c/EPA
United States
Environmental Protection
Agency
Industrial Environmental Research
Laboratory
Research Triangle Park NC 27711
EPA-600/7-80-107
May 1980
Effect of Physical Coal
Cleaning on Sulfur
Content and Variability
Interagency
Energy/Environment
R&D Program Report
-------
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tems. The goal of the Program is to assure the rapid development of domestic
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tion Service, Springfield, Virginia 22161.
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EPA-600/7-80-107
May 1980
Effect of Physical Coal
Cleaning on Sulfur
Content and Variability
by
D.H. Sargent, B.A. Woodcock,
J.R. Vaill, and J.B. Strauss
Versar, Inc.
6621 Electronic Drive
Springfield, Virginia 22151
Contract No. 68-02-2136
Task No. 300
Program Element No. EHE623A
EPA Project Officer: James D. Kilgroe
Industrial Environmental Research Laboratory
Office of Environmental Engineering and Technology
Research Triangle Park, NC 27711
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Research and Development
Washington, DC 20460
-------
ABSTRACT
Sulfur content and heating value data for 53 different coal source -
cleaning plant combinations were statistically analyzed, to document the
effectiveness of commercial operating coal cleaning plants in reducing
sulfur and enhancing heating value , and to investigate the effect of physical
coal cleaning upon sulfur variability.
Cleaning plants for which matched pairs of feed and product coal data
were available exhibited reductions (from feed to product) in the mean
Ibs S02/MM Btu of 24 to 50 percent. These empirical data fall within the range
(8 to 81 percent reduction) of the calculated design performance of coal
cleaning plants. The wide ranges reflect the sensitivity of performance to coal
washability and to plant design.
These matched pairs of empirical feed and product coal data exhibited a
reduction in sulfur variability averaging 55 percent and ranging from 9 to
90 percent. An indirect analysis of a larger data base, where matched pairs
of data were not available, resulted in similar reductions in sulfur variability
attributable to physical coal cleaning.
Much of the coal data exhibited autocorrelation, verifying
expectations based upon geology and engineering rationale. Analysis of
the data resulted in estimates of the long-term (geostatistical) component
of variability, in the short-term component of variability, and in the
component of variability attributable to coal sampling and analysis. By
removing the long-term conponent (which includes autocorrelation), an
inverse relationship between relative standard deviation and lot size was
empirically demonstrated.
-------
CONTENTS
Abstract i
Figures iv
Tables v
Acknowledgements vii
1. Introduction 1
1.1 Objectives of the study 1
1.2 Background on coal cleaning effectiveness as a
sulfur dioxide control technology 2
1.3 Importance of coal sulfur variability 8
1.4 Expected attenuation of variability by coal
cleaning processes 9
2. Sources of Sulfur Variability 11
2.1 Characterization of variability in coal and
in coal data 11
2.2 Permissible values for the sampling component
of variance 12
2.3 Experimental values for the sampling component
of variance 14
3. Description of The Data Base 19
3.1 Data sets 19
3.2 Data points 22
3.3 Sampling procedures utilized 22
4. Analysis of Paired Coal Peed and Product Data Sets from
Individual Plants 25
4.1 Effect of coal cleaning upon sulfur content, heating
value, and heat-specific S02 content 25
4.2 Effect of coal cleaning upon sulfur variability .... 29
5. Analysis of Unpaired Data Sets 31
5.1 Approach and limitations 31
5.2 Statistics for the data sets 32
-------
CONTENTS (Continued)
5.3 Variability of heat-specific sulfur content calculated
from variabilities of sulfur and of heating value 32
5.4 Autocorrelation of data points 35
5.5 Distribution of the data points 42
5.6 Comparison of variabilities: uncleaned vs.
cleaned coals 49
6. Components of Variance 55
6.1 Analysis of autocorrelated data sets 55
6.2 Generalized estimates for components of variance 58
7. Effect of Lot Size Upon Variability 60
7.1 Results of previous study 60
7.2 Analysis of total variability, all data sets 60
7.3 Analysis of select data sets 62
8. Conclusions 66
9. References 70
Appendices
A. Listing of the data base A-l
B. Detailed chi-square analysis B-l
111
-------
FIGURES
Number Page
1 Relative standard deviation of Ibs S02/MM Btu:
actual vs. predicted .................... 36
2 Fitted normal curve and histogram of grouped
data for batch C-8 ..................... 50
3 Fitted normal curve and histogram of grouped
data for batch U-ll .................... 51
4 Fitted normal curve and histogram of grouped SO2
data for batch C-3 ..................... 52
5 Effect of lot size upon percent sulfur relative
standard deviation ..................... 61
6 Effect of lot size upon long-term RSD select
data sets ......................... 63
7 Effect of lot size upon short-term RSD select
data sets ......................... 64
IV
-------
TABLES
Number Page
1 Average Calculated Potential for Desulfurization by
Physical Coal Cleaning 3
2A Calculated Design Performance of Cleaning
Plants 5
2B Calculated Design Performance of Cleaning
Plants Raw Coal: Upper Freeport "E" Seam,
Butler, Pennsylvania 6
2C Calculated Design Performance of Cleaning
Plants 7
3 Calculated Values of Mean Coal-to-Emission
Limit Ratio (p/E) 10
4 Components of Ash Variance in Sampling and
Analysis 15
5 Laboratory (Sample Preparation and Analysis) Variance
for Total Sulfur 17
6 Data Set Identification - Unwashed Coals 20
7 Data Set Identification - Washed Coals 21
8 Contents of Data Set 208 23
9 Statistics for Preparation Plant Peed and Product 26
10 Changes in Mean Values from Cbal Cleaning: Direct
Comparison of Feed and Product for Individual Plants ... 27
11 Reductions in Variability from Coal Cleaning: Direct
Comparison of Feed and Product for Individual Plants ... 30
12 Statistics for Variability of Sulfur, Heating Value,
and Ibs SOz Per Million Btu's, Unwashed Coal 33
13 Statistics for Variability of Sulfur, Heating Value,
and Ibs S02 Per Million Btu's Washed Coal 34
14 Autocorrelation Test, Unwashed Coal Data Sets
Parameter Tested: Ibs SOa/MM 3tu 40
v
-------
TABLES (Continued)
Number
15 Autocorrelation lest, Washed Goal Data Sets
Parameter Tested: Ibs SO2/MM Btu 41
16 Statistics for Variability of Sulfur, Heating
Value, and Ibs S02/MM Btu's-lJhcleaned Coal 43
17 Statistics for Variability of Sulfur, Heating.
Value, and Ibs S02/MM Btu's-Cleaned Coal 44
18 Statistics for Variability of Sulfur, Heating
Value, and Ibs S02AM Btu's-lMcleaned Coal 45
19 Statistics for Variability of Sulfur, Heating
Value, and Ibs S02/MM Btu's-Cleaned Coal 46
20 Computed Chi-Square Values 48
21 Comparison of Variabilities 54
22 Analysis of Autocorrelated Data Sets Parameters:
Ibs SOz/MM Btu 57
VI
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ACKNCWLEDGEMENTS
This study was made possible by the cooperation of the National Coal
Association and several of its member companies in supplying the extensive
data required for statistical analysis. The authors also thank Mr. Carl
Nelson of PEDCo Environmental, Inc., for his help in supplying the original
detailed data used in his prior study of sulfur variability, much of which
has been incorporated into the data base for this study.
Two mandates for this study had to be carefully balanced: the need for
a useful product and the requirement for meticulous statistical treatment.
Fortunately, the authors were guided in this effort by EPA Project Officers
and advisors with the required sensitivity for this balance: Mr. James D.
Kilgroe, Mr. David Kirchgessner, Mr. Robert Lagemann and Dr. Kenneth E. Rowe.
Coir special gratitude is extended to Dr. Constancio F. Miranda, for his
guidance, for his careful and constructive reviews of the drafts leading to
this final document, and for his active participation in the detailed
analytical work.
VII
-------
SECTION 1
INTRODUCTION
_.l OBJECTIVES OF THE STUDY
The Office of Research and Development (ORD), Industrial Environmental
Research Laboratory of the U.S. Environmental Protection Agency (EPA) at
Research Triangle Park is studying coal cleaning technology to determine its
potential for controlling the emissions of sulfur dioxide from coal-fired
boilers. Two mechanisms are straightforward: lowering of the mean sulfur
content in coal by removal of pyritic sulfur, and lowering of the mean
pounds of sulfur (or equivalent S02) per million Btu by enhancing the heating
value. The original purpose of this study was to document the performance of
U.S. coal preparation plants by gathering and analyzing existing data. This
documentation of sulfur reduction and of heating value enhancement varifies
the effectiveness of existing and operating coal cleaning technology as a
sulfur dioxide control for boilers.
The ability of boiler operators to comply with existing or proposed emission
regulations, and the costs associated with such compliance, also depend upon the
variabilities of coal sulfur content and heating value. An emission limitation,
expressed as a maximum heat-specific SOa value (Ihs SOa/MM Btu), has the effect
of requiring combustion of a coal with a mean Ibs SOa/MM Btu value lower than
the emission limit, to prevent exceeding the limit when the coal sulfur excur-
sions about the mean are positive. Two factors determine how much lower the
mean heat-specific SOa value must be than the emission limit: the fractional
time that the regulations permit a boiler to axceed the nominal limit
(confidence level), and the characteristic variability in the coal feed
(standard deviation or relative standard deviation).
-------
Quantification of this second factor, i.e., the characteristic variability
of heat-specific sulfur content in ooal, is a second prime objective of this
study. A previous EPA-sponsored studyt1) served as a beginning in quantifying
this factor. This present study extends the data base to include higher sulfur
coals. The primary objective of this study (which the previous study did not
address) is to quantify the reduction of sulfur variability achieved by
physical coal cleaning. Secondary objectives are to better understand
the fundamental variability of sulfur and heating value in coal, and to
add to the understanding of how lot size affects variability.
1.2 BACKGROUND ON COAL CLEANING EFFECTIVENESS AS A SULFUR DIOXIDE CONTROL
TECHNOLOGY
The available information on the effectiveness of physical coal cleaning in
reducing the Ibs SO2/MM Btu values of coal is generally limited to calculated
performance, for specific coals and for specific plant designs, using
washability data as the basis. An objective of this study is to provide
actual performance data from operating plants to supplement the published
calculated performance values.
The calculated data may be classified into two types. In the first type,
the theoretical potential for reduction of Ibs SOa/lM Btu was calculated using
coal washability data and some arbitrary degree of crushing and operating speci-
fic gravity. The U.S. Bureau of Mines, in RI 8118, published washability data
for 455 coal samples, representing mines which currently provide more than 70
percent of the utility coal. Table 1 lists the raw coal characteristics composited
by region, the calculated theoretical product characteristics (upon crushing to
3/8-inch top size and separating, with no misplaced material, at 1.60 specific
gravity), and the resulting percent reduction in Ibs S02/MM Btu. Under the
conditions stated, the average potential reduction in Ibs S02/1XM Btu ranged (by
region) from 16 to 43 percent.
For the second type of published effectiveness data, a coal cleaning plant
of a desired level of complexity was tailored for each coal considered, and the
performance of that plant was calculated, taking into consideration the ineffi-
ciencies cf separation on a commercial scale. Each cleaning level includes
one or more of the major unit operations. Although the levels may oversimplify
a complex technology, they illustrate and identify the basic coal preparation
principles.
2
-------
TfMK 1. AVEKAC*: CAIX.UIAI12B WI1WIA). l-OH IJiSUl KJltt ZAT10N
BY I1IYSTCAL CUA1, CUSANfNU*
(Cnisluncj to 3/8-l.icli Top Size, Separation at 1.60 S.C.)
Ox.il ivy ion
NlmJA.'r r>l: samples
i
in
•H
H fll
s«
Jfiu,
S ** H
3 Vi
U 4J
ijy
lYcitic S, v.
•ibuil :.;, %
Ash, '4
ni-.ii/ III
Ibs iU)L./l()''nni
lYritJu S, 'i
•total .S, 'i
Ash, %
HI u/ll)
Jl-ii Uouovory, %
^•.iijht liajuvery, V,
inuruiisti in liLu/lb, %
».i:rtiimj in IYr-it-Jc S, %
UcnjriiMj in 'Ibtiil S, %
Uis ;XV.
Vjcroiisu in — '-, 'i
10'htu
Nor diem
Analauhia
227
2.0J
3.01
15.1
12,693
4.74
0.85
1.86
8.0
13,766
2.70
92.5
80.3
8.5
58
38
4.3
Sou then i
Appalcichiii
35
0.37
1.03
11.0
13,314
1.55
0.19
0.91
5.1
.14,197
1.28
96.1
90.1
f>.6
49
J2
17
Al £ll tuitl
10
O.C9
1.33
9.5
13,696
1.94
0.49
1.16
5.8
14,264
1.63
96.4
92.6
4.1
29
13
16
l£ist:ern
Midwest
95
2.29
3.92
14. 2
12,189
6.43
1.03
2.74
7.5
13,138
4.17
94.9
88.0
7.8
55
30
35
Western
Midwest
44
3.58
5.25
16.2
12,072
8.69
1.80
3.59
8.3
13,209
5.43
91.7
83.8
9.4
50
32
38
Western
44
0.23
0.68
8.9
12,437
1.09
0.10
0.56
6.3
12,779
0.88
97.6.
95.0
2.7
57
18
19
•total
U.S.
455
1.89
3.00
14.0
12,573
4.77
0.85
2.00
7.5
13,530
2.D5
93.8
87.2
7.6
55
33
38
U.S. liureciu of Mi lies
-------
Level 1 - Breaker for top size control and for the removal of coarse
refuse.
Level 2 - Ooarse beneficiation - where larger fractions of coal (plus
3/8 inch) are treated. The separated and untreated minus
3/8 inch portion of the coal is combined with the cleaned
coarse coal for shipment.
Level 3 - Fine and coarse size beneficiation - where all the feed is
wetted. Plus 28M is beneficiated; 28M x 0 material is
dewatered and either shipped with clean coal or discarded
as refuse.
level 4 - Very fine beneficiation - where all the feed is wetted and
washed. Thermal drying of 1/4" x 0 fraction generally is
often desired to limit moisture content.
Level 5 - Full beneficiation resulting in multiproducts - where the
raw coal is crushed to much finer sizes, resulting in
multistage cleaning and multiproduct operation. A plant
optimized to remove both pyritic sulfur and ash from
amenable coals would most likely be of this type.
Tables 2A, 2B, and 2C summarize the performance calculations conducted
(8)
by Bechtel Corporation for the Department of Energy and by Versar,. Inc.,
(9 10)
for the Environmental Protection Agency. ' The calculated reductions in
Ibs SO2/MM Btu ranged from 8 to 81 percent. The data in Tables 2A and 2C
clearly show that the effectiveness of coal cleaning as an SO 2 control tech-
nology depends to a large extent upon the cleanability potential of the raw
coal, which varies widely from coal to coal. The data in Table 2B, all for
the same raw coal, clearly show that the effectiveness is highly sensitive
to the complexity of the cleaning plant design. These data demonstrate that no
valid "typical" effectiveness can be quoted for physical coal cleaning technology.
Because the existing published measures of coal cleaning effectiveness are
based upon design calculations for hypothetical plants, a verification was
needed. Acquiring actual data from operating plants to fulfill this need was
one of the original objectives of this study.
-------
TABLE 2A.
CALCULATED DESIGN PERFORMANCE OF CLEANING PLANTS
Cleaning level
Coal
source
Raw coal
character
istics
3 .
Cleaned co
• character
istics
Pyritic S, %
Total S, %
Ash, %
Btu/lb
Ibs S02/106 Btu
Pyritic S, %
Total S, %
Ash, %
Btu/lb
lbs/S02/106 Btu
Btu Recovery, %
Weight Recovery, %
Increase in Btu/lb, %
Decrease in Pyritic S, %
Decrease in Total S, %
Decrease in Ibs SO2/1QS Btu, %
II
West Va.
Cedar Grove
0.11
0.81
22.7
11,810
1.37
0.06
0.75
17.0
12,655
1.19
97.4
90.9
7.2
45
7
13
III
Colorado
Montrose
0.25
0.80
19.4
11,790
1.36
0.19
0.73
10.5
13,120
1.11
94.3
84.7
11.3
24
9
18
IV
Pennsylvania
Lower Kittaning
2.19
2.77
13.0
12,830
4.32
0.22
0.80
4.7
14,250
1.12
76.2
68.6
11.1
90
71
74
V - Multiproduct plant
Pennsylvania
Upper Freeport
2.79
3.40
23.4
11,486
5.92
Clean Pdt
0.22
0.83
3.3
14,608
1.14
61.2
48.1
27.2
92
76
81
Middlings
1.56
2.17
17.5
12,342
3.52
30.1
28.0
7.5
44
36
41
Composite
0.71
1.32
8.5
13,774
1.92
91.3
76.1
19.9
75
61
68
*Source: Bechtel Corporation
(s)
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TABLE 2B.
CALCULATED DESIGN PERFORMANCE OF CLEANING PLANTS
RAW COAL: UPPER FREEPO:?'i' "E" SEAM, BUTLER, PENNSYLVANIA
**
Cleaning
level
Product
Total S, %
Ash, %
Btu/lb
Ibs S02/1Q6 Btu
Btu recovery, %
Weight recovery, %
In
De
De
crease in Btu/lb, %
crease in total S, %
. Ibs SO2 .
crcaoc in 1Q6 Btu, o
II
3.00
20.0
12,260
4.89
97.0
92.8
6.5
13
18
III
1.89
11.5
13,551
2.79
84.0
73.2
17.7
45
53
IV
1.30
7.6
14,000
1.85
87.5
70.0
21.6
62
69
V - Multiproduct plant
Clean Pdt
1.08
5.80
14,426
1.50
43.4
35.3
25.3
69
75
Middlings
1.69
11.31
13,612
2.48
44.0
38.0
18.3
51
59
Composite
1.53
8.66
14,004
2.01
87.4
73.3
21.7
56
66
*Source: Versar Inc.
**Upper Freeport Coal:
Pyritic S, 2.51%
Total S, 3.45%
Ash, 23.90%
Btu/lb 11,510
Ibs S02/106 Btu, 5.99
-------
TABLE 2C. CALCUIATED DESIOJ PERFORMANCE OF CIEANING PLANTS
Jleaning level
Coal
source
1
1
j
Pyritic S, %
•total S, %
Ash, %
Btu/lb
Ibs SO2/106Btu
Pyritic S, %
total S, %
Ash, %
Utu/lb
Ibs S02/106Btu
Btu recovery, %
height recovery, %
Increase in Btu/lb, %
Dec. in Pyritic S, %
Dec. in Total S, %
• Ibs SO2 a
Dec- U1 lbe'Btu' %
IV
Upper
Freeport, PA.
2.51
3.45
23.9
11,510
5.99
0.95
1.57
9.7
13,704
2.30
88.7
74.5
19.1
62
54
62
IV
Lower
Kitt. , PA
1.34
1.86
12.8
13.50G
2.75
0.67
1.22
8.7
14,139
1.72
96.9
92.6
4.7
50
34
37
III
Upper
Freeport, PA
2.51
3.45
23.9
11,510
5.99
1.34
2.21
14.4
12,971
3.41
94.2
83.6
12.7
47
36
43
IV
Bakerstown,
WV
0.92
28.7
10,750
1.71
0.82
19.9
12,072
1.35
90.3
80.5
12.3
11
22
IV
Clintwocd,
VA
0.87
11.2
13,891
1.25
0.83
8.1
14,382
1.15
93.0
89.9
3.5
5
8
III
Upper Cliff,
AL
0.41
0.85
10.9
13,845
1.23
0.34
0.75
9.5
14,094
1.06
98.0
96.3
1.8
17
12
14
IV
Splash
Dam, VA
1.56
25.9
11,275
2.77
1.24
9.7
13,960
1.77
92.1
74.4
23.8
21
36
IV
Eagle,
VA
1.18
10.4
13,622
1.73
U.94
4.7
14,487
1.30
89.3
84.0
6.4
20
25
17
llagy.
VA
2.95
23.1
11,688
5.04
2.31
15.5
13,002
3.55
93.8
84.3
11.2
22
30
III
No. 6
IL
3.13
4.35
29.9
9,782
8.89
1.80
3.30
11.4
12,370
5.34
91.6
72.4
26.5
42
24
40
IV
No. 5
IL
2.01
2.88
16.4
12.120
4.75
1.06
1.99
7.5
13,407
2.97
92.9
84.0
10.6
47
31
37
IV
No. 5
IL
2.01
2.88
16.4
12,120
4.75
0.91
1.85
7.1
13,464
2.75
88.6
79.8
11.1
55
36
42
IV
Bevier,
MO
5.22
27.2
8,011
13.04
4.05
8.0
10,123
7.99
83.1
65.8
26.4
22
39
*Source: Versar, Inc.
(10)
-------
1.3 IMPORTANCE OF COAL SULFUR VARIABILITY
The variability of ooal has a pronounced effect upon the ability and costs for
boiler operators to comply with existing or proposed emission regulations. An
emission limitation, expressed as a maximum value in Ibs SOa/MM Btu,
to be exceeded only for a specified percentage of the time, has the effect of
requiring a coal with a mean Ibs S02/iyM Btu value lower than the emission limit.
The relationship between y, the mean coal value for Ibs S02/MM Btu and E,
the emission limitation value or maximum permissible emission in Ibs SOa/toM Btu,
may be described by the equation:
(3)
E = 3(y + taS) = 3y(l + taRSD)
(1)
where 3 = the fraction of sulfur in the coal which is emitted (less losses to
bottom ash and fly ash). Although 3 has a distribution of its own,
its variability is comparatively small, and 3 is generally assumed
constant at 0.95.
RSD = the relative standard deviation for Ibs S02/MM Btu, defined as the
standard deviation divided by the mean.
S = the absolute standard deviation for Ibs S02/MM Btu.
t = the one-tailed students' "t" value assuring a fractional compliance
time of a. For the purpose of illustrating the importance of
coal sulfur variability in this section, it is assumed that the
data follow a quasinormal or "t" distribution. The validity of
this assumption is discussed in Section 5.5.
Values of t for large numbers (>100) of observations are^2':
a, Fractional compliance time
Sx
0.80
11.85
0.90
1.29
0.95
1.66
0.99
2.36
0.9995
3.37
A prior EPA study^1) of sulfur variability in coal resulted in RSD values
ranging from 5 to 34 percent (excluding core samples which resulted in higher
RSD values).
-------
Table 3, calculated from Equation 1, lists the ratio of y (the required
mean coal value for Ibs S02/MM Btu) to E (the emission limitation value). It
is apparent that this ratio is much less than unity for typical RSD values,
and is also quite sensitive to RSD. Hence, the variability of sulfur in coal
assumes importance in formulating new emission standards and in complying with
existing or new standards. This study addresses the variability of sulfur and
of heating value in coal with the objectives of better understanding the sources
of variability, of better quantification of variability for a given coal, and
ultimately of suggesting means for attenuating this variability.
1.4 EXPECTED ATTENUATION OF VARIABILITY BY GOAL CLEANING PROCESSES
Three reasons exist for expecting washed coals to exhibit a lower sulfur
variability than raw coals. First, is the reduction of the variance in coal
sampling and sample preparation, as a result of coal cleaning. Most cleaning
plants include a size reduction step, ameliorating the influence of large integral
impurity particles upon each sample. The cleaning process removes much of these
integral impurity particles, thereby making the product more uniform. The in-
creased precision of sampling washed coals (as opposed to raw coals) has been
experimentally documented. 5 Keller has proposed a revision to the ASTM coal
sample preparation method in which half as much of the reduced sample quantity was
required for cleaned coals as for raw coals. •
The second reason is that the coal preparation process contains many oppor-
tunities for blending. Coal unloading, loading, and storage operations,
size reduction operations, and some separation operations feature mixing of
the coal, which should reduce short-term variability. A third reason is that
specific gravity separation processes should dampen the feed variations. If the
instantaneous pyritic sulfur and/or ash content is greater than nominal, the in-
stantaneous refuse stream should be larger, thereby resulting in a product stream
of greater uniformity.
These reasons for expecting attenuation of variability, coupled with the im-
portance of sulfur variability, led to the primary objective for this study -
to quantitatively determine, by analyzing data from operating coal cleaning
plants, the attenuation of sulfur variability achieved by physical coal cleaning.
9
-------
TABLE 3. CALCULATED VALUES OF MEAN COAL-TO-EMISSION LIMIT RATIO (p/E)
RSD of ooal
0.05
0.10
0.15
0.20
0.30
0.40
Fractional compliance time
0.90
0.99
0.93
0.88
0.84
0.76
0.69
0.95
0.97
0.90
0.84
0.79
0.70
0.63
0.99
0.94
0.85
0.78
0.72
0.62
0.54
0.9995
0.90
0.79
0.70
0.63
0.52
0.45
-------
SECTION 2
SOURCES OF SULFUR VARIABILITY
2.1 CHARACTERIZATION OF VARIABILITY IN COAL AND IN COAL DATA
One approach to characterizing variability in coal is to relate measured
coal properties to the geologic history and current geologic characteristics of
the deposit. Included in this approach is the documentation of the precise mining
location for each lot of coal sampled and analyzed. Also included in this approach
is the correlation of sulfur and heating value data to petrographic data and to
the mineralogical and chemical composition of the impurities in coal. These sub-
jects are currently under study by the U.S. Geological Survey.
An alternative approach, taken in this study, is to characterize sulfur vari-
ability from existing coal analysis data itself. This approach is empirical,
compared to the more fundamental .approach described above. The ultimate objective,
however, is the same : to be able to predict with some precision the variability
of each coal resource, and further, to find ways of attenuating or accomodating
this variability.
To implement this empirical approach, the observed variance for each coal source
was divided into three basic categories:
1. Long-Term Component. For each coal source, the ooal characteristics
change as mining progresses, and mining and processing methods may
change as well. From a utilization standpoint (althouah the rationale
is based upon geology and technology), the long-term component of
variance is defined in this study as the month-to-month variation.
?. Short-Term Component. This is defined, for practicality, as lot-to-
lot variability. The lot is the smallest unit for which coal character-
istics data are reported and maintained for each source. The lot size
may be a daily quantity, a unit-train quantity, or some other discrete
value. Rationale for day-to-day variance may include local coal varia-
tions within the mine and short-term variations in processing efficien-
11
-------
cies. This component of variance nay depend upon the quantity of coal
in a lot for each source.
3. Sampling/Sample Preparation/Analysis Component. This component of the
variance depends upon whether ASTM methods are employed. It also depends
upon whether or not the coal has been washed.
In summary, the model adopted for examining sulfur variability has the
following generalized components of variability:
Total Long Short Sampling
Term Term & Analysis
This model is applicable to data from a specific coal source. There are addi-
tional components of variance, when considering multiple coal sources, that are
geographical and source-specific in nature. The sulfur level and its variability
are unique according to the region and the seam of the deposit, and to the particu-
lar mine and mining method. Components of variance may be defined as region-to-
region, seam-to-seam, and (mining or processing) source-to-source. Rationale for
the first two and for part of the third is geology; part of the source-to-source
variance may be attributable to mining methods and coal preparation methods employed.
2.2 PERMISSIBLE VALUES FOP. THE SAMPLING CCMPONENT OF VARIANCE
As defined above, the "sampling" component of variance includes sample prepa-
ration (both field and laboratory steps) and laboratory analysis, as well as
sampling itself. The American Society for Testing and Materials (ASTM) Standards
D-492 and D-2234 widely adopted in the commercial sampling of coal, are intended
to provide an accuracy of +_ 10 percent (of the ash content) in 95 out of 100 test
results. It may be implied that the sampling accuracy intended for ash content .
applies as well to sulfur content and to heating value. At a confidence level of
95 percent, approximately equivalent (for the two-tailed "t" distribution) to two
standard deviations, the ASTM-intenued relative standard deviation is 0.05.
Other ASTM standards address laboratory analysis precision. The permissible
variance for ash analysis is 20 percent of the total sampling and analysis variance.
The implied permissible relative standard deviation of ash analysis is therefore
0.05/0.2 = 0.0224. The permissible sampling relative standard deviation (which is
also valid for sulfur content and for heating value) is 0.05/0.8 = 0.0447.
12
-------
For sulfur determinations, the following precision limits are specified by
ASTM:
Coal containing less than 2 percent sulfur, 0.1 percent
Coal containing 2 percent sulfur or more, 0.2 percent.
Translating into relative standard deviation (assuming a 95 percent confidence
level for a two-tailed "t" distribution is implied),
Mean sulfur '
content %
0.5
1.0
1.5
2.0
2.5
3.0
4.0
5.0
6.0
Permissible
analysis
std. dev. %
0.05
0.05
0.05
0.10
0.10
0.10
0.10
0.10
0.10
Permissible
analytical
BSD
0.100
0.050
0.033
0.050
0.040
0.033
0.025
0.020
0.017
Permissible
total
RSD for sulfur*
0.110
0.067
0.056
0.067
0.060
0.056
0.051
0.049
0.048
*The last column is derived (since sampling and analytical RSDs are independent)
fron: Permissible Total RSD = [0.04472 + (Permissible Analytical RSD)2]V2
The ASTM precision limits for the laboratory determination of heating value
is 100 Btu/lh. At an assumed 95 percent confidence level, the corresponding
relative standard deviations are:
Mean heating
value , Btu/lb
9,000
10,000
11,000
12,000
13,000
14,000
Permissible
for RSD
0.0056
0.0050
0.0045
0.0042
0.0038
0.0036
Permissible total
RSD for heating value*
0.045
0.045
0.045
0.045
0.045
0.045
*Including permissible sampling variance.
Assuming the total RSD for sulfur value is independent from the total value
for heating value (see Section 5.3), the permissible RSD for Ihs SOa/MM Btu is:
I (RSD for S)2 + (RSD for Heating Value) 2J
13
-------
The derived values are listed below:
Mean sulfur
content, %
0.5
1.0
1.5
2.0
2.5
3.0
4.0
5.0
6,0
Permissible total RSD
for Ibs. SOa/feM Btu
0.119
0.081
0.072
0.081
0.075
0.072
0.068
0.067
0.066
These values, for the permissible RSDs in Ibs SOa/MM Btu, based upon ASTM
sampling and analysis protocols, are 7 or 8 percent of the mean (for mean sulfur
contents greater than one percent).
2.3 EXPERHXENTAL VALUES FOR THE SAMPLING COMPONENT OF VARIANCE
Keller and Aresco and Omingv experimentally determined for ash the
components of the coal sampling, sample preparation, and analysis variance. In
their tests, field sampling, field sample preparation, laboratory sample prepara-
tion, and laboratory analyses were conducted according to ASTM standards. Their
results, in terms of the components of variance in ash content, are listed in
Table 4. Also listed in Table 4 are the calculated relative standard deviations
for each component of variance. These were pooled according to:
Pooled RSD = I ZN (RSD) 2 "I ly/2
L EN J
where N = number of tests in each data set. Since RSDs have been arithmetically
averaged in prior work,^1) average RSDs were also calculated. The results are:
RSD for Sampling
PSD for Sample Preparation
P
RSD for Lab Analysis
Raw coals
d.f.
146
206
206
(RSD)p
0.0291
0.0149
0.0080
R3D
0.0275
0.0148
0.0071
Washed coals
d.f.
54
156
156
(RSD)p
0.0160
0.0126
0.0114
RSD
I
o.oiso ;
0.0122
i
0.0073
14
-------
TABUS 4. OOMTONI-N'iS OF ASH VARIANCE IN SAMPLING AND ANALYSIS
Ul
Data
source*
K
K
K
K
K
AO
AO
AO
AO
AO
AO
AO
K
K
K
K
K
K
AO
AO
AO
AO
AO
AO
Sourae
ID
A
B
C
K
I.
1
2
3
4
5
6
7
D
F
I
M
N
P
8
9
10
11
12
13
Coal
oondi-
tion
Raw
Raw
Raw
Raw
Raw
Raw
Raw
Raw
Raw
Raw
Raw
Raw
Waslicd
Wasted
Washed
Washed
Washed
Washed
Waslied
Washed
Washed
Washed
Waslied
Wasted
No.
bests
10
20
10
10
10
22
34
17
12
28
29
4
30
42
10
20
10
10
18
6
3
6
16
5
Ash content;, percent
Mean
12
12.5
29
22
16
9.05
9.22
10. 95
5.11
8.21
11.96
15 . 14
7.0
5.5
4.5
4.2
6.5
7.0
8.25
7.02
8.54
5.11
8.34
10.44
V
s
—
—
—
—
—
0.0644
0.0627
0.1472
0.0234
0.0442
0.1498
0.0471
—
—
—
—
—
—
0.0195
0.0062
0.0315
0.0026
0.0223
0.0187
V
P
0.0407
0.03uO
0.2935
0.0329
0.2948
0.0090
0.0153
0.0162
0.0063
0.0112
0.0175
0.0245
0.0036
0.0045
0.0090
0.0030
0.0064
0.0027
0.0100
0.0064
0.0070
0.0003
0.0086
0.0103
VA
0.0961
0.0054
0.0052
0.1471
0.0036
0.0012
0.0015
0.0017
0.00.12
0.001.1
0.0018
0.0028
0.0037
0.0098
0.0050
0.0015
0.0009
0.0037
0.0012
0.0004
0.0006
0.0008
0.0010
0.0009
VT
—
—
—
—
—
0.0746
0.0795
0. 1651
0.0309
0.0565
0. 1691
0.0744
—
—
—
—
—
0.0307
0.0130
0.0391
0.0117
0.0329
0.0299
RSD
s
—
—
—
—
—
0.0280
0.0272
0.0350
0.0299
0.0256
0.0324
0.0143
—
—
—
—
—
—
0.0169
0.0112
0.0208
0.0100
0.0179
0.0131
RSI)p
O.OL68
0.0152
0.0187
O.OOH2
0.0339
0.0105
0.0134
0.0116
0.01.55
0.0129
0.0111
0.0103
0.0086
0. 0122
0.0211
0.0130
0.01.23
0.0074
0.0121
0.0114
0.0098
0.0178
0.0111
0.0097
RSD^
0.0258
0.0059
0.0025
0.0174
0.0038
0.0038
0.0042
0.0030
0.0068
0.0040
0.0035
0.0035
0.0087
0.01.80
0.0157
0.0092
0.0046
0.0087
0.0042
"0.0028
0.0029
0.0055
0.0031!
0.0029
RSP ;
—
—
_...
0.0)02
0.030C
0.0371
O.OJ44
0.0290
0.0344
0.01 till
_..
—
—
—
—
_..
0.0212
0.0162
0.0232
0.0212
0.0217
0.01 Of.
K = Keller ' , AO = Aresoo and Orning
V = Variance
RSD = Relative Standard Deviation
Subscripts = S = Saiipling
P = Scinple Preparation
A = laboratory Analysis
T = Ttotal
-------
(RSD) refers to the pooled PSD, and RSD to the average PSD. Although PSD
is always less than (PSD) , the differences are slight.
The tDtal PSD, calculated from
(RSD^p = [(RSDs)2 + (RSDp)2 + (RSDA)2 ] 1/2
is: (RSD) = 0.0337 for raw coals,
(RSD ) = 0.0233 for washed coals.
These values are smaller than the permissible maximum relative standard deviation
for ash analysis, derived from the ASTM standard, of 0.05.
The combined RSDs for sample preparation and laboratory analysis are:
(RSD_ ) = [0.01492 + 0.00802] 1/2 = 0.0169 for raw coals,
r,A p
(PSD,, _) = [0.01262 + 0.01142] 1/2 = 0.0170 for washed coals.
P,A p
Combined PSD values are virtually equal for raw and washed coals, leading
to the conclusion that the larger total PSD for raw coals (compared to washed
coals) results from coal sampling differences and not from laboratory
differences. This conclusion is rational, since washed coal is expected to
have a smaller particle size and to be more uniform in composition, leading .to
lower sampling-induced variability. The empirical sampling RSD , which
o
should apply to sulfur content and heating value as well as to ash content, are:
(PSD ) = 0.029 for raw coals ,
s p
(RSD ) = 0.016 for washed coals.
s p
Keller also reported the variances for total sulfur in coal, and for sample
preparation and analysis. His data, listed in Table 5, did not include the vari-
ance for sampling.
The pooled values for RSD (laboratory) for sulfur are:
0.019 for raw coals,
0.006 for washed coals.
16
-------
TABLE 5. LABORATORY (SAMPLE PREPARATION AND ANALYSIS) VARIANCE FOR TOTAL SULFUR
SOURCE: KELLER*5)
Coal
ID
A
B
C
K
L
F
M
N
O
P
Coal
condition
Raw
Raw
Raw
Raw
Raw
Washed
Washed
Washed
Washed
Washed
Number of
tests
10
50
10
10
10
30
10
10
10
10
ffean sulfur,
peroent
3.30
2.38
1.20
0.72
1.30
0.60
0.65
1.09
1.70
1.52
Variance
(laboratory)
0.0040
0.0014
0.0003
0.0004
0.0013
0.0000
0.0000
0.0001
0.0004
0.0001
RSD
(laboratory)
0.019
0.016
0.014
0.028
0.028
0.000
0.000
0.009
0.012
0.007
-------
It appears that the sample preparation and analysis component of variance for
raw coals is considerably greater than for washed coals. This observation is
different from that reached for ash analysis, where the RSDs were equivalent at
0.017.
Since the sampling procedures for coal are the same (and in practice
the identical samples are utilized) for the ash determination and for the
sulfur and the heating value determinations, it is reasonable to adopt the
experimental sampling RSDs for ash both to the sulfur and heating value.
The total RSDs for sulfur are:
[(0.029)2 + (0.019)2] 1/2 = 0.035 for raw coals,
[(0.016)2 + (0.006)2] 1/2 = 0.017 for washed coals.
No experimental data were found for the laboratory heating value determina-
tion. Adopting the permissible laboratory RSD of 0.004 and the experimental
(for ash) sampling RSD, the total sampling and analysis RSDs for heating value
are:
[(0.029)2 + (0.004)2] 1/2 = 0.029 for raw coals,
[(0.016)2 + (0.004)2] 1/2 = 0.016 for washed coals.
Finally, the sampling and analysis RSDs for Ibs SO2/MM Btu, based primarily upon
experimental data, would be:
[(0.035)2 + (0.029)2 ] 1/2 = 0.045 for raw coals,
[(0.017)2 + (0.016)2 ] 1/2 = 0.023 for washed coals.
These values represent the best current estimates for the actual sampling
and analysis components of variance, consistent with ASTM standards for sampling
and analysis. They are considerably less than the maximum permissible values.
18
-------
SECTION 3
DESCRIPTION OF THE DATA BASE
3.1 DATA SETS
The data base for this study consists of 53 individual data sets, with a
total of 3,204 data points. Each data set represents an identifiable and unique
coal stream, either raw coal or cleaned coal, from a particular cleaning plant
or loading facility, with the source of the coal (seam and county) and cleaning
level specified. Tables 6 and 7 list the data sets for unwashed coals and for
washed coals (respectively) together with the characteristics of the data sets.
Unwashed coals were defined as either run-of-mine (RDM) coals, where no prepara-
tion at all was conducted, or coals cleaned at Level I (crushing and sizing),
with removal of large pieces of rock and overburden). Washed coals were defined
as coals cleaned at Levels II and above, where specific gravity separation is
conducted on one or more size fractions.
The data sets were obtained in three different ways. Forty-one data
sets resulted from a request by Versar to coal preparation plant owners
through the National Coal Association (NCA). Nine data sets published in
a previous EPA study *1' were abstracted for use in this study. Three data
sets from the Homer City, Pennsylvania, preparation plant were obtained from EPA.
The NCA data request was aimed at obtaining matching pairs of plant feed
(unwashed coal) and product (washed coal) data sets so that direct comparisons
could be used to determine the effectiveness of coal cleaning plants. The NCA
contacted a number of companies which, taken together, operate 111 preparation
plants (over 25 percent of the national total) in different coal regions. Since
most such plants are in the East and the Midwest, these are the primary areas
covered by the study — although data was also requested from one (non-NCA)
company which operates four coal preparation plants in the Alabama region.
Eight separate coal companies responded to the data request; eight coal prepara-
tion plants provided data sets for both feed and product coal; and approximately
19
-------
TABLE 6.
DATA SET IDENTIFICATION - UNWASHED COALS
Data set
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
C-l
08
U-4
U-5
U-ll
U-12
U-13
State
Ky.
Ky.
Ky.
Ky.
Ky.
Ky.
Ky.
Ky.
Ky.
Ky.
Ky.
11.
11.
11.
Oh.
Pa.
Pa.
Va.
WV.
Mt.
Ok.
W.
Oh.
Ky.
Ky.
Pa.
Pa.
Pa.
County
Ohio
Ohio
Ohio
Ohio
Ohio
Muhlenberg
Muhlenberg
Muhlenberg
Muhlenberg
Muhlenberg
Muhlenberg
Randolph
Christian
Randolph
Perry
Indiana
Indiana
-
Hancock
Rosebud
Craig,
Nowata
-
_
-
-
-
-
Seams
9,14
9
9,11
9
9,11,13
11,12
9
9
11
12
9,12
6
6
6
6
Cleaning
level
I (F)
I (F)
ROM
I
I
I (F)
I
I
I
I
I
I
ROM (F)
ROM (F)
I (F)
Upper Free. ROM
Upper Free. ROM
SW
Low Kitt.
Rosebud
Ft. Scott
-
_
-
-
-
-
ROM (F)
ROM (F)
I
I
Number of
data points
6
6
25
25
25
4
25
25
25
25
25
26
6
12
6
44
44
5
5
25
24
ROM 704
ROM
ROM
ROM
275
162
250
ROM j 250
I ; 250
I '• 250
i i
20
-------
TABLE 7.
DATA SET IDENTIFICATION - WASHED COALS
Data set
201
1
202
203
204
205
, 206
! 207
' 208
; 209
210
; 211
212
213
214
215
216
217
218
219
220
221
222
223
C-2
C-3
State
Ky.
Ky.
Ky.
Ky.
Ky.
11.
11.
11.
11.
11.
11.
Oh.
Oh.
In.
In.
In.
In.
In.
Pa.
Mo.
MO.
Va.
wv.
Ky.
Ky.
County
Ohio
Ohio
Ohio
Ohio
Muhlenberg
Randolph
Christian
St. Clair
Gal la tin
Gallatin
Randolph
Perry
Perry
Greene,
Knox
Warrick
Warrick
Greene,
Sullivan
Vermillion
Indiana
Henry
Henry
-
Hancock
Seams
9,14
9,14
9
9
11,12
6
6
6
6
5
6
6
6
5, 6
5, 6
5, 6
3, 4, 5,
6, 7
6
Upper Free.
Beviar
Lit. Tabo
Beviar
SW
Low.Kitt.
Cleaning
level
V
V
V
V
V
V
VT
VI
V
VI
III
V
V
V
VI
V
V
V
VI
VI
VI
V
III
II
V
Number of
data points
6
24
6
25
6
24
6
26
25
25
12
6
24
25
25
25
25
25
46
6
18
5
5
115
115
21
-------
40 others submitted only single values for feed and product measurements. The
remaining plants provided product data without the corresponding feed values.
The matched pairs of feed and product data sets for individual coal prepara-
tion plants are as follows:
Plant ID
1
2
3
4
5
6
7
8
Feed data set ID
101
114
113
102
106
115
119
118
Product data set ID
201
211
207
203
205
212
223
222
3.2 DATA POINTS
Each of the data points within each data set represents a "lot" of coal
from the coal stream. A "lot" may be a day's or a month's contiguous quantity
from the coal stream, or it may be a car load, a unit train load, or a barge load.
The lots (data points) are ordered chronologically, from earliest to latest,
within each data set. Associated with each lot (data point) is the lot size (in
tons), and single reported values for measured total sulfur content (percent, dry
basis) and for calculated equivalent pounds SOz per million Btu (Ibs SO-^/MM Btu) .
Table 8 illustrates the contents of a representative data set. Appendix A
is a listing of all of the data acquired in this study.
3.3 SAMPLING PROCEDURES UTILIZED
Little specific information was provided with each data set regarding
the procedures used (sampling, analyzing, compositing, or mathematical averaging)
to generate the single reported values of percent sulfur and heating value
for each data point. The coal companies were asked to describe their sampling
procedure, and the replies were that specific procedures differ from plant to
plant relative to how the sample is taken, sampling frequency, the method of
22
-------
TABLE 8.
CONTENTS OF DATA SET 208
6" x 100M Cleaned Coal (Level VI), Illinois, St. Clair County
Data point
(lot) no.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
Lot size
tons
2,806
2,626
1,023
4,201
6,870
8,361
5,463
2,790
7,983
5,652
6,837
4,060
2,621
5,598
7,015
1,388
7,961
2,847
5,231
1,353
9,864
2,844
2,798
5,675
1,426
1,395
Total S,
%
4.29
4.20
4.15
4.13
3.96
4.04
4.03
4.31
4.08
4.04
4.12
4.10
4.00
4.08
3.87
3.99
4.15
4.09
4.24
4.20
3.83
3.98
4.25
4.28
3.55
3.44
Heating value ,
BtuAb
12,215
12,171
12,115
12,300
12,162
12,085
12,099
11,934
12,134
11,805
12,284
12,001
12,105
12,192
12,109
12,232
12,279
12,271
12,421
11,991
12,016
11,896
11,671
12,074
11,831
12,622
Ibs S02
MM Btu
7.02
6.90
6.84
6.71
6.51
6.68
6.66
7.22
6.72
6.84
6.70
6.83 .. .
6.60
6.69
6.39
6.52
6.75
6.66
6.82
7.00
6.37
6.69
7.28
7.08
6.00
5.45
23
-------
producing a composite sample, and sampling locations for feed and product
coals .
For feed coal, infrequent, manual sampling is the norm. The terms
"occasionally," "weekly," "only when we have problems," and "periodically"
were used to describe feed coal sample frequency. In a majority of the
cases the feed coal belt is stopped and an American Society for Testing
and Materials (ASTM) belt sample is taken. The sample provides a depend-
able representation of the input coal at that time; however, it should
not be considered to reliably represent actual coal properties in the long- and
medium-term. This was an overriding factor that led some of the coal
companies to send monthly and yearly average values, rather than the
daily, weekly, or lot shipment information requested. The values provided
to Versar were generally weighted averages of feed coal belt sample analyses.
In contrast the product coal is extensively sampled and analyzed. The
coal companies typically take a one or two hour composite sample of the
product, if the plant has an automatic sampler, or manually sample
unit train carloads or barges according to ASTM sampling procedures. The
automatically sampled composites consist of individual samples taken at
5-15 minute intervals. The manual samples are usually taken off a conveyor
discharge as the railroad car or barge is loaded.
The frequency of product sampling is determined in part by the origin
of the coal feed to the preparation plant. For a mine mouth coal cleaning
plant, only one composite sample per day may be analyzed; at the other extreme,
where specifications are tight and contract coal is blended and cleaned,
the composite samples may be taken and analyzed every 30 minutes. Where
possible, Versar has specified data which were received from plants with
automatic product samplers.
In Table 6, most of the data sets represent product coal (despite the
lack or low level of cleaning) . Those data sets in Table 6, which
represent feed coal to a preparation plant and are not subjected to the
more extensive product coal sampling requirements, are signified by an
(F) in the cleaning level column.
24
-------
SECTION 4
ANALYSIS OF PAIRED GOAL FEED AND PRODUCT DATA SETS FROM INDIVIDUAL PLANTS
Table 9 lists the statistics calculated for the eight data sets from
the individual coal preparation plants which provided multiple data
samples for both feed and product coal. For each plant (and separately
for both feed and product samples) the mean (Y), the standard deviation
(Sy) , and the relative standard deviation (BSD = Sy/Y) were calculated for:
YI = Total sulfur content (percent)
Y2 = Heating value (Btu/lb)
Y3 = Heat-specific S02 content (Ibs S02/MM Btu)
4.1 EFFECT OF GOAL CLEANING UPON SULFUR CONTENT, HEATING VALUE, AND HEAT-
SPECIFIC S02 CONTENT
Table 10 lists, for each plant, the changes (between the feed coal
and the product coal) in the mean values of YI, Y2/ and Y3. The percentage
changes are also listed. It is observed that (except for Plant No. 8),
•the coal cleaning process resulted in reductions in sulfur content (Yi)
of 14 to 45 percent, in increases in heating value (Y2) of 6 to 23 percent,
and in reductions in heat-specific S02 content (Y3) of 24 to 50 percent.
Goal cleaning plant No. 8 operated upon a very high ash feed, and the heating
value was increased by 45 percent, but in the process, the sulfur content
was also increased.
To test whether the observed changes in the mean values are statisti-
cally significant, the "t" statistics were calculated for each plant:
t = ^product - *feed"/S>
where s is the pooled standard deviation for both feed and product coal for
that plant.
25
-------
TABU-; 9. STATISTTCS FOR PRUPAIWITDN 1'IANT FKKI1 AND PUTTXICI1
Cleaiiincj plant II)
Cleaning level
State
County
Seams
coal statistics
I
in
.y
L statist
8
0.
Data set no.
No. points
Y,=
brocit
Tot.S.
Y2=
ntu/
lb
Yi=
IhsSOz
MM 13 tu
Y
SY
SY/Y
Y
SY
SY/7
Y
SY
SYA"
Data set no.
No. points
Y,=
V-roanl
•Itot.S.
Qtu/
lb
Y3=
IbsSOj
M»intu
Y
SY
SYA~
Y
SY
SYA
Y
SY
SYA"
1
V
KY
Ohio
9 f. 14
101
6
4.16
0.249
0.060
11,320
581
0.051
7.35
0.427
0.058
201
6
3.19
0.046
0.015
13,000
55
0.0043
4.90
0.123
0.025
2
III
II,
Randolph
6
114
12
4.75
0.461
0.097
10,762
248
0.023
8.82
0.938
0. 106
211
12
4.10
0.316
0.077
12,177
1.36
0.0112
6.73
0.447
0.067
3
vr
1L
Christian
6
113
6
5.12
0.199
0.039
10,650
242
0.023
9.60
0.301
0.031
207
6
4.39
0.065
0.015
12,300
37
0.0030
7.13
0.097
0.014
4
V
KY
Ohio
9
102
6
4.29
0.477
0.111
12,230
371
0.030
7.01
0.786
0.112
203
6
3.37
0.038
0.011
12,970
48
0.0037
5.18
0.066
0.013
5
V
KY
Muhlenberg
11 & 12
106
4
4.26
0.550
0.129
10.270
500
0.049
8.33
1.405
0.169
205
6
3.22
0.148
0.046
12 ,650
119
0.0094
5.09
0.280
0.055
6
V
Oil
Perry
6
115
6
3.94
0.339
0.086
11,070
331
0.030
7.13
0.730
0.102
212
6
3.01
0.077
0.026
1.2,460
22
0.0018
4.83
0.124
0.026
7
11 1
wv
Hancock
Iowr;r Ki tt
ll'J
5
1.94
0.5118
0.303
12,950
624
0.048
3.00
0.864
0.2H8
223
5
1.07
0.166
0. 1 55
14,370
0.0127
1.49
0.240
0.161
fl
V
VA
-
sw
na
r»
0.93
0.233
0.250
9.980
636
0.064
1.85
0.389
0.210
222
5
1..J7
0. 2311
0.197
14,470
145
O.OIOL
1.61
0. 307
0. I'JI
en
-------
TABLE 10. CHANGES IN MEAN VALUES FROM COAL CLEANING:
DIRECT COMPARISON OF FEED AND PRODUCT FOR
INDIVIDUAL PLANTS
Plant
number
1
2
3
4
5
6
7
8
Change in Y
Yi
-0.97
-0.65
-0.73
-0.92
-1.04
-0.93
-0.87
+0.24
Y2
+1680
+1415
+1650
+ 740
+2380
+1390
+1420
+4490
Y3
-2.45
-2.09
-2.47
-1.83
-3.24
-2.30
-1.51
-0.24
% change in Y
Yi
-23
-14
-14
-21
-24
-24
-45
+26
Y2
+15
+12
+15
+ 6
+23
+13
+11
+45
Y3
-33
-24
-26
-26
-39
-32
-50
-13
"t" statistics
Yi
10.7
9.1
8.6
4.8
3.5
7.4
3.8
2.7
Y2
7.5
9.3
18.5
4.8
9.4
10.5
6.5
16.7
Y3
14.1
11.7
19.9
5.7
4.4
5.0
4.5
1.5
d.f.
5
11
5
5
3
5
4
4
t.95
2.02
1.80
2.02
2.02
2.35
2.02
2.13
-2.13
27
-------
These values of t are listed in Table 10. It is apparent from Table 9
that for each plant, the standard deviations for feed coal are not equal
to the standard deviations for product coal. The values for s in the
above equation were therefore determined by the method of Crow, Davis,
and Maxfield,(2)
s =
Where n]_ n]_
Q = ni l Ui2 - / z Ui
ui = Yli - Y2iJs (i = 1,2 ni)
1«2 :
Y]J_ and Y2j_ are paired individual observations such that n^<_ n2.
It may be observed that for plant Nos. 1 through 7, the reductions
in sulfur content, the increases in heating value, and the reductions
in heat-specified S02 content are all significant at the 95 percent
confidence level. For plant No. 8, only the decrease in Ibs SOz/MM Btu
was not significant at this confidence level.
The table on the following page summarizes the ranges of effectiveness
in physical coal cleaning, comparing the calculated average potential by
coal producing region, the calculated design performance of hypothetical plants,
and the measured performance of operating plants. Effectiveness is measured by
the decrease in total sulfur content, the increase in heating value, and the
decrease in Ibs SO2/m Btu.
28
-------
Calculated Average
Potential (Table 1)
Calculated Performance
of Hypothetical Plants
(Tables 2A, 2B, 2C)
Measured Performance of
Operating Plants (Table
10, plants 1-7)
Decrease in
total sulfur
percent
12-38
5-76
14-45
Increase in
heating value
percent
4-9
5-27
6-23
Decrease in Ibs
S02/tm Btu,
percent
16-43
8-81
24-50
These ranges of effectiveness are wide, reflecting the sensitivity of
coal cleaning efficiency to the washability characteristics of specific
coals and to the complexity and sophistication of the plant design. The
ranges of measured performance, however, fall within the ranges of calculated
performance. The effectiveness as measured in operating coal cleaning
plants does in fact confirm the effectiveness calculated for many hypo-
thetical plants, although the very highest removal efficiencies (greater
than 50 percent decrease in Ibs SOa/MM Btu) were not empirically validated
by the available data.
4.2 EFFECT OF COAL CLEANING UPON SULFUR VARIABILITY
In each of the eight plants, both the absolute standard deviation and
the relative standard deviation were reduced (for all three coal character-
istics) by the coal preparation process. The percent reductions are
summarized in Table 11. The average reductions in relative standard
deviation attributable to cleaning are 57 percent (for Yi, percent sulfur) ,
81 percent (for Y2, Btu/lb), and 54 percent (for Y3, Ibs S02/MM Btu) .
Although data from only eight plants were available for this direct
analysis of individual cleaning plant variability reduction, the results
appear to be relatively consistent from plant to plant. Both percent
sulfur and Ibs S02/MM Btu variabilities (as measured by relative standard
deviation) were reduced by an average of 55 percent, while heating value
variability was reduced by an average of 80 percent.
29
-------
TABLE 11. SEDUCTIONS IN VARIABILITY FROM GOAL CLEANING: DIRECT
COMPARISON OF FEED AND PRODUCT FOR INDIVIDUAL PLANTS
Plant
number
1
2
3
4
5
6
7
8
Averages
Percent reductions in SY
Y!
72
31
45
92
73
77
72
3
Y2
91
45
85
87
76
93
71
77
Y3
71
52
68
92
80
83
72
21
Percent reductions in SY/Y
Y!
75
21
62
90
64
70
49
21
57
Y2
92
51
87
88
81
94
74
84
81
Y3
57
37
55
88
67
75
44
9
54
30
-------
SECTION 5
ANALYSIS OF UNPAIRED DATA SETS
5.1 APPROACH AND LIMITATIONS
The analysis of matched pairs of feed and product data for eight
coal cleaning plants, presented in Section 4, was a straightforward
comparison of the means and variabilities before and after the coal
cleaning process. This analysis followed the approach that was intended
at the time of the data request.
As explained in Section 3, however, the preponderance of the
responses did not provide matched pairs of feed and product data. Twenty
coal data sets in Table 6, out of a total of 28, were for raw coals or
for coals cleaned at Level I, with no matching data sets for corresponding
washed product coals. Similarly, 17 coal data sets in Table 7, out of a
total of 25, were for washed product coals, with no matching data sets
for the corresponding feed coals. A second statistical analysis, distinct
from the direct comparison of Section 4, was conducted to exploit the
entire available data base. This second analysis was an indirect compari-
son between feed and product variabilities for the data sets of all
washed coals relative to the data sets of all unwashed coals.
This approach is not nearly as satisfying as the direct approach
of analyzing matched pairs of data sets, but it does allow consideration of
more of the available data. A major difficulty in the indirect approach
is that neither the group of unwashed coal data sets nor the group of
washed coal data sets forms a logically consistent or homogeneous popula-
tion susceptible to rigorous statistical analysis. Indeed, much of the
reported data is mixed with respect to mining method, cleaning method,
sampling frequency and procedure, methods of compositing or averaging,
31
-------
(definition of a "lot" of coal and the nominal lot size, and the analytical
laboratory precision. Each of the two groups of data sets (unwashed and
washed coals) is comprised of coals from different regions, seams, and
mines, with inherent geological and engineering differences. Furthermore,
the data sets are not necessarily representative of their respective
regions or seams.
Because of these inherent comparability problems, the results of
this second statistical analysis are not as definitive as those of the
first analysis. Ihe comparison of mixed data sets can lead to
only a rough picture of the effects of coal cleaning on sulfur
variability.
5.2 STATISTICS FOR THE DATA SETS
When the data sets were assembled, those with large lot sizes
(>105 tons) were deleted because they were unlikely to represent single
analyses of single coal sample composites.
For each data set, the mean, the standard deviation, and the coefficient
of variation (relative standard deviation) were calculated for:
YI = total sulfur content (%)
Y2 = heating value (Btu/lb)
Y3 = heat-specific S02 content (Ibs S02/MM Btu)
These statistics are listed in Table 12 (for unwashed coals) and in Table
13 (for washed coals).
5.3 VARIABILITY OF HEAT-SPECIFIC SULFUR CONTENT CALCULATED FROM VARIABILITIES
OF SULFUR AND OF HEATING VALUE
In the previous EPA Study , a contingency table analysis showed that
the percent total sulfur data was independent from the heating value data.
There are potential mechanisms for explaining either the existence or
non-existence of a correlation between the two measurements. Since total
sulfur is measured in the laboratory by different tests from heating value,
measurement errors should be independent. Fundamentally, the sample-to-
sample variation of heating value should be similar to that of ash content,
32
-------
TABLE 12. STATISTICS FOR VARIABILITY OF SULFUR, HEATING VALUE, AND
LBS SO2 PER MILLION BTU'S UNWASHED OOAI
U)
U)
Batch ID.
103
104
105
107
108
109
110
111
112
116
117
120
121
01
08
U-4
U-5
U-ll
U-12
U-13
N=
No. of
lots
25
25
25
25
25
25
25
25
26
44
44
25
24
704
275
164
250
250
250
250
X = Mean
lot size
tons
2,800
10,900
11,200
5,300
6,800
7,100
1,100
6,700
3,800
7,600
3,400
10,300
17,300
12,000
10,000
12,000
13,000
Y, = sulfur, (%)
5,
4.44
4.11
4.85
5.04
4.16
5.21
4.80
4.66
4.22
2.00
3.09
1.49
3.78
2.79
2.60
1.04
0.92
3.13
2.34
2.31
SY,
0.45
0.16
0.58
0.47
0.23
0.47
0.49
0.35
0.24
0.28
0.24
0.44
0.19
0.23
0.13
0.16
0.15
0.44
0.26
0.22
SY./Y,
0.10
0.039
0.12
0.093
0.055
0.090
0.101
0.075
0.057
0.14
0.078
0.30
0.050
0.082
0.050
0.15
0.16
0.14
0.11
0.095
Y? =Btu/lb
*2
11,840
12,030
12,000
12,310
11,900
11,520
10,350
11,610
11,510
11,440
11,090
11,400
12,550
13,052
12,481
12,000
11,856
11,522
12,046
12,135
SY2
333
172
340
255
169
461
371
216
418
322
263
250
226
231
703
310
299
378
257
273
SYz/Y-2
0.0281
0.0143
0.0283
0.0207
0.0142
0.0400
0.0358
0.0186
0.0363
0.0281
0.0237
0.0219
0.0180
0.0177
0.0563
0.026
0.025
0.0328
0.0213
0.0225
Y = i§S S°j
*3
7.51
6.82
8.11
8.20
6.99
9.04
9.28
8.03
7.35
3.50
5.59
2.63
6.00
4.27
4.17
1.73
1.55
5.44
3.88
3.81
SY,
0.81
0.30
1.22
0.88
0.44
0.89
1.01
0.67
0.62
0.55
0.48
0.79
0.29
0.36
0.27
0.28
0.25
0.85
0.46
0.35
SY,/7,
0.11
0.044
0.15
0.11
0.063
0.098
0.11
0.083
0.084
0.16
0.086
0.30
0.048
0.084
0.065
0.16
0.16
0.16
0.12
0.092
-------
TABLE 13. STATISTICS TOR VARIABILITY OF SULFUR, HEATING VALUE, AND LBS SO2 PER MILLION BTU'S WASHED COAL
00
Batch ID.
202
203
204
206
208 '
209
210
213
214
215
216
217
218
219
?.20
221
222
223
C-2
C-3
N=
No. Of
lots
24
6
25
24
26
25
25
24
25
25
25
25
25
46
6
18
5
5
115
115
X= Mean
lot size
tons
6,500
100,000
18,300
3,900
4,500
6,300
4,200
10,300
16,900
2,100
5,400
4,700
51,500
7,600
4,200
5,400
2,700
600
5,600
2,500
Yi= Sulfur (%)
Y"I
3.18
3.37
3.36
3.85
4.05
2.77
3.34
2.97
2.58
3.47
3.75
2.92
2.59
1.66
4.14
4.46
1.17
1.07
0.66
0.78
SY,
0.15
0.04
0.12
0.20
0.21
0.20
0.13
0.15
0.24
0.16
0.21
0.28
0.13
0.18
0.55
0.44
0.23
0.17
0.03
0.08
SYi/Yi
0.047
0.012
0.036
0.052
0.052
0.072
0.039
0.050
0.093
0.046
0.056
0.10
0.050
0.11
0.13
0.10
0.20
0.16
0.045
0.103
Y2= Btu/lb
YJ
13,000
12,970
12,990
12,060
12,120
12,760
12,990
12,440
12,670
12,740
12,620
12,510
12,250
12 , 350
12,290
12,780
14,470
14,370
13,240
12,179
S*2
76
48
80
210
200
172
107
68
93
144
121
205
119
428
265
194
145
182
162
373
SY2/Y2
0.0058
0.0037
0.0062
0.0174
0.0165
0.0135
0.0082
0.0055
0.0073
0.0113
0.0096
0.0164
0.0097
0.0346
0.0216
0.0152
0.0100
0.0127
0.0122
0.0306
Y 3 =
Y3
4.88
5.18
5.18
6.38
6.69
4.33
5.14
4.78
4.07
5.44
5.94
4.66
4.21
2.69
6.72
6.97
1.61
1.49
0.99
1.28
Ibs SO2
MM Btu
SY3
0.25
0.07
0.20
0.38
0.37
0.32
0.22
0.25
0.38
0.26
0.34
0.46
0.22
0.33
0.95
0.70
0.31
0.24
0.05
0.12
SY3Aa
0.051
0.014
0.039
0.060
0.055
0.074
0.043
0.052
0.093
0.048
0.057
0.099
0.052
0.12
0.14
0.10
0.19
0.16
0.051
0.094
-------
since Btu per pound for a given coal is almost a monotonic decreasing
function of ash content. Conversely, the percent total sulfur is, to a
considerable extent, sensitive to the organic sulfur content, which is not
at all linked to ash-forming inorganic impurity concentrations. However,
two factors may cause total sulfur variability measurements to be corre-
lated to heating value variability measurements: first, whatever contribu-
tion the inadequacies of coal sampling make to the observed variabilities
should be the same for total sulfur as for heating value; second, the
reduction of variability by coal preparation processes (either by blending
operations or by attenuation in specific-gravity separation processes)
should be effective for both percent sulfur and for heating value.
Accepting the conclusion of independence established in the previous EPA
study means that Yi varies about its mean in a random fashion relative
to the variations of Y2 about its mean. In this case, the relative
standard deviation of Y3 may be predicted by:
The statistics in Tables 12 and 13 may be used to verify the above
equation. Figure 1 is a plot of the actual values of the relative standard
deviation of Y3 vs. the value as calculated from equation (2). It can be
seen that the points scatter above, but generally parallel to, the 45-degree
line. This would confirm that, in fact, the variation in total sulfur
content (in both cleaned and uncleaned coals) is essentially independent
of the variation in heating value; and the utility of such a conclusion
is that the relative standard deviation of heat-specific S02 content can
be estimated via equation (2) using the relative standard deviations of
percent sulfur and heating value.
5.4 AUTOCORRELATION OF DATA POINTS
Elementary statistical tests and confidence intervals are based on
the assumptions that the individual data points are samples of a single
35
-------
0.3
0.0
0.3
Predicted RSD (¥3) by equation (1)
Figure 1. Relative standard deviation
of Ibs S02/MM Btu:
actual vs. predicted.
36
-------
population and that they are independent of each other - that they are
randomly distributed about a mean.
As Thomas pointed out, however, there is good reason why coal
data points are neither samples of a single population nor independent.
Even within a given mine, geological factors are responsible for the
inhomogeneity of the deposit. The deposit likely consists of multiple
populations, separated by distance along the seam (or by time of extrac-
tion) . The coals mined on successive days are potentially highly
correlated because they are geologically related.
The science of geostatistics is being applied to coal data to
measure and account for autocorrelation. The total variance in a set of
data points is separated into two components: the "nugget" component
Co associated with samples taken close together and the long-range compon-
ents C.. Co is conceptually associated with samples taken close together
in. the mine, and thus represents the imprecision of replicate samples
due to local discontinuities or inhomogeneities in the coal and to
sampling and analytical uncertainties. C is conceptually associated with
samples taken far apart, so that it represents geologic differences in
the deposit . \7here may be several distinctly different mineralized zones
within a deposit with different values of C.. The values of Co and C. are
determined empirically from a data set (in which the data points are spatially
or chronologically ordered*) by generating a variogram: a plot of y(k) vs k, where:
n n-k 2
K,] , k = l,2,...,n/3
For small values of k, as k approaches zero, y(k) approaches Co, the
"nugget" variance. At large values of k, y(k) typically becomes constant
with k and is equivalent to the combined long-range variance Co + C = S2,
where S2 is the classical variance computed by:
-in ,
n
*0ne-dimensional spatial and time-correlated variances are analogous.
37
-------
For the special case of k = 1, where y (k) should approach Go,
An alternative method for detecting a trend in data (an autocorrelation)
is given by Crow
by:
/ O \
The mean square successive difference 62 is calculated
-r-
n-1
n~1
£
._.
[x. ,,-x.
i+l i
An estimate of the component of variance that reduces the trend effect
is 6^2, which is the same as yd) -an estimate of the "nugget" variance-
in the geostatistical approach. Crow's test for autocorrelation consists
of computing 62/S2 (= 2 y(l)/S2). If the data are not serially correlated,
a value of 62/S2 near 2 is expected. Values of 62/S2 less than 2 occur
with autocorrelation, and values greater than 2 occur with serial oscilla-
tion greater than random variation.(2)
The computed value of 62/S2 is compared with the appropriate critical
value from a table given by Crow and abstracted below for illustrative
purposes:
n
4
10
20
40
60
Autocorrelation
P=0.95
0.7805
1.0623
1.2996
1.4921
1.5814
P=0.99
0.6256
0.7518
1.0406
1.2934
1.4144
P=0.999
0.5898
0.4816
0. 7852
1.0850
1.2349
Rapid oscillation
P=0.95
3.2195
2.9378
2.7004
2.5079
2. 4186
P=0.99
3.3744
3.2482
2.9593
2.7066
2.5856
P=0.999
3.4102
3.5184
3.2148
2.9151
2.7651
38
-------
The Ibs S02/MM Btu. values for the data sets listed in Tables 6 and
7 were tested. Tables 14 and 15 list (respectively), for unwashed coal
data sets and for washed coal data sets, values of y(l) = 52/2, of S2 ,
and of the ratio 62/S2 . The appropriate critical values (at the 95
percent confidence level) are also listed, and those data sets meeting
the test for autocorrelation or for rapid oscillation are noted by
an asterisk. A double asterisk signifies that the test was positive at
the 99 percent confidence level, and a triple asterisk refers to a positive
test result at 99.9 percent confidence.
Only one data set (No. 103) out of 48 in Tables 14 and 15 had a
positive rapid-oscillation test at the 95 percent confidence level, and
the test was not positive at the 99 percent level. This result is
discounted ; one of 20 data sets with true randan variation mav be
expected to erroneously give positive test results.
The autocorrelation test, however, gave positive results in 6 of
23 unwashed coal data sets and in 10 of 25 washed coal data sets, at
the 95 percent confidence level. Of these 16 data sets giving positive
results, 9 were positive at the 99 percent level, and 4 were positive at
the 99.9 percent confidence level. There is little doubt that much
of these coal data are serially correlated, verifying the expectations
based upon geology and engineering rationale.
Several reasons may be proposed to explain why autocorrelation was
not evident in all the data sets:
• The measurement (sampling and analysis) inprecision in some data
sets may be so large as to overshadow serial correlations.
• The local coal inhomogeneities and discontinuities in some data
sets may be of such magnitude as to overshadow serial
correlations -
• There may be significant blending of coal in some data sets which
overshadows serial correlation. This blending might be the
result of simultaneous mining from multiple mine faces (or
39
-------
TABI£ 14 .
AUTOCORRELATION TEST, UNWASHED COAL DATA SETS
PARAMETER TESTED: LBS SOj/MM BTU
Data
set
101
102
103
104
105
106
107
108
109
110
in
112
113
114
115
116
117
118
119
120
121
C-l
C-8
n
6
6
25
25
25
4
25
25
25
25
25
26
6
12
6
44
44
5
5
25
24
704
275
Yd) = <52/2
0.265
0.789
0.907
0.059
1.324
2.235
0.893
0.248
0.991
1.037
0.544
0.253
0.138
0.255
0.486
0.261
0.223
0.146
0.159
0.492
0.065
0.093
0.034
S2
0.182
0.618
0.656
0.090
1.488
1.974
0.774
0.194
0.792
1.020
0.449
0.384
0.091
0.880
0.533
0.303
0.230
0.151
0.740
0.624
0.084
0.130
0.073
52/S2
2.91
2.55
2.77
1.31
1.78
2.26
2.31
2.56
2.50
2.03
2.42
1.32
3.03
0.58
1.82
1.72
1.94
1.93
0.43
1.58
1.55
1.43
0.92
(62/S2
Autocorr.
0.89
0.89
1.37
1.37
1.37
0.78
1.37
1.37
1.37
1.37
1.37
1.38
0.89
1.13
0.89
1.52
1.52
0.82
0.82
1.37
1.36
1.87
1.80
0.95
Oscill.
3.11
3.11
2.63
2.63
2.63
3.22
2.63
2.63
2.63
2.63
2.63
2.62
3.11
2.87
3.11
2.48
2.43
3.18
3.18
2.63
2.64
2.13
2.20
Auto-
oorrel.
*
*
**
**
***
***
Rapid
oscill.
*
40
-------
TABLE 15.
•AUTOCORRELATION TEST, WASHED COAL DATA SETS
PARAMETER TESTED: IBS SO2/tfll BTU
Data
set
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
C-2
C-3
n
6
24
6
25
6
24
6
26
25
25
12
6
24
25
25
25
25
25
46
6
18
5
5
115
115
Yd) = 62/2
0.0024
0.0708
0.0033
0.0395
0.0219
0.1648
0.0078
0.0672
0.0633
0.0292
0.0637
0.0192
0.0574
0.0934
0.0773
0.1101
0.1922
0.0379
0.0773
0.7194
0.4571
0.0514
0.0521
0.0017
0.0109
S2
0.0151
0.0625
0.0044
0.0400
0.0784
0.1444
0.0094
0.1369
0.1024
0.0485
0.1998
0.0154
0.0625
0.1444
0.0676
0.1156
0.2116
0.0484
0.1089
0.9025
0.4900
0.0942
0.0576
0.0078
0.0136
62/S2
0.32
2.27
1.50
1.98
0.56
2.28
1.66
0.98
1.24
1.20
0.64
2.49
1.84
1.29
2.29
1.90
1.82
1.57
1.42
1.59
1.87
1.09
1.81
0.44
1.60
(<52/S2) 0.95
Autocorr.
0.89
1.36
0.89
1.37
0.89
1.36
0.89
1.38
1.37
1.37
1.13
0.89
1.36
1.37
1.37
1.37
1.37
1.37
1.53
0.89
1.27
0.82
0.82
1.69
1.69
Oscill.
3.11
2.64
3.11
2.63
3.11
2.64
3.11
2.62
2.63
2.63
2.87
3.11
2.64
2.63
2.63
2.63
2.63
2.63
2.47
3.11
2.73
3.22
3.22
2.31
2.31
Auto-
carrel.
***
**
**
*
it
**
*
*
***
*
Rapid
oscill.
41
-------
longwall mining with the sane effect) , feed ooal to a preparation
plant being composed of shipments from multiple mines, or
blending in the feed coal or product coal storage, handling, or
shipping operations .
• The coal seam may not exhibit large inhomogeneities at distances
equivalent to a "lot" quantity for some data sets.
• An equivalent effect to the previous hypothesis vould be achieved
if, for some data sets, the "lot" quantity is very large compared
to the zones of influence in the coal seam.
5.5 DISTRIBUTION OF THE DATA POINTS
Many statistical tests and confidence intervals are based upon the
assumption that the data populations have normal distributions. The data
sets in Tables 12 and 13 vere examined for normality. In addition, twD
variance-stabilizing transformations ware applied in an attempt to obtain
some approximation of normality. For each data set, the individual data
points of total sulfur content (Yi) , heating value (Y2) , and Ibs SCz/MM Btu
(Y3) vere transformed into natural logarithms:
Zi = In
Z2 = In (Y2)
Z3 = In (Y3)
The resulting statistics for the transformed data sets are listed in
Table 16 (for uncleaned coals) and in Table 17 (for cleaned coals) .
Similarly, the original data points vrere transformed into radical
form:
W2 =
W3 = A7
Table 18 (for uncleaned coals) and Table 19 (for cleaned coals) list the
resulting statistics.
42
-------
TABIE 16. STATISTICS FOR VARIABILITY OF SULFUR, HEATING VALUE, AND LBS SOZ PER MILLION BTU'S UNCLEANED COAL
(Logarithmic Transformation)
Batch ID.
103
104
105
107
108
109
110
111
112
116
117
120
121
C-l
C-8
U-4
U-5
U-ll
U-12
U-13
N=
No. of
lots
25
25
25
25
25
25
25
25
26
44
44
25
24
704
275
164
250
250
250
250
X- Mean
lot size,
tons
2,800
10,900
11,200
5,300
6,800
7,100
1,100
6,700
3,800
7,600
3,400
10,300
17,300
12,000
10,000
12,000
13,000
-
-
-
Z,=ln(SiUfur(%))
Zi
1.49
1.41
1.57
1.61
1.42
1.65
1.56
1.54
1.44
0.68
1.13
0.36
1.33
1.02
0.96
0.02
0.09
1.13
0.85
0.83
SZi
0.10
0.038
0.11
0.090
0.056
0.089
0.101
0.075
0.056
0.17
0.078
0.29
0.050
0.08
0.05
0.15
0.13
0.15
0.10
0.09
SZ./Z,
0.067
0.027
0.070
0.056
0.039
0.054
0.065
0.049
0.039
0.25
0.069
0.80
0.038
0.078
0.052
7.50
-1.44
0.13
0.12
0.11
Z2=Li (Btu/U>
Z2
9.38
9.39
9.39
9.42
9.38
9.35
9.24
9.36
9.35
9.34
9.31
9.34
9.44
9.477
9.430
9.392
9.380
9.352
9.396
9.404
SZi
0.028
0.014
0.029
0.021
0.014
0.041
0.036
0.019
0.036
0.028
0.024
0.022
0.018
0.018
0.058
0.026
0.025
0.032
0.021
0.023
SZ2/Zj
0.0030
0.0015
0.0031
0.0022
0.0015
0.0044
0.0039
0.0020
0.0038
0.0030
0.0026
0.0024
0.0019
0.0019
0.0062
0.0028
0.0027
0.0034
0.0022
0.0024
Z3= Jnflbs SO2\
Z3
2.01
1.92
2.08
2.10
1.94
2.20
2.22
2.08
1.99
1.24
1.72
0.92
1.79
1.45
1.43
0.53
0.43
1.68
1.35
1.33
VMM Btu/
SZ3
0.11
0.043
0.14
0.10
0.063
0.15
0.11
0.083
0.082
0.18
0.085
0.31
0.049
0.09
0.06
0.15
0.13
0.17
0.11
0.09
SZ3/Z3
0.055
0.022
0.067
0.048
0.032
0.068
0.050
0.040
0.041
0.14
0.049
0.34
0.027
0.062
0.042
0.28
0.30
0.10
0.081
0.068
OS-
LO
-------
TABLE 17. STATISTICS FOR VARIABILITY OF SULFUR, IIFATJNG VALUE, AND LBS SO2 PER MILLION BTU'S-CLEANED COAL
(Loqarithmic Transformation)
Batch ID.
202
203
204
206
208
209
210
213
214
215
216
217
218
219
220
221
222
223
C-2
C-3
N=
No. of
lots
24
6
25
24
26
25
25
24
25
25
25
25
25
46
6
18
5
5
115
115
X— m*^«
- Mean
lot size,
tons
6,500
100,000
18,300
3,900
4,500
6,300
4,200
10,300
16,900
2,100
5,400
4,700
51,500
7,600
4,200
5,400
2,700
600
5,600
2,500
Z,=ln(Sulfur(%))
Zi
1.15
1.21
1.21
1.35
1.40
1.015
1.206
1.09
0.945
1.24
1.32
1.065
0.95
0.50
1.41
1.49
0.14
0.055
-0.42
-0.24
SZ,
0.049
0.011
0.035
0.052
0.053
0.070
0.040
0.050
0.096
0.046
0.056
0.098
0.047
0.107
0.14
0.097
0.20
0.164
0.05
0.10
sz,/z,
0.043
0.0091
0.029
0.038
0.038
0.069
0.033
0.046
0.10
0.037
0.042
0.092
0.049
0.21
0.099
0.065
1.43
2.98
-0.12
-0.40
Z2=ln (Btu/lb)
Z2
9.473
9.471
9.471
9.40
9.40
9.45
9.47
9.43
9.45
9.45
9.44
9.43
9.41
9.42
9.42
9.46
9.58
9.57
9-491
9.407
SZ2
0.0059
0.0037
0.0062
0.018
0.016
0.013
0.0080
0.0054
0.0073
0.011
0.0096
0.016
0.010
0.035
0.021
0.015
0.010
0.013
0.012
0.032
SZ2/Z2
0.00062
0.00039
0.00065
0.0019
0.0017
0.0014
0.00084
0.00057
0.00077
0.0012
0.0010
0.0017
0.0011
0.0037
0.0022
0.0016
0.0010
0.0014
0.0013
0.0034
Z3=
Z3
1.58
1.64
1.64
1.86
1.90
1.46:
1.637
1.56
1.40
1.69
1.78
1.53
1.44
0.98
1.90
1.94
0.463
0.38
-0.01
0.25
In/ Ibs SO2 \
'MM Btu /
SZ3
0.051
0.013
0.038
0.058
0.058
0.074
0.044
0.053
0.095
0.048
0.057
0.103
0.050
0.12
0.14
0.10
0.19
0.17
0.05
0.09
SZ3/Z3
0.032
0.0079
0.023
0.031
0.030
0.050
0.027
0.034
0.068
0.028
0.032
0.067
0.035
0.12
0.074
0.052
0.41
0.45
-5.00
0.36
-------
TABLE 18.
STATISTICS FOR VARIABILITY OF SlIIJUR, HEATING VAJJJIJ, AND IflS SOj 1'ER MIIJ/ION BTIJ'S UNCLEANED COAL
(Radical Transformation)
Batch ID.
103
104
105
107
108
109
110
111
112
116
117
120
121
C-l
C-8
U-4
U-5
U-ll
U-12
U-13
N=
No. of
lots
25
25
25
25
25
25
25
25
26
44
44
25
24
704
275
164
250
250
250
250
X= Mean
lot size,
tons
2,800
10,900
11,200
5,300
6,800
7,100
1,100
6,700
3,800
7,600
3,400
10,300
17,300
12,000
10,000
12,000
13,000
-
-
-
w,= >/Sulfur (%)
W~i
2.11
2.03
2.20
2.24
2.04
2.28
2.19
2.16
2.05
1.41
1.76
1.21
1.94
1.67
1.61
1.02
0.96
1.76
1.53
1.52
SW,
0.11
0.039
0.13
0.10
0.057
0.10
0.11
0.081
0.058
0.11
0.069
0.17
0.048
0.07
0.04
0.08
0.07
0.13
0.08
0.07
sw,/w,
0.052
0.019
0.059
0.045
0.028
0.044
0.050
0.038
0.028
0.078
0.039
0.14
0.025
0.60
0.025
0.078
0.073
0.074
0.052
0.046
W2= ^3tu/l*>
w?
108.8
109.7
109.5
110.9
109.1
107.3
101.7
107.7
107.3
106.9
105.3
106.8
112.2
114.2
111.7
109.5
108.9
107.3
109.7
110.2
SW,
1.53
0.78
1.57
1.15
0.77
2.17
1.83
1.01
1.95
1.49
1.26
1.17
1.01
1.0
3.2
1.4
1.4
1.7
1.2
1.2
sWjM2
0.014
0.0071
0.014
0.010
0.0071
0.020
0.018
0.0094
0.018
0.014
0.012
0.011
0.0090
0.0088
0.029
0.013
0.013
0.016
0.011
0.011
W3=
w"a
2.74
2.61
2.84
2.86
2.64
3.00
3.04
2.83
2.71
1.86
2.36
1.60
2.45
2.07
2.04
1.31
1.24
2.32
1.97
1.95
Vlbs SO2
MM Btu
SW3
0.15
0.056
0.20
0.15
0.083
0.097
0.16
0.12
0.11
0.15
0.101
0.24
0.059
0.09
0.07
0.10
0.09
0.19
0.11
0.09
SWs/Wj
0.055
0.021
0.070
0.052
0.031
0.032
0.053
0.042
0.041
0.081
0.043
0.15
0.024
0.043
0.034
0.076
0.073
0.082
0.056
0.046
-------
TABLE 19. STATISTICS FOR VARIABILITY OF SULFUR, HEATING VAUJE, AND LDS SO2 PER MIU.ION m\J• S-CLEANED CQA1
(Radical Transformation)
Batch ID.
202
203
204
206
208
209
210
213
214
215
216
217
218
219
220
221
222
223
C-2
C-3
N=
No. of
lots
24
6
25
24
26
25
25
24
25
25
25
25
25
46
6
18
5
5
115
115
X= ftean
lot size,
tons
6,500
100,000
18,300
3,900
4,500
6,300
4,200
10,300
16,900
2,100
5,400
4,700
51,500
7,600
4,200
5,400
2,700
600
5,600
2,500
W,= V Sulfur («)
Hi
1.78
1.83
1.83
1.96
2.01
1.68
1.83
1.72
1.61
1.86
1.94
1.705
1.61
1.28
2.03
2.11
1.08
1.031
0.81
0.88
SW,
0.043
0.010
0.03
0.051
0.052
0.059
0.037
0.043
0.077
0.043
0.054
0.083
0.038
0.069
0.15
0.103
0.106
0.082
0.02
0.04
SW,/H,
0.024
0.0055
0.016
0.026
0.026
0.035
0.020
0.025
0.048
0.023
0.028
0.049
0.024
0.054
0.074
0.049
0.098
0.080
0.025
0.045
W2= V Btu/lb
w.
114.0
113.9
114.0
109.8
110.1
112.9
114.0
111.5
112.6
112.9
112.3
111.8
110.7
111.1
110.8
113.0
120.3
119.9
115.1
110.3
SW2
0.33
0.21
0.35
0.096:
0.91
0.76
0.468
0.30
0.412
0.64
0.54
0.92
0.54
1.94
1.19
0.86
0.605
0.761
0.7
1.7
SW2/W2
0.0029
0.0018
0.0031
0.00088
0.0083
0.0067
0.0041
0.0027
0.0037
0.0057
0.0048
0.0082
0.0049
0.017
0.011
0.0076
0.0050
0.0063
0.0061
0.015
W3=
Wj
2.21
2.28
2.27
2.53
2.58
2.08
2.27
2.18
2.02
2.33
2.44
2.16
2.05
1.64
2.59
2.64
1.26
1.22
1.00
1.13
Vlbs SO
MM Bt
SW3
0.056
0.015
0.043
0.074
0.073
0.077
0.049
0.058
0.095
0.056
0.069
0.11
0.052
0.10
0.18
0.13
0.12
0.100
0.03
0.05
2
u
SW3/W3
0.025
0.0066
0.019
0.029
0.028
0.037
0.021
0.027
0.047
0.024
0.028
0.051
0.025
0.061
0.069
0.049
0.095
0.082
0.030
0.044
-------
Now, to test the hypothesis that a (random) sanple comes from a pop-
ulation having a normal distribution, a normal curve can be fitted to
the data and a chi-square test (for goodness of fit) applied to determine
whether the hypothesis is justified. In such a case, the mean and standard
deviation for the fitted normal curve is usually estimated from grouped
sample data because the chi-sguare test requires the presence of several
(>_ 5) observations in each class if the Stirling-approximation (used
in the classical derivation of the test) is to be valid. Inspection of
Tables 12 and 13 shows that sufficient lot numbers exist (for known mean
lot-sizes) for seven batches of uncleaned coals (Cl, C8, U4, U5, Ull, U12,
and U13) and two batches of cleaned coals (C2 and C3). Taking the correspond-
ing sample means and standard deviations as estimates for the population means
and standard deviations*, chi-square tests at the 5 percent level of signifi-
cance were made to determine whether the (transformed and untransformed)
data could be assumed to have come from a normal distribution. Detailed
chi-quare analyses for three data sets (C-8, U-ll, and C-3) in their three
forms (original, logarithmic transformation, and radical transformation)
are included in Appendix B. Table 20 presents the summarized results of
these calculations for all data sets, with italicized entries designating
acceptance of the hypothesis at the 5 percent level of significance.
As can be seen, the general tendency is that, if the actual data
satisfies the test**, the transformed data does also. The exceptions in
U-12 and U-13 can be seen to have failed the test** by a relatively small
margin. Observe, however, that all of the data for both cleaned coal
batches satisfy the acceptance criteria.** Recalling that uncleaned coals
are generally subject to far less stringent sampling procedures than are
* Using the sample standard deviation as an estimate of the population
standard deviation is admittedly tenuous, for those samples exhibiting
autocorrelation (Section 5.4).
** The chi-square test is designed to refute an hypothesis of normality, not to
validate it. Therefore, "satisfying the test" means an absence of evidence (at
the stated level of significance) to reject the hypothesis, and "failing the
test" means rejection of the hypothesis of normality.
47
-------
T7V3IE 20. OOMPUrED CIII-fiQUTW, VALUES
00
a-ita
set
Unwashed
Cl
Cfl
U4
U5
Illl
U12
U13
Washed
C2
C3
No. of
data
points
704
275
164
250
250
250
250
115
115
Degrees
of
freedom
17
13
5
7
13
13
13
9
9
S
31.8
23.5
80.6
186.7
44.2
32.0
37.3
10.?,
G.f,
In (S)
3.1.8
35.7
91.3
197.5
54.1
36.0
29.1
7. 7
ir,.!.
s
so,
z.". -;
«;:.^
55.2
78.1
53.1
2Z.fi
13. S
14.7
7.1
In (SO,)
;M . n
1,1.0
31.7
28.0
74.4-
23.1
l?t. n
l.y.. 1.
?.!>
. ;:
/fi.,i
47. f,
34.5
72.6
17.!',
/.'.. /
Z*.3
fi. ."?
chi-sr.)uate
(0.05)
27.59
22.16
.1.1.07
14.07
22.36
22.36
22.36
1.6.92
16.92
lkalj.c'i.xp.rl nwnhfrR i.nrU.cnte af!CG\>1:finafi of Uir> In/fiatliani.a Mt
iionnal at. thr .ri? Icvf.l of
th" niiinjtj.ca MCIV. olil.fii.nfil fivm iv.>i'n/.nl.i«nn
-------
the cleaned (product) coals, no satisfactory conclusions can be drawn
from assumptive distribution testing before the sampling and analysis
protocols which produce the data are sufficiently defined and standard-
ized. Indeed, the results of the chi-sguare evaluation tend to indicate
the absence of sensible evidence for preferring any one distribution
over the others, and Figures 2, 3, and 4 (where graphs of the fitted normal
curve are plotted on the same scale as the histogram of the grouped data)
illustrate this characteristic for three of the data sets of Table 20.
It should also be noted that there exists an inherent difficulty in
judging "by eye" how much departure from the normal pattern should be
expected in such figures. In fact, the plots for a sample of 1,000
data points drawn from a population known to be normal often exhibit
substantial irregularity — which is why the chi-square test is generally
taken to be far superior to graphical methods for testing the fit of a
distribution.*
5.6 CDMPARISON OF VARIABILITIES: UNCLEANED VS. CLEANED ODALS
The conclusion reached in Section 5.5 was that no sensible evidence
exists for preferring any one distribution (original data points,
logarithmic transformation, or radical transformation) over the others.
In general, if the original data satisfied the chi-square test for
normality, then the transformed data does also. The converse is also
generally true. For reasons of simplicity, then, the following comparison
of variabilities was conducted using the original (untransformed) data.
The following comparison of variabilities was conducted with due
respect to the limitations and caveats expressed about this analysis in
Section 5.1., and especially with respect to the evidence of autocorrela-
tion in Section 5.4. It would be a mistake to construe the results of
this comparison beyond the point of being, perhaps, roughly indicative
of the effects of the coal cleaning process.
The statistics for individual (untransformed) data sets are listed
in Tables 12 and 13. The variances (S2y , S2y2/ and S2Y;j) for all of
the uncleaned coal data sets in.Table 12 were pooled according to:
* More rigorous tests of normality should also include tests for skewness
and kurtosis.
49
-------
40
20
S02
i
2 -1.0 1 2
Distance frcm Mean (Standard Deviations)
20
In (S02)
f\
-3
-2 -1 _,0 1 2
Distance from Mean (Standard Deviations)
40
20
N
\
-3 -2 -1 0 . . 2 1
Distance from Mean (Standard Deviations)
Figure 2. Fitted Normal Curve and Histogram of
Grouped S02 Data for Batch C-8
50
-------
40
S02
^20
-3
-2 -1 0.1 2
Distance fron Mean (Standard Deviations)
40
20
-3
40
In (S02)
-2-10 1 2
Distance from Mean (Standard Deviations)
20
-3
-2-1012
Distance from Mean (Standard Deviations)
Figure 3 . Fitted iMormal Curve and Histogram of
Grouped S02 Data for Batch U-ll
51
-------
15
-3
\
S02
\
\
-2-1012
Distance from Mean (Standard Deviations)
15
.10
u
b 5
In (S02)
\
-3-2-10123
Distance from Mean (Standard Deviations)
.10
-3
\
\
-2 -1 0 12
Distance from Mean (Standard Deviations)
Figure 4. Fitted Normal Curve and Histogram of
Grouped SO2 Data for Batch C-3
52
-------
J J=1 J ^ J
where N. = number of data points (lots) in data set j
J = the number of data sets in Table 12.
The same calculation was performed for the cleaned coal data sets in
Table 13.
Similarly, the squares of the relative standard deviations were
pooled according to:
i /pooled
and (PSD.) pooled =
Finally, because we wish to evaluate average RSDs,
J
(BSDi> average = 5 - ' ^ \ 'i = 1'2'3 •
" Yi / J
The results of these calculations are listed in Table 21. The
reductions in variability, depending upon how variability is measured,
range from 25 to 64 percent. Despite the limitations of the statistical
treatment, these results surely suggest that the variability is reduced
by the coal cleaning process. Moreover, these results are consistent
with the percent reductions derived (in Section 4.2) from the eight
paired coal feed and product data sets.
53
-------
TABLE 21.
COMPARISON OF VARIABILITIES
Pooled variances
(Sy,2) pooled
Pooled RSDs
r/SyA2 1l/2
( Y1 (pooled
\Yi /
Average
RSDs
Uncleaned ooals
Cleaned coals
Percent reduction
Uncleaned coals
Cleaned coals
Percent reductions
Uncleaned coals
Cleaned coals
Percent reductions
% Total sulfur
0.0710
0.0303
57
0.111
0.078
30
0.104
0.078
25
Btu/lb
126,100
56,800
55
0.0291
0.0192
34
0.0265
0.0134
49
Ib S02/MM Btu
0.236
0.084
64
0.118
0.078
34
0.114
0.080
30
-------
SECTION 6
COMPONENTS OF VARIANCE
As outlined in Section 2.1, the model adopted for examining sulfur varia-
bility has the following generalized components of variance:
Total ~ Long + Short + Sampling &
Term Term Analysis
V tal represents the variability of the data points within each data set about
the mean for that data set. No attempt has been made in this study to evaluate
the additional geographical and source components of variance which apply among
data sets. Hence, V_ ., for each coal source (e.g., each data set) will be
influenced by characteristics of the coal region, the coal seam, the particular
mine, the mining methods employed, and the coal preparation methods employed.
For example, the coal shipped from an eastern underground mine may originate
from several quite-different coal faces, i.e., the sulfur content at one face
may have a mean of one percent, and may be three percent at another, face-. - A
large value for vTotai an<^ for Vxr>ncr-T^rm wou^-^ result. In contrast, another
mine might have a single face in operation at any one time, and the deposit
may be relatively homogeneous, resulting in a smaller value for V_ .,.
The model for examining sulfur variability is a temporal model. Further,
the definition of long-term as the month-to-month variation is rather arbitrary,
and is influenced by the definition of short-term as considerably less than
one-month (e.g., daily variation). There is no fundamental reason, such as
matching "long-term" in a temporal model with "long-range" in a corresponding
geostatistical spatial model, for choosing a month as the long-term/short-term
boundary.
6.1 ANALYSIS OF AIJIOaJRRELATED DATA SETS
In Section 5.4, tests for autocorrelation of the heat-specific sulfur
content yielded positive results Cat the 95 percent confidence level) for 16
data sets. These "select" data sets differ from the broader group of data sets
55"
-------
specifically because the long-term component of variance was discernible above
the noise level of lot-to-lot Cshort-term) variance. An opportunity therefore
exists to use the select group of data sets to estimate a generalized long-term
component of variance.
Table 22 presents these selected data sets. The values for the total
(source-specific) variance, S2, and the estimates of the "nugget" variance,
yCl), are taken from Tables 14 and 15. For .the purposes of this analysis, y(D
is used as a conveniently calculated surrogate for the true nugget variance,
VCO) , with due appreciation of possible added uncertainty. This "nugget" variance
includes both the short-term variance and the sampling-and-analysis
variance. The difference, S2 - yd) / is listed in Table 22 as represent-
ing the long-term component of variance. The transformation of variances
to relative standard deviations (also shown in Table 22) serves to
normalize the variability data for the "geographical" component which
influences the mean for each data set:
Total RSD = (S2)1//2/?3
(Short-Teim + S/A) RSD =
Lang-Term RSD = (S2-y (D )
The RSDs of Table 22 were then pooled according to:
1/2
RSD
pooled
resulting in:
Uncleaned coals
Cleaned coals
All coals
Pooled RSD
Total
0.0815
0.0882
0.0834
Short + S/A
0.0649
0.0665
0.0653
Long
0.0493
0.0580
0.0519
56
-------
TABLE 22.
ANALYSIS OF AtfKXX3RRELATED DATA SETS
PARAMETER: LBS 902/)W BTU
Data
set
104
112
114
119
C-l
08
201
205
208
209
210
211
214
219
C-2
C-3
n
25
26
12
5
704
275
6
6
26
25
25
12
25
46
115
115
Average lot
size, tons
10,900
3,800
319,700
640
12,000
10,000
214,500
228,300
4,500
6,300
4,200
251,900
16,900
7,600
5,600
2,500
Mean,
y3
6.82
7.35
8.82
3.00
4.27
4.17
4.90
5.09
6.69
4.33
5.14
6.73
4.07
2.69
0.99
1.28
Variances
S2
0.090
0.384
0.880
0.740
0.130
0.073
0.0151
0.0784
0.1369
0.1024
0.0485
0.1998
0.1444
0.1089
0.0078
0.0136
•
Y(l)
0.059
0.253
0.255
0.159
0.093
0.034
0.0024
0.0219
0.0672
0.0633
0.0292
0.0637
0.0934
0.0773
0.0017
0.0109
S2-Y(1)
0.031
0.131
0.625
0.581
0.037
0.039
0.0127
0.0565
0.0697
0.0391
0.0193
0.1361
0,0510
0.0316
0.0061
0.0027
RSD
Ibtal
0.0440
0.0843
0.1064
0.2867
0.0844
0.0648
0.0251
0.0550
0.0553
0.0739
0.0428
0.0664
0.0934
0.1227
0.0892
0.0911
Short + S/A
0.0356
0.0684
0.0573
0.1329
0.0714
0.0442
0.0100
0.0291
0.0387
0.0581
0.0332
0.0375
0.0751
0.1034
0.0416
0.0816
Long
0.0258
0.0492
0.0896
0.2541
0.0450
0.0474
0.0230
0.0467
0.0395
0.0457
0.0270
0.0548
0.0555
0.0661
0.0789
0.0406
-------
The total RSDs above for the select group of autooorrelated data sets
may be compared with the total RSDs for all data sets (from Table 21):
Uhcleaned Coals, 0.118
Cleaned Coals, 0.078
The results of the analysis of the select group of data sets are
then useful in estimating a generalized value for the long-term RSD.
This long-term RSD, defined as a month-to-month component of variance,
is 0.052, which is the best estimate applicable to all of the coals
in the data base. No difference should exist for this long-term
component between uncleaned coals and cleaned coals.
6.2 GENERALIZED ESTIMATES FDR CCMPONENTS OF VARIANCE
In Section 2.3, experimentally based estimates were derived for
the actual sampling and analysis components of variability of Ibs S02/MM Btu:
(RSD) S&A for Uhcleaned Coals =0.045
(RSD) S&A for Cleaned Coals = 0.023
In Section 5.6 (Table 21), estimates were derived for the total
RSD (of each coal source about the mean for that source) for Ibs S02/lyiM Btu:
(RSD) Total, Each Source, for Uncleaned Coals = 0.118
(RSD) Total, Each Source, for Cleaned Coals = 0.078
In Section 6.1, an estimate was derived for the long-term component
of variability, applicable to all coal data sets:
(RSD) Lang-Term = 0.052
The determination, by difference, of the short-term component of varia-
bility is therefore possible:
(RSD) Short-Term for Uncleaned Coals
[1 1 /+\
(0.118)2 - (0.052)2 - (0.045)2 1/2 = 0.096
(RSD) Short-Term for Cleaned Coals
I
1
= (0.078)2 - (0.052)2 - (0.023)2 = 0.053
58
-------
The table below summarizes these estimates for the components of
variability;
BSD for long-term
PSD for short-term
BSD for S&A
(RSD) total for each source
Uncleaned
coals
0.052
0.096
0.045
0.118
Cleaned
coals
0.052
0.053
0.023
0.078
It must be emphasized that these are generalized estimates, represent-
ing aggregated data sets. In no way may these values be utilized to
characterize any one particular coal. Actual variabilities of individual
data sets, as evidenced by Tables 12 and 13, may be quite different
from the generalized values shown above.
59
-------
SECTION 7
EFFECT OF LOT SIZE UPON TORI ABILITY
7.1 FESULTS OF PREVIOUS STUDY
In a previous study of sulfur variability sponsored by EPA , it was
pointed out on both theoretical and empirical grounds that the sulfur
variability of small lots of coal should be greater than that of large lots.
A qualitative explanation was the application of the Central Limit Theorem
to the component of variance which corresponds to the averaging process.
However, the evidence in the present study (Section 5.4) for serial
correlation of coal sulfur variability data places doubt upon the validity
of applying the Central Limit Theorem to such data.
The empirical rationale in this previous study was based upon 12 data
sets for coals with less than one percent sulfur, where each data point
represented a unit train (approximately 10,000 tons). Despite averaging
across heterogeneous populations (different regions, both unwashed and
washed coals, etc.), the average PSD among data points (unit trains) within
each month was 0.143, while the average PSD from month-to-month (perhaps
16 unit J;rains per month) was 0.059. This inverse relationship between
PSD and lot size was not, however, demonstrated with consistency in the
previous study.
7.2 ANALYSIS OF TOTAL VARIABILITY, ALL DATA SETS
The data of Tables 12 and 13 are plotted on Figure 5. Shown are the
relative standard deviation of percent sulfur as the ordinate, and the lot
size (on a logarithmic scale) as the abcissa. As observed, the data in
Figure 5 are highly scattered, but it may be argued that the general inverse
relationship (higher RSD's at lower lot sizes) does exist.
60
-------
0.20-
LEGEND:
® UNWASHED COALS
WASHED COALS
z
lit
o
®
HYPOTHETICAL CURVE,
O
Q
A®
A ®
® A
0.00-
200 3OO BOO
l.OOO 2.OOO
6.0OO 10.000 20.000
LOT SIZE. TONS
6O.OOO IOO.OOO 2OO.OOO
600.000
FIGURE 5. EFFECT OF LOT SIZE UPON PERCENT SULFUR RELATIVE STANDARD DEVIATION
-------
Also shown (for reference) in Figure 5 is a curve developed in the
previous EPA study for a "hypothetical" coal. The origin of this curve
has both theoretical and empirical rationale, but the prior study pointed
out that a different curve would result for any specific coal deposit (data
set) or for different groups of data sets. Hie RSD data points (from the
database in this study) are generally lower than the hypothetical curve.
7.3 MAIYSIS OF SEIECT DATA SETS
It is possible that an observed difference between a relative standard
deviation for data points within months, and a relative standard deviation
for month-to-month aggregated data, may be explained either by a lot size
difference (the month-to-month aggregated data would, of course, be
associated with large lots) or by the difference between the short-term
and the long-term components of variability.
The 16 select data sets of Table 22, where autocorrelation was
demonstrated, provide an opportunity for discerning lot-size effects from
long-term/short-term effects, because the long-term and short-term components
of variability were independently estimated. Table 22 also lists the average
lot sizes for these select data sets. Figure 6 is a plot of the long-term
component of the relative standard deviation (for Ibs S02/MM"1 Btu> vs. lot
size. Except for the one data set (No. 119) with an average lot size of
640 tons, the long-term variability data of Figure 6 does not exhibit a
dependence of PSD upon lot size.
Figure 7 is a plot of the short-term (including sampling and analysis)
component of the RSD vs. lot size. Although these data are scattered to a
large extent, the inverse relationship is clearly observable. This result
is expected, since the short-term component of variability has been separated
from the component which is associated with autocorrelation effects. A
least-squares straight line (shown in Figure 7) through the data points of
Figure 7 is:
62
-------
o
s
LEGEND:
UNWASHED COALS
CJ
o
s
K
A
A
A °A A 00
A 0
A
O
A
400 600 1.OOO 2.000 4.OOO
10.0OO 20.OOO 40.OOO
LOT SIZE. TONS
100.OOO 20O.OOO 400.000
FIGURE 6. EFFECT OF LOT SI2E UPON LONG TERM HSO SELECT DATA SETS.
-------
CT>
o
LEGEND:
UNWASHED COALS
WASHED COALS
A
4OO 60O
I
1.OOO
I
2.000
I
4.000
o
IO.OOO 20.OOO
LOT SIZE. TONS
200.OOO 400.0OO
FIGURE 7. EFFECT OF LOT SIZE UPON SHORT TERM RSO SELECT DATA SETS
-------
(RSD) Short-Tsrm = 0.150 - 0.0223 logio (lot size, tons)
The correlation coefficient of this least-square line is 0.59. Hence,
34 percent of the total variance of short-term BSD values was accounted for
by the regression on (the log of) lot size. Considering that the 16 data
sets are from non-homogeneous populations - different coal regions,
seams, and mines, both unwashed and washed coals, and non-uniform sampling
and analytical procedures - the remaining variance is explainable.
65
-------
SECTION 8
CONCLUSIONS
The analysis of the collected data in this report supports the
following conclusions:
• In seven of eight coal cleaning plants, for which matched pairs
of feed and product coal data were available, the coal cleaning
process resulted in significant changes in coal properties. The
mean total sulfur content was reduced by 14 to 45 percent, the
mean heating value was increased by 6 to 23 percent, and the mean
Ibs S02/TyiM Btu was reduced by 24 to 50 percent. The range of
effectiveness of physical coal cleaning as a sulfur dioxide control
technology is demonstrated by these data from operating commercial
preparation plants. These empirical data fall within the range of
calculated physical coal cleaning performance of hypothetical
plants. The ranges of both demonstrated and calculated effective-
ness are wide, reflecting the sensitivity of coal cleaning
efficiency to the washability characteristics of specific coals
and to the complexity of the plant design. These actual and
calculated data demonstrate that no valid "typical" effectiveness
can be quoted for physical coal cleaning technology.
• In each of the eight plants for which iratched pairs of feed and
product data were available, both the absolute standard deviation
and the relative standard deviation for all three coal character-
istics were reduced by the coal preparation process. The reduc-
tions in both percent sulfur variability and Ibs SOzAM Btu
variability averaged approximately 55 percent and ranged from 9
to 90 percent, while the heating value variability reduction
averaged approximately 80 percent and ranged from 51 to 94 percent.
66
-------
Data from 20 sets of unwashed coal data and from 17 sets of washed
coal data did not permit direct comparison of feed and product
pairs. A second statistical analysis, conducted to exploit the
entire available data base, compared the data sets of all
unwashed coals to the data sets of all washed coals. This indirect
approach is hampered because the two groups of data sets do not
form logically consistent or homogeneous populations sufficient
for rigorous statistical analysis. Because of these inherent
compatibility problems, the results of this second statistical
analysis should not be regarded as definitive as those of the
first analysis. Despite the limitations of the statistical
treatment, the comparison of variabilities of the two groups of
data sets surely suggest that the variability is reduced by the
coal cleaning process. The reductions, from unwashed coals to
washed coals, range from 25 to 64 percent depending upon how
variability is measured. These results are consistent with the
percent reductions in variability derived from the paired feed/
product data sets.
Nine data sets (which accounted for 2,373 data points) were
examined in three ways: without transformation, with a logarithmic
transformation, and with a radical transformation. The distributions
of the untransformed and transformed data were tested for normality.
Six of the nine batches satisfied the chi-square test (for Ibs
S02/MM BTU) for normality, with either the untransformed data or
the transformed data. The three batches failing the test failed
regardless of whether the data were transformed or not. These
results indicate the absence of sensible evidence for preferring any
one distribution over the others.
Tests for autocorrelation of the data points within data sets gave
positive results in 16 of 48 data sets (at the 95 percent confidence
level). There is little doubt, therefore, that much of these coal
data are serially correlated, verifying the expectations based upon
geology and engineering rationale.
67
-------
For each of 16 data sets which exhibited autocorrelation, the total
variance (of Ibs S02/MM Btu) was resolved into the long-term component,
associated with the serial correlation according to geostatistical
concepts, and the residual short-term (including sampling and
analysis) component. An estimate of a generalized long-term com-
ponent of relative standard deviation was 0.052, applicable to both
unwashed coals and washed coals.
From previously published data representing actual commercial
practice, the component of relative standard deviation attributable
to ASTM coal sampling, sample preparation, and laboratory analysis
(in terms of Ibs S02/MM Btu) was 0.045 for unwashed coals and
0.023 for washed coals. Ihese values are smaller than the 0.07 to
0.08 maximum permitted by the ASTtl protocols.
Estimates of the components of variability are:
FSD for long-term
PSD for short-term
FSD for S&A
(FSD) total for each source
Unc leaned
coals
0.052
0.096
0.045
0.118
Cleaned
coals
0.052
0.053
0.023
0.078
It must be emphasized that these are generalized estimates,
representing aggregated data sets. In no way may these values be
utilized to characterize any one particular coal. Actual variabilities
of individual data sets may be quite different from the generalized
values shown above.
A prior study concluded that the relative standard deviation should
be inversely related to lot size. By removing the long-term com-
ponent of variability (which includes autocorrelation) from data
68
-------
in this study, an inverse relationship betoreen the short-term
component of PSD and lot size was discerned. A least-squares
line had a correlation coefficient of 0.6, indicating a much
clearer inverse relationship than was previously demonstrated.
69
-------
SECTION 9
REFEFENCES
1 Preliminary Evaluation of Sulfur Variability in Low-Sulfur Goals from
Selected Mines. EPA 450/3-77-044, November 1977.
2 Crow, E. L., F. A. Davis, and M. W. Maxfield. Statistics Manual.
Dover Publications Inc., New York. (S599).
3 Kilgroe, J. D. Coal Sulfur Variability Estimates for Industrial
Boiler Study. EPA/IERL/RTP Memo. (October 20, 1978).
"* Leonard, J. W., and D. R. Mitchell (ed.) . Coal Preparation.
3rd edition. The American Institute of Mining, Metallurgical,
and Petroleum Engineers, Inc., New York, 1968.
5 Keller, G. E. Determination of Quantities Needed in Coal Sample
Preparation and Analysis. Transactions Society of Mining Engineers,
September 1965. pp. 218-26.
6 Aresco, S. J., and A. A. Orning. A Study of the Precision of Coal
Sampling. Sample Preparation and Analysis. Transactions Society
of Mining Engineers, September 1965. pp. 258-64.
7 Cavallaro, J. A., M. T. Johnson, and A. W. Deurbrouck. Sulfur
Reduction Potential of the Coals of the United States. Report of
Investigations 8118. U.S. Department of the Interior, Bureau of
Mines, 1976.
8 Bechtel Corporation. Environmental Control Implications of
Generating Electric Power frcm Coal. Appendix A (Part 1).
Argonne National Laboratory, U.S. Department of Energy,
December 1977.
70
-------
Technology Assessment Report for Industrial Boiler Applications:
Coal Cleaning and Low Sulfur Coal. EPA-600/7-79-178c. EPA Contract
No. 68-02-2199, Task No. 12. December 1979.
10
Versar, Inc. Coal Cleaning Sensitivity Analysis. (Draft) for U.S.
Environmental Protection Agency. July 1979.
11 Thonas, R. E. Interpreting Statistical Variability. Battelle-Columbus
Laboratories. In Proceedings: Symposium on Coal Cleaning to Achieve
Energy and Environmental Goals. September 1978. Hollywood, Florida.
Volume 1. EPA-600/7-79-098a, April 1979. pp. 126-147.
71
-------
APPENDIX A
LISTING OF THE DATA BASE
A-l
-------
TABLE A-l. DATA SETS
tota
Set
No.
101
102
103
Lot
Size,
Tons
271,402
238,303
275,873
270,487
394,101
271,355
143,854
134,79D
118,004
106,709
104,390
88,544
4,120
2,871
1,358
1,404
4,276
1,530
2,825
4,339
2,908
4,181
5,642
4,201
5,392
1,245
1,465
1,421
1,409
1^343
1,438
1,427
10,100
1,383
1,432
1,383
1,436
Ibtal Data lot Total Iteta lot Total
Sulfur, ntu Ibs SO2 Set Size, Sulfur, Btu ibs SO2 Set Size, Sulfur, ntu Ibs SO,
% ~IU io'Stu' No. Tons % "ib 108Btu No. Tons % ll> To* ntu
4.17 11,035 7.55 .104 13,129 3.91 12,360 6.45 106 399,192 3.99 10,H()3 7.31)
4.64 11,827 7.84 8,983 3.86 12,151 6.35 344,441 4.25 9,821 8.C.5
4.08 12,009 6.79 11,787 1.30 12,218 7.03 371,490 3.77 10,590 7.11
3.96 10,529 7.51 15,092 1.14 12,007 6.89 272,336 5.03 9,268 10. LH
3.98 11,611 6.85 11,662 3.01 11,942 6.59 L07 0,613 4.7 12,360 7.60
4.13 10,914 7.56 16,837 4.07 11,912 6.83 8,495 4.9 12,240 U.OO
4.72 12,447 7.50 13,618 -1.13 12,021 6.86 3,629 5.1 12,600 ::.09
4.07 12,385 ft. 57 7,604 4.43 11,890 7.44 7,786 5.3 12,280 8.02
3.99 12,019 6.63 5,825 4.16 12,128 6.85 3,384 5.1 12,440 8.19
3.96 11,664 6.78 12,055 4.46 12,126 7.35 4,613 4.6 12,340 7.45
5.05 12,15-1 8.30 12,828 4.10 12,124 6.76 4,693 4.7 12,380 7.59
3.9.3 12,728 6.17 11,982 3.95 12,210 6.46 5,382 5.5 11,900 9.23
4.61 11,813 7.80 11,175 3.93 12,042 6.52 5,125 4.9 11,840 B.27
4.22 11,498 7.33 5,992 4.05 12,314 6.57 5,047 6.5 11,980 10.84
5.39 11,834 9.10 7,579 4.01 12,146 6.60 0,821 4.7 12,320 7.62
3.94 12,027 6.55 16,131 3.RO 12,040 6.46 5,618 5.4 12,340 8.74
4.54 12,189 7.44 4,412 4.08 12,000 6.79 5,670 4.5 12,100 7.43
3.99 12,342 6.46 10,376 4.05 11,640 6.95 9,079 4.9 12,200 8.03
4.83 12,010 8.04 14,163 4.23 11,896 7.10 4,233 4.6 12,600 7.29
3.91 12,063 6.48 13,533 4.11 11,965 6.86 4,407 5.3 12,060 0.78
4.25 12,185 6.97 10,389 4.25 1.1,673 7.27 3,597 4.8 12,580 7.62
5.41 11,939 9.05 11,501 ' 4..">6 11,902 7.15 4,817 4.3 12,780 f>. 72
4.00 12,110 6.60 8,360 3.99 11,907 6.70 4,311 5.4 12,400 8.70
4.44 11,905 7.45 8,612 3.9fl 12,028 6.61 3,486 4.7 12,620 7.44
4.57 11,974 7.63 9,903 4.27 12,177 7.01 4,727 5.6 12,240 9.14
3.40 12,088 5.62 105 10,974 5.14 11,766 8.73 3,734 5.5 1.2,100 9.0U
4.99 11,707 8.52 11,111 5.88 11,119 10.57 3,350 4.7 12,640 7.43
4.49 11,338 7.91 11,237 4.53 12,055 7.51 5,272 5.0 12,460 8.02
4.13 11,558 7.14 11,009 4.36 12,169 7.16 3,614 5.4 11,900 ').07
4.46 12,435 7.17 11,170 1.48 12,264 7.30
4.57 11,472 7.96 10,957 4.83 12,175 7.93
4.28 11,812 7.24 11,912 4.56 1.1,940 7.63
4.63 11,902 7.77 11,499 5.15 12,063 8.53
4.74 11,515 8.22 9,668 4.41 12,178 7.24
4.48 11,636 7.69 10,910 4.30 12,087 7.11
4.15 11,032 7..S2 9,632 4.59 12,215 7.51
4.64 1.1,479 8008 11,073 5.20 12,244 8.49
11,185 4.35 12,051 7.21
11,912 5.20 11,666 8.91
10,862 5.04 1.1,908 8.46
12/417 6.61 11,100 11.90
11,834 4.49 12,227 7.34
11,313 4.20 12,253 6.85
1.1,330 4.48 12,123 7.38
11,549 5.33 12,081 8.82
11,91.1 5.71 11,472 9.95
11,488 4.70 11,866 7.91
11,304 5.04 1.7,404 fi.12
11,737 4.4? 12,350 7.15
NJ
-------
TABLE A-2. DATA SETS
Data
Sot
No.
108
109
Lot
Size,
'tons
6,052
6,927
6,727
7,01.0
7,142
7,083
7,058
6,872
6,746
7,001
7,055
6,009
7,017
6,700
6,900
6,793
7,030
6,026
7,008
5,456
7,165
6,743
6,672
0,608
6,351
8,807
9,135
8,233
1,709
8,1.71
7,976
1,004
7,256
1,499
10,350
2,932
10,317
6,575
9,193
.16,731
4,095
9,041
5,253
3,555
4,912
6 , 1.66
5,365
5,615
10,1.29
5,406
Tot/il Data Lot 'total lota Lot Total n]a, 11 ,s ;»,
Sulfur, Utn Ibs SO2 Set Size, Sulfur, 15tu Ibs M)2 9et Size Sulfur Ib WFVbT
% Ib 10" Btu No. Ttms % Ib 10bBtu No. "tons %
4.29 11,744 7.30 Ho 2,320 4.7 10,100 9.30 112 1,113 4.27 12,106 7.05
4.03 11,760 6.85 1,455 4.4 9,240 9.51 2,842 4.35 1 1., 172 7.78
3.92 11,742 6.67 1,434 5.2 9,980 10.11 2,851 1.79 11,103 8.62
4.14 11,664 7.09 755 4.1 11,140 7.35 1,424 4.42 1.1,779 7.50
4.39 11,774 7.45 973 4.8 10,440 9.19 2,090 4.24 11,397 7.43
4.23 11,898 7.10 1,155 4.6 1.0,360 8.87 2,829 4.34 11,953 7.25
3.86 11,852 6.51 1,200 4.8 10,660 9.00 2,851 4.26 11,175 7.62
4.03 12,009 6.67 1,037 4.6 10,600 8.67 2,842 4.10 10,683 7.07
4.58 11,853 7.72 1,066 4.7 10,680 0.79 2,826 4.18 11,409 7.32
4.15 12,126 6.84 761. 5.3 10,280 10.30 8,489 4.06 11,197 7.25
3.95 11,975 6.59 666 4.5 10,940 8.22 5,585 4.35 11,226 7.74
4.32 11,948 7.22 887 4.7 10,600 8.79 2,833 4.75 10,717 0.86
1.01 12,032 6.60 2,043 5.0 10,540 9.48 2,803 1.33 11,115 7.70
4.29 11,643 7.36 858 3.9 10,240 7.61 5,750 4.10 11,402 7. L3
3.91 11,901 6.5T. 8G6 4.9 10,280 9.52 2,069 4.34 11,350 7.6'1
4.23 11,641 7.26 1,126 4.9 10,600 9.21 7,089 1.06 11,832 0.8".
3.85 12,202 6.30 890 5.2 10,560 9.81 2,004 4.02 12,035 6.67
4.47 11,771 7.59 1,014 4.6 10,240 8.98 2,873 3.91 11,595 6.74
3.80 12,035 6.31 800 5.4 10,100 10.68 8,333 4.04 12,007 6.72
3.96 11,917 6.64 955 4.1 10,260 7.98 1,407 4.11 11,800 6.91
4.39 11,818 7.4.? gfll 4.2 .10,060 8.34 2,800 3.85 11,760 6.54
4.33 12,029 7.19 1,170 5.0 10,140 9.85 5,744 4.63 11,033 8.39
4.04 11,978 6.74 970 5.6 10,120 11.06 1,250 1.18 11,792 7.08
4.15 12,262 6.76 726 4.8 10,100 9.50 5,647 4.20 11,443 7.33
4.66 11,803 7.89 751 6.0 10,500 11.42 4,260 1.05 11,935 6.78
4.9 11,800 8.30 HI 6,227 5.0 11,620 8.60 1,426 3.87 12,109 6.39
5.7 11,780 9.67 10,570 4.5 11,300 7.96 113 299,805 4.87 10,304 9.44
4.8 12,080 7.94 7,484 4.7 12,000 7.03 300,584 5.16 10,70"' 9.63
5.2 11,320 9.18 9,403 4.2 11,580 7.25 318,967 5.05 10,956 9.21
4.5 10,240 8.78 5,247 4.5 11,440 7.06 280,974 5.44 10,741 10.12
5.4 11,700 9.22 9,885 4.4 11,820 7.44 303,269 4.98 .10,417 9.55
6.2 11.000 10.50 5,692 5.1 11,060 9.21 244,479 5.20 10,705 9.05
5.2 11,920 8.72 3,068 4.8 11,420 8.10 .114 - 3.98 11,11.3 7. .10
5.0 11,220 8.90 9,177 5.0 11,600 8.61 - 4.27 10,780 7.91.
5.3 11,820 8.96 3,133 4.4 .1.1.640 7.55 - 4.74 .10,9:.") 8.67
4.8 11,620 8.25 8,877 4.6 11,680 7.87 - 4.72 10,991. 8.50
6.0 11,560 10.37 9,600 5.4 11,340 9.51 - 4.10 10,940 7.49
4.8 12,000 7.95 7,909 4.2 11.640 7.21 - 4.45 10,499 0.47
4.7 11,740 8.00 7,782 4.6 11,620 7.9L - 4.87 1.0,304 9.44
5.0 11,640 8.58 7,452 4.1 11,700 6.97 - 5.16 10,707 9.03
5.9 1.1,720 10.06 6,101 4.9 11,740 8.34 - 5.05 10,956 9.21
4.9 11,420 8.57 3,426 4..4 11,320 7.77 - 5.44 10,741 10.12
5.9 11,100 10.62 r>,45.4 ".6 11,780 7.80 - 4.98 10,417 9.55
5.5 10,600 10.37 5,979 4.3 11,920 7.21 - 5.20 10,705 9.65
4.5 11,260 7.99 14,585 4.8 11,800 8. hi 115 212,17.3 4.07 11,054 7.30
5.2 11,200 9.28 4,824 5.1 11,760 8.67 .196,633 3.73 11,005 6.39
5.3 11,900 8.85 5,043 4.7 11,680 0.04 222,090 3.90 11,17') 7.11
4.0 11,960 8.02 3,537 5.2 1.1,500 0.97 203,91.9 4.46 10,742 H. 50
5.6 10,840 10.32 3,674 4.2 11,740 7.15 202,582 3.90 10,030 7.30
5.1 11,740 8.60 3,122 4.9 11,300 0.60 2.?6,344 3.45 10,92') 6.11
co
-------
TABLE A-3. DATA SETS
Data lot
Set Size,
No. 'Tons
116 2,1.08
2,280
•1,088
5,554
6,213
6,357
6,391
6, 494
6,762
6,952
7,143
7,344
7,350
7,354
7,465
7,634
7,645
7,649
7.672
7,674
7,702
7,704
7,741
7,851
7,914
7,974
7,981
8,053
8,119
8,169
8,176
8,310
8,413
8,488
8,584
8,627
8,766
8,896
(1,942
9,134
9,310
9,824
9,923
10,782
Total
Sulfur,
%
2.15
2.21
2.15
1.97
2.11
2.05
2.09
2.26
2.15
2.00
1.79
1.94
1.64
2.36
2.07
2.03
1.96
2.07
1.88
1.93
2.18
1.82
2.01
2.25
2.11
1.82
2.01
2.93
1.89
1.76
2.11
2.27
2.10
1.93
1.91
1.99
1.97
1.98
2.05
0.81
1.K9
1.55
1.82
1. 82
Dtu
Ib
11,562
11,192
11,181
11,161
11,356
11,171
11,030
10,951
10,859
1.1,329
11,538
11,607
11,253
11,247
11,432
11,565
11,467
1.1,523
11,466
11,732
12,833
11,328
11,540
11,326
11,5P9
11,769
11,317
10,833
11,616
11,708
11,272
11,279
11,609
11,321
11,692
11,386
11,481
11,329
1 1,117
11,782
11,757
11,643
11,615
11,493
Ibs SO
ToW
3.72
3.95
3.85
3.53
3.72
3.67
3.79
4.13
3.96
3.53
3.10
3.34.
2.91
4.20
3.62
3.51
3.42
3.59
3.28
3.29
3.40
3.21
3.48
3.97
3.64
3.09
3.55
5.41
3.25
3.01
3.74
4.03
3.62
3.41
3.27
3.50
3.43
3.50
3.69
1.37
3.22
2.66
3.13
3.17
Cata lot
Set Size,
No. 'tons
117 1,500
1,526
1,576
1,895
2,009
2,235
2,273
2,401
2,478
2,501
2,506
2,754
2,770
2,808
2,813
2,828
2,936
3,072
3,171
3,310
3,304
3,406
3,422
3,450
3,518
3,542
3,635
3,732
3,800
3,800
3,891
3,953
4,007
4, OK,
4,084
4,374
4,432
4,742
4,770
4,801
4,99.8
5,126
5,414
5,590
Total
Sulfur
%
3.09
3.01
3.14
3.42
2.83
3.30
3.06
2.97
2.92
3.07
3.53
2.82
.3.09
3.11
3.04
3.10
3.16
2.95
2.64
2.91
3.02
3.00
3.01
3.00
2.87
3.52
2.89
2.67
3.36
3.24
.3.51
2.86
2.72
2.94
3.60
3.25
3.01
2.75
3.12
3.31
3.39
2.99
3.27
3.29
, ntu
HE
11,445
11,191
10 , 889
10,976
11,200
11,345
11,034
11,162
11,574
11,132
10,398
10,849
11,137
11,206
11,106
11,420
11,141
10,972
11,105
11,308
11,312
11,375
11,490
10,118
10,898
11,259
11,271
11,257
11,000
10,656
11,182
10,938
11,199
10,903
1.0,976
11,10G
11,011
11,055
11,098
11,268
11,081
11,078
10,908
11,013
Ibs SO?
ioGntu
5.40
5.38 j
5.77 '
6.23
. 5.05
5.96
5.55
5.32
5.05
5.52
6.79
5.20
5.55
6.09
5.47
5.43
Data lot
Set Size,
No. Tons
118
-
-
-
-
119
-
-
-
-
120 LI, 269
10,160
10,137
10,380
10,285
10,437
5.67 ] 10,769
5.38 10,284
4-75 10,254
5-15 io,112
5.34 1 10,202
5.27 io,177
5.24 10,704
5.93 10,4110
5.27 9/r,27
("'•25 9,065
5.1,3
4.74
6.11
6.08
6.28
5.23
4.86
5.39
6.56
5.8r,
5.47
4. 98
5.62
5.88
6.12
5.40
6.00
5.97
9,145
10,016
10,526
10,292
10,463
10,297
10,143
10,740
10,471.
Total
SII.I.CIIK
%
1.20
0.92
0.82
0.61.
1.10
2.80
2.24
1.84
1.46
1.38
0.90
1.20
1.51
1.74
1.98
1.76
2.34
1.29
l.OU
1.89
1.22
1.41
0.9B
1.62
1.95
1.18
1.38
0.98
1.39
1.78
1.16
1.52
0.83
1.92
2.33
, IJ tu
ll>
10,834
10,377
9,77.1
9, 1(12
9,752
13,485
12,879
12,102
12,657
13,629
11 , 287
11,41)9
11,006
1.1,126
11,053
10,987
11,300
11,592
11,5')4
11,370
ll,38f.
11,407
11,629
11,585
1.1, 4. 12
11,657
1.1,345
11,663
11,709
11,120
1.1,581
11., 518
11,848
11,019
1.1,150
Ibs SO,
.10 6 Illu
2.21
1.77
1.68
1.33
:p.25
4. 15
3.48
3.04
2.30
2.02
1.50
2.09
2.74
3.12
3.58
3.20
4. 14
2.22
1 . »r,
3.3:-!
2. 14
2.47
1.68
2.79
3. 19
2.02
2.43
1.68
2.37
3.20
2.00
2.63
1.40
3.4H
4. L8
-------
TABLE A-4. DATA SETS
Data
Set
No.
121
lot
Size,
Tons
18,889
30,903
17,362
13,442
23,145
10,574
18,169
10,921
6,004
16,925
29,162
24,219
14,619
5,777
14,691
20,468
6,007
22,728
31,152
17,662
8,100
7,998
22,065
18,100
Total
Sulfur,
%
3.79
3.74
3.94
3.99
3.88
3.66
3.71
3.78
3.69
3.74
3,90
3.40
3.69
3.34
3.69
3.59
3.80
3.72
3.76
4.01
4.15
3.85
3.72
4.07
Btu
Ib
12,364
12,507
12,629
12,740
12,831
12,974
12,978
12,545
12,727
12,610
12,630
12,400
12,477
12,330
12,477
12,435
12,247
12,273
12,616
12,597
12,692
13,092
12,510
12,314
Ihs S02
10bBtu
6.12
5.98
6.23
6.26
6.04
5.64
5.71
6.02
5.79
5.93
6.17
5048
5.91
5.41
5.91
5.77
6.20
6.06
5.96
6.36
6.53
5.88
5.94
6.60
A-5
-------
TABLE A-5.DATA SETS
nit.a lot
Set Size,
No. Ibus
201 203,873
179,374
209,200
201,994
293,460
1913,878
202 6,810
6,548
5,502
6,603
6,404
6,613
6,120
6,841
6,761
6,556
6,517
6,129
6,7R4
6,418
5,9<13
6,459
6,687
6,575
6 , 607
6,762
6,714
6,271
6 , 259
6,407
203 124,662
116,037
10.1,978
91,848
90,102
75,501
Total
Sulfur, Dtu Ibs SO2
% Ib. 10''Btu
3.21 13,052 4.91
3.23 13,063 4.94
3.24 13,030 4.97
3.14 12,927 4.85
3.13 12,977 4.82
3.18 12,956 4.90
3.20 1.3,026 4.91
3.22 13,062 4.93
3.39 13,071 5.10
2.89 13,145 4.39
3.30 13,051 5.05
3.16 .13,118 4.81
3.15 .13,052 4.82
3.19 13,095 4.07
3.34 13,015 5.13
3.11 13,084 4.75
2.95 13,044 4.52
3.02 12,883 4.68
3.30 12,927 5.10
3.12 12,959 4.01
3.38 12,978 5.20
3.30 12,899 5.11
3.27 12,947 5.0S
2.89 13,039 4.43
3.10 12,944 4.79
3. 20 12,936 5.07
3.04 12,956 4.69
3.24 12,887 5.02
3.30 12,924 5.23
2.97 13,047 4.55
3.40 13,021 5.22
3.40 12,887 5.27
3.36 12,995 5.17
3.30 12,993 5.07
3.35 12,954 5.17
3.38 12,988 5.20
Tata rot
Set Size,
No. -tons
204 10,498
19,6f>f,
22,867
17,399
26,023
24,458
21,620
4,177
12,558
18,030
23,770
0,209
24,577
15,878
9,006
30,906
26,560
13,407
17,816
21,954
10,340
2C,OOS
13,840
13,0139
10,960
205 1^4,662
116,037
101,978
91,848
90,102
75,501
'Ibtal nnta lot Total
SulEur, Btu Ibs S Set Hizo, Sul.Eur, yj_u H'S M)^
% .lh To^'n- Mo. Tons ' "I'' I"* lUii
3.32 13,075 5.07 206 2,912 3.99 11,937 f,.r,H
3.38 13,1.59 5.13 5,721 3.79 12,044 6.2')
3.32 12,996 5.10 5,094 4.05 12,074 6.70
3.54 12,944 5.46 5,696 3.91 12,107 6.4r,
3.30 12,930 5.10 5,554 3.57 u,2V> 5.03
3.<,5 12,898 5.34 1,378 4.27 11,552 7.19
3.39 12,924 5.24 4, 205 3.67 12, 21 11 6.00
3.26 13,133 4.96 2,800 3.42 12,037 5.68
3.35 13, (,65 5.12 2,868 3.84 1.2,022 6.3H
3.51 12,094 5.44 2,830 3.00 12,397 6.12
3.29 12,891 5.10 1,434 3.77 ]J/J63 fi. 10
3.25 13,001 4.99 l(374 3.87 ]lfr)27 G.7]
3.24 13,026 4.97 2,051 3.99 11,937 6.60
3.42 12,901 5.30 2,925 4.32 12,403 f,.'i6
3.18 13,107 4.85 8,734 3.70 12,30') 6.01
3.29 12,989 5.06 2,787 3.69 12,103 6.09
3.21 12,969 4.95 2,860 3.72 1.2,070 6.15
3.32 12,935 5.13 2,834 3.96 12,171 6.50
3.67 12,919 5.60 If4f)0 3. ;B U,979 6. VI
3.41 12,930 5.27 1,428 3.71 12,042 6.16
3.55 13,057 5.4.3 4,263 3.09 11,94') 6.r,l
3.24 12,980 4.99 9,959 3.89 12,226 6.34
3.34 12,954 5.15 r)(703 3-Vr) 12,051. 6. 23
3.49 12,924 5.40 4,720 4.05 12,01.7 6.73
3.39 13,091 5.17 207 237,056 4.40 12,297 7.15
3.31 12,552 5.27 244,514 4.34 1.2,2711 7.06
3.39 12,495 5.42 251,592 4.44 1.2,370 7.1.7
3.29 12,633 5.20 226,517 4.46 12,320 7.23
3.20 12,689 5.04 242,190 4.42 12,267 7.20
3.15 12,692 4.96 197,603 4.29 12,292 6.97
2.97 12,832 4.62
cr\
-------
TABLE A-6. DATA SETS
Data l>ot
Set Size,
No. Tons
208 2,006
2,626
1,023
4,201
6,070
8,361
5,463
2,790
7,983
5,652
6,837
4,060
2,621
r.,598
7,015
1,388
7,961
2,047
5,231
1,353
9,864
2,844
2,798
5,675
1,426
1,395
Total
Sulfur, utu
% ~Tb
•4.2'J 12,215
4.20 12,171
4.15 12,115
4.13 12,300
3.96 12,162
4.04 12,085
4.03 12,099
4.31 11,934
4.08 12,134
4.04 11,805
4.12 12,284
4.10 12,001
4.00 12,105
4.08 12,192
3.87 12,109
3.99 12,232
4.15 12,279
4.09 12,271
4.24 12,421
4.20 11,991
3.83 12,016
3.98 11,896
4.25 11,671
4.28 12,074
3.55 11,831
3.44 12,622
Ibs SO;
10"Btu
7.02
6.90
6.04
6.71
6.51
6.60
6.66
7.22
6.72
6.84
6.70
6.83
6.60
6.69
6.39
6.52
6.75
6.66
6.82
7.00
6.37
6.69
7.28
7.08
6.00
5.45
Data lot
Set Size,
Mo. Tons
209 7,150
6,230
6,02.3
5,444
5,972
6,255
5,906
6,556
5,720
5,817
5,964
6,597
6,260
6,099
5,974
8,067
7,498
6,570
6,196
6,224
5,972
6,258
6,1.43
5,081
6,252
210 4,17/J
4 , 269
4,356
4,219
4,464
4,402
4,444
4,307
4,383
4,367
4,593
4,1.29
4,018
2,755
4,147
4,139
4,291
4,395
4,290
4,345
4,109
4,2P5
4,351
4,200
4,375
Total Data Lot Total
Sulfur, Ctu His SO2 Set Size, Sulfur, utu Ibs SO,
% lb 10" Btu No. 'lions % Ib i')^m.u
2.45 12,930 3.78 211 150,234 3.64 12,073 6.02
2.79 12,844 4.34 315,719 3.93 12,073 6.50
2.56 12,902 3.96 295,914 3.83 12,011 6.37
2.76 12,873 4.28 320,532 3.94 12,047 6.53
2.69 12,880 4.17 294,042 3.83 12,059 6.35
2.46 12,712 3.87 246,346 3.71 1.2,032 6.46
2.68 12,715 4.21 237,056 4.40 12,297 7.15
2.84 1.3,119 4.33 244,514 4.34 12,270 7.06
2.54 12,471 4.07 251,592 4.44 .12,370 7.1.0
2.96 12,652 4.67 226,517 4.46 12,320 7.23
2.76 12,802 4.31 242,190 4.42 12,267 7.20
2.84 12,895 4.40 197,683 4.29 12,292 6.97
2.73 12,851 4.24 212 170,413 3.03 1.2,494 4.85
3.04 1.2,754 4.76 152,329 2.86 12,464 4.50
3.27 12,742 5.13 178,680 3.06 12,462 4.91
2.95 12,439 4.74 159,949 3.05 12,443 4.90
2.81 12,674 4.43 208,650 3.06 12,465 4.91.
2.96 12,752 4.64 179,994 2.99 12,420 4.81
2.97 12,631 4.70 213 9,829 2.07 12,459 4.60
2.67 12,707 4.20 1.0,558 3.27 12,439 5.25
2.75 12,376 4.44 10,402 3.02 12,425 4.86
2.68 12,596 4.25 10,072 2.0') 12,536 4.61
2.69 12,808 4.20 9,731 2.84 12,470 4.55
2.45 12,981 3.77 10,521 3.01. 12,503 4.01
2.84 12,849 4.42 10,292 2.96 12.390 4.77
3.12 12,997 4.00 10,565 2.66 12,530 4.24
3.35 13,011 5.14 1.0,467 3.0L 12,467 4.82
3.20 13,131 4.07 9,990 2.99 12,453 4.00
3.20 13,094 4.88 1.0,002 2.79 12,588 4.43
3.45 12,835 5.37 .10,610 3.12 12,392 5.03
3.13 12,900 4.82 10,508 3.05 12,412 4.91
3.36 13,020 5.16 10,336 3.15 12,354 5.09
3.29 13,035 5.04 10,000 2.08 12,430 4.63
3.51 13,011 5.39 P 10,532 3.20 12,365 5.17
3.51 1.3,06.3 5.37 1 10,534 3.09 12,281 5.01
3.65 12,968 5.62 9,842 3.10 12,430 4.98
3.05 13,157 4.63 ' 10,069 3.02 12,365 4.00
3.44 13,034 5.27 . 10,447 3.02 12,370 4.00
3.35 13,070 5.12 9,799 2.85 12,44S 4.57
3.34 12,970 5.15 ' 10,205 2.96 12,495 4.73
3.43 13,061. 5.25 10,078 2.76 12,474 4.42
3.28 13.187 4.97 • 10.6K6 2.83 12,430 4.55
3.35 13,059 5.16
3.29 12,982 5.06 .
3.34 12,823 5.20
3.42 12,934 5.28
3.32 12,934 5.13
3.35 12,800 5.23
3.43 12,095 5.31
3.41 17,779 5.33
-------
TABLE A-7. DATA SETS
llnta lot
Set Size,
NJ. Tais
214 13,1.15
14,897
15,428
24,:>17
9,580
18,826
28,960
17,473
11,551
32,901
15,247
15,815
11,800
24,806
10,042
7,169
13,873
8,512
4,3J2
17,981
28,434
25,009
15,] 32
15,248
10,906
215 2,570
589
2,373
4,079
1,587
2,277
868
2,405
2,729
1,522
2,57f,
481
2,576
4,962
.1,547
1,303
2,055
1,566
1,984
615
4,996
2,350
1,374
1 ,472
2,733
'total
Sulfur,
0
2.87
2.20
2.40
2.56
2.22
2.77
2.77
2.82
2.80
2.82
2.25
2.24
2.47
2.83
2.78
2.78
2.78
2.34
2.24
2.28
2.58
2.77
2.51
2.74
2.79
3.13
3.84
3.54
3.23
3.44
3.60
3.57
3.65
3.42
3.53
3.40
3.49
3.42
3.36
3.33
3.50
3.1.8
3.65
3.65
3..41
3.39
3.39
3.55
3.54
3.52
11 tu
Tb
12,932
12,716
12,757
12,660
12,723
12,801
12,702
12,638
12,683
12,714
12,781
12,568
12,638
12,733
12,598
12,554
12,751
12,636
12,569
12,625
12,565
12,541
12,653
12,722
12,580
12,917
12,731
12,906
12,862
12,724
12,776
12,792
12,853
12,536
12,576
12,573
12,825
12,897
12,839
12,92.r,
12,413
12,762
12,694
12,738
12,620
12,474
12,635
1.2,719
12,906
12,757
Ibs S07
10" Btu
4.43
3.46
3.76
4.04
3.49
4.32
4.36
4.46
4.41
4.43
3.52
3.56
3.91
4.44
4.41
4.42
4.36
3.70
3.56
3.61
4. in
4.41
3.96
4.30
4.43
4.84
6.03
5.48
5.02
5.40
5.63
5.58
5.67
5.4.r.
5.61
5.40
5.44
5.30
5.13
5.r
5.63
4.98
5.75
5.73
5.40
5. '4 3
5.36
5.58
5.48
5.51
Data Lot
Set Size,
No. Tons
216 900
5,700
9,667
2,866
3,825
1,075
5,925
5,400
5,775
6,450
7,650
5,625
5,925
3,450
6,450
4,575
4,575
6,450
5,850
6,600
5,100
5, 100
4,800
8,475
5,925
217 2,221
5,759
5,712
2,025
1,664
4,003
3,873
4,342
5,800
4,466
5,455
2,820
2,207
1,294
5,213
5,835
7,504
4,859
7,732
4,344
4,483
6,033
5,674
6,614
6,420
'Ibtal
Sulfur,
%
4.28
3.38
3.UO
4.08
3.49
3.76
3.69
3.75
3.68
3.90
3.84
4.00
3.7?
3.95
3.R5
3.67
3.86
4.01
3.62
3.51
3.4'l
3.63
3. 71
3.53
3.57
3.34
2.34
2.99
2.91
3.18
2.97
2.36
2.55
2.75
2.86
2. 55
.?. 66
3.16
2.97
3.27
2.67
3.3fl
?.r>7
T.14
3.00
3.26
2.8)
2.95
2.90
3.01
13 til
lb
12,652
.12,549
12,509
12,380
]2,61l
12,738
12,688
12,599
12,766
12,702
12,735
12,803
12,41.5
12,395
12,652
12,707
12,693
12,665
12,543
12,662
12,513
12,636
12,569
12,778
12,538
.1.2,650
12,461
12,373
12,3.36
12,142
12,473
12,603
12,667
12,484
12,606
12,729
12,700
12,923
12,741
12,567
1.2,706
.12,627
1.2,183
12,584
12,593
12,314
12,441
12,058
12,440
12,353
Ibs SO2
i.O'-Ulu
6.76
5.38
6.07
6.59
5.53
5.90
5.81
5.95
5.76
6.10
6.02
6.24
5.99
6.37
6.08
5.77
6.08
6.33
5.77
5.54
5.57
5.74
5.90
5.52
5.09
5.28
3.75
4.83
4.71
5.23
4.76
3.74
4.02
4.40
4.53
4.00
4.19
4.118
4.66
5.20
4.20
5.22
4.87
4.99
4.76
5.29
4.51
4.89
4.60
4.87
Data U>t
Set Size,
No. T-TIIS
218 29,086
31,875
45,584
54,055
65,572
51,656
65,654
54,053
63,352
54,144
31,839
8,861
55,367
40,727
61,182
44,064
49,681
55,536
47,273
73,512
78,538
53,775
41,351
43,733
79,239
•njl.nl
Sulfur,
?i
2.90
2.43
2.54
2.62
2.55
2.58
2.65
2.56
2.58
2.60
2.56
2.72
2.54
2.70
2.53
2.69
2.57
2.63
2.69
2.55
2.39
2.44
2.41
2.42
2.85
JiUJ
Ih
12,250
12,200
12,060
12,171
12,086
12,070
12,1.20
12,146
12,169
12,138
12,1.92
12,409
12,376
12,301.
12,397
12,308
12,453
.12,403
12,359
12,324
12,374
12,362
12 , 267
12,228
12, KG
]bs :u>z
TO^HLii
4.73
3.98
4.21
4.30
4.22
4.27
4.37
4.21
4.24
4.30
4.20
4.38
4. 10
4.39
4.08
4.37
4.12
4.24
4.35
4.1 \
3.06
3.94
3.93
3.95
4.69
CO
-------
TABLE A-8. DATA SETS
Data Lot
Set Size,
yo. Ttons
219 45
1,737
1,916
3,102
3,161
3,373
4,471
4,473
4,673
5,240
5,505
5,616
5,931
6,292
6,307
6,982
7,016
7,165
7,467
7,517
7,658
7,749
8,109
3,173
8,473
3,536
3,602
8,611
3,733
3,362
9,030
9,045
9,131
9,177
9,914
9,961
9,934
9,989
10,040
10,198
10,206
10,444
11, 1«0
11,233
12,100
13,314
Total
Sulfur,
%
1.57
1.44
1.75
1.92
1.59
1.88
1.48
1.36
1.31
1.44
1.57
1.53
1.63
1.60
1.64
1.53
1.45
1.73
1.5.
1.55
1.44
1.49
1.58
1.85
1.77
1.45
1.93
1.72
1.33
1.45
1.50
1.74
1.64
1.54
1.70
1.57
1.47
1.90
1.70
1.80
2.01
2.05
2.01
1.31
1.30
1.62
Stu
li
12,818
12,641
13,040
11,518
11,745
12,419
12,524
12,196
12,860
12,726
12,913
12,065
12,528
12,233
12,173
12,439
12,909
12,446
12,539
12,211
12,972
12,441
12,686
12,316
12,661
12,555
12,340
12,109
12,235
11,783
12,003
10,977
12,262
12,643
12,636
12,675
12,577
12,315
12,706
12,152
12,400
12,010
12,204
11,327
11,912
11,432
Ibs S02
10'Btu
2.45
2.28
2.68
3.33
2.71
3.03
2.34
2.23
2.81
2.26
2.43
2.6?.
2.50
2.62
2.59
2.62
2.25
2.78
2.40
2.70
2.: 22
2.40
2.49
3.00
2.80
2.31
3.13
2.34
2.26
2.46
2.50
3.17
2.67
2.44
2.68
2.48
2.34
3.09
2.68
2.96
3.24
3.41
3.29
3.06
3.02
2.33
Data Lot
Set Size,
>!o. Tons
220 5,760
3,120
3,920
3,920
6,400
2,320
221 1,050
4,720
4,560
6,380
4,240
4,320
4,640
5,360
7,200
4,560
3,791
4,260
9,108
2,374
5,340
8,240
6,300
8,889
222 2,700
2,700
2,700
2,700
2,700
223 640
640
640
640
540
Total
Sulfur,
%
3.79
3.31
4.16
4.95
J.94
4.66
4.35
4.30
4.57
4.45
4.97
4.14
3.97
4.48
4.72
4.37
4.46
5.14
4.14
3.78
4.73
3.85
4.01
5.31
1.43
' 1.31
0.39
1.06
1.10
1.11
1.20
1.22
0.92
0.99
Stu
1J3
12,455
12,170
12,276
12,126
11,972
12,715
12,486
12,575
12,932
12,497
12,983
13,093
12,903
D,039
12,747
12,626
12,739
12,324
12,931
12,913
12,577
12,546
12,906
12,710
14,591
14,449
14,260
14,428
14,624
14,622
14,249
14,146
14,392
14,435
Ibs SO,
10sBtu
6.02
5.43
6.77
3.16
6.53
7.32
6.96
7.63
7.06
7.11
7.65
6.32
6.15
6.37
7.40
6.92
7.00
3.01
6.40
5.85
7.51
6.13
6.21
8.35
2.03
1.31
1.25
1.47
1.50
1.52
1.68
1.72
1.14
1.37
A-9
-------
APPENDIX B
DETAILED CHI-SQUARE ANALYSIS
(N.-E.)'
E.
N. = Cbserved frequency in group i
e. = Theoretical (normal distribution) frequency in group i
r = Number of Groups
f = Degrees of freedon = r-3, when both Y and S
are estimated from the data. ^
B-l
-------
Table n.l. DATA SET C-8, 275 DATA POIN'IV,.
CO
Y-Y
SV
-1.75
-1.50
-1.25
-1.00
-0.75
-0.50
-0.25
Onn
• \j\i
0.25
-.50
0.75
i nn
-L • UU
1.25
i ^n
J. • ^U
1.75
-(. ro
Group
i
1
2
3
4
5
6
7
0
9
10
11
12
13
14
15
16
Theoretical
Frequency, e.
11.0275
7.3425
10.6700
14.6025
18.6725
22.5225
25.5200
27.1425
27.1425
25.5200
22.5200
18.6725
14.6025
10.6700
7.3425
11.0275
Observer! Frequency, N^
Y, log Yi ^Y, Yj log Y2 .''YT Y3 log Y3 A',
12 15 12 1.5 15 15 5 6 f,
75 8 If. 15 15 35 4
10 9 9 19 18 18 11 1.1 1.0
11 11 11 lit 19 19 19 17 19
11 11 11 15 14 15 26 25 25
23 23 23 10 11 10 30 2R 20
33 21 2.1 1 11 34 33 34
27 39 39 3 22 27 23 23
24 24 24 5 66 1.8 22 22
37 37 37 38 35 38 24 26 24
27 27 27 54 61 56 20 18 20
14 14 14 67 70 70 13 14 12
11 11 11 15 8 10 12 14 14
15 20 20 0 00 10 10 10
10 5 50 00 99 9
33 30 0 0 14 14 14
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Table D.2. IJTCTA SET
, 250 IOTA ItUNIS.
U)
Y-Y
sy
_ tn
-1.75
-1.50
-1.25
-1.00
-0.75
-0.50
-0.25
0.00
Ope;
.
-------
Table D.3. DftTA SET C-3, 115 DATA POINTS.
V
Y-Y
sy
_ 00
-1.27
-1.00
-0.75
-0.50
-0.25
0.00
0.25
0.50
0.75
1.00
1.25
Group
1
1
2
3
4
5
6
7
8
9
10
11
12
Theoretical
Frequency, e.
12.1440
6.1065
7.8085
9.4185
10.6720
11.3505
11.3505
10.6720
9.4185
7.8085
6.1065
12.1440
Oiserved Frequency, N.
Yi log Y| ^Y7 Y2 log Y2 *^7 Yj loj Y3 •'57
8 11 88 78 99 9
63 66 65 65 6
10 10 10 4 45 11 12 11
12 12 12 12 10 11 11 9 10
10 10 10 16 17 16 9 10 9
14 14 14 7 98 10 10 11
12 7 12 11 11 11 14 13 14
9 12 9 15 16 15 11 13 11
11 7 5 12 13 14 11 11 11
4 15 10 1.1 11 9 11 11 13
87 85 40 44 4
11 7 11 8 77 88 8
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. 3EPORT NO.
EPA-600/7-80-107
2.
3. RECIPIENT'S ACCESSION NO.
J. TITLE AND SUBTITLE
Effect of Physical Coal Cleaning on Sulfur Content
and Variability
5. REPORT DATE
May 1980
6. PERFORMING ORGANIZATION CODE
7. AUTHORIS)
D.H.Sargent, B. A. Woodcock, J.R. Vaill, and
J. B.Strauss
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Versar, Inc.
6621 Electronic Drive
Springfield, Virginia 22151
10. PROGRAM ELEMENT NO.
EHE623A
11. CONTRACT/GRANT NO.
68-02-2136, Task 300
12. SPONSORING AGENCY NAME AND ADDRESS
F. REPORT AND PERIOD COVERED
EPA, Office of Research and Development
Industrial Environmental Research Laboratory
Research Triangle Park, NC 27711
11 TYPE OF. REPORT AND PERIOD
Task Final; 6/78-4/80
14. SPONSORING AGENCY CODE
EPA/600/13
is. SUPPLEMENTARY NOTES T£RL-RTP project officer is James D. Kilgroe, Mail Drop 61,
919/541-2851.
16. ABSTRACT
rep0rt gjves results of a statistical analysis of the sulfur content and
heating value data for 53 different coal-source/cleaning-plant combinations , both to
document the operational effectiveness of commercial coal cleaning plants in redu-
cing sulfur and enhancing heating value, and to define the effect of physical coal
cleaning on sulfur variability. Cleaning plants , for which matched pairs of feed and
product coal data were available, showed 24-50% reductions (from feed to product)
in the mean Ib SO2/million Btu. These empirical data are consistent with the calcu-
lated performance of hypothetical coal cleaning plants. The wide ranges reflect the
sensitivity of performance to both coal washability and plant design. These matched
pairs of data showed a 60% reduction in sulfur variability. An indirect analysis of
a larger data base, where matched pairs were not available, showed similar sulfur
variability reductions , attributable to physical coal cleaning. Much of the coal data
showed serial autocorrelation, verifying expectations based on geology and engineer-
ing rationale. Data analysis resulted in estimates of the long-term (geostatistical)
and short-term components of variability, and in the component of variability attri-
butable to coal sampling and analysis. Removing the long-term component empiri-
cally showed an inverse relationship between relative standard deviation and lot size.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
COSATI Field/Group
Pollution
Coal Preparation
Sulfur
Desulfurization
Variability
Calorific Value
Pollution Control
Stationary Sources
Physical Coal Cleaning
Sulfur Content
13B
081
07B
07A,07D
14G
20M
13. DISTRIBUTION STATEMENT
Release to Public
19. SECURITY CLASS (This Report)
Unclassified
21. NO. OF PAGES
93
20. SECURITY CLASS (This pagef
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
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