EPA/600/A-93/095
Eric G. Eckert1, Joseph W. Maresca, Jr.2, Robert W. Hillger1" and James j~._iczzj	
LOCATION OF LEAKS LN PRESSURIZED PETROLEUM PIPELINES BY
MEANS OF PASSIVE-ACOUSTIC SENSING METHODS
Reference: Eckert, E. G., Maresca, J. W., Jr., Hillger, Robert W., and Yezzi, James J.,
"Location of Leaks in Pressurized Petroleum Pipelines By Means of Passive-
Acoustic Sensing Methods," Leak Detection Monitoring for Underground Storage
Tanks, A.STM STP 1161, Philip B. Durgin and Thomas M. Young, Eds., American
Society for Testing and Materials, Philadelphia, 1992.
Abstract: Experiments were conducted on the underground pipeline at the EPA's 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 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-diameter pressurized petroleum pipeline. The
range of line pressures and hole diameters used in the experiments were 70 to 140 kPa
(10 to 20 psi), and 0.4 to 0.7 mm (0.015 to 0.030 in.), respectively. Application of a
leak location algorithm based upon the technique of coherence function analysis
resulted in mean differences of approximately 10 cm between predicted and actual leak
locations. Standard deviations of the location estimates were approximately 30 cm.
Spectra computed from leak-on and leak-off time 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.
Keywords: leak location, leak detection, acoustics, pipelines, underground storage
tanks, passive-acoustics, acoustic emissions
INTRODUCTION
Millions of underground storage tanks (USTs) are used to store petroleum and other
chemicals. The underground pressurized pipelines associated with USTs containing
Research engineer. Vista Research, Inc., 100 View Street, Mountain View, CA 94041.
2Staff scientist. Vista Research, Inc., 100 View Street, Mountain View, CA 94041.
3Environmental scientist, U.S. Environmental Protection Agency, Releases Control Branch, Risk
Reduction Engineering Laboratory, Edison, NJ 08837
4Senior environmental engineer, U.S. Environmental Protection Agency, Releases Control Branch, Risk
Reduction Engineering Laboratory, Edison. NJ 08837

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A/D
~T~
COMPUTER -*
A/D

A/D

ACOUSTIC TRANSDUCERS
T*
ACOUSTIC SIGNAL
LEAK
FIG. 1 - Example of a passive-acoustic leak location system.
petroleum motor fuels arc typically 5 cm (2 in.) in diameter and 15- to 60-m (50- to
200-ft) in length. These pipelines typically operate at pressures of 140 to 210 kPa (20
to 30 psi). Longer lines, with diameters up to 10 cm (4 in.), are found in some
high-volume facilities. There are many systems that can be used to detect leaks in
underground pressurized pipelines. When a leak is detected, the first step in the
remediation process is to find its location. Passive-acoustic measurements, combined
with advanced signal-processing techniques, provide a nondestructive method of leak
location that is accurate, relatively simple to perform, and can be applied to a wide
variety of pipelines and pipeline products. 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 pressurized 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. Acoustic systems have been successfully used to detect and locate
leaks in nuclear reactors for many years [1]. 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 approximately 230 L/h (60 gal/h) 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 [2]. Theoretical
predictions based on [2] suggest that leaks of 450 L/h (120 gal/h) could be pinpointed
to within several meters with sensors spaced at several hundred meters. Using
monitoring frequencies less than 25 kHz makes this wider spacing possible; frequencies
between 1 and 5 kHz appear to give the best results. 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.
Figure 1 shows a simple representation of a passive-acoustic leak location system
in which three transducers simultaneously sample the acoustic signal. The output of
each transducer is digitized and stored as a time series. These time series, recorded by
spatially separated sensors, then serve as input to a leak location algorithm. The
primary function of the location algorithm is to estimate the time delay between
acoustic leak signals received by pairs of sensors. The measured time delay can be used
to estimate the source location (for signals received by sensors bracketing the leak) or
the propagation speed of the acoustic waves (for signals received by non-bracketing
sensor pairs).
Location algorithms that measure the time delays by means of cross-correlation
analysis work well provided that the signal is very strong or that the background noise
is not excessive. When the acoustic signal is wealc in relation to the level of
background noise or has a finite frequency bandwidth, more sophisticated signal
processing techniques are available. One such technique is coherence function analysis.
2

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If the correspondence between received signals is frequency-dependent, or if the phase
dependence of the correspondence is a nonlinear function of frequency, the application
of coherence function analysis is the means by which the source of the signal is best
located. For the purpose of signal estimation and source location, coherence function
analysis represents a significant improvement over correlation analysis [3]. Advanced
signal processing is required for the successful application of this technology to the
problem of leak location for UST pipelines. This paper presents the results of leak
location estimates obtained through application of a location algorithm based upon
coherence function analysis, and a brief summary of the physics associated with
pipeline leak location. A more detailed presentation of these results can be found in [4].
LOCATION OF A CONTINUOUS LEAK SIGNAL
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 similarity
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 (turbulent flow, 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 (SNR) provides a reasonable estimate of the frequency band for
which accurate leak locations may be obtained, a more sensitive measure of signal
similarity is required for the location of small (e.g., 10 L/h or less) leaks.
Consider two time series of acoustic signals, m^t), and m2[t), where each
represents the sum of a desired acoustic leak signal, s(*), and a contaminating noise
component, n(t). The contaminating noise component could be a combination of
ambient acoustic noise in the measurement environment that is uncorrelated at the
separated sensors, and electronic noise associated with the data acquisition system. The
coherence function, 72(f), is the normalized cross spectrum of the two measurements,
where the upper-case letters denote the Fourier transform of the respective quantities
and the overbar denotes the ensemble average. The magnitude of the complex
coherence function measures the similarity between signals and tn2(t) received at
spatially separated sensor locations. The coherence phase, 4>{f), measures the relative
time delay between the two signals as a function of frequency. The coherence function
ranges in magnitude from 0 (signals completely uncorrelated) to 1 (signals completely
correlated). Values of 72(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
MxiWiU)
(1)
27r/ = kV,
(2)
3

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LEAK	B
S~
¦x 	*4**— x —*4*—x —~I
AL	^	BL " BC n
	 X,
AB
FIG. 2 - Three-sensor approach to acoustic location of leaks.
where k is the wavenumber and V is the propagation speed, the differential separation
between two sensors, Ax, and the frequency-dependent phase, are simply related
by
m = 2(3)
Through the use of coherence function analysis, it is possible to isolate portions of the
acoustic spectrum within which the linear dispersion relation is obeyed. The measured
phase shift, 4>{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 confined to the range —180° < 4> < 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 72(f) is
high; thus, a differential form of Eq. (3) must be used to relate sensor separation,
propagation speed, and coherence phase:
d 27rAx
df = V '
(4)
in which it is assumed that the medium is nondispersive.
The three-sensor approach illustrated in Figure 2 is used to locate leaks in an
underground pipeline. 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. Because the wave
speed associated with a particular product and pipeline geometry is usually unknown,
an experimental estimate of the wave speed improves the accuracy of the leak location
estimate.
Application of Eq. (4) to sensor pair A-B, which bracket the leak, yields a simple
relationship between measured phase, wave speed, and leak location:
vr	Xab V dAB
Xal = ~r ~ Ti~dT	(5)
Vr	XAB , V dAB
Xbl = ~r+	(6)
where the subscript L denotes the location of the leak. The wave speed is estimated
from the measured phase between sensor pair B-C:
v = 2 tXbc(^)-\	(7)
The one-standard-deviation uncertainty in the location estimate, ct(XAl), associated
with an ensemble of measurements {XAl} obtained through application of Eqs.(5) and
'4

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(7) is related to the uncertainty in the derivative of the measured coherence phase and
the sensor geometry by:
/df\ V
XAL represent ensemble average values of the propagation speed and leak location,
respectively. Two important observations should be made regarding Eq. (8): (1) errors
in the measurement of d/df translate directly into errors in location estimate, and (2)
the magnitude of the predicted location error is affected by both the overall sensor
geometry and by the position of the leak relative to the bracketing sensor-pair. For a
given uncertainty in the phase-derivative, /df is calculated by
applying a linear regression to n data points, {<£;, /<}, contained within a frequency
band A/, 
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LEAK APERTURE (0.3-0.8 mm)
0.3 m
LEAK SIMULATOR
PRESSURIZED CO,
GASOLINE
0.35 m » ¦ —VALVE
A
C
i
15 m
8 m
FIG. 3 - Diagram of the pressurized petroleum pipeline at the UST Test Apparatus. Pressurized
CO2 is used to generate static line pressure. A cross section of the leak simulator is also shown.
static line pressure and the diameter of the aperture through which the product was
allowed to leak. Leak apertures between 0.4 and 0.7 mm 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 pipeline. The range of flow rates generated during
the experiments was between 2 and 20 L/h (0.5 and 5.0 gal/h). The backfill materials
used in the experiments were fine-grain sand and pea gravel.
Three types of acoustic measurements (calibration, leak-on, and leak-off) were
performed 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 1.7 s in duration were recorded at one-minute intervals. The
leak-on measurements were bracketed by a pair of recordings obtained under leak-off
conditions.
DATA
The raw data consist of time series of acoustic leak signals and ambient noise
sampled simultaneously by three sensors. The first step toward 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/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 something of the character of the leak 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
frequency, 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
6
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B v*
LEAK OFF
1
ni'iln-;i'i'M!i,rij''
r f I rlfr

50.0
150.0
100.0
TIME (mS)
FIG. 4 - Time series of acoustic leak signals generated by a 11.4 L/h leak. Sample rate is 10
kHz. A no-leak time series recorded by sensor B is shown for reference.
domain (i.e., power spectra and complex coherence).
Time series of acoustic leak signals generated by a 11.4-L/h (3.0-gal/h) gasoline
leak into a sand backfill are shown in Figure 4; 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 presented here
represent unfiltered data. Due to the low level of ambient acoustic noise associated with
the underground pipeline, the fluctuations observed in the leak-off time series of Figure
4 are determined largely by electronic noise within the amplifiers. The distance between
the simulated leak and sensors A and B is approximately 15 m; sensor C is located
approximately 23 m from the leak. The line pressure used in this experiment was 100
kPa (15 psi) and the hole diameter was 0.7-mm. Two important observations should be
made regarding the time series of Figure 4: (1) a comparison of the leak-on and leak-off
measurements clearly shows that the leak is detectable, and (2) the relative arrival time
of the leak signal 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 location of the leak, can be estimated.
The strength of the acoustic signal produced by a leak in a buried pipeline is
proportional to the flow rate, for a hole of a given diameter. Estimates of the
signal-to-noise ratio (SNR) for pipeline leaks into a sand backfill at flow rates of 11.4,
5.7, 3.8, and 1.9 L/h are shown in Figures 5a-d. The hole diameters and line pressures
used to establish the flow rates were 0.7 mm at 100 kPa (15 psi), 0.5 mm at 100 kPa
(15 psi), 0.4 mm at 100 kPa (15 psi), and 0.4 mm at 35 kPa (5 psi), respectively. The
1
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10
10
a: 2
2 10
C/D
a:
2
CO
10
10
10
10
10
10
10
M I I I i I |l 111 I I l I | III I i I l |IL I I I I I -
=- (A) 11.4 L/h
I 1 111 111 I	i i 11'in!	1 i mini	i inn"
9) 11 I
rrn—iiiim : .—|iniin i d
g- (C) 3.8 L/h
a 11 I i i pT
=- (B) 5.7 L/h
nil 11 I I I prim I I =
i ' i mill i i i Mini i i i mill i i i n"
Willi I
TH	llllli I
llllll I I ^
(D) 1.9 Uh

U_LUlJ	' ' 		 1 ""III	I I 11 "71 r ¦ ' mini	' ' ' "'"I 	'I	' "ii"
1	2	3
10 10 10
1	2	3
10 10 10
FREQUENCY (Hz)
FIG. S - Signal-to-noise ratio (SNR) for pipeline leaks at flow rates of 11.4 L/h (A), 5.7 L/h
(B), 3.8 L/h (C), and 1.9 L/h (D). Dashed line indicates SNR=1.
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 overlapping,
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 6a shows the coherence amplitude as a function of frequency for acoustic
leak signals received by sensors bracketing a 5.7-L/h leak. The sensor separation is 38
m. 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 f2 is not statistically
significant at all Fourier frequencies. Figure 6b shows the coherence amplitude for
acoustic leak signals received by sensors bracketing a leak through a 0.4-mm-diameter
hole pressurized to 35 kPa (5 psi); the flow rate is 1.9 L/h and the sensor separation is
8
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10
FREQUENCY (Hz)
FIG. 6 - Coherence amplitude as a function of frequency for acoustic signals generated by 5.7
L/h (A) and 1.9 L/h (B) leaks. Sensor separation is 38 m (A) and 30 m (B). Dashed lines
indicate 95% and 99% levels of statistical significance.
30 m. As the line pressure is reduced, the frequency band within which signal
similarity is maintained is narrowed considerably.
LOCATION RESULTS
Table 1 summarizes the results of leak location and wave speed estimates for flow
rates of 11.4, 5.7, and 3.8 L/h. Leak location estimates are reported as a difference
between the computed and actual location. 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), 3.6 cm (5.7 L/h), and
-11.6 cm (3.8 L/h). Standard deviations of the location estimates were 26.1 cm (11.4
L/h), 26.3 cm (5.7 L/h), and 39.1 cm (3.8 L/h). The mean propagation speed was 915
m/s with a standard deviation of 146 m/s.
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 coherence 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. (5) through
(7), using the known sensor positions and the computed regression slopes.
9
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o
o
UJ
UJ
cc
o
UJ
Q
to
o
m
X
0)
UJ
0)
<
X
0.
o
FIG. 7 - Unwrapped coherence phase between 2.0 and 2.5 kHz for sensor pairs A-B, A-C, and
B-C of Figure 3. Least-squares regression lines through actual data points are included. The
flow rate is 11.4 L/h.
TABLE 1— Leak location and propagation speed measurements.
Flow
Rate
D
P
Af1
Mean
Error
(AB)2
Std.
Dev.
(AB)2
Mean
Error
(AC)3
Std.
Dev.
(AC)3
V
av
4
nl
(L/h)
(mm)
(kPa)
(Hz)
(cm)
(cm)
(cm)
(cm)
(m/s)
(m/s)

11.4
0.7
140
2100-2400
8.6
16.4
-2.4
23.7
1048
37
25
11.4
0.7
140
3800-4050
18.7
29.9
14.2
31.8
917
89
18
5.7
0.5
140
2100-2400
14.4
15.8
15.8
14.9
930
136
23
5.7
0.5
140
3800-4050
I
1ft
00
19.8
-12.2
20.4
775
81
15
3.8
0.5
76
3800-4050
-2.5
47.9
-20.7
28.1
715
150
8
* Location algorithm analysis frequency band
2 A-B used as bracketing sensors
^ A-C used as bracketing sensors
Number of independent location estimates
B-C
A-C
A-B

2100	2200	2300	2400
FREQUENCY (Hz)
If the coherence amplitude is statistically significant for each Fourier component
within a given frequency band, a simple phase-unwrapping procedure can be applied to
the coherence phase. Figure 7 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. 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
10
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-5 0 5
TIME DELAY (mS)
FIG. 8 - 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 1.0 and 4.0
kHz (A) and 2.0 and 2.5 kHz (B) prior to computing p^. tbc and tCb represent predicted
time delays for primary and reflected acoustic waves propagating at V=1000 m/s.
the three sensor pairs at a given Fourier frequency. The regression slopes of Figure 7
can be used to calculate the time delays between signals received by the three sensor
pairs. The measured dtfrjdf 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, 5.8, 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 8a shows the normalized cross-correlation
coefficient as a function of lag time, />*y(r), between the time series B and C used in
Figure 7. The time series were bandpass filtered in order to isolate the high-SNR, 1.0-
to 4.0-kHz portion of the leak signal spectrum 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 8b 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 used to generate the phase curves of Figure 7, correlation analysis and
11
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coherence function analysis 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 frequency 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).
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 3).
Multi-mode wave propagation results from the excitation, by the leak flowfield, 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, experimental data
and simple simulations show that the effects of multi-path and multi-mode propagation
are detectable.
The reflective nature of the pipeline is illustrated by the cross-correlation plot
shown in Figure 8b. The primary peak, which occurs at the lag time r a 7 ms,
corresponds to signals propagating in the direction from sensor B to sensor C at speed
c a 1000 m/s. A secondary peak, which occurs at the lag time r a -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 flowfield: (1) transverse waves propagating in steel, (2)
longitudinal waves propagating in steel, and (3) longitudinal waves propagating within
the product contained in the pipeline. The nominal propagation speeds for each type of
wave motion are 6000 m/s (longitudinal, steel), 3000 m/s (transverse, steel), and 1200
m/s (longitudinal, gasoline). The similarity between the measured wave speed (a 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 longitudinal waves propagating in steel was investigated
through a calibration test in which an impulsive signal was generated by breaking a
pencil lead near the leak location. Figure 9 shows 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 6250 m/s for the leading edge of the impulse. This
speed is consistent with the nominal value of 6000 m/s for longitudinal waves
propagated within steel. While the calibration data do not indicate the degree to which
the longitudinal wave mode in steel is excited by the leak flowfield, it does show that
such waves, if emitted by the leak, will be detected by sensors mounted externally on
the pipeline wall.
The excitation of transverse waves by the leak flowfield, and their detectability,
were investigated through a series of experiments in which CO2, rather than gasoline.
12
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c
B
19.0
15.0
16.0
17.0
20.0
18.0
TIME (mS)
FIG. 9 - Time series of impulsive calibration signals recorded by sensors B and C. The
estimated propagation speed (6250 m/s) is consistent with the nominal speed of sound in steel.
was used as the product. Time series of acoustic leak signals produced by the flow of
C02 through a 0.7-mm-diameter hole under 100-kPa line pressure were recorded by the
three-element sensor array. Application of Eq. (7) to the phase plot corresponding to
sensor pair B-C yielded a propagation speed of approximately 2400 m/s. Two important
observations should be noted regarding this experiment: (1) the measured wave speed is
similar to the nominal value for freely propagating transverse waves in steel, and (2)
the measured wave speed is much higher than the speed of acoustic waves propagated
in C02(c~ 270 m/s). The SNR of the C02 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 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.
The effect of multi-path and multi-mode wave propagation can also be observed in
the coherence phase. Figure 10 shows a plot of the phase shift between sensors B and
C in which the linear trend has been removed. The residual phase shift is dominated by
a non-random, periodic oscillation that occurs at intervals of approximately 50 Hz 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
comparable to those observed in the data.
13
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o
Tf
B-C
ID
ID
LU
O
CM
O
o
c\i
111
o
Tf
2250
2150
2350
FREQUENCY (Hz)
FIG. 10 - 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.
PHASE UNWRAPPING
Accurate source location requires that the location algorithm distinguish between
useful information 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 1.0 to 4.0 kHz frequency band used in Figure 8a). While the location estimates
given in Table 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 width.
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 d^/df over a wide range of frequencies. Such unwrapping
algorithms are easily implemented, provided that the coherence phase is reliably
measured (i.e., that the coherence amplitude is high) at many frequencies 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 predicted phase shifts can be viewed over an arbitrarily wide
frequency band.
Figures 11 and 12 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 (f) lines (shown as solid lines in the figures). Reliable
phase measurements (indicated by markers in the plots) correspond to coherence
amplitudes that exceed the 95% level of statistical significance; the flow rates are 11.4
L/h (Figure 11) and 5.7 L/h (Figure 12). The frequency distribution of reliable phase
measurements for the 11.4-L/h data is such that all of the information contained in the
2.0- to 4.0-kHz band can be used in the location estimate if a straightforward
14
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	I	1111
2000	3000	4000
FREQUENCY (Hz)
FIG. 11 - 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.
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phase-unwrapping algorithm is implemented. As the flow rate is reduced, however, the
simple unwrapping algorithm works only within a small number of narrow frequency
bands (e.g., 2.2 to 2.5 kHz, and 3.7 to 4.0 kHz in Figure 12). The similarity 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.
CONCLUSIONS
4
Passive acoustic measurements, combined with advanced signal processing
techniques based on coherence analysis, offer a promising method for the location of
small leaks in the pressurized 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, 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
location algorithm and the instrumentation.
Experiments were conducted on a 2-in.-diameter underground pipeline at the UST
Test Apparatus in which three acoustic sensors separated by a maximum distance of 38
m were used to monitor signals produced by 11.4-, 5.7-, and 3.8-L/h gasoline leaks.
Application of a leak location algorithm based upon the technique of coherence
function analysis resulted in mean differences of approximately 10 cm between
predicted and actual leak locations. Standard deviations of the location estimates were
approximately 30 cm.
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. At a line pressure
of 140 kPa (20 psi) this resulted in a leak rate of 3.8 L/h (1 gal/h). Additional
experiments need to be performed with smaller holes and at higher line pressures (150
to 350 kPa) to determine the minimum leak rate that can be reliably located.
Spectra computed from leak-on and leak-off time 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. Energy propagation from leak to sensor was observed via three
forms of wave motion: longitudinal waves in the product, transverse waves in the steel,
and longitudinal waves in the steel. 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 fluctuations in the measured phase difference
between sensor pairs.
The SNR was observed to be generally high within the entire 1.0- to 4.0-kHz
frequency band; however, continuous regions of high coherence appropriate for source
location were typically 100 to 500 Hz in width. Several data sets recorded in the
presence of the 11.4-L/h leak exhibited high coherence over a 2-kHz bandwidth.
Location estimates obtained by means of cross-correlation showed that without the
detailed knowledge 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 1.0-
to 4.0-kHz analysis 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.
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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 passive 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 and preamplifiers used in these experiments was incapable of resolving the low
levels of ambient acoustic noise associated with the pipeline. Improved system
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.
ACKNOWLEDGEMENTS
This work was funded by the U.S. EPA under contract No. 68-03-3409. The
authors gratefully acknowledge CTI, Inc., for the loan of the acoustic sensing
equipment used in the experiments.
REFERENCES
[1]	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).
[2]	D.S. Kupperman and D.E. Karvelas, "Acoustic Leak Detection for District Heating
Systems," Technical Report No. ANL-87-60, Argonne National Laboratory,
Axgonne, Illinois (February 1988).
[3]	P.R. Roth, "Effective Measurements Using Digital Signal Analysis," IEEE
Spectrum, Vol. 8 (April 1971).
[4]	E.G. Eckert and J.W. Maresca, Jr.,"Location of Leaks in Pressurized Petroleum
Pipelines by Means of Passive-Acoustic Sensing Methods," EPA Contract
68-03-3409, Risk Reduction Engineering Laboratory, U.S. Environmental
Protection Agency, Edison, New Jersey (1991).
[5]	J.S. Bendat and A.G. Piersol, Engineering Applications of Correlation and
Spectral Analysis (New York: John Wiley & Sons, 1980).
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