Dimensional Analysis

Practical Guides in Chemical Engineering

Jonathan Worstell

• Publisher: Butterworth-Heinemann
• Year: 2014
• Print ISBN: 9780128012369
• eBook ISBN: 9780128012550
• Topic: Technology & Engineering
• Subtopic: Linear Algebra
• Index: Technology & Engineering

Practical Guides in Chemical Engineering are a cluster of short texts that each provides a focused introductory view on a single subject. The full library spans the main topics in the chemical process industries that engineering professionals require a basic understanding of. They are 'pocket publications' that the professional engineer can easily carry with them or access electronically while working. Each text is highly practical and applied, and presents first principles for engineers who need to get up to speed in a new area fast. The focused facts provided in each guide will help you converse with experts in the field, attempt your own initial troubleshooting, check calculations, and solve rudimentary problems. Dimensional Analysis provides the foundation for similitude and for up and downscaling. Aeronautical, Civil, and Mechanical Engineering have used Dimensional Analysis profitably for over one hundred years. Chemical Engineering has made limited use of it due to the complexity of chemical processes. However, Chemical Engineering can now employ Dimensional Analysis widely due to the free-for-use matrix calculators now available on the Internet. This book shows how to apply matrices to Dimensional Analysis. - Practical, short, concise information on the basics will help you get an answer or teach yourself a new topic quickly - Supported by industry examples to help you solve a real world problem - Single subject volumes provide key facts for professionals

Chapter 1

Introduction

This chapter discusses the historical procedures used by chemical engineers when developing a new process or modifying an existing process. It also explains why we are generally unable to use the three conservation laws for scaling a process during its development. This chapter notes that we can use Dimensional Analysis and experimentation to define the functional relationships of the variables pertinent to a process, thereby placing a mathematical foundation under our scaling procedures. We briefly discuss in this chapter the two most common methods of Dimensional Analysis taught to chemical engineers. We also discuss the shortcomings of these two Dimensional Analysis methods.

This chapter demonstrates how Dimensional Analysis can reduce process development cycle time and costs. This feature of Dimensional Analysis is important in light of the three revolutions that occurred during the second half of the twentieth century. Those revolutions were in transportation, communication, and finance.

Keywords

Process development; Dimensional Analysis; Method of Indices; number of experiments; twentieth-century revolutions

1.1 Process Development

We generally classify chemical processes by their size: laboratory, pilot plant, or commercial. Process development entails moving technology from the laboratory to the commercial plant. Process development usually begins with an idea that is later successful in laboratory experiments. The proven idea then moves into a pilot plant and if successful there, progresses to a purpose-built commercial plant or into an existing commercial plant. Process support involves moving from an existing commercial plant into a laboratory or pilot plant to solve a problem. We may solve that problem by a small change to the process or with a major overhaul of the process, but, in either case, the solution is first tested in a laboratory or pilot plant, and then confirmed in a test run at the commercial plant.

Process development and process support involve identifying the variables pertinent to and controlling the chemical process, then designing experiments to establish the functional relationship between the variable of interest; i.e., the dependent variable—the variable that will make us money or is costing us money—and the independent variables of the process. These experimental programs must be doable and within the financial ability of the organization sponsoring them.

A good portion of such an experimental program involves collecting information that allows us to move the process from its current size to the next larger size. We call moving from one size to another “scaling.” Thus, process development involves upscaling and process support utilizes downscaling and upscaling. Upscaling involves starting with an idea, then proceeding from laboratory to commercial plant. Downscaling involves starting at a commercial plant and conducting laboratory experiments or operating a pilot plant to mimic the commercial plant problem, then upscaling the solution into the commercial plant.

At some point in your chemical engineering career, you will be asked either to develop a process or to provide technical support to an existing process. You are at that point in your career; otherwise, you would not be reading this book.

There are three methods for developing and upscaling a chemical process:

1. Build successively larger plants until you reach a defined commercial size.

2. Derive and solve the various conservation and transport equations describing your process, then use them to size the commercial process.

3. Establish the empirical relationships between the variables of your process, then use similarity to size the commercial process.

During the first 65–75 years of chemical engineering, we employed the first method when developing and upscaling a chemical process. There are several reasons why we used this method. First, during those years, most chemical processes were new and novel and chemical engineers possessed little information about them, particularly with regard to their safety. Therefore, chemical engineers incrementally increased, stepwise, the size of the process and established the operating conditions and monitored the interaction of the chemicals at each completed step. Second, chemical engineers used each successively larger processing unit as an analog computer, sampling the contents of each unit, then plotting the resulting data to obtain the solution to the differential equations describing the chemical process. Third, during those years, chemical and metallurgical engineers had to develop new materials of construction to meet the specifications of their new chemical processes, particularly with regard to high pressure, high temperature, and corrosion resistance. Fourth, physical property databases were rudimentary during those years. In many cases, intermediate-sized processing units; i.e., pilot plants, were built primarily to measure the physical properties of the chemical components comprising the new process. This process development method, while having advantages, is capital intensive, time consuming, and operationally expensive.

The second method arose with the advent of digital computing during the mid-1940s. Digital computing extends the hope that we can step directly from laboratory-sized equipment to commercial-sized equipment via calculation. The realization of this hope requires extensive, robust databases. Thus, the effort during the third and fourth quarters of the twentieth century to establish the physical properties of a wide variety of chemicals and to develop methods for estimating, via calculation, the physical properties of all chemicals. Also, during these years, computing power doubled many times and software became evermore user-friendly. But, even with these advances, the conservation and transport equations for a given chemical process remain difficult to solve numerically. Much of this difficulty arises from the “stiff” differential equations describing the chemical process. Stiff means some of the differential equations have characteristic times much smaller than the other differential equations.¹ Numerical solutions are also difficult to obtain for catalyzed chemical processes. In a catalyzed chemical process, the catalyst is present at parts per million levels while the reactants are present at moles per liter levels. The same constraint occurs when impurities or by-products are included in a digital model. Again, impurities and by-products are present at parts per million levels while reactants and products are present at moles per liter levels. Such sets of differential equations demonstrate the same characteristics of stiff sets of differential equations; namely, numerical calculations will not “close,” will not approach a stable result. Today, it is possible to design portions of a chemical process directly from laboratory data, distillation showing the most success, but we are far from designing a complete commercial-sized chemical process via calculation.

Downsizing occurs when a commercial plant exists but a pilot plant for the chemical process does not exist. This situation occurs quite frequently for well-established commercial products, particularly commodity products. Unfortunately, processing issues still arise in such commercial plants, issues which require study in a nonexistent pilot plant. In such cases, you will be asked to design a pilot plant that mimics the commercial plant in order to develop solutions to commercial plant problems. Downsizing a chemical process sounds easy, until you try it. Traditionally, we have simply built a miniature “look-alike” plant when downsizing a commercial plant. This approach depends upon “luck” to reproduce the problem requiring solution. If we alter the controlling regime of the process due to downsizing, then we spend time, capital, and incur operating expense solving a problem related to the pilot plant rather than solving the commercial plant problem. This situation occurs many more times than we care to admit. To successfully downsize a chemical process, we must first identify the regime, either momentum transfer, energy transfer, or mass transfer, causing the problem in the commercial ...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Dedication
• Chapter 1. Introduction
• Chapter 2. History of Dimensional Analysis
• Chapter 3. Dimensions and Systems of Units
• Chapter 4. Foundation of Dimensional Analysis
• Chapter 5. Mechanical/Physical Examples of Dimensional Analysis
• Chapter 6. Thermal Examples of Dimensional Analysis
• Chapter 7. Mass Transfer and Reaction Examples of Dimensional Analysis
• Chapter 8. Dimensional Analysis and Scaling
• Chapter 9. An Assessment of Dimensional Analysis