Simulation and Process Optimization


The main objective of this curricular unit is to provide an advanced training in Process Systems Engineering (PSA), focused on the design and operation of complex production systems, with emphasis on the development and application of modelling and computing methods for the simulation, design, control and optimization of chemical and biological processes. These processes are studied through the mathematical description of the underlying physico-chemical and biochemical phenomena. At the end of this course unit the student will have acquired knowledge, skills and competences to:

- Understand the fundamental concepts of PSE, namely the notions of system, stationary and dynamic model, parameters, degrees of freedom, continuous and integer decision variables, constraints, objective function;

- Understand the principles of methods of solving systems of equations (simulation), namely systems of algebraic equations, systems of differential/algebraic equations, and systems of differential equations, and optimization methods for linear (continuous and mixed) and non-linear problems;

- Understand the concepts and methods of modular simulation, involving sequential approach with partitioning and convergence of loops, or simultaneous modular approach.

- Be able to build mechanistic models, involving conservation laws and constitutive relationships, in the form of aggregate or distributed parameter models.

- Be able to carry out parameter estimation, involving data acquisition, application of parameter estimation methods and error analysis.

- Be able to work with simulation and optimization tools specific to the area of chemical and biological engineering, namely flowsheeting tools (Aspen Plus), generic dynamic modelling tools (gPROMS), and optimization languages (AMPL).

General characterization





Responsible teacher

José Paulo Barbosa Mota


Weekly - 3

Total - 5

Teaching language



This curricular unit has not precedences.


  • R. G. Rice, D. D. Do. Applied Mathematics and Modelling for Chemical Engineers. John Wiley & Sons, 1995.
  • K. Hangos, I. Cameron, Process Modelling and Model Analysis, Academic Press, 2001.
  • L. Biegler, Nonlinear Programming: Concepts, Algorithms, and Applications to Chemical Processes, MOS-SIAM, 2010.
  • H.P. Williams, Model Building in Mathematical Programming, 5th ed., Wiley, 2013.
  • Aspen Plus Users Guide (version 12.1). AspenTech, 2005.
  • gPROMS Advanced Users Guide (release 5.0). Process Systems Enterprise Ltd, 2016.
  • gPROMS Introductory User Guide (release 5.0). Process Systems Enterprise Ltd, 2016.
  • R. Fourer, D.M. Gay, B.W. Kernighan, AMPL: A Modeling Language for Mathematical Programming, 2nd ed., Durbury/Thomson, 2003.

Teaching method

The theoretical subjects are taught in theoretical classes in the usual format where the theoretical principles are taught according to the program using the computer as an interaction tool with the students. Practical classes take place in a computer laboratory and aim to consolidate the knowledge acquired in theoretical classes by its application to solving concrete problems. These classes, with strong practical component, are based on the intensive use of commercial software for simulation of chemical and biochemical processes (gPROMS and Aspen Plus), and the mathematical programming interface (optimization) AMPL.

The evaluation has 3 components:

Evaluation method

The evaluation has 3 components:

A - Theoretical test;

B - Practical work of simulation;

C - Practical work of optimization;

FINAL GRADE = 0.5 * A + 0.25 * B + 0.25 * C

Subject matter

  1. Introduction and general concepts: system, model, simulation, optimization.
  2. Mechanistic models: conservation laws, constitutive relations, dynamic and steady-state models, lumped and distributed models.
  3. Solution of systems of equations (simulation): systems of algebraic equations, systems of algebraic-differential equations, systems of partial differential equations.
  4. Parameter estimation: data acquisition, parameter estimation methods, error analysis.
  5. Modular simulation: sequential approach, partitioning, convergence of loops, simultaneous modular approach.
  6. Statistical/data modelling: regression models, artificial neural networks, hybrid models.
  7. Introduction to process optimization: continuous, integer and mixed-integer linear mathematical programming. Optimality conditions. Dual problem. Simplex method. Nonlinear optimization.
  8. Application of modelling, simulation and optimization tools:
  • Flowsheeting – ASPEN Plus, case studies.
  • Generic, equation-oriented dynamic modelling – gPROMS, case studies.
  • Optimization – AMPL, case studies.


Programs where the course is taught: