vvEPA
United States
Environmental Protection
Agency
Office of
Research and Development
Washington, DC 20460
EPA/600/R-92/143
August 1992
Acoustic Location of
Leaks in Pressurized
Underground Petroleum
Pipelines
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EPA/600/R-92/143
August 1992
ACOUSTIC LOCATION OF LEAKS IN PRESSURIZED
UNDERGROUND PETROLEUM PIPELINES
by
Eric G. Eckert and Joseph W. Maresca, Jr.
Vista Research, Inc.
Mountain View, California 94042
Contract No. 68-03-3409
Project Officer
Robert W. Hillger
Superfund Technology Demonstration Division
Risk Reduction Engineering Laboratory
Edison, New Jersey 08837
RISK REDUCTION ENGINEERING LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CINCINNATI, OHIO 45268
Printed on Recycled Paper
U.S. Environmental Protection Agency
Region 5, '..:_;re~>~ ;~'-]o-> '
- 12th
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DISCLAIMER
This material has been funded wholly or in part by the United States Environmental Pro-
tection Agency under Contract 68-03-3409 to CDM Federal Programs Corporation. It has been
subject to the Agency's peer and administrative review, and it has been approved for publication
as an EPA document. Mention of trade names or commercial products does not constitute
endorsement or recommendation for use.
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FOREWORD
Today's rapidly developing and changing technologies and industrial products frequently
carry with them the increased generation of materials that, if improperly dealt with, can threaten
both public health and the environment. The U. S. Environmental Protection Agency is charged
by Congress with protecting the nation's land, air, and water resources. Under a mandate of
national environmental laws, the agency strives to formulate and implement actions leading to a
compatible balance between human activities and the ability of natural systems to support and
nurture life. These laws direct the EPA to perform research to define our environmental prob-
lems, measure the impacts, and search for solutions.
The Risk Reduction Engineering Laboratory is responsible for planning, implementing,
and managing research, development, and demonstration programs to provide an authoritative,
defensible engineering basis in support of the policies, programs, and regulations of the EPA
with respect to drinking water, wastewater, pesticides, toxic substances, solid and hazardous
wastes, and Superfund-related activities. This publication is one of the products of that research
and provides a vital communication link between the researcher and the user community.
The work reported in this document has application to the remediation of leaks from
underground pressurized pipelines containing petroleum or other hazardous chemicals.
E. Timothy Oppelt, Director
Risk Reduction Engineering Laboratory
111
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ABSTRACT
Experiments were conducted at the UST Test Apparatus Pipeline in which three acoustic
sensors separated by a maximum distance of 38.1 m (125 ft) were used to monitor signals pro-
duced by 11.4-, 5.7-, and 3.8-L/h (3.0-, 1.5-, and 1.0-gal/h) leaks in the wall of a 5-cm- (2-in.-)
diameter pressurized petroleum pipeline. The line pressures and hole diameters used in the
experiments ranged from 69 to 138 kPa (10 to 20 psi) and 0.4 to 0.7 mm (0.01 to .03 in.), respec-
tively. Application of a leak location algorithm based upon the technique of coherence function
analysis resulted in mean differences between predicted and actual leak locations of
approximately 10 cm. The standard deviations of the location estimates were approximately
30 cm. This is a significant improvement (i.e., smaller leaks over longer distances) over the
cross-correlation-based techniques which are currently being used.
Spectra computed from leak-on and leak-off time series indicate that the majority of acous-
tic energy received in the far field of the leak is concentrated in a frequency band from 1 to
4 kHz. The strength of the signal within this band was found to be proportional to the leak flow
rate and line pressure. Energy propagation from leak to sensor was observed via three types of
wave motion: longitudinal waves in the product, and longitudinal and transverse waves in the
steel. The similarity between the measured wave speed and the nominal speed of sound in gaso-
line suggests that longitudinal waves in the product dominate the spectrum of received acoustic
energy. The effects of multiple-mode wave propagation and the reflection of acoustic signals
within the pipeline were observed as non-random fluctuations in the measured phase difference
between sensor pairs.
Additional experiments with smaller holes and higher pressures (138 to 345 kPa [20 to
50 psi]) are required to determine the smallest leaks that can be located over distances of several
hundred feet. The current experiments indicate that improved phase-unwrapping algorithms
and/or lower noise instrumentation are required to optimize system performance.
This report was submitted in fulfillment of Contract No. 68-03-3409 by Vista Research,
Inc., under the sponsorship of the U.S. Environmental Protection Agency. This report covers a
period from 23 January 1991 to 31 October 1991, and work was completed as of
30 September 1991.
IV
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TABLE OF CONTENTS
Disclaimer ii
Foreword iii
Abstract iv
List of Figures vi
List of Tables ix
List of Abbreviations x
Acknowledgments xi
1 Introduction 1
2 Conclusions 5
3 Recommendations 7
4 Location of a Continuous Leak Signal 8
4.1 Location Algorithm 9
4.2 Location Errors 11
4.3 Estimates of Measurement Uncertainty 13
4.4 Accuracy 16
4.5 Performance of the Leak Location System 17
5 Experiment Design 20
6 Data 24
6.1 Signal Strength 26
6.2 Coherence and Phase Measurements 27
7 Location Results 33
8 Leak Signal Propagation 37
9 Phase Unwrapping 41
10 References 44
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LIST OF FIGURES
Figure 1.1. Example of a passive-acoustic leak location system 3
Figure 4.1. Three-sensor approach to acoustic location of leaks 10
Figure 4.2. G{§AB(f)} for sensor separation distance as a function of n between 5 and
50 and values of ^AB(f) equal to 0.8,0.6,0.4, and 0.2 estimated for any frequency with
Eq. (4.9) 14
Figure 4.3. G{XAB} for sensor separation distance between two sensors, A and B, as a
function of n between 5 and 50 and values of *&B(f) equal to 0.8,0.6,0.4, and 0.2
estimated with Eqs. (4.9), (4.12), and (4.14) for the following conditions: XAB = 38.1
m (125 ft), XBC = 7.6 m (25 ft), X^ = 3.8 m (12.5 ft) (Le., 10% of XAB), Af = 2373 -
2119 = 254 Hz, N = 26, and = 1,000 m/s 14
Figure 4.4. G{XAB} for sensor separation distance between two sensors, A and B, as a
function of n between 5 and 50 and values of rfAB(f) equal to 0.8,0.6,0.4, and 0.2
estimated with Eqs. (4.9), (4.12), and (4.14) for the following conditions: XAB = 38.1
m (125 ft), XBC = 7.6 m (25 ft), XAL = 9.7 m (31.75 ft) (i.e., 25% of XAB), Af = 2373 -
2119 = 254 Hz, N = 26, and = 1,000 m/s 15
Figure 4.5. G{XAB} for sensor separation distance between two sensors, A and B, as a
function of n between 5 and 50 and values of iAB(f) equal to 0.8,0.6,0.4, and 0.2
estimated with Eqs. (4.9), (4.12), and (4.14) for the following conditions: XAB = 38.1
m (125 ft), XBC = 7.6 m (25 ft), X^ = 19.0 m (62.5 ft) (i.e., 50% of XAB), Af = 2373 -
2119 = 254 Hz, N = 26, and = 1,000 m/s 15
Figure 4.6. G{XAB} for sensor separation distance between two sensors, A and B, as a
function of n between 5 and 50 and values of ^fi(/) equal to 0.8, 0.6, 0.4, and 0.2
estimated with Eqs. (4.9), (4.12), and (4.14) for the following conditions: XAB = 38.1
m (125 ft), XBC = 7.6 m (25 ft), X^. = 9.7 m (31.75 ft) (i.e., 25% of XAB), Af = 2373 -
2119 = 254 Hz, N = 5, and = 1,000 m/s 16
Figure 4.7. Estimates of PD and PFA as a function of SNR = d developed for normally
distributed noise. (Urick [6]) 18
Figure 5.1. Diagram of the pressurized petroleum pipeline at the UST Test Apparatus.
Pipe material is 5-cm- (2-in.-) diameter) steel; product is gasoline. Pressurized CO2 is
used to generate 0- to 172-kPa (0- to 25-psi) static line pressure. Valves in connecting
branches were closed during all experiments 21
VI
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Figure 5.2. Diagram of the coupling between the acoustic transducer (CTI-30) and the
steel pipeline 22
Figure 5.3. Diagram of the data acquisition system used in the experiments 22
Figure 5.4. Apparatus used to generate simulated pipeline leak. Backfill materials are
fine-grain sand and coarse gravel. Leak apertures between 0.3 and 0.8 mm (0.01 to
0.03 in.) were introduced into the pipeline via carburetor jets 23
Figure 6.1. Time series of acoustic leak signals generated by a 11.4-L/h (3-gal/h) leak
into a sand backfill. Line pressure is 103 kPa (15 psi) and hole diameter is 0.7 mm
(0.03 in.). Sample rate is 10 kHz. A no-leak time series recorded by sensor B is shown
for reference 25
Figure 6.2. Time series of acoustic leak signals generated by a 1.9-L/h (0.5-gal/h) leak
into a sand backfill. Line pressure is 345 kPa (5 psi) and hole diameter is 0.3 mm (0.01
in.). Sample rate is 10 kHz. A no-leak time series recorded by sensor B is shown for
reference 26
Figure 6.3. Signal-to-noise ratio (SNR) for pipeline leaks into a sand backfill at flow
rates of 11.4 L/h (3.0 gal/h) (A), 5.7 L/h (1.5 gal/h) (B), 3.8 L/h (1.0 gal/h) (C), and
1.9 L/h (0.5 gal/h) (D). Dashed line indicates SNR=1. SNR estimates are computed by
averaging the received power at each of the sensor locations shown in Figure 6.1 29
Figure 6.4. Signal-to-noise ratio (SNR) for pipeline leak into a gravel backfill. Flow
rate is 11.4 L/h (3.0 gal/h) 30
Figure 6.5. Strength of acoustic leak signal as a function of static line pressure for a
fixed hole diameter (0.5 mm [0.02 in.]). Error bars indicate the standard deviation of
six measurements used to compute the SNR at each pressure level 30
Figure 6.6. Coherence amplitude and coherence phase as a function of frequency for
acoustic leak signals bracketing a 5.7-L/h (1.5-gal/h) leak. Sensor separation is 38.1 m
(125 ft). The coherence function represents an ensemble average of 15 overlapping,
1024-point data segments. Dashed lines indicate 95% and 99% levels of statistical
significance 31
Figure 6.7. Coherence amplitude and coherence phase for acoustic leak signals
bracketing a 1.9-L/h (0.5-gal/h) leak. Line pressure is 34 kPa (5 psi); sensor separation
is 30 m (100 ft). Dashed lines indicate 95% and 99% levels of statistical significance.
32
Figure 6.8. Unwrapped coherence phase, <)>(/), between 3.8 and 4.0 kHz for sensor
pair B-C of Figure 5.1. Least-squares regression line through actual data points is
included. The flow rate is 11.4 L/h (3 gal/h) 33
vu
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Figure 7.1. Unwrapped coherence phase between 2.0 and 2.5 kHz for sensor pairs
A-B, A-C, and B-C of Figure 5.1. Least-squares regression lines through actual data
points are included. The flow rate is 11.4 L/h (3 gal/h) 35
Figure 7.2. Normalized cross-correlation coefficient, p^(t), as a function of time
delay (T) between time series recorded by sensors B and C. The time series were
bandpass-filtered between 1.0 and 4.0 kHz prior to computing p^. The flow rate is
11.4 L/h (3 gal/h). 1BC represents the predicted B-C time delay at V = 1000 m/s 36
Figure 7.3. Normalized cross-correlation coefficient as a function of time delay
between time series recorded by sensors B and C. The time series were bandpass-
filtered between 2.0 and 2.5 kHz prior to computing p^. The flow rate is 11.4 L/h
(3 gal/h). IBC and TCB represent predicted time delays for primary and reflected
acoustic waves propagating at V = 1000 m/s 37
Figure 8.1. Time series of impulsive calibration signals recorded by sensors B and C
of Figure 5.1. The estimated propagation speed (6250 m/s) is consistent with the
nominal speed of sound in steel 39
Figure 8.2. Unwrapped coherence phase between 2.7 and 3.0 kHz for sensor pair B-C
of Figure 5.1 in which CO2 is used as the product. The line pressure is 103 kPa
(15 psi); the hole diameter is 0.7 mm. The estimated propagation speed (2400 m/s) is
consistent with the nominal speed of transverse waves in steel 40
Figure 8.3. Unwrapped coherence phase between 2.1 and 2.4 kHz for sensor pair B-C
in which the linear trend has been removed. The flow rate is 11.4 L/h (3 gal/h) 41
Figure 9.1. Unwrapped coherence phase between 1.5 and 4.5 kHz for sensor pairs
A-B, A-C, and B-C. Solid lines indicate predicted coherence phase for linearly
propagating plane waves based upon known leak location and propagation speed.
Flow rate is 11.4 L/h (3 gal/h) 43
Figure 9.2. Unwrapped coherence phase between 1.5 and 4.5 kHz for sensor pairs
A-B, A-C, and B-C. Solid lines indicate predicted coherence phase for linearly
propagating plane waves based upon known leak location and propagation speed.
Flow rate is 5.7 L/h (1.5 gal/h) 44
Vlll
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LIST OF TABLES
Table 4.1. Estimates of the Total Uncertainty in Measuring the Separation Between
Sensors and the Location of a Leak as a Function of the Number of Incoherent
Averages and -&,(/) Computed for L = 95 and 99% 17
Table 4.2. Estimates of PFA and a PD of 50% as a Function of SNR 18
Table 7.1. Leak Location and Propagation Speed Measurements 36
IX
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LIST OF ABBREVIATIONS
cm = Centimeters
dB = Decibels
0 = Degrees
<> = Expectation value or average value
f = Frequency
ft = Feet
y2 = Squared complex coherence function
gal = Gallons
h = Hours
Hz = Hertz
in. = Inches
k = Wavenumber
kHz = Kilohertz
kPa = Kilopascals
L = Liters
m = Meters
mm = Millimeters
m (t) = Measured quantity (time domain)
M (f) = Measured quantity (frequency domain)
P = Pressure; level of statistical significance
PD = Probability of detection
PFA = Probability of false alarm
(j) = Phase angle
71 = Pi
psi = Pounds per square inch
pxy = Normalized cross-correlation coefficient
s = Seconds
a = Standard deviation
SNR = Signal-to-noise ratio
t = Time
1 = Time
v = Wave speed
x = Measurement of distance
EPA = Environmental Protection Agency
RREL = Risk Reduction Engineering Laboratory
UST(s) = Underground Storage Tank(s)
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ACKNOWLEDGMENTS
This research report for evaluating the feasibility of locating small leaks in undergound
pressurized pipelines containing petroluem and other hazardous liquids by means of a passive
acoustic sensing system was prepared for the U.S. Environmental Protection Agency's (EPA's)
Risk Reduction Engineering Laboratory (RREL) on Contract No. 68-03-3409. Robert W.
Hillger and James J. Yezzi were the Technical Program Monitors on the Work Assignment for
EPA/RREL. Technical review was provided by Messrs. Hillger and Yezzi and by Anthony N.
Tafuri, Section Chief, Underground Storage Tank Program. The authors would especially like to
acknowledge CTI, Inc., for the loan of the acoustic sensing equipment used in the experiments.
This document was edited by Monique Seibel and prepared for publication by Pamela Webster
and Christine Lawson.
XI
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SECTION 1
INTRODUCTION
Underground pressurized pipelines are frequently used to transfer liquid products for many
industrial applications. Some of these pipelines are associated with the underground storage
tanks typically found at retail stations, and others with tanks at industrial storage facilities; they
can contain petroleum products or a variety of other chemicals. There are many systems that can
be used to detect leaks in underground pressurized pipelines. These leak detection systems are
designed for use on pipelines that are typically 5 cm (2 in.) in diameter and generally 15.2 to
61.0 m (50 to 200 ft) in length. The EPA regulations [1] require that the leak detection equip-
ment used to test a pipeline monthly be capable of detecting leaks at least as small as 0.76 L/h
(0.2 gal/h) with a probability of detection (PD) of 95% and a probability of false alarm (PFA) of
5%. If the equipment is used to test the line annually, it must be able to detect leaks as small as
0.38 L/h (0.1 gal/h); in the regulations, this type of test is designated as a line tightness test.
If a leak is found, remediation must follow. The first step in any remediation is to find the
location of the leak. At the present time, there are two methods being used, but neither method is
totally acceptable. The first method is to systematically uncover the line and perform a visual
inspection for leaks. While this method works, it is time consuming, disruptive to operations,
and costly. In addition, the line is subject to damage during the excavation process. The second
method is to use a helium- or halogen-tracer technique, but both tracer techniques have opera-
tional and accuracy problems. There is a need for a nondestructive method of leak location that
is accurate, relatively simple to use, and applicable to a wide variety of pipelines and pipeline
products.
One method of expediting the remediation process is the application of remote sensing
techniques to the pipeline in order to accurately locate the leak. Passive-acoustic measurements,
combined with advanced signal-processing methods, may provide a means by which to locate
small leaks in limited-access pipeline delivery systems. The concept of using passive acoustics
to determine the spatial location of leaks has been around for some time, but this approach has
not been applied to underground petroleum pipelines. While it is known that a pressurized
underground pipeline that is leaking emits an acoustic signal, the strength and characteristics of
the signal associated with the leak are not well known.
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Acoustic systems have been successfully used to detect and locate leaks in nuclear reactors
for many years [2]. By means of a cross-correlation analysis, 100- to 400-kHz acoustic sensors
spaced at 5- to 10-m intervals can be used to detect leaks of about 3.8 L/min (1 gal/min) with an
accuracy that is within 0.5 m. A similar approach has been tested for locating water leaks in 10-
to 25-cm- (4- to 10-in.-) diameter underground district heating and cooling pipes [3]. Theoretical
predictions based on Kupperman et al. [3] suggest that leaks of 7.6 L/min (2 gal/min) could be
pinpointed to within several meters with sensors spaced at several hundred meters. Using moni-
toring frequencies less than 25 kHz makes this wider spacing possible; frequencies between 1
and 5 kHz appear to give the best results. In the program of experiments conducted in
Kupperman et al. [3], the sensors were externally mounted to the steel pipe. Interestingly, leaks
that occurred in a steel pipe covered with insulation material (urethane and a rubber jacket)
showed a higher level of signal intensity than leaks that occurred in an uncovered pipe. This
suggests that if a pipeline is located underground rather than above ground, the surrounding
backfill and soil may enhance the acoustic leak signal. The predictions were based upon models
that were validated using a 25.9-m- (85-ft-) long, 7.6-cm- (3-in.-) diameter aboveground pipeline
that contained water and in which leaks of 5.7 L/min (1.5 gal/min) were induced at a pressure of
827 kPa (120 psi). Field tests on an operational line were also done.
Figure 1.1 shows a simple representation of a passive-acoustic leak location system in
which a pair of transducers bracketing a leak simultaneously sample the acoustic signal. The
leak emits an acoustic wave, which propagates down a pressurized pipeline, and is received at
the two transducers. A microcomputer system acquires and analyzes the data needed to find the
location of the leak. The data are converted from an analog signal to a digital signal with an A/D
converter. These time series, recorded by spatially separated sensors, then serve as input to a
leak location algorithm.
Cross-correlation analysis works well provided that the signal is very strong or that the
background noise is not excessive. When the acoustic signal is weak in relation to the level of
background noise or has a finite frequency bandwidth, more sophisticated signal processing tech-
niques are available. Advanced signal processing is required if any of the following objectives
are to be achieved: (1) detection of leaks smaller than several gallons per hour, (2) a reduction in
the number of false alarms and missed detections due to operational or ambient noise, and (3) an
increase in the distance between sensors bracketing the leak. One such technique is coherence
function analysis.
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PIPE WALL
ACOUSTIC
SIGNAL
LEAK
Figure 1.1. Example of a passive-acoustic leak location system.
The application of coherence function analysis to signals measured by two or more trans-
ducers is the means by which the source of the signal is best located. Coherence function analy-
sis, which estimates the correspondence between two measurements as a function of frequency,
is analogous to the squared correlation coefficient, but is afar more powerful tool in signal
estimation and location. The coherence magnitude measures the strength of the correspondence,
and the coherence phase measures the relative time delay. In contrast, the correlation coefficient
is a measure of correspondence that is the result of an integration over all frequencies. If the
correspondence is frequency-dependent, or if the phase dependence of the correspondence is a
nonlinear function of frequency, the correlation is degraded. By contrast, coherence is a direct
measure of the complex frequency correspondence between two measurements, and, therefore,
preserves the actual correspondence between the two measurements of the signal.
In the last five to ten years there have been significant advances in commercially available
acoustic sensors, in powerful computers that are both small and inexpensive, and in digital signal
processing. This means that acoustic leak location can be made available in a portable package,
a possibility that makes it an attractive and viable option. Acoustic systems are attractive from
an operational standpoint because the test is short (a few minutes) and the sensors can be
mounted directly on the outside of the pipeline. Acoustic systems have direct application to the
15.2- to 61.0-m (50- to 200-ft) pipelines found at retail service stations because the sensors can
be placed at each end of the line. Acoustic systems are also applicable to longer pipelines, but
access at several points along the line must be provided.
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The objective of this work was to make an estimate of the accuracy of locating a leak in a
pressurized petroleum pipeline, by means of passive acoustic sensors mounted on the outside
wall of the pipeline, as a function of leak rate and distance between acoustic sensors. While
there are regulatory standards for detection of leaks in underground pressurized pipelines, there
are no standards for leak location. For rapid remediation, it would be highly desirable if the leak
could be located within 10% of the length of the pipeline in the case of a line longer than 30.5 m
(100 ft), or within 3.0 m (10 ft) in the case of a line shorter than 30.5 m (100 ft). This limits the
excavation to only a small fraction of the line. As will be shown below, theoretical estimates
suggest that the accuracy of the proposed technique should be better than 25 cm. These theoreti-
cal estimates, however, assume that the leak signal is large compared to the noise.
It would be desirable if the acoustic system could locate leaks as small as the detection
standards in EPA's regulations (i.e., either 0.38 or 0.76 L/h [0.1 or 0.2 gal/h]). However, the
system can be useful nonetheless, even if it does not meet these standards, since many of the
leaks actually detected are much larger. One to two drops of liquid per second produces leaks as
large as 0.38 L/h (0.1 gal/h); such a leak might occur if, for example, the threaded connection
between two pipes or between a pipe and another appurtenance is not tight. Any type of small
hole in the pipeline system will produce a large leak. A 0.08-cm- (1/32-in.-) diameter hole in a
pipeline pressurized to 138 kPa (20 psi) would, for example, result in a flow rate of approxi-
mately 19 L/h (5.0 gal/h). Leaks of this magnitude should be large enough to locate with an
acoustic system providing that the length of the line is not too long.
The results of this work are described below and are summarized in a peer-reviewed jour-
nal article being published by the American Society for Testing and Materials [4].
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SECTION 2
CONCLUSIONS
Passive acoustic measurements, combined with advanced signal processing techniques
based on coherence analysis, offer a promising method for the location of small leaks in pressur-
ized petroleum pipelines found at retail service stations and industrial storage facilities. While
the results presented in this work represent a significant improvement over previous pipeline leak
location efforts, additional research and development are required in order to optimize system
performance. Location of leaks of several tenths of a gallon per hour over distances of several
hundred feet should ultimately be possible.
Experiments were conducted on a pipeline at the UST Test Apparatus in which three
acoustic sensors separated by a maximum distance of 38 m (125 ft) were used to monitor signals
produced by 3.8-, 5.7-, and 11.4-L/h (1.0-, 1.5-, and 3.0-gal/h) gasoline leaks. These flow rates
were generated through drilled holes 0.4 to 0.7 mm (0.01 to 0.03 in.) in diameter. The three-
transducer system enabled the propagation speed of acoustic waves to be measured for particular
combinations of product, pipeline geometry, and analysis frequency band. Data recorded at the
higher flow rates (5.7 and 11.4 L/h [1.5 and 3.0 gal/h]) correspond to full line pressure (103 to
138 kPa [15 to 20 psi]), while data recorded at the lower flow rate (3.8 L/h [1.0 gal/h]) were
obtained under partial line pressure (69 kPa [10 psi]) due to the limitation imposed by the mini-
mum available hole diameter (0.4 mm [0.01 in.]). Application of a leak location algorithm based
upon the technique of coherence function analysis resulted in mean differences between
predicted and actual leak locations of 8.7 cm (11.4 L/h [3.0 gal/h]), 3.6 cm (5.7 L/h [1.5 gal/h]),
and -11.6 cm (3.8 L/h [1.0 gal/h]). Standard deviations of the location estimates were 26.1 cm
(11.4 L/h [3.0 gal/h]), 26.3 cm (5.7 L/h [1.5 gal/h]), and 39.1 cm (3.8 L/h [1.0 gal/h]). The mean
propagation speed was 915 m/s with a standard deviation of 146 m/s.
Data recorded in the presence of a 1.9-L/h (0.5-gal/h) leak were obtained as part of an
investigation of signal strength as a function of line pressure for a fixed-diameter hole (0.4 mm
[0.01 in.]). The 1.9-L/h (0.5-gal/h) leak produced a detectable signal; however, because of the
reduced line pressure, the algorithm, as applied, yielded no location estimates.
Spectra computed from leak-on and leak-off time series indicate that the majority of acous-
tic energy received in the far field of the leak is concentrated in a frequency band from 1 to
4 kHz. The strength of the acoustic signal within this band was observed to be proportional to
the leak flow rate and line pressure, as expected. Energy propagation from leak to sensor was
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observed via three forms of wave motion: longitudinal waves in the product, and both transverse
and longitudinal waves in the steel. Isolation of each of these propagation modes was achieved
. through the use of gasoline and CO2 as the product fluids, and through the generation of impul-
sive calibration signals. Though each of these propagation modes is believed to contribute to the
overall received signal, longitudinal wave motion in the product was clearly the dominant
propagation mode for liquid-filled pipelines. The effects of multiple-mode wave propagation
and the reflection of acoustic signals within the pipeline were observed as non-random fluctua-
tions in the measured phase difference between sensor pairs.
Accurate leak location requires the identification of frequency bands within which a high
degree of similarity is maintained between acoustic signals propagated along different paths from
leak to sensor. Coherence function analysis provides the best means of gauging this similarity,
and thus separating useful information concerning the leak location from ambient or system
noise. While the signal-to-noise ratio (SNR) was observed to be generally high within the entire
1- to 4-kHz frequency band, continuous regions of high coherence appropriate for source loca-
tion were typically 100 to 500 Hz in width. Several data sets recorded in the presence of the
11.4-L/h (3-gal/h) leak exhibited high coherence over a 2-kHz bandwidth. Location estimates
obtained by means of the cross-correlation technique showed that without the detailed knowl-
edge of signal similarity provided by the coherence function, cross-correlation analysis cannot
locate small leaks with acceptable accuracy. The observed correspondence between measured
and predicted phase shifts within the 1- to 4-kHz frequency band demonstrates the need to
develop a more sophisticated location algorithm such that a greater fraction of the information
contained in coherent leak signals may be processed.
Buried pipelines provide a generally quiet ambient environment in which to perform
acoustic measurements. Since the SNR for a given leak largely determines the ability of a pas-
sive acoustic system to locate the leak, the system noise level should be determined by ambient
acoustic noise, rather than electronic noise. The combination of sensors (CTT-30s) and
preamplifiers (Panametrics 5660-Cs) used in this work was incapable of resolving the low levels
of ambient acoustic noise associated with the pipeline at the UST Test Apparatus. Improved sys-
tem performance may be attained through the use of transducers with greater sensitivity in the
low frequency range (1 to 10 kHz) and low-noise preamplifiers.
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SECTION 3
RECOMMENDATIONS
The full capability of the location algorithm was not evaluated in these tests. The smallest
hole used to generate a leak in the experiments was 0.4 mm (0.01 in.). At a line pressure of
138 kPa (20 psi) this resulted in a leak rate of 3.8 L/h (1.0 gal/h). It is recommended that addi-
tional experiments be performed with smaller holes at higher line pressures (138 to 345 kPa [20
to 50 psi]) to determine the minimum leak rate that can be reliably located. The current work
indicates that further improvement can be realized through the application of better phase-
unwrapping algorithms and better instrumentation. A better understanding of the underlying
physics of pipeline acoustics, including the propagation modes and source mechanisms of the
acoustic leak signal, will help optimize the algorithms and the hardware. It is recommended that
the following work be performed to extend the technology:
• development of a location algorithm capable of processing the coherence phase over
an arbitrarily wide frequency band
• characterization of the wave propagation modes excited by the acoustic leak signal
and the degree to which each mode enhances or degrades the leak location estimate
• reduction of system noise through transducers specifically designed for low-
frequency, high-sensitivity applications, and through the use of low-noise, audio-
range preamplifiers
• automation of the data acquisition system and signal processing algorithm, and evalu-
ation of system performance on a variety of actual pipelines
-------
SECTION 4
LOCATION OF A CONTINUOUS LEAK SIGNAL
The primary function of the location algorithm is to estimate the time delay between
acoustic leak signals received by a pair of sensors. The time delay, which is estimated from
phase measurements made in the frequency domain for continuous leak signals, can be used to
estimate the source location (for sensors bracketing the leak) or the propagation speed of the
acoustic waves (for non-bracketing sensor pairs). Two criteria must be satisfied in order that
accurate location estimates result from the application of the location algorithm: (1) the received
signals must originate primarily at a single, localized source and propagate as plane waves along
(or within) the pipeline, and (2) the received signals must maintain a reasonable degree of simi-
larity over the maximum sensor separation. If criterion (1) is satisfied, the difference in phase
between received waves of a given frequency is simply related to the time delay between signals
that arrive at the different sensor locations. The accuracy with which the time delays can be
measured is related to criterion (2). The similarity between signals emitted from a localized
source and received at separate locations is determined by the signal strength relative to ambient
noise (i.e., the signal-to-noise ratio) and the difference in propagation path between the source
and each sensor. Due to the complex manner in which the acoustic leak signal is produced (tur-
bulent flow and cavitation) and the many variations in the propagation medium (valves,
branches, reflective ends), the degree of signal similarity is not uniform over a broad range of
frequencies. Though the signal-to-noise ratio provides a reasonable estimate of the frequency
band for which accurate leak locations may be obtained, a more sensitive measure of signal simi-
larity is required for the location of small leaks (e.g., 11.4 L/h [3 gal/h] or less).
The proposed detection algorithm is designed to locate leaks with a high signal-to-noise
ratio1. As the leak becomes smaller or the line becomes longer, the SNR will eventually become
small enough that routine location estimates cannot be made. The accuracy of the location esti-
mate depends on the estimate of the sound speed, the resolution of the data acquisition system,
the strength of the signal compared to the noise, and the signal processing algorithm. The
experimental uncertainty in locating a leak can be estimated from the standard deviation of the
location estimates made from many realizations of the measurement of the leak for one or more
1 The signal-to-noise ratio is estimated from the ratio of the received power at the output of the measurement system
over a specified frequency band while a signal is present, divided by the output power measured at the receiver over
the same frequency band while a signal is not present.
8
-------
leak rates and at one or more separation distances of the sensors bracketing the leak. The algo-
rithms proposed for leak location and the estimates of the uncertainty in applying these algo-
rithms are described below.
4.1 Location Algorithm
Consider two measurements of the signal, m^t) and m2(t), where each represents the
sum of a desired signal, s(t), and a contaminating noise component, n(t). The signal, s(t),
would be the acoustic signal emanating from the leaking pipeline, and the contaminating
noise component, n(t), could be ambient noise in the measurement environment that is uncor-
related at the separated acoustic sensors. The coherence function, f(f), is the normalized
cross spectrum of the two measurements,
where upper-case letters denote the Fourier transform of the respective quantities and the
overbar denotes the ensemble average. As noted above, the coherence is complex and the
phase, <()(/), measures the relative time delay between the two signals at a given frequency f.
The coherence function ranges in magnitude from 0 (signals completely uncorrelated) to 1
(signals completely correlated). Values of f(f) exceeding 95% of the noise fluctuations are
usually taken as indicating a reliable phase measurement.
If the acoustic leak signal is approximated as a collection of propagating acoustic plane
waves that obey the simple linear dispersion relation
(4.2)
where k is the wavenumber and V is the propagation speed, the differential separation
between two sensors, Ax, and the frequency-dependent phase, <|>(f), are simply related by
27Iy (4.3)
Through the use of coherence function analysis, it is possible to isolate portions of the acous-
tic spectrum within which the linear dispersion relation is obeyed. The measured phase shift,
<|>(f), within these frequency bands can then be used to estimate either the propagation speed
of acoustic waves or the differential sensor separation. Because the coherence phase is con-
fined to the range -180° < <)> < 180°, the measured phase generally differs from the actual
phase by an unknown factor of 360°, except at very low frequencies and/or very small sensor
-------
separations. As a consequence, the measured phase cannot be accurately unwrapped except
within frequency bands where J2(f) is high; thus, a differential form of Eq. (4.3) must be used
to relate sensor separation, propagation speed, and coherence phase:
df
(4.4)
in which, for the sake of simplicity, it is assumed that the medium is nondispersive.
The three-sensor approach illustrated in Figure 4.1 was used to locate leaks in an
underground pipeline. This configuration is similar to the one shown in Figure 1.1, except
that sensor pair B-C is used to measure the in situ wave speed, while sensor pairs A-B or A-C
are used to estimate the leak location. Knowledge of the wave speed improves the accuracy
of the leak location estimate. However, the wave speed associated with a particular product
and pipeline geometry is usually unknown. Therefore, it is useful to make an experimental
estimate of the wave speed.
A LEAK B C
L
* x to-
^ ^AL ^
•* Y
\
.* x ».
^ ABL ^
^ AAB "
.* X -tor-
^ ABC ^
Figure 4.1. Three-sensor approach to acoustic location of leaks.
Application of Eq. (4.4) to sensors A and B, which bracket the leak, yields a simple
relationship between measured phase, wave speed, and leak location:
XAL=~
AB
df
df
(4.5)
(4.6)
where L denotes the location of the leak. The wave speed is estimated from the measured
phase between sensors B and C:
fid
-i
(4.7)
10
-------
4.2 Location Errors
The coherence phase required for the estimation of the leak location and wave speed is
most accurately measured (i.e., has a low probability of being a noise fluctuation) when the
coherence amplitude, ^(f), is significantly above the noise. The value of the coherence
amplitude associated with a level of statistical significance, P, is given by
(4.8)
where n is the number of independent data segments used to compute rf(f). If P is 0.95 and n
is 15, then for any value f(/) greater than 0.35, there is less than a 0.05 (5%) chance that f(f)
was produced by a noise fluctuation.
An estimate of the one-standard-deviation uncertainty in the phase measurements,
o{(J)/4B(/)}, derived from coherence measurements between any two sensors (e.g., A and B) is
given by
(4.9)
by Bendat and Piersol [5]. Eq. (4.9) indicates that the random error associated with phase
measurement is controlled by n and by the magnitude of YAB(/)-
The one-standard-deviation uncertainty, o{XAL}, in estimating the location of a leak
with respect to sensor A, when sensors A and B bracket the leak and the mean propagation
velocity, , is measured between sensors B and C, is given by
2Y/2
(4.10)
OS
df
Because the average rate of change of the phase with respect to frequency is directly related
to physical distances, it can be shown that
(XAB-2)
(4.11)
Assuming that v{dty/df} = a{d$AB/df} = G{dtyBC/df}, and using Eq. (4.11), Eq. (4.10)
reduces to
11
-------
. (4.12)
where
, (XAB-2f
K2=— - a . (4.13)
^BC
The uncertainty, Cf{Xxz,}, in the estimate of the location of the leak, X^, is affected by
the three-sensor measurement geometry and the location of the leak. The term K accounts
for this effect; clearly, the largest uncertainty occurs when K is largest. Eqs. (4. 12) and
(4.13) suggest that the minimum uncertainty in X^ occurs when the leak is midway between
A and B; in fact, when X^ = 0.5 XAB, the uncertainty in XAL is independent of the uncer-
tainty, G{d$BC/df}, in the measurement of the propagation velocity. The maximum uncer-
tainty in XAL occurs when the leak is very near sensor A (or B), or when the separation
distance, XBC, used to estimate the propagation velocity is very small.
The estimates of uncertainty, G{XAL], can be written in terms of the standard deviation
of the phase, a{<|)}, using the equation
df\
where N is equal to the number of independent data points in the frequency band, A/, used to
estimate the rate of change of the phase. In general, there is some correlation between data
points, and so the number of degrees of freedom is usually less than the number of data
points used to derive dtydf. Estimates of G{XAL} are made in the next section for different
sensor geometries, levels of statistical significance, and frequency bands.
The most accurate estimates of leak location are made when (1) the number of indepen-
dent data sets, n, used to compute coherence and phase, the number of degrees of freedom, N,
and the frequency bandwidth used to estimate dty/df are large, and (2) the leak is
approximately at the mid-point between the two bracketing sensors.
4.3 Estimates of Measurement Uncertainty
A theoretical estimate of the standard deviation of the location estimate, a{XAL}, can be
made with Eqs. (4.9), (4.12) and (4.14). A field estimate of c{XAL} can be made, from repet-
itive measurements, with Eq. (4.10).
12
-------
Figure 4.2 shows the uncertainty in phase determined from Eq. (4.9) as a function of
the number of independent data segments, n, used to compute the coherence and for rfAB(f) =
0.2, 0.4, 0.6, and 0.8. When n = 15 (which is the number of independent data segments used
in the leak location estimates in this paper), and fAB(f) = 0.5 (which is typical of the values of
coherence for many of the leak location estimates), G{$AB(f)} = 10.5°.
Figures 4.3 through 4.5 show the uncertainty in the location estimate, aiX^}, when the
distances between sensors A and B and sensors B and C are nominally 38.1 m (125 ft) and
7.6 m (25 ft), respectively, and the distance between the leak and sensor A is 3.8 m (12.5 ft),
9.7 m (31.75 ft), and 19.0 m (62.5 ft). The curves are derived in terms of the number, n, of
independent data segments used to estimate the coherence and fAB(f). The estimates assume
that dtydf is computed from N = 26 points over the frequency band 21 19 to 2373 Hz; the
254-Hz band represents the larger bands for which the location estimates were made. In
many instances a frequency band closer to 100 Hz was used. The conditions used to generate
Figure 4.6 are identical to those used to generate Figure 4.4, except that N = 5 points.
An estimate of the leak location and sensor separation is best made when the value of
*?(/) is significantly above the noise. Table 4.1 shows the one standard deviation in phase,
sensor separation, and leak location as a function of n for the three geometries described
above for values of JAB(f) at the 95% and 99% levels of statistical significance. As n
increases, the value ofy^B(f) required to maintain the same level of statistical significance
decreases. Obviously, more accurate estimates of the location of the leak can be made if the
values of rfAB(f) or n are greater than the values in Table 4.1. The results in Figures 4.3
through 4.5, as well as in Table 4.1, suggest that the largest uncertainty in leak location is less
than 20 cm (7.88 in.).
13
-------
LU
111
DC
o
LU
Q
I
tr
O
DC
DC
LU
LU
36 -
32 -
28 -
24 -
20 -
16 -
12 -
8 -
4 -
—i—
15
—i—
25
—i—
35
—i—
45
NUMBER OF INDEPENDENT DATA SEGMENTS
Figure 4.2. a{$AB(f)} for sensor separation distance as a function of n between 5 and 50 and values of *&,
equal to 0.8,0.6,0.4, and 0.2 estimated for any frequency with Eq. (4.9).
60
u
I
DC
O
DC
DC
LU
LU
O
50-
40-
30 -
CO
Q
co 20 -
10 -
15
25
35
45
NUMBER OF INDEPENDENT DATA SEGMENTS
Figure 4.3. a{XAB} for sensor separation distance between two sensors, A and B, as a function of n between 5
and 50 and values of -fAB(f) equal to 0.8,0.6, 0.4, and 0.2 estimated with Eqs. (4.9), (4.12), and (4.14) for the
following conditions: X^ = 38.1 m (125 ft), XBC = 7.6 m (25 ft), X^ = 3.8 m (12.5 ft) (i.e., 10% of X^), Af =
2373 - 2119 = 254 Hz, N = 26, and = 1,000 m/s.
14
-------
36
o
i
DC
O
DC
DC
LLJ
LU
O
Q
NUMBER OF INDEPENDENT DATA SEGMENTS
Figure 4.4. o{XAB} for sensor separation distance between two sensors, A and B, as a function of n between 5
and 50 and values of fAB(f) equal to 0.8,0.6,0.4, and 0.2 estimated with Eqs. (4.9), (4.12), and (4.14) for the
following conditions: XAB = 38.1 m (125 ft), XBC = 7.6 m (25 ft), X^ = 9.7 m (31.75 ft) (i.e., 25% of XM), Af =
2373 - 2119 = 254 Hz, N = 26, and = 1,000 m/s.
o
DC
O
DC
DC
LU
LU
O
I
Q
12 -
5 15 25 35 45
NUMBER OF INDEPENDENT DATA SEGMENTS
Figure 4.5. Q{XAB} for sensor separation distance between two sensors, A and B, as a function of n between 5
and 50 and values of -fAB(f) equal to 0.8,0.6,0.4, and 0.2 estimated with Eqs. (4.9), (4.12), and (4.14) for the
following conditions: X^ = 38.1 m (125 ft), XBC = 7.6 m (25 ft), X^ = 19.0 m (62.5 ft) (i.e., 50% of X^), Af =
2373 - 2119 = 254 Hz, N = 26, and = 1,000 m/s.
15
-------
o
tr
O
cc.
tr
m
UJ
o
1
Q
o 20 -
10 -
NUMBER OF INDEPENDENT DATA SEGMENTS
Figure 4.6. a{XAB} for sensor separation distance between two sensors, A and B, as a function of n between 5
and 50 and values of -?AB(f) equal to 0.8, 0.6,0.4, and 0.2 estimated with Eqs. (4.9), (4.12), and (4.14) for the
following conditions: X^ = 38.1 m (125 ft), XBC = 7.6 m (25 ft), X^ = 9.7 m (31.75 ft) (i.e., 25% of X^), Af =
2373 - 2119 = 254 Hz, N = 5, and = 1,000 m/s.
4.4 Accuracy
The accuracy of the acoustic measurement system for locating a leak along the pipeline
is defined as the mean difference between the actual and estimated location of the leak. The
accuracy is affected by any biases that may result from the phase measurement estimates, by
the uncertainty in the estimate of the average propagation speed (as affected by an error in
the location of the sensors with respect to each other), and by differences in the wave speed
along different propagation paths from the leak to the sensors.
A bias in the phase measurements can occur for a variety of reasons: biases in the
power spectral and cross spectral estimates used to compute phase, ambient noise that is
highly directional, and other signals that are correlated with the input signal. These may
include errors due to multiple modes of propagation that occur in the liquid product and the
pipe wall and errors due to reflections of the signal within the pipe due to boundaries, joints,
couplings, elbows, etc. Accurate theoretical estimates of bias errors are difficult to make
and require information about the signal and noise field; as a consequence, none will be
attempted here. It is anticipated, however, that the bias errors in the phase measurements will
be small compared to the other two sources of error mentioned above.
16
-------
Table 4.1. Estimates of the Total Uncertainty in Measuring the Separation between Sensors and the Location of
a Leak as a Function of the Number of Incoherent Averages and "&B(f) Computed for L = 95 and 99%
•&(/) Number of SNR a{*AS} a{XAB}' a{XAL}" c{XAL}'" a{XAL}""
Averages
(o) (cm) (cm) (cm) (cm)
L = 95%
0.78
0.49
0.35
0.27
0.22
0.12
L = 99%
0.90
0.64
0.48
0.38
0.32
0.17
5
10
15
20
25
50
5
10
15
20
25
50
3.5
0.9
0.5
0.4
0.3
0.1
9.0
1.8
0.9
0.6
0.5
0.2
9.7
13.2
14.3
14.9
15.2
15.9
6.0
9.6
10.8
11.5
11.8
12.6
35.5
48.0
52.2
54.3
55.5
57.9
22.0
35.0
39.5
41.8
43.2
45.9
14.3
19.4
21.1
21.9
22.4
23.4
8.9
14.1
16.0
16.9
17.5
18.6
9.2
12.5
13.6
14.1
14.4
15.1
5.7
9.1
10.3
10.9
11.2
12.0
3.5
4.7
5.1
5.3
5.4
5.7
2.2
3.4
3.9
4.1
4.2
4.5
'Sensor separation error estimated between 2119 and 2373 Hz for V = 1,000 m/s and N = 26 assuming that the
velocity is measured and the nominal sensor separations are X^ = 38.1 m (125 ft) and XBC = 7.6 m (25 ft), and
XAL = 9.7m(31.75ft).
"Leak location error estimated between 2119 and 2373 Hz for V = 1,000 m/s and N = 26 assuming that the
velocity is measured and the nominal sensor separations are XM = 38.1 m (125 ft) and XBC = 7.6 m (25 ft), and
XAL= 3.8m (12.5 ft).
'"Sensor separation error estimated between 2119 and 2373 Hz for V = 1,000 m/s and N = 26 assuming that the
velocity is measured and the nominal sensor separations are XAB = 38.1 m (125 ft) and XBC = 7.6 m (25 ft), and
XAL = 9.7m(31.75ft).
""Leak location error estimated between 2119 and 2373 Hz for V = 1,000 m/s and N = 26 assuming that the
velocity is measured and the nominal sensor separations are X^ = 38.1 m (125 ft) and XBC = 7.6 m (25 ft), and
XAL= 19.0m (62.5 ft).
Ultimately, the accuracy of a leak location estimate depends on the speed of sound
used to covert the time-of-arrival or phase measurements to distance. Any errors in the esti-
mate of the wave propagation speed will translate directly into distance errors. Sound speed
estimates should be measured experimentally to minimize these errors.
4.5 Performance of the Leak Location System
A leak detection system requires a high probability of detection (PD) to be effective.
The EPA regulation requires that a detection system have a PD of at least 95%. On the other
hand, a leak location system does not require a high PD, but does require a low probability of
false alarm (PFA), 5% or less, to be effective. There is no recommended PFA or PD for a loca-
tion system. However, a PD of 50% or less should be sufficient because it is presumed that
the leak location system is being used only after the existence of a leak has been confirmed.
17
-------
The PFA and PD can be estimated directly from the SNR for normally distributed noise. These
estimates can be made with the standard curves shown in Figure 4.7; these curves were
reproduced directly from Urick [6] and can be found in many textbooks.
I
3
99 999
99 99
99 9
99 8
99 5
qq n
90 0
50 0
10 0
c, p,
2 0
1 0
0 5
0 2
0 01
0 00'
/
*
/
i\
A
/
/I
/
00
A
/
/
r"
/
y
t
/
/
<
/
/
/[
01
c
/
/
/
/
f
/
/
/
/
*
/
s
s
/
/
/
0.1
-V
>/
/
/
/
/
4
/
o
fe/
I/
/
^
A
1
/
/
0
/
'I
/
/
S
/i
/
5
/
;/
/\
f
t
/
A
/
,2
/
/
/
s/
t
/
/
f
/
/
/
t
/
/
/
0)
/
/
/
S
/i
1
/
/
/
/
6>
/
/
/
3
<
/
•
/
\
(
,
^
/
/
3
/
/
/
•V
/
3
r
/
s
/
(
r
<'
/
5
/
S
f
r
/
i
/
3
/
/
\
/
/
7
/
/
/
t
/
/
0
f
y
/
/
/
/
9
/
/
/
L/
3
7-
/
/
/
9
(
1,
'
/
'
8
/
/
/
99
/
/
/
.5
/
/
/
/
/
99.
y
99
/
00001 0.01 0.2 1
20 40 60 80
p (FAS, percent
95 99 999 99.999
Figure 4.7. Estimates of PD and PFA as a function of SNR = d developed for normally distributed noise. (Urick
[6])
Table 4.2 presents, as a function of SNR, estimates of the PFA for a PD of 50% and PD
for a PFA of 5%. For most detection applications, an SNR over 9 will more than suffice. The
PFA and PD can be further improved by averaging the results of multiple tests.
Table 4.2. Estimates of PFA and a PD of 50% as a Function of SNR
SNR
PFA for
PD = 50%
PFA = 5%
0
1
2
4
9
16
25
50
16
9
2.5
0.15
0.008
< 0.0001
5
26
40
62
90
98
99.93
18
-------
The SNR can be computed from the coherence estimates made over the signal band of
interest for any two sensors bracketing a leak in the pipeline [7], The relationship between
and the SNR is given by
Eq. (4.8) can be used to estimate the probability of a false alarm as a function of SNR
and the number of independent data segments used to compute the coherence. Thus, with
Figure 4.7 (or Table 4.2) and Eqs. (4.8), and (4.15), (1) an estimate of the PFA and PD can be
made for a leak location test based on the value of n used in the analysis and the value of "f(f)
measured, or (2) the minimum specifications of n and rf(f) required to achieve a given PFA
and PD can be estimated. The latter can be done by
• selecting the desired PFA and PD, and computing SNR from Figure 4.7,
• solving Eq. (4.15) for *f(f) and computing °f(f) for the SNR required to achieve the
desired PFA and PD, and
• computing n from Eq. (4.8) for "f(f) and PFA.
The following example provides an estimate of the minimum number of independent data
segments, n, and the minimum coherence, "f(f), required to achieve a given performance. If
a PFA of 5% and a PD of 50% are desired, the SNR estimated from Figure 4.7 must be approx-
imately 3 (6 dB). The value of "/*(/) estimated from Eq. (4.15) is 0.75, and the value of n
estimated from Eq. (4.8) is 5. If n is increased and the value of rf(f) remains at 0.75, the PFA
will be less than 5% and the PD will greater than 50%.
The PD and PFA can be estimated for a given measurement by
• computing the PFA for a given n and the measured *?(f) by means of Eq. (4.8),
• computing SNR for the measured ^(f) by means of Eq. (4. 15), and
• computing PD for the given PFA and SNR by means of Figure 4.7.
19
-------
SECTION 5
EXPERIMENT DESIGN
The experiments were conducted on the pressurized 5-cm- (2-in.-) diameter steel pipeline
at the UST Test Apparatus and were done in accordance with the quality assurance project plan
[8]. A diagram of the pipeline at the UST Test Apparatus is shown in Figure 5.1. Access ports
required for the attachment of transducers to the pipeline were located at intervals of approxi-
mately 8 m (25 ft); the coupling between the pipeline and an acoustic transducer is shown in
Figure 5.2. Sensor positions shown in Figure 5.1 were used during all experiments. The
transducers chosen for this work were CTI-30 resonant sensors. Though the CTI-30 is designed
primarily for acoustic emissions applications, its sensitivity at low frequencies (1 to 5 kHz) is
adequate for the detection of acoustic leak signals in pipelines. The acoustic signals were ampli-
fied by 80 dB, in two stages, by means of battery-operated Panametrics 5660-C preamplifiers
and line-driven Krohn-Hite 3342 amplifying filters. A Western Graphtec TDA-3500 transient
recorder was used to digitize the acoustic wave forms at a sampling rate of 10 kHz. Data were
stored and analyzed with a COMPAQ-386 portable computer. A diagram of the data acquisition
system is shown in Figure 5.3.
Figure 5.4 shows a diagram of the apparatus used to generate a leak in the pipeline. The
flow rate of the leak was controlled by the static line pressure (0 to 172 kPa [0 to 25 psi]) and the
diameter of the aperture through which the product was allowed to leak. Leak apertures between
0.3 and 0.8 mm (0.016 and 0.031 in.) were introduced into the pipeline via carburetor jets in
order to avoid the difficulty of drilling small-diameter holes through the steel wall of the pipe-
line. The range of flow rates generated during the experiments was between 1.9 and 18.9 L/h
(0.5 and 5.0 gal/h). The backfill materials used in the experiments were fine-grain sand and
coarse gravel.
Three types of acoustic measurements (calibration, leak-on, and leak-off) were made for
each combination of line pressure, hole diameter, and backfill material. The calibration signal
was produced by breaking a pencil lead on the pipe surface near the location of the simulated
leak. The relative arrival times of this impulsive signal at the three transducer locations were
used to verify that the sensors and data acquisition system were operating properly. After the
initiation of the leak, approximately eight leak-on measurements, each 1.7 s in duration, were
recorded at 1-min intervals. The eight leak-on measurements were bracketed by a pair of record-
ings obtained under leak-off conditions.
20
-------
r
LEAK SIMULATOR
PRESSURIZED CO,
GASOLINE
B
c
I
0.35 m
t. **— VALVE
15m
8 m
Figure 5.1. Diagram of the pressurized petroleum pipeline at the UST Test Apparatus. Pipe material is 5-cm-
(2-in.-) diameter steel; product is gasoline. Pressurized CO2 is used to generate 0- to 172-kPa (0- to 25-psi) static
line pressure. Valves in connecting branches were closed during all experiments.
21
-------
PIPELINE
n
STEEL
COUPLING
ACOUSTIC
TRANSDUCER
Figure 5.2. Diagram of the coupling between the acoustic transducer (CTI-30) and the steel pipeline.
CTI-30 P
SENSORS
n
REAMPLIFIERS AMPLIFYING
(+60 dB) FILTERS (+20 dB)
PANAMETRIC
5660-C
PANAMETRIC
5660-C
PANAMETRIC
5660-C
—
KROHN-HITE
3342
KROHN-HITE
3342
KROHN-HITE
3342
—
A/D
CONVERSION
WESTERN
GRAPHTEC
TDA-3500
TRANSIENT
RECORDER
». PC
Figure 5.3. Diagram of the data acquisition system used in the experiments.
22
-------
BACKFILL
CONTAINER
0.3 m
0.3m
Figure 5.4. Apparatus used to generate simulated pipeline leak. Backfill materials are fine-grain sand and coarse
gravel. Leak apertures between 0.3 and 0.8 mm (0.01 to 0.03 in.) were introduced into the pipeline via carburetor
jets.
23
-------
SECTION 6
DATA
The raw data consist of time series of acoustic leak signals and ambient noise sampled
simultaneously by three sensors. The first step toward deriving and applying a leak location
algorithm to the raw data is to view the data in three forms: (1) time series, (2) power spectral
density, and (3) complex coherence. Viewed in the time domain, the leak-on and leak-off data
(i.e., time series) provide convincing evidence that an acoustic leak signal exists and is detectable
over the dimensions of the pipeline. In addition, the time series reveal the continuous character
of the leak signal, as compared to the impulsive signal generated by the pencil-lead calibration
signal. However, the time series alone offer no clues as to the location of the leak or the types of
processing required to perform a source location estimate. The distribution, with respect to fre-
quency, of acoustic energy emitted by the leak and the way in which this energy is propagated
from source to sensor is revealed by viewing the data in the frequency domain (i.e., power
spectra and complex coherence).
Time series of acoustic leak signals generated by a 11.4-L/h (3-gal/h) gasoline leak into a
sand backfill are shown in Figure 6.1; a time series recorded under no-leak conditions by one of
the sensors is shown for reference. Aside from an anti-alias filter applied to the analog signals
prior to digitization, the time series shown here represent unfiltered data. The distance between
the simulated leak and sensors A and B is approximately 15m (50 ft); sensor C is located
approximately 23 m (75 ft) from the leak. The line pressure used in this experiment was 103 kPa
(15 psi) and the hole diameter was 0.7 mm (0.03 in). Two important observations are made
regarding the time series of Figure 6.1: (1) the leak is clearly detectable from the difference
between the leak-on and leak-off measurements, and (2) the relative arrival time of the leak sig-
nal at the different sensor locations cannot be obtained through inspection of the time series. The
continuous nature of the acoustic leak signal requires that some type of signal processing be
applied to the leak signal time series in order that the relative arrival times, and hence the loca-
tion of the leak, can be estimated.
Figure 6.2 shows time series of acoustic leak signals generated by a 1.9-L/h (0.5-gal/h)
leak into a sand backfill along with a no-leak time series for reference. The line pressure used in
this experiment was 34 kPa (5 psi) and the hole diameter was 0.3 mm (0.014 in.); the sensor
geometry is the same for all experiments. At the reduced flow rate of 1.9 L/h (0.5 gal/h), the
24
-------
acoustic leak signal cannot be clearly identified in the raw time series. In order to detect the
presence of small leaks, the data collected in the time domain must be transformed into the fre-
quency domain.
B
LEAK OFF
50.0
100.0
TIME (mS)
150.0
Figure 6.1. Time series of acoustic leak signals generated by a 11.4-L/h (3-gal/h) leak into a sand backfill. Line
pressure is 103 kPa (15 psi) and hole diameter is 0.7 mm (0.03 in.). Sample rate is 10 kHz. A no-leak time series
recorded by sensor B is shown for reference.
25
-------
B
LEAK OFF
B
50.0
100.0
TIME (mS)
150.0
Figure 6.2. Time series of acoustic leak signals generated by a 1.9-L/h (0.5-gal/h) leak into a sand backfill. Line
pressure is 34 kPa (5 psi) and hole diameter is 0.3 mm (0.01 in.). Sample rate is 10 kHz. A no-leak time series
recorded by sensor B is shown for reference.
6.1 Signal Strength
The strength of the acoustic signal produced by a leak in a buried pipeline is primarily
a function of flow rate, but is influenced somewhat by the surrounding backfill material.
Estimates of the signal-to-noise ratio for pipeline leaks into a sand backfill at flow rates of
11.4, 5.7, 3.8 and 1.9 L/h (3.0,1.5, 1.0 and 0.5 gal/h) are shown in Figures 6.3(a) through
6.3(d). The hole diameters and line pressures used to establish the flow rates were 0.7 mm at
103 kPa (15 psi) (i.e., 11.4 L/h [3.0 gal/h]); 0.5 mm at 103 kPa (15 psi) (i.e., 5.7 L/h)
[1.5 gal/h]); 0.4 mm at 76 kPa (11 psi) (i.e., 3.8 L/h [1.0 gal/h]); and 0.4 mm at 34 kPa (5 psi)
26
-------
(i.e., 1.9 L/h [0.5 gal/h]). The SNR at each flow rate was obtained by dividing the power
spectral density computed with the leak present by a similar spectrum computed with no leak
present. The power spectra for each of the three individual sensors, computed using 31 over-
lapping, 1024-point FFT segments, were averaged together prior to computing the SNR. The
time series used were 1.7 s in duration and were sampled at a frequency of 10 kHz. The SNR
spectra show that the energy associated with the acoustic leak signal is not equally distributed
over the 1- to 5000-Hz sampling bandwidth, but is instead concentrated within a relatively
narrow 1- to 4-kHz frequency band. The frequency domain representation of acoustic data
offers a means by which the location algorithm can separate useful information concerning
the leak from unwanted noise.
Figure 6.4 shows the SNR computed from time series recorded in the presence of an
11.4-L/h (3-gal/h) leak with coarse gravel as the backfill material. A comparison of
Figures 6.4 and 6.3(a) indicates that the acoustic signal produced by the turbulent flow of
product into a backfill of fine-grain sand represents a slight enhancement over that produced
when the backfill consists of gravel. A similar relationship between the backfill material and
the strength of the acoustic leak signal has been reported for studies of simulated leaks in the
floor of aboveground storage tanks [9-11].
An estimate of the strength of the acoustic signal as a function of line pressure for a
fixed-diameter hole is shown in Figure 6.5. The line pressures used in this experiment were
172 kPa (25.0 psi), 128 kPa (18.5 psi), 83 kPa (12.0 psi), and 41 kPa (6.0 psi); the hole diam-
eter was 0.5 mm (0.020 in.). The average SNR computed over the 1- to 4-kHz frequency
band is used as the measure of acoustic leak signal strength. As expected, the leak signal
increases in strength as the line pressure is increased.
6.2 Coherence and Phase Measurements
Figure 6.6 shows the coherence amplitude and coherence phase as a function of fre-
quency for acoustic leak signals received by sensors bracketing a 5.7-L/h (1.5-gal/h) leak.
The sensor separation is 38 m (125 ft). The coherence plot represents an ensemble average
of 15 overlapping, 1024-point segments, each individually detrended and weighted with a
cosine bell prior to Fourier transforming. Statistically significant coherence (as indicated by
the 95% confidence level) is observed primarily within the frequency bands 0.9 to 1.2 kHz
and 2.0 to 4.0 kHz. It should be noted that within both of these frequency bands y2 is not
statistically significant at all Fourier frequencies. Figure 6.7 shows the coherence amplitude,
), and coherence phase,
-------
1.9-L/h (0.5-gal/h) leak. The sensor separation is 30 m (100 ft). As the flow rate is reduced
(in this case by lowering the line pressure to 34 kPa [5 psi]), the frequency band within which
signal similarity is maintained is narrowed considerably.
If the coherence amplitude is statistically significant for each Fourier component within
a given frequency band, a simple phase-unwrapping procedure may be applied to the coher-
ence phase. Figure 6.8 shows the unwrapped phase shift as a function of frequency between
3.8 and 4.0 kHz for sensors B and C of Figure 5.1; the flow rate is 11.4 L/h (3 gal/h).
28
-------
PERIOD (SECONDS)
10"1 10~2 10"3
10
-1
-
10
-
10
10
10
i 102
CO
10
10
10
10
DC 2
Z 10
CO
1
10
10
=- (A) 3 GPH
=- (C) 1.0 GPH
= • (B) 1.5 GPH
s- (D)0.5 GPH
II II IN I I I I I III
1 2 3
10 10 10
io2 io3
FREQUENCY (Hz)
Figure 6.3. Signal-to-noise ratio (SNR) for pipeline leaks into a sand backfill at flow rates of 11.4 L/h
(3.0 gal/h) (A), 5.7 L/h (1.5 gal/h) (B), 3.8 L/h (1.0 gal/h) (C), and 1.9 L/h (0.5 gal/h) (D). Dashed Une indicates
SNR=1. SNR estimates are computed by averaging the received power at each of the sensor locations shown in
Figure 6.1.
29
-------
PERIOD (SECONDS)
10
-1
10
'2
10
'3
cc
10
10
Hn
10
10
illi
101 102 103
FREQUENCY (Hz)
Figure 6.4. Signal-to-noise ratio (SNR) for pipeline leak into a gravel backfill. Flow rate is 11.4 L/h
(3.0gal/h).
0
I
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cc
01
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o
C\J
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25
LINE PRESSURE (PSI)
Figure 6.5. Strength of acoustic leak signal as a function of static line pressure for a fixed hole diameter
(0.5 mm [0.02 in]). Error bars indicate the standard deviation of six measurements used to compute the SNR at
each pressure level.
30
-------
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PHASE (DEGREES)
SQUARED COHERENCE
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PHASE (DEGREES)
SQUARED COHERENCE
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<
Q.
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3850
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FREQUENCY (Hz)
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Figure 6.8. Unwrapped coherence phase, <(»(/), between 3.8 and 4.0 kHz for sensor pair B-C of Figure 5.1.
Least-squares regression line through actual data points is included. The flow rate is 11.4 L/h (3 gal/h).
33
-------
SECTION 7
LOCATION RESULTS
The procedure used to estimate the leak location and wave speed for a given set of time
series is as follows: (1) compute the coherence function between the three sensor pairs (i.e.,
A-B, A-C, and B-C), (2) identify frequency bands of at least 100-Hz width for which the coher-
ence amplitude exceeds the 95% level of statistical significance, (3) unwrap the coherence phase
within these frequency bands, (4) compute the linear regression lines through each of the three
<(>(/) curves, and (5) apply Eqs. (4.5) through (4.7) using the known sensor positions and the com-
puted regression slopes.
Figure 7.1 shows the unwrapped phase differences between sensor pairs A-B, A-C, and
B-C for the frequency band 2.0 to 2.5 kHz. The flow rate used in this experiment was 11.4 L/h
(3 gal/h). Included in this plot are least-squares regression lines through the actual data points
corresponding to each sensor pair. The criterion for the inclusion of a phase measurement in the
estimation of leak location and wave speed is that the coherence amplitude exceed the 95% level
of statistical significance for each of the three sensor pairs at a given Fourier frequency.
Table 7.1 summarizes the results of leak location and wave speed estimates for flow rates of
11.4, 5.7, and 3.8 L/h (3.0, 1.5, and 1.0 gal/h). Leak location estimates are reported as a differ-
ence between the computed and actual location.
The regression slopes of Figure 7.1 can be used to calculate the time delays between sig-
nals received by the three sensor pairs. The measured dty/df values of -0.47°/Hz (A-B), 2.07°/Hz
(A-C), and 2.55°/Hz (B-C) correspond to time delays of -1.3 ms, 5.8 ms, and 7.1 ms,
respectively.
An alternative method of extracting the time delays from the time series is to apply the
technique of cross-correlation. Figure 7.2 shows the normalized cross-correlation coefficient,
p^(T), as a function of lag time (T) between time series recorded by sensors B and C. The time
series were bandpass-filtered in order to isolate the high SNR portion of the leak signal spectrum
(1 to 4 kHz) prior to computing the correlation coefficient. Without the detailed knowledge of
the distribution of leak signal energy provided by the coherence function, correlation analysis
fails to give an accurate measurement of the time delay between leak signals received by sensors
B and C. Figure 7.3 shows the correlation coefficient computed between B and C time series in
which the data are bandpass-filtered from 2.0 to 2.5 kHz. Within the high-coherence interval
34
-------
o
o
o
CO
HI
LU
DC
CD
UJ
O
I
CO
LU
CO
<
CL
O
O
UO
B-C
A-B
2100
2200
FREQUENCY (Hz)
2300
2400
Figure 7.1. Unwrapped coherence phase between 2.0 and 2.5 kHz for sensor pairs A-B, A-C, and B-C of
Figure 5.1. Least-squares regression lines through actual data points are included. The flow rate is 11.4 L/h
(3 gal/h).
used to generate the phase curves of Figure 7.1, correlation analysis and coherence function anal-
ysis result in approximately equal estimates of the time delay. Although this result suggests that
the two techniques for measuring time delays are equivalent, accurate correlation analysis
requires a priori knowledge of the frequency bands within which the acoustic leak signal is
strong and composed of linearly propagating waves. Coherence function analysis identifies fre-
quency bands for which the SNR is high (through the coherence amplitude) and for which the
phase behavior is appropriate for leak location (through the coherence phase).
35
-------
Table 7.1. Leak Location and Propagation Speed Measurements
Flow
Rate1
(L/h)
11.4
11.4
5.7
5.7
3.8
D
(mm)
0.7
0.7
0.5
0.5
0.5
P2
(kPa)
138
138
138
138
76
Af
(Hz)
2100 - 2400
3800 - 4050
2100-2400
3800 - 4050
3800 - 4050
Mean
Error
(AB)4
(cm)
8.6
18.7
14.4
-5.8
-2.5
Std.
Dev.
(AB)4
(cm)
16.4
29.9
15.8
19.8
47.9
Mean
Error
(AC)5
(cm)
-2.4
14.2
15.8
-12.2
-20.7
Std.
Dev.
(AC)5
(cm)
23.7
31.8
14.9
20.4
28.1
V
(mis)
1048
917
930
775
715
aV
(m/s)
37
89
136
81
150
N6
"LOC
25
18
23
15
8
1) 11.4 L/h = 3.0 gal/h; 5.7 L/h = 1.5 gal/h; and 3.8 L/h = 1.0 gal/h
2) 128 kPa = 20 psi and 76 kPa = 11 psi
3) Location Algorithm Analysis Band
4) A-B used as bracketing sensors
5) A-C used as bracketing sensors
6) Number of independent location estimates
-15 -10 -505
TIME DELAY (mS)
10
15
Figure 7.2. Normalized cross-correlation coefficient, p^,(T), as a function of time delay (T) between time series
recorded by sensors B and C. The time series were bandpass-filtered between 1.0 and 4.0 kHz prior to computing
p^. The flow rate is 11.4 L/h (3 gal/h). TBC represents the predicted B-C time delay at V = 1000 m/s.
36
-------
-15
-10
-505
TIME DELAY (mS)
10
Figure 7.3. Normalized cross-correlation coefficient as a function of time delay between time series recorded by
sensors B and C. The time series were bandpass-filtered between 2.0 and 2.5 kHz prior to computing p^. The flow
rate is 11.4 L/h (3 gal/h). TBC and TO, represent predicted time delays for primary and reflected acoustic waves prop-
agating at V = 1000 m/s.
37
-------
SECTION 8
LEAK SIGNAL PROPAGATION
The analysis of acoustic data from pipelines is complicated by the presence of multi-path
and multi-mode wave propagation. Multi-path signals are produced by reflections within the
complex pipeline geometry or by signal leakage, across the connecting arms, from one main
branch of the pipeline to the other (see Figure 5.1). Multi-mode wave propagation results from
the excitation, by the leak flow field, of wave motion in different materials (e.g., gasoline and
steel), or of waves in the same material that propagate at different speeds (e.g., longitudinal and
transverse waves). While the analysis presented above suggests that the acoustic leak signal is
dominated by a single propagation mode that traverses a single path from leak to sensor, exper-
imental data and simple simulations show that the effects of multi-path and multi-mode propaga-
tion are detectable.
The reflective nature of the pipeline is illustrated by the cross-correlation plot shown in
Figure 7.3. The primary pxy peak, which occurs at the lag time 1 ~ 7 ms, corresponds to signals
propagating in the direction from sensor B to sensor C at speed c ~ 1000 m/s. A secondary peak,
which occurs at the lag time I ~ -7 ms, is consistent with reflection signals propagating at the
same speed, but in the opposite direction.
Energy propagation along the pipeline results from the excitation of three types of wave
motion by the leak flow field: (1) transverse waves propagating in the steel, (2) longitudinal
waves propagating in the steel, and (3) longitudinal waves propagating within the product con-
tained in the pipeline. The nominal propagation speeds for each type of wave motion are
6,000 m/s (longitudinal, steel), 3,000 m/s (transverse, steel), and 1,200 m/s (longitudinal,
gasoline). The similarity between the measured wave speed (~ 1000 m/s) and the speed of
acoustic waves in gasoline suggests that in the far field of the leak, the sensors respond primarily
to longitudinal waves propagating through the product. These longitudinal waves are sensed
indirectly through stresses induced in the steel in response to the fluctuating pressure field within
the pipe. If other forms of wave motion are produced by the leak and are detectable, the phase
measurements, and thus the location estimates, will be degraded. The detectability of longitudi-
nal waves propagating in steel was investigated through a calibration test in which an impulsive
signal was generated by the breaking of a pencil lead near the leak location. Figure 8.1 shows
the time series of the calibration impulse received by sensors B and C. The measured time delay
(1.2 ms) and sensor separation (7.5 m) yield a propagation speed of 6,250 m/s for the leading
38
-------
edge of the impulse. This speed is consistent with the nominal value of 6,000 m/s for longitudi-
nal waves propagated within the steel. While the calibration data do not indicate the degree to
which the longitudinal wave mode in steel is excited by the leak flow field, it does show that
such waves, if excited by the leak, will be detected by sensors mounted externally on the pipeline
wall.
B
15.0
16.0
17.0 18.0
TIME (mS)
19.0
20.0
Figure 8.1. Time series of impulsive calibration signals recorded by sensors B and C of Figure 5.1. The estimated
propagation speed (6250 m/s) is consistent with the nominal speed of sound in steel.
The excitation of transverse waves by the leak flow field, and their detectability, were
investigated through a series of experiments in which CO2, rather than gasoline, was used as the
product. Figure 8.2 shows the unwrapped phase shift between sensors B and C measured in the
presence of a 103-kPa (15-psi), CO2 leak. The hole diameter was 7 mm (0.029 in.). Application
of Eq. (4.7) to the phase plot yields a propagation speed of approximately 2,400 m/s. Two
important observations should be noted regarding this experiment: (1) the measured wave speed
is similar to the nominal value for transverse waves propagating freely in steel, and (2) the mea-
sured wave speed is much higher than the speed of acoustic waves propagated in CO2
(c ~ 270 m/s). The SNR of the CO2 leak was approximately 15 dB less than the SNR recorded in
the presence of a gasoline leak at the same line pressure and hole diameter. Two conclusions
may be drawn from these measurements: (1) freely propagating transverse waves are produced
39
-------
by the leak and are detectable in the far field, and (2) the coupling between acoustic waves in the
product and stresses induced in the surrounding pipeline is a function of the product contained
within the pipeline. Liquid leaks appear to be sensed primarily through energetic, low-velocity
acoustic waves, while gas leaks are sensed via less energetic, high-velocity transverse waves
propagating in the steel.
en
LU
LLJ
DC
O
LU
Q
CO
UJ
CO
<
Q.
O
O
-------
odic oscillation that occurs at approximately 50-Hz intervals with an average amplitude of 40°.
If the signal received at each sensor is represented as a summation of a direct-path signal
propagating at the observed wave speed and contaminating signals caused by multi-path and
multi-mode propagation, an estimate can be made of the fraction of total energy received via the
contaminating signals. A simple simulation in which approximately 15% of the total received
energy was propagated by multi-path and multi-mode waves produced residual phase shifts com-
parable to those observed in the data.
CO
UJ
111
cc
O o
tU CM
O,
t
I
UJ O
CO
Q.
CO
UJ
cc
O
T
2150
2200 2250
FREQUENCY (Hz)
2300
2350
Figure 8.3. Unwrapped coherence phase between 2.1 and 2.4 kHz for sensor pair B-C in which the linear trend has
been removed. The flow rate is 11.4 L/h (3 gal/h).
41
-------
SECTION 9
PHASE UNWRAPPING
Accurate source location requires that the location algorithm distinguish between the infor-
mation provided by the leak signal, and ambient or system noise. The continuous nature of the
acoustic leak signal further requires that the separation of signal from noise take place in the
frequency domain, through coherence function analysis, rather than in the time domain. It has
been demonstrated that source location through cross-correlation analysis is not accurate when
applied to wide frequency bands (e.g., the 1- to 4-kHz frequency band used in Figure 7.2).
While the location estimates given in Table 7.1 are based upon the successful application of
coherence function analysis to relatively narrow frequency bands (100 to 500 Hz), the possibility
exists that a similar location algorithm may be applied to frequency bands of arbitrary wi
dth.
Information concerning the leak location is contained in the coherence phase. Because the
measured phase differs from the actual phase shift by an unknown multiple of 360°, the deriv-
ative of the coherence phase with respect to frequency, dtydf, is required in order to estimate the
relative arrival time of leak signals at spatially separated sensor locations. When the relative
separation between a pair of sensors is large compared to the wavelength of the received signals,
some form of phase-unwrapping algorithm must be applied in order to measure dtyldf over a
wide range of frequencies. Such unwrapping algorithms are easily implemented, provided that
the coherence phase is reliably measured (i.e., the coherence amplitude is high) at many frequen-
cies within the desired band. As the distribution of reliable phase estimates within a frequency
band becomes more sparse, the ability to simply unwrap the phase is diminished, and the
information provided by the phase measurements must be discarded. If the leak location and
propagation speed of acoustic waves are known, the correspondence between measured and pre-
dicted phase shifts can be viewed over an arbitrarily wide frequency band.
Figures 9.1 and 9.2 show the unwrapped phase shift between sensors A-B, A-C, and B-C
in which the unknown multiples of 360° required to unwrap the phase were computed from the
predicted <)>(/) lines (shown as solid lines in the figure). Reliable phase measurements (indicated
by markers in the plots) correspond to coherence amplitudes that exceed the 95% level of statis-
tical significance; the flow rates are 11.4 L/h (3 gal/h) (Figure 9.1) and 5.7 L/h (1.5 gal/h)
(Figure 9.2). The frequency distribution of reliable phase measurements for the 11.4-L/h
(3-gal/h) data is such that all of the information contained in the 2- to 4-kHz band can be used in
42
-------
the location estimate by implementing a straightforward phase-unwrapping algorithm. As the
flow rate is reduced, however, the simple unwrapping algorithm works only within a small num-
ber of narrow frequency bands (e.g., 2.2 to 2.5 kHz, and 3.7 to 4.0 kHz in Figure 9.2). The simi-
larity between the measured and predicted phase shift outside of these narrow bands suggests
that a more robust unwrapping algorithm may be capable of exploiting a greater fraction of the
available phase information for the purpose of leak location.
co 8
LU in
in co
DC
o
LJLJ
Q
•r o
111
co
O
O
in
B-C
2000
2500 3000
FREQUENCY (Hz)
3500
4000
Figure 9.1. Unwrapped coherence phase between 1.5 and 4.5 kHz for sensor pairs A-B, A-C, and B-C. Solid lines
indicate predicted coherence phase for linearly propagating plane waves based upon known leak location and propa-
gation speed. Flow rate is 11.4 L/h (3 gal/h).
43
-------
o
o
ID
CO
tu
111
CC
O
ULJ
Q
T °
s §
HI V
CO
T
O.
O
CO
B-C
2000
2500 3000
FREQUENCY (Hz)
3500
4000
Figure 9.2. Unwrapped coherence phase between 1.5 and 4.5 kHz for sensor pairs A-B, A-C, and B-C. Solid lines
indicate predicted coherence phase for linearly propagating plane waves based upon known leak location and propa-
gation speed. How rate is 5.7 L/h (1.5 gal/h).
44
-------
SECTION 10
REFERENCES
1. U.S. Environmental Protection Agency, "40 CFR 280 - Technical Standards and Correc-
tive Action Requirements for Owners and Operators of Underground Storage Tanks,"
Federal Register, Vol. 53, No. 185 (23 September 1988).
2. D. S. Kupperman, T. N. Claytor, T. Mathieson, and D. Prine, "Leak Detection Technology
for Reactor Primary Systems," Nuclear Safety, Vol. 28 (April-June 1987).
3. D. S. Kupperman and D. E. Karvelas, "Acoustic Leak Detection for District Heating Sys-
tems," Technical Report No. ANL-87-60, Argonne National Laboratory, Argonne, Illinois
(February 1988).
4. E. G. Eckert, J. W. Maresca, Jr., R. W. Hillger, and J. J. Yezzi, "Location of Leaks in
Pressurized Pipelines by Means of Passive-Acoustic Sensing Methods," Leak Detection
Monitoring for Underground Storage Tanks, ASTM STP 1161, Philip B. Durgin and Tho-
mas M. Young, Eds., (Philadelphia: American Society for Testing and Materials, 1992).
5. J. S. Bendat and A. G. Piersol, Engineering Applications of Correlation and Spectral
Analysis (New York: John Wiley & Sons, 1980).
6. R. J. Urick, Principles of Underwater Sound (New York: McGraw-Hill Book Company,
1967).
7. P. R. Roth, "Effective Measurements Using Digital Signal Analysis," IEEE Spectrum,
Vol. 8 (April 1971).
8. J. W. Maresca, Jr., and R. H. Nakata, "Quality Assurance Project Plan: Remediation of
Leaks in Underground Pressurized Pipeline Systems," Vista Research Project 1036, Vista
Research, Inc., Mountain View, California (August 1991).
9. E. G. Eckert, and J. W. Maresca, Jr., "Detection of Leaks in the Floor of Aboveground
Storage Tanks by Means of a Passive Acoustic Sensing System," Proceedings of the 84th
Annual Meeting and Exhibition of the Air and Waste Management Association, Van-
couver, British Columbia (1991).
10. E. G. Eckert and J. W. Maresca, Jr., "Field Tests of Passive Acoustic Leak Detection Sys-
tems for Aboveground Storage Tanks When In Service," Proceedings of the 85th Annual
Meeting and Exhibition of the Air and Waste Management Association, Kansas City,
Missouri (1992).
11. E. G. Eckert and J. W. Maresca, Jr., "An Engineering Assessment of Acoustic Methods of
Leak Detection in Aboveground Storage Tanks," Final Report for API, Vista Research,
Inc., Mountain View, California (October 1991).
45
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TECHNICAL REPORT DATA
(Please read Inarucnons on the reverie before comntering)
1. REPORT NO. 2.
EPA/600/R-92/143
•i. TITLE AND SUBTITLE
ACOUSTIC LOCATION OF LEAKS IN PRESSURIZED UNDERGROUND
PETROLEUM PIPELINES
7. AUTHORISJ
Eric G. Eckert and Joseph W. Maresca, Jr.
Vista Research, Inc., Mountain View, CA 94042
9. PERFORMING ORGANIZATION NAM6 AND ADDRESS
CDM Federal Programs Corporation
13135 Lee Jackson Memorial Highway — Suite 200
Fairfax, Virginia 22033
12. SPONSORING AGENCY NAME AND ADDRESS
Risk Reduction Engineering Laboratory — Cin. , OH
Office of Research and Development
US Environmental Protection Agency
Cincinnati, Ohio 45268
3. RECIPIENT'S ACCESSION-NO.
PB92-207 687
5. REPORT DATE
August 1992
6. PERFORMING ORGANIZATION CODE
8. PERFORMING ORGANIZATION REPORT NO.
10. PROGRAM ELEMENT NO.
CBRD1A
11. CONTIRACT/GRANT NO.
68-^3-3409
13. TYP* OF REPORT AND PERIOD COVERED
Prop act Report
14. SPONSORING AGENCY CODE
EtfA 600/14
15. SUPPLEMENTARY NOTES
Project Officer: Robert W. Hillger (FTS) 340-6639 Comm: ($08) 321-6603
Experiments were conducted at the UST Test Apparatus Pipeline in which three acoustic sensorts separated by a maximum
distance of 38 m (125-ft) were used to monitor signals produced by 3.0-, 1.5-, and 1.0-gal/h leaksjn the wall of a 2-in.-diameter
pressurized petroleum pipeline. The range of line pressures and hole diameters used in the experiments were 10 to 20 psi, and 0.4
to 0.7 mm, respectively. Application of a leak location algorithm based upon the technique of coherence function analysis
resulted in mean differences between predicted and actual leak locations of approximately 10 cm. The standard deviations of the
location estimates were approximately 30 cm. This is a significant improvement (i.e., smaller leaks over longer distances) over
the cross-correlation-based techniques, which are currently being used. Spectra computed from leak-on and leak-off lime series
indicate that the majority of acoustic energy received in the far-field of the leak is concentrated in a frequency band from 1 to
4 kHz. The strength of the signal within this band was found to be proportional to the leak flow rate and line pressure. Energy
propagation from leak to sensor was observed via three types of wave motion: longitudinal waves in the product, and longitudinal
and transverse waves in the steel. The similarity between the measured wave speed and the nominal speed of sound in gasoline
suggests that longitudinal waves in the product dominate the spectrum of received acoustic energy. The effects of multiple-mode
wave propagation and the reflection of acoustic signals within the pipeline were observed as non-random fluctuations in the
measured phase difference between sensor pairs. Additional experiments with smaller holes and higher pressures (20 to 50 psi)
are required to determine the smallest leaks that can be located over distances of several hundred feet. The current experiments
indicate that improved phase-unwrapping algorithms and/or lower noise instrumentation are required to optimize system
performance. This report was submitted in fulfillment of Contract No. 68-03-3409 by Vista Research, Inc., under the sponsorship
of the U.S. Environmental Protection Agency. This report covers a period from 23 January 1991 to 31 October 1991, and work
was completed as of 30 September 1991.
!CE-r7VOHDS ANO DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS \C.COSATI Field/Group
'Iptection
Pipeline
Petroleum
Gasoline
Acoustic
UST
Underground Storage Tank:
Leak
ji3. OI5TRI3UTION STATEMENT
Release to Public
19. SECURITY CLASS /Tha Report)
Unclassified
21. NO. OF PAGES
57
20. SECURITY CLASS (This page I
Unclassified
22. PRICE
£PA Form 2220-1 (9-73)
46
•&U.S. GOVERNMENT PRINTING OFFICE: 1992 - 648-003/60010
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