EPA-650/4-74-033



SEPTEMBER 1974
Environmental Monitoring Series
                                                 ilUDY


                                                    \
                                                     UJ
                                                     O

-------
                               EPA-650/4-74-033
      COLLABORATIVE STUDY
OF METHOD FOR  DETERMINATION
     OF STACK  GAS  VELOCITY
  AND VOLUMETRIC  FLOW RATE
          IN  CONJUNCTION
        WITH  EPA  METHOD 5
                   by

           H. F. Hamil and R. 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. R. 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

                September 1974

-------
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 tho Agency,
nor does mention of trade names or commercial products constitute
endorsement or recommendation for use.
                                  11

-------
                                  SUMMARY AND CONCLUSIONS
     This report presents the results of a statistical analysis on data collected in the use of EPA Method 2 in
conjunction with collaborative testing of Method 5 (Particulate Emissions). Method 2 is for the determination of
stack gas velocity and volumetric flow rate and specifies that the stack gas velocity be determined from the gas
density and from measurement of the velocity head using a Type S Pitot tube.

     The collaborative tests of Method 5 were conducted at three sites: a Portland cement plant, a coal-fired
power plant, and a municipal incinerator. There were 15, 16 and 12 sampling runs, respectively, at the three sites
and four collaborating laboratories at each.  The data from one laboratory at the power plant site were not used,
and some determinations were not made due to equipment failure during the sampling run. This resulted in a
total of 150 separate determinations of both velocity and flow rate being used in the analyses.

     The runs at each site were grouped into blocks based upon the velocity heads. The precision components,
within-laboratory, between-laboratory and laboratory bias, are shown to be proportional to the mean of the deter-
minations and are expressed as percentages of the true mean, denoted by 6. The results are summarized below for
each factor.

     Velocity-The between-laboratory standard deviation estimate is 5.0% of 6 with 8 degrees of freedom. The
               within-laboratory standard deviation estimate is 3.9% of 5 with 113 degrees of freedom. From
               these, a laboratory bias standard deviation of 3.2% of 5 may be estimated.

     Volumetric Flow Rate—The estimated between-laboratory standard deviation is 5.6% of 8 with 8 degrees of
               freedom. The estimated within-laboratory standard deviation is 5.5% of 5 with 113 degrees of
               freedom. These give a laboratory bias standard deviation of 1.1%  of 6.

     The emission rate, denoted by r, is defined in the Federal Register as the product of the volumetric flow
rate and the pollutant concentration. Using the estimates for the precision of the flow rate determination and
estimates for  the precision of Methods 5,6, and 7, the precision of r is estimated for each Method.

     Based upon the results obtained, the precision of  the volumetric flow rate seems adequate for use with other
test methods  in determining the  emission rate. The precision of r depends primarily upon the precision of the test
method used, which is the desirable result.
                                                  in

-------
                                TABLE OF CONTENTS

                                                                                   Page

LIST OF ILLUSTRATIONS	     vi

LIST OF TABLES	     vi

I.    INTRODUCTION	      1

II.   COLLABORATIVE TESTING	      2

     A.   Collaborative Test Sites	      2
     B.   Collaborators and Test Personnel	      2

III.  STATISTICAL DESIGN AND ANALYSIS	      7

     A.   Statistical Terminology   	      7
     B.   Test Data	      8
     C.   Test Design and Analysis	      9

IV.  VELOCITY DETERMINATION PRECISION  ESTIMATES	     12

V.   VOLUMETRIC FLOW RATE PRECISION ESTIMATES	     13

VI.  EMISSION RATE VARIATION	     14

APPENDIX A—Method 2. Determination of Stack Gas Velocity and Volumetric Flow Rate (Type S
     PitotTube)	     15

APPENDIX B-Statistical Methods	     19

     B.1   Proportional Relationship Between Mean and Standard Deviation in the
          Velocity  Determinations	      21
     B.2  Proportional Relationship Between Mean and Standard Deviation in the Flow
          Rate Determination	      22
     B.3   Unbiased Estimation of Standard Deviation Components	      25
     B.4   Weighted Coefficient of Variation Estimates	      26
     B.5   Estimating Precision Components For Velocity Determination	      29
     B.6   Estimating Precision Components For Volumetric Flow Rate	      30
     B.7   Emission  Rate Variability	      33

LIST OF REFERENCES	      35

-------
                                 LIST OF ILLUSTRATIONS

Figure                                                                                   Page

    1     Typical Velocity Profiles, Lone Star Portland Cement Plant	     3

    2     Typical Velocity Profiles, Allen King Power Plant	     4

    3     Typical Velocity Profiles, Holmes Road Incinerator	     5


                                      LIST OF TABLES

Table                                                                                   Page

    1     Average \Mp's and Block Designations	    10

    2     Stack Gas Velocity Data, Arranged by Block	    10

    3     Volumetric Flow Rate Data, Arranged by Block	    11

    4     Precision Estimates for Emission Concentrations	    14

  B-l     Velocity Transformation Results	    21

  B-2     Run Means and Standard Deviations (Velocity, ft/sec)	    22

  B-3     Collaborator-Block Means and Standard Deviations (Velocity, ft/sec)	    23

  B-4     How Rate Transformation Results	    23

  B-5     Run Means and Standard Deviations (Volumetric Flow Rate, ft3/hr X 10'4)  .  ...    24

  B-6     Collaborator-Block Means and Standard Deviations (Volumetric Flow Rate,
          ft3/hrX 10-4)	    25

  B-7     Run Beta Estimates and Weights (Velocity)	    30

  B-8     Collaborator-Block Beta Estimates and Weights (Velocity)	    31

  B-9     Run Beta Estimates and Weights (Volumetric Flow Rate)	    32

B-10     Collaborator-Block Beta Estimates and Weights (Volumetric Flow Rate)	    32
                                               vi

-------
                                         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 determination of stack gas velocity and volumetric flow rate with use of Method 5 for particulate
emissions as given in "Standards of Performance for New Stationary Sources"'  '.

     This report describes the statistical analysis of data from collaborative tests conducted in a Portland cement
plant/2^ a coal-fired power plant/  * and a municipal incinerator/ *

     The collaborative tests of the method for determination of stack gas velocity and volumetric flow rate were
not run as separate tests of Method 2 but as this method is used in conjunction with Method 5 for particulate
emissions/1*

     The results of the data analyses are given in this report.

-------
                                   II. COLLABORATIVE TESTING
 A.   Col laborative 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 fed into a 300-foot-high stack.( '
 Samples were taken at the sample ports located on the stack 150 feet above grade. Inside diameter of the stack
 at the sample ports is 13 feet.* The cross-sectional area of the stack at the sample ports is 132.73 ft2 .*  The
 average stack gas velocity ranged from about 50 to 60 ft/sec* during the test period.  A typical velocity profile
 is shown in Figure 1.  The typical volumetric flow rate was about 12 X 106 fr /hi* dry gas basis at 70°F and
 1 atmosphere.

      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 precipitatofs. The twin emission gas streams are
 fed into an 800-foot-high stack through two horizontal ducts/3* The sample  ports were located in the south
 horizontal duct upstream of the entrance to the stack. The inside duct dimensions are 12 feet wide by 27 feet
 high. The duct cross sectional area is 324 ft2. The average gas velocity was about 50 ft/sec. A typical velocity
 profile is shown in Figure 2. The typical total volumetric flow rate (flow rate in the duct times 2) was about
 70 X 106ft3/hr.

      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  participates. 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.  The
 inside diameter of both stacks is  6.5 ft.  The cross-sectional area of each  stack is 33.18 ft2. The  typical stack
 gas velocity for both stacks was about 50 ft/sec (Fig. 3). The typical volumetric flow rate for either unit was about
 3.5 X 106 ft3/hr. Determinations were made on both stacks during the test.  Only one furnace train was operating
 at any time during the test.

 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
 Environmental Research Corporation, St. Paul, Minn.

     The collaborators  for the Holmes  Road Incinerator test were Mr. Mike Taylor and Mr. Rick Hohmann of South-
west Research Institute, Houston Laboratory, Houston, Texas; Mr. Charles Rodriguez and Mr. Ron Hawkins of

*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 factors are:

              1  ft = 0.3048 meters                1.0 ft*= 0.0929 meters2
           1 ft/sec = 0.3048 meters/sec             1 ft3/hr = 0.0283 meters3/hr

-------
  70
   65-
c
8
r.  60
c
c
   55
   50
   45
                                              Stack Diameter, feet
                                                  B-D Ports
10
                                                                                                ~
   45
                                                   6              8
                                                Stack Diameter, feet
1C
                                                     A-C Ports
                                   FIGURE 1. TYPICAL VELOCITY PROFILES,
                                    LONE STAR PORTLAND CEMENT PLANT

-------
6bi



fin

8
4-
£r 55

g


j._
t>u



,f.
G
Ea



















;t







































































































































































































:






























B



















_—



















•^-



















5


























































2>-





1



4



















.








i



















-






































-i



















-



























































^



















-











£







•*-<



















i.


























































g







































-»















































































•\












3






,-



















'**



















-



















5



















-
















































































































.



















































































































































































1
iA



















2
est
                                            Duct Width, Feet
                                       Profile Across Upper Ports
0)
DO
50
45
40
35
1
Ea






























































































































































































































































g
'^



















•~>



















^»,


















a


















-,


















-,

















- »

















,r

















**

















?


















/


















t



















4

















<
P

















/
















i |










J
fee
2H














2 4
st








^






























_^-
gw*"t;















































! ' • i
















t












V












s













-





1



















\




















^



















1
11

















V,




















•^s







































—
^-'























































































































































































































































6 8 10 12
West
                                       Profile Across Lower Ports
                     FIGURE 2. TYPICAL VELOCITY PROFILES, ALLEN KING POWER PLANT

-------
  c
   •
   B
50
4E

     36             48


 Stack Diameter, inches


   Profile, East Stack
72      78

        C
                  •:

      36             48

   Stack Diameter, inches



     Profile, West Stack

D    Axis through ports A, C

O    Axis through ports B, D


                  FIGURE 3. TYPICAL VELOCITY PROFILES, HOLMES ROAD INCINERATOR

-------
 Southwest Research Institute, San Antonio Laboratory, San Antonio, Texas; Mr. Quirino Wong, Mr. Randy Creighton,
 and Mr. Steve Byrd, City of Houston, Department of Public Health; Mr. John Key, Mr. James Draper, Mr. Tom
 McMickle, 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, and may differ from the code numbers assigned in the previous reports.^>^

-------
                           III.  STATISTICAL DESIGN AND ANALYSIS
A.   Statistical Terminology

     To facilitate the understanding of this report and the utilization of its findings, this section explains the statis-
tical terms used in this report. The procedures for obtaining estimates of the pertinent values are developed and
justified in the subsequent sections.
                             A                                                  A
     We say that an estimator, 9 , is unbiased for a parameter 6 if the expected value of 0 is 6 , or expressed in nota-
tional form, E(ff) = 6 . From a population of method determinations made at the same true level, /z, let Xi , .... xn
be a sample of n replicates. Then we define:

               1  "
     (1)   3c = — /_* Xj as the sample mean, an unbiased estimate of the true determination mean, 5, the center of
               ni=l
           the distribution of the determinations. For an accurate method, 5  is equal to M, the true level.

                 1    n
     (2)   s2  = - y")C*i ~ * )2 as the sample variance, an unbiased estimate of the true variance, o1 .  This
               «-i,tt
           term gives a measure of the dispersion in the distribution of the determinations around 6.
      (3)   s = Vs  as the sample standard deviation, an alternative measure of dispersion, which estimates a, the true
           standard deviation.

      The sample standard deviation, s, however, is not unbiased for o/5^ so a correction factor needs to be applied.
The correction factor for a sample of size n is an, and the product of an and s is unbiased for a. That is, E(ans) = a.
As n increases, the value of an decreases, going for example from a3 = 1.1284,04 = 1.0854 too^o = 1.0281. The for-
mula for <*„ is given in Appendix B.3.

      We define
as the true coefficient of variation for a given distribution. To estimate this parameter, we use a sample coefficient
of variation, @, defined by
where 0 is the ratio of the unbiased estimates of a and 5 . The coefficient of variation measures the percentage
scatter in the observations about the mean and thus is a readily understandable way to express the precision of
the observations.

      There were a total of 43 sampling runs for the three tests. Since the actual velocity, and hence the flow rate,
fluctuates, one can in general expect different true levels for each run. To permit a complete statistical analysis,
the individual runs are grouped into blocks, where each block has approximately the same true level.

      We can apply the statistical terms of the preceding paragraphs both to the collaborators' values during a
given run and to each collaborator's values in a given block.  In this report, statistical results from the first situa-
tion are referred to as run results.  Those from the second situation are referred to as collaborator-block results.

-------
For example, a run mean is the average of all the determinations made in a run as obtained by Method 2. A col-
laborator-block coefficient of variation is the ratio of the unbiased standard deviation to the sample mean for all
the collaborator's runs grouped in the block.

      The variability associated with a Method 2 determination is estimated in terms of the within-laboratory and
the between-laboratory precision components. In addition, a laboratory bias component can be estimated. The
following definitions of these terms are given with respect to a true level, M-

      •     Within-laboratory-Jhe within-laboratory standard deviation, a, measures the dispersion in replicate single
            determinations made using Method 2 by one laboratory team (same field operators, laboratory analyst,
            and equipment) sampling the same true level, /*. The value of a is estimated from within each col-
            laborator-block combination.

      •     Between-laboratory '-The between-laboratory standard deviation, aj,, measures the total variability in
            a determination due to simultaneous Method 2 determinations by different laboratories sampling
            the same true stack level, ji. The between laboratory variance, a|, may be expressed as
            and consists of a within-laboratory variance plus a laboratory bias variance, o| . The between-laboratory
            standard deviation is estimated using the run results.

      •     Laboratory Mzs-The laboratory bias standard deviation, ff/, = ya \ - a2 , is that portion of the total
            variability that can be ascribed to differences in the field operators, analysts and instrumentation, and
            due to different manners of performance of procedural details left unspecified in the method. This
            term measures that part of the total variability in a determination which results from the use of the method
            by different laboratories, as well as from modifications in usage by a single laboratory over a period of time.
            The laboratory bias standard deviation is estimated from the within- and between -laboratory estimates
            previously obtained.

 B.   Test Data

      This study is based upon velocities and volumetric flow rates obtained in the use of Method 5.  The average
 velocity, (Fs)aVg, i& calculated as
                                                                     ft/sec
                                                             P^s

where

      Kp = 85.48 for the units used,

      Cp         - the pitot tube coefficient

      (\/^)avg  — the average square root of the velocity head of the stack, inches H20

      (5rs)avg     — the average absolute stack gas temperature, °R

      Ps          — the absolute stack gas pressure, inches Hg

and

      Ms         - the molecular weight of the stack gas (wet basis), Ib/lb-mole.

-------
      The data used in the calculation of the velocities and flow rates were obtained during the sampling runs and
 not from the preliminary velocity traverses. These, then, represent 2-hour average velocities and flow rates across
 the stack. The volumetric flow rate, Qs, is calculated as


                            Qs = (3600X1 -


 where A is the cross-sectional area of the stack, and Bwo is the volume fraction of water vapor in the gas stream.

      In conjunction with the testing of Method 5, the collaborators calculated average stack velocities but not
 volumetric flow rates, since the concentration determinations in the previous studies were the final results used in
 the analysis.  The velocities were recalculated to ensure their accuracy, and the flow rates calculated using these
 velocities and the other test data.

      The results obtained by Lab 201 were excluded from the analysis. In a study on moisture fraction determination,
 Lab 201 was eliminated due to the probable development of leakage during some runs and filter contamination due
 to use of a low-melting ground-joint lubricant. Since this would adversely affect the volume of liquid collected due
 to the introduction of ambient air into the train, their moisture fractions were not usable.  Since the moisture
 fraction is involved directly in the Qs determination and indirectly, throughMs, in the (Kj)avg determination,
 these data were not judged acceptable.

 C.   Test Design and Analysis

      The data were arranged in blocks where the true velocity was  assumed to be essentially constant.  The velocity
 determination has been shown*  ' to be principally dependent upon the value of (v^)aVg  - Thus, this provides
 a valid means of determining when there was a change in the stack gas velocity.  The actual reading of the velocity
 head is a function of the particular pitot tube that is used, but by comparing the values of all collaborators, the
 increases and decreases in velocities can be determined. The average v^'s are shown in Table 1, along with the
 blocks to which the runs were assigned. The determinations used in the analyses are shown arranged in blocks
 in Table 2 and 3.

      To determine the best method of analyzing the data, Bartlett's test for homogeneity of variance was used to
 determine the appropriateness of an analysis of variance approach. The data were then transformed using the
 logarithmic transformation and retested by Bartlett's test. The details are contained in Appendices B.I and B.2.

      For the velocity data, significance levels under both transformations indicate suitability.  If a logarithmic
 transformation is accepted, the conclusion is that there is a proportional relationship between the true mean and
 true standard deviation.  If a linear transformation is accepted, then the indication is that the variance is
 independent  of the mean. An investigation of the proportional relationship was conducted on an empirical
 basis to determine which of the two models should be used.
      The correlation between the sample means and standard deviations is determined for both the run data and
the collaborator-block data. The model chosen is a no-intercept model, meaning that when the sample mean is
zero, the sample standard deviation must also be zero.  The coefficient of determination, r2, is the measure of the
appropriateness of the model.  For the run data, the value of r2 was 0.80, which  gives a correlation coefficient,
r = VT% of 0.89  based on  43 pairs.  This value is significant at the 5 percent level. For the collaborator-block
data, the value of r2 was  0.75, and the correlation coefficient, r, was 0.86, based on 37 pairs. This value also
exceeds the value for the  5 percent significance level.

      Thus, there is evidence of a proportional relationship between the mean and the standard deviation for
the velocity data. This is equivalent to saying that the standard deviations, a/, and a, change as the mean, 6,
changes. That is,

-------
TABLE 1. AVERAGE v/A^'s AND BLOCK
           DESIGNATIONS.
TABLE 2. STACK GAS VELOCITY DATA,
     ARRANGED BY BLOCK.
          Velocity, ft/sec
Run
Labs
Block
Site 1

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
101
0.83
0.83
0.83
0.75
0.75
0.78
0.68
0.72
0.74
0.74
0.72
0.73
0.72
_*
0.67
102
0.82
0.83
0.84
0.75
0.78
0.75
0.69
0.76
0.74
0.73
0.72
0.76
0.73
0.69
0.70
103
_*
0.91
1.02
0.77
0.76
0.76
0.69
0.73
0.73
0.74
0.72
0.73
0.71
0.67
0.69
104
0.83
0.83
0.83
0.79
0.75
0.79
0.74
0.72
0.77
0.73
0.75
0.76
0.75
0.70
0.70

1
1
1
2
2
2
4
3
2
3
3
3
3
4
4
Site 2

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
202 203
0.75 0.80
0.74 0.75
0.70 0.79
0.78 0.80
0.73 0.75
0.74 0.79
0.69 0.76
0.79 0.80
0.68 0.71
0.73 0.74
0.72 0.75
0.71 0.73
0.76 0.75
0.76 -*
0.71 0.73
0.75 0.80
204
0.76
0.76
0.77
0.78
0.73
0.77
0.74
0.76
0.74
0.77
0.75
0.67
0.75
0.74
0.75
0.72

1
2
1
1
2
1
2
1
3
2
2
3
2
2
2
2
Site 3

1
2
3
4
5
6
7
8
9
10
11
12
301
0.79
0.77
0.78
0.78
0.83
0.82
0.79
0.83
0.68
0.84
0.77
0.82
302
0.81
0.91
1.00
0.73
0.86
0.90
0.86
0.89
0.75
0.84
0.83
0.87
303
0.78
0.73
0.79
0.73
0.78
0.74
0.75
0.70
0.67
0.78
0.77
0.76
304
_*
0.88
0.78
0.86
0.83
0.81
0.84
0.74
0.72
0.87
0.84
0.94

3
2
1
3
2
2
3
3
4
1
3
1
*Run not made due to equipment failure.
Block
Run
Labs
Site 1

1


2



3




4



1
2
3
4
5
6
9
8
10
11
12
13
7
14
15
101
62.4
61.1
61.7
56.5
55.9
57.6
51.9
49.5
52.6
51.2
51.9
51.7
46.9
_*
52.0
102
62.3
63.2
63.1
56.5
60.3
56.0
52.8
53.9
53.4
54.1
55.3
53.2
48.7
52.0
51.5
103
_*
59.0
66.1
57.3
56.3
56.4
52.3
51.7
53.0
52.4
53.3
51.9
49.0
48.6
49.9
104
58.2
60.7
63.3
60.1
57.6
60.4
55.6
51.8
53.8
55.9
57.0
55.3
51.9
52.9
52.2
Site 2

1




2








3


1
3
4
6
8
2
5
7
10
11
13
14
15
16
9
12
202
51.2
47.3
53.1
50.2
53.7
50.1
49.8
46.5
48.8
48.1
51.9
51.3
48.2
50.6
46.0
48.6
203 204
52.3 47.6
51.8 51.3
52.5 49.6
52.0 49.3
51.3 47.5
48.7 49.9
49.3 48.1
48.8 45.4
48.3 44.8
46.6 48.8
47.6 48.8
-* 49.8
46.8 48.6
51.7 47.0
45.0 49.5
46.5 43.0
Site 3

1


2


3




4

3
10
12
2
5
6
1
4
7
8-
11
9
301
46.9
50.9
50.5
48.0
51.7
51.1
48.6
48.0
48.8
51.6
47.4
41.7
302
52.3
51.8
50.2
48.2
51.6
48.9
51.0
47.9
49.6
46.1
51.0
44.8
303
57.9
53.5
55.5
58.4
55.6
57.5
55.9
56.7
55.3
56.5
53.4
48.7
304
47.7
53.0
57.6
54.2
53.2
50.2
_*
54.3
52.0
46.0
51.5
48.5
*Run not made due to equipment failure.
                                       10

-------
TABLE 3. VOLUMETRIC FLOW RATE DATA,
         ARRANGED BY BLOCK
     Volumetric Flow Rate, ft3/hi X 10'4
°b =
Block
Run
Labs
Site 1

1















1
2
3
4
5
6
9
8
10
11
12
13
7
14
15
101
1267.6
1244.2
1238.5
1101.3
1123.3
1183.7
1257.4
1243.9
1240.1
1241.7
1208.4
1184.5
1078.2
_*
1136.8
102
1176.5
1243.7
1220.3
1141.6
1065.6
1110.5
1256.7
1335.0
1245.9
1167.2
1198.1
1160.7
1261.9
1086.1
1118.8
Site

1




2








3


1
3
4
6
8
2
5
7
10
11
13
14
15
16
9
12
202
7170.8
6617.2
7324.7
6995.2
7445.7
6895.3
6935.4
6555.7
6835.6
7364.3
7173.4
7119.1
6694.1
7093.1
5819.7
6835.7
103
_*
1384.0
1496.7
1250.2
1238.4
1248.5
1403.8
1337.1
1341.2
1255.8
1257.8
1266.2
1270.0
1152.5
1205.0
2
203
7145.4
7110.8
7162.2
7011.5
7199.8
6606.4
6741.9
6850.2
6861.3
6534.0
6887.8
_*
6586.4
7177.6
6582.5
6730.8
104
1254.2
1251.4
1410.4
1274.7
1158.1
1220.9
1330.8
1320.1
1255.2
1198.7
1192.6
1240.5
1431.5
1114.7
1135.8

204
6947.2
7240.3
6855.4
6880.2
6683.3
6958.7
6823.1
6551.8
6364.2
6839.9
7015.9
6928.9
6830.0
6602.6
7101.8
6107.2
Site 3

1












3
10
12
2
5
6
1
4
7
8
11
9
301
335.8
354.1
319.8
311.3
261.3
335.4
309.3
301.4
308.4
323.8
312.6
273.6
302
371.7
369.1
367.6
355.5
350.9
349.5
368.3
329.5
339.4
323.4
348.7
311.7
303
333.5
317
342
334
.3
.2
.6
310.5
325.6
357
.1
316.6
325.4
352.0
303
.7
276.7
304
311.8
353.9
374.5
345.1
284.5
320.2
_*
317.8
326.2
281.1
329.0
289.5
*Run not made due to equipment failure.
                                              and
                                              where fo and (1 are the true coefficients of variation for between-
                                              laboratory and within-laboratory, respectively. The standard
                                              deviations are estimated, then, as
                                              and
                                              where &b and 0 are the estimated coefficients of variation.

                                                   For the volumetric flow rates obtained, a similar
                                              investigation is done. For these values, the only acceptable
                                              transformation is the logarithmic, which implies, on a theoretical
                                              basis, an underlying proportional relationship between the
                                              population mean and the population standard deviation for
                                              both the run data and the collaborator-block data.

                                                   To establish this empirically, the paired sample means
                                              and standard deviations are fit to a no-intercept regression
                                              model. The run data give an r2 of 0.73 and a correlation
                                              coefficient of 0.85, based on 43 pairs. The collaborator-block
                                              r2 is 0.63, with r = 0.79 based on 37 pairs. Both r values are
                                              significant at the 5 percent significance level.

                                                   As a result, the volumetric flow rate within-laboratory
                                              and between-laboratory standard deviations can be said to
                                              be proportional to the  mean level.  The estimates of these
                                              standard deviations will be expressed using coefficients of
                                              variation times an unknown mean in the same manner as
                                              the velocity data.

                                                   At each site, there were occasional missing values due to
                                              equipment malfunctions and varying block sizes, so that not
                                              all coefficients of variation are based on the same number of
                                              observations. To account for this, for each site the individual
                                              beta estimates are weighted so that a greater contribution to
                                              the final estimate, is made by those values based on larger
                                              samples. The weighting technique is based upon the number
                                              of values in each run or block  and is discussed in detail in
                                              Appendix B.4.  The beta values from all three sites form a
                                              composite estimate of the coefficients of variation for
                                              both velocity and flow rate.
                                                 11

-------
                   IV. VELOCITY DETERMINATION PRECISION ESTIMATES
       The between-laboratory standard deviation, aj, and the within-laboratory standard deviation, a, for (Vs) avg
 are estimated as
 and
 In Appendix B.5, the data from the three sites are used to obtain estimates of these terms using a linear combination
 of the individual values.

      The between-laboratory coefficient of variation is |3j = (0.050). This gives a between-laboratory standard
 deviation of
                                                  = (0.050)5

 or 5.0% of the mean. This estimate has 8 degrees of freedom associated with it.

      The within-laboratory coefficient of variation is estimated as $ = (0.039). This gives an estimated within-
 laboratory standard deviation of

                                                0 = 08

                                                  = (0.039)6

 or 3.9% of the mean.  There are 1 13 degrees of freedom associated with this term.

      From the formula in Section IIIA, the laboratory bias standard deviation, a/, , is given by

                                             °L =

 Substituting the estimates above into this formula gives
                                               = V(0.050)282-(0.039)262

                                               = >/[(0.050)2-(0.039)2]62
                                               = >/(0.001)52

                                               = (0.032)5

or 3.2% of the mean level.
                                                    12

-------
                    V. VOLUMETRIC FLOW RATE PRECISION ESTIMATES
     The between-laboratory standard deviation, ffft, and the within-laboratory standard deviation, 6 , for Qs are
estimated as
and
where 0& and 0 are the estimated coefficients of variation.  In Appendix B.6 the individual beta estimates are com-
bined to obtain estimates of these from the run data and collaborator-block data, respectively.

     The estimated between-laboratory coefficient of variation is fa = (0.056). This gives an estimated between-
laboratory standard deviation of
                                              = (0.056)5

or 5.6% of the mean. This estimate has 8 degrees of freedom associated with it.

     The within-laboratory coefficient of variation is estimated by 3 = (0.055). This gives an estimated within-
laboratory standard deviation of

                                            a=J36

                                             = (0.055)6

or 5.5% of the mean. There are 113 degrees of freedom associated with this estimate.

     The laboratory bias standard deviation is defined as
Substituting ab and a into this formula gives

                                    5/.=V°J
= Jal-P
                                       = x/(0.056)252 - (0.055)262

                                       = N/[(0.056)2-(0.055)2]62

                                       = (0.011)5

or 1.1% of the mean level.
                                                 13

-------
                               VI.  EMISSION RATE VARIATION
     The standards of performance*1* for certain sites (e.g., power plants, nitric acid plants, Portland cement plants)
specify that the product of the volumetric flow rate and the emission concentration obtained by the appropriate
method be used in determining compliance with the regulations.  The rate is denoted in this study by r, where
It is of interest to determine the precision of this product based upon the precision of the individual components.

      In Appendix B.7, the formula is developed for estimating a precision component for this product when both
the flow rate and the concentration determination follow the coefficient of variation hypothesis. The formulas for
the within-laboratory and between-laboratory variances are given by
and
where ^(G4) and P(QS) are the between and within-laboratory coefficients of variation for flow rate, $b(c) and
|3(c) are the coefficients of variation for emission concentrations, and 5r is the mean emission rate.

TABLE 4. PRECISION ESTI-        In Table 4 are listed values of $b(c) and  0(c) for Methods 5, 6 and 7 based upon
.  MATES FOR EMISSION     previous collaborative studies. Using these and the coefficients of variation for Qs
   CONCENTRATIONS       developed in this study, estimates can be made of the precision associated with r.
Method
5<4>
6(7)
7(8)
0(0
0.253
0.040
0.066
*>
0.387
0.058
0.095
                                Method J-The between-laboratory standard deviation estimate is 39.2% of dr,
                           and the within-laboratory standard deviation estimate is 25.9% of 6r. This gives a
                           laboratory bias term of 29.4% of 6r.

                                Method 6—The estimated between-laboratory standard deviation is 8.1% of 5r,
                           with an estimated within-laboratory standard deviation of 6.8% of 5r. From these, the
                           laboratory bias standard deviation is estimated as 4.5% of 8r.

     Method 7-The estimated between-laboratory standard deviation is 11.0% of 8r. The estimated within-laboratory
standard deviation is 8.6% of 8r.  Using these, the laboratory bias standard deviation is estimated as 7.1% of 5,-.

     As can be seen from these results, the precision in r depends primarily upon the  precision of the emission con-
centration determination, and little variation is introduced by the volumetric flow rate determination.
                                                  14

-------
                   APPENDIX A

METHOD 2. DETERMINATION OF STACK GAS VELOCITY AND
     VOLUMETRIC FLOW RATE {TYPE S PITOT TUBE)
                       15

-------
24884
      RULES AND  REGULATIONS
METHOD  a—DETERMINATION  Or  STACK  GAS
  VELOCITY AND VOLUMETRIC HOW BATE (TYPE
  S Pl'ruT TUBE)

  1. Principle and applicability.

  I.I  Principle. Stack gas velocity Is deter-
mined from the gas density Bud from meas-
urement of the velocity head using a Type S
(SUuisohelbe or reverse type) pltot tube.
  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.

  2. Apparatus.
  2.1  Pttot tube—Type S  (Figure 2-1), or
equivalent, with a coefficient  within ±5%
over the working range.
  2.2  Differential pressure gauge—Inclined
manometer, or equivalent, to measure velo-
city head to within  10%  of the minimum
value.
  2.3  Temperature gauge—Thermocouple or
equivalent attached  to the  pltot tube to
measure stack temperature to wrthln 1.5% of
the  minimum absolute stack, temperature.
  2.4  Pressure gauge—Mercury-filled U-tube
manometer, or equivalent, to measure stack
pressure to'within 0.1 In. Hg.
  2.5  Barometer—To measure atmospheric
pressure to within 0.1 In. Hg.
  2.6  Oas analyzer—To analyze gas composi-
tion for determining molecular weight.
  2.7  Pltot tube—Standard  type, to cali-
brate Type S pltot tube.

  3. Procedure.
  3.1  Set up the apparatus as shown In Fig-
ure 2-1.  Make sure all connections are-tight
and leak free. Measure the velocity head and
temperature at the traverse  points specified
by Method 1.
  3.2  Measure  the  static pressure  in  the
stack.
  3.3  Determine  the stack  gas molecular
weight by gas analysis and appropriate  cal-
culations as Indicated In Method 3.
                                                                                          4. Calibration.

                                                                                          4.1  To calibrate the pitot tube, measure
                                                                                        the velocity head at some point In a flowing
                                                                                        gas stream with both a Type S pltot tube and
                                                                                        a standard  type pltot tube with  known  co-
                                                                                        efficient. Calibration should be done  In  the
                                                                                        laboratory and the velocity of the flowing gas
                                                                                        stream should  be  varied over the  normal
                                                                                        working range. It  is recommended that  the
                                                                                        calibration  be repeated after use at each field
                                                                                        site.
                                                                                          4.2  Calculate the  pitot tube  coefficient
                                                                                        using equation 2-1.
                             equation 2-1
where:
  Cp,,.,=Pltot tube coefficient  of  Type  S
            pitot tube.
   Cp,tJ=Pitot tube coefficient of standard
            type pltot tube (if unknown, use
            0.99) .
   Apnd= Velocity head measured by stand-
            ard type pitot tube.
  Apt. .t=: Velocity head measured by Type S
            pitot tube.
  4.3 Compare the coefficients of the Type S
plbot tube determined first with  one leg and
then the other pointed downstream. Use the
pitot tube only if the two coefficients differ by
no more than 0.01.
  6.  Calculations.
  Use equation 2-2 to calculate the stack gas
velocity.
                                     PIPE COUPLING
                                                                 TUBING ADAPTER
                                                                                                                     Equation 2-2
                                                                                         where :
                                                                                            (V»)«c.= Stack gas velocity, feet per second (f.p.s.).
                                                                                                Cp=Pltot tube coefficient, dimensionl'1ss
                                                                                            (T.)«£.=A7erage absolute stack gas temperature
                                                                                                      R.
                                                                                          ( VAP) >T,.= Average velocity head of stack gas, inches
                                                                                                     HiO (see Fig. 2-2).
                                                                                                P.=Absohite stack gas pressure, Inclips \JK.
                                                                                                M.= Molecular weight of stack gaa (wet basis).
                                                                                                     Ib./Ib.-mole.
                                                                                                      Mj(l-Bwo)+18Bwo
                                                                                                Md=Dry molecular weight of stack gas (from
                                                                                                     Methods).
                                                                                               B»0=Proportion by volume of water vapor in
                                                                                                     the gas stream (from Method 4).

                                                                                           Figure 2-2 shows a sample recording sheet
                                                                                        for velocity  traverse data.  Use the averages
                                                                                        In the last two columns of Figure 2-2 to de-
                                                                                        termine the average stack gas velocity from
                                                                                        Equation 2-2.
                                                                                           Use Equation  2-3  to calculate the stack
                                                                                        gas volumetric flow rate.
                                                                                            .=3600 a-
                                                                                                                     Equation 2-3
                                                                                        where:
                                                                                           Q.=Volumetric flow rate, dry basis, standard condi-
                                                                                                tions. ft.'/hr.
                                                                                            A =Cross-secttonal area of stack, ft."
                                                                                          T,td= Absolute temperature at standard conditions,
   Figure 2-1.  Pttot tube-manomotar assembly.
                                              P.id= Absolut* pressure at standard conditions, 29.92
                                                    inches Hg.
                            fEOHAL UGISRR, VOL M. NO. 247—THURSDAY, DECEMBER 23, 1971
                                                            17

-------
                          RULES AND  REGULATIONS
                                                                                                24885
  6. References.

  Mark. L. 3., Mechanical Engineers' Hand-
book. McGraw-Hill Book Co., Inc.. New York,
N.T., 1951.
  Ferry, J. H.,  Chemical Engineers' Hand-
book, McGraw-Hill Book Co., Inc., New York,
N.Y., 1960.
  Shigehara, R. T., W. P. Todd,  and W. 8.
Smith, Significance of Errors In Stack Sam-
             pling Measurements. Paper presented at the
             Annual Meeting of the Air Pollution Control
             Association, St. Louis, Mo., June 14-18, 1970.
               Standard Method for Sampling Stacks for
             Paniculate Matter,  In: 1971 Book of ASTM
             Standards, Pan 23. Philadelphia, Pa,  1971,
             ASTM Designation D-2S29-71.
               Vennard, J. K., Elementary Fluid Mechan-
             ics, John Wiley & Sons, Inc., New York, N.Y,
             1947.
   PIANT_

   DATE
   RUN NO.
   STACK DIAMETER, in..
   BAROMETRIC PRESSURE, in. Hg._
  STATIC PRESSURE IN STACK (Pg). in. Hg._

  OPERATORS	
                              SCHEMATIC OF STACK
                                CROSS SECTION
          Traverse point
              number
Velocity head.
   in. HjO
                                                              Stack Temperature
                                 AVERAGE:
                        .Figure 2-2.  Velocity traverse data.
          FEDERAl REGISTER, VOL. 36, NO. 247—THURSDAY,  DECEMBER 23, 1971
                                              18

-------
     APPENDIX B



STATISTICAL METHODS
          19

-------
                           APPENDIX B.  STATISTICAL METHODS
     This appendix consists of various sections which contain detailed statistical procedures carried out in the
analyses of the Method 2 data. Reference to these sections has been made at various junctures in the body of this
report. Each Appendix B section is an independent ad hoc statistical analysis pertinent to a particular problem
addressed in the body of the report.

B.1  Proportional Relationship Between Mean and Standard Deviation in the Velocity
     Determinations

     The velocities shown in Table 2 are tested to determine if the variance is independent of the mean level in
their original form (linear) and after having undergone a logarithmic transformation.  Bartlett's test for homogeneity
of variance^ is used to determine the suitability of each transformation.  The obtained values of the statistic with
degrees of freedom and significance levels are shown in Table B-l.  The significance levels are obtained from a
chi-square distribution with the degrees of freedom shown.
      TABLE B-l. VELOCITY TRANSFORMATION RESULTS
Data
Run

Collaborator-Block

Transformation
Linear
Logarithmic
Linear
Logarithmic
Test
Statistic
44.391
46.219
47.932
48.084
DF
42
42
36
36
Significance
Level
0.371
0.302
0.088
0.086
                                                              For both the run data and the collaborator-
                                                        block data, either form is acceptable. The
                                                        acceptance of the linear form of the data implies
                                                        that the variance is independent of the mean,
                                                        that is, constant regardless of the mean value.
                                                        The acceptance of the logarithmic transforma-
                                                        tion implies a proportionality between the pop-
                                                        ulation mean and the population standard
                                                        deviation, or that as the mean level rises (falls),
                                                        the standard deviation rises (falls) in a propor-
                                                        tional manner.
      Both transformations are acceptable at nearly equal significance levels.  To determine if there is further
evidence of a proportional relationship between the mean and standard deviation, a regression model is fit to the
data. The model chosen is a no-intercept model,

                                               y = bx

so that a sample mean of zero implies a sample standard deviation of zero. Define

     Xjjk as the determination by collaborator i on run k in block/.
      1
x .  = —
                     k as the mean of run k in block / for p collaborators
and
 »/* =
                                     as the run standard deviation.
The paired means and standard deviations, (jc ./#, Sjk), shown in Table B-2 are fit to the model, and the degree of fit
determined by the coefficient of determination, r2.  For this model, r2 is calculated as^
                                                  21

-------
TABLE B-2. RUN MEANS AND STANDARD
    DEVIATIONS (Velocity, ft/sec)
Run
Mean
Velocity
Standard
Deviation
Site 1
1
2
3
4
5
6
9
8
10
11
12
13
7
14
15
61.0
61.0
63.5
57.6
57.5
57.6
53.1
51.7
53.2
53.4
54.4
53.0
49.1
51.2
51.4
2.4
1.7
1.8
1.7
2.0
2.0
1.7
1.8
0.5
2.0
2.2
1.7
2.1
2.3
1.0
Site 2
1
3
4
6
8
2
5
7
10
11
13
14
15
16
9
12
50.4
50.1
51.7
50.5
50.8
49.6
49.1
46.9
47.3
47.8
49.4
50.5
47.9
49.8
46.8
46.0
2.5
2.5
1.9
1.4
3.1
0.8
0.9
1.7
2.2
1.1
2.2
1.1
0.9
2.5
2.4
2.8
Site 3
3
10
12
2
5
6
1
4
7
8
11
9
51.2
52.3
53.4
52.2
53.0
51.9
51.8
51.7
51.4
50.0
50.8
45.9
5.1
1.2
3.7
5.0
1.9
3.8
3.7
4.5
2.9
5.0
2.5
3.3
For the run data, r2 = 0.80, which indicates that 80 percent of the
variation in the magnitude of the standard deviation is attributed to
variation in the magnitude of the mean. The correlation coefficient,
r = V^3", is 0.89 based on 43 pairs of observations, which is significant
at the 5 percent level.

     For the collaborator-block data, we define
                                                  _J_  "V
                                              determinations.
                                                                 as the mean of collaborator-block ij, for
                                         and
                                                                  - x ,y.)2  as the collaborator-block standard
                                              deviation.
                                         The values obtained are shown in Table B-3. Fitting these to a no-
                                         intercept model, we have a coefficient of determination of r2 = 0.75
                                         and a correlation coefficient of 0.86. This value is also significant at
                                         the 0.05 level, based upon 37 pairs of observations.

                                              Thus, we have that on a theoretical basis, from the acceptability
                                         of the logarithmic transformation, and an empirical basis, from the regres-
                                         sion model, there is strong evidence that a proportional relationship exists
                                         between the mean and standard deviation for the velocity data.  This
                                         is equivalent to saying that the coefficients of variation for both between-
                                         and within-laboratory components remain constant. This gives the
                                         equations
                                         and
                                              Then we estimate the standard deviations by estimating the
                                         coefficients of variation and defining new estimators 8& and d,
                                         and
                                         where fe and |3 are the estimated coefficients of variation for between-
                                         laboratory and within-laboratory, respectively.  Thus, the standard deviations
                                         are estimated as percentages of an unknown mean, 5.
B.2  Proportional Relationship Between Mean and Standard Deviation in the Flow Rate Determination

      The calculated volumetric flow rates in Table 3 are tested for equality of variance in two forms: their original
form (linear) and after having been passed through a logarithmic transformation.  Bartlett's tesr  ' for homogeneity
of variance is used to determine the adequacy of each transformation, and the test statistic is compared to a chi-square
                                                    22

-------
TABLE B-3. COLLABORATOR-BLOCK MEANS
     AND STANDARD DEVIATIONS
            (Velocity, ft/sec)
TABLE B-4. FLOW RATE TRANSFORMATION RESULTS
Block
Collaborator
Mean
Velocity
Standard
Deviation
Site 1
1



2



3



4



Lab 101
Lab 102
Lab 103
Lab 104
Lab 101
Lab 102
Lab 103
Lab 104
Lab 101
Lab 102
Lab 103
Lab 104
Lab 101
Lab 102
Lab 103
Lab 104
61.73
62.87
62.55
60.73
55.47
56.40
55-57
58.42
51.38
53.98
52.46
54.76
49.45
50.73
49.17
52.33
0.65
0.49
5.02
2.55
2.49
3.07
2.23
2.26
1.16
0.82
0.69
2.02
3.61
1.78
0.67
0.51
Site 2
1


2


3


Lab 202
Lab 203
Lab 204
Lab 202
Lab 203
Lab 204
Lab 202
Lab 203
Lab 204
51.10
51.98
49.06
49.48
48.47
47.91
47.30
45.75
46.25
Site 3
1



2



3



4*



Lab 301
Lab 302
Lab 303
Lab 304
Lab 301
Lab 302
Lab 303
Lab 304
Lab 301
Lab 302
Lab 303
Lab 304
Lab 301
Lab 302
Lab 303
Lab 304
49.43
51.43
55.63
52.77
50.27
49.57
57.17
52.53
48.88
49.12
55.56
50.95
41.70
44.80
48.70
48.50
2.55
0.47
1.58
1.72
1.62
1.82
1.84
1.06
4.60

2.20
1.10
2.20
4.95
1.99
1.80
1.43
2.08
1.62
2.12
1.33
3.52
_
-
-
-
*No standard deviations since block contains
only one run.
Data
Run

Collaborator-Block

Transformation
Linear
Logarithmic
Lineal
Logarithmic
Test
Statistic
192.451
48.401
192.416
62.844
DF
42
42
36
36
Significance
Levei
0.000
0.230
0.000
0.004
                                           distribution with the appropriate degrees of freedom. The values
                                           for both the run and collaborator-block data are shown in Table B-4.

                                                Clearly, for the run data the logarithmic transformation is
                                           acceptable, while the linear form of the data is not. The reason for
                                           this is apparent from the formula for Qs. The principal factor upon
                                           which Qs depends is (f^avg, but the use of the multipliers of (3600)
                                           and the cross-sectional area of the stack increases the magnitude of
                                           the velocity variation. However, the relative variation, as expressed
                                           by the coefficient of variation, tends to remain constant from site
                                           to site.  For the collaborator-block data, the logarithmic  transformation
                                           would not be considered acceptable but is an improvement over the
                                           linear form. The acceptance of the logarithmic transformation implies,
                                           on a theoretical basis, a proportional relationship between the mean
                                           and standard deviation of the distribution.

                                                To further investigate the proportional relationship, a least
                                           squares model is fit to the paired sample means and sample standard
                                           deviations. For the run data, define

                                                Xjjk  — the flow rate determined by collaborator /on run k
                                                in block/.
 V   - _ V
 *•/'*"   L,
                                                collaborators
                                                                 as the run mean, where p is the number of
                                           and
                                                     P ~ 1 i = 1
                                                                             the run standard deviation.
                                           A no-intercept model is fit to the pairs (x./jt, s/jt), since a mean of zero
                                           automatically implies a standard deviation of zero.  The paired means
                                           and standard deviations are shown in Table B-5.  The fit to this model
                                                     23

-------
TABLE B-5. RUN MEANS AND STANDARD
   DEVIATIONS (Volumetric Flow Rate,
              ft*/hrX lO'4)
is measured by the coefficient of determination, r2. For the no-intercept
model, r2 is calculated as*  ^
Run

1
2
3
4
5
6
9
8
10
11
12
13
7
14
15
Mean
Flow Rate
Standard
Deviation
Site 1
1232.8
1280.8
1341.5
1191.9
1146.3
1190.9
1312.2
1309.0
1270.6
1215.8
1214.2
1213.0
1260.4
1117.8
1149.1
49.2
68.9
134.3
83.7
72.3
59.8
70.3
44.1
47.5
40.5
29.8
48.8
144.4
33.3
38.2
Site 2
1
3
4
6
8
2
5
7
10
11
13
14
15
16
9
12

3
10
12
2
5
6
1
4
7
8
11
9
7087.8
6989.4
7114.1
6962.3
7109.6
6820.1
6833.5
6652.6
6687.0
6912.7
7025.7
7024.0
6703.5
6957.8
6501.3
6557.9
Site 3
338.2
348.6
351.0
336.6
301.8
332.7
344.9
316.3
324.8
320.1
323.5
287.9
122.4
328.8
238.3
71.6
389.1
187.8
97.2
171.2
279.9
419.9
143.1
134.5
122.1
310.5
644.9
393.8

24.8
22.0
25.0
18.9
38.4
12.9
31.3
11.5
12.7
29.2
19.8
17.3
                                               For the run data, r2 = 0.73 based on 43 pairs of observations.  This
                                          indicates that 73% of the variation in the magnitude of the standard deviation
                                          is attributed to variation in the magnitude of the mean.  The correlation
                                          coefficient, r = v^3", is 0.85 which is a significant value at the 5 percent
                                          level.

                                               Similarly, for the collaborator block data define

                                                     1   "9
                                               x ff = — V  Xijk as the collaborator-block mean for collaborator
                                                    "'/"  * = i
                                               i in block/, and n,y determinations in the collaborator-block
                                          and
                                                                            as the collaborator-block standard
                                               deviation.
                                          The paired values (*#., s/y) are shown in Table B-6.  For the no-intercept
                                          model,/-2 = 0.63 and the correlation coefficient, r, is 0.79 based on
                                          37 pairs. As in the case of the transformations, the proportional relation-
                                          ship does not appear as strong for the collaborator-block data. However,
                                          a correlation coefficient of 0.79 is significant at the 5 percent level.

                                               As a result, then, we have the model for the between-laboratory
                                          and within-laboratory standard deviations of
                                          and
                                                                         = 05
                                         where fa and |3 are the true between-laboratory and within-laboratory
                                         coefficients of variation, and 6 is an unknown mean. The coefficients
                                         of variation remain constant, and the standard deviation may be expressed
                                         as a percentage of the mean value. Thus, the standard deviations are
                                         estimated by obtaining estimates of the coefficients of variation, fo and 0,
                                         and expressing the estimators as
                                                                     »&=!
                                                        and
                                                                      5 = 1
                                                    24

-------
TABLE B-6.  COLLABORATOR-BLOCK MEANS AND
           STANDARD DEVIATIONS
      (Volumetric Flow Rate, ft'/hr X lO'4)
Block
Collaborator
Mean
Flow Rate
Standard
Deviation
Site 1
1
2
3
4
Lab 101
Lab 102
Lab 103
Lab 104
Lab 101
Lab 102
Lab 103
Lab 104
Lab 101
Lab 102
Lab 103
Lab 104
Lab 101
Lab 102
Lab 103
Lab 104
1250.10
1213.50
1440.35
1305.33
1166.42
1143.57
1285.22
1246.12
1223.72
1221.38
1291.62
1241.42
1107.50
1155.60
1209.17
1227.33
15.42
34.11
79.69
91.00
69.94
81.63
79.22
73.87
26.32
71.89
43.59
51.45
41.44
93.50
58.86
177.13
Site 2
1
2
3
Lab 202
Lab 203
Lab 204
Lab 202
Lab 203
Lab 204
Lab 202
Lab 203
Lab 204
7110.72
7125.94
6921.28
6962.89
6780.70
6768.34
6327.70
6656.65
6604.50
323.46
71.54
203.17
251.59
210.72
215.90
718.42
104.86
703.29
Site 3
1
2
3
4*
Lab 301
Lab 302
Lab 303
Lab 304
Lab 301
Lab 302
Lab 303
Lab 304
Lab 301
Lab 302
Lab 303
Lab 304
Lab 301
Lab 302
Lab 303
Lab 304
336.57
369.47
331.00
346.73
302.67
351.97
323.57
316.60
311.10
341.86
330.96
313.52
273.60
311.70
276.70
289.50
17.16
2.07
12.64
31.96
37.80
3.14
12.18
30.46
8.19
17.65
22.95
22.13
-
*No standard deviations since block contains
only one run.
B.3 Unbiased Estimation of Standard Deviation
     Components

     In Appendices B.I and B.2, the theoretical and empirical
arguments from the collaborator-block data indicate that a
suitable model for the within-lab standad deviations of both
variables is
                                                                       o =
                                               ship
                                                     To estimate this standard deviation, we use the relation-
                                               where Cis a constant, representing the proportionality. As
                                               previously discussed, s,y is a biased estimator for the true
                                               standard deviation, a. The correction factor for removing
                                               the bias is dependent on the sample size n, and is given by
Ziegler
                                                     (5)
                                                         as
                                               where T represents the standard gamma function. Thus, we
                                               can say that
                                               or
                                                                     a =
                                                                      = anCE(xi/.)
                                                                      = 06
                                                so that in obtaining an unbiased estimate of 0, we can obtain
                                                an unbiased estimate of a as well. Thus, we define an estimator
                                                for a, a, where
     From Appendices B.I and B.2, we determine that a suitable model for the run data from both variables is
                                               ab =
                                                   25

-------
where oj, = VOL +o2 is the between-lab standard deviation. Empirically, we have

                                              Sjk = CbX.jk

and Sjk is a biased estimator for o/,. Thus, for p collaborators,

                                             E(apSjk) = o

and we have

                                           a = E(apsjk)

                                             = apE(Cbxjk)
                                            = 0*6-

      Obtaining an estimate of ft,, we have a new estimator, <% , of <;& given by
But a^ = Vffi + °2 implies
and substituting our estimates of 
-------
for a sample of size n.  This estimator is shown in B.5 to be unbiased for the true coefficient of variation.  However,
since we are dealing with small samples to obtain our individual estimates, weighting is more desirable in that it pro-
vides for more contribution from those values derived from larger samples. There is more variability in the beta
values obtained from the smaller samples, as can be seen by inspecting the variance of the estimator. We have that
for normally distributed samples/ 1 1 * and true coefficient of variation, j3. Rewriting this expression, we have
and all terms are constant except for c?n and n. Thus, the magnitude of the variance changes with respect to the
factor <&ln. Now, since an decreases as n increases, the factor o£/n must decrease as n increases, and the variance
is reduced.

     The weights, w,-, are determined according to the technique used in weighted least squares analysis(6), which
gives a minimum variance estimate of the parameter. The individual weight, w,-, is computed as the inverse of the
variance of the estimate, ft, and then standardized. Weights are said to be standardized when
                                              1   *
 To standardize, the weights are divided by the average of the inverse variances for all the estimates.  Thus, we can
 write
                                                     "i
                                                     r
                                                     u
 where
                                                   Vaitf/)

 and

                                                1   *     1
                                                k fa Vaitf/)

      Now, from the above expressions we can determine «,-, u  and w,- for the beta estimates. For any estimate, ft,
                                                      27

-------
for sample size «/, and
Thus, the ith weight, w,-, is
                                              1   *    1
                                               ; =
                                                *   «/  r     2
                                             I      2
     The estimated coefficient of variation is
                                               k ^
                                               */-1
                                               * A f
                                                     / -1
                                                   28

-------
B.5  Estimating Precision Components For Velocity Determination

      In Appendix B.I the models are given for the between-laboratory and within-laboratory standard deviations,
a}, and a, respectively,

                                               <>b =

and
where jjj and|3 are the true coefficients of variation for between-laboratory and within-laboratory, respectively.
The coefficients of variation remain constant for changing mean levels.

     Estimates of o^ and a are obtained using the technique of Appendices B.3 and B.4. The coefficients of
variation are estimated as a linear combination of beta values obtained from each run or collaborator-block.  The
estimator is of the form
where k is the number of individual estimates and w; is the weight applied to the Mi beta estimate.

     From the run data, the estimated between-laboratory coefficient of variation is estimated as


                                             -—  V
                                           fe~43  ^ Wjfc


The individual beta estimate and the weights applied are shown in Table B-7. Substituting these into the above
formula gives

                                             ft, =(0.050).

The estimated between-laboratory standard deviation, then, is
                                                  = (0.050)6.

     The degrees of freedom associated with this estimate are determined by taking the number of collaborators
at a site less one, summed for all three sites. This gives (4 —  1) + (3 - 1) + (4 - 1) = 8 degrees of freedom for this
estimate.
                                                    29

-------
      TABLE B-7.  RUN BETA ESTIMATES AND WEIGHTS
                     (Velocity)
Run

1
2
3
4
5
6
9
8
10
11
12
13
7
14
15

1
3
4
6
8
2
5
7
10
11
13
14
15
16
9
12

3
10
12
2
5
6
1
4
7
8
11
9
Beta Hat
Site 1
0.0444
0.0307
0.0315
0.0322
0.0375
0.0374
0.0342
0.0377
0.0105
0.0416
0.0477
0.0339
0.0457
0.0500
0.0220
Site 2
0.0551
0.0555
0.0408
0.0307
0.0694
0.0172
0.0201
0.0417
0.0520
0.0265
0.0506
0.0263
0.0223
0.0557
0.0569
0.0693
Sir e 3
0.1073
0.0244
0.0748
0.1047
0.0382
0.0800
0.0810
0.0938
0.0616
0.1092
0.0535
0.0789
Weight

0.723
1.043
1.043
1.043
1.043
1.043
1.043
1.043
1.043
1.043
1.043
1.043
1.043
0.723
1.043

1.030
1.030
1.030
1.030
1.030
1.030
.030
.030
.030
.030
.030
0.556
.030
.030
.030
.030

1.026
1.026
1.026
1.026
1.026
1.026
0.712
1.026
1.026
1.026
1.026
1.026
     The within-laboratory coefficient of
variation, j3, is estimated from the collaborator-
block data as

                 1    37

                37  ~j

The collaborator block beta estimates and their
corresponding weights are shown in Table B-8.
Substituting into the above equation gives

                 0 = 0.039

and the within-laboratory standard deviation estimate
is
                                                                              = (0.039)6.

                                                                There are are (n,y - 1) degrees of freedom for
                                                           this estimate from each collaborator-block, where
                                                           n,y is the number of determinations in the col-
                                                           laborator block. Summing over the 37 blocks gives
                                                           113 degrees of freedom.

                                                           B.6  Estimating Precision Components For
                                                                Volumetric Flow Rate

                                                                In Appendix B.2, the models are developed
                                                           for the standard deviation components, a/, and a,
                                                                            ob =
                                                           and
                                                                               = 06,
                                                           where |3j and (3 are the between-laboratory and
                                                           within-laboratory coefficients of variation, and 8
                                                           is the mean method determination. The coefficients
                                                           of variation are shown to remain constant as the
                                                           mean changes. To estimate a^ and a, then, estimators
                                                           % and a are defined as
                                                           and
Estimated coefficients of variation are used to estimate the standard deviations as percentages of the mean value, 6.

      The technique used in estimating fa and ft is discussed in Appendices B.3 and B.4. The estimator is a linear
combination of beta values,
                                                    30

-------
TABLE B-8. COLLABORATOR-BLOCK BETA
   ESTIMATES AND WEIGHTS (Velocity)
Block
Collaborator
Beta Hat
Weight
Site 1
1
2
3
4
Lab 101
Lab 102
Lab 103
Lab 104
Lab 101
Lab 102
Lab 103
Lab 104
Lab 101
Lab 102
Lab 103
Lab 104
Lab 101
Lab 102
Lab 103
Lab 104
0.0119
0.0089
0.1006
0.0474
0.0486
0.0591
0-0435
0.0420
0.0241
0.0162
0.0139
0.0392
0.0914
0.0396
0.0153
0.0111
0.786
0.786
0.425
0.786
1.133
1.133
1.133
1.133
1.475
1.475
1.475
1.475
0.425
0.786
0.786
0.786
Site 2
1
2
3
Lab 202
Lab 203
Lab 204
Lab 202
Lab 203
Lab 204
Lab 202
Lab 203
Lab 204
0.0531
0.0095
0.0342
0.0360
0.0346
0.0391
0.0487
0.0291
0.1245
0.960
0.960
0.960
1.837
1.618
1.837
0.277
0.277
0.277
Site 5
1
2
3
4*
Lab 301
Lab 302
Lab 303
Lab 304
Lab 301
Lab 302
Lab 303
Lab 304
Lab 301
Lab 302
Lab 303
Lab 304
Lab 301
Lab 302
Lab 303
Lab 304
0.0503
0.0241
0.0447
0.1059
0.0446
0.0409
0.0282
0.0447
0.0352
0.0458
0.0254
0.0749
-
0.796
0.796
0.796
0.796
0.796
0.796
0.796
0.796
1.494
1.494
1.494
1.148
-
*No estimates possible since this block
contains only one run.
                                                                     /-!
                                        where $,- is the ith beta estimate from a run or collaborator-block, w/
                                        is the weight assigned, and k is the number of estimates.

                                             From the run data, there are 43 separate estimates of 0j, which gives
                                                                        43
                                        The values and their weights are shown in Table B-9. Substituting
                                        these into the above formula gives

                                                                 & = 0.056.

                                        The between-laboratory standard deviation is estimated as
                                                                     = (0.056)5
                                        or 5.6% of its mean value.
                                              The degrees of freedom for this estimate are determined by
                                        taking the number of collaborators less one at each site, and summing
                                        over the three sites. This gives (4 - 1) + (3 - 1) + (4 - 1) = 8 degrees
                                        of freedom for this estimate.

                                              The collaborator-block data gives an estimate of the within-lab-
                                        oratory precision components. The within-laboratory coefficient of
                                        variation is estimated as

                                                                  1    37
                                                               *B     Z "A
                                        The individual beta estimates and weights are shown in Table B-10.
                                        Substituting into this equation gives

                                                                 $ = 0.055

                                        and a standard deviation estimate of

                                                                   &=|35

                                                                     = (0.055)5.
Thus, the within-laboratory standard deviation is estimated as 5.5% of the mean level.  Letting n/y be the number
of determinations in a collaborator-block, there are («/y - 1) degrees of freedom for this estimate from each. Sum-
ming, there are a total of 113 degrees of freedom from the 37 collaborator-blocks for this estimate.
                                                    31

-------
TABLE B-9. RUN BETA ESTIMATES AND
   WEIGHTS (Volumetric Flow Rate)
Run
Beta Hat
Weight
Site 1
1
2
3
4
5
6
9
8
10
11
12
13
7
14
15
0.0450
0.0584
0.1087
0.0762
0.0685
0.0545
0.0581
0.0365
0.0406
0.0362
0.0266
0.0436
0.1244
0.0336
0.0361
0.723
1.043
1.043
1.043
1.043
1.043
1.043
1.043
1.043
1.043
1.043
1.043
1.043
0.723
1.043
Site 2
1
3
4
6
8
2
5
7
10
11
13
14
15
16
9
12
0.0195
0.0531
0.0378
0.0116
0.0618
0.0311
0.0160
0.0290
0.0472
0.0685
0.0230
0.0240
0.0205
0.0504
0.1119
0.0678
1.030
1.030
1.030
1.030
1.030
1.030
1.030
1.030
1.030
1.030
1.030
0.556
1.030
1.030
1.030
1.030
Site 3
3
10
12
2
5
6
1
4
7
8
11
9
0.0796
0.0686
0.0774
0.0610
0.1381
0.0420
0.1025
0.0396
0.0425
0.0991
0.0664
0.0653
1.026
1.026
1.026
1.026
1.026
1.026
0.712
1.026
1.026
1.026
1.026
1.026
TABLE B-10. COLLABORATOR-BLOCK BETA
    ESTIMATES AND WEIGHTS
       (Volumetric Flow Rate)
Block
Collaborator
Beta Hat
Weight
Site 1
1



2



3



4



Lab 101
Lab 102
Lab 103
Lab 104
Lab 101
Lab 102
Lab 103
Lab 104
Lab 101
Lab 102
Lab 103
Lab 104
Lab 101
Lab 102
Lab 103
Lab 104
0.0139
0.0317
0.0693
0.0787
0.0651
0.0775
0.0669
0.0643
0.0229
0.0626
0.0359
0.0441
0.0469
0.0913
0.0549
0.1628
0.786
0.786
0.425
0.786
1.133
1.133
1.133
1.133
1.475
1.475
1.475
1.475
0.425
0.786
0.786
0.786
Site 2
1


2


3


Lab 202
Lab 203
Lab 204
Lab 202
Lab 203
Lab 204
Lab 202
Lab 203
Lab 204
0.0484
0.0107
0.0312
0.0373
0.0322
0.0329
0.1423
0.0197
0.1335
0.960
0.960
0.960
1.837
1.618
1.837
0.277
0.277
0.277
Site 3
1



2



3



4*



Lab 301
Lab 302
Lab 303
Lab 304
Lab 301
Lab 302
Lab 303
Lab 304
Lab 301
Lab 302
Lab 303
Lab 304
Lab 301
Lab 302
Lab 303
Lab 304
0.0575
0.0063
0.0431
0.1040
0.1409
0.0101
0.0425
0.1086
0.0280
0.0549
0.0738
0.0766
	
-
—
-
0.796
0.796
0.796
0.796
0.796
0.796
0.796
0.796
1.494
1.494
1.494
1.148
_
_
-
-
*No estimates possible since block contains
only one run.
                                  32

-------
B.7  Emission Rate Variability

     The emission rate, r, is given by
where
and
     Qs is the volumetric flow rate of the stack, ft3/hr
     c is the concentration of pollutant, determined by the applicable test method, appropriate weight units/scf.
     The flow rate calculation does not involve the mass or volume of pollutant obtained, and the concentration
of pollutant is determined separately from the velocity calculation.  Thus, it is reasonable to say that Qs and c are
independent variables. Under this assumption, we can estimate a variance component for r, V(r), from the estimated
terms for Qs and c.

     In this section, these relationships will be used.

     [1 ]   The variance of any random variable, x , is defined as
      [2]   For independent variables jc and y
and


for any two functions /i and/2 .

     [3]  For any variables x and y
                                                      (jc)] -E\f2(y)}
                                                                ~ E(y2)[E(x)]2 + [E(x)]2 [E(y)]
          This can be derived easily from [1] .

     For the variable r, from [1]
                                                    •
-------
Rearranging terms gives
and from  1
where

     6|    —  the mean pollutant concentration, and

     6gs  —  the mean flow rate

     When both the flow rate and pollutant concentration have constant coefficients of variation, &(QS) and 0(c
respectively, the variances are written as
and substituting these into the equation for K(r) gives
where

     Br is the mean emission rate, 5r =
                                                    34

-------
                                     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.     Hamil, H.F. and Camann, D.E., "Collaborative Study of Method for the Determination of Paniculate Matter
        Emissions from Stationary Sources (Portland Cement Plants)," Southwest Research Institute report for
        Environmental Protection Agency, May, 1974.

 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.     Ziegler, R.K., "Estimators of Coefficients of Variation Using k Samples," Technometrics, Vol. 15, No. 2,
        May 1973, pp 409414.

 6.     Hamil, H.F., "Laboratory and Field Evaluations of EPA Methods 2, 6  and 7." Southwest Research Institute
        report for Environmental Protection Agency, October, 1973.

 7.     Hamil, H.F. and Camann, D.E., "Collaborative Study of Method for the Determination of Nitrogen Oxide
        Emissions from Stationary Sources," (Fossil Fuel-Fired Steam Generators) Southwest Research Institute
        report for Environmental Protection Agency, October 5, 1973.

 8.     Hamil, H.F. and Camann, D.E., "Collaborative Study of Method for the Determination of Sulfur Dioxide
        Emissions From Stationary Sources (Fossil Fuel-Fired Steam Generators)." Southwest Research Institute
        report for Environmental Protection Agency, December 10, 1973.

 9.     Dixon, W.J. and Massey, F.J., Jr., Introduction to Statistical Analysis, 3rd Edition. McGraw-Hill, New York,
        1969.

10.     Searle, S.R., Linear Models. Wiley, New York, 1971.

11.     Cramer, H., Mathematical Methods of Statistics. Princeton University Press, New Jersey, 1946.

12.     Hogg, R.V. and Craig, A.T., Introduction to Mathematical Statistics, 3rd Edition. The Macmillan Company,
        New York, 1970.
                                                  35

-------
TECHNICAL REPORT DATA
(Please read Ituouctions on the reverse before completing)
1. REPORT NO. 2.
EPA-650/4-74-033
4. TITLE AND SUBTITLE
Collaborative Study of Method for Determination of Stack Gas Velocity and
Volumetric Flow Rate in Conjunction with EPA Method 5
7. AUTHOR(S)
H.F. Hamil, R.E. Thomas
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Southwest Research Institute
8500 Culebra Road
San Antonio, Texas 78284
12. SPONSORING AGENCY NAME AND ADDRESS
Quality Assurance and Environmental Monitoring Laboratory
National Environmental Research Center
Research Triangle Park, North Carolina 277 1 1
3. RECIPIENT'S ACCESSION-NO.
5. REPORT DATE
September, 1974 (date of issue)
6. PERFORMING ORGANIZATION CODE
8. PERFORMING ORGANIZATION REPORT NO.
10. PROGRAM ELEMENT NO.
1HA327
11. CONTRACT/GRANT NO.
68-02-0626
13. TYPE OF REPORT AND PERIOD COVERED
Task Order
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
!
I
 16. ABSTRACT
        This study concerns itself with the determination of stack gas velocity and volumetric flow rate (EPA Method 2) as
   used with EPA Method 5 (Particulates).  The determinations were calculated from data obtained in collaborative testing of
   Method 5 at three sites:  a Portland cement plant, a coal-fired power plarit and a municipal incinerator.  These data were
   submitted to statistical analysis to obtain estimates of the precision that can be expected with the use of Method 2. The
   standard deviations for both velocity and flow rate are shown to be proportional to the mean value.

        The between-laboratory standard deviations are estimated as 5.0% of the mean and 5.6% of the mean for velocity and
   volumetric flow rate, respectively. The volumetric flow rate is used to calculate the emission rate for compliance testing.
   The precision of the emission rate is shown to be primarily a function of the precision of the pollutant test method used. The
   conclusion, then, is that the volumetric flow rate determination is sufficiently precise as it appears in Method 2.
17.
                                         KEY WORDS AND DOCUMENT ANALYSIS
                       DESCRIPTORS
                                                            b.lDENTIFIERS/OPEN ENDED TERMS  c.  COSATI Field/Group
   Air Pollution 1302
   Flue Gases
  Collaborative Testing
  Method Standardization
   13-B
   07-B
18. DISTRIBUTION STATEMENT

   Release Unlimited
19. SECURITY CLASS (This Report)
     UNCLASSIFIED
21. NO. OF PAGES
        40
                                                            2O. SECURITY CLASS (This page)
                                                                 UNCLASSIFIED
                                                                                               22. PRICE
EPA Form 2220-1 (9-73)

-------
                                                          INSTRUCTIONS
     1.   REPORT NUMBER
         Insert the EPA report number as it appears on the cover of the publication.
     2.   LEAVE BLANK
     3.   RECIPIENTS ACCESSION NUMBER
         Reserved for use by each report recipient.
     4.   TITL E AND SUBTITL E
         Title should indicate clearly and briefly the subject coverage of the report, and be displayed prominently.  Set subtitle, if used, in smaller
         type or otherwise subordinate it to main title. When a report is prepared in more than one volume, repeat the primary title, add volume
         number and include subtitle for the specific title.
     5.   REPORT DATE
         Each report shall carry a date indicating at least month and year. Indicate the basis on which it was selected (e.g., date of issue, date of
         approvc.1, date of preparation, etc.).
     6.   PERFORMING ORGANIZATION CODE
         Leave blank.
     7.   AUTHOR (S)
         Give name(s) in conventional order (John R. Doe, J. Robert Doe, etc.).  List author's affiliation if it differs from the performing organi-
         zation.
     8.   PERFORMING ORGANIZATION REPORT NUMBER
         Insert if performing organization wishes to assign this number.
     9.   PERFORMING ORGANIZATION NAME AND ADDRESS
         Give name, street, city, state, and ZIP code. List no more than two levels of an organizational hirearchy.
     10.  PROGRAM ELEMENT NUMBER
         Use the program element number under which the report was prepared. Subordinate numbers may be included in parentheses.
     11.  CONTRACT/G RANT NUMBE R
         Insert contract or grant number under which report was prepared.
     12.  SPONSORING AGENCY NAME AND ADDRESS
         Include ZIP code.
     13.  TYPE OF REPORT AND PERIOD COVERED
         Indicate interim final, etc., and if applicable, dates covered.
     14.  SPONSORING AGENCY CODE
         Leave blank.
     15.  SUPPLEMENTARY NOTES
         Enter information not included elsewhere but useful, such as: Prepared in cooperation with, Translation of, Presented at conference of,
         To be published in, Supersedes, Supplements, etc.
     16.  ABSTRACT
         Include a brief (200 words or lets)  factual summary of the most significant information contained in the report.  If the report contains a
         significant bibliography ot literature survey, mention it here.
     17.   KEY WORDS AND DOCUMENT ANALYSIS
         (a) DESCRIPTORS - Select from the Thesaurus of Engineering and Scientific Terms the proper authorized terms that identify the major
         concept of the research and are sufficiently specific and precise to be used as index entries for cataloging.
         Cb) IDENTIFIERS AND OPEN-ENDED TERMS - Use identifiers for project names, code names, equipment designators, etc.  Use open-
         ended terms written in descriptor form for those subjects for which no descriptor exists.
         (c) COSATI FIELD GROUP - Field and group assignments are to be taken from the 1965 COSATI Subject Category List. Since the ma-
         jority of documents are multidisciplinary in nature, the Primary Field/Group assignment(s) will be specific discipline, area of human
         endeavor, or type of physical object.  The application(s) will be cross-ieferenced with secondary Field/Group assignments that will follow
         the primary posting(s).
    18.   DISTRIBUTION STATEMENT
         Denote releasability to the public or limitation for reasons other than security for example  "Release Unlimited." Cite any availability to
         the public, with address and price.
    19. & 20. SECURITY CLASSIFICATION
         DO NOT submit classified reports to the National Technical Information service,
    21.   NUMBER OF PAGES
         Insert the total number of pages, including this one and unnumbered pages, but exclude distribution list, if any.
    22.   PRICE
         Insert the price set by the National Technical Information Service or the Government Printing Office, if known.
EPA Form 2220-1 (9-73) (Revert*)

-------