ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK - CHAPTER 7 docx

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 vol

Trang 1

PART III

Math Concepts: Air Pollution Control

L1681_book.fm Page 149 Tuesday, October 5, 2004 10:51 AM

Trang 2

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

Trang 3

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

Ozone (O3) 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 O3 is created by a chemical reaction between oxides of nitrogen (NOx) 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 NOx 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 + NOx + Heat + Sunlight = Ozone

Trang 4

AIR POLLUTION FUNDAMENTALS 153

7.1.1.2 Nitrogen Oxides

Nitrogen oxides (NOx) 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; NO2; NO3; N2O; N2O3; N2O4; and N2O5; however, only two are important in the study of air pollution: nitric oxide (NO) and nitrogen dioxide (NO2) Many of the nitrogen oxides are colorless and odorless However, nitrogen dioxide (NO2), 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 NOx 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

Sulfur dioxide (SO2) belongs to the family of sulfur oxide gases (SOx) 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 SO2 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 SO2 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 SO2 released to the air, or more than 13 million tons per year, come from electric utilities, especially those that burn coal Other sources of SO2 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 SO2 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

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

Trang 5

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

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

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/m3) — 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

Trang 6

(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

molecular wtmg/m

3

=

mg/m molecular wt

24.45 ppm

3=

Trang 7

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 ).

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

P1 = the initial pressure of the gas

V1 = the initial volume of the gas

P2 = the ﬁnal pressure of the gas

V2 = 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)

100 equal divisions — 180 equal divisions —

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.

P V1 1 = P V2 2

Trang 8

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:

Charles observed that hydrogen (H2), carbon dioxide (CO2), oxygen (O2), 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:

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) = x( atm)(2.5 L)

x = 1.6 atm

V /T1 1 = V /T2 2

2 L/313 K = xL/353 K

x = 2.26 L

P /T1 1 = P /T2 2

Trang 9

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

This gas lawcombines 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

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 )/T1 1 1 = (P V )/T2 2 2

V /T1 1 = V /T2 2

PV = nRT

Trang 10

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

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)

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 × ))(300 K)K

Định dạng
Số trang	13
Dung lượng	635,25 KB