The Stack Height Requirements Implicit In the Federal Standards of Performance For New Stationary Sources

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1 Journal of the Air Pollution Control Association IN: (Print) (Online) Journal homepage: The tack ight Requirements Implicit In the Federal tandards of Performance For New tationary ources Wilbert L. Lee & Arthur C. tern To cite this article: Wilbert L. Lee & Arthur C. tern (1973) The tack ight Requirements Implicit In the Federal tandards of Performance For New tationary ources, Journal of the Air Pollution Control Association, 3:6, , DOI: / To link to this article: Published online: 15 Mar 01. ubmit your article to this journal Article views: 944 View related articles Citing articles: 3 View citing articles Full Terms & Conditions of access and use can be found at

2 The tack ight Requirements Implicit In the Federal tandards of Performance For New tationary ources Wilbert L. Lee and Arthur C. tern University of North Carolina The promulgation of Federal standards of performance for certain classes of new stationary sources requires that such sources have minimum stack heights to meet also the requirements of national air quality standards. The determination of minimum stack height is complicated by the fact that the performance and air quality standards are stated on different averaging time bases; that the extent of preemption of the assimilative capacity of the air by any individual source will vary among jurisdiciions and, in some cases, among different geographic areas of a single jurisdiction; and that some new sources will be designed to emit appreciably less than the performance standard requirement. However, these complications can be resolved and equations and charts prepared from which minimum stack height can be selected. On April 30, 1971, the Environmental Protection Agency (EPA) promulgated primary and secondary national air quality standards for particulate matter, sulfur oxides, and nitrogen dioxide 1 and on December 3, 1971, EPA promulgated emission standards for the emission of these three pollutants from new fossil-fuel fired steam generating plants, of particulate matter from new Portland cement plants and new incinerators, of sulfur oxides from new sulfuric acid plants, and of nitrogen oxides from new nitric acid plants (Table I). If one of the foregoing types of new plants were to be the only source of the regulated pollutant in a region, we can argue that its stack should be sufficiently high, that when its emission is at the maximum permissible limit, the secondary air.quality standard should not be exceeded at any point in the region. By selecting an appropriate stack plume dispersion formula and proper input parameters for use therein, a computation can be made for the stack height required. Air Quality The problem is more complex when either or both of the following occur. First, when the region is unwilling to have % of the air quality standard pre-empted by the new sole source, it may decide to commit only a given percentage, P, e.g., 0%, of the air quality standard to the new source, in which case the computation for effective stack height is based upon PC, e.g., 0.C s, where C s is the national air quality standard, instead of 1.0C s. The second case is where the air of the region is already polluted by the regulated pollutant. The level of present pollution can be called background level, C b, with respect to pollution from the proposed new source; or in fact, all new sources. When the level of C b is O.QC, then, if (1-0.6) C s or 0AC s were allowed exclusively to the new source, its effective stack height, H e, could be computed by using 0AC s, instead of 1.0C s, in the required computation. It is apparent that if C b exceeds C s, no new plant could be built since it would cause C b to still further exceed C s. Realistically, a region may wish to invoke both of the foregoing constraints by applying a working factor,, to C s in the effective stack height computation such that = - C b /C s ) (1) June 1973 Volume 3, No

3 / (mil Btu/hr) - 10,000 '- 9, ,000-7,000-6,000 5,000-4,000-3,000 -,000 1, ' 40 Figure 1. Effective stack height, H e, for particulate emission from fossil fuel fired steam generators. = Pf(l - Cb/Cs)(Eq. ) For given and plant capacity, K, the effective stack height is found from the nomogram when emission equals the emission standard, E s. For emission less than E l the effective stack height required should be calculated by using Equation ' O50' 0.30' Table I. Emission standards and air quality standards for new stationary sources. ource Fossil-fuel fired steam generator Portland cement Kiln Clinker cooler ulfuricacid plant Nitric acid plant Incinerator Pollutant Particulates ulfur dioxide Liquid fossil-fuel olid fossil-fuel Nitrogen Oxides Gaseous fossil-fuel Liquid fossil-fuel olid fossil-fuel Particulates Particulates ulfur Dioxide Nitrogen Oxides Particulates Emission tandard, E a Cone. 0.1 Ib/mil Btu Ib/ton 0.1 Ib/ton 4Ib/ton 3Ib/ton 0.08 gr/scf corr. to 1% CO Averaging time, hr 50' 90' ' 180' 00' ' ' econdary Air Quality tandard, C 3 Cone. Mg/m Averaging time 4 hr 4 hr 4 hr Annual Annual Annual 4 hr 4 hr 4 hr Annual 4 hr The factor, P, reflects not only the region's assessment of its intended future growth, but also its assessment of the relevance of the national air quality standard to its regional needs. It might be willing to use a higher value of P, if it felt that C s had in it a high factor of safety with respect to its region, even if the factor of safety were lower for some other part of the country. Another function that is served by P is to allow introduction into a standardized computational procedure for effective stack height of a means for accounting for geographic differences in topography. The topographical condition assumed in most dispersion computations is level terrain without substantial obstruction to wind flow. Where the topography is worse than an unimpeded level terrain, the appropriate corrective factor that needs to be applied is most easily introduced into the value of. Thus, if the topographic corrective factor is called /, and if P is allowed to retain its original definition of the percentage of the air quality standard the community is willing to have pre-empted by the new source, Equation 1 becomes = - C b /C s ) () Recommended values of / (Table II) were derived from the work of Berlyand. 3 Emissions The emission, Q, from new stationary sources can be expressed in compatible units by multiplying national emission standard, E s, by plant capacity, K, and a conversion factor, G. Thus: = E KG (3) Effective tack ight For the purpose of these computations, we have chosen to follow the Gaussian dispersion model 4 to establish the relationship among H e, K, and, when C s and E s are assigned the values promulgated by EPA (Table I). The basic equation for the centerline maximum ground level concentration is: n "max (4) where a v and a z are lateral and vertical dispersion parameters, respectively, e is the base of natural logarithms, and u is average wind speed through the layer between the effective stack height and the ground. 5 In the computation above, a y, a z, and u need to be chosen to represent the meteorological condition assumed. This basic relationship is subject to the interrelationships among a v, <r z, and u and the differences in averaging times implicit in the value of E s and C s, as stipulated in the promulgating regulations. Taking these matters into 506 Journal of the Air Pollution Control Association

4 account, the operative critical relationship derived for air quality standards on 4 hr averaging time basis, i.e., particulates and O is (Appendix I): H e = /_Q_\l/.J \scj (5) For fossil-fuel fired plants, for which the unit of capacity, KMB/H, is million Btu/hour, this equation becomes: H < - *(- sc, '-) (5a) For Portland cement and sulfuric acid plants, for which the unit of capacity, -KT/D, is tons/day, the equation becomes: H e = 8.87^ (5b) sc, For incinerators, for which the unit of capacity, K sc im, is standard cubic feet of flue gas per minute, corrected to 1% CO, the equation becomes: H, = 4.39(^ 1/-5 (5c) For air quality standards on annual averaging time basis, i.e., nitrogen oxides, the operative critical relationship that corresponds to equation 5 can be expressed as (Appendix I): ( O \ 1/- For fossil-fuel fired plants, for which the unit of capacity, KMB/H, is million Btu/hr, this equation becomes: K MB/H (mil Btu/hr; r- 10,000 9,000 8,000 7,000 6,000 5,000 : 4,000 3,000, a » H ( = 18.9l(- C (6a) For nitric acid plants, for which the unit of capacity, KT/D, is tons/day, the equation becomes: 1, ' = 4.6l(- scs (6b) By incorporating values of C s and E s from Table I into Equations 5, a-c and 6, a-b, nomograms of the H e -K- relationships for the several pollutants and new source categories previously noted have been derived (Figures 1-8). In using these nomograms, the known value is usually plant capacity K and the unknown value sought is the required effective stack height H e. The line connecting these two must pass through the appropriate value of *, which must be computed using Equation in which the value of C s is from Table I and the value of C b is obtained from air quality data summaries of the community in which the plant is to be located. The value of P is entirely judgmental; the value of / may be tentatively chosen from Table II ' Figure. Effective stack height, H e, for nitrogen oxides emission from solid fossil fuel fired steam generators (Equation ). For given and plant capacity, K, the effective stack height is found from the nomogram when emission equals the emission standard, E s, for solid fuel. When liquid or gas fuel is burned, and/or when emission is less than E 3, the effective stack height required should be calculated by using Equation 8,11, or both. June 1973 Volume 3, No

5 Table II. Recommended value of topographic factor. Factor f Level 1.00 Topography Hilly 0.70 Valley 0.50 K MB/H (mil Btu/hr) -10,000 r 9,000-8,000-7,000-6,000-5,000 ^4,000-3,000 -,000 1, q 0.50" ^ ^ ^ 50' 60 70' 80' ^ -^ ' Figure 3. Effective stack height, H e, for sulfur dioxide emission from solid fossil fuel fired steam generators (Equation ). For given and plant capacity, K, the effective stack height is found from the nomogram when emission equals the emission standard, E s, for solid fuel. When liquid or gas fuel is burned, and/or when emission is less than E l the effective stack height required should be calculated by using Equation 8,11, or both. 180' Emissions Lower than the Emission tandard In plotting Figures 1-8, E s has been given the value of the emission standard from Table I. If, however, it is known that the design of the new plant will limit the emission to less than E ) the stack need not be as high as the nomograms would indicate. Thus, if plant design limits emission to LE, where L is a factor less than unity, e.g., 0.8 E s, it will be seen that: Q = (LE )KG = (LK)E G (7) ince the nomograms are based on Equation 3, stack height under these circumstances may be read from the nomograms by entering capacity in the nomogram as a reduced capacity K\ in which: = LK (8) In Equations 7 and 8, the separate values of L for particulate matter, sulfur oxides, and nitrogen dioxide emissions should be designated as L P) L s, and L n, respectively. Physical tack ight Once the effective stack height required for a new stationary source is found, the physical stack height can be determined for any stack design conditions. The most convenient parameter that characterizes the plume rise of stack effluent is heat flux, F, which is given by F = where g is the acceleration of gravity, V s gas exit velocity, D stack inside diameter, T s and T a, gas and ambient temperature, absolute. There are a large number of formulae proposed for plume rise estimation. We have chosen Briggs' formula 6 for use in these computations. Ah =.67F 3l5 H s l5 /u (10) The physical stack height, H s, is then obtained by subtracting the plume rise, Ah, from the effective stack height, H e. This computational process has been converted into the two nomograms, 508 Journal of the Air Pollution Control Association

6 Figures 9 and 10, from which one can read the physical stack height, H s, for a given effective stack height, H e, obtainable from Figures 1-8, the stack parameters, V s, D, and T s, and the ambient temperature, T a (Appendix III). Nomograms For fossil-fuel fired steam generating plants, we have provided separate nomograms (Figures 1-3) for particulate matter, nitrogen oxides, and sulfur dioxide from solid-fuel fired plants. Each pollutant may be the determining factor for the required stack height when the applicable value of L is high. For liquid and gas fuel fired plants, a multiplier, A, which has been provided (Table III) for each pollutant can be directly applied to the effective stack height for solid fuel fired plants (Figures 1-3) such that where = AH. (11) H = effective stack height for liquid or gas-fuel-fired plants A = multiplier H es = effective stack height for solidfuel fired plants It can be assumed that Portland cement plants will have separate stacks for the kiln and the clinker cooler. Therefore, separate nomograms are operative for each, these nomograms (Figures 4 and 5) being derived from Equation 5b. ince incinerator and sulfuric acid plants must meet only one criterion each, one equation suffices for the determination of the stack height for each type of new plant. The nornogram for sulfuric acid plants (Figure 6) is derived from Equation 5b; the one for incinerators (Figure 7) from Equation 5c; and the one for nitric acid plants (Figure 8) from Equation 6b. Figure 9 represents the relation between the heat flux, F, the other stack parameters, V s, D, and T s, and ambient temperature, T a. For given F and H e, one can obtain the physical stack height, H s, from Figure 10. KT/D (tons/day) r- 7,000 H e 6, ,000-3,000 -,000 1,000 ^ ' "o.5b : ' ^ 8 """" ""*"" "-» ^. 30 ""** ^, 3 " ' J 1 00 Figure 4. Effective stack height, H e, for particulate emission from Portland cement plant kilns (Equation ). For given and plant capacity, K, the effective stack height is found from the nomogram when emission equals the emission standard, E s, for kilns. For emission less than E s, the effective stack height required should be calculated by using Equation 8. Table III. Fuel fired olid Liquid Gas Values of multiplier A in Eq. (ll). a Pollutant Particulates NO X (Fig. 1) (Fig. ) 1 1 l a l a O (Fig. 3) a ee Eq. 8 for reduction in stack height for design limits below E s. June 1973 Volume 3, No

7 K T/D (tons/day; - 7,000-6,000-5,000 4,000-3,000 -,000 1, " Figure 5. Effective stack height, H e, for participate emission from Portland cement plant clinker coolers (Equation ). For given and plant capacity, K, the effective stack height is found from the nomogram when emission equals the emission standard, E 3, for clinker coolers. For emission less than E s, the effective stack height required should be calculated by using Equation 8. ummary A set of nomograms are presented by the use of which effective and physical stack heights required for new steam generating, Portland cement, sulfuric acid, incinerator and nitric acid plants may be determined to meet simultaneously EPA requirements for air quality and emission standards. Acknowledgment This research was supported by Research Grant Number APO-1130 from the Environmental Protection Agency, Research Triangle Park, N. C. Appendix I Derivation of Equations 5 and 6 Centerline ground level concentration downwind from an elevated point source is given by the Gaussian dispersion model as: C{x, 0, 0, H e ) = KdyGzU Xexp\-U ) I a-d ' ' The ground level concentration is affected not only by plant design parameters Q and H e, but also by mean wind speed u, and dispersion parameters <j v and <7z. According to the Nashville study on atmospheric stability 7 the slightly unstable condition, Bi, has been observed with the highest frequency. ince for standardized computations the most commonly observed meteorological condition should be used, the Brookhaven gustiness class, Bi, has been chosen. The dispersion parameters for Bi gustiness class are expressed in terms of downwind distance x as = 0.36a; 0-86 (1-) = 0.33a; 0-86 (1-3) The mean wind speed, u, can be estimated from the following relation: 1 C u = I uo ttejo dz (1-4) where z is a height from the ground, and Wo is the wind speed at the reference elevation z 0. Referring to the Brookhaven gustiness class 7 and the Pasquill stability categories, 4 the value of u 0 and Zo are set to be 3.8 m/sec and 10 m, and the exponent, n, is set to be Then Equation (1-4) becomes: u = 1.687ff P 0-5 (1-5) The maximum ground level concentration, C max, can be derived from Equation (1-1) as: n (1-6) \j max ~~ we u H P where e is the base of natural logarithm, (vz/o-y) is given by Equation (1-) and (1-3), and u by Equation (1-5). While Equation (1-6) is valid for the range of sampling time from few minutes to 90 min, the national air quality standard for O and particulate matter are specified on 4-hr averaging time. A conversion procedure can be obtained from Hino's extensive study on the effect of sampling time on the maximum concentration. 10 If Ci and C denote the maximum ground level concentrations at different averaging times, U and t, respectively, then we have: tt = d-7) ubstituting & = C ma x, C = C, k = 1 hr, and t = 4 hr into Equation (1-7) we have: (1-8) Combination of Equations (1-5), (1-6), and (1-8) leads to the final computational formula for effective stack height as: ( O 1/-5 ince the air quality standard for NO is based upon annual averaging time, the following procedures have been adopted to convert annual averaging time to hourly averaging time and where C d = y = Cy \i) (C d)so = air quality standard of O on 4-hr averaging time, 60Mg/m 3 (C sv )so = air quality standard of O on annual averaging time, 60 Mg/ m3 th, t d, and t v = hourly, daily and annual averaging times, respectively. Ch, C d) and C y = concentration of NO Z on averaging times, t h, td, and t y, respectively. 510 Journal of the Air Pollution Control Association

8 Figure 6. Effective stack height, H e, for sulfur dioxide emission from sulfuric acid plants (Equation ). For given and plant capacity, K, the effective stack height is found from the nomogram when emission equals the emission standard, E s, for sulfuric acid plants. For emission less than E 3, the effective stack height required should be calculated by using Equation 8. KT/D (tons/day) 5,000 4,000 3, Combination of Equations (I-10a) and (I-10b) yields:, ' (1-11) ubstituting Ch = C max, C y = C, h = 1 hr, and t y = 8760 hr into Equation (1-11) leads to: C max = 1.C, (1-1) The final computational formula for effective stack height, therefore, is obtained as Q \ 1/.5 1, s Appendix II Derivation of Equations 5a through 6b The basic equations used in the standardized computation are: Q = E KG (II-l) and for sulfur dioxide and particulates, Q \ 1/.5 H e = 0197^j and for nitrogen oxides ( 0 ic 1/-5 ince the national air quality standard, C ) is expressed in terms of ng/m 3, the emission rate, Q, should be expressed in terms of /ig/sec. For fossil-fuel fired steam plants, the emission standard, E s, is specified in terms of lb/mill Btu, and the plant capacity, KUB/H, is expressed in terms of mill Btu/hr. Therefore, the factor, G, to convert the emission rate unit lb/hr to ^g/sec is: X 106 G = 3600 sec/hr = 1.6 X 10 6 [(Mg c)/(lb/hr)] Figure 7. Effective stack height, H e, for particulate emission from incinerators (Equation ). For given and plant capacity, K, the effective stack height is found from the nomogram when emission equals the emission standard, E s, for incinerators. For emission less than E s, the effective stack height required should be calculated by using Equation K scfm (scfm) r- 30,000-0,000 10,000 9,000 8,000 7,000 6,000 5,000-4,000-3,000 -,000 1, June 1973 Volume 3, No l.oo-q O ' ^

9 KT/D (tons/day) - 5,000-4,000-3,000 s 1.00-q 5-i Figure 8. Effective stack height, H e, for nitrogen oxides emission from nitric acid plants (Equation ). For given and plant capacity, K, the effective stack height is found from the nomogram when emission equals the emission standard, E 8, for nitric acid plants. For emission less than E s, the effective stack height required should be calculated by using Equation 8.., "0.0 45' 50' Then, Equation (II-l) becomes: 1, v s (m/sec) ' ' Q = 1.6 X 10 5 KMB/HE (II-3) ubstitution of Equation (II-3) into Equations (II-a) and (II-b), separatively, yields: H ( and = 0.197( - 6 X 105 ijc MB /H^A 1/i!5 C / ( IT ; sc. C \ 1/ 5:5 [m] For Portland cement, sulfuric acid, and nitric acid plants, the emission standard, E s, is specified in terms of lb/ ton, and the plant capacity, KT/D, is expressed in terms of tons/day. Therefore, the factor, G, to convert the emission rate unit lb/day to Mg/sec is: X 10 6 Mg/lb ~ 3600 X 4 sec/day = 5.5 X 10 3 [(jug/sec)/(lb/day)] -6 Then, the working equation can be obtained by substituting this conversion factor, G, and Equation (II-l) into Equations (II-a) and (II-b), separatively: /5.5 X 103 E \ 1/. H, = \ C [m] (H-5a) and H e. = 4. sc, [m] (n-5b) Figure 9. Calculation of heat flux, F, of hot plume from stationary sources. For given plant design parameters, stack exit velocity V s, stack exit temperature Ts, and stack diameter D, and ambient air temperature T a, the heat flux can be obtained from the nomogram. For example, when V s = 14.9 m/sec, T a = 70 F = 530 R, T s = 40 F = 880R", T /(T T a) =.51, D = 5 m, F = 365 mvseca 51 Journal of the Air Pollution Control Association

10 For incinerators, the emission standard, E ) is specified in terms of grains/scf corrected to 1% CO, and the plant capacity, K ac tm, is expressed in terms of scfm corrected to 1% CO. Therefore, the conversion factor, G, is: X 10 6 Mg/lb ~ 7000 grains/lb X 60 sec/min = 1.08 X 10 3 [(Mg/sec)/(grains/min) ] and the working equation is: F (m 4 /sec 3 ) 5,000 4,500 4,000 sc s [m] (II-6) Appendix III Determination of Physical tack ight The effective stack height is the sum of the physical stack height and the plume rise, i.e., H e = H s + Ah (III-l) According to Briggs 6 the plume rise of stack effluent is given by Ah =.67F 3 ' 5 H s /u (111-) ubstitution of Equation (III-) into Equation (III-l) yields, 3,000,000 (HI-3) In the above equation, wind speed, u, is the average wind speed through the layer from the ground to the effective stack height, H e, which is given by Equation (1-5). For simplicity, however, the wind speed at the physical stack height is used instead, i.e., ( H M =.19 (III-4) The difference in wind speeds given by Equations (1-5) and (III-4) is, in general, negligibly small. From Equations (III-3) and (III-4), one can obtain the equation that has been used in preparing the nomogram; i.e. Figure 10. Calculation of physical stack height, H a, from effective stack height, H e, and heat flux, F. For given H e and F obtained from Figures 1-9, the physical stack height required is found from the nomogram. H e = H s + 1.5F 3 > 5 H s s w (III-5) References 1. Environmental Protection Agency, "National primary and secondary ambient air quality standards," Federal Register, 36: 8187 (April 30, 1971).. Environmental. Protection Agency, "tandards of performance for new stationary sources," Federal Register, 36: M. E. Berlyand, "Investigations of atmospheric diffusion providing a meteorological basic for air pollution control," Atmos. Environ., 6: 379 (197). 4. F. Pasquill, "The estimation of the dispersion of windborne material," Meteorol. Mag., 90(1063): 33 (1961). 5. G. H. trom, "Atmospheric Dispersion of tack Effluents," in Air Pollution, nd Ed., Vol. I. Edited by A. C. tern, Academic Press, New York, p G. A. Briggs, "Plume Rise," AEC Critical Review eries, U.. Atomic Energy Commission, Nov. 1969, pp D. M. Baulch, "Relation of gustiness to sulfur dioxide concentration," /. Air Poll. Control Assoc, 1(11): 539 (Nov 196). 8. I. A. inger and M. E. mith, "Atmospheric dispersion at Brookhaven National Laboratory," Intern. J. Air Water Poll, 10: 15 (Feb. 1966). 9. P. M. Jones, M. A. B. DeLarrinage, and C. B. Wilson, "The urban wind velocity profile," Atmos. Environ., 5: 89 (Feb. 1971). 10. M. Hino, "Maximum concentration and sampling time," Atmos. Environ., : 149 (March 1968). Mr. Lee is associated with, and Mr. tern is a professor in the Department of Environmental cience and Engineering, chool of Public alth, University of North Carolina, Chapel Hill, N.C This paper was presented as Paper No at the 65th Annual Meeting of APCA in Miami Beach in June 197. June 1973 Volume 3, No