CBE 255. Introduction to Chemical Process Modeling

CBE Faculty

Department of Chemical and Biological Engineering

University of Wisconsin

Madison, Wisconsin

Course Overview

This course provides an overview of the chemical engineering curriculum and develops facility with using modern computational software for numerical problem solving.

The course provides an integrative overview of the entire chemical engineering curriculum. The faculty instructors for the latter courses in the curriculum have identified the key modeling concepts that they would like students entering their courses to be exposed to early in their education in our department. We will select 10-12 key topics from this list and structure the course around one key concept per week. The lectures will introduce these concepts and the students will immediately begin to apply them in smaller discussion sections. We will introduce computational tools motivated by these key concepts. By the end of this course, the students will have a set of tools that have been selected by the faculty in the latter courses as most useful to them as instructors.

Technology is an essential component of this course. The college has invested in classrooms with laptop projection capability and wireless internet connections. Many engineering undergraduates bring their own laptops to campus. The department will loan the additional laptops so every student can bring their laptop to class. The course requires intensive problem solving in small groups to educate the students in how to use advanced computational tools for engineering decision making in complex situations. We envision using undergraduates who have mastered the course in previous semesters as the leaders for the smaller discussion sections. The professor in charge of the course will also cover one discussion section on a rotating basis.

The course may be broken into two parts, with the first part taught to sophomores and the second part to juniors. In this way, the students will find almost immediate use of all the tools they have learned in their next semester courses.

Given the following features: (i) the course provides an integrated view of the entire curriculum, (ii) the course instructors select the concepts and computational tools presented, and (iii) the senior students lead discussion sections with the junior students, we hope to foster a learning community in the department in which using technology to solve complex engineering problems becomes an integral part of our students' educational experience.

Complete collections of the M-files for both Matlab and Octave in zip or tar.gz file formats are available for download from the following links:

Matlab:

cbe255-matlab-m-files-v0.8.zip

cbe255-matlab-m-files-v0.8.tar.gz

Octave:

cbe255-octave-m-files-v0.8.zip

cbe255-octave-m-files-v0.8.tar.gz

Module 1: Programming and programming languages

Computational concepts: introduction to Matlab, purpose of Matlab windows, accessing the online help system

COE Support Page for Matlab

Module 2: Stoichiometry of chemical reactions

Chemical and biological engineering concepts: chemical reactions, linear independence of reactions, reaction rates, production rates

Computational concepts: matrices, rank of a matrix, submatrices, reshaping matrices, solving least squares problems

Programming concepts: looping, conditionals, plotting, loading data from files, writing to the screen

Broader applications of these concepts: electrical circuit theory, network models, linear programming and game theory, financial models and optimization

Tutorial

	Exercise 2.1: Finding independent sets of reactions.			Exercise 2.9: Reaction rates from production rates.
	Exercise 2.11: Download this data set with a browser and save it to a file.

Module 3: Diffusion and heat transfer

Chemical and biological engineering concepts: heat transfer and mass diffusion, gradient and flux, thermal conductivity, heat capacity, diffusivity, dimensionless variables

Computational concepts: partial differential equations, implicit differential equations, differential-algebraic equations, orthogonal collocation, semi-infinite domains

Programming concepts: colloc program, functions, scripts, global statement, ODE solvers in Matlab, ode15i

Broader applications of these concepts: transport phenomena, rate processes, dimensional analysis

Tutorial

	Figure 3.1: Temperature profile versus position at several times during heating of a slab.			Figure 3.2: Temperature profile of the semi-infinite slab at different tau = kt/(\rho \CP).
	Figure 3.5: Dimensionless concentration versus dimensionless radial position for different numbers of collocation points.			Figure 3.6: Relative error in the effectiveness factor versus number of collocation points.
	Figure 3.7: The solution to the full model for the series reaction A -> B -> C; ODE model.			Figure 3.8: The solution to the reduced QSSA model; DAE model.
	Exercise 3.1: The function sin 2 pi x with 10 collocation points.			Exercise 3.2: The function e^(-10x) with 10 collocation points.
	Exercise 3.5: Cooking the turkey.

Module 4: Process systems steady-state modeling and design

Chemical and biological engineering concepts: process systems, reaction, separation, flash tank, recycle, material balances, degrees of freedom

Computational concepts: solving sets of nonlinear algebraic equations, Newton's method, Jacobian matrix,

Programming concepts: looping, iteration, formatted output to the screen, user input from the keyboard, nonlinear algebraic equation solvers in Matlab

Broader applications of these concepts: process industries and chemical manufacturing, designing processes

Tutorial

	Figure 4.2: Solving f(x)=x^3 - 2x^2 + 3x -6 = 0 with Newton's method.
	Exercise 4.1: Solving f(x)=x^3 - 2x^2 + 3x -6 = 0 with Newton's method.			Exercise 4.2 : Solving f(x)=x^3 - 3x - 2 = 0 with Newton's method.
	Exercise 4.3: Solving f(x)=x^3 - 2x^2 + 3x -6 = 0 with Newton's method.
	Exercise 4.5 : Solving the process flowsheet example.

Module 5: Chemical kinetics in well-mixed reactors

Chemical and biological engineering concepts: chemical kinetics, law of mass action, material balance, well-mixed reactor, reaction rates, production rates, complex dynamics, oscillations, Zhabotinsky reaction, coupled mass and energy balance for the CSTR

Computational concepts: ordinary differential equations, Euler method, stepsize, relative and absolute errors

Programming concepts: functions, scripts, global statement, ODE solvers in Matlab, ode15s

Broader applications of these concepts: dynamical systems, complex dynamics, oscillations, multiple steady states

Tutorial

	Figure 5.2 : First-order, irreversible kinetics in a batch reactor.			Figure 5.3 : First-order, irreversible kinetics in a batch reactor, log scale.
	Figure 5.4 : First-order, reversible kinetics in a batch reactor, k1 = 1, k-1 = 0.5, cA0 = 1, cB0 = 0.
	Figure 5.5 : Concentrations of Ra, Rn, Po, He versus time for radioactive decay reactions.			Figure 5.6 : Concentrations of Ra, Rn, Po, He versus time for radioactive decay reactions --- log scale.

Module 6: Staged separations

Chemical and biological engineering concepts:

Computational concepts:

Programming concepts:

Broader applications of these concepts:

Tutorial

Module 7: Estimating parameters from data

Chemical and biological engineering concepts: fitting chemical and biological engineering models to data

Computational concepts: optimization, least squares, statistical confidence intervals, normal and uniform distributions, sampling, mean, variance

Programming concepts: parest.m, ellipse.m, Sundials package, hist, chi2inv, sqrtm, rand, randn

Broader applications of these concepts: Decision making under uncertainty, model discrimination, statistical methods, random variables, sampling

Tutorial

Figure 7.4:
Histogram of 10,000 samples of Matlab's randn function Figure 7.5:
The 15 samples of measurement, pressure, and concentration.

Figure 7.8:
One thousand samples of the random variable x = N(m, P) and 95% probabilty contour. Figure 7.10:
Antoine model fitted to the acetone vapor pressure data of Example 7.5

Figure 7.11:
Measurements of species concentrations in Reactions A-> B -> C versus time. Figure 7.12:
Fit of model to measurements using estimated parameters.

Course Review

Study guide

Table 1 :
Summary of Matlab commands used in CBE 255.

	Figure 7.4: Histogram of 10,000 samples of Matlab's randn function			Figure 7.5: The 15 samples of measurement, pressure, and concentration.
	Figure 7.8: One thousand samples of the random variable x = N(m, P) and 95% probabilty contour.			Figure 7.10: Antoine model fitted to the acetone vapor pressure data of Example 7.5
	Figure 7.11: Measurements of species concentrations in Reactions A-> B -> C versus time.			Figure 7.12: Fit of model to measurements using estimated parameters.