Intended Audience

This book is for the chemical engineering student or the professional engineer who is interested in solving problems that require numerical methods by using mathematical software packages on personal computers. This book provides many typical problems throughout the core subject areas of chemical engineering. Additionally, the “nuts and bolts” or practical applications of numerical methods are presented in a concise form during example problem solving, which gives detailed solutions to selected problems.

Background

The widespread use of personal computers has led to the development of a variety of tools that can be utilized in the solution of engineering problems. These include mathematical software packages like MathCAD, Maple, Mathematica, Matlab, Polymath, and spreadsheets like Excel. While there is great potential in the hands of individual PC users, often this potential is not well developed in current engineering problem solving.

In the past the computer was used only for the difficult tasks of rigorous modeling and simulation of unit operations, processes, or control systems, while the routine calculations were carried out using hand-held calculators (or spreadsheet programs more recently), using essentially the same techniques that were used in the slide rule era. Limiting the use of the computer solely to the difficult tasks was justified before the introduction of interactive numerical packages because the use of the computer was very time consuming.

A typical computer assignment in that era would require the student to carry out the following tasks: (1) Derive the model equations for the problem at hand, (2) find an appropriate numerical method to solve the model, (3) write and debug a FORTRAN program to solve the problem using the selected numerical algorithm, and (4) analyze the results for validity and precision.

It was soon recognized that the second and third tasks of the solution were minor contributions to the learning of the subject matter in most chemical engineering courses, but they were actually the most time consuming and frustrating parts of a computer assignment. The computer enables students to solve realistic problems, but the time spent on the technical details that were of minor relevancy to the subject matter was much too long.

The introduction of interactive numerical software packages brought about a major change in chemical engineering calculations. This change has been called a “paradigm shift” by Fogler. ² Using those packages the student’s (or the practicing engineer's) main task is to set up the model equations. The interactive program provides accurate solutions to these equations in a short time, displaying the results in graphical and numerical forms. The meaning of the paradigm shift, however, is that using the old calculation techniques with the new computer tools brings very little benefit. This is emphasized in the following observation made by deNevers and Seader ¹ : “Since the advent of digital computers, textbooks have slowly migrated toward computer solutions of examples and homework problems, but in many cases the nature of the examples and problems has been retained so that they can be solved with or without a computer.”

In most of the examples and problems provided in this book, new solution techniques are presented that require the use of the computer. Thus the full benefits of a computer solution can be gained even for routine, simple problems, not just for complicated ones.

In spite of many available numerical problem-solving packages, advanced problem solving via personal computers continues to be under utilized in chemical engineering education. A recent survey by Jones ⁵ has indicated that “across the country, computers are usually not used effectively in undergraduate engineering science courses. Often they are not used at all. Problem solving approaches and calculation methods are little influenced by the availability of computers.” There are several major reasons for this situation.

First, many of the current engineering textbooks and reference books have been very slow to react to the enhanced problem-solving capabilities that are currently available. Unfortunately, the current textbooks in most engineering subject areas have been slow to react to this emerging capability. The lack of properly framed standard problems in various engineering disciplines is accompanied by a lack of faculty interest in the use of new tools and the creation of appropriate problems that utilize these tools.

Another important reason for the lack of mathematical software usage for advanced problem solving is the actual cost of the software for individual students. While there are many educational benefits to having problem solving close at hand on student-owned personal computers, often the cost to the individual students is prohibitively high. Fortunately, the costs to major colleges and universities for site licenses for the use of software only in computer labs is much more reasonable. However, this pricing structure forces students to use problem-solving software only in computer labs and does not allow interactive use of the software at other locations. Thus advanced problem-solving capabilities are not currently as close at hand as the nearest personal computer.

Finally, there is a significant learning curve to most of the advanced problem-solving software. This requires users to become familiar with a command structure that is often not intuitive and thus difficult to use. This is a significant impediment to student, professional, and faculty use of many packages.

Purposes of This Book

The main purpose of this book is to provide a comprehensive selection of chemical engineering problems that require numerical solutions. Many problems are completely or partially solved for the reader. This text is intended to be supplementary to most of the current chemical engineering textbooks, which do not emphasize numerical solutions to example and posed problems. This book is highly indexed. The reader can only consider a particular subject area of interest or the application of a particular numerical method in actual problem solving. In either area, problems or methods, the book gives concise and easy-to-follow treatments.

The problems are presented in a general way so that various numerical problem-solving computer packages can be utilized. Many of the problems are completely solved so as to demonstrate a particular problem-solving approach. In other cases, problem-solving skills of the reader need to be applied.

This book has been designed for use with any mathematical problem solving package. The reader is encouraged to use the mathematical software package of his or her choice to achieve problem solutions. However, the POLYMATH package has been used as an example package, and a complete version of POLYMATH is included in the companion web site that is available for this text. This allows the convenient use of POLYMATH throughout the book, as many of the problems have some part of the solution in POLYMATH files that are available on the companion web site.

General Problem Format

All problems presented in the book have the same general format for the convenience of the reader. The concise problem topic is first followed by a listing of the chemical engineering concepts demonstrated by the problem. Then the numerical methods utilized in the solution are indicated just before the detailed problem statement. Typically a particular problem presents all of the detailed equations that are necessary for solution, including the appropriate units in a variety of systems, with Système International d’