United States
Environmental Protection
Agency
Air and Energy Engineering
Research Laboratory
Research Triangle Park NC 27711
Research and Development
EPA/600/S7-85/024 Aug. 1985
&EBA Project Summary
Coal Sampling and Analysis:
Methods and Models
Alan Gleit, William Moran, and Arthur Jung
New Source Performance Standards
for large coal-fired boilers and certain
State Implementation Plans require op-
erators to monitor SO2 flue gas emis-
sions. As an alternative to stack gas
monitoring, sampling and analysis of
feed coal has been proposed to esti-
mate SO2 emissions. This report pro-
vides information on coal sampling and
analysis (CSA) techniques and proce-
dures and presents a statistical model
for estimating SO2 emissions. In partic-
ular, this study assesses the various
coal sampling techniques and equip-
ment, the various sample preparation
and analytic methods, and common
practices for CSA. It describes the vari-
ables associated with the prediction of
SO2 emissions from CSA data; e.g., sul-
fur retention, variability, measuring
errors, and auto-correlation. Finally, it
presents a time series model for pre-
dicting emissions which takes into con-
sideration the correlation of the sulfur
content of the coal, the measuring er-
rors, and the sampling procedures for
coal collection. The model is used to fit
53 data sets with little evidence of non-
fit.
This Project Summary was devel-
oped by EPA's Air and Energy Engineer-
ing Research Laboratory, Research Tri-
angle Park, NC, to announce key
findings of the research project that is
fully documented in a separate report
of the same title (see Project Report or-
dering information at back).
Introduction
The purpose of this study was to eval-
uate the use of CSA techniques for esti-
mating SO2 emissions from coal-fired
boilers. Coal sampling, whether per-
formed manually or automatically,
must extract a quantity of coal much
smaller than the original lot for labora-
tory analysis. The sample, to be repre-
sentative, must have the same charac-
teristic qualities and constituents as the
entire coal lot. However, inherent vari-
ability in the coal parameters and the
imprecision of the entire measurement
process make sampling a rather techni-
cal subject. This report addresses the
methodology, equipment, and model-
ing of the CSA procedures. The full re-
port covers:
• Assessment and statistical evalua-
tion of coal sampling techniques
and equipment.
• Assessment and statistical evalua-
tion of coal sample preparation and
analytical techniques.
• Sulfur loss (not emitted as S02) in
coal-fired utility boilers.
• Common industry practices in CSA,
• Important mathematical parame-
ters used to describe coal sulfur
variability.
• A statistical time series model for
characterizing coal sample and
emission data.
• The consideration of measurement
errors.
• The consideration of sampler bias.
• The analysis of CSA and emission
data with a time series model.
This Summary briefly discusses some
.of the topics covered in the full report.
Objectives of Coal Sampling
The sampling of coal, whether per-
formed manually or automatically,
must extract a quantity of coal much
smaller than the original lot but with
proportionately the same characteristic
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qualities and quantities present in the
entire lot. It has long been realized that
the properties in coal are not distributed
uniformly. The variability of coal makes
it difficult to collect a sample that is rep-
resentative of a large mass of coal. For
instance, grab samples of coal from the
same source may show different analyt-
ical values if tested in different laborato-
ries or by different technicians in the
same laboratory.
Besides coal's inherent variability,
other factors (e.g., how the coal was
handled, or how the samples were ob-
tained) affect the collection of a repre-
sentative sample. The coal may have
become segregated during loading,
transport, or unloading so that the parti-
cles are grouped together by size. When
samples are taken from a stationary
source (e.g., a coal storage pile or rail-
road car), it is difficult to obtain an accu-
rate sample because the material in the
center of the pile will be inaccessible
when conventional sampling tech-
niques are used. Generally, samples
taken around the pile will be limited by
the depth of penetration of the sampling
device into the stationary source. Simi-
larly, when samples are taken from a
moving stream (e.g., a conveyor), they
should be taken from the entire width of
the belt to avoid biasing the sample.
To be effective, a sampling plan must
employ measures to reduce the effect of
segregated particles, minimize the ef-
fect of the variability of the coal proper-
ties, and identify any mechanical bias
due to the sampling method. Sampling
material from a conveyor or a chute
through which the coal is flowing pro-
vides access to a cross-section cut of the
entire stream. This cross-sectional cut
will provide a characteristic sample
even though the vertical distribution of
material on the conveyor may be segre-
gated by particle size.
Manual sampling bias may be re-
duced by the use of automatic equip-
ment which is not dependent on human
discretion for operation. These systems
are generally elaborate and have been
designed for a specific plant's applica-
tion. Manual sampling methods can be
used, but care must be taken to ensure
that the sampling technique has been
consistently applied.
Sampling personnel must consider
the variability between discrete units of
coal when attempting to collect a sam-
ple which is representative of a specific
lot; e.g., a 10,000-ton lot of coal may
consist of 100 discrete units or railroad
cars of 100 tons each. If the variability
between railroad cars is high because of
differences in loading procedures and
coal characteristics, a composite made
up of one increment collected from
every tenth car may be insufficient to
represent the entire 10,000-ton lot. In
this case, increasing the number of in-
crements (or increasing the number of
railroad cars sampled) will produce a
composite which better characterizes
the entire lot. On the other hand, if the
variability is expected to be relatively
low, then sampling from each car may
be an extensive effort with little or no
extra benefit.
Sampling Guidelines
With all these factors contributing to
the inaccuracy of coal sampling, there
has been concern over the reliability of
coal analysis data. Inaccurate data,
whether due to an error in sampling,
poor analytical techniques, or some
other factor, can result in data misuse.
Because of this, there are many opin-
ions concerning guidelines for sam-
pling coal and the establishment of
standard methods.
The most widely regarded standards
were established by the American Soci-
ety for Testing and Materials (ASTM).
The ASTM issued recommended proce-
dures for a variety of sampling situa-
tions. ASTM Method D 2234 details the
minimum number and weight of incre-
ments and the amount of the gross
sample needed to provide a stated level
of precision.
The ASTM also evaluates conditions
under which an increment is collected;
e.g., stopped-belt cut, full-stream cut,
part-stream cut, and stationary sam-
pling. ASTM points out that an auto-
matic or mechanical sampling method,
without human discretion, is more pre-
cise than manual sampling. They clas-
sify each condition under which an in-
crement is collected. The highest
classification, or most precise method,
is the stopped-belt cut removed by a
mechanical cutter with increments
spaced systematically. The stopped-belt
technique allows all of the particles in a
cross-section of the belt to be collected,
eliminating segregation due to particle
size. ASTM specifications restrict the
cutter speed to 18 in./sec and indicate a
minimum cutter width (size of the open-
ing of 2-1/2 to 3 times the topsize of the
coal.
ASTM also considered the ratio of
maximum particle size and the large
variation of ash content among coe
pieces of different size. Ash content wa
used because it was believed to be th
most sensitive measure of variations ii
coal quality. ASTM specifies that no les
than the minimum increment weight bi
collected so as to reduce the bias due t<
particle size and ash content.
Table 1 summarizes sampling guide
lines recommended by various expert;
and authorities.
Sampling Equipment
Although the recommended proce
dure for collecting a coal sample is witl
an automatic sampler, manual sam
pling is sometimes the only alternative
Manual samples can be taken from i
stationary source or, more reliably
from a moving stream.
In stationary source sampling (e.g.
from railroad cars or storage piles)
manual techniques which employ shov
els, buckets, probes, augers, and othe
instruments can be used. The simplest
and perhaps most inaccurate, mean;
would be sampling with shovels o
scoops frqm a stationary source. Al
though discouraged, there are severa
guidelines for this type of sampling: al
of them recommend taking several in
crements from different points and at<
consistent depth. This method will no
always produce a representative sam
pie of the entire lot because only tht
uppermost particles in the storage pile
or transport vehicle are accessible to the
sampling device.
An auger can be used to obtain a core
sample of consistent depth into the pile
The augering technique may not accu
rately represent fine particles because
they tend to fall out of the sampler prioi
to discharge into the sample collection
container. Although the use of an augei
allows deeper penetration into a pile
than shoveling, quite often the innei
portions of the pile remain unsampled.
At least one manufacturer offers slot-
ted sampling probes of varying lengths
and diameters. These devices may be
inserted into a pile but are limited to
materials with a nominal topsize of less
than 0.5 in.
Samples taken from a moving stream
by manual techniques are more precise
than samples from a stationary source,
but they are subject to human error. The
human factor involved in accurately re-
peating the cutting process adds to the
sampling error. For sampling material
from a falling stream, the simplest de-
vices include shovels, scoops, and
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Table 1. Summary of Sampling Guidelines
Author
USBM/G.S. Pope
Recommended
Method
From a mov-
ing stream
Number of
Increments
Spaced syste-
matically over
entire lot
Size of
Increments, Ib
10-30
Gross
Sample, Ib
1,000
Recommendations
Larger increments result in
more accurate sample
USBM/B.A. Landry
From a mov-
ing stream
IN)W
All increments
must be same
size
Not considered
Sampling is based on vari-
ability of coal and desired
precision
U.S. Steel
USBM/N.H. Snyder
ASTM
A.A. Orning
W.M. Bertholf
P. Gy
Full cross-
section,
stopped belt
Full cross-
section, mov-
ing stream
Full cross-
section,
stopped belt
Not specified
Not specified
Mechanical
One every
30 minutes
50
Minimum of 15
Number and size
Minimum num-
ber based on
coal's variabil-
ity
40 to 50, based
on estimated
sample size
6-8
10-30
2-15
1,000
500-1,500
Dependent on in-
crement number
and size
Orderly spacing of increments
to represent entire lot
Increment size dependent on
coal topsize
Increment size dependent on
coal topsize
of increments depend on variability of coal's size and properties.
Not specified
Dependent'on
speed and width
of cutter
Not specified
Dependent on size
and shape of par-
ticles
Proposes collection of a pri-
mary increment, which is
then resampled
Recommends a mechanical
sampler with a large cutter
width
buckets. The shovel or similar device
should have raised sides and capacity
sufficient to hold a cross-sectional cut
without overflowing.
The collection of coal samples by me-
chanical means is considered a much
more precise and representative
method than manual sampling. The
ASTM bases this assumption on the fact
that an automatic sampler will not se-
lect an increment on a discretionary ba-
sis. There is no human element in-
volved.
Mechanical samplers are nearly al-
ways associated with coal conveyor
belts on coal chutes. Most manufactur-
ers of mechanical samplers have used
designs based on ASTM standards.
Some commercial mechanical samplers
use primary, secondary, and tertiary au-
tomatic samplers (combined). The pri-
mary sampler collects a large sample
which is subsequently sampled by a
secondary sampler. In some cases the
coal from the secondary sampler is
crushed prior to division by an auto-
matic tertiary sampler. In other cases
size reduction and further subdivision
of the primary or secondary sampler is
performed manually. Samplers now in
use include cross-stream cutters, rotat-
ing scoops, augers, and rotary arm sam-
plers. The reliability and accuracy of dif-
ferent automatic systeYns is difficult to
quantify and is a function of the installa-
tion of the equipment, the physical char-
acteristics of the material to be sam-
pled, and the operating techniques used
by the facility personnel.
The many different approaches to
mechanical sampling allow for many
different applications and consideration
of specific requirements. Although me-
chanical sampling is more precise than
manual, not all mechanical methods
collect equally representative samples.
The design should include a means for
taking a sample from the entire cross-
section of the coal stream. Other impor-
tant factors to consider are the speed of
the cut and the size of the cutter open-
ing.
In general, the cutter should move at
a uniform speed to ensure that the en-
tire cross-section is represented in
equal proportions. The speed should
also be slow enough to prevent segre-
gation and rejection of particles due to
disturbances of the coal stream. The
cutter opening should be large enough,
at least three times the size of the larger
coal particles, to allow equal represen-
tation of all size particles.
The preferred method of sampling
would be the method that obtained the
most precise representative increment.
Table 2 shows the order of preference
for each samplng scheme discussed
here.
Sample Preparation
The collection of a representative
gross sample using manual or auto-
matic methods often yields a bulk quan-
tity of material which may weigh as
much as several hundred pounds. Nor-
mally, 50 to 100 g of material are neces-
sary to meet the analytical require-
ments of most coal characterization
tests. The method used to reduce the
gross sample to the analytical sample
must maintain the integrity and repre-
sentativeness of the sample while meet-
ing the particle size and weight require-
ments as specified by the particular
analytical methods.
The preparation of a gross sample for
coal analysis requires several process-
ing steps. Air drying is used to bring the
moisture content of the sample to equi-
librium with the air in the room where
further preparation will take place. Sam-
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Table 2. Order of Preference of Sampling Procedures and Methods
Collection Procedure Collection Method Order of Preference
Stopped belt cut
Stopped belt cut
Full stream cut
Full stream cut
Part stream cut
Part stream cut
Stationary sampling
Stationary sampling
Mechanical, automatic
system
Manual sampling
Mechanical, automatic
system
Manual sampling
Mechanical, automatic
system
Manual sampling
Mechanical, automatic
system
Manual sampling
1
2
3
4
5
8
pies are reduced or crushed from a
nominal 3-in. topsize to minus No. 4 or
No. 8 mesh used to pptimize the repro-
ducibility of subsequent processing
procedures. Sample division or splitting
results in a smaller quantity of material
without a loss in the sample's represen-
tativeness. Another sample reduction
process, pulverizing to minus 60 mesh,
is generally required for specific analyti-
cal procedures. Thoroughly mixing and
homogenizing the analytical sample is
necessary so that the small aliquots
which are taken for individual tests are
representative of the sample.
Sample Analysis
Proximate and ultimate analyses are
often used to characterize selected coal
properties. Proximate analysis refers to
the determination by prescribed meth-
ods of moisture, volatile matter, fixed
carbon (by difference), and ash. Ulti-
mate analysis includes: the determina-
tion of carbon and hydrogen in the ma-
terial (as found in the gaseous products
of its complete combustion); the deter-
mination of sulfur, nitrogen, and ash (in
the materials as a whole); and the esti-
mation of oxygen by difference (ASTM
D121-78). Although it is common to find
several different methods for measur-
ing each parameter, it is generally
through agreement between parties,
such as the coal supplier and customer,
that specific methods and operating
conditions are selected.
The most important analyses for eval-
uating coal S02 emission are moisture,
ash, total sulfur and calorific value.
Standardized techniques for performing
these analyses are summarized in
Table 3. In addition to these standard
methods, a number of automated tech-
niques substantially reduce the analysis
time and hence the costs of these analy-
ses. A brief summary of some of these
techniques is provided in the full report.
Sulfur Loss in Coal-Fired Utility
Boilers
Coal feedstock is usually sampled as
it is bunkered. When it is removed, it
moves on to the pulverizers and then to
the boilers. Sulfur is removed during
pulverizing and combustion from path-
ways other than the emission of gase-
ous S02 in the flue gas. Hence the
amount of gaseous S02 in the flue gas is
not simply related to the measured sul-
fur in a CSA program. As S02 is regu-
lated by EPA, guidelines need to be de-
veloped to estimate the SO2 based on
as-bunkered coal sulfur measurements.
Several factors must be considered in
this development: the coal characteris-
tics (ash constituents, organic and
pyritic sulfur content, and heating
value), the combustion process (boiler
size, firing type, and generating load),
and possible fuel additives.
In general, insufficient knowledge is
currently available concerning the ef-
fects and interrelationships of the vari-
ous factors involved in sulfur retention
in the pulverization and combustion
process to allow a blanket recommen-
dation for sulfur loss credits. However,
some possibilities for giving credits for
sulfur loss can be given:
a. A constant 5% rate seems a rea-
sonable compromise between reg-
ulatory demands for conservancy
and industrial demands for "re-
ality."
b. Each utility can take a constant rate
(say 5%) or can, using mass bal-
ance, prove it is entitled to more.
The regulatory difficulty here is
that the retention rate is so vari-
able that past or current informa-
tion may bear little relation to the
future.
c. Allow no retention rate. This is the
most conservative approach, forc-
ing the sources to bear the entire
burden of the retention if they wish
to use CSA.
d. Allow no retention in general but
allow each source, using mass bal-
ance, to prove it is entitled to one.
The drawback stated in (b) applies.
CSA Practices in the Utility In-
dustry
Several common CSA techniques are
currently used by coal-fired utilities to
evaluate their fuel. A brief study was
conducted to determine the extent of
use of these methods and any quality-
control measures associated with them.
This information is important to the
study because it indicates how closely
current industry practices match the
proposed EPA Reference Method 19A
requirements (48 FR 48960, October 21,
1983) and because it may show where
alternative procedures need to be incor-
porated or approved for use some-
where within the proposed regulation.
Two major sources of information
were used to evaluate CSA practices in
the utility industry. The first source was
a report entitled "Electric Utility Coal
Sampling and Analysis Practice: A
Comparison to Proposed EPA Refer-
ence Method 19A Requirements Based
on Utility Responses to FERC Survey."
This report tabulated and analyzed cer-
tain data collected from a survey of 190
utility plants for CSA information. The
tabulations were set up so they could be
compared with the proposed Reference
Method requirements; therefore, the
sampling method was not specifically
defined beyond a group of ASTM meth-
ods. The sampling location was not
specified other than "as-received" or
"as-fired," and the method of sulfur
analysis was not defined if any method
other than the ASTM standards was
used.
The other source of information was
individual contacts at 24 utility plants
with which Versar had previously
worked. These plants were part of a na-
tionwide sampling program and, as
such, represent a variety of boiler types,
coal types, and geographic^ locations.
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Table 3. Summary of Selected Standards for Coal Analysis
Standard Determination . Brief Description
ASTM D3173
ISO 1171*
Moisture
Moisture
ISO 388
ASTM D3174
ISO 1171
ASTM D3377
Moisture
Ash
Ash
Sulfur
ISO 351
ASTM D3286 and
ISO 1928
ASTM D2015 and
ISO 1928
Sulfur
Calorific Value
Calorific Value
A sample is air dried in an oven under
controlled conditions. The moisture con-
tent is determined from the sample weight
loss.
A stream of preheated, oxygen-free dry ni-
trogen is passed through a retort contain-
ing the coal sample. Moisture from the ni-
trogen is collected in a weighing tube
containing a desiccant. The moisture con-
tent is determined from the weight in-
crease of the desiccant.
The coal sample is distilled with toluene.
The moisture is condensed from the coal/
toluene mixture, and the coal moisture
content is determined from the volume of
condensed water.
A coal sample is completely combusted,
and the ash content is determined by the
weight of residue.
Similar to ASTM method but with different
heating rates and maximum temperature.
There are three alternative methods:
a. Eschka Method—A weighed sample
and Eschka mixture [2 parts MgO, 1
part /VaycO/3/ are ignited together, and
the sulfur is precipitated from the re-
sulting solution of barium sulfate
(BaS04). The precipitate is filtered,
ashed, and weighed.
b. Bomb Washing Method—Sulfur is pre-
cipitated as BaSOt from oxygen-bomb
calorimeter washings. The precipitate is
filtered, ashed, and weighed.
c. High Temperature Combustion Meth-
od—A sample is burned with oxygen in
a tube furnace generating sulfur and
chlorine oxides. The oxides are col-
lected in absorption bottles and con-
verted to acids. The acids are titrated to
determine the equivalent amount of sul-
fur formed during combustion.
Similar to ASTM High Temperature Com-
bustion Method, above.
The gross calorific value is determined
using an isothermal-jacket bomb calorime-
ter.
The gross calorific value is determined
using an adiabatic bomb calorimeter.
a/SO = International Organization for Standardization
An analysis of these sources of infor-
mation indicates that the following CSA
procedures-are common in current util-
ity practice:
1. Sampling from conveyor belts
using automated full-stream cut
equipment is used by about 50% of
all plants considered by Versar,
and probably 67% of all the plants
considered in this survey.
2. Sampling from a conveyor by tak-
ing random manual grab samples
is used by 38% of the plants con-
tacted by Versar, and probably
36% of all the plants considered.
3. Sampling coal to define as-
received quality is used by 43% of
all plants considered as opposed
to 4% taking as-fired samples;
however, no location was speci-
fied for 48% of the plants.
4. Determining heat content with an
adiabatic calorimeter is used by
74% of all plants considered.
5. Analyzing for sulfur by the bomb-
washing method is used by 45% of
those plants which report that wet
chemical procedures are used.
6. Analyzing for sulfur using auto-
mated infrared-detector-equipped
analyzers may be more prevalent
than use of standard wet-chemical
procedures.
7. Using ASTM standard methods for
the analysis of residual moisture,
total moisture, and ash is univer-
sal.
8. Calibrating equipment with stand-
ard samples, duplicates, or blanks,
is done most frequently on a daily,
every-other-day, or weekly basis.
9. Analyzing standard samples is
done for each batch (usually 5 to
10 samples}.
Modeling SO2 Emission with
CSA DATA
The practical application of CSA data
for estimating S02 emission is influ-
enced by several factors. With current
CSA techniques it is impossible to.mea-
sure the sulfur and Btu content of all
coal being fired in a boiler. For this rea-
son it is important to adopt a statistical
theory that will allow the modeling of a
large population from a relatively lim-
ited data set. This model should provide
statistical information on the coal popu-
lation being burned and errors which
are attributed to the CSA techniques
employed.
An appropriate statistical theory for
developing a model relating the CSA
data to S02 emissions is time series
analysis. In developing the CSA emis-
sion model it was assumed that the
time-dependent nature of a coal or
emission stream could be represented
by an auto-regressive model of order
one [AR(1,1(]. An auto-regressive mov-
ing average [ARMA(1,D] model was
then used to relate the CSA data to the
underlying coal properties. By using the
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• 24 Hours •
Coal Flow
Past
Sampling Point
Gi
G2
• • •
GL L,
to
...
G2L
II 1
1
\
G = actual value of the coal property in each
discrete coal packet.
J = each potential sampling unit.
I = actual sampling units.
Q = LMN
Q = 1,008,000 discrete coal packets per 24 hour
period.
L = n of coal packets collected in each potential
increment (determined by coal sampler cutter
speed).
M - difference between increment numbers for
actual sample increments.
N = # of increments actually collected to form a
composite.
IfL = 24 and N = 35 then: M = 1.008.000/(24 x 35) = 1200.
>/2M
\
\
/N
C = Composite of Increments
Figure 1. • Increment collection and composite in a CSA program.
models to analyze CSA data it is possi-
ble to develop estimates of CSA errors
and statistical properties of the time de-
pendent coal emission stream. The sta-
tistical properties and error estimates
can in turn be used to obtain the follow-
ing information.
1. The average SO2 emission level
that is needed to comply with a
given emission standard.
2. The probability of exceeding or
complying with a specified emis-
sion standard.
3. The effect of sampling and analy-
sis frequency on the sampling and
analysis error confidence interval.
Model Description
The model simulated the statistical
properties present in either a moving
stream of coal or stack emissions. In ei-
ther case, the coal or stack gas passing
the sampling point can be thought of as
being made up of Q discrete packets of
homogeneous material per day (Fig-
ure 1). The computer implementation js
based on the assumption that Q
= 1,008,000 discrete packets pass the
sampling point each 24-hour period.
When applied to a CSA program the nu-
merical results are based on the as-
sumption that the action of the sampler
cutting through the coal stream takes
about 2 seconds. Therefore, roughly 24
discrete packets would be collected
with each pass of the sampler.
The actual value of the coal property
in each discrete coal packet is G; e.g., G,
can be the total sulfur contained in the
ith discrete packet of coal. Each poten-
tial sampling unit is J. Thus, for coal
sampling, every collection of 24 coal
packets is a potential sampling unit.
The increments, I, are the actual sam-
pling units, which correspond to the po-
tential sampling units (J) that were actu-
ally collected. The collected increments
are composited to form C as shown in
Figure 1.
A slightly different approach is used
when describing emissions data. By the
time flue gases reach the stack they
have become so well mixed that each
unit of gas has part of the products of
combustion from hundreds of the coal
packets. For a continuous emission
monitor (CEM) system, hourly emission
values are based on four equally spaced
data points. Daily averages are the aver-
age of the 24 hourly averages. In term!
of our model, N = 96 increments make
up the daily composites. We assume
that a sampling unit J is made eacr
minute so M = 15. Hence, L = Q/MIS
= 700 coal units make up each sampling
unit.
A continuous bubbler (CB)* system is
modeled in a similar manner. Since the
CB system is continuously withdrawing
well-mixed stack gases, it receives pan
of the products of combustion from
each coal packet. Thus, L = Q
= 1,008,000 and M = N = 1.
The variability associated with the
coal property G is subject to correlated
and random elements. This stochastic
process is modeled by an autoregres-
sive model of order one [i.e., an AR(1)
process].
Since the variability associated with
the discrete coal packets is modeled by
an AR(1) model, J(J = J1r J2...JNM) is
modeled as an average of an AR(1]
model. This latter time series model is
termed an auto-regressive moving av-
erage model, ARMA(1,1). Since I is a
. "thinned" version of J, it too is an
ARMA(1,1) model. Next, consider thai
6
-------
one composite sample is formed each
day from the N increments:
C = ft di + I2 + - + IN)
The composites are then used to deter-
mine the quantities that are of interest;
e.g., total sulfur (weight %), since the
actual measurements in the laboratory
represent the composites (C) and not
the potential sampling units (J), nor the
increments (I), nor the packets (G).
Again, C is an averaged value derived
from the I values, so C is also modeled
by an ARMA(1,1) model.
In all cases the daily composite value,
C, is defined as the actual value of the
coal or stack emission. It is provided by
the model. In actuality the estimation of
emissions involves using measured val-
ues (X) of coal properties as determined
by the analysis of composited labora-
tory samples. The measured value X
does not equal C because X includes
some unavoidable measurement error.
The measurement error consists of vari-
ations in the sampling and analysis pro-
cedures.
The ARMA(1,1) model that describes
the actual coal supply (C) can be ex-
tended to a model for the measured
value (X) of the daily composites. Using
the parameters that describe X and the
properties of the model, the parameters
that describe the actual coal supply can
be derived.
To apply the ARMA(1,1) model which
describes C there must be some relation
between its parameters and the param-
eters that describe X. The relationship
between C and X is:
X = C + ME
where ME is the measurement error of
the sampling and analysis procedures.
ME is modeled as a normally distributed
random variable that is independent of
all past history and of C. The measure-
ment error, ME, and the actual value of
the composites, C, can be determined
from the model once the parameters
that estimate the value of the measured
daily composites (X) are known. The
auto-regressive model can also be used
to provide estimates for all the parame-
ters describing the processes G, J, and I.
Evaluation of Models
The statistical models were evaluated
using 53 data sets: 19 for CSA, 25 for
CEM, and 9 for Method 6B (continuous
bubbler). Each of the data sets was ana-
lyzed using the appropriate ARMA(1,1)
model. Each data set was then sub-
jected to goodness-of-fit analysis to de-
termine if the model provided an ade-
quate description of the original data
set. A few analyses were performed to
determine if the models adequately de-
scribe the coal variability and measure-
ment error phenomena.
A computer routine was developed
and implemented to analyze the data
using the ARMA(1,1) and other appro-
priate time series models. Important
statistical parameters developed for
each data set with the ARMA(1,1) model
included the mean value, the estimated
variance of the underlying coal struc-
ture [Var (C)], the estimated variance of
the measurement error [VaV (ME)], and
relative standard deviation of the mea-
surement error [RSD (ME)]. The vari-
ance is a measure of the variability or
spread of data points around the mean
value. The RSD is defined as the square
root of the variance divided by the mean
value, and the ratio is multiplied by 100
to convert the ratio to a percentage.
Table 4 summarizes the analysis re-
sults for the CSA data sets.
One of the longer CSA data sets eval-
uated was the 226 point Republic Steel
clean coal. Set 2. The coal variance for
this data set (0.0080) represented 65.6%
of the total variance, and the measure-
ment error \4ariance (0.0035) repre-
sented 30.5% of the total variance. The
relative standard deviation of the mea-
surement error [RSD (ME)] was 44%.
To determine if the fitted ARMA(1,1)
model adequately fit the data, three in-
dicators were considered: residual anal-
ysis, overfit, and R2.
The residuals are estimated by the dif-
ference between the forecast of the next
data point at each time and the actual
observed data point:
residual = (X,+1 - X) - AR(X)(X, - X) .
If the model fits, then these residuals
should form an independent sequence
of random variables. If they do, then
95% of their correlations should be in
the interval ±1.96/Vn - 1 and
Q = (n)(sum of squared correlations)
should be small. For the Republic set,
the computer calculated the first 20 cor-
relations for the residuals. It was found
that 2 of these 20 were not in the interval
±0.12 and that Q = 21.31. Neither of
these tests shows that the ARMA(1,1)
model is inadequate (but, on the other
hand, neither is very compelling either).
The second method used was
"overfitting" of the model. The data was
fit with ARMA(1,2) and ARMA(2,1) mod-
els to see if either was significantly bet-
ter. For the Republic set analyzed above,
neither the ARMA(1,2) nor ARMA(2,1)
model provided a fit which was signifi-
cantly better than the ARMA(1,1) model.
The third indicator of fit is the overall
R2 defined by:
R2 _ 1 _ residual variance _
total variance
"% of variance explained
by model."
In the above example for the Republic
set, R2 = 0.748.
In general, the CSA results indicated
that VAR (ME) increased as VAR (C) in-
creased. The analysis of variance from
the R&F data sets, in which the labora-
tory analytical samples were split for
duplicate analyses, indicated that the
principal component of the measure-
ment error was the sampling and sam-
ple preparation error (the analytical
error was nearly constant for three of
the four sets analyzed). From these ob-
servations it is postulated that the major
component of the measurement error is
the sampling error and the sampling
error increases with the increased vari-
ability of the underlying coal popula-
tion. This is to be expected since the
probability that any given sample will
be representative of the mean value de-
creases as the variability of the underly-
ing coal population increases. This sam-
pling representational error can be
reduced by increasing the sampling fre-
quency.
Conclusions and Recommenda-
tions
Coal sampling and analysis (CSA)
procedures cannot guarantee "correct"
results. Inherent coal variability and the
representativeness of the sampling and
preparation procedures lead us to con-
clude that the resulting 50-100 g of coal
per day analyzed in the laboratory may
not have coal parameters exactly equal
to the daily average of the coal. The lab-
oratory results rely on fallible humans,
who may introduce additional inaccura-
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cies. Thus, any discussion of CSA must
address the statistical issues of estimat-
ing the true emissions from the scat-
tered sulfur data.
This study presents a theoretical
model for coal sulfur data involving
time series modeling. Extensive verifi-
cation of the model using real coal data
does not suggest any widespread lack
of fit. On the contrary, the model seems
to do a very credible job in fitting the
data. The model can be used by EPA to
evaluate the impact of various stack
emission standards and/or averaging
periods on the mean level of compli-
ance coal. Alternatively, it can be used
by EPA to offer guidelines to the indus-
try as to how it could meet proposed
stack emission standards.
Table of Conversion Factors
Multiply To Obtain
English Unit by SI Unit
pound (lb> 453.59 gram
ton (2000 Ib) 0.907 megagram
(Mg) = metric
ton
inch (in.) 0.0254 meter (m)
Tyler Screen Size Mesh
Mesh Size
14
24
48
100
200
270
ooc
J£O
Openings
mm
1.18
0.60
0.30
0.15
0.075
0.053
n rt/if:
U.UQD
Table 4. Summary of Results for CSA
Data Set
1. R&F, A, ROM, Even Splits
2. R&F, A, ROM, Odd 'Splits
3. R&F, BC, ROM, Even Splits
4. R&F, BC, ROM, Odd Splits
5. R&F, A, Clean, Even Splits
6. R&F, A, Clean, Odd Splits
7. R&F, BC, Clean, Even Splits
8. R&F, BC, Clean, Odd Splits
9. Republic, Clean, Set 1
10. Republic, Clean, Set 2
1 1. Republic, ROM, Set 1
12. Republic, ROM, Set 2
13. Iowa P.S.
14. Homer City, Unit 1 (Time 1)
15. Homer City, Unit 2, Set 1
(Time 1)
16. Homer City, Unit 2, Set 2
(Time 1)
17. Homer City, Unit 3, Set 1
(Time 1)
18. Homer City, Unit 3, Set 2
(Time 1)
19. Homer City, Unit 3, Set 3
(Time 1)
Average
2.93
2.92
3.32
3.32
2.53
2.50
2.82
2.83
1.42
1.38
2.70
2.69
0.54
2.57
2.49
2.76
2.66
2.57
2.47
Vaf(C)
0.0352
0.0358
0.0610
0.0578
0.0039
0.0041
0.0557
0.0591
0.0033
0.0080
0.0643
Var(ME)
0.0109
0.0096
0.0668
0.0594
0.00945
0.0087
0.0314
0.0316
0.0050
0.0035
0.00375
RSD(ME)
28
29
13
14
26
27
16
16
20
23
44
R2
0.675
0.705
0.902
0.911
0.797
0.805
0.852
0.869
0.849
0.748
0.452
negative split
negative split
0.0107
0.0095
26
0.619
negative split
0.0326
0.0294
16
0.583
negative split
0.0091
0.0282
0.0147
0.0440
21
12
0.794
0.968
AC (Residuals)
out of Range'
none
3
none
none
none
1
none
none
1
2
none
1
1
none
none
none
none
none
none
Q"
21.5
29.9
11.6
10.7
11.7
22.2
11.2
11.9
24.7
21.3
8.2
9.8
24.2
18.4
7.3
8.3
11.9
28.5
15.0
Overfit
Improvement
No
Yes (Both)
No
No
No
Yes (1,2)
No
No
No
No
No
Yes (both)
Yes (1,2)
No
No
No
No
No
No
"Expected number out of range is 1; i.e., 5% of 20 is 1.
"Significance levels for 10% = 26.0, for 5% = 28.9, for 1% = 34.8.
cYes means white noise variance may be reduced by 10% by ARMA (1,2) or ARMA
(2,1)
8
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A. Gleit, W. Moran, and A. Jung are with Versar, Inc., Springfield, VA 22151.
James D. Kilgroe is the EPA Project Officer (see below).
The complete report, entitled "Coal Sampling and Analysis: Methods and
Models,"(Order No. PB 85-216 604/AS; Cost: $17.50, 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:
Air and Energy Engineering Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
US GOVERNMENTPBINTOiaOFFICE-IMS 539-111/20642
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