Designation: D 2013 – 04

Standard Practice for

Preparing Coal Samples for Analysis1
This standard is issued under the fixed designation D 2013; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.

1. Scope D 4749 Test Method for Performing the Sieve Analysis of

1.1 This practice2 covers the reduction and division of gross Coal and Designating Coal Size
or divided samples, and the preparation of composite samples, E 11 Specification for Wire-Cloth Sieves for Testing Pur-
up to and including the individual portions for laboratory poses
analysis. E 177 Practice for Use of the Terms Precision and Bias in
1.2 Reduction and division procedures are prescribed for ASTM Test Methods
coals of the following groups: E 456 Terminology Relating to Quality and Statistics
1.2.1 Group A includes coals that have been cleaned in all 3. Terminology
sizes.
1.2.2 Group B includes all other coals. Unknown coals are 3.1 Definitions of Terms Specific to This Standard—No
to be considered under Group B. terms are used which are specific to this practice. Many terms
1.2.3 Group A allows smaller weight laboratory samples to used in this practice may be found in Terminologies D 121 and
be retained than Group B. These lower weights may be used for E 456 and in Practice E 177.
particular coals if they have been shown, by using the 4. Summary of Practice
procedures of Annex A1.2, to give a sample preparation and
analysis variance which is no more than 20 % of the total 4.1 Three processes of sample division and reduction are
analysis variance. covered as follows:
1.3 This standard does not purport to address all of the 4.1.1 Procedure A—Manual riffles are used for division of
safety concerns, if any, associated with its use. It is the the sample and mechanical crushing equipment for the reduc-
responsibility of the user of this standard to establish appro- tion of the sample.
priate safety and health practices and determine the applica- 4.1.2 Procedure B—Mechanical sample dividers are used
bility of regulatory limitations prior to use. for the division of the sample and mechanical crushing
1.4 The values stated in SI units are to be regarded as equipment for the reduction of the sample.
standard. The values given in parentheses are provided for 4.1.3 Combined Procedure A and B—The two procedures
information purposes only. may be combined at any stage.

2. Referenced Documents 5. Significance and Use

2.1 ASTM Standards: 3 5.1 Other standards are used to collect the gross sample:
D 121 Terminology of Coal and Coke Practice D 2234/D 2234 M allows for one division of the gross
D 2234/D 2234 M Practice for Collection of a Gross sample before crushing. The mass and top size of the gross or
Sample of Coal divided sample collected by using these guides and practices
D 3174 Test Method for Ash in the Analysis Sample of Coal are usually too large for chemical or physical testing. Practice
and Coke from Coal D 2013 provide instructions for reducing and dividing the
D 3302 Test Method for Total Moisture in Coal gross or divided sample, by on-line or off-line processes, or
both, to a top size and mass suitable to the performance of
testing. Any bias in the gross or divided sample before
1
This practice is under the jurisdiction of ASTM Committee D05 on Coal and adherence to this practice will remain in the final sample
Coke and is the direct responsibility of Subcommittee D05.23 on Sampling. resulting from use of this practice. Therefore, carefully select
Current edition approved Nov. 1, 2004. Published November 2004. Originally
approved in 1962. Last previous edition approved in 2001 as D 2013 – 03.
the standard to be used to collect the gross sample.
2
For more detailed explanation of this practice see Keller, G. E., “Determination 5.2 Division and reduction of a sample may occur at more
of Quantities Needed in Coal Sample Preparation and Analysis,” Transactions, Vol than one location. Most often, the sample is collected, reduced,
232, 1965, pp. 218-226. and divided (one or more times) by use of a mechanical
3
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website.

Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.

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sampling system. The remaining sample may be further di- 6.3 Mixing Wheel—One type of a mechanical device used
vided on-site to facilitate transporting it to the laboratory where for mixing the analysis sample. In this device, the samples are
further reduction and division likely occurs before analysis. in closed containers attached to the rim of a wheel at an angle
5.3 In places, this practice requires air drying the sample of 45° with the horizontal wheel shaft. The wheel provides
before subsequent reduction. Procedures for air drying and space for a number of containers depending on its diameter and
air-dry loss determination are provided in Test Method D 3302. is turned slowly by a small motor and reduction gear. The
5.4 Most often, samples are reduced and divided to an wheel should be rotated at a speed so that the particles fall
analysis sample. However, some tests may require a sample of gently from top to bottom of the container, mixing the sample
different mass or top size. This procedure may be used to thoroughly. The container should be about half full and never
provide a sample of any mass and size consist from the gross more than two thirds full to obtain good mixing of the sample.
or divided sample to, and including, the analysis sample. 6.4 Sieves—A set of sieves whose dimensions are in accor-
5.5 This practice also specifies how to prepare composite dance with Specification E 11, of the following sizes, with
samples, if required. cover and receiver:
No. Size
6. Apparatus
4 4.75 mm
6.1 Crushers or Grinders—Jaw, cone, or rotary crusher; 8 2.36 mm
hammer mill; roll; or other suitable crusher to reduce the 20 850 µm
60 250 µm
sample to pass the sieve designated in 6.4. Hard steel or chilled
iron plate with tamper, sledge, or hand bar may be used for 6.5 Laboratory Sample Containers—Heavy vapor-
preliminary crushing of any large lumps in the sample before impervious bags, properly sealed, or noncorroding cans such as
feeding into the crusher. Crushers should be designed and those with an airtight top, friction top, or screwtop sealed with
operated in a manner to minimize the effect of induced air a rubber gasket and pressure-sensitive tape for use in storage
circulation and thus the potential for drying the coal. and transport of the laboratory sample. Glass containers, sealed
6.1.1 Pulverizer or Mill—For final reduction of laboratory with rubber gaskets, may be used, but care must be taken to
sample to the 250-µm (No. 60) sieve size, the following avoid breakage in transport.
equipment may be used:
6.1.2 Hammer Mill—Completely enclosed to avoid loss of 7. Precautions
dust or moisture.
7.1 General—The preparation of the gross or divided
6.1.3 Porcelain-Jar Ball Mill—This mill shall be approxi- sample, or the composite sample, shall be performed by, or
mately 230 mm (9.0 in.) in diameter and 250 mm (10.0 in.) in under the direct supervision of, personnel knowledgeable of
height with smooth, hard, well-rounded, flint pebbles, or proper sample handling practices. Sample preparation should
equivalent, that do not increase ash content of the sample. be checked at intervals by the methods described in Annex A1
6.1.4 Bucking Board (Chrome Steel) or Mortar (Agate or or Annex A2. It is necessary that the variance of sample
Equivalent) and Pestle—Only for reducing the small fraction division and analysis Sda2 be not more than 20 % of the total
of sample, not passing a 250-µm (No. 60) sieve after pulveri- variance of sampling, division, and analysis So2.
zation.
7.1.1 The sample preparation operations should be per-
6.2 Sample Dividers:
formed in an enclosed space, roofed, cool, and free from
6.2.1 Mechanical—A mechanical sample divider using a
excessive air movements.
reciprocating or rotating cutter, a rotating hopper and spout, a
rotating slotted cone, a reciprocating hopper and fixed cutter, 7.2 Number of Tests—Before preparing the gross or divided
bucket cutter with either bottom dump or inverting discharge, sample, or the composite sample, consider the number and
slotted belt, rotary disk divider, mechanical stopped or moving nature of the analysis and tests to be performed. A separate
belt sweeper, or other acceptable devices for dividing the moisture laboratory sample may be required, and portions may
sample. Typical mechanical sample dividers are shown in Fig. be required for grindability and other tests. Also, a reserve
1. These illustrate various designs, but other acceptable designs sample may be desired in case a check analysis or test is
are available. required.
6.2.2 Riffle—A manual sample divider that splits the coal 7.3 This practice specifies situations when air drying the
stream into a number of alternate elements. Riffle slots should sample is necessary during sample preparation. Test Method
be at least three times the top size of coal being divided. A D 3302 specifies procedures for air drying and calculation of
typical riffle is shown in Fig. 2. It is preferable that feed chutes percent air dry loss.
and enclosed riffles be used. The slope of feed chutes and riffles 7.3.1 Calculate and record air-dry loss determination each
must be at least 60°. time air drying is performed.
6.2.2.1 Feed Scoop—A feed scoop or pan having straight 7.3.2 In handling, reducing, and dividing the sample, all
sides and a width equal to the effective width of the riffle shall operations shall be done rapidly and in as few operations as
be used to feed the riffle. possible, since moisture loss depends on several factors other
6.2.2.2 Feed Chute—A feed chute shall be used as shown in than total moisture content, such as time required for crushing,
Fig. 2. The minimum discharge opening of the feed chute shall atmospheric temperature and humidity, and type of crushing
be the same width as the riffle slot opening. equipment.

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(a) Reciprocating Cutter—Fig. 1(a) shows a section of a cutter which is moved across a stream of coal. At regular intervals, the cutter movement is reversed and a sample
increment is collected on each trip through the coal stream.
(b) Rotating Cutter—Fig. 1(b) shows two cutters attached to a hollow, rotating shaft. Each cutter is designed to extract increments from the feed and to discharge these
into the hollow shaft. One or more cutters may be used.
(c) Rotating Hopper and Spout—Fig. 1(c) shows the totaling hopper that receives the crushed sample and discharges it through a spout over one or more stationary
cutters.
(d) Rotating Cone—A sampler developed by the British National Coal Board. Two slotted cones are locked together and rotated on a vertical shaft so that on each
revolution the common slot operating intercepts the falling stream of coal and collects an increment.
FIG. 1 Mechanical Sample Dividers

7.3.3 While awaiting preparation, the gross or divided subsample shall be weighed and its moisture equilibrated with
sample shall be protected from moisture change as a result of the new atmosphere, and the loss or gain in mass shall be used
exposure to rain, snow, wind, and sun on contact with in the calculation of moisture content.
absorbent materials.
7.3.4 Whenever subsamples are stored or transported, the 8. Sieve Tests
containers and subsample shall be weighed and equilibrated to
the new atmosphere by air drying, and the weight loss or gain 8.1 The errors of sample division are sensitive to the top
shall be used in the calculation of moisture content. size, and therefore, it is important to make a periodic sieve test
7.4 Whenever a distinct change of humidity occurs during of the product of the sample crusher. Sieve tests shall be made
the course of preparation of an air-dried subsample, the and reported in accordance with Test Method D 4749.

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FIG. 2 Sample Divider (Riffle)

9. Procedure interest in determining the air-dry loss value before crushing.

9.1 Mass—The minimum allowable mass of the sample at Air dry in accordance with Test Method D 3302.
any stage depends on the top size, the variability of the 9.2.2 In the reduction and division of gross or divided
constituent sought, and the degree of precision desired (Table samples for which total moisture content is to be determined,
1). the precautions in 7.3 and 7.4 must be followed.
9.2 Reduction and Division (See Fig. 3 for flowchart): 9.2.3 Procedure A—Manual Riffling:
9.2.1 It is permissible to air dry the sample before crushing. 9.2.3.1 Reduce the gross or divided sample to a top size of
Samples may require air drying to feed properly through the 4.75-mm (No. 4) or 2.36-mm (No. 8) sieve taking precautions
reduction and dividing equipment. Sometimes there is an in accordance with Section 7.
9.2.3.2 Determine the number of passes required in the
TABLE 1 Preparation of Laboratory Sample riffling operation from the total mass of the gross sample and
Divide to a minimum the minimum permissible mass in accordance with Table 1.
Crush to pass at least 95 weight of, gA 9.2.3.3 Divide the crushed sample by using a large riffle.
% through sieve
Group A Group B Riffles properly used will reduce sample variability but cannot
No. 4 (4.75-mm) 2000 4000 eliminate it. A typical enclosed riffle is shown in Fig. 2 and
No. 8 (2.36-mm) 500 1000 described in 6.2.2. Pass the coal through the riffle from a feed
No. 20 (850 µm) 250 500
No. 60 (250 µm) 50 50
scoop, feed bucket, or riffle pan having a lip or opening the full
(100 % through) width of the riffle. When using any of the preceding containers
A
If a moisture sample is required, increase the quantity of No. 4 (4.75-mm) or to feed the riffle, spread the coal evenly in the container, raise
No. 8 (2.36-mm) sieve subsample by 500 g. the container, and hold it with its front edge resting on top of

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FIG. 3 Sample Preparation Flowchart

the feed chute, then slowly tilt it so that the coal flows in a the riffle from a small-mouthed container. Do not allow the
uniform stream through the hopper straight down over the coal to build up in or above the riffle slots. If it does not flow
center of the riffle into all the slots, then into the riffle pans, one freely through the slots, shake or vibrate the riffle to facilitate
half of the sample being collected in each pan. Under no even flow.
circumstances shovel the sample into the riffle or dribble into

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9.2.3.4 If the initial crushing was only to 4.75-mm (No. 4) 10. Preparation of Composite Samples to Represent Lot-
sieve size, reduce to 2.36-mm (No. 8) sieve size after dividing Size (or Consignment-Size) Quantities of Coal
to no less than the quantity specified in Table 1 for a 4.75-mm 10.1 There are several issues to consider when deciding
(No. 4) sieve size. whether to make a physical composite of separate samples
9.2.3.5 After reducing to 2.36-mm (No. 8) sieve size, divide collected to represent different parts of the same lot (or
the subsample by riffling to no less than the quantity specified consignment). When the analytical parameters of interest are
in Table 1 for a 2.36-mm sieve size. additive (for example, proximate and ultimate analyses) the
9.2.3.6 With suitable pulverizing equipment (see 6.1), re- preferred method is to test the individual samples and perform
duce the 2.36-mm (No. 8) sieve size subsample to a 250-µm a ton-weighted mathematical average to determine the result
(No. 60) sieve size. Divide the ground subsample by riffling, for the lot (or consignment). See Note 2. On the other hand,
using the small riffle (see 6.2.2) until a minimum of 50 g is when the sought-after parameters are non-additive (for ex-
obtained. Quickly pass the subsample through a 250-µm (No. ample, ash fusibility and Hardgrove grindability), analysis of a
60) sieve. Reduce the particles retained on the screen, on a composite sample is the only way to achieve a meaningful test
bucking board or mortar and pestle to pass the sieve, and add result. Another consideration is that since there are no provi-
to what passed through the sieve and mix thoroughly. This is sions in this standard for dividing samples of top size larger
the analysis sample. than 250 µm (No. 60) by means other than riffling or mechani-
9.2.3.7 As an alternative to the procedure of 9.2.3.6, the cally subsampling, the exact weights needed for preparation of
2.36-mm (No. 8) sieve size subsample may be reduced to pass composite samples containing larger particles are not attain-
95 % through a 850-µm (No. 20) sieve. Divide this subsample able. Taking these and other issues into account leads to the
by riffling with the small riffle to not less than the quantity requirement that preparation of composites be performed with
specified in Table 1, and then reduce to 250-µm (No. 60) sieve strict adherence to the procedures which are described below
size in accordance with 9.2.3.6. and are summarized in Table 2. The details pertaining to the
9.2.3.8 Thoroughly mix, preferably by mechanical means, preparation of composite samples must be agreed to by all
the analysis sample, weighing not less than 50 g, before concerned parties.
extracting portions for analysis (see 6.3).
9.2.4 Procedure B—Mechanical Division: NOTE 2—As used in this standard, parameters which are additive are
those having values that are not affected by interactions between the
9.2.4.1 Reduce the gross or divided sample in stages and physical and chemical properties of the combined individual samples.
divide by suitable mechanical sample dividers (see 6.2.1) to Non-additive parameters are those for which such interactions may occur
quantities not less than those shown in Table 1. or those for which definitive information on interactions is not available.
9.2.4.2 Mechanical division of the sample consists of auto- 10.2 If two or more samples have been collected by a single
matically collecting a large number of increments of the mechanical coal sampling system operated under constant
properly reduced sample. Distribute this large number of settings resulting in a constant sampling ratio (see Practice
increments equally throughout the entire discharge from the D 2234/D 2234 M), or by multiple sampling systems with
sample crusher because crushers can introduce appreciable identical sampling ratios, prepare the composite by directly
segregation. At each stage of division, take at least 60 combining all of the material from all samples. If it is desired
increments. to decrease the total weight of the composite, it is acceptable to
NOTE 1—It is recommended that, in the case of mechanical division in combine equal percentages (for example, 75 % or 50 %) of
which an increment is not thoroughly mixed with other increments before each individual sample, all of which have been divided in the
division, a portion of each increment be collected by the subsequent stage same manner and according to this standard. Determine
increment collection process. whether sample masses have been decreased, and by what
9.2.4.3 Thoroughly mix the analysis sample, 100 % through percentage, prior to arrival of samples at the laboratory.
250-µm (No. 60) sieve and weighing not less than 50 g, in Account for that information when making the composite. The
accordance with 9.2.3.8 before extracting portions for analysis. samples may be reduced in nominal top size (for example, to
TABLE 2 Preparation of Composite Samples
For Analysis of Additive Parameters For Analysis of Non-additive Parameters
Source of Samples to be Required Nominal Top Size Required Nominal Top Size
Combined Required Nominal Top Size Required Nominal Top Size
is Larger than 250 µm (No. is Larger than 250 µm (No.
is 250 µm (No. 60) Sieve Size is 250 µm (No. 60) Sieve Size
60) Sieve Size 60) Sieve Size
Single mechanical coal Test samples individually Test samples individually Combine large particle-size Combine large particle-size
sampling system with a (preferred), or combine large (preferred), or combine large samples directly per 10.2 samples directly per 10.2
constant sampling ratio, or particle-size samples directly particle-size samples directly
multiple sampling systems per 10.2 per 10.2
having identical sampling
ratios

Multiple mechanical coal Test samples individually Test samples individually (do Combine minus 250 µm (No. Combine large particle-size
sampling systems which do (preferred), or combine minus not combine) 60) sieve size samples per samples using close-
not have identical sampling 250 µm (No. 60) sieve size 10.3 approximation procedure per
ratios, or manual sampling samples per 10.3 10.4
practices

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pass a 2.36 mm (No. 8) sieve) to facilitate the compositing sampling ratios, or if manual sampling practices have been
process. Adhere to the minimum weights required in Table 1. used, and particles larger than 250 µm (No. 60) sieve size are
Observe the precautions of Practice D 2234/D 2234 M and Test required for analysis of non-additive parameters (such as for
Method D 3302, as well as those found in this standard, to Hardgrove grindability), prepare a close-approximation com-
guard against unaccounted-for changes in moisture. It is posite sample as follows.
advisable to mix the composite sample thoroughly, but without 10.4.1 Ascertain the mass of the sub-lot or lot represented
altering the moisture content, before reducing or dividing to by each sample and the total mass represented by all samples.
smaller quantities. Calculate the percentage of the total sub-lot or lot which each
10.3 If two or more samples have been collected by multiple sample represents. Select an approximate desired mass for the
mechanical coal sampling systems which do not have identical composite sample. Multiply the desired composite mass by the
sampling ratios, or if manual sampling practices have been percentage of the total which each sample represents to find the
used, and only 250 µm (No. 60) sieve size samples are required exact number of grams which are desired for each sample to be
for analysis (such as for proximate, ultimate, ash fusibility, used in making the composite.
etc.) prepare the composite sample using the 250 µm (No. 60) 10.4.2 Using a riffle, divide one sample to obtain approxi-
sieve size samples as follows. mately the number of grams for that sample as calculated
10.3.1 Determine the residual moisture content of each 250 above. Do not produce riffle portions which are smaller in mass
µm (No. 60) sieve size sample according to Test Method than stated in Table 1 of this standard. Select and combine the
D 3173 or Test Method D 3302. Designate the results R1, R2, riffle portions which yield a close approximation of the desired
R3... Rn. mass. See Note 3. Repeat for all samples, then combine the
10.3.2 Ascertain the mass of coal in the lot or sub-lot riffled portions of the original samples to form the composite.
represented by each sample and designate these values L1, L2, NOTE 3—It is highly unlikely that the exact number of grams needed
L3... Ln. Add the individual lot or sub-lot masses to find the for each sample can be obtained using a riffle while adhering to the
total sampled lot (or consignment) mass (Ltotal). requirements of Table 1. Do not add or delete particles without using a
10.3.3 Select an approximate desired mass (Mc) for the riffle in order to obtain the exact desired mass. The user must exercise
composite sample. judgment to assess when the riffled mass is sufficiently close to the desired
10.3.4 Calculate, according to the following, the mass of mass so as to not materially affect the results of the test(s) for which the
each sample (M1, M2, M3... Mn) to be combined to make the composite sample is being prepared.
composite sample. 10.4.3 Prepare and use close-approximation composites
~Mc! ~L1! / ~Ltotal! only when particles larger than 250 µm (No. 60) sieve size are
M1 5 (1) required for analysis of non-additive parameters. Indicate on
~100 2 R1! / 100
the laboratory report that data were obtained by testing a
10.3.5 Obtain the calculated mass of each sample to the close-approximation composite, and that the results may there-
nearest 0.0001 g and combine to form the composite sample. fore not fully reflect the properties of the originally sampled
Mix by mechanical means before extracting portions for material.
analysis. 10.5 Table 2 presents a convenient summary of the con-
10.3.6 Calculation of as-received basis data (see Test straints for preparation of composites depending on the source
Method D 3302 and Practice D 3180) from the as-analyzed of samples, the required nominal top size for testing, and
basis data obtained by testing the composite sample requires whether the anticipated analytical parameters are additive or
the equivalent air-dry loss of the composite (ADLc). Compute non-additive.
that value as shown below:
ADLc 5 ~ADL1! ~L1/Ltotal! 1 ~ADL2! ~L2/Ltotal!... 1 ~ADLn! ~Ln/Ltotal! 11. Precision and Bias
(2) 11.1 The precision of sample preparation (and analysis) can
where: be checked by Annex A1 and Annex A2. Since this practice
ADL1 = air-dry loss of first sample, does not produce a numerical result, determination of bias is
ADL2 = air-dry loss of second sample, and not applicable.
ADLn = air-dry loss of nth sample.
10.4 If two or more samples have been collected by multiple 12. Keywords
mechanical coal sampling systems which do not have identical 12.1 coal; composite; division; reduction

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ANNEXES

(Mandatory Information)

A1. METHOD OF CHECKING THE PRECISION OF SAMPLE PREPARATION AND ANALYSIS

A1.1 Scope A1.2.6.1 Make calculations on the first set of ten samples so
A1.1.1 This method covers procedures for checking preci- that the variance for each of the stages may be checked and
sion of sample preparation and analysis of the various stages. corrective action, if needed, may be taken.
The data obtained from tests using consistent sample prepara- A1.2.6.2 Continue this cycle of tests until three successive
tion and analysis method are used to estimate the random errors sets of ten samples are satisfactory.
in the various stages of sample division and analysis.
A1.1.2 Coals used in each series of tests should be of similar A1.3 Calculation
ash content.
A1.3.1 The analysis of variance is based upon the calcula-
A1.2 Procedure tions of mean squared differences with the eight determinations
A1.2.1 Reduce the gross sample to 95 % through 4.75-mm for each sample taken in different combinations. Calculate the
(No. 4) sieve and divide, using either riffles or mechanical variances of these combinations: VP, the variance of the
sample dividers, into two equal parts. difference between duplicate analyses; VQ, the variance of the
A1.2.1.1 Many laboratories are crushing directly to difference between the averages of duplicate analyses; and VR,
2.36-mm (No. 8) size instead of to No. 4; but for purpose of the variance of the difference between the average of each four
test it is usually best to use both No. 4 and 8 sizes since we can analyses, as follows:
assume that crushing directly to No. 8 would give a variance no VP 5 ~1/4N! ([X1 – X2!2 1 ~X3 – X4!2 1 ~Y1 – Y2!2 1 ~Y3 – Y4!2#
greater, and probably less, than crushing to No. 4 and then to (A1.1)
No. 8. If, however, it is desired to crush directly to No. 8,
follow the same procedure as if crushed to No. 4 and then to where:
No. 8. N = number of tests and
A1.2.2 Divide each subsample by riffling or mechanically to X1, X2, X3, X4, Y1, Y2, Y3, Y4 = individual ash deter-
no less than weights as outlined in Table 1. minations.
A1.2.2.1 Individual weights should not vary more than 6
20 % from the weights given in Table 1, and the average of all S D FS
1
VQ 5 2N (
X1 1 X2 X3 1 X4
2 – 2 D S
2
1
Y1 1 Y2 Y3 1 Y4 2
2 – 2 DG
tests should be within 610 % of the weights. (A1.2)
A1.2.3 Reduce the 4.75-mm (No. 4) sieve laboratory
sample 95 % through 2.36-mm (No. 8) sieve and divide, using
either riffles or mechanical sample dividers, into two equal
VR 5 ~1/N!( FS X1 1 X2 1 X3 1 X4 Y1 1 Y2 1 Y3 1 Y4
4 – 4 DG
2

parts without discarding. Divide each subsample to no less than (A1.3)

the minimum weights as outlined in Table 1. A1.3.2 The variances can be resolved further in terms of
A1.2.4 Reduce each part of the No. 8 subsample to 100 % variance caused by the first stage of sample preparation, V1;
through 250-µm (No. 60) sieve and divide to no less than 50 g. variance caused by the second stage of sample preparation, V2;
A1.2.5 Determine ash in accordance with Test Method and the variance of analysis, Va.
D 3174 in duplicate on each analysis sample.
A1.2.5.1 This test can be used for sulfur, Btu, or other where:
determinations, instead of ash, if desired. Va = 1⁄2 VP,
A1.2.5.2 If possible, the duplicate determinations should be V2 = 1⁄2 VQ – 1⁄4 VP, and
made at different times and preferably by different analysts. V1 = 1⁄2 VR – 1⁄4 VQ.
The purpose of these tests is not to find out how accurate a A1.3.3 The total variance of sample preparation and analy-
laboratory can be, but to find out actual variances of prepara- sis, Sda2, is given by the equation:
tion and analysis in the normal routine of a laboratory
Sda2 5 Va 1 V2 1 V1 (A1.4)
following a prescribed procedure.
A1.2.6 Treat three sets of ten samples each in the preceding A1.3.4 The calculations of the variances of sample prepa-
manner. ration are illustrated in Table A1.1.

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TABLE A1.1 Illustrations of the Calculation of the VariancesA of Sample Preparation at the Various Stages and Analysis
Test No. X1 X2 Difference Difference2 X3 X4 Difference Difference2
1 12.13 12.10 0.03 0.0009 12.03 12.05 −0.02 0.0004
2 10.67 10.73 −0.06 0.0036 10.69 10.78 −0.09 0.0081
3 10.93 11.10 −0.17 0.0289 11.36 11.45 −0.09 0.0081
4 12.05 12.02 0.03 0.0009 12.17 12.23 −0.06 0.0036
5 12.74 12.70 0.04 0.0016 12.71 12.76 −0.05 0.0025
6 12.47 12.30 0.17 0.0289 12.21 12.14 0.07 0.0049
7 11.94 11.99 −0.05 0.0025 12.08 12.17 −0.09 0.0081
8 12.52 12.63 −0.11 0.0121 12.76 12.82 −0.06 0.0036
9 12.01 12.05 −0.04 0.0016 11.94 11.77 0.17 0.0289
10 10.96 10.88 0.08 0.0064 11.37 11.40 −0.03 0.0009
Total 118.42 118.50 0.0874 119.32 119.57 0.0691
Average 11.84 11.85 11.93 11.96
Test No. Y1 Y2 Difference Difference2 Y3 Y4 Difference Difference2
1 12.00 12.01 −0.01 0.0001 12.00 12.00 0.00 0.0000
2 10.53 10.65 −0.12 0.0144 10.60 10.62 −0.02 0.0004
3 11.37 11.47 −0.10 0.0100 11.22 11.35 −0.13 0.0169
4 12.13 12.10 0.03 0.0009 12.01 12.04 −0.03 0.0009
5 12.60 12.60 0.00 0.0000 12.51 12.40 0.11 0.0121
6 12.09 12.15 −0.06 0.0036 12.18 12.20 −0.02 0.0004
7 11.93 11.87 0.06 0.0036 11.71 11.73 −0.02 0.0004
8 12.57 12.57 0.00 0.0000 12.58 12.61 −0.03 0.0009
9 11.81 11.88 −0.07 0.0049 11.70 11.84 −0.14 0.0196
10 11.57 11.48 0.09 0.0081 11.54 11.36 0.18 0.0324
Total 118.60 118.78 0.0456 118.05 118.15 0.0840
Average 11.86 11.88 11.81 11.82
Test No. X(1 + 2)/2 X(3 + 4)/2 Difference Difference2 Y(1 + 2)/2 Y(3 + 4)/2 Difference Difference2
1 12.11 12.04 0.07 0.0056 12.00 12.00 0.00 0.0000
2 10.70 10.73 −0.03 0.0012 10.59 10.61 −0.02 0.0004
3 11.01 11.40 −0.39 0.1521 11.42 11.28 0.13 0.0182
4 12.03 12.20 −0.16 0.0272 12.11 12.02 0.09 0.0081
5 12.72 12.73 −0.01 0.0002 12.60 12.45 0.14 0.0210
6 12.38 12.17 0.21 0.0441 12.12 12.19 −0.07 0.0049
7 11.96 12.12 −0.16 0.0256 11.90 11.72 0.18 0.0324
8 12.57 12.79 −0.21 0.0462 12.57 12.59 −0.02 0.0006
9 12.03 11.85 0.17 0.0306 11.84 11.77 0.07 0.0056
10 10.92 11.38 −0.46 0.2162 11.52 11.45 0.07 0.0056
Total 118.46 119.44 0.5491 118.69 118.10 0.0969
Average 11.85 11.94 11.87 11.81
Test No. X(1 + 2 + 3 + 4)/4 Y(1 + 2 + 3 + 4)/4 Difference Difference2
1 12.07 12.00 0.07 0.0056
2 10.71 10.60 0.11 0.0138
3 11.21 11.35 −0.04 0.0203
4 12.11 12.07 0.04 0.0022
5 12.72 12.52 0.20 0.0400
6 12.28 12.15 0.12 0.0156
7 12.04 11.81 0.23 0.0552
8 12.68 12.58 0.10 0.100
9 11.94 11.80 0.13 0.0182
10 11.15 11.48 −0.33 0.1122
Total 118.95 118.39 0.2932
Average 11.90 11.84

VP = 1⁄40 (0.0874 + 0.0691 + 0.0456 + 0.0840) = 0.0071

VQ = 1⁄20 (0.5491 + 0.0969) = 0.0323
VR = 1⁄10 (0.2932) = 0.0293
Then:
Va = 1⁄2 (0.0071) = 0.0035
V2= 1⁄2 (0.0323) − 1⁄4 (0.0071) = 0.0144
V1= 1⁄2 (0.0293) − 1⁄4 (0.0323) = 0.0066
Sda2= 0.0035 + 0.0144 + 0.0066 = 0.0245
A
This table contains data taken from a computer printout with rounding errors that are not involved in the overall calculation. Data taken at intermediate steps are not
consistent within limits of these rounding errors. Thus, the difference 0.072 shows a result of 0.0056 which is correct when all places are carried in the calculation.

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 D 2013 – 04

A2. METHOD FOR DETERMINING THE OVERALL VARIANCE OF DIVISION AND ANALYSIS

A2.1 Scope where:

A2.1.1 Legitimate estimates of the variance of division and Sda2 = variance of division and analysis,
analysis, Sda2, can only be made using data obtained from tests x2 = sum of the squares of the four ash results, and
that were run using consistent division and analysis methods. ((x)2 = sum of the ash results, quantity squared.
Coals used in these variance tests should be of similar ash A2.2.3 Make progressive checks as the work is carried out
content. Any gross change in the division and analysis methods by using the data in groups of 5. In any group of 5 estimates of
or in the ash characteristics of the test coal will nullify the test Sda2 based on 4 subsamples for each estimate, the ratio of the
results. largest estimate to the average of the group should not exceed
2.99, in 19 out of 20 cases. Investigate values in excess of this
A2.2 Procedure
ratio before proceeding with the test. In addition, after com-
A2.2.1 The following four-step method uses the regular pleting 30 sets, by groups of 5, the ratio of the largest group
gross or divided samples obtained from normal sampling average to the overall average should not exceed 1.88 in 19
operations: cases out of 20. If these criteria are met, the variance of
A2.2.1.1 Crush the gross sample to the same mesh as that
division and analysis may be taken as the overall average Sda2
normally obtained when preparing the gross sample for pro-
of the 30 sets of data. If these criteria are not met, follow the
cessing,
procedure described in Practice D 2013 for the necessary
A2.2.1.2 Divide the sample into four equal parts, according
to the normal routine laboratory procedure, information to improve techniques of division and analysis.
A2.2.1.3 Reduce the four subsamples to laboratory analysis A2.2.4 Example—A complete example illustrating the pro-
samples, and cedure for determining the variance of division and analysis is
A2.2.1.4 Analyze each analysis sample for dry ash content. given in Table A2.1. In this example, gross sample No. 24, the
A2.2.2 Calculate the variance of division and analysis for highest individual ash sample in the group (19.28 % ash), has
each gross or divided sample from the “within set sums of an unusually high variance of division and analysis. The
squares” for the replicate determinations as follows: behavior of samples 21 to 30 indicates that trouble can be
Sda2 5 [(x 2 2 ~ (x!2/4]/3 (A2.1) expected when the ash exceeds 15 % (see Table A2.1).

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 D 2013 – 04
TABLE A2.1 Determination of Variance of Division and Analysis—Use of Four Analysis Samples for Each Gross Sample
NOTE 1—Ten percent ash was subtracted from each of the ash results listed to simplify the calculations.
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)
Gross Analysis Samples Average
Sample (x (x2 ((x)2/4 (6)–(7) (8)/3 = Sda2 Sets of CiA CiB
Number 1 2 3 4 5 Sda2
1 1.22 1.37 1.56 1.71 5.86 8.7230 8.5849 0.1381 0.0460 1.62
2 1.29 1.17 1.70 1.57 5.73 8.3879 8.2082 0.1797 0.0599 2.11
3 1.56 1.66 1.58 1.64 6.44 10.3752 10.3684 0.0068 0.0023 0.08
4 5.63 5.57 5.93 5.52 22.65 128.3571 128.2556 0.0015 0.0005 0.02
5 3.90 3.87 3.58 3.56 14.91 55.6769 55.5770 0.0999 0.0333 1.17
Average ... ... ... ... 12.78 ... ... ... ... 0.0284 ... 0.61
6 0.64 0.42 0.80 0.73 2.59 1.7589 1.6770 0.0819 0.0273 1.12
7 2.47 2.44 2.74 2.68 10.33 26.7445 26.6772 0.0673 0.0227 0.93
8 3.70 3.53 3.43 3.43 14.09 49.6807 49.6320 0.0487 0.0162 0.66
9 3.59 3.73 4.13 3.80 15.25 58.2979 58.1406 0.1573 0.0524 2.15
10 2.14 2.17 2.25 2.11 8.67 18.8031 18.7922 0.0109 0.0036 0.15
Average ... ... ... ... 12.55 ... ... ... ... 0.0244 ... 0.52
11 5.71 5.61 5.61 5.71 22.64 128.1524 128.1424 0.0100 0.0033 0.09
12 3.21 3.40 2.86 2.90 12.37 38.4537 38.2542 0.1995 0.0665 1.87
13 4.99 4.80 5.51 4.93 20.23 102.6051 102.3132 0.2919 0.0973 2.74
14 3.26 3.15 3.17 3.09 12.67 40.1471 40.1322 0.0149 0.0050 0.14
15 3.48 3.65 3.59 3.53 14.25 50.7819 50.7656 0.0163 0.0054 0.15
Average ... ... ... ... 14.11 ... ... ... ... 0.0355 ... 0.76
16 2.89 2.84 2.85 2.89 11.47 32.8923 32.8902 0.0021 0.0007 0.02
17 2.35 2.48 2.90 2.71 10.44 27.4270 27.2484 0.1786 0.0595 1.86
18 4.23 3.92 4.13 4.05 16.33 66.7187 66.6672 0.0515 0.0172 0.54
19 5.46 5.13 5.13 5.38 21.10 111.3898 111.3025 0.0873 0.0291 0.91
20 3.15 2.98 3.42 3.47 13.02 42.5402 42.3801 0.1601 0.0534 1.67
Average ... ... ... ... 13.62 ... ... ... ... 0.0320 ... 0.69
21 2.88 2.81 2.80 2.59 11.08 30.7386 30.6916 0.0470 0.0157 0.17
22 4.94 4.32 4.40 4.39 18.05 81.6981 81.4506 0.2945 0.0982 1.05
23 4.04 4.28 4.47 4.48 17.27 74.6913 74.5632 0.1281 0.0427 0.46
24 8.38 8.28 8.93 9.28 34.87 304.6461 303.9792 0.6669 0.2223 2.39
25 6.93 6.97 6.37 6.54 26.81 179.9543 179.6940 0.2603 0.0868 0.93
Average ... ... ... ... 15.40 ... ... ... ... 0.0931 ... 2.00C
26 4.52 4.27 3.66 4.07 16.52 68.6238 68.2276 0.3962 0.1321 2.02
27 4.53 4.46 4.54 4.65 18.18 82.6466 82.6281 0.0185 0.0062 0.09
28 2.18 2.42 2.45 2.31 9.36 21.9474 21.9024 0.0450 0.0150 0.23
29 8.84 9.21 8.69 8.55 35.29 311.5883 311.3460 0.2423 0.0808 1.24
30 5.03 4.73 5.47 5.11 20.34 103.7068 103.4289 0.2779 0.0926 1.42
Average ... ... ... ... 14.98 ... ... ... ... 0.0653 ... 1.40
Overall ... ... ... ... ... ... ... ... ... 0.0465 ...
average
Sda2
A
“C” for individuals in subgroup. Divide individual Sda2 values (Column 9) by average Sda2 (Column 10). Results should be below 2.99 in 19 cases out of 20.
B
“C” for subgroup averages. Divide average Sda2 (Column 10) by overall averages Sda2. Result should be below 1.88 in 19 cases out of 20.
C
Above limit of 1.88.

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