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Statistical and Numerical Methodsfor Chemical Engineers
(401-0675-00L)
Dr. Roger Käppeli
Dr. Patric Müller
Lecture for D-CHAB Autumn Semester 2017
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Statistical and Numerical Methodsfor Chemical Engineers
● Part one: Numerical methods (Roger Käppeli)Lecture: Wednesday, 08:15-10:00, HG E 33.1
From 20.09.17 until 15.11.17● Part two: Statistical methods (Patric Müller)
Lecture: Wednesday, 08:15-10:00, HG E 33.1From 22.11.17 until 20.12.17
● Exercises (Daniel Baur & Michael Sokolov)– Tuesday, 07:45-09:30, HCI G 174
From 26.09.17 until 19.12.17
● Case study week: 13.11.17 – 17.11.17
Start next week! This week MATLAB introduction
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MATLAB introduction
● Instructors: Daniel Baur & Michael Sokolov● Thursday, 21.09.17, 09:00-16:00, HCI G 174
For Bsc students● Friday, 22.09.17, 09:00-16:00, HCI G 174
For all other students
https://de.wikipedia.org/wiki/Matlab
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Exam
● Mode of examination: Oral 30 minutes
● Two parts:– 20 minutes Numerical Methods– 10 minutes Statistical Methods
● “Sample” exam for Numerical Methods part in last lecture
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Part one: Numerical Methods
● Lecture webpage:– http://www.sam.math.ethz.ch/~karoger/numci/2017/index.html
– Lecture Notes (handwritten)– Script (work in progress… still)– Slides– Some MATLAB codes
● Exercises webpage:– https://www.ethz.ch/content/specialinterest/chab/chemical-n-
bioengineering/morbidelli-group/en/education/snm.html
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Part one: Numerical Methods
● Outline
1.Interpolation and Numerical Calculus
2.Non-linear Equations
3.Ordinary Differential Equations
4.Partial Differential Equations
5.Linear and Non-linear Least Squares
● This is a lot...
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Part one: Numerical Methods
● What are Numerical Methods?
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Part one: Numerical Methods
● What are Numerical Methods?
– They are methods to give approximate solutions to hard problems (difficult or even impossible)
● Why can’t I just use a Numerical Method?
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Part one: Numerical Methods
● What are Numerical Methods?
– They are methods to give approximate solutions to hard problems (difficult or even impossible)
● Why can’t I just use a Numerical Method?
– Like with any other equipment (e.g. lab apparatus) one needs to have a basic understanding to judge the results
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Example 1: CSTR
● CSTR operated isothermally, with negligible volume change, in inflow mode with constant fluid volume, and with two elementary reactionsPerfectly mixed
Continuously Stirred-Tank Reactor
INLET
OUTLET
Input concentration
Output concentrationVolumetric flow rate
Reactor volume
Rate constants
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Example 1: CSTR
● Concentration of each species governed by set of mass balances
Continuously Stirred-Tank Reactor
Inflow Reactions
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Example 1: CSTR
● Concentration of each species governed by set of mass balances
Continuously Stirred-Tank Reactor
Set of coupled nonlinear Ordinary Differential EquationsSolve Numerically!!! Chap. 3
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Example 1: CSTR
● Concentration of each species governed by set of mass balances
Continuously Stirred-Tank Reactor
Set of coupled nonlinear EquationsSolve Numerically!!!
Steady state
Chap. 2
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Example 2: Tubular Reactor
Mass balance:
Diffusion Advection/Convection
Reaction
Boundary conditions:
Solve Numerically!!! Chap. 4
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Example 2: Tubular Reactor
Discretize in space
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Example 2: Tubular Reactor
Discretize in space
ODEs
Chap. 1,2,3,4
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Part one: Numerical Methods
● Outline
1.Interpolation and Numerical Calculus
2.Non-linear Equations
3.Ordinary Differential Equations
4.Partial Differential Equations
5.Linear and Non-linear Least Squares
● This is a lot…
Only an overview…
Starter kit!
… “Preparation” for Statistical part
https://commons.wikimedia.org
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Literature
● Not really needed…
● But see e.g.– Press et al., “Numerical Recipes”– Ascher & Greif, “A First Course in Numerical Methods”– Beers, “Numerical Methods for Chemical Engineering”– ...