炉物理の研究 第 70 号（2018 年 4 月）

Supercritical transient analysis in possible fuel debris systems at Fukushima Daiichi
NPS by multi-region approach based on integral kinetic model
Delgersaikhan Tuyaa and Toru Obarab*aDepartment of Nuclear Engineering, Tokyo Institute of Technology, Ookayama 2-12-1-N1-19,
Meguro-ku, Tokyo 152-8550, Japan;b
Laboratory for Advanced Nuclear Energy, Institute of Innovative Research, Tokyo Institute ofTechnology, Ookayama 2-12-1-N1-19, Meguro-ku, Tokyo 152-8550, Japan

Introduction

Shortly after the accident at the Fukushima Daiichi NPS (1FNPS) occurred an effort tosafely decommission the damaged reactors has started and been steadily going forward. One of
the important topics surrounding the decommissioning activity is criticality safety during a
retrieval of fuel debris formed inside the damaged reactors. As a full- or partial-submersion
method, in which fuel debris is flooded with water, is likely to be a preferred method for fueldebris retrieval, there is possibility of criticality accident under an appropriate condition thatcan be formed due to presence of fuel debris and light water.
According to a study by some experts in the nuclear criticality safety field in Japan, arisk-informed criticality control is preferable over a deterministic control, a method thatprevents criticality accident by, for example, poisoning a water with strong neutron absorbing
materials, which was employed for defueling of Three-Mile Island Unit 2 (TMI-2) (Tonoike etal., 2015). Such risk-informed criticality control of fuel debris allows small possibility ofcriticality accident and provides a mitigation system should the accident occur. Whether it be
the risk-informed criticality control or the deterministic control, for overall criticality control
of fuel debris, analyses on possible accident can be important for establishing safety measuresagainst criticality accident in order to eventually protect on-site workers.
To realistically analyze possible criticality accident during fuel debris retrieval, acondition of fuel debris and its possible change in terms of geometry, composition, and amountof water are must be known first. However, currently the condition of fuel debris is unknown
and fuel debris retrieval methods are not yet completely determined, making it hard to do anyrealistic analysis. Secondly, an appropriate method should be used for such analyses. Since it
is highly likely that fuel debris contains coupled distinct regions in terms of geometry orcomposition interacting with one another via neutron transport, a method which takes aspace/region-dependency into account is preferred.
Due to the current uncertain condition of fuel debris, we made several simple andhypothetical coupled fuel debris systems that are helpful as a preliminary systems for the1FNPS. These systems also clarifies the use of the space/region-dependent method. In specific,
in the current study, we used a multi-region approach based on the integral kinetic model (IKM),
which models a system in region-wise manner by taking their interaction into account using
secondary-fission probability density functions (Gulevich and Kukharchuk, 2004; Takezawa
and Obara, 2012, 2010). During the time of our analyses on several types of fuel debris systems,
we have also been continuously developing and improving the multi-region approach itself. In
this study, the earlier version of the multi-region approach was used for supercritical transient
analyses in simple fuel debris systems of single or coupled two regions with symmetric andasymmetric geometry, while the latter version, which is the base of Multi-region Integral
Kinetic (MIK) code that we have developed, was used for supercritical analyses in the
hypothetical fuel debris systems with more realistic geometry and composition than theprevious systems.
In general, the purpose of this study was to establish the multi-region approach as anapplicable method to supercritical transient in various fuel debris systems ranging from thesimple systems of two coupled regions with simple composition and geometry to the rather
realistic yet hypothetical systems consisting of three coupled regions with more complicatedcomposition and geometry.
As this article is intended as a short introduction of this study, in the remaining part of*Corresponding author. Email: tobara@lane.iir.titech.ac.jp1炉物理の研究 第 70 号（2018 年 4 月）

it we will briefly present some of the results and the main conclusion of the study.
Brief results of the study
Here we show the descriptions and analysis results of each type of system briefly alongwith analysis method. A feedback due to Doppler broadening was considered in all systems
except the validation problem of the improved multi-region approach involving Godiva core,in which a feedback due to change in physical density was considered. In addition, in all systems,a heat transfer between the regions was not modeled.
The first systems we analyzed involved single and two symmetrical spherical regions
inside of light water. Each region consisted of small spherical fuel debris particles, whose
composition is simple UO2 with 5.0 wt% enrichment of 235U. As for the two-region systems,
the regions were separated by certain distances. The distance between the regions was changed
while the inserted reactivity kept constant, so that the effect of distance on the transient result
could be investigated. In total, we made three two-region systems by changing the distance,plus one single-region system. For each system, the earlier version of the multi-region approach
was applied to obtain time- and region-dependent fission rate and temperature profile, andregion-wise and total energy release during the first power spike following the step-wise
reactivity insertion above prompt-critical level. In short, it was found from the results that as
the distance between the regions increased, total energy release decreased in spite of nearly thesame inserted reactivity in all systems. More on the results of these analysis can be found in thereference (Tuya and Obara, 2016).
The next systems were consisted of symmetric or asymmetric two spherical regions
separated by certain distances inside of light water similar with the previous systems. Again,
the regions consisted of small spherical UO2 particles with 5.0 wt% enrichment. The difference,
however, is that the different amount of reactivity was inserted into each system by changing
the distance between the regions, while the geometrical size of each region kept constant. The
main purpose of the analysis involving these systems was to compare the multi-region approachwith a conventional kinetic analysis method known as a one-point kinetics model (PKM). The
earlier version of the multi-region approach and the PKM were applied to supercriticaltransients in these systems. The obtained results were region-wise fission rate and temperature
profile as well as region-wise and total energy releases by the multi-region approach; total
fission rate and temperature profile and total energy release by the PKM during the first power
spike following the step-wise reactivity insertion. In brief, the results showed that in all systems
the PKM overestimated energy release compared to that by the multi-region approach. Moreon these analyses can be found in the reference (Tuya and Obara, 2017).
In the next part of this study, we introduced the improved multi-region approach (i.e.,the MIK code) and then attempted to validate it through supercritical transient in simple Godiva
core by comparing the results with that of the Godiva experiment. The experimental results
were obtained from the work by Wimett et at (Wimett et al., 1956). In short, the results by theimproved multi-region approach were in reasonably good agreement with the experimental
results despite its simpler geometry and feedback models. However, the tail region of the power
profile, which was caused by the short-lived delayed neutron precursors, observed in theexperiment was not simulated by the improved multi-region approach as it did not take thedelayed neutrons into account. The detailed discussion of the improved multi-region approachand the results of these analyses can be found in the reference (Tuya et al., 2017).
And in the last part of this study, we performed supercritical transient analysis in themore practical yet hypothetical fuel debris systems as a preliminary fuel debris system possibleat the 1FNPS using the improved multi-region approach. These systems are more practicalcompared to the previous systems in terms of geometry and composition. The hypothetical fueldebris systems were based on the scenario in which some fragmented small fuel particles drop
on top of some consolidated fuel debris region forming supercritical system inside of light water.
The composition of fuel debris was homogeneous mixture of fuel, structural materials, andsome concrete and was based on the study on fuel debris melting and spreading analysis
performed elsewhere (Kevin R. and Matthew W., 2013). The hypothetical systems weremodeled as three-region system in the improved multi-region approach. The obtained results
included region-wise fission rate and temperature profile, and region-wise and total energy
release during the first spike of the transient. It was aimed also in these analyses to evaluate2炉物理の研究 第 70 号（2018 年 4 月）

relative impact of certain parameters on the result, specifically on total energy release, of thesupercritical transient. In brief, from the results it was found that the enrichment of 235U was
the parameter with the highest impact followed by the angle of repose of fragmented conicaldebris region and the height of consolidated cylindrical debris region.
Brief conclusion
In this study, supercritical transient analyses in various simple and rather complicatedfuel debris systems were performed using the multi-region approach based on the integral
kinetic model (IKM). In all systems, the feedback due to either Doppler broadening or change
in physical density was considered.
In general, this study established the multi-region approach based on the integral kinetic
model as an applicable method to supercritical transient in various fuel debris systems that canbe possible at the Fukushima Daiichi NPS to some extent, and showed that the multi-region
approach can be useful tool to investigate characteristics of supercritical transient involving fueldebris.
While the analyses introduced in this study were being conducted, at the same time wehave also been improving and further developing the multi-region approach itself. The latest
development of the multi-region approach, referred to as the improved multi-region approachin this study, was named the Multi-region Integral Kinetic (MIK) code.
As for the MIK code, several topics such as treatment of delayed neutrons, more realistic
feedback mechanisms including heat transfer, and practical reactivity insertion are being
considered to be developed and included it in near future.
Partial references
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1: Melt spreading and core-concrete interaction analyses with MELTSPREAD andCORQUENCH. Technical report. ORNL/TM-2012/455.
Takezawa, H., Obara, T., 2012. New Approach to Space-Dependent Kinetic Analysis by theIntegral Kinetic Model. Nucl. Sci. Eng. 171, 1–12. doi:10.13182/NSE09-59
Takezawa, H., Obara, T., 2010. Calculation of the Integral Kinetic Model Transient Parametersby the Monte Carlo Method for Space-Dependent Kinetic Analysis. Nucl. Sci. Eng. 164,80–86. doi:10.13182/NSE08-91
Tonoike, K., Yamane, Y., Umeda, M., Izawa, K., Sono, H., 2015. Study on criticality control offuel debris by Japan Atomic Energy Agency to support Nuclear Regulation Authority ofJapan, in: International Conference on Nuclear Criticality Safety (ICNC 2015). pp. 20–27.
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