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

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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
JŁO




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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