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Scheda Riassuntiva
Anno Accademico 2018/2019
Scuola Scuola di Ingegneria Industriale e dell'Informazione
Insegnamento 051426 - FISSION REACTOR PHYSICS II + TRANSPORT OF RADIOACTIVE CONTAMINANTS
Docente Giacobbo Francesca Celsa
Cfu 10.00 Tipo insegnamento Monodisciplinare

Corso di Studi Codice Piano di Studio preventivamente approvato Da (compreso) A (escluso) Insegnamento
Ing Ind - Inf (Mag.)(ord. 270) - BV (478) NUCLEAR ENGINEERING - INGEGNERIA NUCLEARE*AZZZZ051426 - FISSION REACTOR PHYSICS II + TRANSPORT OF RADIOACTIVE CONTAMINANTS
097675 - FISSION REACTOR PHYSICS II
052601 - FISSION REACTOR PHYSICS II + EXPERIMENTAL NUCLEAR REACTOR KINETICS
097680 - TRANSPORT OF RADIOACTIVE CONTAMINANTS

Obiettivi dell'insegnamento

The course is offered in a 10-CFU annual version (Fission Reactor Physics II + Transport of Radioactive Contaminants). In alternative the students can attend one of the two 5-CFU courses into which the annual version is parted (Fission Reactor Physics II - first semester and Transport of Radioactive Contaminants - second semester). Moreover the 5-CFU course Fission Reactor Physics II is also part of the integrated 10-CFU course Experimental Nuclear Reactor Kinetics + Fission Reactor Physics II.

The detailed descriptions reported below define aims, educational outcomes and programs for both of the two 5-CFU courses that compose the 10 CFU annual course.

FISSION REACTOR PHYSICS II (5 ECTS)

The aim of the course is to provide knowledge of the main methods for the solution of the neutron transport equation and of the fundamental concepts necessary for the use of deterministic and stochastic neutron transport codes.

The Boltzmann neutron transport equation, both in Integral and integrodifferential formulation, is derived and the main deterministic solution methods are illustrated and discussed. Subsequently the adjoint equation is derived and its application to perturbation problems is addressed. Finally the theoretical formulation of the Monte Carlo method applied to the neutron transport equation is dealt with.

 

TRANSPORT OF RADIOACTIVE CONTAMINANTS (5 ECTS)

The aim of the course is to provide knowledge of the main physical concepts necessary to analyze and model the transport of radioactive contaminants through natural and artificial porous media and groundwater and learning of the fundamentals required for the use of deterministic and stochastic codes.

To this aim the principal processes of radionuclide transport in aqueous solution through porous and fractured media are illustrated and discussed. The advection dispersion equation is derived. The stochastic Kolmogorov Dmitriev model is applied to describe radionuclide transport through porous media. Exercises with codes and experimental activities are provided to better understand the adopted models.

 

At the end of the course a visit to the Joint Research Centre of Ispra is foreseen. The visit is comprehensive of seminars regarding the following topics:  Nuclear Safeguards and Security; Decommissioning and Nuclear Waste Management issues.


Risultati di apprendimento attesi

FISSION REACTOR PHYSICS II

The student:

  • knows the main physical assumptions under which the Boltzmann equation of neutron transport can be derived, is able to derive the Boltzmann equation in integrodifferential and integral form and knows the main mathematical methods for its deterministic solution
  • knows the fundamentals of the theoretical formulation of the Monte Carlo method applied to the transport of neutrons in a multiplying medium
  • knows the physical interpretation of the adjoint flux and is able to derive the adjoint transport equation and to apply the adjoint transport equation to a perturbation problem
  • is able to use an appropriate and scientifically rigorous language to describe the topics covered by the course

 

TRANSPORT OF RADIOACTIVE CONTAMINANTS

The student:

  • knows the main processes that govern water flow through aquifers and transport of radionuclides through porous media and is able to derive the Advection Dispersion equation and a probabilistic equation of transport by means of the Kolmogorov Dmitriev approach
  • knows how to study experimentally, at the lab scale  (i) the transport of a tracer through a porous medium and (ii) the exchange processes between aqueous and solid phases to obtain equilibrium isotherms
  • is able to discuss the problem of radioactive repositories assessment with reference to the main processes to be taken into account and to the main properties of the host geological formations
  • is able to use an appropriate and scientifically rigorous language to describe the topics covered by the course

Argomenti trattati

FISSION REACTOR PHYSICS II

Recalls of Statistics. Probability theory, random data analysis.

The Boltzmann equation. The neutron transport equation. Fundamental physical assumptions for the derivation of the equation of neutron transport. Neutron angular density and angular flux. Neutron current. Transfer probabilities for scattering and fission. Derivation of the Boltzmann equation of neutron transport in Lagrangian and Eulerian form on the basis of neutron conservation. Integrodifferential formulation. General characteristics of the transport operator. Integration in the entire reactor. Linearity and Green’s functions. Integral formulation and its derivation by means of the characteristics method and on the basis of neutron conservation.

Solution methods. Integral formulation. Von Neumann method. Integrodifferential formulation. Analysis of non-stationary case by means of the alpha eigenvalue method. Effective multiplication factor eigenvalue method. Expansion of flux in Legendre polynomials for plane geometry. Pn approximation. P1 approximation. Derivation of the diffusion equation. Discrete ordinate method. Sn approximation. The Multigroup method. Numerical solutions and organization of modern computer codes (outline).

The adjoint transport equation. The adjoint to the transport operator. The adjoint function and neutron importance. Derivation of the adjoint transport equation for the neutron importance. Physical interpretations of the adjoint flux to certain kinds of adjoint source. Spectrum of the adjoint operator and criticality. Application of the perturbation theory. Perturbation of the effective multiplication factor. Application to a PWR core barrel oscillations. Derivation of the Point Kinetics equation.

Monte Carlo method. Application of the Monte Carlo method to the stochastic simulation of transport of neutrons and photons. Collision, transfer, and transport kernels. Von Neumann expansion. Iterated fission sources method.

Neutronic simulation of a TRIGA Reactor (*) (monographic topic in collaboration with the course 'Experimental Nuclear Reactor Kinetics') Monte Carlo approach to transport theory with application to the TRIGA reactor by Serpent code: 1) Determination of multiplication coefficient, kinetic parameters and neutron flux distribution, 2) Determination of group constants for defining a diffusive model for several energy groups.

Statistics of Neutron Fluctuations (*) (monographic topic). Probability generating functions. The convolution theorem. Fluctuations of the number of particles in a Markovian system of different types of particles: the branching model of Kolmogorov and Dmitriev. The Chapman-Kolmogorov identity. The Kolmogorov equations. Application to the propagation of neutrons in multiplying system with a neutron source variable in time. The Fokker-Planck equation.

Neutron Noise (*) (monographic topic). Introduction to the analysis of random data and neutron noise. Stationary processes. Ergodic processes. Analysis in the time domain and frequency. Application to the determination of the directions and frequencies of oscillation of the core-barrel of PWR reactor. Estimate of the rate of rise of bubbles in a liquid two-phase within a vertical channel.

 (*) the monographic topics can be activated at the discretion of the professor in charge of the course

 

TRANSPORT OF RADIOACTIVE CONTAMINANTS

Recalls of Statistics (*). Probability theory, random data analysis.

Monte Carlo method (*). Outline of the application of the Monte Carlo method to the stochastic simulation of transport of neutrons and photons. Collision, transfer, and transport kernels. Von Neumann expansion.

Repositories of radioactive waste. Characteristics and types of radioactive waste. Concepts of deposit and barriers. Main processes of leakage of radionuclides from deposits. Transport in the near-field and in the far field. Determination of the source term.

Transport of toxic and radioactive pollutants in aqueous solution in porous and fractured media. Basics concepts of hydrogeology. Porosity and water content. Hydraulic conductivity . Storage coefficient. Darcy law. Darcy velocity. Pore velocity. Models of water flow in saturated and unsaturated porous media. Flow field in a saturated porous medium: confined and unconfined aquifers. Main transport phenomena in hydrogeology. Derivation of the Advection Dispersion equation. Main physical and chemical parameters and their determination. Hydrodynamic dispersion. Reactive transport. Exchange processes between the phases. Isothermal linear equilibrium. Freundlich and Langmuir nonlinear Isotherms. Processes of decay, dissolution, degradation, adsorption, competition, colloidal transport. Dual porosity media. Two Region Model.  

Stochastic approach. Probability generating functions. The convolution theorem. Fluctuations of the number of particles in a Markovian system of different types of particles: the branching model of Kolmogorov and Dmitriev. The Chapman-Kolmogorov identity. The Kolmogorov equations. Probabilistic Kolmogorov equations and their application to the propagation of radionuclides in a porous media. Derivation of main rates by comparison with the advection dispersion deterministic model. Application of the Monte Carlo method to the stochastic simulation of the transport of contaminants in saturated and unsaturated media in presence of linear and nonlinear processes. .

Informatics laboratory. 1D model with Matlab. 3D Model with Groundwatervistas: MODFLOW, MODPATH, MT3D; compartment code AMBER and 3D code FEFLOW (outline). 

Laboratory. Experimental techniques for the study and measurement of the dispersion of contaminants in porous media. Batch tests to study the phenomena of exchange between the phases and the determination of the equilibrium isotherms. Column tests of 1D transport. Determination of the effective porosity and coefficient of dispersivity Spectrophotometry. Liquid chromatography. Mass spectrometry.

The inverse problem (outline). Definition of the problem. Direct and indirect methods. Examples of methods for the solution of inverse problems for the determination of characteristic parameters of the models of flow and transport.

Transport of pollutants in the atmosphere (**) (monographic topic). Vertical movements and conditions of stability and instability of the atmosphere. Equation of diffusion of contaminants into the atmosphere. Decay and chemical reactions. The theory and assumptions underlying the simulation models of Gaussian type. Chemical and physical parameters. Source term.

 (*) recalls for the students that attend only the 5CFU course Transport of Radioactive Contaminants

(**) the monographic topics can be activated at the discretion of the professor in charge of the course

 

At the end of the 10FU course a visit to the Joint Research Centre of Ispra is foreseen for all the students that attend any of the 5CFU versions of the course. The visit is comprehensive of the following seminars:

Seminar on Nuclear Safeguards and Security (outline). Illustration of issues related to nuclear safeguards.

Seminar on Decommissioning and Waste management (outline). Illustration of a decommissioning project.

 


Prerequisiti

The two 5FCU courses are self consistent, i.e.  one is not needed for the other.

 

FISSION REACTOR PHYSICS II

To attend the 5CFU course Fission Reactor Physics II a knowledge of the subjects contained in the program of Fission Reactor Physics, or of an equivalent course, is assumed. Moreover, to attend the course a knowledge, at least at an elementary level, of the subjects contained in the program of Metodi matematici per l’ingegneria (Mathematical Methods for Engineering), or of an equivalent course, can be helpful.

 

TRANSPORT OF RADIOACTIVE CONTAMINANTS

To attend the 5CFU course Transport of Radioactive Contaminants a knowledge of partial differential equations, at least at an elementary level, is required.


Modalità di valutazione

FISSION REACTOR PHYSICS II + TRANSPORT OF RADIOACTIVE CONTAMINANTS

FISSION REACTOR PHYSICS II

TRANSPORT OF RADIOACTIVE CONTAMINANTS

The evaluation consists in an oral examination. It aims at verifying the knowledge of the course topics, with particular reference to the knowledge of the mathematical description of the fundamental physical processes under consideration, to the ability of deriving the fundamental equations of transport of neutrons in multiplying media and of transport of radionuclides in porous media and to the ability to use an appropriate and scientifically rigorous language to describe the topics covered by the course.

The student will be asked to explain the physical meaning of the adopted mathematical models and to derive and discuss the following main topics:

  • Fission reactor physics II : Boltzmann equation, deterministic and stochastic (i.e. Monte Carlo) solution methods of the Boltzmann equation, adjoint transport equation, application of the adjoint transport equation to a perturbation problem;
  • Transport of Radioactive Contaminants: deterministic models of water flow and transport of radionuclides through porous media and Kolmogorov Dmitriev stochastic model of transport of radionuclides through porous media. The ability to discuss the relevance of parameters of transport through porous media with respect to the assessment of radioactive repositories is addressed as well. The student will also be asked to describe in detail the experiments held in the lab.

Bibliografia
Risorsa bibliografica obbligatoriaG. Bell and S. Glasstone, Nuclear Reactor Theory, Editore: Van Nostrand Reinhold Co, Anno edizione: 1970
Risorsa bibliografica obbligatoriaD. Savage, The scientific and Regulatory basis for geological disposal of radioactive waste, Editore: John Wiley and Sons,, Anno edizione: 1995
Risorsa bibliografica obbligatoriaAdditional notes are given by the professor in charge of the course and are made available on the one-drive site

Forme didattiche
Tipo Forma Didattica Ore di attività svolte in aula
(hh:mm)
Ore di studio autonome
(hh:mm)
Lezione
65:00
97:30
Esercitazione
20:00
30:00
Laboratorio Informatico
10:00
15:00
Laboratorio Sperimentale
5:00
7:30
Laboratorio Di Progetto
0:00
0:00
Totale 100:00 150:00

Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua Inglese
Disponibilità di materiale didattico/slides in lingua inglese
Disponibilità di libri di testo/bibliografia in lingua inglese
Possibilità di sostenere l'esame in lingua inglese
Disponibilità di supporto didattico in lingua inglese
schedaincarico v. 1.6.5 / 1.6.5
Area Servizi ICT
11/08/2020