Criticality Study on Different Pebble Arrangement inside HTR Reactor Core

Simplification on modeling of high temperature reactor core (HTR) of pebble bed type has been widely developed before. The last calculation that writer develop on modeling and simplification for HTR modelling has been done on TRISO and single pebble, especially on it is KINF and burnup calculation. From that calculation, it is known that TRISO modeling that using fuel kernels and cover (homogenized buffer, PyC and SiC) gives K-INF values that are not (much) different than the complete TRISO modeling (fuel kernel, buffer, PyC and SiC on each different cell). Then the purpose of this study was to analyze the effect on KEFF and calculation time of combined TRISO particle arrangement modeling in the HTR fuel pebble and this pebble arrangement inside reactor core using MCNPX. The modeling variations that will be carried out include modeling of HTR fuel pebble using simplified TRISO (fuel kernel and homogenized TRISO coating layers) that uniformly dispersed inside pebble using HCP, SC, FCC and BCC lattice, that arranged inside reactor core (also) using HCP, SC, FCC and BCC lattice. For all variations mentioned above, K-EFF calculations has been done for each fuel height variation from 90-190 cm inside reactor core, with 50% fuel pebble to fuel-moderator pebble ratio, in 61% pebble volume fraction ratio except Simple Cubic (SC) lattice (max. 52.36%). Whole modelling gives K-EFF that have not much deviation except all modelling using SC pebble arrangement inside reactor core, because its low packing fraction. SC-type TRISO dispersion mode inside pebble always need more calculation time than other model. The modeling using HCP TRISO unit inside HCP pebble unit inside reactor core gives consistently short calculation time, same as almost all calculation using FCC TRISO unit inside pebble always have shortest calculation time compare to other TRISO unit. FCC and BCC pebble unit inside reactor core using less calculation time compare to HCP at most calculation.


Introduction
Previously on finding simpler way to modelling pebble bed high temperature reactor (HTR) core, Indonesia has found that the homogenized TRISO cover model (homogenized buffer, PyC and SiC) can be used as an initial approach for TRISO modeling of HTR full-core. Then selection of TRISO unit types that can facilitate full core modeling still requires further research, but SC (simple Cubic) type modeling can be chosen as initial approach [1,2,3,4,5,6,7,8,9]. As part of modeling of HTR to calculate equilibrium condition, the initial approach to see the effect of modeling and simplification that will be used in full-scale HTR modeling can start to be done on the next level, the reactor core itself.
The criticality calculation of HTR-10 has been done by INET as part of HTGR Test Module Core Physics Benchmarks using VSOP 2D and MCNP [10]. Tsinghua University has also been done the criticality calculation of HTR-10 using Random geometry capability in RMC code [11]. That last calculation is an improvement from previous calculation using RMC code on benchmarking HTR-10 [12].

Main Parameter
The main parameter of HTR that will be used inside this study could be seen on Figure 1 and its radial dimension on Figure 2. On Figure 2, we could see that hexagonal lattice has been used as part of HCP pebble dispersion inside core. Other pebble dispersion mode will be used like square lattice for SC, FCC and BCC and this type of lattice will also be used for TRISO dispersion inside pebble.   3 TRISO modelling that chosen from pervious study is TRISO which all coating layers is made into one homogenized cover region. This fuel kernel cover is made up of the buffer material, PyC and SiC with the mass of each component and the overall size of TRISO unchanged. Dimension of TRISO modelling that used in this study could be seen in Figure 3. Density of UO2 is set to 10.4 gr/cc (17% 235 U) and homogenized TRISO cover has density for about 1.929 gr/cc from combination of buffer material (1.04 gr/cc), PyC (1.88 gr/cc) and SiC (3.15 gr/cc). In this study, reactor using helium as coolant paired with 1.73 gr/cc dummy pebbles density and reactor using dry air as coolant paired with 1.84 gr/cc dummy pebble density will calculated as 2 bonus variation beside TRISO or pebble dispersion mode and loading height. Temperature of all cell set to 27℃ with default MCNPX cross section library, calculated using 2.5GHz dual core processor, 8GB RAM, 500 GB HDD.

Fueled Pebble and Dummy
TRISO unit variation that used inside pebble's fuel zone are HCP using hexagonal lattice, SC, FCC and BCC using square lattice. To maintain the number of TRISOs in a pebble of 8335 particles, the dimensions of each unit will be adjusted to achieve the desired packing fraction (5.0248%vol of TRISO inside the fuel zone). The dimensions for each TRISO unit can be seen in Figure 4. The number of TRISO particles in HCP, SC, FCC and BCC-shaped unit are 6, 1, 4 and 2 TRISO particles respectively. Then TRISO unit is auto-fill to fuel region of fueled pebble that have dimension as seen on Figure 5. Dummy pebble has same dimension like fueled pebble, 3 cm pebble radius, but its only filled with graphite with uniform density, without fueled zone.

Pebble dispersion inside core
Pebble unit variation that used inside reactor core are HCP using hexagonal lattice, SC, FCC and BCC using square lattice. The dimensions of each unit will be adjusted to achieve the desired pebble packing fraction 61%, except SC that only has maximum packing fraction 52.36%. The dimensions for each TRISO unit can be seen in Figure 6. For this calculation, 3 type of pebble configuration has been done. First configuration is configuring the position of "pebble unit that filled with fueled pebble only" and "pebble unit that filled with dummy pebble only" that makes 4 variation of pebble unit will fill the reactor core as shown in Figure 7 to Figure 10. Within simulation, we named it X-version.
Second variation of pebble configuration that selected is variation in positioning fueled pebble and dummy pebble inside each pebble unit. Because SC unit consist of 1 pebble per unit, so SC unit mode wasn't included in this variation. Then because HCP unit consist of 6 pebble per unit that has more than 1 configuration mode that available, so HCP unit has 2 variation of fueled pebble and dummy pebble inside its unit, and we called it "HCP 3 center" and "HCP 2 center" to define number of pebbles on its center that variated. Within simulation, we named second variation as Xa-version and it could be seen in Figure 11.
Then, third variation of pebble configuration is also a combined version of fueled pebble and dummy pebble inside each unit, but the different is only on reversed version of second variation. So, every dummy pebble in Xa-version will changed to fueled pebble and vice versa, as shown in Figure 12. We name it with Xb-version.  Figure 7. HCP X-version pebble dispersion mode  For second and third variation, they don't need any further configuration within core, so lattice input for this variation is simpler than the first one. Figure 13 to Figure 16 will show you an axial and radial cutaway of HTR reactor using two configuration that mentioned before.  All TRISO unit variation (4) will combined with pebble unit variation (4), and make this study have 16 combination that will be used to calculate K-EFF of difference loading height of HTR from 90-190 cm with 10 cm increment. KCODE is used on this case that use 1000 neutron per cycle with 50 cycle skipped (inactive) from 200 total cycle. KSRC that used in this calculation is set to the middle of zero lattice element of each pebble unit.

Results and discussion
.1. Helium as coolant and 1.73 gr/cc dummy pebble density In this section, Helium coolant and 1.73 gr/cc dummy pebble density used to calculate K-EFF of different loading height from 16 variation that mention before. The K-EFF data for X-version of pebble unit (consist of HCP, SC, FCC, and BCC TRISO unit that combined with HCP, SC, FCC and BCC pebble unit) could be seen in Figure 17. Then, data for Xa and Xb-version of pebble unit (consist of HCP, SC, FCC, and BCC TRISO unit that combined with HCP 3 center, HCP 2 center, FCC and BCC pebble unit) could be seen in Figure 18 and 19 respectively. Its KEFF deviation from INET VSOP 2D could be seen in Figure 20 to 22.  It can be seen from Figure 17, that SC pebble unit always has a lower K-EFF than other pebble unit type because it has limitation on geometry that make SC only could achieve 52.67% packing fraction, lower that other type of pebble unit that could achieve 61% or higher. Then it could be seen that HCP, FCC and BCC could give us minimum deviation from other calculation that has been done before.
From Figure 19 we could see that some curve from Xb-version has more deviation that X-version or Xaversion. It could be seen on Figure 20 to 22 that there is higher deviation from INET VSOP 2D K-EFF value on Xb-version of TRISO and pebble unit variation. Yellow lines (SC TRISO unit var) gives more deviation than other variation, followed by black lines (FCC TRISO unit var), blue lines (HCP TRISO unit) and green lines (BCC TRISO unit) are overlapping each other.
From Table 1 to 3, we could see that SC TRISO unit are more often on red label (longer computing time) for computing time than other TRISO unit type even though it always had a minimum code lines because its simplicity. Then shortest computing time are more often happen when using FCC TRISO unit, followed by HCP unit and BCC unit.
Trend for computing time of pebble unit are a bit more difficult because of fluctuation on calculation time value that affected by computer that used for this calculation is also used for daily task, sometimes it's on maximum load but on the other minute it's on normal load. So, it's glad to see that there is some trend on TRISO unit level, but it's pretty normal if there are no explicit trend within some variation, even after averaging its value. Generally, HCP, FCC and BCC pebble unit give us shortest average calculating time, but only on specific combination, like HCP pebble unit with HCP unit or FCC TRISO unit. FCC pebble unit has second short average computing time when combined with FCC and BCC, close enough to BCC pebble unit that has shortest average computing time when combined with FCC and BCC TRISO unit on Xb-version.

.2. Dry air as coolant and 1.84 gr/cc dummy pebble density
In this section, Dry air is chosen as coolant and 1.84 gr/cc dummy pebble density used to calculate K-EFF of different loading height from 16 variation that mention before. The K-EFF data for X-version of pebble unit could be seen in Figure 23. Then, data for Xa and Xb-version of pebble unit could be seen in Figure 24 and 25 respectively. Its KEFF deviation from HCP TRISO unit variance (this reference chosen because HCP input code complexity is higher than other TRISO unit type) could be seen in Figure 26 to 28.