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Equilibrium core depletion and criticality analysis of the HTR-10 for Uranium and
Thorium fuel cycles
Godart van Gendt May 8th – August 17th 2006
Supervisors Dr. Ir. Jan Leen Kloosterman Professor Zhou Zhiwei Ir. Brian Boer Dr. Chang Hong TU Delft INET, Tsinghua University Beijing NETHERLANDS CHINA
ABSTRACT Although the current design of the pebble bed High Temperature Reactor (HTR) uses coated particle uranium oxide fuel, extensive research performed in the past has shown advantages of mixing other fertile and fissile isotopes to the fuel. Fertile fuel is added to increase the conversion ratio and thus realize a higher burnup potential and longer pebble residence times. Thorium has been used in combination with 235U and to a limited extent with 233U and 239Pu in several experimental prototype high temperature gas cooled reactors. Fabrication of pebbles of 235U enriched UO2-ThO2 coated particles has been well mastered. Research performed at the Thorium High Temperature Reactor (THTR) mixed thorium with highly enriched (93 w% 235U) uranium. A new deterministic method has been developed for the neutronic analysis of a pebble-bed reactor (PBR). The method accounts for the flow of pebbles and couples the flow to the neutronics. The method allows modeling of once-through cycles as well as cycles in which pebbles are recirculated through the core an arbitrary number of times. The burnup calculations are run using the code PEBBLEBURN developed at TU Delft. The code calculates equilibrium core nuclide densities at a desired burnup given an initial flux (FASTBURN), cross-sections (XS), and the resulting k-effective (DALTON). Uniform radial pebble-velocity is assumed. The deterministic SCALE and ORIGEN-S package is used within these codes. The design parameters of the existing HTR-10, including fuel design, reactor core dimensions and power, have been taken as fixed parameters. The research internship studied the possible use of low enriched 235U (max 20 w%) together with thorium to maximize burnup. In addition, 233U (100 w%) was mixed with 232Th. Very high burnups, higher than 150 000 MWd / ton, were achievable. It is confirmed that adding 232Th to a given amount of fissile 235U or 233U increases the conversion ratio. However, the k-effective of an homogeneous mix of 232Th and 235U decreases rapidly with decreasing overall enrichment, making high burnups impossible. Due to the better fissile properties of 233U, both a higher conversion ratio and a higher burnup can be obtained. However, there are proliferation dangers associated with the use of high-enriched 233U.
TABLE OF CONTENTS 1 Introduction to the Pebble Bed HTR-10 ..................................................................... 5
1.1 Pebbles ................................................................................................................ 6 1.2 TRISO particles .................................................................................................. 7 1.3 Reactor Structure ................................................................................................ 7 1.4 Multiple passes.................................................................................................... 7
2 Nuclear Fuel Cycles.................................................................................................... 8 2.1 235Uranium vs. 233Uranium.................................................................................. 8 2.2 Addition of thorium and its effect on reactor criticality ................................... 10 2.3 Other aspects of the thorium cycle.................................................................... 11
2.3.1 Fuel fabrication ......................................................................................... 11 2.3.2 Reactivity 233Pa effect in 232Th – 233U fuel ............................................... 11 2.3.3 Proliferation .............................................................................................. 11 2.3.4 Reprocessing ............................................................................................. 11
3 Reactor parameters.................................................................................................... 12 3.1 Fuel composition during burnup and decay...................................................... 12 3.2 Conversion Ratio .............................................................................................. 13 3.3 K-effective ........................................................................................................ 14 3.4 Burnup and Fission of Initial Metal Atoms (FIMA)......................................... 14 3.5 Velocity of pebble through the core.................................................................. 15
4 Cross-section preparation and program description ................................................. 16 4.1 Shielding ........................................................................................................... 16
4.1.1 Grain Cell.................................................................................................. 16 4.1.2 Pebble cell................................................................................................. 17
4.2 Homogenized cross-section preparation ........................................................... 17 4.2.1 Average cross-sections.............................................................................. 17 4.2.2 Cell Weighting .......................................................................................... 18 4.2.3 Zone Weighting ........................................................................................ 18
4.3 Visualization of Grain and Pebble Cell ............................................................ 19 4.4 Program PEBBLEBURN description ............................................................... 20
4.4.1 DISPLAY.................................................................................................. 20 4.4.2 FASTBURN.............................................................................................. 21 A) Background – depletion code .............................................................................. 21 B) Cross-section preparation – grain cell calculation .............................................. 22 C) Reactor type ......................................................................................................... 22 4.4.3 Ilustration of PEBBLEBURN iteration .................................................... 22
5 Benchmark equilibrium core calculation .................................................................. 24 5.1 Results benchmark and the comparison with INET ......................................... 24 5.2 Potential for deep-burn ..................................................................................... 25
6 Addition of Thorium to different fissile fuels........................................................... 26 6.1 Using 235U as fissile fuel ................................................................................... 26
6.1.1 Decreasing k-effective with increasing thorium loading .......................... 26 6.1.2 Conversion Ratio ...................................................................................... 27 6.1.3 Flux iteration for multiple passes.............................................................. 28
6.2 Using 233U as an alternative fissile fuel ............................................................ 29 6.2.1 K-effective ................................................................................................ 30
6.2.2 Increasing conversion ratio with burnup................................................... 30 7 Recommendations & Discussion .............................................................................. 33
7.1 Improvements of the PEBBLEBURN code.......Error! Bookmark not defined. 7.1.1 Velocity of the pebbles through the core .................................................. 33 7.1.2 Cross-section calculation comparison....................................................... 33
8 Conclusions............................................................................................................... 34 9 References................................................................................................................. 35 10 APPENDIX........................................................................................................... 36
10.1 Appendix A: SCALE, CSAS and ORIGEN-S.................................................. 36 10.1.1 Master vs. working library........................................................................ 36 10.1.2 SCALE...................................................................................................... 36
10.2 Appendix B – K-effective and conversion ratio of PEBBLEBURN calculations 38
10.2.1 Mixing 232Th to 238U and 235U............................................................. 38 10.2.2 Mixing 232Th to 233U ............................................................................. 39
10.3 Appendix C: VSOP........................................................................................... 39
1 Introduction to the Pebble Bed HTR-10 At the moment, much interest is shown for the inherent safety characteristics and high efficiencies, as well as the hydrogen production and transmutation capabilities, of the pebble bed High Temperature Reactor (HTR). The HTR is one of the six designs of the Generation IV initiative. The experimental HTR-10 reactor at INET, Tsinghua University, Beijing, is the only existing experimental pebble bed reactor in the world at this moment. The experimental results that have been obtained with the HTR-10 are used extensively during the current design phase of the Pebble Bed 200 MWth modular HTR Demonstration Reactor. The HTR-10 has a power of 10 MWth and a volume of 5 m3. The average power density is 2 MWth / m3, which is comparatively very low. The low power density allows for passive heat removal through convection, radiation and conduction in case of cooling system shutdown. As the reactor has a strong negative temperature reactivity coefficient, the nuclear chain reaction will shutdown without external intervention. The passive safety of the HTR-10 is one of its most important advantages compared to fast reactors and higher power density thermal reactors.
Figure 1: Sketch of HTR-10 reactor vessel, including reactor core
The following specifications of the experimental HTR-10 have been used in the equilibrium core calculations.
Table 1: Key Design Parameters of the HTR-10 Test Reactor (IAEA report [1]) The following parts of the HTR pebble bed reactor are described:
- Pebble fuel - TRISO particles - Reactor structure - Multiple pass fuel cycle
1.1 Pebble fuel The HTR-10 is fueled by pebbles that consist predominantly of graphite. The pebble has a fuel region that is surrounded by a layer of carbon. In the fuel region, a great number of TRISO particles are loaded (ranging from 8.000 – 16.000). The total number of pebbles in the core is determined by the volume of each pebble and the total volume of the reactor core, taking into consideration a packing fraction of pebbles of 61%. Around 27.000 pebbles are loaded.
1.2 TRISO particles In each pebble, the fuel is packed in the form of TRISO particles. These particles allow for fuel confinement at very high temperatures, and have robust properties even at very high burnups. The core of the TRISO particle consists of a fuel kernel. In this paper, the fuel kernel has been loaded with different ratio’s of UO2 and ThO2. The fuel kernel is surrounded by a number of protective coatings of carbons. The fuel kernel of each TRISO particle has a theoretical density of 99%. Thus, it is impossible to increase the Heavy Metal (HM) loading of each pebble by increasing the density of the TRISO particles. When increasing the loading of the pebble, the number of TRISO particles in the pebble is increased.
1.3 Reactor Structure Graphite is chosen as the main material of the reactor core structures which primarily consist of the top, bottom and side reflectors. An important advantage of graphite is its high heat capacity. The ceramic core structures are housed in a metallic core vessel which is supported by a steel pressure vessel. The side reflector has a thickness of 100 cm; the top- and bottom reflectors are 120 and 160 cm respectively.
1.4 Multiple passes The pebbles travel through the core from the top to the bottom. The pebbles are extracted at the bottom of the core by a discharging machine, after which their HM content (burnup) is measured. Once this appears to be sufficient, the pebble is reloaded at the top of the core. This is repeated until the pebble has reached its target burnup.
2 Nuclear Fuel Cycles Nuclear fuel cycles using different fissile isotopes have been studied. At the moment, almost every fuel cycle is based on 235U enriched Uranium. However, breeding of 233U fissile fuel using fertile 232Th could have fuel cycle advantages.
2.1 235Uranium vs. 233Uranium From a neutronic viewpoint, 233U bred from thorium is the best of the three nuclear fissile fuels (235U, 239Pu, 233U). This is the case for most neutron energies practically envisaged for power reactors. The eta (η) ratio, relating neutron yield per fission, fission cross-section, and absorption cross-section, is more favorable compared to the ratio of 235U or of 239Pu.
Figure 2: Illustration of eta (η) ratio f
a
νση
σ= .
An important parallel exists between natural uranium (containing 99.3% fertile 238U) and thorium (almost exclusively composed of fertile 232Th). The artificial fissile isotopes that are comparable to the small natural 235U fraction are 239Pu for 238U fuels and 233U for 232Th fuels. Natural thorium is composed almost exclusively of the fertile isotope 232Th, which, by neutron capture, becomes 233Th; 233Th transmutes into 233Pa and then into fissile 233U, with a corresponding half life of 22 minutes and 27 days, respectively.
Figure 3: Parallel between the 232Th – 233U and 238U – 239Pu fuel cycles In the research performed, a comparison has been made between HTR’s using UO2 and HTR’s using a mixture of UO2 and ThO2. In addition, the total heavy metal (HM) loading of the pebbles, and the desired burnup, have been varied.
Figure 4: Simulation studies of both fissile fuels have been performed
HTR-10
Use of UO2: fissile fuel 235U
Use of ThO2 / UO2: fissile fuel 233U
232Th + 1 neutron
233Pa β decay 27.4 days
233U + 1 neutron 90% fission 10% capture
234U + 1 neutron
235U + 1 neutron 80% fission 20% capture
236U + 1 neutron
238U + 1 neutron
239Np β decay 2.3 days
239Pu + 1 neutron 65% fission 35% capture
240U + 1 neutron
241Pu + 1 neutron 75% fission 25% capture
242Pu + 1 neutron
FERTILE
FISSILE
FERTILE
PARASITE
FISSILE
2.2 Addition of thorium and its effect on reactor criticality
Increasing the amount of thorium in a pebble decreases the k-effective significantly. The most important reason for the decrease in k-effective is the extra neutron absorption in the fertile fuel as the atomic density of fertile fuel increases. The enrichment of HM fuel loaded in a core is defined as follows:
[%] TotalFissileFuelEnrichmentTotalFissileFuel TotalFertileFuel
=+
As the amount of fertile material loaded in the reactor core increases, the initial enrichment of the fuel decreases. Although increasing the amount of fertile material in the core increases the conversion ratio (see section 3.2), the increasing number of captures of neutrons in the fertile material has a negative effect on the multiplication constant (k-effective).
Enrichment fuel for different composition - max 100 MWd / kg
6%
8%
10%
12%
14%
16%
18%
0 20 40 60 80 100 120
Burnup (MWd / kg)
Enri
chm
ent (
%)
Benchmark - 5 gram UThorium - 2.5 gram
Figure 5: Increasing the amount of fertile fuel decreases the overall enrichment, affecting the potential criticality of the reactor during burnup
2.3 Other aspects of the thorium cycle 2.3.1 Fuel fabrication
One of the principal drawbacks of the thorium cycle is the presence of hard gamma emitters (2–2.6 MeV) among the descendants of the 232Th isotope, and of 232U, an alpha emitter with a 72-year half-life which is always present with 233U. The presence of 232U necessitates the manufacture of 233U based fuels completely remotely in a gamma-shielded environment. This is a very expensive technique which only starts to be mastered with MOX fuel element fabrication.
2.3.2 Reactivity 233Pa effect in 232Th – 233U fuel The rather long half-life of 233Pa (decaying into 233U) can result in a reactivity surge a long time after reactor shutdown due to fissile 233U production. This must be taken into account in the reactor design and safety features. As can be recalled, by neutron absorption, 232Th produces 233Th and 233Pa (half-life 27-days), to produce 233U. This is called the 233Pa effect.
2.3.3 Proliferation From the proliferation viewpoint, 233U is as ‘good’ a potential weapon as 235U or 239Pu. It is somewhat better than 239Pu in that there are fewer spontaneous neutrons, which may simplify weapon fabrication. However, U-233 is rather proliferation-resistant due to the presence of gamma-radiation emitting 232U, which causes very serious handling difficulties and improves its traceability. There are methods that can be studied to allow for a more proliferation-resistant way of using 233U in combination with the isotopes 235U and 238U. Blanket regions containing 232Th with some 238U would allow for safe chemical separation of uranium. The 233U would not be useable for weapons, denatured by the 238U and the 239Pu present in the irradiated blankets.
2.3.4 Reprocessing Recently, more emphasis has been placed on decreasing the long-term toxicity of nuclear waste. In this respect, the fact that the toxicity of minor actinides (MA’s) resulting from thorium reactors is at least one order of magnitude less compared to MA’s resulting from uranium reactors favors the thorium fuel cycle. Such a fuel cycle will generate a minimum quantity of actinide waste, the radiotoxicity of which would be lower than the existing reactors working on 238U-235U /239Pu fuel cycle for the first 50 000 years after disposal.
3 Reactor parameters The equilibrium core atomic densities are defined as the densities which would be obtained when continuously adding a predetermined fresh fuel pebble to the core and removing pebbles of a predetermined burnup. Prior to running an equilibrium core code, a refueling strategy is defined, including the number of passes of pebbles through the core, and the maximum burnup allowed. The equilibrium core code calculated the following parameters of the HTR equilibrium core:
- Fuel composition during burnup and decay - Conversion Ratio - K-effective - Burnup and Fission of Initial Metal Atoms (FIMA) - Speed through the core
3.1 Fuel composition during burnup and decay The fission, absorption and capture cross-sections used in the depletion formula are the so called ‘average cross-sections’ (see chapter 4). We assume a constant flux during the burnup step in each axial zone of the HTR. The initial densities are calculated using the composition of the fresh fuel, and the geometry of the reactor core and pebble. The atomic densities of subsequent burnup steps are calculated using the following formula:
, ,
,
:
ii a i i j i j c k i k i l i f l
j i l
ii
i a i
i i i
j i j ij i
c k i k k i
i
dN N N N N Q ydt
withdN ChangeNuclideDensitydt
N AbsorptioninNuclideN DecayofNuclide
N DecaytoNuclide
N AbsorptioninNuclide toNuclideQ
σ ϕ λ λ σ ϕ σ ϕ
σλ
λ
σ ϕ
→ → →≠
→≠
→
= − − + + + +
=
==
=
=
∑ ∑ ∑
∑
∑
,l i f l l il
ExternalSourcey FissionYieldofNuclide toNuclideσ ϕ→
=
=∑
- The first term represents loss by neutron absorption, with a spectrum averaged microscopic cross section including fission and capture. - The third term represents production by radioactive decay of a precursor species. This could be caused by more than one precursor.
- The fourth term represents production by neutron interaction in a precursor species by neutron capture with a spectrum averaged microscopic capture cross section. - The sixth term represents the production term for fission products, where the value of the fission product yield ‘y’ is dependent on both the fissioning isotope and the energy of the neutron causing fission. The other terms are related to nuclide decay and an external fission source.
3.2 Conversion Ratio A higher conversion ratio of fertile to fissile fuels allows for longer burnups and a smaller burnup reactivity swing. In the research that follows, the maximum burnup given a initial fuel composition has been studied in detail. The conversion ratio is defined as:
PrFissile oductionConversionRatioFissileDestruction
=
Production of fissile isotopes occurs when a fertile isotope, such as 238U or 232Th, absorbs a neutron. After a number of decays, 239Pu and 233U are produced. These isotopes are fissile in a thermal reactor. Destruction of isotopes can be calculated using the number of days that the reactor is run and the total thermal power of the reactor. Using the total calculated energy (units MWd), and the average of 200 MeV per fission of a fissile atom, the number of fissioned atoms is calculated.
Fissile Fuel Destroyed - for different HM loadings
0
10
20
30
40
50
70 80 90 100 110 120 130 140 150
Burnup (MWd / kg)
Mas
s (k
g) 5 gram HM
7.5 gram HM
10 gram HM
Figure 6: Fissile mass (233U) destroyed given the power and burnup for different initial loadings. In the research performed, it was apparent that for a homogeneously mixed thorium / uranium fuel of an acceptable enrichment, it is impossible to reach conversion ratio’s above 25%. In a thermal breeder, the conversion ratio must be greater than 100%.
3.3 K-effective The multiplication factor, also called k-effective, is the ratio comparing the total production of neutrons by fission to the total loss of neutrons in a reactor core by capture and leakage. The reactor is critical when production is equal to loss. When the core is assumed to have infinite dimensions, k-infinity is used rather than k-effective. This benchmark calculates k-effective for each equilibrium core composition. When k-effective exceeds one, the reactor can be operated critically. Supercriticality would be compensated by insertion of control rods in the core and in the control assemblies of the reflector regions.
3.4 Burnup and Fission of Initial Metal Atoms (FIMA) The burnup of the pebble in the reactor is a measure for the amount of energy that is extracted from a total amount of initial Heavy Mass (HM) loaded per pebble. It is defined as follows:
* *AtomicDensity VolumeFuel EnergyperFissionBurnupHMperPebble
Δ=
The conventional units of burnup are MWd / kg. Another measure that it used to indicate the change in composition of the initial pebble is the fission of initial metal atoms (FIMA, %). FIMA is defined as:
[%] HMdensityFIMAInitialHMdensity
Δ=
As is clear from these formulas, FIMA is linearly related to the burnup (MWd / kg) of the reactor core. FIMA is not related to the number of passes through the core or the number of grams of fertile thorium loaded in the pebble.
FIMA vs. Burnup
0%
5%
10%
15%
20%
25%
60 80 100 120 140 160 180 200
Burnup (MWd / kg)
FIM
A (%
)
Figure 7: Linear relationship between burnup (MWd / kg) and FIMA (%)
3.5 Velocity of pebble through the core The velocity of the pebble through the core determines the residence time of the pebble before being removed from the core. The velocity of the pebble through the core is dependent on the following variables:
- desired burnup [MWd / kg] - number of passes through the core - height of the core [m] - thermal power of the reactor [MWth] - HM loading of the pebble [kg] - number of pebbles in the core
The formula used to calculate the velocity of the pebble through the core is:
(# )( )( )( )(# )( )
thpasses H eight Pow erVelocityM axB urnup pebbles H M loading
=
An appropriate unit conversion factor is needed to express velocity in m/s, cm / d, or other desired units. In the paper below, the speed of the pebbles through the core changes throughout the simulation, as the HM loading of the pebble, the desired burnup and the number of passes is changed regularly. The height of the reactor core, the number of pebbles and the thermal power have been kept constant throughout the simulation. A uniform radial velocity distribution of the pebbles is assumed. Thus, the pebbles move throughout the core with the same speed, regardless of the radial position in the core. The difference between a burnup of 60 MWd / kg and 180 MWd / kg translates itself in core residence time for pebbles that is three times as long.
Residence time of pebble as function of burnup7.5 gram HM, 6 passes
3456
789
80 90 100 110 120 130 140 150 160
Burnup (MWd / kg)
Num
ber o
f yea
rs
Figure 8: Core residence time for pebbles for different burnups
4 Cross-section preparation and program description
The nuclear cross-sections for capture, fission and scattering are most important when calculating the changing atomic densities of a running reactor core. In this chapter, cross-section preparation for the pebble-bed reactor is described. As described in Section 3.1, the following depletion formula is solved when simulating the depletion of a nuclear reactor core.
, ,i
i a i i j i j c k i k i l i f lj i l
dN N N N N Q ydt
σ ϕ λ λ σ ϕ σ ϕ→ → →≠
= − − + + + +∑ ∑ ∑
Before being able to calculate the cross-sections for depletion analysis, the cross-sections must be corrected for shielding effects. After the shielding correction, the cross-sections are homogenized. Both shielding and homogenization is discussed below. In addition, the interactions between different parts of the PEBBLEBURN code are displayed.
4.1 Shielding An important part of the unit-cell calculations is the generation of shielded fine-group cross sections in the resonance energy range. The code package SCALE (See Appendix B) takes spatial self-shielding effects into account. A key-parameter to shielding calculations is the volume-to-surface ratio of the fuel lump, i.e. the fuel kernel in case of the HTR. If the distance between the fuel kernels is small compared to a neutron’s mean free path length in the pebble graphite, the kernels ’interact’ and, hence, the volume-to-surface of the fuel kernel becomes effectively larger. This ’fuel shadowing’ phenomenon is quantified by the Dancoff factor. [2] A pile of pebbles can be considered a double-heterogeneous system. The first heterogeneity, on the smallest geometric scale, is the fuel kernel that is surrounded by the coating layers and the graphite matrix. The second heterogeneity is of the fuel zone and the pebble shell, including the coolant. Below, descriptions are given of the ‘grain’ and the ‘pebble’ cell.
4.1.1 Grain Cell A standard simulation starts with the preparation of group cross sections on the finest geometric scale, which in the case of an HTR would be the fuel kernel surrounded by coating layers and graphite. The heterogeneity of the fuel kernel surrounded by the coatings and graphite matrix is translated into a grain cell. On this geometric level, the resonance-shielding calculations take place, and hence, a Dancoff factor for the fuel kernel has to be provided. For the analytical calculation of this Dancoff factor, we consider an equivalent grain cell with white boundary conditions. This grain cell consists of an inner sphere which corresponds to the fuel kernel, and a spherical shell which contains the coating layers and the graphite matrix, homogeneously mixed. The resonance absorption is usually calculated by the collision probability method applied for a unit cell with a fuel and moderator region. For simple lattice cells, the
Dancoff factor is usually internally calculated by the resonance-shielding code. However, if the geometry is more complicated, such as the double-heterogeneous system of a pile of pebbles, it has to be given as an input parameter.
4.1.2 Pebble cell The stochastically stacked pile of fuel pebbles is also modeled as a spherical two-region unit cell with white boundary conditions. This equivalent pebble cell consists of an inner sphere, representing the fuel zone of the pebble (radius of 2.5 cm), and an outer spherical shell. The outer shell contains a homogeneous mixture of the 0.5-cm pebble shell and the void between the pebbles (packing fraction is 61%). The Dancoff factor is equal to the sum of the inter- and intrapebble Dancoff factors.
4.2 Homogenized cross-section preparation Homogenization of regions of the reactor core is performed to calculate cross-sections. These homogenizations have been performed on the following levels, the:
- grain cell - pebble cell
To calculate the power over the entire reactor core, the macroscopic zone weighted cross-sections are used.
4.2.1 Average cross-sections The average cross-section is a function of the integral of the energy dependent cross-section and the energy-dependent flux over the entire energy range, divided by the integral over the energy-dependent flux.
0
0
( ) ( )
( )
E E dE
E dE
σ ϕσ
ϕ
∞
∞=∫
∫
The “averaged” cross sections are defined in a manner that conserves reaction rates. In multigroup notation, conservation is expressed as:
:
' '
( , )
applicable applicablespatial spatialregions regions
j j j j jG D g g g
j g G j g G
G
jD
jg j g
jg
N W N W
with
AverageCrossSectioninGroupG
N NumberDensityZone j
W WeightingSpectrum dr dE E r
CrossSectionUnreduced
σ σ
σ
ϕ
σ
∈ ∈
=
=
=
= =
=
∑ ∑ ∑ ∑
∫ ∫
There are two ways to calculate average cross-sections. One way is called ‘cell weighting’, the other ‘zone weighting’.
4.2.2 Cell Weighting Cell weighting homogenizes the cross sections in a heterogeneous cell. Cell weighted cross sections preserve the reaction rates which occur in a representative cell from the reactor. Cell weighting calculates the average number density of an isotope as follows:
:' '
cellj j
jjD cell
j
j
j
V NN
V
withV VolumeZone j
=
=
∑
∑
4.2.3 Zone Weighting Zone weighting in a unit cell defines the flux in the fuel, structures and coolant. Within the different zones, the flux is constant. When the weighting is done for a complete reactor core calculation, the flux is constant in the zones defined in the core. Each zone produces a unique set of cross sections which preserves reaction rates for that zone.
4.3 Visualization of Grain and Pebble Cell The figure below visualizes the above explanation of the grain- and the pebble-cell. The calculations of cross-sections in the HTR are done after performing shielding calculations and homogenization using the grain- and pebble-cell models.
Figure 9: Schematic drawing of the grain cell, and the pebble cell
4.4 Program PEBBLEBURN description The complete solution of the core physics problem in the pebble-bed reactor must simultaneously account for the movement of the fuel, the changing composition of the fuel as it is burned, the distribution of flux that results from the core geometry and the spatial variation of the composition. In this section, the PEBBLEBURN code is described. The PEBBLEBURN code is broken down in the following functions:
- Calculation of initial atomic densities and speed through core (DISPLAY) - Calculation of equilibrium core atomic densities (FASTBURN) - Calculation of the cross-sections in the reactor core (XS) - Calculation of the k-effective using diffusion theory (DALTON)
XS and DALTON calculate the two-dimensional flux over the reactor, and the k-effective of the equilibrium core. Below, the programs DISPLAY and FASTBURN are explained in more detail.
Figure 10: Illustration of the logical flow of the PEBBLEBURN code
4.4.1 DISPLAY DISPLAY is used to calculate the initial atomic densities and the speed through the reactor core, which are consequently used in the FASTBURN code. DISPLAY can calculate the densities when uranium and thorium oxide fuels are included in the initial fuel composition. DISPLAY uses basic information such as the geometry of the fuel TRISO’s, the pebble, and the reactor, the composition of the fuel kernel, cladding and coolant, as well as the isotopic vectors of different elements. In addition, the desired maximum burnup, the number of passes through the core, and the number of grams of heavy metal per pebble, are given as input parameters. These parameters are used for calculating the speed through the reactor core.
FAST BURN
( )zkN
DALTON ( ),i r zΣ
Calculate XS
max layersm n×( ), zk mN
( )zϕ ( )zϕ
4.4.2 FASTBURN In FASTBURN, equilibrium core nuclide densities are calculated, taking into consideration the temperature and the geometry of the components of the unit cell, as well as the nuclide densities The flux per axial zone is taken together with the average isotopic cross-sections per zone and is input into ORIGEN-S to calculate new initial densities. The desired maximum burnup determines the speed through the core, and thus the residence time of pebbles in the core. The code iterates until the desired burnup is reached.
A) Background – depletion code In general, a depletion code has a qualitative structure as indicated in the figure below.
Figure 11: General lay-out of a depletion code TUD worked with the SCALE 4.4 system to calculate the average cross-sections in the unit-cells of the reactor core. ORIGEN-S was used to calculate the change of nuclide densities of the heavy metals during burnup and decay. An AMPX master library is used with an energy structure for thermal reactor applications (172-group XMAS). The code solves the 1D transport equation. FASTBURN is used to couple several SCALE modules together. Appendix B explains the workings of the SCALE code.
1 Reactor and control system geometry and material volume fractions
2 Multigroup cross-section library
3 Initial fuel composition and range of operating parameters
4 Calculation of spectrum averaged group cross-sections for unit cell
5 Core Power level and fuel arrangement
6 Power distribution calculation
7 Fuel composition change with burnup
B) Cross-section preparation – grain cell calculation As described in the section on shielding, the burnup simulation involves a double heterogeneous cell-calculation. First, a ’grain-cell’ calculation is performed. Thereafter a ‘pebble cell’ calculation is performed. Below, the calculation of the ‘grain-cell’ cross-sections with SCALE is explained. The ‘pebble-cell’ calculation is done in a similar manner. First, the codes BONAMI-S and NITAWLII process shielded group cross sections, using the 172-group XMAS library based on JEF2.2. BONAMI-S performs the resonance shielding for the unresolved resonances, whereas NITAWL-II does the same for the resolved resonances by the Nordheim Integral Method. Both codes use an externally calculated Dancoff factor. Thereafter, the one-dimensional discrete ordinate code XSDRNPM uses the shielded group cross sections and solves the eigenvalue equation in radial coordinates. The grain cell has a spherical geometry. It consists of the kernel, surrounded by a spherical shell containing the four coatings in a homogenized sense, a shell containing the inter-granular matrix material, as well as a shell containing the pebble shell and the inter-pebble void. The volume ratios between the various spherical shells in this grain cell are the same as in the real pebble bed. After the spatial flux calculation is performed by XSDRNPM, the cross sections of the inner three zones are weighted (so-called inner-cell weighting), but not collapsed. These weighted cross sections are passed on to a second XSDRNPM calculation.
C) Reactor type For all nuclides not included in the spectrum calculation, it is necessary to indicate the type of reactor used during the burnup calculation. In our case, we used the thermal High Temperature Reactor (HTR) option. Other options include the Liquid Metal Fast Breeder Reactor (LMFBR), and the Sodium Fast Reactor (SFR). Indication of the type of reactor influences the fission yield cross-sections of the ORIGEN-S library. It is also used as an indication which nuclides are important to the calculation. There are usually only five nuclides per library for which all fission yield data is known.
4.4.3 Ilustration of PEBBLEBURN iteration The initial guess (Fast 1) of the axial flux over the reactor determines the shape of the axial flux. The first FASTBURN calculation scales the value of the flux until the desired burnp is obtained. The DALTON code calculates the two-dimensional flux over the reactor in such a way that the power of the reactor is 10 MWth. The shape of the flux changes (DALTON 1). As can be seen below, using the iterated flux from DALTON in a second run of the FASTBURN code, the calculated flux once again is scaled only in magnitude. The process continues until the flux calculated by FASTBURN is the same as the flux calculated by DALTON.
Flux iteration using FASTBURN and DALTON
1.0E+13
1.5E+13
2.0E+13
2.5E+13
3.0E+13
3.5E+13
4.0E+13
0 5 10 15 20 25
Axial layer from top of reactor
Flux
(neu
trons
/ cm
2 * s
ec)
Fast 1DALTON 1Fast 2DALTON 2Fast 3
Figure 12: Illustration of the flux iteration for multiple iterations * The results are shown for the 80 MWd / kg, 1 pass benchmark burnup using 5 gram of HM. In the calculations that have been performed, only one iteraton of DALTON has been used to calculate the k-effective and the equilibrium core nuclide densities. It was seen that the calculated nuclide densities and k-effective in the equilibrium core changed slightly when using the flux obtained using multiple iterations. This can be seen below for the atomic density of 235U for different number of iterations.
Uranium-235 burnup in HTR-10
00.00050.001
0.00150.002
0.00250.003
0.00350.004
0.0045
0 200 400 600 800 1000 1200
Burnup (days)
Atom
ic d
ensi
ty (a
tom
/ ba
rn
* cm
) 1st iteration2nd iteration3rd iteration
Figure 13: Equilibrium core nuclide densities for different number of iterations * The results are shown for the 80 MWd / kg, 1 pass benchmark burnup using 5 gram of HM.
5 Benchmark equilibrium core calculation The benchmark calculation uses 5 gram of Uranium per pebble. The pebbles have a desired burnup of 80 MWd / kg. All other variables of the benchmark calculation are determined by the design parameters of the HTR-10, including the 17% enrichment of the uranium fuel. The number of passes through the core is varied.
5.1 Results benchmark and the comparison with INET The k-effective of the equilibrium core varies between 1.13 and 1.19 for different number of passes through the core.
K-effective - 80 MWd / kg Benchmark
1.10
1.12
1.14
1.16
1.18
1.20
1 pass 3 passes 6 passes
Number of passes
K-e
ffect
ive
Figure 14: K-effective of the benchmark composition for different number of passes INET has calculated the equilibrium core using the same benchmark reactor core parameters using the VSOP code. In the Appendix D, a short description of the VSOP code has been included. The k-effective of the INET calculation is 10% less than that PEBBLEBURN calculation. This is a very significant amount, indicating either that a number of assumptions in the PEBBLEBURN code were invalid, or that the input deck of one of the codes contains a mistake. Future research should be done using an improved deterministic equilibrium core code to see whether a k-effective that is more similar to INET’s calculation, can be found.
5.2 Potential for deep-burn The data shows that there is a significant potential for deep-burn without addition of thorium.
Potential for deepburn
1.0201.0401.0601.0801.1001.1201.1401.1601.1801.200
70 110 150 190
Burnup (MWd / kg)
K-e
ffect
ive
Figure 15: Increasing burnup of the benchmark composition – 5 gram of U per pebble, 17 w% enrichment It has already been noted that the k-effective of our calculations is much higher than the calculation of INET. When using INET’s calculation of the equilibrium core k-effective, there is little room for increasing the burnup further than 80 MWd / kg.
6 Addition of Thorium to different fissile fuels In addition to the benchmark calculation, differing amounts of thorium have been added to the pebble. Varying the mass of HM loading per pebble has an effect on the calculated flux and the atomic densities in the equilibrium core. In this chapter, some of the results of loading fertile thorium fuel in pebbles with fissile 235U and fissile 233U are presented. The results of all of the simulations that have been performed can be found in Appendix C.
6.1 Using 235U as fissile fuel Loading additional 232Th fissile fuel would potentially increase the Conversion Ratio and thus allow higher burnups. However, this section shows that the negative effect on k-effective dominates any positive effect due to a higher Conversion Ratio.
6.1.1 Decreasing k-effective with increasing thorium loading As can be expected, when increasing the fertile loading per pebble, the k-effective of the equilibrium core decreases. Below you will find a graph of the decreasing k-effective with addition of thorium for a desired burnup of 80 MWd / kg and 1 pass through the core. Similar slopes have been found when for increased number of passes and increased burnups. As can be seen, adding only 2.5 g of 232Th to the benchmark fuel decreases the k-effective from 1.13 to 1.01. Further increasing the burnup or the amount of fertile fuel loaded would result in a subcritical reactor.
Decreasing k-effective with thorium loading
1.001.021.041.06
1.081.101.121.14
4.5 5 5.5 6 6.5 7 7.5 8
Total mass of HM per pebble
K-ef
fect
ive
Figure 16: Decreasing k-effective when increasing fertile (HM) loading - maximum burnup 80 MWd / kg
6.1.2 Conversion Ratio The Conversion Ratio increases when increasing the amount of fertile fuel and increases with burnup. However, only a small increase in the Conversion Ratio is observed with increasing burnup and with increasing fertile loading. This increase is insufficient to allow for high burnups in under the constraint of reactor criticality. Below, you’ll find graphs showing the increasing conversion ratio with increasing fertile loading and increasing burnup.
Conversion Ratio increases with increasing burnup7.5 gram HM, Initial loading: U-235, U-238 and Th-232
0%5%
10%15%20%25%30%35%
70 80 90 100 110 120 130
Burnup (MWd / kg)
Con
vers
ion
Rat
io (%
)
Figure 18: Increasing conversion ratio with increasing burnup: 235U, 238U fuel
Conversion Ratio increases with increasing fertile loading80 MWd / kg maximum burnup
0%10%20%30%40%50%
4.5 5.5 6.5 7.5 8.5 9.5 10.5
Number of grams per pebble (g)
Con
vers
ion
Rat
io
(%)
Figure 19: Increasing conversion ratio with increasing fertile loading: 235U, 238U fuel
6.1.3 Flux iteration for multiple passes The flux iterates to a different value for simulations of pebbles that undergo multiple passes. In addition, the nuclide densities iterate to different values for different number of passes. The k-effective of the equilibrium core increases when you increase the number of passes. Below, this is illustrated for a maximum pebble burnup of 80 MWd / kg and a HM load of 7.5 gram.
Flux iterated for different number of passes80 MWd / kg, 7.5 gram HM
0.00E+00
1.00E+13
2.00E+13
3.00E+13
4.00E+13
5.00E+13
0 5 10 15 20 25
Axial layer
Flux
(neu
trons
/ cm
2 *
sec)
1 pass3 passes6 passes
Figure 20: Iterated flux over the HTR for different number of passes
Average atomic density U-235 for different number of passes80 MWd / kg, 7.5 gram HM
0.00E+005.00E-041.00E-031.50E-03
2.00E-032.50E-033.00E-03
0 5 10 15 20 25
Axial layer
Ato
mic
den
sity
(ato
m /
barn
* c
m)
1 pass3 passes6 passes
Figure 21: Average atomic density of 235U per reactor core axial layer for different number of passes
K-effective for different number of passes80 MWd / kg, 7.5 gram HM
1.00
1.01
1.02
1.03
1.04
1.05
1 pass 3 passes 6 passes
Number of passes
K-e
ffect
ive
Figure 22: Increasing the number of passes of the pebble through the core increases the k-effective.
6.2 Using 233U as an alternative fissile fuel A combination of low-enriched Uranium (max 20 w% 235U ) with fertile fuel has shown very little high burnup potential under the constraint of reactor criticality. Replacing fissile 235U with fissile 233U would possibly allow for greater burnups due to the better fissile potential of 233U (see Chapter 2). Once again, increasing the number of passes has a positive effect on the k-effective of the equilibrium core. For this reason, a further analysis of a 233U-232Th core was done ‘recycling’ pebbles six times through the core. It is important to realize that there are also significant disadvantages when using 233U as fuel. - Using pure 233U does not respect the current fuel practice of using low-enriched fissile fuel. Where previous research limited the fuel enrichment to 20%, using pure 233U in combination with 232Th is the proliferation equivalent of using 100% enriched 235U. - 233U must be bred in the blankets surrounding a reactor core. Possible breeding could take place after capture of neutrons that have leaked from the reactor core. After sufficient breeding, such blankets could be reprocessed. When discussing future research, a number of other points concerning reprocessing will be made. Thus, there are significant barriers to using 233U. However, as will be shown below, an HTR fueled by 233U and 232Th does have a much greater capacity for higher burnups.
6.2.1 K-effective Below, the k-effective of an equilibrium core loaded with pebbles containing 7.5 gram of HM and for 6 passes through the core have been compared. It can be clearly seen that 233U is a much better fissile fuel than 235U. In addition, the even greater potential for high burnups is displayed.
K-effective for different fissile fuel loading
1.021.041.061.081.1
1.121.141.161.181.2
1.22
50 70 90 110 130 150 170 190
Burnup (MWd / kg)
K-ef
fect
ive
U-233U-235
Figure 23: Higher k-effective at similar equilibrium core burnups when using 233U as fissile fuel
6.2.2 Increasing conversion ratio with burnup The Conversion Ratio of fissile material in a pebble increases with burnup when analyzing the results of mixing 233U to the reactor as fissile fuel. The reasons for the increase are similar to the increase of the Conversion Ratio when using 235U as fissile fuel. First of all, the FIMA (%) increases with burnup. As can be seen, the FIMA (%) for a 140 MWd / kg pebble is very similar for different loadings of the pebble. However, the number of days that a pebble must burn to reach this similar amount of FIMA (%) increases by a factor 2 when going from 5 to 10 gram loaded per pebble. In other words, although the number of days burnt increases by a factor 2, the end atomic density of fissile fuel remains more or less the same!
Burnup of U-233 expressed in FIMA (%)
40%
50%
60%
70%
80%
90%
70 80 90 100 110 120 130 140 150
Burnup (MWd / kg)
FIM
A (%
) 5 gram HM7.5 gram HM10 gram HM
Figure 24: Increasing FIMA for increasing burnup
Number of days burnup for a pebble to reach 140 MWd / kgLoading varied between 5 and 10 gram HM
150020002500300035004000
4.5 5.5 6.5 7.5 8.5 9.5 10.5
HM loaded per pebble (g)
Bur
ntim
e (d
ays)
Figure 25: Increasing residence time of pebble in reactor core for increasing loading
Burnup of U-233 - fissile mass per pebble140 MWd / kg, 6 passes
0.0
0.2
0.4
0.6
0.8
1.0
0 500 1000 1500 2000 2500 3000 3500 4000
Burnup (days)
Mas
s U
-233
(g)
5 gram HM7.5 gram HM10 gram HM
Figure 26: Fissile mass per pebble for different loadings, burnup 140 MWD /kg
The reason for this equilibrium is a production rate in the pebble of fissile 233U from fertile 232Th that is equal to the destruction rate in the pebble. During the last 940 days of the burnup of the 10 g HM loaded pebble (from 2840 days until 3780 days), the FIMA (%) remains the same (about 82%). The production rate of 233U from 232Th is the about the same as the production in a fresh pebble, however, the destruction of 233U is much lower, as the pebble is almost depleted. As the reactor is loaded with a mix of pebbles that are undergoing there first until sixth passage through the reactor, it is still possible for the reactor as a whole to be critical.
Production and destruction for 10 grams of HM in pebble
0.0
0.4
0.8
1.2
70 90 110 130 150
Burnup (MWd / kg)
Mas
s of
fiss
ile m
ater
ial
(g)
Production U-233
Destruction
Linear (Production U-233)
Linear (Destruction)
Figure 27: Production and destruction of fissile fuel in the pebble
Conversion Ratio - 10 gram HM - different burnups
30%
35%
40%
45%
50%
55%
70 80 90 100 110 120 130 140 150
Burnup (MWd / kg)
Con
vers
ion
Rat
io (%
)
Figure 28: Increasing Conversion ratio for higher pebble burnups As shown in the results, using fertile material in the reactor core increases the conversion ratio per pebble, but does not result in a significant amount of fissile material remaining in the waste fuel. The pebbles used in such a cycle would be regarded as waste after these high-burnups. Reprocessing of these pebbles would not be economically viable. However, when implementing blankets of thorium to breed 233U, reprocessing of these blankets is necessary.
7 Recommendations: Improving PEBBLEBURN A number of improvements can be made to the analysis of the equilibrium fuel cycle of the HTR-10. Changes can be made to the PEBBLEBURN code. In addition, a comparison can be made of the cross-sections used to calculate burnup in the SCALE system vs. the VSOP system.
7.1 Velocity of the pebbles through the core The different rates at which the fuel spheres move through the reactor core, and the different flux values and flux spectra in the different areas in the core, cause the fuel depletion to become largely dependent on the space-time history of the fuel sphere. Using VSOP, INET was able to simulate aspects of the pebble source terms that we were not able to simulate. For reactors with a small diameter / height ratio (such as HTR-10), a parabolic velocity distribution should be used to accurately describe pebble movement through the core. It is possible to alter the deterministic PEBBLEBURN code in such a way that, instead of a uniform radial velocity, a parabolic (or a distribution that better describes pebble movement) velocity is used.
7.2 Cross-section calculation comparison In addition, a source in the literature has been found which describes an important difference between the calculated burnup of HM in a pebble bed using the codes VSOP and ORIGEN-S [3]. Although ORIGEN-S is a more widely used code, and is thus exposed to much more frequent evaluation, the article mentions that the accuracy of a fuel recycling with ORIGEN-S in comparison with a more realistic fuel recycling in VSOP needs to be evaluated.
The composition of the pebbles for an approximate 90 MWd/kgU burnup is tabulated for different HM: 235U, 238U-238, 239Pu and 241Pu. The spent fuel mass differences between the ORIGEN-S and VSOP are larger than expected. They have compared the ORIGEN-S one-group isotopic cross-sections with the VSOP values, and have concluded that the ORIGEN-S 238U capture cross-section was about 7% larger than the VSOP value, and the ORIGEN-S 235U fission cross-section was about 5% larger than the VSOP value. It was shown, for example, that the Pu-239 mass in a fuel sphere at discharge burnup could
differ with a factor 1.7. It is likely that there are differences in the one-group 238U capture and 235U fission cross-sections between SCALE and VSOP.
8 Conclusions The deterministic method, developed for the neutronic analysis of a pebble-bed reactor should be improved, as the results of the benchmark equibrium calculation differed significantly from the equilibrium core calculation that was performed by INET. Homogeneously mixing low enriched 235U (max 20 w%) together with thorium decreases the k-effective significantly. Although the Conversion Ratio increases, the number of days the pebble is able to burn decreases due to the quick subcriticality of the equilibrium core with increased fertile material. Due to the better fissile properties of 233U, both a higher conversion ratio and a higher burnup can be obtained. However, there are proliferation dangers associated with the use of high-enriched 233U. 233U (100 w%) was mixed with 232Th. Very high burnups, higher than 150 000 MWd / ton, were achievable. However, it should be noted that the excellent neutronic properties of 233U for neutrons over a broad energy range, and smaller reactivity change with burnup resulting in longer core life cycles, were not attractive enough in the past to continue emphasis of the thorium fuel cycle. This was due to the necessity of adapting to a new fuel cycle with its particular problems, especially in reprocessing and handling of 233U. There are high costs associated with fuel fabrication due partly to the high radioactivity of U-233 which is always contaminated with traces of U-232. Much development work is still required before the thorium fuel cycle can be commercialised, and the effort required seems unlikely while abundant uranium is available.
9 References [1] IAEA TecDoc, “Evaluation of high temperature gas cooled reactor performance: Benchmark analysis related to initial testing of the HTTR and HTR-10”, November 2003. [2] Bende E. E., Hogenbirk A. H., Kloosterman J. L., Van Dam, H., “Analytical Calculation of the Average Dancoff Factor for a Fuel Kernel in a Pebble Bed High-Temperature Reactor”,NRG and TU DELFT, The Netherlands, NUCLEAR SCIENCE AND ENGINEERING: 133, 147–162, 1999. [3] Stoker C.C., Reitsma F., “PBMR fuel sphere source terms”, PBMR (Pty), South Africa, 2nd International Topical Meeting on HIGH TEMPERATURE REACTOR TECHNOLOGY Beijing, CHINA, September 22-24, 2004. Other refereces used: Terry W., Gougar H., Ougouag A.,”Direct deterministic method for neutronics analysis and computation of asymptotic burnup distribution in a recirculating pebble-bed reactor”, INEEL, Annals of Nuclear Energy, 29 (2002) 1345-1364. Lung M., Gremm O., “Perspectives on the thorium cycle”, Nuclear Engineering and Design 180 (1998) 133-146. Nabielek H., Kaiser G. , “Fuel for pebble-bed HTR’s”, September 1983. Nam S., “The hazards of waste arising from the use of thorium fuels in power reactor systems”, Central Electricity Generating Board, Berkeley Nuclear Laboratories, Annals of Nuclear Energy, Vol. 5, pp. 259 to 266. Talamo A., Gudowski W. , “Performance of the gas turbine-modular helium reactor fuelled with different types of fertile TRISO particles”, Department of Nuclear and Reactor Physics, Royal Institute of Technology, Stockholm, Annals of Nuclear Energy 32 (2005) 1719–1749. Jing Xingqing, Yang Yongwei, “Physical design and calculations for the full power operation of the 10 MW high temperature gas-cooled reactor – test module (HTR-10)”, Institute of Nuclear Energy Technology, Tsinghua University, Beijing, 2nd International Topical Meeting on HIGH TEMPERATURE REACTOR TECHNOLOGY Beijing, CHINA, September 22-24, 2004. Gauld I.C., Hermann O.W., Westfall R.M., “ORIGEN-S: SCALE system module to calculate fuel depletion, actinide transmutation, fission product buildup and decay, and associated radiation source terms”, ORNL, April 2005. Green N.M. et. al., “NITAWL-II: SCALE System Module for Performing Resonance Shielding and Working Library Production”, March 2000. SCALE 4.4, “Modular code system for performing standardized computer analyses for licensing evaluation”, ORNL, 1994. SCALE: A Modular Code System for Performing Standardized Computer Analyses for Licensing Evaluations, ORNL/TM-2005/39, Version 5, Vols. I–III, April 2005. Available from Radiation Safety Information Computational Center at ORNL as CCC-725.
10 APPENDIX
10.1 Appendix A: SCALE, CSAS and ORIGEN-S Most internal programming necessary to calculate k-effective and atomic densities during burnup is written by the SCALE, CSAS and ORIGEN-S system. User errors are thus minimized.
10.1.1 Master vs. working library A master library is different from a working library. All information about each nuclide is present in the master library. Programs such as NITAWL, BONAMI and XDRNPM get the necessary information from the master library. NITAWL creates a working library. This working library is subsequently used by the other programs.
Figure A-1: Creation of problem dependent Master and Working Libraries
10.1.2 SCALE Calculations utilize the multi-energy-group cross sections from standardized JEFF3 data. The SCALE system or the AMPX system, developed at Oak Ridge National Laboratory (ORNL), compute the flux-weighted cross sections, simulating conditions within any given reactor fuel assembly, and converts the data into a library that can be input to ORIGEN-S. Time-dependent libraries may be produced, reflecting fuel composition variations during irradiation. In the SCALE system, general microscopic cross-section data is made problem-dependent through NITAWL-II and XSDRNPM. Then the COUPLE module updates the ORIGEN-S cross-section libraries with the neutron flux-averaged constants from XSDRNPM. Thus, the SCALE system provides the capability of executing ORIGEN-S with data that have been rigorously processed for a particular reactor core. CSAS The Criticality Safety Analysis Sequences (CSAS) were developed within the SCALE code system. CSAS allows for automated, problem dependent cross-section calculations followed by the calculation of the neutron multiplication factor. Below, the different functional modules of CSAS are described. ORIGEN-S calculates the depletion and decay of nuclides.
AMPX Master
Master Master for Problem
Calculate initial densities
BONAMI NITAWL Working for Problem
BONAMI and NITAWL The cross-sections in the AMPX master library for each isotope are known for many energy groups. However, cross-sections of isotopes are assumed to be in a homogeneous environment. Cross-sections in a fuel mixture must be corrected for unit cell effects, including self shielding and rod shadowing. BONAMI and NITAWL correct for these self-shielding effects. BONAMI is a module of the SCALE system which is used to perform Bondarenko calculations for resonance self-shielding. Cross sections and Bondarenko factor data are input from an AMPX master library. The output is written as a problem dependent AMPX master library. [11] NITAWL-II is a module to produce an AMPX working cross-section library that can be used for transport calculations (XSDRNPM). The module provides the Nordheim Integral Treatment for resonance self-shielding. [12] XSDRNPM XSDRNPM is a discrete-ordinates code that, in our case, solves the one-dimensional transport equation, determining the eigenvalue. XSDRNPM uses the fluxes determined from its spectral calculation to collapse input cross sections and write these into different formats. A variety of weighting options are allowed, including zone and cell. COUPLE The average cross-sections are calculated by COUPLE. It solves the formula:
0
0
( ) ( )
( )
E E dE
E dE
σ ϕσ
ϕ
∞
∞=∫
∫
using problem dependent cross-sections and flux (f.e. from XSDRNPM). ORIGEN-S ORIGEN-S is a functional module in the SCALE system and is one of the modules invoked in control module within CSAS. The ORIGEN-S system takes the flux and averaged cross-sections, after which it solves for the depletion equation presented in the previous section. [8] ORIGEN is used as a depletion code with the high temperature reactor at 10 MWth.
10.2 Appendix B – K-effective of calculations 10.2.1 Mixing 232Th to 238U and 235U
Below, you will find the results of the simulation of the k-effective for varying number of passes, Thorium loading, and burnups. The fissionable material at the start of the burnup consists of 235U. 1 pass HM (gram) Burnup 5 7.5 10 60 0.977 80 1.133 1.014 100 1.074 120 1.054 1.007 135 0.939 140 160 3 pass HM (gram) Burnup 5 7.5 10 60 80 1.182 1.031 100 0.992 0.927 120 140 1.069 6 pass HM (gram) Burnup 5 7.5 10 60 1.074 0.998 80 1.190 1.039 100 120 140 1.085 160 1.06 180 1.03
Table B-1: K-effective for different simulations of equilibrium core HTR using 235U.
10.2.2 Mixing 232Th to 233U Below, you will find the results of the simulation of the k-effective for six passes through the core and varying thorium loading and burnups. The fissionable material at the start of the burnup consists of 233U. 6 pass HM (gram) Burnup 5 7.5 10 60 80 1.324 1.193 1.104 100 120 0.991 140 1.235 1.112
Table B-2: K-effective for different simulations of equilibrium core HTR using 233U.
10.3 Appendix C: VSOP The well-known code VSOP, developed by Julich research center in Germany, is suitable for the calculation and analysis of pebble bed HTR gas-cooled reactors with coated particles. It has been used for the physical designs of HTR-10. A four-group energy structure and the two-dimensional R-Z geometry model are used for the physical calculations of the HTR-10. The following essentials in pebble-bed high temperature gas-cooled reactor are taken into account in the physical calculation, including: a) The double heterogeneity of the fuel element with coated particles; b) The streaming correction of the diffusion constant in the core.; c) The buckling feedback in the spectrum; d) The anisotropic neutron diffusion constants correction for the top cavity; e) The effective thermal conductivity in the bed of pebbles. An important difference between VSOP and PEBBLEBURN is that VSOP considers the non-uniform velocity profile of the pebbles through the core.
