A New Model for the Stochastic Point Reactor: Development and Comparison with Available Models

Alamir Elsayed,Shorooq Al-Qahtani,Amnah Al-Juhani,Mohamed El-Beltagy

doi:10.3390/en14040955

Alamir Elsayed, Shorooq Al-Qahtani + Show 2 more

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https://doi.org/10.3390/en14040955

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Journal: Energies	Publication Date: Feb 11, 2021
Citations: 2	License type: CC BY 4.0

Affiliation: Cairo University, University of Tabuk

Abstract

The point kinetic model is a system of differential equations that enables analysis of reactor dynamics without the need to solve coupled space-time system of partial differential equations (PDEs). The random variations, especially during the startup and shutdown, may become severe and hence should be accounted for in the reactor model. There are two well-known stochastic models for the point reactor that can be used to estimate the mean and variance of the neutron and precursor populations. In this paper, we reintroduce a new stochastic model for the point reactor, which we named the Langevin point kinetic model (LPK). The new LPK model combines the advantages, accuracy, and efficiency of the available models. The derivation of the LPK model is outlined in detail, and many test cases are analyzed to investigate the new model compared with the results in the literature.

Highlights

Comparison with Available Models.Point kinetic equations (PKEs) [1] are a system of coupled ordinary differential equations (ODEs) that describes concentrations/populations of neutrons and precursors in the nuclear reactor
This was the first model in which the space variations are neglected and the analysis is reduced by avoiding the need to solve a space-time of coupled partial differential equations (PDES)
We reviewed two procedures to construct stochastic differential equation models and applied them to the point reactor

Summary

Introduction

Comparison with Available Models.Point kinetic equations (PKEs) [1] are a system of coupled ordinary differential equations (ODEs) that describes concentrations/populations of neutrons and precursors in the nuclear reactor. Random variation fluctuations of neutron and precursor concentrations are significant during low-power operation, e.g., the startup or the shutdown of the reactor. To overcome these difficulties, the authors in [2] derived a model of the stochastic point kinetic (SPK) equations that can be solved for these fluctuations, which we refer to as the SPK model. The model [2] requires the computing of the square root of a matrix in the diffusion term, which is computationally inefficient and could cause instabilities To overcome these drawbacks, a second model [3] utilizes alternative modeling following a procedure developed before in [4]. The SSPK model was further considered in [5] by using the Wiener-Hermite expansion (WHE) spectral technique to avoid sampling of the stochastic terms and to allow for random variation of the model parameters [6]

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