Multiobjective optimization increases safety, cost efficiency of final disposal of spent nuclear fuel in Finland

The disposal of spent nuclear fuel is an important part of the sustainable and responsible use of nuclear power. The international focus is on Finland, because Posiva Oy is going to start the final disposal of high-level spent nuclear fuel first in the world.

The final disposal has a remarkable temporal and economic scale, and it also challenges the scientific world in many different sectors in those countries making progress toward final disposal.

The final disposal project in Finland involves geologists, chemists as well as nuclear physicists and there is also an important role for mathematicians in the project.

Mathematicians of the University of Turku have been responsible for optimizing the disposal schedule and loading of canisters in the project.

Researchers have developed a multiobjective scheduling model and a canister loading optimization algorithm to support the decision making in the final disposal process in collaboration with Fortum Power and Heat Oy, Teollisuuden Voima Oyj, and Posiva Oy.

Decisions in the final disposal process have a significant impact on safety and cost efficiency

Before fuel assemblies can be disposed of, they are stored in reactor pools and interim storages for decades in order to decrease their decay heat power and radioactivity to the level required for disposal.

Thereafter, the fuel assemblies are loaded to disposal canisters in the encapsulation plant and the canisters are deposited into the disposal holes drilled on the floor of the disposal tunnels in the bedrock at Olkiluoto.

Decisions are made during the final disposal process, such as when to dispose of the canisters, how to choose the canister powers together with the spacings between the canisters and the disposal tunnels, and how to choose which fuel assemblies to load to which canisters.

These decisions have a significant impact on the safety and cost efficiency of the final disposal. There are tens of thousands of fuel assemblies to be disposed of during the next hundred years, and therefore it is important to use optimization to support the decision-making.

Optimization of the final disposal process is based on long-lasting research

In Timo Ranta's doctoral dissertation completed in 2012, a two-stage hierarchical method for optimizing the disposal process was developed. In the first stage, the canister disposal schedule is defined and in the second stage the fuel assemblies loaded to each canister are defined. For implementing each stage, a distinct single-objective application of optimization was developed.

"I acted as Timo Ranta's opponent and the idea to apply multiobjective optimization matured during the post-doctoral party. Hence, after the doctoral dissertation defense, we have continued the research in collaboration by applying multiobjective optimization to the disposal process, making it possible to simultaneously optimize different cost and safety drivers of the process in addition to the total costs," says Professor of Applied Mathematics Marko Mäkelä.

After 2018, the research has been carried out in two projects at the Department of Mathematics and Statistics of the University of Turku. The purpose of the research has been to increase safety and cost efficiency of the final disposal. To reach this goal, the mathematicians of the University of Turku have developed a distinct multiobjective application of optimization for implementing each stage of the two-stage method, which provides compromise solutions between conflicting objectives.

Requirements for the applications are defined in collaboration with Fortum Power and Heat Oy, Teollisuuden Voima Oyj, and Posiva Oy. To ensure the reliability of solutions, special attention is given to uncertainties in initial data and nonlinear relations between different physical entities.

"It has been great to collaborate with my fellow mathematicians and the experts of the nuclear industry in this pioneering research whose results have worldwide significance," says Ranta who has been working as a research manager in these projects.

Multiple goals and tens of thousands of variables are taken into account in scheduling the final disposal

Mathematicians have computed optimal disposal schedules for different future scenarios in collaboration with Posiva and the power companies. The results are meant to support the decision making at these companies.

For defining the canister disposal schedule, a multiobjective scheduling model is formed. In the interactive method developed for solving the model, a decision-maker first defines a reference point that is the preferred objective value for the solution.

There are eight objectives in total and they are attached to the safety and cost drivers of the process. In the model, the time window of disposal is divided into periods and different decisions are made in each period, for example, how much spent nuclear fuel is disposed of in that period.

There are about 20,000 variables to be solved in the optimization problem when using the most accurate time interval of one year. In addition to the problem size, there are about 600 discrete variables and 300 nonlinear constraints, making the problem even harder to solve.

Despite the complexity of the problem, good solutions can be found. When a time interval of one year is used, the problem is made easier to solve by using only a single-objective. When solving the multiobjective problem, the most accurate time interval is two years.

As a result of the optimization problem, the decision-maker obtains mathematically equally good solutions, although different in practice, having the objective values in some sense as close as possible to the reference point given by the decision-maker. If needed, the reference point could be updated according to the decision maker's wishes to find new optimal compromise solutions.

Loading of canisters has been simulated a hundred years forward

In addition to the scheduling model described above, a distinct mathematical model is formed for defining which fuel assemblies to load to which canisters and a loading optimization algorithm is developed for solving it.

Mathematicians have simulated the loading of canisters about a hundred years into the future in collaboration with Posiva and the power companies. The results show that the loading of canisters can be implemented according to the objectives.

The loading optimization algorithm is integrated into Posiva's spent nuclear fuel database. Posiva is going to define which fuel assemblies are loaded to which canisters using the loading optimization algorithm developed in this research.

"It has been rewarding to be able to utilize the skills acquired during my studies to solve practical problems," says Project Researcher Ville-Pekka Eronen, who has been responsible for algorithm development.

The optimization problem related to the loading of canisters has millions of discrete variables, making the problem very challenging to solve. Therefore, a heuristic algorithm has been developed, which finds small improvements to the solution until they are no longer found.

In the algorithm, the canisters disposed of in the near future are considered more carefully because the canisters disposed of later are more exposed to uncertainties related to the initial data.

For the canisters disposed of in the near future, goal heat powers are specified, and the most important objective of the algorithm is to choose fuel assemblies to these canisters such that their decay heat powers are within a given accuracy from their goal heat powers.

The other objectives of the algorithm are to maximize the number of fuel assemblies with a priority in the canisters with goal heat powers and to minimize the maximum weighted decay heat power of other canisters.

The algorithm takes into account, for example, the uncertainties in the decay heat powers of fuel assemblies and their mutual dependencies as well as different types of conditions, such as the date when a pool in the Olkiluoto interim storage should be empty. The algorithm is also capable of simulating the loading of all canisters one production batch at a time.

"In the first project, a scheduling model was produced, and the model utilized iterative decision-making, where further calculations were focused on the most interesting solutions. In the first project, a loading optimization algorithm was also produced, which was integrated into Posiva's spent nuclear fuel database.

"In the second project, development work was continued, and results were produced with more accurate data. Furthermore, as the most important point, the uncertainties in the decay heat powers of fuel assemblies were defined and the loading optimization algorithm was developed further to take those into account," says Jani Huttunen from Posiva, who has been working as a client-side project manager in the projects.

"The safe disposal of spent nuclear fuel is part of nuclear safety work. The comprehensive optimization of final disposal accomplished in the safety framework gives additional information to the decision-making and makes possible the more optimal use of interim storage capacity and disposal facilities as well as increasing safety, among other things. The projects produced important information, and the objectives were achieved excellently," says Ari Posti, Posiva's Business Development Manager.

"Posiva Solutions Oy offers tailored services for spent nuclear fuel disposal, where Posiva's decades-long experience brings added value and has played an important role in these projects as well," says Posiva Solutions' Managing Director Mika Pohjonen.

"Finland is going to start the final disposal as the first country in the world. Posiva has a solution for the final disposal due to years-long research and development work, and shortly Posiva is going from construction phase to actual production phase," says Posiva's CEO Ilkka Poikolainen.

Provided by University of Turku