Chapter 5 Dispersion Models

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Chapter 5 Dispersion Models

• 5.1 Dispersion of pollutants in the atmosphere
• 5.2 Models
• 5.3 Gaussian Dispersion Model
• 5.4 Effective stack height
• 5.5 Area and line sources

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Introduction

• Connection between Source and Atmosphere
• Emissions of pollutants from sources
• Air quality in the atmosphere
• Emission ?Air Quality (Imission)
• Connection MODELS
• Very wide variety of models

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What is MODEL?

• A mathematical relation (equation or a set of
  equations) to estimate some parameter(s) (i.e.
  Outputs) by using some other set of parameter(s)
  (i.e. Inputs)

MODEL Yj f(Xi)
Output(s), Yj
Input(s), Xi
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MODELS

• Deterministic ModelsInitially KNOWN relationship
  between inputs and outputs
• Box Models (Simple Box Model, Eulerian Box
  Model, Lagrangian Box Model) Receptor
  Models Dispersion Models

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MODELS

• Stochastic Models
• Initially UNKNOWN relationship between inputs
  and outputs
• Mathematical approximations such as polynomial
  equations, neural networks, fuzzy networks etc

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General Structure of Air Pollution Models
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Detailed Structure of Atmospheric Chemical
Transport Models
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Parameters in Models

• Source Parameters (Emission Characteristics) Emis
  sion rates of pollutants (mass/time) Physical
  location of source Temperature of gas
  release Plume Rise
• Meteorology Atmospheric temp. Atmospheric
  stability (needed for Dipersion coefficients)
  Wind velocity
• Atmospheric Chemistry Chemical Reaction in the
  atm. Depositions (wet or dry)
• Surface Parameters Surface geometry, roughness,
  seas, urban or rural areas etc

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Scope of this Chapter

• Dispersion Models
• GAUSSIAN DISPERSION MODEL

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Theory Behind Gaussian Dispersion Model (GDM)

• A Mass Balance on the basis of a specific
  pollutant In a Control Volume
• Accumulation Rate (mass/time)
• All Flows In
• All Flows Out
• Formation Rate
• - Destruction Rate

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Theory Behind Gaussian Dispersion Model (GDM)
Inputs
Diffusion
Outputs
Advection (by wind)

• Two main transportation mechanisms are involved
• Diffusion on molecular basis in all directions
  (i.e.in x, y and z directions)
• Transportation by wind in only wind direction
  (i.e. in x direction)

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Theory Behind Gaussian Dispersion Model (GDM)

• Molecular diffusion
• 
  (Ficks Law)
• Nx Mass diffusion flowrate of gas pollutant in
  x direction (mass/time)
• Dx Diffusivity (turbulent mixing coefficient)
  in x direction (area/time)
• C Concentration (mass / volume)
• A Cross-sectional area (Adydz) in the
  direction of transportation (i.e. x direction)

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Theory Behind Gaussian Dispersion Model (GDM)

Ci concentration of pollutant i, µg/m3 u
mean convective velocity in x-direction (wind
velocity), m/sec dy mean convective velocity
in y-direction, m/sec dz mean convective
velocity in y-direction, m/sec Dx mass
diffusivity in x-direction, m2/sec Dy mass
diffusivity in y-direction, m2/sec Dz mass
diffusivity in z-direction, m2/sec F pollutant
removal or accumulation rate, µg/sec
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Theory Behind Gaussian Dispersion Model (GDM)
Dividing both sides by control volume dxdydz
Assuming mass diffusivities are constant due to
continuity principle, that is
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Theory Behind Gaussian Dispersion Model (GDM)

• Last equation becomes
• Basic dispersion equation
• We need to evaluate Gaussian Dispersion mechanism
  to further go on

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Gaussian Dispersion Mechanismin 2D
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Gaussian Dispersion Mechanismin 3D
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Gaussian Dispersion Mechanism

• In order to obtain Gaussian Model, we need to
  simplify the Basic dispersion Equation
• Assumptions
• Pollutant emission rate (Qi) from the source is
  constant
• Wind velocity in y and z directions is zero
• Wind velocity in x direction is constant
• Advective transportation is dominant over
  diffusion in x direction

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Gaussian Dispersion Mechanism

• Pollutant accumulation or removal is zero
• F0
• With all these assumptions Basic Eqn
• Becomes a second order differential eqn

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Gaussian Dispersion Mechanism

• Solution
• K is an indefinite integration constant
• To find K we need to determine the integration
  limits depending upon the dispersion geometry.
• In the plume we have

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Gaussian Dispersion Mechanism

• Integration limits for a ground source
• y -infinity to infinity
• z 0 to infinity
• Result
• K is

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Gaussian Dispersion Mechanism

• Inserting into main eqn
• By definition we have the following relations
  between diffusion and dispersion coefficients
• Inserting them into main eqn,we have
• Gauss Dispersion Eqn for ground level source

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Concepts about GDM

• Ground Level Source

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Concepts about GDM

• Stack Dip Downwash
• If
• Stack dipdownwash is neglected
• Otherwise Reduced Stack height

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Concepts about GDM

• Plume Orientation

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Concepts about GDM

• Elevated source

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Concepts about GDM

• Ground Reflection

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Concepts about GDM

• Ground Reflection
• (Vertical Concentration profile)

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Concepts about GDM

• Ground Reflection
• (Horizontal concentration change)

Cmax and its location (xmax) is important
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Most General Form of GDM

• Terms in GDM

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Plume Shapes depending on Stability
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Plume Shapes depending on Stability
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Plume Shapes depending on Stability
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Plume Shapes depending on Stability
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Plume Shapes depending on Stability
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Plume Shapes depending on Stability
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How to use GDM?

• Need to know proper orientations of both Source
  and ReceptorSource at (0,0,H) and Receptor at
  (x,y,z) ?C(x,y,zH)
• Pollutant Emission Rate from source Q (mass of
  pollutant/time) NOT Volume flowrate of
  Stackgas
• Atmospheric Stability Category (A, B, C. etc.)
• Wind velocity at stack height u
• Dispersion Coefficients sy and sz
• Effective Stack height H hs ?h ?
  Calculation of Plume rise (?h )
• THEN USE GDM ? C(x,y,zH) .

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Source-to-Receptor Orientation

• A source is emitting pollutant stack gas from its
  stack of 100m. Define the location of a ground
  level receptor site 5 km North (N) of the source
  if the wind blows from SouthWest (SW) direction.
• ?Draw the geographical orientation of source and
  receptor and calculate x, y and z coordinates
  for GDM.

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• Solution

Distance x (5 km) Cos 45
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Receptor-to-Source Orientation

• A park area is located in 10 km west (W) of a
  thermal power plant having 200m tall stack.
  Determine the geographical positions of receptor
  and source points if the wind blows from
  East-NorthEast (ENE) direction.
• ?Draw the geographical orientation of source and
  receptor and calculate x, y and z coordinates
  for GDM

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• Solution

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Dispersion Coefficients sy, sz
As plume goes away from source, dispersion
increases in both y and z directions ? As x
increases ? sy and sz icrease depending upon
stability
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Dispersion Coefficients sy, sz

• First developed graphical representations

sy
sz
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Dispersion Coefficients sy, sz

• Mathematical simulations for Disp. Coeffs.

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Calculation of Plume Rise (?h)
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Calculation of Plume Rise (?h)
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Calculation of Plume Rise (?h)
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Calculation of Plume Rise (?h)
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Calculation of Plume Rise (?h)

• Parameters in Briggs Equations

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EXAMPLES
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EXAMPLES
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EXAMPLE
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Graphical representation of concentration versus
x distance
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Ground Level Max Concentration and Location

• Turners Graphical Solution
• A Graph for
• Cu/Q versus xmax
• Max Concentration depends on
• Stability category
• Effective stack height
• GRAPH

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Analytical Solution for Cmaxvalid for all
stability categories
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Analytical Solution for Cmaxvalid only for
Slightly stable and Neutral conditions