Application of the Laplace transform method for computational modelling of radioactive decay series
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D. L. Oliveira
Abstract
It is well known that when spent fuel is removed from the core, it is still composed of considerable amount of radioactive elements with significant half-lives. Most actinides, in particular plutonium, fall into this category, and have to be safely disposed of. One solution is to store the long-lived spent fuel as it is, by encasing and burying it deep underground in a stable geological formation. This implies estimating the transmutation of these radioactive elements with time. Therefore, we describe in this paper the application of the Laplace transform technique in matrix formulation to analytically solve initial value problems that mathematically model radioactive decay series. Given the initial amount of each type of radioactive isotopes in the decay series, the computer code generates the amount at a given time of interest, or may plot a graph of the evolution in time of the amount of each type of isotopes in the series. This computer code, that we refer to as the LTRadL code, where L is the number of types of isotopes belonging to the series, was developed using the Scilab free platform for numerical computation and can model one segment or the entire chain of any of the three radioactive series existing on Earth today. Numerical results are given to typical model problems to illustrate the computer code efficiency and accuracy.
Kurzfassung
Wenn abgebrannte Brennelemente aus dem Kern entfernt werden, enthalten sie immer noch beträchtliche Mengen radioaktiver Elemente mit signifikanten Halbwertszeiten. Die meisten Aktinide, insbesondere Plutonium, fallen in diese Kategorie und müssen deshalb sicher entsorgt werden. Eine Lösung ist die Lagerung langlebiger abgebrannter Brennelemente durch Einschließung und Lagerung in tiefen, stabilen geologischen Formationen. Dazu ist es erforderlich, die Transmutation dieser Radionuklide mit der Zeit zu bestimmen. In dem vorliegenden Beitrag wird die Anwendung des Laplace Transformationsverfahrens in Matrixformulierung beschrieben, um analytisch Fragestellungen zu lösen und die radioaktiven Zerfallsreihen mathematisch zu modellieren. Ausgehend von der ursprünglichen Menge eines jeden radioaktiven Isotops in der Zerfallsreihe, erzeugt der Rechencode die Menge eines jeden radioaktiven Isotops zu einem bestimmten interessierenden Zeitpunkt, oder druckt eine Kurve der zeitlichen Evolution der Menge eines jeden radioaktiven Isotops in der Serie. Dieser Rechencode, der sogenannte LTRadL Code, wobei L die Anzahl der zu der Reihe gehörenden Isotope, wurde entwickelt mit Hilfe der Scilab Plattform für numerische Berechnungen und kann ein Segment oder die gesamte Kette einer jeden der drei radioaktiven Reihen, die heute existierenden Reihen modellieren. Numerische Ergebnisse werden auf typische Fragestellungen angewendet um die Efficiency und die Genauigkeit zu demonstrieren.
References
1 Scilab – Copyright (c) 1989–2007, Consortium Scilab (INRIA, ENPC) (www.scilab.org)Suche in Google Scholar
2 Kreyszig, E.: Advanced Engineering Mathematics. John Wiley and Sons, New York, 1967Suche in Google Scholar
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© 2012, Carl Hanser Verlag, München
Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- Analytical assessment for stress corrosion fatigue of CANDU fuel elements under load following conditions
- Development of a thermal-hydraulic analysis code for annular fuel assemblies
- Reduction of fluid property errors of various thermohydraulic codes for supercritical water systems
- Computational fluid dynamics validation study of steam condensation on the containment walls
- CFD analysis of a hydraulic valve for cavitating flow
- Thermal plume behaviour in the Kadra reservoir at Kaiga atomic power station – Part 2: studies for the case of four and six units in operation
- 124I production for PET imaging at a cyclotron
- Investigation of ground state features of some medical radionuclides
- Solution of the radiative transfer equation with the successive order scattering transport approximation and its application to a biological medium
- Solving the constant source problem for the quadratic anisotropic scattering kernel using the modified FN method
- Application of the Laplace transform method for computational modelling of radioactive decay series
- A standing wave reactor by continuous radial fuel shuffling
- Technical Notes/Technische Mitteilungen
- On the radial flux shape of a fast standing wave reactor operated by radial fuel shuffling
Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- Analytical assessment for stress corrosion fatigue of CANDU fuel elements under load following conditions
- Development of a thermal-hydraulic analysis code for annular fuel assemblies
- Reduction of fluid property errors of various thermohydraulic codes for supercritical water systems
- Computational fluid dynamics validation study of steam condensation on the containment walls
- CFD analysis of a hydraulic valve for cavitating flow
- Thermal plume behaviour in the Kadra reservoir at Kaiga atomic power station – Part 2: studies for the case of four and six units in operation
- 124I production for PET imaging at a cyclotron
- Investigation of ground state features of some medical radionuclides
- Solution of the radiative transfer equation with the successive order scattering transport approximation and its application to a biological medium
- Solving the constant source problem for the quadratic anisotropic scattering kernel using the modified FN method
- Application of the Laplace transform method for computational modelling of radioactive decay series
- A standing wave reactor by continuous radial fuel shuffling
- Technical Notes/Technische Mitteilungen
- On the radial flux shape of a fast standing wave reactor operated by radial fuel shuffling
