EPA-650/4-74-026
June 1974
Environmental Monitoring Series
m
:*£•
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EPA-650/4-74-026
COLLABORATIVE STUDY
OF METHOD FOR STACK GAS
ANALYSIS AND DETERMINATION
OF MOISTURE FRACTION
WITH USE OF METHOD 5
by
Henry F. Hamil and Richard E. Thomas
Southwest Research Institute
8500 Culebra Road
San Antonio, Texas 78284
Contract No. 68-02-0626
ROAP No. 26AAG
Program Element No. 1HA327
EPA Project Officer: M. Rodney Midgett
Quality Assurance and Environmental Monitoring Laboratory
National Environmental Research Center
Research Triangle Park, North Carolina 27711
Prepared for
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
June 1974
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This report has been reviewed by the Environmental Protection Agency
and approved for publication. Approval does not signify that the
contents necessarily reflect the views and policies of the Agency,
nor does mention of trade names or commercial products constitute
endorsement or recommendation for use.
ii
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SUMMARY AND CONCLUSIONS
This report presents the analyses of data which were obtained in the performance of EPA Method 3 (Gas Analysis
for Carbon Dioxide, Excess Air, and Dry Molecular Weight) and in the determination of stack moisture content with
the use of EPA Method 5 for particulate matter determination. The data were obtained during collaborative testing of
Method 5.
The collaborative tests were conducted at a Portland cement plant, a coal-fired power plant, and a municipal incin-
erator, using four sampling teams at each site. For this study, each sampling run at a test site is considered a repetition
at the same true level for both the stack gas analysis and the moisture determination. This assumption is made since
there were no independent methods for the determination of true values, and since at a given site there were no signifi-
cant changes in the determined values. At the cement plant, power plant, and incinerator, there were 15, 16, and 12
runs, respectively. Not all collaborators completed all runs, and thus there were missing values for the statistical analyses.
A total of 160 Method 3 determinations and 150 moisture determinations were submitted to statistical treatment.
Precision estimates are obtained for the various parameters, with the exception of excess air, from an analysis of
variance based on a nested experimental design. These estimates are expressed in terms of within-laboratory, laboratory
bias, and between-laboratory components, and are presented below in terms of standard deviations. Since the actual
gas composition undoubtedly varied slightly from run to run, with within-laboratory components contain source varia-
tions as well as sampling error and are probably larger than would be expected in the use of these analytical procedures
in the field. The laboratory bias component is essentially free of this added variation due to the manner in which it is
calculated. The results obtained for each component are summarized below.
Method 3- All collaborators used Orsat apparatus to perform their stack gas analyses. The average of three con-
secutive analyses was used, but the requirement that they differ by no more than 0.2% by volume was not enforced.
There was no detectable CO at any of the test sites:
(1) CO-i . The within-laboratory standard deviation is estimated as 1 .44% C02 by volume, with 149 degrees of
freedom. The laboratory bias standard deviation is estimated as 1 .06% CO2 , with 9 degrees of freedom. This
gives a between-laboratory standard deviation of 1 .78% C02 . Particulate concentrations from compliance
tests at municipal incinerators are corrected to 12% C02 . The demonstrated variation in a C02 determina-
tion would cause the reported particulate concentrations of two laboratories who obtained the same
uncorrected particulate concentrations to differ from each other by 36% at low C02 levels, and 16%
at high CO2 levels.
(2) O2 . The within-laboratory standard deviation for O2 is estimated as 1.70% O2 by volume, with 149 degrees
of freedom. The laboratory bias standard deviation is estimated as 1 .29% 02 , with 9 degrees of freedom.
This results in an estimated between-laboratory standard deviation of 2.14% 02 .
(3) Dry Molecular Weight. The within-laboratory standard deviation for dry molecular weight determination is
0.20 Ib/lb-mole with 149 degrees of freedom. The estimated laboratory bias standard deviation is 0.14
Ib/lb-mole with 9 degrees of freedom. From these, the between-laboratory standard deviation is estimated
as 0.24 Ib/lb-mole. Thus, this determination is precise, even though there is considerable variation in the C02
and O2 values used in the calculation.
(4) Excess Air. The excess air determination is shown to be a function of the O2 level, increasing exponentially
as the % 02 increases. The least squares estimation of the model is
with a coefficient of determination, r2 , of 0.993. The equation was obtained using one quarter of the excess
air values from the three sites. From this model and the precision demonstrated for % 02 , normal deviation
in % 02 determination can be expected to produce a variation of from 30% to 60% in the excess air value.
fli
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Moisture Fraction—The within-laboratory standard deviation is estimated as 0.032 with 140 degrees of freedom.
The laboratory bias standard deviation estimate is 0.032 with 8 degrees of freedom. This gives a between-laboratory
standard deviation of 0.045.
The following conclusions and recommendations are made based upon the results presented above:
(1) In a great deal of compliance testing, Method 3 is used only for the determination of the dry molecular
weight of the stack gas, i.e., the CO2 and excess air values are not used in subsequent calculations. When
this is the case, the requirement that 3 consecutive analyses differ by no more than 0.2% by volume may be
relaxed. The precision shown for the dry molecular weight in this study without the restriction would be
sufficient for field tests usage.
(2) When correction factors based upon the Orsat analysis are to be used, e.g. correction to 12% CO2 or correc-
tion for excess air, it is imperative that the stack gas composition be determined precisely. Small variations
in the C02 and 02 levels can produce relatively large variations in these factors, and thus three consecutive
analyses differing by no more than 0.2% by volume is a reasonable requirement.
(3) To allow more precise determination of stack gas composition, two relatively simple modifications of the
standard Orsat gas analyzer could be made.
(a) The gas buret could be modified to allow direct reading to 0.1 mfi, with interpolation to the nearest
0.05 mfi.
(b) A more accurate method of adjusting the pressure in the gas buret to atmospheric pressure could be
installed. The present hand-held leveling bulb could be replaced with a leveling bulb mounted in a
screw-adjustable leveling clamp. Incorporation of a small sidearm manometer at the top of the buret
would allow precise adjustment of the pressure via the screw adjustment on the leveling clamp. In-
stallation of a stopcock in the sidearm manometer would be necessary to block off the manometer
during filling of the gas buret and during transfer of the gas to and from the absorbing burets.
IV
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TABLE OF CONTENTS
Page
LIST OF ILLUSTRATIONS w
LIST OF TABLES n
I. INTRODUCTION 1
II. TEST DESCRIPTION 2
A. Collaborative Test Sites 2
B. Collaborators and Test Personnel 2
III. STATISTICAL DESIGN 4
A. Terminology 4
B. Experimental Design 5
C. Data Handling and Analysis 5
IV. METHODS 7
A. Carbon Dioxide 7
B. Oxygen 9
C. Dry Molecular Weight 11
D. Excess Air 12
V. MOISTURE FRACTION 15
APPENDIX A-Method 3. Gas Analysis for Carbon Dioxide, Excess Air, and Dry Molecular Weight ... 17
APPENDIX B-Moisture Fraction Determination from Method 5 21
APPENDIX C-Statistical Methods 25
LIST OF REFERENCES 37
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LIST OF ILLUSTRATIONS
Figure Page
1 Schematic Test Han, Method 3 5
2 Schematic Test Plan, Moisture Fraction 5
LIST OF TABLES
Table Page
1 Carbon Dioxide Data 8
2 Oxygen Determination Data 10
3 Dry Molecular Weight Data 11
4 Percent Excess Air Data 12
5 Moisture Fraction Data 16
C.I Analysis of Variance for % C02 28
C.2 Analysis of Variance for % 02 30
C.3 Analysis of Variance for Dry Molecular Weight 31
C.4 Analysis of Variance for Moisture Fraction 34
VI
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I. INTRODUCTION
This report describes the work performed on Contracts 68-02-0623 and 68-02-0626 and the results obtained on
Southwest Research Institute Project 01-3462-008, Contract 68-02-0626, which includes collaborative testing of the
method for stack gas analysis and the method for determination of stack gas moisture fraction with use of Method 5 for
particulate emissions as given in "Standards of Performance for New Stationary Sources"*1 \
This report describes the statistical analysis of the data from collaborative tests conducted at a Portland cement
plant/2* a coal-fired power plant*3), and a municipal incinerator*4 ^
The collaborative tests of the method for stack gas analysis and the method for determination of the stack gas
moisture fraction were not conducted as separate tests of Methods 3 and 4 O but as these methods are used in con-
junction with Method 5 for particulate emissions.
The results of the data analyses and the conclusions and recommendations based on these analyses are given in
this report.
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II. TEST DESCRIPTION
A. Collaborative Test Sites
The site of the Portland cement plant test was the Lone Star Industries Portland Cement Plant in Houston, Texas.
This plant utilizes the wet feed process and operates three kilns. The flue gas from each kiln passes through a separate
electrostatic precipitator. The flue gases are then combined and feed into a 300-foot-high stack/2 * Samples were taken
at the sample ports located on the stack 150 feet above grade.
Typical stack gas composition was about 7.5% C02 and 13.5% O2. No CO was detected. Moisture fraction (Bwo)
was about 0.25.
The site of the coal-fired power plant was the Allen King Power Plant, The Northern States Power Company, near
St. Paul, Minnesota. The exhaust gas from the combustion chamber passes through the heat exchanger and splits into
two identical streams upstream of twin electrostatic precipitators. The twin emission gas streams are fed into an 800-foot-
high stack through two horizontal ducts/3)
Samples were taken from sample ports located in the south horizontal duct upstream of the entrance to the stack
flue. Typical stack gas composition was about 11.8% C02 and 6.4% O2. No CO was detected. Moisture fraction (Bwo)
was about 0.10.
The site for the municipal incinerator test was the Holmes Road Incinerator, City of Houston, Houston, Texas.
The facility consists of two independent parallel furnace trains. Refuse feeds continuously onto traveling grate stokers in
the furnaces. Gases leaving the furnaces are cooled in water spray chambers, and then enter the flue gas scrubbers to remove
particulates. The gases are then drawn through induced draft fans and exhaust into the 148-foot-high stacks. Samples
were taken from the sample ports located on the stacks 102 feet above grade. During the test, samples were taken from
both units at the incinerator. Typical stack gas composition was about 5.2% CO2 and 14.1% O2. No CO was detected.
Moisture fraction (Bwo) was about 0.40.
Stack gas samples were taken at all three sites during the performance of Method 5 determinations. Equal quan-
tities of gas were taken at each traverse point to provide an integrated sample. Stack gas was transferred from the stack
to a gas sample bag by means of a one-way squeeze bulb. Stack gas samples were analyzed by the Orsat procedure after
each day's runs.
Moisture determination was made by the impinger method in conjunction with the Method 5 determinations.
B. Collaborators and Test Personnel
The collaborators for the Lone Star Industries Portland Cement Plant test were Mr. Charles Rodriguez and
Mr. Nollie Swynnerton of Southwest Research Institute, San Antonio Laboratory, San Antonio, Texas; Mr. Mike Taylor
and Mr. Ron Hawkins of Southwest Research Institute, Houston Laboratory, Houston, Texas; Mr. Quirino Wong,
Mr. Randy Creighton, and Mr. Vito Pacheco, Department of Public Health, City of Houston, Houston, Texas; and
Mr. Royce Alford, Mr. Ken Drummond, and Mr. Lynn Cochran of Southwestern Laboratories, Austin, Texas.
The collaborators for the Allen King Power Plant test were Mr. Mike Taylor and Mr. Hubert Thompson of
Southwest Research Institute, Houston Laboratory, Houston, Texas; Mr. Charles Rodriguez and Mr. Ron Hawkins of
Southwest Research Institute, San Antonio Laboratory, San Antonio, Texas; Mr. Gilmore Sem, Mr. Vern Goetsch,
and Mr. Jerry Brazelli of Thermo-Systems, Inc, St. Paul, Minn.; and Mr. Roger Johnson and Mr. Harry Patel of Environ-
mental Research Corporation, St. Paul, Minn.
The collaborators for the Holmes Road Incinerator test were Mr. Mike Taylor and Mr. Rick Hohmann of Southwest
Research Institute, Houston Laboratory, Houston, Texas; Mr. Charles Rodriguez and Mr. Ron Hawkins of Southwest
Research Institute, San Antonio Laboratory, San Antonio, Texas; Mr. Quirino Wong, Mr. Randy Creighton, and
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Mr. Steve Byrd, City of Houston, Department of Public Health; Mr. John Key, Mr. James Draper, Mr. Tom McMicklc,
Mr. Tom Palmer, Mr. Michael Lee, and Mr. Charles Goerner, Air Pollution Control Services, Texas State Department of
Health.*
The Portland cement plant test was conducted under the supervision of Dr. Henry Hamil, and the power plant
and municipal incinerator tests were conducted under the supervision of Mr. Nollie Swynnerton, both of Southwest
Research Institute.
Collaborators for all three tests were selected by Dr. Hamil.
•"Throughout the remainder of this report, the collaborative laboratories are referred to by randomly assigned code numbers. For the
cement plant test, code numbers 101,102,103, and 104 are used. For the power plant test, code numbers 201, 202, 203, and 204 are
used. For the cement plant test, code numbers 301, 302, 303, and 304 are used. These numbers do not correspond to the above ordered
listing of laboratories. The ordering is the order that was used in the particulate collaborative studies. The first digit has been changed
to correspond to the site numbers used in this report.
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III. STATISTICAL DESIGN
A. Terminology
To facilitate the understanding of this report and the utilization of its findings, this section explains the statistical
terms used in this report. The estimates of the pertinent values are developed in the subsequent sections.
We say that an estimator, 0, is unbiased for a parameter 6 if the expected value of 0 is 6 , or in notational form ,
E(d) = 6. From a population of method determinations made at the same true level, y., let xt , x2 , . . . ,xn be a sample
of n replicates. Then we define:
n
1 ^-^
(1) x = — j ^ X( as the sample mean, an unbiased estimate of the true mean of the population of determina-
n ~™
i= i
tions, 5. The sample mean gives an estimate of the center of the distribution of the determinations. If
the method is accurate, 5 is equal to n, the true level.
(2) SS= (Xi — x)2 as the sum of squares for the sample, which is used to estimate the dispersion of the
i = 1
population of determinations around 5.
(3) d/as the degrees of freedom, an indication of the amount of confidence in the estimate. A larger number
of d/implies more confidence in the estimate.
(4) d2 = SS/df, as a variance estimate, or mean square, unbiased for a2 , the true variance of the determinations.
The variance is a measure of the dispersion in the determinations around the true mean, 6 .
(5) a = vS2, as the estimated standard deviation of the determinations. This term is a biased estimate of
a = \Ar and is an alternative measure of dispersion.
The variability in a method determination is expressed in terms of within-laboratory, laboratory bias and between-
laboratory components. The following definitions of these terms are given with respect to a true value, M.
• Within-laTjoratory—The within-laboratory component measures the dispersion in replicate single method
determinations of the same true value, ju, made by one laboratory. The within-laboratory variance is
estimated from the results of each laboratory at each test site and is denoted by a2 .
• Laboratory Was-The laboratory bias component measures the dispersion in determinations made of the
same true value, p, due to use of the method by separate laboratories. These differences can be ascribed
to such factors as different analysts and instrumentation, and the variance, a£, is estimated by comparing
the results obtained by different laboratories at each test site.
• Between-laboratory— The between-laboratory component is estimated from the within-laboratory and
laboratory bias terms. The between-laboratory standard deviation is an estimate of the variation that can
be expected between two single determinations made of the same true value, n, by two laboratories work-
ing independently. The between-laboratory variance, a2, , is defined as
a2=(i2+a2.
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B. Experimental Design
The data were collected from three separate tests of Method 5 at three sources covered by the new source per-
formance standards/1' At each site, four collaborating laboratories were used, but the laboratories and collaborators
varied from one test site to another. The number of sampling runs also varied from site to site.
The model chosen is a nested or hierarchical moder ' with three factors: sites, labs-within-sites, and repetitions-
within-labs-within-sites or error. There were three sites; a cement plant, a power plant, and an incinerator.
The determinations from each of the laboratories are considered only within the particular site where they were
made. For each laboratory during each run of the test, determination of the stack gas composition by Method 3 and
moisture fraction determination by Method 5 were called for.
For the analysis of the particulate matter determination at both the power plant and the cement plant, one labor-
atory's results were excluded. At the cement plant, Lab 102 deviated from Method 5 in the laboratory analysis of the
particulate matter. However, this had no bearing on either the Method 3 data or the moisture fraction data, and thus
Lab 102's results are included in this study. At the power plant, Lab 201 was eliminated due to the probable develop-
ment of leakage during some runs and filter contamination due to use of a low-melting ground joint lubricant. Since
this would adversely affect the volumes of stack gas and liquid collected due to the introduction of ambient air into
the train, their moisture fractions are not usable. The Method 3 data from Lab 201 are unaffected and are included in
the analysis.
The schematic of the design for the treatment of the various Method 3 results is shown in Figure 1. The schematic
design for the analysis of the moisture fraction data is shown in Figure 2. The number of repetition, r/, varies slightly
SITE 1 SITE 2 SITE 3
I I I
I I I I I I I I I I T I
LAB 101 LAB 102 LAB 103 LAB 104 LAB 201 LAB 202 LAB 203 LAB 204 LAB 301 LAB 302 LAB 303 LAB 304
rl rl4 r! ri3 . -rl rl6 r-i ("is /"i r16 rj r15 /^ r12 /"i <"12
FIGURE 1. SCHEMATIC TEST PLAN, METHOD 3
SITE 1 SITE 2 SITE 3
I I I I I I
LAB 101 LAB 102 LAB 103 LAB 104 LAB 202 LAB 203 LAB 204 LAB 301 LAB 302 LAB 303 LAB 304
r1 r14 r-i /-15 r, r14 r-t r14 ^ r16 r, r16 r, r15 /^ r12 r, r12 r, r12 r, /•-, ,
FIGURE 2. SCHEMATIC TEST PLAN, MOISTURE FRACTION
from lab to lab at each site due to a failure to complete the run, or in the case of Lab 303, failure to perform an
Orsat analysis.
C. Data Handling and Analysis
The raw data from the tests were used to obtain the determination values used in the analysis. All Method 3
values shown were calculated using the three stack gas content determinations as a starting point, and the moisture
fractions were calculated from the dry gas volume and volume of liquid collected.
Method 3 specifies that three consecutive analyses be made which differ by no more than 0.2 percent by volume
for each of C02 , 02 and CO. This requirement was not enforced in the collaborative tests due to time and difficulty
-------
factors. It has been demonstrated* ^ that this requirement is stricter than can reasonably be expected by a qualified
analyst using the specified equipment. Thus, the data as shown are the averages of three consecutive analyses on an
integrated gas sample.
The statistical model for this experiment is of the form
where
Yjjic is the fcth repetition by lab; at site /.
IJL is the overall mean.
•Yt is the effect of the i*h site.
tyl/ is the effect due to laboratory; at site i.
is the random error associated with Yiik.
The site factor is not of interest, since it merely reflects the differences in the levels of the parameters of
interest from site to site. Its inclusion in the analysis serves as a restriction on the error term by removing
these effects.
The lab factor, X/|/, provides an estimate of the laboratory bias variance by comparing the results from different
laboratories at the same site. The error term, ejtl/lj, is the source of the within-laboratory variance, assumed constant,
and comes from comparison of results by the same laboratory at the same site.
The sampling runs at each site are considered replicate determinations of the same true level for the various factors
studied. This is done since the true levels were unknown, no independent means were available to measure them, and
since inspection of the data does not indicate a great disparity in the level of any factor. As a result, the error term
reflects both normal sampling error and fluctuation in the true level and is probably larger than the true within-labora-
tory variance. The laboratory bias term is essentially free from any error due to level fluctuation, since it is determined
by comparing the averages of all the runs.
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IV. METHODS
Method 3 is for the determination of C02, dry molecular weight, and percentage of excess air. The method calls
for the use of an Orsat analyzer or equivalent to determine the CO2,O2 , and CO content of the stack gas. All the
analyses in this study were performed using Orsat equipment. At all sites tested, there was no detectable percentage
of CO, and thus the resultant variables for study with regard to Method 3 were:
(1) %C02.
(2) %02.
(3) Dry Molecular Weight (Md.).
(4) Excess Air (%EA).
These variables were considered both with respect to the precision that can be expected in their determination and,
where applicable, to the degree that their imprecision could affect the results of a performance test for compliance.
The results of the statistical treatment are presented in the following sections, while more detail of the analyses is
contained in the appropriate Appendix C section.
A. Carbon Dioxide
The C02 determinations made by the collaborators for the three test sites are shown in Table 1. These values
were used in an Analysis of Variance (AOV) on the nested design to give the following results in terms of the precision
associated with a single C02 determination by Method 3 using an Orsat analyzer. The precision estimates are
Obtained in Appendix C.2.
The within-laboratory variance estimate for the % CO2 determinations is
a2 = 2.06
This estimate has 149 degrees of freedom associated with it. The estimated within-laboratory standard deviation is
given by
= V2^06
= 1.44%CO2
The laboratory bias variance, a\, is estimated as
with 9 degrees of freedom. The estimated laboratory bias standard deviation is
= 1.06%CO2.
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TABLE 1. CARBON DIOXIDE DATA
%CO, by volume
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Run
1
2
3
4
' 5
6
7
8
9
10
11
12
13
14
15
16
Run
1
2
3
4
5
6
7
8
9
10
11
12
Sitel
Labs
101
9.0
7.4
6.0
7.0
7.0
10.0
4.6
4.6
6.5
5.8
6.8
7.0
6.0
_*
4.7
102
9.0
9.0
9.0
7.0
10.4
10.5
4.0
7.2
7.6
8.0
8.0
7.6
9.6
9.6
8.6
103
_*
9.0
9.2
11.4
9.1
9.1
5.4
5.8
7.1
7.6
7.2
7.2
6.6
8.5
8.3
104
2.9
7.2
5.1
8.3
4.0
10.0
4.6
_*
7.5
7.4
7.2
6.7
_*
8.1
6.4
Site 2
Labs
201
7.6
7.6
9.4
9.7
8.7
10.3
9.9
9.8
9.7
10.0
8.1
10.2
12.8
13.1
11.7
12.4
202
5.2
8.0
12.6
12.0
13.0
12.6
10.5
11.5
13.2
13.6
12.7
12.2
13.1
12.4
10.6
10.2
203
13.4
13.3
12.7
12.6
12.9
12.7
13.1
13.7
12.9
13.4
12.9
12.3
12.8
13.0
13.4
13.1
204
13.2
12.1
11.6
13.2
13.0
12.5
12.4
12.6
11.9
12.8
12.7
12.4
12.5
_*
13.0
12.6
Site 3
Labs
301
6.4
4.3
6.2
6.0
7.2
5.2
5.7
5.0
5.1
5.5
6.1
5.7
302
4.8
4.0
4.3
6.8
7.1
5.6
6.4
6.1
6.6
5.9
7.9
4.9
303
4.8
4.0
1.0
5.0
5.0
5.2
6.1
_*
-t
-t
-t
-t
304
_*
3.8
3.0
3.7
3.7
3.2
4.1
5.4
5.3
4.3
4.8
3.0
*Run aborted, no Great data taken.
fNo analyses made.
Combining the previous estimates, the between-laboratory
variance, oj , is estimated as
= 2.06 + 1.12
= 3.18.
This gives an estimated between-laboratory standard deviation of
= 1.78%C02
The percent C02 determination is used as a correction factor
in the determination of particulate emissions from incinerators accord-
ing to the formula
12
%C02
The effect of a deviation from the actual %CO2 upon this correction
factor and upon the particulate concentration determination can
be demonstrated by considering the case where the determined
value differs from the actual by one standard deviation. The between-
laboratory standard deviation is used since this gives an indication
of the comparative results of two independent testing facilities
working at the same true particulate concentration and C02 level.
Let,
F,- be the corrected concentration value for lab i
C be the uncorrected concentration
j be the correction factor determined by lab /.
Then
Suppose that one laboratory determines the correct CO2
percent and the other differs by one between-laboratory standard
deviation. Then the factors are
12
%CO2
k 12
%CQ2±ob'
and the concentrations are reported as
-------
/ 12
2 ~ \%C02 ±
The error that would be induced by a one standard deviation error can be shown by taking the ratio of the
two concentration values, V\ / F2.
12
%CO2
12
% C02 ± ofc
12C %CO2±ab
~%C02 12C
_ % CO2 ± Qfr
%CO2
Assuming true values of 5, 8, and 1 1 percent for % CO2 , the resultant error can be demonstrated. For 5 per-
cent, one standard deviation high gives
V2 5%
6.78
5
= 1.36.
One standard deviation low gives
5% -1.78%
5%
3.22
= 0.64.
Similarly, for true values of 8 and 11 percent the ratios are 1.22 and 0.78, and 1.16 and 0.84, respectively. Thus,
the data from these tests indicate that variation of one standard deviation in the CO2 level would cause the reported
particulate concentrations of two laboratories to differ by 36 percent at low C02 levels, and 16 percent at high CO2
levels, when corrected to 12% CO2.
B. Oxygen
The percentage of oxygen in the stack gas is also measured by the Orsat analyzer. There is no direct application
of this to a standard of performance, but it is used in the computation of both the dry molecular weight of the gas
stream and the percentage of excess air. The 02 determinations from the three sites are presented in Table 2.
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TABLE 2. OXYGEN DETERMINATION DATA
% O, by volume
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Run
1
2
3
4
5
6
7
8
9
10
11
12
Sitel
Labs
101
12.0
13.6
14.2
13.7
13.7
10.7
16.2
16.2
13.2
14.1
13.9
13.7
14.2
_*
14.7
102
L2-2
12.2
12.8
14.8
11.4
11.5
17.0
14.4
14.0
14.0
13.2
14.0
12.2
12.6
13.0
103
_*
15.4
11.5
10.6
11-7
11.4
16.0
14.2
13.0
13.6
13.4
13.8
14.2
12.3
12.3
104
16.8
6.1
16.5
13.4
17.8
11.2
16.2
_*
13.8
12.7
13.9
14.5
_*
13.0
14.8
Site 2
Labs
201
8.1
8.1
8.2
8.2
9.3
7.3
8.0
8.1
8.0
7.8
9.0
7.0
4.3
4.8
4.7
4.2
202
14.3
11.4
5.3
6.7
5.2
6.2
7.0
6.1
5.1
4.9
5.8
6.3
6.3
6.5
7.3
8.2
203
4.6
5.0
5.5
5.9
5.3
5.4
5.0
4.6
5.5
5.4
5.0
6.0
6.0
5.0
5.0
5.0
204
4,8
6.4
6.4
5.2
5.0
6.0
5.8
5.9
6.4
5.6
5.8
6.2
5.8
_*
5.5
5.8
Site3
Labs
301
14.0
15.3
13.7
13.7
13.5
14.7
14.1
14.5
14.6
14.3
13.8
14.2
302
14.2
14.0
13.4
10.8
10.3
11.0
10.3
10.0
10.3
10.2
8.6
10.2
303
15.0
11.5
20.0
15.0
15.0
14.9
14.1
-t
-t
-t
-t
-t
304
_*
15.7
16.7
20.0
17.0
16.8
16.7
14.8
14.1
15.3
16.6
17.5
*Run not made.
t Orsat data not taken.
In Appendix C.3, the AOV table is shown for these deter-
minations and the appropriate variance components estimated.
Under the assumption that the 02 level remained essentially con-
stant over the testing period, we can estimate a within-laboratory
variance, a2 , of
a2 = 2.90
with 149 degrees of freedom. This gives an estimated within-
laboratory standard deviation of
= \/2~90
= 1 .70% 02 by volume.
From the laboratory factor of the analysis, the laboratory
bias variance, o\ , may be estimated as
&L = 1.66
with 9 degrees of freedom. Then the estimated laboratory bias
standard deviation is
= 1.29% O2 by volume.
Combining the above components, we can estimate a between-
laboratory variance, a|, by the formula in section IIIA. The estimated
value is
dl = (1.66) + (2.90)
= 4.56
Then the between-laboratory standard deviation is estimated by
= 2.14%02 by volume.
Thus, the between-laboratory standard deviations for both
C02 and 02 are in fairly close agreement. This is consistent with
comments made by users of the Orsat method that there is a trade-
off between COZ and 02 . That is, a loss of CO2 results in an
equivalent gain in 02 .
10
-------
TABLE 3. DRY MOLECULAR WEIGHT DATA
Ib/lb-mole
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Run
1
2
3
4
"5
6
7
8
9
10
11
12
13
14
15
16
Run
1
2
3
4
5
6
7
8
9
10
11
12
Site 1
Labs
101
29.92
30.01
29.53
29.67
20.67
30.03
29.38
29.38
29.57
29.49
29.64
29.67
29.53
_
29.34
102
29.93
29.93
29.95
29.71
30.12
30.14
29.32
29.73
29.78
29.84
29.81
29.78
30.02
30.15
29.90
103
_*
30.06
29.93
30.53
29.92
29.91
29.50
29.22
29.38
29.76
29.69
29.70
29.62
29.85
29.82
104
29.14
29.40
29.48
29.86
29.35
30.05
29.38
_*
29.75
29.41
29.71
29.65
_*
29.82
29.62
Site 2
Labs
201
29.54
29.54
29.83
29.96
29.76
29.94
29.90
29.89
29.87
29.91
29.66
29.91
30.22
30.29
30.06
30.15
202
29.40
29.74
30.23
30.19
30.29
30.26
29.96
30.08
30.32
30.37
30.26
30.20
30.35
30.24
29.99
29.96
203
30.33
30.33
30.25
30.25
30.28
30.25
30.30
30.38
30.28
30.36
30.26
30.21
30.29
30.28
30.34
30.30
204
30.30
30.19
30.11
30.04
30.28
30.24
30.22
30.25
30.16
30.27
30.26
30.23
30.23
—
30.30
30.25
Site3
Labs
301
29.58
29.30
29.54
29.51
29.69
29.48
29.48
29.38
29.40
29.45
29.53
29.48
302
29.34
29.20
29.22
29.52
29.27
29.34
29.44
29.38
29.47
29.35
29.61
29.19
303
29.65
29.10
28.96
29.40
29.40
29.43
29.54
-t
-t
-t
-t
-t
J04
_
29
29.24
29.15
29.27
29.18
29.32
29.46
29.41
29.30
29.43
29.18
*Run not made.
fNo Orsat data taken.
Note: EPA policy is to express all measurements in
Agency documents in metric units. When
implementing this practice will result in undue cost or
difficulty in clarity, NERC/RTP is providing
conversion factors for the particular non-metric units
used in the document. For this report, the factor is:
1 Ib/lb-mole o 1 gm/gm-mole.
C. Dry Molecular Weight
The dry molecular weight (Ma) of the stack gas is determined
from the stack gas analysis. The formula is
Md = (0.44) % C02 + (0.32) % O2 + (0.28) (%N i + % CO).
The sites tested had no detectable CO, and since the percent N2
is determined by subtraction, the values for Md used in this report
depend solely on theC02 and 02 determinations. Thus, in this
section the precision of the Ma determination is given, along with
the relationship of that precision to the precision of the C02 and
02 determinations.
The dry molecular weights used in the analysis are shown in
Table 3. Submitting these to an AOV according to the model
discussed gives the precision estimates desired. The values are
obtained in Appendix C.4.
The within-laboratory variance, o2 , is estimated as
o2 = 0.04
with 149 degrees of freedom. From this, the estimated within-
laboratory standard deviation is
= 0.2 Ib/lb-mole.
The estimated laboratory bias variance is
al = 0.02
with 9 degrees of freedom. Thus, the estimated laboratory bias
standard deviation is
OL = V0.02
= 0.14 Ib/lb-mole.
Combining estimates, the between-laboratory variance, a2,,
for the determination of dry molecular weight is estimated as
= (0.02) + (0.04)
= 0.06,
and the estimated between-laboratory standard deviation is
ab = -v/0.06
= 0.24 Ib/lb-mole.
11
-------
TABLE 4. PERCENT EXCESS AIR DATA
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
IS
16
Run
1
2
3
4
5
6
7
8
9
10
11
12
Site 1
Labs
101
135.5
180.9
206.8
189.4
189.4
104.5
344.0
344.0
165.0
200.1
197.6
189.4
206.8
_*
223.5
102
141.8
141.8
163.2
253.2
123.3
126.5
440.9
228.7
209.0
212.4
173.6
209.0
144.5
156.6
168.9
103
_*
337.8
121.9
103.4
127.1
118.9
336.8
213.3
166.0
188.8
177.2
195.6
211.7
142.9
142.0
104
381.9
36.3
393.1
184.3
625.7
116.6
344.0
_»
197.8
156.2
200.6
230.0
_*
166.0
246.5
Site 2
Labs
201
57.2
57.2
60.5
60.9
75.3
50.5
58.5
59.7
58.3
56.1
69.8
47.1
24.5
28.4
27.1
23.6
202
205.7
115.4
32.4
45.4
31.7
40.7
47.4
39.0
31.0
29.5
36.9
41.4
42.1
43.6
50.8
61.5
203
27.0
30.2
34.2
37.8
32.5
33.3
30.1
27.1
34.3
33.7
30.0
38.5
38.9
30.0
30.0
30.1
204
28.5
42.3
42.0
32.3
30.0
38.7
36.7
37.8
42.2
35.1
36.9
40.6
36.8
_*
34.3
36.8
Site 3
Labs
301
199.6
258.2
184.0
182.7
181.6
226.2
199.4
214.8
221.2
208.1
187.8
204.4
302
197.7
183.1
160.9
98.6
91.6
99.8
88.1
82.3
88.5
85.4
64.0
83.5
303
233.0
106.4
2336.4
245.1
245.1
240.6
202.4
-t
-t
-t
-t
-t
304
282.8
371.2
13966.5
432.0
388.9
396.8
236.2
196.4
258.2
400.0
501.7
*Runs not made.
|No Orsat data taken.
Thus, there is little variation in the computed dry molecular
weights, especially in light of the variation demonstrated previously
for the CO2 and O2 determinations. This has been noted in
other studies on the Orsat method/7 > The trade-off between C02
and 02 mentioned earlier is responsible for this small deviation
in Md. If we assume a loss of 2% CO2 by volume and a result-
ant gain of 2% 02 by volume, the net effect on Md would be:
Ma = (0.44) (% C02 - 2%) + (0.32) (% O, + 2%)
+ (0.28)(%N2 +%CO)
= (0.44) (% C02)- (0.44) (2%) + (0.32) ($O2) + (0.32)(2%)
+ (0.28)(%N2 +%CO)
= (0.44) (%C02 ) + (0.32) (%02 ) + (0.28) (%N2 + % CO)
+ (032) (2%) - (0.44) (2%)
= dry molecular weight + (0.32 - 0.44) 2%
= dry molecular weight - 0.24.
The result would be an estimate that fell 0.24 below the actual
value. A comparison of the between-laboratory standard
deviations for CC^ ,02 and Md gives credence to this trade-off
explanation.
D. Excess Air
The excess air percentage is determined according to the
formula
%£A =
(%02)-0.5(%CO)
(0.264)(%N2 ) -
X 100 percent
Using the data from Tables 1 and 2, the excess air deter-
minations were computed, and the values are shown in
Table 4.
It is apparent from the data that there is a great deal of
imprecision in this computation. Rather than apply an AOV
approach to obtain precision estimates, the factor or factors
upon which the %EA determination depends is investigated.
In the absence of CO, the above formula can be expressed as
%EA =
%02
(0.264)(%N2)-%0,
X 100 percent
and since %N 2 = 100 - % O2 - % CO2,
%EA =
%02
(0.264X100- %02 - %CO2)- %02
%02
" 26.4- (1.264)%02 - (0.264)% C02
X 100 percent
X 100 percent.
12
-------
Thus, the excess air is the ratio of the oxygen content to a constant less a percentage of the 02 and C02 fractions.
But since only about one-quarter of the % CO2 is involved in the denominator, this amounts usually to a relatively
small contribution to the overall determination. As a result, the factor making the significant contribution to the
estimate is the oxygen percentage.
Based upon this and the nature of the data, an exponential model for the excess air was proposed as
where
y is % EA
x is % O2
e is the base of the natural logarithms
and
a0,a\ are constants.
A least squares fit of a sample of the excess air determinations taken from all three sites was used to estimate
a0 and a\ and to determine the degree of fit. The steps used are shown in Appendix C.5. The model obtained was
The degree of fit, as measured by the coefficient of determination, r2 , is
r2 = 0.993
indicating an extreme closeness of the determinations to the model .
By using this model and the previously determined precision estimate for % 02 determination, it is possible to
demonstrate the imprecision of the excess air determination. Using the between-laboratory standard deviation of
2.14% 02 , we can estimate the effect on the excess air determination of an error of one standard deviation in the 02
determination.
If we let x = % O2 be the actual percentage of O2 in the gas, and y be the actual percentage of excess air, then
a standard deviation of 2.14% O2 implies
where yc is the calculated excess air. Then
yc = (10.47)e <°-
= [(10.47)e (°-
13
-------
Thus a normal error in 02 determination would result in a 57% error in the excess air determination. Similarly, a
one standard deviation error in the negative direction implies
= (0.64)y
From the above, it can be seen that the excess air determination can only be as reliable as the O2 determination,
and due to the exponential relationship, small deviations in 02 result in large deviations in excess air.
14
-------
V. MOISTURE FRACTION
The moisture fractions for this study were obtained using the formula given in Method 5. The equation is
where
Vw td-the volume of water vapor collected, corrected to standard conditions.
Vm .— the volume of gas collected, dry basis, corrected to standard conditions.
The water vapor collected is determined by adding the water volume increase in the impingers to the weight increase in
the silica gel tube in grams, and multiplying by a constant factor. Using the above formula, the moisture fractions used
in the analysis were obtained, and these are shown in Table 5.
The precision estimates for the moisture fraction determination are obtained using an AOV in the design that was
shown in Figure 2. The AOV table and related data are shown in Appendix C.6.
The within-laboratory variance, a2 , is estimated as
&2 = 0.001
with 140 degrees of freedom. This gives an estimated within-laboratory standard deviation of
= 0.032
The laboratory bias variance estimate obtained was
Of, = 0.001
with 8 degrees of freedom. The laboratory bias standard deviation, then, is given by
= 0.032
Using the above values, the estimated between-laboratory variance is
6« = &i + d3
= (0.001) + (0.001)
= 0.002.
and the between-laboratory standard deviation is estimated as
= 0.045
15
-------
TABLE 5. MOISTURE FRACTION DATA
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Run
1
2
3
4
5
6
7
8
9
10
11
12
Sitel
Labs
101
0.26
0.30
0.30
0.32
0.31
0.31
0.20
0.22
0.23
0.23
0.25
0.26
0.26
_*
0.26
102
0.33
0.31
0.33
0.30
0.38
0.32
0.21
0.23
0.26
0.26
0.28
0.28
0.28
0.30
0.28
103
_*
0.19
0.24
0.27
0.28
0.26
0.21
0.22
0.18
0.22
0.23
0.21
0.22
0.24
0.23
104
0.28
0.27
0.23
0.30
0.32
0.30
0.16
0.22
0.25
0.24
0.28
0.28
_*
0.29
0.28
Site 2
Labs
202
0.10
0.10
0.10
0.10
0.11
0.10
0.11
0.10
0.10
0.10
0.11
0.11
0.10
0.10
0.11
0.10
203
0.05
0.09
0.09
0.10
0.09
0.10
0.08
0.09
0.09
0.09
0.10
0.09
0.09
0.10
0.10
0.10
204
0.10
0.08
0.09
0.10
0.10
0.10
0.10
0.10
0.09
0.09
0.11
0.10
0.10
_*
0.10
0.10
SiteS
Labs
301
0.37
0.37
0.30
0.38
0.42
0.35
0.37
0.38
0.35
0.32
0.35
0.38
302
0.29
0.27
0.30
0.32
0.33
0.29
0.32
0.31
0.32
0.29
0.32
0.28
303
0.37
0.43
0.41
0.44
0.44
0.40
0.41
0.38
0.43
0.41
0.43
0.39
304
_*
0.40
0.40
0.23
0.32
0.37
0.40
0.42
0.43
0.40
0.42
0.36
*Runs not made.
16
-------
APPENDIX A
METHOD 3. GAS ANALYSIS FOR CARBON DIOXIDE,
EXCESS AIR, AND DRY MOLECULAR WEIGHT.
17
-------
24886
RULES AND REGULATIONS
MKTHOD .1—GAS ANALYSIS FOR CAHBON DIOXIDK,
KXCKSS AIR. AND CUT MOLECOLAJt WEIGHT
1 Principle and applicability.
1.1 Principle. An Integrated or grab gas
sample is extracted from a sampling point
and analyzed for Its components using an
Orsat analyzer.
1.2 Applicability. This method should be
applied only when specified by the test pro-
cedures for determining compliance with the
New Source Performance Standards. The test
procedure will Indicate whether a grab sam-
ple or an integrated sample Is to be used.
2. Apparatus.
2.1 Grab sample (Figure 3-1).
2.1.1 Probe—Stainless steel or Fyrex>
glass, equipped with a filter to remove partic-
ulate matter.
2.1.2 Pump—One-way squeeze bulb, or
equivalent, to transport gas sample to
analyzer.
1 Trade name.
2.2 Integrated sample (Figure 3-2).
2.2.1 Probe—Stainless steel or Pyrez1
glass, equipped with a filter to remove par-
ticulate matter.
2.2.2 Air-cooled condenser or equivalent—•
To remove any excess moisture.
2.2.3 Needle valve—To adjust flow rate.
2.2.4 Pump—Leak-free, diaphragm type,
or equivalent, to pull gas.
2.2.5 Rate meter—To measure a now
range from 0 to 0.035 cfm.
2.2.6 Flexible bag—Tedlar,1 or equivalent,
with a capacity of 2 to 3 cu. ft. Leak test the
bag in the laboratory before using.
2.2.7 Pitot tube—Type S, or equivalent,
attached to the probe so that the sampling
flow rate can be regulated proportional to
the stack gas velocity when velocity Is vary-
ing with time or a sample traverse is
conducted.
2.3 Analysis.
2.3.1 Orsat analyzer, or equivalent.
PROBE
FLEXIBLE TUBING
TO ANALYZER
LTER(G
FILTER (GLASS WOOL)
SQUEEZE BULB
3. Procedure.
3.1 Crab sampling.
3.1.1 Set up the equipment as shown in
Figure 3-1, making sure all connections are
leak-free. Place the probe in the stack at a
sampling point and purge the sampling line.
3.1.2 Draw sample into the analyzer.
3.2 Integrated sampling.
3.2.1 Evacuate the flexible bag. Set up the
equipment as shown In Figure 3-2 with the
bag disconnected. Place the probe in the
stack and purge the sampling line. Connect
the bag, making sure that all connections are
tight and that there are no leaks.
3.2.2 Sample at a rate proportional to the
stack velocity.
3.3 Analysis.
3.3.1 Determine the CO., o,. and CO con-
centrations as soon as possible. Make as many
passes as are necessary to give constant read-
ings. If more than ten passes are necessary.
replace the absorbing solution.
3.3.2 For grab sampling, repeat the sam-
pling and analysis until three consecutive
samples vary no more than 0.5 percent by
volume for each component being analyzed.
3.3.3 For Integrated sampling, repeat the
analysis of the sample until three consecu-
tive analyses vary no more than 0.2 percent
by volume for each component beinir
analyzed.
4, Calculations,
4.1 Carbon dioxide. Average the three con-
secutive runs and report the result to the
nearest 0.1% r
4.2 Excess air. Use Equation 3-1 to calcu-
late excess air. and average the runs. Report
the result to the nearest 0.1% excess air.
% EA =
0.264(%
CO)
X100
Figure 3-1. Grab-sampling train.
RATE)
AIR-COOLED CONDENSER
PROBE
FILTER [GLASS WOOL)
QUICK DISCONNECT
RIGID CONTAINER
Figure 3-2. Integrated gas • sampling train.
equation .'!- 1
where:
%EA=Percent excess air.
%O3:= Percent oxygen by volume, dry basis.
%Na=Percent nitrogen by volume, dry
basis.
%CO=Percent carbon monoxide by vol-
ume, dry basis.
0.264= Ratio of oxygen to nitrogen in air
by volume.
4.3 Dry molecular weight. Use Equation
3-2 to calculate dry molecular weight and
average the runs. Report the result to the
nearest tenth.
Md = 0.44(%CO..)+0.32(%O.)
+b.28(
-------
6. Reference*.
AHshuller, A. P., et a.],, Storage of Oases
and Vapon In Plastic Bags, Int. J. Air ft
Water Pollution, 6:75-81. 1983.
Conner, William D., and J. S. Nader, Air
Sampling with Plastlo Bags, Journal of the
American Industrial Hygiene Association,
25:291-297, May-June 1964.
Devorkln, Howard, et al., Air Pollution
Source Testing Manual, Air Pollution Con-
trol District, Los Angeles, Calif., November
1083.
to
O
'///////////////////A
§
I
m
O
O
5
FEDERAL REGISTER, VOL. 36, NO. 247—THURSDAY, DECEMBER 33, 1971
$
-3
-------
APPENDIX B
MOISTURE FRACTION DETERMINATION FROM METHOD 5
21
-------
RULES AND REGULATIONS
24889
////A
s/777.
'7/77.
'7/77,
/777s
////A
44444
'7/7.
7-7-,
444
,44
7777,
///y
'777.
77.
777.
444^444^244
444
444
444
444
777
777,
7ZZ;
s///
777
777
777;
777>
'77.'
7/7;
7777
7777
77
4444
/777
S/7/
777
777
777;
777:
7777
777.
777
777;
Y//,
777y
Container No. 3. Weigh the spent silica gel
and report to the nearest gram.
5. Calibration.
Use methods and equipment which have
been approved by the Administrator to
calibrate the orifice meter, pltot tube, dry
gas meter, and probe heater. Recalibrate
after each test series.
6. Calculations.
6.1 Average dry gas meter temperature
and average orifice pressure drop. See data
sheet (Figure 5-2).
6.2 Dry gas volume. Correct the sample
volume measured by the dry gas meter to
standard conditions (70° P., 29.92 Inches Hg)
by using Equation 5-1.
mi
17-71
in. H6
T.
Tm= Average dry gas meter temperature,
"R.
Pb.r= Barometric pressure at the orifice
meter, inches Hg.
AH = Average pressure drop across the
orifice meter, Inches H,O.
13.6= Specific gravity of mercury.
P. u= Absolute pressure at standard con-
ditions, 28.92 Inches Hg.
8.3 Volume of water vapor.
RT..
0.0474
equation ~>-2
where:
V».td= Volume of water vapor In the gas
sample (standard conditions) ,
cu. ft.
Vi.= Total volume of liquid collected in
implngers and silica gel (see Fig-
ure 9-3). ml.
on.,o= Density of water, 1 g./ml.
Mn.,o= Molecular weight of water. 18 lb./
Ib.-mole.
B= Ideal gas constant, 21.83 Inches
Hg— cu. ft./lb.-mole-°R.
T,I4= Absolute temperature at standard
conditions, 630* R.
P.tJ=AbsQlute pressure at standard con-
ditions. 29.92 Inches Hg.
6.4 Moisture content.
B.0=
'-.id
V..U+V...,
equation 5-3
where:
Bwo = Proportion \>y volume of water vapor in tin-pas
stream, dime-iisionless.
v*.ui=VoIume of water in the pas sample (standard
conditions), cu. ft.
v».w=Volume of gas sample tlirougli the dry ciu innter
(standard conditians), cu. ft.
X*
. equation &-1
where:
V«,,4= Volume of gas sample through the
dry gas meter (standard condi-
tions) , cu. ft.
V_= Volume of gas sample through the
dry gas meter (meter condi-
tions) , cu. ft.
T.tl= Absolute temperature at standard
conditions, 530* R.
tfOUTO, VOL M, NO. 247—THURSDAY, OECEMUI 23, 1971
23
-------
24890
RULES AND REGULATIONS
PLANT
DATE.
RUN NO,
CONTAINER
NUMBER
TOTAL
WEIGHT OF PARTICULAR COLLECTED,
mg
FINAL WEIGHT
TARE WEIGHT
Figure5-3. Analytical data.
FINAL
INITIAL
LIQUID COLLECTED
TOTAL VOLUME COLLECTED
VOLUME OF LIQUID
WATER COLLECTED
IMPINGER
VOLUME.
ml
-
SILICA GEL
WEIGHT.
9
8TJ nil
CONVERT WEIGHT OF WATER TO VOLUME BY DIVIDING TOTAL WEIGHT
INCREASE BY DENSITY OF WATER. (1 g. ml):
FEDERAL REGISTER, VOL 36, NO. 247—THURSDAY, DECEMBER 23, 1971
24
-------
APPENDIX C
STATISTICAL METHODS
25
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APPENDIX C. STATISTICAL METHODS
This appendix consists of various sections which contain details of statistical procedures carried out in the analysis
of the data. Reference to these sections has been made at various junctures in the body of the report. Each section is
an independent analysis pertinent to a particular portion of the report.
C.I Expected Mean Squares
In an analysis of variance, the mean square for each factor is computed. The mean squares are variance estimates,
and they are used to determine which factors affect the overall mean level. However, if the expected values of these
variance estimates or expected mean squares are known, the individual variance components of interest can also be
estimated.
The basic design used in this study is a nested design with unequal levels of the various factors. That is, the num-
ber of labs per site and repetitions per lab vary from one site to the next. The expected mean squares for this design
are not determined in a straightforward manner, but rather they are obtained as a weighted average of the varying
sample sizes. The F-tests obtained using these expected mean squares are inexact with the exception of the lowest or-
der comparison made with respect to the error term. However, that is the only test of interest in this study.
The expected mean square (EMS) for the labs/sites factor consists of a within-laboratory term, a2, and a multiple
of the laboratory bias term, a\. What is needed is to determine the multiple, k, for a given set of determinations. The
formula was developed by Anderson and Bancroft*s* and is given by
i I
where
HI: is the number of determinations at site / by lab /
fii =
df
Hj is the total number of determinations at site i
and
of/is the degrees of freedom for labs.
As an example, we have the following sample sizes for the analysis of the Method 3 data:
nt =56 «2 =63 «3 = 42
itn = 14 «2i = 16 «3i = 12
= 12
«14 = 13 «24 = 15 «34 = 11
27
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and there are 9 degrees of freedom. So
= y yV"'/""'/ „ ..2
' i i 9
^fCH)"'
Thus, we can say that for the labs/sites factor, the expected mean square is a2 + (13.37)a£, and using this rela-
tionship we can estimate a£ from the AOV table.
C.2 Precision Estimates For % CO2
This section presents the analysis of variance table and develops the variance estimates for the % CO2 determina-
tion. There were 161 determinations used, which results in a total degrees of freedom of 160 for this analysis. Of
this number, 2 are attributed to the site factor. The labs/sites degrees of freedom are obtained by taking the number
of labs at a site less one and summing for all sites, or 3(4 — 1) = 9. The remaining degrees of freedom are attributed to
the error term, which is calculated from the repetitions within each laboratory at each site. The AOV is summarized
in Table C-l.
TABLE C.I ANALYSIS OF VARIANCE FOR % CO2.
The F value for labs/sites is the ratio of the mean
square for labs/sites to the mean square for error.
This ratio exceeds the critical value of 1 .95, taken
from a table of the F-distribution at the 5 percent
level of significance with 9 and 149 degrees of free-
dom. This implies that there is a laboratory effect,
or equivalently, that the laboratory bias variance, a\ ,
is greater than zero.
Using the expected mean squares, we can ob-
tain precision estimates for the within-laboratory and
laboratory bias components. The expected mean
square of the error term is a2 , the within-laboratory variance. Thus, the estimated within-laboratory variance is the
mean square for error, or
a2 = 2.06.
This gives an estimated within-laboratory standard deviation of
Source
Sites
Labs/Sites
Error
Total
DF
2
9
149
160
SS
1222.82
152.84
306.59
1682.25
MS
611.41
16.98
2.06
F
_*
8.24f
EMS
_*
a* + (13.37)a}
o- L
*Not of interest.
fSignificant value at 5% level.
= N/2~06
= 1.44%C02 by volume.
This estimate has 149 degrees of freedom associated with it.
28
-------
The laboratory bias variance is estimated from the labs/sites mean square. The manner of obtaining the expected
mean square is discussed in Appendix C. 1. Since the expected mean square is
EMS = o2 + 13.37a2,
a\ is estimated by
>2 _MSL-d*
°L 13.37
where MS/, is the mean square for labs/sites. Then
f2_ 16.98-2.06
13.37
14.92
13.37
= 1.12.
The estimated laboratory bias variance has 9 degrees of freedom associated with it. The laboratory bias standard devia-
tion, OL , is estimated as
= 1.06%C02 by volume.
The between-laboratory variance, a2,, is defined as
°l = oi + o\
Substituting the estimates for a2 and a£ gives
dl = a2 + a2
= (1.12) + (2.06)
= 3.18
and the between-laboratory standard deviation estimate is
= 1.78%CO2 by volume.
C.3 Precision Estimates For % O2
The analysis of variance table for % 02 determination is presented here, and the variance component estimates
derived. There are 161 determinations used in the analysis, for a total of 160 degrees of freedom. Of these, 3 — 1 = 2
are due to sites, while 3(4 — 1) = 9 are due to labs/sites. The remainder form the error term. The analysis of variance
table is shown in Table C.2.
29
-------
TABLE C.2 ANALYSIS OF VARIANCE FOR % O2.
Source
Sites
Labs/Sites
Error
Total
DF
2
9
149
160
SS
2127.80
225.37
432.55
2785.72
MS
1063.90
25.04
2.90
F
_*
8.63f
EMS
_*
a2 + (13.37)4
a2
*Not of interest.
tSignificant value at 5% level.
The F-value shown for labs/sites is the ratio of
the mean squares for labs/sites and error. The value
exceeds the tabled value of 1.95 taken from a table
of the /""-distribution at the 5 percent significance
level with 9 and 149 degrees of freedom. This implies
that there is a significant laboratory effect on the O2
determination, or that a\ is greater than zero.
Using the expected mean squares, the within-
laboratory and laboratory bias variances may be
estimated. The expected mean square for error is a2,
the within-laboratory variance. Thus, the estimated
within-laboratory variance is
a2 = 2.90,
the mean square for error. There are 149 degrees of freedom associated with this variance estimate. The within-
laboratory standard deviation, a, is estimated as
= 1.70%O2 by volume.
The expected mean square for labs/sites is a2 + (13.37)a£. Then o£ is estimated by
8?=-
where MSL is the mean square for labs/sites. Thus,
13.37
25.04 - 2.90
13.37
22.14
13.37
= 1.66,
with 9 degrees of freedom. The estimated laboratory bias standard deviation, OL , is
= 1.29%02 by volume.
The between-laboratory precision components are estimated from the above. The between-laboratory variance,
, is estimated by
= (2.90) + (1.66)
= 4.56
30
-------
The between-laboratory standard deviation, then, is estimated as
= 2.14%O2 by volume.
C.4 Precision Estimates For Dry Molecular Weight.
The dry molecular weight precision components are estimated by using an analysis of variance on the values in
Table 3. There were 161 total determinations made, which gives 160 total degrees of freedom. The site factor accounts
for 3 — 1 = 2 of these, and the labs/sites accounts for 3(4 — 1) = 9, the number of labs less one at each site, summed
for the three sites. The remaining 149 degrees of freedom are attributable to the repetitions per lab, or error term.
The analysis of variance table is shown in Table C.3.
TABLE C.3 ANALYSIS OF VARIANCE
FOR DRY MOLECULAR WEIGHT
Source
Sites
Labs/Sites
Error
Total
DF
2
9
149
160
SS
14.62
2.33
5.95
22.90
MS
7.31
0.26
0.04
F
_*
6.25f
EMS
_*
a* + (13.37)4
a2
*Not of interest.
• f Significant at 5% level.
The F-value given for labs/sites is the ratio of
the mean squares for labs/sites and error. This value
may be said to be significant at the 5 percent level
if it exceeds a tabled value taken from the F-distribu-
tion with 9 and 149 degrees of freedom. The
critical value is 1.95, so that the labs/sites factor has
a significant effect on the overall mean level. This is
equivalent to saying that the laboratory bias variance,
0£, is greater than zero.
To estimate the precision components, the
expected mean square (EMS} column is used. The
EMS of the error term is o-2, the within-laboratory
variance. Thus,
error
= 0.04
is the estimated within-laboratory variance, with 149 degrees of freedom. The within-laboratory standard deviation,
then, is estimated by
The EMS of the labs/sites factor is a2 + (13.3 7)o£, as developed in Appendix C.I. Thus, the estimated labora-
tory bias variance is
2
where MSL is the mean square for labs/sites. Then
MSL - a
13.37
0.26 - 0.04
13.37
31
-------
0.22
07 - -
L 13.37
= 0.02.
The laboratory bias variance estimate has 9 degrees of freedom associated with it. The estimated laboratory bias standard
deviation is
= 0.141b/lb-mole.
The between-laboratory components are estimated using the above estimates. The between-laboratory variance
is defined as
so that the estimated value,
&* = a*+&2
= (0.02) + (0.04)
= (0.06).
This gives an estimated between-laboratory variance of
= 0.24 Ib/lb-mole.
C.5 Distribution of Excess Air.
The excess air determinations were used to propose a distribution model for these determinations which could
predict the excess air percentage at a given level of O2. The formula in the absence of CO, as derived in Section IV
of the report,
%02
%EA = - X 100 percent
(26.4) - (1 .264) % 02 - (0.264) % CO2
indicates that the chief contribution to the %EA was made by % O2 . A model was proposed, then, that did not con-
tain the % CO2 as an independent variable. Due to the nature of the determinations, an exponential model,
was proposed where
y is%EA
x is % O2
and
a0, a i, are unknown constants.
32
-------
A least squares regression^6* is used to estimate a0 and a, . Taking the natural log of the equation gives
which is of the form
This is the usual form of a simple linear regression, and by using the formulas
E>. — i
Xjyj/n - xy
and
where
n is the total determinations used
3c is the mean % O2
y' is the mean of the (^j')'s
the least squares estimates of a'0 and Oi are obtained. These are derived using one quarter of the data points.
a, =0.21
a'0 = 2.35
Then to fit the proposed model,
a'0 =&n.a0
which implies
= e(2.35)
= 10.47.
Thus, we have
The closeness of this model to the determinations is measured by the coefficient of determination, r2. The
formula for r2 is
n ~|
£ (xt-^W-y'n
='J
1=1 ii = 1
33
-------
The value of r2 was 0.993, which indicates an extremely good fit to the model.
C.6 Moisture Fraction Precision Estimates.
The moisture fractions which appear in Table 5 are used to develop precision estimates. The determinations are
used in an analysis of variance on a nested design, with 150 total determinations used. This gives 149 total degrees of
freedom. Of these, 2 are attributed to sites, while the labs/sites factor accounts for (4 — 1) + (4 — 1) + (3 — 1) = 8
degrees of freedom, the number of labs per site less one, summed over all sites. The remaining 140 are attributed to
the repetitions per lab or error term. The analysis of variance is summarized in Table C.4.
TABLE C.4 ANALYSIS OF VARIANCE
FOR MOISTURE FRACTION
Source
Sites
Labs/Sites
Error
Total
DF
2
8
140
150
SS
1.699
0.103
0.136
1.938
MS
0.8SO
0.013
0.001
F
_*
13.000t
EMS
_*
o3 + (13.78)ai
o1
•Not of interest.
fSignificant at 5% level.
The F-value shown is the ratio of the labs/sites
mean square to the error mean square. This value is
significant at the 5 percent level if it exceeds the
tabled value taken from the /"-distribution with 8
and 140 degrees of freedom. The table value is
approximately 2.02, which implies that there is a
significant laboratory effect, or that the laboratory
bias variance, 0£, is greater than zero.
Using the expected mean squares, the variance
components may be estimated. The EMS of the error
term is a2, the within-laboratory variance. Thus the
estimated value of a2 is
a2 = 0.001
the error mean square. This estimate has 140 degrees of freedom associated with it. Then the estimated within-
laboratory standard deviation is
= 0.032.
The EMS of the labs/sites factor is a2 + 13.78o|. The factor 13.78 is obtained according to the formula in
Appendix C.I, substituting the values for the sample sizes and degrees of freedom for this study. Thus
E(MSL) = a2 + 13.7802,
where MSi is the mean square for labs/sites. This implies
5^MSL-o2
1 13.78
0.013-0.001
13.78
0.012
13.78
'0.001
34
-------
with 8 degrees of freedom. The estimated laboratory bias standard deviation, then, is
oi=V0.001
= 0.032.
The between-laboratory variance is o2b = o2L 4- a2 . Substituting into this equation, gives
dl=ai + o*
= (0.001) + (0.001)
= (0.002).
From this, the estimated between-laboratory standard deviation is
= 0.045.
35
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LIST OF REFERENCES
1. Environmental Protection Agency "Standards of Performance for New Stationary Sources," Federal Register,
Vol. 36, No. 247, December 23, 1971, pp 24876-24893.
2. Harnil, H.F. and Camann, D.E., "Collaborative Study of Method for the Determination of Particulate Matter
Emissions from Stationary Sources (Portland Cement Plants)," Southwest Research Institute report for
Environmental Protection Agency, in preparation.
3. Hamil, H.F. and Thomas, R.E., "Collaborative Study of Method for the Determination of Particulate Matter
Emissions from Stationary Sources (Fossil Fuel-Fired Steam Generators)," Southwest Research Institute
report for Environmental Protection Agency, June 30,1974.
4. Hamil, H.F. and Thomas, R.E., "Collaborative Study of Method for the Determination of Particulate Matter
Emissions from Stationary Sources (Municipal Incinerators)." Southwest Research Institute report for
Environmental Protection Agency, July 1, 1974.
5. Anderson, R.L. and Bancroft, T.A., Statistical Theory in Research. McGraw-Hill, New York, 1952.
6. Dixon, W.J. and Massey, F.J. Jr., Introduction to Statistical Analysis, 3rd Edition. McGraw-Hill, New York,
1969.
7. Mitchell, WJ. and Midgett, M.R., "Studies of the Field Reliability of the Orsat Analyzer," Environmental
Protection Agency, QAEML, (To be published).
37
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TECHNICAL REPORT DATA
(Please read Instructions an the reverse before completing)
1. REPORT NO.
EPA-650/4-73-026
3. RECIPIENT'S ACCESSION"NO.
4. TITLE AND SUBTf'.E
Collaborative Study of Method for Stack
Gas Analysis and Determination of Moisture Fraction
with Use of Method 5
5. REPORT DATE
June 1974
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Henry F. Harnil
Richard E. Thomas
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Southwest Research Institute
8500 Culebra Road
San Antonio, Texas 78284
10. PROGRAM ELEMENT NO.
Task Order 8
11. CONTRACT/GRANT NO.
68-02-0626
12. SPONSORING AGENCY NAME AND ADDRESS
Quality Assurance and Environmental Monitoring Laboratory
National Environmental Research Center
Research Triangle Park, North Carolina 27711
13. TYPE OF REPORT AND PERIOD COVERED
Task Order
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
16. ABSTRACT
Statistical analyses are performed on data from EPA Method 3 (Stack Gas Analysis for Carbon Dioxide, Excess Air
and Dry Molecular Weight) and from the stack gas moisture fraction determination obtained in the collaborative testing
of EPA Method 5 (Particulates). Using data from Method 5 tests at a Portland cement plant, a coal-fired power plant
and a municipal incinerator, estimation is made of the precision that can be expected with the use of these methods. For
Method 3, the precision of CO2 and 02 determination using an Orsat analyzer is investigated, as well as the effect of
this on the dry molecular weight and excess air calculations. In addition, the effect of variability in CO2 and 02 deter-
minations on correcting particulate determinations to a common base is studied. The precision of the determination of
the moisture fraction of the stack gas by the formula in Method 5 is studied. Recommendations are made for the improve-
ment of the precision of the Orsat method.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
Air Pollution, 1302
Flue Gases
Collaborative Testing
Methods Standardization
Orsat
13-B
07-B
18. DISTRIBUTION STATEMENT
Release Unlimited
19. SECURITY CLASS (This Report)
UNCLASSIFIED
21. NO. OF PAGES
45
20. SECURITY CLASS (This page)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
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