United States
Environmental Protection
Agency
Industrial Environmental Research
Laboratory
Research Triangle Park NC 27711
Research and Development
EPA-600/S7-83-055 Feb. 1984
Project Summary
Variability and Correlation in Raw
and Clean Coal: Measurement
and Analysis
B. Cheng, K. Crumrine, A. Gleit, A. Jung, D. Sargent, and B. Woodcock
The ability of a coal to comply with an
emission regulation depends on a
statistical appraisal of the coal sulfur
content and heat content determined
by random spot or composite sample.
Previous studies of the ability of coal to
comply with emission regulations have
been hampered by inadequacies in the
coal sampling method sets which can
be used to statistically characterize the
variations in coal properties. In this
project coal samples were collected at
1/2- or 1 -hour intervals at the inlet to, and
outlet from, two coal preparation plants
(R&F Coal Company and Republic
Steel Corporation). Coal samples from
the plants were analyzed for total
sulfur, pyrite sulfur, heating value, ash
content, and moisture. Values for the
organic sulfur and SO2 emission param-
eter (lbSO2/106Btu) were calculated with
ASTM or equivalent procedures. The
sample data were evaluated statistically
to determine the mean value, variance,
relative standard deviation (standard
deviation -r mean), correlation struc-
ture, and skewness. The correlation
structure was evaluated by time-series
and geostatistic techniques. Time-
series techniques proved the most
useful.
From this the coal cleaning processes
at the R&F and Republic plants reduced
the mean SO2 emission parameter by
about 23 and 63 percent, respectively.
The relative standard deviation (RSD)
of the SOa emission parameters were
reduced by 26 and 44 percent, respec-
tively. Differences in the reductions in
mean and RSD values between plants
resulted primarily from differences in
the raw coal properties.
For much of the data acquired in this
study, strong autocorrelation was
indicated. The 30-minute increment
data were more highly autocorrelated
than composite data collected over
longer time intervals.
Currently used time-series models
were used to estimate the average
number of emission violations produced
by a power plant burning the R&F coal
(either raw or cleaned) using old
procedure. For an emission limit 2.5
standard deviations greater than the
mean, and for a 24-hour averaging
time, the time series models predicted
12 violations per year for raw coal and
49 for clean coal. Under these circum-
stances the expected number of viola-
tions for clean coal is higher than that
for raw coal because of the stronger
reliance on autocorrelations used in the
clean coal model. These violation
frequencies are much greater than the
two violations per year that would be
predicted from (erroneous) assumption
of serially independent coal data. These
model results show the importance of
considering the effects of autocorrela-
tions when estimating the potential for
emission limit exceedance with raw or
cleaned coal.
This Project Summary was developed
by EPA's Industrial Environmental
Research Laboratory, Research Triangle
Park. NC, to announce key findings of
the research project that is fully docu-
mented in a separate report of the same
title (see Project Report ordering
information at back).
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Introduction
Previous studies, to determine if a coal
complied with SOz emission limits, were
based on Gaussian statistics that assume
an independently varying sulfur and
energy content in coal. Accordingly, the
time sequence of the data was ignored,
and a distribution curve was used to
determine the mean coal sulfur value that
ensures compliance. Recent studies
indicate that this method may be inappro-
priate for handling coal data.
These recent studies, however, were
hampered because the data sets did not
form logically consistent or homogeneous
populations sufficient for rigorous statisti-
cal analysis. Indeed, much of the reported
data were mixed with respect to location,
mining method, cleaning method, samp-
ling frequency and procedure, methods of
compositing or averaging, definition of a
"lot" of coal and the nominal lot size, and
analytical laboratory precision. The data
sets consisted of coals from different
regions, seams, and mines, with inherent
geological and engineering differences.
Furthermore, the data sets did not
necessarily represent their respective
regions or seams.
Prior studies were also hampered by
the commercial practice of compositing
samples and reporting data for relatively
large quantities of coal. The relative
paucity of data for short time increments
(i.e., small coal quantities) has made it
difficult to observe and analyze the
components of coal variability.
Because of these inherent comparability
problems in studying available data that
were originally acquired for quite different
objectives, prior studies led to only a
rough picture of coal sulfur variability.
This study, featuring intensive sampling
and analysis at selected Coal cleaning
plants, was designed to overcome the
data deficiencies of prior studies.
Objectives of the Study
This program was a controlled experi-
mental study to accurately collect and
analyze representative samples of raw
and clean coal. By using the same
sampling procedures, sample preparation
procedures, and laboratory analysis
methods for both raw and clean coal
samples, representative composite sam-
ples of different size lots provided a
measure of correlation and variability in
the coal sources tested and of the
attenuation of sulfur variability from coal
preparation plants.
The study had the following major
objectives:
1. To measure and evaluate the re-
duction of variability of sulfur and
heating value of raw versus clean
coal by collecting and analyzing
samples of raw and clean coal at two
commercial plants.
2. To measure and quantify the ob-
served variance of sulfur, heating
value, and ash associated with the
day-to-day changes in raw and clean
coal and the variance associated
with sampling, sample preparation,
compositing, and analysis of raw
and clean coal; i.e., measurement
uncertainty.
3. To evaluate the relationship between
serial correlation and variability by
determining if the measured param-
eters in sequential coal samples
are random and, if they are not, to
separate the variability of the param-
eters into correlated and random
components.
4. To determine the relationship be-
tween lot size and variability.
General Characteristics of Coal
Data
Because of the nature of coal formation,
there is some structure (as opposed to
complete randomness) in the properties
of a coal deposit. Superimposed on this
structure is a certain amount of random-
ness. Thus, if samples are taken from a
deposit, the statistical treatment of these
data should recognize both structural and
random characteristics of the samples.
Mining transforms the spatial charac-
teristics of coal into a time sequence of
varying coal properties. Alternative
mining approaches or schemes within the
same deposit provide different time
sequences of potential sulfur emissions.
These sequences are subsequently
modified by coal preparation, coal trans-
portation, coal blending and sulfur
emission control. Moreover, the sequence
for one coal data set cannot be assumed
to be applicable to other coals.
Coal fired utility plants burn raw
(unwashed) coal, clean (washed) coal, or
a blend of the two. Variability in sulfur
content of these coals can produce
variability in the level of emissions from
the utility stack. The components of
variability in coal relate to (1) variability
within any one source of coal, (2)
variability between the sources of coal
being studied, (3) variability associated
with sample collection and laboratory
analysis, and (4) variability with different
size lots of coal.
The autocorrelation properties of coal
data are important and must also be
evaluated. Ignoring them may result in
incorrect statistical models that lead to
errors in decisions on the ability of a coal
to comply with SOz emissions regulations.
Important Statistical Properties
Three statistical measures are impor-
tant in evaluating coal sulfur data: (1)
mean value; (2) variance, a measure of
the data spread; and (3) autocovariance or
autocorrelation, the statistical relationship
of data points to other data points in the
same time (or space) series.
The usefulness of autocovariance or
autocorrelation is in forecasting future
data from past data. Small autocorrelations
may indicate that the correlations between
past and present values are small, and so
past data provide little useful information
in predicting future events. If the autocor-
relation is large, it is essential to
determine the time dependent effect of
events through modeling in order to
predict future trends. Once these trends
have been forecast, the variance can be
used to estimate their accuracy.
Experimental Approach and
Procedures
Raw and clean coal samples were
collected from the R&F Coal Company
and Republic Steel Corporation coal
preparation plants so that hour-to-hour
and day-to-day changes in the coat
characteristics could be monitored.
These samples were collected and
analyzed consistently during the study,
using standard techniques so that the
variance associated with sampling and
analysis would not mask the coal charac-
teristics. The data sets produced were of
suitable size to allow application of
Gaussian statistics, geostatistics, and
time series analysis.
At the R&F plant, the feed and product
conveyors were equipped with automatic
sampling systems. The raw coal primary
sampler took periodic cross-stream cuts
of the 4-in.* x 0 feed material, reduced it to
28 mesh x 0 in a hammermill crusher, and
split it again through the secondary
sampler. The sample collection vessel
was left in place for 8 production hours to
collect composites; the vessel was removed
every 30 minutes during intensive study
periods. The clean coal sampling system
was similar to the feed system except the
clean coal being sampled had a topsize of
2 in. x 0. Both primary samplers were
*EPA policy is to use metric units; however, non-
metric units are used here for convenience.
Readers more familiar with the metric system
may use the conversion factors at the back.
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programmed to take cross-sectional cuts
every 6-7 minutes.
The sampling scheme used at the R&F
plant was designed to provide as much
information on the characteristics of
varying lot sizes as possible. Samples
were collected at 30-minute increments
during two intensive efforts for 22 and 40
hours, respectively. Concurrently, 8-hour
composites were collected during the
entire study period. The sampling frequen-
cies and time composites represent clean
coal lot sizes based on an average 660
tons/hour production rate. Therefore, a
30-minute increment sample represents
a 330 ton lot, an 8-hour composite
represents 5, 280 tons of clean coal, and
a weekly composite is equivalent to a
48,000 ton lot size.
At the Republic plant, the feed and
product conveyors were equipped only
with primary sampling devices. Unlike
the R&F system, the samplers at Republic
consisted of a cutter which emptied the
material into a hopper for acquisition. The
sampler was activated manually through
a relay control mechanism. The size of the
sample was proportional to the amount of
coal on the belt. Normally, the cross-
stream cuts produced 200 Ib of sample
material. No crushing took place during
the cleaning operation; therefore, the
topsize of both the feed and product coals
was 1 -1/2 in. x 0.
The sample scheme used at the
Republic plant was designed to provide as
many samples or data points as possible
during a production day. Samples were
collected hourly during the first and
fourth weeks, and on the half-hour during
the second and third weeks. The data can
therefore be compiled to represent hourly
samples for a continuous 4-week period
and half-hour samples for a continuous
2-week span.
Based on the average clean coal
production rate, hourly samples represent
458 tons of coal, a daily composite (6.4 hr)
represents 2,932 tons, and a Weekly
composite is equivalent to 14,663 tons of
clean coal.
Results
For much of the data acquired in this
study, strong autocorrelation was indica-
ted. The 30-minute increment data from
the R&F plant were more highly autocor-
related than composite data over longer
time intervals. The data from the Republic
plant exhibited weaker autocorrelation
than the R&F data. However, results from
both plants confirm that serial correlation
of coal data does exist over short time
intervals.
Two analytical techniques were used to
quantify the correlated and random
components of the variability in coal data:
geostatistics and time-series analysis.
Time-series models can be used predic-
tively to generate data sets much longer
than the empirical (measured) data set.
The random component in the predictive
model is obtained from a random number
generator. Since a time series model is
probabilistic, many different time series,
equally likely, may be generated, all
based on the same mean, same variance,
and same correlation structure. From
many time series based on models for one
raw and one clean coal data set from the
R&F plant, the average number of
emission violations by a power plant
burning this coal (either raw or cleaned)
was determined.
For an emission limit 2.5 standard
deviations greater than the mean, and for
a 24-hour averaging time, 12 violations
per year were predicted for raw coal and
49 for clean coal. These violation
frequencies are much greater than the
two violations per year predicted from the
(erroneous) assumption of serially indepen-
dent coal data. It should be emphasized
that the prediction of violations for the
time-series or Gaussian model is derived
from the same mean and variance values for
the coal.
5000
Histograms were constructed for the
raw and clean coals, based on the
measured R&F coal data and using the
time-series predictive model (see Figures
1 and 2). Each figure shows two emission
limits: (1) the limit considered achievable
for this coal (2.5 standard deviations
above the mean), assuming that the value
of each data point is not dependent on the
value of any other data point as indicated
on the graphs as the Gaussian Emission
Limit; and (2) the limit that must be set to
ensure an actual average of two violations
per year, labelled the Cutoff Emission
Limit. These histograms are useful in
relating the number of expected violations
per year for this coal, for any emission
limitation. The histograms based on time-
series generation are broader, with higher
tails, than corresponding Gaussian curves,
demonstrating that many more violations
are expected with actual coal than under
the misapplication of data independence.
Sampling of both feed and product
coals from each of two coal preparation
plants, under carefully controlled condi-
tions, has confirmed the results of prior
studies. These results indicate that both
the mean total sulfur content and the
mean emission parameter (Ib SO2 per
million Btu) are significantly reduced by
the cleaning process, as shown in Table
1.
Gaussian Cutoff
emission Emission
Limit Limit
6.065 6.175
.140
5.340
5.540 5.740 5.940 6.140
Daily Average Emission Rate. Ib SOz/W Btu
6.340
Figure 1.
R&F Coal Company—histogram of daily average emission rate based on 100-year
time-series generation at 30 minute increments, ROM coal.
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10000-
S 8000-
8
»..
.c
2. 6000-
4000 —
2000^
Clean Coal
Gaussian
Emission
Limit
4.550
Cutoff
Emission
Limit
4.755
3.910 4.070 4.230 4.390 4.550 4.710
Daily Average Emission Hate, Ib SOx/10* Btu
4.870
Figure 2. R&F Coal Company—histogram of daily average emission rate based on 100-year
time-series generation at 30 minute increments, clean coal.
Table 1. Sampling Results
Total
Sulfur.
percent
Emissions
lbSO2
10* Btu
Raw Coal
Cleaned Coal
Reduction
Raw Coal
Cleaned Coal
.Reduction
R&F Plant
30-min
Increments
3.076
2.612
15.1%
5.476
4.237
22.6%
Republic Plant
1 -hour
Increments
2.576
1.309
49.2%
5.117
1.875
63.4%
The extent of the reduction is quite
different for the two plants. \n fact, the
63.4 percent SOa emission reduction at
the Republic plant is uncharacteristically
high for most commercial coal preparation
plants. This large reduction in potential
sulfur emission results primarily from the
washability characteristics of lower Kit-
tanning coal and the operating conditions
of a preparation plant processing coal to
metallurgical grade specifications. A
wide range of reductions between differ-
ent coal types and preparation plants is
consistent with prior findings.
Also confirming the results of prior
studies, this investigation documented
significant reductions, attributable to the
coal preparation process, of the variability
in total sulfur and in the emission
parameter, as shown in Table 2.
Prior to analyzing the variability in coal
data, the measurement uncertainty in the
data was independently determined. This
uncertainty, attributable to the process of
sampling, compositing, sample prepara-
tion, and laboratory analysis, provides a
quantitative limitation to subsequent
explanations of coal variability. All values
for aggregate measurement uncertainty
were significantly less than the total
variations. Real variability in coal charac-
teristics therefore was observed, over
and above the measurement noise level.
The time-series predictive model was
also used to develop the effect of lot size
on variability. The data generated by the
time series were mathematically compo-
sited into successively longer time
intervals (corresponding to successively
larger quantities of coal in each interval).
The effects of compositing may be
expressed either in terms of the averaging
time or number of data points (reference
lots). For teh R&F plant, a 30-minute
clean coal averaging time (a single
sample increment) corresponds to a
reference lot size of 330 tons. The sample
mean variance decreases with increasing
lot size, but at a smaller rate than would
be expected from serially independent
data. This relationship was more pro-
nounced for clean coal than for ROM coal
at the R&F plant (see Figures 3 and 4).
Conclusions and
Recommendations
Serial dependence (also called autocor-
relation) of coal characteristics must be
incorporated into any analysis of the
ability of either raw' or clean coals to
comply with SOz emission regulations.
The misapplication of Gaussian statistics,
which assumes serial independence of
coal data, leads to a gross underestima-
tion of the frequency of short-term
emission violations, time series analysis,
which combines serial dependence with
a stochastic component to construct a
predictive model, provides an alternative
to Gaussian statistics. The techniques
and computer programs for applying
time-series analysis are generally availa-
ble for use.
Although the two diverse coals studied
in detail both exhibited autocorrelation,
the magnitude of the autocorrelation
component of the total variance differed
from one coal to another and from raw to
cleaned coal. Therefore, each coal's
ability to meet short-term emission
regulations must be determined separa-
tely until the number of different coals
characterized is sufficient to generalize
the variability of coal characteristics.
Based on results from the two coal
preparation plants studied, one can
expect the serial dependence of a coal to
be adequately characterized by analysis
of consecutive samples, each represent-
ing a 30- or 60-minutetime increment, if
each primary sample is a full-stream cut
obtained by an automatic sampler.
Extension to 8 hours of the time interval
between analyses does not appear
acceptable, since the coal properties
apparently have a shorter time lag of
autocorrelation. Therefore, the conven-
tional sample collection frequencies
recommended by ASTM appear to be
inadequate to characterize coal variability
for short-term emission compliance.
The duration of an extensive sampling
and analysis study to characterize the
variability of a specific coal should be
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Table 2. Data Analysis
R&F Plant 130-min Increments)
Measure
Variance
Relative
Standard
Deviation
Parameter
Total Sulfur, %
Ib SOz/10*Btu
Total Sulfur, %
Ib SOz/1(f Btu
Raw
Coal
0.194
0.559
0.143
0.137
Clean
Coal
0.082
0.188
0.109
0.102
Percent
Reduction
57.7
66.4
23.8
25.5
Republic Plant (1-hour Increments)
Raw
Coal
0.101
0.419
0.123
0.126
Clean
Coal
0.0072
0.0172
0.065
0.070
Percent
Reduction
92.9
95.9
47.2
44.4
several days, sufficient to provide about
80 -100 consecutive data points at a 30-
or 60-minute frequency. The integrity of
the consecutive data requirement is of
utmost importance in characterizing
autocorrelation, and requires that all
efforts be directed to avoiding data gaps.
To verify the results and to evaluate
longer term effects, the intensive study
of several days should be repeated at
regular intervals over a much longer time
span (e.g., 6-12 months).
For this report, intensive testing was
conducted at only two preparation
plants. The results obtained should be
verified for coals other than the ones
intensively studied. In particular, cost
from other regions and with higher and
lower mean sulfur contents should be
investigated. The additional studies
should address coal feeds to power
plants in order to characterize the time
variation of coals responsible for boiler
emissions. Those studies should include
the effects upon variability of blending,
stockpiling, and pulvering at the power
plants.
Conversion Factors
Nonmetric
Btu
in.
ton
Multiplied
bv
1055. 1
2.54
907.2
Yields
Metric
J
cm
kg
0.6-
Averaging Time, hours
10 15
20
25
0.5-
I
to
!
<55
0.4-
0.3-
0.2-
0.1-
0.0-
ROM
Coal
A Correlated
Q Uncorrelated
10
20 30
Number of Samples (N)
40
50
Figure 3. R&F Coal Company—sample mean variance of ROM coal as a function of averaging
time, uncorrelated vs. correlated data.
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0.75
0.00
Averaging Time, hours
10 15
A Correlated
Q Uncorrelated
10
20 30
Number of Samples (N)
40
50
Figure 4. R&F Coal Company—sample mean variance of clean coal as a function of averaging
time, uncorrelated vs. correlated data.
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B. Cheng, K. Crumrine, A. Gleit, A. Jung. D. Sargent, and B. Woodcock are with
Versar, Inc., Spring field, MA 22151.
James D. Kilgroe is the EPA Project Officer (see below).
The complete report, entitled "Variability and Correlation in Raw and Clean Coal:
Measurement and Analysis," (Order No. PB 84-118 223; Cost: $26.50, subject
to change} will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Industrial Environmental Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
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United States
Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati OH 45268
Official Business
Penalty for Private Use $300
HICAGO IL
ft U.S. GOVERNMENT PRINTING OFFICE: 1984-759-102/851
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