Leak location in pipelines using transient reflection

by

Lee, P.J., Simpson, A.R., Lambert, M.F., Vítkovský, J.P. and Misiunas, D.

Australian Journal of Water Resources

Citation: Lee, P.J., Simpson, A.R., Lambert, M.F., Vítkovský, J.P. and Misiunas, D. (2007). “Leak location in pipelines using transient reflection.” Australian Journal of Water Resources, Vol. 11, No. 1, pp. 53-66.

For further information about this paper please email Angus Simpson at angus.simpson@adelaide.edu.au

Leak location in single pipelines using transient reflections

PJ Lee Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand

MF Lambert and AR Simpson

School of Civil and Environmental Engineering, University of Adelaide, Adelaide, Australia

JP Vitkovský Water Assessment Group, Queensland Department of Natural Resources and Water, Indooroopilly

D Misiunas

Department of Industrial Electrical Engineering and Automation, Lund University, Lund, Sweden SUMMARY: The use of controlled, small amplitude transient (water hammer) signals for the detection of leaks in pipeline systems is a promising area of research. A pressure transient travels along the system at high speed and is modified by the system during its travel. Leaks within a pipeline partially reflect these pressure signals and allow for the accurate location of a leak by tracing the reflection to its source – a technique commonly known as time domain reflectometry. This paper discusses and provides possible solutions to a number of practical issues associated with leak detection methods of this type, including the impact of the system configuration and methods for detecting leak reflected signals within a transient trace. A set of equations has been derived to locate leaks in a pipeline for all locations of the transient source and measurement stations, and is essential for an automated monitoring system that uses more than one simultaneous measurement of the transient signal. A change detection algorithm is used in this paper to provide an automated approach for detecting leak reflections, which can reduce the ambiguity associated with simple visual inspection of the transient trace. This procedure was validated by both operational and offline (pipeline shutdown) experimental tests conducted at the University of Adelaide. NOTATION AL = leak area AV = valve orifice area Cd = leak orifice discharge coefficient L = length of pipeline T = fundamental period of the pipeline To = disturbance occurrence time after the generation of transient TT = disturbance occurrence time after the start of period a = wave speed gt

1, gt2 = positive and negative cumulative sum at time t

h = head st

1, st2 = positive and negative residual error at time t

t = time ! = level of random fluctuation within the transient trace ∆H = magnitude of the residual at the time when the CUSUM alarm is triggered ∆HRmax = maximum residual induced by the reflected signal 1 INTRODUCTION Leak detection techniques that use fluid transients are becoming increasingly popular. Approaches to leak detection in pipelines are numerous and include inverse transient methods that match a modeled transient trace to experimental data (Liggett & Chen, 1994; Nash & Karney, 1999, Vitkovský et al, 1999; Vitkovský et al, 2001), a method that uses the damping rate of the transient trace (Wang et al, 2002), methods based on the analysis of the system response in the frequency domain (Ferrante et al, 2001; Lee et al, 2002, 2003, 2005a, 2005b), and methods that measure the time of arrival of partially reflected signals to determine leak location – also known as time-domain reflectometry (TDR) techniques (Jönsson & Larson 1992; Silva et al, 1996; Brunone, 1999; Covas & Ramos, 1999; Ferrante & Brunone, 2001; Vitkovský et al, 2003). Among the different families of transient leak detection techniques, the methods based on TDR are attractive due to their simplicity in application and analysis. Development of leak detection procedures has thus far concentrated on numerical studies, with limited research on overcoming the difficulties that are encountered in a field application. The reluctance to address these

issues has limited the applicability of the technology in the industry. This paper identifies three problems that can arise with the field application of TDR techniques and provides possible solutions to these issues. TDR for fault detection has been used in structural and geotechnical applications and is similar to the concepts behind the use of electromagnetic waves in radar, or the use of geoseismic shockwaves in geosurveys. In all these cases, a signal is sent out from a source with the aim of detecting objects or abnormalities in the area. The arrival times of reflected signals indicate the position of objects located away from the source. In a pipeline, the transient wave will travel back and forth along the pipe, reflecting off system boundaries, generating an oscillation in head at locations within the system. The signal will travel past any object repeatedly, generating reflected signals at regular intervals. In the case of a transient wave in a pipeline, the signal and the leak-reflected signals could take multiple wave paths due to boundary reflections. A transient event in a pipeline is shown in figure 1. The figure illustrates the two different wave paths that the signal could have travelled to generate a leak reflected signal labelled (a) and (b). The time of arrival of the reflected signal can be associated with either one of these wave paths, each generating a different position of the leak if the wave path is not known. Note that the leak will also reduce the magnitude of the transmitted signal, but this effect alone cannot be used to locate the leak.

Figure 1: Operation mechanism of time-domain reflectometry in pipeline systems.

The procedure of TDR for leak detection is as follows:

• Generate a sharp disturbance within the system. This disturbance should be small in magnitude (5 m in head) to prevent damage to the pipeline. Such head variations are of a similar magnitude (but of a different shape) to those caused by normal flow fluctuations in the pipeline. These tests should be conducted during off-peak hours to minimise disruption to users and also to minimise background noise in the data. A standpipe to an existing connection (eg. a fire hydrant) may be used for this purpose, where a sudden release or closure of the flow through this pipe will generate the required transient.

• Detect and locate the possible leak reflected disturbance in the signal by comparing the obtained transient trace to numerically generated or historical leak-free trace of the system under similar background flow conditions.

• Using the observed wave speed, determine the position of the leak within the pipeline from the time of arrival of the leak-reflected signals at the measurement positions.

While conceptually simple, the application of the TDR techniques for leak detection involves a number of practical complications. This paper discusses the following issues:

• Automatic detection of leak reflected signals. • Impact of the measurement and transient generation positions. • Sensitivity to the wave speed measurement.

2 DETECTABILITY OF REFLECTED SIGNALS TDR requires the detection of leak reflected disturbances within the transient trace. Previous publications have used visual inspection of the transient trace for detecting these reflections. For real pipeline systems, disturbances from non-leak related sources (such as pipeline vibrations), reflections from minor losses and reflections from existing hydraulic elements (such as sharp bends), can create traces where the existence of leak reflected signals cannot be easily verified. An automated procedure can remove some of the uncertainty often associated with visual inspection and moves towards the development of a

real-time monitoring system. In this paper, the leak reflected signals are detected by a change detection algorithm between the measured experimental transient trace and numerical (intact pipe) result derived from the method of characteristics. It is necessary to know the nominal response of the system to a transient event such that leak-reflected signals within the pressure signal can be identified. Such a nominal response can be produced numerically using a model of the system. Alternatively, if the transient event can be controlled and made repeatable using electronic valves with a fixed closure pattern, then valid comparisons of the measured transient behaviour before and after leak occurrence can be made. The occurrence of a leak reflected disturbance within the trace can be determined from the detection of any significant and prolonged deviation of the transient behaviour from the model predicted results. The cumulative sum algorithm (CUSUM) is selected as the change detection algorithm due to its speed and ability to detect changes and is widely used in online monitoring of chemical processes (Basseville et al, 1993). The two-sided CUSUM algorithm requires the determination of the positive and negative discrepancies, st

1, st2, between the data and the modelled benchmark. These discrepancies are defined

as:

!!! = ℎ! ! − ℎ! !

!!! = ℎ! ! − ℎ! ! where hE and hM are the observed and modelled head response at time t. Real data will be contaminated by background noise and an expected variance level, !, is required to set the magnitude of the norminal discrepancy between the experimental and the expected responses. Any discrepancies below this magnitude will be ignored. Discrepancies higher than this value are added to the cumulative sums, gt

1, gt

2.

!!! = max   !!!!! + !!! − !, 0

!!! = max   !!!!! + !!! − !, 0 where gt

1, gt2 = positive and negative cumulative sum of discrepancies between the experimental result

and the expected response at time t. A change is detected when the value of gt

1 or gt2 builds up to a preset tolerance (alarm) level, in which

case, the change time is recorded and the alarm triggered. The alarm will remain on until the sign of the residual no longer contributes positively to the magnitude of the cumulative sums. The cumulative sums are reset to zero when the alarm is switched off. The value of ! and the tolerance level have significant impacts on the accuracy of the CUSUM procedure. For the greatest change detection accuracy, the value of the expected variance should be determined directly from the measured trace, accounting for the background electrical and mechanical noise within the system. Before the application of the leak-detection procedure, the minimum size of a leak that can be detected using the input transient must be determined in-situ by placing artificial leaks of different sizes on the pipe. The smallest leak-reflected signal that can be observed is set as the tolerance (alarm) level, with as half the size of this value (Basseville et al, 1993). This value marks the lower limit of the leak-detection sensitivity in this system. 3 IMPACT OF SYSTEM CONFIGURATION ON TDR LEAK DETECTION TECHNIQUES In the case of a simple pipeline system, with the transient generation point and the measuring transducer both located at the same position, the distance of the leak from the measurement point is given by:

!!"#$ =!!!2

where DLeak is the distance of the leak from the transducer, a is the wave speed and T0 is the occurrence time of the disturbance, measured from the start of any oscillation period to the position of the leak induced disturbance. The application of equation (5) has been central to TDR leak detection methodology in the past and has shown success in situations where both the transient generation and

(1)  

(2)  

(3)  

(4)  

(5)  

measurement of the pressure response occurs at the same system boundary (Jönsson & Larson, 1992; Brunone, 1999; Covas & Ramos, 1999; Ferrante & Brunone, 2001). It is not, however, always possible to have the transient source and measurement point both located at this optimum position. While most single pipeline systems have flow controlling devices at boundaries that can be adapted for transient generation, the use of fast-acting side discharge valves for transient generation often requires the use of access points that may not coincide with system boundaries. In such situations, equation (5) no longer applies. A set of mathematical equations describing the relationship between the arrival time of the leak reflected wave-front and the location of the leak is determined to overcome this sensitivity to the system configuration. These equations allow the leak location to be determined in a pipeline regardless of the location of the transient source and measurement stations, which is essential for an automated monitoring system. The expansion of the conventional TDR procedure to cater for any configuration of the transient source and measurement station increases the scope of the technique, and also allows for the use of multiple measurement stations to give higher confidence in the detection result. The arrival time of the first reflected wave front is associated with all the possible paths over which the original and the reflected wave are expected to have travelled. This results in a set of possible leak locations for a given leak induced disturbance in the transient trace. For a measurement point and transient source located within a single pipeline, a leak can be located in three zones, between a boundary and the measuring point, between a boundary and the transient source and between the transient source and the measuring transducer. The approach is illustrated with the pipeline configuration shown in figure 2, with the leak between the transient generation point and the pressure transducer. The list of known distances in figure 2 are X, (L-X-Y-Z) and L. Figures 3 and 4 (which, for the purpose of nomenclature, shall be called mechanisms #1 and #2) are the sequences of events that can lead to the formation of the leak disturbance at the measurement point for this pipeline configuration. In figure 3 (mechanism #1), the total time of travel since the generation of the transient (TT) for a disturbance to appear in the transient trace measured by the transducer (hence the time between generation of the transient and the arrival of the leak reflected wave at the transducer) is given by summation of the total distance travelled along paths ([A1, A2, A3], [A4, A5], A7) divided by the wave speed:

!! =!!+3!!+2(! − ! − ! − !)

!

The time of commencement of the transient event, as measured by the transducer, occurs only after a time lag of (Y+Z)/a following the generation of the transient (paths [A1, A2]). The time of occurrence of the leak reflected signal, TO, measured from the start of the transient trace for mechanism #1 is therefore:

!! =!!+3!!+2(! − ! − ! − !)

!−(! + !)

!

which simplifies to

!! =2!!−2!!−2!!

Now, considering figure 4 for mechanism #2, the total time of travel along paths ([B1], [B3, B4], [B5, B6, B7]) is given by:

!! =3!!+2!!+!!

and the time of disturbance after subtraction of the time lag of (Y+Z)/a is ([B1, B2])

!! =2!!+2!!

(6)  

(7)  

(8)  

(9)  

(10)  

Figure 2: Configuration of the system used for mathematical derivation of the relationship between

occurrence time and leakage location.

Figure 3: Mechanism #1 for generating a leak-induced disturbance in the transient trace measured at the

transducer.

Figure 4: Mechanism #2 for generating a leak-induced disturbance in the transient trace measured at the

transducer. Equations (8) and (10) describe the shortest occurrence time of a leak-reflected signal for a leak located between the measurement transducer and the transient source, and relates this time with the location of the leak within this zone. To fully cater for all cases, similar derivations need to be performed for all leaks located in other zones, with the aim of producing a conclusive set of equations that are able to detect leaks located anywhere within the simple pipeline. The details of these derivations follow the same procedure as previously shown and the results are presented in table 1. The results show that four possible locations of the leak are expected from each measured occurrence time from a single transducer depending on which arrangement from table 1 is present in the pipeline. It will be illustrated later in the paper that for a particular system configuration, some of these equations will yield clearly impossible results, reducing the number of possible leak positions. In addition, the use of multiple transducers can reduce the number of possible locations knowing that a solution common to all the transducer results would be the true location of the anomaly. Note that for the case where the measurement and transducer points are coincident, it is suggested that equation (5) be used to determine the distance of the leak away from the source/measurement point.

Table 1: Summary of the complete set of derived leak location equations (symmetric systems are considered to be identical).

Diagram of Configurations Equations

A ! =  −!!!2

+ ! − !

B ! =!!!2

− !

C ! =!!!2

D ! =!!!2

4 IMPACT OF THE WAVE SPEED APPROXIMATION Regardless of whether equation (6) or the results of table 1 are used to determine the location of the leak, the estimation of the wave speed is central to the accuracy of the leak location. A 5% error in the wave speed estimate will result in a predicted leak location that is 2.5% of the total pipeline length away from the true leak position. While the theoretical expressions in Wylie et al (1993) can be used to determine the wave speed based on pipeline material and structural restraints, the variability of system characteristics means that a more accurate measurement of the wave speed needs to be performed in-situ. Jönsson (2001) has calculated the observed wave speed by determining the period of the pipeline from the transient trace. Knowing the length of the pipeline and the boundary conditions, the wave speed can be determined from a = 4L/T for open/closed boundary conditions, and a = 2L/T for open/open boundary conditions, where T=the period of the transient oscillation and a boundary is defined as “open” when the impedance of the boundary is less than the impedance of the pipe (Wylie et al, 1993). Ferrante & Brunone (2001) proposed a similar method of wave speed determination using the location of the resonance peaks in the frequency response diagram and is mathematically identical to that proposed by Jönsson (2001). 5 LABORATORY CONFIGURATION The TDR approach for leak detection was tested on the laboratory system at the University of Adelaide. The schematic of the pipeline is in figure 5. The apparatus comprises a straight 37.53 m copper pipe, 22 mm internal diameter and 1.6 mm wall thickness. The pipe slope is constant throughout with a vertical to horizontal ratio of approximately 1:18.5 and a roughness height of 1.5 x 10-6 m. The pipe connects two electronically regulated pressure tanks with inline ball valves located at the boundaries. There is an elevation difference of 2 m between the two ends of the pipe. Brass blocks with Druck PDCR 810 flush-fitted pressure transducers are located at five locations along the pipe. The pressure transducers have a rise time of 5 x 10-6 s. The data acquisition card has a maximum sampling rate of 100 kHz and the pressures are sampled at a frequency of 2000 Hz. To simulate leaks within the system, side-discharge orifices of varying diameter are connected with manual ball valves. Figure 6 shows the transient trace within the leak-free single pipeline system at the University of Adelaide generated by the closure of the solenoid valve next to an open reservoir boundary. This system configuration allows the generation of sharp pulses within the transient trace whose peak can be used as a clear indicator of the signal location, increasing the accuracy of the wave speed determination. For all

the measurement positions, a 113 ms period was observed in traces, which corresponds to a wave speed of 1328 ms-1, given that the downstream boundary is closed and the total length of the pipe is 37.53 m.

Figure 5: Schematic of laboratory system at the University of Adelaide.

Figure 6: Experimental determination of wave speed in experimental apparatus.

The magnitude of the smallest detectable leak reflection in the laboratory system at the University of Adelaide is 3.5% of the magnitude of the incident transient signal and is set as the threshold for the CUSUM detection procedure. The expected variance of the signal is half the size of this threshold. 6 EXPERIMENTAL VALIDATION OF TECHNIQUE The experimental validation of the above TDR leak detection procedure has been undertaken at the University of Adelaide for two operational situations, a flowing and a static test. In the flowing test, both boundaries are open with a constant base flow through the system, simulating real pipeline operation conditions. For the static test, the downstream valve is closed and the system is at rest. For each test, the transient traces from two measurement transducers on the pipeline are compared to the model predicted results for the system if no leak exists. The discrepancies from this comparison are inputs into the CUSUM algorithm. Predicted leak positions that are common to both measurement stations are accepted as true leak location within the pipeline. 6.1 Flowing test The flowing test was conducted with the boundary heads at 49.2 and 39.64 m, with fully opened valves giving an initial flow with a Reynolds number of 26,200. The transient was generated by the closure of an initially open, side discharge brass solenoid valve located 18.82 m downstream of the supply reservoir. The lumped CdAV parameter for the valve at the steady state head is 1.7 x 10-6 m2. Note that this parameter is the coefficient of the orifice equation,

! = !!!! 2!∆!

which relates the flow through the valve, Q, given a head difference across the valve of ∆H. A leak is located at 30.83 m downstream from the supply tank of a size that is 0.465% of the area of the pipe (orifice diameter of 1.5 mm). The transient was measured by two transducers, one located at the transient source, the other at 0.345 m upstream of the downstream tank. The measured transient trace, model prediction, residual and alarm status for each measurement station are shown in figures 7 and 8. The change detection alarm status from the CUSUM algorithm using the above value of variance is also plotted on these figures, where “1” represents the activated status. The point where the alarm was first activated is stored, and the arrival times of disturbances are 0.02 and 0.012 s for figures 7 and 8, respectively. Using Equation (4) for the results of figure 7, the leak was located at 13.28 m away from the transient source, which is either 5.54 or 32.10 m downstream from the supply tank (with the true position at 30.83 m). Using equation A in table 1 with the arrival time of 0.012 s for the trace of figure 8, gives the leak position at 29.56 m from the upstream boundary. For this situation, equations B, C and D in table 1 yield results that are either negative, outside the physical boundaries of the system, or inconsistent with the configuration for which the equations were derived.

Figure 7: Transient trace measured at measuring station located 18.82 m from upstream reservoir for

flowing test.

Figure 8: Transient trace measured at measuring station located 0.345 from downstream reservoir for

flowing test.

The three possible leak locations from the CUSUM analysis are therefore 5.54 and 32.10 m for figure 7, or 29.56 m from the upstream boundary for figure 8. As the true leak position must be consistent with the results observed from both transducers, the leak location of 5.54 m is discarded. When comparing the predicted leak locations with the true value of 30.83 m, it appears that both values deviate from the correct solution, with results that indicate a leak location that is further away from the transducer than reality. The apparent inaccuracy is a result of the following three uncertainties in the measurement of the arrival time of the leak reflected signals:

• Time lag in the determination of the exact arrival time – this is an intrinsic source of error for the technique. Transient signals with gradual rising slopes will create reflections with arrival times that are difficult to ascertain. This error can be reduced with multiple sampling stations, or the use transient signals that have a sharp and definable maximum (eg. a pulse).

• Discrete sampling – the point where the threshold is exceeded may also be affected by the sampling frequency, where the maximum time lag error that can occur is one sampling period, corresponding to a wave travel distance of 0.664 m.

• Error in wave speed approximation – as mentioned previously, errors in the estimation of the wave speed can also incur errors on the final leak location.

The final solution for the leak position for this flowing test was given by the average of the two results, and is equal to 30.83 m from the upstream boundary with minimal error from the true solution. 6.2 Static test The static test is conducted with the upstream reservoir set at a head of 39.6 m and the downstream valve, located 0.08 m from the closed downstream boundary. The transient is generated by the closure of the initially open brass side discharge solenoid valve located at 37.285 m from the upstream boundary. Two transducers are used to measure the transient, one located 18.705 m and the other 28.06 m from the upstream boundary. For this head condition, the lumped CdAV parameter of the solenoid valve is 1.8 x 10-6 m2. A leak is located at 6.70 m downstream from the supply tank, of a size that is 0.465% of the area of the pipe (orifice diameter = 1.5 mm). The CUSUM results for the transducer measured 18.71 and 28.06 m from the upstream boundary, are shown in figures 9 and 10. The predicted leak locations for the two measurement stations are 6.42 and 5.76 m from upstream boundary. The final predicted leak location is 6.09 m from the upstream boundary, and differs from the true leak position of 6.70 m by 0.60m.

Figure 9: Transient trace measured at measuring station located 18.705 m from upstream reservoir for

static test. The application of the proposed leak detection technique hinges on the ability of the system to be modelled numerically or a measured leak-free response exists. In a field situation, it is accepted that a significant level of variation can occur with the possibility of air pockets, blockage, partially closed valves and unknown friction factors. The application of the leak detection technique without a good knowledge of the behaviour of fluid transients within such systems may result in predictions that are low in confidence.

Figure 10: Transient trace measured at measuring station located 28.055 m from upstream reservoir for

static test. 7 CONCLUSIONS This paper illustrates the implementation of TDR techniques in a pipeline system for detecting reflected signals in a transient trace due to leaks and investigates the sensitivity of the technique to system configuration. A cumulative sum change detection algorithm is used as an automated procedure for detecting significant deviation of the experimental results from the method of characteristics model predictions. This automated approach reduces the ambiguity associated with visual inspection of the transient trace for detecting leak reflections and moves towards the development of a real-time monitoring system for pipelines. A set of equations has been determined to describe the relationship between the arrival time of the leak reflected signal with the location of the leaks within the pipe for different system configurations. Using these equations, multiple measuring points can be used in each test to remove spurious errors in the prediction. The technique has been tested under both flowing and static operating conditions. This investigation has also highlighted some of the shortcomings with the TDR method of problem detection within a single pipeline. The current method relies heavily on the sharpness of the input transient and an accurate numerical model for finding discrepancies from the trace from the expected response. In situations where the system geometry is complex (for example containing multiple pipes or appurtenances) the technique will still apply but the no-leak benchmark will be more complicated. In these cases, the numerical model will require prior knowledge of the system parameters, but could be replaced with real field transient response data recorded soon after construction as a no-leak benchmark. ACKNOWLEDGEMENT The authors would like to acknowledge the detailed and helpful review of the paper by one of the anonymous reviewers. REFERENCES

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