AGH University of Science and Technology
Faculty of Energy and Fuels
Department of Nuclear Energy
AGH WEiP KEJ/2013/5
AGH University of Science and Technology
Faculty of Energy and Fuels
Department od Nuclear Energy
Transition to the Adiabatic-LFR: preliminary
definition of the start-up core and MA-burning
capabilities evaluation
Report for the LEADER project
of European Union's 7th FP EURATOM
AGH WEiP KEJ / 2013/ 5
Kraków 2013
Jerzy Cetnar, Przemys aw Stanisz, Gra yna Doma ska
Editor: Jerzy Cetnar
Akademia Górniczo-Hutnicza im. Stanis awa Staszica w Krakowie
Wydzia Energetyki I Paliw, Katedra Energetyki J drowej
Al. A. Mickiewicza 30, 30-059 Kraków
ISBN 978-83-911589-4-4
SUMMARY: This report concerns the core performance and fuel cycle assessment of the
ELFR reactor during its evolution from beginning of life (BOL) along with adiabatic multicycling towards reaching the fuel equilibrium state. Few options of the fuel loading at BOL
concerning its composition have been assessed, where MOX and MA from LWR spent fuel
was assumed for the initial fuel, while for the reloading the depleted uranium replaces
removed fission products in equal mass. Major goals of the carried out investigation using
an advanced Monte Carlo method – MCB – were: to establish what fuel composition at BOL
allows the ELFR core to transit into the equilibrium core within the reactivity control
margin, to assess to what extent the external MA can be utilised for this purpose, and to
characterise the core neutronic performance over the multi-cycling time including the
evolution of the fuel nuclides. The analysis includes burn-up calculations in two-batch fuel
reloading scheme in adiabatic multi-cycling over period longer than century, which is
needed to reach the equilibrium state. For the considered core configurations, assessments
have been performed for power distribution, radial and axial power factors, influence of
control rod insertion, burn-up swing and fuel composition evolution. Reactivity effects such
as void effect, coolant temperature coefficient, Doppler coefficient, core expansion coefficient
are also evaluated at BOL.
2
Table of Contents
Table of Contents ........................................................................................ 3
List of Figures ............................................................................................. 4
List of Tables ............................................................................................... 7
Scope .......................................................................................................... 8
1. Introduction ......................................................................................... 8
2.
BOL fuel scenarios ............................................................................... 9
3.
Calculation methodology .................................................................... 11
3.1. General features of MCB ..................................................................... 11
3.2. MCB added values in applications for LFR analysis ............................. 12
4.
LFR calculation model ........................................................................ 12
5.
Fuel cycle analysis ............................................................................. 14
5.1. Criticality evolution ............................................................................. 15
5.1.1.
Observation of reactivity evolution ........................................... 16
5.1.2.
Reactivity range shift............................................................... 17
5.2. Transmutation characteristics ............................................................. 17
5.2.1.
Nuclide mass flow in transmutations ....................................... 18
5.2.2.
Transmutation of elements ...................................................... 22
5.2.3.
Full transition to the equilibrium composition ............................ 23
6.
Power distributions. ........................................................................... 23
7.
Safety coefficients ............................................................................... 24
8.
Conclusions ....................................................................................... 25
References
.............................................................................................. 26
Figures
.............................................................................................. 27
Tables
.............................................................................................. 66
3
List of Figures
Figure 1. Evolution of neutron multiplication factor of LFR .................................. 27
Figure 2. Effect of control rods insertion on criticality (k-eff) evolution of LFR
core case B with 2.5 % of MA at BOL. ......................................................... 28
Figure 3. Effect of control rods insertion on criticality (k-eff) evolution of LFR
core case C with no MA at BOL................................................................... 28
Figure 4. Comparison of criticality (k-eff) evolution assessment using coarse and
fine steps of burn-up calculation in MCB system ........................................ 29
Figure 5. Batch mass flow of U234 in three cases of fuel strategy options ............ 30
Figure 6. Batch mass flow of U235 in three cases of fuel strategy options ............ 31
Figure 7. Batch mass flow of U236 in three cases of fuel strategy options ............ 31
Figure 8. Batch mass flow of Np237 in three cases of fuel strategy options ........... 32
Figure 9. Batch mass flow of Pu238 in three cases of fuel strategy options ........... 32
Figure 10. Batch mass flow of Pu239 in three cases of fuel strategy options ......... 33
Figure 11. Batch mass flow of Pu240 in three cases of fuel strategy options ......... 33
Figure 12. Batch mass flow of Pu241 in three cases of fuel strategy options ......... 34
Figure 13. Batch mass flow of Pu242 in three cases of fuel strategy options ......... 34
Figure 14. Batch mass flow of Am241 in three cases of fuel strategy options ........ 35
Figure 15. Batch mass flow of Am242m in three cases of fuel strategy options ..... 35
Figure 16. Batch mass flow of Am243 in three cases of fuel strategy options ........ 36
Figure 17. Batch mass flow of Cm242 in three cases of fuel strategy options ........ 36
Figure 18. Batch mass flow of Cm243 in three cases of fuel strategy options ........ 37
Figure 19. Batch mass flow of Cm244 in three cases of fuel strategy options ........ 37
Figure 20. Batch mass flow of Cm245 in three cases of fuel strategy options ........ 38
Figure 21. Batch mass flow of Cm246 in three cases of fuel strategy options ........ 38
Figure 22. Batch mass flow of Cm247 in three cases of fuel strategy options ........ 39
Figure 23. Batch mass flow of Cm248 in three cases of fuel strategy options ........ 39
Figure 24. Batch mass flow of uranium in three cases of fuel strategy options ...... 40
Figure 25. Batch mass flow of plutonium in three cases of fuel strategy options ... 40
Figure 26. Batch mass flow of americium in three cases of fuel strategy options ... 41
Figure 27. Batch mass flow of curium in three cases of fuel strategy options ........ 41
Figure 28. Plutonium enrichments evolution in three cases of fuel strategy
options ...................................................................................................... 42
Figure 29. Breeding gains for every fuel batch in three cases of fuel strategy
options.. .................................................................................................... 42
Figure 30. Zoom on breeding gains after 60 years form BOL evolution. ................ 43
Figure 31. CR effect on breeding gains in LFR – case C without MA. .................... 43
Figure 32. CR effect on Pu240 batch mass flow – case C without MA. .................. 44
Figure 33. CR effect on Cm245 batch mass flow – case C without MA. ................. 44
Figure 34. U235 system inventory evolution in three cases of fuel strategy
options ...................................................................................................... 45
Figure 35. Uranium system inventory evolution in three cases of fuel strategy
options ...................................................................................................... 45
Figure 36. Pu238 system inventory evolution in three cases of fuel strategy
options ...................................................................................................... 46
4
Figure 37. Pu239 system inventory evolution in three cases of fuel strategy
options ...................................................................................................... 46
Figure 38. Pu240 system inventory evolution in three cases of fuel strategy
options ...................................................................................................... 47
Figure 39. Pu241 system inventory evolution in three cases of fuel strategy
options ...................................................................................................... 47
Figure 40. Pu242 system inventory evolution in three cases of fuel strategy
options ...................................................................................................... 48
Figure 41. Plutonium system inventory evolution in three cases of fuel strategy
options ...................................................................................................... 48
Figure 42. Am241 system inventory evolution in three cases of fuel strategy
options ...................................................................................................... 49
Figure 43. Am242m system inventory evolution in three cases of fuel strategy
options ...................................................................................................... 49
Figure 44. Am243 system inventory evolution in three cases of fuel strategy
options ...................................................................................................... 50
Figure 45. Americium system inventory evolution in three cases of fuel strategy
options ...................................................................................................... 50
Figure 46. Cm242 system inventory evolution in three cases of fuel strategy
options ...................................................................................................... 51
Figure 47. Cm244 system inventory evolution in three cases of fuel strategy
options ...................................................................................................... 51
Figure 48. Cm245 system inventory evolution in three cases of fuel strategy
options ...................................................................................................... 52
Figure 49. Cm246 system inventory evolution in three cases of fuel strategy
options ...................................................................................................... 52
Figure 50. Cm247 system inventory evolution in three cases of fuel strategy
options ...................................................................................................... 53
Figure 51. Cm248 system inventory evolution in three cases of fuel strategy
options ...................................................................................................... 53
Figure 52. Curium system inventory evolution in three cases of fuel strategy
options ...................................................................................................... 54
Figure 53. MA system inventory evolution in three cases of fuel strategy options .. 54
Figure 54. Radial density power factor at beginning and end of first cycle
(BOC=BOL); LFR case A (BOL MA 1.347%); CR withdrawn.......................... 55
Figure 55. Radial density power factor at beginning and end of eight cycle (BOC =
17.25 years); LFR case A (BOL MA 1.347%); CR withdrawn ........................ 55
Figure 56. Radial density power factor at beginning and end of first cycle
(BOC=BOL); LFR case B (BOL MA 2.5%); CR withdrawn ............................. 56
Figure 57. Radial density power factor at beginning and end of eight cycle (BOC =
17.25 years); LFR case B (BOL MA 2.5%); CR withdrawn ............................ 56
Figure 58. Radial density power factor at beginning and end of first cycle
(BOC=BOL); LFR case C (no MA at BOL); CR withdrawn ............................. 57
Figure 59. Radial density power factor at beginning and end of eight cycle (BOC =
17.25 years); LFR case C (no MA at BOL); CR withdrawn ............................ 57
Figure 60. Radial density power factor at beginning and end of first cycle
(BOC=BOL); LFR case B (BOL MA 2.5%); CR fully inserted ......................... 58
5
Figure 61. Radial density power factor at beginning and end of eight cycle (BOC =
17.25 years); LFR case B (BOL MA 2.5%); CR fully inserted ........................ 58
Figure 62. Radial density power factor at beginning and end of first cycle
(BOC=BOL); LFR case C (no MA at BOL); CR fully inserted ......................... 59
Figure 63. Radial density power factor at beginning and end of eight cycle (BOC =
17.25 years); LFR case C (no MA at BOL); CR fully inserted ........................ 59
Figure 64. Linear power factor at beginning and end of first cycle (BOC=BOL);
LFR case A (BOL MA 1.347%); CR withdrawn ............................................. 60
Figure 65. Linear power factor at beginning and end of eight cycle (BOC = 17.25
years); LFR case A (BOL MA 1.347%); CR withdrawn .................................. 60
Figure 66. Linear power factor at beginning and end of first cycle (BOC=BOL);
LFR case B (BOL MA 2.5%); CR withdrawn ................................................ 61
Figure 67. Linear power factor at beginning and end of eight cycle (BOC = 17.25
years); LFR case B (BOL MA 2.5%); CR withdrawn ..................................... 61
Figure 68. Linear power factor at beginning and end of 1st cycle (BOC=BOL); LFR
case C (no MA at BOL); CR withdrawn ........................................................ 62
Figure 69. Linear power factor at beginning and end of 8th cycle (BOC = 17.25
years); LFR case C (no MA at BOL); CR withdrawn ..................................... 62
Figure 70. Linear power factor at beginning and end of 18th cycle (BOC = 17.25
years); LFR case C (no MA at BOL); CR withdrawn ..................................... 63
Figure 71. Linear power factor at beginning and end of 28th cycle (BOC = 17.25
years); LFR case C (no MA at BOL); CR withdrawn ..................................... 63
Figure 72. Linear power factor at beginning and end of first cycle (BOC=BOL);
LFR case B (BOL MA 2.5%); CR fully inserted............................................. 64
Figure 73. Linear power factor at beginning and end of eight cycle (BOC = 17.25
years); LFR case B (BOL MA 2.5%); CR fully inserted .................................. 64
Figure 74. Linear power factor at beginning and end of first cycle (BOC=BOL);
LFR case C (no MA at BOL); CR fully inserted ............................................ 65
Figure 75. Linear power factor at beginning and end of eight cycle (BOC = 17.25
years); LFR case C (no MA at BOL); CR fully inserted .................................. 65
6
List of Tables
Table 1. Comparison of fuel vectors and compositions at BOL and in adiabatic
equilibrium in reference case of 1.347% MA. ............................................... 66
Table 2. Reactivity evolution with control rod effect in LFR case B, with fuel cycle
strategy using 2.5% MA at BOL. ................................................................. 67
Table 3. Reactivity evolution with control rod effect in LFR case C, with fuel cycle
strategy using no MA at BOL. ..................................................................... 68
Table 4. Nuclide mass flow in selected points of fuel reprocessing and recycling.
Second batch of LFR case A, with reference fuel cycle strategy using 1.347%
MA at BOL. ................................................................................................ 69
Table 5. Nuclide mass flow in selected points of fuel reprocessing and recycling.
Second batch of LFR case B, with fuel cycle strategy using 2.5% MA at BOL. 70
Table 6. Nuclide mass flow in selected points of fuel reprocessing and recycling.
Second batch of LFR case C, with fuel cycle strategy using no MA at BOL. ... 71
Table 7. Fuel power density and rating distribution in the first fuel cycle from
BOL of LFR – Case A (initial MA content 1.347%) ........................................ 72
Table 8 Fuel power density and rating distribution in 35 th fuel cycle (from 83.8
years) of LFR – Case A (initial MA content 1.347%) ...................................... 73
Table 9. Fuel power density and rating distribution in the first fuel cycle from
BOL of LFR – Case B (Initial MA content 2.5%) BOL ................................... 74
Table 10 Fuel power density and rating distribution in the first fuel cycle from
BOL of LFR – Case C (Initial MA content 0%) BOL ....................................... 75
Table 11. FIMA on discharge of the first batch in seven service cycles (1800 days)
in LFR with three fuel strategy options....................................................... 76
Table 12. Fuel Burnup on discharge of the first batch in seven service cycles
(1800 days) in LFR with three fuel strategy options .................................... 77
Table 13. Safety related coefficients in the first fuel cycle from BOL of LFR for
three fuel strategy options with CR-s fully withdrawn. ................................. 78
7
depleted uranium at the same time eliminating long lived heavy metal waste. These
features are very promising, however at the first implementation stage of new ELFR
reactors we will have no elements of the adiabatic fuel vector composition, therefore
a detailed analysis of the transitional period from BOL must be carried out, which
will result in the definition of the BOL core and possible fuel scenarios. Here the
inherent stability of the adiabatic core is the result of nuclear transmutation
processes in the neutron field characteristic for LFRs especially of adiabatic
configuration. This process of transmutation in series of multi cycles constrained to
the same main parameters of the cycles will tend to the final equilibrium
composition regardless from the initial composition. This feature is very important
for the strategy of defining the BOL core because hopefully it should allow us for a
simple core adjustment limited to the fuel material composition. What can be
adjusted are the contributions of the fuel elements while their isotopic vectors must
reflect the isotopic fractions characteristic of LWR waste, which are different from
that of the adiabatic fuel composition. The definition of the ELFR core at BOL
should be as close as possible to that in the adiabatic equilibrium at the technical
specification level, yet leading to small deviations of its performance parameters. It
generally should enable to control the reactor using the same control system as well
as to keep constraints of the fuel cycle concerning target burn-up, irradiation and
cooling times in the reprocessing. In other words the initial excess reactivity should
be kept below the margin of CR system reactivity worth, and remain in the positive
region with the burn-up in the consecutive cycles.
2.
BOL fuel scenarios
The core configuration at BOL is based on the configuration defined by the
adiabatic cycle state, which was determined in the scope of deliverable D05 [3],
where the only difference is the fuel vector composition at BOL for which few fuel
scenarios are being examined. If the assumed core design strategy has to be
successful the fuel composition differences must not result in substantial
increasing of the initial excess of reactivity as well as its swing during the reactor
lifetime. There are two major sources of composition differences:
a) the fission product component, which is absent at BOL;
b) the fuel vector composition.
Ad a) Since we are dealing with two-batch reloading scheme a significant
difference between adiabatic core at beginning of cycle (BOC) and the BOL core will
be caused by fission product content in the core. In case of equilibrium core half of
it is filled with the second batch fuel of 50% target burn-up whereas the BOL core
is free from fission product. This difference of about 2.8% of fission products is the
main culprit for the BOL reactivity excess and the following reactivity swing during
fuel burn-up in which the fission product content is saturating.
Ad b) As BOL core must resort to physically available fuel material the vector
compositions of LWR spent fuel are used, which are shown in Table 1 in
comparison with the adiabatic fuel. What influences the initial reactivity are the
concentrations of fissionable nuclides. One should keep in mind that in the fast
neutron spectrum of LFRs the division between nuclides that is characteristic for
thermal reactors: fissile and fertile, is not rigid since fast neutrons can fission every
nuclide; nevertheless generally at the level of elements, plutonium is dominated by
nuclides of high fissionability, whereas other transuranic elements are more
9
neutron capture prone than fission prone. By comparison a higher amount of
highly fissionable nuclides in the BOL vectors is observed for:





U235;
Pu239;
Pu241;
Am241;
Am243,
while for the adiabatic equilibrium vector:





U233;
Am242m;
Cm243;
Cm245;
Cm247.
Owing to orders of magnitude higher concentrations of the first group, the BOL
vectors are more fission prone than the equilibrium one. This feature means that at
BOL the fuel vector will not increase reactivity, but along with transmutation it will
increase the negative reactivity swing. This means that lowering the fissile
concentrations at BOL in order to reduce the initial reactivity excess would not be
feasible due to its leading to falling the reactivity below zero level in one of the
following cycles.
As the nuclear transmutations will ultimately lead from BOL composition to
the equilibrium one, it is apparent what isotopic composition changes are to be
expected, however their rates or transitional concentrations levels are not known a
priori. The fuel loading scenarios in the initial cycles must tackle the reactivity
problem, in order to avoid running the reactivity beyond controllable range.
Therefore the fuel loading scenarios should lead to a reduction of the reactivity
swing, which can be achievable through reduction of the fissile content and
enhancement of the fuel breeding at the initial cycles. Different effects on the
breeding gain during initial few cycles will be caused by increasing content of
uranium than MA. Depleted uranium is overwhelm by U238, which is strongly
fertile since only one neutron capture is sufficient to initiate its transmutation into
fissile Pu239, which is not the case for the most of minor actinides. This difference
in the number of neutron capture needed for the transmutation will be reflected in
breeding ratio, therefore increased content of MA can cause a time shift in
increasing the breeding and thus reducing the negative reactivity swing. Also the
neutron capture probability is different, which will differently balance current
breeding ratio. Fuel composition at BOL can be tailored appropriately by balancing
the uranium, plutonium and MA contributions. There is room here for making
strategic options concerning fuel management, which can depend on the needs of a
particular nuclear power industry. Since the equilibrium composition contains MA
by 1.347%, this amount will be generated in systems that have no MA in the core at
BOL. Introduction of MA in this amount to the initial fuel will result in no net
breeding of MA, which will help solving the problem of existing MA waste from
LWRs. Introduction of a larger amount of MA than in equilibrium will result in their
net burning. All cases have their advantages as well as week points, but each of
them can be of industrial interest in particular situations, therefore they need to be
examined in order to recognise and address their pros and cons. Three most
characteristic fuel scenarios with concern of MA fraction were selected and then,
the initial cycle analysis was carried out in order to check what is the range of
10
Scope
This report describes the work done under the scope of Task 2.1 of WP2 for the
LEADER project [1], which is part of the European Union’s 7th Framework
Programme. It concerns the core performance and fuel cycle assessment of the
ELFR reactor during its evolution from beginning of life (BOL) along with adiabatic
multi-cycling towards reaching the fuel equilibrium state [2]. The ELFR core
configuration and fuel cycle reloading schemes which were developed for the
adiabatic fuel cycle as described in deliverable D05 [3] define constrains for the
reference ELFR core at BOL. Few options of the fuel loading at BOL concerning its
composition have been assessed in regards to the core neutronic performance along
with the fuel multi-cycling ultimately leading to the equilibrium composition. For
this the utilisation of MOX and MA from LWR spent fuel is assumed for the initial
fuel, while for the reloading the depleted uranium replaces removed fission
products in equal mass. Major goals of the carried out investigation using an
advanced Monte Carlo method - MCB [4] - are: to establish what fuel composition
at BOL allows the ELFR core to transit into the equilibrium core within the
reactivity control margin, assess to what extent the external MA can be utilised for
this purpose, and to characterise the core neutronic performance over the multicycling time including the evolution of the fuel nuclides. The analysis includes
burn-up calculations in two-batch fuel reloading scheme in adiabatic multi-cycling
over period longer than century, which is needed to reach the equilibrium state. For
the considered core configurations, assessments have been performed for power
distribution, radial and axial power factors, influence of control rod insertion, burnup swing and fuel composition evolution. Reactivity effects such as void effect,
coolant temperature coefficient, Doppler coefficient, core expansion coefficient are
also evaluated at BOL. Neutronic and burn-up analyses have been done applying
an advanced Monte Carlo method – MCB, the same used in D05 analysis.
1.
Introduction
The definition of the adiabatic ELFR core to be complete needs to cover the
transition period from beginning of life to the equilibrium state. The definition of the
main technical parameters of the core like its dimensions in all levels starting from
the core through subassemblies to the fuel elements, has been carried out within
the design analysis of the ELFR core loaded with the fuel of equilibrium
composition in adiabatic operation. All that complex design process is described in
deliverable D05. Once the adiabatic equilibrium fuel is available the ELFR core
becomes invariant cycle to cycle as long as the major cycle parameters are kept
constrained to the defined values. Those parameters are the reactor power and the
irradiation and cooling times. The adiabatic equilibrium is a stable one in regards
to some parameters, which means that small deviation of the cycle parameters will
result in a system response that will counteract the deviation. This effect can be
illustrated by the case of the average power of the system, which is directly
translated into fuel burn-up, that influences the breeding gain. If the average power
decreases it will increase the breeding gain keeping it positive which will result in
higher fuel enrichment after reprocessing and thus lowering the breeding ratio in
the cycle loaded with the reprocessed fuel and consequently counteract the initial
increase of the breeding gain. All this process is directly reflected in the fuel
composition. The stable equilibrium of the adiabatic ELFR is its inherent feature
which makes this kind of system advantaged for two main reasons: firstly it
establishes well defined regime of system operation and fuel processes for all
reactor generations, secondly it allows for the fuel sustainability basing only on
8
reactivity change during reactor operation from BOL through multi-cycling,
primarily to learn if CR system is able to handle this change, and if needed to
modify plutonium and uranium fraction in order to keep the constraints.
3.
Calculation methodology
3.1. General features of MCB
The main goal of a burnup code is to calculate the evolution of material
densities. It concerns all possible nuclides that may emerge in the system after
nuclides decays, transmutations, or particles emissions. Transmutation process
includes fission product breakdown into nuclides as well as helium and hydrogen
atoms formed from emitted α particles and protons respectively. There is no
required predefined list of nuclides under consideration since all transmutation
chains are being formed automatically on-line basing on physical conditions that
constrain the system under the control of user-defined thresholds. These
thresholds concern contribution to the nuclide mass change from constructed
transmutation trajectories. In a real system under irradiation or decay, the nuclide
composition undergoes evolution that generally can be described with a continuous
function of time. An approximation of this function is obtained in MCB through the
time step procedure which starts from assessing reaction and decay probabilities of
every possible channel by means of stationary neutron transport calculations. In
the next step, the transmutation chain is formed and then solved to produce the
nuclide density table in required time points. The main features of the code can be
outlined as follows below.
 The decay schemes of all possible nuclides and their isomeric states are
formed and analysed on the basis of the decay data taken from two sources. The
first one – TOI.LIB, which is based on Table of Isotopes [5] describes decay schemes
for over 2400 nuclides including formation of nuclides in the excited states.
 Numerous cross-section libraries and data sets can be loaded into computer
memory to calculate adequately reaction rates and nuclide formation probabilities.
It includes possibility of separate treatment of cross sections for different burnable
zones, to account for thermal effects, employment of energy dependent distribution
of fission product formation, and energy dependent formation of isomer nuclides.
 Thermal-hydraulic coupling with FLUENT or POKE is available.
 Reaction rates are calculated exclusively by continuous energy method with
the usage of the point-wise transport cross-section libraries and, in case of lack of
proper library, by using the dosimetry cross section library. The contributions to
reaction rates are being scored at every instant of neutron collision occurring in
cells filled with burnable material by using the track length estimator of neutron
flux.
 Fission products yield is calculated from incident energy dependent
distributions of fission products prepared separately for every fissionable nuclide.
 Heating is automatically calculated in a similar way as the reaction rates
during neutron transport simulation by using heating cross sections, which are
KERMA factors included in standard cross section tables. The code calculates
automatically also the heating from natural decay of nuclides, what allows for
consideration of afterheat effects. The energies of decays are taken from the
ORIGEN library.
11
 Time evolutions of nuclide densities are calculated with the complete set of
linear transmutation chains that is prepared for every zone and time step so it is
being automatically adjusted to the transmutation conditions evolving with time.
 The code uses the extended linear chain method, which is based on the
Bateman approach, to solve prepared-on-line a set of linear chains that noticeably
contribute to nuclide formation [6].
 Detailed analysis of transmutation transitions from nuclide to nuclide is
performed. The transmutation chains that are formed by the code can be printed
for nuclides of interest.
 Material processing is available along with material allocations to geometry
cells during the burnup. Using this feature the user can simulate the fuel shuffling
or CR operation.
3.2. MCB added values in applications for LFR analysis
Due to the existing complexity of burnup process and reactor physics itself in
LFR cores, with evolving fuel from BOL to adiabatic equilibrium, in order to ensure
high quality of design, particularly with its safety features, it is reasonable to apply
few different tools of reactor core analysis. This can bring about results obtained
from few different perspectives. Here, the Monte Carlo methods, although
demanding more computer power, are characterised by higher level of model
complexity and fidelity, thus the results can be obtained in an integrated way,
possibly displaying important effects that can be hidden or neglected in other
approaches. For this purpose, the integrated Monte Carlo burnup calculation code
MCB is very suitable. It is a fully integrated calculation system, which allows the
user taking into consideration spatial effects of full heterogeneous reactor models
with continuous energy representation of cross section and the thermo-hydraulic
coupling. Here, a particular importance lays in a proper assessment of the power
distribution, but not merely at BOL but as a function of burnup with consideration
of the CR operation. The power distribution affects many core safety features,
therefore a simplified approach can lead to biased conclusions. As Monte Carlo
approach presents some benefits, it is not free from their intrinsic problems, which
need to be treated accurately. Namely, statistical fluctuations, which are
intrinsically present in Monte Carlo methods, need to be discriminate from an
expected real solution.
4.
LFR calculation model
The LFR core model for MCNP[7]/MCB calculations was prepared according to
the reference specifications from Deliverable 5 [3]. The major objective of our Monte
Carlo study is to understand deeply the neutronic and burnup characteristic of the
deep burn core in the reference configuration by consideration of the core features
in the models that were neglected so far, or are difficult to be considered using
other methods. We pay a particular attention to the modelling of CR operation as
the CR insertion level is adjusted along with the reactivity loss during burnup. For
the power distribution analysis and burnup calculations, the active core is divided
into burnup zones.
The adopted fuel cycle analysis features are summarised below.

The two-batch fuel cycle is assumed with no fuel shuffling.
12



The core has been divided into burnup zones in 16 radial regions and 10
axial segments, which makes 160 fuel burnable zones.
Fuel reprocessing and recycling is fully modelled for five fuel batches that
are needed for serving two batches in the core and three batches in cooling
or reprocessing.
Influence of CR insertion has been assessed by performing fuel cycle
analysis with CR withdrawn and inserted.
13
5.
Fuel cycle analysis
Confirmation about the chosen component fractions of the fuel at BOL is
sought at the first place in the calculation of system reactivity, which is derived
from the effective neutron multiplication factor, shortly called criticality. As
operational reactivity equals zero its value with control rods fully withdrawn must
be positive, while with the rods fully inserted negative over entire life of the system
from its transition from BOL state to the equilibrium. In other words the reactivity
of the system with CR fully withdrawn, which is called excess reactivity must be
positive and remain in the range of the CR system reactivity margin.
Common practice in calculation of the excess reactivity evolution in fuel cycle is to
carry out criticality calculations with CR fully withdrawn. Actually this procedure
gives the correct result regarding excess reactivity just at BOL, but with time
evolution the transmutations are calculated in different neutron spectrum than in
reality where CR insertion would suppress a part of the thermal neutron flux.
Keeping in mind this week point for the common approach, we will use it but with
the additional assessment of CR insertion influence on the mass and criticality
evolution.
Calculation of the ELFR core evolution from BOL to the adiabatic equilibrium
state is highly demanding in regard to the computation time. The primary reason is
the complexity of the fuel strategy definition, even if kept reasonably simple, which
involves two batch reloading strategy and fuel reprocessing. Yet, transition from
BOL to the equilibrium conditions requires many fuel reprocessing and recycling
steps, which should also include independent nuclides evolution during the cooling
time. For the assumed two-batch reloading scheme and cooling time that is trice
the reloading interval, we are dealing with five independent fuel batches, which for
two reloading periods of 900 days are in reactor service and for 7.5 years (which is
about three periods) remain discharged for cooling and simple reprocessing. Core
criticality evolution for three representative cases was calculated for initial
assumptions where plutonium and MA vectors of adiabatic core were substituted
by that of LWR spent fuel vectors; also, their contribution to the fuel composition
was fixed for the reference case, while for other cases, which are defined by
different MA fractions, additional adjustments of the uranium fraction were also
done. Comparison between the fuel compositions is shown in Table 1.
Initial cycle analysis was carried out in order to check what is the range of the
reactivity change during reactor operation from BOL through multi-cycling,
primarily to learn if CR system is able to handle this change. Change in isotopic
composition of plutonium and minor actinides is fully manageable by the CR
system designed for adiabatic equilibrium, while once we change the MA fraction
the plutonium fraction needs adjustment in order to reduce the initial excess
reactivity and the reactivity swing. This adjustment, in case of increased MA, is not
a must, but once the initial plutonium fraction is lowered to 17.8% the criticality
evolution is centred in the range of CR reactivity margin. For the case of no MA at
BOL the initial plutonium adjustment is not sufficient so that the first reprocessing
needs an addition of plutonium. After this initial assessment, the following BOL
fuel scenarios were examined in detail:
A. Reference case; MOX with MA in adiabatic equilibrium proportions between
U, Pu and MA vectors: U - 80.503%, Pu - 18.15%, MA - 1.347%.
The equilibrium proportions in the BOL core make no major problems in
maintaining the criticality swing in the margin range of the CR system designed for
adiabatic equilibrium. However, the reactivity swing, which occurs from BOL to
14
time of reactivity stabilisation spans almost the entire range of the CR system
reactivity margin.
B. MA burner case; MOX with increased fraction of the MA component: U 79.7%, Pu - 17.8%, MA - 2.5%.
Increasing MA to 2.5% at BOL has positive influence on the reactivity swing
reduction due to lowering the reactivity loss rate in initial cycles. This in turn
allowed for the reduction of the initial content of Pu as compared with the reference
case, which reduced the initial reactivity.
C. No MA case; MOX without MA: First loads of fresh fuel batches have Pu
fraction lowered - 17.2%/18.1%, which are increased during the first
reprocessing to 18.9%.
Case without MAs at BOL and the standard reprocessing approach (replacement of
FP by depleted uranium), here referred to as C0, would be characterised by the
highest initial reactivity, which is above the margin manageable by the CR system,
and the strongest reactivity swing. This would bring the core into negative reactivity
just after few initial cycles. The proposed solution to this problem is to reduce the
initial inventory of plutonium, which will lower the BOL reactivity, and then
increase it in the reprocessing of few initial cycles. Possible reduction and
restoration of plutonium inventory can be done by changing the number of fuel
assemblies loaded into the core, but that could have an adverse effect on the power
and temperature distributions, therefore a simple and more elegant solution of
varying plutonium fraction in the initial loads is proposed. The proposed solution is
the following:
 The BOL core is loaded in the first half by fuel of 17.2 % plutonium content
and in the second half by fuel with 18.1% of plutonium.
 After the first cycle of 2.5 years, the fuel of the first half is discharged and
cooled by three cycles (that is 7.5 years). This fuel, as well as that of the next
two loads are replaced by fresh fuel of 18.1% plutonium enriched MOX.
 After 10 years from BOL, the first fuel batch has been cooled already for 7.5
years and now is reprocessed with the increase of plutonium fraction to
18.9%. This procedure is applied to the next four fuel batches, each one after
5 years of irradiation and 7.5 years of cooling.
 From the second reprocessing of each fuel batch, they are carried out in the
standard way (with replacement of entire FP by depleted uranium). The first
batch of such a fuel will be reloaded to the core after 22.5 years from BOL.
5.1. Criticality evolution
Criticality evolutions for all cases A,B & C with control rods fully withdrawn
are presented in Figure 1, where also case C0 is shown, for comparison. In this
two-batch refuelling scheme of 900 day cycles and 7.5 years cooling time, every
batch but the first one is twice burnt and trice cooled before reprocessing and
reloading into the core. Five batches make the system inventory, out of which two
are on load while three are off load. The values of system reactivity at beginning
and end of cycles for the fuel strategy with enhanced plutonium content - case B are presented in Table 2, while for the fuel strategy without MA at BOL – case C –
they are shown in Table 3. The effect of CR insertion on the criticality evolution is
shown in Figure 2 for the fuel strategy with enhanced plutonium content - case B while in Figure 3 for the fuel strategy without MA at BOL – case C. For these cases
15
the values of system reactivity at beginning and end of cycles are presented in Table
2 - case B - and in Table 3 - case C. There are presented the values of the reactivity
swing on load - under irradiation - and off load – due to reprocessing and reloading.
Both tables present data obtained in two opposite assumptions concerning control
rod insertion – fully withdrawn or fully inserted, and the difference in the swings
due to CR insertion. The effect of CR insertion on the reactivity and the magnitude
of this effect needs to be understood in order to be aware of how much a deeper CR
insertion during a cycle shortens the cycle length. A deeper insertion might be the
consequence of differences between theory and reality or deviation from assumed
fuel strategy. In Figure 4 the comparison of criticality evolution of case C obtained
in calculation model with coarse steps and fine steps is shown in order to validate
the former calculation model, which is faster and was used in the first place during
extensive analysis of different options. Generally we observe good agreements
between applied models – within the range of calculation uncertainty.
5.1.1. Observation of reactivity evolution
The following observations have been made concerning the reactivity evolution
in the analysed cases.

The reactivity is highest at BOL and drops with every cycle until the equilibrium
level is reached.

The initial reactivity excess is manageable by CR system reactivity margin in all
cases, but lack of MA at BOL increases the reactivity level, which must be
compensated by a reduction of the plutonium fraction at BOL.

The reactivity swing is negative on load (under irradiation) while positive off load
(during reprocessing and reloading).

Fuel scenarios with MA content at the level of adiabatic composition and higher,
are positively influenced to what concerns the reactivity evolution through a
reduction of both the initial reactivity excess and the negative reactivity swing.

The fuel scenario without MA (case C0) needs to have plutonium added during
the first reprocessing of each fuel batch in order to compensate its reduction in
the fresh fuel and thus to avoid running the reactivity into the negative territory.
This requirement resulted in the evolution of this scenario to case C.

The reactivity range in the refuelling cycle (900 days) shifts down in periods of
five cycles, owing to the difference of the overall burnup history of reprocessed
and reloaded fuel batch compared to that of the discharged batch. This process
is explained in one of the subchapters bellow.

Criticality reaches the equilibrium level the quickest for case B (increased MA
content) after about 25 years, whereas in case A (reference fuel fraction) after 35
years, and in case C (no MA) after about 60 years of reactor operation.

The highest reactivity swing on load, of about 2789 (±50) pcm during the first
cycle, occurs for case C (no MAs) with CRs fully inserted.
16

The smallest reactivity swing on load, of about 1146 (±50) pcm during the first
cycle, occurs for case B (2.5% MAs) with CRs fully withdrawn.

CR insertion increases cycle reactivity swings - negative on load and positive off
load. The insertion increases the negative reactivity over the entire cycles, where
the additional negative swing would reach level of 1200 pcm in case B with CRs
fully inserted over 50 years of operation. For case C (no MAs) the corresponding
number equals about 900 pcm. Since in reality the CRs are substantially
inserted only in the initial cycles, the CRs insertion in case B can give estimated
value of additional swing below 300 pcm, while for case C below 150 pcm.

The ELFR cores with all defined and analysed scenarios can be fully managed
by the designed CR system reactivity margin, which at BOL equals 5400(±50)
pcm in case A (1.347% MA), 5250(±50) pcm in case B (2.5% MA) and 5600(±50)
pcm in case C (no MA).
5.1.2. Reactivity range shift
As the core at BOL is loaded entirely with fresh fuel, the reactivity is the
highest and then drops at the highest rate during the first cycle. The first batch in
its first load is only once bunt and it is replaced by new fresh batch number three
in the second cycle. This and the next two cycles (2nd to 4th) show identical
evolutions owing to their fuel of similar burnup history – fresh fuel batch has the
BOL composition while once burnt fuel batch was on load over one reloading cycle.
In this period the reactivity lost on load is regained off load. This pattern changes in
the 5th cycle, which starts after 9,86 years, where the first batch is reloaded after
reprocessing. Off load reactivity gain cannot compensate its loss during previous
cycle since the reloaded fresh fuel batch has its burnup history. Similar situation
occurs in next - 6th - cycle while during the next three cycles from 7th to 9th the
evolutions are similar owing to the same reason as in the case of cycles 2 nd to 4th.
This periodical behaviour can be observed in latter cycles also but with decreasing
magnitude. The cycle reactivity changes its cycle range in two consecutive cycles:
5th & 6th, 10th & 11th and so on, while replicates it in next three cycles: 2 nd to 4th , 7th
to 9th, 12th to 14th and so on. This periodic effect decreases with the number of
batch reprocessing since the fuel composition transforms closer to the equilibrium
one and the differences reprocessing to reprocessing are getting smaller.
5.2. Transmutation characteristics
The transition from the start-up core to the equilibrium one is a complex
process that can be followed in terms of core performance parameters, but also in
terms of nuclide mass evolution. Nuclide mass density flow has been analysed and
presented in transition from start-up core towards equilibrium core with CR fully
withdrawn and 2-batch refuelling scheme of 900 days refuelling cycles and 7.5
years cooling time. In presenting the results we focus on heavy metal elements up
to curium. In the Figures from 5 to 25 the nuclide mass flow in the three cases A, B
and C is shown independently in each of the five batches over the reactor operation
time of over 86 years, which spans seven reprocessing cycles of 12,32 years of the
second batch. We will call this moment EOL only for the sake of a simpler
description process. Every batch is twice burnt (colour lines) and trice cooled (grey
lines), two batches make core inventory, five batches make the system inventory.
17
The second batch is the most representative since it was loaded to the core at BOL
for two cycles, differently than the first batch. For the second fuel batch its mass
flow is presented in Tables 4, 5 and 6 for fuel strategies A, B and C respectively,
where transmutation changes are shown as they occur in initial cycles and over the
analysed life time.
5.2.1. Nuclide mass flow in transmutations
Fuel mass flow from BOL over 35 refuelling cycles that correspond to 7
reprocessing cycles for 5 batches is characterised nuclide by nuclide as follows.
U234
U234 mass initially as low as about 650 grams per batch is growing with every
reprocessing while its mass flow during irradiation increases in initial cycles
decreases starting from the 5th batch reprocessing as Figure 5 shows. Overall
transmutation mass flow is positive and it is higher with higher MA content at BOL.
U234 alpha decay to Th230 with half-life time of 2.455×105 years, therefore the
decay plays no role in the ELFR cycle. Addition of U234 in every reprocessing is
also not a significant factor. Increasing mass during off load time, is result of Pu238
alpha decay, therefore U234 build-up depends on Pu238 evolution. This in turn
differentiates significantly depending on the initial Am242m, at least over 50 years.
After that time as Pu248 in considered MA strategies will converge, U234 will also
follow. The maximum should be reached about after a century. Its highest batch
mass at EOL (after the 7th reprocessing) of about 58 kg in case B is still below
equilibrium value of 67,6 kg.
U235
The transmutation mass flow of U235 shown in Figure 6 is very similar for all
cases. Owing to its fissionability, it decreases during irradiation and is
compensated during the reprocessing. Balance of that processes brings
stabilization of U235 mass flow but in slightly different levels, which might be
explained by different fission probability in function of MA content. EOL mass of
30,5 kg in case B is slightly above the equilibrium level of 28 kg. In case B the
equilibrium level is actually reached.
U236
U236 is growing with time both on load and off load, without obvious
dependence on MA fraction at BOL. Mass at EOL of about 30 kg is still below the
equilibrium level of 48 kg. U236 alpha decays to Th232 with half-life of 2.342×107
years. It is formed by neutron capture on U235. U236 is mainly removed in neutron
capture to U237. Since U235 mass stabilises earlier, U236 concentration will be
increasing until production and destruction rates will balance each other. Time to
reach equilibrium is in range of 200 years.
U238
Mass flow of U238 is ruled by a simple principle – transmutation loss to
Np239 on load is compensated in reprocessing. What can be interesting is U mass
flow convergence of all three cases, which started with different uranium content at
18
BOL. Figure 24 shows mass flow of uranium, which is overwhelmed by U238 at the
same level at EOL in all cases.
Np237
The only noticeable neptunium isotope evolves starting with different BOL
levels since it contributes to the MA vector. Its mass flow shown in Figure 8
undergoes a steady convergence in all cases, very close to the equilibrium level of
about 26 kg. The evolution patterns during irradiation show that with higher MA
content Np237 is produced during every first cycle after batch reload while being
destroyed in the second cycle. This process occurs once the Np237 batch mass has
grown above 25 kg.
Pu238
Pu238 alpha decays to U234 with half-life time of 87,7 years, which
influences the mass flow in the studied cases. Pu238 is mainly produced in neutron
capture on Np237 with following beta - decay of Np238 of 2,1 days half-life time. The
second production channel is alpha decay of Cm242 with half-life time of 160 days.
The main removal channel of Pu238 is the neutron capture leading to the formation
of Pu239. This production channels explain the observed Pu238 evolution
dependence on the initial MA fraction because the main precursors of Pu238
contribute to MA. Figure 9 shows mass flow for this isotope, which takes different
directions depending on the MA fraction. Since this nuclide has substantial removal
rates, its balance depends heavily on the stabilization of its precursors. This,
however, comes relatively quickly, after extremes of mass flow reach their peaks
after about 30 years and start to converge. At EOL the case A is at equilibrium
levels while cases B and C are about 20% above or below it respectively.
Pu239
Pu239 is the most abundant fissile isotope in the ELFR and is being
constantly generated as well as destroyed. Figure 10 shows the mass flow for this
isotope, which converges to equilibrium level in a reasonable speed. The initial
difference of Pu239 results from defined strategy parameters, in which case C –
without MA - has the higher plutonium mass, yet introduced to the system in
addition during the first reprocessing. This is represented by jumps in mass flow
during off load times after the first discharge of each batch. Evolution patterns
during irradiations show that Pu239 at initial cycles is net destroyed but while
converging to equilibrium stabilises, even if with oscillations. The oscillations are
caused by its net production in every first cycle on load, and net destruction in the
second on load cycle. Other kind of mass oscillations is attributed to odd number of
fuel assemblies in the core which affects batch mass flow. Masses at EOL in all
there cases are very close to the equilibrium mass of about 2660 kg.
Pu240
Pu240 alpha decays to U236 with half-life time of 6540 years, is removed in
neutron capture to Pu241, and is produced after neutron capture on Pu239. Since
applied plutonium vectors at BOL have different mass ratios than in the adiabatic
equilibrium regarding Pu239 and Pu240, and since Pu239 levels out early, the
transmutation process leads to build-up of Pu240 over entire observed time, which
is shown in Figure 11. At EOL the biggest mass of 1660 kg of Pu240 in case A is
19
still below equilibrium level of about 1780 kg, which can be met about after 120
years.
Pu241
Pu241 beta decays to Am241 with half-life time of 14 years, which makes
this isotope very sensitive to the cooling times. Pu241 is produced in neutron
capture on Pu240 and removed in fission as well as in neutron capture to Pu242.
The mass flow of Pu241 shown in Figure 12 is similar in all cases and weekly
depends on MA fraction but mostly on Pu240, which will grow over 100 years.
Pu241 for being fissionable decreases fast during initial periods both on load and
off load. While strong destruction due to its decay remains, the production term
grows in time with increasing mass of Pu240, therefore after initial strong net
destruction, Pu241 becomes net produced after about 20 years. EOL mass of about
115 kg is close to the equilibrium value of 125 kg.
Pu242
Pu242 alpha decays to U238 with half-life time of 370 000 years. It is
produced in neutron capture on Pu241 and removed in neutron capture to Pu243.
Since initial fraction are more than twice higher than in adiabatic equilibrium its
mass flow in all considered cases is decreasing – which occurs only during on load
cycles, while off load periods change nothing, which is shown in Figure 13. The
evolutions are independent from the MA content. As EOL batch mass is about 250
kg and equilibrium is about 180 kg, it will be required at least additional 50 years
to reach the equilibrium.
Am241
Am241 alpha decays to Np237 with half-life of 432,8 years. The main source of
Am241 in the system is beta decay of Pu241 with half-life of 14.3 years. Am241 is
destroyed in fission or converted to Am242 or Am242m in neutron capture process.
Due to the short half-life of Pu241, the mass flow of Am241 is strongly growing
during off load periods which is clearly visible for all considered cases as shown in
Figure 14. Its destruction during on load periods depends mostly on its
concentration, therefore a simple path to reach equilibrium in all cases is formed
here. Equilibrium levels of 215 kg is almost reached by all cases at EOL, since all
cases converge considerably quickly.
Am242m
As the neutron capture on Am241 leads to the formation of Am242m, with
half-lives of 141 years, that leads mostly to Am242 through the isomeric transition.
Am242 beta decays in hours to Cm242, while Am242m substantially undergoes
fission as competitive channel to its isomeric transition. The mass flow presented in
Figure 15 shows that a strong temporary build-up of Am242m is observed in case
of a larger MA content – case B, but after 30 years it decreases toward equilibrium
level of about 17 kg, which is approached reasonably quickly in all cases. In cases
B and C the EOL mass differs by about 10% from the equilibrium level, which is
already met in case A then.
20
Am243
Am243 is formed in the neutron capture of Am242m. It is removed in neutron
capture to Am244 and Am244m. It alpha decays to Np239 with half-live time of
7370 years. As it depends on Am242m evolution on the sources side and
transmutation to Am244 on destruction side, its mass flow will follow pattern
similar to that of its precursor Am242m. This will lead to grow of Am243 in cases A
and C while for case B of 2.5% MA content the destruction rate is stronger, which is
manifested by the reduction of the mass flow. Reaching equilibrium requires over
100 years.
Cm242
Cm242 emits neutrons in spontaneous fission and alpha decays to Pu238 with
half-life of 160 days. Therefore, it is important for radiological safety. It is formed in
beta decay of Am242 with 16 hours half-life. Due to the very short life of Am242 its
decay practically occurs during on load time when Am242 is produced from
Am241. As shown in Figure 17 Cm242 is built-up only temporarily for the time of
its irradiation, and decays out quickly during off load cooling times. At EOL its
batch mass in case B is as low as 44 grams comparing to 6 kg on discharge.
Cm243
Cm243 alpha decays to Pu239 with half-life time of 29 years. Cm243 is
produced in neutron capture on Cm242 and is removed by fission or converted to
Cm244 on neutron capture. It is the most abundant curium isotope, mainly
because of its substantial production rate. Owing to its half-life time it decreases
noticeably during off load periods. Its production rate depends on Cm242 which is
restored during every on load period and is converted into Cm243 piling it up until
balance with its decay is established. This occurs in few decades depending on
initial MA fraction on a rather steady process, where in case B (2.5%MA) the
maximum mass is observed after about 20 years. After that time all cases start to
converge, also owing to lower production of Cm242. At equilibrium its batch mass
(at BOC) will be about 0.55 kg.
Cm244
Cm244 is important for the radiological safety because it emits neutrons in
spontaneous fission and decays to Pu240 in alpha decay with half-life time of 18.1
years. It is produced in neutron capture on Cm243 and beta decay of Am244. The
last channel is the most important and it is initiated by conversion of Am242 by
neutron captures to Am243 and then Am244. It is converted in neutron capture to
Cm245. It is the most abundant curium isotope mainly due to its substantial
production rate. Owing to its half-life time it decreases noticeably during off load
periods. Its production rate depends on Am243. The mass flow stabilizes after few
decades of growth depending on the initial MA fraction on a rather steady process,
where in case B (2.5%MA) the maximum mass is observed after about 50 years.
Case A reaches a broad maximum around 60-70 years, while case C later – about
90 - 100 years. After that time all cases start to converge tending to BOC mass of
about 25 kg - after around 150 years.
Cm245
21
Cm245 alpha decays to Pu241with half-life time of 8 500 years. It is produced
in neutron capture on Cm244 and removed in fission. The mass flow evolution is
determined by that of Cm244 but with a certain delay. The broad mass maximum
in case B occurs after around 70 years, while for other cases beyond analyzed EOL;
in all cases the maximum should however be below 13 kg per batch. The
equilibrium level is lower at about 8 kg and could be reached even after 2 centuries.
Cm246, Cm247, Cm248
Heavier isotopes of curium show similar patterns of mass flow in the analyzed
period, which is: growth with time. The function of growth looks exponential for low
mass fraction, below one kilogram, linear above it, and for masses of few kilograms
inflection point occurs, after which the growth slows down to reach its maximum
and eventually approach its balance level. All nuclides should eventually follow the
evolution pattern of lighter isotopes but extended in time even over two centuries
for the heavier ones. Equilibrium batch mass levels for Cm246, Cm247 and Cm248
are 5.8, 1.18 and 1.06 kg respectively.
5.2.2. Transmutation of elements
Element transmutations are dominated by one or two of the most abundant
nuclides, the masses of which convert to their equilibrium levels the earliest. They
are U238, Pu239 & Pu240, Am241 & Am243 and Cm244. As nuclide compositions
are important for nuclear physics reasons, the elements decide about fuel
chemistry, particularly of chemical stability. As shown in Figure 24,Figure 25Figure
26Figure 27, the masses of all elements convert form their BOL levels to the
equilibrium levels or close to them in analysed time of 35 cycles. Since BOL vectors
differ from the equilibrium ones we observe mass flows between elements in every
analysed strategy, which, in Table 4Table 5 and Table 6, are shown in details for
every analysed strategy – A, B and C respectively. These mass flows can be
summarised as follows.

Uranium is fully ruled by U238, its most dominant natural isotope, which mass
at BOL for cases B and C differs from that of case A - the reference one,
marginally - up to 2.5%. The most of the difference is reduced before EOL (after
35 cycles). In cases with initial MA content the uranium consumption is lower.

Plutonium consumption is highest in case C with no MA since that case
requires addition of plutonium during the first reprocessing for maintaining the
reactivity. For case B of higher MA content, less plutonium is needed since MAs
become fuel that is net burnt.

Americium is a MA component but LWR spent fuel vector contains it in higher
amount than the adiabatic composition, therefore even in the reference case
8.14% of it is burnt. For case without MA about 277 kg of Am is being produced
per batch over 14 cycles. For case B of 2.5 % MA about 288 kg of Am is net
burnt per batch, which amounts to burnout of 1440 kg Am during 35 reloading
cycles. The difference between the extreme options over 35 cycles is 2835 kg of
americium in the system inventory.

Curium is net produced in all cases since its production rate at the operating
concentrations has not saturated yet. Curium net production is lower with
22
higher concentrations, and per batch over 14 cycles equals 29.6, 34.9 and 41.8
kg in cases B, A and C respectively. The difference between the extreme options
over 35 cycles is 61 kg of curium in the system inventory.
5.2.3. Full transition to the equilibrium composition
Full transition to the equilibrium composition occurs when all nuclides have
reached their equilibrium levels. The physics of MA transmutations tells us that to
satisfy this idealistic condition the equilibrium of Cf-252 must be reached, which
will occur not earlier than after few centuries. Shorter times but longer than a
century are expected for heavier curium isotopes. In presented analysis build-up of
berkelium and californium is not included since it requires strategy definition
because of their high market possible value.
6.
Core characteristics
Calculated core characteristics contain power distribution at BOC and EOC,
used for burnup assessment (fuel power densities) and linear power ratings used
for thermal hydraulic assessments. Distributions of that functions are usually the
same, but in our case the fuel pellet has not uniform cross section therefore that
distribution differs. The burnup characteristic is presented in terms of FIMA as well
as in terms of specific energy deposition. For the safety assessments some basic
coefficients were calculated for all considered fuel scenarios.
6.1. Power distributions.
Power distributions were calculated for all considered cases at the beginning
and the end of cycle for selected representative cycles, including in all cases the 1 st
cycle, which starts at BOL. The distributions of fuel power densities that are
applicable for burnup calculations are given together with linear power ratings that
are applicable to thermal hydraulic assessment. In the most cases the CRs were
withdrawn, but in some cases the calculations were also done with the CRs fully
inserted in order to assess their influence on the considered results. Table 7 and
Table 8 show the power distribution in the reference case of MA content of 1.347%
for 1st and 35th fuel cycles respectively. Table 7Table 9 and Table 10 show the power
densities in the 1st cycle for case B and C respectively. The average fuel burnup on
discharge in terms of FIMA are shown in Table 11 for all considered cases, while in
terms of energy [MWd/kg] is shown in Table 12. Power density factors for reference
case are depicted in Figure 54 for 1st cycle and in Figure 55 for 8th cycle. For the
same cycles the power densities plots are presented for cases B and C in Figure 56,
Figure 57, Figure 58Figure 59 respectively. In that cases (B and C) power
distributions with the CR-s fully inserted are shown in Figure 60,Figure 61,Figure
62 and Figure 63. For all above cases the power distributions in terms of linear
ratings are shown in Figures fromFigure 64 to Figure 75.
6.1.1. Fuel power density
Power distributions at BOL cores are not of any concern as they are more
equalized comparing to that of the equilibrium core. Fuel power density is always
higher at BOC, where the case C with no MA has the highest peak density of 470
W/cm3. At EOC the peak density is smaller by about 2% than at BOC. In the
23
reference case the power peak at BOL is about 5% smaller than in 35 th cycle, which
has very similar power distribution to the equilibrium one.
6.1.2. Power linear ratings
The average radial form factor of linear power ratings is below 1.5 in all cases
during 1st cycle and varies marginally in the cycle. In the reference case the BOL
value of average radial form factor equals 1.454 which corresponds to the peak
ratings of 23.36 kW/m. With the time evolution the peak linear rating raises to
24.84 kW/m at equilibrium which is about 6% higher than at BOL.
6.1.3. Average burnup
Burnup is generally bounded to the constrained thermal power of the system
and the cycle period time therefore the fuel average burnup discharge values
should not fluctuate substantially. Some fluctuations in terms of specific energy
deposition can occur due to possible change of the heating fraction outside the fuel.
A part of fluctuations can be also attributed to batch to batch fluctuations since the
number of core fuel assemblies is an odd number thus slightly different amount of
HM is loaded every time. FIMA can also float slightly since the fuel vector
transmutation changes the HM vector, which affects to some extend the fission
heating number. As shown in Table 11 average discharge FIMA grows slightly with
the number of fuel reprocessing from 5.66% to 5.77% in case of reference case.
Other cases differ slightly but rather in the range of statistical fluctuations. The
FIMA peak values in all cases is similar, about 8.75% maximum. The above
numbers were obtained with CR withdrawn. The effect of the CR insertion
introduces to the distribution additional suppression of local flux, which leads to an
increment of the peak FIMA to 9.27%. The burnup in terms of specific energy is
shown in Table 12. The peak burnup in reference case equals 75.31 MWd/kg while
the average 49.64 MWd/kg.
6.2. Safety coefficients
Safety coefficient were calculated for the first cycle for all three cases and are
shown in Table 13. They were obtained with all CR withdrawn, one section above
the active core and the second section below the active core. The Doppler constants
are negative in range between 600 to 825 pcm, while the core expansion coefficient
are negative in the range of 242 to 330 pcm for 2% axial expansion, and in the
range of 822 to 942 pcm for 2% radial expansion. The void worths are generally
negative for entire vessel voiding but active core voiding is rather strongly positive.
Safety parameters do not change significantly due to different MA content or
fractions at BOL. Also voiding the vessel to the bottom fuel level brings positive void
reactivity between 906 to 1697 pcm. It was noticed that very strong effect on void
coefficients is brought by CR insertion level. In applied model all CR are in the most
remote positions from the core centre. The insertion of the bottom CRs can shift
down the void worth more than 1500 pcm (independently from bringing the
reactivity down), therefore with CR inserted the vessel voiding should decrease the
reactivity. Generally, increased MA content at BOL increases positive terms in
reactivity coefficients, therefore it will need an attention, and possible consideration
of additional reactivity countermeasures at reactor peripheries
24
7.
Conclusions

All investigated BOL cores bring the fuel into equilibrium composition.
Differences occur in time needed for reaching it.

Several nuclides are observed for transitional build-up of their mass peak before
reaching the equilibrium levels.

Temporary build-up of some actinides is increased with increasing fraction of
MA at BOL, notably Am242m, Am243, Cm243, Cm244, Cm245, Cm246 and
Cm247.

Peaking time extends with higher Z and A nuclide numbers.

Americium peaks relatively earlier whereas higher curium isotopes do peak after
50 years of reactor residence time, which corresponds to about 200 years real
time assuming 7.5 years of cooling before each fuel reprocessing.

Maximum concentrations of curium isotopes grow with initial fraction of MA and
can exceed the equilibrium level by 80%.

Strong influence of cooling periods on transmutation patterns is noticed, which
is explainable by Pu241 decay into Am241. It influences the reactivity swings in
fuel cycle as well as it sullies the nuclide fractions in the equilibrium
composition, generally increasing the content of curium.

Addition of MA from LWRs into the BOL fuel has positive influence on the
reactivity swing by both reduction of the initial excess and the reactivity loss
rate in initial cycles.

All analysed cores can be fully manageable by the designed CR system.

The fuel containing 2.5% MAs is characterised by the smallest reactivity swing.

In the core without MA at BOL about 277 kg of Am is being produced per batch
over 14 cycles, which amounts to burnout of 1440 kg Am during 35 reloading
cycles.

The core of 2.5% MA at BOL burns about 288 kg of Am per batch over 14 cycles.
The difference between the extreme options over 35 cycles is 2835 kg of
americium in the system inventory.

Curium is net produced in all cases. Its net production is lower with higher
concentrations, and equals: 29.6, 34.9 and 41.8 kg per batch over 14 cycles in
cases of 2.5% MA, 1.347% MA and no MA respectively. The difference between
the extreme options over 35 cycles is 61 kg of curium in the system inventory.
25
References
[1] EURATOM Seventh Framework Programme. Lead-cooled European Advanced
DEmonstration Reactor (LEADER). Proposal/Contract no. FP7 - 249668 (2010),
http://www.leader-fp7.eu/default.aspx.
[2] C. Artioli, G. Grasso and C. Petrovich. A new paradigm for core design aimed at
the sustainability of nuclear energy: the solution of the extended equilibrium
state. Ann. Nucl. Energy 37:915 (2010).
[3] C. Döderlein et al. Definition of the ELFR core and neutronic characterization.
Technical Report LEADER-DEL005-2011, revision 1, EURATOM, 2013.
[4] J. Cetnar, W. Gudowski and J. Wallenius "MCB: A continuous energy Monte
Carlo Burnup simulation code", In "Actinide and Fission Product Partitioning
and Transmutation", EUR 18898 EN, OECD/NEA (1999) 523.
[5] Firestone, R., B., et al.: ”Table of Isotopes, 8E” John Wiley & Sons, Inc.(1996)
[6] J. Cetnar “General solution of Bateman equations for nuclear transmutations”
Annals of Nuclear Energy Volume: 33, Issue 7, May 2006, pp. 640-645
[7] X-5 Monte Carlo Team, “MCNP — A General Monte Carlo N-Particle Transport
Code, Version 5”, LA-UR-03-1987, Los Alamos National Laboratory, 2003
26
Figures
Figure 1. Evolution of neutron multiplication factor of LFR from BOL for few fuel
strategy options basing on two-batch refuelling scheme of 900 day refuelling cycles
and 7.5 years cooling time; every batch is twice burnt and trice cooled; five batches
make the system inventory; CRs are fully withdrawn.
Figure 2. Effect of control rods insertion on criticality (k-eff) evolution of LFR core
case B with 2.5 % of MA at BOL.
Figure 3. Effect of control rods insertion on criticality (k-eff) evolution of LFR core
case C with no MA at BOL.
28
Figure 4. Comparison of criticality (k-eff) evolution assessment using coarse and
fine steps of burn-up calculation in MCB system; LFR core case C with no MA at
BOL with CR fully withdrawn.
29
Figures from 5 to 33 below concern LFR core with CR fully withdrawn and 2-batch
refuelling scheme of 900 day refuelling cycles and 7.5 years cooling time. Every
batch is twice burnt (colour lines) and trice cooled (grey lines), two batches make
core inventory, five batches make the system inventory. Three cases are shown with
0%, 1.347% and 2.5% of MA at BOL. In case of no MA, additional plutonium is
imported to every batch during their first reprocessing that increases plutonium
fraction to 18.9% of HM vector)
Figure 5. Batch mass flow of U234 in three cases of fuel strategy options
30
Figure 6. Batch mass flow of U235 in three cases of fuel strategy options
Figure 7. Batch mass flow of U236 in three cases of fuel strategy options
31
Figure 8. Batch mass flow of Np237 in three cases of fuel strategy options
Figure 9. Batch mass flow of Pu238 in three cases of fuel strategy options
32
Figure 10. Batch mass flow of Pu239 in three cases of fuel strategy options
Figure 11. Batch mass flow of Pu240 in three cases of fuel strategy options
33
Figure 12. Batch mass flow of Pu241 in three cases of fuel strategy options
Figure 13. Batch mass flow of Pu242 in three cases of fuel strategy options
34
Figure 14. Batch mass flow of Am241 in three cases of fuel strategy options
Figure 15. Batch mass flow of Am242m in three cases of fuel strategy options
35
Figure 16. Batch mass flow of Am243 in three cases of fuel strategy options
Figure 17. Batch mass flow of Cm242 in three cases of fuel strategy options
36
Figure 18. Batch mass flow of Cm243 in three cases of fuel strategy options
Figure 19. Batch mass flow of Cm244 in three cases of fuel strategy options
37
Figure 20. Batch mass flow of Cm245 in three cases of fuel strategy options
Figure 21. Batch mass flow of Cm246 in three cases of fuel strategy options
38
Figure 22. Batch mass flow of Cm247 in three cases of fuel strategy options
Figure 23. Batch mass flow of Cm248 in three cases of fuel strategy options
39
Figure 24. Batch mass flow of uranium in three cases of fuel strategy options
Figure 25. Batch mass flow of plutonium in three cases of fuel strategy options
40
Figure 26. Batch mass flow of americium in three cases of fuel strategy options
Figure 27. Batch mass flow of curium in three cases of fuel strategy options
41
Figure 28. Plutonium enrichments evolution in three cases of fuel strategy options
Figure 29. Breeding gains for every fuel batch in three cases of fuel strategy options.
Reprocessed and reloaded batches loose breeding gain during cooling time, which is
represented by the batch-charge-in staring points lowered correspondingly.
42
Figure 30. Zoom on breeding gains after 60 years form BOL evolution.
Figure 31. CR effect on breeding gains in LFR – case C without MA.
43
Figure 32. CR effect on Pu240 batch mass flow – case C without MA.
Figure 33. CR effect on Cm245 batch mass flow – case C without MA.
44
Figure 34. U235 system inventory evolution in three cases of fuel strategy options
Figure 35. Uranium system inventory evolution in three cases of fuel strategy options
45
Figure 36. Pu238 system inventory evolution in three cases of fuel strategy options
Figure 37. Pu239 system inventory evolution in three cases of fuel strategy options
46
Figure 38. Pu240 system inventory evolution in three cases of fuel strategy options
Figure 39. Pu241 system inventory evolution in three cases of fuel strategy options
47
Figure 40. Pu242 system inventory evolution in three cases of fuel strategy options
Figure 41. Plutonium system inventory evolution in three cases of fuel strategy options
48
Figure 42. Am241 system inventory evolution in three cases of fuel strategy options
Figure 43. Am242m system inventory evolution in three cases of fuel strategy options
49
Figure 44. Am243 system inventory evolution in three cases of fuel strategy options
Figure 45. Americium system inventory evolution in three cases of fuel strategy options
50
Figure 46. Cm242 system inventory evolution in three cases of fuel strategy options
Figure 47. Cm244 system inventory evolution in three cases of fuel strategy options
51
Figure 48. Cm245 system inventory evolution in three cases of fuel strategy options
Figure 49. Cm246 system inventory evolution in three cases of fuel strategy options
52
Figure 50. Cm247 system inventory evolution in three cases of fuel strategy options
Figure 51. Cm248 system inventory evolution in three cases of fuel strategy options
53
Figure 52. Curium system inventory evolution in three cases of fuel strategy options
Figure 53. MA system inventory evolution in three cases of fuel strategy options
54
1,6
1st fresh load (BOC)
Power density factor
1,4
2nd fresh load (BOC)
1st fresh load (EOC)
1,2
2nd fresh load (EOC)
1
0,8
0,6
0,4
0,2
0
1
2
3
4
5
6
7
8
Radial regions
Figure 54. Radial density power factor at beginning and end of first cycle (BOC=BOL);
LFR case A (BOL MA 1.347%); CR withdrawn
1,6
1st fresh load (BOC)
Power density factor
1,4
2nd continue load (BOC)
1st fresh load (EOC)
1,2
2nd continue load (EOC)
1
0,8
0,6
0,4
0,2
0
1
2
3
4
5
6
7
8
Radial regions
Figure 55. Radial density power factor at beginning and end of eight cycle (BOC = 17.25
years); LFR case A (BOL MA 1.347%); CR withdrawn
55
1,6
1st fresh load (BOC)
Power density factor
1,4
2nd fresh load (BOC)
1st fresh load (EOC)
1,2
2nd fresh load (EOC)
1
0,8
0,6
0,4
0,2
0
1
2
3
4
5
6
7
8
Radial regions
Figure 56. Radial density power factor at beginning and end of first cycle (BOC=BOL);
LFR case B (BOL MA 2.5%); CR withdrawn
1,6
1st fresh load (BOC)
Power density factor
1,4
2nd continue load (BOC)
1st fresh load (EOC)
1,2
2nd continue load (EOC)
1
0,8
0,6
0,4
0,2
0
1
2
3
4
5
6
7
8
Radial regions
Figure 57. Radial density power factor at beginning and end of eight cycle (BOC = 17.25
years); LFR case B (BOL MA 2.5%); CR withdrawn
56
1,6
1st fresh load (BOC)
Power density factor
1,4
2nd fresh load (BOC)
1st fresh load (EOC)
1,2
2nd fresh load (EOC)
1
0,8
0,6
0,4
0,2
0
1
2
3
4
5
6
7
8
Radial regions
Figure 58. Radial density power factor at beginning and end of first cycle (BOC=BOL);
LFR case C (no MA at BOL); CR withdrawn
1,6
1st fresh load (BOC)
Power density factor
1,4
2nd continue load (BOC)
1st fresh load (EOC)
1,2
2nd continue load (EOC)
1
0,8
0,6
0,4
0,2
0
1
2
3
4
5
6
7
8
Radial regions
Figure 59. Radial density power factor at beginning and end of eight cycle (BOC = 17.25
years); LFR case C (no MA at BOL); CR withdrawn
57
1,6
1st fresh load (BOC)
2nd fresh load (BOC)
1st fresh load (EOC)
2nd fresh load (EOC)
Power density factor
1,4
1,2
1
0,8
0,6
0,4
0,2
0
1
2
3
4
5
6
7
8
Radial regions
Figure 60. Radial density power factor at beginning and end of first cycle (BOC=BOL);
LFR case B (BOL MA 2.5%); CR fully inserted
1,6
1st fresh load (BOC)
2nd continue load (BOC)
1st fresh load (EOC)
2nd continue load (EOC)
Power density factor
1,4
1,2
1
0,8
0,6
0,4
0,2
0
1
2
3
4
5
6
7
8
Radial regions
Figure 61. Radial density power factor at beginning and end of eight cycle (BOC = 17.25
years); LFR case B (BOL MA 2.5%); CR fully inserted
58
1,6
1st fresh load (BOC)
Power density factor
1,4
2nd fresh load (BOC)
1st fresh load (EOC)
1,2
2nd fresh load (EOC)
1
0,8
0,6
0,4
0,2
0
1
2
3
4
5
6
7
8
Radial regions
Figure 62. Radial density power factor at beginning and end of first cycle (BOC=BOL);
LFR case C (no MA at BOL); CR fully inserted
1,6
1st fresh load (BOC)
Power density factor
1,4
2nd continue load (BOC)
1st fresh load (EOC)
1,2
2nd continue load (EOC)
1
0,8
0,6
0,4
0,2
0
1
2
3
4
5
6
7
8
Radial regions
Figure 63. Radial density power factor at beginning and end of eight cycle (BOC = 17.25
years); LFR case C (no MA at BOL); CR fully inserted
59
1,6
1st fresh load (BOC)
Linear power factor
1,4
2nd fresh load (BOC)
1st fresh load (EOC)
1,2
2nd fresh load (EOC)
1
0,8
0,6
0,4
0,2
0
1
2
3
4
5
6
7
8
Radial regions
Figure 64. Linear power factor at beginning and end of first cycle (BOC=BOL); LFR case
A (BOL MA 1.347%); CR withdrawn
1,6
1st fresh load (BOC)
Linear power factor
1,4
2nd continue load (BOC)
1st fresh load (EOC)
1,2
2nd continue load (EOC)
1
0,8
0,6
0,4
0,2
0
1
2
3
4
5
6
7
8
Radial regions
Figure 65. Linear power factor at beginning and end of 8th cycle (BOC = 17.25 years);
LFR case A (BOL MA 1.347%); CR withdrawn
60
1,6
1st fresh load (BOC)
Linear power factor
1,4
2nd fresh load (BOC)
1st fresh load (EOC)
1,2
2nd fresh load (EOC)
1
0,8
0,6
0,4
0,2
0
1
2
3
4
5
6
7
8
Radial regions
Figure 66. Linear power factor at beginning and end of first cycle (BOC=BOL); LFR case
B (BOL MA 2.5%); CR withdrawn
1,6
1st fresh load (BOC)
Linear power factor
1,4
2nd continue load (BOC)
1st fresh load (EOC)
1,2
2nd continue load (EOC)
1
0,8
0,6
0,4
0,2
0
1
2
3
4
5
6
7
8
Radial regions
Figure 67. Linear power factor at beginning and end of 8th cycle (BOC = 17.25 years);
LFR case B (BOL MA 2.5%); CR withdrawn
61
1,6
1st fresh load (BOC)
Linear power factor
1,4
2nd fresh load (BOC)
1st fresh load (EOC)
1,2
2nd fresh load (EOC)
1
0,8
0,6
0,4
0,2
0
1
2
3
4
5
6
7
8
Radial regions
Figure 68. Linear power factor at beginning and end of 1 st cycle (BOC=BOL); LFR case C
(no MA at BOL); CR withdrawn
1,6
1st fresh load (BOC)
Linear power factor
1,4
2nd continue load (BOC)
1st fresh load (EOC)
1,2
2nd continue load (EOC)
1
0,8
0,6
0,4
0,2
0
1
2
3
4
5
6
7
8
Radial regions
Figure 69. Linear power factor at beginning and end of 8th cycle (BOC = 17.25 years);
LFR case C (no MA at BOL); CR withdrawn
62
1,6
1st fresh load (BOC)
Linear power factor
1,4
2nd continue load (BOC)
1st fresh load (EOC)
1,2
2nd continue load (EOC)
1
0,8
0,6
0,4
0,2
0
1
2
3
4
5
6
7
8
Radial regions
Figure 70. Linear power factor at beginning and end of 8 th cycle (BOC = 17.25 years);
LFR case C (no MA at BOL); CR withdrawn
1,6
1st fresh load (BOC)
Linear power factor
1,4
2nd continue load (BOC)
1st fresh load (EOC)
1,2
2nd continue load (EOC)
1
0,8
0,6
0,4
0,2
0
1
2
3
4
5
6
7
8
Radial regions
Figure 71. Linear power factor at beginning and end of 8 th cycle (BOC = 17.25 years);
LFR case C (no MA at BOL); CR withdrawn
63
1,6
1st fresh load (BOC)
Linear power factor
1,4
2nd fresh load (BOC)
1st fresh load (EOC)
1,2
2nd fresh load (EOC)
1
0,8
0,6
0,4
0,2
0
1
2
3
4
5
6
7
8
Radial regions
Figure 72. Linear power factor at beginning and end of first cycle (BOC=BOL); LFR case
B (BOL MA 2.5%); CR fully inserted
1,6
1st fresh load (BOC)
2nd continue load (BOC)
Linear power factor
1,4
1st fresh load (EOC)
1,2
2nd continue load (EOC)
1
0,8
0,6
0,4
0,2
0
1
2
3
4
5
6
7
8
Radial regions
Figure 73. Linear power factor at beginning and end of eight cycle (BOC = 17.25 years);
LFR case B (BOL MA 2.5%); CR fully inserted
64
1,6
1st fresh load (BOC)
Linear power factor
1,4
2nd fresh load (BOC)
1st fresh load (EOC)
1,2
2nd fresh load (EOC)
1
0,8
0,6
0,4
0,2
0
1
2
3
4
5
6
7
8
Radial regions
Figure 74. Linear power factor at beginning and end of first cycle (BOC=BOL); LFR case
C (no MA at BOL); CR fully inserted
1,6
1st fresh load (BOC)
Linear power factor
1,4
2nd continue load (BOC)
1st fresh load (EOC)
1,2
2nd continue load (EOC)
1
0,8
0,6
0,4
0,2
0
1
2
3
4
5
6
7
8
Radial regions
Figure 75. Linear power factor at beginning and end of eight cycle (BOC = 17.25 years);
LFR case C (no MA at BOL); CR fully inserted
65
Tables
Table 1. Comparison of fuel vectors and compositions at BOL and in adiabatic
equilibrium in reference case of 1.347% MA.
Vector
fraction
Nuclide
in HM
[wt%]
Uranium vector
U233
U234
80.50%
U235
U236
U238
Plutonium vector
Nuclide fraction in HM
[wt%]
Nuclide fraction in the
vector [wt%]
Element fraction in
the vector [wt%]
BOL
Adiabatic
BOL
Adiabatic
0.0020%
0.325%
0.008%
80.17%
0.000015%
0.253%
0.094%
0.181%
79.97%
0.0025%
0.40%
0.010%
99.58%
0.000018%
0.31%
100%
0.12%
0.22%
99.34%
100%
0.479%
9.86%
6.65%
0.483%
0.679%
0.00035%
2.33%
56.87%
27.00%
6.10%
7.69%
-
2.64%
54.35%
36.61%
2.66%
3.74%
0.0019%
100%
100%
0.112%
0.814%
0.058%
0.208%
0.0001%
0.0022%
0.0913%
0.0305%
0.0218%
0.0044%
0.0040%
3.81%
75.41%
0.254%
16.17%
0.067%
3.04%
1.16%
0.090%
0.0017%
0.0001%
8.35%
60.42%
4.33%
15.45%
0.011%
0.163%
6.78%
2.26%
1.62%
0.32%
0.29%
3.81%
8.35%
91.84%
80.20%
4.35%
11.45%
Pu238
0.423%
Pu239
10.32%
Pu240
4.90%
18.15%
Pu241
1.108%
Pu242
1.396%
Pu244
MA vector (Np+Am+Cm)
Np237
0.051%
Am241
1.016%
Am242m
0.003%
Am243
0.218%
Cm242
1.347% 0.0009%
Cm243
Cm244
0.041%
Cm245
0.016%
Cm246
0.0012%
Cm247
0.000023%
Cm248
0.000002%
BOL
Adiabatic
Table 2. Reactivity evolution with control rod effect in LFR case B, with fuel cycle
strategy using 2.5% MA at BOL.
CR OUT
BOS
Time
0
2.4641
4.9281
7.3922
9.8563
12.32
14.784
17.248
19.713
22.177
24.641
27.105
29.569
32.033
34.497
36.961
39.425
41.889
44.353
46.817
49.281
51.745
54.209
56.674
59.138
61.602
64.066
66.53
68.994
71.458
73.922
76.386
78.85
81.314
CR IN
Reactivity [pcm]
Reactivity
swing
BOC
EOC
On load
3614±32
3073±35
3054±35
3091±30
1826±33
1098±37
1049±34
1039±32
970±27
833±33
735±34
794±33
685±35
646±35
754±32
764±36
715±33
764±32
744±34
813±33
784±32
705±32
735±30
813±32
774±30
725±33
754±32
715±34
784±32
764±30
774±35
695±32
685±33
666±31
2458±37
1749±32
1749±35
1768±31
1196±29
675±31
695±29
725±30
666±32
656±31
577±30
567±30
606±30
596±31
656±33
587±31
587±32
626±31
547±33
626±27
626±31
587±25
626±32
626±33
596±30
606±30
577±30
606±34
606±34
675±32
636±31
567±34
587±32
587±33
646±32
83.778 685±31
Reactivity [pcm]
Reactivity
swing [pcm
Off load
BOC
EOC
On load
Off load
-1156±49
-1324±47
-1305±49
-1323±43
-631±44
-422±48
-354±45
-314±44
-305±42
-177±45
-158±46
-227±44
-79±46
-49±47
-99±46
-178±48
-128±46
-138±44
-197±47
-187±43
-158±45
-118±41
-109±44
-187±46
-178±43
-118±45
-178±44
-109±48
-178±47
-89±43
-138±47
-128±47
-99±46
-79±45
615±51
1305±47
1343±46
58±45
-98±47
373±46
344±44
246±40
167±46
79±46
217±45
119±46
40±46
158±44
108±49
128±46
178±45
118±46
266±47
158±42
79±45
148±39
187±45
148±45
128±45
148±44
138±45
178±47
158±45
99±47
59±45
119±47
79±45
99±45
-1638±35
-2443±34
-2370±38
-2417±37
-3842±35
-4810±36
-4853±34
-4888±35
-4899±35
-5109±36
-5389±33
-5504±36
-5353±30
-5422±32
-5452±36
-5475±39
-5522±33
-5555±32
-5641±33
-5559±31
-5631±34
-5729±30
-5672±30
-5702±32
-5635±32
-5572±31
-5681±35
-5726±33
-5617±35
-5630±38
-5752±30
-5779±31
-5763±31
-5867±36
-3191±34
-3991±32
-3976±33
-3964±36
-4778±31
-5340±31
-5339±29
-5467±34
-5333±32
-5519±33
-5646±31
-5817±32
-5738±29
-5762±32
-5716±35
-5710±31
-5845±34
-5795±31
-5826±33
-5770±36
-5806±36
-5864±30
-5813±35
-5854±32
-5850±35
-5961±27
-5922±33
-5837±31
-5894±33
-5890±33
-5856±29
-5923±31
-5985±33
-5924±33
-1552±49
-1548±47
-1606±50
-1547±52
-936±47
-530±48
-486±45
-580±48
-434±48
-409±49
-257±46
-313±48
-385±42
-340±45
-264±50
-235±50
-323±48
-240±44
-184±47
-211±47
-174±49
-134±42
-141±46
-152±45
-216±47
-389±41
-241±48
-111±45
-277±48
-259±50
-104±42
-145±44
-222±45
-57±49
747±48
1621±49
1559±49
122±51
-32±48
487±46
451±45
569±49
224±48
130±47
142±48
464±44
317±43
310±48
241±52
189±46
289±47
154±45
267±45
139±49
76±47
191±42
112±47
219±45
278±47
280±44
196±47
220±47
264±51
138±45
77±43
160±44
118±49
96±47
-39±44
-
-5828±34 -5858±28
Additional
swing due
to full CR
insertion
[pcm]
-263
-171
-256
-415
-655
-649
-674
-616
-690
-870
-1045
-785
-815
-953
-986
-984
-1067
-1133
-1119
-1162
-1182
-1154
-1262
-1156
-1044
-1183
-1188
-1148
-1141
-1273
-1221
-1195
-1280
-1260
-30±44
67
Table 3. Reactivity evolution with control rod effect in LFR case C, with fuel cycle
strategy using no MA at BOL. Off load reactivity swing after eight initial cycles
includes effect of adding plutonium in the first reloads and reprocessing of each
batch.
CR OUT
BOS
Time
0
2.4641
4.9281
7.3922
9.8563
12.32
14.784
17.248
19.713
22.177
24.641
27.105
29.569
32.033
34.497
36.961
39.425
41.889
44.353
46.817
49.281
51.745
54.209
56.674
59.138
61.602
64.066
66.53
68.994
71.458
73.922
76.386
78.85
81.314
83.778
CR IN
Reactivity [pcm]
Reactivity
swing
BOC
EOC
On load
4771±32
4735±35
4726±35
4717±30
4997±33
5096±37
4689±34
4689±32
4726±27
3251±33
2277±34
2162±33
2210±35
2095±35
1546±32
1049±36
1049±33
1059±32
1049±34
744±33
705±32
646±32
656±30
606±32
398±30
498±33
458±32
478±34
488±32
339±30
339±35
448±32
478±33
448±31
319±31
2286±37
2105±32
2133±35
2200±31
2733±29
3016±31
2865±29
2847±30
2828±32
1874±31
1303±30
1205±30
1235±30
1254±31
843±33
626±31
626±32
616±31
567±33
448±27
369±31
329±25
279±32
369±33
379±30
359±30
339±30
259±34
359±34
319±32
299±31
309±34
349±32
379±33
339±32
-2484±49
-2630±47
-2592±49
-2516±43
-2264±44
-2080±48
-1824±45
-1843±44
-1898±42
-1377±45
-974±46
-957±44
-975±46
-841±47
-703±46
-423±48
-423±46
-442±44
-482±47
-296±43
-336±45
-317±41
-376±44
-238±46
-20±43
-139±45
-119±44
-218±48
-129±47
-20±43
-40±47
-139±47
-129±46
-69±45
20±44
Reactivity [pcm]
Reactivity
swing [pcm
Off load
BOC
EOC
On load
Off load
2448±51
2621±47
2583±46
2797±45
2363±47
1673±46
1824±44
1879±40
423±46
403±46
859±45
1005±46
861±46
292±44
206±49
423±46
433±45
433±46
178±47
257±42
277±45
327±39
327±45
30±45
119±45
99±44
139±45
228±47
-20±45
20±47
149±45
169±47
99±45
-60±45
-
-829±35
-934±37
-834±34
-939±37
-636±29
-747±29
-1061±33
-1063±32
-1119±34
-2601±36
-3841±31
-3974±30
-3944±36
-4046±30
-4754±37
-5260±36
-5270±34
-5243±34
-5237±33
-5578±34
-5834±34
-5698±32
-5783±34
-5896±31
-5984±35
-6126±32
-5984±32
-6042±30
-6061±33
-6151±33
-6170±29
-6059±28
-6203±38
-6054±31
-6076±31
-3618±32
-3761±34
-3792±29
-3773±34
-3211±30
-2954±33
-3046±34
-3076±34
-3112±31
-4122±31
-4860±30
-4996±36
-5002±32
-4976±30
-5516±31
-5776±33
-5793±33
-5825±32
-5811±34
-5952±33
-6082±32
-6108±27
-6122±35
-6045±35
-6220±30
-6171±30
-6165±28
-6179±30
-6218±31
-6247±31
-6173±31
-6212±32
-6200±32
-6288±31
-6280±30
-2790±47
-2828±50
-2958±45
-2834±51
-2575±42
-2207±44
-1985±47
-2013±46
-1993±46
-1521±48
-1019±43
-1022±47
-1059±48
-929±43
-763±48
-517±49
-523±48
-581±47
-575±47
-375±47
-248±46
-409±42
-339±48
-148±47
-236±46
-45±44
-181±42
-136±43
-157±46
-96±46
-3±42
-153±43
3±50
-234±44
-204±43
2685±49
2927±48
2853±48
3137±45
2464±42
1893±47
1983±46
1956±48
511±48
281±43
886±42
1052±51
956±44
222±47
257±48
507±47
550±47
588±46
233±48
119±47
383±45
324±44
226±46
61±50
95±44
187±44
123±41
117±45
67±46
78±43
114±42
9±50
146±45
212±44
Additional
swing due to
full CR
insertion
[pcm]
-69
40
-55
-33
-243
-151
-153
-245
-252
-518
-536
-554
-542
-700
-709
-719
-702
-686
-722
-939
-744
-839
-903
-782
-1023
-842
-920
-949
-891
-909
-907
-1081
-902
-795
68
Table 4. Nuclide mass flow in selected points of fuel reprocessing and recycling.
Second batch of LFR case A, with reference fuel cycle strategy using 1.347% MA at
BOL.
BOL content
Pu 18.15%
MA 1.347%
A
B
C
D
BOL
4.93 [y]
End of 2nd
cycle
12.32 [y]
After 1st
reprocess.
86.24 [y]
After 7th
reprocess.
[g]
Change
B-A
C-A
D-A
[%]
U234
6.42E+02
4.64E+03
1.20E+04
5.18E+04
623%
1775%
7971%
U235
8.64E+04
5.33E+04
5.97E+04
2.78E+04
-38.30%
-30.93%
-67.84%
U236
2.14E+03
9.86E+03
1.11E+04
3.06E+04
361%
417%
1329%
U238
2.13E+07
1.99E+07
2.14E+07
2.13E+07
-6.42%
0.29%
0.01%
U
2.14E+07
2.00E+07
2.15E+07
2.14E+07
-6.49%
0.27%
0.11%
Np237
1.36E+04
1.68E+04
1.76E+04
2.52E+04
23.02%
29.03%
84.73%
Pu238
1.13E+05
1.23E+05
1.23E+05
1.22E+05
9.56%
9.50%
8.60%
Pu239
2.74E+06
2.71E+06
2.71E+06
2.66E+06
-1.34%
-1.27%
-3.01%
Pu240
1.30E+06
1.37E+06
1.37E+06
1.64E+06
5.02%
5.41%
25.99%
Pu241
2.94E+05
2.19E+05
1.52E+05
1.13E+05
-25.69%
-48.21%
-61.67%
Pu242
3.71E+05
3.54E+05
3.54E+05
2.42E+05
-4.59%
-4.57%
-34.69%
Pu244
0.00E+00
7.77E+00
7.77E+00
5.04E+01
-
-
-
Pu
4.82E+06
4.77E+06
4.71E+06
4.78E+06
-1.10%
-2.33%
-0.93%
Am241
2.70E+05
2.24E+05
2.87E+05
2.06E+05
-16.97%
6.43%
-23.83%
Am242m
9.11E+02
1.23E+04
1.19E+04
1.61E+04
1248%
1202%
1669%
Am243
5.79E+04
7.18E+04
7.18E+04
8.03E+04
24.05%
23.97%
38.65%
Am
3.29E+05
3.08E+05
3.71E+05
3.02E+05
-6.25%
12.83%
-8.14%
Cm242
0.00E+00
7.18E+03
2.88E+01
3.91E+01
-
-
-
Cm243
2.39E+02
6.13E+02
5.11E+02
5.50E+02
157%
114%
130%
Cm244
1.09E+04
2.53E+04
1.90E+04
3.43E+04
133%
74.85%
216%
Cm245
4.14E+03
4.74E+03
4.74E+03
1.10E+04
14.33%
14.26%
166%
Cm246
3.23E+02
7.17E+02
7.17E+02
4.07E+03
122%
122%
1160%
Cm247
6.05E+00
4.97E+01
4.97E+01
6.00E+02
722%
722%
9812%
Cm248
4.93E-01
3.25E+00
3.25E+00
1.43E+02
560%
560%
28940%
Cm
1.53E+04
3.80E+04
2.51E+04
5.02E+04
148%
63.26%
227%
69
Table 5. Nuclide mass flow in selected points of fuel reprocessing and recycling.
Second batch of LFR case B, with fuel cycle strategy using 2.5% MA at BOL.
BOL content
A
B
C
D
BOL
4.93 [y]
End of 2nd
cycle
12.32 [y]
After 1st
reprocess.
86.24 [y]
After 7th
reprocess.
U234
[g]
6.35E+02
5.23E+03
1.48E+04
U235
8.56E+04
5.29E+04
U236
2.12E+03
U238
Pu 18.15%
MA 2.50%
Change
B-A
C-A
D-A
6.57E+04
723%
2225%
10244%
5.94E+04
3.05E+04
-38.12%
-30.64%
-64.40%
9.69E+03
1.09E+04
3.11E+04
357%
414%
1370%
2.11E+07
1.97E+07
2.12E+07
2.12E+07
-6.41%
0.41%
0.73%
U
2.12E+07
1.98E+07
2.13E+07
2.14E+07
-6.48%
0.40%
0.91%
Np237
2.53E+04
2.60E+04
2.86E+04
2.81E+04
2.55%
12.88%
10.91%
Pu238
1.10E+05
1.57E+05
1.60E+05
1.44E+05
42.13%
44.58%
30.04%
Pu239
2.69E+06
2.66E+06
2.67E+06
2.65E+06
-1.00%
-0.93%
-1.40%
Pu240
1.28E+06
1.34E+06
1.35E+06
1.63E+06
4.99%
5.71%
27.80%
Pu241
2.89E+05
2.14E+05
1.49E+05
1.11E+05
-25.90%
-48.35%
-61.39%
Pu242
3.64E+05
3.56E+05
3.56E+05
2.52E+05
-2.12%
-2.09%
-30.76%
Pu244
0.00E+00
1.21E+01
1.21E+01
6.04E+01
-
-
-
Pu
4.73E+06
4.73E+06
4.68E+06
4.79E+06
0.01%
-1.06%
1.30%
Am241
5.01E+05
3.75E+05
4.35E+05
2.16E+05
-25.13%
-13.17%
-56.86%
Am242m
1.69E+03
2.13E+04
2.06E+04
1.82E+04
1162%
1120%
975%
Am243
1.07E+05
1.06E+05
1.06E+05
8.77E+04
-0.97%
-1.03%
-18.34%
Am
6.10E+05
5.03E+05
5.62E+05
3.22E+05
-17.59%
-7.89%
-47.22%
Cm242
0.00E+00
1.20E+04
5.01E+01
4.41E+01
-
-
-
Cm243
4.43E+02
1.07E+03
8.95E+02
6.15E+02
142%
102%
38.7%
Cm244
2.02E+04
4.20E+04
3.15E+04
3.85E+04
108%
56.27%
91.04%
Cm245
7.69E+03
8.46E+03
8.45E+03
1.30E+04
9.97%
9.90%
69.03%
Cm246
6.00E+02
1.31E+03
1.31E+03
5.47E+03
119%
119%
812%
Cm247
1.13E+01
9.10E+01
9.10E+01
8.49E+02
706%
706%
7419%
Cm248
9.03E-01
5.99E+00
5.99E+00
2.19E+02
563%
563%
24100%
Cm
2.85E+04
6.39E+04
4.23E+04
5.81E+04
124%
48.66%
104%
70
Table 6. Nuclide mass flow in selected points of fuel reprocessing and recycling.
Second batch of LFR case C, with fuel cycle strategy using no MA at BOL.
A’
BOL content A
B
Pu 18.1%
MA 0%
4.93 [y]
12.32 [y]
12.32 [y]
86.24 [y]
B-A
st
st
st
End of 1 Added in 1 After 1
After 7th
cycle
reprocess. reprocess. reprocess.
BOL
C
D
Transmutation change
C-(A+A’) D-(A+A’)
U234
[g]
6.53E+02 3.83E+03 3.24E+01
8.49E+03
3.68E+04
[%]
487%
U235
8.79E+04 5.32E+04 4.37E+03
5.82E+04
2.49E+04
-39.45% -36.92% -73.01%
U236
2.18E+03 1.03E+04 1.08E+02
1.14E+04
3.00E+04
371%
398%
1211%
U238
2.17E+07 2.02E+07 1.08E+06
2.13E+07
2.13E+07
-6.64%
-6.50%
-6.50%
U
2.18E+07 2.03E+07 1.08E+06
2.14E+07
2.14E+07
-6.71%
-6.47%
-6.47%
Np237
0.00E+00 6.31E+03 0.00E+00
4.97E+03
2.23E+04
-
-37.74% 0.00%
Pu238
1.12E+05 8.05E+04 8.47E+03
8.57E+04
1.01E+05
-28.24% -28.86% -16.16%
Pu239
2.74E+06 2.72E+06 2.07E+05
2.93E+06
2.67E+06
-0.64%
-0.58%
-9.40%
Pu240
1.30E+06 1.37E+06 9.81E+04
1.47E+06
1.67E+06
5.51%
5.14%
19.45%
Pu241
2.94E+05 2.20E+05 2.22E+04
1.75E+05
1.16E+05
-25.23% -44.66% -63.31%
Pu242
3.70E+05 3.42E+05 2.80E+04
3.70E+05
2.40E+05
-7.56%
-7.04%
-39.70%
Pu244
0.00E+00 2.79E+00 0.00E+00
2.79E+00
3.89E+01
-
-
-
Pu
4.81E+06 4.73E+06 3.63E+05
5.03E+06
4.80E+06
-1.66%
-2.76%
-7.21%
Am241
0.00E+00 4.78E+04 0.00E+00
1.13E+05
1.99E+05
-
-
-
Am242m
0.00E+00 1.56E+03 0.00E+00
1.51E+03
1.42E+04
-
-
-
Am243
0.00E+00 3.17E+04 0.00E+00
3.17E+04
7.43E+04
-
-
-
Am
0.00E+00 8.10E+04 0.00E+00
1.46E+05
2.87E+05
-
-
-
Cm242
0.00E+00 1.42E+03 0.00E+00
3.67E+00
3.45E+01
-
-
-
Cm243
0.00E+00 6.30E+01 0.00E+00
5.25E+01
4.90E+02
-
-
-
Cm244
0.00E+00 5.84E+03 0.00E+00
4.38E+03
3.02E+04
-
-
-
Cm245
0.00E+00 3.96E+02 0.00E+00
3.96E+02
8.88E+03
-
-
-
Cm246
0.00E+00 1.62E+01 0.00E+00
1.62E+01
2.36E+03
-
-
-
Cm247
0.00E+00 4.91E-01
0.00E+00
4.91E-01
2.90E+02
-
-
-
Cm248
0.00E+00 1.32E-02
0.00E+00
1.32E-02
4.71E+01
-
-
-
Cm
0.00E+00 7.67E+03 0.00E+00
4.85E+03
4.18E+04
-
-
-
1139%
5269%
71
Table 7. Fuel power density and rating distribution in the first fuel cycle from BOL of
LFR – Case A (initial MA content 1.347%)
BOL
Total Power in
burnable zones
Average Power
Density
Total Form Factor
Average radial Form
Factor
1.496E+09 [W]
259.7 [W/ccm]
1.762
1.454
Average Radial
Power Density
[W/ccm]
Maximum Radial
Power Density
[W/ccm]
Average Linear
Radial Power
[kW]/[m]
Maximum Linear
Radial Power
[kW]/[m]
1st fresh 2nd fresh 1st fresh 2nd fresh 1st fresh 2nd fresh 1st fresh 2nd fresh
load
load
load
load
load
load
load
load
377.58
377.41
455.95
457.49
19.28
19.27
23.28
23.36
358.66
357.16
436.17
431.55
18.31
18.23
22.27
22.03
340.17
342.63
413.19
416.79
17.37
17.49
21.09
21.28
313.22
313.18
385.65
384.87
18.94
18.94
23.32
23.28
274.51
274.54
338.28
337.48
16.60
16.60
20.46
20.41
226.81
227.57
278.49
279.34
13.72
13.76
16.84
16.89
169.93
169.58
207.25
207.99
10.28
10.26
12.53
12.58
129.62
129.77
158.06
159.12
7.84
7.85
9.56
9.62
End of 1st cycle (900 days)
Total Power in
burnable zones
Average Power
Density
Total Form Factor
Average radial Form
Factor
1.465E+09 [W]
254.0 [W/ccm]
1.746
1.454
Average Radial
Power Density
[W/ccm]
Maximum Radial
Power Density
[W/ccm]
Average Linear
Radial Power
[kW]/[m]
Maximum Linear
Radial Power
[kW]/[m]
1st fresh 2nd fresh 1st fresh 2nd fresh 1st fresh 2nd fresh 1st fresh 2nd fresh
load
load
load
load
load
load
load
load
369.26
368.66
438.78
441.13
18.85
18.82
22.40
22.52
352.60
352.44
419.20
419.24
18.00
17.99
21.40
21.40
333.40
332.25
400.99
399.64
17.02
16.96
20.47
20.40
304.47
304.24
366.48
369.24
18.41
18.40
22.16
22.33
267.84
268.38
325.75
327.36
16.20
16.23
19.70
19.80
221.99
221.99
271.10
269.93
13.43
13.42
16.39
16.32
166.58
166.78
201.77
201.78
10.07
10.09
12.20
12.20
127.45
127.44
155.05
155.37
7.71
7.71
9.38
9.40
72
Table 8 Fuel power density and rating distribution in 35th fuel cycle (from 83.8 years)
of LFR – Case A (initial MA content 1.347%)
BOC (83.778 years)
Total Power in
burnable zones
Average Power
Density
Total Form Factor
Average radial Form
Factor
1.479E+09 [W]
256.8 [W/ccm]
1.894
1.564
Average Radial
Power Density
[W/ccm]
Maximum Radial
Power Density
[W/ccm]
Average Linear
Radial Power
[kW]/[m]
Maximum Linear
Radial Power
[kW]/[m]
1st fresh
2nd load
load
1st fresh
2nd load
load
1st fresh
1st fresh
2nd load
2nd load
load
load
401.54
394.69
486.48
478.96
20.50
20.15
24.84
24.45
372.04
366.47
450.66
444.11
18.99
18.71
23.01
22.67
343.13
338.45
415.91
409.32
17.52
17.28
21.23
20.90
308.29
305.65
374.62
374.09
18.64
18.48
22.66
22.62
267.46
265.26
329.41
326.38
16.18
16.04
19.92
19.74
219.99
217.74
271.25
267.68
13.30
13.17
16.40
16.19
162.50
162.13
199.34
197.75
9.83
9.81
12.06
11.96
122.67
122.14
148.80
148.04
7.42
7.39
9.00
8.95
EOC (86.242 years)
Total Power in
burnable zones
Average Power
Density
Total Form Factor
Average radial Form
Factor
1.463E+09 [W]
254.0 [W/ccm]
1.774
1.468
Average Radial
Power Density
[W/ccm]
Maximum Radial
Power Density
[W/ccm]
Average Linear
Radial Power
[kW]/[m]
Maximum Linear
Radial Power
[kW]/[m]
1st fresh
1st fresh
1st fresh
1st fresh
2nd load
2nd load
2nd load
2nd load
load
load
load
load
371.53
372.93
447.96
450.47
18.97
19.04
22.87
23.00
353.35
356.16
422.82
429.52
18.04
18.18
21.59
21.93
331.40
333.80
399.64
403.54
16.92
17.04
20.40
20.60
302.28
305.72
367.42
372.84
18.28
18.49
22.22
22.55
268.19
269.41
325.05
329.65
16.22
16.29
19.66
19.94
223.30
222.02
271.73
270.10
13.50
13.43
16.43
16.33
165.56
165.76
202.26
202.79
10.01
10.02
12.23
12.26
125.08
124.71
151.84
152.12
7.56
7.54
9.18
9.20
73
Table 9. Fuel power density and rating distribution in the first fuel cycle from BOL of
LFR – Case B (Initial MA content 2.5%) BOL
BOL
Total Power in
burnable zones
Average Power
Density
Total Form Factor
Average radial Form
Factor
1.495E+09 [W]
259.7 [W/ccm]
1.793
1.485
Average Radial
Power Density
[W/ccm]
Maximum Radial
Power Density
[W/ccm]
Average Linear
Radial Power
[kW]/[m]
Maximum Linear
Radial Power
[kW]/[m]
1st fresh 2nd fresh 1st fresh 2nd fresh 1st fresh 2nd fresh 1st fresh 2nd fresh
load
load
load
load
load
load
load
load
385.69
384.52
465.46
462.94
19.69
19.63
23.76
23.63
364.93
364.63
439.37
439.02
18.63
18.61
22.43
22.41
341.33
340.41
409.75
410.47
17.42
17.38
20.92
20.95
309.45
310.64
373.93
377.92
18.71
18.79
22.61
22.85
272.67
272.95
332.55
330.10
16.49
16.51
20.11
19.96
224.77
226.02
273.32
275.55
13.59
13.67
16.53
16.66
169.03
168.53
205.60
204.79
10.22
10.19
12.43
12.38
128.57
128.45
156.86
155.47
7.78
7.77
9.49
9.40
End of 1st cycle (900 days)
Total Power in
burnable zones
Average Power
Density
Total Form Factor
Average radial Form
Factor
1.461E+09 [W]
253.7 [W/ccm]
1.703
1.410
Average Radial
Power Density
[W/ccm]
Maximum Radial
Power Density
[W/ccm]
Average Linear
Radial Power
[kW]/[m]
Maximum Linear
Radial Power
[kW]/[m]
1st fresh 2nd fresh 1st fresh 2nd fresh 1st fresh 2nd fresh 1st fresh 2nd fresh
load
load
load
load
load
load
load
load
357.74
355.41
432.09
425.37
18.26
18.14
22.06
21.72
346.99
346.73
417.88
419.12
17.71
17.70
21.33
21.40
331.32
331.04
398.46
398.10
16.91
16.90
20.34
20.32
306.06
305.14
371.93
368.62
18.51
18.45
22.49
22.29
270.14
270.19
328.40
328.74
16.34
16.34
19.86
19.88
226.29
225.17
276.45
274.99
13.68
13.62
16.72
16.63
167.72
168.76
204.70
205.01
10.14
10.21
12.38
12.40
128.11
127.61
154.32
155.15
7.75
7.72
9.33
9.38
74
Table 10 Fuel power density and rating distribution in the first fuel cycle from BOL of
LFR – Case C (Initial MA content 0%) BOL
BOL
Total Power in
burnable zones
Average Power
Density
Total Form Factor
Average radial Form
Factor
1.496E+09 [W]
259.7 [W/ccm]
1.809
1.494
Average Radial
Power Density
[W/ccm]
Maximum Radial
Power Density
[W/ccm]
Average Linear
Radial Power
[kW]/[m]
Maximum Linear
Radial Power
[kW]/[m]
1st fresh 2nd fresh 1st fresh 2nd fresh 1st fresh 2nd fresh 1st fresh 2nd fresh
load
load
load
load
load
load
load
load
371.59
387.97
448.69
469.70
18.97
19.81
22.91
23.98
354.71
371.23
430.41
449.15
18.11
18.95
21.97
22.93
334.24
349.62
404.49
423.48
17.06
17.85
20.65
21.62
306.45
320.59
373.10
390.18
18.53
19.39
22.56
23.60
267.59
279.38
328.78
341.02
16.18
16.90
19.88
20.62
218.75
230.81
269.87
283.81
13.23
13.96
16.32
17.16
163.51
171.95
200.19
210.61
9.89
10.40
12.11
12.74
126.29
132.25
153.88
161.97
7.64
8.00
9.31
9.80
End of 1st cycle (900 days)
Total Power in
burnable zones
Average Power
Density
Total Form Factor
Average radial Form
Factor
1.465E+09 [W]
254.3 [W/ccm]
1.747
1.467
Average Radial
Power Density
[W/ccm]
Maximum Radial
Power Density
[W/ccm]
Average Linear
Radial Power
[kW]/[m]
Maximum Linear
Radial Power
[kW]/[m]
1st fresh 2nd fresh 1st fresh 2nd fresh 1st fresh 2nd fresh 1st fresh 2nd fresh
load
load
load
load
load
load
load
load
362.82
372.97
435.39
444.30
18.52
19.04
22.23
22.68
342.03
355.15
406.39
422.85
17.46
18.13
20.75
21.59
325.13
334.91
390.50
400.44
16.60
17.10
19.94
20.44
298.86
308.34
361.55
373.02
18.07
18.65
21.86
22.56
263.84
274.24
322.01
333.67
15.96
16.58
19.47
20.18
220.96
228.16
269.44
278.52
13.36
13.80
16.29
16.84
166.05
172.64
202.49
210.79
10.04
10.44
12.25
12.75
127.71
133.64
154.03
161.58
7.72
8.08
9.32
9.77
75
Table 11. FIMA on discharge of the first batch in seven service cycles (1800 days) in
LFR with three fuel strategy options
Average FIMA [%] on discharge
Discharge
time [year]
Full
cycles in
service
CASE_A
(MA
1.347%)
CASE_B
(MA 2.5 %)
CASE_C
(MA 0%)
CASE_C
(MA 0%)
CR in
4.93
1
5.66
5.69
5.71
5.74
17.25
2
5.73
5.74
5.69
5.65
29.57
3
5.74
5.75
5.73
5.75
41.89
4
5.77
5.76
5.76
5.72
54.21
5
5.76
5.76
5.76
5.79
66.53
6
5.77
5.77
5.78
5.74
78.85
7
5.77
5.76
5.77
5.80
Peak FIMA [%] on discharge
Discharge
time [year]
Full
cycles in
service
CASE_A
(MA
1.347%)
CASE_B
(MA 2.5 %)
CASE_C
(MA 0%)
CASE_C
(MA 0%)
CR in
4.93
1
9.21
9.50
9.22
9.74
17.25
2
9.68
9.55
9.35
9.29
29.57
3
9.52
9.76
9.68
9.64
41.89
4
9.66
9.68
9.80
9.67
54.21
5
9.76
9.70
9.89
9.67
66.53
6
9.69
9.79
10.06
9.35
78.85
7
9.87
10.01
9.80
9.88
76
Table 12. Fuel Burnup on discharge of the first batch in seven service cycles (1800
days) in LFR with three fuel strategy options
Average burnup [(MW days)/kg] on discharge
Discharge
time [year]
Full
cycles in
service
CASE_A
(MA
1.347%)
CASE_B
(MA 2.5 %)
CASE_C
(MA 0%)
CASE_C
(MA 0%)
CR in
4.93
1
49.50
49.53
49.96
50.26
17.25
2
49.68
49.66
49.73
49.42
29.57
3
49.59
49.61
49.69
49.96
41.89
4
49.75
49.72
49.79
49.49
54.21
5
49.65
49.63
49.71
49.97
66.53
6
49.76
49.75
49.78
49.50
78.85
7
49.64
49.65
49.68
49.97
Peak burnup [(MW days)/kg] on discharge
Discharge
time [year]
Full
cycles in
service
CASE_A
(MA
1.347%)
CASE_B
(MA 2.5 %)
CASE_C
(MA 0%)
CASE_C
(MA 0%)
CR in
4.93
1
84.99
86.08
85.05
86.97
17.25
2
87.23
87.56
84.12
84.28
29.57
3
89.94
88.40
86.67
87.93
41.89
4
88.18
90.00
88.76
86.87
54.21
5
88.81
88.34
88.99
88.30
66.53
6
88.56
88.72
89.45
88.55
78.85
7
89.15
89.64
88.54
90.60
77
Table 13. Safety related coefficients in the first fuel cycle from BOL of LFR for three
fuel strategy options with CR-s fully withdrawn.
A: Initial MA 1.347%
CASE:
EOS
[2.464 y]
BOL
Source of change
B: Initial MA 2.5%
EOS
[2.464 y]
BOL
C: Initial MA 0.0%
EOS
[2.464 y]
BOL
Reactivity change [pcm]
Doppler constant
-825 ±70
-730 ±38
-717 ±37
-606 ±20
-815 ±33
-747 ±44
Core 2% axial expansion
-242 ±23
-277 ±23
-330 ±23
-330 ±37
-298 ±23
-284 ±22
Core 2% radial expansion
-823 ±23
-822 ±23
-884 ±23
-942 ±32
-877 ±22
-866 ±20
Cladding 2% expansion
93 ±24
40 ±23
0 ±23
44 ±22
39 ±22
81 ±20
200K coolant temp. change
91 ±22
77 ±23
68 ±23
58 ±21
-5 ±22
77 ±22
463 ±25
844 ±25
1270 ±25
439 ±23
841 ±23
1296 ±22
389 ±23
836 ±24
1260 ±24
437 ±22
885 ±23
1286 ±21
344 ±23
712 ±22
1142 ±23
459 ±22
880 ±21
1269 ±21
3897 ±25
4093 ±23
4155 ±25
4309 ±23
3649 ±23
4085 ±24
Entire vessel voiding (100%)
-1549 ±25
-1383 ±26
-1170 ±26
-1089 ±23
-2106 ±23
-1748 ±23
Reactor vessel
voiding to the
level of fuel
elements:
top
bottom
-1075 ±24
1299 ±25
-1135 ±23
1524 ±23
-1145 ±24
1609 ±25
-1166 ±22
1697 ±23
-1195 ±20
906 ±25
-1184 ±21
1269 ±21
Control rod worths (12 CR)
-5293 ±25
-5327 ±23
-5327 ±23
-5338 ±21
-5610 ±23
-5585 ±21
Void worths:
Active core coolant
density change:
-10%
-20%
-30%
Active core voiding (100%)
78
ISBN 978-83-911589-4-4