Atmospheric Dispersion Flashcards
Air quality/ Dispersion Modeling
use mathematical and numerical
techniques to simulate the physical and chemical
processes that affect air pollutants as they disperse and
react in the atmosphere.
What are the 5 major physical processes in air pollution dispersion modeling?
Emission
Chemical reaction
Pollutant advection
Diffusion
Deposition
Simple One Box Model
Stationary atmospheric box
Global Atmosphere: Fin + Fout = 0
Transport A flow of x into the box (Fin) and out of the box (Fout)
Rate of change of X will depend on sources (Fin + E + P) and Sinks (Fout - L - D)
dm/dt = Σsources - Σ sinks = Fin + E + P - Fout - L - D
Multi Box Model
Change in concentration in one box will depend on the other box.
✘ In a steady state, dm1/dt = dm2/dt = 0
Assuming that the flux is proportional to the mass, Fij = kij*mij
Ex. 2-Box Model
3-Box Model
Advection Model
Qa/ Zi = u ∆C/ ∆x
c =∆xQa/ uZi
Assuming:
steady-state emissions and atmospheric conditions
○ Complete mixing of pollutants up to zi is produced.
○ The turbulence is strong enough that the pollutant concentration
is C uniform in the whole volume of air
○ The wind blows in x direction with velocity u. This velocity is constant
and is independent of time, location or elevation.
○ The air pollution emission rate is Qa. It is constant and unchanging
with space and time.
Atmospheric Diffusion assumptions:
○ Pollutant material takes on Gaussian distribution in both y
and z directions
○ Not reacting chemically in the atmosphere
○ Steady-state condition
○ Uniform continuous emission rate
○ Homogenous, horizontal wind field. Wind speed constant
○ The aerosol diameter to be smaller than 20 μm for
residence time to be large
○ Flat terrain
Characteristics of an average plume
WInd, M
Plume centerline
Plume spread
Plume rise
Source or stack height
Centerline height, zcL
Plume rise is the additional height owing to the
buoyancy of the hot gases and the momentum of the
gases leaving the stack.
Atmospheric Diffusion: Gaussian Model
C (x,y,z) = Q/ (2pi* σy σzu) * e ^[-1/2(y/ σy)^2]* {e^[-1/2(Z-ZcL/ σz)^2]+ e^[-1/2(Z+ZcL/ σz)^2]}
Where:
- C(x,y,z) : concentration of pollutant at point (x,y,z), expressed in μg/m3
- Q the emission rate expressed in μg/s
- u the wind velocity (m/s)
- σy & σz the plume-spread standard deviations in y and z direction
- ZcL = H + ∆h is the height of the plume centerline above ground,
- U is the average ambient wind speed at the plume centerline height
Concentration at ground level (z = 0) (with ground reflection): c (x, y, 0)
C (x,y,z) = Q/ (pi* σy σzu) * e ^[-1/2(y/ σy)^2]* {e^[-1/2(ZcL/ σz)^2]
Concentration at ground level (z = 0) on centerline (y=0) (with
ground reflection): c (x, 0, 0)
C (x,y,z) = Q/ (pi* σy σzu)]* {e^[-1/2(ZcL/ σz)^2]
Concentration at ground level (z = 0, y = 0, h = 0)(with ground
reflection): c (x, 0, 0), h = 0
C (x,y,z) = Q/ (pi* σy σzu)]
Plume rise
∆h = (1.6 F^1/3* x^(2/3)f)/ u
Following approximations for x
xf = 120 F^0.4 if F >_ 55 m^4/s^3
xf = 50 F^5/8 if F < 55 m^4/s^3
F = gVs (d^2/4)* (Ts-Ta/ Ts)
F is the coefficient of flux buoyancy (m^4* s^-3)
g is the coefficient of the acceleration gravitational settling (ms^-2)
d is the stack diameter (m)
Ta is the air temperature at the height of the stack (K)
Ts is the temperature at the height of the stack (K)
Vs is the exit velocity from the stack (m/s)
Mean Wind speed formula
u (z) = u0 (z/z0) ^p
where:
u(z) = wind speed at plume height, z
u0 = wind speed at instrument height
z = plume height (m)
z0 = instrument height (m)
p = factor which depends on stability condition of atmosphere
