Air Quality Modeling

Dr. Wesam Al Madhoun

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Overview

Overview

• Air Quality Models are mathematical formulations that

include parameters that affect pollutant concentrations.

• They are used to

– Evaluate compliance with NAAQS and other

regulatory requirements

– Determine extent of emission reductions required

– Evaluate sources in permit applications

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Types of AQ Models

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SourceDispersion

Model

ReceptorModel

EmissionModel

MeteorologicalModel

ChemicalModel

Temporal and spatial emission ratesTopography

Chemical TransformationPollutant Transport

Equilibrium between Particles and gasesVertical Mixing

• Emission Model– Estimates temporal and spatial emission rates

based on activity level, emission rate per unit of activity and meteorology

• Meteorological Model– Describes transport, dispersion, vertical mixing

and moisture in time and space

• Chemical Model– Describes transformation of directly emitted

particles and gases to secondary particles and gases; also estimates the equilibrium between gas and particles for volatile species

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• Source Dispersion Model– Uses the outputs from the previous models to

estimate concentrations measured at receptors; includes mathematical simulations of transport, dispersion, vertical mixing, deposition and chemical models to represent transformation.

• Receptor Model– Infers contributions from different primary source

emissions or precursors from multivariate measurements taken at one ore more receptor sites.

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Classifications of AQ Models

• Developed for a number of pollutant types and time periods– Short-term models – for a few hours to a few

days; worst case episode conditions– Long-term models – to predict seasonal or annual

average concentrations; health effects due to exposure

• Classified by – Non-reactive models – pollutants such as SO2 and

CO– Reactive models – pollutants such as O3, NO2, etc.

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AQ Models

• Classified by coordinate system used– Grid-based

• Region divided into an array of cells• Used to determine compliance with NAAQS

– Trajectory• Follow plume as it moves downwind

• Classified by level of sophistication – Screening: simple estimation use preset, worst-

case meteorological conditions to provide conservative estimates.

– Refined: more detailed treatment of physical and chemical atmospheric processes; require more detailed and precise input data.

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9

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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Fixed-Box Models

Assumptions:1. Rectangular city. W and L are the dimensions, with one side

parallel to the wind direction.

2. Complete mixing of pollutants up to the mixing height H. No mixing above this height.

3. 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).

4. The wind blows in the x direction with velocity u , which is constant and independent of time, location, & elevation.

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… Assumptions

5. The concentration of pollutant in the air entering the city is

constant and is equal to b (for background concentration).

6. 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.

7. 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. Let’s 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

uH

qLbc

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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

uH

qLbc

m 1000m/s 3

m 15000m . sg

104

m

μg 5 26

3

c

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Comments on the simple fixed-box model

• The fixed-box models does not distinguish between area sources and point sources.

• Both sources are combined in the q value. We know that raising the release point of the pollutant will decrease the ground-level concentration.

• 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 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

iesmeteorolog allover ymeteorolog

thatof occurrence

offrequency

ymeteorolog

for that

ionconcentrat

ionConcentrat

Average

Annual

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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 →

333

iesmeteorolog allover

m

μg 15 0.6

m

μg8.33 0.4

m

μg 25

ionConcentrat

Average

Annual

ymeteorolog

thatof occurrence

offrequency

ymeteorolog

for that

ionconcentrat

ionConcentrat

Average

Annual

3

26

3

m

g 8.33

m 1000m/s 6

m 5000m . sg

104

m

μg 5

c

c

Note that L is now 5km, not 15km

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Gaussian Dispersion Models• Most widely used , Lakes Environnemental Software: http://www.weblakes.com

• Plume spread and shape vary in response to meteorological conditions

Fig. 6.3 De Nevers

Fig 7.11

H

X

Y

Z

u

Q

Model Assumptions

• Gaussian dispersion modeling based on a number of assumptions including– Steady-state conditions (constant source emission

strength)– Wind speed, direction and diffusion characteristics

of the plume are constant.– Conservation of mass, i.e. no chemical

transformations take place– Wind speeds are >1 m/sec. – Limited to predicting concentrations > 50 m

downwind

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y

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Where; c(x,y,z) = mean concentration of diffusing substance at a point (x,y,z) [kg/m3]

x = downwind distance [m], y = crosswind distance [m], z = vertical distance above ground [m], Q = contaminant emission rate [mass/s], = lateral dispersion coefficient function [m], = vertical dispersion coefficient function [m], ῡ = mean wind velocity in downwind direction [m/s], H = effective stack height [m].

The general equation to calculate the steady state concentration of an air contaminant in the ambient air resulting from a point source is given by:

z

2

2

2

2

2

1exp

2,,

zyzy

Hzy

u

QzyxC

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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 σy & σz 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 σy & σz values

2) Diffusion Models

Stability Classes

• Table 3-1 Wark, Warner & Davis

• Table 6-1 de Nevers

Dispersion Coefficients: Horizontal

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Fig 7.12

Dispersion Coefficients: Vertical

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Fig 7.13

Gaussian Dispersion Equation

If the emission source is at ground level with no effective plume rise then

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2

2

2

2

2

1exp,,

zyzy

zy

u

QzyxC

• H is the sum of the physical stack height and plume rise.

Plume Rise

stackactualriseplume hhH

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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

2) Diffusion Models

s

ass

T

TTPD

u

DVh 31068.25.1

Δh = plum rise in mVs = stack exit velocity in m/sD = stack diameter in mu = wind speed in m/sP = pressure in millibarsTs = stack gas temperature in KTa = atmospheric temperate in K

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Example 6.3

Q = 20 g/s of SO2 at Height H

u = 3 m/s,

At a distance of 1 km, σy = 30 m, σz = 20 m (given)

Required: (at x = 1 km)

a) SO2 concentration at the center line of the plume

b) SO2 concentration at a point 60 m to the side of and 20 m below the centerline

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… solution of example 6.4

33

0

2

2

2

2

g/m 1770 g/m 00177.m) m)(20 m/s)(30 (32

(g/s) 20

2

1 0 0,

centerline At the a)

2

)(

2exp

2

zy

zyzy

u

Qc

ez - Hy

Hzy

u

Qc

33

2

2

2

2

g/m 145)0818.0)(g/m (1770

)20(2

)20(

)30(2

60exp

m) m)(20 m/s)(30 (32

(g/s) 20

m 20- m, 06

CL thebelow m 20 and side the to60mpoint aAt b)

c

z - Hy

Chemical Mass Balance Model• A receptor model for assessing source apportionment using

ambient data and source profile data.• Available at EPA Support Center for Regulatory Air Models -

http://www.epa.gov/scram001/tt23.htm

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81

23,4,5,12

6

7

9

1011

1314

PM10 emissions from permitted sources in Alachua County (tons) (ACQ,2002)

2000 Values1. GRU Deerhaven 144.22. Florida Rock cement plant 34.353. Florida Power UF cogen. plant 3.19

1997 Values4. VA Medical Center incinerator 0.25. UF Vet. School incinerator 0.26. GRU Kelly 1.97. Bear Archery 9.58. VE Whitehurst asphalt plant 4.99. White Construction asphalt plant 0.710. Hipp Construction asphalt plant 0.311. Driltech equipment manufacturing 0.2

Receptor Sites12. University of Florida13. Gainesville Regional Airport14. Gainesville Regional Utilities (MillHopper)

Cij = Σ(aik×Skj) • Cij is the concentration of species ith in the sample jth measured

at the receptor site:• aik is the mass fraction of the species in the emission from

source kth, and • Skj is the total mass contribution from source kth in the jth

sample at the receptor site.04/19/23 33

Principles• Mass at a receptor site is a linear combination of the

mass contributed from each of a number of individual sources;

• Mass and chemical compositions of source emissions are conserved from the time of emission to the time the sample is taken.

Example• Total Pb concentration (ng/m3) measured at the site: a linear

sum of contributions from independent source types such as motor vehicles, incinerators, smelters, etc PbT = Pbauto + Pb incin. + Pbsmelter +…

• Next consider further the concentration of airborne lead contributed by a specific source. For example, from automobiles in ng/m3, Pbauto, is the product of two cofactors: the mass fraction (ng/mg) of lead in automotive particulate emissions, aPb, auto, and the total mass concentration (mg/m3) of automotive emission to the atmosphere, Sauto

• Pbauto = aauto (ng/mg) × Sauto (mg/m3air)

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Assumptions

• Composition of source emissions is constant over period of time,

• Chemicals do not react with each other,• All sources have been identified and have had their

emission characterized, including linearly independent of each other,

• The number of source category (j) is less than or equal to the number of chemical species (i) for a unique solution to these equations, and

• The measurement uncertainties are random, uncorrelated, and normally distributed (EPA, 1990).

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