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Air Quality Modeling

• Overview of AQ Models

• Gaussian Dispersion Model

• Chemical Mass Balance (CMB) Models

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Overview

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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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SourceDispersion

Model

ReceptorModel

EmissionModel

MeteorologicalModel

ChemicalModel

Temporal and spatial emission ratesTopography

Chemical TransformationPollutant Transport

Equilibrium between Particles and gasesVertical Mixing

Types of AQ Models

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• 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.

http://www.epa.gov/scram001/images/grid4.jpg

http://www.epa.gov/scram001/images/smokestacks.jpg

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• Screening models available at: http://www.epa.gov/scram001/dispersion_screening.htm

• Preferred models available at: http://www.epa.gov/scram001/dispersion_prefrec.htm – A single model found to outperform others

• Selected on the basis of other factors such as past use, public familiarity, cost or resource requirements and availability

• No further evaluation of a preferred model is required

• Alternative models available at: http://www.epa.gov/scram001/dispersion_alt.htm – Need to be evaluated from both a theoretical and a performance

perspective before use• Compared to measured air quality data, the results indicate the

alternative model performs better for the given application than a comparable preferred model

• The preferred model is less appropriate for the specific application or there is no preferred model

USEPA AQ models

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USEPA AQ models

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Gaussian Dispersion Models• Most widely used• Based on the assumption

– plume spread results primarily by molecular diffusion – horizontal and vertical pollutant concentrations in the plume are

normally distributed (double Gaussian distribution)

• Plume spread and shape vary in response to meteorological conditions

Fig 7.11

H

X

Y

Z

u

Q

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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– Mass transfer due to bulk motion in the x-direction far

outshadows the contribution due to mass diffusion– 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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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:

y

z

2

2

2

2

2

1exp

2,,

zyzy

Hzy

u

QzyxC

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Atmospheric Stability Classes

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Dispersion Coefficients: Horizontal

Fig 7.12

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Dispersion Coefficients: Vertical

Fig 7.13

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Gaussian Dispersion Equation

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

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

• For neutral and unstable atmospheric conditions, buoyant rise can be calculated by

)/ 55F( 425.21 34

75.0

smu

Fh riseplume

)/ 55F( 71.38 34

6.0

smu

Fhplume rise

Sass TTTdgVF 4/)(2 where buoyancy flux is

Vs: Stack exit velocity, m/sd: top inside stack diameter, mTs: stack gas temperature, KTa: ambient temperature, Kg: gravity, 9.8 m/s2

Buoyant plume: Initial buoyancy >> initial momentumForced plume: Initial buoyancy ~ initial momentumJet: Initial buoyancy << initial momentum

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Carson and Moses: vertical momentum & thermal buoyancy, based on 615 observations involving 26 stacks.

(stable) 24.204.1

(neutral) 64.235.0

(unstable) 15.547.3

u

Q

u

dVh

u

Q

u

dVh

u

Q

u

dVh

hsriseplume

hsriseplume

hsriseplume

asph TTCmQ

MWRT

PV

dm

ss4

2

(heat emission rate, kJ/s)

(stack gas mass flow rate. kg/s)

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Wark & Warner, “Air Pollution: Its Origin & Control”

2

2

2

2

2

2

2exp

2exp

2exp

2,,

zzyzy

HzHzy

u

QzyxC

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Ground level concentration

2

2

2

2

2exp

2exp

zyzy

Hy

u

QC

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Maximum Ground Level Concentration

Under moderately stable to near neutral conditions,

zy k 1The ground level concentration at the center line is

2

2

21 2

exp0,0,zz

H

uk

QxC

The maximum occurs at

2 0/

HddC zz

Once z is determined, x can be known and subsequently C.

u

Q

u

QxC

zyzy

1171.01exp0,0,

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Example

• An industrial boiler is burning at 12 tons (10.9 mton) of 2.5% sulfur coal/hr with an emission rate of 151 g/s. The following exist : H = 120 m, u = 2 m/s, y = 0. It is one hour before sunrise, and the sky is clear. Determine downwind ground level concentration at 10 km.

Stability class =

y =

z =

C(10 km, 0, 0) =

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• If emissions are from a ground level source with H = 0, u = 4 m/s, Q = 100 g/s, and the stability class = B, what is downwind concentration at 200 m?

At 200 m:

y =

z =C(200 m, 0, 0) =

Exercise

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• Calculate H using plume rise equations for an 80 m high source (h) with a stack diameter = 4 m, stack velocity = 14 m/s, stack gas temperature = 90o C (363 K), ambient temperature = 25 oC (298 K), u at 10 m = 4m/s, and stability class = B. Then determine MGLC at its location.

F =

h plume rise =

H =

z =

y =

Cmax =

Example

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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

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)

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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.

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.

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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).