AIMS AND CONTENT

AIMS AND LEARNING OUTCOMES

The participation to the training activities is instrumental to:

knowing the basics of the theory of development of chemical processes;

understanding the logical basis which a predictive model relies upon;

giving examples about the application of such models to the chemico-physical processes of the industrial production;

identifying and estimating the main parameters describing the kinetics of a chemical process;

developing process simulation algorithms with deterministic or statistic models (Monte Carlo);

choosing the most suitable algorithm for solving a problem of industrial optimization;

applying numerical discretization criteria to a model containing differential equations.

PREREQUISITES

A basic knowledge of  mathematics, chemistry and physics is required, but there is no need for the student to have previously passed other exams.

TEACHING METHODS

The course is structured in frontal lessons and exercises carried out by the teacher.

SYLLABUS/CONTENT

1. Basics of theory of applied statistics (15 hours)

Independent and mutually exclusive events – Stochastic variables and their operations – Uniform and Gaussian distribution functions – Central tendency and dispersion measures – Sample sizes and quantities  – Central limit theorem – Test of hypothesis: statistical inference applied to the mean and standard deviation of a population – Student t, Chi square, and F distributions with relevant tests. Applications to the quality control of a productive process.

1. Simulation of stochastic processes (15 hours)

Monte Carlo methods: simulation of a pure and biased Brownian motion – Applications of the Monte Carlo method to aggregation-disaggregation processes.  Diffusion- and reaction-limited control regimes. Applications to etching and chemical lithography processes.  Simulation of percolation processes. Applications to electrochemistry and to leaching processes.

1. Theory of estimates (10 hours)

Regression methods (determination of parameters contained in a given model) – Estimators: least squares, minimax, maximum likelihood – Linear and non-linear regression. Applications to  chemical reactor engineering.

1. Process optimization (10 hours)

Numerical methods for the determination of local singular points of a multivariate function. Derivative methods: gradient, Newton, Marquardt and Quasi Newton methods.

Non-derivative methods:  direct search, simplex and Powell methods.

1. Numerical methods for the solution of algebraic and ordinary differential equations (10 hours)

Algebraic equations: sequential substitution, bisection, regula falsi. Newton, continuation and homotopy methods.

Ordinary differential equations (ODEs): finite difference discretization criteria, computational molecules and discrete approximations of derivative operators. Explicit and implicit methods.

RECOMMENDED READING/BIBLIOGRAPHY

G. Vicario, R. Levi. Calcolo delle probabilità e statistica per ingegneri. Progetto Leonardo, Bologna 1997.

D.M. Himmelblau, K.B. Bischoff.  Process analysis and simulation : deterministic systems.

New York : Wiley, 1968

TEACHERS AND EXAM BOARD

Exam Board

ANDREA REVERBERI (President)

PATRIZIA PEREGO

LESSONS

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam consists of an oral discussion.

ASSESSMENT METHODS

The exam aims at checking:

• the learning level ;
• the skilfulness in applying the learned concepts to solve problems concerning the themes proposed.

The assessment standards concern the ability to stay on topic, the quality of expression, the logic pattern of the reasoning and the critical reasoning skills.

Exam schedule