ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK - CHAPTER 9 docx

Calculate the particle terminalvelocity assume the particles are spherical and determine how far each will fall in 30 sec.Given: Air temperature and pressure = 238°F, 1 atm Specific gravi

CHAPTER 9 Particulate Emission Control

Fresh air is good if you do not take too much of it; most of the achievements and pleasures of life are in bad air.

Oliver Wendell Holmes

Particle or particulate matter is defined as tiny particles or liquid droplets suspended in the air; theycan contain a variety of chemical components Larger particles are visible as smoke or dust andsettle out relatively rapidly The tiniest particles can be suspended in the air for long periods oftime and are the most harmful to human health because they can penetrate deep into the lungs.Some particles are directly emitted into the air from pollution sources

Constituting a major class of air pollutants, particulates have a variety of shapes and sizes; aseither liquid droplet or dry dust, they have a wide range of physical and chemical characteristics.Dry particulates are emitted from a variety of different sources in industry, mining, constructionactivities, and incinerators, as well as from internal combustion engines — from cars, trucks, buses,factories, construction sites, tilled fields, unpaved roads, stone crushing, and wood burning Dryparticulates also come from natural sources such as volcanoes, forest fires, pollen, and windstorms.Other particles are formed in the atmosphere by chemical reactions

When a flowing fluid (engineering and science applications consider liquid and gaseous states

as fluid) approaches a stationary object (a metal plate, fabric thread, or large water droplet, forexample), the fluid flow will diverge around that object Particles in the fluid (because of inertia)will not follow stream flow exactly, but tend to continue in their original directions If the particleshave enough inertia and are located close enough to the stationary object, they collide with the

9.1.1 Interaction of Particles with Gas

To understand the interaction of particles with the surrounding gas, knowledge of certain aspects

of the kinetic theory of gases is necessary This kinetic theory explains temperature, pressure, meanfree path, viscosity, and diffusion in the motion of gas molecules (Hinds, 1986) The theory assumesgases — along with molecules as rigid spheres that travel in straight lines — contain a large number

of molecules that are small enough so that the relevant distances between them are discontinuous.Air molecules travel at an average of 1519 ft/sec (463 m/sec) at standard conditions Speeddecreases with increased molecule weight As the square root of absolute temperature increases,molecular velocity increases Thus, temperature is an indication of the kinetic energy of gas

208 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK

molecules When molecular impact on a surface occurs, pressure develops and is directly related

to concentration Gas viscosity represents the transfer of momentum by randomly moving moleculesfrom a faster moving layer of gas to an adjacent slower moving layer of gas Viscosity of a gas isindependent of pressure but will increase as temperature increases Finally, diffusion is the transfer

of molecular mass without any fluid flow (Hinds, 1986) Diffusion transfer of gas molecules isfrom a higher to a lower concentration Movement of gas molecules by diffusion is directlyproportional to the concentration gradient, inversely proportional to concentration, and proportional

to the square root of absolute temperature

The mean free path, kinetic theory’s most critical quantity,is the average distance a moleculetravels in a gas between collisions with other molecules The mean free path increases withincreasing temperature and decreases with increasing pressure (Hinds, 1986)

The Reynolds number characterizes gas flow, a dimensionless index that describes the flowregime The Reynolds number for gas is determined by the following equation:

(9.1)

where

Re = Reynolds number

The Reynolds number helps to determine the flow regime, the application of certain equations,and geometric similarity (Baron and Willeke, 1993) Flow is laminar at low Reynolds numbers andviscous forces predominate Inertial forces dominate the flow at high Reynolds numbers, whenmixing causes the streamlines to disappear

9.1.2 Particulate Collection

Particles are collected by gravity, centrifugal force, and electrostatic force, as well as by impaction,interception, and diffusion Impaction occurs when the center of mass of a particle diverging fromthe fluid strikes a stationary object Interception occurs when the particle’s center of mass closelymisses the object but, because of its size, the particle strikes the object Diffusion occurs whensmall particulates happen to “diffuse” toward the object while passing near it Particles that strike

Figure 9.1 Particle collection of a stationary object (Adapted from USEPA-84/03, p 1-5.)

η

PARTICULATE EMISSION CONTROL 209

the object by any of these means are collected if short-range forces (chemical, electrostatic, and

Different classes of particulate control equipment include gravity settlers, cyclones, electrostaticprecipitators, wet (Venturi) scrubbers, and baghouses (fabric filters) In the following sections wediscuss many of the calculations used in particulate emission control operations Many of thecalculations presented are excerpted from USEPA-81/10

As we have said, particulate air pollution consists of solid and/or liquid matter in air or gas Airborneparticles come in a range of sizes From near molecular size, the size of particulate matter ranges

concentrations of particulate matter are by mass

Liquid particulate matter and particulates formed from liquids (very small particles) are likely

to be spherical in shape To express the size of a nonspherical (irregular) particle as a diameter,several relationships are important These include:

would have the same settling velocity as the particle or aerosol in question Note that becauseUSEPA is interested in how deeply a particle penetrates into the lung, the agency is more interested

in nominal aerodynamic diameter than in the other methods of assessing size of nonsphericalparticles Nevertheless, a particle’s nominal aerodynamic diameter is generally similar to its con-ventional, nominal physical diameter

9.2.2 Equivalent Diameter

as that of the nonspherical particle and is given by

(9.2)

9.2.3 Sedimentation Diameter

settling velocity and density as the particle In density particles, it is called the reduced sedimentationdiameter, making it the same as aerodynamic diameter The dynamic shape factor accounts for anonspherical particle settling more slowly than a sphere of the same volume

210 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK

9.2.4 Cut Diameter

(9.3)

9.2.5 Dynamic Shape Factor

sedimentation diameters:

(9.4)

The d e equals d sfor spherical particles, so χ for spheres is 1.0

Air pollution control devices collect solid or liquid particles via the movement of a particle in thegas (fluid) stream For a particle to be captured, the particle must be subjected to external forceslarge enough to separate it from the gas stream According to USEPA-81/10, p 3-1, forces acting

on a particle include three major forces as well as other forces:

• Gravitational force

• Buoyant force

• Drag force

• Other forces (magnetic, inertial, electrostatic, and thermal force, for example)

The consequence of acting forces on a particle results in the settling velocity — the speed atwhich a particle settles The settling velocity (also known as the terminal velocity) is a constantvalue of velocity reached when all forces (gravity, drag, buoyancy, etc.) acting on a body arebalanced — that is, when the sum of all the forces is equal to zero (no acceleration) To solve for

an unknown particle settling velocity, we must determine the flow regime of particle motion Oncethe flow regime has been determined, we can calculate the settling velocity of a particle

The flow regime can be calculated using the following equation (USEPA-81/10, p 3-10):

(9.5)

where

K = d (gp p /µ )p p a 2 0.33

PARTICULATE EMISSION CONTROL 211

USEPA-81/10, p 3-10, lists the K values corresponding to different flow regimes as:

• Laminar regime (also known as Stokes’ law range): K < 3.3

• Transition regime (also known as intermediate law range): 3.3 < K, 43.6

• Turbulent regime (also known as Newton’s law range): K > 43.6

fluid-particle dynamic laws that apply

• For a laminar regime (Stokes’ law range), the terminal velocity is

When particles approach sizes comparable with the mean free path of fluid molecules (also

particles can fall between the molecules at a faster rate than that predicted by aerodynamic theory.Cunningham’s correction factor, which includes thermal and momentum accommodation factors

values, is introduced into Stoke’s law to allow for this slip rate (Hesketh, 1991; USEPA-84/09, p 58):

212 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK

Solution:

Step 1 Use Equation 9.5 to calculate the K parameter to determine the proper flow regime:

The result demonstrates that the flow regime is laminar.

Step 2 Use Equation 9.9 to determine the settling velocity:

Example 9.2

Problem:

Three differently sized fly ash particles settle through the air Calculate the particle terminalvelocity (assume the particles are spherical) and determine how far each will fall in 30 sec.Given:

Air temperature and pressure = 238°F, 1 atm

Specific gravity of fly ash = 2.31

Because the Cunningham correction factor is usually applied to particles equal to or smaller than 1 µ m, check how it affects the terminal settling velocity for the 0.4- µ m particle.

PARTICULATE EMISSION CONTROL 213

(USEPA-84/09, p 167)

Determine the flow regime (K):

For d p = 0.4 µ m:

where 1 ft = 25,400(12) µ m (USEPA-84/09, p 183) For d p = 40 µ m:

For d p = 400 µ m:

Step 2 Select the appropriate law, determined by the numerical value of K:

K < 3.3; Stokes’ law range 3.3 < K < 43.6; intermediate law range 43.6 < K < 2360; Newton’s law range For d p = 0.4 µ m, the flow regime is laminar (USEPA-81/10, p 3-10) For d p = 40 µ m, the flow regime is also laminar

For d p = 400 µ m, the flow regime is the transition regime For d p = 0.4 µ m:

214 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK

For d p = 400 µ m (use transition regime equation):

Step 4 Calculate distance.

For d p = 40 µ m, distance = (time)(velocity):

For d p = 400 µm, distance = (time)(velocity):

For d p = 0.4 µm, without Cunningham correction factor, distance = (time)(velocity):

For d p = 0.4 µm with Cunningham correction factor, the velocity term must be corrected For our

purposes, assume particle diameter = 0.5 µm and temperature = 212°F to find the C f value Thus,

C f is approximately equal to 1.446

Example 9.3

Problem:

Determine the minimum distance downstream from a cement dust-emitting source that will be

free of cement deposit The source is equipped with a cyclone (USEPA-84/09, p 59)

Given:

Specific gravity of the cement dust = 1.96

Wind speed = 3.0 mi/h

The cyclone is located 150 ft above ground level Assume ambient conditions are at 60°F and

1 atm Disregard meteorological aspects

Calculate the air density (p) Use modified ideal gas equation, PV = nR u T = (m/M)R u T

Determine the flow regime (K):

For d p = 2.5 µm:

where 1 ft = 25,400(12) µm = 304,800 µm (USEPA-84/09, p 183)

Step 3 Determine which fluid-particle dynamic law applies for the preceding value of K Compare the K value of 0.104 with the following range:

K < 3.3; Stokes’ law range

3.3 ≤ K < 43.6; intermediate law range 43.6 < K < 2360; Newton’s law range

The flow is in the Stokes’ law range; thus it is laminar.

Step 4 Calculate the terminal settling velocity in feet per second For Stokes’ law range, the velocity is

Step 5 Calculate the time for settling:

Step 6 Calculate the horizontal distance traveled:

Different classes of particulate control equipment include gravity settlers; cyclones; electrostatic

the following section, we discuss calculations used for each of the major types of particulate controlequipment

9.4.1 Gravity Settlers

Gravity settlers have long been used by industry for removing solid and liquid waste materials

actually nothing more than a large chamber in which the horizontal gas velocity is slowed, allowingparticles to settle out by gravity Gravity settlers have the advantage of having low initial cost andare relatively inexpensive to operate because not much can go wrong Although simple in design,

Figure 9.2 Gravitational settling chamber (From USEPA, Control Techniques for Gases and Particulates, 1971.)

gravity settlers require a large space for installation and have relatively low efficiency, especially

9.4.2 Gravity Settling Chamber Theoretical Collection Efficiency

The theoretical collection efficiency of the gravity-settling chamber (USEPA-81/10, p 5-4) is given

by the expression:

(9.10)

where

v y = vertical settling velocity

L = chamber length

H = chamber height (greatest distance a particle must fall to be collected)

As mentioned, the settling velocity can be calculated from Stokes’ law As a rule of thumb, Stokes’

(9.11)

where

g = acceleration due to gravity, 9.8 m/sec2 (32.1 ft/sec2)

Figure 9.3 Baffled gravitational settling chamber (From USEPA, Control Techniques for Gases and

Particu-lates, 1971.)

η (v L)(v H)= y x

vt=[g(d ) (pp 2 p−p )a µ)

18]/(

µ = gas viscosity, pascal-seconds (pound-feet-second)

p a = N/m2

N = kilogram-meters per sec2

Equation 9.11 can be rearranged to determine the minimum particle size that can be collected

(9.12)

(9.13)where

(9.15)

Howard settling chamber

Equation 9.15 can be written as:

(9.16)and the overall efficiency can be calculated using

(9.17)

where

When flow is turbulent, Equation 9.18 is used

In using Equation 9.10 through Equation 9.16, note that Stokes’ law does not work for particlesgreater than 100 µm

9.4.3 Minimum Particle Size

Most gravity settlers are precleaners that remove the relatively large particles (>60 µm) before thegas stream enters a more efficient particulate control device such as a cyclone, baghouse, electro-static precipitator (ESP), or scrubber

Example 9.4

Problem:

A hydrochloric acid mist in air at 25°C is collected in a gravity settler Calculate the smallestmist droplet (spherical in shape) collected by the settler Stokes’ law applies; assume the acidconcentration is uniform through the inlet cross-section of the unit (USEPA-84/09, p 61)

Given:

Dimensions of gravity settler = 30 ft wide, 20 ft high, 50 ft long

Specific gravity of acid = 1.6

Solution:

Step 1 Calculate the density of the acid mist using the specific gravity given:

Step 2 Calculate the minimum particle diameter in feet and microns, assuming that Stokes’ law applies For Stokes’ law range:

Example 9.5

Problem:

A settling chamber that uses a traveling grate stoker is installed in a small heat plant Determinethe overall collection efficiency of the settling chamber, given the operating conditions, chamberdimensions, and particle size distribution data (USEPA-84/09, p 62)

Given:

Chamber width = 10.8 ft

Chamber height = 2.46 ft

Chamber length = 15.0 ft

Volumetric flow rate of contaminated air stream = 70.6 scfs

Flue gas temperature = 446°F

Flue gas pressure = 1 atm

Particle concentration = 0.23 gr/scf

Particle specific gravity = 2.65

Standard conditions = 32°F, 1 atm

Particle size distribution data of the inlet dust from the traveling grate stoker are shown in Table9.1 Assume that the actual terminal settling velocity is one-half of the Stokes’ law velocity

Solution:

Step 1 Plot the size efficiency curve for the settling chamber The size efficiency curve is needed to calculate the outlet concentration for each particle size (range) These outlet concentrations are then used to calculate the overall collection efficiency of the settling chamber The collection efficiency for a settling chamber can be expressed in terms of the terminal velocity, volumetric flow rate of contaminated stream, and chamber dimensions:

where

η = fractional collection efficiency

v = terminal settling velocity

B = chamber width

L = chamber length

Q = volumetric flow rate of the stream

Table 9.1 Particle Size Distribution Data Particle size

range, µm

Average particle diameter, µm

Step 2 Express the collection efficiency in terms of the particle diameter dp Replace the terminal settling velocity in the preceding equation with Stokes’ law Because the actual terminal settling velocity is assumed to be one half of the Stokes’ law velocity (according to the given problem statement), the velocity equation becomes:

Determine the viscosity of the air in pounds per foot-second:

Determine the particle density in pounds per cubic foot:

Determine the actual flow rate in actual cubic feet per second To calculate the collection ciency of the system at the operating conditions, the standard volumetric flow rate of contami- nated air of 70.6 scfs is converted to actual volumetric flow of 130 acfs:

effi-Express the collection efficiency in terms of d p , with d p in feet Also express the collection

effi-ciency in terms of d p , with d p in microns.

Use the following equation; substitute values for p p , g, B, L, µ, and Q in consistent units Use the conversion factor for feet to microns To convert d p from square feet to square microns, d p is di- vided by (304,800) 2

Table 9.2 provides the collection efficiency for each particle size The size efficiency curve for the settling chamber is shown in Figure 9.4; read off the collection efficiency of each particle size from this figure.

Calculate the overall collection efficiency ( Table 9.3 ).

Figure 9.4 Size efficiency curve for settling chamber (Adapted from USEPA-84/09, 136.)

Table 9.2 Collection Efficiency

for Each Particle Size

60 50

40 30 20 10 0

9.4.4 Cyclones

Cyclones — the most common dust removal devices used within industry (Strauss, 1975) — removeparticles by causing the entire gas stream to flow in a spiral pattern inside a tube They are the

the larger particles move outward and collide with the wall of the tube The particles slide downthe wall and fall to the bottom of the cone, where they are removed The cleaned gas flows out the

Cyclones have low construction costs and relatively small space requirements for installation;they are much more efficient in particulate removal than settling chambers However, note that the

size, and they do not handle sticky materials well The most serious problems encountered withcyclones are with airflow equalization and with their tendency to plug (Spellman, 1999) They areoften installed as precleaners before more efficient devices such as electrostatic precipitators andbaghouses (USEPA-81/10, p 6-1) are used Cyclones have been used successfully at feed and grainmills; cement plants; fertilizer plants; petroleum refineries; and other applications involving largequantities of gas containing relatively large particles

9.4.4.1 Factors Affecting Cyclone Performance

The factors that affect cyclone performance include centrifugal force, cut diameter, pressure drop,collection efficiency, and summary of performance characteristics Of these parameters, the cutdiameter is the most convenient way of defining efficiency for a control device because it gives anidea of the effectiveness for a particle size range As mentioned earlier, the cut diameter is defined

is a characteristic of the control device and should not be confused with the geometric mean particlediameter of the size distribution A frequently used expression for cut diameter where collectionefficiency is a function of the ratio of particle diameter to cut diameter is known as the Lapple cutdiameter equation (method) (Copper and Alley, 1990):

(9.19)

where

[d p]cut = cut diameter, feet (microns)

Table 9.3 Data for Calculation of Overall

Figure 9.5 Convection reverse-flow cyclone (From USEPA, Control Techniques for Gases and Particulates, 1971.)

Zone of inlet interference

Inner vortex

Outervortex

Gas outlet

Body

Inner cylinder (tubular guard)

Gas inlet Top view

Side view

Outer vortex

Inner vortex

Dust outlet

Core

n t = effective number of turns (5 to 10 for common cyclones)

Specific gravity of the particle = 2.9

Inlet gas velocity to cyclone = 50 ft/sec

Effective number of turns within cyclone = 5

Cyclone diameter = 10 ft

Cyclone inlet width = 2.5 ft

Particle size distribution data are shown in Table 9.4

Solution:

Step 1 Calculate the cut diameter [d p]cut, which is the particle collected at 50% efficiency For cyclones:

where

µ = gas viscosity, pounds per foot-second

B c = cyclone inlet width, feet

n t = number of turns

v i = inlet gas velocity, feet per second

p p = particle density, pounds per cubic foot

p = gas density, pounds per cubic foot

Determine the value of p p – p Because the particle density is much greater than the gas density,

Calculate the cut diameter:

Step 2 Complete the size efficiency table (Table 9.5) using Lapple’s method (Lapple, 1951) As mentioned, this method provides the collection efficiency as a function of the ratio of particle diameter to cut diameter Use the equation

Step 3 Determine overall collection efficiency:

Example 9.7

Problem:

An air pollution control officer has been asked to evaluate a permit application to operate acyclone as the only device on the ABC Stoneworks plant’s gravel drier (USEPA-84/09, p 68)

Given (design and operating data from permit application):

Average particle diameter = 7.5 µm

Total inlet loading to cyclone = 0.5 gr/ft 3 (grains per cubic foot)

Cyclone diameter = 2.0 ft

Inlet velocity = 50 ft/sec

Specific gravity of the particle = 2.75

Number of turns = 4.5 turns

Table 9.5 Size Efficiency Table