Engenharia dos Processos e Sistemas

Mathematics, Algebra, Separation Processes and Reaction Engineering

Theoretical teaching based on the oral presentation of subject topics. Practical teaching based on problem solving.

Provide students with the ability to:

1. Develop models of processes/systems of interest in Chemical Engineering/Biological Engineering;
2. Solving them using analytical tools for the solution of ODEs;
3. Solving them using numerical analysis techniques
4. Formulating a system in the form of state space and understand dynamic evolution
5. Analyse and troubleshoot typical first and second order systems through the use of Laplace Transforms;
6. Analyse feedback control systems.

1. Modelling Module

1. Modelling: Model definitions
2. Types and uses of models
3. Lumped parameter models
4. Distributed parameter models
5. Extension balances: mass, energy, and momentum
6. Additional constitutive relationships
7. Definition of states, inputs, and outputs in a physical context and in a systemic context

2. Numerical Methods Module

1. Solving Ordinary Differential Equations using dedicated software
2. Analytical solution of ODEs (separable, linear, and homogeneous)

3. Systems Analysis Module

1. Introduction to Laplace transforms
2. Final value and initial value theorems
3. Inversion of dynamics
4. Notion of transfer function
5. Analysis of first order systems – Responses to different types of disturbances
6. Parameterization of 1st order systems based on experimental data
7. Parameterization based on dynamic response
8. Analysis of higher order systems – Responses to different types of disturbances
9. Characterization based on the damping factor
10. Effect of the location of poles and zeros of the transfer function on dynamics
11. Parameterization of 2nd order systems based on experimental data

4. Feedback Control Systems Analysis Module

1. Control loop elements
2. Dynamic response of the open control loop
3. Dynamic response of the closed control loop

NAO

1. Bequette, B.W., “Process Dynamics – Modeling, Analysis and Simulation”, Prentice Hall PTR, Upper Saddle River, N.J. (1998)
2. Biran, A., Breiner, M., “Matlab 5 for Engineers”, Addison Wesley, Dorchester (1999)
3. Cutlip, M.B., Shacham, M., “Problem solving in Chemical Engineering with Numerical Methods”, Prentice Hall PTR, Upper Saddle River, N.J. (1999)
4. Gerald, C.F., Wheatley, P.O., “Applied Numerical Analysis”, 5th Ed., Addison-Wesley Publishing Company, N.Y (1994)
5. Rice, R.G., Do, D.D., “Applied mathematics and modeling for chemical engineers”, John Willey & Sons, Inc., N.Y (1995)
6. Contantinides, A., Mostoufi, N., “Numerical Methods for Chemical Engineers with Matlab Applications”, Prentice Hall PTR, Upper Saddle River, N.J. (1999)
7. Duarte, B.P.M., “Apontamentos de Engenharia dos Processos e Sistemas”, ISEC, Coimbra (2013)