&EPA
United States
Environmental Protection
Agency
Industrial Environmental Research EPA-600/7-79-1 55
Laboratory July 1979
Research Triangle Park NC 27711
Total Particulate Mass
Emission Sampling Errors
Interagency
Energy/Environment
R&D Program Report
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
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The nine series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
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6. Scientific and Technical Assessment Reports (STAR)
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This report has been assigned to the INTERAGENCY ENERGY-ENVIRONMENT
RESEARCH AND DEVELOPMENT series. Reports in this series result from the
effort funded under the 17-agency Federal Energy/Environment Research and
Development Program. These studies relate to EPA's mission to protect the public
health and welfare from adverse effects of pollutants associated with energy sys-
tems. The goal of the Program is to assure the rapid development of domestic
energy supplies in an environmentally-compatible manner by providing the nec-
essary environmental data and control technology Investigations include analy-
ses of the transport of energy-related pollutants and their health and ecological
effects; assessments of, and development of, control technologies for energy
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This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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EPA-600/7-79-155
July 1979
Total Participate Mass Emission
Sampling Errors
by
E. F. Brooks
TRW Systems and Energy
One Space Park
Redondo Beach, California 90278
Contract No. 68-02-2165
Task No. 104
Program Element No. INE624
EPA Project Officer: Robert M. Statnick
Industrial Environmental Research Laboratory
Office of Energy, Minerals, and Industry
Research Triangle Park, NC 27711
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Research and Development
Washington, DC 20460
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CONTENTS
Page
Foreword iii
List of Tables iv
Sections
1 . Conclusions 1
2. Recommendations 2
3. Introduction 3
4. Particulate Mass Transport 4
5. Error Analysis 6
6. Evaluation of Error Sources 9
7. Summary and Discussion of Results 15
References 17
Glossary 18
Appendices
A. Derivation of Mass Transport Equations 20
B. Error Source Evaluation 24
C. Comments on Data and Error Analyses 42
ii
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FOREWORD
This report is an analysis of sampling errors in the determination of
total participate mass emissions from stationary sources. In particular
it examines the accuracy which is obtainable with EPA-IERL Level 1 assess-
ment procedures and hardware. It was prepared under Task 26 of EPA Contract
68-02-2165, "Sampling and Analysis of 'Reduced1 and 'Oxidized1 Species in
Process Streams".
This work was conducted under the direction of Dr. R. M. Statnick,
Environmental Research Center, Research Triangle Park, North Carolina.
The Fluid Physics Department and Applied Chemistry Department, Applied
Technology Division, TRW Systems and Energy, Redondo Beach, California,
were responsible for the work performed on this task. Dr. C. A. Flegal,
Applied Chemistry Department, was Program Manager, and the Task Manager
was E. F. Brooks. The author wishes to thank Southern Research Institute
for stratification background data and discussions on sampling techniques.
m
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List of Tables
Page
1. Values for Minor Error Sources 10
2. Values for Velocity Measurement Parameter Errors 11
3. Values for Collected Particulate Mass Error 13
4. Values for Mapping Error 14
5. Single Point and System Errors for Total Particulate Mass
Sampling 15
iv
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1. CONCLUSIONS
Level 1 total participate mass emission assessments:
• A SASS train operated in accordance with "IERL-RTP Procedures
Manual, Level 1 Environmental Assessment" sampling at a single
point will have a sampling accuracy of a factor of ±2 or better
in most locations such as stacks or control device inlets.
Under worst case conditions, such as at an ESP outlet, it will
have an accuracy of about a factor of ±3.
• The degree of anisokinetic sampling induced by the SASS train
design and operation has a negligible effect on system accuracy.
• In single point sampling, the mapping error (non-representative-
ness of the selected point) will be the largest individual error
in the system.
• Sampling accuracy using the SASS train could be improved to
about ±25% by using a 16 point traverse rather than sampling
at a single point.
General
• For traverse sampling, the largest individual error will normal-
ly be in collected particulate mass, due to anisokinetic sampling
and flow/probe misalignment.
• System accuracies of ±10% to ±16% can be achieved using com-
mercially available equipment and a 16 point traverse. These
accuracy levels, while not required for environmental assessment,
indicate potential accuracies for control device evaluation
testing.
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2. RECOMMENDATIONS
The SASS train in its present state is recommended for Level 1
assessment work, using single point sampling. A modified traverse
(along a single line) should be considered for places such as ESP
outlets to minimize errors due to stratification.
Additional stratification data should be obtained at sites such
as full scale coal fired power plants for the three general types
of most important locations: control device inlets, control device
outlets, and stacks. Such data should be obtained with a single
(or identical) train(s) to isolate the stratification data.
Development of methodology to optimize single point sampling
accuracy through judicious selection of the sampling point should
be pursued through analysis of stratification data and proof of
principal source testing for proposed techniques.
There is a need for lightweight, high volumetric flow sampling
hardware and associated procedures to perform quick (1-2 hour)
surveys to determine particulate stratification in sources so
that appropriate techniques can be used for longer term source
assessment testing.
Additional error analysis work should be performed for size
fractionating sampling techniques. The present analysis applies
only to the total particulate mass determination.
Although this report does not deal specifically with Method 5
hardware and procedures, results suggest that for hardware of a
given accuracy, there will exist specific procedures to optimize
system performance (achieve close to maximum accuracy while
minimizing manpower requirements and sampling times). Work
should be continued to prepare an IERL-RTP Procedures Manual in
this area.
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3. INTRODUCTION
The purpose of this report is to present a "first cut" estimate of
sampling errors in the measurement of total particulate mass emissions
from stationary sources. In "IERL-RTP Procedures Manual: Level 1
Environmental Assessment" (Reference 1), the desire is expressed to per-
form measurements which are accurate "to within a factor of ±2 to 3."
Measurement errors are divided into two general categories: sampling
errors and analysis errors. This report deals with evaluation of total
particulate mass sampling errors, within the framework of a system error
analysis. A mass transport expression is developed in terms of measured
parameters to serve as the basis for the analysis. A standard explicit
error analysis is performed on the derived expression for mass transport.
Since there are also important non-explicit error sources, terms are added
to the explicit equation to handle them. The individual error terms are
then evaluated on the basis of previous analyses, available empirical data,
and, where no data are available, guesses. The evaluation leads to a
ranking of individual error sources and estimates of total system error.
For single point sampling, which is recommended in Level 1 work,
the analysis shows that accuracies within a factor of two to three should
normally be achieved. This conclusion is, however, tentative at present
due to a shortage of quantitative data on particulate stratification.
Results of this study show that particulate stratification causes the
greatest individual error in the system. For traverses using sixteen or
more sampling points, it can be said with reasonable certainty that the
system error should be less than ±25% when proper hardware and techniques
are used. For traverses, the largest error will usually be due to velocity
measurement and collected mass uncertainties.
Conclusions are that single point sampling will usually be acceptable
for a Level 1 assessment, but additional mapping error work is needed to
provide better justification. In addition, methodology development should
be pursued to optimize single point sampling techniques — the present method
of sampling at a point of average velocity is a step in the right direction,
but further refinements are needed.
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4. PARTICULATE MASS TRANSPORT
For cases of current interest, it is reasonable to describe the flow
stream as consisting primarily of a gas, with small amounts of entrained
solid and/or liquid aerosol. The mass transport of the gas is given by
(Reference 2):
""G = //PG "G ' " dA 0)
A
where
trig = total gaseous mass flow rate, g/s
PQ = local gas density, g/cm3
UG = local gas velocity vector, m/s
n = unit vector normal to measurement plane, dimensionless
A = area of measurement plane, m2
Aerosol mass transport can be handled in a number of ways. The most exact
would be to consider the particles individually, and use statistical methods
dealing with single particle mass and velocity. Since the sampling hardware
operates on the particle as being entrained in a gas flow, it is most appro-
priate from an engineering standpoint to use an entrainment model. This
allows us to represent aerosol mass transport in a manner analogous to
gaseous mass transport:
"A" //cAa "G • "dA
A
where
mA = total aerosol (liquid and solid) mass flow rate, g/s
C. = local aerosol concentration, g/cm3
<* = correction factor to account for local difference
between mass mean aerosol velocity and gas velocity
(i.e., particle slip velocity).
Equation (2)-can be considered an exact representation of aerosol mass
transport if the proper value of « is selected for each application.
For particles of diameter 10 microns or less, we can expect 0.99 < <* < l
in most streams. The correction factor « is more fully discussed in
Appendix B.
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The transformation of equation (2) into measured engineering parameters
is performed in Appendix A. This transformation is needed to perform a
meaningful error analysis. We are presently concerned with two cases:
single point sampling and traverse sampling. For these cases, the engineer-
ing representations are:
mA /2Ap R ~
Single point: m. = « A g- k cos e */ —— (3)
N m.
"A /^prrrco
Traverse: m^ = « k\/2lT^ >^ ^— cos 6 -t/— • _""• • (4)
n=l 9n °°n n
where
k = calibration factor for S probe, dimensionless
e = angle between local velocity vector and the vector
normal to the measurement plane
Ap = measured differential pressure, torr
2
R = universal gas constant, 8314.32 —? ' ? 6|/
mole s2 K
T^ = local static temperature, °K
p^ = local static pressure, torr
M = local average molecular weight (of the gas), g/mole
m,, = mass of collected aerosol, g
V = volume of withdrawn gas at stream temperature, pressure
9 and gas composition, cm3
( ) = value of parameters at traverse point n
N = total number of traverse points
These relations are in terms of parameters which are measured directly
with the sampling hardware or for which values are established through
prior calibration or assumption. The forms of the relations, as is shown
in the next section, determine the relative contributions of the individual
parameters to total system error.
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5. ERROR ANALYSIS
The function of this error analysis is to identify individual sources
which contribute to total system error, and to quantify their relative
contributions to that error. The value of the analysis lies in two areas —
the estimate of total error reflects reliability of the data and can be used
to accept or reject individual data points; the estimates of individual
errors identify leading error sources, thus indicating where resources
should be allocated to improve system accuracy.
The following error analysis is carried out under the assumption of a
normal distribution of random errors. This assumption will be valid for
most, but not all, of the parameters involved. Reference 3, "The Analysis
of Physical Measurements" is a recommended text for appropriate background.
The logic of the analysis below is identical to that of error analyses for
total volumetric flow and gaseous emissions presented in detail in Reference
2. Consider the general relation (Reference 3);
G = f (Hr H2, H3 — Hr) (5)
where
G = dependent variable (quantity to be calculated)
H = independent variable (parameter to be measured)
f = functional relationship
Define the error in the measurement of variable Hr as er- The standard
deviation of the measurement of Hr is then given by
N
V
• ». •** w
where
ar = standard deviation of Hr
N = number of measurements
By derivation, the standard deviation of G is then given as
2 /af \\/3f v2 '-' v2
«< *• -^ i __ f^ i^i - r\
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For the present case, it is convenient to analyze the single point relation,
equation (3), and then generalize to the traverse case.
Applying equation (7) we obtain:
2 22
m. a a. a. m. V
"A
2
1 / c
(/ ^ a a-r
^*-£*-
AP2 M2 p2 T2
Equation (8) is presented in a non-dimensional form which will allow us to
speak of dimension!ess errors rather than the actual standard deviations,
which are usually dimensional (e.g., we can consider a temperature error
OT /T^ in percent rather than a-r in °K).
00 °° <»
The individual error terms in equation (8) correspond to errors which
will occur at each point in the stream where a sample is obtained. They
are explicit errors in that they are due to identifiable performance
aspects of the sampling hardware itself. In addition to these error sources
there will also be non-explicit errors due to limitations of the methodology
employed. Whenever possible, it is desirable to separate hardware errors
from methodology errors so that appropriate hardware and technique can be
selected separately to achieve optimum accuracy in any given sampling
situation. To accomplish this in the present analysis, we will consider
the hardware related errors in equation (8) as those which occur at a
given point in the stream. Methodology error terms, introduced below,
basically deal with distinctions between the sample obtained at a single
point or points and the true total particulate mass emission rate. By
definition, then, let a- in equation (8) be the sampling uncertainty
occurring at a point in the stream.
x 100% (9)
°SPE -
where
°SPE = P°int error, percent
7
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We can then define a system error as
°SE = °SPE + °ME + °TE + °AE
where
a^c = total system uncertainty, percent
OJ,.E = mapping uncertainty, percent
a,-r = temporal uncertainty, percent
o.r = assumption uncertainty, percent
Significance of the individual terms is as follows:
°SPE ~~ as exPlained above> tni's represents the system's capability
to extract a representative sample at any one point in the
stream, and is determined by the accuracy of the hardware.
OME — the mapping uncertainty is associated with stratification in
the sample plane. If all other errors are zero, o.,E is a
measure of how accurately the sample point or points represent
the total aerosol emission.
o,.,: — temporal uncertainty is that due to changes in stream condi-
tions during the sampling period, and applies to traverses.
aAE — the assumption error accounts for inaccuracies in the math-
ematical model used in a given situation. For example, if
the temperature is assumed constant during a traverse when
in fact it varies by a few percent in the sample plane, the
resulting error will show up in a^ by definition.
aSE — this represents the total system error, and is the final
desired quantity.
Equations (8), (9), and (10) specifically identify thirteen separate error
sources which occur during total particulate mass emission sampling. Of
the thirteen, ten are hardware related, and three are methodology related.
In the following section, the individual terms are quantitatively evaluated
and the leading sources of error are specifically identified.
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6. EVALUATION OF ERROR SOURCES
This section deals with quantitative evaluation of the thirteen error
terms identified in Section 5, with the objective of producing realistic
estimates of total system error. Emphasis is placed on a summary of evalu-
ations and comments on leading error sources. A more detailed evaluation
of individual terms is presented in Appendix B. Two points should be kept
in mind when considering the data presented below: (1) The errors, presented
in terms of standard deviations, are random errors, rather than systematic
errors due to causes such as instrument calibration shifts or mistakes due
to operator error. (2) For normally distributed errors, the standard 95%
engineering confidence interval is represented by a ± 2o interval. Most,
but not all, of the errors can be reasonably represented by a normal dis-
tribution. For non-normally distributed errors, emphasis is placed on the
"95% confidence" aspects rather than on trying to determine the appropriate
type of distribution.
Of the thirteen error sources, seven are generally rather small and
well understood. These are treated briefly as a group. Following that is
commentary on the three terms related to velocity measurement, which are
well understood but are not always small. The section concludes with indi-
vidual discussion of the temporal error, collected particulate mass error,
and mapping error.
6.1 Generally Small, Well Understood Error Sources
Errors in static pressure and temperature, duct cross-sectional area,
and average molecular weight of the gas are usually small because the
parameters are not difficult to measure in most applications. When sig-
nificant errors do occur, they are usually systematic in nature and are
due to such things as improper calibration practices, unaccounted for wall
deposits which reduce the flow area, and other procedural errors. The
error due to particle slip velocity is typically small due to the particle
size distribution and density encountered in most process streams. The
slip velocity, represented by «, is treated further in Appendix B. The
other terms mentioned above are discussed at length in Reference 2.
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The assumption error will be small as long as adequate attention is
paid to sampling details. This means that each of the parameters in
equation (3) should be measured at each sampling point. The form of
equation (3) is sufficiently exact and inclusive that assumption errors
will be relatively small. Assumption errors are also treated at greater
length in Reference 2.
The error in the volume of withdrawn gas will be small when adequately
calibrated equipment is used and it is acknowledged that V is based upon
stack temperature, pressure, and composition, which usually means that the
instrument reading (e.g., from a dry test meter) must be properly corrected
for temperature and pressure, and condensible and volatile stream components
must be accounted for.
Achievable errors for the above parameters are presented below in
Table 1. The listed accuracies are not difficult to obtain with generally
available equipment as long as adequate care is taken to avoid systematic
errors.
Table 1. Values for Minor Error Sources
Parameter
M
Poo
T
A
oc
V9
Assumption
Error
2a (95% Confidence Interval)
Error, Percent
±2
±2
±2
±2
±2
±2
±2
6.2 Velocity Measurement Parameter Errors
These are errors associated with the parameters k, 9, and Ap. They
are discussed at considerable length in References 2 and 4. Errors for
various types of hardware and flow conditions are given in Appendix B,
and summarized in Table 2.
10
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Table 2. Values for Velocity Measurement
Parameter Errors
Parameter
Related Component
Error
Pi tot-static probe
S-type probe
x 100% = ±0.5%
x 100% = ±156
a. near flow
disturbance
b. far from flow
disturbance
Pitot-static
S-type
Pitot-static
S-type
2(tan e) a0 x 100% = ±1.3%
y
2(tan e) a. x 100% = ±8%
t>
2(tan e) aQ x 100% = ±0.5%
2(tan e) CTQ x 100% = ±2%
AP
U-tube manometer
SASS train1
Baratron
2aAp = ±0.065 Torr
x 100% = ±14%
Ap
100% = ±0.16%3
IAP read on 0-.5 or 0-4 in ^0 Magnehelic gage
2nominal velocity range 6-40 m/s
3nominal velocity range 1.7-55 m/s
The SASS train, selected for Level 1 assessments, employs an S-type pi tot
probe and two Magnehelic differential pressure gages. These components
comprise a low cost, reasonable accuracy system. The high accuracy
Baratron/pitot-static probe combination has been used in the field by TRW
without handling problems (Reference 4), and is recommended, especially
for very low flow velocities (< 5 m/s), in situations where accuracy takes
precedence over hardware cost.
11
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6.3 Temporal Variation Errors
The temporal error, OT^, is difficult if not impossible to evaluate
when significant changes occur during the period of traverse. The best
way to handle the problem is the standard approach of being sure that
plant operating conditions are held constant during the sampling period,
and discarding the data if they are not. Concurrently, it is also
desirable to minimize the sampling time by maximizing the sample flow
rate, as is done with the SASS train. The constant attention of the
sampling team is required during the sampling period to detect variations
in flow or other critical parameters. The estimated value for 2aTE in
sources such as power plants is ±4%.
6.4 Collected Particulate Mass Errors
The term am. gives the accuracy with which the sampling probe obtains
an aerosol sample representative of the point at which the probe is placed.
The major error contributions result from anisokinetic sampling and from
sample loss or gain within the collection system. Anisokinetic errors, due
to improper sampling rate and/or probe misalignment, are treated at length
in Appendix B. Sample gain or loss is usually due to improper hardware
design or procedures. The appropriateness of condensing some types of
vapors and considering the result as particulate is a philosophical
battleground which will not be trod upon here. A 2o error of ±4% in col-
lected mass due to aerosol gain or loss is considered reasonable for a
sampling system such as the SASS train.
Isokinetic sampling is achieved for different gas velocities through
variation of the sampling rate, the nozzle orifice diameter, or both.
Size fractionating devices like the SASS train require a constant, fixed
flow rate so that adjustments to approximate isokinecity must be done by
varying the nozzle I.D. Nozzle diameters are typically available in .32 cm
(.125 in.) intervals, which allows maximum deviation from isokinetic sam-
pling to be calculated, as is done in Appendix B.
The magnitude of achievable isokinetic sampling errors depends on the
type of hardware used (e.g., fixed or variable sample rate), component
12
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accuracy, and stream conditions (particle size distribution and local flow
direction). Collected mass errors, as determined in Appendix B, are sum-
marized below in Table 3 for several general cases.
Table 3. Values for Collected Particulate Mass Error
Sampling Location
m.
Collected Mass Error, 2—- x 100%
SASS Train
Maximum Accuracy Train*
Control device inlet
Control device outlet
In stack, z 8 diameters
above breeching
±20%
±16%
±10%
±8%
±6%
Hypothetical train using best readily available hardware components.
6.5 Mapping Errors
In the case of single point sampling, which is the method recom-
mended for Level 1 assessments, the mapping error will usually be the
largest single error in the system. Consequently, the mapping error
deserves considerable attention. The major problem encountered so far
has been a shortage of particulate stratification data, which is essen-
tial in evaluation of mapping techniques. The bulk of the data examined
to date has been comparisons of single point impactor measurements and
Method 5 type traverses. Due to significant differences between the
types of sampling trains, it is difficult to isolate the differences in
output which are due solely to stratification. Data examined and discus-
sion thereof are presented in Appendices B and C, respectively. Mapping
error estimates for single point sampling and 16 point traverses are
presented in Table 4 for various types of conditions.
13
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Table 4. Values for Mapping Error
Sampling Location
Control device inlet
Control device outlet
In stack, *8 diameters
above breeching
Mapping Error, 2oME
Single Point
+60%, -40%
+150%, -60%
+50%, -33%
16 Point Traverse
±8%
±12%
±5%
As Table 4 shows, maximum mapping errors tend to occur at a control device
outlet, especially for electrostatic precipitators, meaning that stratifi-
cation is increased by the control device. Just as it is a general rule
for velocity measurement to avoid working immediately downstream of a large
flow disturbance, it is wise in particulate sampling to avoid sampling
immediately downstream of a stratification source. When sampling is done
near such a source, such as an ESP outlet, knowledge of the ductwork and
characteristics of the source can be used to select a single sampling
point which would be more representative than a randomly selected point.
14
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7. SUMMARY AND DISCUSSION OF RESULTS
Error values in Tables 1-4 were substituted into equations 8-10 to
obtain single point and system errors, which are shown in Table 5. The
point error, OSPE;» is indicative of. hardware accuracy, while the
system error, ar, indicates the combined hardware and procedure accuracy.
Table 5. Single Point and System Errors for Total
Parti culate Mass Sampling
Sampling
Train
.^•— • "~
SASS
Maximum
Accuracy
Sampling
Location
Control device
inlet
Control device
outlet
Stack, * 8 dia.
above breeching
Control device
inlet
Control device
outlet
Stack, > 8 dia.
above breeching
Error
20SPE
*Jl L.
±23%
±20%
±13%
±9%
±9%
±7%
2°SE
Single Point
+64%, -46%
+150%, -64%
+52%, -36%
+60%, -42%
+150%, -60%
+50%, -34%
16 Point
±24%
±24%
±15%
±13%
±16%
±10%
Largest Error
Source
Single
Point
aMF
ric.
a
Oijr-
ME
aME
aME
OK • ^
ME
16
Point
mft
a
mA
a
mA
CTME,
a
mA
aME
a
mA
Hypothetical train using best readily available hardware components.
The "Maximum Accuracy" train in Table 5 is a train which would consist of
the highest accuracy components readily available commercially. For example,
it would include a high accuracy differential pressure transducer. The
purpose in showing the "Maximum Accuracy" train error estimates is only to
illustrate the best state of the art capabilities.
15
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A comparison of relative accuracies of hardware and procedures is
given by aspE and o^. For single point sampling, OSE is invariably large
compared with aspE, due to the single point mapping error. Thus hardware
improvements in the SASS train would not improve the system accuracy when
single point sampling is used. For traverses, the situation is different.
The SASS train system accuracy is limited by the hardware rather than by
procedure, while for the Maximum Accuracy train, the respective hardware
and procedure errors are about equal.
There has been a twofold reason for performing the above analyses.
The first has been to determine whether hardware and procedures recommended
for Level 1 assessments are adequate to produce the desired "factor of
± 2 to 3" accuracy. The second has been to determine optimum accuracy
capabilities and to show where future efforts should be devoted to optimize
system accuracy. Results of the analyses show that a Level 1 assessment
should have a sampling accuracy of better than a factor of i 2 except at
a control device outlet, where the accuracy is more likely to be a
factor of 3, especially if the control device is an ESP. It is likely
true that the error at a control device outlet can be reduced by making
use of known device characteristics in selecting a sample point. This
type of methodology should be pursued. For very high accuracy work,
Table 5 indicates that there is a good match between the accuracies of
currently available hardware and traverse sampling procedures. Future
work in this area would involve integration of high accuracy components
into a viable system for efficient traverse sampling.
In conclusion on the matter of Level 1 assessments, it is recommended
that sampling after a control device be done in a stack whenever feasible-
rather than directly at the control device outlet. This will be the best
way to optimize accuracy. In addition, development of methodology for
single point sampling and/or modified traverse sampling (along a single
line to minimize moving of equipment) directly at a control device outlet
should be pursued to minimize the error due to particulate stratification.
16
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REFERENCES
1. "IERL-RTP Procedures Manual: Level 1 Environmental Assessment,"
EPA-600/2-76-160a, Hamersma, Reynolds, and Maddalone, June 1976.
2. "Flow and Gas Sampling Manual," EPA-600/2-76-203, Brooks and Williams,
July 1976.
3. The Analysis of Physical Measurements, E. Pugh and G. Winslow;
Addison-Wesley, 1966.
4. "Continuous Measurement of Total Gas Flowrate from Stationary Sources,"
EPA-650/2-75-020, Brooks, et al., February 1975.
(See Appendices for additional references.)
17
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GLOSSARY
SYMBOL USAGE
A flow cross-sectional area, m2
C. true aerosol concentration in the stream ahead of the
probe, g/cm3
C aerosol concentration inside probe entry, g/cm3
D particle diameter, cm
D sample probe orifice diameter, cm
f empirical functional relationship; functional relationship
G dependent variable (quantity to be calculated)
H independent variable (parameter to be measured)
k pi tot probe calibration factor, dimensionless
mA mass of collected aerosol, g
m total aerosol (liquid and solid) mass flow rate, g/s
ITU total gaseous mass flow rate, g/s
M local gas average molecular weight, g/mole
n unit vector normal to measurement plane, dimensionless
N number of measurements; total number of sampling points
D local static pressure, torr
roo
p local stagnation pressure, torr
Ap P ~ POO ' tfie Pressure differential between the local
stagnation and static pressures, torr
g-m2
universal gas constant, 8314.32
mole S2 °K
}K
local gas velocity vector, m/s
local gas static temperature, °K
UG true gas velocity ahead of the probe, cm/s
U mean velocity at probe inlet, cm/s
18
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SYMBOL USAGE
V volume of withdrawn gas at stream temperature, pressure,
9 and gas composition, cm3
( ) value of parameter at sample point n
correction factor to account for local difference between
mass mean aerosol velocity and gas veloctity (i.e.,
particle slip velocity).
Dn Pn ur
P P »
3 -^~j;—
lop u
e angle between local velocity vector and duct axis
y gas viscosity, poise
PG gas density, g/cm3
p particle density, g/cm3
a.r assumption uncertainty, percent
aME mapping uncertainty, percent
OSE total system uncertainty, percent
a standard deviation of H
point error, percent
Oyr temporal uncertainty, percent
19
-------
APPENDIX A. DERIVATION OF MASS TRANSPORT EQUATIONS
This appendix deals with the transformation of t!)e participate conser-
vation of mass equation (equation (2) in Section 4) into the engineering
representations shown in equations (3) and (4) in Section 4. The conser-
vation of mass equation is:
"•A = J[/CA « "G ' " dA (A-D
M
where
m = total aerosol (liquid and solid) mass flow rate, g/s
C. = local aerosol concentration, g/cm3
« = Correction factor to account for local difference
between mass mean aerosol velocity and gas velocity
(i.e., particle slip velocity).
A = flow cross-sectional area, m2
Equation (A-l) is a convection model which states that the local aerosol
concentration is convected downstream with the gas at a speed equal
to the gas velocity component in the axial flow direction multiplied by
a correction factor <* which accounts for inertial and gravitational forces
on the particles. As the particle mass to cross-sectional area ratio
becomes small, « goes to unity, which represents complete entrainment.
As that ratio becomes large, <* goes to zero, representing non entrainment.
For most processes of interest, <* will be very close to unity, and is not
measured in practice.
For purposes of the error analysis, we need to take equation (A-l)
and put it in terms of actual engineering parameters. In most cases, it
is not practical to take the entire gas stream and process it to determine
the particulate content. Standard techniques involve obtaining samples
from one or more discrete points in the stream. For these two cases,
single point and traverse sampling, equation (A-l) becomes
20
-------
Single point: m^ % CA « UG • n A (A-2)
N , A
Traverse: rhA £ V* (CA <*n UG • njAAn (A-3)
n=l
where
N = total number of sampling points
( ) = value of parameter at sample point n.
For a typical sampling train, the aerosol concentration is measured as
CA = r- (A-4)
g
where
m. = mass of collected aerosol, g
V = volume of withdrawn gas at stream temperature, pressure,
9 and gas composition, cm3
The aerosol mass mA is determined by weighing the collected samples, and
the gas volume is measured with a dry gas meter or similar device, with
correction being made for moisture removed ahead of the meter.
The flow cross-sectional area, A, is usually determined from blue-
prints, especially in the case of rectangular ducts. For traverses, all
common techniques divide the area up into segments of equal size, so that
AAn = ff (A"5)
The axial component of the gas velocity is usually measured by means of
a pitot probe and differential pressure device for the primary measurement.
The transformation is as follows:
uG-n = |UG| cos e (A-6)
where
e = angle between local velocity vector and duct axis
21
-------
For notational simplicity, define
UG E "G (A-7)
We will normally be dealing with incompressible gas flows, so that
2Ap
ur = k
6 - >G
where
Ap = pQ - p^ , the pressure differential between the local stagnation
and static pressures, torr
PG = gas density, g/cm3
k = pi tot probe calibration factor
Substituting the equation of state,
P
.
fT
where
p^ = local static pressure, torr
R = universal gas constant, 8314.32
mole S2 °K
M = local gas average molecular weight, g/mole
T^ = local gas static temperature, °K
for P£, we obtain
V2Ap R T
-^
UG "n = UG COS 9 =
p M
roo
Substituting into equations (A-2) and (A-3), we obtain
Single point:
R T
00
A \rk cos e
(A-9)
22
-------
Traverse:
n=l n I °°n n
The conservation of mass equation is now presented in terms of normal
engineering parameters. Of the terms in equations (A-ll) and (A-12), the
following are usually measured directly with sample train components and
support equipment: mA> V , Ap, T^. The area A is either measured or
determined from blueprints. The static pressure p^ is often determined
by adding (or subtracting, as required) the differential pressure between
the stream pressure and ambient pressure to barometric pressure, which is
usually available. The average molecular weight, fT, is either measured or
estimated from plant operating conditions. The pitot probe calibration
constant should be determined by pre- and post-test calibration. The slip
velocity factor « is usually ignored (therefore considered to be unity).
Flow angularity is also typically ignored, meaning cos 8=1, but it is
possible to use a velocity probe which automatically compensates for
angularities up to 30°, as is discussed in Appendix B. Equations (A-ll)
and (A-12), which appear as equations (3) and (4) in Section 4, serve as
the basis for the error analysis in Section 5.
23
-------
APPENDIX B. ERROR SOURCE EVALUATION
The purpose of this appendix is to provide background to support the
summaries of evaluations presented in Section 6. Emphasis here will be
placed on understanding the physics of some of the key parameters, and on
presentation of empirical data, in particular for stratification. Emphasis
is placed on three areas: velocity measurement, collected particulate
mass, and stratification.
1. Particle Slip Velocity Factor
Of the "generally small, well understood error sources", only
the slip velocity factor a warrants additional treatment here.
Particle velocities will differ from the gas velocity due to gravity
forces and inertial forces, the latter arising when there is a change
in flow direction. The magnitude of the particle/gas velocity differen-
tial is most easily illustrated for the case of a flow going directly
up a vertical stack. In this situation, gravity produces a downward
force which makes the particle velocity less than the gas velocity.
The result is a local Stokes flow condition in which the differential
velocity is identified as the settling velocity of the particles.
Settling velocity is plotted in Figure B-l as a function of particle
size (spherical particles) for two different values of particle density
and gas viscosity. The slip velocity factor would then be calculated
from the particle settling (terminal) velocity and the gas velocity.
As Figure B-l shows, the settling velocity will be at most a few
centimeters/second for particles smaller than 10 microns. A vertical
flow represents the worst case in terms of gravitational effects.
Inertial effects can usually be ignored due to the velocities involved.
It typically takes a special effort, as in the case of cyclones and
impactors, to produce the high velocities and sharp turning angles
required to make inertial effects important.
24
-------
60 r-
ro
tn
50
40
30
a.
oo
cu
10
IN A STACK, WE HAVE
CURVE
1
8.0
-4
j , poise 1.7x10
10 20 40 70
PARTICLE DIAMETER, MICRONS
100
MOST PROCESS STREAM
CONDITIONS FALL
IN THIS REGION
200
Figure B-l. Settling speed of spherical particles in a combustion
stream as a function of particle size
-------
2. Gas Velocity Measurement
Present concern is limited to measurement techniques involving a
pitot probe and differential pressure measurement device. The most
common types of pitot probes are the S-type probe typically used in
field testing, and the pi tot-static probe, which has tended to acquire
a reputation of being acceptable for use only in the laboratory. The
2a calibration factor accuracies of +_ .5% and + 1% for the pitot-static
probe and S probe, respectively, shown in Table 2 in the main text were
obtained from References B-l and B-2. Angularity sensitivity data in
Table 2 were obtained from the same sources. The data are shown in
Table B-l below.
Table B-l. Errors due to Flow Angularity for
S-Type and Pi tot-Static Probes
Flow Angularity
yaw, degrees
± 5
±10
±20
±30
pitch, degrees
+ 5
+10
+20
+30
- 5
-10
-20
-30
2a Velocity Error, 2 (tan e) a0xlOO%
t)
"S" Pitot Probe
+1.6
+3.5
+4.5
+7.5
+1.5
+2.0
+3.5
+4.5
-1.5
-2.5
-5.0
-8.0
Pitot Static Probe
+0.3
+1.0
+1.3
+0.2
+0.3
+ 1.0
+1.3
+0.2
+0.3
+1.0
+1.3
+0.2
26
-------
For the "near flow disturbance" case in Table 2, a flow angu-
larity range of ±30° was assumed, while the range was selected to be
±5° for the "far from flow disturbance" case. As the data show, the
pitot static probe has the more desirable characteristics.
Accuracy of differential pressure measurement devices is presented
in Figure B-2. The zig-zag in the SASS train curve corresponds to a
switch from the low range to the high range Magnehelic gage. Summary
data in Table 2 were taken from this plot.
3. Collected Particulate Mass
The Level 1 particulate collection procedure has been questioned
(Reference B-3) for single point sampling and for not sampling in a
strictly isokinetic manner. The isokinetic problem is addressed here,
while single point sampling (mapping) errors are discussed in the fol-
lowing section.
The term am gives the accuracy with which the sampling probe
obtains an aerosol sample representative of the point at which the
probe is placed. The major contributions to error come from anisoki-
netic sampling and from sample loss or gain within the probe. Loss
of sample could occur due to poor system design or procedural errors,
while sample gain is due to vapor condensation, which would also be
hardware and/or procedure related. Sample alteration should not be a
major problem in a properly designed and operated system.
Isokinetic sampling errors will occur in even the most careful
work due to equipment random errors and stream conditions. Some
general comments about the concept of isokinetic sampling are in
order here. Textbook explanations of isokinetic sampling show
smooth streamlines in the flow around the sample probe inlet, with
streamline deviations illustrating anisokinetic conditions. In
reality, such a situation exists only in steady laminar flows, as
can be produced in a good wind tunnel. Laminar flows will not^ be
encountered in the field. In steady, laminar flows, streamlines are
27
-------
1.5
100
APPROXIMATE VELOCITY, M/S
5 15
r~
45
U-TUBE
MANOMETER
10
o
cc.
oo
3
GO
CO
.1
SASS
TRAIN
ARATRON 145
(MKS INSTRUMENTS)
.01
1
.01
Figure B-2.
.1 1
DIFFERENTIAL PRESSURE, TORR
Differential pressure measurement
accuracy of various devices
28
10
-------
steady state entities, which makes flow visualization techniques such
as smoke filaments in air flow or dye filaments in liquid flow viable.
In a turbulent stream, streamlines exist instantaneously only-- the
streamline pattern varies greatly from millisecond to millisecond.
These changes are typically not small. In a fully developed turbulent
pipe flow, the turbulence is structured such that turbulent eddies
tend to move downstream as units (Reference B-4). Experimental studies
have shown that the size of these turbulent eddies is about 7% of the
pipe diameter (Reference B-5). In a fully developed turbulent pipe
flow, the velocity component parallel to the sample probe axis can be
expected to fluctuate over about a ±10% (of axial flow velocity) range,
with similar fluctuations in the angle of the velocity vector at the
probe tip (Reference B-6). For operation near an elbow or other large
disturbance, these fluctuations will be even worse due to the larger
local scale of turbulence caused by flow detachment.
What this all means is that in real life, isokinetic sampling is
a type of averaging process. In all cases, we can expect that the
stream turbulence scale will be large with respect to the sampling
orifice, so there is no easy way to get around the turbulence problem.
The primary reason for the above commentary is to illustrate that
while isokinetic sampling*can be performed in a good laminar flow wind
tunnel, it can only be approximated in actual process streams.
Watson's expression for isokinetic sampling errors (Refereces
B-7 and B-8), the experimental verification for which was obtained in
a low turbulence wind tunnel, is as follows:
' C
UG
A
(B-l)
29
-------
where
C = aerosol concentration inside probe entry, g/cm3
C. = true aerosol concentration in the stream ahead of the
probe, g/cm3
Ug = true gas velocity ahead of the probe, cm/s
U = mean velocity at probe inlet, cm/s
- DP PP UG
"
Ds
f = empirical functional relationship
D = particle diameter, cm
p = particle density, g/cm3
u = gas viscosity, poise
DS = sample probe orifice diameter, cm
Equation (B-l) is plotted in Figure B-3 for different values of the
various parameters. In practice, the plot says that anisokinetic
sampling does not lead to concentration errors as the particles become
very small, while in the limit of large, dense particles, the concen-
tration error is inversely proportional to the velocity error, i.e.
C U6
~— -v TT- for large, dense particles.
LA um
In normal practice, the stream velocity is measured with a pitot
probe and the sampling velocity Um is set equal to the measured
velocity. For this mode of operation, the measured aerosol mass
flux at the sampling point becomes (ignoring <* for the moment)
= CmUm
30
-------
4 i-
co = UI
"$»r
a - K •
) UG
o
o
o
C£
_ •>
f(B) DIAMETER, MI^ONS
0 >50
40
30
22
13
CP =
V
s
FOR
1 g/cm3
10 m/s
1.27 cm
-4
= 2.3 x 10 poise
UG TRUE GAS SPEED
Um ' SAMPLING SPEED
Figure B-3. Particulate measured concentration error as a function of sampling
velocity (Anisokinetic) error for various aerosol conditions
(from Watson, Reference B-7)
-------
while the true mass flux is
= CAUG
(B-3)
applying the small and large particle limits of equation (B-l), we
obtain
0 <
meas
true
(B-4)
where zero error occurs for the case of large particles, while non-zero
error occurs for very small particles and is in fact solely a velocity
measurement error unrelated to the sampling process. In other words,
as long as sampling velocity and measured velocity are kept identical,
anisokinetic sampling of large particles compensates for velocity
measurement errors, while anisokinetic sampling of small particles
does not lead to a concentration measurement error. For total particu-
late measurement errors, then, we may make the following statement:
Particle mass emission errors at a point will not be larger
than errors in the measured stream velocity as long as the
sample velocity is maintained equal to the measured velocity
and the sampling probe is properly aligned with the stream.
It must be noted that the above statement applies only to particle
mass emission and only at individual points. The relationship between
point measurements and the total emission is related to stratification,
which is treated below. The important point is that isokinetic errors
and velocity measurement errors are compensating rather than additive.
Concentration measurement errors due to anisokinetic sampling
depend, of course, on all the factors shown in equation B-l. Reference
B-7 recommends the values shown in Table B-2 "for the size distribution
of dusts encountered in practice". The following general rule is also
32
-------
Table B-2. Effect of Departure from Isokinetic Conditions
on Sample Concentrations (from Reference B-7)
UG
US
0.6
0.8
1.2
1.4
1.6
1.8
C
Co
RANGE
0.75-0.90
0.85-0.95
1.05-1.20
1.10-1.40
1.15-1.16
1.20-1.80
TYPICAL VALUE
0.85
0.90
1.10
1.20
1.30
1.40
33
-------
recommended in Reference B-7:
"Isokinetic sampling is unnecessary for smoke and fumes which
are not admixed with particulate matter over 5y in size."
It is clear that for purposes of error analysis, the term o- should
m/\
be coupled with the velocity error terms due to the compensating aspects.
Aside from the traditional isokinetic sampling aspects, we must also be
concerned with misalignment of the sampling probe with respect to the
local stream direction. As explained above, the flow direction goes
through instantaneous changes, but these average out reasonably over
the sampling period in most cases when the volumetric flow rate stays
constant. Any misalignment of the sampling probe reduces the number
of large particles (> 5y) collected, while collection of small particles
is affected little, if at all. Failure of the sampling team to align
the sampling probe parallel to the duct or stack axis within two or
three degrees constitutes a mistake rather than a random error. Non-
alignment of the flow itself with the stack axis must generally be
considered a random error since the sampling team will usually not
have the instruments to properly determine flow direction. The best
way to avoid flow angularity is to use the standard "eight diameters
downstream and two diameters upstream of a disturbance" approach when
possible. In stacks, the flow will tend to be axially aligned within
a few diameters from the breaching except in the case of swirling
(cyclonic) flow, which can persist much longer. Reference B-9 makes
the following statements about such flows:
"....severe cyclonic motion has not been observed in large
power plant stacks."
Unfortunately, it is also concluded that
"Little qualitative data is available defining flow angularity
in large (>100 MW) power plant stacks."
To summarize the above commentary and relate it to actual hard-
ware, it can be said that the major error sources for collected
34
-------
particulate mass are non-isokinetic sampling, probe/flow misalignment,
and sample gain or loss within the probe. For the SASS train, non-
isokinetic sampling occurs because the sample flow rate must be held
constant. Since a sampling crew will have a limited number of inlet
nozzle sizes, there will be a differential between the nozzle inlet
velocity and the local stream velocity. In addition, this configuration
does not allow for adjustments in sampling rate during a run to com-
pensate for any free stream velocity changes. In an optimum train,
the sampling velocity would be continually adjusted so that it matched
the measured stream velocity. The discussion associated with equation
(B-4) says that if this can be accomplished, errors in isokinetic
sampling tend to compensate for velocity measurement errors. In the
turbulent flows which occur in real life, it will not be possible to
match the sample flow rate to the measured velocity, since the latter
will fluctuate more rapidly than the sample flow can be adjusted.
The error estimates in Table 3 of the text for a are based on
known SASS train characteristics, accuracies (velocity measurement in
particular) of other commercially available hardware, and estimates of
actual flow conditions to be encountered at the three types of designated
sampling locations. For the SASS train, the greatest source of error
is the anisokinetic error, while misalignment will be the largest
source for the hypothetical "maximum accuracy train". The basic
difference between the two trains would be greater velocity measurement
accuracy and continuously variable sampling velocity for the "maximum
accuracy train". Errors are predicted highest at a control device inlet
due to the size distribution (maximum number of large particles) and
anticipated flow angularities. (See Reference B-9 for compilations of
control device inlet and outlet size distributions.) Errors will be
at a minimum in a stack due to smaller flow angularities and removal
of large particles in a control device.
35
-------
4. Mapping (Handling of Stratification)
There are three major difficulties involved in dealing with
stratification problems: (1) The stratification level itself is
often very large, which leads to large errors, especially for single
point sampling. (2) More background data are needed to assess the
severity of the problem. (3) There is a shortage of methodology for
sampling techniques in stratified streams. The first point is illustrated
in Table B-3, taken from Reference B-10. Particulate mass concentra-
tion maps were taken for the four cases listed (the ESP data is true
field data). Large variations from the mean concentration were ob-
served in each case. Of particular interest is the ESP data, which
shows that the device was definitely a source of stratification. The
variations shown in Table B-3 clearly indicate that single point
sampling is likely to result in large mapping errors.
There is no question that much more stratification data exist
than were examined for this report. As much data was examined as
could be obtained within the scope of work. Comparison data between
single point impactor sampling and multiple point Method 5 type
sampling is shown in Tables B-4 and B-5. The data were obtained from
References B-ll and B-12, respectively, supplied by Joe McCain of
Southern Research Institute. The data in Table B-4 represent a
summary of many runs. The "minimum" and "maximum" errors are the
best and worst correlations obtained among the individual runs, while
the "nominal" error was the average error for all runs in the category.
The data in Table B-5 are for individual runs. A very important item
to keep in mind when examining these data is that entirely different
types of sampling trains were used to obtain the single point (im-
pactors were used here) and multiple point (Method 5 type train) data.
This makes it impossible to isolate the mapping error due to single
point sampling. Data type and quality are discussed further in
Appendix C. What is needed is more mapping data obtained with a single
36
-------
Table B-3. Summary of Particulate Mapping Data from
Fluidyne "Particulate Sampling Strategies"
Report (Reference B-9)
DESCRIPTION
Downstream of ESP
Upstream of ESP
"Theoretical" distri-
bution downstream of
ESP
Laboratory scale
model flow
CENTER POINT
CONCENTRATION
ERROR, %
-16
+13.5
-62.8
- 2.33
VARIATION IN SAMPLE PLANE
FROM MEAN CONCENTRATION, %
LOW
-74
-35
-63
-19
HIGH
+268
+ 30
+160
+117
Table B-4. Summary of Comparison of Single Point Impactor
Data Versus Method 5 Traverse at an ESP Outlet,
from Southern Research Institute EPRI Report
(Reference B-ll)
OPERATING
MODE*
With S03
Without S03
SINGLE POINT ERROR USING METHOD 5 TRAVERSE AS A REFERENCE, %
MINIMUM
- 5
-68
NOMINAL
-33
-75
MAXIMUM
-61
-94
*SOo injection was used as a mechanism to minimize re-entrainment due to
rapping. Lower loading and less stratification occurred with SO.,
injection.
37
-------
Table B-5. Grain Loading Errors for Single Point Impactor
Sampling, Using Conventional (ASME, EPA) Mass
Train Traverse Measurement As Reference Data
(Data taken from Reference B-12)
SITE
1
2
3
4
RUN NO.
1
2
3
4
5
6
7
1
2
3
1
2
3
1
2
3
4
SINGLE POINT MASS LOADING ERROR, %
+711
+256
+227
+ 26
+ 6
+ 5
+131
- 34
- 35
- 43
- 38
- 19
- 50
- 6
- 45
- 48
- 50
Sites: At all sites, location was control device outlet
1 - Coal fired power plant
2 - Coal fired power plant
3 - Electric arc smelting furnace
4 - Coal fired power plant
38
-------
instrument, as was done to obtain the data summarized in Table B-3.
The data in Table B-4 are a good illustration of the need for
better sampling methodology. The impactor sampling point used was
not representative of the distribution in the stream, leading to
errors of as high as a factor of 16. The Level 1 approach of using
a point of average velocity as the sampling point is a step in the
right direction since such a point is less likely than most to result
in misalignment errors, will not be in a recirculation region, and at
least will be representative of total mass transport. For stack
sampling, it may be the case that further refinements to this approach
will not be needed. For sampling at a control device outlet, however,
Table B-4 points out the need for taking the device's characteristics
into account in the selection of a sampling point or points.
Particulate stratification originates where the particles
originate, e.g. in the furnace of a coal fired power plant. Strati-
fication can be made worse by in-leakage of air. Removal devices can
make stratification either more or less severe, according to their
operating characterisitics. Changes in ducting shape and direction
simultaneously promote convective mixing (reduces stratification) and
inertial separation (increases stratification). The combination of
desired accuracy and stratification provides the answer to the ques-
tion, "To single point or not to single point?". This question has
been studied more extensively for flow measurement and gas sampling
than for particulate sampling, but should apply to that case as well.
Reference B-13, which is basically a summarization of the velocity
measurement data in Reference B-10, and Reference B-14 conclude that
the 2o mapping error of a 12-to-16 point traverse is about a factor
of five less than that for a single point measurement for volumetric
flow (References B-12 and B-13) and gas composition (Reference B-13).
As the mean particle size becomes small (<5p), particulate stratifica-
tion is almost identical in mechanism to gas stratification because of
39
-------
the dominance of convective mixing in both cases. In Reference B-15,
the average 2o single point gas composition mapping error was found to
be ±15%. There is no reason to believe the single point participate
sampling mapping error would be better than this figure, and indeed
will be much worse in most cases. The data which have been examined
are not sufficient to establish good bounds for single point particulate
sampling. Accumulated data for volumetric flow and gas composition
lead to the conclusion that a properly performed traverse using about
16 points will result in o^ not being the major source of system
error.
The single point mapping error estimates in Table 4 in the text
were derived from Tables B-3 and B-5, taking into account the difference
in trains in the latter. The traverse error estimates were obtained
by comparing the maps in Reference B-10 with gas composition maps in
Reference B-14. The mapping error itself is independent of the
sampling equipment used. The mapping error estimates must at present
be considered the least firm of all the error estimates in the text,
which is unfortunate since the mapping error is by far the largest
error in the system for single point sampling. The need for more data
to "firm up" the estimates is discussed in Appendix C.
40
-------
APPENDIX B. REFERENCES
B-1. "Continuous Measurement of Total Gas Flowrate from Stationary
Sources," EPA-650/2-75-020, Brooks, et al.. February 1975.
B-2. The Measurement of Air Flow, E. Ower and R. C. Pankhurst; Pergamon
Press, 1966.
B-3. "Recent Environmental Assessment Studies," (Draft Copy), Monsanto
Research Corporation, November 1976.
B-4. Boundary Layer Theory, H. Schlichting; McGraw-Hill Book Company, 1968.
B-5. "Correlation Measurements in a Turbulent Flow Through a Pipe," G. I.
Taylor, Proc. Roy. Soc. A 157. 537-546,1936.
B-6. "The Structure of Turbulence in Fully Developed Pipe Flow," J. Laufer,
NACA TN 2954, 1953.
B-7. Air Pollution. Volume II, A. Stern, ed., Academic Press, 1968.
B-8. H. H. Watson, Am. Ind. Hyg. Assoc. Quart. 15, 21, 1954.
B-9. "Particulate Sampling Strategies for Large Power Plants Including
Non-uniform Flow," EPA-600/2-76-170, Hanson, et a!.. June 1976.
B-10. "Fine Particle Emissions Information System: Summary Report (Summer
1976)," EPA-600/2-76-174, Schrag and Rao, June 1976.
B-ll. "Proceedings on the Workshop on Sampling, Analysis, and Monitoring of
Stack Emissions," EPRI SR-41, Southern Research Institute, April 1976.
B-12. "Particulate Sizing Techniques for Control Device Evaluation,"
EPA-650/2-74-102-a, Smith, et al.f August, 1975.
B-13. "The Number of Sampling Points Needed for Representative Source
Sampling," K. T. Knapp, paper presented at Fourth National Conference
on Energy and Environment, October 1976.
B-14. "Flow and Gas Sampling Manual," EPA-600/2-76-203, Brooks and Williams,
July 1976.
B-15. "Continuous Measurement of Gas Composition from Stationary Sources,"
EPA-600/2-75-012, Brooks, et al.. July 1975.
41
-------
APPENDIX C. COMMENTS ON DATA AND ERROR ANALYSES
As stated in the text, the error analysis performed was identical in
form to that in Reference C-l. The explicit portion of the error analysis
is similar in concept to that in Reference C-2. A nominal 2o system error
of ±16% was obtained for a total participate mass measurement involving a
traverse. This estimate is similar to those for traverses in Table 5.
A more encompassing error discussion is given in Reference C-3, and treats
both explicit and non-explicit error sources. However, error bounds were
not well established in this analysis.
The nature of the measurement for total particulate mass dictates that
two distinct groups of information must be consulted to determine system
accuracy - sampling hardware characteristics and source characteristics.
For parameters such as temperature and static pressure, it is normally the
case that measurement accuracy can be determined from the hardware alone.
The accuracy of parameters such as velocity and collected particulate mass
usually depend on both hardware and source characteristics. At the other
extreme, mapping errors depend only on source characteristics. The great
variety of source characteristics makes it impossible to perform a system
error analysis and arrive at a single number for system accuracy, just as
it would be impossible to arrive at a single number result for an analysis
of a variety of sampling trains. The final selected approach of looking
at two types of trains in three generalized sampling situations was in-
tended to show the relative impact of hardware and source on system
accuracy.
Most error analysis work deals with identification and evaluation of
specific error sources. The interrelationship of hardware and source
characteristics for particulate sampling necessarily complicates isolation
of errors. During the present study, this problem caused the most diffi-
culty in evaluation of the error terms a and o^. As was mentioned in
Appendix B, evaluation of anisokinetic sampling errors has traditionally
been performed in laminar flow wind tunnels. The turbulent, unsteady flows
42
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in process streams make it difficult to adapt laminar flow data to the real
life case. That approach has been used of necessity, however, since it has
not been possible to obtain high accuracy reference data needed for an
error assessment in the field.
The bulk of the mapping data summarized in Appendix B has the problem
that the single point data was obtained with significantly different hard-
ware than the traverse data. This makes it impossible to separate the
hardware error from the mapping error. There is no question that mapping
data of the type desired (a concentration map obtained with a single probe)
is difficult, time consuming, and costly to obtain. In this instance, it
is felt that the effort would be justified due to the magnitude of mapping
errors, in addition to supporting error analysis work, the same data would
be essential to the development of methods for obtaining representative
samples through judicious selection of a single sampling point or a small
number of sampling points.
The functional purpose of a system error analysis, in addition to
producing the bottom line number for total system accuracy, is to determine
the relative importance of the individual error sources. This information
tells the worker which hardware components in a given system should be
upgraded to achieve a desired accuracy, and which components may be replaced
with less expensive, less accurate ones without significantly altering the
system accuracy. The same is true of sampling procedures, the most obvious
example being selection of single or multiple point sampling techniques to
achieve a given accuracy. A proper error analysis is thus the technical
foundation for optimum allocation of funds and manpower to achieve sampling
data of appropriate quality for the tasks at hand.
43
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APPENDIX C. REFERENCES
C-l. "Flow and Gas Sampling Manual," EPA-600/2-76-203, Brooks and Williams,
July 1976.
C-2. Industrial Source Sampling. Brenchley, Turley, and Yarmac, Ann Arbor
Science Publishers, Inc., 1973.
C-3. "A Manual of Electrostatic Precipitator Technology, Part I - Funda-
mentals," NTIS PB-196 380, Oglesby, etal., August 1970
44
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
REPORT NO.
EPA-600/7-79-155
2.
3. RECIPIENT'S ACCESSION NO.
4.TITLE AND SUBTITLE
I Total Particulate Mass Emission Sampling Errors
5. REPORT DATE
July 1979
6. PERFORMING ORGANIZATION CODE
7. AUTHORIS)
E.F. Brooks
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
TRW Systems and Energy
One Space Park
Redondo Beach, California 90278
10. PROGRAM ELEMENT NO.
INE624
11. CONTRACT/GRANT NO.
68-02-2165, Task 104
12. SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
Industrial Environmental Research Laboratory
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
Task Final; 11/76 - 4/77
14. SPONSORING AGENCY CODE
EPA/600/13
is. SUPPLEMENTARY NOTES gPA project officer R. M. Statnick is no longer with
for details, contact F.E. Briden, Mail Drop 62, 919/541-2557.
16. ABSTRACT The repOrt gives a first-cut estimate of sampling errors in the measure-
ment of total particulate mass emissions from stationary sources. IERL-RTP Pro-
cedures Manual: Level 1 Environmental Assessment expresses the desire to mea-
sure at accuracies within a factor of -f or - 2 to 3. Measurement errors are divided
into two general categories: sampling errors and analysis errors. The report deals
with evaluation of total particulate mass sampling errors , within the framework of
a system error analysis. A mass transport expression is developed in terms of
measured parameters to serve as the basis for the analysis. A standard explicit
error analysis is performed on the derived expression for mass transport. Since
there are also important non-explicit error sources, terms are added to the explicit
equation to handle them. The individual error terms are then evaluated on the basis
of previous analyses, available empirical data and, where no data are available,
estimates. The evaluation leads to a ranking of individual error sources and esti-
mates of total system error. Analysis results show that a Level 1 should have a sam-
pling accuracy of better than a factor of + or -2, with a confidence of 95%, except at
a control device outlet where the accuracy is more likely to be a factor of + or -3,
especially if the control device is an electrostatic precipitator.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
Pollution
Dust
Emission
Sampling
Analyzing
Error Analysis
Pollution Control
Stationary Sources
Particulates
Mass Emissions
. COSATl Field/Group
13B
11G
14B
12A
8. DISTRIBUTION STATEMENT
Release to Public
19. SECURITY CLASS (ThisReport/
Unclassified
21. NO. OF PAGES
49
20. SECURITY CLASS (This page}
Unclassified
22. PRICE
epA Form 2220-1 (9-73)
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