# XWT-35305 Computational Methods in Water Technology

## Vak

Studiepunten 5.00

 Onderwijstype Contacturen Lecture 18 Practical 30 Independent study 0
 Course coordinator(s) ir. PHA van Dorenmalen Prof. dr. ir. KJ Keesman Lecturer(s) Prof. dr. ir. KJ Keesman Examiner(s) Prof. dr. ir. KJ Keesman

EN

### Assumed knowledge on:

XWT-23805 Transport Phenomena in Water Technology and XWT-33305 Chemical Reactor Design

### Contents:

Nowadays, computers are more and more used to support the understanding of water treatment processes and the design, optimization and control of reactors and reactor networks in water technological applications. The basic principles of computational methods for water technology will be outlined and demonstrated on typical reactor configurations in water and wastewater treatment. Topics discussed during the course include:
- matrix algebra: operations, determinants, eigenvalues and eigenvectors;
- solving sets of linear equations: inverse and pseudo-inverse;
- linearization: non-linear functions with one or more variables;
- linear dynamic systems: state-space representation, LTI systems, steady state, stability;
- simulation: single state LTI system, solutions, discretization, aeration tank, hydrolysis;
- simulation: partial differential equation (PDE), multiple state LTI system, discretization, plug flow reactor;
- non-linear systems: state-space representation, linearization, time scales;
- simulation: set of ordinary differential equations, phase portrait, co-current water-adsorbent contactor;
- reactor networks: mass and energy balances, steady state solutions, sensitivity, economic evaluation.

### Learning outcomes:

After successful completion of this course students are expected to be able to:
- understand mathematical concepts and apply mathematical knowledge, insights and methods to solve problems in water technological sciences using a systematic approach;
- represent a physical (linear/linearized differential equations) model in LTI state-space form with matrices {A,B,C,D};
- numerically calculate the solution of sets of differential equations or the solution of a partial differential equation and knows how to interpret the solution;
- analyze, via linearization and/or spatially/temporally discretization techniques, the dynamic and steady-state behavior and stability of general dynamic systems;
- critically reflect upon the results by verifying them.

### Activities:

- attending lectures and instruction hours;
- studying the presented material and hand-out;
- preparing and performing (intensive) computer practicals;
- working on take-home exams.

### Examination:

Observations during computer practicals. Exam consist of a set of take-home exams. The final mark is the average of the individual take-home exams, with individual scores of at least 5.5.

### Literature:

Slides & book chapters
Recommended
1. Stewart, J., Calculus (2011), Early Transcendentals, 7th ed., 1308p., Cengage Learning Services, ISBN13 - 9780538498876.
2. Lay, D.C. (2006), Linear Algebra and its applications, 3rd international ed., Pearson Education, ISBN13 -9780321417619.
3. Akker H. van den & Mudde R.F., Transport Phenomena, the art of balancing, 1st edition, ISBN13 - 9789065623584.
4. Ogata, K. Modern Control Engineering, Prentice Hall, 5th Ed, 2010.

Opleiding Fase Specialisatie Periode MWT Water Technology (joint degree) MSc 4WD