# 1.1: Introduction

• • R.L. Cerro, B. G. Higgins, S Whitaker
• Professors (Chemical Engineering) at University of Alabama at Huntsville & University of California at Davis

This text has been prepared for use in what is normally the first chemical engineering course in a typical chemical engineering program. There are essentially two major objectives associated with this text. The first objective is to carefully describe and apply the axioms for conservation of mass in multicomponent, reacting systems. Sometimes these ideas are stated as

mass is conserved

or

mass is neither created nor destroyed

and in this text we will replace these vague comments with definitive mathematical statements of the axioms for conservation of mass. Throughout the text we will use these axioms to analyze the macroscopic transport of molecular species and their production or consumption owing to chemical reaction. The macroscopic mass and mole balances presented in this text are often referred to as material balances. A course on material balances is generally taken after students have completed courses in calculus, vector analysis, and ordinary differential equations, and these subjects will be employed throughout the text. Since a course on linear algebra is often taken simultaneously with the first chemical engineering course, the elements of linear algebra required for problem solving will be introduced as needed.

The second objective of this text is to introduce students to the types of problems that are encountered by chemical engineers and to use modern computing tools for the solution of these problems. To a large extent, chemical engineers are concerned with the transport and transformation (by chemical reaction) of various molecular species. Although it represents an oversimplification, one could describe chemical engineering as the business of keeping track of molecular species. As an example of the problem of “keeping track of molecular species” we consider the coal combustion process illustrated in Figure $$\PageIndex{1}$$. Coal fed to the combustion chamber may contain sulfur, and this sulfur may appear in the stack gas as $$\ce{SO2}$$ or in the ash as $$\ce{CaSO3}$$. In general, the calcium sulfite in the ash does not present a problem; however, the sulfur dioxide in the stack gas represents an important contribution to acid rain. Figure $$\PageIndex{1}$$: Coal combustion

The sulfur dioxide in the stack gas can be removed by contacting the gas with a limestone slurry (calcium hydroxide) in order to affect a conversion to calcium sulfite. This process takes place in a gas‐liquid contacting device as illustrated in Figure $$\PageIndex{2}$$. There we have shown the stack gas bubbling up through a limestone slurry in which $$\ce{SO2}$$ is first absorbed as suggested by

$\left(\mathrm{SO}_{2}\right)_{g a s} \rightleftarrows\left(\mathrm{SO}_{2}\right)_{l i q u i d} \label{eq1}$

The absorbed sulfur dioxide then reacts with water to form sulfurous acid

$\mathrm{H}_{2} \mathrm{O}+\mathrm{SO}_{2} \rightleftarrows \mathrm{H}_{2} \mathrm{SO}_{3} \label{eq2}$

which subsequently reacts with calcium hydroxide according to

$\mathrm{Ca}(\mathrm{OH})_{2}+\mathrm{H}_{2} \mathrm{SO}_{3} \rightleftarrows \mathrm{CaSO}_{3}+2 \mathrm{H}_{2} \mathrm{O} \label{eq3}$

Here we have used Equation \ref{eq1} to represent the process of gas absorption, while Equations \ref{eq2}-\ref{eq3} are stoichiometric representations of the two reactions involving sulfurous acid. The situation is not as simple as we have indicated in Equation \ref{eq3} for the sulfurous acid may react either homogeneously with calcium hydroxide or heterogeneously with the limestone particles. This situation is also illustrated in Figure $$\PageIndex{2}$$ where we have indicated that homogeneous reaction takes place in the fluid surrounding the limestone particles and that heterogeneous reaction occurs at the fluid-solid interface between the particles and the fluid. It should be clear that “keeping track of the sulfur” is a challenging problem which is essential to the environmentally sound design and operation of coal‐fired power plants. Figure $$\PageIndex{2}$$: Limestone scrubber for stack gases

There are other mass balance problems that are less complicated than those illustrated in Figures $$\PageIndex{1}$$ and $$\PageIndex{2}$$, and these are problems associated with the study of a single chemical component in the absence of chemical reaction. Consider, for example, a water balance on Mono Lake which is illustrated in Figure $$\PageIndex{3}$$. It is not difficult to see that the sources of water for the lake are represented by the average rainfall and snowfall in the Mono Lake watershed. Over time, these “sources” must be balanced by the two “sinks” i.e., evaporation and shipments to Los Angeles1. There are two questions to answer concerning the impact of Los Angeles on Mono Lake:

1. What will be the final configuration of the lake?
2. When will this configuration occur? Figure $$\PageIndex{3}$$: Water balance on Mono Lake

The water balance for Mono Lake can be analyzed in a relatively simple manner, and both of these questions will be discussed in Chapter $$3$$.

The biological processes that occur in Mono Lake are altered by the changing level and the changing chemical composition of the lake. The analysis of these natural processes is very complex; however, commercial biological reactors, such as the chemostat illustrated in Figure $$\PageIndex{4}$$, can be analyzed using the techniques that are Figure $$\PageIndex{4}$$. Continuous cell growth in a chemostat developed in this text. In a chemostat, nutrients and oxygen enter a well‐mixed tank containing a cell culture, and biological reactions generate new cells that are harvested in the product stream. This biological process will be analyzed in Chapter $$8$$. Figure $$\PageIndex{4}$$: Continuous cell growth in a chemostat