Air Pollution Control EENV 4313

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Air Pollution Control EENV 4313

• Chapter 6
• Air Pollutant Concentration Models

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Why do we need them?

• To predict the ambient air concentrations that
  will result from any planned set of emissions for
  any specified meteorological conditions, at any
  location, for any time period, with total
  confidence in our prediction.
• The perfect model should match the reality, which
  is impossible. Therefore the model is a
  simplification of reality.
• The simpler the model, the less reliable it is.
  The more complex the model, the more reliable it
  is.

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General Form of Models

• The models in this chapter are material balance
  models. The material under consideration is the
  pollutant of interest.
• The General material balance equation is
• Notes 1) we need to specify some set of
  boundaries.
• 2) The model will be applied to one air pollutant
  at a time. In other words, we cannot apply the
  model to air pollution in general.

Accumulation rate (all flow rates in)
(all flow rates out) (creation rate)
(destruction rate)
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Three types of Models (in this chapter)

• Fixed-Box Models
• Diffusion Models
• Multiple Cell Models
• These models are called source-oriented models.
  We use the best estimates of the emission rates
  of various sources and the best estimate of the
  meteorology to estimate the concentration of
  various pollutants at various downwind points.

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1) Fixed-Box Models

• The city of interest is assumed to be
  rectangular.
• The goal is to compute the air pollutant
  concentration in this city using the general
  material balance equation.

Fig. 6.1 De Nevers
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1) Fixed-Box Models

• The city of interest is assumed to be
  rectangular.
• The goal is to compute the air pollutant
  concentration in this city using the general
  material balance equation.
• Assumptions
• Rectangular city. W and L are the dimensions,
  with one side parallel to the wind direction.
• Complete mixing of pollutants up to the mixing
  height H. No mixing above this height.
• The pollutant concentration is uniform in the
  whole volume of air over the city (concentrations
  at the upwind and downwind edges of the city are
  the same).
• The wind blows in the x direction with velocity u
  , which is constant and independent of time,
  location, elevation.

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• Assumptions
• The concentration of pollutant in the air
  entering the city is constant and is equal to b
  (for background concentration).
• The air pollutant emission rate of the city is Q
  (g/s). The emission rate per unit area is q
  Q/A (g/s.m2). A is the area of the city (W x L).
  This emission rate is assumed constant.
• No pollutant enters or leaves through the top of
  the box, nor through the sides.
• No destruction rate (pollutant is sufficiently
  long-lived)

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• Now, back to the general material balance eqn
• ?Destruction rate zero (from assumptions)
• ?Accumulation rate zero (since flows are
  independent of time and therefore steady state
  case since nothing is changing with time)
• ? Q can be considered as a creation rate or as a
  flow into the box through its lower face. Lets
  say a flow through lower face.

Accumulation rate (all flow rates in)
(all flow rates out) (creation rate)
(destruction rate)
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• the general material balance eqn becomes
• The equation indicates that the upwind
  concentration is added to the concentrations
  produced by the city.
• To find the worst case, you will need to know the
  wind speed, wind direction, mixing height, and
  upwind (background) concentration that
  corresponds to this worst case.

0 (all flow rates in) (all flow rates out) 0
u W H b q W L u W H c Where c is the
concentration in the entire city
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Example 6.1

• A city has the following description W 5 km,
  L 15 km, u 3 m/s, H 1000 m. The upwind, or
  background, concentration of CO is b 5 µg/m3.
  The emission rate per unit are is q 4 x 10-6
  g/s.m2. what is the concentration c of CO over
  the city?
• 25 µg/m3

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Comments on the simple fixed-box model

• 1) The third and the sixth assumptions are the
  worst (why?).
• 2) The fixed-box models does not distinguish
  between area sources and point sources.
• Area sources small sources that are large in
  number and usually emit their pollutants at low
  elevations such as autos, homes, small
  industries, etc.
• Point sources large sources that are small in
  number and emit their pollutants at higher
  elevations such as power plants, smelters,
  cement plants, etc.
• Both sources are combined in the q value. We
  know that raising the release point of the
  pollutant will decrease the ground-level
  concentration.

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Comments on the simple fixed-box model

• 3) If you are laying out a new city, how would
  you lay it? (page 125).
• In light of this, would it be preferable to put
  your city in a valley?
• 4) For an existing city, what actions would you
  take in order to minimize air pollutant
  concentrations? (answer in words that people can
  understand and act according to)
• 5) So far, the fixed-box model predicted
  concentrations for only one specific
  meteorological condition. We know that
  meteorological conditions vary over the year.

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Modifications to improve the fixed-box model

• 1) Hanna (1971) suggested a modification that
  allows one to divide the city into subareas and
  apply a different value of q to each. (since
  variation of q from place to place can be
  obtained q is low in suburbs and much higher in
  industrial areas).
• 2) Changes in meteorological conditions (comment
  5) can be taken into account by
• a. determine the frequency distribution of
  various values of wind direction, u, and of H
• b. Compute the concentration for each value using
  the fixed-box model

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Modifications to improve the fixed-box model

• c. Multiply the concentrations obtained in step b
  by the frequency and sum to find the annual
  average

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Example 6.2

• For the city in example 6.1, the meteorological
  conditions described (u 3 m/s, H 1000 m)
  occur 40 percent of the time. For the remaining
  60 percent, the wind blows at right angles to the
  direction shown in Fig. 6.1 at velocity 6 m/s and
  the same mixing height. What is the annual
  average concentration of carbon monoxide in this
  city?
• First we need to compute the concentration
  resulting from each meteorological condition and
  then compute the weighted average.
• For u 3 m/s and H 1000 m ? c 25 µg/m3

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example 6.2 cont.

• For u 6 m/s and H 1000 m ?

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Graphical Representation of the Fixed-Box Model
Equation (Fig. 6.2 in your textbook)
Slope (L/uH)
Ambient air concentration, c
Emission rate, q, g/s.km2
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Example

• A pollutant concentration was calculated to be c1
  with emission rate q1. If the Environmental
  Authority wishes to reduce the concentration to
  c2, compute the new allowable emission rate (q2)
• We can use graphical interpolation
• OR
• Note this can be done only when the
  meteorological parameters are constant

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Example 6.3 (fractional reduction in emission
rate)

• The ambient air quality standard for particulates
  (TSP) in the USA in 1971 was 75 µg/m3 annual
  average. In 1970 the annual average particulate
  concentration measured at one monitoring station
  in downtown Chicago was 190 µg/m3. The background
  concentration was estimated to be 20 µg/m3. By
  what percentage would the emission rate of
  particulates have to be reduced below the 1970
  level in order to meet the 1971 ambient air
  quality standard?
• c1 190 µg/m3 , c2 75 µg/m3

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Example 6.3 (fractional reduction in emission
rate)

• c1 190 µg/m3 , c2 75 µg/m3
• OR you can use interpolation from
• the graph

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2) Diffusion Models

• Called as diffusion models. However, they are
  actually dispersion models.
• Such models usually use the Gaussian plume idea.

Fig. 6.3 De Nevers
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2) Diffusion Models
Problem Statement

• Point source (smoke stack) located at (0, 0, H)
  that steadily emits a pollutant at emission rate
  of Q (g/s)
• The wind blows in the x-direction with velocity
  u.
• The goal is to compute the concentration due to
  point source at any point (x, y, z) downwind.

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2) Diffusion Models
Description of Situation in Fig. 6.3

• The origin of the coordinate system is (0, 0, 0),
  which is the base of the smoke stack.
• Plume is emitted form a point with coordinates
  (0, 0, H)
• H h ?h , h physical stack height
• ?h plume rise
• Plume rises vertically at the beginning (since it
  has higher temperature and a vertical velocity),
  then levels off to travel in the x-direction
  (wind direction).
• As the plume travels in the x-direction, it
  spreads in the y and z directions.
• The actual mixing mechanism is the turbulent
  mixing not the molecular diffusion.
• What will happen if the molecular diffusion was
  the only mechanism?

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2) Diffusion Models
cont. Description of Situation in Fig. 6.3

• If we place a pollutant concentration meter at
  some fixed point in the plume, we would see the
  concentration oscillating in an irregular fashion
  about some average value (snapshot in Fig. 6.4).
  This is another evidence of the turbulent mixing.
  This average value is the value that the Gaussian
  plume model calculates
• The model does not calculate the instantaneous
  concentration value. It only calculates the
  average value.
• Therefore, results obtained by Gaussian plume
  calculations should be considered only as
  averages over periods of at least 10 minutes, and
  preferably one-half to one hour.
• The Gaussian plume approach calculates only this
  average value

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2) Diffusion Models
The Basic Gaussian Plume Equation

• Where sy horizontal dispersion coefficient
  (length units)
• sz vertical dispersion coefficient (length
  units)
• The name Gaussian came from the similarity
  between the above equation and the Gauss normal
  distribution function used in statistics.
• The previous equation can also be written the
  following form

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Example 6.4

• Q 20 g/s of SO2 at Height H
• u 3 m/s,
• At a distance of 1 km, sy 30 m, sz 20 m
  (given)
• Required (at x 1 km)
• SO2 concentration at the center line of the plume
• SO2 concentration at a point 60 m to the side of
  and 20 m below the centerline

2) Diffusion Models
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solution of example 6.4
2) Diffusion Models
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What about sy and sz? (Dispersion coefficients)

• sy ? sz ?? Spreading in the two directions are
  not equal
• Most often sy gt sz ?? Elliptical contour
  concentration at a given x .
• Symmetry is disturbed near the ground.
• To determine sy gt sz , use figures 6.7 and 6.8

2) Diffusion Models
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Figure 6.7 De Nevers

• Horizontal dispersion coefficient

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• Vertical dispersion coefficient

Figure 6.8 De Nevers
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Notes on Figures 6.7 and 6.8

• Both sy sz are experimental quantities. The
  derivations of equations 6.24 and 6.25 do not
  agree with reality.
• We will only use figures 6.7 and 6.8 to find sy
  sz.
• Plotted from measurements over grasslands i.e.
  not over cities
• However, we use them over cities as well since we
  have nothing better
• Measurements were made for x 1 km. Values
  beyond 1 km have been extrapolated.

2) Diffusion Models
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What are the A to F categories?

• A to F are levels of atmospheric stability (table
  6.1).
• Explanation
• For a clear hot summer morning with low wind
  speed, the sun heats the ground and the ground
  heats the air near it. Therefore air rises and
  mixes pollutants well.
• ?? Unstable atmosphere and large sy sz values
• On a cloudless winter night, ground cools by
  radiation to outer space and therefore cools the
  air near it. Hence, air forms an inversion layer.
• ?? Stable atmosphere and inhibiting the
  dispersion of pollutants and therefore small sy
  sz values

2) Diffusion Models
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Stability Classes

• Table 3-1 Wark, Warner Davis
• Table 6-1 de Nevers

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Example 6.5
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Some Modifications of the Basic Gaussian Plume
Equation

• The effect of the ground
• Mixing height limits and one dimensional
  spreading

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a) The Effect of the Ground

• Equation 6.27 assumes that the dispersion will
  continue vertically even below the ground level!
  The truth is that vertical spreading terminates
  at ground level.
• To account for this termination of spreading at
  the ground level, one can assume that a pollutant
  will reflect upward when it reaches the ground

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the Effect of the Ground

• This method is equivalent to assuming that a
  mirror-image plume exists below the ground.
• The added new concentration due to the image
  plume uses zH instead of z H . (draw the plume
  to check!)

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Example 6.6 (effect of ground)

• Q 20 g/s of SO2 at Height H
• u 3 m/s,
• At a distance of 1 km, sy 30 m, sz 20 m
  (given)
• Required (at x 1 km)
• SO2 concentration at a point 60 m to the side of
  and 20 m below the centerline a) for H 20 m
• b) for H 30 m

2) Diffusion Models
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example 6.6

• a) For H 20 m i.e. the concentration at the
  ground level itself (z 0)
• (z H)2 (-H)2 H2
• (z H)2 (H)2 H2
• Therefore the answer will be exactly twice that
  in the 2nd part of example 6.4
• c (145 µg/m3) 2 290 µg/m3 .
• b) For H 30 m
• i.e. about 22 greater than the basic plume
  equation (since the basic plume eqn does not take
  ground reflection into account.

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Ground-Level Equation

• Set z 0 in the equation accounting for the
  ground effect
• This is the most widely used equation because it
  applies directly to the problem of greatest
  practical interest, which is the ground-level
  concentration.

This is the ground-level modification of equation
6.27. It takes reflection into account.
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Using Figure 6.9 to estimate Ground-Level
concentration

• Figure 6.9 in your text book describes a way of
  finding the concentration at the line on the
  ground directly under the centerline of the
  plume.
• ? z 0 and y 0
• cu/Q can be plotted against x to obtain figure
  6.9. Note that the right-hand side depends on H,
  sy, and sz . Therefore, we should have a group of
  H curves. Also figure 6.9 is for category C
  stability only.

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Example 6.8 (using figure 6.9)

• Q 100 g/s at Height H 50 m
• u 3 m/s, and stability category is C
• At a distance of 1 km, sy 30 m, sz 20 m
  (given)
• Required
• Estimate the ground-level concentrations
  directly below the CL of the plume at distances
  of 0.2, 0.4, 0.5, 1, 5, 10 km downwind

2) Diffusion Models
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example 6.8 (using figure 6.9)

• Using figure 6.9, we can read the values of cu/Q
  at each distance
• The third column is obtained by multiplying the
  2nd column by Q/u
• It is obvious that one of the benefits of figure
  6.9 is that one can know the maximum ground level
  concentration its distance downwind by
  inspection only

Distance (km) cu/Q (m-2) c (µg/m3)
0.2 1.710-6 57
0.4 4.410-5 1467
0.5 5.310-5 1767
1 3.610-5 1200
5 2.710-6 83
10 7.810-7 24
2) Diffusion Models
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Plume Rise

• This equation is only correct for the
• dimensions shown.
• Correction is needed for stability classes other
  than C
• ? For A and B classes multiply the result by 1.1
  or1.2
• ? For D, E, and F classes multiply the result by
  0.8 or 0.9

?h plum rise in m Vs stack exit velocity in
m/s D stack diameter in m u wind speed in
m/s P pressure in millibars Ts stack gas
temperature in K Ta atmospheric temperate in K
2) Diffusion Models
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Example 6.9

2) Diffusion Models
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Multiple Cell Models

• Complex simultaneous reaction rate expressions
  (Figure 1.2)
• Multiple cell modeling is used. The Urban Airshed
  Model UAM is an example this modeling type.

• Model Description
• The airspace above the city is divided into
  multiple cells. Each cell is normally from 2 to 5
  km each way and is treated separately from the
  other.
• Four or six layers in the vertical direction,
  half below the mixing height and half above.

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How does the Model Work?

• Mass balance for each cell. To start the
  simulation, we should have initial distribution
  of pollutants.
• The program calculates the change in
  concentration of the pollutant for a time step
  (typically 3 to 6 minutes) by numerically
  integrating the mass balance equation (eqn 6.1)
• Complex computations requiring data on
• Wind velocity and direction
• Emissions of the ground-level cells
• Solar inputs

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How does the Model Work?

• The concentrations from the end of the previous
  time step are used to first compute the changes
  in concentration due to flows with the winds
  across the cell boundaries, and then compute the
  changes due to chemical reactions in the cell.
  These two results are combined to get the
  concentration in each cell at the end of the time
  step.
• Therefore, the model needs subprograms for the
  chemical transformations during the time step in
  any cell and subprograms for deposition of the
  pollutant from the ground-level cells.

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How does the Model Work?

• Complex computations requiring data on
• Wind velocity and direction
• Emissions of the ground-level cells
• Solar inputs
• The previous data are needed to simulate a day or
  a few days in an urban area. What if such data
  are not available?
• ?The program has ways of estimating them. The
  following is a common procedure
• Choose a day on which the measured pollutant
  concentration was the maximum for the past year.
• The model is run using the historical record of
  the wind speeds and directions, solar inputs, and
  estimated emissions for that day.
• The models adjustable parameters are modified
  until the calculated concentrations match well
  with the observed ambient concentrations for that
  day.

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How does the Model Work?

• Then the model is re-run with different emission
  rates corresponding to proposed (or anticipated)
  future situations and the meteorology for that
  day.
• In this way the model performs a prediction of
  the worst day situation under the proposed future
  emission pattern.

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Receptor-Oriented Models

• The previous models are called source-oriented
  models. We use the best estimates of the
  emission rates of various sources and the best
  estimate of the meteorology to estimate the
  concentration of various pollutants at various
  downwind points.
• In receptor-oriented models, one examines the
  pollutants collected at one or more monitoring
  sites, and from a detailed analysis of what is
  collected attempts to determine which sources
  contributed to the concentration at that
  receptor. This source differentiation is not an
  easy process for example
• If the pollutant is chemically uniform (e.g. CO,
  O3, SO2), then there is no way to distinguish
  between sources.
• If the pollutant is not chemically uniform i.e.
  consisting of variety of chemicals within the
  pollutant itself (e.g. TSP, PM10, PM2.5), one can
  analyze their chemical composition and make some
  inferences about the sources. (Aluminum and
  silicon example in page 148)

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Receptor-Oriented Models

• When results of both types disagree
  significantly, we tend to believe the
  receptor-oriented model because we have more
  confidence in chemical distribution data than we
  have in the meteorological data.
• If the goal is to estimate the effects of
  proposed new sources (e.g. for permitting
  issues), source oriented models are used.
  Receptor-oriented models cannot be used in such
  cases.
• Therefore receptor-oriented models are mostly
  used to
• test the estimates made by source-oriented models
• Simultaneously test the accuracy of the emissions
  estimates that are used in source-oriented models

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Building Wakes Aerodynamic Downwash

• When the wind flows over the building, a plume
  may get sucked and trapped into low-pressure wake
  behind the building. This will lead to high local
  concentration.
• A simple rule of thumb for avoiding this problem
  is to make the stack height at least 2.5 times
  the height of the tallest nearby building.
• Another simple rule of thumb
•   downwash unlikely to be a problem if
• hs ? hb 1.5 Lb
•   hs stack height
• hb building height
• Lb the lesser of either building height or
  maximum projected building width.

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Building Wakes
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Building Wakes
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Building Wakes
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• Structure Influence Zone (SIZ) For downwash
  analyses with direction-specific building
  dimensions, wake effects are assumed to occur if
  the stack is within a rectangle composed of two
  lines perpendicular to the wind direction, one at
  5L downwind of the building and the other at 2L
  upwind of the building, and by two lines parallel
  to the wind direction, each at 0.5L away from
  each side of the building, as shown below. L is
  the lesser of the height or projected width. This
  rectangular area has been termed a Structure
  Influence Zone (SIZ). Any stack within the SIZ
  for any wind direction shall be included in the
  modeling.

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For US EPA regulatory applications, a building is
considered sufficiently close to a stack to cause
wake effects when the distance between the stack
and the nearest part of the building is less than
or equal to five (5) times the lesser of the
building height or the projected width of the
building. Distancestack-bldg lt 5L
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• Figure 4.6 GEP 360 5L and Structure Influence
  Zone (SIZ) Areas of Influence (after U.S. EPA).