Modeling Simulation and Optimization

Recommended Prerequisites

Linear Algebra and Analytic Geometry, Calculus I, II and III, Programing and Numerical Methods.

Teaching Methods

Integration of specific Chemical Engineering applications in the generic modelling/simulation/optimization methodologies. In the theoretical lectures the concepts will be introduced and discussed, supported by real case studies. The practical classes include selected problems to be analysed and solved mostly by computational means (MATLAB and GAMS platforms). The application of these computational tools will be also encouraged outside the classes by the development of small work projects assigned to student working groups.

Learning Outcomes

With this course, students will learn relevant aspects of modeling, simulation and decision in Chemical Engineering. The transient state modeling will be addressed, giving an integral perspective of the topic and introducing an appropriate methodology. Students will also be trained in the numerical resolution of these models, which often involve the solution of partial differential equations with diverse auxiliary conditions. Another objective of the course is to approach optimization methods for model resolution and decision making problems, with different levels of complexity (linear or nonlinear; without or with restrictions; continuous or discrete domains).

Skills to be developed: ability to integrate knowledge; practice with computation tools; ability to acquire knowledge autonomously; critical thinking; synthesis capacity; skills to work in a team.

Work Placement(s)

No

Syllabus

1. Modelling strategies and model classifications. A systematic approach for the construction of process models. Examples of application of models in chemical processes.

2. Numerical solution of ordinary differential equations - boundary value problems: shooting method; discretization techniques and finite differences method. Numerical solution of partial differential  equations: method of the lines, finite differences methods (explicit and implicit); stiff problems. Matlab programming for differential equations.

3. Optimization of non-linear functions without constrains (R and Rn): Fibonacci and Golden Section methods; Powell's, gradient, Newton's and Marquardt's methods. Optimization with constrains. Optimization of staged/discrete processes. Formulation and solving of optimization problems using the GAMS platform.

Head Lecturer(s)

Luísa Maria Rocha Durães

Assessment Methods

Assessment
Resolution Problems: 40.0%
Frequency: 60.0%

Bibliography

Hangos, K., Cameron, I., Process Modelling and Model Analysis, 4th vol. of Process Systems Engineering, Academic Press, San Diego (2001).

Chapra, S., Applied Numerical Methods with MATLAB for Engineers and Scientists, 4th Ed., McGraw-Hill, Boston (2018).

Edgar, T.F., Himmelblau, D.M., S.L. Leon, Optimization of Chemical Processes, 2nd Ed., McGraw-Hill, N.Y. (2001).

Vande Wouwer, A., Saucez, P., Vilas, C., Simulation of ODE/PDE Models with MATLAB, OCTAVE and SCILAB, Springer International Publishing, Cham, Switzerland (2014).

GAMS Development Corp. (n.d.). GAMS User's Guide. Acedido a partir de https://www.gams.com/latest/docs/UG_MAIN.html

The MathWorks Inc. (n.d.). MATLAB Documentation. Acedido a partir de

https://www.mathworks.com/help/matlab/index.html