IPA Contract No.: 68-DO-0125 . EPA/400/1-91/029
1
FINAL REPORT
DEVELOPMENT OF ANNUAUZEO
SO, EMISSION CONVERSION FACTORS
Prepared by:
Radian Corporation
Prepared for
Larry Montgomery
Office of Atmospheric and Indoor Air Progran
U.S. Environmental Protection Agency
401 M Street, SW
Washington, DC 20460
June 5,1991
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ABSTRACT
m
*
This report documents the results of a study to develop factors that can be used to estimate
utflity untts's sulfur dioxide (SOj) allowable emissions uw'er the Qean Air Act Amendments of 1991. To
accomplish the objective, a database of utility units continuous emission monitoring systems' results was
constructed and factors were developed based on accepted EPA statistical methods. The database is a
cross-sectional representation of utflity plants with units of different sizes, with or without flue gas
desuNurization systems, and different coals. Factors were developed using various averaging periods
end exeeedanca policies being Implemented by the States. Results are presented for utOity units with
and without flue gas desuHurization systems.
1
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*:•.>
CONTENTS
Page
Figures '•. v
Tablet vl
1.0 Introduction 1
1.1 Objective 2
1.2 Technical Approach 2
2.0 Data Review and Analysis 3
* ' *
3.0 Factors Development 6
4.0 Results 10
*
Conclusions 18
6.0 References 19
Appendix A Descriptive Statistics of Utility Bolers
Used In This Analysis A-l
Appendbc B Comparison of Two Emission Factors Calculation Methods B-1
Appendix C Summary of Conversion Factors C-1
Appendbc D Conversion Factors for Selected ProbaMJUes D-1
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figure
I
f
2
3
Non-FCC • Low-SuJfur Coal
FGDLovt-SutfurCoal
FGDHIgh-SiifurCaaJ
13
14
15
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UST OF TABLES
1
2
3
Ust of Utlfty Units
Estimated Mean With Minimum and Maximum Values
Mean and Cumulative Probablfty to Cow 06and 99 Percent
of tha Unit Population
11
17
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•r.
TWe IV of the Qean Air Act Amendments of 1990 establishes a system of allowances for sulfur
dioxide (SOj) emissions from utility units. The legislation provides for a two-phase program. In Phase I,
annual emission Omit of 2.5 Ib/MMBtu Is Imposed on 110 plants. In Phase II. a maximum limit of
1.2 to/MMBtu win be applied to afl utility units. The Environmental Protection Agency (EPA) Office of
Atmospheric and Indoor Air Program (OAIAP) Is responsible for calculating SCfe allowances for ail utility
unto, as defined in the Amendments, and developing a national allowance data base that contains all the
units covered under Title IV.
*
The term •allowance" is defined In the Amendments as the tonnage of SQj that an affected unit
may emit during a specified calendar year. Allowances are allocated by the EPA Administrator. One
allowance is equal to one ton of SO, emissions. The SOj allowance for each utility unit is calculated by
multiplying the annual quantity of fossil fuel consumed, in miiions of Btu, by the actual or allowable
emission rate, in Ib SOj/MMBtu, for a previous or anticipated time period.
* *
Under Phase II, utility units that are burning high-sulfur fossa fuels and. as a result, emitting more
than 1.2 Ib SQ/MMBtu wfll receive an allowance of 1.2 Ib SQ/MMBtu. For units with low to medium
SO, emissions, actual or allowable emissions, whichever is lower (and they are usually less than 1.2),
must be used.
To estimate SO, allowances for utility units. EPA can use available data bases such as the
Department of Energy Form 767. the National Acid Precipitation Assessment Program (NAPAP) Emission
Inventory version 2, the National Utility Reference File (NURF), or a corrected data base, as established
by the Administrator, as a base reference. However, some of the above data bases contain
shortcomings, such as incomplete lists of plants covered under Title IV, different bases (e.g., different
averaging periods), different units of measure, or incorrect data.
In order for EPA to set an allowable emissions level, all current regulatory limits must be
converted to the same units - Ib SOj/MMBtu per year. The regulatory limits in effect across the nation
use varying averaging periods. Converting these limits to an annual basis is not straightforward, since
averaging time, compliance policy, and emissions variabaity all affect the emissions limit that a facility
can meet.
The variabQity In emissions Is particularly important to consider. Facilities with high variability In
their emissions need to operate at a mean emission rate below the regulatory limit in order to avoid .
•JOJpt-2
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exceedances. The higher the variability, the lower the mean emissions need to be in order to avoid an
The averaging period affects the mean only sJightt>'. but ft has considerable effect on the standard
deviation (a measure of variabBity). As averaging periods are lengthened, the standard deviation goes
down. Thus, a facility may be able to meet a given limit If a 24-hour averaging period is used, but
perhaps not V a 3-hour averaging period is used. •
In order to convert existing regulatory limits1 to an annual basis, a factor Is needed that reflects the
differences in variability and, thus, In attainable emission limits, between utility boilers. Since variability in
emissions b largely a function of coal characteristics and control equipment It should be possible to
group bolers based on these characteristics and assign a specific factor to each grouping.
» • •
1.1 OBJECTIVE
* i
The objective of this study was to assist EPA in developing conversion and equivalency factors to
be used in the national allowance data base. These factors could be used to normalize the different
forms of existing SOj regulations data (e.g., data given in percent sulfur or in different averaging periods)
Into an annual average basis (In Ib SO,/MMBtu). The conversion factors can be used to estimate total
tons of allowable emissions for units not included In the data bases or to correct the existing data bases.
To estimate total tons of allowable SOj emissions for a given utility unit conversion factors could be
multiplied by the emission limits (In Ib Spj/MMBtu) and annual average heat input (in MMBtu) of that
unit divided by 2000.
1.2 TECHNICAL APPROACH
» ' m
Conversion factors were developed by performing the following technical tasks:
• The various averaging periods being implemented by the States were reviewed.
• Continuous Emission Monitoring (CEM) data on emission variability for 23 coal-burning
plants were collected and reviewed. When inconsistent or inaccurate data were identified,
they were deleted from the analysis.
• A telephone survey of utilities and suppliers was conducted, and the literature was reviewed
to estimate sulfur variability In oi.
• SOj variability characteristics were analyzed and power plants were categorized
accordingly.
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• Conversion factors for each power plant were developed based on accepted EPA statistical
methods.
2.0 DATA REVIEW AND ANALYSIS
Mdafly, the averaging periods Implemented by each State were reviewed. One or more of the
fcflowing averages were used by each State: 1-hr, 2-hr, 3-hr, 24-hr block. 24-hr rolling, 7-day. 30-day
block. 30-day rolling. 90-day block, and 90-day rolling.
A data base of CEM data on 23 coal-burning utility units was assembled and used to analyze the
vartabitty characteristics of SC> emissions from coal-burning units subject to the acid rain provisions of
the Amendments. The data from these units were screened for errors and deviations from normal
operating variability. .Two types of data were collected: (1) hourly CEM SO, emissions; and
(2) summary statistics, including means, standard deviations, and, in some cases, autocorrelation factors
found in other reports. Detailed hourly CEM data were not available for the second type of data
* " * " j
Due to the lack of data for oil-burning units, utilities and suppliers were contacted to estimate
sulfur variabBity In oB. As such, the SQ variability in oi-buming units was qualified based on the
telephone and literature survey, and a data base was not assembled.
r
After ail relevant data sets had been identified, the following approach was taken to develop the
.factors:
Identify ail relevant utility boaer data and sort into a small number of categories. Categories
were based on boner and coal characteristics that might affect the variability as well as the
average SQ emissions; " ~ ' .
Calculate means and standard deviations at various averaging periods and for different
compliance policies;
Develop a set of factors (using different averaging periods and compliance policies) based
on the mean emissions and the maximum expected emissions; and
Determine the probability distribution of these (actors so that a statistical method can be
used to choose an 'appropriate' factor for each category.
Two types of data were collected: (1) data with hourly CEM SO, emissions; and (2) summary
statistics, Ir^uding means, standard deviations, and. In some cases, autocorrelation factors. SO,
emissions values have been found to have a relatively high amount of autocorrelation (greater than 0.5).1
autocorrelation factor to a measure of the degree of association between observations in a.time
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series. The factor can range from -1.0 tor Inversely related observations to +1.0 for extremely linear
fattens. The standard formula for calculating autocorrelations factors* is:
M
» sample data point at tone t
- sample data point at time t+k; and
1 » sample data average,
The autocorrelation factors for this data set ranged from 0.59 to 0.98. ,.,,....
Oetaled hourly CEM data were not available for all of the data sets. Means and standard
deviations for one averaging period were available for some utility units. For these units, means and
standard deviations for other averaging periods were estimated. The estimate was based on a ratio of
averaging periods with a simBar boier with known mean and standard deviation for the particular
averaging period.- . ^^^
A unit was considered simiar if It was similarly equipped (with or without an FGO) and If it burned
the same (or dose to the same) percent sulfur coal. For example, plants A and 8 are considered
simiar. Both plant A and B have known means for the 3-hour averaging period, plant A has known
mean for the 24-hour averaging period, and the mean for the 24-hour averaging period for plant B Is
unknown. A ratio of this information allows for the estimation of the mean for the 24-hour averaging •
period for plant B:
A simiar ratio Is established for the standard deviation. These estimates are then used to calculate the
mean for the particular plant and averaging period.
Emissions data were collected from a total of 23 units burning coal. Table 1 summarizes the coal-
bumlng utility units by Identification number, type of coal being used, scrubber avaBabDity, and unit size.
Appendix A presents means, standard deviations, and autocorrelations factors for an the units
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TABLE 1. UST OF UTILITY UNITS
' 10
Number
1
2
3
5
6
7
8
9
10
11
'?
13
14
15
16
17
18
19
20
21
22
23
24
Coal Supply
Low Sulfur
Low Sulfur4
High Sulfur
Low Sulfur
Low Sulfur*
Low .Sulfur
Low Sulfur
Low Sulfur
Low Sulfur
Low Sulfur
Low Sulfur
Low Sulfur
High Sulfur
High Sulfur
High Sulfur
High Sulfur
High Sulfur
High Sulfur
Low Sulfur
High Sulfur
High Sulfur
Medium Sulfur
High Sulfur
(% Sulfur) .
(P.32)
(0.68)
(3-82)
(0.34)
(NA)
(NA)
(NA)
(NA)
(NA)
(0.33)
(0.33)
(0.33)
(2.33)
(3.6)
(3.75)
(3.41)
(3.85)
(3.85)
(0.3)
-(2.8)
(2.8)
(1.7)
(2.5)
Scrubber
NoFGD
No FGD
FGD
NoFGD .
No FGD
No FGO
No FGD
FGO
FGD
FGD
FGO
FGO
FGO
FGD
FGO
FGO
FGO
FGO
FGO
FGD
FGD
FGD
FGD
Size
(MW)
512
750
195
640
795
725
.'580
445
550
720
720
720
235
195
835
272
265
265
NA
684
684
65
NA
'Washed coal.
NA - not available.
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considered In this analysis. The data base Is a cross-sectional representation of utility plants with units
of different sizes, wfth or without flue gas desutturizatlon (FGD) systems burning low- or high-sulfur
coals, using .washed or unwashed coals, having different averaging periods, and having different
policies. . -
These units were subdivided into three groups: sfac (6) non-FGD units burning low sulfur coal.
eleven (11) FGD units burning high sulfur coal, and six (6) FGD units burning low sulfur coal. These
groups were used in the statistical analysis described below. . .f .. .
3.0 FACTOR DEVELOPMENT
A utility plant has a specific SO; emissions limit Due to the random fluctuation in emission levels
_ both above and below the long-term average, the mean emission rate must be maintained at an
.emission level below the emission standard in order to assure compliance. Ideally,- a unit would never
exceed the emissions limit In fact 'compliance policies' are established to ensure a limited number of
exceedances. Typically one exceedance per year.-one exceedance per ten (10) years, etc., have been
used to set emission limit standards.
Through analysis of the variability in emissions, GIguere1 developed a procedure that allows the
^projection of long-term mean SO, emission levels required to meet a desired Ib SQ/MMBtu emission
limit The method requires knowledge of the following variables:
• Standard delation and relative standard deviation;
• Autocorrelation;
• Emissions distribution (normal vs. lognormal); '
• Length of averaging period and averaging method; and
• Compliance policy (exceedance rate).
The relative standard deviation (RSD) is defined as the ratio of the standard deviation to the
average or mean and is typically used to describe emissions variability. Autocorrelation (defined above)
Is not as Important as RSD In determining SQ variability and predicting long-term mean emission levels.
Longer averaging periods dampen the effects of variability, allowing plants to operate with SOj emission
rates doser to the actual emissions limit
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The probability of violating the limit can be calculated for a specific averaging period and
exceedance policy. For example, consider a 30-day rolling averaging period In combination with a one
» _ *
exceedance per ten (10) year policy. There are 3,650 days over a 10-year period, so that one
exceedance divided by the total number of potential exctedances yield* 0.00027. Therefore, the
probability of violating the limit each day is a constant of 0.00027. TM daily exceedance probability of
0.00027 translates to a standard normal distribution Z value of 3.46.
*
* . . '
The implication of the above Is that In order to comply with the emission limit, the unit should be
run at a target level that is less than the given limit by an amount equal to Z times the standard deviation
of the 30-day rolling averages. Thus, the maximum expected emissions is the target level plus Z times
the standard deviation.
Given the mean and maximum expected emissions for a specific averaging period and
exceedance policy, a factor can be created that could be used to adjust the emission limits for the
^averaging periods: • ' * * .
Factor-*?**!
Max
The factor is simply a ratio of mean emissions to expected maximum emissions. For a facility with low
variability (and therefore operating very near the limit), this factor will be dose to 1. Also for any facility,
• the factor should approach 1 as the averaging period lengthens. The compliance policy assumed to be
used by a facility will also affect the factor.
The Glguere method adjusts the standard deviation to account for the autocorrelation of the data.
However, autocorrelations were not available for most of the facility data Therefore, for each different
unit and averaging period, the expected maximum emissions under a particular exceedance policy were
calculated using the following formula:
Max • x * Z • 3
where
Max - expected maximum emissions;
X - average emissions for averaging period;
Z » z-score for compliance policy and averaging period; and
s - (sample) standard deviation for averaging period.
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To test the validity of this approach, the data sets for which an autocorrelation value was avalabie
were used to conduct a comparison of the Giguere method and the simplified method shown in the
above equation. Factors were computed using both methods to estimate the expected maximum, and
the differences between the resulting factors of the two methods were computed. In looking at the
results from the two methods, there does not appear to be a significant difference between them.
Therefore, the simplified method requiring only the mean and standard deviation was used for
determining factors for the 23 units since it gives results that are comparable to the Giguere method.
The resulting equation used for factor development was:
X
to order to use this methodology to develop conversion factors for SO, emission limits, it is
necessary to determine the mean and expected maximum for each facflity using different averaging
periods and compliance policies. In the analysis below, the effects of three different compliance policies
were included:
• One exceedance allowed In a 10-year period:
• One exceedance allowed in one year; and
• A 1 percent exceedances (that is. 1 percent of the emission averages in a year may be in
excess of the limit).
» «
For example, a faculty under a 3-hour block average regulation will have 8,760 hrs/yr/3 nrs * 2920
chances to exceed. A 1 percent exceedance policy would allow the possibility of 29 exceedances in a
year. Appendix B gives a comparison of the effects of various compliance policies.
The set of factors in each category can be used to statistically characterize the category. The
probabllty distribution of factors for a given category could be used to choose the factor that applies to
• specific percentage of the Deputation of bolers within a category. For example, on* half the boilers
would have a factor less than or equal to the 50th percentle factor. Choosing a factor at the 95th
percentle would mean that 95 percent of the bolers could meet (or do better than) the emission limit
caJcuteted by using that factor.
The derived factors are not normally distributed. The famOiar methods of calculating means of
distributions, sample standard deviations of normal distributions, and percentDes of normal
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distributions are not applicable. Because the (actors are continuous and bounded above and below,
they can be represented by a beta distribution. A beta distribution Is defined by the data points, the end
points, and by two shape parameters, v > 0 and w > 0. It is necessary to calculate the end points for
•ten group exceedance policy and averaging period. Lower end points are chosen to be below the
minimum BSD for the particular averaging perkxl under a gKwn exc»edance Ddtey and group. The
upper end points are selected to be above the maximum BSD for the particular averaging period under
a given exceedance policy and group. The factors are then normalized as follows:
x - a
b -a
a
b
x,
lower bound
upper bound, and
normalized factor.
Next, K is necessary to calculate the shape parameters for each category averaging time and
exceedance policy based on the sample data. The shape parameters are estimated as follows1:
v-
where
x - arithmetic mean and
s* - sample variance.
For each category averaging period and exceedance policy, a beta distribution has been defined
by the shape parameters v and v* as described above. The mean and standard deviation for a given
beta distribution are then calculated as follows3:
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v w
Variance • —
(v » wftv * w * 1)
Standard Deviation • /variance
Foflowing the calculation of the summary statistic* for each category and exceedance policy and
averaging period, the probability values from each beta distribution were calculated. The probability
density function of a beta distribution is given by1 :
where
x - value at which the distribution is to be evaluated and
v.w * shape parameters.
Calculations were performed to determine the value where 5 percent 25 percent 50 percent 75 percent.
95 percent or 99 percent of the sample factors were below it
4.0 RESULTS
Table 2 presents the estimated means, minimum and maximum values, and standard deviations
for aD 23 coal-burning units for different averaging periods and exceedance policies. Originally the units
were divided into three categories: (1) non FGD units burning low sulfur coals (6 units), (2) FGD units
burning low sulfur coals (7 units), and (3) FGD units burning medium to high sulfur coals (10 units).
Figures t through 3 show the factors for different averaging periods. Coals containing less than one
percent of sulfur by weight were categorized as low sulfur coals. Above one percent sulfur, coals were
considered as medium- to high- sulfur coals. Units with FGD systems burning low. and high-sulfur coals
examined separately and a summary of conversion factors is presented in Appendix C. Units with
systems demonstrated similar conversion factors regardless of coal sulfur content Therefore, two
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categories were used for the final analysis: units without FGO (6 units), and units with FGD (17 units). In
addition, all cases (23 units) were combined to give average values to all units.
Appendix 0 presents (actors for all cases considered In this study for different averaging periods,
different cumulative probabilities ranging from 5 percent to 99 percent, and two exceedance cases. For
this study, two exceedance cases as being used by States were considered: (1) one exceedance per
10 years, (2) one exceedance per year. As Appendix 0 shows, both cases have similar results. For ail
units combined with a 1-hour block average, a conversion factor of 0.74 would cover about 75 percent
of tiie population. In another word, 75 percent of the units considered in this analysis have conversion
tutors equal to or less than 0.74. Table 3 summarizes means and conversion factors with cumulative
probability for covering 95 and 99 percent of the population for units without FGD, with FGO, and all
units combined.
^
Conversion factors were hot developed for the following averaging periods: 24-hr block, 30-day
r • ' *
block, 90-day block, and 90-day rolling. The conversion factors for the above averaging periods.
however, can be estimated using the trend in the factors from one averaging period to the next For •
example. 30-day rolling average for 95 percent confidence limit and one exceedance per year for FGO
units is 0.99. Therefore. 90-day averages should be between 0.99 and 1.0.
As specified in a 1980 EPA report.4 the sample statistics from the analyses of coals failed to
identify any consistent, predictable relationships that would explain coal sulfur variabilities.
Emission data were typically reported as Ib SOj/MMBtu, Ib S/MMBtu. or percent sulfur in the fuel.
In order to put ail data on the same basis, data reported in Ib S/MMBtu or percent sulfur were converted
to Ib SQ/MMBtu using the following equations:
COAL
Ib SCfc/MMBtU • 2 * Ib S/MMBtu.
Ib SCfe/MMBtu - 18143 * (HHV)** * S%
Ib SOj/MMBtu » 1.1 • S% • DEN
where
HHV • higher heating value. Btu/lb
S% » sulfur percent . ,
• DEN » oO density. Ib/gallon
OB heating value was assumed to be 6.2 MMBtu/bbl.
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TABLE 3. MEAN AND CUMULATIVE PROBABILITY TO COVER 95 AND 99 PERCENT
OF THE UNIT POPULATION1
Averaging Period
No FGD1
Mean
95% Probabaily
99% Probability
FGD Equipped
Mean
95% Probability
99% Probability
AflCaserf
Mean
95% Probability
99% Probability .
NoFGCr5
Mean
95% Probability
99% Probability
FGO Equipped
Mean
95% Probability
99% Probability
All Cases'
Mean
95% Probability
99% Probability
IHr
0.54
0.86
0.92
0.45
0.83
t
0.92
0.48
0.88
0.94
0.55
0.82
0.89
0.42
0.80
0.89
.'.
0.45
0.84
0.92
2Hr
0.61
0.88
0.93
0.47
0.85
0.93
0.51
0.91
0.97
0.61
0.80
0.87
0.44
0.81
0.91
0.47
0.88
0.95
3Hr
*
0.60
0.84
0.90
0.49
0.87
0.94
0.5)2
0.92
0.97
0.60
0.79
0.86
0.45
0.83
0.92
0.48
0.88
0.95
24 Hr
0.62
•0.83
0.90
0.54
0.88
0.94
0.56
0.91
0.96
0.63
0.79
0.88
0.51
0.85
0.93
0.53
0.88
0.95
7 Day
0.75
0.89
0.94
0.70
0.95
0.98
0.72
0.97
0.99
0.75
0.85
0.92
0.66
0.93
0.97
0.69
0.94
0.98
30 Day
0.85
0.92
0.96
0.86
0.99
1.00
0.86
0.99
0.99
0.83
0.90
0.96
•
0.86
0.99
1.00
0.83
0.99
0.99
'Factors are for one exceedance per year.
"Factors are for one exceedance per 10 years.
17
-------
-------
5.0 CONCLUSIONS
For utility unfts, SQ concentration in the flue gas varies due to variability In fuel sulfur content,
healing value, and control device variability. The various analyses of coal sulfur variability identified no
reliable method for coal suppliers or consumers to predict variability. The conclusion was that the
primary factors affecting coal sulfur distributions are possibly geologic factors, mining techniques, and
coal handling procedures. For units equipped with FGD, this variability Is also due to random
fluctuations in operating parameters such as Inlet SOj concentration, sorbent quality, flue gas flow rate,
and liquid to gas ratio.
In order to meet an emission standard, a unit must operate In a manner that accommodates the
natural variability in coal and control device such that the average emission rate does not exceed the
permit limit for the specific averaging time. This ensures that any emission variations due to coal
characteristics and control device are normalized over the averaging time period. As a result, the
shorter the emission averaging time the lower the mean emission will be to ensure compliance.
r
The analysis of the limited CEM data indicated that significant reductions in the relative variability
of emissions can be achieved by increasing the averaging time interval from 1 hour to 3 hours. 24 hours,
30 days. This vend could also be seen in Figures 1 through 3 where the conversion factors were
otted versus different averaging time periods. These figures show the tendency of the conversion
factors to approach 1.0 as the averaging time period increases. The conversion factors for converting.
data on 1-hour and 30-day averages to annual averages for 95 percent cumulative probabOity will be in
the range of 0.83-0.88 and 0.92-0.99. respectively.
OB purchased from refineries has a known sulfur and heating value content Suppliers generally
guarantee these two values. The price of o3 with different sulfur content can be the same depending on
the local oil market if the oil sulfur content from different suppliers is below the standard, pricing is the
main driver for choosing a supplier. Oi-fired source operators sample the oil from the transport
container or pipelines upon delivery to ensure that it conforms with the contract specifications. In
addition, the oi in the storage tanks is well mixed and has a uniform sulfur content As such, the
emissions from a utility unit burning oi from the same supplier has low variabilities. However, oB sulfur
content can vary from one shipment to the next particularly if the oB was purchased from different
suppliers. .
18
-------
-------
6.0 REFERENCES
1. Giguere, Gregory C., "Determination of Mean SC* Emission Levels Required to Meet a 1.2 Ib
Spj/Mfllion Btu Emission Standard For Various Averaging Times and Compliance Policies,"
prepared for Walter H. Stevenson, US EPA, Emission Standards and Engineering Division,
Durham. North Carolina 27711. March 1985.
2. Pankratz, Alan. Forecasting with Unlvariate Box-Jenkins Models. Concepts and Cases. John Wiley
& Sons, New York, 1983.
3. • Hastings. NJU.. and J.B. Peacock. Statistical Distributions. A Handbook far Students and
Practitioners. John WOey & Sons, New York, 1975.
4. Warhoflc, G.R., et al. 'A Statistical Study of Coal Sulfur Variability and Related Factors." NTIS
PB81.111585, US. Environmental Protection Agency, Research Triangle Park. North
Carolina 27709. May 1980. • -
19
-------
-------
APPENDIX A .
DESCRIPTIVE STATISTICS OP UTILITY BOILERS USED IN THIS ANALYSIS
\
-------
-------
DESCRIPTIVE STATISTICS OF UTILITY BOILERS USED IN THIS ANALYSIS
Table A-1 presents the descriptive statistics for ttn utility units used In this study. For a given
averaging period, an arithmetic mean and sample standard deviation were either calculated or
estimated under the assumption that SCfe emissions are normally distributed. A description of the
method of estimation ft found In this report For those units for which ft was available, the
autocorrelation factor for a given averaging period is also presented A description of autocorrelation
factors Is found in Section 2.0 of this report
-------
-------
TABLE A-1. DESCRIPTIVE STATISTICS OF THE UTILITY UNITS
k 10 Averaging
P * Period
1 1-hr
2-hr
3-hr
24-hrB
24-hr R
- " ' * 7-day R
30-day R
2 1-hr
2-hr
3-hr
24-hr B
24-hr R
7-day R
- . 3 1-hr
2-hr
3-hr
24-hr B
24-hr R •
7-day R
5 1-hr
^ 2-hr
M 3-hr
" 24-hr B
24-hr R
7-day R
30-day R
6 1-h' .
2-hr
3-hr
24-hr R
7-day R
30-day R
7 • 1-hr
2-hr
3-hr
24-hr R
7-day R
30-dayR
8 1-hr
2-hr
3-hr
24-hr R
7-day R
^ 30-day R
Mean •.
0.603
0.602
0.602
0.602
0.602
0.601
0.606
0.875
0.875
0.875
0.875
0.875
0.871
0.612 '
0.613
0.613
0.614
0.585
0.546
0.569
-0.8
0.8-
0.8
0.8
0.8
0.8
6.5
0-5'
0.5
0.5
0.5
0.5
0.78
0.78*
0.78
0.78
0.77
0.77
Standard
Deviation •
O.IT;
0.115.
0.114
0.100
0.099
0.060
0.016
0.084
0.081
0.078
0.059
0.058
0.029
0.396
0.384
0.379
0.329
0.262
0.099
0.074
0.09
0.07*
0.08
0.06
0.05
0.02
0.09
0.07*
0.08
0.08
0.06
0.04
0.15
0.12*
0.14
0.12
0.08
0.05
Auto-
Correlation
0.97
0.71
.
0.92
.
0.73
0.69
0.72 ,
0.93
0.81
0.94
0.90
0.79
0.96
0.98
0.88
0.84
0.59
0.94
0.94
-------
*
TABLE A-1. CONTINUED
ID Averaging
* Period
9 1-hr
2-hr
3-hr
24-hr R
7-day R
30-day R
10 1-hr
2-hr
3-hr
24-hr R
7-day R
30-day R
11 1-hr
2-hr
•3-hr
24-hr 8
24-hr R
7-day R
30-day R
12 1-hr
2-hr
3-hr
24-hr B
24-hr R
7-day R
. 30-day R
13 1-hr
2-hr
3-hr
24-hr B
24-hr R
7-day R
30-day R
14 1-hr
2-hr
3-hr
24-hr B
24-hr R
7-day R
30-day R
Mean .
0.9
0.9*
0.9
0.9
0.9
0.9
0.8
0.8*
as
0.8
0.8
0.8
0.352*.
0.353* '
0,352*
0.352
0.352
0.352*
0.352*
0.609*
0.610*
0.609*
0.609
0.609
0.609* _
0.609*
0.29*
0.29*
0.29*
0.29
0.29
0.29*
0.29*
1.005*
1.007*
1.001*
0.947
0.947
Standard
Deviation
0.12
0.12*
*0.11
0.08
0.06
0.02
0.09
0.09*
0.09
0.07
0.05
0.02
0.224*
0.218*
0.214*
0.161
0.161
0.118*
0.043*
0.213*
0.207*
0.204*
0.153
0.153
0.112*
0.041*
0.281*
0.273*
0.269*
0.202
0.202
0.148*
0.054*
0.204*
0.198*
0.188*
0.124
0.124
Auto-
Correlation ^^
0.74 ^P
0.76
0.67
0.95
0.95
0.94
0.88
0.73
0.95
0.91
• - *
•
.
•
-------
TABLE A-1. CONTINUED
>ID Averaging
# Period
15 1-hr
2-hr
3-hr
24^rB
24-hr R
.. 7-day R
30-day R .
16 1-hr
2-hr
3-hr
24-hr B
24-hr R
7-day R
30-day R
* » . *
17 1-hr
2-hr
3-hr
24-hr B . .
24-hr R
7-day R
30-day R
I 18 1-hr
f 2-hr
3-hr
24-hr B
24-hr R
7-day R
* . 30-day R
19 1-hr
2-hr
3-hr
24-hr B
24-hr R
7-day R
30-day R
20 1-hr
2-hr
3-hr
24-hr B
24-hr R
7-day R
30-day R
Mean .
0.998'
1.000*
1.000*
1.001*
0.953
0.891*
O326*
O326*
0.326*
0.327'
0.311
0.291*
• "
0.303*
0.303*
0.303*
0.304*
0.289
0.270*
0.707*
0.708*
0.708*
0.709*
0.675
0.631*
0.838*
0.839*
0.839*
0.841*
0.800
0.748*
0.3*
0.3'
0.3'
O3
0.3
0.3'
0.3'
Standard Auto-
Deviation Correlation
O224*
OJ17*
•0^14*
0.186*
0.148
0.056*
0.121 *
0.117*
0.116*
0.100*
0.080
0.030*
• \i »f
0.131 *
0.128*
0.126*
0.109*
0.087
0.033*
0.286*
0.277*
0.273*
0.237*
0.189
0.071*
0.186*
0.180*
0.178*
0.154*
0.123
0.046*
0^51*
0^62*
0^39*
0.180
0.180
0.132*
0.048*
-------
I TABLE A-1. CONTINUED
ID Averaging
* Period
21 1-hr
2-hr
3-hr
24-hr B
24-hr R
7-day R
30-day R
22 1-hr
2-hr
3-hr
24-hr B
24-hr R
7-day R
30-day R
23 • 1-hr
2-hr
3-hr
3-hour R
24-hr S
24-hr R
24 1-hr
2-hr
3-hr
3-hrR
24-hr B
24-hr R
30-day R
Mean .
0.87*
0.88*
0.87*
0.87*
0.87
0.88*
0.988*
0.990*
0.983*
0.982*
0.983
0.989*
0.2607
0.2612*
0.2597
0.2584
0.2422
0.2456
0.6737
0.6749*
0.6699
0.6697.
0.6697
0.6702
0.6742
Standard Auto-
Deviation Correlation ^fe
0414* . ^
0.208*
"0.188*
0.127*
0.128
0.006*
0.102*
0.099*
0.090*
0.061 *
0.061
0.003* . .
0.2799
0.2718* .
0.2578
0.2583
0.1837
0.1702
0.1832 ^
0.1779* M
0.1606 ^r
0.1604
0.1089
0.1094 *
0.0050
* Estimate
-------
APPENDIX B
COMPARISON OF TWO EMISSION FACTORS CALCULATION METHODS
-------
-------
COMPARISON OF TWO EMISSION FACTORS CALCULATION METHODS
For five (5) utility units used in this study, an autocorrelation factor was available for five (5)
different averaging periods. These units were used to compare two methods of factor calculations.
The simplified factors resulting from the method requiring only the mean and standard deviation are
designated Mean/Exp. Max or A, These factors were compared to those derived using the Giguere
method, designated Target Level/Limit, or B. The difference between the two factors was calculated
for each unit for each of the averaging periods for three different exceedance policies. In looking a?
the results from the two methods, there does not appear to be a significant difference between them.
Table irt also shows how the factors (either A or B) increase with increasing averaging period
length and the effect the exceedance policy has on the factors.
-------
-------
TABLE B-1. EMISSION FACTOR COMPARISON
*
6
•
7
*
Averging
Period
1-hr
3-hr
24-hr
7-day R
30-day R
1-hr
3-hr
24-hr R
7-day R
30-day R
1-hr
3-hr
24-hr R
7-day R
30-day R
14ir
3-hr
24-hr R
7-day R
30-day R
i-hr
3-hr
24-hr R
7-day R
30-day R
1-hr
3-hr
24-hr R
7-day R
30-day R
Exceedance
Policy
One/10 yr
One/10 yr
One/10 yr
One/10 yr
One/10 yr
One/yr
One/yr
One/yr
One/yr
One/yr
1%
1%
1%
1%
1%
One/10 yr
One/10 yr
One/10 yr
One/10 yr
One/10 yr
One/yr
One/yr
One/yr
One/yr
One/yr
1%
1%
1%
1%
1%
Expected
Maximum
1.1812
1.1185
1.0541
0.9728
0.8691
1.1317
1.0716
1.0211
0.9389
0.8555
1.0094
0.9861
0.9398
0.9163
0.8465
0.8812
0.8185
0.8388
0.7074
0.6382
0.8317
0.7716
0.7948
0.6666
0.6111
0.7094
0.6861
0.6861
0.6398
0.5931
Mean/Exp.
Max (A)
0.6773
0.7152
0.7589
0.8224
0.3205
0.7069
0.7465
0.7834
0.8521
0.9351
0.7926 .
0.8113
0.8514
0.8731
0.9450
0.5674
0.6109
0.5961
0.7068
0.7834
0.6012
0.6480
0.6291
0.7500
0.8182
0.7048
0.7287
0.7287
0.7818
0.8431
Target
Level
0.8528
0.9018
0.9452
0.9635
1.0993
0.8861
0.9360
0.9720
1.0023
1.1177
0.9807
1.0057
1.0453
1.0296
1.1303
0.6900
0.7480
0.7489
0.8235
0.9175
0.7303
0.7919
0.7873
0.8776
0.9619
0.8535
0.8868
0.9014
0.9176
0.9940
Target
Level/Limit
(B)
0.7107
0.7515
0.7877
0.8029
0.9160
0.7384
0.7800
0.8100
0.8352
0.9314
0.8173
0.8381
0.8710
0.8582
0.9419
0.5750
0.6233
0.6241
0.6863
0.7646
0.6086
0.6599
0.6561
0.7313
0.8016
0.7112
0.7390
0.7514
0.7647
0.8283
Difference
(B-A)
0.033
0.036
0.029
-0.019
•0.004
0.032
0.033
0.027
•0.017
•0.004
, 0.025
. 0.027
0.020
-0.015
-0.003
0.008
0.012
0.028
-0.021
-0.019
0.007
0.012
0.027
-0.019
•0.017
0.006
0.010
0.023
-0.017
-0.015
-------
ID Averglng
* Period
8 1-hr
3-hr
24-hr R
7-dayR
30-day R
- 1-hr
3-hr
24-hr R
7-day R
30-day R
1-hr
3-hr
' 24-hr R
7-day R .
30-day R
9 1-hr
3-hr
24-hr R
7-day R
30-day R
1-hr
3-hr
24-hr R
7-day R
30-day R
1-hr
3-hr
24-hr R
7-day R
30-day R
Exceedanca
Policy
One/10 yr
One/10 yr
One/10 yr
One/10 yr
One/10 yr
One/yr
One/yr
. One/yr
One/yr
One/yr
1%
1%
1%
1%
1%
One/10 yr
One/10 yr
One/10 yr
One/10 yr
One/10 yr
One/yr
One/yr
One/yr
One/yr
One/yr
1%
1%
1%
1%
1%
' TABLE B-1
Expected
Maximum
1.4153
1.3374
1.2882
1.0465
• 0.9428
1.3328
1.2554
1.2223
0.9922
0.9089
1.1290
1.1057
1.0592
. 0.9561
0.8863
1.4082
1.3380
1.2388
1.1074
0.9691
1.3423
1.2735
1.1948
1.0666
0.9555
1.1792
1.1559
1.0861
1.0396
0.9465
. CONTINUED
Mean/Exp.
Max (A)
0.5511
0.5832
0.6055
0.7358
0.8167
0.5852
0.6213
0.6382
0.7761
0.8472
0.6909
0.7054
0.7364
0.8053
0.8688
0.6391
0.6727
0.7265
0.8127
0.9287
0.6705
0.7067
0.7532
0.8438
0.9419
0.7633
0.7786
0.8286
0.8657
0.9508
•
Target
Level
0.6803
6.7251
0.7997
0.8257
0.9351
0.7208
0.7699
0.8359
0.8796
0.9775
0.8453
0.8679
O.S412
0.9195
1.0078
0.8077
0.8426
0.9173
0.9416
1.0995
0.8435
0.8812
0.9463
0.9832
1.1178
0.9472
0.9616
1.0263
1.0129
1.1304
_
Target
Level/Limit
(B)
6.5669
0.6042
0.6665
0.6881
0.7793
0.6007
0.6416
0.6966
0.7330
0.8146
0.7044
0.7232
0.7844
0.7662
0.8399
0.6731
0.7021
0.7644
0.7847
0.9162
0.7029
0.7343
0.7886
0.8193
0.9315
0.7894
0.8014
0.8552
0.8441
0.9420
t
• *,
Difference
III | ^
0.016 -
0.021
0.061
•0.048
•0.037
0.015
0.020
0.058
-0.043
-0.033
0.013
0.018
0.048 :
-0.039
-0.029
0.034
0.029
0.038
•0.028
•0.012
0.032 ^
0.028 ^B
0.035 ^*
•0.024
-0.010
0.026
0.023
0.027
•0.022
-0.009
-------
TABLE 6-1. CONTINUED
^B * Averging
™ Period
10 1-hr
3-hr
24-hr R
7-dayR
30-day R
1-hr
3-hr
244vR
7-dayR
30-day R
1-hr
3-hr .
24-hr R
7-day R
30-day R
Exceedance
Policy
One/10 yr
One/10 yr
One/10 yr
One/10 yr
One/10 yr
One/yr
One/yr
One/yr
One/yr
One/yr
1%
1%
1%
1%
1%
Expected
Maximum
1.1812
1.1583
1.0965
0.9728
0.8691
1.1317
1.1056
1.0580
0.9389
0.8555
1.0094
1.0094
0.9628
0.9163
0.8465
Mean/Exp.
Max (A)
0.6773
0.6906
0.7296
0.8224
0.9205
0.7069
0.7236
0.7562
0.8521
0.9351
0.7926
0.7926
0.8309
0.6731
0.9450
Target
Level
0.8208
0.8450
0.9114
0.9628
1.0944
0.8559
0.8834
0.9408
1.0016
1.1137
0.9571
0.9635
1.0222
1.0293
1.1268
Target
Level/Limit
(B)
0.6840
0.7041
0.7595
0.8023
0.9120
0.7133
0.7362
0.7840
0.8347
0.9281
0.7976
0.8029
0.8518
'0.8577
0.9390
Difference
(B-A)
0.007
0.013
0.030
-0.020
-0.008
0.006
0.0136
0.028
-0.017
-0.007
0.005
0.010
0.0021
-0.015
-0.006
-------
-------
APPENDIX C
SUMMARY OF CONVERSION FACTORS
-------
-------
SUMMARY OF CONVERSION FACTORS
Table C-l presents the calculated conversion factors, using the simplified method, for each FGD-
equipped utflJty units used in this study. Conversion (actors were calculated for two different
txeeedance policies for a variety of averaging periods. Footnote V indicates that the unit bums
high-sulfur coal and V Indicates that the unit burns tow-sulfur coal. Footnote "c" indicates that the
factor was derived from estimated means and standard deviations, as described in Section 2.
-------
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APPENDIX 0
CONVERSION FACTORS FOR SELECTED PROBABILITIES
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CONVERSION FACTORS FOR SELECTED PROBABILITIES
Because the conversion factors are continuous aid bounded above and below, they can be
represented by a beta distribution. The statistics presented in Table D-1 and r>2 were calculated
using a beta distribution to generate cumulative probabilities for two different exceedance policies.
Table D-1 summarize* the one-exceedanee-per-year policy and Table D-2 the one-exceedance-per-
tan-years policy.
t *
The units were divided Into two categories according to FGD equipment; statistics for the
combined categories are also shown. Means and standard deviations were calculated for each
averaging period under a given exceedance policy. Factors were calculated at selected cumulative
probabiIJty levels of 5 percent. 25 percent. 50 percent 75 percent, and 95 percent For example, for
jion-RSD equipped units under a compliance policy of one exceedance per year-and a 1-hour block
averaging period, 95 percent of the conversion factors are less than (or equal to) 0.85, whereas for a
30-day rolling averaging period, 95 percent of the conversion factors are less than (or equal to) 0.95.
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