Modelling of Processes
FSI-IMPAcad. year: 2018/2019
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 at a steady state
• Model of process equipment describing a transient 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.
Learning outcomes of the course unit
Students will understand the basic principles of mathematical model design for processing and energy 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 and should understand the basic principles of those models.
Basic knowledge of mathematics and physics from the first four semesters at FME.
Recommended optional programme components
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 problems using the knowledge from lectures, mostly computer aided, program MS Excel.
Assesment methods and criteria linked to learning outcomes
SEMINARS: Regular and active attendance is required and checked. All assignments have to be delivered and written test must be passed successfully. Test is successfully passed if more than half points are obtained. The student has the possibility of one repeat.
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
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 seminars is checked, necessary condition to pass the course is regular attendance (i.e. maximum of 3 absences at seminars). Attendance at lectures is not checked, but assignments in seminars require the knowledge from lectures.
Type of course unit
39 hours, optionally
Teacher / Lecturer
1. Basics of modelling. Definition of system. Oriented graph. Branches and nodes. Unit operations. General balance equation, system boundaries.
2. Steady state system. Extensive and intensive properties. Mass balance, species balance, energy balance, material and energy streams,
3. Open and closed system. Simple models: Mixers, splitters, manipulators, heat exchangers.
4. Algebraic systems of equations, application to process system balancing. Degrees of freedom, solvability, sequential modular simulation. System description by equations.
5. Chemical equilibrium, conversion degree. Elemental balance. Crystallization, solvability.
6. Optimization, objective function, feasible set. Hierarchy of process/equipment model and optimization.
7. Recycle stream, bypass, iterative solution, solution using least squares method.
8. Pipe networks, Hardy Cross method, solution using least squares method.
9. Sensitivity analysis, design of experiment, sensitivity indices, sub-optimum strategies.
10. Transient process. Differential balance. Ordinary differential equation of 1st order. Explicit and implicit Euler methods.
11. Transient process with higher order equation. Conversion to a system of 1st order ordinary differential equations. Numerical solution of the system.
12. Application of the general balance equation to a system with distributed parameters. Model for structural mechanics. Model for fluid flow.
13. Repetitions, solution of problems covering the whole extent of the lectures.
26 hours, compulsory
Teacher / Lecturer
Computer-aided seminars. Solution of assignments related to lecture subjects, mostly in MS Excel.