scholarly journals MATRIX EXPONENTIAL METHODS FOR PARALLEL COMPUTING OF ISOTOPIC DEPLETION AND SPECIES TRANSPORT FOR MOLTEN SALT REACTOR ANALYSIS

2021 ◽  
Vol 247 ◽  
pp. 06047
Author(s):  
Zack Taylor ◽  
Benjamin Collins ◽  
Ivan Maldonado
Keyword(s):  
Differential Equations ◽  
Molten Salt ◽  
Fission Products ◽  
Matrix Exponential ◽  
Fissile Material ◽  
Species Transport ◽  
The Matrix ◽  
Exponential Method ◽  
Reactor Loop ◽  
Exponential Methods

Matrix exponential methods have long been utilized for isotopic depletion in nuclear fuel calculations. In this paper we discuss the development of such methods in addition to species transport for liquid fueled molten salt reactors (MSRs). Conventional nuclear reactors work with fixed fuel assemblies in which fission products and fissile material do not transport throughout the core. Liquid fueled molten salt reactors work in a much different way, allowing for material to transport throughout the primary reactor loop. Because of this, fission product transport must be taken into account. The set of partial differential equations that apply are discretized into systems of first order ordinary differential equations (ODEs). The exact solution to the set of ODEs is herein being estimated using the matrix exponential method known as the Chebychev Rational Approximation Method (CRAM).

scholarly journals Fourth-Order Approximation of the Fundamental Matrix of Linear System of Differential Equations

1997 ◽  
Vol 2 ◽  
pp. 57
Author(s):  
A.M. Hussein
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Fundamental Matrix ◽  
Mixed Boundary ◽  
Order Approximation ◽  
Boundary Value ◽  
Mixed Boundary Conditions ◽  
Matrix Exponential ◽  
The Matrix ◽  
Linear Differential

A fourth-order approximation to the fundamental matrix of a system of linear differential equations is presented in closed form as a matrix exponential. The matrix exponential is then discretized over the interval of integration l‘adc approximation together with the method of scaling and squaning (Moler et at 1978) is used to evaluate the matrix exponential. This approach is suitable for solving both initial and boundary value problems with mixed boundary conditions. The approximating matrix can also be used as an integrating operator for methods which require information about the solution along the discretized subintervals. An example of a boundary value problem with mixed boundary condition is presented.

scholarly journals Pyrochemical reprocessing of molten salt fast reactor fuel: focus on the reductive extraction step

Nukleonika ◽  
2015 ◽  
Vol 60 (4) ◽  
pp. 907-914 ◽  
Author(s):  
Davide Rodrigues ◽  
Gabriela Durán-Klie ◽  
Sylvie Delpech
Keyword(s):  
Molten Salt ◽  
Fast Reactor ◽  
Liquid Fuel ◽  
Noble Metals ◽  
Fission Products ◽  
Selective Extraction ◽  
Fissile Material ◽  
Metallic Lithium ◽  
Fuel Salt ◽  
Static Conditions

Abstract The nuclear fuel reprocessing is a prerequisite for nuclear energy to be a clean and sustainable energy. In the case of the molten salt reactor containing a liquid fuel, pyrometallurgical way is an obvious way. The method for treatment of the liquid fuel is divided into two parts. In-situ injection of helium gas into the fuel leads to extract the gaseous fission products and a part of the noble metals. The second part of the reprocessing is performed by ‘batch’. It aims to recover the fissile material and to separate the minor actinides from fission products. The reprocessing involves several chemical steps based on redox and acido-basic properties of the various elements contained in the fuel salt. One challenge is to perform a selective extraction of actinides and lanthanides in spent liquid fuel. Extraction of actinides and lanthanides are successively performed by a reductive extraction in liquid bismuth pool containing metallic lithium as a reductive reagent. The objective of this paper is to give a description of the several steps of the reprocessing retained for the molten salt fast reactor (MSFR) concept and to present the initial results obtained for the reductive extraction experiments realized in static conditions by contacting LiF-ThF4-UF4-NdF3 with a lab-made Bi-Li pool and for which extraction efficiencies of 0.7% for neodymium and 14.0% for uranium were measured. It was concluded that in static conditions, the extraction is governed by a kinetic limitation and not by the thermodynamic equilibrium.

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