The Korea Atomic Energy Research Institute (KAERI) is currently developing a process-based performance assessment model known as APro. Distinguished from the previous system-level safety assessment model developed by KAERI, APro exhibits the capacity to encompass a threedimensional biosphere domain, evolving over the long term. In this study, we elucidate the methodology employed in developing the dose assessment module of APro and present the module’s functionalities. The procedural steps underlying radiation dose calculations within the APro framework can be succinctly outlined as follows: 1) Definition of a landscape model, utilizing information derived from a specified snapshot period provided by the APro biosphere transport module; 2) Generation of unit biotope objects spanning the landscape; 3) Evaluation of radionuclide transfer within the soil medium; 4) Calculation of activity concentration for flora and fauna groups; 5) Assessment of the distribution of effective dose among representative human groups; 6) Progressing through successive time steps. The APro dose calculation module exhibits notable capabilities that encompass: 1) Accounting for radionuclide decay and ingrowth; 2) Facilitating transfer through unsaturated porous media; 3) Considering sorption effects; 4) Addressing the inheritance of radioactivity between various landscape models; 5) Offering customizable ecosystem parameters; 6) Providing flexibility for user-defined exposure pathways. Leveraging these functionalities of the dose assessment module, APro is proficient in evaluating the distribution of radiological doses and associated risks for representative population groups, all while accounting for the dynamic, long-term evolution of the biosphere, including alterations in land cover.

APro, a process-based total system performance assessment (TSPA) tool for a geological disposal system, has a framework for simulating the radionuclide transport affected by thermal, hydraulic, mechanical or geochemical changes occurred in the disposal system. APro aims to be applied for the TSPA to long-term (> 100,000) evolution scenarios in real-world repository having more than 10,000 boreholes. In this large-scale TSPA, it is important not only to develop a high-performance numerical approach, but also to apply an efficient post-processing approach to massive spatiotemporal data. The post-processing refers to validating numerical analysis results, analyzing and evaluating target systems through data processing or visualization. Since APro uses COMSOL interface, the postprocessing function in COMSOL can be used. However, when the data size increases due to largescale numerical analysis, the time for the COMSOL post-processing increases, resulting in a problem that the analysis and evaluation are not performed effectively. In this case, it is possible to extract necessary data using the COMSOL exporting function and importing it into an external postprocessing program for the analysis and evaluation. In this study, the efficiency of external post-processing with extracted data from COMSOL was reviewed. And, we derived a proper data extraction approach (format and structure) that can increase efficiency of external post-processing.

The safety of deep geological disposal systems has to be ensured to guarantee the isolation of radionuclides from human and related environments for over a million years. Over such a long timeframe, disposal systems can be influenced by climate change, leading to significant long-term impacts on the hydrogeological condition, including changes in temperature, precipitation and sea levels. These changes can affect groundwater flow, alter geochemical conditions, and directly/ indirectly impact the stability of the repository. Hence, it is essential to conduct a safety assessment that considers the long-term evolution induced by climate change. In this context, the Korea Atomic Energy Research Institute (KAERI) is developing the Adaptive Process-based total system performance assessment framework for a geological disposal system (APro). Currently, numerical modules for APro are under development to account for the longterm evolution that can influence groundwater flow and radionuclide transport in the far-field of the disposal system. This study focuses on the development of two numerical modules designed to model permafrost formation and buoyance force due to relative density changes. Permafrost is defined as a ground in which temperature remains below zero-isotherm (0°C) continuously for more than two consecutive years. In regions where permafrost forms, the relative permeability of porous media is significantly reduced. The changes in permeability due to permafrost formation are modelled by calculating the unfrozen fluid content within a porous medium. Meanwhile, buoyancy force can occur when there is a difference in density at the boundary of two distinct water groups, such as seawater (salt water) and freshwater. Sea level change associated with climate change can alter the boundary between seawater and freshwater, resulting in changes in groundwater flow. The buoyancy force due to relative density is modelled by adjusting concentration boundary conditions. Using the developed numerical modules, we evaluated the long-term evolution’s effects by analyzing radionuclide transport in the far-field of the disposal system. Incorporating permafrost and buoyancy force modelling into the APro framework will contribute valuable insights into the complex interactions between geological and climatic factors, enhancing our ability to ensure the secure isolation of radionuclides for extended periods.

Understanding the long-term geochemical evolution of engineered barrier system is crucial for conducting safety assessment in high-level radioactive waste disposal repository. One critical scenario to consider is the intrusion of seawater into the engineered barrier system, which may occur due to global sea level rise. Seawater is characterized by its high ionic strength and abundant dissolved cations, including Na, K, and Mg. When seawater infiltrates an engineered barrier, such dissolved cations displace interlayer cations within the montmorillonite and affect to precipitation/ dissolution of accessory minerals in bentonite buffer. These geochemical reactions change the porewater chemistry of bentonite buffer and influence the reactive transport of radionuclides when it leaked from the canister. In this study, the adaptive process-based total system performance assessment framework (APro), developed by the Korea Atomic Energy Research Institute, was utilized to simulate the geochemical evolution of engineered barrier system resulting from seawater intrusion. Here, the APro simulated the geochemical evolution in bentonite porewater and mineral composition by considering various geochemical reactions such as mineral precipitation/dissolution, temperature, redox processes, cation exchange, and surface complexation mechanisms. The simulation results showed that the seawater intrusion led to the dissolution of gypsum and partial precipitation of calcite, dolomite, and siderite within the engineered barrier system. Additionally, the composition of interlayer cation in montmorillonite was changed, with an increase in Na, K, and Mg and a decrease in Ca, because the concentrations of Na, K, and Mg in seawater were 2-10 times higher than those in the initial bentonite porewater. Further studies will evaluate the geochemical sorption and transport of leaked uranium-238 and iodine-129 by applying TDB-based sorption model.

APro, developed in KAERI for the process-based total system performance assessment (TSPA) of deep geological disposal systems, performs finite element method (FEM)-based multiphysics analysis. In the FEM-based analysis, the mesh element quality influences the numerical solution accuracy, memory requirement, and computation time. Therefore, an appropriate mesh structure should be constructed before the mesh stability analysis to achieve an accurate and efficient process-based TSPA. A generic reference case of DECOVALEX-2023 Task F, which has been proposed for simulating stationary groundwater flow and time-dependent conservative transport of two tracers, was used in this study for mesh stability analysis. The relative differences in tracer concentration varying mesh structures were determined by comparing with the results for the finest mesh structure. For calculation efficiency, the memory requirements and computation time were compared. Based on the mesh stability analysis, an approach based on adaptive mesh refinement was developed to resolve the error in the early stage of the simulation time-period. It was observed that the relative difference in the tracer concentration significantly decreased with high calculation efficiency.

The Korean Nuclear Safety and Security Commission has established a general guideline for the disposal of high-level waste, which requires that radiological effects from a disposal facility should not exceed the regulatory safety indicator, a radiological risk. The post-closure safety assessment of the disposal facility aims to evaluate the radiological dose against a representative person, taking into account nuclide transport and exposure pathways and their corresponding probabilities. The biosphere is a critical component of radiation protection in a disposal system, and the biosphere model is concerned with nuclide transport through the surface medium and the doses to human beings due to the contaminated surface environment. In past studies by the Korea Atomic Energy Research Institute (KAERI), the biosphere model was constructed using a representative illustration of surface topographies and groundwater conditions, assuming that the representative surface environment would not change in the future. Each topography was conceptualized as a single compartment, and distributed surface contamination over the geometrical domain was abstracted into 0D. As a result, the existing biosphere model had limitations, such as a lack of quantitative descriptions of various transport and exposure pathways, and an inability to consider the evolution of the surface environment over time. These limitations hinder the accurate evaluation of radiological dose in the safety assessment. To overcome these limitations, recent developments in biosphere modeling have incorporated the nuclide transport process over a 2D or 3D domain, integrating the time-dependent evolution of the surface environment. In this study, we reviewed the methodology for biosphere modeling to assess the radiological dose given by distributed surface contamination over a 2D domain. Based on this review, we discussed the model requirements for a numerical module for biosphere dose assessment that will be implemented in the APro platform, a performance assessment tool being developed by the KAERI. Finally, we proposed a conceptual model for the numerical module of dose assessment.

In the engineered barrier system of deep geological disposal repository, complex physicochemical phenomena occur throughout the entire disposal time, consequently impacting the safety function. The bentonite buffer, a significant component of the engineered barrier system, can be geochemically altered due to the changes in host rock groundwater, temperature, and redox condition. Such changes may have direct or indirect effects on radionuclide migration in case of canister failure. Therefore, a modeling tool that accounts for coupled thermal-hydraulic-mechanical-chemical (THMC) processes is necessary for the safety assessment. To this end, the Korea Atomic Energy Research Institute (KAERI) has developed the APro, a modeling interface for conducting safety assessment of deep geological disposal repository. The APro considers coupled THMC processes that influence radionuclide migration. Here, the solute transport considering thermal and hydraulic processes are calculated using the COMSOL multi-physics, while geochemical reactions are carried out in PHREEQC. The two software are coupled using a sequential non-iterative operator splitting approach, and transport of non-water H, non-water O, and charge were additionally considered to enhance the coupling model stability. Finally, the applicability of APro to simulate long-term geochemical evolution of bentonite was demonstrated through benchmark studies to evaluate the effects of mineral precipitation/dissolution, temperature, redox, and seawater intrusion.

The most important thing in development of a process-based TSPA (Total System Performance Assessment) tool for large-scale disposal systems (like APro) is to use efficient numerical analysis methods for the large-scale problems. When analyzing the borehole in which the most diverse physical phenomena occur in connection with each other, the finest mesh in the system is applied to increase the analysis accuracy. Since thousands of such boreholes would be placed in the future disposal system, the numerical analysis for the system becomes significantly slower, or even impossible due to the memory problem in cases. In this study, we propose a tractable approach, so called global-local iterative analysis method, to solve the large-scale process-based TSPA problem numerically. The global-local iterative analysis method goes through the following process: 1) By applying a coarse mesh to the borehole area the size of the problem of global domain (entire disposal system) is reduced and the numerical analysis is performed for the global domain. 2) Solutions in previous step are used as a boundary condition of the problem of local domain (a unit space containing one borehole and little part of rock), the fine mesh is applied to the borehole area, and the numerical analysis is performed for each local domain. 3) Solutions in previous step are used as boundary conditions of boreholes in the problem of global domain and the numerical analysis is performed for the global domain. 4) steps 2) and 3) are repeated. The solution derived by the global-local iterative analysis method is expected to be closer to the solution derived by the numerical analysis of the global problem applying the fine mesh to boreholes. In addition, since local problems become independent problems the parallel computing can be introduced to increase calculation efficiency. This study analyzes the numerical error of the globallocal iterative analysis method and evaluates the number of iterations in which the solution satisfies the convergence criteria. And increasing computational efficiency from the parallel computing using HPC system is also analyzed.

With the increasing demand for a repository to safely dispose of high-level radioactive waste (HLW), it is imperative to conduct a safety assessment for HLW disposal facilities for ensuring the permanent isolation of radionuclides. For this purpose, the Korea Atomic Energy Research Institute (KAERI) is currently developing the Adaptive Process-based total system performance assessment framework for a geological disposal system (APro). A far-field module, which specifically focuses on fluid flow and radionuclide transport in the host rock, is one of several modules comprising APro. In Korea, crystalline rock is considered the host rock for deep geological disposal facilities due to its high thermal conductivity and extremely low permeability. However, the presence of complex fracture system in crystalline rock poses a significant challenge for managing fluid flow and nuclide transport. To address this challenge, KAERI is participating in DECOVALEX-2023 Task F1, which seeks to compare and verify modeling results using various levels of performance assessment models developed by each country for reference disposal systems. Through the benchmark problems suggested by DECOVALEX-2023 Task F1, KAERI adopts the Discrete Fracture-Matrix (DFM) as the primary fracture modeling approach. In this study, the transport processes of reactive tracers in fractured rock, modeled with DFM, are simulated. Specifically, three different tracers (conservative, decaying, adsorbing) are introduced through the fracture under identical injecting conditions. Thereafter, the breakthrough curves of each tracer are compared to observe the impact of reactive tracers on nuclide transport. The results of this study will contribute to a better understanding of nuclide behavior in subsurface fractured rock under various conditions.

Various linear system solvers with multi-physics analysis schemes are compared focusing on the near-field region considering thermal-hydraulic-chemical (THC) coupled multi-physics phenomena. APro, developed at KAERI for total system performance assessment (TSPA), performs a finite element analysis with COMSOL, for which the various combinations of linear system solvers and multi-physics analysis schemes should to be compared. The KBS-3 type disposal system proposed by Sweden is set as the target system and the near-field region, which accounts for most of the computational burden is considered. For comparison of numerical analysis methods, the computing time and memory requirement are the main concerns and thus the simulation time is set up to one year. With a single deposition hole problem, PARDISO and GMRESSSOR are selected as representative direct and iterative solvers respectively. The performance of representative linear system solvers is then examined through a problem with an increasing number of deposition holes and the GMRES-SSOR solver with a segregated scheme shows the best performance with respect to the computing time and memory requirement. The results of the comparative analysis are expected to provide a good guideline to choose better numerical analysis methods for TSPA.

이 논문은 대중음악의 리듬에 큰 영향을 끼친 펑크 리듬과 아프로 큐반 리듬을 구조적 관점으로 분석하여 그 연관성과 응용과정을 연구하였다. 펑크 리듬은 1965년 제임스 브라운과 그의 밴드들 에 의해 발생 및 발전되었으며, 아프리카에서 온 흑인들에게 영향을 받은 라틴 음악의 리듬을 미 국 대중음악에 적용하고 융합하여 만들어 낸 리듬이다. 대중음악 리듬에 큰 영향을 끼치고 있는 펑크 리듬의 발생과 발전에 대해 체계적으로 분석하여, 리듬의 응용과 융합 방법의 원리를 제시하 는 것이 이 연구의 목적이다. 연구 방법은 대중음악 리듬의 혁명으로 불리는 1960년대 중반 이후 의 제임스 브라운의 앨범에 정착된 펑크 리듬과 아프로 큐반 음악의 리듬 구조를 비교하여 연관성 을 분석하였고, 대중음악 리듬으로 응용 및 적용하는 과정에 대해 추론하였다. 연구 결과 아프로 큐반의 대표적인 리듬들과 대중음악에서 사용되는 펑크의 중심 리듬에서 그 연관성을 찾을 수 있 었으며, 특히 드럼의 킥 패턴과 킥과 스네어 드럼 조합의 패턴을 응용하여 대중음악 리듬으로 만 들었다는 것을 도출해 내었다. 마지막으로 이 방법을 활용하여 좀 더 많은 전통 리듬들을 응용하 여 새로운 대중음악의 리듬을 응용하고 만들어내는 가능성을 제시하였다.

APro, a modularized framework of the process-based total system performance assessment, has been developed by KAERI to simulate the radionuclide transport in geological disposal system considering multi-physics phenomena. However, the target problem including more than 10,000 boreholes and over 100,000 years of simulation time is computationally challenging to deal with numerical solvers provided by COMSOL Multiphysics constituting APro. To alleviate the computational burden, machine learning (ML) techniques have been studied to develop a surrogate model replacing the heavy computation part. In recent studies, attempts have been made to integrate the knowledge of physics and numerical methods into the ML model for partial differential equations (PDEs). Unlike conventional ML approaches solely relying on data-driven method, the integration can help to make the ML model more specialized for solving PDEs. The hybrid neural network (NN) solver method is one of the strategies to develop more efficient PDE solver by interleaving NN with numerical solvers like finite element method (FEM). The hybrid NN model on the premise of numerical solver is easier to train and more stable than the purely data-driven model. For example, one previous study has used the hybrid NN model as a corrector for an incomplete numerical solver for the advection-diffusion problem. In every time step of simulation, NN corrects the error of incomplete solution obtained by a relaxed numerical solver with coarse meshing. The simulation in the next time step starts from the corrected solution, so NN interacts with the numerical solver iteratively. If the corrector is successfully trained, the incomplete but fast solver with corrector can provide reliable results comparable to the original massive solver. This study adopts the hybrid concept to develop a surrogate model for the near-field region, which is the heavy computation part in the simulation of geological disposal system. Various incomplete models such as coarse meshing or emptying the borehole domain are studied to construct a hybrid NN solver. This study also covers how to embed the hybrid NN in COMSOL Multiphysics to train and use it during the simulation.

Domain decomposition method (DDM) has been widely employed for the numerical analysis of large-scale problems due to its applicability to parallel computing. DDM divides the modeling domain into a set of subdomains and obtains the entire solution iteratively until the values of each subdomain which are shared with other subdomains, such as boundary values, are converged. Therefore, in general, DDM is a memory-efficient iterative algorithm with inherent parallelism on the geometric level. APro, the process-based total system performance assessment model, aims for simulating the radionuclide transport considering coupled multi-physics phenomena occurring in large-scale geological disposal system, which are inevitably accompanied by huge memory burden. Therefore, DDM is applicable for the large-scale problem of APro and its performance in parallel computing needs to be examined. The DDM solvers provided by COMSOL which constitute APro can be classified into two methods. One is the overlapping Schwarz method that each subdomain overlaps its neighboring domains and the other is the Schur complement method that subdomains are non-overlapping and separated by boundary domains. For the Schwarz method, the additive, hybrid, multiplicative and symmetric methods can be selected according to the solution update scheme. And for the Schur method, the additive and multiplicative ordering options can be chosen for solving Schur complement system. In this study, the calculation efficiency of the DDM solvers in COMSOL and the applicability to the cluster environment were examined. In aspect of efficiency, the memory requirements with different number of subdomains and calculation schemes were compared in a single node. Then, the memory requirements with increasing number of disposal tunnels and deposition holes were investigated in multiple nodes. As a result, on the cluster environment, with the help of distributed memory architecture which enables efficient memory usage, the applicability of DDM solvers to the large-scale problem of APro was confirmed.

APro, developed by KAERI as a process-based total system performance assessment model, can simulate the radionuclide transport affected by thermal, hydraulic, mechanical and geochemical changes that may occurs in the engineering and natural barriers of a geological disposal system. APro targets a large-scale and heterogeneous 3D system that includes more than 10,000 boreholes located about 500 m underground and hundreds of fractures of different sizes distributed within an area of several km2. Simulating transport and reaction phenomena for such a system through the global implicit approach (GIA) may require considerable computational resources or be intractable in some cases. Therefore, APro adopts the sequential non-iterative approach (SNIA), one of the operator splitting (OS) methods, to separate the mass transport and reaction phenomena into independent problems. By using SNIA, the parallel computation performance in APro with multiple cores is expected to be improved. In this study, the effect of SNIA on the parallel computation performance was analyzed through a simple 1D reactive transport problem. Without SNIA, finite difference equations, discretized from the partial differential equations (PDEs) describing the reactive transport problem, have to be solved at once because all dependent variables are nonlinearly and spatially interconnected through reaction and mass transport terms. When the reaction and mass transport terms are separated through SNIA, the mass transport problem can be converted into independent linear equations for each chemical and the efficient linear system solver can be applied to each linear equation. In particular, since the reaction problem is changed to independent nonlinear equations for each node, the parallel computation performance can be greatly improved. To verify this, the 1D reactive transport problem was implemented in MATLAB, and SNIA and GIA were applied to solve the problem. As a result, there was no significant difference in results between SNIA and GIA for proper spatial and temporal discretization, which verified the accuracy of SNIA. In order to see the parallel computation performance, the calculation times for SNIA and GIA with increasing number of cores were measured and compared. As the number of cores increased, the SNIA calculation speed became faster than that of GIA, which verified that SNIA could improve parallel computation performance in APro. In the future, the effect of SNIA on the parallel computation performance will be verified for the numerical analysis of large-scale geological disposal systems.

국내 고준위 방사성폐기물 심층처분시스템에 대한 프로세스 기반의 종합성능평가체계(APro) 개발을 위하여 사용자 편의성이 향상된 모델링 인터페이스를 구축하였다. APro의 모델링 인터페이스는 프로그래밍 언어인 MATLAB을 이용하여 구축되었고, 다중물리현상 모사가 가능한 COMSOL과 지화학반응 계산이 가능한 PHREEQC를 계산 엔진으로 활용하여 연산 자분리 방식을 적용하였다. APro는 모델링 영역을 기존의 정형화된 처분시스템으로 제한함으로써 모델의 자유도는 낮지만, 사용자 편의성을 향상시켰다. 처분시스템에서 고려되는 주요 현상들을 모듈화하였고, 이를“Default process”와 다수의“Alternative process”로 구분하여 사용자가 선택할 수 있도록 함으로써 모델의 유연성을 높였다. APro는 크게 입력자료 부분과 계산실행 부분으로 구성된다. 기본 입력자료는 하나의 EXCEL 파일에 일정한 포맷으로 정리되고, 계산실행 부분은 MATLAB을 이용하여 코딩되었다. 최종적인 전체 계산 결과는 독립적인 COMSOL 파일 형태로 생성되도록 하여 COMSOL을 이용한 계산 결과의 후처리가 가능하도록 하였다.