1
Introduction
This Chapter 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 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 presesnted 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
thoughout 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 1-1.
stack gases
containing SO2
ash containing
CaSO3
combustion
chamber
coal containing
sulfur
air
Figure 1-1. Coal combustion
1
energy to
steam plant
Chapter 1
2
Coal fed into the combustion chamber may contain sulfur, and this sulfur may appear in the stack gas as
SO2 or in the ash as Ca SO3 . 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.
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 the gasliquid contacting device illustrated in Figure 1-2 where we have shown the stack gas bubbling up through a
limestone slurry in which SO 2 is first absorbed as suggested by
SO2 gas
SO2 liquid
(1-1)
The absorbed sulfur dioxide then reacts with water to form sulfurous acid
H 2O SO2
H 2SO3
(1-2)
which subsequently reacts with calcium hydroxide according to
Ca(OH)2 H 2SO3 CaSO3 2H 2O
(1-3)
Here we have used Eq. 1-1 to represent the process of gas absorption, while Eqs. 1-2 and 1-3 are
stoichiometric representations of the two reactions involving sulfurous acid. The situation is not as simple
as we have indicated in Eq. 1-3 for the sulfurous acid may react either homogeneously with calcium
hydroxide or heterogeneously with the limestone particles. This situation is also illustrated in Figure 1-2
Figure 1-2. Limestone scrubber for stack gases
Introduction
3
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.
There are other mass balance problems that are less complicated than those illustrated in Figures 1-1
and 1-2, 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 1-3. It is not difficult to see that the sources of water for the lake are actually represented by the
average rainfall and snowfall in the Mono Lake watershed. Over time, these sources must be balanced
Figure 1-3. Water balance on Mono Lake
by the two sinks i.e., evaporation and shipments to Los Angeles 1 . 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?
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 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 1-4, can be analyzed using the techniques
that are 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.
1. For details see the Mono Lake Committee at http://www.monolake.org.
Chapter 1
4
Figure 1-4. Continuous cell growth in a chemostat
1.1 Analysis versus Design
In this text, we will generally concern ourselves with the analysis of systems of the type illustrated in
Figures 1-1 through 1-4. For example, if we know how much SO2 is entering the scrubber shown in
Figure 1-2 and we can measure the amount of Ca SO3 leaving with the slurry, then we can use material
balance techniques to determine the amount of SO 2 leaving the scrubber in the clean gas. The design of
a limestone slurry scrubber is a much more difficult problem. In that problem we would be given the
amount and composition of the stack gas to be treated, and the allowable amount of SO 2 in the clean gas
would also be specified. The task of the chemical engineer would be to determine the size of the
equipment and the flow rate of the limestone slurry required to produce the desired clean gas. The design
of a stack gas scrubber is not a trivial problem because the rate of transfer of SO2 from the gas to the
liquid is influenced by both the homogeneous and heterogeneous chemical reactions. In addition, this rate
of transfer depends on the bubble size and velocity, the viscosity of the slurry, and a number of other
parameters. Because of this, there are many possible designs that will provide the necessary concentration
of SO2 in the stack gas; however, it is the responsibility of the chemical engineer to develop the least
expensive design that minimizes environmental impact, protects the health and safety of plant personnel,
and assures a continuous and reliable operation of the chemical plant.
1.2 Representation of Chemical Processes
Chemical processes are inherently complex. In a continuous chemical plant 2 , such as we have
illustrated in Figure 1-5, raw materials are prepared, heated or cooled, and reacted with other raw materials.
2. Shreves Chemical Process Instutries, 1998, 5th Edition, edited by J. Saeleczky and R. Margolies, McGraw-Hill
Professioinal, New York.
Introduction
5
Figure 1-5. Simplified flowsheet for the manufacture of ethyl alcohol from ethylene
The products are heated or cooled and separated according to specifications. A chemical plant, including
its utilities, has many components such as chemical reactors, distillation towers, heat exchangers,
compressors and pumps. These components are connected to each other by pipelines or other means of
transportation for carrying gases, liquids, and solids. To describe these complex chemical
engineers systems use two fundamental elements:
(a) Structure: This is the manner in which the components of a plant are connected to each
other with pipelines or other means of transportation. The structure is unique to a plant. Two
components connected in different sequences can completely alter the nature of the products.
Structure is represented using flowsheets. A complete version of a flowsheet, including all
utilities, control, and safety devices is known as the Piping and Instrumentation Diagram
(P+ID). Figure 1-5 is a pictorial representation of a simple flowsheet.
(b) Performance: This is the duty or basic operating specifications of the individual units. The
duty is described using Specification Sheets for all units of the process and by listing the
properties of the streams connecting the units. The properties of the streams include flow rates,
composition, pressure and temperature. In relatively simple systems, a single document
includes the flowsheet and the properties of the streams. To describe complex systems, one
needs several flowsheets as well as a collection of specification sheets.
To perform material balances for complex systems, one uses information about the structure of the
flowsheet and the performance of the units to determine the properties of the connecting streams. The
processes illustrated in Figures 1-1 through 1-5 appear to be dramatically different; however, the
fundamental concepts used to analyze these systems are the same. Hidden behind the complexity of these
Chapter 1
6
processes is a simplicity that we will describe in subsequent chapters. To make this point very clear, we
consider the complex system illustrated in Figure 1-5 and we identify the scrubber as the object of a
separate analysis as illustrated in Figure 1-6. In this text, most of our effort will be directed toward the
Figure 1-6. Analysis of an individual unit
analysis of single units such as scrubbers, distillation columns, chemical and biological reactors, in additon
to systems such as Mono Lake. After establishing the framework for the analysis of single units, we will
move on to a study of more complex systems in Chapters 7. Transient processes are examined briefly in
Chapter 8, and an introduction to reaction kinetics is provided in Chapter 9.
The concept of analyzing small parts of a problem and then assembling the small parts into a
comprehensive representation of the whole problem is extremely important. In addition, the concept of
studying the whole problem and then breaking it apart into smaller problems is also extremely important.
For example, the ethyl alcohol plant shown in Figure 1-5 could also be viewed from the perspective of the
ethyl alcohol production system shown in Figure 1-7. That production system consists of a natural gas
plant that provides feed for an ethylene plant that provides feed to an ethyl alcohol plant that produces
ethyl alcohol. Within the ethyl alcohol plant there are various units such as the reactor, the scrubber, etc.,
in addition to feed preparation units, secondary distillation units, utilities, and emergency systems such as
the flare and the vessels associated with it. Similar units exist in the natural gas plant and the ethylene
plant, and we have not shown those details in Figure 1-7; however, we have shown the details of the
scrubber that must be analyzed as part of the design of the ethyl alcohol plant, and we have illustrated the
details of the gas-liquid mass transfer process that lies at the foundation of the scrubber design. Clearly
there is an hierarchy of length scales associated with the production of ethyl alcohol and there is important
analysis to be done at each length scale.
The circles illustrated in Figure 1-7 represent control volumes that we use for accounting purposes,
i.e., we want to know what goes in, what goes out, and what is accumulated or depleted. In some cases, we
do not need to know what is happening inside the control volume and we are only concerned with the
Introduction
7
Figure 1-7. Hierarchy of length scales associated with the production of ethyl alcohol.
inputs and outputs of a control volume. This situation is suggested by Figure 1-8 where we have shown
only the inputs and outputs for the ethyl alcohol plant. If both the steady state and dynamic behavior of the
control volumes associated with the natural gas plant, the ethylene plant, and the ethyl alcohol plant are
known, the behavior of the ethyl alcohol production system is also known. However, to learn how those
systems behave, we need to move down the length scales to determine the details of the various processes.
This is illustrated in Figure 1-7 where we have shown a scrubber that is one element of the ethyl alcohol
plant, and we have shown a bubble at which mass transfer takes place within the scrubber. The concept
illustrated in Figure 1-7 is that we must be able to keep track of molecular forms at a variety of length
scales.
Chapter 1
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Figure 1-8. Control volume representation of the ethyl alcohol plant
As another example of the importance of keeping track of molecular species in both large and small
regions, we consider a problem of lead contamination. The title of the article by Steding, Dunlap and
Flegal 3 on lead contamination suggests that we should keep track of lead in the San Francisco Bay estuary
system; however, the lead that appears in the estuary comes from several sources. Endless weathering of
granite in the Sierra Nevada mountains releases lead that is transported by streams and rivers and
eventually arrives in the bay. Other lead comes from hydraulic mine sediments transported across the
Central Valley and into the bay during the nineteenth century. Finally, the more recent influx of lead from
the combustion of leaded gasoline makes its way into the estuary by a variety of paths. Within the estuary
itself, the impact of lead contamination varies. In the shallow salt marshes, seasonal floods and daily tidal
flows have a smaller effect on the transport of lead, and the local bio-reactors are confronted with an
unhealthy diet. Clearly the study of lead contamination in the San Francisco Bay estuary requires keeping
track of lead over a variety of length scales as we have indicated in Figure 1-9. The analysis of this lead
contamination process in Northern California has some of the same characteristics as the analysis of water
conservation in Mono Lake, stack gas scrubbing in a coal-fired power plant, cell growth in a chemostat,
and ethanol production in an ethyl alcohol production system. In this text we will develop a framework
that allows us to analyze all of these systems from a single perspective based on the axioms for the mass of
multicomponent systems. This will allow us to solve mass balance problems associated with a wide range
of phenomena; however, chemical engineers must remember that in addition to these physical problems,
there are economic, environmental, and safety concerns associated with every process and these concerns
must also be addressed.
1.3 Problems
1-1. Read the MSDS (Material Safety Data Sheet) and write a one-paragraph description of the hazards
associated with: dimethyl mercury (students with last names ending in (A to E), methanol (F to J), ethyl
ether (K to O), benzene (P to T), phosgene (U to Z). Information is available on the Internet, at your
campus library, and on the Web page of your local department of environmental health and safety.
3. Steding, D.J., Dunlap, C.E. and Flegal, A.R. 2000, New isotopic evidence for chronic lead contamination in the San
Francisco Bay estuary system: Implications for the persisitence of past industrial lead emmisions in the biosphere,
Proceedings of the National Academy of Science 97 (19), 11181-11186.
Introduction
9
Figure 1-9. Multiple regions associated with lead contamination