| Optimization of the reload pattern for a nuclear reactor using perturbation theory |
Title: Optimization of the reload pattern for a nuclear reactor using perturbation theory
Author(s): Johan Koolwaaij
Reference: MSc thesis, Dept. Mathematical Physics, Technical Mathematics, Delft University of Technology
Keywords: Mathematical Modelling
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The core of a nuclear reactor contains a large number of fuel elements (uranium dioxide: UO2). During operation, energy in the form of heat is extracted. The fissile material is consumed by fission and a number of fission products are formed. The core has to be refueled with fresh fuel once a year. Generally, not all the fuel is replaced, but only a fraction. When, for example, a fraction 1/n is replaced by fresh fuel, the core contains n age groups of fuel. The oldest fuel bundles are replaced by fresh fuel bundles. For optimal results a total redistribution of the different fuel elements is required. The description of this redistribution is called the reloading pattern. There too many possible reloading patterns to evaluate each one.
The aim of this research project is to provide a tool that can help in optimizing the reloading pattern. The adjoint equation is used in developing a method to quickly estimate the effects of a whole series of reloading patterns, patterns that are variations of one reloading pattern. The optimal variation can be varied again and so on until no improvement is possible.
The reloading pattern of a reactor can be optimal in a number of ways. Often, we want to produce as much energy as possible with the available fuel. Or, we want to use the oldest fuel batch as much as possible to decrease the amount of nuclear waste. So the objective function will be a weighted sum of energy costs, produced energy, burnup of the fuel elements, etc.
In chapter 1 a general description of the fission process inside a nuclear reactor core is given and reactor control is also treated. In chapter 2 the essential equations are introduced: the neutron transport equation and the burnup equations. Attention is paid to diffusion theory and homogenization of the cross sections. In chapter 3 the finite difference method to solve the diffusion equation is described. In chapter 4 the adjoint equation is introduced and with perturbation theory a fast forward algorithm is developed, which is described in chapter 5. To get an impression of the performance of this fast forward algorithm, we implemented the algorithm in MatLab, in chapter 6. The conclusions are given in the last chapter.
Key words: reactor physics, reloading patterns,
perturbation theory, optimization
AMS(MOS) subject classifications: 81V35