also taken into account (Table 9) options b and c suggest a significant increase of uncertainty to higher than 8%. 5.2. Depressurization reactivity effect Due to the low thermal inertia of the core depressurized accidents present the most challenging situations in a GFR. Therefore the reactivity effect of the most serious of such accidents was determined, i.e. when the core suffers total depressurization and the He pressure decreases from nominal (7 MPa) to atmospheric

(0.1 MPa) conditions. The results can be seen in Table 18 and show more significant model dependence than the Doppler effect. Especially the results obtained by diffusion theory seem to underpredict the reactivity increase, the transport results are more consistent, however both the homogenization of the assemblies and the use of two-dimensional calculations have noticeable effects (up to 8% and 4% respectively). The isotopic decomposition of the reactivity effect is shown in Table 19 both for the ERANOS and for SCALE calculations. The reactivity effect can be attributed almost solely to the elastic scattering of 4He (again, all anisotropy is manifested in leakage in the ERANOS calculations). The spatial decomposition of the effect shows that a significant contribution comes from the low density rod follower (RF) regions, which explains the underprediction by diffusion theory. As expected neither the plenums (bottom and top e BP and TP respectively) nor the reflectors (radial, bottom and top e RR, BR and TR) affect the results significantly. The obtained reactivity effect of 315  330 pcm is somewhat lower than the value of 350.1 pcm reported in (Aliberti et al., 2006) for a similar GFR design, more important is however the fact that it is significantly below the effective delayed neutron fraction of 400 pcm precluding super-prompt-criticality in the core, as well as confirming that the design satisfies this major safety goal. Table 16 shows the uncertainty of the depressurization reactivity effect obtained by both transport and diffusion calculations.

Table 15 The decomposition of the Doppler constant calculated with ERANOS and SCALE applying three-dimensional transport. Isotope

Table 14 The Doppler constant with different codes, models and cross section data. ERANOS

SCALE

Model details Doppler constant

33 group 172 group Diffusion, 33 group Diffusion, 172 group

Model details

Doppler constant þ50 K

Homogeneous FA

Heterogeneous FA

2D

3D

2D

e e e

1078 e 1080

1076 1067 1063 At 20  C, 1059 1055 238 group e 1064 Expanded, 1084 238 group e 1056

e

e

þ100 K

3D 1076 1084

Capturea

Fissiona

Elastica

Inelastica

Totala

ER

SC

ER

SC

ER

SC

ER

SC

ER

SC

U-238 Pu-238 Pu-239 Pu-240 Pu-241 Pu-242 C-000 Si-028 Si-030

1069 0 57 30 0 2 0 0 1

1172 2 55 27 1 4 0 0 0

1 1 98 5 6 0 0 0 0

0 3 113 6 4 0 0 0 0

12 0 0 0 0 0 6 1 0

55 0 1 2 0 0 0 0 0

2 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

1060 0 40 24 5 2 6 1 1

1116 1 59 20 4 4 0 0 0

Total

1163

1261

97

127

5

56

2

0

1063b

1076

a

All values given in units of pcm. Value includes the 12 pcm transport component which is not separated in the SCALE breakdown. b


, Z., et al., Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor, Progress in Nuclear Please cite this article in press as: Perko Energy (2014), http://dx.doi.org/10.1016/j.pnucene.2014.09.016


et al. / Progress in Nuclear Energy xxx (2014) 1e22 Z. Perko

14

Table 16 The uncertainty of the Doppler, depressurization and thermal expansion reactivity effects along with target accuracy values. Parameter

Doppler

Method

2Da

3Db

2Da

3Db

2Da

3Db

2Da

3Db

1095 5.11 7%

1091 5.11

343 8.12 7%

302 8.87

0.223 1.98 7%d

0.220 1.98

0.640 1.41 7%d

0.669 1.38

c

Value [pcm,pcm/K] 1s-uncertainty [%] Target accuracy [%] a b c d

Depress.

Axial expansion

Radial expansion

Two-dimensional transport calculations. Three-dimensional diffusion calculations. The Doppler and depressurization reactivity effects are presented in units of pcm, the expansion effects in units of pcm/K. Assumed to be the same as the Doppler and depressurization reactivity effect target accuracies.

Again, sufficient agreement is seen between the two methods and taking a look at the isotopic decomposition in Table 17 one can once more identify 238U as the main source (6.8%), alongside 4He (4.86%), natural carbon (1.8%), 241Pu (1.59%) and 239Pu (1.25%), the other contributions being less than 1%. The obtained value of 8.1e8.9% is somewhat higher than the 7.1% report in (Aliberti et al., 2006) even without the Re contributions, when those are assessed the uncertainty ranges up to 11% (see in Table 9). When comparing the isotopic decomposition one can conclude that the higher uncertainty in this study is mostly caused by the higher contribution of 238U (6.8% vs. 3.9%) and a significant fraction coming from 4He (4.86%).

computed axial and radial core expansion coefficients calculated as Dr/DT with the different models. Good agreement is found between the two- and three-dimensional transport models, however the use of diffusion theory overpredicts the radial coefficient. The uncertainty of the axial and radial core expansion reactivity coefficients is summarized in Table 17. Once again, taking a look at the isotopic decompositions it is revealed that the uncertainty of the axial expansion reactivity coefficient is mainly caused by 238U (1.12%, inelastic scattering), 241Pu (1.08%, fission and production) and 28Si (0.85%, inelastic scattering), while that of the radial coefficient by 238U (0.84%) and 241Pu (0.88%). These uncertainty values are well below the 7% target value, though do not contain the effects of Re.

5.3. Expansion reactivity effects Core expansion effects were also investigated with ERANOS. The axial expansion reactivity effect was determined by lowering the fuel temperature used for computing the axial expansion (with the non-bonded approach) from Thot ¼ 990  C to Tcold ¼ 180  C corresponding to the full power and decay heat conditions. The radial expansion reactivity effect was gained by a hypothetical reduction of inlet coolant temperature used to calculate the expansion of the diagrid by 300  C from the nominal value of 400  C, the unit cell radii being correspondingly decreased as well. Table 16 shows the

Table 17 Isotopic decomposition of the uncertainties of the Doppler, depressurization and thermal expansion reactivity effects (based on three-dimensional diffusion calculations with ERANOS using 33 group cross sections and the BOLNA covariance library). Only the total isotopic contributions and their most important reactions are listed as % contributions. Nuclide Doppler

Deppresurization Axial expansion Radial expansion

a

Main Total Maina reaction reaction

Total

Maina reaction

Total

Maina reaction

Total

U-235 C-000 U-238 Pu-238 Pu-239 Pu-240 Pu-241 Pu-242 Am-241 He-004 Si-028 Zr-090 Zr-091 Zr-092 Zr-094 B-010 Fe-056

0.18 1.91 3.99 0.40 0.95 0.53 1.95 0.36 0.04 0.05 0.45 0.04 0.02 0.03 0.03 0.08

(c) (e) (i) (f) (c) (f) (f) (c) (c) (e) (i) (e) (c) (i) (i) (c) (i)

0.24 1.80 6.80 0.33 1.25 0.65 1.59 0.65 0.04 4.86 0.69 0.03 0.03 0.08 0.09 0.12 0.02

0.08 0.54 0.82 0.15 0.48 0.14 1.08 0.15 0.02 0.07 0.69 0.02 0.01 0.01 0.01 0.04

(f) (e) (i) (f) (c) (f) (f) (c) (c) (e) (i) (i) (c) (c) (i) (c)

0.11 0.54 1.12 0.15 0.63 0.15 1.08 0.17 0.02 0.07 0.85 0.02 0.02 0.02 0.02 0.04

0.03 0.18 0.79 0.24 0.22 0.29 0.88 0.23 0.01 0.19 0.17 0.03 0.03 0.02 0.02 0.27

(f) (e) (i) (f) (f) (f) (f) (f) (f) (e) (i) (i) (c) (c) (i) (c)

0.04 0.19 0.84 0.24 0.23 0.29 0.88 0.23 0.01 0.19 0.20 0.04 0.03 0.03 0.03 0.27

Total

4.03 (i)

5.11 6.67 (i)

8.87

1.18 (f)

1.98

1.04 (f)

1.38

a

(c) (e) (i) (f) (c) (f) (f) (f) (c) (e) (i) (i) (c) (i) (i) (c)

0.18 1.92 4.04 0.40 1.11 0.54 1.96 0.51 0.05 0.05 0.55 0.04 0.02 0.03 0.03 0.08

0.22 1.80 6.63 0.32 1.03 0.59 1.58 0.45 0.03 4.86 0.65 0.02 0.02 0.08 0.09 0.11 0.02

Reaction labels: capture (c), fission and production (f), elastic scattering (e), inelastic scattering (i).

5.4. Water ingress reactivity effect As mentioned in Section 2.2 refractory metals (W and Re) are used in the GFR2400 pins as cladding liners in order to improve their fission product retention. Though the liners are thin and they make up less than 1% of the total inventory mass they cause a a significant neutronic penalty in normal operation due to their high absorption cross sections, well signaled by the high sensitivity of the k-effective (see Table 7). They have however a favorable effect in accidental situations in which spectrum softening is expected, which can be caused by the unwanted presence of moderating material in the system. In the analyzed GFR design water is used as the working principle of the secondary side of the decay heat removal loops. In case of pipe leak or rupture in these circuits it is possible to have water and/or steam entering the core directly. Such a scenario has various impacts, of which the most rapid one is the disruption of the neutron balance. In a fast reactor this variation is due to two main effects: the softening of the neutron spectrum and the increased absorption in the water itself. The consequence of the latter is a decrease in reactivity whereas the neutron spectrum change has a combined effect: it clearly increases the k-effective due to the high

Table 18 The depressurization reactivity effect with different codes, models and cross section data. ERANOS

SCALE

Model details Depressurization effect

Model details

33 group 172 group Diffusion, 33 group Diffusion, 172 group

Homogeneous FA

Heterogeneous FA

2D

3D

2D

3D

e e e

303 e 276

343 348 e

329 334 302

e

e

e

307

Depressurization effect

At 20  C, 315.4 238 group Expanded, 315.8 238 group


, Z., et al., Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor, Progress in Nuclear Please cite this article in press as: Perko Energy (2014), http://dx.doi.org/10.1016/j.pnucene.2014.09.016


et al. / Progress in Nuclear Energy xxx (2014) 1e22 Z. Perko

15

Table 19 He depressurization reactivity effect and its decomposition. Only the most relevant elastic scattering of He-4 and the leakage in case of ERANOS calculations are shown. Region

Elastic

Leakage

ERANOS a

OC IC RR BR þ TR BP þ TP RF a b

SCALE b

3D

2D

þ127.7 þ168.9 þ6.32 þ2.34 þ24.6 þ40.3

þ125.9 þ174.3 þ6.5 þ1.8 þ20.0 þ42.9

Total

ERANOS a

3D

3D

þ110.5 þ157.8 þ1.046 þ0.876 þ11.18 þ34.70

16.28 8.75 2.91 0.38 20.26 44.80

ERANOS 2D

b

15.82 11.09 2.72 0.45 12.17 5.34

3D

a

þ111.4 þ160.2 þ3.41 þ1.97 þ4.27 4.46

SCALE 2D

b

þ110.1 þ163.2 þ3.82 þ1.39 þ7.85 þ37.54

3D þ110.5 þ157.8 þ1.046 þ0.876 þ11.18 þ34.70

Diffusion calculation with 136 groups. Transport calculation with 136 groups and P1S16 approximation in r-z geometry.

contribution of the thermally fissile 235U and Pu isotopes to the neutron multiplication, but also changes the absorption rates of other materials in accordance with their resonance structure. The reactivity effect of having various amounts of water or steam injected into the core was assessed by neutronic calculations with the water being homogeneously mixed into the coolant in the fuel assemblies. To cover a wide range of water/steam densities the values were varied from 0.1 to 1.0 g/cm3. The behavior of the effective multiplication factor as a function of the smeared water/ steam density is depicted in Fig. 11. As can be seen there is a good agreement between the two Monte Carlo codes using continuous energy cross sections in the whole domain of the investigated water densities. For the nuclear data libraries the agreement is less satisfactory, especially at nominal conditions, nevertheless the reactivity differences are in the range of 200 pcm regardless of the water density. Consequently, there is no indication that the neutron spectrum thermalisation would not be properly accounted for. Fig. 11 shows that in GFR2400 the effect of the spectrum softening is counterbalanced by the increased absorption in almost the whole domain. The k-effective immediately starts to decrease, at 0.1 g/cm3 water density it is 4000 pcm smaller than the nominal value and it goes down by approximately 8000 pcm (corresponding to a negative reactivity insertion of roughly 7000 pcm) before it starts to increase from 0.4 g/cm3. It only exceeds its nominal value around 0.9 g/cm3 and even in the fully flooded core it is only 2000 pcm higher than that. This is primarily a consequence of the increased absorption rate of W and Re in the 1/v energy range,

Fig. 11. Multiplication factor as a function of smeared water/steam density in the GFR core: comparative results.

having a rapid surge till 0.3 g/cm3 and only decreasing back to its nominal value when the core is completely filled with water (Mikityuk et al., 2013). This shows the significant benefits of W and Re in case of this particular type of accident for the GFR from the neutronic point of view. The observation of the substantial decrease of the multiplication factor in response to the water ingress has an important message for core safety. It suggests that it is worthwhile to study the injection of borated water into the primary circuit of the GFR as a countermeasure to remove decay heat in the most penalizing accidental scenarios, i.e. in depressurized conditions. With this in mind, obviously other aspects of the water/steam ingress e such as chemical interaction with core materials, dynamic response of the reactor and the primary circuit, thermal-mechanical fuel behavior, etc. e should also have to be carefully evaluated and their interconnections should be well understood before any final recommendation can be made. 5.5. Control rod worths and movable reflectors The worth of control rods was also investigated by determining the k-effective for several insertion combinations with a threedimensional model of the reactor using homogenized fuel assemblies in SCALE. As a reference continuous energy MCNP5 v1.6 (MCNP5, 2003) calculations were also done. The obtained control rod worth values can be seen in Table 20 and one can easily conclude that the results show large shadowing and antishadowing effects. For instance the sum of the reactivity worth of both CSD rings is 6264 pcm, corresponding to only 76.5% of the roughly 8200 pcm computed worth of all CSD devices. On the other hand the individual worth of the outer DSD devices is around 310 pcm, whereas the total worth of the whole ring of 12 rods is 4400 pcm, approximately 15% higher than the sum. Both the CSD and DSD device group is able to provide a sufficient reactivity margin to shut down the reactor separately, i.e. without the requirement of the simultaneous insertion of the other group. Moreover even if the central ring of CSD devices was stuck outside the active core the use of the outer ring could still make the system sufficiently sub-critical. Since the neutron flux is almost constant in the radial direction in most of the core (see Fig. 9) the worth of control rods located at different radial positions is rather uniform, approximately 310 pcm for the inner CSD ring and the DSDs, and a slightly lower value of 260 pcm for the outer CSD ring. The total worth of all control rods is approximately 32beff, which is comparable to pressurized light water reactors and previous fast reactor designs (Waltar et al., 2012). Fig. 12 shows the spatial distribution of the neutron flux in case of having all control and safety rods fully inserted in the core. Though the rods introduce sufficient negative reactivity to shut down the reactor there are symmetrically distributed hot spots


, Z., et al., Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor, Progress in Nuclear Please cite this article in press as: Perko Energy (2014), http://dx.doi.org/10.1016/j.pnucene.2014.09.016


et al. / Progress in Nuclear Energy xxx (2014) 1e22 Z. Perko

16

Table 20 The reactivity worth of control rods in several combinations. Six CSDs (CSD 1e6) constitute the inner ring, 12 (CSD 7e18) the outer ring. The DSDs are split into a central rod (DSD 0) and a ring of 12 (DSD 1e12) between the inner and outer CSD rings. CSDs

DSDs

Combination

Worth [pcm]

Combination

Worth [pcm]

CSD 2 CSD 10 CSD 11 CSD 1e6 CSD 7e18 All CSD

317 260 263 1550 4714 8182

DSD 0 DSD 4 DSD 5 e DSD 1e12 All DSD

325 310 319 e 4401 4556

All rods (CSDs&DSDs) worth [pcm]

12825

corresponding to groups of 6e7 fuel assemblies located on the inner side of the outer core, where the distance from all absorber rods is relatively big. To provide a flatter power profile and avoid having decoupled neutronic zones in the core an additional system of partially movable reflector assemblies was investigated, which allows for a larger fraction of neutrons to leak out from the core. The two most promising options are (1) the withdrawal of six groups of six reflector assemblies symmetrically located in the innermost reflector ring near the hot spot areas (involving 36 assemblies); and (2) the removal of the entire first, innermost ring of reflector assemblies (involving 90 assemblies). In both cases the reflector movement was modelled by shifting the radial reflector assemblies (shown in light violet in Fig. 3) downwards, such that their top was at the same height as the bottom of the active core and the space above was simply filled with the coolant. The results are summarized in Table 21. During normal operation when the absorber rods are located above the core the removal of the reflector assemblies leads to a change of 466 pcm (option 1) and 1100 pcm (option 2) in reactivity, which is equivalent to the worth of 1.5 and 4 control rods respectively. When all control and safety rods are inserted in the core the withdrawal of six reflector groups (option 1) leads to a decrease of 1345 pcm in reactivity, whereas the worth of the complete first ring (option 2) is 2582 pcm. Comparing the values to Table 20 one can

Fig. 12. The spatial distribution of the normalized neutron flux in case of having all rods fully inserted in the core. The six symmetrically located hot spots can clearly be identified.

Table 21 The reactivity worth of movable reflectors at different control rod positions. Rod position (CSDs and DSDs)

Movable reflector option

Total worth [pcm]

Worth per reflector assembly [pcm]

All All All All

Option Option Option Option

467 1101 1345 2582

13 12 37 29

up up down down

1 2 1 2

conclude that the movable reflectors can significantly improve the shutdown of the core by introducing an extra 10e20% negative reactivity, at the same time they also flatten the power profile somewhat (see Fig. 13) due to the increased leakage from the hot spot areas (Vrban and Pelloni, 2013). Since the efficiency of the individual reflector assemblies is lower when the whole innermost ring is removed, the removal of only the 6 groups of reflector assemblies is a more promising option. 6. Fuel cycle studies In this section the open and closed cycle operation of GFR2400 as well as several transmutation scenarios are discussed. The results were obtained with the two different methods presented in Section 3.4, which have been designed for slightly different purposes. Both tools similarly provide the fuel composition evolution, however they differ in the assumptions. In the EQL3D procedure the fuel is fully recycled and the feed composition is fixed. Accordingly, the overall breeding gain of the equilibrium cycle is zero and the breeding capability of the core can be determined from the excess reactivity. In the FITXS burnup model the share of recycled fuel and the feed composition is controlled so that the core is critical at the end of equilibrium cycle. Accordingly, the equilibrium reactivity excess is close to zero and the breeding capability of the core is given by the cycle average breeding gain. Both these assumptions have some advantages and disadvantages and the respective results are in accordance with them. 6.1. Open and closed fuel cycle simulations for GFR2400 The first investigations considered open and closed cycles without recycling from other reactors. Besides the study of the breeding performance of the GFR and core characterization in various fuel cycle states, these cases are also suited to compare the different simulation methods. 6.1.1. Investigation of fuel cycle parameters A single simulation of the EQL3D procedure was used to obtain information about four fuel cycle states. These are labeled in the presented results as A, B, C, and D. First there is transition from the beginning of life state to the open cycle equilibrium in region A. Region B represents the actual open cycle equilibrium with fresh fuel operation. Region C corresponds to the most important transition between the open and closed cycles with fuel recycling and finally region D represents the fully converged equilibrium closed fuel cycle. The evolution is presented using effective full power year units, note however that in the last region D these units do not correspond to the reality, i.e. the equilibrium state is reached later than indicated time values. The evolution of the GFR reactivity and breeding gain in these four regions is presented in Fig. 14. As can be seen from region B the reactivity swing in open cycle equilibrium corresponds roughly to 900 pcm and respective reactivity values at the end of the batches are slightly negative. In the transition phase C between the open


, Z., et al., Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor, Progress in Nuclear Please cite this article in press as: Perko Energy (2014), http://dx.doi.org/10.1016/j.pnucene.2014.09.016


et al. / Progress in Nuclear Energy xxx (2014) 1e22 Z. Perko

17

Fig. 13. The spatial distribution of the normalized neutron flux in case of having all rods fully inserted and applying the movable reflectors. The six hot spots are somewhat reduced with both options.

Fig. 14. Evolution for the GFR reactivity and breeding gain in four region: (A) transition from BOL to open cycle equilibrium (B), (C) transition to closed cycle equilibrium (D).

and closed cycle equilibria, the reactivity first drops and later rises to the final values above 3000 pcm. The initial decrease is caused by the negative breeding gain of the initial core. The later increase of breeding gain can be partly explained by the 241Pu-241Am couple (see Fig. 15). The mass of fissile 241Pu, but also of 235U, is reduced, whereas the mass of fertile Am-241 grows. The reactivity increase in the equilibrium closed cycle is generally driven by its better neutron economy, illustrated for instance by the decreased 242Pu amount. The reactivity increase towards the equilibrium closed cycle is much higher when compared to the predecessor GFR core and also more comparable with other fast reactors (Krepel et al., 2012). The FITXS method was also used to simulate the open cycle in order to provide a comparison case with EQL3D, as well as to calculate two different closed cycle options. The first investigated option assumed only Pu recycling into the GFR to serve as a reference case for further studies. This simulation showed that the GFR is self-breeder since the breeding gain reaches 0.02 in equilibrium (see the ’0% MA’ case in Fig. 18) and no external feed of Pu is required, a small amount of Pu is even produced and fed to the storage (29 kg/cycle which is roughly 0.25% of the total Pu content of the core). The initial 14.8% Pu content of the core increases to

Fig. 15. Evolution of the GFR fuel composition in four region: (A) transition from BOL to open cycle equilibrium (B), (C) transition to closed cycle equilibrium (D).


, Z., et al., Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor, Progress in Nuclear Please cite this article in press as: Perko Energy (2014), http://dx.doi.org/10.1016/j.pnucene.2014.09.016

18


et al. / Progress in Nuclear Energy xxx (2014) 1e22 Z. Perko

Fig. 16. Evolution of the GFR depressurization reactivity and Doppler constant in three core states: (A) transition from BOL to open cycle equilibrium (B), and in closed cycle equilibrium (D).

16.8% due to the pile up of 240Pu and the decrease of the fissile 241Pu which is typical of fast reactors (see Figs. 19e20). The second option was the recycling of Pu and MAs into GFR without adding MAs from LWRs (referenced as ‘re MA’ in Figs. 18e19). An important question in this case is whether an equilibrium can be reached or not, and if yes, at what MA concentrations this is possible. The results show that the equilibrium is reached at approximately 1% of MA concentration in the core, hence satisfies the original design constraint. Isotopic compositions also reach equilibrium which means that all MAs are consumed by fission and no Cm accumulation occurs due to the MA recycling (see Fig. 21). This proves that the GFR can be applied as a MA burner. Since the assumptions of the above fuel cycle calculations with the EQL3D and the FITXS methods are not too different, a comparison of the two methods is possible. Table 22 shows the comparison for the charged and discharged fuel composition (the inner and the outer core zones are averaged in the EQL3D case). It can be seen that the two methods agree well in the isotopic compositions. Small differences are observed in the amount of the fission products, which is directly related to the burnup level. Since the same power and cycle length were assumed in the calculations this difference can be accounted for the differences in the modelling of energy release from fission and radiative capture reaction. Slight deviations in the EOC compositions can also be accounted for the

6.1.2. Core characterization in different fuel cycle states by EQL3D EQL3D was also used to determine the evolution of other integral core parameters (i.e. other than the reactivity) in different regimes of the core operation. As an example of safety related parameters the change of the depressurization reactivity effect (depressurization of the reactor from nominal conditions to atmospheric pressure) and the Doppler constant (calculated based on nominal and a þ1000  C elevated temperatures) are shown in Fig. 16. The equilibrium open cycle only shows a small deterioration when compared to the BOL state, however the deterioration in the equilibrium closed cycle is more significant. Several other core integral parameters are presented in Table 23. The most important

Fig. 17. Radial power peaking for all studied core states.

Fig. 18. Breeding gain in the case of different MA loading options.

different cooling times considered (4.2 and 5 years in case of EQL3D and FITXS respectively). As FITXS sets the BOC reactivity (see Equation (1)), while EQL3D does not, a difference can also be observed in the reactivity values. The breeding gain values in Table 22 were calculated based on the reaction rates at the given conditions (i.e. at BOC or EOC). The self-breeding property of the GFR core and the approximately 1% equilibrium concentration of the MAs are also confirmed by both calculations. The detailed analysis of the differences between the two methods are subject to further investigations.


, Z., et al., Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor, Progress in Nuclear Please cite this article in press as: Perko Energy (2014), http://dx.doi.org/10.1016/j.pnucene.2014.09.016


et al. / Progress in Nuclear Energy xxx (2014) 1e22 Z. Perko

Fig. 19. Pu content of the core at BOC in the case of different MA load options.

result is that depressurization reactivity in the closed fuel cycle exceeds the respective beta effective. Accordingly, depressurization can lead to super-prompt-criticality, hence deeper analysis and several transient simulations may be necessary before final conclusions can be drawn. Fig. 17 shows the radial power peaking for the studied core states. As can be seen the core is well designed for the open cycle operation. Both BOL and open cycle equilibrium provide very flat power distributions in radial direction. However, the results for the equilibrium closed cycle are much worse. This deterioration is mainly caused by the unrealistic assumption that the inner and outer burned fuel are reprocessed separately and not mixed together. In reality the fuel vectors would be mixed together in the reprocessing facility, possibly even with the spent fuel of several other reactors. Using this mixture, the reprocessed inner and outer fuel could be fabricated with different Pu contents, similar to the initial fuel in order to flatten the power profile. 6.2. Simulation of minor actinide burning in a nuclear energy system with the FITXS method The realization of transmutation is generally envisaged on the level of the complete nuclear energy system, where the different

19

Fig. 21. MA content of the core at BOC with the MA recycling option (re MA case).

reactor types can play different roles (Salvatores, 2002). In such a system fast reactors are expected to be able to consume minor actinides produced in other reactors. Therefore it is important to investigate these fast reactor designs at a system level where MA loading from other reactors is considered. Several studies addressed the comparison of the different fast reactors (Tu cek et al., 2008; Salvatores and Palmiotti, 2011) in the past indicating that the selection of the coolant (sodium, lead or gas) can influence the performance in MA burning. Investigation of the earlier 600 MWth GFR design (van Rooijen et al., 2007; van Rooijen and Kloosterman,
et al., 2012) already proved the favorable features of 2009; Perko the GFR in this aspect since in its fast spectrum almost all the actinide isotopes are fissionable. However the present 2400 MWth GFR design was not assessed previously from this point of view. In this study the FITXS method was applied for this purpose and numerous recycling options were investigated. The MA equilibrium concentration of 1% found in Section 6.1.1 suggests that a higher MA concentration in the core is possible allowing external feed of MAs and turning the GFR into a net MA burner. In order to verify this statement simulations were performed with the assumption of a fixed ratio of MAs in the charged fuel varying from 0.5% to 5%. As was expected, with 0.5 and 1% MA ratios the need for external MA feed diminishes as the equilibrium is approached, while for a ratio of 1.5% and above a significant external MA feed is possible (see Fig. 22). The increasing MA content also increases the breeding gain (see in Fig. 18) which can be explained by the fact that the fissile MA isotopes (mainly 242mAm and 245Cm) partly replace the fissile Pu in the core, while other MA isotopes behave as fertile material. This also results in a decreasing Pu content in the core with the increasing MA content (Fig. 19). In the isotopic composition of Pu shown one can observe an increasing amount of 238Pu which is produced from the high amount of 237Np fed from LWR waste. 7. Conclusions and future work

Fig. 20. Pu isotopic composition without MA recycling (0% MA case).

This paper presented a comprehensive neutronic characterization of the GFR2400 Gas Cooled Fast Reactor design that was investigated within the European FP7 GoFastR project. The parties involved in the collaboration performed a consistent assessment of all major neutronic parameters using several different code systems, models and cross section libraries, and in general found a good agreement between the calculated quantities, giving confidence about the used methodologies and the results.


, Z., et al., Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor, Progress in Nuclear Please cite this article in press as: Perko Energy (2014), http://dx.doi.org/10.1016/j.pnucene.2014.09.016


et al. / Progress in Nuclear Energy xxx (2014) 1e22 Z. Perko

20

Table 22 Comparison of the results of the EQL3D and FITXS methods for different fuel cycle options. Element

Open cyclea

Closed cyclea

Loaded EQL3D

Discharged FITXS

EQL3D

Loaded FITXS

EQL3D

Discharged FITXS

EQL3D

FITXS

U-all

84.20

84.20

78.48

78.46

81.40

82.34

76.17

76.86

234

U 235 U 236 U 238 U

0.00 0.59 0.00 83.62

0.00 0.61 0.00 83.60

0.01 0.35 0.05 78.06

0.01 0.36 0.09 78.00

0.18 0.14 0.17 80.91

0.21 0.14 0.45 81.54

0.17 0.10 0.16 75.74

0.18 0.10 0.44 76.13

Pu-all

15.68

15.69

15.93

15.87

17.49

16.59

17.59

16.88

0.43 8.84 4.09 1.17 1.15

0.43 8.85 4.09 1.17 1.15

0.32 9.34 4.36 0.82 1.08

0.31 9.32 4.33 0.83 1.09

0.44 9.79 6.16 0.53 0.57

0.40 9.65 5.58 0.44 0.52

0.43 9.78 6.15 0.65 0.57

0.41 9.73 5.62 0.61 0.52

238

Pu 239 Pu 240 Pu 241 Pu 242 Pu MA

0.11

0.11

0.40

0.36

1.11

1.07

1.04

0.96

237

0.00 0.11 0.00 0.00 0.00

0.00 0.11 0.00 0.00 0.00

0.03 0.22 0.01 0.10 0.02

0.01 0.22 0.01 0.09 0.01

0.14 0.63 0.04 0.17 0.09

0.13 0.65 0.04 0.15 0.07

0.13 0.51 0.04 0.17 0.10

0.12 0.49 0.04 0.15 0.09

Np 241 Am 242m Am 243 Am 244 Cm FP Total k-effective Breeding gain Pu/238U

239 a

0.00

0.00

5.20

5.31

0.00

0.00

5.20

5.30

100.00

100.00

100.00

100.00

100.00

100.00

100.00

100.00

1.00786 0.043 0.106

1.01569 0.035 0.106

0.99886 0.053 0.120

1.00443 0.021 0.120

1.03625 0.118 0.121

1.00769 0.062 0.118

1.03146 0.025 0.129

1.00582 0.034 0.128

Isotopic concentrations given in m/m%.

For benchmarking purposes the following neutronic parameters were determined at beginning of life conditions: excess reactivity, Doppler-coefficient, depressurization reactivity effects, effective delayed neutron fraction and generation time. Most results agree within 0.5%, with the notable exception of beff (3%) and L (5%). Core expansion reactivity effect and power distribution were also determined at BOL conditions. It was confirmed that the GFR2400 design is an improvement compared to previous concepts in several aspects. It is a more conventional pin bundle configuration with a workable concept compared to the previous plate type design. It features a manageable 10 t/GWel initial plutonium inventory at 45% plant efficiency and in case of self-recycling the mass fraction of MAs stays close to 1% of the fuel at equilibrium. The coolant

depressurization reactivity effect is smaller than the effective delayed neutron fraction in the fresh core (i.e. at BOL) and in an open equilibrium cycle, excluding super-prompt-criticality in case of a loss of coolant accident. Meanwhile the Doppler and expansion reactivity effects are similar to previous GFR designs and are sufficiently negative to enhance safety. Both groups of absorber rods (CSDs and DSDs) were shown to be able to shut down the reactor independently of each other, moreover the outer CSD ring provides satisfactory negative reactivity on its own. However local hot spots exist even when all control rods are fully inserted into the core, needing further attention and design refinement. A potential idea of using movable reflectors to enhance leakage for this purpose was assessed and it was found that the withdrawal of the innermost ring of reflector assemblies is equivalent to

Table 23 Overview of integral core parameters for several fuel cycle states. Integral core parameters

Average burn up [EFPD] k-effective Reactivity [pcm] Breeding gain Pu-239/U-238 mass ratio Depressurization reactivity [pcm] Doppler constant [pcm] Depressurization reactivitya [pcm] Doppler constantb [pcm] beff [pcm] Generation time [ms] Radial expansionc [pcm/ C] Axial fuel expansionc [pcm/ C] Cladding expansiond [pcm/ C] a b c d

BOL

0 1.01848 1815 0.067 0.106 334 1026 344 1010 403 0.608 0.6817 0.2502 0.1318

Equilibrium open cycle

Equilibrium closed cycle

Beginning

End

Beginning

End

481 1.00786 779 0.043 0.111 353 970 363 953 394 0.598 0.6813 0.2553 0.1324

962 0.99886 114 0.053 0.115 370 920 379 903 385 0.584 0.6767 0.2572 0.1357

481 1.03625 3498 0.118 0.124 392 782 401 766 357 0.501 0.6352 0.2461 0.1314

962 1.03146 3050 0.025 0.126 397 745 405 731 355 0.498 0.6351 0.2486 0.1318

At Doppler temperature, i.e. at þ1000  C elevated fuel temperature. In depressurized core. Calculated for a þ100  C temperature increase under the same assumptions as in Section 5.3. Calculated for simultaneous axial and radial expansion of the cladding due to a þ100  C temperature increase.


, Z., et al., Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor, Progress in Nuclear Please cite this article in press as: Perko Energy (2014), http://dx.doi.org/10.1016/j.pnucene.2014.09.016


et al. / Progress in Nuclear Energy xxx (2014) 1e22 Z. Perko

Fig. 22. External MA feed in the case of different MA load options.

approximately 4 control rods (1100 pcm) when all rods are in their parking position above the core and can help alleviate the problems of the local hot spots. The cladding liners made from refractory metals (W and Re) which are envisaged to ensure fission product confinement were shown to have a significant penalty on the neutron economy during normal operation due to their high absorption, however they could be favourable in accidental situations involving spectrum softening. In case of steam or water ingress e despite the neutron spectrum softening e the increased absorption in these thin liners leads to a very significant maximum negative reactivity insertion of 7000 pcm (compared to the 12,000 pcm full worth of the control rods). This suggests it is worthwhile to study the injection of borated water into the primary circuit as one of the possible and effective ways to remove decay heat when depressurization is expected, naturally taking into account other aspects of the presence of steam or water in the reactor as well, such as chemical interactions, dynamic response, thermal-mechanical fuel behavior, etc. An extensive sensitivity and uncertainty assessment was also carried out for the most relevant parameters at BOL conditions. The excess reactivity was shown to be most sensitive to the 239Pu and 238 U data, however the sensitivities to the Re and W isotopes in the metallic liners are also non-negligible. It was shown that uncertainty of several quantities exceed their target value, most notably the effective multiplication factor (by a factor of 6), depressurization reactivity effect (by 25%) and the power peaking factor (by 6%). In particular the inelastic scattering of 238U, the fission and production of 239Pu, 240Pu and 241Pu were found to be significant sources of uncertainty, but Re isotopes also contribute somewhat. Moreover, these uncertainty results should in general be considered as underpredictions due to certain approximations that were used (e.g. Re covariance data missing from the BOLNA covariance library). The excellent agreement of the sensitivity and uncertainty results for the k-effective between SCALE and ERANOS however gives confidence about the uncertainties calculated with ERANOS alone, despite the use of the less accurate 15 group covariance library. Fuel cycle studies were also performed for the GFR2400 core using two different methods, the ERANOS based EQL3D procedure and the FITXS method based on SCALE calculations. Both the open and closed cycle operation as well as several transmutation scenarios were simulated. A comparison of the results obtained by the two methods showed good agreement in the main parameters. The

21

results confirm the capability of the GFR2400 core to work in open and closed cycles and to self-recycle its own Pu and MA vector. By assuming external MA load from LWRs it was also shown that the GFR can be a net MA burner in a nuclear energy system. The investigation of the safety related parameters in different fuel cycle states however showed that in the closed cycle equilibrium those are slightly deteriorated, most importantly depressurization may lead to prompt criticality. Hence deeper analysis and several transient simulations may be necessary before final conclusions can be drawn. Lastly, the presented results indicate that for neutronics studies of such conceptual designs current commercial codes seem to be adequate in terms of accuracy and consistency. For further development however there is still a need for better nuclear data and uncertainty information, with special attention to the fast energy region. Both traditional isotopes like 238U and Pu nuclides, as well as less traditional materials like Re should be investigated in order to have reliable results with acceptable uncertainties for fast reactor applications. Acknowledgement The work presented in this paper was funded by the GoFastR project in the 7th Euratom Framework Programme of the European Union under contract No. 249678. The authors wish to thank all partners of this collaboration: AMEC, Areva, CEA, CIRTEN, EA, KIT-G, Imperial College, IRSN, JRC, NRG, PSI, Rolls-Royce, STU BA, TU Delft, TUV, SRS, BME, ENEA, Ansaldo, AEKI, FZJ,RC-Rez, NNLL. Appendix A. Abbreviations AIM1 BG BOC BOL CSD DSD EFPD EFPY EOC FA FP GFR HLW IC LR LWR MA MOX OC RF RR UR

Special steel alloy envisioned for certain structural parts Breeding gain Beginning of cycle Beginning of life Control system device (control rod) Diverse safety device (safety rod) Effective full power day Effective full power year End of cycle Fuel assembly Fission Product Gas Cooled Fast Reactor High level waste Inner core Lower reflector Light water reactor Minor actinide Mixed oxide Outer core Rod follower Radial reflector Upper reflector

References Aliberti, G., Palmiotti, G., Salvatores, M., Kim, T.K., Taiwo, T.A., Anitescu, M., Kodeli, I., Sartori, E., Bosq, J.C., Tommasi, J., 2006. Nuclear data sensitivity, uncertainty and target accuracy assessment for future nuclear systems. Ann. Nucl. Energy 33, 700e733. http://dx.doi.org/10.1016/j.anucene.2006.02.003. Bosq, J.C., Peneliau, Y., Rimpault, G., Vanier, M., 2006. Fine 3D Neutronic Characterization of a Gas-cooled Fast Reactor Based on Plate-type Sub-assemblies, pp. 1e10. Boucher, L., Velarde, F.A., Gonzales, E., Dixon, B.W., Edwards, G., Dick, G., Ono, K., 2010. International comparison for transition scenario codes involving COSI, DESAE, EVOLCODE, FAMILY and VISION. In: Proceedings of Actinide and Fission


, Z., et al., Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor, Progress in Nuclear Please cite this article in press as: Perko Energy (2014), http://dx.doi.org/10.1016/j.pnucene.2014.09.016

22


et al. / Progress in Nuclear Energy xxx (2014) 1e22 Z. Perko

Product Partitioning and Transmutation 11th Information Exchange Meeting, San Francisco, California, USA, pp. 61e71. Chauvin, N., Malo, J.Y., Garnier, J.C., Bertrand, F., Bosq, J., Ravenet, A., Lorenzo, D., Pelletier, M., Escleine, J.M., Munoz, I., Bonnerot, J.M., 2007. GFR fuel and core pre-conceptual design studies. In: International Conference on Advanced Nuclear Fuel Cycles and Systems (GLOBAL '07), Boise, Idaho, USA, pp. 423e433. da Cruz, D.F., Hogenbirk, A., Bosq, J.C., Rimpault, G., Prulhiere, G., Morris, P., Pelloni, S., 2006. Neutronic benchmark on the 2400 MW Gas-cooled fast reactor design. In: PHYSOR 2006: ANS Topical Meeting on Reactor Physics, Vancouver, BC, Canada, pp. 1e10. Dumaz, P., Bassi, C., Cadiou, T., Conti, A., Garnier, J.C., Malo, J.Y., Tosello, A., 2007. Gascooled fast reactors e status of CEA preliminary design studies. Nucl. Eng. Des. 237, 1618e1627. http://dx.doi.org/10.1016/j.nucengdes.2007.03.018. European Commission, 2006. FISA 2006 e EU Research and Training in Reactor Systems. Office for Official Publications of the European Communities, Luxembourg.
sz, M., Szieberth, M., Fehe
r, S., Reiss, T., 2013. Fuel cycle studies on the uranium Hala utilization efficiency and minor actinide burning in Gas cooled fast reactors. In:
fok, Procedings of 4th International Youth Conference on Energy 2013, Sio Hungary. Hartman, C., 2012. Effects of Geometrical Uncertainties in a Gas Cooled Fast Reactor. Bachelor thesis. Delft University of Technology. Keepin, G.R., Wimett, T.F., Zeigler, R.K., 1957. Delayed neutrons from fissionable isotopes of uranium, plutonium and thorium. J. Nucl. Energy 6, 1e21. Krepel, J., Pelloni, S., Mikityuk, K., 2012. Comparison of open and closed U-Pu equilibrium fuel cycles for generation-IV fast reactors with the EQL3D procedure. Nucl. Eng. Des. 250, 392e402. http://dx.doi.org/10.1016/j.nucengdes.2012.06.004. URL: http://dx.doi.org/10.1016/j.nucengdes.2012.06.004. Krepel, J., Pelloni, S., Mikityuk, K., Coddington, P., 2009. EQL3D: ERANOS based equilibrium fuel cycle procedure for fast reactors. Ann. Nucl. Energy 36, 550e561. http://dx.doi.org/10.1016/j.anucene.2009.01.008. URL: http://dx.doi. org/10.1016/j.anucene.2009.01.008. Krepel, J., Pelloni, S., Mikityuk, K., Coddington, P., 2010. GFR equilibrium cycle analysis with the EQL3D procedure. Nucl. Eng. Des. 240, 905e917. http:// dx.doi.org/10.1016/j.nucengdes.2009.12.007. URL: http://dx.doi.org/10.1016/j. nucengdes.2009.12.007. Krepel, J., Saliba, J., Mikityuk, K., Chawla, R., 2011. Comparison of safety related parameters of generation-IV fast reactors in equilibrium closed cycle. In: Proceedings of GLOBAL 2011, Makuhari, Japan. Lepp€ anen, J., 2010. Serpent Monte Carlo reactor physics code. In: Proc. 20th AER Symposium on VVER Reactor Physics and Reactor Safety, Espoo, Finland.
, Z., Girardin, G., 2013. Reactivity effect of steam/water ingress in Mikityuk, K., Perko generation-IV gas-cooled fast reactor core. In: Procedings of International Conference on Fast Reactors and Related Fuel Cycles: Safe Technologies and Sustainable Scenarios (FR13), Paris, France, pp. 1e7. Pelowitz, D.B.E., 2011. MCNPX User's Manual. Technical Report. Los Alamos National Laboratory, Los Alamos.
, Z., Fehe
r, S., Kloosterman, J.L., 2012. Minor actinide transmutation in GFR600. Perko Nucl. Technol. 177, 83e97. Piksaikin, V.M., Isaev, S.G., Goverdovski, A.A., 2002. Characteristics of delayed neutroncs: systematics and correlation properties. Prog. Nucl. Energy 41, 361e384. http://dx.doi.org/10.1016/S0149-1970(02)00018-5. Rearden, B.T., Williams, M.L., Jessee, M.A., Mueller, D.E., Wiarda, D.A., 2011. Sensitivity and uncertainty analysis capabilities and data in scale. Nucl. Technol. 174.
neliau, Y., Zabie
go, M., 2010. Reference GFR 2400 MWth Core DefiRichard, P., Pe nition at Start of GOFASTR. GoFastR Project Deliverable. CEA/DEN/CAD/DER/ SESI/LC4G DO2 26/03/10. Rimpault, G., Plisson, D., Tommasi, J., Jacqmin, R., Rieunier, J.M., Verrier, D., Biron, D., 2002. The ERANOS Code and Data System for Fast Reactor Neutronics Analyses. Physor 2002, Seoul, Korea, October 7e10, 2002.

van Rooijen, W.F.G., Kloosterman, J.L., 2009. Closed fuel cycle and minor actinide multirecycling in a gas-cooled fast reactor. Sci. Technol. Nucl. Instal. http:// dx.doi.org/10.1155/2009/282365. van Rooijen, W.F.G., Kloosterman, J.L., van der Hagen, T.H.J.J., van Dam, H., 2005. Fuel design and core layout for a gas-cooled fast reactor. Nucl. Technol. 151, 221e238. van Rooijen, W.F.G., Kloosterman, J.L., van der Hagen, T.H.J.J., van Dam, H., 2007. Definition of breeding gain for the closed fuel cycle and application to a gascooled fast reactor. Nucl. Sci. Eng. 157, 185e199. Salvatores, M., 2002. Transmutation: issues, innovative options and perspectives. Prog. Nucl. Energy 40, 375e402. Salvatores, M., Aliberti, G., Dunn, M., Hogenbirk, A., Ignatyuk, A., Ishikawa, M., Kodeli, I., Koning, A.J., Mcknight, R., Wills, R.W., Oblozinsky, P., Palmiotti, G., Plompen, A., Rimpault, G., Rugama, Y., Yang, W.S., 2008. Uncertainty and Target Accuracy Assessment for Innovative Systems Using Recent Covariance Data Evaluations. Nuclear Science NEA/WPEC-26. Salvatores, M., Palmiotti, G., 2011. Radioactive waste partitioning and transmutation within advanced fuel cycles: achievements and challenges. Prog. Part. Nucl. Phys. 66, 144e166. http://dx.doi.org/10.1016/j.ppnp.2010.10.001. URL. http://dx. doi.org/10.1016/j.ppnp.2010.10.001. SCALE, 2009. A Modular Code System for Performing Standardized Computer Analyses for Licensing Evaluations. Version 6, Available from Radiation Safety Information Computational Center at Oak Ridge National Laboratory as CCC750. ORNL/TM-2005/39. Oak Ridge National Laboratory, Oak Ridge, Tenn, USA. Stainsby, R., Haas, D., Somers, J., Mikityuk, K., Pouchon, M., Guedeney, P., Garnier, J.C., Touron, E., Mizuno, T., 2014. The gas-cooled fast reactor system. Prog. Nucl. Energy. XXXeYYY. Stainsby, R., Peers, K., Mitchell, C., Poette, C., Mikityuk, K., Somers, J., 2011. Gas Cooled Fast Reactor research in Europe. Nucl. Eng. Des. 241, 3481e3489. http:// dx.doi.org/10.1016/j.nucengdes.2011.08.005. URL: http://linkinghub.elsevier. com/retrieve/pii/S0029549311006303.
r, S., Reiss, T., 2012. Fuel cycle studies on minor Szieberth, M., Hal
asz, M., Fehe actinide burning in Gas Cooled Fast Reactors. In: Procedings of 12th Information Exchange Meeting on Actinide and Fission Product Partitioning and Transmutation, Prague, Czech Republic. Szieberth, M., Reiss, T., 2013. Fuel cycle studies on minor actinide burning in Gas Cooled Fast Reactors. In: International Conference on Fast Reactors and Related Fuel Cycles: Safe Technologies and Sustainable Scenarios (FR13), Paris, France. Tommasi, J., 2007. ERANOS User's Manual e Applications for Perturbation Theory with Finite Difference Diffusion and SN Transport Flux Solvers. SPRC/LEPh 07e003. CEA. Cadarache. Tu cek, K., Carlsson, J., Vidovi c, D., Wider, H., 2008. Comparative study of minor actinide transmutation in sodium and lead-cooled fast reactor cores. Prog. Nucl. Energy 50, 382e388. http://dx.doi.org/10.1016/j.pnucene.2007.11.021. US DOE, 2002. A Technology Roadmap for Generation-IV Nuclear Energy Systems. Technical Report. US Department of Energy. Vrban, B., Pelloni, S., 2013. Investigation of the coupled reactivity effects of the movable reflector and safety control rods in the GFR. In: Procedings of International Conference on Fast Reactors and Related Fuel Cycles: Safe Technologies and Sustainable Scenarios (FR13), Paris, France, pp. 1e11. Waltar, A.E., Todd, D.R., Tsvetkov, P.V., 2012. Fast Spectrum Reactors. Springer, New York. http://dx.doi.org/10.1007/978-1-4419-9572-8. Williams, M.L., Wiarda, D., Arbanas, G., Broadhead, B.L., 2009. SCALE Nuclear Data Covariance Library (SCALE, VOL III, Sect. M19). Technical Report ORNL/TM2005/39. Oak Ridge National Laboratory, Oak Ridge, Tenn, USA. X e 5 Monte CarloTeam, 2003. MCNP e a General N e Particle Transport Code, Version 5.
neau, C., Briottet, L., Ingremeau, J.J., Ravenet, A., Zabiego, M., Sauder, C., David, P., Gue
deney, P., Le Flem, M., Se
ran, J.L., 2013. Overview of Lorrette, C., Chaffron, L., Gue CEA's R&D on GFR fuel element design: from challenges to solutions. In: Procedings of International Conference on Fast Reactors and Related Fuel Cycles: Safe Technologies and Sustainable Scenarios (FR13). Paris, France.


, Z., et al., Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor, Progress in Nuclear Please cite this article in press as: Perko Energy (2014), http://dx.doi.org/10.1016/j.pnucene.2014.09.016