Empirical Relationships Between Time-Averaged SO2 Concentrations Thomas L. Montgomery* and Jesse H. Coleman Tennessee Valley Authority, Muscle Schoals, Ala. 35660
w This paper presents values for two types of SO:! concentration ratios: (1) ratios of peak-to-mean concentrations and (2) ratios of maximum concentrations. These ratios may be used to project measured or calculated concentrations from one time period to another. Peak-to-mean SO:! concentration ratios have been derived from 2f/2 years of ambient SO:! data collected by 14 SO2 monitors near the TVA Paradise coal-fired power plant in Kentucky. Regressions of peak-to-mean ratios vs. ratio percentile were computed for mean time periods of 1,2, 3, and 24 hr, 1 month, and 1 year. From these regressions peak-to-mean ratios for the 99th, 95th, 50th, and 5th percentiles were reported. Average peak-to-mean ratios are also reported. Ratios of maximum SO:! concentrations were derived from data collected at eight of TVA’s coal-fired power plants. For each of these plants, ratios were computed for maximum 1-hr concentrations to maximum T-hour concentrations, where the Thour period ranged over times of 3 and 24 hr, 1 month, and 1 year. The relationships between these ratios and stack height are presented graphically.
Ground-level concentrations of sulfur dioxide (SO:!) emitted from coal-fired power plants are highly variable in time. A monitor near such a plant may record concentrations ranging over two or three orders of magnitude. These variations, as seen on the record of a stationary groundlevel SO:! monitor, depend primarily on meteorological conditions, the relative position of the monitor and plume, and on data averaging time resulting from instrument response time and data handling (1-4). Information on the relationships between concentration variations and averaging times is needed now because air quality standards have been promulgated for SO2 and other gases in terms of averaging times ranging from less than 1 hr to 1 year. Most dispersion equations are used to predict concentrations for periods of 1 hr or less. Concentrations for longer periods can be predicted by projecting the concentrations for these short periods to longer periods using ratios of time-averaged concentrations. This paper provides empirical values for two types of SO:! concentration ratios (peak-to-mean and maximum ratios) used to project concentrations from one averaging time to another. These two types of ratios are computed differently and must be interpreted differently. They have complementary uses, however. Ratios of peak SO:! concentrations (maximum 5-min average) to mean SO:! concentrations were developed from data recorded over 2.5 years by a network of 14 ambient SO2 monitors at the TVA Paradise Steam Plant in Kentucky. These peak-to-mean concentration ratios are reported for mean time periods of 1, 2, 3, 24, 730 (1 month), and 8760 (1year) hr. For each of these ratio classes, the average ratio and the 5th, 50th, 95th, and 99th percentile ratios were determined. The dependence of peak-to-mean ratios upon the length of time of the mean concentration period was determined and is presented graphically. From this, peak-to-mean ratios may be determined for time periods other than those listed above. A limitation of the above peak-to-mean ratios, as developed in this analysis, is that they cannot be used to project
maximum concentrations. However, a second type of ratio, ratios of maximum SO:! concentrations defined as maximum ratios, may be used to project maximum 1-hr concentrations to maximum concentrations of 3 hr, 24 hr, 1 month, and annual time periods. These ratios were developed from data collected at eight TVA coal-fired power plants. The relationships between these maximum ratios and stack height are also presented graphically. Ambient SO:! Monitoring Data for Peak-to-Mean Ratios Ambient SO:! monitoring data from the Paradise Steam Plant air monitoring network were used to develop peakto-mean concentration ratios. The Paradise Steam Plant, one of the world’s largest coal-fired power plants, has two 704-MW units with stacks 183 meters tall and one 1150MW unit with a stack 244 meters tall. The plant is located among rolling hills 60-90 meters high in the western Kentucky coal basin about 130 km north of Nashville, Tenn. The terrain in the area is aerodynamically rough, consisting of woodland, small farms, and strip mine spoil areas. The atmospheric dispersion condition associated with the highest ground-level SO:! concentrations a t Paradise Steam Plant is plume trapping ( 5 ) ,which occurs about 40 days a year at Paradise (6).On these days, elevated concentrations of SO2 persist for about 2-4 hr. Coning and inversion break-up dispersion conditions ( 5 ) occur more frequently but cause lower concentrations. No attempt was made in this analysis to identify ratios of time-averaged concentrations mitored during the above individual dispersion conditions. Also, no attempt was made to account for concentration ratios based on differences in plant emissions or meteorological conditions. The Paradise air-monitoring network for this peak-tomean ratio analysis included 14 Instrument Development Corp. conductivity-type SO:! monitors. These monitors are checked twice weekly for proper operation and interference from small local SO2 sources such as burning coal waste piles and home heating by coal. Interferences are noted and disregarded when the record is read. Serious sources of interference are eliminated or, if this cannot be done, monitors are relocated. The monitors were located within 3-17 km of the plant in the 22.5-degree prevailing downwind sector (Figure 1).Data from the SO:! monitors were collected in the form of cumulative digitized readings taken a t 5-min intervals. These data were telemetered to a central facility where all data were recorded on paper punched tape. Ambient SO2 Monitoring Data for M a x i m u m Ratios Sulfur dioxide data from the ambient air-monitoring networks at eight of TVA’s coal-fired power plant including Paradise were used to develop maximum ratios. These eight plants are listed in Table I. For these plants, unit sizes range from 125-1150 MW, and the stack heights range from 76-244 meters (Table I). Various numbers of ambient Son-monitoring instruments are located around each of the eight plants. Paradise Steam Plant is monitored by 16 instruments, including the 14 Instrument Development Corp. instruments described earlier and two Thomas autometers, not in the prevailing downwind direction (Figure 1).The SO:! instruments a t the other seven plants are Thomas autometers-conductivity Volume 9, Number 10, October 1975
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instruments that record continuous SO2 concentrations and also 1-hr averages. Each of these SO2 monitors is checked for interferences in the same manner as the monitors in the Paradise network. The number of instruments and the number of years of SO2 records used in this analysis for each of the plants are given in Table I. Data Reduction and Determination of Concentration Ratios Peak-to-Mean Ratios. The punched paper tape data collected a t Paradise Steam Plant were processed to calculate the basic parameters used in evaluating the peak-tomean ratios. Data reduction consisted of the following three steps: 1. Average SO2 concentrations for each instrument were computed for 1-, 2-, 3-, and 24-hr, 1-month, and 1-year periods by averaging all 5-min averages within the selected period. Daily averages were computed from midnight to midnight. Two-hr averages were taken from midnight to 2 a.m., 2 to 4 a.m., and so foith. Three-hour averages were taken from midnight to 3 a.m., 3 to 6 a.m., and so forth. 2. The highest 5-min average concentration which occurred during each of the above time periods was determined and defined as the peak concentration during that time period. 3. Peak-to-mean ratios were then computed for each time period for each instrument; that is, a peak-to-1-hr ratio was computed for each hour of data collected by each instrument, and so forth. In an attempt to exclude data resulting from sources other than the power plant plume, hourly periods with average SO2 concentrations less than 0.10 ppm were excluded. Also, any 2-, 3-, or 24-hr period in which there was not at least 1 hr with an average SO2 concentration of 0.10 ppm or greater was also excluded. Monthly concentrations were excluded if the peak SO2 concentration did not equal or exceed 0.3 ppm.
Maximum Ratios. Strip charts were removed from the Thomas autometers weekly, checked for indications of instrument malfunction, and then interpreted. Values 'for 1-hr SO2 averages were punched on data cards and computer processed to calculate T-hour averages for 3-, 24-, 730- (1month), and 8760-hr (1year) periods. Concentration records for each year were examined for each instrument in each of the eight power plant monitoring networks. The maximum 1-hr-average concentration recorded by a given instrument during a single year was identified as were the maximum 3- and 24-hour, and monthly concentrations during the same year. From these data and the annual average, four maximum ratios were computed: maximum 1-hr average to maximum 3-hr average; maximum 1-hr average to maximum 24-hr average;
Table I. T V A Coal-Fired Power Plant Design and SO, Monitoring Network Information No. of
so,
Power plant
Shawnee Kingston Jo hnsonvil le Colbert Allen Gallatin Pa ra d ise Bull R u n
Total rated capacity, MW
No. of stacks
1,750 1,700 1,485 1,396 990 1,255 2,558 950
10 9 8 5 3 2 3 1
0
0
Figure 1. Paradise steam plant ambient air monitoring network 0 SO2 instrument Meteorologicalstation
954
Environmental Science & Technology
instruments in Time Average network of stack for this record, height, m analysis years
76 86 92 104 122 152 203 244
1
2
3
5 3 4 1 1 3 16 6
4
k , lometerr
5
6
3 4 3 3 3 2 3 3
assigned. A p t h percentile is the ratio that is equaled or exceeded by p percent of the ratios in its peak-to-mean ratio class. For example, the 95th percentile of a peak-to-mean ratio class is that ratio equaled or exceeded by 95% of the ratios in that class. Data in many of the peak-to-mean classes appear to follow a log-normal distribution except that they have a lower bound of 1 instead of zero. Thus, a new parameter, "peak-to-mean ratio minus 1," was introAnalysis of Concentration Ratios duced to adjust the lower bound to zero. This parameter was used for the peak-to-mean ratio classes of time periods Peak-to-Mean Ratio Analysis. Peak-to-mean ratios of 1, 2, 3, and 24 hr but not for peak-to-month and peakhave upper and lower bounds governed by two conditions. to-year ratio classes since all of the ratios in these two First, no peak-to-mean ratio can be less than 1. Second, classes were large compared to unity. For the averaging peak-to-mean ratios have upper bounds determined by the times of 1, 2, 3, and 24 hr, the peak-to-mean-minus-1 averaging times involved. For example, since the peak values were plotted against their corresponding percentile values discussed here are 5-min (l/12 hr) averages, peak-tovalues on logarithmic-probability graph paper. The line of 1-hr averages have an upper bound of 12, which occurs best fit was then determined by the method of least when an instrument registers zero for all but one of the squares-that is, a regression of the logarithm of the peak5-min periods during an hour. Similarly, peak-to-2-hr and to-mean ratios minus 1 upon the probit of the correspondpeak-to-24-hr ratios have upper bounds of 24 and 288, reing percentile values was computed for each of these four spectively. ratio classes. For ratio classes with averaging times of 1 Peak-to-mean ratios were grouped into frequency month and 1 year, the parameter "peak-to-mean" was groups, and to each of these groups a percentile value was treated similarly. Each of these regressions had a correlation coefficient of -0.98 or better. Examples of the graphs obtained are shown in Figures 2 and 3, where the peak-to1-hr ratio minus 1 and peak-to-24-hr ratio minus 1 data are Table II. Maximum SO, Concentration Ratios TVA Coal-Fired Power Plants displayed with the corresponding regression lines. Figures 2 and 3 also illustrate that no correction was made to account Maximum ratio for the fact that the log-normal distribution, which has no (Maximum I-hr average to maximum T-hr average concentration ratio) upper bound, was used to describe data that have an upper (dimensionless) bound. This is seen by observing that the regression lines, T= T = 730 when extended to the left, intersect the line segments T = 24 hr, Av stack 8760 hr, marking the upper bounds. However, no data points were 1 month 1 year hr height, m T = 3 hr Power plant found near the upper bounds, and as mentioned by Ledbet( 7 ) , extrapolation of the log-normal curve to extreme ter 82 Shawnee 76 1.6 5.8 32 values is poor practice. The 5th, 50th, 95th, and 99th per86 1.5 6.0 51 120 Kingston centiles were calculated from regression lines for all pre92 1.5 5.8 61 130 Johnsonville viously mentioned ratio classes (Table 111). Average values 5.8 50 110 Colbert 104 1.2 and corresponding number of data points were also calcu110 6.8 64 Allen 122 1.7 lated for each of the ratio classes (Table 111). 5.1 34 120 Gal la t in 152 1.3 Peak-to-mean ratios were compared to the length of time 120 6.2 60 203 1.4 Pa rad i se over which the me-n concentrations were computed. Data 8.2 56 190 Bull R u n 1.7 244 ~-from Table I11 were subjected to the most appropriate remaximum 1-hr average to maximum monthly average; and maximum 1-hr average to annual average. For given time class ratios, the ratios for all the instruments in a plant's network and for all its years of data were averaged to obtain a single ratio of that class that could be associated with the plant. The results are recorded in Table I1 and are associated with average plant stack height.
, c , I
I
:?
I
,,-,us.
ZG",,.\S
5
5;
3 :IcIc'Ic
::.,:,,
ij
t L 0 .
1,
2.
";
z=>o
,lr.I3::::,-
Figure 2. Cumulative frequency distribution of parameter pea k-toI-hr SO2 concentration ratio minus 1"
L1 7-+-
"
I
a
9'
99
939
QYY
> I
Figure 3. Cumulative frequency distribution of parameter "peak-to24-hr SOp concentration ratio minus 1" Volume 9, Number 10, October 1975
955
gression analysis as follows: Linear regression was used for averaging times up to 3 hr and logarithmic regression was used for averaging times of 24 hr and greater. The resulting regression lines were extrapolated and smoothly joined. The linear regressions were computed under the constraint that the line pass through the point representing 5 min and a peak-to-mean ratio of 1 since the ratio of peak concentration (maximum 5-min average) to a 5-min-average concentration is exactly 1.0. The resulting lines from these analyses were plotted on logarithmic paper as shown in Figure 4. T o increase the accuracy of the approximations of peakto-mean ratios for short time periods, the above linear regressions were plotted on linear paper for averaging times of 1 , 2 , and 3 hr (Figure 5 ) . The lines in Figure 5 have correlation coefficients of 0.98 or greater and provide for more accurate estimation of the ratios for mean time periods of 3 hr and less. Analysis of Maximum Concentration Ratios. There was a wide range in the stack heights of the power plants from which the ratios of maximum concentrations were derived. Thus, it was possible to determine the relationship between stack height and maximum concentration ratios. The data in Table I1 were used as the basis for linear regression analysis. A least-squares regression was performed for each type of ratio listed in Table 11. The regression lines that were obtained are plotted along with intervals indicating the standard error of estimate in Figure 6.
Discussion Since peak-to-mean ratios are highly variable, great care should be exercised in choosing an appropriate ratio when
needed. The data presented in Figures 2 and 3 indicate that peak-to-mean ratios, for mean time periods of 1 and 24 hr, vary by considerably large factors. Examination of the range of the 5th and 95th percentile ratios (Table 111) indicates that this variability extends to all ratio classes. In all cases within a given ratio class, the 5th percentile ratio was more than three times greater than the 95th percentile ratio. In general, peak-to-mean ratios presented here are lower than those of Gifford (8) for elevated sources and those of Singer (2). However, as shown in both of these papers, lower ratios are expected with increasing distance from the source. Most of the SO2 monitors used in this study are a t greater distances than those used in either of these previous studies. Peak-to-mean ratios are strongly dependent upon the time periods of the concentrations. Gifford (8) and Singer ( I ) suggest a power law dependence of peak-to-mean ratios upon averaging times. This type of dependence is demonstrated by a high correlation between peak-to-mean ratios and mean time periods ranging from 24 hr to 1 year (Figure 4). However, Ramsdell and Hinds (4), using data for shorttime periods, suggest that peak-to-mean ratios increase more slowly than would be predicted by a power law dependence. Examination of peak-to-mean ratios for time periods of only a few hours (Table 111) suggest a linear relationship for these time periods (Figure 5). Figures 4 and 5 can be used to obtain peak-to-mean ratios not given in Table 111. The method used here to arrive a t ratios of maximum concentrations involves nothing more than an inspection of monitoring records and the identification of various maxi-
Paradise Steam Plant
,I
Peak-to-meanratio for given mean time period (dimensionless) 1
Ratio parameter
1 hr
2 hr
3 hr
24 hr month 1 year
-
1r i: I
LYEPlG:ib
1
-
12
-
,
I
9 0 -
I -
/
T l M l !*In)
Flgure 4. Relationship between peak-to-mean ratios and averaging time for averaging times of 1 year and less
956
-
11
Table I II. Peak-to-Mean SO, Concentration Ratios
Environmental Science & Technology
Figure 6. Relationship between maximum SO:! concentration ratios and stack height
mum concentrations. This data analysis method produces a less complete display of data than the method of Larsen (3, 9-1 1), and does not allow the projection of lower concentrations than the maximum. These disadvantages are perhaps balanced by two advantages. First, the method used here is simple to apply since even a vast record may be inspected rapidly without recourse to large electronic computers. Second, no assumptions are made about the shape of the concentration frequency distribution. As Larsen (9) and Pollack (12) point out, the frequency distribution of concentrations from single sources is not always log normal, not well known, and probably quite complicated. Thus, this method might be applicable to other applications where projections of maximum concentrations must be made from data of unknown distribution. Regressions of maximum concentration ratios against power plant stack height (Figure 6) indicated that ratios of maximum l - h r concentration to maximum 3- and 24-hr concentrations do not vary significantly with stack height. However, ratios of maximum l - h r concentration to maximum monthly and annual concentrations do increase with increasing stack height. This indicates the effectiveness of
tall stacks in reducing maximums of SO2 concentrations for long time-averaging periods. Literature Cited Singer, I. A., J. Air Pollut. Control Assoc., 11, 336 (1961). (2) Singer, I. A., et al., ibid., 13,40 (1963). (3) Larsen, R. I., ibid., 19,24 (1969). (4) Ramsdell, J. V., Hinds, W. T., Atmos. Enuiron., 5 , 483 (1971). ( 5 ) Carpenter, S. B., et al., J . Air Pollut. Control Assoc., 21, 491
(1)
(1971). (6) Leavitt, J. M., et al., ibid., 400. (7) Ledbetter, J. O:, Enuiron. Lett., 3, 159 (1972). (8) Gifford, F., Znt. J . Air Water Pollut., 3, 253 (1960). (9) Larsen, R. I., J . Air Pollut. Control Assoc., 23,933 (1973). (10) Larsen, R. I., ibid., 24,551 (1974). (11) Larsen, R. I., “A Mathematical Model for Relating Air Quali-
t y Measurements to Air Quality Standards,” US.Environmental Protection Agency AP-89 (1971). (12) Pollack, R. I., “Studies of Pollutant Concentration Frequency Distributions,” PhD Dissertation, Polytechnic Institute of
Brooklyn, 1974.
Received for review October 29, 1974. Accepted J u n e 2, 1975. A preliminary version of this paper was presented at the American Meteorological Society Conference on Air Pollution Meteorology, Raleigh, N.C., April 5-8, 1971.
Determination of Dissolved Gases in Water by Diffusion and Gas Chromatographic Techniques Heinz P. Kollig,* James W. Falco, and Frank E. Stancil, Jr. Environmental Protection Agency, Southeast Environmental Research Laboratory, College Station Road, Athens, Ga. 30601
w A method has been developed for the determination of dissolved oxygen, nitrogen, and carbon dioxide in water. The gases diffuse from the water through a plastic membrane. A stream of helium gas carries the diffused gases to a dual column gas chromatographic trace gas analyzer equipped with Helium Ionization Detectors. Calibration of the gas probes is performed in a water bath through which analyzed air containing a predetermined amount of carbon dioxide has been bubbled. The system is estimated to have a sensitivity of 5-10 Mg/l. of dissolved gas in water. A knowledge of the distribution of dissolved gases, in particular oxygen, nitrogen, and carbon dioxide, in aquatic ecosystems is of utmost importance to the understanding of microbial behavior in these systems. The literature contains numerous procedures for the determination of dissolved oxygen in aqueous systems. Standard Methods ( I ) describes the Winkler and the electrometric methods, and McKeown et al. ( 2 ) compared them. Clark et al. ( 3 ) introduced the oxgyen-permeable membrane in solid electrode systems. Various modifications of the membrane electrode, both the polarographic as well as the galvanic type, have been published since (4-9). However, to date, no simple method has been available for the determination of nitrogen gas or free carbon dioxide in aqueous systems. The Aquatic Ecosystem Simulator (AEcoS) of the U S . Environmental Protection Agency, Southeast Environmental Research Laboratory, Athens, Ga., required an instrumental method for the simultaneous analysis of dissolved gases in aquatic ecosystems. The AEcoS houses a flow
channel 19.5 meters long, 46 cm wide, and 46 cm deep. Sampling stations are located at 2.4-meter intervals for chemical characterization of the water, including determination of dissolved gases. Investigations led to the development of an automatic system that will accept nine different sample streams for the analysis of oxygen, nitrogen, and carbon dioxide. Experimental Silastic, a silicone rubber manufactured by Dow Corning Corp. (Midland, Mich. 48640), was chosen as the membrane material for the dissolved gas probe. The material should have the following properties: does not change in composition over a period of time by leaching of its components has a high transmission rate for gases does not provide nutrients for bacterial and fungal growth does not harden, oxidize, or deteriorate over long periods of use can withstand repeated sterilization without altering shape, strength, clarity, or flexibility may be bonded to itself or other materials has a transmission rate for dissolved gases of about 100 times that of Teflon. After one year of operation in the laboratory, Silastic, which was also tested by Chuck (10) in the cardiovascular system, appears t o meet these requirements. The gas probe was constructed by mounting a 60-mm piece of Silastic tubing (6 mm i.d. X 1 2 mm 0.d.) between two pieces of 6-mm stainless steel tubing, using an epoxy glue, so that 50 mm of the Silastic tubing was exposed for Volume 9, Number IO, October 1975
957
