EPA-450/3-77-044
November 1977
PRELIMINARY EVALUATION
OF SULFUR VARIABILITY
IN LOW-SULFUR COALS
FROM SELECTED MINES
~
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Air and Waste Management
Office of Air Quality Planning and Standards
Research Triangle Park, North Carolina 27711
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EPA-450/3-77-044
PRELIMINARY EVALUATION OF SULFUR
VARIABILITY IN LOW-SULFUR COALS
FROM SELECTED MINES
Prepared l>\
PKDCo Km iionmciilal. I in
11499 Chester Koad
(Cincinnati, Ohio 45246
Conliact No. hK-OJ
Task \<>. U
I'.PA Project Officers: (ilan< i» Miriuid,
anil David K n c |IL''--H' i
IVcparrd lor
U.S. ENVIRO.NMKNTAL I'KOTKCTION \(;i:\
Office of Air and ^asle Manafremenl
Office of Air Ouality Planning and StandanK
Research Triangle Park.. IVorth (Carolina 2771 I
November 1V77
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This report is issued by the Environmental Protection Agency to report
technical data of interest to a limited number of readers. Copies are
available free of charge to Federal employees, current contractors and
grantees, and nonprofit organizations - in limited quantities - from the
Library Services Office (MD-35) , Research Triangle Park, North Carolina
27711; or, for a fee, from the National Technical Information Service,
5285 Port Royal Road, Springfield, Virginia 22161.
This report was furnished to the Environmental Protection Agency by
PEDCo Environmental, Inc. , Cincinnati, Ohio, in fulfillment of Contract
No. 68-02-1312, Task 41. The contents of this report are reproduced herein
as received from PEDCo Environmental, Inc. The opinions, findings, and
conclusions expressed are those of the author and not necessarily those
of the Environmental Protection Agency. Mention of company or product
names is not to be considered as an endorsement by the Environmental Protection
Agency .
Publication No. EPA-450/3-77-044
11
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ACKNOWLEDGEMENT
A study of this complexity cannot be conducted without
the cooperation of many companies and individuals. The
project was initiated at a meeting with representatives of
four companies: Peabody Coal Company, Consolidation Coal,
AMAX Coal Company and Island Creek Coal Sales Company, all
of whom supplied data. Individuals at Penelec, Duke Power
Company, Tennessee Valley Authority, Virginia Electric Power
Company, and Carolina Power and Light also provided data
that are included in the study. The cooperation of those
who supplied data and reviewed the report is greatly appre-
ciated.
PEDCo also expresses appreciation to David Kirchgessner
and Constancio Miranda, EPA Project Officers, for their
active interest in the project: arrangement of meetings,
participation in the meetings, and review of the report. In
particular we appreciate the contribution by Constancio
Miranda of Appendix C to the report. We also appreciate the
recommendations and timely suggestions of other members of
the Energy Strategies Branch: John Fink and Rayburn Morrison.
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CONTENTS
Page
SUMMARY vi
1.0 INTRODUCTION 1-1
2.0 VARIABILITY OF SULFUR IN COAL 2-1
2.1 Background 2-1
2.2 Approach 2-6
3.0 DATA BASE 3-1
4.0 DATA ANALYSIS 4-1
5.0 IMPLICATIONS OF STATISTICAL ANALYSIS 5-1
5.1 Background and Introduction 5-1
5.2 Data Analysis 5-3
5.3 Average Sulfur Content Required 5-7
for Compliance
5.4 Examples 5-19
6.0 CONCLUSIONS AND RECOMMENDATIONS 6-1
7.0 REFERENCES 7-1
APPENDIX A - SELECTED DATA SETS A-l
APPENDIX B - METHODS OF DATA ANALYSES B-l
APPENDIX C - SULFUR VARIABILITY WITH LOT SIZE C-l
APPENDIX D - SELECTED REVIEW COMMENTS D-l
iv
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FIGURES
No. Page
2-1 Variation in Pyritic and Organic 2-2
Sulfur Contents of Pittsburgh Seam
Coal (West Virginia)
2-2 Hypothetical Distribution of Sulfur 2-3
in 30-Ysar Coal Reserve
4-1 Histogram of Weekly Averages for 4-5
Data Set U-l
4-2 Cumulative Frequency Graph of 4-6
Data Set U-l
4-3 Average Weekly Sulfur Content of Coal 4-8
of Data Set U-l Vs. the Number of the
Week
5-1 RSD Vs. Averaging Period/Tons of Coal 5-8
(Days/Hours/Tons)
5-2 Determination of Required Average 5-10
Sulfur Content
5-3 Sulfur Content Vs. Heating Value of 5-13
Coal Required to Yield 1.2 Ib SO-/
MM Btu
5-4 Determination of Required Average Sul- 5-14
fur Content Assuming Lognormal Distri-
bution
5-5 Required Average Sulfur Content Vs. 5-18
Sulfur Variability
A-l Variation in Sulfur Content, Ib SO / A-3
MM Btu, with Time, Data Set C-2
A-2 Variation in Weekly Average Sulfur A-4
Content, Ib S02/MM Btu
A-3 Variation in Sulfur Content, Ib SO / A-6
MM Btu, Vs. Time, Data Set C-3
A-4 Minimum and Maximum Values of Sulfur A-9
Content, Ib SOVMM Btu, for Unit
Trains Within One Month, Data Set C-5
A-5 Comparison of Core Data and Run- A-39
of-Mine Data
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FIGURES (continued)
No. Page
A-6 Frequency Distribution of One Day A-40
Averages of Weight Percent Sulfur
in Coal
A-7 Frequency Distribution for Data A-41
Set U-18
B-l Scatter Diagram of a Sample of B-14
Data Set U-l
B-2 Relationship of Standard Deviation B-17
to Mean Sulfur Content
B-3 Frequency Distribution for Data B-18
Set U-l
B-4 Application of Quality Control Chart B-26
to Control Sulfur Variability
B-5 Moving Average and Moving Range B-29
Quality Control Charts
C-l Hypothetical Example Illustrating C-3
Lot Size Variability
C-2 Statistics for Normal Distribution C-4
C-3 Data Set C-2: RSD Vs. Lot Size Tons ' C-8
C-4 Data Set C-2: Variability Effect C-9
on the Mean SO-
C-5 RSD of SO vs. Lot Size for Mines 1160, C-10
4186 and 8150
C-6 RSD of SO vs. Lot Size for Mines 4830 C-ll
and 5717
C-7 RSD of SO2 vs. Lot Size for NGS Data C-12
C-8 Unit Train and Monthly Variation of C-15
SO-/106 Btu for Data Set C-2
vi
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TABLES
No. Page
2-1 Pertinent Factors in Studying 2-5
Sulfur Variability
3-1 Summary of Data Sources 3-2
4-1 Summary of Sulfur Variability Data 4-2
4-2 Comparison of Average and RSD of 4-3
Sulfur content of Run-of-Mine Coal
and Corresponding Core Drilling
Samples
4-3 Frequency Tabulation of Weekly 4-4
Weighted Average of Sulfur (Dry Basis)
for Data Set U-l
5-1 Expected Values of the Relative Stan- 5-9
dard Deviation of Weight Percent
Sulfur Vs. Number of Composite Samples
Per Indicated Averaging Period/Tons
5-2 Summary of Compliance Computations 5-17
A-l Minimum, Maximum and Average Sulfur A-43
Weight Percent for Each Data Set
B-l Analysis of Variance B-4
B-2 Analysis of Variance for Data Set U-l B-4
B-3 Estimation of Means and Standard B-6
Deviations (Components of Variation)
of Sulfur Content
B-4 Estimation of Means and Standard B-7
Deviations (Components of Variation)
of Sulfur Content (Coals with Less
Than 1 Percent Sulfur)
B-5 Expected Values and Limiting Values for B-8
Absolute and Relative Standard Devia-
tion for Each Component of Variance
B-6 Cross-Tabulation of Sulfur and Btu B-13
Contents
B-7 Data and Computation of Control Chart B-28
Limits for Moving Average Charts for
Sulfur Content
C-l Analysis of Data Set C-2 C-7
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SUMMARY
Data on the variability of sulfur content and heating
value of coal were obtained from several coal and utility
companies. These data were analyzed to estimate the mean,
standard deviation, and the frequency distribution of weight
percent sulfur (dry basis) and the impact of this variability
on the average sulfur content required for compliance with
an emission regulation. Analysis of composite samples of
coal from unit trains indicates that the values of weight
percent sulfur are skewed to the rightthat is, they tail
off slowly at the higher sulfur levels. This finding suggests
the use of a skewed distribution such as the logarithmic
normal or the inverted gamma distribution in empirical
approximations of the frequency distribution of the weight
percent sulfur. The data on heating values (Btu/lb) do not
appear to be skewed. The ratio of sulfur dioxide emitted
per million Btu (Ib SO?/MM Btu) is also skewed because of
the dominating influence of the variation of sulfur content.
This report indicates that the relative standard deviation
(RSD, the ratio of the standard deviation to the mean
expressed as a percent) for sulfur content expressed as Ib
S02/MM Btu is 1.02 to 1.05 times the RSD for weight percent
sulfur. The statistical correlation between sulfur content
and heating value was found to be relatively low but sig-
nificant in a few cases, and insignificantly different from
zero for almost all of the data sets used in this study.
In order to assess the implications of sulfur vari-
ability in coal for compliance with emission regulations
such as those specified in State Implementation Plans (SIP)
and New Source Performance Standards (NSPS), the relative
standard deviation of weight percent sulfur was estimated
viii
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as a function of the amount of coal sampled and the number
of composite samples for the specified averaging period,
e.g. 1 week, 1 month..
These RSD's were then used to estimate the average
sulfur .content required to yield 95 and 99 percent compliance
with the NSPS emission limitation of 1.2 Ib S02/MM Btu.
Detailed computations are given for two sizes of power
plants, 500 MW and 25 MW* (250 MM Btu/hour, the smallest
plant covered by the IJSPS). Based on averaging periods of
1 month (3 hours), the required averages of weight percent
sulfur to achieve 95 percent compliance are estimated to be
0.65 and 0.60 (0.52 and 0.49) for the 500-MW and 25-MW plant,
respectively. As the percent of compliance increases, the
average sulfur content required for compliance decreases
and rapidly approaches sulfur levels at which the availability
of uncleaned coal that would allow the user to comply with
the NSPS would approach zero.
A methodology is provided whereby an analyst may substi-
tute values of sulfur content variability expressed as an
RSD into a computation or use a graph to estimate the average
sulfur content, in Ib SO^/MM Btu or weight percent, that is
required for compliance with NSPS. Several hypothetical
examples are given to illustrate application of the data and
methodology. If an analyst cannot obtain data specific to a
coal supply, he may use typical or nominal values given in
this report. These values may be adjusted upward or down-
ward if the variation would be expected to be greater or
less than that presented in the summary tables and graphs of
this report.
Assumes 10,000 Btu/kWh heat rate
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PRELIMINARY EVALUATION
OF SULFUR VARIABILITY
IN LOW-SULFUR COALS
FROM SELECTED MINES
1.0 INTRODUCTION
The primary objectives of this report are (1) to
summarize results of a study on sulfur variability in coals
and (2) to determine the effect of this variability on com-
pliance with Federal emission regulations. Data were ob-
tained from coal companies, utility companies, EPA files,
and earlier reports. The data do not permit a study of
sulfur variability for coals from all mines or seams within
a district or region, because the data do not represent a
random sample of coals from a geographical area. A back-
ground discussion concerning variability of sulfur content
is given in Section 2, sources of the data used in this
study are reported in Section 3, summary results are pre-
sented in Section 4, and implications of the results with
respect to compliance with emission regulations are dis-
cussed in Section 5. Because the volume of data used in the
study is too large to include in the report, selected data
summaries are given in Appendix A. These data were analyzed
by standard statistical methods, described in Appendix B. A
possible application of a quality control technique is
described in Appendix B.4. Appendix C presents an analysis
of the variability of sulfur content as a function of the
tonnage of coal sampled. Appendix D gives some comments of
reviewers with respect to practical applications of the
methods presented herein.
1-1
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One of the primary objectives of this study is to
assess the effect of the variability of sulfur content of
coals on compliance with the Federal New Source Performance
Standard (NSPS) limiting the emissions of sulfur dioxide
from coal-fired steam-generating units. The pertinent
portion of this standard follows:
The provisions of this subpart are applicable to
each fossil fuel-fired steam generating unit of more
than 63 million kcal per hour heat input (250 million
Btu per hour), which is the affected facility. Any
change to an existing fossil fuel-fired steam gener-
ating unit to accomodate the use of combustible mate-
rials, other than fossil fuel as defined in this sub-
part, shall not bring that unit under the applicability
of this subpart.
On and after the date on which the performance test
required to be conducted by Part 60.8 of the Federal
Register is completed, no owner or operator subject
to the provisions of this subpart shall cause to be
discharged into the atmosphere from any affected
facility any gases which contain sulfur dioxide in
excess of 2.2 g per million cal heat input (1.2 Ib
per million Btu) derived from solid fossil fuel.*
The essence of this report consists of the methodology
presented in Section 5 and use of the tables and graphs of
that section in analysis of the effect of sulfur variability
on compliance with emission regulations. Several examples
are given to demonstrate application of the results. The
user is in no way restricted to the data given in this
report. To the extent possible, the user should obtain data
on variability of sulfur content of specific coal supplies
under consideration; the user can then apply the appropriate
methodology in Section 5.
The scope of this study does not include determination
of how the emission regulations will affect the sale and
utilization of coals; the attempt here is to provide the
information needed for such a determination.
Code of Federal Regulations 40, Protection of the Environment,
Parts 60, §60.40 and 60.43 (a) (2), (July 1, 1975, page 743.)
1-2
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2.0 VARIABILITY OF SULFUR IN COAL
2.1 BACKGROUND
The sulfur content of coal occurs as the mineral
pyrite, as organically sound sulfur, and in trace amounts as
sulfate sulfur. The ratio of organically bound sulfur to
inorganic sulfur varies widely from coal seam to coal seam,
from mine to mine operating in the same seam and to a lesser
extent within the same mining complex.
An example of the seam variability is shown in the data
displayed in Figure 2-1 for Pittsburgh seam (West Virginia)
coal. The range of organic sulfur is between 1.0 and 2.92
percent by weight, with a mean and standard deviation of
1.62 and 0.52 percent, respectively. The pyritic sulfur
content of these same coals ranges from 0.87 to 4.69 per-
cent, with a mean and standard deviation of 2.07 and 0.95
percent, respectively.
In midwestern coals, the organic sulfur content is
higher on the average than in eastern coals; however, the
organic sulfur occurs in a relatively narrow range of con-
centrations as compared with the pyritic sulfur in these
coals. In most western coals the pyritic sulfur content is
extremely low, and therefore little or no reduction in the
total sulfur content is achieved by present economical
cleaning processes; although in some cases the reduction in
sulfur content of western coals would be sufficient to
upgrade the coal to NSPS.
In a specific coal reserve, the distribution of total
sulfur may occur as shown hypothetically in Figure 2-2,
which identifies iso-sulfur contours. The range of sulfur
content shown is from 1 to 5 percent. If this reserve
were mined by surface or strip mining, the variability of
sulfur content from month to month or year to year would
2-1
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I
to
a ORGANIC SULFUR
o PYRITIC SULFUR
2.0 2.5 3.0 3.5
PERCENT SULFUR BY HEIGHT
Figure 2-1. Variation in pyritic and organic sulfur contents
of Pittsburgh seam coal (West Virginia).
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Figure 2-2. Hypothetical distribution of
percent sulfur in 30-year coal reserve.
2-3
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be significant, since a single large stripping machine is
usually operated along a designated path. In deep mining,
however, a number of mining machines operate in different
sections of the reserve, generally advancing at a constant
rate. Variability of sulfur content of the mined product on
a daily basis would be higher than the variability of the
average sulfur content on a monthly or annual basis. The
daily variability would reflect the in-seam variability, the
number of machines operating, the type of deep mining and
the relative productivity of these machines.
Study of sulfur content of coals requires consideration
of a number of variables such as those summarized in Table
2-1. Many of these factors are interrelated. For example,
the measured differences in sulfur content can reflect not
only differences in the coal in the mine or differences in
the mining method, but also differences in the methods of
sampling, averaging, and measurement. Variability of sulfur
content can be determined on the basis of (1) individual
samples, e.g., one composite sample taken from each unit
train (60 to 100 cars or 6,000 to 10,000 tons) by the
Standard ASTM Method and/or (2) weighted averages of these
individual samples, corresponding to weekly or monthly
averages of coal as received at a utility plant. The four
coal companies providing coal data for this study use this
ASTM method. The data on sulfur variability can then be
used in determining the required average sulfur content of
the coal for the user to comply with a given regulation.
?--
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Table 2-1 PERTINENT FACTORS IN STUDYING SULFUR VARIABILITY
1. Type of coal
Organic and inorganic sulfur content.
Distribution of sulfur in coal (coarse pyrite or
finely disseminated throughout the coal).
The form in which the sulfur occurs is
significant when the coal is washed.
2. Stage of sampling
Core drilling (or channel samples after operation),
Run-of-mine production.
After preparation, cleaning.
As received at utility plant/consumer.
As burned.
3. Coal blending and processing
4. Mining plan (selective)
5. Mining technique
Number and location of machines, type of mining
6. Location of coal
Seam.
Mine.
Region or district.
7. Averaging times/tonnages
Daily.
Weekly.
Monthly.
Other.
8. Sampling procedure
Amount of coal sampled.
How the sample is formed as a composite of a large
amount of coal.
Sample variation.
9. Analytical method
10. Cleaning technique
2-5
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Variability in sulfur content and heating value of
coals could be associated with each of the factors listed in
Table 2-1. A detailed analysis would not be practical,
however, in view of the large number of factors and their
interdependence. Even though some of this information is
available in the records of operating mines and steam plants,
the cost of assembling and analyzing the data would be
prohibitive.
2.2 APPROACH
The approach used in this study was to obtain data on
sulfur contents and heating values of coal from several
sources and to analyze these data by standard statistical
techniques to obtain the following summary information:
1. Averages of sulfur content (weight percent sul-
fur) , heating value (Btu/lb), and sulfur emissions
(Ib SOp/MM Btu) over different averaging times
(per unit train, weekly, monthly, etc.).
2. Standard deviations of weight percent sulfur,
Btu/lb, and Ib S02/MM Btu.
a. Among individual samples from unit trains.
b. Within and among weekly averages.
c. Within and among monthly averages.
3. Frequency distribution of weight percent sulfur,
Btu/lb, and Ib SO2/MM Btu
a. Histograms of data.
b. Cumulative frequency distribution.
Depending upon the particular data set, one or more of these
analyses was conducted for each summary statistic.
No attempt was made to obtain random samples of coals
from different mines and seams in a given region or district,
even though this approach was considered early in the study.
2-6
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Because data sources do not coincide with a region or
district, inferences cannot be made with respect to the
overall variability of all coals in a sampled region.
The results are nonetheless useful in assessing the impact
of variability of sulfur content on compliance with emission
regulations.
It would be desirable to know the long-term variability
of sulfur content because compliance with emission control
regulations is required for the life of the plant. None
of the data, however, extend over a long enough period to
permit estimation of long-term variability.
No attempt was made to isolate the variation in measured
sulfur content that is due to the analytical measurement.
With respect to coals containing less than 2 weight percent
sulfur, one study indicates that the analytical reproduci-
bility (the differences between two or more determinations
carried out by different laboratories on representative
samples taken from the same bulk sample) should be within
0.10 percent in absolute terms. For example, if the
mean sulfur content were 0.70 weight percent, the values
measured by different laboratories should fall within an
interval of 0.65 to 0.75 weight percent. Reference 4 and
Appendix B.I.3 provide further details of the analytical
method and its precision.
2-7
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3.0 DATA BASE
The data base is comprised of 35 data sets. Table 3-1
lists the data sets with comments on each; the sets aro
numbered serially with a prefix U or C to denote utility or
coal company as the source. All of the sets represent coals
mined in recent years (1974, 1975 and 1976), and the sulfur
measurements reflect either core samples or composite samples
from unit trains. A composite sample may represent 1,000 to
20,000 tons of coal.
Of the 35 data sets, 13 were supplied by coal companies
in voluntary support of this study; 8 (U-14 thru U-21) were
taken from a published report on the Navajo Generating
Station; and 1 (U-22) was extracted from Federal Power
Commission reports (FPC Form 423) of utility coal purchases.
U-22 deals with coal purchased from coal districts 3, 7, and
8, for which the mean emission level of all purchases by a
specific plant was less than 1.2 Ib S02/MM Btu (the NSPS
limit).
A statistical summary of all data sets is given in
Section 4, Table 4-1. More detailed statistical summaries
are given in Appendix A.
3-1
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Table 3-1. SUMMARY OF DATA SOURCES
Source of data
Comments
Coal companies
Appalachian coals
Data Set C-l
Data Set C-2
Data Set C-3
Other coals
Data Set C-4
Northern W VA, deep mines, 1972-76. Two-
mine operation, crushed to 2 inches,
Bradford breaker, shipped to one plant.
Raw coal, as loaded, seven continuous
and one long wall miners. 702 samples
each representing an average of about
12,000 tons of coal.
Kentucky, deep mine, 1975. Coal was
cleaned at the mine using a jig washer
in which the total raw coal stream was
cleaned. This is a relatively simple
cleaning operation in an older cleaning
plant. Sampling of coal was done at the
utility plant, 115 samples, each repre-
senting about 5600 tons.
Kentucky, deep mine, 1975. Coal was
cleaned in a modern cleaning plant. The
+l/4-inch coal was cleaned in a heavy
media vessel, the -1/4-inch coal on a
deister table. Filter cake -28M was re-
jected. 157 samples, each representing
about 2500 tons, shipped to one plant.
Montana, 1975-76. Two-seam operation
with blending of each seam or possible
loading of each seam separately. This
depends entirely upon the mining
3-2
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Table 3-1. (continued)
Source of data
Comments
Data Set C-5
Data Set C-6
Data Set C-7
Data Set C-8
Data Set C-9
Data Set C-10
Data Set C-ll
operation and geological factors. Raw
coal shipments, no cleaning. 370 samples,
each representing about 10,000 tons,
shipped to one plant.
Arizona, 1974-1976. Multiple seam
operation with all or part of the seams
loaded simultaneously. Raw coal ship-
ments with the as-mined coal passing
through a Bradford breaker to remove
large rock. No further cleaning. 316
samples, each representing about 3000
tons, shipped to one plant.
Montana, Core data for one seam of data
set C-4, raw coal, 72 cores.
Montana, Core data for other seam of
data set C-4, raw coal, 110 cores.
SE Ohio, Deep mine, 1973-76. One mine
operation crushed to 4 inches, no picking,
shipped to one plant. ASTM sampling and
analysis as loaded. Raw coal, 8 con-
tinuous miners, 272 samples, each repre-
senting about 10,000 tons.
Western PA, Upper Freeport Seam.
data, raw coal.
Core
Central Utah Coal Reserve, I & J Seams.
Core data, bottom bench, raw coal.
Central Utah Coal Reserve, I & J Seams.
Core data, top bench, raw coal.
(continued)
3-3
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Table 3-1. (continued)
Source of data
Comments
Data Set C-12
Data Set C-13
Utility companies:
Appalachian coals
Data Set U-l
Data Set U-2
Data Set U-3
Data Set U-4
Data Set U-5
SE Ohio, Seams 8 and 9. Raw, strip
mining coal, 3 large shovels. ASTM
sampling and analysis as loaded. (559
samples, each representing about 10,000
tons.)
Wyoming. Core data, raw coal. 140
cores, raw coal.
As received at one plant, coal as-burned,
103 weekly averages, 721 samples each
representing about 5700 tons of coal.
1973-1975.
Eastern KY, 1972-1975. Raw coal, as
received at one plant. Sampling and
analysis at plant, ASTM procedure.
312 samples each representing about
11,000 tons.
Eastern Kentucky, 1972-1975. Raw coal,
same coal as above, sampling as burned.
103 samples, each representing about
40,000 tons.
Eastern Kentucky, 1974-1976. Raw coal,
as received at one plant. Modified
ASTM sampling at plant. 162 samples
each representing about 12,000 tons.
Eastern Kentucky, 1974-1976. Raw coal,
as received at one plant. Modified
ASTM sampling at plant. 250 samples
each representing about 13,000 tons.
(continued)
3-4
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Table 3-1. (continued]
Source of data
Comments
Data Set U-6
Data Set U-7
Data Set U-8
Data Set U-9
Data Set U-10
Data Sets U-ll,
and U-13
Other Coals
Data Set U-14
Data Set U-15
West Virginia, District 7, 1975-1976.
As received at one plant. 90 samples
each representing about 2500 tons.
West Virginia, District 7, 1974. As
received at one plant. 120 samples,
each representing about 1800 tons.
West Virginia, District 7, 1974. As
received at one plant. 61 samples, each
representing about 1000 tons.
West Virginia, District 7, 1974. As
received at one plant. 74 samples, each
representing about 1500 tons.
West Virginia, 1975. As received from
one supplier for one plant. Hand sampled
in part, ASTM for almost all samples.
50 samples each representing about 20
cars on the average.
Pennsylvania coal, 1975. Run-of-mine coal,
U-12 receives sizing operation in a Bradford
breaker which reduces the coal to 1 1/4-inch
maximum while removing some shale in the
process. Magnetic pulley removes any tramp
iron in the raw coal stream. All three data
sets - single mine operation. Raw coal.
About 250 samples each representing about
4000 to 12000 tons.
Arizona, Core data. 82 core samples,
raw coal.
Arizona, Core data. 83 core samples,
raw coal.
(continued)
3-5
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Source of data
Comments
Data Set U-16
Data Set U-17
Data Set U-18
Data Set U-19
Data Set U-20
Data Set U-21
Data Set U-22
Arizona, Core data. 395 core samples,
raw coal.
Arizona, Core data. 132 core samples,
raw coal.
Arizona, As received data corresponding
to U-14. 770 samples.
Arizona, As received data corresponding
to U-15. 113 samples.
Arizona, As received data corresponding
to U-16. 768 samples.
Arizona, As received data. 1766 samples.
Districts 3, 7, and 8 purchases by
utilities during 1974 and 1975. FPC form
423 data. 63 samples, each representing
all purchases for which the mean Ib
S02/MM Btu for one plant was less than
1.2.
Data sets U-14 through U-21 are described in greater detail
in reference 1.
3-6
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4.0 DATA ANALYSIS
The methods of data analysis are described in Appendix
B, except for some standard methods that are given in
c f: *j
statistical texts. ' ' The data sets are presented in
Appendix A, with results of pertinent analyses. This
section summarizes the results of the analyses.
Table 4-1 summarizes sulfur variability data by
data set. The arithmetic mean (or average) and the standard
deviation of the measurements of sulfur content are given
in columns 2 and 3. The relative standard deviation*
(RSD) is the ratio of the standard deviation to the mean,
expressed as a percentage, and is given in column 4. For
example, for Data Set C-5, the mean is 0.42, the standard
deviation is 0.048, and the RSD is 11.5 percent. There is
a preference for using the RSD's when the standard deviation
depends on the average concentration. Comparison of the
RSD's for the core data with those of the run-of-mine data
indicates clearly that the core data show larger variations
by factors ranging from 1^ to 4, as illustrated in Table
4-2. This is an expected result; the core sample repre-
sents a very small amount of coal relative to a composite
sample from a unit train of several thousand tons.
Similar analyses were performed with respect to heating
value or Btu content. It is readily apparent that the
RSD of Btu content is much smaller, 2 to 5 percent, than
that for sulfur content which is 5 to 25 percent.
*The RSD is also referred to as the coefficient of variation,
4-1
-------
I
ro
Data
set
C-l
C-2
C-3
C-4
C-5
C-6
C-7
C-8
C-9
C-10
C-ll
C-12
C-13
U-l
U-2
U-3
U-4
U-5
U-6
U-7
U-8
U-9
U-10
U-ll
U-12
U-13
U-14
U-15
U-16
U-17
U-18
U-19
U-20
U-21
0-22
Weight percent sulfur
Average
2.30
0.60
0.81
1.38
0.42
Standard
deviation
0.224
0.030
0.088
0.253
0.049
2.14 0.705
1.50
2.60
1.G3
0.58
0. 88
3.42
0.58
0.74
0.88
0.82
1.04
0.93
0.79
0.80
0.84
0.81
1.74
3. 10
2.25
2.15
0.49
0.53
0.68
0.66
0.37
0.46
0.60
0.55
0.405
0.130
0.780
0.247
0.535
1). 344
0.090
0.129
0.103
0.160
0.180
0.170
0.150
0.170
0.220
0.160
0.59
0.366
0.157
0.152
0.195
0.164
0.180
0.180
0.035
0.055
0.092
0.086
RSDa of
variation, %
8.0
5.0
10.9
18.3
11.7
33.0
27.0
5.0
47.8
42.6
60.7
10.1
15.5
17.4
11.7
19.5
17.3
18.3
19.0
21.3
26.2
19.8
33.9
11.8
7.0
7.1
39.8
30.9
26.5
27.3
9.5
12.0
15.3
15.6
Btu/lb
Average
13,050
Standard
deviation
224
RSD of
variation, %
1.7
12,310 161 ! 1.3
12,250 276 ' 2.3
11,540 263 2.3
12,150 , 197 1.6
11,540 i 291 2.5
11,480 283 2.5
12,480 708 5.7
14,190
142 1.0
13,170 332 2.5
12, 700 291 . 2.3
12,000 160 , 1.3
11,970 191 1.6
12,500 250 2.0
12,000 250 2.1
11,000 210 1.9
12,000
11,900
11,800
12,300
12,200
12,000
12,070
11,030
11,770
11,480
280 , 2.3
280 ', 2.4
400 3.4
488 4.0
636 5.2
665 5. 5
382 \ 3.2
332 ! 3.0
251
267
2.1
2. 3
Ib SO2/MM Btu
Average
4. 21
0.93
1.26&
2. 34
0.65b
3.52b
2.48b
4.08
2.25
0.88
1. 39
5.69
0.95
1.16
1. 39b
1.42b
1.73
1.55
1. 34
1.29
1.37
1 . 35
2.83
5. 34b
3.36b
3.56b
1.03C
Standard
deviation
0. 34
0.07
0. 14
0.43
0.08
1.20
0.67
0. 30
1.08
0.38
0.86
0.59
0.15
0.21
0.17
0.28
0.23
0.18
0.27
0.28
0. 34
0. 27
0.96
0.65
0.25
0.27
0.16
RSD of
variation, %
8.1
7.1
11.1
Core data
18.4 i
33.1
27.1
7.6
47.8
42.7
60. 7
10.4
15.6
17.5
11.9
19.6
16.2
11.6
20.1
21.7
26.7
20.0
34.1
12.2
7.4
7.6
15.8
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
RSD (relative standard deviation) is the ratio of the standard deviation to the average, multiplied
by 100 to yield the standard deviation as a percent of the average.
Estimated from weight percent sulfur and Btu/lb data, not by direct computation.
Positive square root of pooled variance estimates, coals purchased in Districts 3, 7, and 8,
for which the mean or average sulfur content is less than 1.2 Ib SO2/MM Btu.
-------
Analysis of sulfur content in Ib S02/MM Btu was
performed by two methods:
1. Using Ib S02 computed by multiplying weight per-
cent by 1.90 (Ib SC>2 emitted per Ib sulfur in
coal), dividing by the Btu content, and expressing
the results in Ib S02/MM Btu.
2. By direct use of results from analysis of weight
percent sulfur and Btu/lb.
In case 2, the RSD of Ib S02/MM Btu is given by the ap-
proximation, square root of the sum of squares of the RDS's
of weight percent sulfur and Btu content. See Appendix
B.I.5 for the explanation of this method. Also in case
2, the average Ib SC^/MM Btu is given by the quotient of
the corresponding average of weight percent sulfur x 1.90
by average Btu/lb x 10~ .
Table 4-2. COMPARISON OF AVERAGE AND RSD OF
SULFUR CONTENT OF RUN-OF-MINE COAL AND
CORRESPONDING CORE DRILLING SAMPLES
Run-of-mine data
Data set
C-4
U-18
U-19
U-20
x
1.38
0.37
0.46
0.60
RSD, %
18.3
9.5
12.0
15.3
Core drilling data
Data set
/C-6
\C-7
U-14
U-15
U-16
x
2.14
1.50
0.49
0.53
0.68
RSD, %
33
27
39.8
30.9
26.5
Standard frequency tabulations were made of almost all
the data sets with low sulfur content, less than or equal
to 1 percent. The tabulation for Data Set U-l is given
in Table 4-3. A histogram and a cumulative frequency
distribution are given for these same data in Figures 4-1
and 4-2, respectively. The cumulative frequency is plotted
on logarithmic normal probability paper because the data
4-3
-------
Table 4-3. FREQUENCY TABULATION OF WEEKLY WEIGHTED
AVERAGE OF SULFUR (DRY BASIS) FOR DATA SET U-l3
Weighted
average, %
0.62 -
0.64 -
0.66 -
0.68 -
0.70 -
0.72 -
0.74 -
0.76 -
0.78 -
0.80 -
0.82 -
0.84 -
0.86 -
0.38 -
0.90 -
0.92 -
0.94 -
0.96 -
0.98 -
0.63
0.65
0.67
0.69
0.71
0.73
0.75
0.77
0.79
0.81
0.83
0.85
0.87
0.89
0.91
0.93
0.95
0.97
0.99
Frequency
1
6
5
14
21
13
6
11
8
3
2
4
1
4
0
1
1
1
1
x = 0.742
s = 0.0732
Each weekly weighted average is a weighted average of the
seven daily measurements of weight percent sulfur for a
composite sample from an average of about 5700 tons of coal,
4-4
-------
0.575 0.655 0.735 0.815 0.895 0.975
WEIGHT PERCENT SULFUR
Figure 4-1. Histogram of weekly averages for data set U-l,
4-5
-------
2.0
ex:
UJ
1.0
0.90
0.80
0.70
0.60
0.50
I I
12 5 10 20 30 40 50 60 70 80 90 95 98 99
PERCENT OF AVERAGES AT OR BELOW CORRESPONDING ORDINATE
Figure 4-2. Cumulative frequency graph of data set U-l
-------
are skewed toward the high values. This skewing is obvious
upon examination of the histogram in Figure 4-1, which
shows tail-off of the data at the higher values of weight
percent sulfur. Reference 1 discusses this point in
considerable detail and suggests the inverted gamma fre-
quency distribution. The lognormal is another good empir-
ical approximation, which is more convenient than the
inverted gamma and gives results that are identical for
all practical purposes. Rational explanations for the
logarithmic normal distribution are given in statistical
literature.
One other graphical analysis that is useful in inter-
preting the variability of sulfur content in coal is a
time series plot of the sulfur measurements by unit train
and by weekly average, as shown in Figure 4-3 for Data
Set U-l. This plot allows comparison of short-term
variation (week-to-week) and a 4-week moving average. The
definite tendency is for the values of successive weeks
to be closer than those that are more separated in time
(that is, a greater correlation among the weight percent
sulfur values with a short time lag). No sophisticated
time series analyses were conducted because the time
increments between unit train samples are not typically
the same within data sets. Data set U-l is unique in
this respect in that there is one data value for each day.
Several analyses were made of the correlation between
the sulfur and Btu contents of the coal; these were done
by a combination of cross-tabulation and computation of
the correlation coefficient. Results are given in Appen-
dix A (cross-tabulations) and Appendix B (for Data Set
U-l) .
4-7
-------
1.00
4 WEEK MOVING AVERAGE
MEAN VALUE * 0.742
0.60
25 30
MUMKR OF WEEK
Figure 4-3. Average weekly sulfur content of coal of data set U-l
vs. the number of the week.
-------
5.0 IMPLICATIONS OF STATISTICAL ANALYSIS
5.1 BACKGROUND AND INTRODUCTION
The purpose of this section is to provide a methodology
for estimating the impact of the variability of sulfur as
a function of the tons (e.g., per 3 hours) and/or the
number of composite samples analyzed and averaged (per
week, month, etc.) on determination of compliance with SIP
or NSPS emission regulations. Since the impact will be
similar for both types of regulations, only NSPS compliance
is considered here. (An example is given for a regulation
other than NSPS.)
THE NSPS 1.2 Ib SO-/MM Btu, is stated as a maximum
value never to be exceeded. A legal interpretation of
the NSPS would require that at no instant of time would
the value 1.2 be exceeded. An interpretation of the NSPS
based on a continuous monitoring procedure is that the
maximum 3-hour average should not exceed 1.2 Ib SO-/MM Btu.
A typical plant of 500 MW capacity will burn about 600
tons of coal in three hours. The smallest plant covered
by the NSPS, 25 MW, will burn about 33 tons of coal in
3 hours. Although no data sets in this study contain
samples that represent an amount of coal as small as
either 600 or 33 tons, data set C-12 and other selected
data sets provide statistical evidence of a trend toward
smaller RSD's as the quantity (tons) of coal sampled
increases. (See Appendix C for a detailed discussion of
this relationship.) This tendency is consistent with that
5-1
-------
expected from the standpoint of a physical explanation
of the sampling process (see ASTM procedure ). The .avail-
able data are extrapolated to yield a reasonable estimate
of the RSD as a function of quantity of coal sampled in
order to estimate the impact of the variability in sulfur
content on compliance with NSPS. It will be more difficult
for a small plant to comply with the NSPS, on the assump-
tion that the coal burned during each 3-hour period will
vary more in sulfur content than will that burned at a
typical 500-MW plant. This problem is discussed further
in Section 5.2.
If the interpretation of NSPS involved a longer
period, such as 1 week or 1 month, and if several composite
samples were analyzed and the results averaged for the
longer period of compliance, then the impacts on compliance
with NSPS can be estimated by use of the data and methods
presented in this section.
Compliance in this case would be determined by
averaging, for example, all the composite analyses of sulfur
content for the specified period, say 1 month. If this
average is less than some specified value, such as 1.2 Ib
S02/MM Btu, one would infer that the coal would provide
compliance. In this case, the variability of the average
depends on (1) the amount of coal represented by each
composite sample and (2) the number of composite samples
averaged during the specified period. The results will
vary less as either the tonnage and/or the number of
samples increases. The smaller plants are expected to
receive smaller quantities per sample as well as fewer
samples per month, and hence, the averages for a specified
period of 1 month will vary more than those of a larger
plant. A methodology is presented wherby an analyst or
5-2
-------
company may use estimates of the RSD based on computations
with available data or perhaps by computer simulation
models to yield a measure of the likelihood of compliance
with NSPS or other emission regulations.
As an illustration of the determination of the impact
of sulfur variability on compliance with the NSPS, consider
the following example. A typical 500-MW plant uses 600
tons of coal per 3 hours, 4800 tons per day, and receives
coal four times per week (four unit trains), averaging
8400 tons each delivery. Thus 16 composite samples are
analyzed for Ib S02/MM Btu averaged for 1 month. If this
monthly average is used as a basis for compliance, what is
the expected frequency with which the average exceeds 1.2
Ib SC>2/MM Btu? What is the average required sulfur content
(weight percent) that will enable compliance with the
regulation assuming that variability is (1) as estimated
in this study and (2) as estimated from data available to
the company?
Although NSPS does not legally permit a single value
to exceed a standard, in practice it is necessary to admit
noncompliance for some minimal number or percentage of
cases (averaging periods). The percentage of noncompliance
can be maintained at a small value that will provide a
reasonable trade-off between availability of coals (costs)
and average emission levels. Several hypothetical examples
are posed at the end of this section to illustrate use
of the methodology.
5.2 DATA ANALYSIS
Analyses were performed on the data to (1) relate the
variability of sulfur content to the amount (tonnage) of
the coal from which the composite sample was taken and/or
the number of composite samples used in obtaining the
5-3
-------
average, (2) estimate the form of the frequency distribution
of the individual analyses of composite samples from unit
trains, and (3) estimate the impact of sulfur-content varia-
bility on the determination of compliance with emission
regulations.
Appendix B.I.2 presents a brief description of the
statistical methods and a summary of the means and the
estimates of the standard deviations of the several sources
of variation corresponding to the number of composite samples
analyzed and averaged during one week, month, etc. All of
these analyses were performed using the data in their ori-
ginal scale, that is, with no transformations. Logarithmic
transformations are often used to stabilize the variance if
the standard deviation in the original scale varies directly
as the mean (see Figure B-2). In several analyses essen-
tially the same result was obtained with and without the
transformation. It can be readily established that the
standard deviation of In x is approximately equal to the RSD
of x. Thus the use of RSD's results in a stabilization of
the variance in situations where the logarithmic transfor-
mations are indicated. The RSD's are also more useful for
making comparisons in the study of the variability of sulfur
in coal. At the bottom of Table B-5 are given the weighted
average or pooled standard deviations and the average
relative standard deviations. These are typical values that
might occur for a particular application. The coals repre-
sented in this table have had different degrees of preparation
and cleaning and have been mined by different techniques.
If one knows that the mining and processing techniques of a
given operation will provide a coal of less (or greater)
variation in sulfur content than the average, then the
lower (or upper) limits in Table B-6 might be used, as
5-4
-------
described in Appendix B.I.3. NOTE; It is emphasized that
the values are based on a collection of coal data made
available by selected companies. Each company using the
approach presented herein is urged to use its own data in
estimating the variability of sulfur content for specified
averaging times or tonnages.
As stated earlier, the data for estimating sulfur
variability are based on analyses of composite samples from
unit trains in quantities ranging from about 1,000 tons to
20,000 tons; none of the data extended to the range of 33
tons or 600 tons, as required to estimate the impact of
variability on compliance in a 3-hour averaging time for
either a small plant or an average plant. Thus, an attempt
is made to extrapolate the available data to smaller amounts
of coal (in tons) by use of specific data sets as a basis
for obtaining a relationship between the relative standard
deviation and the amount of coal sampled. For the region
of extrapolation, this relationship is assumed to be linear
in the logarithm of the amount of coal sampled in tons, i.e.,
the RSD is given by
RSD = a + b log,0T (Equation 5-1)
where
RSD = relative standard deviation of weight
percent sulfur,
T = tons of coal sampled,
log,QT = log of T, base 10 (common logarithms), and
a,b = constants to be determined by the data.
Data set C-12, gives the following results for the
relative standard deviation as a function of the amount of
coal sampled.
5-5
-------
Weight percent sulfur
Amount of coal
sampled, tons
2,000
10,000
Minimum
1.76
2.54
Maximum
5.04
4.34
Mean, X
3-. 42
3.42
Standard
deviation,
0.4251
0.3436
RSD =
s s/X
0.1243
0.1005
Using these data and equation 5-1, one obtains
0.1005 = a + b log1Q10,000
0.1243 = a + b Iog1()2,000,
and hence, upon solving for a and b,
a = 0.237
b 0.0341,
and
RSD = 0.289 - 0.0341 log1()T.
For this particular coal (Data Set C-12) the RSD is slightly
smaller than the average for all of the coal data analyzed;
hence, the value of RSD was adjusted by increasing the
constant term, a, from 0.237 to 0.289. Thus the final
equation for RSD , i.e., the predicted RSD, is
RSD = 0.289 - 0.0341 log1QT. (Equation 5-2)
Because this equation is based on a small amount of data,
it is desirable to extrapolate the result to the extreme,
comparable to a core sample representing, say, 50 pounds
of coal. For T = 50/2000 = 0.0250,
RSD = 0.289 - 0.0341(log 0.025) = 0.344,
which is consistent with the core sample data. That is,
in Table 4-1 the RSD's for core sample data (indicated by
a yes in the last column) range from 26 to 48 percent
and one value is at 61 percent. Thus, the 34 percent
value is a reasonable extrapolation of the results.
5-6
-------
These results are given in Table 5-1 above the dashed
line for a 25-MW plant (33 tons of coal burned in 3 hours)
and below the dashed line for a 500-MW plant (600 tons of
coal burned in 3 hours, 4800 tons per day, 4 unit trains
per week, 16 sample results averaged per month). Figure
5-1 also shows the impacts on the RSD of the weight percent
sulfur of the amount of coal represented by a composite
sample and/or the number of sample results averaged
during the specified averaging period. The extrapolation
to 33 tons for the 25-MW plant is shown by a dashed line.
At the extreme right-hand portion of the curve it is
desired that the RSD tend to zero as the averaging time
approaches the life of the typical mine, say 20 years.
The RSD for the left-hand portion of the curve approaches
that of core samples. Hence, the two ends of the curve
in Figure 5-1 are reasonably well determined, as are
some of the central portions, particularly for the amount
of coal represented by one unit train and for averages
of results of 16 composite samples per month.
5.3 AVERAGE SULFUR CONTENT REQUIRED FOR COMPLIANCE
Computation of the average sulfur content required
for compliance with the 1.2 Ib SO /MM Btu regulation is
based on appropriate assumptions concerning the frequency
distribution of the data. The computations assume a
typical 500-MW plant or 25-MW plant, as indicated.
5.3.1 Averaging Period of One Month, Assuming Normality,
500-MW Plant
Let m be the mean required sulfur content, then for
16 samples per month, RSD = 0.069 for weight percent sulfur,
Table 5-1. It is assumed that the RSD for Ib S02/MM Btu =
1.05 x RSD for weight percent sulfur. See Appendix B.I.5
5-7
-------
I
00
»
in
0.24
0.20
0.16
0.12
0.08
0.04
48
33 TONS
(3 HOURS FOR
-THE 25 MM PLANT)
480
TONS OF COAL
4800
48,000
480,000
4.8 x 10"
600 TONS (3 HOURS FOR 500 MM PLANT)
Q*V REGION OF EXTRAPOLATION
-4800 TONS (1 DAY FOR 500 MM PLANT)
-8400 (1 UNIT TRAIN FOR 500 MH PLANT)
AVERAGING PERIOD 3 HOURS 1 DAY 7
(500 MM)
AVERAGING PERIOD/TONS OF COAL (DAYS/HOURS/TONS)
30 90 180 360
Figure 5-1. RSD versus averaging period/tons of coal (days/hours/tons)
-------
Table 5-1. EXPECTED VALUES OF THE RELATIVE STANDARD
DEVIATION3 OF WEIGHT PERCENT SULFUR VS. NUMBER OF COMPOSITE
SAMPLES PER INDICATED AVERAGING PERIOD/TONS .
(Based on data for coals with 1.0 percent sulfur or less)
Averaging period/ (tons)
3 hours/ 33 tons, 25 MW plant
3 hours/ 600 tons, 500 MW plant
Among unit trains
(composite samples of
8400 tons, 500 MW plant)
Weekly averages
n= 2C
Monthly averages 11.7%
Quarterly averages 6.8%
Semiannual averages 4.8%
Annual averages 3.4%
Expected variation
23.7%
19.4%
15.5%
w=l w=2 w =
15.5% 14.2% 12
n = 4 n=8 n =
9.3% 7.8% 6.
5.4% 4.5% 4.
3.8% 3.2% 2.
2.7% 2.3% 2.
(RSD)
4 w =
.3% 11
16 n =
9% 6.
0% 3.
8% 2.
0% 1.
7
.4%
28
5%
8%
7%
9%
The relative standard deviation can be used for a wide range
of levels of sulfur content. For example, if the coal is
1 weight percent sulfur, the values in the table also serve
as the absolute standard deviation; if, however, the coal is
1.5 percent sulfur, the values should be multiplied by 1.5 to
yield the absolute standard deviation. The data in this
study cover the range up to 1.5 percent, and these percentages
seem to be appropriate over this range. See Figure B-2.
w is the number of unit trains (composite samples averaged)
per week.
Q
n is the number of unit trains (composite samples averaged)
per month.
5-9
-------
for a discussion of this relationship between the RSD's.
Hence, the RSD for Ib SO?/MM Btu for averages of composite
samples from 16 unit trains, is given by
0.069(1.05) = 0.0725.
Figure 5-2 illustrates the determination of the value m,
in that for 95 percent compliance the distance between m
and 1.2 must be equal to 1.645 a where a is the absolute
standard deviation of Ib S02/MM Btu and is 0.0725 m, i.e.,
the product of the RSD by the mean value, m. The value
1.645 is obtained from a table for areas under a standard
g
normal curve, corresponding to the 95th percentile.
Figure 5-2. Determination of required
average sulfur content
Hence,
u
1.2 - m
0.0725m
= 1.645
(Equation 5-3)
or
m = 1.072.
5-10
-------
The weight percent sulfur for a coal with heating value of
11,500 Btu/lb is given by 0.727 x (1.072/1.2) = 0.65. The
value is then adjusted by the ratio 1.072/1.2. Similarly
the calculation of m for 99 percent compliance is made by
using 2.326 in place of 1.645. Values of m for different
amounts of coal sampled/numbers of samples averaged are
obtained by multiplying the RSD given in Table 5-1 by 1.05
and substituting it for the 0.0725 in equation 5-3.
5.3.2 Averaging Period of One Month, Assuming Lognormal
Distribution, Small Plant
In this case, the number of composite samples averaged
per month will be smaller than that for the 500-MW plant.
For example, if 33 tons are required per 3 hours, 264 tons
per day, or 7920 tons per month, it is possible that the
entire month's supply would be obtained at one time. For
the purpose of illustration, assume that four shipments of
about 2000 tons each are received in one month and that the
average sulfur content of four composite samples is used
to determine compliance with the emission regulation. From
Figure 5-1, the expected RSD of weight percent sulfur for
samples of 2000 tons is about 18.2 percent. On the assumption
that four composite samples are averaged each month, from
Table 5-1 we read that RSD is 9.3 percent. However, this
is based on samples from a larger tonnage of coal, 8400
tons rather than the 2000 in this example. Hence, assuming
the same percentage reduction in the RSD is given for 4
composite samples from the 2000 ton lot as for the 8400
ton lots, an estimate of the RSD is the product of 18.2
by (9.3/15.5) or about 10.9 percent. The RSD of Ib S02/MM
Btu is estimated to be 11.5 percent (= 10.9 x 1.05). This
value is then used along with the lognormal distribution
to obtain an estimate of the required mean sulfur content.
5-11
-------
The normality assumption is not good for averages of
a small number of measurements, say less than 5; hence, the
lognormal distribution was assumed for this example.
The lognormal distribution is skewed toward the larger
values as shown in Figure 5-4, upper sketch. The lower
distribution is that of the transformed variable, Y = InX,
which should be approximately normally distributed. As
stated earlier, the lognormal distribution provides a very
good empirical fit to several of the data sets, and because
of its mathematical convenience, the impact of sulfur con-
tent is first determined by use of this distribution. The
value of 0.115, is determined as follows: If Y = InX, and
the standard deviation of X is (1.05) x 10.9% or 0.115, where
m is the mean of X, m1 the mean of Y, then the standard
deviation of Y is approximately,
0{Y} = i 0{X} = RSD{X).
That is, the estimated standard deviation of InX is essentially
equal to the RSD of X. Hence, the transformation Y = InX
is a variance stabilizing one, provided the RSD's are approxi-
mately the same for all levels of sulfur content. Calcu-
lations using the RSD of the sulfur content are essentially
equivalent to those using the standard deviation of the
logarithm of sulfur content.
From Figure 5-3, the sulfur content required for 95
percent compliance with 11,500 Btu/lb heating value would
be 0.727 x (0.993/1.2) = 0.60 weight percent sulfur. The
multiplication by 0.993/1.2 provides for the adjustment
from 1.2 to 0.993 as the required average.
5-12
-------
13,000
12,000
o
»
z
CO
11,000
10,000
I
I
0.60
0.70 0.80
WEIGHT PERCENT SULFUK
Figure 5-3. Sulfur content versus heating value of
coal required to yield 1.2 Ib S02/MM Btu
(1.90 Ib S02/lb S assumed)
5-13
-------
NODE
MEDIAN
1.2
0.182
Y « InX
Figure 5-4. Determination of required average
sulfur content assuming lognormal distribution
Referring to Figure 5-4, lower sketch, the following
approximate relationship applies, where m1 is the mean of
the lognormal distribution, 0.182 = In 1.2.
0.182 - m1 , ,At.
u = 0.115 = 1'645
m1 = -0.0072
m ~ em' = 0.993 Ib
Btu.
5-14
-------
5.3.3 Three-Hour Average, Lognormal Distribution ,
500-MW Plant
Now consider the implication of the expected variation
in 3-hour averages for the 500-MW plant with respect to
compliance with the NSPS. In this case the graph of Figure
5-1 provides an estimate of the RSD of the weight percent
sulfur to equal to 19.4 percent, or 19.4 * 1.05 or 20.4
percent for Ib SO^/MM Btu. Using the same procedure as
in earlier computations
_ 0.182 - m'
U
04
m1 = -0.1536
m - em = 0.858 Ib S02/MM Btu.
Using Figure 5-3, the weight percent sulfur assuming 11,500
Btu/lb, must average 0.727 (0.858/1.2) = 0.52 weight percent
sulfur.
This computation is also performed in Appendix B.3
assuming the inverted gamma distribution; the result is 0.875
compared with the 0.858 obtained using the lognormal distri-
bution. This same close relationship was found for a large
number of cases computed with both lognormal and inverted
gama distributions.
5.3.4 Three Hour Average, Lognormal Distribution,
Small Plant
For this case, the RSD as read from Figure 5-1 for 33
tons is about 23.7 percent, or about 24.9 percent for Ib
SO2/MM Btu. Hence, the estimated mean for 95 percent com-
pliance is estimated to be about 0.80. In terms of sulfur
content, this transforms to 0.727 x (0.80/1.2) = 0.49
average weight percent sulfur.
5-1!
-------
The results of these four analyses are tabulated in
Table 5-2 for convenience of subsequent discussion.
Table 5-2 shows clearly that the mean weight percent
sulfur required for compliance with the NSPS decreases as
the averaging period changes from 1 month to 3 hours and
also as the plant size decreases. As the percentage of
compliance increases, the mean will decrease still further
and will rapidly approach a value for which the availability
of raw coal for compliance with NSPS tends to be very limited.
Figure 5-5 provides a general procedure for determining
the average sulfur content of a coal (Ib S02/MM Btu) required
to achieve compliance with the NSPS of 1.2 Ib S02/MM Btu for
90, 95, and 99 percent of the averages of individual unit
train samples for specified RSD's. Results are given for
assumptions of both normal and lognormal distribution of
sulfur content (Ib S02/MM Btu). For example, if a company
has determined that the monthly averages vary by approxi-
mately 7 percent of the mean (RSD = 7%), then for 95 percent
compliance, the required mean sulfur content would be about
1.08 (1.07) Ib S02/MM Btu assuming normal (lognormal) dis-
tribution. If one does not have information from which to
derive the sulfur variability in terms of the RSD, then
Figure 5-1 may be used to obtain an estimated value. These
values would be multiplied by 1.05 to estimate the RSD of Ib
S02/MM Btu in terms of that for weight percent sulfur. The
RSD's read from Figure 5-1 would be applicable to coals with
sulfur content up to 3 percent, the limit of data used in
this study. It is expected, however, that the RSD's also
would apply to higher sulfur levels.
5-16
-------
Table 5-2. SUMMARY OF COMPLIANCE COMPUTATIONS
(95 AND 99% COMPLIANCE WITH EMISSION RATE OF
1.2 Ib SO /MM Btu)
Averaging
period
1 month
3 hours
Information
Number of composite samples
per month
Tonnage of coal represented
by each sample
RSD (Ib S02/MM Btu)
Assumed heating value
Required mean (Ib SO2/MM
Btu) for 95% compliance
Required mean (weight
percent sulfur) for 95% com.
Required mean (Ib SO?/
MM Btu) for 99% compliance
Required mean (weight
percent sulfur) for 99% com.
Tonnage of coal represented
by each sample
RSD (Ib S02/MM Btu)
Assumed heating value
Required mean (Ib SO2/
MM Btu) for 95% compliance
Required mean (weight
percent sulfur) for 95% com
Required mean (Ib S02/
MM Btu) for 99% compliance
Required mean (weight
percent sulfur) for 99% com
500-MW
plant
16
8,400
7.25%
11,500
1.072
0.65
1.014
0.61
600
20.4
11,500
0.86
0.52
0.75
0.45
25-MW
plant
4
2,000
11.5%
11,500
0.993
0.60
0.918
0.56
33
24.9
11,500
0.80
0.49
0.67
0.41
5-17
-------
ASSUMING NORMAL
DISTRIBUTION
ASSUMING LOG NOftMAL
DISTRIBUTION
0 5 10 15 20 25
SULFUR VARIABILITY EXPRESSED AS RELATIVE STANDARD DEVIATION (*)
Figure 5-5. Required average sulfur content
vs. sulfur variability.
5-18
-------
5.4 EXAMPLES
The essence of this report is application of the tables
and graphs of this section, together with necessary back-
ground information as described in other sections, to real
problems of compliance with NSPS or other emission limita-
tions. As an aid in understanding the application of these
graphs and tables, several examples are given to represent
some typical problems.
Example 1
A coal is assumed to vary in a manner consistent with
the data in Figure 5-1, having an average weight percent
sulfur equal to 0.70. Assume that four unit trains are
received each week, i.e., Table 5-1 under w=4. What is the
expected range of variation of sulfur content (weight
percent) of 95 percent of the weekly averages (2a limits)?
Monthly averages? Quarterly averages?
Weekly (7 days) averages: 0.70 + 2(0.123) (0.70) =
0.70 + 0.17,
Monthly (30 days) averages: 0.70 + 2(0.069)(0.70) =
0.70 + 0.10,
Quarterly (90 days) averages: 0.70 + 2 (0.04) (0.70) =
0.70 + 0.056.
Example 2
Only two unit trains are received per week (eight per
month), and the limits of variation specified in Example 1
are required. In this case one must refer to Table 5-1,
third column. The results are as follows:
Weekly averages: 0.70 + 2(0.142)0.70 =
0.70 + 0.199,
Monthly averages: 0.70 + 2(0.078)0.70 =
0.70 + 0.109,
Quarterly averages: 0.70 + 2(0.045)0.70 =
0.70 + 0.063.
5-19
-------
Example 3
Data are available from which it has been determined
that monthly averages vary by 10 percent of the mean (RSD =
10%) about an average sulfur content of 0.70 weight percent
and that the heating values vary by 2 percent about an
average of 12,000 Btu/lb. Would this coal enable the plant
to meet the NSPS regulation for 95 percent of the monthly
averages? The average and standard deviation of Ib S02/MM
Btu is given by the very good approximation,
- 0.70 x 1.90 ,n4 _ , n,
x 12,000 x 10 ~ 1'11'
s -x /tO. 10)2 + (0.02)2 = 1.11(0.102) = 0.113.
Using Figure 5-5, for RSD of 10.2 percent and 95 percent
compliance, the required average must not exceed 1.03 (1.01)
Ib SO2/MM Btu assuming normal (lognormal) distribution.
Because x = 1.11 is larger than 1.03^ the relative frequency
of compliance will not be 95 percent. The expected fre-
quency of compliance can be estimated, assuming normality,
by use of the standard normal variable, u,
- l-2 - * _ 1.2 - l.ll _ 0 a
u - -- - --- -- -- 0.80,
Q
and a table of normal probabilities to obtain 0.788, or
compliance about 79 percent of the time.
Example 4
It has been determined that the variability of sulfur
content (weight percent) of a unit train sample has an RSD
equal to 15 percent. The average sulfur content required
for compliance 95 percent of the time is about 0.96 (0.94)
Ib SO-/ MM Btu, as read from Figure 5-5 for the assumption
5-20
-------
of normal (lognormal) distribution. Note that Figure 5-5
can be used in many applications.
Example 5
A state agency has decided that the monthly averages of
sulfur content must provide compliance with the NSPS reg-
ulation 99 percent of the time. Assume that a plant receives
four unit trains each week, or sixteen per month. What is
the average sulfur content required for compliance with the
regulation 1.2 Ib S02/MM Btu? It is assumed that Table 5-1
is applicable, that is, the RSD of weight percent sulfur is
0.069 and the RSD for Ib S02/MM Btu is given by 0.069 (1.05)
= 0.0725.
From Figure 5-5, the 30-day average for 99 percent
compliance and assuming normal distribution is read as 1.025
Ib SO_/MM Btu. From Figure 5-3, for heating value of 11,500
Btu/lb, we read 0.727 percent sulfur to yield 1.2 Ib or
0.727 (1.025/1.2) = 0.62 as the required average weight
percent sulfur. Figure 5-3 was derived on the assumption
that 1.9 pounds of SO_ is emitted per pound of sulfur.
Example 6
Same as in Example 5, except that weekly averages are
used and 95 percent compliance is acceptable. Using Table
5-1, the RSD for weekly averages (four unit trains) is 12.3
percent; from the 95 percent curve on Figure 5.5 (lognormal
distribution), the required average sulfur content should be
0.98 Ib S02/MM Btu. From Figure 5-3, the average sulfur
content in weight percent sulfur is determined by reading
the value corresponding to 11,500 (i.e., 0.727) and multi-
plying by 0.98/1.2 to obtain 0.59 weight percent sulfur.
Example 7
An SIP requires compliance 95 percent of the time on
emission standard of 2.0 Ib SO_/MM Btu, based on monthly
5-21
-------
averages of 16 unit trains. Assume that the RSD values
in Table 5-1 are applicable. From the table, we read the
RSD value 6.9 percent. For compliance 95 percent of the
time, the standard normal variable u = (2.0 - m)/0.069(1.05)m
must equal 1.645 (2.326 for 99 percent compliance). The
1.05 multiplier is used to account for the higher variability
of Ib SO2/MM Btu relative to the variability of percent
sulfur. Solving the equation,
2.0 - m _ . ..At.
0.0725m - 1'645'
we obtain m = 1.787 Ib S02/MM Btu. From Figure 5-3, the
required average weight percent sulfur is obtained for an
assumed heating value of 12,500 Btu/lb: 0.790 x (1.787/1.2)
=1.18 percent.
5-22
-------
6.0 CONCLUSIONS AND RECOMMENDATIONS
CONCLUSIONS
1. The distribution of weight percent sulfur for com-
posite samples from unit trains is skewed to the right (has
a long tail of large values). This is particularly im-
portant when decisions are based on only one or two composite
samples from unit trains.
2. The logarithmic normal distribution is used to
approximate the skewed distribution. This is a good empir-
ical approximation and is convenient for making predictions
concerning compliance. The inverted gamma distribution has
also been proposed as an empirical fit to the skewed fre-
quency distribution. Differences in estimates made using
these two distributions are very small.
3. The distribution of Btu content of coals is rea-
sonably symmetrical and is approximated rather well using
the normal distribution.
4. The distribution of Ib SO_/MM Btu is skewed because
of the dominating effect of the distribution of weight
percent sulfur.
5. The variation of weight percent sulfur from com-
posite samples (unit trains) is approximately 15 percent of
the mean sulfur content, with almost all of the values
between 10 and 25 percent of the mean. The lower percent-
ages result from coal cleaning and/or from mining techniques,
such as the number of machines in operation. The higher
values would occur with no cleaning or with a mining tech-
nique that does not tend to mix or "blend" the coals within
6-1
-------
the mining area. Greater variation also results from mixing
coals from two seams with different sulfur content, par-
ticularly when the proportions of the two coals also vary.
NOTE: It is emphasized that the values provided in this
report are not necessarily representative of a specific
coal, mining or processing technique. The values are based
on a collection of coal data made available by selected
companies. Each company using the approach presented herein
is urged to use its own data in estimating the variability
of sulfur content for specified averaging times or tonnages.
6. The RSD of Btu content is smaller than that of sulfur
content; that is, the RSD of Btu content is about 2 to 5
percent of the mean Btu content compared to the RSD of sulfur
content that is 10 to 25 percent of the mean sulfur content.
7. The RSD of Ib S02/MM Btu is about 1.02 to 1.05 times
the RSD for weight percent sulfur because of the dominating
effect of the variation of sulfur. This is not true for the
absolute standard deviation (see Appendix B.I.5). Through-
out this report a conservative estimate of the RSD of Ib
S02/MM Btu is 1.05 * RSD of weight percent sulfur.
8. The sulfur contents of samples from consecutive unit
trains will differ by much less than the sulfur contents of
samples from trains far apart in time; that is, there is a
statistical dependence in the time series of data. Hence,
the statistical analysis includes a subdivision of the
variation into two components (1) that among unit trains
within a week (or month) and (2) that among weekly (or
monthly) averages. For a few data sets the year-to-year
component can be estimated. These values are then used to
determine the impact of averaging period/amount of coal
sampled (week, month, quarter; 33 T, 600 T, etc.).
6-2
-------
9. The average sulfur content required for compliance
with the 1.2 Ib S02/MM Btu standard must decrease as the
amount of coal in tons and/or the averaging period decreases
and as the percentage of compliance time (95%, 99%, etc.)
increases. Theoretically, if 100 percent compliance is
required, then the average sulfur content approaches zero.
10. The RSD of sulfur content of coal from core drillings
is greater by a factor of 1-1/2 to 4 than the variability of
sulfur content among unit trains. This indicates the
impact of small-increment samples on sulfur variability,
since the core sample is a composite sample from a very
small amount of coal, approximately 50 pounds.
11. Although sulfur variability is expected to decrease
as the stage at which the sample is taken proceeds from core
drilling -> run-of-mine coal -» as-cleaned coal -* as-received
at plant -> as-burned, the reduction is difficult to detect
beyond the first stage core drillings to run-of-mine coal.
The reduction of variability in the latter stages should be
relatively small; considerable data would be required to
verify an expected reduction, if any.
12. Given an estimate of the RSD of sulfur content
(weight percent), Figure 5-5 provides a straightforward
means of determining the sulfur content in Ib SO2/MM Btu
required for compliance with the regulation of 1.2 Ib
SO2/MM Btu.
13. A quality control chart is suggested as one means
of monitoring the sulfur content of coal to detect signifi-
cant trends or changes in either the average or variation
of sulfur content over time. Section B.4 of Appendix B
discusses this approach, proposing either a standard chart
for averages or one for moving averages.
6-3
-------
14. The correlation of Btu content and sulfur content
is relatively low and in almost all cases is insignificantly
different from zero.
RECOMMENDATIONS
1. As further coal cleaning data become available, it
would be desirable to assess the variability of sulfur
content before and after cleaning.
2. Additional long-term data (over several years) must
be analyzed to determine long-term contractual implications.
Recall from Section 2 that for strip mining operations with
one machine the long-term variations are expected to be
large. Not enough data have been obtained to assess this
potential impact with the low-sulfur coals.
3. A computer program incorporating the types of anal-
yses proposed in this report would have long-term utility.
Furthermore, it would enable the analysis of some of the
remaining data available to EPA.
4. Further consideration should be given to impact of
sulfur variability, meteorological conditions, and other
factors on the environmental SO2 concentrations.
5. A study of the cost impacts of schemes for reducing
the average and/or standard deviation of sulfur content
would be helpful.
6. Additional data relating the variability of sulfur
content to the stages of sampling (core drillings, channel
samples, run-of-mine, after cleaning, and as received at
the plant) would yield estimates of the expected average re-
duction (if any) at each stage. In this report the analysis
is limited to a comparison of the core drillings and as-
received data.
6-4
-------
7. An ideal program for further study would be based
on composite samples from smaller amounts of coal than the
tonnages of unit trains, e.g., 50, 250, 1000, 5000, and
10,000 tons. At least 15 to 25 samples at each level would
be needed. Analysis of these data would provide a basis for
validating or adjusting the extrapolated region of the curve
in Figure 5-1.
8. A study of the correlation between the RSD of data
collected by a continuous stack monitor and the RSD of the
as-burned coal would enhance the understanding of the poten-
tial change in variability at this stage.
6-5
-------
7.0 REFERENCES
1. Navajo Generating Station Sulfur Dioxide Field
Monitoring Program, Volume I. Air Monitoring
Center, Rockwell International, Meteorological
Research, Inc., Systems Applications, Inc.
September 1975.
2. Sulfur Reduction Potential of U.S. Coals: A Re-
vised Report of Investigation, EPA-600/2-76-091,
Bureau of Mines Rl 8118, April 1976.
3. Standard Methods for Collection of a Gross Sample
of Coal. American Society for Testing and Materials,
Designation: D 2234-72.
4. Standard Methods of Test for Total Sulfur in the
Analysis of Coal and Coke. American Society of
Testing Materials, Part 26. Designation: D 3177-
73, pp. 674-677.
5. Dixon, Wilfrid J. and Frank J. Massey, Jr. In-
troduction to Statistical Analysis. New York,
McGraw-Hill Book Co., 1951. 370 p.
6. Hald, A. Statistical Theory with Engineering
Applications. New York, John Wiley and Sons,
Inc., 1952. 783 p.
7. Anderson, R.L. and T.A. Bancroft. Statistical
Theory in Research - I. Basic Statistical Theory,
II. Analysis of Experimental Models by Least
Squares. New York, McGraw-Hill Book Co., 1952.
399 p.
8. Hald, A. Statistical Tables and Formulas, John
Wiley and Sons, Inc., New York, 1952.
9. Bauer, Edward L. A Statistical Manual for Chemists.
New York. Academic Press. 1971. 193 p.
10. Grant, E. I. and R. S. Leavenworth. Statistical
Quality Control, McGraw-Hill Book Co., New York,
1972.
7-1
-------
APPENDIX A
SELECTED DATA SETS
Paqe
DATA SET C-l A-l
DATA SET C-2 A-2
DATA SET C-3 A-5
DATA SET C-5 A-7
DATA SET C-10 A-10
DATA SET C-ll A-10
DATA SET C-12 A-ll
DATA SET C-13 A-12
DATA SET U-l A-13
DATA SET U-2 A-18
DATA SET U-3 A-19
DATA SET U-4 A-20
DATA SET U-5 A-23
DATA SET U-6 A-25
DATA SET U-7 A-28
DATA SET U-8 A-31
DATA SET U-9 A-34
DATA SET U-ll A-37
DATA SETS U-14 to a-21 A-38
DATA SET U-22 A-42
-------
Data Set C-l
Variability of Sulfur Content versus Amount of Coal Sampled
Weight percent
sulfur
2.1 - 2.2
2.2 - 2.3
2.3 - 2.4
2.4 - 2.5
2.5 - 2.6
2.6 - 2.7
2.7 - 2.8
2.8 - 2.9
2.9 - 3.0
3.0 - 3.1
3.1 - 3.2
3.2 - 3.3
3.3 - 3.4
3.4 - 3.5
3.5 - 3.6
3.6 - 3.7
Total
Mean
Standard
deviation
RSD
Amount of coal sampled (1000 tons)
< 8
0
2
4
4
3
4
9
5
10
5
1
3
0
1
0
1
52
2.801
0.301
0.107
8-12
2
2
12
29
36
48
67
66
68
52
24
4
1
1
0
1
413
2.803
0.226
0.081
12 - 16
0
0
1
3
3
12
11
9
7
6
0
1
1
0
0
0
54
2.788
0.199
0.072
16 - 20
0
0
1
6
15
35
39
41
24
5
9
3
4
0
0
1
183
2.805
0.200
0.072
Total
2
4
18
42
57
99
126
121
109
68
34
11
6
2
0
3
702
2.802
0.224
0.080
A-l
-------
DATA SET C-2
CROSS-TABULATION OF SULFUR AND BTU CONTENT
BtU
< 12,000
12,000-12,100
12,100-12,200
12,200-12,300
12,300-12,400
12,400-12,500
12,500-12,600
12,600-12,700
12,700-12,800
Subtotals
Weight Percent Sulfur
0.54-
0.55
2
1
0
2
0
0
1
0
0
6
0.56-
0.57
1
1
1
2
3
1
0
0
0
9
0.58-
0.59
0
1
1
4
9
1
0
0
0
15
0.60-
0.61
0
3
7
5
9
8
4
1
0
37
0.62-
0.63
0
0
7
9
5
3
3
0
1
28
0.64-
0.65
0
0
4
2
3
1
4
0
0
14
0.66-
0.67
0
0
0
1
2
0
0
0
0
3
0.68-
0.69
0
0
0
1
0
0
0
0
0
1
0.70-
0.71
0
0
1
0
0
0
0
0
1
2
Subtota
3
6
21
26
30
14
12
1
2
115
Weight Percent Sulfur
x = 0.61 weight percent sulfur
s = 0.03 weight percent sulfur
Btu
x = 12,310 Btu
s = 158 Btu
ANALYSIS OF VARIANCE OF SULFUR CONTENT
Source of Variation
Sum pf Squares
Degrees of
Freedom
Mean
Square
Among months 0.03 11 0.0027
Within months 0.07 103 0.0007
Estimated Standard Deviation (within months) = (0.0007)15
= 0.026
Estimated Standard Deviation (among months) -
'0.0027 - 0.0007
= 0.015
-------
3>
I
GO
1.10
1.05
1.00
0.95
DATA SET C-2
UNIT TRAIN AND MONTHLY AVERAGES
FOR SULFUR CONTENT. LB S02/MM BTU
EACH UNIT TRAIN REPRESENTS ABOUT
_ 5600 TONS OF COAL
0.90
0.85
0.80
WT $ SULFUR
MONTHLY AVERAGE
(NONOVERLAPPING)
10 20 30 40 50 60 70 80
SERIAL NUMBER OF UNIT TRAIN/COMPOSITE SAMPLE
90
100
110
120
Figure A--1. Variation in sulfur content,
Ib SO /MM Btu with time, Data Set C-2.
-------
I
.t*.
1.10
1.05
1.00
« 0.95
CM
a
>
_«
0.90
0.85
0.80 -
DATA SET C-2
MEEKLY AVERAGES FOR SULFUR
CONTENT, LI ay** ITU
T i i
UT X SULFUR
BTU/LB
0.605 x " 12.310
0.03 s 161
LB S02/m BTU
x - 0.93
S 0.066
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 4i
SERIAL NUMBER OF MEEK
Figure A-2. Variation in weekly average sulfur content, Ib SO /MM Btu.
-------
DATA SET C-3
CROSS-TABULATION OF SULFUR AND BTU CONTENT
Btu
< 11,700
11,700-11,800
11,800-11,900
11,900-12,000
12,000-12,100
12,100-12,200
12,200-12,300
12,300-12,400
12,400-12,500
12,500-12,600
12,600-12,700
12,700-12,800
12,800-12,900
12,900-13,000
13,000-13,100
13,100-13,200
Subtotals
Weight Percent Sulfur
0.54-
0.57
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0.58-
0.61
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.62-
0.65
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0.66-
0.69
3
0
1
2
1
1
1
0
1
0
0
0
0
0
0
0
10
0.70-
0.73
0
4
2
3
3
1
2
5
1
1
1
0
0
0
0
0
23
0.74-
0.77
0
1
1
5
4
2
2
4
1
0.78-
0.81
2
1
1
2
8
4
6
-
6
0 1 2
4
0
0
0
0
0
24
0
1
0
0
0
0
38
0. 82-
0.85
0
0
0
1
2
5
5
4
6
4
2
0
0
0
0
0
29
0.86-
0.89
0
0
0
0
2
2
2
3
3
3
2
1
0
0
1
0
19
0.90-
0.93
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
5
0.94-
0.97
0
0
0
0
0
0
0
0.98-
1.01
0
0
0
0
0
0
0
1 0
0
0
0
0
0
1
0
0
0
0
0 0
0 I 0
0
1
0
1
>1.02
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
Sub
1
Weight Percent Sulfur
x = 0.807 weight percent sulfur
s = 0.088 weight percent sulfur
Btu
x = 12,250 Btu
s = 276 Btu
ANALYSIS OF VARIANCE OF SULFUR CONTENT
Source of Variation
Sum of Squares
Degrees of
Freedom
Mean
Square
Among months 0.201 11 0.0182
Within months 0.841 146 0.0057
Estimated Standard Deviation (within months) = ,(0.0057)^ = 0.0V76
'0.0182 - 0.0057^
Estimated Standard Deviation (among months) =
13
= 0\ 031
-------
1.70-
DATA SET C-3
WT. X SULFUR
UNIT TRAIN AND MONTHLY AVERAGES FOR
SULFUR CONTENT, LB S02/MM BTU
EACH UNIT TRAIN REPRESENTS ABOUT
5600 TONS OF COAL
X - 0.802 X - 12,260
S - 0.088 S Z7«
Lft S6,/m BTU
X - 1.24
S - 0.121
MONTHLY AVERAGE
10
40 50 60 70 80
NUMBER OF UNIT TRAIN/COMPOSITE SAMPLE
110
120
Figure A-3. Variation in sulfur content, Ib SO-/MM Btu, vs. time, Data Set C-3
-------
DATA SET C-5
CROSS-TABULATION OF SULFUR AND Btu VALUES
Btu
11,000-11,200
11,200-12,400
11,400-11,600
11,600-11,800
11,800-12,000
12,000-12,200
12,200-12,400
12,400-12,600
12,600-12,800
12,800-13,000
Total
Weight Percent Sulfur
£0.33
0
0
0
0
0
0
5
1
0
0
6
0.34-
0.38
0
0
0
1
1
18
42
10
0
0
72
0.38-
0.42
0
0
0
0
11
37
27
2
0
0
77
0.42-
0.46
0
1
1
6
12
55
30
4
0
1
110
0.46-
0.50
0
0
0
2
9
6
10
0
0
0
27
0.50-
0.54
0
0
1
2
5
5
2
0
0
0
15
^0.55
0
0
0
0
7
2
0
0
0
0
9
Total
0
1
2
11
45
123
116
17
0
1
316
Sulfur
Mean, x = 0. 42
Standard Deviation, s = 0.0491
Btu
Mean, x = 12,149
Standard Deviation,
s = 197
A-7
-------
DATA SET C-5
MEAN AND STANDARD DEVIATION (WEIGHT PERCENT)
(Based on a Sample of 10 Values Per Month)
Month
January
February
March
April
May
June
July
August
September
October
November
December
Mean
Year
1974
0.43
0.38
0.37
0.36
0.39
0.35
0.37
0.38
0.36
0.38
0.38
0.47
1975
0.37
-
0.39
0.42
0.40
0.42
0.40
0.39
0.40
0.42
0.42
0.40
1976
0.48
0.38
0.43
0.37
-
-
-
-
-
-
-
~
Standard Deviation
Year
1974
0.05
0.05
0.02
0.02
0.04
0.03
0.03
0.04
0.04
0.03
0.05
0.10
1975
0.03
-
0.02
0.05
0.04
0.05
0.05
0.02
0.04
0.04
0.04
0.04
1976
0.03
0.03
0.03
0.04
-
-
-
-
-
-
-
~
A-8
-------
0.90
0.80
0.70
-------
CORE DATA - TWO SEAMS
July 1976
Data Set C-lO
Bottom Bench
Sulfur
Btu
S02
Minimum
0.35
12134.00
0.52
Maximum
1.45
13570.00
2.39
Mean
0.58
13174.63
0.88
Variance
0.0612
109920.5625
0.1597
Standard
Deviation
0.2474
331.5564
0.3996
Data Set C-ll
Top Bench
Sulfur
Btu
so2
Minimum
0.29
12042.00
0.44
Maximum
2.53
13283.00
3.99
Mean
0.88
12685.27
1.39
Variance
0.2858
84752.0625
0.7488
Standard
Deviation
0.5346
291.1221
0.8653
A-10
-------
SHIPMENT DATA - TWO SEAMS
July 1976
Data Set C-12
Sulfur
By 2,000 tons
By 10,000 tons
By month
By year
Btu
By 2,000 tons
By 10,000 tons
By month
By year
SO2
By 2,000 tons
By 10,000 tons
By month
By year
Minimum
ll?6
2.54
3.08
3.18
9737.75
10964.39
11813.69
11935.29
3.00
4.31
5.09
5.29
Maximum
5.04
4. 34
3.98
3.54
12719.95
12337.29
12227.21
12054.81
9.52
7.33
6.68
5.93
Mean
3.42
3.42
3.42
3.42
12004.30
12003.53
12003.23
12003.22
5.69
5.69
5.69
5.69
Variance
0.1807
0.1181
0.0682
0.0142
64764.4688
25670.6094
11930.5195
3006.3992
0.5230
0.3451
0.1994
0.0468
Standard
deviation
0.4251
0.3436
0.2611
0.1193
254.4886
160.2205
109.2269
54.8306
0.7232
0.5875
0.4466
0.2163
A-ll
-------
DATA SET C-13
CROSS-TABULATION OF SULFUR AND BtU VALUES
Btu
11,000-11,200
11,200-11,400
11,400-11,600
11,600-11,800
11,800-12,000
12,000-12,200
12,200-12,400
12,400-12,600
Total
Weight Percent Sulfur
0.38-
0.42
0
0
0
0
1
0
1
0
2
0.42-
0.46
0
0
0
2
1
3
0
0
6
0.46-
0.50
0
0
1
3
9
6
3
1
23
0.50-
0.54
0
1
1
8
11
6
0
1
28
0.54-
0.58
0
0
2
4
10
11
0
0
27
0.58-
0.62
0
0
0
2
3
5
0
0
10
0.62-
0.66
0
0
0
0
0
7
0
0
7
0.66-
0.70
0
0
0
0
7
17
0
0
24
0.70-
0.74
0
0
0
0
0
7
0
0
7
0.74-
0.78
0
0
0
0
0
4
0
0
4
>_ 0.78
0
0
0
0
0
2
0
0
2
Tota
0
1
4
19
42
68
4
2
14(
I-1
to
Sulfur
Mean, x = 0.5768
Standard Deviation, s = 0.0905
Btu
Mean, x = 11,974
Standard Deviation,
s = 191
-------
DATA SET U-l
Date
(1st day of wk)
1973, May 31
June 7
14
21
28
July 5
12
19
26
Aug 2
9
16
23
30
Sept 6
13
20
27
Oct 4
11
18
25
Nov 1
8
15
22
29
Dec 6
13
20
27
1974, Jan 3
10
17
24
31
Feb 7
14
21
28
Dry Basis
Weighted
Weekly
Average
Sulfur
0.72
0.76
0.73
0.83
0.85
0.71
0.78
0.74
0.72
0.72
0.70
0.78
0.84
0.78
0.88
0.94
0.99
0.78
0.78
0.71
0.70
0.68
0.68
0.70
0.64
0.93
0.76
0.74
0.68
0.65
0.64
0.68
0.64
0.62
0.67
0.75
0.71
0.70
0.74
0.77
Weighted
Weekly
Average
Btu
11,512
12,465
12,501
12,915
12,629
12,924
12,638
12,530
12,637
12,262
11,730
12,125
12,423
12,238
12,591
12,730
12,726
12,785
12,830
12,545
12,535
12,733
12,273
12,584
12,566
12,583
11,562
12,765
12,815
12,787
12,916
12,643
12,679
12,499
12,274
12,431
12,772
12,648
12,549
12,726
Weekly
Range of
Sulfur
Content
0.32
0.84
0.25
0.55
0.40
0.11
0.65
0.17
0.32
0.30
0.16
0.33
0.47
0.35
0.56
0.46
1.05
0.48
0.43
0.34
0.29
0.31
0.18
0.24
0.12
0.94
0.70
0.36
0.27
0.26
0.09
0.20
0.08
0.25
0.21
0.36
0.27
0.37
0.32
0.39
Weekly
Range of
Btu
Content
068
1097
678
634
146
370
1217
1369
660
1867
1554
714
941
1069
456
808
1060
633
959
1800
1282
650
939
1041
580
913
342
931
123
1171
877
817
947
1213
846
538
1102
469
411
494
A-13
-------
DATA SET U-l (continued)
Date
(1st day of wk)
Mar 7
14
21
28
Apr 4
11
18
25
May 9
16
23
30
June 6
13
20
27
July 4
11
18
25
Aug 1
8
15
22
29
Sept 5
12
19
26
Oct 3
10
17
24
31
Nov 7
21
28
Dec 5
12
19
26
Dry Basis
Weighted
Weekly
Average
Sulfur
0.78
0.74
0.75
0.68
0.70
0.76
0.69
0.96
0.89
0.81
0.84
0.85
0.89
0.80
0.69
0.89
0.87
0.75
0.71
0.66
0.70
0.73
0.71
0.76
0.73
0.70
0.68
0.70
0.72
0.67
0.63
0.69
0.68
0.66
0.72
0.71
0.70
0.77
0.70
0.68
0.72
Weighted
Weekly
Average
Btu
12,615
12,861
12,440
12,700
12,876
12,591
12,209
12,255
12,465
12,725
12,367
12,517
12,407
12,704
12,333
12,714
12,703
12,620
12,644
12,049
12,192
12,445
12,482
12,266
12,121
12,014
12,166
12,330
12,852
12,464
12,203
12,161
12,310
12,756
12,634
12,687
12,815
12,705
12,318
12,304
12,268
Weekly
Range of
Sulfur
Content
0.66
0.24
0.34
0.24
0.14
0.47
0.21
0.47
0.73
0.24
0.23
0.40
0.58
0.14
0.69
0.50
0.32
0.17
0.63
0.09
0.07
0.26
0.16
0.30
0.26
0.19
0.18
0.14
0.09
0.07
0.10
0.14
0.06
0.09
0.15
0.20
0.18
0.34
0.15
0.11
0.18
Weekly
Range of
Btu
Content
1078
430
1173
800
1015
821
876
638
1326
960
756
607
676
343
1186
538
674
754
1002
724
686
476
861
470
1105
1089
532
623
621
672
1254
620
1320
566
567
503
242
416
448
922
427
A-14
-------
DATA SET U-l (continued)
Date
(1st day of wk)
1975, Jan 2
9
16
23
30
Feb 6
13
20
27
Mar 6
13
20
27
Apr 3
10
17
24
May 1
8
15
22
29
Dry Basis
Weighted
Weekly
Average
Sulfur
0.72
0.64
0.70
0.67
0.71
0.69
0.81
0.71
0.73
0.73
0.73
0.71
0.76
0.69
0.68
0.79
0.82
0.79
0.76
0.76
0.77
0.71
Weighted
Weekly
Average
Btu
12,618
12,646
12,686
12,399
12,279
12,292
12,519
12,282
12,484
12,105
12,278
12,114
12,645
12,537
12,252
12,196
12,321
12,110
12,141
12,270
12,705
12,410
Weekly
Range of
Sulfur
Content
0.23
0.20
0.14
0.09
0.08
0.11
0.21
0.09
0.20
0.39
0.25
0.11
0.45
0.16
0.07
0.40
0.53
0.36
0.58
0.51
0.53
0.14
Weekly
Range of
Btu
Content
1065
411
680
838
837
635
781
854
1941
349
347
865
513
692
721
719
1368
1749
959
1122
1034
1061
A-15
-------
DATA SET U-l (continued)
FREQUENCY TABULATION OP WEEKLY WEIGHTED
AVERAGE OF SULFUR - DRY BASIS
Weighted
Average (%)
.62 - .63
.64 - .65
.66 - .67
.68 - .69
.70 - .71
.72 - .73
.74 - .75
.76 - .77
.78 - .79
.80 - .81
.82 - .83
.84 - .85
.86 - .87
.88 - .89
.90 - .91
.92 - .93
.94 - .95
.96 - .97
.98 - .99
X
8
r
June -
Dec
1973
0
3
0
3
5
4
2
2
5
0
1
2
0
1
0
1
1
0
1
0.762
0.0869
Jan -
June
1974
1
1
1
4
3
0
3
3
1
2
0
2
0
3
0
0
0
1
0
0.761
0.0868
July -
Dec
1974
0
1
3
4
8
5
1.
2
0
0
0
0
1
0 .711
0 .0435
Jan -
May
1975
0
1
1
3
5
4
0
4
2
1
1
0.730
C.0470
Total
1
6
5
14
21
13
6
11
8
3
2
4
1
4
0
1
1
1
1
0 .742
0 .0732
A-16
-------
DATA SET U-l (continued)
FREQUENCY TABULATION OF WEEKLY RANGE
OF WEIGHT PERCENT SULFUR - DRY BASIS
Range ( % )
0 - .05
.06 - .10
.11 - .15
.16 - .20
.21 - .25
.26 - .30
.31 - .35
.36 - .40
.41 - .45
.46 - .50
.51 - .55
.56 - .60
.61 - .65
.66 - .70
.71 - .75
.76 - .80
.81 - .85
.86 - .90
.91 - .95
.96 - 1.0
1.01 - 1.05
s
June -
Dec
1973
0
1
2
4
3
2
6
2
2
2
1
0
1
2
0
0
1
0
0
1
1
0.394
Jan -
June
1974
0
1
2
4
6
1
2
4
0
3
0
1
0
0
1
0.306
July -
Dec
1974
1
6
7
6
0
3
2
0.160
Jan -
May
1975
1
4
3
2
3
1
2
1
1
0
3
1
0.260
Total
2
12
14
16
12
7
12
7
3
5
4
2
1
2"
1
0
1
0
0
1
1
D.287
A-17
-------
DATA SET U-2
FREQUENCY DISTRIBUTION OF WEIGHT PERCENT SULFUR
(As Received at Plant)
% Sulfur
0.7 - 0.8
0.9 - 1.0
1.1 - 1.2
1.3 - 1.4
Total
Frequency for Year
1973
58
64
0
2
124
1974
51
83
2
0
136
1975
7
44
2
0
53
Mean, x = 0.86
Standard
Deviation, s = 0.12
0.88
0.10
0.93
0.08
ANALYSIS OF VARIANCE
Source of Variation
Among Months
Within Months
Sum of Squares
0.54
0.58
Degrees of
Freedom
27
284
Mean Square
0.0200
0.0020
Estimated Standard Deviation (within months) = (0.0020)
= 0.045
Estimated Standard Deviation (among months) =1-
0.0200 - 0.00201
11
= 0.040
A-18
-------
DATA SET U-3
FREQUENCY DISTRIBUTION OF WEIGHT PERCENT SULFUR
(Coal Burned at Same Plant as for Data Set U-2)
% Sulfur
0.5 - 0.6
0.7 - 0.8
0.9 - 1.0
1.1 - 1.2
1.3 - 1.4
1.5 - 1.6
Total
Frequency for Year
1973
1
27
6
2
3
1
40
1974
0
37
6
2
2
0
47
1975
0
12
4
0
0
0
16
Mean, x= 0.86 0.82 0.80
Standard
Deviation, s = 0.22 0.15 0.09
Total
1
76
16
4
5
1
103
ANALYSES OF VARIANCE
Source of Variation
Among Months
Within Months
Sum of Squares
1.37
1.39
Degrees of
Freedom
25
76
Mean Square
0.0548
0.0183
Estimated Standard Deviation (within months) =
(0.0183)31 = 0.135
Estimated Standard Deviation (among months) -
0.0548 - 0.0183
= 0.096
A-19
-------
DATA SET U-4
FREQUENCY DISTRIBUTION OF WEIGHT PERCENT SULFUR
(As received at plant from various seams of coal - 1 county)
% Sulfur
0.7 - 0.8
0.9 - 1.0
1.1 - 1.2
1.3 - 1.4
1.5 - 1.6
1.7 - 1.8
1.9 - 2.0
:> 2.1
Total
Frequency Distribution by Year
1974
6
34
6
2
1
0
0
1 (4.1)
50
1975
1
49
27
7
2
0
1
0
87
1976
0
22
5
0
0
0
0
0
27
Total
7
105
38
9
3
0
1
1 (4.1)
164
Mean, x = 1.04 1.07
(0.98)*
Standard
Deviation, s = 0.47 0.18
(0.15)*
*Omitting 4.1 value
0.99
0.08
A-20
-------
DATA SET U-4
FREQUENCY DISTRIBUTION OF Btu VALUES
Btu
11,200 -
11,400 -
11,600 -
11,800 -
12,000 -
12,200 -
12,400 -
12,600 -
12,800 -
11,400
11,600
11,800
12,000
12,200
12,400
12,600
12,800
13,000
Year
1974
0
0
9
9
13
8
3
2
0
44
1975
3
5
18
19
24
16
5
1
1
92
1976
1
2
5
10
2
4
3
1
0
28
Total
4
7
32
38
39
28
11
4
1
164
Mean, x
Standard
Deviation, s
12,068
276
11,993
310
12,014
319
A-21
-------
DATA SET U-4
FREQUENCY DISTRIBUTION OF Ibs S02/MM Btu
(All Years, 1974 - 1976)
Ibs SO-/MM Btu
1.1 -
1.3 -
1.5 -
1.7 -
1.9 -
2.1 -
2.3 -
2.5 -
2.7 -
2.9 -
3.1 -
3.3 -
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
Total
Frequency
3
7
58
58
22
5
6
1
1
0
0
1
162
x = 1.73
s = 0.28
A-22
-------
DATA SET U-5
FREQUENCY DISTRIBUTION OF Btu VALUES
Btu
11,000 -
11,200 -
11,400 -
11,600 -
11,800 -
12,000 -
12,200 -
12,400 -
12,600 -
11,200
11,400
11,600
11,800
12,000
12,200
12,400
12,600
12,800
Total
Year
1974
0
2
3
3
19
24
9
2
3
70
1975
2
12
22
40
43
26
10
4
0
159
1976
0
0
4
5
5
5
2
0
0
21
Total
2
14
29
53
67
55
21
6
3
250
Mean, x = 12,014
Standard
Deviation, s
286
11,812
293
11,862
258
FREQUENCY DISTRIBUTION OF WEIGHT PERCENT SULFUR
(As received at plant from various seams of coal - 1 county)
Frequency Distribution by Year
% Sulfur
0.7 - 0.8
0.9 - 1.0
1.1 - 1.2
> 1.3
Total
1974
28
42
0
0
70
1975
34
110
14
1 (2.2)
159
1976
1
15
4
1 (2.1)
21
Total
63
167
18
2
250
Mean, x = 0.87
Standard
Deviation, s = 0.10
* Omitting 2.2 value.
0.93
(0.925)*
0.15
(0.11)*
1.03
(0.98)**
0.26
(0.10)**
**Omitting 2.1 value.
A-23
-------
DATA SET U-5
FREQUENCY DISTRIBUTION OF Ibs S02/MM Btu
(All Years, 1974 - 1976)
Ibs SO
1.1
1.3
1.5
1.7
1.9
>
,,/MM Btu
- 1.2
- 1.4
- 1.6
- 1.8
- 2.0
2.1
Frequency
9
56
125
44
14
2
Total =250
x = 1.55
s = 0.18
ANALYSIS OF VARIANCE OF SULFUR CONTENT
Source of Variation
Among months
Within months
Sum of Squares
1.48
3.94
Degrees of
Freedom
22
227
Mean
Square
0.067
0.017
Estimated Standard Deviation (within months) =
Estimated Standard Deviation (among months) -
(0.017K
0.132
r
0.067 - 0.017^
10.4
= 0.069
A-24
-------
DATA SET U-6
FREQUENCY DISTRIBUTION OF WEIGHT PERCENT SULFUR
(As Received at Plant)
% Sulfur
0.6
0.7
0.8
0.9
1.0
1.1
Frequency
22
18
21
12
13
4
Total 90
x = 0.79
s = 0.15
FREQUENCY DISTRIBUTION OF BTU
Btu
10,600-10,700
11,000-11,100
11,100-11,200
11,200-11,300
11,300-11,400
11,400-11,500
11,500-11,600
11,600-11,700
11,700-11,800
11,800-11,900
11,900-12,000
12,000-12,100
12,100-12,200
12,200-12,300
12,300-12,400
12,400-12,500
12,500-12,600
Frequency
4
3
0
5
0
0
8
13
8
17
2
22
. 0
4
0
0
4
Total 90
x = 11,770
s = 393
A-25
-------
DATA SET U-6
FREQUENCY DISTRIBUTION OF Ibs S02/MM Btu
Ibs SOo/MM Btu
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
Frequency
21
4
12
16
7
7
6
9
5
3
Total = 90
x = 1.
s = 0.
34
27
ANALYSIS OF VARIANCE OF SULFUR CONTENT
Source of Variation
Among months
Within months
Sum of Squares
0.71
1.33
Degrees of
Freedom
13
76
Mean
Square
0.055
0.018
Estimated Standard Deviation (within months) =
= 0.134
Estimated Standard Deviation (among months) -
0.055 - 0.018
= 0.073
A-26
-------
DATA SET U-6
CROSS-TABULATION OF SULFUR AND BTU CONTENT
Btu
10,500-10,600
10,900-11,000
11,000-11,100
11,100-11,200
11,200-11,300
11,300-11,400
11,400-11,500
11,500-11,600
11,600-11,700
11,700-11,800
11,800-11,900
11,900-12,000
12,000-12,100
12,100-12,200
12,200-12,300
12,300-12,400
12,400-12,500
Total
Weight Percent Sulfur
0.6
0
1
0
0
0
0
0
0
3
7
0
6
0
4
0
0
1
22
0.7
3
0
0
0
0
0
2
2
0
5
0
3
0
0
0
0
3
18
0.8
1
0
0
0
0
0
0
7
0
2
2
9
0
0
0
0
0
21
0.9
0
0
0
3
0
0
3
0
4
0
0
2
0
0
0
0
0
12
1.0
0
2
0
2
0
0
0
4
2
3
0
0
0
0
0
0
0
13
1.1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
4
A-27
-------
DATA SET U-7
FREQUENCY DISTRIBUTION OF Btu VALUES
(1974 Data)
Btu
11,400
11,600
11,800
12,000
12,200
12,400
12,600
12,800
>
- 11,600
- 11,800
- 12,000
- 12,200
- 12,400
- 12,600
- 12,800
- 13,000
14,200
Frequency
7
12
19
15
24
19
0
22
2
Total 120
Mean, x = 12,278
Standard Deviation, s = 488
FREQUENCY DISTRIBUTION OF WEIGHT PERCENT SULFUR
(As Received at Plant)
% Sulfur
0.6
0.7
0.8
0.9
1.0
> 1.5
Frequency
21
38
23
6
30
2
Total 120
Mean, x = 0. 80
Standard
Deviation, s = 0.17
A-28
-------
DATA SET U-7
FREQUENCY DISTRIBUTION OF Ibs SO-/MM Btu
Ibs SO
0.9
1.1
1.3
1.5
1.7
>
0/MM
- 1.
- 1.
- 1.
- 1.
- 1.
2.3
Btu
0
2
4
6
8
Frequency
23
44
16
24
11
2
Total 120
Mean, x = 1.29
Standard
Deviation, s = 0.28
ANALYSIS OF VARIANCE OF SULFUR CONTENT
Source of Variation
Among months
Within months
Sum of Squares
0.51
2.95
Degrees of
Freedom
11
108
Mean
Square
0.046
0.027
Estimated Standard Deviation (within months) =
(0.027)
0.165
Estimated Standard Deviation (among months) -
/0.046 - 0.027|
\ 10 /
= 0.0436
A-29
-------
DATA SET U-7
CROSS-TABULATION OF SULFUR AND Btu CONTENT
Btu
11,500
11,600
11,700
11,800
11,900
12,000
12,100
12,200
12,300
12,400
12,500
12,600
12,700
12,800
12,900
13,000
14,200
Total
Weight Percent Sulfur
0.6
1
0
0
0
0
0
0
0
0
0
10
0
0
0
0
10
0
21
0.7
0
0
3
9
0
3
0
0
0
16
4
1
0
0
0
0
2
38
0.8
0
0
0
0
0
12
0
0
0
3
0
0
0
0
0
8
0
23
0.9
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
6
1.0
0
6
0
0
0
3
10
1
5
0
4
0
0
0
0
1
0
30
> 1.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
Total
1
6
3
9
0
19
14
1
5
19
18
1
0
0
22
2
120
A-30
-------
DATA SET U-8
FREQUENCY DISTRIBUTION OF Ibs SO2/MM Btu
Ibs SC
0.9
1.1
1.3
1.5
1.7
>
)0/MM Btu
- 1.0
- 1.2
- 1.4
- 1.6
- 1.8
2.3
Frequency
7
22
11
10
7
4
Total 61
Mean, x = 1.37
Standard
Deviation, s = 0.34
ANALYSIS OF VARIANCE OF SULFUR CONTENT
Source of Variation
Among months
Within months
Sum of Squares
0.068
2.758
Degrees of
Freedom
8
51
Mean
Square
0.0085
0.0541
Estimated Standard Deviation (within months) = (0.0541)^
= 0.233
Estimated Standard Deviation (among months) = ( \ < 0
60/9
Occasionally the estimated component of variance is negative
due to chance variation. In these cases the component is
shown as a 0+ value in the report.
A-31
-------
DATA SET U-8
FREQUENCY DISTRIBUTION OF BtU VALUES
BtU
11,400
11,600
11,800
12,000
12,200
12,400
12,600
12,800
>
- 11,600
- 11,800
- 12,000
- 12,200
- 12,400
- 12,600
- 12,800
- 13,000
14,200
Frequency
7
11
14
2
1
7
0
16
2
Total 60
Mean, x = 12,243
Standard Deviation, s = 636
FREQUENCY DISTRIBUTION OF WEIGHT PERCENT SULFUR
(As Received at Plant)
% Sulfur
0.6
0.7
0.8
0.9
1.0
> 1.5
Frequency
5
22
13
3
13
4
Total 60
Mean, x = 0. 84
Standard
Deviation, s = 0.22
A-32
-------
DATA SET U-8
CROSS-TABULATION OF SULFUR AND Btu CONTENT
Btu
11,400-11,600
11,600-11,800
11,800-12,000
12,000-12,200
12,200-12,400
12,400-12,600
12,600-12,800
12,800-13,000
>_ 14,200
Total
Weight Percent Sulfur
0.6
2
0
0
0
0
0
0
3
0
5
0.7
0
11
4
0
0
5
0
0
2
22
0.8
1
0
7
0
1
0
0
4
0
13
0.9
0
0
1
2
0
0
0
0
0
3
1.0
4
0
2
0
0
2
0
5
0
13
1.5
0
0
0
0
0
0
0
4
0
4
Total
7
11
14
2
1
7
0
16
2
60
A-33
-------
DATA SET U-9
FREQUENCY DISTRIBUTION OF Ibs S02/MM Btu
Ibs SO
0.9
1.1
1.3
1.5
1.7
1.9
>
^/MM Btu
- 1.0
- 1.2
- 1.4
- 1.6
- 1.8
- 2.0
2.3
Frequency
8
23
19
15
7
1
1
Total 74
Mean, x = 1. 35
Standard
Deviation, s = 0.27
ANALYSIS OF VARIANCE OF SULFUR CONTENT
Source of Variation
Among months
Within months
Sum of Squares
0.12
1.65
Degrees of
Freedom
11
62
Mean
Square
0.011
0.027
Estimated Standard Deviation (within months)
= (0.027)
= 0.163
Estimated Standard Deviation (among months)
{0.011 - 0.027V
74/12 J
< 0
» oa
a The estimated standard deviation among monthly averages is
taken as zero in this particular case in which the estimated
variance component is negative.
A-34
-------
DATA SET U-9
FREQUENCY DISTRIBUTION OF WEIGHT PERCENT SULFUR
% Sulfur
0.6
0.7
0.8
0.9
1.0
1.1
> 1.5
Frequency
9
18
24
6
15
1
1
Total 74
Mean, x = 0.81
Standard
Deviation, s = 0.16
FREQUENCY DISTRIBUTION OF Btu VALUES
Btu
<_ 10,600
11,000-11,200
11,200-11,400
11,400-11,600
11,600-11,800
11,800-12,000
12,000-12,200
12,200-12,400
12,400-12,600
12,600-12,800
12,800-13,000
> 14,200
,
Frequency
1
8
0
12
11
18
1
1
3
2
16
1
Total 74
Mean, x = 12,003
Standard
Deviation, s = 665
A-35
-------
DATA SET U-9
CROSS-TABULATION OF SULFUR AND Btu CONTENT
Btu
£ 10,600
11,000-11,200
11,200-11,400
11,400-11,600
11,600-11,800
11,800-12,000
12,000-12,200
12,200-12,400
12,400-12,600
12,600-12,800
12,800-13,000
>_ 14,200
Total
Weight Percent Sulfur
0.6
0
2
0
0
0
0
0
0
0
0
7
0
9
0.7
0
0
0
0
11
4
0
0
2
0
0
1
18
0.8
1
0
0
8
0
11
0
0
0
0
4
0
24
0.9
0
4
0
0
0
1
1
0
0
0
0
0
6
1.0
0
0
0
3
0
2
0
1
1
2
4
0
15
1.1
0
0
0
1
0
0
0
0
0
0
0
0
1
1.5
0
0
0
0
0
0
0
0
0
0
1
0
1
Total
1
8
0
12
11
18
1
1
3
2
16
1
74
A-36
-------
DATA SET U-ll
FREQUENCY DISTRIBUTION OF WEIGHT PERCENT SULFUR
(As Received at Plant)
% Sulfur
2.0-2.1
2.1-2.2
2.2-2.3
2.3-2.4
2.4-2.5
2.5-2.6
2.6-2.7
2.7-2.8
2.8-2.9
2.9-3.0
3.0-3.1
3.1-3.2
3.2-3.3
3.3-3.4
3.4-3.5
3.5-3.6
3.6-3.7
3.7-3.8
3.8-3.9
Frequency
1
1
0
6
5
9
15
23
27
20
18
22
12
23
27
16
8
6
1
Total 240
x = 3.1
s = 0.366
A-37
-------
DATA SETS U-14 to U-21
Data Set
U-14
*U-15
U-16
U-17
**U-18
*U-19
U-20
U-21
N
82
83
395
132
770
113
768
1766
Weight Percent Sulfur
Mean , x
0.49
0.53
0.68
0.66
0.37
0.46
0.60
0.55
Standard
Deviation , s
0.19
0.16
0.18
0.18
0.035
0.055
0.092
0.086
*The cumulative frequency functions for these data are given
in the following graphs.
**The histogram is given in addition to the cumulative
frequency graph.
A-38
-------
co
95
i.
X 80
ao
50
40
§ 30
20-
10
I I I I T I I I I
DATA SET U-19J
RUH-Of-MINE,
SET
CORE DATA
J 1
0.20 0.90 0.40 0.50 0.60 0.70 0.80
WEIGHT PERCENT SULFUR
Figure A-5. Comparison of core data and run-of-mine data.
-------
4*
O
.31 .32 .33
.35 .37 .39
WEIGHT PERCENT SULFUR
.41
.43
.45
.47
Figure A-6. Frequency distribution of one day averages of
weight percent sulfur in coal.
(Delivery data for Data Set U-18)
-------
0.30
0.32
0.34
0.36 0.38 0.40
WEIGHT PERCENT SULFUR
0.42
0.44
Figure A-7. Frequency distribution for Data Set U-18.
A-41
-------
DATA SET U-22
Plant Name
Benning, D.C.
Winnetka, 111.
Wood River, 111.
Perry, Ind.
Smith, Md.
Advance , Mich .
Advance, Mich.
Plant #65, Mich.
Missouri Ave., N.J.
Huntley, N.Y.
District
0354
0854
0821
0821
0354
0821
0854
0851
0354
0854
Number of
Analyses
19
6
5
2
13
4
2
2
8
2
Ibs S02/MM Btu
Mean
1.06
1.09
1.10
1.16
0.98
1.03
1.17
1.09
0.97
0.98
Standard
Deviation
0.21
0.04
0.11
0.03
0.13
0.08
0.00
0.15
0.20
0.05
RSD
20%
4%
10%
3%
13%
8%
0
14%
21%
5%
Group 1 - Pooled Estimates 1.03
0.16C
15.8%
Stout, Ind.
Dicker son, Md.
Smith , Md .
Salem Harbor, Mass.
Marysville, Mich.
Trenton Channel, Mich.
Burlington, N.J.
Hudson, N.J.
Kearney A & B, N.J.
Mercer, N.J.
Cape Fear, N.C.
Cape Fear, N.C.
Cliffside, N.C.
Dan River, N.C.
Tait, Ohio
Titus, La.
0821
0821
0851
0821
0751
0751
0751
0854
0751
0751
0851
0854
0821
0751
0854
0821
4
3
3
14
2
2
4
4
2
6
72
32
13
33
28
58
1.36
1.85
1.42
1.35
1.24
1.33
1.36
1.33
1.37
1.36
1.42
1.39
1.58
1.53
1.35
1.26
0.19
0.01
0.16
Q.32
0.10
0.23
0.17
0.33
0.22
0.16
0.18
0.24
0.23
0.18
0-.22
0.25
14%
1%
11%
24%
8%
17%
13%
25%
16%
12%
5%
17%
15%
12%
16%
20%
Group 2 - Pooled Estimates 1.39
0.20a 14.6%J
aThis standard deviation was obtained by weighting the corresponding
variances by the number of degrees of freedom (number of analyses
less^one), dividing by the sum of the weights and then taking the
square root.
The RSD is computed from the ratio of the standard deviation to the
mean, multiplied by 100 to convert to percent.
A-42
-------
Table A-l. MINIMUM, MAXIMUM AND AVERAGE SULFUR
WEIGHT PERCENT FOR EACH DATA SET
Weight Percent Sulfur
Data set
C-l
C-2
C-3
C-4
C-5
C-6
C-7
C-8
C-9
C-10
C-ll
C-12
C-13
U-l
U-2
U-3
U-4
U-5
U-6
U-7
U-8
U-9
U-10
U-ll
U-12
U-13
Minimum
2.10
0.54
0.54
0.65
0.30
0.89
0.75
2.22
0.60
0.35
0. 29
2.54
0.38
0.62
0.70
0.50
0.70
0.70
0.60
0.60
0.60
0.60
0.65
2.00
1.72
1.64
Average
2.80
0.60
0.80
1.38
0.42
2.14
1.50
2.60
1.63
0.58
0.88
3.42
0.58
0.74
0.88
0.82
1.04
0.92
0.79
0.80
1.04
0.81
1.74
3.10
2.25
2.15
Maximum
3.70
0.71
1.02
3.58
0.56
3.97
3.55
3.19
4.90
1.45
2.53
4.34
0.80
0.99
1.40
1.60
2.10
1.30
1.10
1.50
2.30
1.50
3.00
3.90
2.85
2.63
A-43
-------
APPENDIX B
METHODS OF DATA ANALYSES
Page
B.I BASIC STATISTICAL ANALYSES B-l
B.I.I Mean, Standard Deviation, and B-l
Relative Standard Deviation of a
Measurement Tabulated in a Fre-
quency Table
B.I.2 Analysis of Variance (Components B-2
of Variance)
B.I.3 Estimation of Standard Deviation B-5
For Various Averaging Times
B.I.4 Correlation Analysis B-12
B.I.5 Estimated Variance of Ib SO2/ B-15
MM Btu
B.I.6 Relationship Between the Average, B-16
x and Standard Deviation, s
B.2 DETAILED ANALYSIS OF DATA SET U-l B-16
(% SULFUR, DRY BASIS)
B.3 AVERAGES FOR FEWER THAN FIVE MEASUREMENTS B-22
ASSUMING INVERTED GAMMA DISTRIBUTION
B.4 APPLICATION OF QUALITY CONTROL TO B-24
SULFUR VARIABIIITY
-------
B.I BASIC STATISTICAL ANALYSES
This appendix presents the statistical methods used in
data analyses in this report. If the methods are not those
routinely used, some discussion is presented along with the
computational methods. The organization of the appendix
permits the reader to look at only those sections for which
he believes that further explanation would be helpful. It
is assumed that the reader interested in further detail will
refer to recommended references.
B.I.I Mean, Standard Deviation, and Relative Standard
Deviation of a Measurement Tabulated in a Frequency
Table
Refer to Data Set U-l, January to May 1975 data on
weight percent sulfur. The frequency tabulation is repeated
from Appendix A for convenience. The midpoints of the
intervals are added to the table to aid in the computation.
Weighted
weekly average
percent sulfur
0.62 - 0.63
0.64 - 0.65
0.66 - 0.67
0.68 - 0.69
0.70 - 0.71
0.72 - 0.73
0.74 - 0.75
0.76 - 0.77
0.78 - 0.79
0.80 - 0.81
0.82 - 0.83
Midpoint (x)
0.625
0.645
0.665
0.685
0.705
0.725
0.745
0.765
0.785
0.805
0.825
Frequency (f)
0
1
1
3
5
4
0
4
2
1
1
B-l
-------
The following statistics are computed:
Average sulfur content = x = ^|^ = 0.730 weight percent
Standard deviation of sulfur content =
1/2
_[zf (x - x
I n - 1
x)
1 = 0.0470,
and for ease of computation without a preprogrammed cal-
culator
2 . I1/2
s =
Coefficient of variation (CV) or relative standard deviation
(RSD)
CV or RSD = x 100 = ' x IQQ = 6.4%.
x u./ju
The RSD is a very convenient measure of variation
whenever the standard deviation tends to be proportional to
the average value, see Section B.I. 6. It is also useful in
estimating the variance of ratios and products of variables,
as illustrated in Appendix B.I. 5. Three references are
recommended, in order of increasing mathematical complexity. 5/5,6
B.I. 2 Analysis of Variance (Components of Variance)
This section discusses briefly the method of analysis
of variance, including components of variance, the results
of which are used in Section 5 to estimate the impact of
averaging time on the average sulfur content required for
compliance with NSPS.
B-2
-------
The nested model with random components is assumed in
all these analyses. An analysis of variance was conducted
on several data sets to estimate the components of variation
due to the variation of sulfur content among samples (unit
trains) within the same week (or month) and among weekly (or
monthly) averages. Data Set U-l is used here to illustrate
the computational approach. These data are weekly weighted
averages (seven samples per week). Four consecutive weeks
are treated as a month, giving actually a 28-day average.
The analysis method is given in Table B-l, followed by an
example in Table B-2. The weekly averages in Data Set U-l
are denoted by x and the totals of four consecutive values
by T. Thus, there are 25 groups of 4 weeks if the last 3
weeks are eliminated. The analysis is straightforward,
requiring only the sum and sum of squares of the individual
weekly averages and the "monthly" totals. The individual
computations for the example are given below and these are
substituted in the formulas of Table B-l to obtain the
results tabulated in Table B-2.
Zx = 74.13,
Zx2 = 55.5107, and
ZT2 = 220.9187.
The analysis follows methods given in standard texts
such as reference 7. The sum of squares and mean squares
are intermediate steps in the calculation and are used as a
convenience to yield the mean square and the estimate of the
components of variance. The mean square for "among weeks"
within a month is a direct measure of the variance of the
individual weekly averages about their own monthly average.
The mean square for "among"monthly" averages is an estimate
of the variance of the weekly averages plus 4 times the
variance of the monthly averages about an overall mean for
all of the data. Equating the results in Table B-2, the
estimates of the components of variance are obtained and
given at the bottom of Table B-2.
B-3
-------
Table B-l. ANALYSIS OF VARIANCE
Source of
variation
Among "monthly
averages "
Among weekly
averages within
month
Sum of
squares (SS)
2 ?
ZT (Zx)
4 100
- 2 ZT2
Ex - j
Degrees of
freedom (DF)
25 - 1 = 24
(4 - 1)25 = 75
Meana
square (MS)
SS
2T
SS
75
Mean square
estimate
of indicated
variance
components
Var (weekly average) +
(4 x Var (monthly
average) )
Var (weekly averages)
w
The mean square for each source of variation is the corresponding sum of squares
divided by the degrees of freedom.
Table B-2. ANALYSIS OF VARIANCE FOR DATA SET U-l
Source of
variation
Among "monthly
averages
Among weekly
averages within
month
Sum of
squares (SS)
0.277
0.281
Degrees of
freedom (DF)
24
75
Mean
Square (MS)
0.0115
0.0037
Var (weekly averages within a month) * 0.0037
Var (monthly averages) - (0.0115 - 0.0037)/4 = 0.0020
Standard deviation of weekly averages - 0.061
Standard deviation of monthly averages ~ 0.045
-------
The results of this type of analysis for several data
sets are reported in Table B-3 for all coals, and in Table
B-4 for coals with less than 1 percent sulfur. Table B-5
lists the expected values and limiting values of the variance
components. The highest limiting values were obtained by
using the second highest as the upper value and the second
lowest as the lowest value within the week (or month) under
the heading of "unit train" and also for monthly components
of variation.
In previous discussions the distribution of the analyses
of composite samples was assumed to be lognormal or inverted
gamma rather than normal. This would suggest a transformation
of the data, such as InX, with all subsequent analyses
performed on the logarithms and the results transformed
back to X = e = e . This was done on one typical example
and the difference in the results was very small. Although
for this specific analysis the transformation does not seem
to be justified, there will be situations in which such a
transformation would be beneficial.
B.I.3 Estimation of Standard Deviation for Various
Averaging Times
One of the important calculations required in Section 5
involves estimating the variability of average sulfur con-
tent based on various averaging periods of one month.
Discussions of this type of computation appear in several
statistical texts under the subject of nested models and
components of variance. A brief description of the approach
is given here.
First of all, a linear model is assumed to describe the
behavior of the data, that is, the individual sample result
(x) is given by the relationship;
B-5
-------
Table B-3. ESTIMATION OF MEANS AND STANDARD DEVIATIONS
(COMPONENTS OF VARIATION) OF SULFUR CONTENT
Data
Set
C-l
C-2
C-3
C-4
C-5
C-8
U-l
U-2
U-3
U-4
U-5
U-6
U-7
U-8
U-9
U-10
U-ll
U-12
U-13
Absolute standard deviation and relative standard deviation
s (weight
Mean,
(weight
percent)
2.80
0.61
0.80
1.38
0.42
2.60
0.74
0.88
0.83
1.04
0.92
0.79
0.81
0.84
0.80
1.74
3.10
2.25
2.15
Average
standard
deviation - s
Average stan-
dard deviation
RSD (% of mean)
Unit train
s
0.22
0.026
0.076
0.030
0.033
0.13
0.106
0.045
0.135
0.132
0.132
0.134
0.165
0.232
0.164
0.169
0.22
0.157
0.125
0.09°
RSD
7.9
4.4
9.5
2.9
8.2
5.0
14.3
5.1
16.3
12.7
14.3
17.0
20.3
27.8
20.0
9.7
7.1
7.0
5.8
11.4
percent sulfur) RSD (%)
t_
Weekly
s
_
-
-
-
-
0.06(7)
-
-
-
-
-
-
-
-
-
0.144(5)
0.166(5)
0.088(5)
0.102
r ( >
RSD
_
-
-
-
-
8.1
-
-
-
-
-
-
-
-
-
4.6
5.2
4.1
5.5
Monthly ( )
s( )
0.12(20)
0.015(9)
0.031(13)
0.32(18)
0.033(10)
0.08(8)
0.044(28)
0.040(11)
0.096(4)
0.065(11)
0.069(11)
0.078(7)
0.044(10)
0+ (6)
0+ (7)
0.249(5)
0.27(20)
0.109(2)
0.129(20)
0.121C
RSD
4.3
2.5
3.9
23.2
8.2
3.1
5.9
4.5
11.6
6.9
7.4
9.9
5.4
0+
0+
14.3
8.7
4.8
6.0
6.9
Annually ( )
s ( )
0.07(240)
-
-
-
-
0.03(100)
_
-
-
-
-
-
-
-
-
-
-
-
0.05
RSD
2.5
1.2
1.9
w
Variation among composite samples from a unit train within a week or month depending
on the subsequent components of variation.
Values in parentheses denote the average number of samples (measurements) per week
month or year; the number is rounded to the nearest integer.
c 2
These values were determined by adding the product of each s by its corresponding
degrees of freedom, and dividing this sum by the* total degrees of freedom.
-------
Table B-4. ESTIMATION OF MEANS AND STANDARD DEVIATIONS
(COMPONENTS OF VARIATION) OF SULFUR CONTENT
(Coals with less than 1 percent sulfur)
Data
Set
U-l
U-2
U-3
U-4
U-5
U-6
U-7
U-8
U-9
C-2
C-3
C-5
Mean,
(weight
percent)
0.74
0.88
0.83
1.04
0.92
0.79
0.81
0.84
0.80
0.61
0.80
0.42
Average standard
deviation
Average relative
standard devia-
tion (% of the
mean)
Absolute standard deviation (s) and
relative standard deviation (RSD)
Unit train
s
0.106
0.045
0.135
0.132
0.132
0.134
0.164
0.232
0.164
0.026
0.076
0.033
0.109b
RSD
14.3
5.1
16.3
14.0
14.3
17.0
20.3
27.8
20.0
4.4
9.5
8.2
14. 3C
Weekly
s
0.06
-
-
-
-
-
-
_
-
-
0.06
RSD
8.1
-
-
-
-
-
-
_
-
-
8.1
Monthly
s
0.044
0.040
0.096
0.065
0.069
0.078
0.044
0+
0+
0.015
0.031
0.033
0.056
RSD
5.9
4.5
11.6
6.9
7.4
9.9
5.4
0+
0+
2.5
3.9
8.2
5.9
'variation among composite samples from a unit train within
week or month depending on the subsequent component of
variation.
These values were determined by adding the product of each
s* by its corresponding degrees of freedom, and dividing
this sum by the total degrees of freedom.
Q
These averages are ordinary averages, not weighted by
the degrees of freedom or the number of samples analyzed.
The data sets represent coals having varying degrees of
mixing in the mining operation and loading on cars, a
wide range of tonnages of coal sampled, and varying coal
preparation/processing/cleaning procedures. In particular,
data sets C-2 and C-3 are washed coals. Hence, the
average value of the RSD does not correspond to that of
a given coal but is a mid-range value.
B-7
-------
Table B-5 EXPECTED VALUES AND LIMITING VALUES FOR ABSOLUTE AND
RELATIVE STANDARD DEVIATION FOR EACH COMPONENT OF VARIANCE
Component of
variation
Among unit
trains a
Among weeks
within months
Among months
Lower limit
s
0.033
_d
0.031
RSD
5.1%
-
3.9%
Expected value
sb
0.109
0.06
0.056
RSDC
14.3%
8.1%
5.9%
Upper limit
s
0.169
-
0.078
RSD
20.3%
-
9.9%
Variation among composite samples from a unit train within
week or month depending on the subsequent component of
variation.
bThese values were determined by adding the product of each
s2 by its corresponding degrees of freedom, and dividing
this sum by the total degrees of freedom.
GThese averages are ordinary averages, not weighted by
the degrees of freedom or the number of samples analyzed.
The data sets represent coals having varying degrees of
mixing in the mining operation and loading on cars, a
wide range of tonnages of coal sampled, and varying coal
preparation/processing/cleaning procedures. In particular,
data sets C-2 and C-3 are washed coals. Hence, the
average value of the RSD does not correspond to that of
a given coal but is a mid-range value.
Insufficient data
B-8
-------
x = Long-term average (e.g., an average for a year (s) )
+ monthly effect (deviation of monthly average
from the long-term average) , a
+ within month effect (deviation of unit train
result from the monthly average) , 6
vt III
x = y + otm + 6wm, Equation B-l
or
x = Long-term average
+ monthly effect (deviation of monthly average
from the long-term average) , a
+ weekly effect (deviation of weekly averages
from their monthly average) , B
wm
+ within weeks effect (deviation of the indi-
vidual sample result from the weekly average) ,
ww
X - ^ + am + ewm + 6ww Equation B-2
It is assumed that a , 6 / 6 are all normally and
m wm ww
independently distributed with zero means and variances
22 2
°a ' aB ' anc^ °6 ' resPectively- In theory, another effect
can be added to equation B-2, that is, the effect of ana-
lytical variation due to imprecision of the measurement
technique. However, this effect is included in the component
of variation,
-------
component due to the measurement itself. The component of
2
variance, a. , includes two components, one due to the sulfur
2
variability, a,. , and one due to the analytical measurement,
2
aa , that is,
A
Since there is no convenient means of separating these two
components for these data, they are treated as one component
throughout this report. For example, if the standard
deviation of sulfur variation were 0.12 and that for the
analytical technique were 0.05, then the combined variance
would be ax2 = 0.0144 + 0.0025 = 0.0169 or a. = 0.13.
0 0
Hence, if the analytical error is small in comparison to the
sulfur variability, the effect of treating the two components
in combination is small.
Subject to the above assumptions the variance of the
result, x, is given by the sum of the variance of each
component. Hence the variance of x is given by
Var(x) = Var (a ) + Var (B ) . Equation B-3
m wm
or by
Var(x) = Var(a ) + Var (3 ) + Var(6 ) Equation B-4
m wm ww
corresponding to equations B-l and B-2, respectively.
The Var(y) = 0 as y is considered a constant, a long-term
average weight percent sulfur.
Now suppose that eight measurements are obtained per
month and their averages computed, the expected variance of
the average is given by
B-10
-------
Var(x, monthly) = o 2 + _$_ Equation B-5
a 8
where a2 and a? are the variances of a and (3 , respectively,
ct p in \vrii
and equation B-l is the assumed model. That is, the component
of variability within months is divided by the sample size
(8 in this case) and the monthly component is added to this
value to obtain the total variance. The standard deviation
is obtained by taking the square root of the variance. In
general, the variance for the average of n measurements per
month is given by,
Var(x, monthly) = a2 + - , Equation B-5
and for 3 months (quarterly) ,
a2
f"V
Var(x, quarterly) = + - . Equation B-6
a2 a*
The estimates of these variances are obtained by substituting
the corresponding estimates obtained from Table B-4 (coals
with less than 1 percent sulfur) .
An example calculation is given to illustrate the use
of the above approach to calculate the entries in Table
5-1, under the column headed by w = 4, n = 16. From Table
B-4, the following RSD's are obtained:
Among months, RSD = 5.9%.
Among weeks within months, RSD = 8.1%
(data for one set only) .
Among unit trains within weeks (or months), RSD = 14.3%.
B-ll
-------
From these data the following RSD's are obtained assuming
4 unit trains per week and 16 unit trains per month
2 2 1/2
RSD(unit trains = (14.3 + 5.9 ) = 15.5%.
2
RSD(weeks) = (5.92 + 8. I2 + ^-- ) . = 12.3%.
2
RSD (months) =(5.92 + ^-^- ) =6.9%.
ID
2 2 1/2
RSD (quarterly) = (^~ + ±j^. ) =4.0%.
2 2 1/2
RSD(semi-annually) = (^-^ + ^^~ ) =2.8%.
5 92 14 32
RSD (annually) = (^ + ii ) =2.0^
B.1.4 Correlation Analysis
It is also of interest to determine whether the weight
percent sulfur (S) and Btu content (B) are correlated. To
determine this correlation, S and B values are cross-tabulated,
as shown in Table B-6; a scatter diagram of the same data
set is given in Figure B-l. The simple correlation is given
by
I(B. - I) (S. - S)
r = - --
tB..^ - B)2 x Y.(S± - S)2
and for these data, the value for r is 0.18.
B-12
-------
Table B-6. CROSS-TABULATION OF SULFUR AND BTU CONTENTS
Btu/lb
< 12,100
12,100-12,200
12,200-12,300
12,300-12,400
12,400-12,500
12,500-12,600
12,600-12,700
12,700-12,800
12,800-12,900
> 12,900
Weight percent sulfur (S)
< 0.65
5
5
1
3
3
5
2
4
6
2
r 0.66-0.69
6
4
4
4
1
5
3
1
3
4
0.70-0.73
8
4
4
5
5
2
5
1
4
3
0.74-0.77
4
4
2
0
2
0
1
1
2
3
0.78-0.81
0
1
0
1
3
1
2
3
1
1
0.82-0.85
1
0
0
1
1
0
2
0
4
3
> 0.85
2
1
4
1
3
6
3
4
6
3
u>
The correlation coefficient r is given by
_ _ (E(B - B) (S - S)}/(N - 1) =
* r* *"* rt---i
. x £(S - S)^
4.603
[Z(B - i
[_N- 1
1
J
1(303.1)
L
(0.0839
)7*
J
= 0.181'
a Referring to a standard table for confidence intervals for the correlation coefficient, it
is concluded with 95 percent confidence that the correlation is slightly positive, that is,
between about 0.04 and 0.35.
-------
1.3
1.2
1.1
1.0
0.9
O.S
0.7
0.6
n K
1 |
DATA LEGEND
0 ONE POINT
TWO COINCIDENT POINTS
4 THREE COINCIDENT POINTS
FOUR COINCIDENT POINTS o
0
o
o
I
0
* o o 8
o o o
too*.
o o * * * o I
P o ° 8 8
0 8 8 ° \ I 8
0
-
o
o
I 1 °
1 1
o
o
o
-
o o
o
0 0
o _
8
0
o
O 0 O O
8 8 °o * 8 §
o
0 1 0 -
8*»8»°o°
III § f ° 1 -
S S A 5 0
X 0 0
0 o 8
o
1 1
11,500 12,000 12,500 13,000
BTU/lb
Figure B-l. Scatter diagram of a sample of data set U-l.
-------
B.1.5 Estimated Variance of Ib SO^/MM Btu
The estimated standard deviation (or variance) of a
ratio can be obtained very simply using the relative stan-
dard deviations and the relationship,
Relative Variance (kS/B) = Rel. Var(S) + Rel. Var(B),
provided S and B are statistically independent. A cross-
plot of S and B for several data sets indicates that in-
dependence is a reasonable assumption. Now assume that the
relative standard deviation of S is about 15 percent and
that for B it is about 5 percent (a conservative, large value)
The relative variances are the squares of these values;
it is readily seen that the effect of the variation in B
is small in terms of the relative variance in the ratio kS/B
versus the relative variance in S above. For the specific
example,
RSD of S = 15
2 2 1/2
RSD of kS/B = (15 + 5 ) = 15.81,
a 5.4 percent increase in the relative standard deviation.
In this report it is assumed that the RSD of the ratio kS/B
is equal to 1.05 times that for S. This is a matter of
convenience. One must be careful not to make this assumption
for the absolute standard deviation of the ratio (kS/B),
which would increase by a factor of about k times that for
weight percent sulfur (S).
B-15
-------
B.I.6 Relationship Between the Average, x and Standard
Deviation, s
In order to study the relationship between s and x, a
plot was made for s versus x, as shown in Figure B-2. This
figure clearly indicates the dependence of s on x, which is
best approximated by a linear relationship, particularly for
coals with sulfur concentrations less than 1.5 weight percent.
The utility of the lognormal transformation is based on this
indicated dependence of s on x.
B.2 DETAILED ANALYSIS OP DATA SET U-l (% SULFUR, DRY BASIS)
A more detailed analysis was conducted of the weight
percent sulfur, Data Set U-l, to estimate the frequency
distribution of sulfur in the coal as-received at a specific
plant.
To simplify the analysis the 103 values for weekly
weighted averages, and the weekly ranges (largest value less
the smallest value) were tabulated as shown in Appendix A,
Data Set U-l. These two frequency distributions were then
plotted on lognormal probability graph paper; experience
with several data sets has shown that the lognormal distri-
bution is a reasonable empirical approximation of the fre-
quency distribution of sulfur. The results of the Navajo
Report are also used to obtain empirical frequency dis-
tribution. There is no reason that the range should be
lognormally distributed but the plotted frequency distribu-
tion still provides a convenient summary of the data.
Figure B-3 gives the graphical presentation.
The data were subdivided by approximate periods of one-
half year each as an aid in determining any major long-term
trends. The next step in the analysis was to compute the
means, x, and standard deviations, s, of the weekly weighted
averages for each 6-month period (approximate) and for the
2-year period. These results are given in Appendix A, Data
Set U-l, which also gives the mean ranges for the data.
B-16
-------
0.7
0.6
5
5E0.5
$0.4
*
1
|»4
250.3
§
0.2
0.1
00
1.0
2.0 3.0
WEIGHT PERCENT SULFUR
4.0
Figure B-2. Relationship of standard deviation to mean sulfur content.
-------
w
I-1
oo
2.00
UI
Ul
1.00-
.90-
3 ".80
£ .70
I I I
1 I
I 1
.01 .050.1
l i
I I 1 T
PREDICTED DAILY FREQUENCY
DISTRIBUTION ASSUMING X HAS
INVERTED GAMMA DISTRIBUTION
1 I I I I II
WEIGHTED AVERAGE
SULFUR, WEEKLY BASIS
RANGE OF WEEKLY
MEASUREMENTS
I I
I
I
I
I
I
0.5 1
10
Percentile of the Frequency Distribution
Figure B-3. Frequency distribution for Data Set U-l,
1.50
1.00
.90
.80
.70
.60
.50
.40
.30
.20
.10
.05
20 30 40 50 60 70 80 90 95 98 9999.599.899.9 99.99
-------
The overall mean sulfur content is x = 0.742 and the standard
deviation of the weekly weighted averages is s = 0.0732. A
separate analysis was conducted for the In x (natural log of
sulfur content, weight percent); the geometric mean and
standard deviation are 0.762 and 0.0866. The overall mean
weekly range, R, is 0.287. From this value an estimate of
**. s\
the standard deviation, a, within weeks is a = RAU =
0.287/ 2.701 = 0.106, where d_ is the factor that when
divided into the mean range yields an estimate of the standard
A.
deviation, a (see reference 8).
With these results it is easy to estimate (again by
approximate methods) the standard deviation of individual
sulfur measurements on a daily basis. The total variance of
a daily measurement is approximately
/s« ^ O O
a (Total) = a (within weeks) + s (among weeks)
= (0.106)2 + (0.0732)2
= 0.0166
/«y
a (Total) = 0.13
Another line is then shown on the logarithmic probability
paper which has the same median value (50th percentile) but
with a slope consistent with the variability of the daily
/^ y\
measurements, a (Total). This is done by plotting, x + a
^ /\
at the 84th percentile and x + 2o at the 97.5th percentile.
This line provides a reasonable approximation of the dis-
tribution that would have been obtained if all of the data
were plotted as was done for the weekly average values.
(This would have required considerable additional work.)
B-19
-------
The next consideration in the analysis was utilizing
the background information given in the Navajo report.
Therein it is explained that the weight percent sulfur of
the coal to be burned, x, has approximately an inverted
gamma distribution, the form of which is given below for
reference only. It is not used directly in subsequent
calculations,
f(w) = (BX)e(|)3+1 e'B*/x/r(B), x > 0, 3,A > 0.
J^
The results of using this distribution will be compared to
those using the lognormal distribution.
In order to apply the above distribution, it is nec-
essary first to estimate the parameters 3 and X or 3 and 3A
= a, by using the following relationships given in Reference
1.
f"
1^2
V~^ /n
8-1
a2 (Total) = ~x - a
(3 - D2(3 - 2)
-^
where x = the overall mean = 0.742 and a(Total) = 0.129,
a (Total) = 0.0166. Substituting in the first equation above,
0.742 = ir-2
3-1
and thus
0.0166 = (0.5506) ^
3-2
or 3 - 2 = 33, 3 = 35.
Hence, a = 0.742(3 - 1) = 25.23.
Incomplete gamma function tables are not conveniently
2
available, whereas x tables (for special cases of the parameter
o
3) are readily available. Hence, the probability that x,
the weighted percent sulfur for a daily sample, is greater
than some specified value can be obtained directly by interpola-
2
tion in a table for x as shown in the example computation
given below. The probability is estimated by
B-20
-------
Prix > x } = Pr{X2 < ^|f = 26),
0 xo
where the example data
/N
2a = 50.46
2
23 = 70 = v = degrees of freedom used with the x table
(v = f in Hald's table8),
For example, if x = lf
Pr(x2 < 50.46 = 50.46|v = f = 70 degrees of freedom}
= 2.5 + (50'46 " 48>8J2.5 = 3.93 or about 4%.
£> .7 /
If XQ = 1.2 ,
Pr{X2 < 5?'?6 = 42.05|v = 70} = 0.38%,
1.2
If XQ = 0.8 ,
Pr{x2 < 50-f6 = 63.08|v = 70} = 29.35%.
U . o
These values may be plotted on log probability paper.
Theoretically they will not fall on a straight line, but the
approximation will be good. Note that the points almost
coincide with the straight line drawn on the graph based on
the lognormal assumption. Thus it is very difficult to dis-
criminate between two such empirical approximations. The
lognormal frequency distribution is more convenient, and the
results are essentially identical to those obtained with the
inverted gamma distribution.
B-21
-------
B.3 AVERAGES FOR FEWER THAN FIVE MEASUREMENTS ASSUMING
INVERTED GAMMA DISTRIBUTION
Section 5.3.3 refers to the fitting of the inverted
gamma frequency distribution to the case where fewer than
five measurements are averaged. A simple technique for
fitting an inverted gamma to a data set is given herein.
The two parameters, a and 8, of the inverted gamma are esti-
mated by the relationships
^
n- ot
e - i
2 *1 2
s* = o2/(B - ir (B - 2)
Combining the two equations yields a simple system of
equations, i.e.,
B - 1
s2 _ 1
X2 B - 2
The value of m is determined by iteration starting with the
value estimated by the lognormal assumption. Thus for a
/\
given RSD, B can be readily determined and substituted in
the first equation to solve for a. For example, for RSD =
0.204, and x = 0.858 (first iteration) we obtain
0.0416 = T^
B - 2
or
B - 2 = 24.0
B = 26.0
a = 21.48.
5-22
-------
From further results given in Appendix B.2, the probability
that x is greater than the emission standard, 1.2 Ib SO^/MM
Btu, is given by the following relationship
s\
9 9rv ^
P(X > 1.2) - Pr{X < I f = 23)
1.2
= Pr(x2 < 35.8 | f = 52},
2
where x is the chi-square variable for which the distri-
bution is tabulated in reference 8 and f is the associated
number of degrees of freedom. Determination of the proba-
2
bility requires interpolation within the x table,
f_
52.0
Probability
0.01 0.025 0.05 0.10
31.2 34.0 36.4 39.4
The probability is estimated to.be 0.044 for this mean.
A larger mean can be selected and the new probability calcu-
lated. Repeat this process until the mean is consistent with
A
a probability of 0.05. Hence if m = 0.87, g = 26.0 as above
/s,
but a = 21.75.
Pr{x2 < 36.2 | f = 52} = 0.0480
If m = 0.88
Pr{X2 < 36.7 | f = 52} = 0.0528.
Therefore m = 0.875 is the mean required for 95 percent
compliance with 1.2 Ib S02/MM Btu. This mean is slightly
larger than the mean estimated using the lognormal assump-
tion. This same close relationship between the two
assumptions was obtained for all of the example computations;
hence, the lognormal assumption is both adequate and some-
what conservative.
B-23
-------
B.4 APPLICATION OF QUALITY CONTROL TO SULFUR VARIABILITY
Suppose that it is desired to control the long-
term average sulfur content at some specified level, say
0.987 Ib S02/MM Btu. Furthermore, it is desired to control
the variation about this average within limits that are
considered reasonable for "inherent" variability of sulfur
content of coals. These requirements immediately suggest a
reasonably simple application of quality control techniques
to, for example, monthly averages of sulfur content.
On the basis of data in Section 5, the estimated rela-
tive standard deviation of monthly averages of weight per-
cent sulfur based on 16 unit trains was determined to be
about 6.9 percent. Based on the data of Section B.I. 5,
Appendix B, the relative standard deviation of monthly
averages of Ib S02/MM Btu would be slightly higher, say 6.9
(1.05) = 7.2 percent of the mean value. Hence, if it is
desired not to exceed a limit of 1.2 Ib S02/MM Btu except
for a very small portion of the monthly averages determined
by an upper (30) control limit, then the required mean
sulfur content would be
' ,>-! m = 3 (corresponding to 3o limit)
U U / ^ Iu
or
m = 0.987 Ib S02/MM Btu
The mean (or center) line on the control chart would be
0.987, the upper 2a limit (warning limit) would be
0.987 + 2(0.072) (0.987) = 1.13 Ib S02/MM Btu
and the upper control limit would be
0.987 + 3(0.072) (0.987) = 1.20 Ib S02/MM Btu
B-24
-------
as prescribed in the above computation and shown in Figure
B-4. The lower warning and control limits are similarly
obtained by replacing the plus (+) sign by a minus (-) sign
in the above equations. If the mean sulfur content remains
at 0.987 Ib S02/MM Btu, and the RSD remains at or below 0.071
(0.072 x 0.987), then the chance of a monthly average ex-
ceeding 1.2 is very small, less than 2 chances in 1000 if
the average can be assumed to be normally distributed. This
is a reasonable assumption for averages of several unit train
measurements, as previously indicated. It is not a good
assumption for individual unit train analyses or for averages
of less than five composite samples.
Both warning limits are included on the chart cor-
responding to the expected variation determined by analyses
of several data sets, Table 5-1. The upper control should
be used as a signal to take immediate corrective action in
that the sulfur content is considerably high and that, for
example, a coal of lower sulfur content should be used or
mixed in appropriate proportion with the current coal to
yield a long-term maximum of 1.2 Ib SO2/MM Btu. The upper
warning limit may be considered a signal to take action if
two consecutive values fall between the upper warning and
control limits. Corrective action may also be taken if a
series of seven consecutive values lie above the mean value
line 0.987, or if there is a series of seven or more con-
secutively increasing values, even if some of the values
are below the mean line at 0.987.
B-25
-------
1.30
CO
o
to
1.10
0.90
0.70
UCL - » 1.20
A
x * MEAN = 0.987
LWL - = 0.845
A
LCLx
0.774
4 6
NUMBER OF MONTH
8
10
Figure B-4. Application of quality control chart
to control sulfur variability.
The lower warning and control limits do not require
corrective action because they indicate a desirable condition
leading to lower emissions. These limits are entered on the
chart to indicate a possible improvement in coal quality.
From the standpoint of the supplier, it would be beneficial
to know that a potential improvement in quality has resulted
from, say, a change in mining operation.
The potential benefits of this approach are that (1)
compliance with the standard of 1.2 Ib SO-/MM Btu is achieved
for a desired percentage of the averages through careful
monitoring of the sulfur content and (2) this interpretation
of the NSPS permits use of the largest possible quantity of
coal reserve while operating in compliance. The disadvan-
tage is that for periods of 1 month the sulfur content of
B-26
-------
the coal may be outside the control limit before action is
taken. In practice, a within-month check can be maintained
by use of a moving average, as described in the following
paragraphs, to allow more rapid action if the coal is
tending toward the high-sulfur range.
The quality control chart can also be used for moving
averages and ranges of four consecutive weekly averages or
of individual analyses. Data set U-l is analyzed to illus-
trate how the quality control limits are derived and used
to "monitor" the sulfur content of coal. Table B-7 gives
the weekly average weight percent sulfur, the 4-week moving
average, and range. The quality control limits are then
derived from the average of the moving average, x = 0.797
percent sulfur by weight, and of the moving range, R
= 0.141. The formulas given at the bottom of the table
require constants as given in Grant and Leavenworth.
The moving average and range charts provide a moving "monthly"
average and a range of the weekly values during the month,
assuming 4 weeks data are averaged. These data can aid in
detecting trends in the mean or variation of sulfur content.
The quality control chart for this example is given in
Figure B-5. There are potential benefits in plotting simul-
taneously a chart for the averages of the unit trains as
received during one week and the monthly averages. The
crossover points for these two charts are indicative of
trends that may warn the company of a trend toward undesired
values of sulfur content.
B-27
-------
Table B-7. DATA AND COMPUTATION OF CONTROL CHART LIMITS
FOR MOVING AVERAGE CHARTS FOR SULFUR CONTENT
(values in weight percent sulfur)
Number
of week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Total
Average
Weekly
average
0.72
0.76
0.73
0.83
0.85
0.71
0.78
0.74
0.72
0.70
0.78
0.84
0.78
0.88
0.94
0.99
0.78
0.78
0.71
0.70
Four-week
moving average
0.760
0.793
0.780
0.793
0.770
0.738
0.735
0.735
0.760
0.775
0.820
0.860
0.898
0.898
0.873
0.815
0.743
13.543
x = 0.797
Four-week
moving range
0.11
0.12
0.14
0.14
0.14
0.06
0.08
0.08
0.14
0.14
0.10
0.16
0.21
0.21
0.21
0.28
0.08
2.40
R = 0.141
UCL-
X
LCL-
X
UCL =
LCLD =
K
= x +
= 0.80 + 0.73(0.14) =
x - A9R = 0.80 - 0.73(0.14)
<-
D2R = 2.28(0.14) = 0.32
D-.R = 0(0.14) = 0
j
0.90
0.70
B-28
-------
IX
0.90
C3
0.80
0.70
6 11 16
NUMBER OF THE WEEK
6 11 16
NUMBER OF THE WEEK
Figure B-5. Moving average and moving range
quality control charts
B-29
-------
APPENDIX C
SULFUR VARIABILITY WITH LOT SIZE
C.1 INTRODUCTION
Performance of power plants in regard to S02 emissions
is generally governed by the New Source Performance Standards
(NSPS) applicable to new plants commissioned after 1975 or
by a State Implementation Plan (SIP) applicable to existing
plants. These standards normally limit S02 emissions to a
value expressed in pounds of SO2 per million Btu (Ib/MM Btu),
a value never to be exceeded. The test procedure prescribed
for ascertaining whether a plant is in compliance implies,
however, that the value for Ib/MM Btu actually refers to a
3-hour average.
The standard, interpreted in common terms of 3-hour
averages, has different impacts on different sizes of power
plants. A typical 500-MW plant consumes about 600 tons of
coal in a 3-hour period, whereas the smallest plant that
comes under the purview of NSPS, a 25-MW plant (or 250 x 10
Btu/hr), consumes only 33 tons of coal in 3 hours. Thus,
a 500-MW plant consumes a larger tonnage of coal with which
to achieve the 3-hour average emission rate. Compliance
is more difficult for the smaller plant, which has only 33
tons of coal over which it can average to meet the standard.
As a corollary, the small plant also will have a cpmparatively
more difficult task in meeting the standard during nonpeak
hours. This is so because during peak hours the plant
consumes considerably greater quantities of coal than it
does during nonpeak hours.
The compliance problems of small plants are further
C-l
-------
compounded by yet another factor, the greater variability
of sulfur content of composite samples from smaller lot
sizes. If truly representative samples are collected from
600-ton lot sizes, the variance of the sulfur measurements
would be smaller than that in 33-ton lot sizes. This situa-
tion is depicted graphically in Figure C-l. Theoretically,
the above statement derives support from the Central Limit
Theorem, which would assert that the sulfur content of
samples from 33-ton lot sizes (as well as the sums) would
have greater variance than that for 100-ton and 600-ton lot
sizes. The larger lot sizes have a less variance because
of the blending involved in collection of representative
samples from progressively larger lot sizes. Thus, the smaller
plants, because of the greater spread of their sulfur con-
tent measurement, would have to start with smaller nominal
sulfur content if a certain standard is not to be exceeded.
Alternatively, if two plants burn coals with the same nominal
sulfur content from the same mine the smaller plant would
produce a larger number of SO emission violations than would
the larger plant.
C.2 STATISTICS OF NORMAL DISTRIBUTION
Although lognormal and inverted gamma distributions
have been proposed and used in connection with SO2 emissions,
for purposes of this discussion a normal distribution of
emissions is assumed. If one of the skewed distributions
were used, the discussion that follows would have still
greater implications in regard to the number of violations.
Statistics of normal distribution are shown in Figure
C-2, where the figures with arrows to the right indicate
areas under the curve up to a given point and figures with
arrows to the left indicate areas beyond that point. Typi-
cally, at y + 30 (where y = mean and a = standard deviation)
C-2
-------
600 T
100 T
33 T
1.0 1.1 1.2 1.2 1.2 1.5 1.0 1.3 1.3 1.3 1.4 1.5 0.8 0.8 1.4 1.0 1.1 1.5
Figure C-l. Hypothetical example illustrating lot size variability.
-------
o
I
0.68*-
RSD OF 2M
0.36% S-«-
1.2 SO,
0.63% S
Figure C-2. Statistics for normal distribution.
-------
the area up to that point is 99.87 percent and the area
beyond the point is only 0.13 percent. Theoretically, the
normal distribution is asymptotic to the x-axis, but for
all practical purposes we can neglect the curve beyond
y + 30. The resulting error is 0.13 percent. Although
this error appears to be insignificantly small, it can repre-
sent a significant number of violations per year. If for
example, a normal curve represents the distribution of a year's
3-hour overlapping averages (8760 averages/year), then
about 12 of these averages would exceed the y + 30 limit (see
values in parentheses on the figure).
If the emission standard is 1.2 Ib SO_/MM Btu and the
coal is known to have an RSD of say 25 percent for lot sizes
corresponding to a 3-hour coal consumption, then the mean
value of Ib SO2/MM Btu would have to be a much smaller value,
0.68, requiring an extremely low-sulfur coal. Even then,
there may be about 12 violations per year. In an attempt to
reduce the number of violations, the emission standard of
1.2 Ib SO2/MM Btu may be set equal to y + 30, resulting in
about two violations per year. If the standard is set equal
to y + 40, then there will be about 0.28 violations per year;
though negligibly small, there is the finite probability
that violation is likely to occur once every 4 years. If
the standard were set equal to y + 40, however, we would
be faced with the concomitant problem of using coal that
on an average would emit only 0.6 Ib S02/MM Btu, requiring
sulfur content of 0.32 percent with a heating value of
10,000 Btu/lb. As cited previously, if the lognormal dis-
tribution were used, the expected number of violations would
be larger than the values indicated above.
C.3 IMPLICATIONS OF VARIABILITY
With regard to the sulfur variability of coal, if a
certain standard is not to be exceeded except for a finite
0-5
-------
number of times, we seek a coal for which the mean sulfur
content is compatible with the emission standard and the RSD
of sulfur content. Larger RSD's imply that the means must
be decreased. Thus, for RSD's of 10 and 25 percent with
an emission standard of 1.2 Ib SO /MM Btu set equal to
y + 3a, the required mean sulfur contents in Ib SO /MM Btu
would be:
yi + 3 x 0.10 x yj = 1.2 or PJ= 0.92.
y2 + 3 0.25 x u? = 1.2 or U2= 0.69.
C.4 VARIABILITY WITH LOT SIZE
As indicated earlier, the sulfur contents of composite
samples from larger lot sizes shows smaller variance of RSD.
This is also indicated clearly in Figure 5-1 and Table 5-1
of this report. Quantification of the relationship between
the RSD and lot sizes is, however, considerably more diffi-
cult than Figure 5-1 suggests. RSD's of different coal
supplies are highly variable. Furthermore, one can assume
that the RSD's of clean coals are much smaller than those
of the raw coals. Although, theoretically, analyses of sul-
fur content of composite samples from larger lots should
show smaller RSD's, analyses of actual coal data often show
departures from this relationship, probably caused by local
aberrations in the data. The overall trend of smaller
variance with larger lot sizes may be established, but in
a local sense the relationship may not be verified. Several
data sets are discussed below in this context.
C.5 IDENTIFICATION OF DATA
C.5.1 Data Set C-2
Analysis of data set C-2, indicates a monotonic, almost
linear relationship between RSD and lot size. The analysis
is summarized in Table C-l and shown graphically in Figure
C-3. The effect of larger variability on the mean value
C-6
-------
required for the plant not to exceed the standard of 1.2
Ib SO2/MM Btu is also shown in Figure C-4, which points to
the plight of smaller plants (which consume less coal in a
3-hour period) as they attempt to meet the standard.
Table C-l. ANALYSIS OF DATA SET C-2a
Lot Si
No. of data
points
40
40
40
39
*, torn
Range ,
tons
278-
1590
1617-
2275
2282-
3009
3024-
7450
i
Mean,
tons
1174
1970
2604
4089
Su.
Mean
(%/lb/MM Btu)
0.8
1.2
0.8
1.2
0.8
1.2
0.8
1.2
Lfor/ttg
Standard
deviation
(%/lb/MM Btu)
0.096
0.134
0.086
0.120
0.067
0.100
0.055
0.077
RSD,
%
11.8
10.7
10.7
9.6
8.6
8.2
7.0
6.3
See Table 3-1, Data Set C-2, for comments.
C.5.2 Data For Some Other Mines
Figure C-5 depicts data for three mines.
o Mine 4186 - Leatherwood, E. Kentucky.
o Mine 8150 - Velva, North Dakota.
o Mine 1160 - Imboden, Appalachia, Virginia.
The data for all three mines refer to raw low sulfur coal.
All samples were collected during the unloading process at
the same time of delivery to the installation. Although the
three sets of data look alike, their analyses indicate widely
differing RSD's. Each has a slope essentially equal to zero,
suggesting independence of RSD's and lot sizes.
Figure C-6 depicts data for two other mines:
o Mine 4830 - Thick Tiller, Dante, Virginia.
o Mine 5717 - High Splint, Pardee, Virginia
C-7
-------
14.Of
12.0
FOR SO,
SO,
USD * 600 T 11.51
RSO 100 T 12.31
RSD 9 33 T 12.5*
10.0
O
I
oo
8.0-
6.0
4.0
1000
2000
LOT SIZE, TONS
3000
4000
Figure C-3. Data set C-2: RSD vs. lot size tons.
-------
o
1.2
0.90 0.96
Figure C-4. Data set C-2: variability effect on the mean SO2,
-------
J3
30
25
£ 20
Ul
o
? *
M
8»
10
5
0
' ' ' ' ' 'X ' 'A
VELVA. N.D. (8150) ^ A
A
0 n
LEATHER WOOD. EAST KY (4186) U O
D
IMBOOEN. VA (1160) O °
O O
r i i . i i . i i i
) 100 200 300 400 500 600 700 800 900 IOC
LOT SIZE. TONS
Figure C-5. RSD of S02 vs. lot size for mines 1160, 4186, and 8150.
-------
n
i
0
at
70
60-
50
40
30
20
.HIGH SM.IHT. ₯A (5717)
THICK TILLER, VA (4830)
900
1000
LOT SIZE, TONS
Figure C-6. RSD of SO- vs. lot size for mines 4830 and 5717.
-------
20
15
O
10-
HAVAJO GENERATING STATION
O
1
10
12
LOT SIZE, lOOO'S OF TONS
14
Figure C-7. RSD of SO- vs. lot size for NGS data.
16
-------
Both these mines also yield low-sulfur coals, sampled at
the time of delivery. Data for Mine 5717 (raw coal) display
a rather steep downward slope, whereas data for Mine 4830
(washed coal) display a mildly upward sloping line.
Figure C-7 depicts results of an analysis of the NGS
(Unit 1) data for the period 10/1/74 to 1/8/75. The plot
shows local aberration in the data, causing the linear
regression line to slope upward. If one neglects the aber-
rant point, the regression line would slope mildly downward.
C.6 CONCLUDING COMMENTS
The foregoing discussion delineates the relationship
between lot size and RSD. In some cases, however, the data
display either horizontal slope or upward slope with in-
creasing lot size, defying theoretical arguments. Such
cases are explained either by aberrations in data or by
the fact that samples were not truly representative of the
entire lot. Analyses of several other data sets, not in- .
eluded here, confirm at least qualitatively that RSD
decreases with increasing lot size.
This discussion also brings into sharp focus the
relatively greater impact of the emission standard on smaller
plants and the effects of averaging over different quanti-
ties of coal or over different time periods. Consider, for
example, data set C-2. Computations in this report indicate
a mean of 0.93 and standard deviations for monthly averages
over 600-ton lots and over 33-ton lots, by pro-rating as
follows:
Monthly S1 = 0.666 x 0.070/0.153 = 0.034 RSD = 3.62%.
Unit train S2 = 0.066 RSD = 7.10%.
500 ton S3 = 0.066 x 0.194/0.153 = 0.084 RSD = 9.00%.
33 ton S^ = 0.066 x 0.237/0.153 = 0.102 RSD = 11.00%,
C-13
-------
We can now study the spread of the data by computing
the y + 30 limits for y = 0.93 and for various values of
standard deviations:
Monthly Ll = 0.93 + 3 x 0.034 = 1.032.
Unit train L2 = 0.93 + 3 x 0.066 = 1.128.
600 ton L3 = 0>93 + 3 x Q.084 = 1.182.
33 ton L^ = 0.93 + 3 x 0.102 = 1.236.
These limits are shown superimposed on a plot of Ib
SO /MM Btu versus the Serial No. of unit trains in Figure
C-8. These limit lines indicate the extent of probable
maximum fluctuations of the averages for various times/ton-
nages. If the standard is set at 1.2 Ib SO /MM Btu, we can
draw the following conclusion:
1. The 33-ton/3-hour plant would be in violation of
the standard.
2. The 600-ton/3-hour plant would be generally in com-
pliance (with a confidence limit of a little over
99.87 percent).
3. It would be easier to achieve compliance with longer
averaging times/tonnages (notice the difference
between L and L2).
Alternatively, beginning with a standard of 1.2 Ib
SO2/MM Btu and RSD's as computed, we could compute the monthly
average (yi), unit train average (y2), 600-ton average (ys),
and 33-ton average (y^) required to meet the standard:
Monthly \il + 0.0366 x 3 x yt = 1.2 -» V l = 1.08.
Unit train y2 + 0.0710 x 3 x y2 = 1.2 -> y2 - 0.99.
600-ton y3 + 0.0900 x 3 x y3 = 1.2 + y 3 = 0.94.
33-ton y^ + 0.1100 x 3 x y^ = 1.2 * y^ = 0.90.
These calculations point to the same conclusion reached
earlier.
C-14
-------
1.30,
1.20
1.10-
1.00-
0.90
U, -1.08 (HONTHLY AVERAGE)
50 60 70 80
SERIAL NUMBER OF UNIT TRAINS
Figure C-8. Unit train and monthly variation of
S02/106 Btu for data set C-2.
C-15
-------
APPENDIX D
SELECTED REVIEW COMMENTS
Some of the comments of persons reviewing early drafts
of this report deal with application of the approach pre-
sented herein to situations that arise in the mining/distri-
bution/use of diverse coal resources in the United States.
To the extent that these comments deal with real-world
problems and provide insight into the applicability of the
statistical procedures, they are considered to be of po-
tential value to users of this report and are reproduced
verbatim in this appendix.
1. "The basic problem is to determine whether the coal
will be in compliance with applicable standards before the
coal is mined and shipped, in fact before the coal is sold
or the coal mine capital is committed for new mines or
expansion of present mines. There are two possible ap-
proaches, both of which lack the desirable precision to
base multi-million dollar projects.
a. If RSD is unknown, then a value must be assumed ...
The tables in the report can be used for this
purpose.
b. Try to estimate the RSD. After all, the values in
the report for RSD's are only averages based on
various (available) sets of data. From core data
and the mine plan, it may be possible to estimate
(?) the RSD through simulation techniques."
2. "Item # 1 in the recommendations, page 7-3, suggests
that it 'would be desirable to assess the variability of
sulfur content before and after cleaning1. Also, on page 2-
1, it is stated that 'the concentration of organically bound
sulfur in a particular coal seam is usually lower than the
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concentration of inorganic or pyritic sulfur'. The second
statement has a direct bearing on the first statement in
that the major portion of the sulfur removed by processes
that are presently utilized by the coal industry is the
inorganic or pyritic sulfur. But, in the case of many of
our 'low sulfur' western reserves, this does not hold true.
The pyritic sulfur is extremely low or nonexistent and,
therefore, little or no reduction in the total sulfur content
is shown by present economical beneficiation processes.
Therefore, cleaning of these coals by present economical
processes will show little if any promise of bringing these
coals into compliance with the regulations as presently
written. On a raw basis many of these reserves are 'marginal'
as regards the 1.2 Ib SO^/MM Btu (standard) even when they
are considered on a total reserve basis and 'unacceptable1
a large percentage of the time when viewed on a per shipment
basis of 10,000 tons."
3. "The sampling/analytical aspect is another critical
point. Part 26 of the 1975 ASTM book has the following
reproducibility statement for sulfur analysis: 16.2 Repro-
ducibility - The means of results of duplicate determi-
nations carried out by different laboratories on represen-
tative samples taken from the same bulk sample after the
last stage of reduction should not differ by more than the
following:
Coal containing less than the 2% sulfur 0.10%
Coal containing 2% sulfur or more 0.20%
Using these reproducibility figures the following table
demonstrates the spreads that could be expected on an
individual sample basis between two laboratories analyzing
a split of the same sample.
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Ib SO?/MM Btu using ASTM reproducibility figures^
Btu Sulfur less than 2% Sulfur greater than 2%
12000 0.16 Ib S02/MM Btu 0.33 Ib S02/MM Btu
11500 0.17 Ib SO2/MM Btu 0.35 Ib SO2/MM Btu
11000 0.18 Ib S02/MM Btu 0.36 Ib SO2/MM Btu
10500 0.19 Ib S02/MM Btu 0.38 Ib S02/MM Btu
10000 0.20 Ib SO2/MM Btu 0.40 Ib SO2/MM Btu
9500 0.20 Ib S02/MM Btu 0.42 Ib S02/MM Btu
9000 0.22 Ib SO2/MM Btu 0.44 Ib S02/MM Btu
8500 0.24 Ib SO2/MM Btu 0.47 Ib S02/MM Btu
8000 0.25 Ib SO2/MM Btu 0.50 Ib S02/MM Btu
As you can see these differences do get quite large and this
does not take into consideration any error that could be
introduced in the sampling procedure and there are no tolerances
listed for sampling."
4. "Assuming that there is no bias in the sampling/analytical
procedures the reproducibility figures of an average of a
series of analytical results tend to reach zero. This, in
my estimation, is another valid point for the inclusion of
an averaging period for S02 emission regulations."
5. "The procedures and examples for determining the required
average sulfur content of coal to be in compliance with
emission standards, as discussed in Sections 5 and 6 of the
report, are based on simple cases in which all of the coal
utilized by a source is obtained from one supplier and one
mine. When a coal supply is obtained from twenty or more
vendors, many of which use more than one mine, each with its
own average sulfur content and variability, the problem of
specifying and enforcing an average sulfur content becomes
much more complicated. Additional problems are introduced
if some of the various shipments of coal are blended to a
greater or lesser degree in a coal storage pile for use at
an undetermined time in the future while other shipments go
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directly from the unloading facilities to the bunkers for
immediate consumption. Such situations do exist in the real
world today."
6. "Because the problems of procuring a complying fuel
supply vary from source to source, any regulatory agency
which wishes to specify the manner in which fuel analyses
are to be used to demonstrate compliance with NSPS should
word its regulations in such a way as to allow the source
owner to select the procurement policies which will allow
compliance in the most efficient manner. Such a regulation
might specify that the sulfur content of the fuel, when
averaged over a specified time period, must not exceed the
value which will allow compliance with NSPS, more than a
specified percentage of the time. This is the type of
regulation discussed in example 5 on page 5-11 of the report
(the example is of a state agency which requires that monthly
averages of sulfur content must comply with NSPS regulation
99 percent of the time). This allows the owner of the
source to specify to his/her suppliers an average suflur
content which is less than that required for compliance with
NSPS, or to put a portion of the burden for determining the
required average sufur content on the supplier by specifying
a maximum sulfur content, with a penalty to be paid by the
supplier when the sulfur content exceeds the specified
maximum."
7. "In a regulation of the type discussed in the preceding
paragraph, the averaging time should be a period longer than
a week (such as a month) because railroad scheduling problems
could make it very difficult to ensure that weekly receipts
from various suppliers with various sulfur contents would
properly balance out."
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8. "As discussed in my preliminary comments of October 22,
1976, it may not be accurate to base compliance calculations
on the quality of the coal as received, in those cases where
the source utilizes pulverizers which reject a portion of
the pyritic suflur content of the fuel. In those cases, the
sulfur content of the fuel as burned is less than the
sulfur content as received; the type of pulverizer func-
tions almost as a coal cleaning facility. The efficiency of
this 'coal cleaning facility1 is low when compared with
conventional coal washing plants and varies with the pyritic
sulfur content of the coal, but in some cases it is sig-
nificant. "
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TECHNICAL REPORT DATA
(Please read liuouctions OH the rrvene before completing}
1. REPORT NO.
EPA-450/3-77-044
2.
3. RECIPIENT'S ACCESSION*NO.
4. TITLE AND SUBTITLE
Preliminary Evaluation of Sulfur Variability in Low
Sulfur Coals From Selected Mines
6. REPORT DATE
July 1977
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Nelson, A. Carl
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
PEDCo Environmental, Inc.
11499 Chester Road
Cincinnati, Ohio 45245
1O. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
68-02-1321, Task 41
12. SPONSORING AGENCY NAME AND ADDRESS
U.S. Environmental Protection Agency
Office of Air Quality Planning and Standards
Strategies and Air Standards Division
Research Triangle Park, North Carolina 27711
13. TYPE OF REPORT AND PERIOD COVERED
Contract Report
14. SPONSORING AGENCY CODE
EPA 200/04
15. SUPPLEMENTARY NOTES
EPA Project Officer: Constancio Miranda and David Kirchgessner
16. ABSTRACT
Data on the variability of sulfur content and heating value of coal have been
obtained from several coal and utility companies. These data have been analyzed
to estimate the mean, standard deviation, and the frequency distribution of weight
percent sulfur (dry basis) and the impact of this variability on the required
average sulfur content to comply with, an emission regulation.
In order to assess the implications of sulfur variability for compliance with
emission regulations, such as those specified by State Implementation Plans(SIP) and
New Source Performance Standards (NSPS), the relative standard deviation (RSD) of
weight percent sulfur was estimated as a function of the amount of coal sampled and
the number of composite samples for the specified averaging period. These RSD's were
used to estimate'the required average sulfur content to yield 95 and 99 percent
compliance with the emission limitation of 1.2 Ib 50,,/MM Btu. The detailed computa-
tions are given for two sizes of power plants, 500 MW and 25 MW (250 MM Btu/hour, the
smallest plant covered by the NSPS). As the percent of compliance increases the
required average sulfur content decreases and rapidly approaches sulfur levels for
which the availability of uncleaned coal to comply with the NSPS would apporach zero.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
Coal
Sulfur variability
Emission standards
Fuel Standards
Coal sampling
Air pollution
Coal
Sulfur variability
Air pollution control
18. DISTRIBUTION STATEMENT
Unlimited
19. SECURITY CLASS (ThisReport)
Unclassified
21. NO. OF PAGES
152
2O. SECURITY CLASS (This puge)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
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