While Polymath 6.1 is the primary software package for the majority of the problems requiring numerical solutions, Wolfram, Excel, Python, and MATLAB are also available. In addition, one can use COMSOL and Aspen to solve a few selected problems in Chapters 12 and 13 and Chapter 18.

Polymath is an extremely user-friendly software package that is best suited for solving chemical reaction engineering problems. In this text and on the Web site, we mostly use the DEQ for solving coupled differential equations (e.g., conversion and temperature), but also use REG for fitting data to a curve, as well as nonlinear regression to determine the best values of parameters to fit the data to determine the reaction-rate parameters such as the specific reaction-rate *k* and the activation energy, *E*_{A}.

Simultaneous linear algebraic equations

Simultaneous nonlinear algebraic equations

Simultaneous ordinary differential equations

Data regressions (including the following)

Curve fitting by polynomials

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.

Polymath is available free on most universities’ computers. In addition, if you would like to buy a version to load onto your own personal computer, you could first try a free 15-day trial version of Polymath 6.1. The trial version of Polymath 6.1 will execute up to 15 consecutive days after installation. You will be able to install this version only once on a particular personal computer. Detailed information on ordering specially priced educational versions of Polymath 6.1 that will execute for a variety of time periods (e.g., 4 months, 1 year) is available only from *http://www.polymathsoftware.com/fogler/*.

Polymath tutorials (LEQ, NLE, DEQ, REG) for the following Polymath Programs are given on the Web site.

How to Run the LEP Codes (

*http://www.umich.edu/~elements/6e/software/Polymath_LEP_tutorial_new.pdf*)Linear Equation Solver (

*http://www.umich.edu/~elements/6e/software/Linear_Equation_%20Solver_Tutorial.pdf*)Nonlinear Equation Solver (

*http://www.umich.edu/~elements/6e/software/Non_linear_equation_tutorial.pdf*)Ordinary Differential Equation Solver (

*http://www.umich.edu/~elements/6e/software/Ordinary_Differential_Equation_Solver_Tutorial.pdf*)Regression Polynomial Fitting of Data (

*http://www.umich.edu/~elements/6e/software/Polymath_linear_and_polynomial_regression_tutorial.pdf*)Nonlinear Regression Analysis

Find Rate Law Parameters (alpha and k) (

*http://www.umich.edu/~elements/6e/software/Example_7-3_Polymath_nonlinear_regression_tutorial.pdf*)Find Rate Law Parameters for Heterogeneous Reactions (

*http://www.umich.edu/~elements/6e/software/Nonlinear_Regression_Tutorial.pdf*)

Nonlinear Regression Tutorial (

*http://www.umich.edu/~elements/6e/software/nonlinear_regression_tutorial.pdf*)

The Web site shows screen shots of the various steps for each of the Polymath programs. A Polymath tutorial is also given in the LearnChemE videos (*https://www.youtube.com/watch?v=nyJmt6cTiL4*).

The Living Example Problems (LEPs) are available in Wolfram, Python, MATLAB, and Polymath and can be run by first loading the software package on to your computer and then clicking on the problem of interest. A tutorial on how to download and run the LEPs is on the CRE Web site—for example, Polymath 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 departments and 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. Android users can also use PolyMathLite on phones, tablets, and computers. More information is available from the Web site *www.polymathlite.com*.

Wolfram CDF Player is used for viewing .cdf files. Its main feature is creating dynamic and interactive examples, which allow users to vary different parameters using sliders and generate results live (allows users to immediately change parameters, and continuously update the plot), although it is not necessary in order to run the Wolfram LEP. If you wish to also edit the code that generates these programs, you need to purchase and download Wolfram Mathematica 12, which can be found here:

*http://www.wolfram.com/mathematica/*. (Note for all University of Michigan students: CAEN computers have Mathematica 12 installed, so you can easily edit and view the Mathematica files.)

**Getting Started**

Download Wolfram CDF Player for FREE (

*https://www.wolfram.com/cdf-player/*). (Note for all University of Michigan students: CAEN computers have CDF player installed, so you don’t need to install CDF player.)View the tutorial on installing Wolfram CDF Player (

*http://www.umich.edu/~elements/6e/software/CDF_installation_tutorial.pdf*).View the tutorial on running Wolfram LEP codes (

*http://www.umich.edu/~elements/6e/software/Wolfram_LEP_tutorial.pdf*).View the tutorial for the initial settings of the Wolfram variable.

In this edition, Python sliders software is included in the Living Example Problems as a resource. Python is similar to Wolfram in that one uses sliders to change the parameters to study the reactions and reactors in which they take place. A **tutorial** can be found on the Web site (*http://www.umich.edu/~elements/6e/tutorials/Python_tutorials.html*).

MATLAB is a high-performance language for technical computing. It is a matrix-based language that allows matrix manipulations, plotting of functions and data, implementation of algorithms, and interfacing with programs written in other languages. To run MATLAB code you need MATLAB software, which is available on most university computers where it is free for your use. If for some reason it is not available at your university, it can be purchased from *https://www.mathworks.com*.

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.

**Getting Started**

If you already have MATLAB installed on your computer, use the MATLAB program tutorial. If you don’t have MATLAB installed, please visit *https://www.mathworks.com/programs/trials/trial_request.html?ref=ggl&s_eid=ppc_5852767522&q=%252Btrial%20%252Bmatlab* to download a one-month free trial.

**MATLAB Tutorial**

Ordinary Differential Equation (ODE) Solver Tutorial (*http://www.umich.edu/~elements/6e/software/matlab_tutorial_LEP-12-1.pdf*)

Microsoft Excel is a spreadsheet application that uses a grid of cells arranged in rows and columns to perform basic and complex mathematical computations and functions. It features calculation, graphing tools, pivot tables, and a macro programming language. In this text, we use Excel for performing linear regression.

**Getting Started**

The tutorial assumes that you have Excel (Microsoft Office) installed on your computer. If you are a student or faculty at a university, you likely have Excel available to you on university computers. If you don’t have access to Excel, contact your university computing services or visit *products.office.com* to download 30-day free trial or to purchase Excel from Microsoft (*https://products.office.com/en-US/excel?legRedir=true&CorrelationId=f37dfa92-9ec7-41a1-bdd4-d5ccd9210720*). For University of Michigan students, Excel is available on all on-campus computers.

**Excel Tutorial**

Determination of Activation Energy (

*http://www.umich.edu/~elements/6e/software/Excel_tutorial.pdf*)

COMSOL Multiphysics is modeling and simulation software that is 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).

The textbook features model examples that have been formulated and solved using the COMSOL Multiphysics software. At *www.comsol/ecre*, each problem is described and summarized in the documentation, which also includes step-by-step instructions to reproduce the corresponding models and derive the model equations in detail. In the Web modules, there are five different COMSOL modules (e.g., tubular reactor, plug-flow reactor, CSTR) that can be downloaded. In order to run or reproduce these COMSOL models, a valid COMSOL Multiphysics license is required.

We use COMSOL software to solve both ordinary and partial differential equations (*http://www.comsol.com/ecre*). The Chemical Reaction Engineering Module in COMSOL is used to solve space- and time-dependent problems.

**Getting Started**

If you have COMSOL software installed on your computer, then you can develop your own COMSOL files or access a number of COMSOL files present on the COMSOL Web site (*http://www.comsol.com/ecre*). There is a tutorial on downloading and running a COMSOL file from the COMSOL Web site at *http://umich.edu/~elements/6e/software/software_comsol.html*.

If you don’t have COMSOL software, don’t worry! We have created a user interface for COMSOL LEP files that enables you to access and run all the COMSOL files, which are in the library. You can sign in to use the COMSOL models using the University of Michigan’s Web site as a “Guest.” To access and run COMSOL, go to *http://www.umich.edu/~elements/6e/12chap/comsol.html*.

COMSOL tutorials to run COMSOL LEP files for the following COMSOL modules are given on the Web site (*http://www.umich.edu/~elements/6e/software/software_comsol.html*).

Nonisothermal tubular reactor

Startup of a CSTR

Plug-flow reactor with adiabatic operations

Plug-flow reactor with heat exchange

Two CSTR in series

Aspen is a process simulator that is used primarily in 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.

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*).

Instructions for using Aspen Plus to solve chemical reaction engineering problems (software not included) can be found on the Aspen Web site at *www.aspentech.com*.

Chapter 5—Example 5-3: Producing 300 Million Pounds per Year of Ethylene in a Plug-Flow Reactor: Design of a Full-Scale Tubular Reactor (Tutorial, ASPEN Backup File) (

*http://www.umich.edu/~elements/6e/software/aspen-creating.html*)Chapter 8—Supplemental Example: Pyrolysis of Benzene (Tutorial, ASPEN Backup File, Polymath File)

Chapter 11—Example 11-3: Adiabatic Liquid-Phase Isomerization of Normal Butane (Tutorial, ASPEN Backup File) (

*http://www.umich.edu/~elements/6e/software/aspen-example11-3.html*)Chapter 12—Example 12-2a: Adiabatic Production of Acetic Anhydride (Tutorial, ASPEN Backup File) (

*http://www.umich.edu/~elements/6e/software/aspen-example12-2.html#8-6*).Chapter 12—Example 12-2b: Constant Heat Exchange Production of Acetic Anhydride (Tutorial, ASPEN Backup File) (

*http://www.umich.edu/~elements/6e/software/aspen-example12-2.html#8-7*).

Additional information on different types of reactors is available at *http://encyclopedia.che.engin.umich.edu/Pages/Reactors/menu.html*.

Instructions for using ReactorLab to simulate a variety of chemical reactors are available at *http://reactorlab.net*.

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