ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK - CHAPTER 7 docx

P

ART

III
Math Concepts: Air Pollution Control

L1681_book.fm Page 149 Tuesday, October 5, 2004 10:51 AM
© 2005 by CRC Press LLC

151

C

HAPTER

7
Air Pollution Fundamentals

“If seven maids with seven mops
Swept it for half a year,
Do you suppose,” the Walrus said,
“That they could get it clear?”
“I doubt it,” said the Carpenter,
And shed a bitter tear.

Lewis Carroll

7.1 INTRODUCTION

In the last 40 years, the environmental engineering profession has expanded its societal responsi-
bilities to include the control of air pollution from industrial sources. Though not exactly “seven
maids with seven mops trying to get it clear,” increasing numbers of environmental engineers are
confronted with problems in this most vital area. Although the design and construction of air
pollution control equipment today is accomplished with some degree of success, air pollution
problems still exist. Environmental engineers of today and tomorrow must develop proficiency and
improved understanding of the design and selection of air pollution control equipment in order to
cope with these problems and challenges — “to get it clear.”
In this spirit (contrary to point of view of the Walrus and the Carpenter), we present this chapter.
In short, we simply feel that the present situation is not that grim. Why do we feel this way? Simply
put, we know we can do something to control environmental air pollution. Environmental engineers
who are well trained and well equipped with the proper mathematical tools and applications can
make a difference when it comes time to “clear the air” that we breathe.
The USEPA focuses (as it should) enormous amounts of time on research topics related to air
pollution control. In this chapter, we heavily excerpt from USEPA publications on the topic. Much
of the general (basic) information provided is adapted from Spellman (1999)

The Science of Air

.
The excerpted materials have been rearranged and edited to make them more concise for engineers
in training and for general readers to understand the basic concepts of air pollution control math-
ematics and processes.

L1681_book.fm Page 151 Tuesday, October 5, 2004 10:51 AM
© 2005 by CRC Press LLC

152 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK

Controlling environmental air pollution begins with understanding what this pollution is. We

define

environmental air pollution

as the contamination of atmospheric air in such a manner as to
cause real or potential harm to human health or well being, or to damage or harm the natural
surroundings without justification. Contaminants may include almost any natural or artificial com-
position of matter capable of being airborne (friable asbestos, for example). Contaminants may be
in the form of solids particles, liquid droplets, or gases, or in combinations of these forms.
Contaminants fall into two main groups: (1) those emitted directly from identifiable sources; and
(2) those produced in the air by interaction between two or more primary contaminants or by
reaction with normal atmospheric constituents, with or without photoactivation.
The Clean Air Act (CAA) established two types of National Ambient Air Quality Standards
(NAAQS).

• Primary standards are designed to establish limits to protect public health, including the health of
“sensitive” populations such as asthmatics, children, and the elderly.
• Secondary standards set limits to protect public welfare, including protection against decreased
visibility and damage to animals, crops, vegetation, and buildings.

7.1.1 Six Common Air Pollutants

USEPA (2003a) has set national air quality standards for six common pollutants (also referred to
as “criteria” pollutants) discharged from various sources:

• Ground-level ozone
• Nitrogen dioxide
•Particulate matter
• Sulfur dioxide
• Carbon monoxide

• Lead

7.1.1.1 Ground-Level Ozone

Ozone (O

3

) is a highly reactive photochemically produced gas composed of three oxygen atoms.
Although it is not usually emitted directly into the air (rather, as a secondary air pollutant), at
ground level O

3

is created by a chemical reaction between oxides of nitrogen (NO

x

) and volatile
organic compounds (VOC) in the presence of heat and sunlight. In

The Science of Air

(1999), we
characterized ozone as the Dr. Jeckel and Mr. Hyde of air pollutants. Why? Ozone has the same
chemical structure, whether it occurs miles above the Earth or at ground level, and can be “good”
or “bad,” depending on its location in the atmosphere. “Good” (Dr. Jeckel) ozone occurs naturally
in the stratosphere approximately 10 to 30 miles above the Earth’s surface and forms a layer that
protects life on Earth from the sun’s harmful rays. In the Earth’s lower atmosphere, however,
ground-level ozone is considered “bad” (Mr. Hyde).

Motor vehicle exhaust and industrial emissions, gasoline vapors, and chemical solvents are some
of the major sources of NO

x

and VOC that help to form ozone. Sunlight and hot weather cause
ground-level ozone to form in harmful concentrations in the air. As a result, ozone is known as a
summertime air pollutant. Many urban areas tend to have high levels of bad ozone, but even rural
areas are subject to increased ozone levels because wind carries ozone and the pollutants that
combine to form it hundreds of miles away from their original sources.
VOC NO Heat Sunlight Ozone
x
+++ =

L1681_book.fm Page 152 Tuesday, October 5, 2004 10:51 AM
© 2005 by CRC Press LLC

AIR POLLUTION FUNDAMENTALS 153

7.1.1.2 Nitrogen Oxides

Nitrogen oxides (NO

x

) is the generic term for a group of highly reactive gases, all of which contain
nitrogen and oxygen in varying amounts. This group includes NO; NO

2

; NO

3

; N

2

O; N

2

O

3

; N

2

O

4

;
and N

2

O

5

; however, only two are important in the study of air pollution: nitric oxide (NO) and
nitrogen dioxide (NO

2

). Many of the nitrogen oxides are colorless and odorless. However, nitrogen
dioxide (NO

2

), a common pollutant, can often be seen, along with particles in the air, as a reddish-
brown layer of air hanging over affected urban areas. Nitrogen oxides form when fuel is burned
at high temperatures, as in a combustion process. The primary sources of NO

x

are motor vehicles,
electric utilities, and other industrial, commercial, and residential sources that burn fuels.

7.1.1.3 Particulate Matter

Particulate matter (PM) is the term for particles found in the air, including dust, dirt, soot, smoke,
and liquid droplets. Particles can be suspended in the air for long periods of time. Some particles
are large or dark enough to be seen as soot or smoke. Others are so small that, individually, they
can only be detected with an electron microscope. Some particles are directly emitted into the air.
They come from a variety of sources, including cars; trucks; buses; factories; construction sites;
tilled fields; unpaved roads; stone crushing; and wood burning. Other particles may be formed in

the air from the chemical change of gases. They are indirectly formed when gases from burning
fuels react with sunlight and water vapor. These can result from fuel combustion in motor vehicles,
at power plants, and in other industrial processes.

7.1.1.4 Sulfur Dioxide (SO

2

)

Sulfur dioxide (SO

2

) belongs to the family of sulfur oxide gases (SO

x

). These gases dissolve easily
in water. Sulfur enters the atmosphere in the form of corrosive sulfur dioxide gas, a colorless gas
possessing the sharp, pungent odor of burning rubber. Also, sulfur is prevalent in raw materials,
including crude oil, coal, and ore that contains common metals like aluminum, copper, zinc, lead,
and iron. SO

2

gases are formed when fuels that contain sulfur (coal and oil, for example) are burned,
as well as when gasoline is extracted from oil or metals are extracted from ore. SO

2

dissolves in
water vapor to form acid and interacts with other gases and particles in the air to form sulfates and
other products harmful to people and their environment.
Over 65% of SO

2

released to the air, or more than 13 million tons per year, come from electric
utilities, especially those that burn coal. Other sources of SO

2

are industrial facilities that derive
their products from raw materials like metallic ore, coal, and crude oil, or that burn coal or oil to
produce process heat. Examples include petroleum refineries, and cement manufacturing and metal
processing facilities. Large ships, locomotives, and some nonroad diesel equipment currently burn
high sulfur fuel and release SO

2

emissions to the air in large quantities.
Two major environmental problems have developed in highly industrialized regions of the world
where the atmospheric sulfur dioxide concentration has been relatively high: sulfurous smog and
acid rain. Sulfurous smog is the haze that develops in the atmosphere when molecules of sulfuric
acid serve as light screeners. The second problem, acid rain, is precipitation contaminated with
dissolved acids, including sulfuric acid. Acid rain poses a threat to the environment by causing
affected lakes to become devoid of aquatic life. Sulfur dioxide produces white to straw-colored
blotches on the foliage of broad-leafed plants.

7.1.1.5 Carbon Monoxide (CO)

Carbon monoxide (CO) is a colorless, odorless, tasteless gas that is, by far, the most abundant of
the primary pollutants. Formed when carbon in fuel is not burned completely, carbon monoxide is

L1681_book.fm Page 153 Tuesday, October 5, 2004 10:51 AM
© 2005 by CRC Press LLC

154 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK

a component of motor vehicle exhaust, which contributes about 56% of all CO emissions nation-
wide. Other nonroad engines and vehicles (such as construction equipment and boats) contribute
about 22% of all CO emissions nationwide. Higher levels of CO generally occur in areas with
heavy traffic congestion; in cities, 85 to 95% of all CO emissions come from motor vehicle exhaust.
Other sources of CO emissions include industrial processes (such as metals processing and chemical
manufacturing), residential wood burning, and natural sources such as forest fires. Woodstoves, gas
stoves, cigarette smoke, and unvented gas and kerosene space heaters are sources of CO indoors.
The highest levels of CO in the outside air typically occur during the colder months of the year
when inversion conditions are more frequent. The air pollution becomes trapped near the ground
beneath a layer of warm air.

7.1.1.6 Lead

Lead is a metal found naturally in the environment as well as in manufactured products. The major
sources of lead emissions have historically been motor vehicles (primarily cars and trucks) and
industrial sources. At present, because of the phase-out of leaded gasoline, metals processing is
the major source of lead emissions to the air. The highest levels of lead in air are generally found
near lead smelters; other stationary sources are waste incinerators, utilities, and lead-acid battery
manufacturers. In high concentrations, lead can damage human health and the environment. Once
lead enters the ecosystem, it remains there permanently. The good news? Since the 1970s, stricter

emission standards have caused a dramatic reduction in lead output.

7.2 GASES

Gases are important not only because a gas can be a pollutant, but also because gases convey
particulate and gaseous pollutants. For most air pollution work, expressing pollutant concentrations
in volumetric terms is customary. For example, the concentration of a gaseous pollutant in parts
per million (ppm) is the volume of pollutant per million parts of the air mixture. That is,
(7.1)
Note that calculations for gas concentrations are based on the gas laws:

• The volume of gas under constant temperature is inversely proportional to the pressure.
• The volume of a gas under constant pressure is directly proportional to the Kelvin temperature.
The Kelvin temperature scale is based on absolute zero (0°C = 273 K).
• The pressure of a gas of a constant volume is directly proportional to the Kelvin temperature.

Thus, when measuring contaminant concentrations, we must know the atmospheric temperature
and pressure under which the samples were taken. At standard temperature and pressure (STP),
1 g-mol of an ideal gas occupies 22.4 L. The STP is 0°C and 760 mm Hg. If the temperature is
increased to 25°C (room temperature) and the pressure remains the same, 1 g-mol of gas occupies
24.45 L.
Sometimes converting milligrams per cubic meter (mg/m

3

) — a weight-per-volume-ratio —
into a volume-per-unit weight ratio is necessary. If 1 g-mol of an ideal gas at 25°C occupies 24.45 L
is an understood fact, the following relationships can be calculated:
ppm
Parts of contamination

million parts of
=
air

L1681_book.fm Page 154 Tuesday, October 5, 2004 10:51 AM
© 2005 by CRC Press LLC

AIR POLLUTION FUNDAMENTALS 155

(7.2)
(7.3)

7.2.1 The Gas Laws

As mentioned, gases can be pollutants as well as the conveyors of pollutants. Air (which is mainly
nitrogen) is usually the main gas stream. To understand the gas laws, it is imperative to have an
understanding of certain terms.

•

Ideal gas

— an imaginary model of a gas that has a few very important properties:
• The gases are assumed to be infinitely small.
• The particles move randomly in straight lines until they collide with something (another gas
molecule or the side of the container in which they are held).
• The gas particles do not interact with each other (they do not attract or repel one another like
real molecules do).
• The energy of the particles is directly proportional to the temperature in Kelvins (in other
words, the higher the temperature is, the more energy the particles have).

These assumptions are made because they make equations a lot simpler than they would be other-
wise, and because these assumptions cause negligible deviation from the ways in which actual gases
behave.
•

Kelvin

— a temperature scale in which the degrees are the same size as degrees Celsius but where
“0” is defined as “absolute zero,” the temperature at which molecules are at their lowest energy.
To convert from degrees Celsius to Kelvins (not “degrees Kelvins”), add 273.
•

Pressure

— a measure of the amount of force that a gas exerts on the container into which it is
put. Units of pressure include atmospheres (1 atm is the average atmospheric pressure at sea level);
torrey (equal to 1/760 of an atmosphere); millimeters of mercury (1 mm Hg is the same as 1 torr,
or 1/760 atm); and kilopascals (101,325 kPa in 1 atm).
•

Standard temperature and pressure

— a set of conditions defined as 273 K and 1 atm.
•

Standard conditions (SC)

— SC is more commonly used than STP and represents typical room
conditions of 20°C (70°F) and 1 atm. SC units of volume are commonly given as normal cubic
meters or standard cubic feet (scf).

•

Temperature

— a measure of how much energy the particles in a gas have and defined as that
property of a body that determines the flow of heat. Heat will flow from a warm body to a cold
body. Several different temperature scales are in general use that depend on the freezing and boiling
points of water as boundary markers for the scale. In a conventional laboratory thermometer, the
boundary points are conveniently selected to relate to the known properties of water.
• On the Celsius scale, the freezing point of water is assigned a value of 0 and the boiling point
a value of 100; the distance between these two points is divided into 100 equal increments,
with each increment labeled in Celsius degree (Table 7.1).
• On the Kelvin scale, the freezing point of water is assigned a value of 273.15 K and the boiling
point a value of 373.15; the distance between these two points is divided into 100 equal
increments, and each increment is labeled as a Kelvin (Table 7.1).
• On the Fahrenheit scale, the freezing point of water is assigned a value of 32 and the boiling
point a value of 212; the distance between these two points is divided into 180 equal increments
and each increment is labeled as a Fahrenheit degree (Table 7.1).
• Rankine is a temperature scale with an absolute zero below which temperatures do not exist
and using a degree of the same size as that used by the Fahrenheit temperature scale. Absolute
zero, or 0° R, is the temperature at which molecular energy is at minimum; it corresponds to
ppm
24.45
molecular wt
mg/m
3
=
mg/m
molecular wt
24.45

ppm
3
=

L1681_book.fm Page 155 Tuesday, October 5, 2004 10:51 AM
© 2005 by CRC Press LLC

156 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK

a temperature of –459.67°F. Because the Rankine degree is the same size as the Fahrenheit
degree, the freezing point of water (32°F) and the boiling point of water (212°F) correspond
to 491.67°R and 671.67°R, respectively (Table 7.1).
We must make a distinction between the actual temperature (°C and °F) and a temperature incre-
ment (Fahrenheit degree and Celsius degree). This distinction enables the derivation of a relation-
ship between the two temperature scales. For example, a temperature of 100°C is the same as a
temperature of 212°F. A temperature difference of 100 degrees Celsius is equal to a temperature dif-
ference of 180 degrees Fahrenheit.
•

Volume

— the amount of space that an object occupies. The unit of volume can be cubic centimeters
(abbreviated “cc” or “cm

3

”); milliliters (abbreviate “mL”; 1 mL is the same as 1 cm

3

); liters
(abbreviated as “L” and equal to 1000 mL); or cubic meters (abbreviated “m

3

” – a cubic meter
contains 1 million cm

3

).

7.2.1.1 Boyle’s Law

Circa 1662, Robert Boyle stated what has come to be known as Boyle’s law — the volume of any
definite quantity of gas at constant temperature varies inversely as the pressure on the gas:
(7.4)
where

P

1

= the initial pressure of the gas

V

1

= the initial volume of the gas

P

2

= the final pressure of the gas

V

2

= the final volume of the gas
This way, if we know the initial pressure and volume of a gas and know what the final pressure
will be, we can predict what the volume will be after we add pressure to it.

Table 7.1

Comparison of Temperature Scales
Temperature scale
Celsius
(°C)
Kelvin
(K)
Fahrenheit
(°F)
Rankine
(°R)

Boiling point of water +100 +373.15 +212 +671.67
————

————
————

↑

—

↑

—
100 equal divisions — 180 equal divisions —

↓

—

↓

—
————
————
Freezing point of water 0 273.15 +32 +491.67
————
————
————
————
————
Absolute zero –273.15 0 –459.67 0

Note

: Units of temperature important to environmental engineers include degree Celsius and
Kelvins (equal to 273 plus the degree Celsius). The degree symbol (

°

) is not used for
the Kelvin temperature scale.
PV PV
11 2 2
=

L1681_book.fm Page 156 Tuesday, October 5, 2004 10:51 AM
© 2005 by CRC Press LLC

AIR POLLUTION FUNDAMENTALS 157

Example 7.1

Problem

:
If we have 4 L of methane gas at a pressure of 1.0 atm, what will be the pressure of the gas if
we compress it to a volume of 2.5 L?

Solution

:

7.2.1.2 Charles’s Law

Charles observed that hydrogen (H

2

), carbon dioxide (CO

2

), oxygen (O

2

), and air expanded by an
equal amount when heated from 0 to 80°C at a constant pressure:
(7.5)
In this equation, the subscript “1” indicates the initial volume and temperature and the subscript
“2” indicates the volume and temperature after the change. Temperature, incidentally, needs to be
given in Kelvins and not in Celsius because if we have a temperature below 0°C, the calculation
works out so that the volume of the gas is negative — a physical impossibility.

Example 7.2

Problem

:
If we have 2 L of methane gas at a temperature of 40°C, what will be the volume if we heat
the gas to 80°?

Solution

:
The first thing to do is to convert the temperature to Kelvins (by adding 273) because Celsius
cannot be used in this equation. To do this, we get that the initial temperature is 40 + 273 = 313
K and the final temperature is 80 + 273 = 353 K. We are now ready to insert these numbers into
the equation:

7.2.1.3 Gay–Lussac’s Law

Gay–Lussac (1802) found that all gases increase in volume for each one degree Celsius rise in
temperature and that this increase is equal to approximately 1/273.15 of the volume of the gas at 0°C:
(7.6)
(1.0 atm)(4 L) ( atm)(2.5 L)= x
x 1.6 atm=
V/T V/T
11 2 2
=
2L/313 K L/353 K= x
x 2.26 L=
P/T P/T
11 2 2
=

L1681_book.fm Page 157 Tuesday, October 5, 2004 10:51 AM
© 2005 by CRC Press LLC

158 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK

If we increase the temperature of a container with fixed volume, this gas law explains how the
pressure inside the container will increase.

7.2.1.4 The Combined Gas Law

This gas law



combines the parameters of the preceding equations, forming
(7.7)
The advantage of the combined gas law equation is that, whenever we are changing the conditions
of pressure, volume, and/or temperature for a gas, we can simply insert the numbers into this
equation.

Example 7.3

Problem

:
If we have 2 L of a gas at a temperature of 420 K and decrease the temperature to 350 K, what
will be the new volume of the gas?

Solution

:
To solve this problem, we use the combined gas law. Because pressure was never mentioned
in this problem, we ignore it. As a result, the equation will be:
which is the same as Charles’s law. To solve, the initial volume is 2 L; the initial temperature is
420 K; and the final temperature is 350 K. The final volume, after solving the equation, should be
1.67 L.

7.2.1.5 The Ideal Gas Law

The ideal gas law combines Boyle’s and Charles’s laws because air cannot be compressed without
its temperature changing. This gas law is an equation of state, which means that we use the basic
properties of the gas to find out more about it without the need to change it in any way. Because
it is an equation of state, it allows us not only to find out the pressures, volumes, and temperatures,
but also to find out how much gas is present in the first place. The ideal gas law is expressed by
the equation:
(7.8)
where:

P

= the pressure of the gas (in atmospheres or kilopascals)

V

= the volume (in liters)

n

= the number of moles

R

= the ideal gas constant

T

= the temperature (in Kelvins)

The two common values for the ideal gas constant include 0.08206 L

×

atm/mol

×

K, and 8.314

×

kPa/mol

×

K. The question is, which one do we use?



The value of

R

used depends on the pressure
(P V )/T (P V )/T
11 1 22 2
=
V/T V/T
11 2 2

=
PV nRT=

L1681_book.fm Page 158 Tuesday, October 5, 2004 10:51 AM
© 2005 by CRC Press LLC

AIR POLLUTION FUNDAMENTALS 159

given in the problem. If the pressure is given in atmospheres, use the 0.08206 value because the
unit at the end of it contains “atmospheres.” If the pressure is given in kilopascals, use the second
value because the unit at the end contains “kPa.”
The ideal gas law allows us to figure out how many grams and moles of the gas are present in
a sample. After all, “moles” is the “

n

” term in the equation, and we already know how to convert
grams to moles.

Example 7.4

Problem

:
Given 4 L of a gas at a pressure of 3.4 atm and a temperature of 300 K, how many moles of
gas are present?

Solution

:

First, figure out what value of the ideal gas constant should be used. Because pressure is given
in atmospheres, use the first one, 0.206 L

×

atm/mol

×

K. After inserting the given terms for
pressure, volume, and temperature, the equation becomes:

n

= 0.55 mol

7.2.1.6 Composition of Air

The air mixture that surrounds us and that we breathe is a dynamic mixture of many components
(see Table 7.2) in several respects. The moisture content of water vapor, the temperature, the
pressure, and the trace gas constituents can and do vary over time and in space. The bulk of the
air in the biosphere is composed of nitrogen and oxygen with various other trace gases mixed in
(see Table 7.2).

Table 7.2

Approximate Composition of Dry Air (by Volume)
Component Symbol
Concentration
(%)

Concentration
(ppm)

Nitrogen N

2

78.084 780,840
Oxygen O

2

20.9476 209,476
Argon Ar 0.934 9,340
Carbon dioxide CO

2

0.0314 314
Neon Ne 0.001818 18.18
Helium He 0.000524 5.24
Methane CH

4

0.0002 2
Sulfur dioxide SO

2

0–0.0001 0–1
Hydrogen H

2

0.00005 0.5
Krypton Kr 0.0002 2
Xenon Xe 0.0002 2
Ozone O

3

0.0002 2

Note

: ASHRAE also reports that the molecular weight of dry air is
28.9645 g/mol based on the carbon 12 scale.

Source

:

ASHRAE Handbook of Fundamentals

, 1993, Atlanta, Georgia:
The American Society for Heating Refrigeration and Air Conditioning
Engineers, p. 6.1 (based on the atomic weight of carbon of 12.0000).
(3.4 atm)(4 L) n (0.08206 L atm/mol K=××))(300 K)

L1681_book.fm Page 159 Tuesday, October 5, 2004 10:51 AM
© 2005 by CRC Press LLC

160 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK

7.3 PARTICULATE MATTER

Typically, in actual practice, the terms

particulate

(or

particle

) and

particulate matter

are used
interchangeably. According to 40 CFR 51.100-90, particulate matter is defined as any airborne
finely divided solid or liquid material with an aerodynamic diameter smaller than 100

µ

m (micro
= 10

–6

). Along with gases and water vapor, Earth’s atmosphere is literally a boundless arena for
particulate matter of many sizes and types. Atmospheric particulates vary in size from 0.0001 to
10,000

µ

m. Particulate size and shape have direct bearing on visibility. For example, a spherical
particle in the 0.6-µm range can effectively scatter light in all directions, thus reducing visibility.
The types of airborne particulates in the atmosphere vary widely, with the largest sizes derived
from volcanoes; tornadoes; waterspouts; burning embers from forest fires; seed parachutes; spider
webs; pollen; soil particles; and living microbes. The smaller particles (the ones that scatter light)
include fragments of rock; salt and spray; smoke; and particles from forested areas. The largest
portion of airborne particulates is invisible. These particulates are formed by the condensation of
vapors; chemical reactions; photochemical effects produced by ultraviolet radiation; and ionizing
forces that come from radioactivity, cosmic rays, and thunderstorms. Airborne particulate matter
is produced by mechanical weathering, breakage, and solution, or by the vapor–condensation–crys-
tallization process (typical of particulates from the furnace of a coal-burning power plant).
We know very well that anything that goes up must eventually come down. This is typical of
airborne particulates also. Fallout of particulate matter depends, obviously, mostly on size; less
obvious are shape; density; weight; airflow; and injection altitude. The residence time of particulate
matter also is dependent on the atmosphere’s cleanup mechanisms (formation of clouds and
precipitation) that work to remove them from their airborne suspended state. Some large particulates
may only be airborne for a matter of seconds or minutes. Intermediate sizes may be able to stay
afloat for hours or days. Finer particulates may stay airborne for a much longer duration: days,
weeks, months, and even years.
Particles play an important role in atmospheric phenomena. For example, particulates provide
the nuclei upon which ice particles and cloud condensation are formed, and they are essential for
condensation to take place. The most important role airborne particulates play is in cloud formation.
Simply put, without airborne particulate matter, no clouds would exist and, without clouds, life
would be much more difficult; the cloudbursts that eventually erupted would cause an extreme

devastation difficult to imagine or contemplate.
7.4 POLLUTION EMISSION MEASUREMENT PARAMETERS
Because of the gaseous and particulate emissions combustion sources can produce, they constitute
a significant air quality control problem. Combustion processes can add carbon dioxide, water
vapor, and heat to the atmosphere and produce a residue that must be disposed of in concentrated
form. In the past, these environmental costs were tolerated in the interest of producing useful energy.
However, it is becoming increasingly clear that the presence of these emissions in the atmosphere
can result indirectly in a greenhouse effect and exacerbate the problem of acid rain.
Because of the environmental impact of combustion emissions, the USEPA has developed
emission standards for the combustion or incineration industry. These standards usually establish
the maximum allowable limit, based on volume or mass flows at specified conditions of temperature
and pressure, for the discharge of specific pollutants. Emissions are measured in terms of the
concentration of pollutant per volume or mass of stack (flue) gas, the pollutant mass rates, or a
rate applicable to a given process. Standards fall into the following six categories:
L1681_book.fm Page 160 Tuesday, October 5, 2004 10:51 AM
© 2005 by CRC Press LLC
AIR POLLUTION FUNDAMENTALS 161
• Pollutant mass rate standards — based on the fixed rate of emissions (the mass of pollutant emitted
per unit time, pounds per hour or kilograms per hour)
• Process rate standards — establish the allowable emissions in terms of the input energy or the
raw material feed of a process
• Concentration standards — limit the mass (weight) or volume of the pollutants in the gas leaving
the stack
• Ambient concentration standards — pollutants, in micrograms per cubic meter, under this limit
include toxic metals, organics, and hydrogen chloride
• Reduction standards — limits expressed as a percent reduction of the pollutants
• Opacity standards — the limit on the degree to which the stack emissions are visible and block
the visibility of objects in the background. Stack emissions of 100% opacity totally block the view
of background objects and indicate high pollutant levels. Opacity of 0% provides a clear view of
the background and indicates no detectable particulate matter emissions.

7.5 STANDARD CORRECTIONS
Because combustion systems always produce stack gas of a higher temperature and pressure than
those of the standards and because actual levels of pollutants emitted can be made to appear smaller
if excess air is added to the stream, corrections for the differences must be made. In increases or
decreases in gas temperature and pressure and the subsequent effect on gas volume, the EPA
recommends answering these questions (making corrections) using the ideal gas law.
For excess air correction calculations, various federal EPA and state regulations give procedures
for calculations of excess air based on dry gas (Orsat type) analyses. Based on USEPA’s (1980)
Method 3B — gas analysis, the percent excess air can be determined by any of the following three
equivalent relationships.
(7.9)
(7.10)
(7.11)
Theoretical air is the amount required to convert all combustible species (mainly carbon,
hydrogen, and sulfur) stoichiometrically to complete normal products of combustion (CO
2
, H
2
O,
and SO
2
). These relationships are stated as mole ratios of air, which equal volume ratios.
In its Method 3B — gas analysis for the determination of emission rate correction factor or
excess air, the USEPA (2003b) provides the following explanation for determining percent excess
air.
USEPA Example
Percent excess air — determine the percentage of the gas that is N
2
by subtracting the sum of the
percent CO

2
, percent CO, and percent O
2
from 100%. Calculate the percent excess by substituting
the appropriate values of percent O
2
, CO, and N
2
into Equation 7.12.
%Excess Air
Total Air Theoretical Air
Th
=
eeoretical Air
()100
%Excess Air
Excess Air
Theoretical Air
= (1000)
%Excess Air
Excess Air
Total Air Excess
=
AAir
()100
L1681_book.fm Page 161 Tuesday, October 5, 2004 10:51 AM
© 2005 by CRC Press LLC
162 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK
(7.12)
Equation 7.12 assumes that ambient air is used as the source of O

2
and that the fuel does not
contain appreciable amounts of N
2
(as do coke oven or blast furnace gases). For cases in which
appreciable amounts of N
2
are present (coal, oil, and natural gas do not contain appreciable amounts
of N
2
) or when oxygen enrichment is used, alternative methods are required.
REFERENCES
ASHRAE Handbook of Fundamentals (1993). Atlanta: The American Society for Heating Refrigeration and
Air Conditioning Engineers.
CFR 40 51.100-90. Definition, Title 40 Parts 51.100 of Code of Federal Regulations published 1990.
Spellman, F.R. (1999). The Science of Air. Boca Raton, FL: CRC Press.
USEPA (2003a), Six common air pollutants. Accessed at />USEPA (2003b), Method 3B — gas analysis for the determination of emissions rate correction factor or excess
air. Accessed at />USEPA 80/02, Combustion evaluation — Student manual, Course 427, EPA Air Pollution Training Institute
(APTI), EPA450-2-80-063, February 1980.
%EA
%O 0.5 %CO
0.264 %N (%O 0.5
2
–
2
–
2
–
=
%%CO)

()100
L1681_book.fm Page 162 Tuesday, October 5, 2004 10:51 AM
© 2005 by CRC Press LLC