D. Software Packages

While Polymath 6.1 is the primary software package for the majority of the problems requiring numerical solutions, MATLAB and Wolfram are also available. In addition, one can use COMSOL and Aspen to solve a few selected problems.

D.1 Polymath

D.1.A About Polymath

Polymath 6.1 is the primary software package used in this textbook. Polymath is an easy-to-use numerical computation package that allows students and professionals to use personal computers to solve the following types of problems:

• Simultaneous linear algebraic equations

• Simultaneous nonlinear algebraic equations

• Simultaneous ordinary differential equations

• Data regressions (including the following)

• Curve fitting by polynomials and splines

• Multiple linear regression with statistics

• Nonlinear regression with statistics

Polymath is unique in that the problems are entered just like their mathematical equations, and there is a minimal learning curve. Problem solutions are easily found with robust algorithms. Polymath allows very convenient problem solving to be used in chemical reaction engineering and other areas of chemical engineering, leading to an enhanced educational experience for students.

The following special Polymath Web site for software use and updating will be maintained for users of this textbook:

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www.polymath-software.com/fogler

D.1.B Polymath Tutorials

Polymath tutorials (https://www.youtube.com/watch?v=nyJmt6cTiL4) can be accessed in the Summary Notes by clicking on the purple hot buttons Image. Here, screen shots of the various steps are shown for each of the Polymath programs.

Summary Notes

Chapter 1

A. Ordinary Differential Equation (ODE) Tutorial

B. Nonlinear (NLE) Solver Tutorial

Chapter 7

A. Fitting a Polynomial Tutorial

B. Nonlinear Regression Tutorial

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Note: The Living Example Problems (LEPs) need to be copied from the CRE Web site and pasted into the Polymath software. The Polymath software is available in most chemical engineering department computer labs in the United States and in some other countries as well. If you want to have Polymath on your own laptop or desktop computer, you can purchase special low-priced educational versions of the software for various time periods. Polymath versions are compatible with Windows XP, Vista, Windows 7, Windows 8, and Windows 10. The specially discounted Polymath Software is available ONLY from the special Web site www.polymath-software.com/fogler. The minimum educational pricing requires you to refer to your Fogler textbook when you sign on to the special Web site to order Polymath. Android users can also use PolyMathLite on phones, tablets, and computers. More information is available from the Web site www.polymathlite.com

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D.2 MATLAB

MATLAB programs for the LEPs are given on the CRE Web site. The disadvantage of the MATLAB ODE solver is that it is not particularly user-friendly when trying to determine the variation of secondary parameter values. MATLAB can be used for the same four types of programs as Polymath.

D.3 Aspen

Aspen is a process simulator that is used primarily in many senior design courses. It has the steepest learning curve of the software packages used in this text. It has a built-in database of the physical properties of reactants and products. Consequently, one has only to type in the chemicals and the rate law parameters. It is really too powerful to be used for the types of home problems given here. The pyrolysis of benzene using Aspen is given as an example on the CRE Web site in Chapter 5, Learning Resources 4.E, Solved Problem E.5-3 Design. Perhaps one home assignment should be devoted to using Aspen to solve a problem with heat effects in order to help familiarize the student with Aspen.

Aspen example on the CRE Web site

An Aspen tutorial and example problem from Chapters 5, 11, and 12 can be accessed directly from the CRE Web site home page (under Let’s Get Started, click on Additional Software and then click Aspen Plus).

D.4 COMSOL Multiphysics

COMSOL Multiphysics is a modeling and simulation software available commercially from COMSOL Inc. It solves multiphysics problems in 1D, 1D axisymmetry, 2D, 2D axisymmetry, 3D, and at single points (0D). Internally in the program, these problems are formulated using partial differential equations (PDEs for 1D to 3D) or ordinary differential equations (ODEs). At www.comsol.com/ecre, one can download documentation and solve CRE problems, which are formulated in this book.

A dedicated application, with a tailored user interface, solves problems for tubular reactors with heat effects involving both radial axial and radial gradients in concentration. A step-by-step COMSOL tutorial with screenshots for setting up this model and solving the model equations is also given in the CRE web modules.

In the web modules, the first tutorial is “Heat effects in tubular reactors” and the second is “Tubular reactors with dispersion.” In the first section, the four examples focus on the effects of the radial velocity profile and external cooling on the performances of isothermal and nonisothermal tubular reactors. In the second section, two examples examine the dispersion effects in a tubular reactor.

Heat Effects

1. Isothermal reactor. This example concerns an elementary, exothermic, second-order reversible liquid-phase reaction in a tubular reactor with a parabolic velocity distribution. Only the mole, rate law, and stoichiometric balance in the tubular reactor are required in this COMSOL exercise.

2. Nonisothermal adiabatic reactor. The isothermal reactor model is extended to include heat effects whereby the tubular reactor is treated as an adiabatic reactor. The material and energy balances are solved simultaneously in the COMSOL exercise.

3. Nonisothermal reactor with isothermal cooling jacket. A cooling jacket kept at a constant temperature is added to the model described in the second example above. This is a valid assumption if the cooling liquid is supplied in such a large amount that the influence of the heat from the reactor on the coolant’s temperature is negligible. The boundary condition for the energy balance at the radial boundary is changed from the thermal insulation boundary condition to a heat flux boundary condition, where the external temperature corresponding to the coolant is set to a constant value.

4. Nonisothermal reactor with variable coolant temperature. This example extends the third example by including the energy balance on the coolant in the cooling jacket as the temperature of the coolant varies along the length of the reactor.

Dispersion and Reaction

1. One-Dimensional model with Danckwerts boundary conditions. In this example, the mass balance in a tubular reactor with arbitrary reactions is described by an ordinary differential equation with dimensionless variables and in terms of the Peclet number and the Damköhler number.

2. One-Dimensional model with upstream and downstream sections. This example uses the open-vessel boundary conditions where an inlet (upstream) section and an outlet (downstream) section are added to a tubular reactor where dispersion occurs but no reaction.

It is suggested that one first uses and plays with COMSOL Multiphysics for solutions to examples XX and YY before making any changes. One should also review the Web Module for Chapter 12 on Axial and radial gradients in tubular reactors before running the program (www.umich.edu/~elements/5e/web_mod/radialeffects/index.htm and www.umich.edu/~elements/web_mod/radialeffects/comsol_ecre.pdf).

Tutorial

Tutorials with step-by-step instructions and screenshots can be found on the web page www.comsol.com/ecre. Start with the documentation of 1. Isothermal Reactor and then go to the documentation section for each of the other exercises. Tutorial material for this exercise is built on but not repeated in the exercises that follow. Next, go to 2. Nonisothermal adiabatic reactor and read the additional information there before continuing to exercises 3 and 4. Again here, the documentation is built on, not repeated, which also holds for each of the sequential exercises.

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