Course detail

Modelling of Processes

FSI-IMPAcad. year: 2017/2018

In the course, students will get acquainted with basic types of mathematic models used for design, analysis and optimization of process systems and equipment.
• Model of processing line describing mass and energy balance of a continuous process
• Model of process equipment describing a batch process
• Model for the optimization of a process or equipment
• Model for detailed analysis of conditions inside of an equipment
Models included in the course are mostly based on a system of equations (mainly linear) and ordinary differential equations. Besides analytical solution of equations systems students will learn how to apply basic numerical methods to the solution of ODEs and to solve by graphical method linear optimization problems.

Learning outcomes of the course unit

Students will understand the basic principles of mathematical model design for complex systems. They will also learn about model application in practice. They will get an overview of process and energy systems and the types of models that are used for design, analysis and optimization. After finishing the course, students should be able to choose appropriate type of model for the design, analysis or optimization of a system or equipment, they should understand the basic principles of those models, have insight in corresponding solution methods and experience with their application.


Process systems engineering, basic knowledge of mathematics, physics and thermomechanics from the first four semesters at FME.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Perry, Robert H.: Perry’s chemical engineers’ handbook, McGraw-Hill, New York, 2008
R. M. Felder and R. W. Rousseau, Elementary Principles of Chemical Processes, 3rd Update Edition. Wiley, 2004.
Ramirez, W. F.: Computational Methods for Process Simulation, 2 edition. Oxford ; Boston: Butterworth-Heinemann, 1998

Planned learning activities and teaching methods

The course is taught through lectures introducing the basic principles and theory, explaining of solution methods and showing solution methods. Lectures include sample problems that are solved interactively with the students, with emphasis on understanding. Lectures often include repetition of the most important prerequisites that are necessary to master the subject.

Seminars are focused on hands-on solution of sample problems complemented with work in software tools.

Assesment methods and criteria linked to learning outcomes

SEMINARS: Regular and active attendance is required and checked. Written test must be passed successfully. Test is successfully passed if more than half of points are obtained. The student has the possibility of one repeat.

EXAM: The exam is written. The course evaluation is performed by a standard procedure, according to the percent of obtained points (0-50%…F, 51-60%…E, 61-70%…D, 71-80%…C, 81-90%…B, 91-100%…A).

Language of instruction


Work placements

Not applicable.


The objective is to acquaint students with the basic principles of mathematical models for design, analysis and optimization of industrial units (processes) or equipment. Students should be able to choose a proper model type for the solution of typical problems, understand the corresponding solution methods and be able to solve simple problems.

Specification of controlled education, way of implementation and compensation for absences

The attendance at lectures is recommended. The attendance at exercises is compulsory and checked.

Presence at lectures is necessary to understant solution methods, which are not explained at seminars, only practiced on example problems.

Classification of course in study plans

  • Programme B3S-P Bachelor's

    branch B-EPP , 3. year of study, winter semester, 6 credits, compulsory

Type of course unit



39 hours, optionally

Teacher / Lecturer


1. Basics of modelling. Definition of system. Oriented graph. Branches and nodes. Demonstration on a concrete example
2. Mass balance, species balance, energy balance, material and energy streams, unit operations, extensive and intensive properties.
3. Simulation and modelling. Simple models. Mixers, splitters, manipulators, heat exchangers.
4. Degrees of freedom, solvability, sequential modular simulation. System description by equations. Recycle stream and iterative solution.
5. Steady and unsteady, continuous and batch process. Chemical reaction kinetics, equilibrium, conversion.
6. Sensitivity analysis. Objective function, feasible set, optimization. Hierarchy of process/equipment model and optimization.
7. Algebraic systems of equations, application to process system balancing.
8. Example problem – process system balancing.
9. System of ordinary differential equations, application to simulation of process systems.
10. Example problem – Simulation of process systems.
11. System of partial differential equations, application to stress/strain analysis.
12. System of partial differential equations, application to fluid flow analysis.
13. Example problem – fluid flow.


26 hours, compulsory

Teacher / Lecturer


Computer-aided seminars. Work on computers related to lecture subjects.