Course detail

Balancing of Process and Energy Systems

FSI-KBPAcad. year: 2018/2019

The subject introduces to students the issue of balancing in process and energy systems. Students will learn to apply balance equation of the mass and energy conservation laws to a wide array of processes:
• Steady state processes
• Single component and multicomponent processes
• Processes with chemical reactions
• Transient processes
To solve the balances, the subject will provide analytical and numerical methods and student will practice on a number of practical examples. Emphasis will be put on the computer implementation of procedures in a widely available software MS Excel.

Learning outcomes of the course unit

Students will learn that balancing is a general method of working with the conservations laws of mass, energy or species. They will acquire a systematic analytical approach towards balanced process diagram. They will learn, how to apply balancing to a mathematical description of various types of processes. The students will also learn to solve balance equations in the studied types of processes.


Required is the knowledge of mathematics, physics and thermomechanics from the bachelor’s degree.



Recommended optional programme components

Enhancement of the knowledge of English, mainly the ability to understand written text.

Recommended or required reading

Felder R. M. and Rousseau R. W., Elementary Principles of Chemical Processes, 3rd Update Edition. Wiley, 2004 (EN)
Klapka, J., Dvořák, J., Popela, P. Metody operačního výzkumu. Brno: VUTIUM, 2001 (CS)

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 include repetition of the most important prerequisites that are necessary to master the subject.

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

Assesment methods and criteria linked to learning outcomes

SEMINARS: Regular and active attendance is required and checked, delivering all assignments is obligatory and written tests must be passed successfully. The criterion of successful completion of the seminar is obtaining more than half points in tests.

EXAM: The exam is written. Maximum overall number of points that can be obtained within the course is 100. The course evaluation is performed by a standard procedure, according to the number of obtained points (0-50 points …F, 51-60 points …E, 61-70 points …D, 71-80 points …C, 81-90 points …B, more than 90 points …A).

Language of instruction


Work placements



The aim of the course is to prepare students for effective use of balancing as a basic tool of process engineer. The subject will at the same time highlight the interdependence of knowledge in other selected courses.

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

The attendance at seminars is obligatory, 3 absences are allowed. Participation at the lectures is not checked, but completion of assignments in the seminars requires knowledge from the lectures.

Classification of course in study plans

  • Programme M2I-P Master's

    branch M-PRI , 1. year of study, winter semester, 5 credits, compulsory
    branch M-PRI , 1. year of study, winter semester, 5 credits, compulsory
    branch M-PRI , 2. year of study, winter semester, 5 credits, compulsory

Type of course unit



26 hours, optionally

Teacher / Lecturer


1. week: Classification of balances and basic terminology
2. week: Mass balance of a steady state system (without chemical reactions and with chemical reactions)
3. week: Energy balance of a steady state system (single component systems without chemical reaction)
4. week: Procedures for calculating energy flows of selected process streams
5. week: Energy balance of a steady state system (milticomponent systems with chemical reaction)
6. week: Introduction to economic process assessment in the pre-investment phase
7. week: General introduction to optimization (linear and nonlinear problems, least squares method, graphical method )
8. week: Balance of processes with recycle or bypass, tube networks
9. week: Balance based on operating data (overdetermined system)
10. week: Balance of transient process (ordinary differential equations of the 1st order, analytic and numerical solution)
11. week: Balance of transient process (ordinary differential equations of higher order, conversion to a system of 1st order equations, numerical solution)
12. week: Computer implementation of algorithms for the solution of balances
13. week: Advanced applications and advanced balancing methods (unsteady 3D processes)

Computer-assisted exercise

26 hours, compulsory

Teacher / Lecturer


Computer aided seminars. Solution of problems related to the lectured topics, based on information from the lectures.