Conducting a TSPA (Total System Performance Assessment) of the entire spent nuclear fuel disposal system, which includes thousands of disposal holes and their geological surroundings over many thousands of years, is a challenging task. Typically, the TSPA relies on significant efforts involving numerous parts and finite elements, making it computationally demanding. To streamline this process and enhance efficiency, our study introduces a surrogate model built upon the widely recognized U-network machine learning framework. This surrogate model serves as a bridge, correcting the results from a detailed numerical model with a large number of small-sized elements into a simplified one with fewer and large-sized elements. This approach will significantly cut down on computation time while preserving accuracy comparable to those achieved through the detailed numerical model.

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.

Nuclear power generation is expected to be enlarged for domestic electricity supply based on the 10th Basic Plan of Long-Term Electricity Supply and Demand. However, the issues on the disposal of spent nuclear fuel or high-level radioactive waste has not been solved. KBS-3 concept of the deep geological disposal and pyroprocessing has been investigated as options for disposal and treatment way of spent nuclear fuel. In other way, the radionuclide management process with 6 scenarios are devised combining chlorination treatment and alternative disposal methods for the efficient disposal of spent nuclear fuel. Various scenarios will be considered and comprehensively optimized by evaluation on many aspects, such as waste quantity, radiotoxicity, economy and so on. Level 0 to 4 were identified with the specialized nuclide groups: Level 0 (NFBC, Hull), Level 1 (Long-lived, volatile nuclides), Level 2 (High heat emitting nuclides), Level 3 (TRU/RE), Level 4 (U). The 6 options (Op.1 to 6) were proposed with the differences between scenarios, for examples, phase types of wastes, the isolated nuclide groups, chlorination process sequences. Op.1 adopts Level 0 and 1 to separate I, Tc, Se, C, Cs nuclides which are major concerns for long-term disposal through heat treatment. The rest of spent nuclear fuel will be disposed as oxide form itself. Op.2 contains Sr separation process using chlorination by MgCl2 and precipitation by K2CO3to alleviate the burden of heat after heat treatment process. U/TRU/RE will be remained and disposed in oxide form. Op.3 is set to pyroprocessing as reference method, but residual TRU/RE chlroides after electrorefining will be recovered as precipitates by K3PO4. Op.4 introduces NH4Cl to chlorinate TRU/RE from oxides after Op.2 applied and precipitates them. TRU/RE/Sr will be simultaneously chlorinated by NH4Cl without MgCl2 in Op.5. Then, chlorinated Sr and TRU/RE groups will be separated by post-chlorination process for disposal. But, chlorinated Sr and TRU/RE are designed not to be divided in disposal steps in Op.6. In this study, the mass flow analysis of radionuclide management process scenarios with updated process variables are performed. The amount and composition of wastes by types will be addressed in detail.

Nuclear power is responsible for a large portion of electricity generation worldwide, and various studies are underway, including the design of permanent deep geological disposal facilities to safely isolate spent nuclear fuel generated as a result. However, through the gradual development of drilling technology, various disposal option concepts are being studied in addition to deep geological disposal, which is considered the safest in the world. So other efforts are also being made to reduce the disposal area and achieve economic feasibility, which requires procedures to appropriately match the waste forms generated from separation process of spent nuclear fuel with disposal option systems according to their characteristics. And safety issue of individual disposal options is performed through comparison of nuclide transport. This study briefly introduces the pre-disposal nuclide management process and waste forms, and also introduces the characteristics of potential disposal options other than deep geological disposal. And environmental conditions and possible pathways for nuclide migration are reviewed to establish transport scenarios for each disposal option. As such, under this comprehensive understanding, this study finally seeks to explore various management methods for high-level radioactive waste to reduce the environmental burden.

The radionuclide management process is a conditioning technology to reduce the burden of spent fuel management, and refers to a process that can separate and recover radionuclides having similar properties from spent fuels. In particular, through the radionuclide management process, high heat- emitting, high mobility, and high toxicity radionuclides, which have a significant impact on the performance of disposal system, are separated and managed. The performance of disposal system is closely related to properties (decay heat and radioactivity) of radioactive wastes from the radionuclide management process, and the properties are directly linked to the radionuclide separation ratio that determines the composition of radionuclides in waste flow. The Korea Atomic Energy Research Institute have derived process flow diagrams for six candidates for the radionuclide management process, weighing on feasibility among various process options that can be considered. In addition, the GoldSim model has been established to calculate the mass and properties of waste from each unit process of the radionuclides management process and to observe their time variations. In this study, the candidates for the radionuclide management process are evaluated based on the waste mass and properties by using the GoldSim model, and sensitivity analysis changing the separation ratio are performed. And the effect of changes in the separation ratio for highly sensitive radionuclides on waste management strategy is analyzed. In particular, the separation ratio for high heat-emitting radionuclides determines the period of long-term decay storage.

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 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.

To conduct numerical simulation of a disposal repository of the spent nuclear fuel, it is necessary to numerically simulate the entire domain, which is composed on numerous finite elements, for at least several tens of thousands of years. This approach presents a significant computational challenge, as obtaining solutions through the numerical simulation for entire domain is not a straightforward task. To overcome this challenge, this study presents the process of producing the training data set required for developing the machine learning based hybrid solver. The hybrid solver is designed to correct results of the numerical simulation composed of coarse elements to the finer elements which derive more accurate and precise results. When the machine learning based hybrid solver is used, it is expected to have a computational efficiency more than 10 times higher than the numerical simulation composed of fine elements with similar accuracy. This study aims to investigate the usefulness of generating the training data set required for the development of the hybrid solver for disposal repository. The development of the hybrid solver will provide a more efficient and effective approach for analyzing disposal repository, which will be of great importance for ensuring the safe and effective disposal of the spent nuclear fuel.

Korea Atomic Energy Research Institute is developing a radionuclide management processes as a conditioning technology to reduce the burden of spent fuel disposal. The radionuclide management process refers to a process managing radionuclides with similar properties by introducing various technology options that can separate and recover radionuclides from spent fuels. In particular, it is a process aimed at increasing disposal efficiency by managing high-heat, high-mobility, and high-toxic radionuclides that can greatly affect the performance of the disposal system. Since the radionuclide management process seeks to consider various technology options for each unit process, it may have several process flows rather than have a single process flow. Describing the various process flows as a single flow network model is called the superstructure model. In this study, we intend to develop a superstructure model for the radionuclide management process and use it as a model to select the optimal process flow. To find the optimal process flow, an objective function must be defined, and at the fuel cycle system level multiple objectives such as effectiveness (disposal area), safety (explosure dose), and economics (cost) can be considered. Before performing the system-level optimization, it is necessary to select candidates of process flow in consideration of waste properties and process efficiency at the process level. In this study, a sensitivity analysis is conducted to analyze changes in waste properties such as decay heat and radioactivity when the separation ratio varies due to the performance change for each unit process of the radionuclide management process. Through this analysis, it is possible to derive a performance range that can have waste properties suitable for following waste treatment, especially waste form manufacturing. It is also possible to analyze the effect of waste properties that vary according to the performance change on waste storage and management approaches.

APro, a modularized process-based total system performance assessment framework, was developed at the Korea Atomic Energy Research Institute (KAERI) to simulate radionuclide transport considering coupled thermal-hydraulic-mechanicalchemical processes occurring in a geological disposal system. For reactive transport simulation considering geochemical reactions, COMSOL and PHREEQC are coupled with MATLAB in APro using an operator splitting scheme. Conventionally, coupling is performed within a MATLAB interface so that COMSOL stops the calculation to deliver the solution to PHREEQC and restarts to continue the simulation after receiving the solution from PHREEQC at every time step. This is inefficient when the solution is frequently interchanged because restarting the simulation in COMSOL requires an unnecessary setup process. To overcome this issue, a coupling scheme that calls PHREEQC inside COMSOL was developed. In this technique, PHREEQC is called through the “MATLAB function” feature, and PHREEQC results are updated using the COMSOL “Pointwise Constraint” feature. For the one-dimensional advection-reaction-dispersion problem, the proposed coupling technique was verified by comparison with the conventional coupling technique, and it improved the computation time for all test cases. Specifically, the more frequent the link between COMSOL and PHREEQC, the more pronounced was the performance improvement using the proposed technique.

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.

As an alternative technology for the efficient disposal of spent nuclear fuel, various process flows can be selected based on the recovered and separated radioactive nuclide group. This is to examine the efficiency of the disposal area of spent nuclear fuel when various disposal technologies and several treatment processes are applied to spent nuclear fuel, compared to the deep geological disposal of burying the entire spent fuel in the ground. Above all, the biggest advantage of the optional treatment processes is that it can be applied to various disposal methods (deep borehole disposal, deep geological disposal) because it can process spent fuel in various sizes and separate into some groups according to the properties of radionuclides. These optional processes are not new technology and currently available as of today, and the level is classified based on the stepwise separation of high heat emission nuclides and long half-life nuclides. This is to increase the efficiency of the disposal of spent nuclear fuel by separating and managing high-risk radionuclides separately. Relatively various optional processes are possible depending on the level, and characteristic analysis is performed on wastes treated with alternative technologies. The mass balance for each option process is completed, and the amount of waste is also calculated accordingly. These are used as basic data for waste disposal area and economic evaluation. Besides it is easy to process spent fuel of various sizes suitable for deep geological disposal or deep borehole disposal technology when an optional treatment technology is applied to spent fuel. However, since this selective process is based on the process structure constructed in a broad framework, it is considered that additional follow-up studies are needed not only on detailed technology but also on the flow and amount of waste.

Considering the domestic condition with small land area and high population density, it is necessary to develop technology that can reduce the disposal area than the deep geological disposal method. For this, KAERI is developing a nuclide management process that can reduce the environmental burden of spent fuel, and establishing an evaluation model that can evaluate the performance of various process options. It is expected that an optimal option of the nuclide management process can be derived from disposal perspective by applying the evaluation model. The mass flow between processing steps of the radionuclide management process is the basic quantity required to quantify the evaluation criteria. Therefore, we built a generalized block model on GoldSim, which can simulate mass flow of various radionuclide management process options. In addition to the mass flow, this model was established to derive the amount of wastes generated by each processing step, the composition of nuclides, and radiological properties (decay heat, radioactivity, etc.). The mass flow and waste property derived from the models are closely related to the factors that determine the area of disposal concepts. Based on this, a disposal area calculation model was established as a model to evaluate the effectiveness of the radionuclide management process on environmental burden reduction. For verification, three process options, which can manage radionuclides having high decay heat (Cs, Sr) or large volume (U), were selected and evaluated as reference processes. And two disposal options, deep geological disposal and deep borehole disposal concepts were considered to be linked with the processes. As a result, it was confirmed that the disposal area could be reduced in the process separating radionuclides having high decay heat. In the future, other evaluation models for economic viability and safety will be added in the GoldSim model.

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.

Korea Atomic Energy Research Institute (KAERI) has investigated Pyroprocessing technology in order to decrease the burden of disposal system and increase availability of useful radionuclides in the spent nuclear fuel (SNF) for future. The treatment and the disposal of SNF, however, are very sensitive issues socially. In addition, under the energy transition policy phasing out nuclear energy gradually there have been demands for alternatives so far. Thus various alternatives should need to be investigated in preparation for unexpected situations. This study has been conducted roughly in effectiveness point of view of alternative pre-managements for SNF, not pyroprocessing technology, in disposal system, consisting of three stages according to the degree of burden in disposal system. Stage I is the case for making safety increase with removing highly-mobile radionuclides from SNF. Stage II is the case for eliminating high-heat radionuclides additionally, alleviating thermal risk in the disposal system. And Stage III is the case for recovering Uranium in addition to Stage II. These options of pre-management are thought to be able to provide an intuitive strategy for effective diversification of the disposal system. Because several types of waste form from pre-management make it possible to develop the effective, newly-composed waste disposal system according to the properties of radionuclides. And the processability of SNF through pre-management might be combination with available core-drilling technology, being able to design various disposal system as well. Even though the whole, detailed unit processes have not designed yet, mass balance and distributions of radionuclides are performed under the appropriate assumption of engineering processes. As a first step the alternative approaches for SNF pre-management for disposal system might be expected to be widely used in implementing SNF management policy in the future.