Air Pollution Control EENV 4313

Air Pollution Control EENV 4313 Chapter 6 Air Pollutant Concentration Models

Wh do we need them? To predict the ambient air concentrations that will result from an planned set of emissions for an specified meteorological conditions, at an location, for an time period. This prediction is ver important since air pollution law in most industrial countries is based on some kind of permitted concentration of contaminants (NAAQS in the United States) ۲

How accurate is a model? The perfect model should match the realit, which is impossible. Therefore the model is a simplification of realit. The simpler the model, the less reliable it is. The more complex the model, the more reliable it is. ۳

General Form of Models The models in this chapter are material balance models. The material under consideration is the pollutant of interest. The General material balance equation is: Accumulation rate = (all flow rates in) (all flow rates out) + (creation rate) (destruction rate) Notes: 1) we need to specif some set of boundaries. ) The model will be applied to one air pollutant at a time. In other words, we cannot appl the model to air pollution in general. ٤

Three tpes of Models (in this chapter) 1. Fixed-Box Models. Diffusion Models 3. Multiple Cell Models These models are called source-oriented models. We use the best estimates of the emission rates of various sources and the best estimate of the meteorolog to estimate the concentration of various pollutants at various downwind points. ٥

1) Fixed-Box Models The cit of interest is assumed to be rectangular. The goal is to compute the air pollutant concentration in this cit using the general material balance equation. Fig. 6.1 De Nevers ٦

1) Fixed-Box Models The cit of interest is assumed to be rectangular. The goal is to compute the air pollutant concentration in this cit using the general material balance equation. Assumptions: 1. Rectangular cit. W and L are the dimensions, with one side parallel to the wind direction.. 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 cit (concentrations at the upwind and downwind edges of the cit are the same). 4. The wind blows in the x direction with velocit u, which is constant and independent of time, location, & elevation. ۷

Assumptions 5. The concentration of pollutant in the air entering the cit is constant and is equal to b (for background concentration). 6. The air pollutant emission rate of the cit is Q (g/s). The emission rate per unit area is q = Q/A (g/s.m ). A is the area of the cit (W x L). This emission rate is assumed constant. 7. No pollutant enters or leaves through the top of the box, nor through the sides. 8. No destruction rate (pollutant is sufficientl long-lived) ۸

Now, back to the general material balance eqn Accumulation rate = (all flow rates in) (all flow rates out) + (creation rate) (destruction rate) Destruction rate = zero (from assumptions) Accumulation rate = zero (since flows are independent of time and therefore stead 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 sa a flow through lower face. ۹

the general material balance eqn becomes: 0 = (all flow rates in) (all flow rates out) 0 = u W H b + q W L u W H c c = b + ql uh Where c is the concentration in the entire cit The equation indicates that the upwind concentration is added to the concentrations produced b the cit. To find the worst case, ou will need to know the wind speed, wind direction, mixing height, and upwind (background) concentration that corresponds to this worst case. ۱۰

Example 6.1 A cit 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/m 3. The emission rate per unit are is q = 4 x 10-6 g/s.m. what is the concentration c of CO over the cit? ql c = b + uh 6 g 4 10 15000 m 5 μg s. m c = + 3 m 3 m/s 1000 m = 5 μg/m 3 ( )( ) ( ) ۱۱

Comments on the simple fixed-box model 1) The third and the sixth assumptions are the worst (wh?). ) The fixed-box models does not distinguish between area sources and point sources. Area sources: small sources that are large in number and usuall emit their pollutants at low elevations; such as autos, homes, small industries, etc. Point sources: large sources that are small in number and emit their pollutants at higher elevations; such as power plants, smelters, cement plants, etc. Both sources are combined in the q value. We know that raising the release point of the pollutant will decrease the ground-level concentration. ۱۲

Comments on the simple fixed-box model 3) If ou are laing out a new cit, how would ou la it? (page 15). In light of this, would it be preferable to put our cit in a valle? 4) For an existing cit, what actions would ou take in order to minimize air pollutant concentrations? (answer in words that people can understand and act according to) 5) So far, the fixed-box model predicted concentrations for onl one specific meteorological condition. We know that meteorological conditions var over the ear. ۱۳

Modifications to improve the fixed-box model 1) Hanna (1971) suggested a modification that allows one to divide the cit into subareas and appl 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). ) Changes in meteorological conditions (comment #5) can be taken into account b a. determine the frequenc distribution of various values of wind direction, u, and of H b. Compute the concentration for each value using the fixed-box model ۱٤

Modifications to improve the fixed-box model c. Multipl the concentrations obtained in step b b the frequenc and sum to find the annual average Annual Average = Concentration over all meteorologies concentration frequenc of for that occurrence of that meteorolog meteorolog ۱٥

Example 6. For the cit 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 velocit 6 m/s and the same mixing height. What is the annual average concentration of carbon monoxide in this cit? 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 = 5 μg/m 3 ۱٦

example 6. cont. For u = 6 m/s and H = 1000 m c c 5 μg = + 3 m µ g = 8.33 3 m 4 10 6 Note that L is now 5km, not 15km g s. m ( 5000 m) ( 6 m/s)( 1000 m) Annual Average = Concentration Annual Average = Concentration over all meteorologies μg 5 3 m concentration frequenc of for that occurrence of that meteorolog meteorolog μg 0.4 + 8.33 3 m μg 0.6 = 15 3 m ۱۷

Graphical Representation of the Fixed-Box Model Equation (Fig. 6. in our textbook) Ambient air concentration, c Emission rate, q, g/s.km ۱۸

q q 1 Example A pollutant concentration was calculated to be c 1 with emission rate q 1. If the Environmental Authorit wishes to reduce the concentration to c, compute the new allowable emission rate (q ) We can use graphical interpolation: OR = = q q 1 = ( c b) 1 ( c b) ( c b) ( c b) 1 uh L uh L Divide () b (1) to get the same result Note this can be done onl when the meteorological parameters are constant c 1 c b q q 1 ۱۹

Example 6.3 (fractional reduction in emission rate) The ambient air qualit standard for particulates (TSP) in the USA in 1971 was 75 μg/m 3 annual average. In 1970 the annual average particulate concentration measured at one monitoring station in downtown Chicago was 190 μg/m 3. The background concentration was estimated to be 0 μg/m 3. B what percentage would the emission rate of particulates have to be reduced below the 1970 level in order to meet the 1971 ambient air qualit standard? c 1 = 190 μg/m 3, c = 75 μg/m 3 ۲۰

Example 6.3 (fractional reduction in emission rate) c 1 = 190 μg/m 3, c = 75 μg/m 3 Fractional reduction in emission rate Fractional reduction in emission rate = = = = ( q q ) 1 ( c b) 1 ( c1 b) ( 190 75) ( 190 0) 0.67 q 1 = 67% q = 1 q = 1 ( c1 c ) ( c b) 1 c 1 c OR: ou can use interpolation from the graph b q q 1 ۲۱

) Diffusion Models Called as diffusion models. However, the are actuall dispersion models. Such models usuall use the Gaussian plume idea. Fig. 6.3 De Nevers ۲۲

Problem Statement ) Diffusion Models Point source (smoke stack) located at (0, 0, H) that steadil emits a pollutant at emission rate of Q (g/s) The wind blows in the x-direction with velocit u. The goal is to compute the concentration due to point source at an point (x,, z) downwind. ۲۳

Description of Situation in Fig. 6.3 ) Diffusion Models The origin of the coordinate sstem is (0, 0, 0), which is the base of the smoke stack. Plume is emitted form a point with coordinates (0, 0, H) H = h + Δh, h = phsical stack height Δh = plume rise Plume rises verticall at the beginning (since it has higher temperature and a vertical velocit), then levels off to travel in the x-direction (wind direction). As the plume travels in the x-direction, it spreads in the and z directions. The actual mixing mechanism is the turbulent mixing; not the molecular diffusion. What will happen if the molecular diffusion was the onl mechanism? ۲٤

cont. Description of Situation in Fig. 6.3 ) Diffusion Models If we place a pollutant concentration meter at some fixed point in the plume, we would see the concentration oscillating in an irregular fashion about some average value (snapshot in Fig. 6.4). This is another evidence of the turbulent mixing. This average value is the value that the Gaussian plume model calculates The model does not calculate the instantaneous concentration value. It onl calculates the average value. Therefore, results obtained b Gaussian plume calculations should be considered onl as averages over periods of at least 10 minutes, and preferabl one-half to one hour. The Gaussian plume approach calculates onl this average value ۲٥

۲٦ ) Diffusion Models Where = horizontal dispersion coefficient (length units) z = vertical dispersion coefficient (length units) The name Gaussian came from the similarit between the above equation and the Gauss normal distribution function used in statistics. The previous equation can also be written the following form: The Basic Gaussian Plume Equation + = ) ( exp z z H z u Q c π ( ) = exp exp z z H z u Q c π

Example 6.4 Q = 0 g/s of SO at Height H u = 3 m/s, At a distance of 1 km, = 30 m, z = 0 m (given) Required: (at x = 1 km) a) SO concentration at the center line of the plume b) SO concentration at a point 60 m to the side of and 0 m below the centerline ) Diffusion Models ۲۷

solution of example 6.4 Q c = exp π u z a) At the centerline ) Diffusion Models ( z H ) + z 0 = 0, z - H = 0 e = 1 Q 0 (g/s) c = = =.00177 g/m πu z π (3 m/s)(30 m)(0 m) b) At a point 60m to the side and 0 m below the CL = 60 m, z - H = - 0 m 0 (g/s) 60 c = exp π (3 m/s)(30 m)(0 m) (30) 3 3 = (1770 µ g/m )(0.0818) = 145 µ g/m ( 0) + (0) 3 = 1770 µ g/m ۲۸ 3

What about and z? (Dispersion coefficients) z Spreading in the two directions are not equal Most often > z Elliptical contour concentration at a given x. Smmetr is disturbed near the ground. To determine > z, use figures 6.7 and 6.8 ) Diffusion Models ۲۹

Horizontal dispersion coefficient Figure 6.7 De Nevers ۳۰

Vertical dispersion coefficient Figure 6.8 De Nevers ۳۱

Notes on Figures 6.7 and 6.8 Both & z are experimental quantities. The derivations of equations 6.4 and 6.5 do not agree with realit. We will onl use figures 6.7 and 6.8 to find & z. Plotted from measurements over grasslands; i.e. not over cities However, we use them over cities as well since we have nothing better Measurements were made for x 1 km. Values beond 1 km have been extrapolated. ) Diffusion Models ۳۲

What are the A to F categories? A to F are levels of atmospheric stabilit (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 & z values On a cloudless winter night, ground cools b radiation to outer space and therefore cools the air near it. Hence, air forms an inversion laer. Stable atmosphere and inhibiting the dispersion of pollutants and therefore small & z values ) Diffusion Models ۳۳

Stabilit Classes Table 3-1 Wark, Warner & Davis Table 6-1 de Nevers

Example 6.5 ۳٥

Some Modifications of the Basic Gaussian Plume Equation a) The effect of the ground b) Mixing height limits and one dimensional spreading ۳٦

a) The Effect of the Ground Equation 6.7 assumes that the dispersion will continue verticall even below the ground level! The truth is that vertical spreading terminates at ground level. To account for this termination of spreading at the ground level, one can assume that a pollutant will reflect upward when it reaches the ground c = concentration due to plume itself concentration reflected + upward from ground ۳۷

۳۸ the Effect of the Ground This method is equivalent to assuming that a mirror-image plume exists below the ground. The added new concentration due to the image plume uses z+h instead of z H. (draw the plume to check!) ( ) ( ) + + = exp exp exp exp z z z z H z u Q H z u Q c π π ( ) ( ) + + = exp exp exp z z z H z H z u Q c π

Example 6.6 (effect of ground) Q = 0 g/s of SO at Height H u = 3 m/s, At a distance of 1 km, = 30 m, z = 0 m (given) Required: (at x = 1 km) SO concentration at a point 60 m to the side of and 0 m below the centerline: a) for H = 0 m b) for H = 30 m c Q exp exp ( z H ) ( z + H ) + exp = π u z z z ) Diffusion Models ۳۹

example 6.6 a) For H = 0 m i.e. the concentration at the ground level itself (z = 0) (z H) = (-H) = H (z + H) = (H) = H Therefore the answer will be exactl twice that in the nd part of example 6.4 c = (145 μg/m 3 ) = 90 μg/m 3. b) For H = 30 m 0 (60) c exp exp π (3)(30)(0) (30) (0) 1 c = 0.00177 exp( ) exp + exp ( ) ( 0) ( 40) + exp (0) = c = 0.00177 3 ( 0.135)( 0.605 + 0.135) = 0.00177( 0.1) = 177 10 6 g/m i.e. about % greater than the basic plume equation (since the basic plume eqn does not take ground reflection into account. ٤۰

٤۱ Ground-Level Equation Set z = 0 in the equation accounting for the ground effect: This is the most widel used equation because it applies directl to the problem of greatest practical interest, which is the ground-level concentration. ( ) ( ) + + = exp exp exp z z z H z H z u Q c π ( ) ( ) + = exp exp exp z z z H H u Q c π ( ) = exp exp z z H u Q c π ( ) = exp exp z z H u Q c π This is the ground-level modification of equation 6.7. It takes reflection into account.

Using Figure 6.9 to estimate Ground-Level concentration c Q exp exp ( H ) = π u z z Figure 6.9 in our text book describes a wa of finding the concentration at the line on the ground directl under the centerline of the plume. cu 1 ( H ) z = 0 and = 0 = exp Q π z z cu/q can be plotted against x to obtain figure 6.9. Note that the right-hand side depends on H,, and z. Therefore, we should have a group of H curves. Also figure 6.9 is for categor C stabilit onl. ٤۲

Example 6.8 (using figure 6.9) Q = 100 g/s at Height H = 50 m u = 3 m/s, and stabilit categor is C At a distance of 1 km, = 30 m, z = 0 m (given) Required: Estimate the ground-level concentrations directl below the CL of the plume at distances of 0., 0.4, 0.5, 1, 5, 10 km downwind ) Diffusion Models ٤۳

example 6.8 (using figure 6.9) Using figure 6.9, we can read the values of cu/q at each distance Distance (km) cu/q (m - ) c (μg/m 3 ) 0. 1.7 10-6 57 0.4 4.4 10-5 1467 0.5 5.3 10-5 1767 1 3.6 10-5 100 5.7 10-6 83 10 7.8 10-7 4 The third column is obtained b multipling the nd column b Q/u It is obvious that one of the benefits of figure 6.9 is that one can know the maximum ground level concentration & its distance downwind b inspection onl ) Diffusion Models ٤٤

Plume Rise V sd h = 1.5 + u.68 10 This equation is onl correct for the dimensions shown. ( T T ) Correction is needed for stabilit classes other than C: For A and B classes: multipl the result b 1.1 or1. For D, E, and F classes: multipl the result b 0.8 or 0.9 3 PD s T s a Δh = plum rise in m V s = stack exit velocit in m/s D = stack diameter in m u = wind speed in m/s P = pressure in millibars T s = stack gas temperature in K T a = atmospheric temperate in K ) Diffusion Models ٤٥

Example 6.9 ) Diffusion Models ٤٦

Multiple Cell Models Complex simultaneous reaction rate expressions (Figure 1.) Multiple cell modeling is used. The Urban Airshed Model UAM is an example this modeling tpe. Model Description: The airspace above the cit is divided into multiple cells. Each cell is normall from to 5 km each wa and is treated separatel from the other. Four or six laers in the vertical direction, half below the mixing height and half above. ٤۷

How does the Model Work? Mass balance for each cell. To start the simulation, we should have initial distribution of pollutants. The program calculates the change in concentration of the pollutant for a time step (tpicall 3 to 6 minutes) b numericall integrating the mass balance equation (eqn 6.1) Complex computations requiring data on: Wind velocit and direction Emissions of the ground-level cells Solar inputs ٤۸

How does the Model Work? The concentrations from the end of the previous time step are used to first compute the changes in concentration due to flows with the winds across the cell boundaries, and then compute the changes due to chemical reactions in the cell. These two results are combined to get the concentration in each cell at the end of the time step. Therefore, the model needs subprograms for the chemical transformations during the time step in an cell and subprograms for deposition of the pollutant from the groundlevel cells. ٤۹

How does the Model Work? Complex computations requiring data on: Wind velocit and direction Emissions of the ground-level cells Solar inputs The previous data are needed to simulate a da or a few das in an urban area. What if such data are not available? The program has was of estimating them. The following is a common procedure: Choose a da on which the measured pollutant concentration was the maximum for the past ear. The model is run using the historical record of the wind speeds and directions, solar inputs, and estimated emissions for that da. The model s adjustable parameters are modified until the calculated concentrations match well with the observed ambient concentrations for that da. ٥۰

How does the Model Work? Then the model is re-run with different emission rates corresponding to proposed (or anticipated) future situations and the meteorolog for that da. In this wa the model performs a prediction of the worst da situation under the proposed future emission pattern. ٥۱

Receptor-Oriented Models The previous models are called source-oriented models. We use the best estimates of the emission rates of various sources and the best estimate of the meteorolog to estimate the concentration of various pollutants at various downwind points. In receptor-oriented models, one examines the pollutants collected at one or more monitoring sites, and from a detailed analsis of what is collected attempts to determine which sources contributed to the concentration at that receptor. This source differentiation is not an eas process; for example: If the pollutant is chemicall uniform (e.g. CO, O 3, SO ), then there is no wa to distinguish between sources. If the pollutant is not chemicall uniform; i.e. consisting of variet of chemicals within the pollutant itself (e.g. TSP, PM10, PM.5), one can analze their chemical composition and make some inferences about the sources. (Aluminum and silicon example in page 148) ٥۲

Receptor-Oriented Models When results of both tpes disagree significantl, we tend to believe the receptor-oriented model because we have more confidence in chemical distribution data than we have in the meteorological data. If the goal is to estimate the effects of proposed new sources (e.g. for permitting issues), source oriented models are used. Receptor-oriented models cannot be used in such cases. Therefore receptor-oriented models are mostl used to test the estimates made b source-oriented models Simultaneousl test the accurac of the emissions estimates that are used in source-oriented models ٥۳

Building Wakes & Aerodnamic Downwash When the wind flows over the building, a plume ma get sucked and trapped into low-pressure wake behind the building. This will lead to high local concentration. A simple rule of thumb for avoiding this problem is to make the stack height at least.5 times the height of the tallest nearb building. Another simple rule of thumb: downwash unlikel to be a problem if: h s h b + 1.5 L b h s : stack height h b : building height L b : the lesser of either building height or maximum projected building width. ٥٤

Building Wakes ٥٥

Building Wakes ٥٦

Building Wakes ٥۷

Structure Influence Zone (SIZ): For downwash analses with direction-specific building dimensions, wake effects are assumed to occur if the stack is within a rectangle composed of two lines perpendicular to the wind direction, one at 5L downwind of the building and the other at L upwind of the building, and b two lines parallel to the wind direction, each at 0.5L awa from each side of the building, as shown below. L is the lesser of the height or projected width. This rectangular area has been termed a Structure Influence Zone (SIZ). An stack within the SIZ for an wind direction shall be included in the modeling. ٥۸

٥۹

For US EPA regulator applications, a building is considered sufficientl close to a stack to cause wake effects when the distance between the stack and the nearest part of the building is less than or equal to five (5) times the lesser of the building height or the projected width of the building. Distance stack-bldg <= 5L ٦۰

Figure 4.6: GEP 360 5L and Structure Influence Zone (SIZ) Areas of Influence (after U.S. EPA). ٦۱