# Numerical Methods Applied to Chemical and Biological Engineering

## Objectives

The main objective of this curricular unit is to provide an advanced training in the development of computational models for Chemical and Biological Engineering problems. In the end of this curricular unit the student will have acquired knowledge, skills and competencies that will enable:

- Understanding the numerical methods for the resolution of systems of algebraic equations, ordinary differential equations and partial differential equations.

- Understanding the methods for developing models from data by regression analysis, chemometrics, artificial intelligence and hybrid methods.

- To develop numerical solutions of Chemical and Biological Engineering problems.

- To implement computational models of Chemical and Biological Engineering problems and to analyse their solutions.

## General characterization

##### Code

12563

##### Credits

6.0

##### Responsible teacher

Rui Manuel Freitas Oliveira

##### Hours

Weekly - 4

Total - 56

##### Teaching language

Português

### Prerequisites

- Previous formation in numerical methods

- Python programming

### Bibliography

Beers, Kenneth J. Numerical Methods for Chemical Engineering: Applications in MATLAB ® . Cambridge University Press, 2006. ISBN: 9780521859714.

Sedat Biringen and Chuen-Yen Chow. An Introduction to Computational Fluid Mechanics by Example, John Wiley & Sons, Inc., 2011, ISBN: 978-0-470-10226-8.

Gillespie D.T. (2005) Stochastic Chemical Kinetics. In: Yip S. (eds) Handbook of Materials Modeling. Springer, Dordrecht, ISBN 978-1-4020-3287-5

Kevin D. Dorfman (2017) Numerical Methods with Chemical Engineering Applications, Cambridge University Press, ISBN: 9781316471425

### Teaching method

Theory-Practice lessons are provided in standard mode where the theory behind numerical methods are addressed in a context of Chemical and Biological Engineering problems complemented with simple exercises. The practical lessons take place exclusively in computer rooms. In the practical lessons the students develop computational tools in computers where they implement numerical methods in MATLAB and/or Python to solve problems of Chemical and Biological Engineering. A list of assignments is provided to be solved in autonomy outside the classroom covering all topics: solution of systems of algebraic equations, dynamical simulation, model inference, optimization, statistical validation.

### Evaluation method

**Minimal lecture attendance:**

- 2/3 attendance of P sessions (pratical sessions with computer)

**Continuous assessment**

A – Assignments

B – Theoretical assessment

C – Practical assessment with computer (minimal mark is 9,5)

FINAL MARK = 0,2 * A + 0,2 * B + 0,6 * C

**Final exame**

B – Theoretical assessment (only theory is repeated in the final exame)

FINAL MARK = 0,2 * A + 0,2 * B + 0,6 * C

## Subject matter

- Introduction: Types of numerical problems in Chemical and Biological Engineering.
- Solving systems of linear and nonlinear algebraic equations: battery of steady state CSTR, multistage column, theoretical yields in bacterial growth, theoretical metabolic pathways.
- Solving systems of ordinary differential equations: properties of dynamical systems (sability, hysteresis, bifurcation), (Fed-)batch reactor, transient CSTR, Plug-flow reactor, In silico cell.
- Solving systems of Partial Differential Equations (PDE): Navier stokes, Computational Fluid Dynamics (CFD), heterogeneous catalytic reactor.
- Stochastic reaction kinetics: Markov chains. The tau-leaping Algorithm. Viral infection. Gene transcription.
- Monte Carlo Simulation: Application to molecular systems and dynamic molecular simulation.
- Creating models from data: (Non)linear regression. Chemometrics (Principle component analysis, Partial least squares, Artificial Neural Networks). Hybrid models