Mustafa M. Aral - PDF Free Download

Air Pathway Analysis Mustafa M. Aral MESL @CEE,GT http://mesl.ce.gatech.edu/ maral@ce.gatech.edu

Air Pollution Air pollution affects humans more than water pollution. Whereas we can always treat the water before we drink it or use it, the air we breathe must be clean where we happen to be. Air quality tends to be worse in large cities where there are more people and more traffic and unnatural emissions to the atmosphere. Some examples are:

CO Diurnal Pattern Roswell Rd 2400 2000 1600 1994 (8/5-) 1995 1996 1997 1998 1999 2000 2001 2002 2003 (-5/31) CO (ppb) 1200 800 400 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 hour of day

SO 2 Diurnal Pattern Georgia T ech SO2 (ppb) 10 8 6 4 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 hour of day

O 3 Diurnal Pattern Confederate Ave. 80 60 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 O3 (ppb) 40 20 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 hour of day

Concern: Fine Particulate Matter Nearly all of southeast is above 15 µg/m 3 fine PM

Regulations CLEAN AIR ACT with amendments: 1955,, 1963, 1966, 1970 and 1990 NATIONAL AMBIENT AIR QUALITY STANDARDS: 1980 1988

Ambient Air Pollution uv O 3 PM SO 2 PM NO x + HC CO + PM Stationary Sources Mobile Sources

Standards for 6 Chemicals Pollutant Exposure Duration NAAQS Health and Environmental Outcome CO 1 hour 8 hours 35 ppm 9 ppm Headaches, asphyxiation Angina, pectoris NO 2 1 year 0.053 ppm Respiratory disease SO 2 3 hours 1 day 1 year 0.50 ppm 0.14 ppm 0.03 ppm Shortness of breath, Odor, acid precipitation O 3 1 hour 8 hours 0.12 ppm 0.075 ppm Eye irritation, breathing damage, bronchitis, heart attack. Pb 3 months 1.5 µg/m 3 Blood poisoning PM 2.5 24 hours 1 year 35 µg/m 3 Lung damage 15 µg/m 3 PM 10 24 hours 150 µg/m 3 Respiratory disease, Visibility

Computational Sequence Source Emissions Domain Idealization Atmospheric Conditions Selection of the Model Solution and Analysis Uncertainty Analysis

Source Emissions Emission from Land disposal Emission from water surfaces Landfills

Source Emissions Highways

Source Emissions Indoor Air Pollution Stacks

Gaussian model 2 C C C + v = Dx + 2 t x x R v C x 2 C = Dx + 2 x R Key parameter is the Diffusion Coefficient in this calculations And it depends on the atmospheric stability conditions.

Atmospheric Stability Thermal stratification is often observed in the atmosphere, especially over diurnal cycle. When it occurs stratification is characterized by colder denser air sinking below lighter and warmer air. This stratification creates an obstacle to turbulence and dispersion of contaminants. If the air stays stationary in stratified layers instead of mixing vertically, than contaminant concentration will not diminish. Thus understanding of stratification and defining a measure of stratification is important.

Atmospheric Stability is Defined in terms of Lapse Rates Lapse rate is defined as the manner in which the temperature in an air packet changes with altitude or elevation. A positive lapse rate implies a decrease in temperature with elevation. Z ELR Environmental Lapse Rate (ELR) refers to the variation of the temperature with altitude at a certain place and time. (Function of space and time) θ1 T

Lapse Rates Adiabatic Lapse Rate (ALR) (heat exchange is not considered). Diabatic process in which heat is added or subtracted from the system, (solar heating, radiation cooling). Dry Adiabatic Lapse Rate (DALR) and the Saturated Adiabatic lapse Rate (SALR). Moisture contents controls the heat transfer.

Lapse Rates Dry adiabatic lapse rate is the rate at which non-saturated air parcel cools as it rises. This rate is 9.8 o C/km or ~ 1 o C/100m The SALR is variable since it depends on how much the latent heat is made available as the condensation occurs for a saturated air parcel.

Rate Comparisons Z ELR Z θ1 θ2 θ2 θ1 ELR ALR ALR T ALR > ELR ALR < ELR θ 2 > θ θ 1 > θ 2 1 T

Stable Neutral Unstable a. Three mechanical stability conditions [displacement ; tendency] Z P ELR Z P ALR ALR > ELR ALR < ELR T T ALR ELR T b. Thermal stability condition c. Thermal instability condition T

T = Temp on ALR Z P ELR T = Temp on ELR Z1 Z2 ALR T 1 < T 1 b. Thermal stability condition To T 2 < T 2 T

T = Temp on ALR Z P ALR ELR T = Temp on ELR Z1 Z2 T 1 > T 1 To T 2 < T 2 T c. Thermal instability condition

Stability Conditions Absolute instability occurs when ELR is greater than DALR. As we know that DALR is 9.8 o C/km, than we can conclude that absolute instability exists when ELR is equal or greater than 9.8 o C/km. This condition is sometimes identified as super-adiabatic lapse rate since the heat loss is very rapid. Natural instability occurs when the ELR and DALR are equal. In this term the word natural refers to the fact that thermal momentum is not going to be accelerated or decelerated. Conditional instability occurs when ELR is less than DALR but more than SALR. SALR is usually considered to be in the range 3.9 o C/km - 7.2 o C/km. The use of the word condition is associated with the condition that instability will only occur when the thermal becomes saturated and before. Absolute stability occurs when ELR is less than SALR. Potential instability occurs when air at lover elevations is moist but it is dryer at higher elevations. The potential for instability is only realized when the thermal ascends and reaches saturation.

Stability Analysis dp dρ dt unknowns: ; ; dz dz dz Pressure vs Elevation: Z P4 P3 P4 W = 0 P2 dz dx Air Pocket P1 p( z + dz) p( z) = ρgdz P3 W dp dz = ρg = γ X Hydrostatic conditions

Equation of state: The atmosphere is a mixture of gases (78% Nitrogen, 21% Oxygen, 1% other gases) collectively it as called air. Mixture is not so important for this analysis. Let s consider air to be ideal gas, with a molecular weight between oxygen and nitrogen. For an ideal gas Equation of state links pressure, density and temperature as follows: P = RρT T = absolute Temperature degrees Kelvin (= deg Centigrade + 273.15) R=287 J/kg-K 287 m 2 /s 2 -K for air

Equation of state: P = RρT dp dρ dt = R T + Rρ dz dz dz Given the definition of hydrostatic eqn. if a parcel of air rises than its pressure drops. Given above relation, accordingly its density or temperature or both should drop as well

Energy state: But as pressure drops the air parcel expands making its pressure do work against surrounding air parcels. Pd V This work is associated with internal energy loss = mc v dt Cv = Heat capacity Thus internal energy of the parcel drops according to: mcvdt or = Pd V 1 CvdT = Pd ρ dt P dρ Cv = dz 2 ρ dz u vu uv d = v v 2 1 0 dρ d = 2 ρ ρ

Thus we have three independent equations for three derivatives: dp dz = γ Pressure state ρ dp d dt = R T + Rρ dz dz dz Ideal Gas dt Cv dz = P d ρ 2 ρ dz Energy state Which can be solved for each derivative

Solve say for temperature gradient: dt Cv + R = g dz dt g g = = dz C + R C ( ) dt v 2 9.81 m / s = = 2 2 dz 1005 m / s K p 3 9.76 10 K / m = Γ Thus as air pressure decreases as z increases the air temperature also decreases according to the equation above. Meteorologists call this ADIABATIC LAPSE. About 1 deg. drop/100m (that is why it is cold up there)

All this is for natural conditions. However, when the air parcel rises and does work to adjust its temperature according to these principles, it finds an another ambient temperature at the new elevation which it needs to adjust as well. T a = ambient temperature is not equal to T p = natural temperature This temperature difference creates buoyancy forces g Ta Tp = T ( z + dz) T ( z) + dz C dt g Ta Tp + dz dz C p p

Net upward force F = buoyancy force weight F net net = ρa V g ρ p V g = ( ρ ρ ) P P Fnet = V g RTa RT p P F ( ) net = Tp Ta V RT T F net a p T T p a = ρ p Ta V g g a p V g F b W

Newton s law 2 d ( dz) Fnet = m dt 2 earlier F net T T p a = ρ p Ta V g ρ p T p T T a a V 2 d ( dz) g = m = ρ 2 p V dt 2 d ( dz) 2 dt 2 Tp Ta d dz g = 2 Ta dt ( ) ( ) T T dz 2 d dz p a g dt g = g = 2 + dt Ta Ta dz C p earlier dt g Ta Tp + dz dz C p

Stability conditions: 2 d ( dz) g dt g = 2 + dt T a dz C p dt dz dt dz dt dz g = C p g < C p g > C p dz neutural atmosphere unstable atmosphere stable atmosphere

GRAPHICALLY Z Γ T a Stable T a Inversion 100m T a 1 o C Z 2 Unstable Z 1 o C T

This effects plume shape:

Gaussian model 2 C C C + v = Dx + 2 t x x R v C x 2 C = Dx + 2 x R Key parameter is the Diffusion Coefficient in this calculations And it depends on the stability conditions.

Dispersion coefficients is a function of

Stability Classes Z Stable Unstable D E F Inversion C B A T

Air Pollution Models Atmospheric Stability Analysis Necessary for Stack height calculations Necessary for dispersion constant estimates. Air Emission Models This is mostly for input to air dispersion models except for INDOOR AIR models Requires chemical database Based on Fickian Diffusion Analysis Requires numerous background models Air Dispersion Models Requires chemical database Requires Stack height corrections for air dispersion models Requires dispersion constants and several other background models Background correction models are for temperature and density corrections for different chemicals are based on Henry constant for chemicals in use.

EMISSIONS

Farmer s Model The Farmer s model can be used to estimate volatile emissions of a buried contaminant source below the soil surface. Clean Soil Emissions Contaminated Soil d 1 V E = AD e C ( ) vs a ( 2 10 ) d 1 C E: steady state emission rate of the gases (g/s) A: surface area of the contamination source (m2) D e : Effective diffusion coefficient of the contaminant for air (cm2/s) C vs : vapor phase concentration of the contaminant (g/cm3), C a : air concentration of the contaminant at soil surface (g/cm3) (usually assumed to be equal to zero) d 1 : the depth of soil cover (m) And 10 2 is the conversion factor

Farmer s Model The user should also note that the emission rate output is presented in the units of (kg/yr) in the output window. The conversion from (g/s) to (kg/yr) is carried out internally in the ACTS model. There are several internal computations done in ACTS in this case as will be the case for all models: In this model, the soil vapor concentration, C vs (g/cm3) is given by, Cvs = H Cw H is the dimensionless Henry s constant (mg/l)/(mg/l) and is defined as, H = H RT H is the Henry s law constant (atm-m3/mole), R is the universal gas constant (8.21E-5 atm-m3/k) and T is the absolute temperature ( o K).

Farmer s Model The aqueous phase concentration, C w (g/cm3), is calculated by, C w = C ( ) ρ + θ ρ ( ) T b w w θ θ H + θ + ρ K T w w b d C T is the contaminant concentration in the soil (g-contaminant/g-wet soil), θ T : soil porosity (dimensionless), ρ b : soil bulk density (g-dry soil/cm3-wet soil), ρ w : density of water (g/cm3), Θ w : volumetric water content (dimensionless) and K d : soil-water partition coefficient, which is a chemical and soil property dependent parameter ((g/g)/(g/cm3)), K = K f d oc oc K oc : organic carbon partition coefficient ((g/g)/(g/cm3)) f oc : fractional organic carbon content of the soil. Note that the soil porosity value entered should not be less than the volumetric water content,.

Farmer s Model = 3.33 a De D θ air 2 θ T D air is the diffusion coefficient for the chemical in air (cm3/s), Θ a is the air filled porosity of soil (cm3-air/cm3 soil) θ T is the total porosity of soil (cm3-voids/cm3-soil). Again the air filled porosity should be less than the total porosity of the soil,. Temperature correction: T DT D 2 T1 T 2 = 1 T 1 is air temperature at which the diffusion coefficient is known ( o K), T 2 is the air temperature at which the diffusion coefficient is estimated ( o K) D T2 and D T1 are the diffusion coefficients of the chemical (cm3/s) at two temperatures. 1.75

Farmer s Model: Example -1 Data: Clean soil thickness d1 = 400 m Emissions Contaminated soil area A = 200 m 2 Background air concentration C = 0 g/m 3 Clean Soil d 1 Total Soil Contamination Cs = 100 mg/kg Contaminated Soil Soil Density = 1.9 g/cm 3 Soil porosity n = 0.4 cm 3 /cm 3 Moisture content = 0.15 cm 3 /cm 3 Soil carbon content % = 0.1 Air Temperature = 298 o K Air Diffusion coeff. =???

Farmer s Model

Farmer s Model MC

Linking Farmer s Model to Box Model The Farmer s model can be used to estimate volatile emissions of a buried contaminant source below the soil surface. Clean Soil Emissions Contaminated Soil d 1 V E = AD e C ( ) vs a ( 2 10 ) d 1 C E: steady state emission rate of the gases (g/s) A: surface area of the contamination source (m2) D e : Effective diffusion coefficient of the contaminant for air (cm2/s) C vs : vapor phase concentration of the contaminant (g/cm3), C a : air concentration of the contaminant at soil surface (g/cm3) (usually assumed to be equal to zero) D 1 : the depth of soil cover (m) And 10 2 is the conversion factor

Linking Farmer s Model to Box Model

Farmer s Model: Assumptions 1. In Farmer s model it is assumed that the source concentration of contaminants does not decrease as the emissions occur. 2. Also decay of the contaminant source is not considered. This implies that the amount of contaminant mass in the soil is infinite; 3. The location of the contaminant source is fixed at a depth below the surface of the soil; 4. Emissions from the soil originating from the contaminant source are in steady state; 5. The concentration of the chemical in air at the soil surface is negligible as compared to the vapor concentration within the soil.

Thibadeaux-Hwang Model Clean Soil Emissions d 1 ( ) E t V = d D C e vs 2 D At( d d ) C + 2 e 2 1 1 mo vs d 2 Contaminated Soil m = ( d d ) AC o 2 1 b C = C ( ρ + ρ θ ) b T b w w 1 t E '( t) = E( t) dt t 0

Thibadeaux-Hwang Model

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