Air Pollution Control EENV 4313

1. Air Pollution Control EENV 4313 Chapter 6 Air Pollutant Concentration Models

2. Why do we need them? • To predict the ambient air concentrations that will result from any planned set of emissions for any specified meteorological conditions, at any location, for any time period, with total confidence in our prediction. • The perfect model should match the reality, which is impossible. Therefore the model is a simplification of reality. • The simpler the model, the less reliable it is. The more complex the model, the more reliable it is.

3. 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: Notes: 1) we need to specify some set of boundaries. 2) The model will be applied to one air pollutant at a time. In other words, we cannot apply the model to air pollution in general. Accumulation rate = (all flow rates in) – (all flow rates out) + (creation rate) – (destruction rate)

4. Three types of Models (in this chapter) • Fixed-Box Models • Diffusion Models • 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 meteorology to estimate the concentration of various pollutants at various downwind points.

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

6. 1) Fixed-Box Models • The city of interest is assumed to be rectangular. • The goal is to compute the air pollutant concentration in this city using the general material balance equation. Assumptions: • Rectangular city. 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. • The pollutant concentration is uniform in the whole volume of air over the city (concentrations at the upwind and downwind edges of the city are the same). • The wind blows in the x direction with velocity u , which is constant and independent of time, location, & elevation.

7. … Assumptions • The concentration of pollutant in the air entering the city is constant and is equal to b (for background concentration). • The air pollutant emission rate of the city is Q (g/s). The emission rate per unit area is q = Q/A (g/s.m2). A is the area of the city (W x L). This emission rate is assumed constant. • No pollutant enters or leaves through the top of the box, nor through the sides. • No destruction rate (pollutant is sufficiently long-lived)

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

9. 0 = (all flow rates in) – (all flow rates out) 0 = u W H b + q W L – u W H c Where c is the concentration in the entire city the general material balance eqn becomes: The equation indicates that the upwind concentration is added to the concentrations produced by the city. To find the worst case, you will need to know the wind speed, wind direction, mixing height, and upwind (background) concentration that corresponds to this worst case.

10. Example 6.1 A city 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/m3. The emission rate per unit are is q = 4 x 10-6 g/s.m2. what is the concentration c of CO over the city? = 25 μg/m3

11. Comments on the simple fixed-box model 1) The third and the sixth assumptions are the worst (why?). 2) The fixed-box models does not distinguish between area sources and point sources. Area sources: small sources that are large in number and usually 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.

12. … Comments on the simple fixed-box model 3) If you are laying out a new city, how would you lay it? (page 125). In light of this, would it be preferable to put your city in a valley? 4) For an existing city, what actions would you 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 only one specific meteorological condition. We know that meteorological conditions vary over the year.

13. Modifications to improve the fixed-box model 1) Hanna (1971) suggested a modification that allows one to divide the city into subareas and apply 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). 2) Changes in meteorological conditions (comment #5) can be taken into account by a. determine the frequency distribution of various values of wind direction, u, and of H b. Compute the concentration for each value using the fixed-box model

14. …Modifications to improve the fixed-box model c. Multiply the concentrations obtained in step b by the frequency and sum to find the annual average

15. Example 6.2 For the city 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 velocity 6 m/s and the same mixing height. What is the annual average concentration of carbon monoxide in this city? 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 = 25 μg/m3

16. …example 6.2 cont. Note that L is now 5km, not 15km For u = 6 m/s and H = 1000 m →

17. Graphical Representation of the Fixed-Box Model Equation (Fig. 6.2 in your textbook) Slope = (L/uH) Ambient air concentration, c Emission rate, q, g/s.km2

18. Example A pollutant concentration was calculated to be c1 with emission rate q1. If the Environmental Authority wishes to reduce the concentration to c2, compute the new allowable emission rate (q2) We can use graphical interpolation: OR Note this can be done only when the meteorological parameters are constant c1 c2 b q2 q1

19. Example 6.3 (fractional reduction in emission rate) The ambient air quality standard for particulates (TSP) in the USA in 1971 was 75 μg/m3 annual average. In 1970 the annual average particulate concentration measured at one monitoring station in downtown Chicago was 190 μg/m3. The background concentration was estimated to be 20 μg/m3. By what percentage would the emission rate of particulates have to be reduced below the 1970 level in order to meet the 1971 ambient air quality standard? c1 = 190 μg/m3 , c2 = 75 μg/m3 c1 c2 b q2 q1

20. Example 6.3 (fractional reduction in emission rate) c1 = 190 μg/m3 , c2 = 75 μg/m3 OR: you can use interpolation from the graph c1 c2 b q2 q1

21. 2) Diffusion Models • Called as diffusion models. However, they are actually dispersion models. • Such models usually use the Gaussian plume idea. Fig. 6.3 De Nevers

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

23. 2) Diffusion Models Description of Situation in Fig. 6.3 • The origin of the coordinate system 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 = physical stack height Δh = plume rise • Plume rises vertically at the beginning (since it has higher temperature and a vertical velocity), then levels off to travel in the x-direction (wind direction). • As the plume travels in the x-direction, it spreads in the y and z directions. • The actual mixing mechanism is the turbulent mixing; not the molecular diffusion. • What will happen if the molecular diffusion was the only mechanism?

24. 2) Diffusion Models … cont. Description of Situation in Fig. 6.3 • 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 only calculates the average value. • Therefore, results obtained by Gaussian plume calculations should be considered only as averages over periods of at least 10 minutes, and preferably one-half to one hour. • The Gaussian plume approach calculates only this average value

25. 2) Diffusion Models The Basic Gaussian Plume Equation • Where σy = horizontal dispersion coefficient (length units) σz= vertical dispersion coefficient (length units) • The name “Gaussian” came from the similarity between the above equation and the Gauss normal distribution function used in statistics. • The previous equation can also be written the following form:

26. Example 6.4 Q = 20 g/s of SO2 at Height H u = 3 m/s, At a distance of 1 km, σy = 30 m, σz = 20 m (given) Required: (at x = 1 km) • SO2 concentration at the center line of the plume • SO2 concentration at a point 60 m to the side of and 20 m below the centerline 2) Diffusion Models

27. … solution of example 6.4 2) Diffusion Models

28. What about σy and σz? (Dispersion coefficients) • σy ≠ σz ►► Spreading in the two directions are not equal • Most often σy > σz ►► Elliptical contour concentration at a given x . • Symmetry is disturbed near the ground. • To determine σy > σz , use figures 6.7 and 6.8 2) Diffusion Models

29. Figure 6.7 De Nevers • Horizontal dispersion coefficient

30. Figure 6.8 De Nevers • Vertical dispersion coefficient

31. Notes on Figures 6.7 and 6.8 • Both σy & σz are experimental quantities. The derivations of equations 6.24 and 6.25 do not agree with reality. • We will only use figures 6.7 and 6.8 to find σy & σz. • 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 beyond 1 km have been extrapolated. 2) Diffusion Models

32. What are the A to F categories? • A to F are levels of atmospheric stability (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 σy & σz values • On a cloudless winter night, ground cools by radiation to outer space and therefore cools the air near it. Hence, air forms an inversion layer. ►► Stable atmosphere and inhibiting the dispersion of pollutants and therefore small σy & σz values 2) Diffusion Models

33. Stability Classes • Table 3-1 Wark, Warner & Davis • Table 6-1 de Nevers

34. Example 6.5

35. Some Modifications of the Basic Gaussian Plume Equation • The effect of the ground • Mixing height limits and one dimensional spreading

36. a) The Effect of the Ground • Equation 6.27 assumes that the dispersion will continue vertically 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

37. … 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!)

38. Example 6.6 (effect of ground) Q = 20 g/s of SO2 at Height H u = 3 m/s, At a distance of 1 km, σy = 30 m, σz = 20 m (given) Required: (at x = 1 km) SO2 concentration at a point 60 m to the side of and 20 m below the centerline: a) for H = 20 m b) for H = 30 m 2) Diffusion Models

39. … example 6.6 a) For H = 20 mi.e. the concentration at the ground level itself (z = 0) (z – H)2 = (-H)2 = H2 (z + H)2 = (H)2 = H2 Therefore the answer will be exactly twice that in the 2nd part of example 6.4 c = (145 μg/m3) × 2 = 290 μg/m3 . b) For H = 30 m i.e. about 22 % greater than the basic plume equation (since the basic plume eqn does not take ground reflection into account.

40. Ground-Level Equation • Set z = 0 in the equation accounting for the ground effect: This is the most widely used equation because it applies directly to the problem of greatest practical interest, which is the ground-level concentration. This is the ground-level modification of equation 6.27. It takes reflection into account.

41. Using Figure 6.9 to estimate Ground-Level concentration Figure 6.9 in your text book describes a way of finding the concentration at the line on the ground directly under the centerline of the plume. → z = 0 and y = 0 cu/Q can be plotted against “x” to obtain figure 6.9. Note that the right-hand side depends on H, σy, and σz . Therefore, we should have a group of H curves. Also figure 6.9 is for category C stability only.

42. Example 6.8 (using figure 6.9) Q = 100 g/s at Height H = 50 m u = 3 m/s, and stability category is C At a distance of 1 km, σy = 30 m, σz = 20 m (given) Required: Estimate the ground-level concentrations directly below the CL of the plume at distances of 0.2, 0.4, 0.5, 1, 5, 10 km downwind 2) Diffusion Models

43. … example 6.8 (using figure 6.9) Using figure 6.9, we can read the values of cu/Q at each distance The third column is obtained by multiplying the 2nd column by 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 by inspection only 2) Diffusion Models

44. Plume Rise This equation is only correct for the dimensions shown. Correction is needed for stability classes other than C: → For A and B classes: multiply the result by 1.1 or1.2 → For D, E, and F classes: multiply the result by 0.8 or 0.9 Δh = plum rise in m Vs = stack exit velocity in m/s D = stack diameter in m u = wind speed in m/s P = pressure in millibars Ts = stack gas temperature in K Ta = atmospheric temperate in K 2) Diffusion Models

45. Example 6.9 2) Diffusion Models

46. Multiple Cell Models • Complex simultaneous reaction rate expressions (Figure 1.2) • Multiple cell modeling is used. The Urban Airshed Model UAM is an example this modeling type. • Model Description: • The airspace above the city is divided into multiple cells. Each cell is normally from 2 to 5 km each way and is treated separately from the other. • Four or six layers in the vertical direction, half below the mixing height and half above.

47. 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 (typically 3 to 6 minutes) by numerically integrating the mass balance equation (eqn 6.1) • Complex computations requiring data on: • Wind velocity and direction • Emissions of the ground-level cells • Solar inputs

48. …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 any cell and subprograms for deposition of the pollutant from the ground-level cells.

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

50. …How does the Model Work? • Then the model is re-run with different emission rates corresponding to proposed (or anticipated) future situations and the meteorology for that day. • In this way the model performs a prediction of the worst day situation under the proposed future emission pattern.