MONITORING GAS DISTRIBUTION PIPELINES

MONITORING GAS DISTRIBUTION

PIPELINES

A thesis submitted to the University of Manchester

for the degree of Doctor of Philosophy

in the Faculty of Science and Engineering

2017

Linan Tao

School of Electrical and Electronic Engineering

Contents

List of Figures 10

Abstract 16

Declaration 17

Copyright Statement 18

Publications 19

Acknowledgments 20

Glossary 23

1 Introduction 29

1.1 General introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

1.2 Introduction to APR technique . . . . . . . . . . . . . . . . . . . . . . 30

1.3 Aims, objectives and contributions . . . . . . . . . . . . . . . . . . . . 31

1.3.1 Thesis aims and objectives . . . . . . . . . . . . . . . . . . . . . 31

1.3.2 Thesis contributions . . . . . . . . . . . . . . . . . . . . . . . . 32

2

1.4 Layout of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

1.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2 Defects Detection in the Pipeline System 39

2.1 Defects in the pipeline system . . . . . . . . . . . . . . . . . . . . . . . 39

2.2 Defect detection methods . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.2.1 CCTV method . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

2.2.2 Cross-correlation method . . . . . . . . . . . . . . . . . . . . . . 43

2.2.3 Pressure transients method . . . . . . . . . . . . . . . . . . . . 45

2.2.4 APR based detection method . . . . . . . . . . . . . . . . . . . 46

2.2.5 Comparison among different detection methods . . . . . . . . . 48

2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3 Literature Review 50

3.1 Uses of APR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.1.1 Seismic surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.1.2 Medical application . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.1.3 Musical instrument bore reconstruction . . . . . . . . . . . . . . 54

3.1.4 Detection of features and defects in pipelines . . . . . . . . . . . 55

3.1.5 Detection of features and defects in small bore tuning . . . . . . 58

3.2 Reviews on approximation models . . . . . . . . . . . . . . . . . . . . . 59

3.2.1 Model equations . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3

3.2.2 Zwikker and Kosten approximation . . . . . . . . . . . . . . . . 60

3.2.3 Kirchhoff approximation . . . . . . . . . . . . . . . . . . . . . . 61

3.2.4 Keefe approximation . . . . . . . . . . . . . . . . . . . . . . . . 63

3.2.5 Comparisons among different approximation models . . . . . . . 67

3.3 Reviews on numerical simulation models . . . . . . . . . . . . . . . . . 68

3.3.1 Finite Difference Time Domain Model . . . . . . . . . . . . . . 68

3.3.2 Layer peeling Model . . . . . . . . . . . . . . . . . . . . . . . . 70

3.3.3 Summary of the two models . . . . . . . . . . . . . . . . . . . . 71

3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4 Attenuation of the Acoustic Wave 73

4.1 Related theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.1.1 Speed of sound . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.1.2 Boundary of plane wave . . . . . . . . . . . . . . . . . . . . . . 75

4.1.3 Window function comparison . . . . . . . . . . . . . . . . . . . 78

4.2 Experiments validation . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.2.1 Previous research results . . . . . . . . . . . . . . . . . . . . . . 82

4.2.2 Experimental apparatus . . . . . . . . . . . . . . . . . . . . . . 83

4.2.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

4.3 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

4.3.1 Different length tests . . . . . . . . . . . . . . . . . . . . . . . . 90

4.3.2 Different diameters tests . . . . . . . . . . . . . . . . . . . . . . 98

4

4.3.3 Different temperature tests . . . . . . . . . . . . . . . . . . . . . 98

4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

5 Feature/Defects Characterisation 102

5.1 Method for the detection of the defects . . . . . . . . . . . . . . . . . . 102

5.1.1 Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

5.1.2 Blockage and erosion . . . . . . . . . . . . . . . . . . . . . . . . 106

5.2 Experimental apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . 108

5.2.1 Holes detection . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.2.2 Erosion and blockage detection . . . . . . . . . . . . . . . . . . 111

5.3 Application to the real-world . . . . . . . . . . . . . . . . . . . . . . . . 113

5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

6 Pipe Simulators and Experimental Validation 117

6.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

6.2 The single pipeline simulator . . . . . . . . . . . . . . . . . . . . . . . . 119

6.2.1 Reflection and transmission coefficients . . . . . . . . . . . . . . 119

6.2.2 Digital waveguides . . . . . . . . . . . . . . . . . . . . . . . . . 121

6.2.3 The cylindrical model to build pipeline . . . . . . . . . . . . . . 122

6.2.4 Attenuation filter . . . . . . . . . . . . . . . . . . . . . . . . . . 125

6.3 The pipeline network simulator . . . . . . . . . . . . . . . . . . . . . . 127

6.3.1 Reflection and transmission coefficients at joints . . . . . . . . . 127

5

6.3.2 The network model . . . . . . . . . . . . . . . . . . . . . . . . . 130

6.3.3 Summary of the pipe simulators . . . . . . . . . . . . . . . . . . 132

6.4 Laboratory validation of the single pipeline simulator . . . . . . . . . . 133

6.4.1 Experimental setup for single pipeline simulator . . . . . . . . . 133

6.4.2 Results and analysis . . . . . . . . . . . . . . . . . . . . . . . . 134

6.4.3 Further demonstration of experimental tests . . . . . . . . . . . 136

6.5 Laboratory validation of the network pipeline simulator . . . . . . . . . 143

6.5.1 Experimental setup for the network pipeline simulator . . . . . 143

6.5.2 Reflection and transmission coefficients validation tests . . . . . 143

6.5.3 Results and analytics . . . . . . . . . . . . . . . . . . . . . . . . 144

6.5.4 Network Pipeline simulator validation tests . . . . . . . . . . . . 146

6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

7 Industrial Case Studies 154

7.1 A case study for an industrial pipeline - Case 1 . . . . . . . . . . . . . 154

7.1.1 Description of the test . . . . . . . . . . . . . . . . . . . . . . . 154

7.1.2 Results of the industrial testing . . . . . . . . . . . . . . . . . . 156






6

7.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

8 Discussions, Conclusions and Future Work 171

8.1 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

8.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

8.3 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

Bibliography 178

7

List of Tables

2.1 Comparison of Different Methods . . . . . . . . . . . . . . . . . . . . . 48

3.1 Review of Analytical Solutions to the Signal Propagation . . . . . . . . 68

4.1 Extrema: Bessel Functions of the First Kind . . . . . . . . . . . . . . . 76

4.2 Pipe Size vs Cut-frequency . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.3 Comparison Among Different Window Functions . . . . . . . . . . . . . 80

4.4 Details of the Test Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.1 Details of the Features in the Test . . . . . . . . . . . . . . . . . . . . . 109

5.2 Hole Size Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . 111

5.3 Hole Size Estimation Results (Short Pipes) . . . . . . . . . . . . . . . . 112

5.4 Erosion Size Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 113

5.5 Blockage Size Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 114

6.1 Test Rig Feature Table . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

6.2 Equipment Used in the Tests . . . . . . . . . . . . . . . . . . . . . . . 143

6.3 Peak Values at Each Location . . . . . . . . . . . . . . . . . . . . . . . 145

8

6.4 Errors Between the Simulation And Experiment Results . . . . . . . . 146

6.5 Locations That Caused Each Feature in Different Layouts . . . . . . . 149

7.1 Gas Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

7.2 Maximum Detected Distances When Pressure = 6.1 MPa And Temper-

ature = 8.9◦C, with the Distances Measured in Meter . . . . . . . . . . 159

7.3 Features in Layout of Trial Haylie Gardens . . . . . . . . . . . . . . . . 164

7.4 Features in Layout of Trial Newmains Rd, Renfrew . . . . . . . . . . . 166

7.5 Features in Layout of Trial Harburn Ave . . . . . . . . . . . . . . . . . 169

9

List of Figures

1.1 The Schematic Diagram of APR [5] . . . . . . . . . . . . . . . . . . . . 30

1.2 Response of a Straight Pipe . . . . . . . . . . . . . . . . . . . . . . . . 33

1.3 Response of a Pipe with Diameter Changes . . . . . . . . . . . . . . . 34

1.4 The Response of a Pipe with Cross-sectional Changes . . . . . . . . . . 35

1.5 The Response of a Pipe with a Blockage Defect . . . . . . . . . . . . . 36

1.6 The Comparison Between Simulated And Recorded Results . . . . . . . 36

2.1 Gas Hydrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

2.2 Schematic View of a Cleaning Pig . . . . . . . . . . . . . . . . . . . . . 41

2.3 A Diagram of the Optical Detection Method . . . . . . . . . . . . . . . 43

2.4 Setup for Cross-correlation Method . . . . . . . . . . . . . . . . . . . . 44

2.5 Diagram of Cross-correlation Method . . . . . . . . . . . . . . . . . . . 44

2.6 Acoustic Ranger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.1 Applications of APR History . . . . . . . . . . . . . . . . . . . . . . . . 51

3.2 Schematic Diagram for Medical Application . . . . . . . . . . . . . . . 53

3.3 Interleaved Grids of Pressure And Velocity . . . . . . . . . . . . . . . . 69

10

3.4 The Schematic Diagram of Setup . . . . . . . . . . . . . . . . . . . . . 70

4.1 Acoustic Modes in a Cylindrical Pipe . . . . . . . . . . . . . . . . . . . 76

4.2 Kichhoff Attenuation Restrictions . . . . . . . . . . . . . . . . . . . . . 79

4.3 Rectangular Window . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.4 Bartlett Window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4.5 Hamming Window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4.6 Hanning Window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.7 The Set up of the Experiment in the Lab . . . . . . . . . . . . . . . . . 85

4.8 Coiled Pipes for the Experiments . . . . . . . . . . . . . . . . . . . . . 86

4.9 Data Transmission Order of the Test System . . . . . . . . . . . . . . . 86

4.10 RMS Value and Peak Value . . . . . . . . . . . . . . . . . . . . . . . . 89

4.11 50 m Pipe Attenuation Results When D = 39.8 mm . . . . . . . . . . 91

4.12 Error Results When D = 39.8 mm . . . . . . . . . . . . . . . . . . . . . 91

4.13 Error Results of RMS Value . . . . . . . . . . . . . . . . . . . . . . . . 92

4.14 Attenuation Results When D = 25 mm . . . . . . . . . . . . . . . . . . 92

4.15 Error When D = 25 mm . . . . . . . . . . . . . . . . . . . . . . . . . . 93

4.16 Attenuation Results When D = 15.17 mm . . . . . . . . . . . . . . . . 93

4.17 Error When D = 15.17 mm . . . . . . . . . . . . . . . . . . . . . . . . 94

4.18 Attenuation Results When D = 39.8 mm . . . . . . . . . . . . . . . . . 94

4.19 Attenuation Results When D = 25 mm . . . . . . . . . . . . . . . . . . 95

4.20 Attenuation Results When D = 15.17 mm . . . . . . . . . . . . . . . . 95

11

4.21 175 m Pipe Recordings When D = 39.8 mm and f = 500 Hz . . . . . . 97

4.22 175 m Pipe Recordings When D = 39.8 mm and f = 1500 Hz . . . . . 97

4.23 Attenuation Results for Different Size of Pipes . . . . . . . . . . . . . . 98

4.24 Attenuation Changes When the Temperature Changes . . . . . . . . . 99

4.25 Temperature Gradient Model . . . . . . . . . . . . . . . . . . . . . . . 99

5.1 (a) Clean Pipe (b) A Hole Defect in the Pipe (c) An Erosion Defect in

the Pipe (d) A Blockage Defect in the Pipe . . . . . . . . . . . . . . . . 103

5.2 Test Rig . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

5.3 A Reflection Signal Caused by a Hole in the Pipeline . . . . . . . . . . 111

5.4 A Reflection Caused by a 300 mm Erosion in the Pipeline . . . . . . . 112

5.5 50 mm Blockage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

5.6 Illustrated Pipeline with a Feature . . . . . . . . . . . . . . . . . . . . 114

6.1 Layout of a Pipe Network . . . . . . . . . . . . . . . . . . . . . . . . . 118

6.2 The Response of the Pipe Network . . . . . . . . . . . . . . . . . . . . 118

6.3 Pressure Transmission in a Pipeline Unit . . . . . . . . . . . . . . . . . 119

6.4 Waveguide Filter Structure . . . . . . . . . . . . . . . . . . . . . . . . 121

6.5 Discretizing a Pipeline . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

6.6 Signal Propagating Along the Pipe . . . . . . . . . . . . . . . . . . . . 123

6.7 Space-time Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

6.8 Attenuation Comparison Between Kirchhoff’s And Keefe’s Equation . 125

6.9 Pipeline with Branches Discretization . . . . . . . . . . . . . . . . . . 128

12

6.10 A Generic Y-piece-branch . . . . . . . . . . . . . . . . . . . . . . . . . 128

6.11 A Generic Pipeline Network . . . . . . . . . . . . . . . . . . . . . . . . 131

6.12 Signals Change at the Junction . . . . . . . . . . . . . . . . . . . . . . 131

6.13 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

6.14 Attenuation Results for Pipe with ID = 39.8 mm . . . . . . . . . . . . 135

6.15 Error Between the Simulation And Experiment Results . . . . . . . . . 135

6.16 Layout of the Prototype Hardware . . . . . . . . . . . . . . . . . . . . 136

6.17 Diagram of the Prototype System Used for Testing Air Filled Pipes . . 137

6.18 Layout of the 50 mm Pipework Used in Laboratory Testing; L1, L2 and

L4 Represent Pipe Feature Locations While L3 And L5 Are Open Ends,

All Lengths Are in meters . . . . . . . . . . . . . . . . . . . . . . . . . 137

6.19 Comparison Results Between Simulation Results And Experimental Re-

sults in Test 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138


sults in Test 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

6.21 Comparison Results between Simulation Results And Experimental Re-

sults in Test 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140


sults in Test 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140


sults in Test 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141


sults in Test 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

6.25 Pipe Layout A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

13

6.26 Pipe Layout B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

6.27 Layouts of the Pipe Network Setup . . . . . . . . . . . . . . . . . . . . 146

6.28 Comparison Between Simulation And Experiment Results for Layout (a)148

6.29 Comparison Between Simulation And Experiment Results for Layout (b)148

6.30 Comparison Between Simulation And Experiment Results for Layout (c) 149

6.31 Comparison Between the Simulation And Experiment Results for a

Three-branches Pipeline . . . . . . . . . . . . . . . . . . . . . . . . . . 150

6.32 Layout of a Pipe Main Containing a Loop And a Branch . . . . . . . . 150

6.33 Comparison Between the Simulation And Experiment Results for the

Layout in Figure 6.32 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

6.34 Layout of a Pipe Main with 4 Branches . . . . . . . . . . . . . . . . . . 152

6.35 Comparison Between the Simulation and Experiment Results for the

Pipe Main with the Layout Depicted in Figure 6.34 . . . . . . . . . . . 152

6.36 Comparison Between the Simulation and Experiment Results When a

Partial Blockage Was Located in a Pipeline Branch, as per the Layout

in Figure 6.34 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

7.1 Raw Data with the First Distinguished Feature . . . . . . . . . . . . . 156

7.2 Recovered Input Excitation Signal . . . . . . . . . . . . . . . . . . . . 157

7.3 Reflection Signals from the Pipeline . . . . . . . . . . . . . . . . . . . 158

7.4 A 50% Blockage Interpreted by the Simulator . . . . . . . . . . . . . . 158

7.5 Reflection From the End of the Pipe . . . . . . . . . . . . . . . . . . . 159

7.6 Layout of the Testing at Alba . . . . . . . . . . . . . . . . . . . . . . . 161

14

7.7 Comparison Between the Simulation And Experiment Results . . . . . 161

7.8 Test Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

7.9 Layout of Trial Haylie Gardens . . . . . . . . . . . . . . . . . . . . . . 163

7.10 Impulse Response of Trial Haylie Gardens . . . . . . . . . . . . . . . . 164

7.11 Layout of Trial Newmains Rd . . . . . . . . . . . . . . . . . . . . . . . 165

7.12 Impulse Response of Trial Newmains Rd . . . . . . . . . . . . . . . . . 166

7.13 Layout of Trial Crocus Grove . . . . . . . . . . . . . . . . . . . . . . . 167

7.14 Impulse Response of Trial Crocus Grove . . . . . . . . . . . . . . . . . 168

7.15 Layout of Trial 31 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

7.16 Impulse Response of Trial 31 . . . . . . . . . . . . . . . . . . . . . . . . 170

15

AbstractPipelines are a vital tool for transporting materials, such as natural gas, oil, and water.However, in extreme circumstances, defects such as blockages and leakages can occur.To limit the economic loss and environmental consequences of such events, it is impor-tant that any defects can be detected and located at an early stage, preferably beforefailure occurs. Research at the University of Manchester has led to the development ofa tool that uses acoustic pulse reflectometry (APR) to locate and characterise defectsand features in tubes and pipes.

The work described in this thesis began with the modelling and validation of acousticattenuation in pipes. Previously published validation studies focused on short pipes(< 40 m) where high frequencies are dominant. The present work focuses on muchlonger pipelines where low frequencies play a much larger role. As such, comprehensivelaboratory experiments were conducted to measure the attenuation of acoustic signalsof varying frequencies in pipes with lengths of up to 200 m and inner diameters between15 mm and 39.8 mm. The results of these experiments showed that theoreticallyobtained attenuation functions fitted measured results to within 5%. This providedevidence to suggest that, in theory, APR could be applied to high-pressure gas pipelinesto detect full blockages with lengths of up to 100 km. This result was supported bythe successful application of the theory to a pipe with a distance exceeding 12 km.

A major weakness that restricts the deployment of APR technology is that even whenapplied to single pipes with only a few axial features, the results can be difficult tointerpret. To aid the interpretation of the recorded APR measurements, a numericalsimulator was developed, which was able to estimate the acoustic attenuation as ittravels inside a pipe. This simulator models the propagation of acoustic waves in acylindrical tube (waveguide) by considering the effects of both viscous and thermalattenuation, as well as changes in the internal cross section of the tube. The simulatordivides the tube into discrete cylindrical segments, each segment being characterised bya digital filter that defines transmission and attenuation. By comparing the expectedresults from the simulator with those obtained from the real system, defects, such aspartial blockages can be detected and located. The simulator’s ability to characterise arange of defects, such as different forms of blockage, holes and erosion was thoroughlyassessed utilising a number of pipes with lengths of up to 200 m and inner diameters of39.8 mm in the laboratory. These results showed that when there were no uncertaintiesin the pipe layout, the experimental and simulated results were consistent to withinapproximately 3%. As final validation of the simulator, it was applied to an industrialpipeline with a length of more than 12 km. The simulator was able to accuratelyestimate the attenuation of the acoustic signal in the pipe and was also able to locatea blockage within this pipe with an accuracy of less than 5 m.

The single pipe simulator was extended such that it was capable of modelling thebehaviour of acoustic signals in pipeline networks. This is important if APR is tobe applied to pipeline networks, such as those used for gas distribution. A networkmodel was used to build the pipe network simulator; the model considered time, axiallocation and branch number. To validate the accuracy of the pipe network simulator,a series of laboratory tests were conducted using different pipeline network layouts.Data collected from a series of field tests were also used to verify the accuracy of thepipe network simulator. These tests showed that the network simulator was able toaccurately detect and locate a number of features located within pipeline networks.The size of the pipes used in evaluating the simulator ranged from 50 mm to 200 mmwith lengths of 60 m to 400 m.

16

Declaration

No portion of the work referred to in the thesis has been submitted in support of an

application for another degree or qualification of this or any other university or other

institute of learning.

17

Copyright Statement

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third parties. Such Intellectual Property and Reproductions cannot and must not

be made available for use without the prior written permission of the owner(s) of

the relevant Intellectual Property and/or Reproductions.

iv. Further information on the conditions under which disclosure, publication and com-

mercialisation of this thesis, the Copyright and any Intellectual Property and/or

Reproductions described in it may take place is available in the University IP Policy

(see http://documents.manchester.ac.uk/DocuInfo.aspx?DocID=487), in any rele-

vant Thesis restriction declarations deposited in the University Library, The Univer-

sity Library’s regulations (see http://www.manchester.ac.uk/library/aboutus/regul-

ations) and in The University’s Policy on Presentation of Theses.

18

Publications

1). Tao, L., Groves, K., Lennox, B. and Gardner, R. Characterisation of defects in pipe

systems using a newly developed tubular acoustic reflection simulator, Proceedings

of the 26th Leuven Conference on Noise and Vibration, Leuven, Belgium, 15–17

Semptember, (2014).

2). Tao, L., Groves, K. and Lennox, B. The simulation of acoustic wave propagation

within networked pipe systems development and experimental validation, The 22nd

International Congress on Sound and Vibration, Florence, Italy, 12–16 July, (2015).

19

Acknowledgments

I would like to express my sincere appreciation to Professor Barry Lennox for his su-

pervision during the past four years. Without his supervision and help, I would not

complete the whole PhD research and thesis. He did not only offer me the help for

research, but also offer me advice regarding career development. I really enjoyed work-

ing and learning with him. Without the support and encouragement from Professor

Lennox, I would not be able to work and write my thesis at the 4th year. I cannot

say thanks enough to him. He is my real role model no matter in the research filed or

daily life. What I learned from him will inspire me for the rest of my life.

I also would like to appreciate the help from Dr Keir Groves. Dr Groves offered a

lot of advice and suggestions to the construction of the simulator theoretically and

experimentally. Thanks a lot to Richard Gardner for his help in the attenuation test.

Besides, I am glad to work with Omar Aldughayem in the team. Without his help for

the setup in some tests, I would not complete all the tests in time.

Sincere appreciation must go to all control system centre lectures/professors, especially

Dr Zhengtao Ding, who encouraged me a lot during the whole PhD learning process

as my co-supervisor.

All my thanks go to my fellow colleagues, who accompanied me during the past 4

years, especially Shuai Wang, Harun Tugal, Salvador Pacheco Gutierrez and Chunyan

Wang. Also many thanks go to my friends in UK, my colleagues at Continental in

Germany and my families and friends in China for their encouragement and support.

Deepest appreciation to the Vice-president at the University of Manchester, without

the financial support from the PDS Award, I would not be able to accomplish my

20

21

study in UK.

I am glad working and living in Manchester. All the memories at the University of

Manchester would be the best in my life. Thanks again for all the people who helped,

loved and encouraged me during the past four years.

To My Parents

22

Glossary

Chapter 2

Symbol Meaning Units

L distance from feature to optical system m

A illuminated area m2

t time s

x1(t) signal recorded by sensor 1

x2(t) signal recorded by sensor 2

ω angular frequency radians/s

X1(jω) Fourier transform of signal x1(t)

X2(jω) Fourier transform of signal x2(t)

ρ12 correlation coefficient

R11(t) auto-correlation of signal x1(t)

R22(t) auto-correlation of signal x2(t)

R12(t) correlation of signal x1(t) and x2(t)

τm time delay s

c speed of sound m/s

d distance m

23

24

Chapter 3



P (z, ω) acoustic pressure

V (z, ω) particle velocity

Z acoustic impedance

Y shunt admittance

a tube radius m

ν2 Prandtl number

η shear viscosity coefficient

rv, rt dimensionless parameter

ρ density kg/m3


s shear wave number

ρs mean density kg/m3

c0 =√γps/ρs undisturbed velocity of sound

µ absolute fluid viscosity

γ = Cp/Cv ratio of specific heats

Cp specific heat at constant pressure J/kg K

Cv specific heat at constant volume J/kg K

Γ = Γ′ + jΓ′′ propagation constant

Γ′ attenuation per unit distance in ξ direction

Γ′′ phase shift per unit distance in ξ direction

f frequency Hz

j =√−1 imaginary unit

Jn Bessel function of first kind of order n

k reduced frequency

n kind of polytropic constant

σ the square root of the Prandtl number

25

Chapter 3 (Continued ...)

ps mean pressure

s shear wave number

t time

µ shear viscosity N· s/m2

αc attenuation Neppers/m

Pr Prandtl number

κ thermal conductivity (W/m)K

α(ω) absorption coefficient

ϑp(ω) phase velocity

fs sampling frequency Hz

k(from (3.60)) time step s

h Position step m

p(z, t) pressure in time domain

v(z, t) velocity in time domain

S cross section are m2

26

Chapter 4



η shear viscosity coefficient

ρ density kg/m3


K coefficient stiffness

p gas pressure

R molar gas constant J·mol−1· K−1

T absolute temperature K

M mass of gas kg/mol

ϑ = T − 273.15 temperature ◦C

µ absolute fluid viscosity

γ = Cp/Cv ratio of specific heats

Cp specific heat at constant pressure J/kg K

Cv specific heat at constant volume J/kg K

m circumferential wave mode

n radial mode

kz wave number

Jn Bessel function of first kind of order n

j′mn the extrema of Jm

f frequency Hz

R ID m

δν viscous acoustic boundary layer m

αp attenuation in experiment dB/m

α attenuation in theory dB/m

p1, p2 pressure signals recorded by two microphones

l12 length between the two microphones m

27

Chapter 5


p0 amplitude of the reflected signal from end

p amplitude of the reflected signal

p1 amplitude of the input signal

D ID of tested pipe mm

a radius of the hole mm

λ wavelength mm

W pipe wall thickness mm

ρ density kg/m3


fc centre frequency Hz

L distance between the leak and the input m

L0 full length of the pipe m

α attenuation in theory dB/m

A cross section change mm2

l length of the defect mm

F function factor

pnoise noise level

M noise parameter

R diameter of pipe m

28

Chapter 6


pi sound pressure

Ui particle velocity

a pipe radius m


D pipe diameter m

f frequency Hz

fs sampling frequency Hz

k wave number

l segment length m

Z acoustic impedance

A amplitude of input signal

B amplitude of reflection signal

p+i,i(nT ) pressure of the forward input signal at the ith segment

p−i,i(nT ) pressure of the backward input signal at the ith segment

p+i,o(nT ) pressure of the forward output signal at the ith segment

p−i,o(nT ) pressure of the backward output signal at the ith segment

p+i (nT ) pressure of the forward signal at the ith pipe branch

p−i (nT ) pressure of the backward signal at the ith pipe branch

si cross-section area m2

ri,j reflection coefficient from segment i to j

ti,j transmission coefficient from segment i to j

ri reflection coefficient at ith pipe branch

ti transmission coefficient at ith pipe branch

T = lfs

one-way travel time s

xi(nT ) attenuation filter in ith segment

α attenuation coefficient dB/m

αp experimental attenuation coefficient dB/m

γ(ω) complex wavenumber

Chapter 1

Introduction

This chapter introduces the background and motivation for this research that was com-

pleted in the area of Acoustic Pulse Reflectometry (APR). The aims, objectives and

contributions of the thesis are introduced. A roadmap of methodologies is presented

at the end of this chapter.

1.1 General introduction

Pipeline systems are invaluable tools, for both delivering utilities and facilitating in-

dustrial processes, such as transporting heating or cooling fluids. However, they often

operate in harsh environments and as such they are frequently subject to defects such

as holes, blockages and corrosion. To avoid the economic loss and environmental conse-

quences that these defects can cause, it is important that any defects can be detected,

located and characterised at an early stage, preferably before failure occurs. To de-

tect defects in pipelines, University of Manchester researchers have been using APR

based technique for several years [1–4]. APR technique is now becoming an established

technique for identifying, locating and characterising defects and features in tubular

systems.

29

CHAPTER 1. INTRODUCTION 30

1.2 Introduction to APR technique

The APR technique is based on measuring the acoustic signal resulting from the re-

flection and transmission of an acoustic signal from the input as it propagates along

the length of a tubular pipe. A schematic diagram of APR is shown in Figure 1.1. A

typical APR probe comprises a loudspeaker, an amplifier, (a) microphone(s), a source

tube and a data acquisition system. In an APR application test, a pulse, containing

a broad range of frequencies, is used as the injected acoustic signal. The signal is

defined using a computer and then transmitted by a digital-to-analog (D/A) converter

and amplifier to a loud speaker. The amplified signal is injected into the gas inside

the pipe and the reflected signal is recorded using the microphone, which is inserted

into the source tube. The injected pulse travels along the gas within the pipe and is

partially reflected back towards the excitation source whenever it encounters a change

in cross sectional area, which may be caused by the usage of a valve and the existence

of a blockage or a branch for example. The first change in cross sectional area in the

object tube leads to a reflection. To distinguish this reflection from the input signal,

a source tube is used. The reflected signal is stored in the computer after being con-

verted to a digital signal using an analog-to-digital (A/D) converter. As the acoustic

signal travels at the speed of sound inside the pipe, features and defects within a tube

can be characterised and located by analysing the recorded reflected signal.

COMPUTER

D/A A/D

AMPLIFIER

MICROPHONE

LOUDSPEAKER SOURCE TUBE OBJECT

Figure 1.1: The Schematic Diagram of APR [5]


1.3 Aims, objectives and contributions

1.3.1 Thesis aims and objectives

APR technique has been used by a lot of researchers to find defects in pipelines. Pre-

vious work has shown the challenge of interpreting the acoustic response of a pipeline

system, because even for a simple pipeline setup, the response can be relatively com-

plex. The research presented in this thesis aimed to develop a simulator to help

interpret results obtained when APR is used to locate and monitor pipeline defects.

The designed simulator was to serve as a reference regarding which APR data could

be compared to ease the interpretation of the measurements. To build the simulator,

modelling the attenuation played an important role in this process. In the meanwhile,

the characterisation of reflections caused by different features could help estimate the

defects identified by the simulator quickly.

The objectives of this PhD research project were the following.

• To fully review the importance of using pipeline monitoring systems to detect

and locate any unexpected defects.

• To understand how acoustic signals are attenuated in pipes and to identify which

theories have been developed to explain this.

• To use measurements obtained using APR to estimate the size of a defect de-

tected within a pipe or tube.

• To build a single pipe simulator to help interpret the results obtained using APR.

• To expand the single pipe simulator so that the acoustic response of a pipeline

network can be simulated.

• To validate and quantify the developed simulators using data from both labora-

tory experimental setups and industrial gas distribution pipeline systems.

• To determine the capability and limitations of using a simulator when applying

APR to real pipelines.


1.3.2 Thesis contributions

There has been a considerable amount of work investigating the attenuation of acoustic

signals in pipes and the use of APR as a tool for surveying such pipes. However, this

research has focused on relatively short lengths of small-bore pipes. For example, Lewis

provided experimental validation of the attenuation of acoustic signals in pipes with

lengths of 34.5 m and diameters of 50 mm [2]. Furthermore, work reported in [5–7]

demonstrated the successful use of APR in detecting holes in musical instruments.

APR is currently being considered as a tool for surveying the long lengths (tens or

even hundreds of kilometres) of offshore gas pipelines [4] and gas distribution networks

[8]. In contrast to the previous work, which has considered relatively short length of

pipes, this thesis mainly focuses on long and complex pipeline setups. The major

contributions of this study are presented below.

(1) Attenuation validation

The main target of the research is to build a pipeline simulator, how to describe the

attenuated signal is fundamental to build the simulator.

An example of the acoustic response measured from a straight length pipe is shown in

Figure 1.2. The acoustic signal is attenuated along the length of the pipe and is then

reflected by the closed end of the pipe. This reflected signal is subsequently attenuated

as it travels back to the loudspeaker and microphone. Hence the amplitude of the

reflected signal is less than that of the input signals. Attenuation theory, proposed by

Kirchoff [2, 9], is typically used to define acoustic attenuation in pipes. However, this

theory has only been validated over relatively short lengths of small-bore pipes. In

this study, Kirchoff’s theory was evaluated using a comprehensive set of experimental

tests with various lengths of pipe (75 m to 225 m) with diameters ranging from 15 mm

to 40 mm. Furthermore, the theory was evaluated using a broad range of frequencies

from 50 Hz to 2000 Hz and a variety of lengths of pipes from 50 m to 225 m. The

experimental work demonstrated that the theory matched the experimental results to

within approximately 5% in the frequency range of 50 Hz to 200 Hz, which is the main

frequency range of interest when APR is applied to long lengths of pipes.


Inp

ut

Res

po

nse

Time

(a) Pipe Layout

Input Impulse Reflected Impulse

(b) Recorded Response

Loudspeaker

Microphone

Pipe

Figure 1.2: Response of a Straight Pipe

(2) Feature detection and characterisation

The characterisation of features contained within an APR signature is fundamental to

determining the size of a defect within the pipe. For example, Figure 1.3 shows a pipe

containing a small reduction in diameter. The lower graph in Figure 1.3 shows the

response when APR is applied to this pipe. Two reflected features can be seen in the

APR response. The positive part of the first reflection is caused by the reduction in

pipe diameter and the negative part by the subsequent expansion of the pipe diameter.

The second reflection (end part in the plot) is caused by the end of pipe. Chapter 5

describes the work that was conducted using Morgan’s technique [10] to characterise

the size of defects based on the APR measurements. Compared to Morgan’s experi-

ments, a more thorough series of validation tests were performed on a group of pipes

with different sizes of features (e.g. hole, blockage, erosion) machined in the pipe.

The validation was in a more systematic method, which will offer a way to calculate

the size of features in the pipe. Experimental validations showed that the developed

techniques were able to provide accurate sizing of holes and other defects (such as the

length of a section of erosion). The size of the feature which can be detected by APR

is relevant to the length of the pipe and the Signal-to-Noise Ratio (SNR).


Inp

ut

Res

pon

se

(a) Pipe Layout

Microphone

Pipe

Input Impulse Reflected Impulse


Reflected features

Loudspeaker

Reduction

Time

Figure 1.3: Response of a Pipe with Diameter Changes

(3) Single pipe simulator

Based on the attenuation theory, how a signal is transmitted in a pipeline is modelled

by a pipe simulator.

A major goal for APR is for it to be used to detect and locate defects as they form

in pipes. For a pipe network, if the acoustic response of the pipe was measured and

recorded before and after the defect was formed, then the defect can be detected and

located by comparing the two responses. However, there are no procedures in place

for this type of test to be completed, nor are there any standards or expectations

of what information should be stored. Hence, when using APR to characterise a

defect, there will typically be no reference signal recorded prior to the defect forming.

Chapter 6 describes the development of a simulator that offers a means of estimating

the idealised response of a pipe for situations when no reference signature exists.

Although simulators have been developed before, the simulator in this thesis covers

a detection length of up to 12 km, which has never been applied by our researchers

before based on the author’s knowledge. The simulator can simulate the response of

a pipeline over any distance theoretically. However, the restriction for applications

lies in the SNR from the recorded signal. When the reflection signal from a defect


is under the level of the background noise, the simulation results will not help the

identification of the defect in the pipeline any more. Therefore, the application of

the APR for detecting defects along the pipeline is restricted to the SNR in the real

situation.

The pipes in Figures 1.2 and 1.3 can be characterised with relative ease as there are

very few reflections emanating from them. However, the system in Figure 1.4 is much

more challenging to survey because more reflections and re-reflections are produced

within the pipe. If a defect is present within the pipe, then as shown in Figure 1.5,

the reflected signal is so complex that it is difficult to detect it.

Inp

ut

Res

pon

se

Microphone

Pipe

Loudspeaker

(a) Pipe Layout

Input Impulse

Reflected Impulse


Reflected features

Time

Figure 1.4: The Response of a Pipe with Cross-sectional Changes

The benefit of the developed simulator is shown in Figure 1.6. In this figure the

response of the actual pipe is compared with that predicted by the simulator. A slight

difference between the two signals can be identified in Figure 1.6 and this difference is

the result of the defect, which can be readily detected with the use of the simulator.

In the research described in Chapter 5, both laboratory and industrial results were

used to determine the accuracy of the simulator. The industrial results validated the

accuracy and feasibility of the simulator when used to detect a blockage in a pipe with


a length of approximately 12 km and an inner diameter (ID) of 200 mm. Furthermore,

the single pipe simulator was used to predict the longest distance over which the APR

technique is likely to be capable of detecting defects in the presence of background

noise.

Microphone

Pipe

Loudspeaker

(a) Pipe Layout

Input Impulse

Reflected Impulse


Reflected features

Time

Inp

ut

Res

po

nse

Defect

Figure 1.5: The Response of a Pipe with a Blockage Defect

Time

Reference signal

Actual signal

Inp

ut

Res

po

nse

Figure 1.6: The Comparison Between Simulated And Recorded Results


(4) Network simulator

To expand the single pipe simulator so that a complex network can be modelled, a

network simulator is built.

Current work at the University of Manchester is exploring the use of APR to survey

pipeline networks. The acoustic signature of such networks is much more complicated

than for single lengths of pipe and to aid in the interpretation of APR signals, the

simulator was extended to provide estimates of the acoustic response of pipe networks.

The networked simulator used a network model to describe the complex connection

among different pipe branches, so that the pipeline network can be expressed in a

mathematical way. Experimental tests in the laboratory and using industrial mea-

surements were used to validate the accuracy of the simulator. The laboratory tests

consisted of a series of tests using pipe networks containing a single branch, multiple

branches, a loop, a loop with branches and a branch with a loop. Further evaluation

was performed using measurements collected from a number of on-site gas distribution

networks.

1.4 Layout of the thesis

There are seven chapters in this thesis. Following this introduction,

Chapter 2 reviews typical defects, such as holes, erosions and blockages, in the pipeline

and relevant detecting methods for respective defects.

Chapter 3 reviews APR and its applications discussed in the literature, identifies gaps

in research and explains where the research in this thesis fits in to existing technologies.

Some typical methods in this area are introduced and some promising methods are

detailed.

Chapter 4 introduces Kirchoff’s theoretical analysis of acoustic attenuation in pipes

and shows the results, which were obtained using experimental tests to determine the

accuracy of this theory. The validation tests were performed using a range of pipe


lengths with different internal diameters using a variety of frequencies. The chapter

compares the results of these tests with related facts published previously.

Chapter 5 characterises the defects (e.g. holes, blockages and erosion) in pipelines

based on equations proposed by Morgan [10]. The tests were performed on a set of

15 pipes with a range of features (e.g. holes, expansion and reduction of the pipe

diameters) in seamless tubes that were 5 m in length. The experiment results and

theoretical results were compared and the errors were analysed.

Chapter 6 describes the development of the single pipe simulator which approximates

the attenuation of acoustic signals along the length of a straight pipe and the pipe

network simulator which generates the response of a network system. The idealised

impulse response generated by the simulators were used to aid in the interpretation

of the recorded reflections by APR. The validation for the transmission and reflection

coefficients at T-pieces was discussed. A variety of laboratory tests were performed to

validate the simulator.

Chapter 7 presents the industrial cases as the application and validation the pipe

simulators introduced in Chapter 6. The industrial results were validated using the

designed simulators. All the industrial cases were used to determine the accuracy of

the simulators and to determine their capabilities.

Finally, Chapter 8 concludes this research and suggests future research directions.

1.5 Summary

Chapter 1 gave an overview about what motivated the author to conduct the research.

Because of the difficulty in interpreting APR data, it was essential that a simulator

was developed to aid the interpretation. Thesis contributions, objectives and aims

were also included in this chapter. Finally, a roadmap of each chapter was described.

Chapter 2

Defects Detection in the Pipeline

System

This chapter will describe some of the typical defects found in pipelines. Before moving

to the detailed introduction, a feature is defined as any anomaly in the pipe such as

joints, blockages, diameter change etc. and a defect is defined as a feature in the pipe

that should not be there or is undesired such as dents, blockages, holes, etc. The

effects of these defects are also introduced. There are many methods for detecting

defects in pipelines. Some typical detecting methods such as closed circuit television

(CCTV) and cross-correlation, are described in this chapter.

2.1 Defects in the pipeline system

According to the investigation conducted by Transportation Research Board (2004),

a pipeline is one of the safest ways to transport fluids [11]. However, the defects, i.e.

leakages, blockages, and erosion, exist along pipelines, which may lead to financial

losses, environmental damage and human injuries.

Leaks in the transport pipelines are causes for concern, as they may lead to severe

damages or accidents both environmentally and economically. In the worst case, the

pipe system could stop working because of the huge amount of leakage from the pipe.

39

CHAPTER 2. DEFECTS DETECTION IN THE PIPELINE SYSTEM 40

For example, billions of dollars have been spent on the water loss from the leakage

of pipelines according to the White Paper from the United States (US) [12]. In some

underwater situations, contamination resulting from foreign objects may cause outage

of the system leading to expensive damage.

Erosion may occur inside the pipeline after some time under conditions (eg. corrosion

of the metal material) even with proper maintenance. When erosion occurs over a

period of time, this could lead to pits formatting in the pipe, which can lead to

leakage. Furthermore, erosion may occur both inside and outside of metal pipelines.

Some of them may cause severe damage to the transportation of gas or liquids.

Blockage is another major problem in the pipeline system. Deep water environments

were developed to produce more oil and gas energy to fulfil energy demand. However,

the high pressure and cold surroundings could lead to the blockage of pipelines with the

formation of hydrate [13]. In the underwater natural gas pipeline system, gas hydrates

can form because of the low temperature and high pressure [14]. For example, hydrates

are formed when the gas molecules contact come in water at a pressure of over 600 kPa

and a temperature under 300 K. The gas hydrate is a solid form of water that contains

gas molecules, e.g. CH4, C2H6 and CO2.

Figure 2.1: Gas Hydrate

In Figure 2.1, it illustrates that a full gas hydrate was formed, which caused the full

blockage of the pipeline [3]. This caused severe problem as no flow would pass the

hydrate. If the hydrate can be identified before it is fully formed into a blockage,


possible actions can be taken such as injecting an inhibitor, to decrease or diminish

the hydrate [15].

Normally cleaning pigs are used to clean the internal surface of pipes to reduce ac-

cumulation of blockages. As shown in Figure 2.2 [16], a cleaning pig is a cylindrical

plug and the flat disk cup is attached to the pig body. The flat disk cup can either

be conical or cylindrical. The cleaning pig is inserted in the pipe and moved along

by flowing fluids [17]. The fluid flow pressure forces the pig to remove the deposits.

The bypass port is used to control the velocity of the pig and to avoid the deposits

accumulating downstream. However, the pig may become stuck in the pipeline under

some circumstances, which causes a blockage in the pipeline.

Flow

deposits

Pig

body

Flat disk cup

Spacer

(rigid)

Bypass port

Figure 2.2: Schematic View of a Cleaning Pig

2.2 Defect detection methods

Defects detection in pipelines is an active topic in the research and industry area.

According to one study by Kristiansen [18], reliability, sensitivity, accuracy and ro-

bustness are the four standard requirements for a detection system.

There are two categories of pipeline monitoring methods, the non-technical and tech-

nical detection methods.

• Non-technical methods

The non-technical methods are those that do not use any equipment and only

rely on people or animal normal senses, such as seeing, hearing and smelling [19].


In some complicated circumstances, this is unrealistic, for example when the

pipelines are under water or beneath a building; in these circumstances, it is dif-

ficult to use normal senses. Hence, it is necessary to develop technical detection

methods.

• Technical methods

The technical methods are those relying on detection devices and equipment or

monitoring changes of the pipeline parameters, such as pressure or flow rate.

2.2.1 CCTV method

For optical detection, CCTV was used to monitor the inside feature of the pipelines [20]

in 2002. The CCTV-based method used optical sensors inside the pipe to monitor the

inner wall conditions. However, there were two limitations to this method: the interior

of the pipe lacked visibility, and it was sometimes difficult to have enough lighting to

obtain images. Based on the CCTV idea to monitor the inside of the pipe, a new

laser-based inspection system was proposed to inspect the inner surface wall of a pipe.

The location of defects could be detected by analysing the intensity of the projected

laser generated ring [21]. Furthermore, the intensity-based optical system proposed

by Safizadeh et al. consisted of a light ring projector, a pre-calibrated charge coupled

device (CCD) camera and an optical diffuser that was used to expand the laser beam

into a light ring. The schematic diagram is shown in Figure 2.3.

Parameter L is the distance from the location of the surface under investigation to the

optical system and A is the illuminated area. Both of the parameters can be calculated

based on the pipe radius and the diffuser projection angles [21]. A surface map of the

inside pipe wall was generated by extracting the intensity information existed in the

pipe images. The laser light rings were projected onto the pipe wall and the light

signals were received by a CCD camera. The light intensity from the projected rings

helped to identify defects in the pipeline. When defects occurred, the intensity in the

image changed because of the scattered laser light.

However, the optically based technology was restricted by the length of the pipe as it


L A

CCD

Laser

diode

Pipe

Ring

of

light

PC

Figure 2.3: A Diagram of the Optical Detection Method

was difficult to install optical sensors along a long pipeline and the limited range of

the optical sensor was also a problem. The system was only used for a test in a pipe

182 m long with an ID of 0.152 m. Pipes with longer length have not been verified

yet. Another restriction was that the intensity of the projected laser ring may not be

strong enough for the inspection.

2.2.2 Cross-correlation method

The Cross-correlation method [22–24] was developed as a key way to locate leaks

along pipelines. Figure 2.4 shows a typical arrangement for leak detection in a buried

pipe. Two access points around the suspected leaking point were required to install

sensors: either listening rods or hydrophones. Two sensors were used to record the

vibration of acoustic signals. The noise correlator computed the cross-correlation of

the two transmitted signals from sensors and transmitted the results to the operator.

For example, two sensors were attached to each side of the leak with the distances

of d1 and d2. The assumption for the pipe length was infinite so that no reflecting

discontinuities could affect the fluid-borne wave.

The process for the cross-correlation function is shown in Figure 2.5. The two recorded

signals x1(t) and x2(t) from two sensors were transformed using the Fourier transform


d1 d2

d

Sensor

x1(t)

Sensor

x2(t)Leak

Figure 2.4: Setup for Cross-correlation Method

operator to X1(jω) and X2(jω) respectively. The expected correlation result R12 was

the inverse Fourier transform of X∗1 (jω)X2(jω) with ∗ denoting conjugation. Normally

the cross-correlation function is expressed in the normalised form with a scale from -1

to 1. Equation (2.1) defines the correlation coefficient ρ12, where R11(0) and R22(0)

are the results of auto-correlation R11(t) and R22(t) when t = 0. The way to calculate

the correlation R12 of two signals x1(t) and x2(t) was expressed in Figure 2.5

ρ12(τ)

=R12

(τ)√

R11

(0)R22

(0) (2.1)

Fourier

Transform

Fourier

Transform

Inverse

Fourier

Transform

Sensor

x1(t)

Sensor

x2(t)

X1(jω)

X2(jω)

X1*(jω)X2(jω)

R12( )

Sensors inputs Implementation of cross-correlation

Figure 2.5: Diagram of Cross-correlation Method

If there was a leak between the two sensors, a distinguished change could be identified

in the cross-correlation function. The time delay τm could be calculated based on

the difference in arrival time between each sensor and c is the speed of sound being

transmitted in the pipe. With the layout in Figure 2.4,

d2 − d1 = cτm (2.2)

d2 + d1 = d (2.3)


The leak position can be calculated by substituting (2.3) for (2.2) , which is found to

be

d1 =d− cτm

2. (2.4)

There were several limitations to the cross-correlation method.

• The access point of the test sensors was sometimes difficult to find. Not all of

the tested pipeline systems were equipped with many access points for external

devices.

• The prediction of the location of the suspected leak was difficult and could require

extra effort.

• The assumption for the cross-correlation method was that the lengths of the

tested pipe were infinite. However, in practice, there are no infinite pipe systems

available.

• The accuracy of locating the leak was not verified. This method was found to

be accurate within 0.3 m to 0.6 m (one to two feet) according to the American

Water Works Association [25].

2.2.3 Pressure transients method

The pressure transient method [26, 27] was used to detect the existence of blockage

in the pipeline using the interaction between transients and blockages. The transient

was initially produced using inlet flow variation. This was achieved by momentarily

altering the rate of fluid incursion into the pipeline which kept transient propagating

in the pipe. When the transient reached the blockage, some portion would be reflected

and propagated upstream. The characteristics of this reflected transient, which were

monitored at the pipe inlet, gave the profile of pipeline internals. The monitored

signal then became a window for observing the pipelines interior. Sorely it gave a

pressure measurement which could be analysed to determine this profile. Numerical

tests showed that pipeline blockages could be detected from the reflected transients

up to a distance of 1.6 km. However, the detection in real condition would be difficult


because the transient amplitude was only 0.0005% of the base pressure. When too

much fluid was suddenly transmitted to the pipe, the rise of such pressure could cause

the pipe to rupture within a short period of time [27].

2.2.4 APR based detection method

APR based detection method is a non-destructive method for pipeline detection. In the

late 1970s, the Central Electricity Generating Board developed an acoustic instrument

named the Acoustic Ranger that was used to monitor the blockage and leakage of a

tube filled with fluid. The Acoustic Ranger was applied to short length and small bore

pipes [10, 28].

As shown in Figure 2.6, Acoustic Ranger used the pulse echo technique, which was

the fundamental application of APR in pipeline detection.

Source

TubeSeals

Microphone

Test Tube

Signal Generation

Circuit

Amplifier

Filter

Display

Loudspeaker

Figure 2.6: Acoustic Ranger

The initial acoustic ranger equipment was large because of actual size of transmitters

and receivers in 1970s. The transmitter (e.g. loudspeaker) and receiver (e.g. micro-

phone) were connected to one end of the pipe and an acoustic signal was injected,

and any discontinuity, e.g. changes of the pipe’s internal diameter or a hole would

cause an echo (reflection) that would be measured by the receiver and displayed in

the recordings. Because the sound wave was transmitted through the gas (e.g. air or

methane) in the pipe, the location of the discontinuity could be calculated using the

speed of sound inside the pipe and the time recorded by the receiver (usually shown


in the oscilloscope at that time).

The input impulse was generated by discharging a capacitor in the circuit which was

operated manually or repeatedly. The input sound from the signal generation circuit

was amplified by the loudspeaker mounted on one end of the source tube, which was

used to connect to the test pipe and helped to separate the input signal and reflected

signal. The source tube was required to have the same internal diameter as the test

tube with a length of 3 m in operation [10] and to connect to the test tube with air

tight seals. The microphone was located close to the loudspeaker and worked as the

receiver of the equipment. The received signal was passed through the swept gain

amplifier and then filtered to remove noise that came from the high frequency. Finally

the filtered signal could be shown in the display unit.

Two versions of the Acoustic Ranger equipment were AR 100 and AR 1000, which

were in commercial production according to Morgan [10]. The AR 100 instrument

could only detect a range of 30 m of a tube with an internal diameter of 25 mm due

to the restriction of the design. The equipment was designed so that it could be used

by a lowly skilled operator.

Because of this limitation of the test range, AR 1000 was produced. The detection

range was extended to 300 m depending on the internal diameter in a range from 6

mm to 250 mm. Unlike the AR 100 with its own display, the AR 1000 could be used

to a separate oscilloscope so that the details of the recorded signal could be examined.

The AR 1000 was used on both conventional and nuclear power generation plants to

help detect blockages in pipeline systems. It was also used in the civil engineering

field to check the water level of sewers and the location of branch pipes. Another

application was to find the presence of debris in ducting pipes after completing a

bridge building project. As deposits of water inside the pipe could also cause the

reflected wave depending on the depth of the water, the Acoustic Ranger was also

used to identify the water level accumulated inside oil tankers, bore holes and coils.

By introducing the Acoustic Ranger, Morgan [10] also compared the response of a

clean pipe, which acted as a benchmark to the response of the dirty pipe so that


subtle changes in the response could be identified. However, the clean condition of

the detected system might not have been tested earlier and the reconstruction of the

same clean system would incur extra time and costs.

Papadopoulou et al. [1] demonstrated that APR can locate the defect of a 5 km pipe

with a 1 m diameter. For example, when a leakage occurs in the middle of the pipe,

the reflected signal shows a sudden spike compared to the standard one when the pipe

was in the condition without any defects. In this way, by comparing the differences

between the acoustic signal reflected from the change and the standard signal with no

damage at all, researchers have a new way to analyse the condition of the pipelines and

industries, and therefore to decrease the loss caused by damage in pipelines. APR-

based technology can be used to identify and localise the defects in time, even for a

distance of over 5 km. This technology overcomes the limitations of the noise cross-

correlation [29] which is restricted by the length of pipelines and the accessibility of

pipeline system.

2.2.5 Comparison among different detection methods

As stated above, Table 2.1 is a summary of different methods with theory and limita-

tions.

Table 2.1: Comparison of Different Methods

Method Verified detection length Location of sensorsCCTV [20,21] 182 m Tested pipe

Cross-correlation [22–24] 102.6 m Tested pipePressure transient [26, 27] 1.6 km Tested pipe

APR [1,10,28] Over 5 km Source tube

In the CCTV method, optical sensors are used to monitor the inner wall conditions of

a pipe. The location of defects is identified by analysing the intensity of the projected

laser ring. It is limited to the detection length of the pipe regardless of the difficulties

to install the optical sensors. The intensity of the light becomes weaker after 50 m.

The theory of cross-correlation method is that two sensors are installed around the

leak point to record the vibration or acoustic signals. The cross-correlation of the two


signals is computed so that the leak can be located. This method is restricted by

the prediction of the possible defect and sometimes it is almost impossible to install

the sensors close to the defects under extreme conditions, for example, deep down the

ocean or underground. In pressure transient method, the transient is produced using

inlet flow variation. The characteristics of this reflected transient show the profile

of pipeline internals. This is also restricted to the detection length as the transient

amplitude is only 0.0005% of the base pressure.

Overall, the primary restrictions among all aforementioned methods for defects detec-

tion include:

• Detection of the distance and size of the pipe;

• Accessibility of installation of the sensors.

APR overcomes both restrictions by offering a solution with longer detection length

and by installing the sensors at the source tube instead of on the tested pipes. All of

these make APR a particularly promising non-destructive approach that is worthy of

further investigation.

2.3 Summary

Chapter 2 listed defects along the pipeline and the potential impacts they may cause.

To identify the defects inside pipelines, a great deal of detection methods was proposed

in the literature. Four typical methods were introduced and their limitations were

listed. Overall, it was shown that APR was a useful and non-destructive tool for

pipeline detection.

Chapter 3

Literature Review

Since originally applied in seismic research by Ware and Aki [30] in 1969, APR has been

widely used in various applications, such as reconstruction of the bore profile of musical

instruments [5–7] and industrial pipelines [1–4]. In this chapter, the applications

of APR in different industrial areas are described. A short summary is shown in

Figure 3.1.

3.1 Uses of APR

APR technique is based on analysing the reflection signal from the acoustic impedance

changes inside the pipe medium. There are several use cases which apply the APR to

different applications. All the following applications are the illustrations for what APR

can do in the real life and show that APR can be applied in a variety of fields, including

the pipeline industry. Because of the success of APR used in different aspects, it is

promising to research on APR further and deeper.

3.1.1 Seismic surveys

Detection based on changes in acoustic impedance of a medium was originally applied

in seismic surveys, pioneered by Ware and Aki [30]. Although the term APR was

50

CHAPTER 3. LITERATURE REVIEW 51

Ware and Aki 1969

Jackson 1977

CEGB 1970s

Fredberg 1980

Brook 1984

Smith 1988

Watson 1989

Marshall 1992

Sharp & Campbell 1997

Horoshenkov 2003

Papadopolou 2008

Wang et al. 2012

...

Ware and Aki estimated the

location of the seismic source.

CEGB used Acoustic Ranger to

find defects in the heat exchangers.

Jackson et al measured the airway

geometry to help the investigation

of ENT and sleep apnoea etc.

Amir 1996 Sharp et al reconstructed the bore

profile of musical instruments.

Horoshenkov et al detected

damages in the sewage pipelines.

Wang et al applied APR in

monitoring gas pipelines.

Figure 3.1: Applications of APR History

known, it was used to solve inverse-scattering problems. This solution shared the

same idea as APR used in the other areas. The earth is made up of different layers

with a variety of types of rock. These rocks can be regarded as different mediums

that propagate the acoustic signal. The properties of different rocks vary greatly, such

as the impedance of the medium. In both the continuous and discrete time domains,

the impedance of the medium can be regarded as a function of travel time, and the

transfer function used to describe the characteristics of the medium was obtained from

the impulse response. When an impulse pressure wave was produced by a dynamite

source, pressure wave reflections were generated because of the impedance change

between different seismic layers. This formed the basis of the application of APR.


Ware and Aki [30] pointed out that analysing the medium properties of reflected waves

through the medium was an inverse-scattering problem. When the elastic parameters

did not vary significantly over one wavelength, the reduced Helmholtz equation [36]

was the estimation of the seismic problems. The expected results of distance could be

achieved by recovering the impedance of each layer based on the function of delay time.

The assumption for the target area should be considered as cylindrically symmetrical.

In 1970, the forward and inverse discrete time problems on a layered elastic medium [31]

were extended to a more general case by adding the dimension of the matrices from

previous methods. Later on, several methods of inferring the acoustical impedance

of a medium using the reflection response were proposed [32–37]. Weglein et al. [38]

presented the key mathematical-physics framework behind the algorithms for seismic

exploration, considering both the forward and inverse-scattering series construction.

Specifically, the following seismic applications were included:

• In exploration seismology, a wave generated by human beings was given on the

earth surface. As the wave propagated into the subsurface, a sharp change of the

signal meant that some percentage of the signal was reflected back to the surface

instead of continuing to move downwards opposite to the surface. This often

indicated changes in the earth material properties, i.e. impedance differences

between the layers.

• In marine exploration, a series of receivers, such as hydrophones, were placed

below the airwater boundary so that rich information in the reflected signal was

recorded. This information was used for further analysis based on forward and

inverse scattering series methods and appropriate algorithms.

3.1.2 Medical application

APR was also used in the medical field to measure the airway dimensions [39]. The

schematic diagram was shown in Figure 3.2.


Amplifier10kHz Low Pass

Filter

AD

MIC

Wave Tube

Trigger module

Spark gap

Data analysis

Figure 3.2: Schematic Diagram for Medical Application

The spark source generated the acoustic impulse by discharging the high-voltage elec-

trical pulse from the trigger module. A microphone (Bruel & Kjaer 4135) recoded this

acoustic impulse transmitted via the wave tube to the airway and the reflected acoustic

wave caused by the impedance changes. The acoustic signal passed the low-pass filter

and analog-to-digital converter(AD) in Figure 3.2 and was ready for analysis. The

inversion technique helped to find the airway geometry by measuring and analysing

the acoustic response. The first test was performed on a dog to determine the airway

geometry of its trachea and lungs. After that, Fredberg et al [40] used the high fre-

quency acoustic data recorded at the mouth to identify features of upper airway and

tracheal geometry. They extended the research to human patients. Brooks repeated

the same experiment on 10 males to show the reproducibility and accuracy of the


airway area measurements by acoustic reflection [39].

APR offered a non-invasive way to measure human airways, and had more advantages

than computerised tomography (CT) scanning and X-ray cephalometry. The acous-

tic wave reflections at the mouth could help to reconstruct the airway. APR could

help the investigation of ENT (ear, nose and throat) problems and sleep apnoea, and

in the management of anaesthetic usage [41]. Apart from this, the APR technique

was also used for the non-invasive assessment of lungs [42], tracheal stenosis [43], and

nasal airways [44–47]. On routine clinical experiments [48], both acoustic and mag-

netic resonance imaging (MRI) methods were applied to assess pharyngeal and glottal

areas, and the results were compared to show the effectiveness of the acoustic method.

In Louis’ research [49], a two-transducer system was developed, implemented, and

tested with computational algorithms to reconstruct airway dimensions from acoustic

reflection data using a strategy with two transducers.

3.1.3 Musical instrument bore reconstruction

The application of APR in musical instrument aroused interests of researchers. Stud-

ies and experiments were performed to measure the acoustic properties of specific

types of musical instruments, for example bassoon by Sharp [50]. The effectiveness of

the acoustic approach was determined by whether audients could tell the differences

between sounds produced using different crooks. Related studies included those on

tubular instruments by Amir [6, 51] and brass instruments by Kemp [52,53]. Accord-

ing to the characteristics of different musical instruments, researchers showed a special

preference for the work on trumpets and cornets [54] and horns [55]. Measurements

based on APR were also applied on musical instruments [56].

Experiments based on APR were conducted on ducts to measure the input impulse

response of a wind instrument [57,58]. The reconstruction of the internal bore profile

of the musical instrument could be evaluated by the input impulse response using a

proper reconstruction algorithm [59]. Sharp and Campbell [60] used a similar method

to detect the position and size of the leakage in musical instrument.


The pulse reflectometry was used by Sharp and Campbell [7,60,61] to reconstruct the

bore of the musical instrument and the detection of the leak along the instrument. The

schematic diagram of the instrument layout was the same as in Figure 1.1. The impulse

used was generated by a D/A converter of a frequency of 12.5 kHz and a voltage of

5 V. A 6-m long copper source tube was used in the layout. The microphone was

located in the middle of the source tube to avoid the overlap of the input signal and

the first reflected signal.

The reflection coefficients caused by the impedance changes could be calculated from

the IIR. It then was only the geometry knowledge to work out the diameter along the

bore because the object was usually assumed to have a cylindrical symmetry. With a

sampling frequency of 50 kHz, a 356 mm long instrument with a diameter expanding

from 9.4 mm to 12.4 mm to 18.5 mm was reconstructed.

The small diameter source tube and object restricted the reconstruction length of

the instruments because of the high attenuation inside the tube. Furthermore, the

application of the pulse reflectometry was mainly used to reconstruct the musical

instruments, that fell within a certain length (usually less than 1 m). The emphasis

was on the accuracy of the reconstruction shape. Sharp and Campell [60] also used the

impulse reflectometry to find the leak inside the pipe, as the leak could be regarded

as an expansion in the bore. The location of the leak could be identified using the

speed of sound and the reflected time. Under favourable conditions, the size of the

leak could also be estimated depending on the selection of the frequency.

3.1.4 Detection of features and defects in pipelines

Another area in which APR was greatly applied was in the detection of the features

and defects of pipelines. Horoshenkov et al [62] showed that the APR could be used

to detect the damage in sewage pipelines with a series of theoretical and practical

examples. Yunus [63] detected holes in the wall by sending out a relatively short pipe

with a chirp signal and processing the reflected signal with a correlator. Podd [64,65]

monitored sewer pipes using the APR technique with an inside diameter of up to 0.6m

and successfully detected the blockage and water pools inside the pipe. Beck [66–69]


developed a similar method to detect the small features in a number of relatively

short pipes. A similar acoustic reflectometry method has also been demonstrated to be

transferable to liquid-filled (e.g. water and petroleum) pipes, even though the presence

of liquid introduces complexity, and features may not be easily identified directly. For

example, Gao [70] introduced the acoustic-related methods to find the leakage in the

water distribution pipelines and Taghvaei [71] used a special piezoceramic transducer

to detect leakage in a fluid-filled pipeline network.

Furthermore, Papadopoulou [1] used this technique to find small holes in pipe walls

and deposits of water inside the pipe with a distance of up to 500 m. He also showed

that APR could allow some characterisation of a blockage. Similarly, it was confirmed

that solid blockages and pools of water (water blockage) could be located and detected.

Lennox et al. got a patented technique known as Acoustek [4]. This technique could

be used to detect blockages and leakages inside the gas pipelines. The basic idea of this

technique was that an impulse signal was injected into some point of the pipeline (which

is usually the beginning in experiments). At another point of the pipe, a microphone

was inserted to record the obtained signal for future analysis. The received signal

was usually a combination of both the normal inputted signal passing by and the

reflected signal because of features/defects inside the pipeline. If there was no specific

feature/defect in the pipeline and the signal was transmitted from one point to the

other in the same direction, the signal received by the microphone was expected to

be the input pulse and the reflection from the end of the pipe. In this condition, the

pipeline can be considered as a clean pipe. If some features/defects existed in the

pipe, no matter what kind of features/defects they were, the recorded signal from the

pipeline would be different from the clean pipe, with a reflected signal being added.

With the knowledge of the speed of sound, the distance between the microphone and

the feature/defect could be calculated and then it was straightforward to know the

location of the defect in the pipeline.

With acoustic analysis and proper mathematical formulation being applied, certain

types of defects, leakages or hydrates could be identified. In some cases that are

slightly more complex than the normal case, for example, when there is a 90 degree


angle in the pipe, there will be some reflections of the signal because of the shape and

set up of the pipeline itself. Then if there were some reflections in the signal obtained

by microphone, it may be the reflection of the joints instead of the defect itself. This

means that, in order to determine whether there are defects along the pipe, the re-

flection generated by the joint should be predicted before analysing the signal further.

After that, if there is still reflected signal in the obtained wave, this indicates some

features in the other parts of the pipe. Similarly, if other features were included in

the pipe, such as couplings, fittings, or other fillings placed into the pipe for measure-

ment, control, or experimental purposes, the reflected signal could be generated and

added into the microphone detected signal accordingly. This information should all

be considered in acoustic analysis, which increases the difficulty of the application of

this technology.

APR provides a solution to a great number of industrial pipeline problems worldwide.

However, there are still some limitations to the above method.

Firstly, as described above, it is not difficult to apply the method when the overall

environment of the pipe is not complex, however given more than one joint with

different angles, or given multiple locations of couplings, fittings, or fillings, it may

be difficult to know each reflection signal and to remove these signal before acoustic

analysis.

Secondly, only considering the speed of the sound, although it brings great convenience

to measure and calculate the location of the defects, how large the defect is remains

unknown. This could also be solved by making the best use of all information regarding

the sound wave, such as the energy of the signal, or in other words, the strength or

magnitude of the sound wave.

Thirdly, the detected length of a pipe is uncertain. Once the length of the pipe is

increased, the reflected signal will be weak: especially when the energy of the reflective

signal is similar to environmental noise, it is difficult to recognise whether reflection

exists, or which part is reflection and which part is noise. More advanced instruments

for measurement and analysis should be used to increase the accuracy of detection. The

application of both hardware and software filter will also lead to some improvement


in solving this problem.

3.1.5 Detection of features and defects in small bore tuning

The initial APR instrument originated from the research by the Central Electricity

Generating Board UK in the 1970s [10, 28]. An instrument was developed to record

the partial reflections from the leakage or blockage after a small acoustic wave was

injected into the pipe. This instrument was shown to work in pipes with an inside

diameter up to 1m and with a length of up to 300 m [28]. However, there were few

detailed publications or data regarding this instrument and a list of questions were left

unanswered. For example, the distance of the pipe to be detected was not validated

and how to distinguish the defects among all existing features (eg. T-pipe) of the pipe

system, etc. The details of the acoustic ranger have already been explained in the

Section 2.2.4.

The company Acoustic Eye has developed a series of patented products for the de-

tection of a heat exchanger which has contributed to the automation of the whole

detection and analysis procedure. The objects for detection are a branch of small

objects, usually a bundle of tubes. In order to identify the bundle of tubes automat-

ically, a computing device has been developed [72], with the ability to obtain images

and identify which bundle is the objects are the ones that need to be tested. Then the

tester is instructed by this exemplary embodiment. The guidance of this equipment

contributes greatly to the detection. The tester includes a base signal that could be

used as the input signal for testing [73]. The next test signal is then selected from the

data base according to the effectiveness of the previous signal. The reflected signal

is saved in storage for future analysis. The algorithm of this application is similar to

the one used in the detection of features and defects in pipelines, but this is a more

complex case when dealing with multiple tubes in a bundle [74]. Each bundle should

be injected with an input signal and the output in each pipe of this bundle needs to be

collected and saved accordingly. The Acoustic Eye has successfully used this technique

to make a prediction regarding the remaining number of cleaning cycles of a branch

of tubes during the cleaning process. This information is obtained with respect to the


state of the branch of tubes in the current cleaning cycle and is re-assessed every one

or several cleaning cycles.

Another recent application of APR on heater exchangers is a patented PACT-04 de-

vice [75]. It was developed by the Irkutsk Research and Design Institute of Chemical

and Petrochemical Engineering. This product is used to detecting defects of inner

sections of pipes. It has been successfully used in industry. It is reported that the fast

speed of APR forms an obvious advantage with full checking of 1000 heat exchanger

pipes taking roughly 40 min in the test.

3.2 Reviews on approximation models

The problem of the propagation of sound waves in gases contained in cylindrical tubes

is a classical one, to which famous name are connected like Zwikker and Kosten [76],

Kirchhoff [9] and Keefe [77]. There are typically two groups for the solutions of the

propagation problem. The representative of the first group was mainly from the an-

alytical approximation from Kirchhoff [9] . The second group was obtained directly

from Zwikker and Kosten [76], Kerris [78] and Iberall [79], etc. It is often related to

studies dealing with the dynamic response of pressure transmission lines.

3.2.1 Model equations

The equation describing the motion of gas in a circular cylinder is the Navier-Stokes

equation in the axial direction [80]. To build up the mathematical model of the

bore based on impedance formulation, the relationship between the acoustic pressure

P (z, ω) and particle velocity V (z, ω) is used according to earlier results in [81], [82],

and [76]. Given a uniform cylindrical tube with a length of L, axial coordinate z

direction along the tube and angular frequency ω,

∂P

∂z+ ZV = 0 (3.1)

∂V

∂z+ Y P = 0 (3.2)


where Z and Y represent the acoustic impedance and shunt admittance.

Applying partial differentiation on both sides of (3.1) with respect to z,

∂2P

∂z2+ Z

∂V

∂z= 0 (3.3)

Apply (3.2) to (3.3),

∂2P

∂z2= ZY P. (3.4)

This forms a single second-order equation in P in the frequency domain [55].

For z ∈ [0, L], standard forms for Z and Y [83] are

Z(jω) =jωZc

c(1− Fv)(3.5)

Y (jω) =jω

cZc(1 + (γ − 1)Ft). (3.6)

To provide a detailed explanation on the above equations, c denotes the speed of the

wave, followed by Zc = ρc being the characteristic impedance with air density ρ. The

ideal gas constant in air is represented by γ, and

Fv =2J1(√−jrv)√

−jrvJ0(√−jrv)

(3.7)

Ft =2J1(√−jrt)√

−jrtJ0(√−jrt)

(3.8)

with J0 and J1 being the Bessel functions of the 0th and 1st-order, and the dimen-

sionless parameter rv and rt are

rv = a

√ρω

η(3.9)

rt = νa

√ρω

η. (3.10)

Here a is the tube radius, ν2 is the Prandtl number and η is the shear viscosity

coefficient.

3.2.2 Zwikker and Kosten approximation

Zwikker and Kosten’s model is usually expressed in frequency domain in terms of

acoustic impedance. It was demonstrated that nearly all the approximation solutions


are covered by the solution obtained by Zwikker and Kosten. This is the solution

designated as the ’low reduced frequency solution’ when reduced frequency k and

shear wave number s are k � 1 and k/s� 1. k and s are defined as below.

s = a√ρsω/µ (3.11)

k = ωR/c0. (3.12)

ρs, mean density

c0 =√γps/ρs, undisturbed velocity of sound

µ, absolute fluid viscosity

γ = Cp/Cv, ratio of specific heats

Propagation constant Γ of the acoustic signal in frequency domain can be described

as

Γ =

√J0 〈j3/2s〉J2 〈j3/2s〉

√γ

n

with

n =

[1 +

γ − 1

γ

√J0 〈j3/2s〉J2 〈j3/2s〉

]−1.

where J0 and J2 are the 0th and 2nd-order Bessel functions, which can be found in

the Appendix of Kinsler’s book [84].

According to Tijdeman [80], most of the analytical solutions depend on the shear wave

number s only and are covered completely by the “low reduced frequency solution”,

obtained for the first time by Zwikker and Kosten [76]. This confirms that as the

Newton-Raphson method requires an initial value to start the iterative process, it can

be provided by the approximate solution of Zwikker and Kosten.

3.2.3 Kirchhoff approximation

The full solution of the problem has been obtained by Kirchhoff [9] in the form of a

complicated, complex equation. The complex form itself does not reveal itself to any


analytical treatment. The equation in (3.13) is rewritten in the terms of shear wave

number s. The estimation was based on the value from Zwikker and Kosten [76].

Γ = j +1 + j√

2[γ − 1 + σ

σs] (3.13)

The real part of Γ represents the attenuation over a unit distance and the imaginary

part represents the phase shift. γ = Cp/Cv is the ratio of specific heats.

For representative liquids and gases, the classical absorption coefficient is defined

by (3.14) [84]. This equation was conventionally used to describe viscous losses and

heat conduction losses in an unconstrained fluid [84].

αc =ω2µ

2ρc3[34

+γ − 1

Pr

](3.14)

αc attenuation, Neppers/m

ω angular frequency, radians/s

µ shear viscosity, N· s/m2

ρ density, kg/m3

c speed of sound, m/s

γ ratio of specific heats

Pr Prandtl number

This equation has been shown to be valid when the gas is monotonic but when the

gas is polyatomic it will not be suitable [84]. Kirchhoff [9] investigated propagation

of sound waves inside a pipe by considering both the viscous and thermal losses. The

deviations that resulted in the equations are described in [2]. In 1974, the English

translation of Kirchhoff’s work became available in [85] which led to the theory being

studied more widely.

If K0, a propagation constant, is defined as shown in (3.15).

K0 = 1 +1− j

a√ρω/µ

(1 +

γ − 1√Pr

)(3.15)


Then the attenuation (3.16) of the signal wave, is equal to the negative imaginary part

of K0 multiplied by wave number k.

α =ω

cR

[√ µ

2ρω+ (γ − 1)

√K

2ρωCp

](3.16)

a radius of the pipe, m

κ thermal conductivity, (W/m)K

Cp specific heat constant, J/kg K

Based on Kirchhoff’s estimation, Rayleigh [86] had the estimation for “narrow” pipes.

Later on, higher order approximations have been given by Weston [87] for the tran-

sition pipes, which belonged to narrow-wide, wide-narrow, etc. The full analysis of

Kirchhoff’s estimation can be found in Tijdeman [80].

3.2.4 Keefe approximation

Because of thermal and viscous losses, energy loss exists in the propagation of signal.

In order to have a model with acceptable accuracy in practical application, an approx-

imation is needed to deal with these losses. The approximation approaches of losses

inside the pipe have been discussed in [77,81,88].

The real and imaginary parts of the impedance Z = R + jωL are given by

R = − ωρ

πa2Fv sinφvD2

, (3.17)

ωL =ωρ

πa21− Fv cosφv

D2(3.18)

where

D2 = (1− Fv cosφv)2 + (Fv sinφv)

2. (3.19)

The analogous expressions for the real and imaginary parts of the admittance Y =

G+ jωC are

G = −ωπa2

ρc2[(γ − 1)Ft sinφt], (3.20)

ωC =ωπa2

ρc2[1 + (γ − 1)Ft cosφt] (3.21)


where φt and φv are the phase angle which are based on tables provided by Abramowitz

and Stegun [89].

At low frequencies or small tubes, where rv � 1 and rt � 1 with rv and rt given in

(3.9) and (3.10) respectively, the approximation [81] is given as

R→ ωρ

πa28

r2v; (3.22)

ωL→ ωρ

πa24

3; (3.23)

G→ ωπa2

ρc2(γ − 1)

r2t8

; (3.24)

ωC → ωπa2

ρc2(γ) (3.25)

Let s = πa2. Applying (3.22) and (3.23) to (3.1), i.e.

∂P

∂z+ (R + jωL)V = 0 (3.26)

forms∂P

∂z+(ωρs

8

r2v+jωρ

s

4

3

)V = 0. (3.27)

Apply (3.24) and (3.25) to (3.2),

∂V

∂z+[ ωsρc2

(γ − 1)r2t8

+jωs

ρc2γ]P = 0, (3.28)

∂V

∂z= − ωs

ρc2(γ − 1)

r2t8P − jωs

ρc2γP. (3.29)


∂2P

∂z2+( ωρπa2

8

r2v+jωρ

πa24

3

)∂V∂z

= 0. (3.30)

By substituting (3.29),

∂2P

∂z2−(ωρs

8

r2v+jωρ

s

4

3

)[ ωsρc2

(γ − 1)r2t8P +

jωs

ρc2γP]

= 0, (3.31)

∂2P

∂z2−(8ω

r2v+j4ω

3

)[ ωc2

(γ − 1)r2t8

+jωγ

c2

]P = 0, (3.32)

∂2P

∂z2+[4ω2γ

3c2− j8ω2γ

r2vc2− ω2(γ − 1)r2t

r2vc2

− jω2(γ − 1)r2t6c2

]P = 0, (3.33)


∂2P

∂z2+

4ω2γ

3c2P − jω2

c2

[8γ

r2v+j(γ − 1)r2t

r2v

]P = 0. (3.34)

Keefe [77] gives the complex function of frequency that is necessary to predict atten-

uation:

Γ = e−α(ω)e−jω/ϑp(ω) (3.35)

where ω is the angular frequency, α(ω) is the absorption coefficient, which represents

the attenuation and ϑp(ω) is the phase velocity.

α(ω) =(ωc

)(2√γ

rv

){1− 1

2

[(rv

2

6

)− γ − 1

γ

(rt

2

8

)](3.36)

ϑp−1(ω) = c−1

(2√γ

rv

){1 +

1

2

[(rv

2

6

)−(γ − 1

γ

)(rv

2

8

)]}(3.37)

The power series expansions in the above equations have been truncated so as to give

the best fit in the transition region, where rv is of order unity.

Thermodynamic constants are listed below for air at standard pressure. The temper-

ature difference relative to 26.85 ◦C (300 K) is ∆T [90].

ρ = 1.1769× 10−3 (1− 0.00335∆T ) g · cm−3 (3.38)

γ = 1.4017 (1− 0.00002∆T ) (3.39)

ν = 0.8410 (1− 0.0002∆T ) (3.40)

c = 3.4723× 104 (1 + 0.00166∆T ) cm · s−1 (3.41)

At high frequencies or big tubes, where rv � 1 and rt � 1 with rv and rt given in

(3.9) and (3.10) respectively, the approximation [81] is given as

R→ ωρ

πa2

√2

rv; (3.42)

ωL→ ωρ

πa2[1 +

√2

rv]; (3.43)

G→ ωπa2

ρc2[(γ − 1)

√2

rt]; (3.44)

ωC → ωπa2

ρc2[1 + (γ − 1)

√2

rt]. (3.45)

Let s = πa2. Applying (3.42) and (3.43) to (3.1), i.e.

∂P

∂z+ (R + jωL)V = 0 (3.46)


forms∂P

∂z+[(ωρ

s

√2

rv

)+jωρ

s

(1 +

√2

rv

)]V = 0. (3.47)

jωρV

s+∂P

∂z+(√2ρω

srv+

√2jρω

srv

)V = 0 (3.48)

jωρV

s+∂P

∂z+

√2ρω

srv(1 + j)V = 0 (3.49)

Apply (3.44) and (3.45) to (3.2),

∂V

∂z+{ ωsρc2

(γ − 1)

√2

rt+jωs

ρc2

[1 + (γ − 1)

√2

rt

]}P = 0. (3.50)

∂V

∂z+jωs

ρc2P +

[ ωsρc2

(γ − 1)

√2

rt+jωs(γ − 1)

ρc2

√2

rt

]P = 0 (3.51)

∂V

∂z= −jωs

ρc2P −

√2ωs(γ − 1)

ρc2rt(1 + j)P (3.52)


∂2P

∂z2+[jωρs

+

√2ρω

srv(1 + j)

]∂V∂z

= 0 (3.53)

By substituting (3.52),

∂2P

∂z2−[jωρs

+

√2ρω

srv(1 + j)

][jωsρc2

P +

√2ωs(γ − 1)

ρc2rt(1 + j)P

]= 0 (3.54)

∂2P

∂z2−[jωρ+

√2ρω

rv(1 + j)

][ jωρc2

+

√2ω(γ − 1)

ρc2rt(1 + j)

]P = 0 (3.55)

∂2P

∂z2+[ω2

c2− j√

2ω2

rvc2(1 + j)− j

√2ω2(γ − 1)

c2rt(1 + j)

]P = 0 (3.56)

∂2P

∂z2+ω2

c2P − j

√2ω2

c2(1 + j)

[ 1

rv+γ − 1

rt

]P = 0 (3.57)

The above approximation was based on the Taylor expansion of series. In [88] and [77],

other approximations were used with the same first-degree Taylor polynomial but with

different types of remainder. Similarly, the absorption coefficient α(ω) and the phase

velocity ϑp(ω) can be expressed in (3.58) and (3.59).

α(ω) =(ωc

){(rv−1√2

)(1 +

γ − 1

ν

)(3.58)

+ rv−2[1 +

γ − 1

ν− 1

2

γ − 1

ν2− 1

2(γ − 1

ν)2]

+rv−3√

2[7

8+γ − 1

ν− 1

2

γ − 1

ν2− 1

8

γ − 1

ν3− 1

2(γ − 1

ν)2

+1

2

(γ − 1)2

ν3+

1

2(γ − 1

ν)3]}


ϑp−1(ω) = c−1

{1 +

(rv−1√

2

)(1 +

γ − 1

ν

)(3.59)

− rv−3√

2[7

8+γ − 1

ν− 1

2

γ − 1

ν2− 1

8

γ − 1

ν3

− 1

2(γ − 1

ν)2 +

1

2

γ − 12

ν3+

1

2(γ − 1

ν)3]}

Keefe [77] summarised the different approximations for the frequency response of an

acoustic tube. All expressions listed in the paper were valid for the continuous fre-

quency domain. However, the majority of the modern equipment could only deal with

the digital signal. Therefore, the discrete measurement is more practically used. Amir

explained the problems encountered when transforming the continuous frequency do-

main to the discrete time domain were explained in detail [6]. Amir pointed out that

the time domain response had more advantages than the frequency one. Only pressure

data needed to be recorded and the time for a single measurement was short in the

time domain. Keefe [77] took Benade’s analysis [90] and applied it to the situation

when the inner wall of the pipe is not isothermal. However, to increase the accuracy,

more terms were retained in the asymptotic expansion of the Bessel functions.

3.2.5 Comparisons among different approximation models

As described above, the three main approximation models are summaried in Table 3.1.

Most of the analytical solutions depend on the shear wave number s only and are cov-

ered completely by the ’low reduced frequency’ by Zwikker and Kosten. The full

Kirchhoff equation can be solved with the help of the Newton-Raphson procedure.

The simplified format in Table 3.1 can be used for ’wide tube’ situation. These ap-

proximations work for tubes under different conditions defined by k and s. Keefe’s

approximation can be written in two formats under the condition of rv and rt, which

was discussed in Section 3.2.4. Keefe’s approximation is based on the conclusions of

acoustic impedance from Kirchhoff to get the approximation for cylindrical gas duct.


Table 3.1: Review of Analytical Solutions to the Signal Propagation

Author Year Formula for the constant of propagation

Kirchhoff (’wide tube’) 1868 [9] Γ = j + 1+j√2

[γ−1+σσs

]

Zwikker and Kosten 1949 [76,79]

Γ =

√J0〈j3/2s〉J2〈j3/2s〉

√γn

with n =

[1 + γ−1

γ

√J0〈j3/2s〉J2〈j3/2s〉

]−1Keefe 1984 [77] Γ = e−α(ω)e−jω/ϑp(ω)

3.3 Reviews on numerical simulation models

3.3.1 Finite Difference Time Domain Model

Bilbao [91] developed the finite difference time domain methods for the simulation of

brass instrument bore. The dynamics of the acoustic bore are simulated based on the

model of musical instrument, with viscothermal and radiation losses being considered.

Define

k =1

fs(3.60)

where fs is the sampling frequency.

Given a time step k equal to the inverse of sampling rate and a position step h = LN

for a known length L, the interleaved grids [92] in Figure 3.3 is used to show

• the pressure p(z, t) at different location z = lh and time t = nk for nonnegative

integer n and l ∈ [0, N ].

• the velocity v(z, t) at different location z = (l + 12)h and time t = (n + 1

2)k for

nonnegative integer n and l ∈ [0, N − 1].

For convenience, the following forwards and backwards shift operators are defined with

respect to a given grid function gnl at the time n and location l:

• forwards and backwards time shifts: et±gnl = gn±1l ;

• forwards and backwards spatial shifts: ez±gnl = gnl±1;


p

p

p

p

p

p

p

p

p

p

p

p

v

v

v

v

v

v

v

v

v

z=0h z=0.5h z=h z=1.5h z=2h z=2.5h

t=nk

t=(n-0.5)k

t=(n-1)k

t=(n+2)k

t=(n+1.5)k

t=(n+1)k

t=(n+0.5)k

Figure 3.3: Interleaved Grids of Pressure And Velocity.

• forward and backward difference operators in time: δt± = ∓ 1k(1− et±);

• forward and backward difference operators in space: δz± = ∓ 1k(1− ez±);

• averaging operations: µt± = 12(1 + et±).

Using these operations, the model can be written as

ρδt−v + δz+p+ qµt−v + fδt12µt−v = 0 (3.61)

S

ρc2δt+p+ δz−(Sv) + gδ

t12µt+p = 0. (3.62)

with

Sl =1

2(Sl+ 1

2+ Sl− 1

2) (3.63)

and an approximation of δt12.

Time domain methods are another approach to model the wave propagation in acoustic

tubes. A tube is numerically integrated using a time-stepping method. One of the

advantages is the impulse response can be calculated directly. Another advantage is

the possibility of generalizations to the case of nonlinear wave propagation.


3.3.2 Layer peeling Model

Amir et al [6, 51] presented two discrete loss models (short cylindrical and conical

models [90, 93]) for tubular acoustics systems. The pipeline system was discretised

to small cylindrical segments or conical segments in each modeling. The waveguide

filter was described to account for the losses inside the segments. The basis for the

algorithm used by Amir was the layer peeling algorithm in seismic applications. The

experiment apparatus used is shown in Figure 3.4.

As the conical model is more complicated in a simulation, especially for a tube with

a longer length and fewer cross sectional changes, the cylindrical model can be conve-

niently used in a pipeline system. In addition, the conical model can also complicate

the calculation according to the way to obtain the reflection coefficients between the

conical segments.

A trumpet bell was used as an experimental example to show the accuracy of the

simulation results.

Figure 3.4: The Schematic Diagram of Setup

Amir’s discrete model has been widely applied by different groups of researchers, in-

cluding Sharp [60], Kemp [52] and Amir himself [6]. In Sharp’s study [60], Pipe #1

(2m) and Pipe # 2 (2 m) in Figure 3.4 were used as source tubes to ensure that the

IIR could be recorded directly by the microphone without the interference of the in-

put reflections and system reflections of the test instruments (longest up to 1m). The

sampling frequency was 12 kHz because of the excitation pulse spectrum was up to 6

kHz. In this way, the resolution of the reconstruction of the instrument, which was the


length of each segment, was around 0.028 m depending on the speed of sound during

the test [60].

In previous papers [52,55], researchers developed and validated a simulator that models

the transmission and reflection of acoustic waves within a single pipe. After that, the

single pipe simulator was expanded to the one that models the behaviour of acoustic

waves in networked pipe systems. By comparing the signals from an experimental test

with those generated by the simulator, any defects could be identified quickly.

All of the simulators that have been developed in the literature have been configured to

model the behaviour of acoustic signals over relatively short lengths (2.5 m) of limited

bore (50 mm) piping. The focus of the present work is to explore the use of APR over

extended distances of large diameter pipe.

Amir et al [6] built the simulators to reconstruct musical instruments, but a simulator

could also be used widely for industrial applications. The biggest difference between

the pipe simulator and those for musical instruments is the measured length. Generally,

a pipe simulator is required to simulate pipes as long as 10 km, whereas a musical

simulator only works for about a 2.5 m tubular instrument.

Numerical simulations of input impedance are compared with measurement for a va-

riety of musical instruments. The complexity of this method is determined by its

application background - complex model of brass instruments with constraints. This

is the reason for the fact that a number of mathematical approximations are applied

in the model and analyze. Both the pressure and the velocity are considered in simu-

lation, which gives more useful information.

3.3.3 Summary of the two models

Both the FDTD model and layer peeling model essentially used time domain approx-

imation. In the layer peeling model [6,51], it focused on the step by step model using

the cylindrical or conical segements. In FDTD model [91, 94], the bore profile was

treated as a unit to obtain a more complete view of the internal bore of the musical


instruments.

The pipeline simulators, which will be introduced in Chapter 6, will develop and

evaluate the application of the layer peeling model in the pipeline system. As the

signal at each feature segment is important for the analysis of APR, especially when

trying to simulate the defect features, using a step by step model is more applicable.

3.4 Summary

Chapter 3 introduced some typical applications for APR including seismic research,

medical application, tubular musical instrument reconstruction and pipeline detection

and analysed their limitations. Three classical approximation models were reviewed.

At the end of the chapter, two typical models for building a simulator were explained

and compared. Layer peeling model is focused on the step by step model using the

cylindrical or conical segments while FDTD considered the bore, both the mouthpiece

and bell as a unit.

Chapter 4

Attenuation of the Acoustic Wave

Acoustic waves propagating along a pipeline over a short distance, such as a distance

equal to the diameter of the pipe, can be regarded as lossless when the dissipation is

slight. However, in long pipelines, the dissipative terms cannot be neglected because

of the existence of viscous and thermal losses, with all of acoustic energy converted to

thermal and viscous energy in the end when the length of the pipeline is long enough.

In this chapter, Kirchhoff’s wave equations are introduced and used to describe the

attenuation of an acoustic signal in a pipe. In this chapter, the wave equation is

introduced together with the boundary conditions. Lossless sound propagation is

then explained followed by the derivation of the attenuation of the acoustic signal. In

addition, experimental results are provided which validate Kirchhoff’s equation. Using

these data, a comparison is made between previously published data investigating

acoustic attenuation in pipelines and the results obtained in this work.

4.1 Related theory

4.1.1 Speed of sound

When considering the propagation of an acoustic signal along the length of a pipe, it

is important to understand the speed that this signal travels, i.e. the speed of sound

73

CHAPTER 4. ATTENUATION OF THE ACOUSTIC WAVE 74

in the medium. The speed of sound c will vary depending on the conditions in the

pipe [86]. Speed of sound is defined by the equation [95]

c =

√K

ρ, (4.1)

where K is the coefficient stiffness and ρ is the density.

For the ideal gas, K is given by

K = γp, (4.2)

where p is the presure and γ is the ratio of specific heats

γ =√Cp/Cv. (4.3)

In (4.3), Cp is the specific heat at a constant pressure and Cv is the specific heat at a

constant volume.

In this way, (4.1) can be written as

c =

√γp

ρ. (4.4)

Under ideal gas law,

p = nRT/V. (4.5)

The speed of sound can be expressed in

cideal =

√γp

ρ=

√γRT

M, (4.6)

where

• R (approximately 8.314,5 J·mol−1· K−1) is the molar gas constant [96];

• T is the absolute temperature, K;

• M is the molar mass of the gas. The mean molar mass for dry air is about

0.028, 964, 5 kg/mol.


This equation applies only when the it is ideal gas inside of the pipe. Calculated values

for speed of sound of air cair have been found to vary slightly from experimentally

determined values [97].

For air, a simplified symbol is used

R∗ =R

Mair

. (4.7)

Define ϑ = T − 273.15 when T is in degrees Celsius (◦C). Then

cideal =√γ ·R∗ · T =

√γ ·R∗ · (ϑ+ 273.15) =

√γ ·R∗ · 273.15

√1 +

ϑ

273.15. (4.8)

Following numerical substitutions, R = 8.314, 510 J/(mol ·K),Mair = 0.028, 964, 5 kg/mol

and γ = 1.4000, cair can be written as

cair = 331.3

√1 +

ϑ

273.15m/s. (4.9)

In laboratory measurement and simulation, the medium inside of the pipe is air and

the pressure is atmospheric. (4.9) can be used to calculate the speed of sound when

air travels inside of pipeline. For on-site experiments, because of complex environment

and different gas pressure and density, and the inside medium is not air or the inside

pressure is not atmospheric, speed of sound generated by AGA 10: 2003 is used. There

is an online tool for this to get the speed of sound directly under different temperature

and pressure.

4.1.2 Boundary of plane wave

A plane wave is defined as follows: each acoustic wave has a constant amplitude and

phase on any plane perpendicular to the direction of propagation.

Figure 4.1 shows different modes for values of m and n of up to 3 where m is the

angular mode order (line in the figure) and n is the radial mode order (circle in the

figure). kz is the wave number in z direction. In Table 4.1, it is shown the extrema

value of Jm under each mode [84].


m=0 m=1 m=2 m=3

n=0

n=1

n=2

n=3

Figure 4.1: Acoustic Modes in a Cylindrical Pipe (Agarwal and Bull [98])

Table 4.1: Extrema: Bessel Functions of the First Kind

n=1 n=2 n=3 n=4 n=5m=0 0 3.83 7.02 10.17 13.32m=1 1.84 5.33 8.54 11.71 14.86m=2 3.05 6.71 9.97 13.17 16.35m=3 4.20 8.02 11.35 14.59 17.79m=4 5.32 9.28 12.68 15.96 19.20m=5 6.41 10.52 13.99 17.31 20.58

When in mode (0, 0) the acoustic signal travels as a plane wave mode at the velocity of

sound in the particular medium it is travelling through. Kichhoff’s attenuation theory

is only applicable when the signal travels in this mode.

According to Kinsler [84], Bessel functions of the first kind (Jm) are introduced to

solve the boundary conditions, which offers the condition when the signal is travelling

as a plane wave. kmn is the wave number

kmn =j′mna

(4.10)

kz =

[(ωc

)2− k2mn

]1/2(4.11)


a diameter of the pipe, ω angular frequency of the transmitting acoustic wave

j′mn is the extrema of Jm whose values have been tabulated for convenience, where the

m suffix represents a circumferential wave mode and the n suffix a radial mode. Based

on different values of m and n, the wave can be transmitted in different modes (m, n)

within the pipe.

If the wave form is in a higher mode and kz has an imaginary part then the wave will

be evanescent in z direction.

Hence for each higher mode, there is a cut off frequency when

ω

c=j′mna

(4.12)

For the first mode beyond the plane wave, the value of j′mn is 1.84 [84]. Therefore,

provided that the angular frequency is lower than 1.84c/a, only the plane wave will

propagate within the rigid wall of the pipe. For example, when the temperature is

20◦C and according to (4.9) the speed of sound is 343.42 m/s and the ID of the pipe

is 50 mm, then the cut off frequency is

f =ω

2π= 4.02× 103Hz (4.13)

In the work presented in this thesis the test pipelines varied in size from 2.7 mm (0.5

inch) to 254.0 mm (10 inches), with the tested length up to 12 km. In Table 4.2, the

cut-off frequency for each pipe size are listed for reference. Equation (4.12) and (4.13)

define the highest frequency when only plane wave travels along the pipeline, which for

the pipeline considered above means that if the frequency is below 4.02 kHz, then the

signal can be considered to be a plane wave. In the experimental work reported in this

thesis the frequency content of the acoustic signals was primarily below 200 Hz, which

was considerably below cut-off frequency and hence plane wave mode was assumed.

Blackstock [99] placed a restriction on the pipe diameter for which the attenuation

equation could be used. This is defined in (4.14).

δν << R <<c2

ω2δν(4.14)

and

δν =

√2µ

ρω(4.15)


Table 4.2: Pipe Size vs Cut-frequency

Size (mm) Cut-off frequency (kHz)12.7 15.8425.4 7.9250.8 3.9676.2 2.64101.6 1.98127.0 1.58152.4 1.32177.8 1.13203.2 0.99228.6 0.88254.0 0.79

δν is the viscous acoustic boundary layer measured in meters.√2µ

ρω� R� c20

ω

(1 +

T

273

)√ ρ

2µω(4.16)

The range of the diameter, when the Kirchhoff’s equation can be applied, is defined

based on the frequency of the signal and temperature of the environment. Assuming

the temperature is 0 ◦C, then the ranges of diameters for the frequency range 10 to

2000 Hz is shown in Figure 4.2. This figure provides the range of diameters when the

application of Kirchhoff’s equation is valid. Based on the boundary results of the pipe,

for an industrial pipe, the larger the pipe is, the more suitable Kichhoff’s equation will

be applied.

A further assumption that is made when applying Kirchoff’s attenuation theory is that

the pipe is infinitely long. In reality, this is not possible. However, the addition of a

’dissipation pipe’ to the end of pipe systems used in this work simulates the idealised

infinite condition.

4.1.3 Window function comparison

In a practical situation it is not possible to inject acoustic signals with unlimited

lengths and therefore it is necessary to use a signal of finite length. After cutting

or shortening the length of a signal, the frequency spectrum will be affected. This is


0 500 1000 1500 20000

0.5

1

1.5

Frequency (Hz)

Dia

mete

r (m

m)

Lower boundary

0 500 1000 1500 20000

2

4

6

8x 10

7

X: 2000

Y: 2.815e+04

Frequency (Hz)

Dia

mete

r (m

m)

Upper boundary

Figure 4.2: Kichhoff Attenuation Restrictions

known as spectral leakage. A window function can be used to control certain properties

of the wave and help to reduce the frequency leakage. If the side lobes of the window

function are close to 0, then the main energy stays within the main lobe, which can keep

the cut wave close to the original spectrum. There are several window functions that

are typically used for this including rectangular window, triangular window, Hamming

window and Hanning window. In Table 4.3, a comparison of the different windows is

provided. The frequency response of each windowing technique is shown in Figure 4.3

to Figure 4.6.

If the primary frequency in the signal is particularly important, then it is better to

choose a window function with a narrow main lobe, which will result in less leakage.

Theoretically either Hanning window or Hamming window works in this situation

as they both have narrow windows. In the presented analysis the Hanning window


Table 4.3: Comparison Among Different Window Functions

Window Name Advantage Disadvantage

Rectangular window(Figure 4.3)

The main lobe is focused.

Side lobes are high withnegative side lobes as well.High frequency interferenceand leakage, Even withminus frequency spectrum

Bartlett window(Figure 4.4)

Side lobes are smallercompared to rectangularwindow, with nonegative side lobes.

The main lobe is twice widerthan the rectangular window.

Hamming window(Figure 4.5)

Decreases high frequencyinterference and leakage

There are more ringsthan in Hanningwindow.

Hanning window(Figure 4.6)

Decreases high frequencyinterference and leakage

The main lobe is widercompared to rectangularwindow.

was used. The Hamming window showed no improvement in the results when it was

applied.

0 5 10 15 20 25 30 35 40 45 500

0.5

1

Samples

Am

plit

ude

-150 -100 -50 0 50 100 1500

20

40

60

Bins

Am

plit

ude

Figure 4.3: Rectangular Window


Samples

Bins

Am

plitu

de

Am

plitu

de

Figure 4.4: Bartlett Window

Samples

Bins

Am

pli

tud

eA

mp

litu

de

Figure 4.5: Hamming Window


Samples

Bins

Am

plitu

de

Am

plitu

de

Figure 4.6: Hanning Window

4.2 Experiments validation

Previous results published in other research studies highlighted errors between theoret-

ical and measured attenuation to be in the range of 1.5% to 15%, with the majority of

experiments performed on pipelines with lengths of less than 33 m. Furthermore, the

lower frequencies, which are particularly important in the present work, had received

very little attention in these previous studies. To fully understand the suitability of us-

ing the attenuation theory detailed above for experiments in long lengths of industrial

pipeline, a series of validation experiments were conducted.

4.2.1 Previous research results

Several studies have investigated the validity of Kirchhoff’s equation. These studies

are summarised below.


Tijdeman [80] and Davies Rodarte [100] showed that the average error was 11.6% as

summarised in [101].

In work conducted by Mason [102], pipe diameters of 14.98 mm, 11.7 mm, 8.46 mm

and 5.36 mm, with corresponding lengths of 6.22 m, 4.89 m, 4.26 m and 7.63 m were

used, with a frequency range between 200 Hz and 4000 Hz. The maximum error

between the theoretical result and the experimental result was 5.56%. The average

temperature used in the experiment was 23.5◦C.

In Lawleys research [103], five tubes were tested with diameters ranging between 0.3

mm and 2.34 mm. The measurements focused on the frequencies of 60 kHz, 80 kHz,

100 kHz, 120 kHz. Although error metrics weren’t provided a statement of their

[Kirchoff’s equation] accuracy was not high. The temperature used in the experiment

was 27◦C.

Weston [87] compared the theoretical result to the experiment result from Lawley,

using a frequency of 120 kHz in a tube with a diameter of 1.5 mm, containing oxygen.

It was shown that the attenuation error was 10.4%. The temperature used in the

experiment was 27◦C.

Fay [104] used 15 mm diameter pipe, with a length of up to 1 m at temperatures of

26◦C and 27◦C. The value of the attenuation coefficient was approximately 5 % in error

based on the magnitude of the received signal in ranges from 1.5% to 15% compared

to the Kirchhoff theory.

Angona [105] used the frequency range from 2 kHz to 10 kHz. The size of the tested

tube was 16.82 mm with 0.5 m long for attenuation test. The test made on dry air

and nitrogen demonstrated that the attenuation from Kirchhoff was underestimated

by 4.5%.

4.2.2 Experimental apparatus

As discussed earlier, the experiments previously reported in the literature have fo-

cused on measuring attenuation in short lengths of small-bore pipes at relatively high


Table 4.4: Details of the Test Pipes

GroupNumber

ID(mm) OD(mm) Length(m)

1 39.8 50

5075100125150175200

2 25 32

5075100125150175200

3 15.17 20

5075100125150175200

frequencies. The experiments described in this Chapter attempt to validate Kirshoff’s

theory at low frequencies over relatively long lengths of pipe.

The pipes used in the laboratory tests were made of polyethylene, and were new and

clean. The three sets of pipes that were used are listed in Table 4.4. The sizes of

the tested pipes were 15.17 mm (0.6 inch), 25 mm (0.98 inch) and 39.8 mm (1.57

inch). Each size of pipe was tested using different lengths, ranging from 50 m to 200

m, which is the target range for the gas distribution work. The length measurements

were provided by the manufacturers and were considered to be only approximate.

More accurate lengths were determined using acoustic time of flight measurements.

Table 4.4, provides full details of the pipes used in the experiments, where ID and OD

represent inner diameter and outer diameter of the pipeline.

The test equipment is listed below, with a diagram of the set up shown in Figure 4.7.


• A/D NI 9234: 24-bit resolution 51.2 kS/s per channel maximum sampling rate

±5V input

• D/A NI 9263: 16-bit resolution 100 kS/s simultaneous analogue output module

• Amplifier: YAMAHA Natural Sound Integrated Amplifier A-S3000

• Microphones: DeltaTron Pressure-field Microphone Type 4944A

• Loudspeaker: SEAS H1208-08 L22RN4X/P

• USB cable

• BNC cables

MIC1

LOUDSPEAKER TEST TUBE

AMPLIFIER

COMPUTER

A/DD/A

MIC2

DISSIPATION TUBE

Figure 4.7: The Set up of the Experiment in the Lab

A photograph of one test is shown in Figure 4.8. It shows the coiled pipe fitted with two

microphones, a speaker at one end, with the other end open to the environment. The

open end meant that the temperature remained consistent with the temperature in

the laboratory. Microphone 1 was positioned close to the loudspeaker with a distance

of around 0.5 m to avoid any ringing from the loudspeaker. A fitting was designed

to connect the loudspeaker to the tested pipe. The fitting was made of a poly acrylic

sheet with four screws to fit the loudspeaker and one central hole to fit the tested

pipe. An amplifier was used to amplify the signal sent out from D/A NI 9263. The

two microphones could receive the acoustic waves along the pipeline with a time delay

between them. After receiving all of the test data, post processing was performed.


Figure 4.8: Coiled Pipes for the Experiments

25 m and 50 m pipes were used to dissipate the signal beyond the end of the pipes. The

pipes used in the experiment had lengths of either 25 m or 50 m. Therefore, to achieve

the longer lengths they were connected via compression polypropylene coupling.

Figure 4.9 shows the flow of data in the experiments.

Cable

ComputerDAQ

board

Conditioner

Loudspeaker

Microphones

Cable Cable

Cable

Figure 4.9: Data Transmission Order of the Test System

During the entire test, the temperature of the environment was considered to be con-

stant while the test was running.


4.2.3 Analysis

During all the tests reported in this Chapter, the amplitude of recorded data refers

to the pressure of the sound wave that is injected and transmitted inside the coiled

pipes.

To begin, tests were conducted using pipelines of the same diameters, but with fre-

quencies ranging from 50 Hz to 2000 Hz. Taking one set of tests as an example (ID

of 39.8 mm, measured using venire callipers). This test was performed on pipes from

50 m to 200 m in increments of 25 m (i.e. seven sets of data were collected). For

each pipe set up, acoustic signals at each frequency was injected and the measure-

ments taken. This was repeated five times and the results averaged to reduce any

unexpected disturbances in the environment.

Acoustic signals ranging in frequency from 20 Hz to 2000 Hz, in increments of 10 Hz,

were transmitted to the loudspeaker and the signals recorded by two microphones were

collected. The signal sent into the system was a short burst sinusoidal wave with a

single frequency. The sinusoidal signal was the wave that produced the minimum dis-

turbance in the electrical circuits and was the only wave that remained unchanged after

signal processing (using filters or following differentiation). Experimental attenuation

values were calculated using

αp = −8.686× ln(p2p1

)/l12 (4.17)

αp experimental attenuation, dB/m

p1, p2 pressure signals recorded by the two microphones

l12 the length between the two microphones.

The constant, 8.686, was used to change the attenuation unit from Neppers/m to

dB/m, i.e. 1Np = 20 log10 e = 8.686 dB.

To analyse the acoustic measurements taken from the experiments, three methods

were used to evaluate the attenuation of the signals: the root mean square (RMS)

value, the peak amplitude value and the root of the FFT spectrum of the signal.


Using these techniques, the acoustic measurements were analysed in both the time and

frequency domains, which allowed different interpretations of the signals. In related

work, Mason [102] used the power ratio to obtain their attenuation measurements

whilst. Fay [104] used the maximum and minimum values to determine the ratio of

pressure.

In the time domain, the RMS and peak amplitude values were used to evaluate the

attenuation. When using the RMS value, p1 and p2 refer to the RMS values of the

two signals recorded by the two microphones. For the peak evaluation, p1 and p2

refer to the peak values of the two signals recorded by the two microphones. The

measurements collected from the microphones were processed in the following way.

1. The beginning and end sections of the signals were ignored as these parts of the

signal were not stable.

2. Full cycles of the signal data were saved. Incomplete periods were discarded as

these would affect the RMS value.

3. A band-width filter was used to reduce secondary frequency content. This was

necessary because the aim was to focus on specific frequencies.

4. Following the signal processing, two signals were available; one from each mi-

crophone. They are the original signals from each microphone after being filtered.

Equation (4.18) was used to determine the RMS measurement and peak values of

the signals were determined directly from the processed measurements. As the signal

could be affected by background noise, the peak value was read from different periods

and averaged. This resulted in more consistent results. The RMS value of a signal is

defined by

xrms =

√1

n

(x21 + x22 + · · ·+ x2n

)(4.18)

where n is the number of points for the target signal and x1, x2, x3, . . . , xn are the

corresponding values at each point along the entire recorded signal length.

Figure 4.10 illustrates the difference between the RMS and Peak values.


Samples

Am

pli

tude

Figure 4.10: RMS Value and Peak Value

To analyse the attenuation in the frequency domain, FFT was applied to the measure-

ments. p1 and p2 refer to the two signals recorded by the microphones after FFT has

been applied. The FFT measurements were processed as follows:

1. A band-width filter was used to remove the unwanted frequencies of the raw data;

i.e. the frequencies that were not the focus.

2. A Hanning window was applied to decrease the edge affects of the signals from the

two microphones. As the same Hanning window was applied to both of the signals,

the attenuation results were not influenced as the operation involves division.

The Hanning window is defined as

w(n) = 0.5(

1− cos( 2πn

N − 1

))(4.19)

where N is the number of Hanning window.

Finally, FFT was applied to the resulting data to determine the frequency content.

To improve the consistency of the results all the tests were completed five times and

the results averaged.


The error between the theoretical value and the experimental values was determined

using the following equation:

Error =(αp − α

α

)× 100% (4.20)

α theoretical attenuation

αp experimental attenuation

The theoretical attenuation α (dB/m) has already been introduced in section 3.2.3

when Kirchhoff’s attenuation was described.

α = 8.686× ω

cR

(√ µ

2ρω+ (γ − 1)

√K

2ρωCp

)(4.21)

If the result is negative, this means that the experimental result is less than the theo-

retical prediction. In contrast, when the result is positive, it means the experimental

result is larger than the theoretical attenuation. In the following subsections of this

chapter, all the errors were calculated using (4.20).

4.3 Experimental results

4.3.1 Different length tests

Taking the 50 m length as an example, the distance between the two microphones

was 50 m, the diameter of the pipe was 39.8 mm and the ambient temperature was

20 ◦C. Figure 4.11 illustrates the attenuation results by utilising the three different

analysis approaches described earlier, compared with the theoretical results, obtained

using (4.21). This figure shows that there is a high degree of consistency in the results.

Figure 4.12 shows the error that was measured for each of the three analysis techniques.

In Figures 4.14 and 4.16, the attenuation results and errors are presented for the

experiments conducted with pipelines with ID of 25 mm and 15.17 mm respectively.


0 200 400 600 800 1000 1200 1400 1600 1800 20000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Frequency (Hz)

Att

en

uati

on

(d

B/m

)

Attenuation Results

Theoretical Attenuation

RMS attenuation

Peak to Peak attenuation

FFT attenuation

Figure 4.11: 50 m Pipe Attenuation Results When D = 39.8 mm

0 200 400 600 800 1000 1200 1400 1600 1800 2000-20

-15

-10

-5

0

5

10

Frequency (Hz)

Err

or

(%)

Error Analysis(%)

RMS

Peak to peak

FFT

Figure 4.12: Error Results When D = 39.8 mm


200 400 600 800 1000 1200 1400 1600 1800 2000-2

-1

0

1

2

3

4

5

Frequency (Hz)

Err

or

(%)

Error Analysis(%)

Figure 4.13: Error Results of RMS Value

0 200 400 600 800 1000 1200 1400 1600 1800 20000.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency (Hz)

Att

enuation (

dB

/m)

Attenuation Resuts


RMS attenuation


FFT attenuation

Figure 4.14: Attenuation Results When D = 25 mm


200 400 600 800 1000 1200 1400 1600 1800 2000-8

-6

-4

-2

0

2

4

6

8

Frequency (Hz)

Err

or

(%)

Error Analysis(%)

RMS

Peak to peak

FFT

Figure 4.15: Error When D = 25 mm

0 500 1000 1500 20000.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Frequency (Hz)

Att

nu

ati

on

(d

B/m

)


RMS attenuation


FFT attenuation

Figure 4.16: Attenuation Results When D = 15.17 mm


0 200 400 600 800 1000 1200 1400 1600 1800 2000-25

-20

-15

-10

-5

0

5

Frequency (Hz)

Err

or(

%)

RMS

Peak to peak

FFT

Figure 4.17: Error When D = 15.17 mm

0 200 400 600 800 1000 1200 1400 1600 1800 20000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Frequency (Hz)

Att

enuation (

dB

/m)

2D plot for Attenuation

Theory

50m

75m

100m

125m

150m

175m

200m



0 200 400 600 800 1000 1200 1400 1600 1800 20000.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency (Hz)

Att

enuation (

dB

/m)

Theory

50m

75m

100m

125m

150m

175m

200m

Figure 4.19: Attenuation Results When D = 25 mm

0 200 400 600 800 1000 1200 1400 1600 1800 20000.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Frequency (Hz)

Att

enuation (

dB

/m)

Theory

50m

75m

100m

125m

150m

175m

200m



Similar attenuation tests were performed for the other lengths and the results are

shown in Figures 4.18- 4.20.

An initial analysis of the results presented in Figures 4.18 to 4.20.

• The results were consistent with each other and similar to the theoretical results.

The exception to this is Figure 4.18 to 4.20 which shows that the attenuation

is significantly lower than anticipated at higher frequencies in small diameter

pipes. This is discussed further in the following discussion in this section.

• The error tended to be slightly larger at frequencies above 200 Hz than below this

frequency. However, the errors were within 5%, with the minimum error being

approximately 0.5%. As the focus for this work was to validate the suitability of

applying Kirchoff’s theory to approximate the attenuation in industrial piping,

which is likely to contain debris and corrosion then a 5% error was considered

to be acceptable at this stage of the research.

• The RMS value had the lowest error when compared with the other metrics.

However, all errors were below 5% (Figure 4.13).

• All of the results had a positive error, except for three frequencies (190 Hz, 210

Hz, 500 Hz). This means that for these tests, Equation (4.21) tended to under

estimated the attenuation.

Figures 4.18 to 4.20 clearly show that at the higher frequencies the measured attenua-

tion is significantly lower than that calculated using Kirchoff’s theory. The reason for

this was because of experimental limitations. Attenuation in the pipes is quite signifi-

cant, particularly at higher frequencies and small diameter pipes. As the attenuation

increases then the signals can get lost in the background noise and when frequency

analysis is applied errors are introduced. If the results for the 175 m (39.8 mm ID)

pipe are now considered. Figures 4.21 and 4.22 show some of the signals recorded in

this test. The upper plots in each figure compare the injected signal (red, using the

Y label in the left) with the reflected signal (green, using the Y label in the right),

while the lower plots show the FFT analysis of the two signals. When the frequency is

relatively low, for example when f = 500 Hz, the reflected signal can still be identified


clearly as a sinusoidal wave. However, when the frequency is increased to f = 1500 Hz,

then the reflected signal is difficult to be identified and as can be seen in the lower plot

of Figure 4.22, other frequencies are introduced in to the analysis which complicates

the analysis. Although the errors encountered in this study are relatively large, these

errors are only significant (above 5%) at frequencies that are above approximately 200

Hz and in relatively small diameter pipes. The focus of this work is in using APR

over long lengths of large diameter pipes. Since long distances are required then the

important frequencies are those that are below 200 Hz.

0.054 0.056 0.058 0.06 0.062 0.064 0.066 0.068-0.04

-0.02

0

0.02

Time (s)

Pre

ssu

re (

V)

0.054 0.056 0.058 0.06 0.062 0.064 0.066 0.068-10

-5

0

5

x 10-5

0 50 100 150 200 250 300 350 400 450 500 5500

0.5

1x 10

-4

Frequency (Hz)

Am

pli

tud

e (V

)

0 50 100 150 200 250 300 350 400 450 500 5500

0.5

1x 10

-9

Reflection signal

Input Signal

Input Signal

Reflection Signal

Figure 4.21: 175 m Pipe Recordings When D = 39.8 mm and f = 500 Hz

0.045 0.05 0.055 0.06 0.065 0.07 0.075-0.02

0

0.02

Time (s)

Pre

ssu

re (

V)

0.045 0.05 0.055 0.06 0.065 0.07 0.075-1

0

1x 10

-4

0 500 1000 15000

0.5

1x 10

-4

Frequency (Hz)

Am

pli

tud

e (V

)

0 500 1000 15000

1

2x 10

Input Signal

Reflection Signal

Reflection Signal

Input Signal

-13

Figure 4.22: 175 m Pipe Recordings When D = 39.8 mm and f = 1500 Hz


4.3.2 Different diameters tests

The laboratory experiments considered a number of tests with varying pipe diameters.

Considering the experiment using the 50 m length of pipe as an example, Figure 4.23

shows the attenuation results when pipes with three different diameters, 39.8 mm, 25

mm and 15.17 mm, were used, at temperatures of 20◦C, 23◦C and 22◦C, respectively.

In this figure ’TD’ represents the theoretical measurements and ’D’ refers to the actual

measurements. The results show that for most of the results, and particularly those at

the lower frequencies, the experimental and theoretical results are very consistent. It

can be seen that at the higher frequencies and smaller diameter there is a significant

difference in the experimental and theoretical results. As before this was because of

the high attenuation rates and the reflected signal being affected by background noise.

0 200 400 600 800 1000 1200 1400 1600 1800 20000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Frequency (Hz)

Att

enuat

ion (

dB

/m)

Attenuation for different diameters

TD=39.80mm

TD=25mm

TD=15.17mm

D=15.17mm

D=25mm

D=39.80mm

Figure 4.23: Attenuation Results for Different Size of Pipes

4.3.3 Different temperature tests

As mentioned earlier in this Chapter, temperature has a significant impact on the

transmission of acoustic signals in pipelines. Figure 4.24 illustrates how the attenuation


changes as a result of variation in temperature. The attenuation in this figure was

calculated using Kirchoff’s theory (3.16).

0 100 200 300 400 500 600 700 800 900 10000.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Frequency (Hz)

Att

enu

atio

n (d

B/m

)

0°C

5°C

10°C

15°C

20°C

25°C

30°C

Figure 4.24: Attenuation Changes When the Temperature Changes

When determining the attenuation α inside a long length of pipeline, which contains

variations in temperature, the attenuation αn in equally spaced subsections (of length

l) of the pipeline, within which the temperature is constant, can be considered.

α = 8.686× ln(pn+1

p1

)/L (4.22)

where L is the length of the full pipeline. The full pipeline is described in Figure 4.25.

...

Ll

p1 p2 p3 p4 p5 pn pn+1

temp1 temp2 temp4temp3 tempn

Figure 4.25: Temperature Gradient Model

The attenuation αn in each subsection of pipe can be calculated using the following

equations.


α1 = 8.686× ln(p2p1

)/l

α2 = 8.686× ln(p3p2

)/l

αn = 8.686× ln(pn+1

pn

)/l

(4.23)

with

ln(p2p1

)= ln p2 − ln p1

ln(p3p1

)= ln p3 − ln p2

ln(pn+1

pn

)= ln pn+1 − ln pn

ln(pn+1

p1

)= ln pn+1 − ln p1

(4.24)

Then (4.22) can be described by

α =1

n(α1 + α2 + ...+ αn). (4.25)

This means the attenuation for the whole pipeline is equal to the average attenuation

across each of the subsections. The temperature gradient can be considered by intro-

ducing temperature in to the simulator model, which will be explained in Chapter 6.

4.4 Summary

This Chapter has described how three metrics have been applied and compared for

measuring acoustic attenuation in pipes. These three techniques compared and anal-

ysed the RMS, peak value and FFT power of the acoustic signals to provide a measure

of attenuation. A series of experimental tests were used to validate the acoustic at-

tenuation which is predicted using theory developed by Kirchhoff. The results from

these experiments showed that Kirchhoff’s theory was accurate to within approxi-

mately 5% when compared with the experimental attenuation. Errors were measured

for experiments that were conducted at higher frequencies and on pipes with relatively

small diameters. For these tests the attenuation of the acoustic signal was high and

background noise was found to have a significant impact on the results. This is not

a problem for the work described in this thesis as the purpose of this study was to


validate Kirchoff’s theory for relatively large diameter pipes (50 mm and above) over

large distances (hundreds of meters or even kilometers). over the longer distances the

higher frequencies will attenuate and it is the lower frequency signals that are impor-

tant. It can therefore be concluded from the results presented in this Chapter that for

the application area that is of interest in this study, Kirchoff’s equation provides an

acceptable approximation of acoustic attenuation.

Chapter 5

Feature/Defects Characterisation

This chapter will discuss how different sizes of features/defects (e.g. erosion, leakage,

etc), as mentioned in Chapter 2, are determined. Different features were added to the

existing pipes for experimental purpose. Limited research has been conducted on this

topic. Among these studies, Morgan’s theory was consistent with the experimental

results. Based on the equations provided by Morgan [10], different features were

characterised. Attenuation was added to the feature characterisation equations to

improve the accuracy of the size approximation.

5.1 Method for the detection of the defects

The basic idea for sizing the defects used the equations presented by Morgan [10]

in 1978. APR-based equipment was used to record the signal. Morgan pointed out

that by using the Acoustic Ranger, the defects inside a tube can be identified quickly.

However, the information from the directly recorded data was not sufficient to obtain

detailed information about the defects themselves. From experience, it was assumed

that the larger the leakage hole was, the smaller the amplitude of the received signal

amplitude would be. The functional scheme of the Acoustic Ranger was explained

in Chapter 3. It has been widely used to identify defects in heat exchangers, power

plants and conventional boilers, to name a few.

102

CHAPTER 5. FEATURE/DEFECTS CHARACTERISATION 103

The APR based technique was used to detect the defects inside the feed heater tube

in the present study. The initial pulse was sent to the tube and any reflection caused

by defects/features could be recorded by the sensor at the beginning of the pipe.

Different defects are described in Figure 5.1. This figure shows how different defects

are modelled in the sizing procedure. Figure 5.1 (a) shows the clean pipeline without

any defects. Figure 5.1 (b) shows a pipe with a hole in one side of the pipe, the radius of

the hole is a. In Figure 5.1 (c), it is shown that a pipe with erosion, which is equivalent

to partially increase of the ID (2a) and a length of l. Similarly in Figure 5.1 (d), a

pipe with blockage can be equivalent to partially decrease of the ID (2a) and a length

of l.

Inner wall

Outer wall

Hole

Clean pipe

Pipe with

a hole

Erosion

Pipe with

erosion

l

a

ar

Blockage

Pipe with

blockagel

ai

( a )

( b )

( c )

( d )

Figure 5.1: (a) Clean Pipe (b) A Hole Defect in the Pipe (c) An Erosion Defect in thePipe (d) A Blockage Defect in the Pipe


5.1.1 Holes

The amplitude p of the received signal from a hole in the pipe wall is [10]

p = p0

{1 +

(πD2(W + 1.7a)

a2λ

)2} 12

(5.1)

Where p0 = the amplitude of reflected sound pulse from the end of the pipe when the

tube is without a leak

D = ID of the tested pipe (mm)

a = radius of the hole (mm)

λ = the wavelength of the input sound pulse (mm) @ probe central frequency

W = pipe wall thickness (mm)

The pressure is assumed to be at atmospheric.

λ =1000c

fc(5.2)

fc = centre frequency from the input signal (Hz)

c = speed of sound (m/s), as shown in Chapter 3.

Based on the equation from experimental attenuation, attenuation α can be written

as follows

α = −8.686× ln(p

p1)/L (5.3)

α = −8.686× ln(p0p1

)/L0 (5.4)

L = distance between the leak and the beginning of the pipe (m)

L0 = distance between the end of the pipe and the beginning of the pipe (m)

p1 = the amplitude of the input signal

p = the amplitude of the reflection signal from the leak


p0 = the amplitude of the reflection signal from end of the pipe

Deviate -8.686 on both sides

− α

8.686= ln(

p

p1)/L (5.5)

− α

8.686= ln(

p0p1

)/L0 (5.6)

Multiply by L and L0 respectively

− αL

8.686= ln(

p

p1) (5.7)

− αL0

8.686= ln(

p0p1

) (5.8)

It follows by

e−αL

8.686 =p

p1(5.9)

e−αL08.686 =

p0p1

(5.10)

Divide the above two equations

ξ =p

p0= e

α(L0−L)8.686 (5.11)

where the attenuation α can also be achieved using Kirchhoff’s attenuation equation.

ξ =

√(1 +

((πD2(W + 1.7a)

a2λ

)2(5.12)

ξ2 = 1 +((πD2(W + 1.7a)

a2λ

)2(5.13)

ξ2 − 1 =((πD2(W + 1.7a)

a2λ

)2(5.14)

Take square root √ξ2 − 1 =

(πD2(W + 1.7a)

a2λ(5.15)√

ξ2 − 1 =πD2W

a2λ+πD21.7

aλ(5.16)

Multiply by a2 and λ

a2λ√ξ2 − 1 = πD2W + πD21.7a (5.17)

Subtract πD21.7a

a2λ√ξ2 − 1− πD21.7a = πD2W (5.18)


Subtract πD2W

a2λ√ξ2 − 1− πD21.7a− πD2W = 0 (5.19)

Solve this equation as the quadratic equation

Aa2 +Ba+ C = 0, (5.20)

where

A = λ√ξ2 − 1 (5.21)

B = −πD21.7 (5.22)

C = −πD2W (5.23)

Because a can only be positive as it is the diameter of the pipe, (the negative a has

already been neglected)

a =−B +

√B2 − 4AC

2A(5.24)

For the size of the hole, the error might be introduced because of the error of Kirchhoff

attenuation theory, the speed of sound and the centre frequency.

5.1.2 Blockage and erosion

Some defects such as erosion and blockage can be modeled to the decrease or increase

of the pipe inlet wall as shown in Figure 5(c) and (d).

According to Morgan, when the alteration in an area is longer than the length of 100

mm, the change, the amplitude from the reflected signal of the feature can be written

as [10]

p = p0

( A

2− A

)(5.25)

A is the cross section change at the defect

p and p0 have the same definitions as in the last section

ξ =A

2− A(5.26)

Multiply by (2− A)

2ξ − ξA = A (5.27)


Add ξA

2ξ = A+ ξA (5.28)

Divide by (1 + ξ)

A = 2ξ/(1 + ξ) (5.29)

By definition

A = π(D

2+ ∆)2 − π(

D

2)2 (5.30)

∆ is the change of the radius. Add πD2

π(D

2+ ∆)2 = A+ π(

D

2)2 (5.31)

Divide by π

(D

2+ ∆)2 =

A+ π(D2

)2)

π(5.32)

Square root

D

2+ ∆ =

√A+ π(D

2)2)

π(5.33)

Minus D/2

∆ =

√A+ π(D

2)2)

π− D

2(5.34)

∆ =

√(4A+ πD2)

4π− D

2(5.35)

If ∆ > 0, the new internal diameter increases. In this way, it is an expansion of the

internal diameter, which can sometimes be the defect of erosion.

If ∆ < 0, the new internal diameter decreases. In this way, it is a contraction of the

internal diameter, which can sometimes be the defect of blockage.

This equation applies to both expansion and contraction conditions in the pipe. Nor-

mally it is the case when the reflections from the start and end do not interfere with

each other.

When the length l is less than 100 mm and the start and rear signals interfere with

each other. The ratio ξ between p and p0 can be written as [10]

ξ = (1− eFl) A

2− A, (5.36)


where l = length of the defect F is a function of shape factor and wavelength of

sound. When the defect is rod or bar, F = 36 and when the defect is a sphere,

F = 25. Multiply by (2− A)

ξ(2− A) = (1− e−Fl)A (5.37)

2ξ − ξA = (1− e−Fl)A (5.38)

Add ξA

2ξ = (1− e−Fl)A+ ξA (5.39)

2ξ = (1− e−Fl + ξ)A (5.40)

Divide (1− e−Fl + ξ) on both sides

A =2ξ

1− e−Fl + ξ(5.41)

5.2 Experimental apparatus

To locate and determine the size of the defects along the pipes, an experiment was

performed to identify specific defects. These pipes were made of aluminum and dif-

ferent kinds of defects, i.e. holes of varying diameters were machined into the pipe

manually .

The test rig shown in Figure 5.2 was built for the experimental test with manually

induced defects along the pipeline at the designated location. Six seamless tubes

(labeled 5, 7, 9, 10, 11 and 12) of 5 m long, 18.6 mm ID, 25.4 mm OD and with a wall

thickness of at least 3.4 mm, were used for the test with some specific features and

only one tube (labeled 15) was kept in a clean state and use as a comparison standard.

The other tubes in the picture were not used for the characterisation test.The details

of the pipes used in the experiment are listed in Table 5.1. The test rig as shown

in Figure 5.2 was AR 6000 with the gas gun. It included a microphone (Sennheiser

ke-4-211-2), a compression driver (Faital HF104) and a DAQ board (NI 4431).


Table 5.1: Details of the Features in the Test

Number Feature Size(mm)Distance fromthe end(mm)

Total length(mm)

5 hole 0.25 400 50007 hole 0.5 400 5000

9 blockage50 long,

0.2 � reduction1172 5000

10 blockage50 long,

0.4 � reduction1420 5000

11 erosion300 long,

0.2 � reduction940 5000

12 erosion300 long,

0.4 � reduction627 5000

15 clean 5000A hole 2.5 1500 3750B hole 2.5 2500 3750C hole 2.5 700 3750D hole 2.5 3300 3750

5.2.1 Holes detection

Firstly, to obtain the signal caused by the feature, the original signal recorded by

the loudspeaker was filtered and the background noise was removed from the original

signal. Figure 5.3 illustrates the signal after filtering and the zoomed in part is the

signal caused by a hole along the pipe.

Secondly, to determine the centre frequency of the feature signal, which would be used

in the estimation equation, a low-pass filter was applied to both the defect signal and

the reflection from the end of the tube. After that, the centre frequency was defined

as the frequency with the highest energy in the frequency domain.

Thirdly, Short Fourier Transform (SFT) was adopted to the feature signal and com-

pensated the loss due to the attenuation of the pipe in the frequency domain. The

same procedure was applied to the echo from the end of the tube.

Finally, IFFT was applied to the frequency signal. The signal could be recovered

without any attenuation. After the previous processing, the signal could be regarded

as transmitted without any energy loss.


Figure 5.2: Test Rig

For sizing the holes, Equation (5.21) to (5.24) were used to calculate the size of the

defect (radius measured in mm). The input signal for the first test was a signal with

the amplitude that did not exceed the range of the loudspeaker. Similarly to the first

test, the second test used a signal that was twice larger than the first input signal.

Table 5.2 shows the results from the pipes mentioned in Table 5.1. Table 5.3 illustrates

four pipes with a hole in different positions. The hole sizes, i.e. the radius of the hole,

was 2.5 mm. The error e was obtained by using Equation (5.42).

e =rp − rεrp

× 100% (5.42)

rp actual size machined in the metal pipe (mm)

rε estimated size (mm)

Based on the results in Table 5.2 and Table 5.3, theoretically the error was as high as 6

%. This error could be caused by the error from the speed of sound, the measurement

of the center frequency and the attenuation. Practically there was little difference

if a hole was predicted to measure 0.47 mm but in fact measured 0.5 mm. Potential


Time (s)

0 0.005 0.01 0.015 0.02 0.025 0.03

Imp

uls

e re

spo

nse

-2

-1

0

1

2

3

-4

10

Figure 5.3: A Reflection Signal Caused by a Hole in the Pipeline

Table 5.2: Hole Size Estimation Results

Test 1Estimatedsize (mm)

Practicalsize (mm)

Distancefrom the end(mm)

Error(%)

Tube 5 0.24 0.25 400 4Tube 7 0.48 0.5 400 4Test 2 Doubled amplitudeTube 5 0.24 0.25 400 4Tube 7 0.47 0.5 400 6

methods yo decrease the error are the calibration of the temperature of the room, which

affects both the speed of sound and attenuation, and detecting the centre frequency

correctly.

5.2.2 Erosion and blockage detection

For long erosion, the reflection signals of the defects could be separated (Figure 5.4);

Equations (5.29) and (5.35) were used to determine the equivalent size of the defect.

Similar to the test for hole sizing, the second set of tests used a signal that was twice as

large as the first signal. The estimated size means the equivalent decrease or increase of

the diameter. Test results are listed in Table 5.4. From the observation of the results,


Table 5.3: Hole Size Estimation Results (Short Pipes)


Practicalsize (mm)


Error(%)

Tube A 2.39 2.5 1500 4.4Tube B 2.36 2.5 2500 5.6Tube C 2.35 2.5 700 6Tube D 2.51 2.5 3300 0.4

improving the amplitude of the input signal, it did not improve the performance of

the equipment. Theoretically the error was up to 5 %. The main error came from ξ

was dependent on the ratio between reflection signal amplitude and the end reflection

amplitude. By improving the accuracy of measuring the two amplitudes, the accuracy

of the prediction can be increased. Practically, it did not make a huge difference when

the prediction was 0.21 mm and the measurement was 0.2 mm in the actual pipe.

Time (s)

0 0.005 0.01 0.015 0.02 0.025 0.03

Imp

uls

e re

spo

nse

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-3

10

Figure 5.4: A Reflection Caused by a 300 mm Erosion in the Pipeline

For partial blockages with a length the reflection signals of the defects could not

be separated (Figure 5.5). Equations (5.35) and (5.41) were used to calculate the

size of the defect. The test results are shown in Table 5.5. The error in the un-

separated condition was up to 5 %, which was mainly caused by the shape factor and

the measurement of the length. The accuracy of the shape factor can be calibrated by

the pipe with a known feature so that it can be calibrated by the known parameters


Table 5.4: Erosion Size Estimation


Practicalsize (mm)


Error(%)

Tube 11 0.21 0.2 increase 1172 5.0Tube 12 0.41 0.4 increase 1420 2.5Test 2 Doubled amplitude

Tube 11 0.22 0.2 increase 1172 10.0Tube 12 0.3728 0.4 increase 1420 7.5

as shown in the equation below. However, the effect of measuring the amplitude still

exists and is unavoidable. Practically it was also acceptable with a difference between

0.38 mm and 0.4 mm.

F = −ln(

1− ξ 2−AA

)l

(5.43)

Time (s)

0 0.005 0.01 0.015 0.02 0.025 0.03

Imp

uls

e re

spo

nse

-2

-1

0

1

2

3

4

5

-3

10

Figure 5.5: 50 mm Blockage

5.3 Application to the real-world

This chapter aims to complete a series of validation tests for the new version of Acoustic

Ranger AR 6000. A series of tests were performed to validate Morgan’s equations to


Table 5.5: Blockage Size Estimation


Practicalsize (mm)


Error(%)

Tube 9 0.20 0.2 increase 1172 0Tube 10 0.38 0.4 increase 1420 5.0Test 2 Doubled amplitudeTube 9 0.21 0.2 increase 1172 5.0Tube 10 0.38 0.4 increase 1420 5.0

characterise a series of features (e.g. holes, blockages and erosion) in the pipeline. All

the tubes in the experiments were machined to match the requirements of the testing,

which can give a thorough picture how the AR 6000 performs.

Based on Equation (5.9) and (5.10), acoustic pressure p at location L and p0 at location

L0 in Figure 5.6 can be expressed as

p = p1e− αL

8.686 (5.44)

p0 = p1e− αL0

8.686 (5.45)

Define M as the minimum parameter (determined by the user) compared to the

L

L0

p1 p p0

Figure 5.6: Illustrated Pipeline with a Feature

background noise of the recorded signal pnoise. As both p and p0 are the key parameters

to locate the size of defects, this means both p and p0 should meet the following

requirements.

p ≥M · pnoise (5.46)

p0 ≥M · pnoise (5.47)


As p > p0, if (5.47) is met, both p and p0 meet the requirement.

α > 8.686 ln(Mpnoisep1

)/L0 (5.48)

Apply (4.21) to (5.48),

ω

cR

(√ µ

2ρω+ (γ − 1)

√K

2ρωCp

)> ln(

Mpnoisep1

)/L0 (5.49)

All the parameters can be referred to glossary for Chapter 3.

As long as the signal frequency ω, length of the pipe L0 match (5.49), the defect can be

identified based on the different types in Section 5.1.1 and 5.1.2 and the corresponding

size can be calculated by (5.24) or (5.35).

Short length test result is a way to verify the feature equations. Long length with

feature location and size characterisation is similar to the short ones. The short

length verification tests provided a systematic way of testing and verification. The

narrow error offered a promising future research area by applying the equation to

longer length in the later of the thesis regarding simulator when a defect was detected.

This technique can help to provide more details.

According to the theory, as long as the reflection can be identified the size can be cal-

culated based on the reflection amplitude and frequency spectrum. As a validation for

AR 6000, this chapter is mainly as a reference for further research. In the next chapter,

pipeline simulators will be introduced. The defects interpreted by the simulator can

be analysed using the results listed in this chapter. The only barrier is sometimes,

the clean pipe response is not available, which is the majority situations in the actual

situation. This means p0 is not available anymore. Other sizing methodologies should

be explored. The rest of the analysis is out of the focus in this thesis.

5.4 Summary

By using Morgan’s method, a normal hole in the pipe wall could be detected and even

the small one (0.25 mm) could also be sized. The expansion of the pipe diameter can

also be detected. The error of sizing was up to 6% under the normal test.


The revised equations were presented for the blockage and erosion detection. Even

though the equivalent diameter change of the pipe was not totally proper, it was

useful for the start of the research at the beginning part as a simple equivalence.

By changing the amplitude of the input signal, the results show that the normal input

signal was enough to detect the defect and there was no need of to increase the input

signals energy. The error for estimating the size of the defects was within 8% if the

input signal amplitude was not boosted.

Chapter 6

Pipe Simulators and Experimental

Validation

As explained in Chapter 1, features in a simple pipeline system may cause numerous

reflections in the impulse response. However, for APR to be of value then it is essential

that these complex signals can be interpreted. To help with the interpretation of the

results recorded in a pipeline system by the APR equipment, a single pipe simulator

and a pipeline network simulator were designed and validated.

6.1 Background

The data obtained by APR from the real pipeline system is difficult to interpret because

of background noise and overlapped reflection and re-reflection signals caused by cross

section changes in pipes, e.g. T-piece or branches. For example, one pipe main had

three pipeline branches as shown in Figure 6.1 and the recorded impulse response was

plotted in blue in Figure 6.2.

An acoustic signal is split into three at each branch location, which makes it more

difficult to directly identify the signal features associated with defects, even for a

simple pipe setup. In Papadopoulou’s research [1], the idea of comparing the signals

before and after the defects was presented. However, in a number of situations, the

117

CHAPTER 6. PIPE SIMULATORS AND EXPERIMENTAL VALIDATION 118

1

30

0.0254

36

0.04

14

0.77

50 25 50 100

MIC

Figure 6.1: Layout of a Pipe Network

Distance from microphone (m)

Imp

uls

e re

spo

nse

0 50 100 150 200

-6

-4

-2

0

2

4

6

8

10

10-6

Figure 6.2: The Response of the Pipe Network

signal before the defects may not be recorded. This is one of the reasons to use the

simulator. To help interpret the results obtained using APR, research into an industrial

simulator has been conducted. The simulator generated the expected response of the

tested system. By comparing the signals from a field test with those generated by

the simulator, any defects will be identified in a more effective and efficient way. In

the example, it is difficult to identify whether there was a defect in the system in

Figures 6.1, as there were many reflections and re-reflections from the joints.


6.2 The single pipeline simulator

The single pipeline simulator was designed to help interpret the response of a single

pipeline system. The single pipeline system is defined as a pipe system without any

branches or T-pieces.

6.2.1 Reflection and transmission coefficients

When a plane wave propagates inside an air-filled cylinder, changes in the cross section

area cause partial reflections. The changes in acoustic pressure as the wave propagates

down the pipe are illustrated using a basic pipeline in Figure 6.3 [84].

The acoustic pressure of the wave before and after the cross section are represented

as p1 and p2 respectively. The particle velocities before and after the cross section

are represented as U1 and U2 respectively. As previously defined, + indicates that

the direction is the same as the propagation direction and − indicates the opposite

direction. According to the continuity of pressure and flow

p+1 + p−1 = p+2 (6.1)

and

U+1 + U−1 = U+

2 (6.2)

p1-

p1+

p2+

Figure 6.3: Pressure Transmission in a Pipeline Unit


Divide (6.1) by (6.2)p+1 + p−1U+1 + U−1

=p+2U+2

(6.3)

Given the acoustic impedance Z, then according to Kinsler [84]

± Z =p

U±, (6.4)

(6.3) can be rearranged:

p+1 + p−1p+1Z1

+p−1−Z1

= Z1. (6.5)

It therefore follows that

Z1(p+2 + p−1 ) = Z2(p

+2 − p−1 ) (6.6)

Z1p+2 + Z1p

−1 = Z2p

+2 − Z2p

−1 (6.7)

Z1p+2 − Z2p

+2 = −Z2p

−1 − Z1p

−1 (6.8)

Then the reflection coefficient r1,2

r1,2 =p−1p+1

=Z2 − Z1

Z2 + Z1

. (6.9)

As the impedance Z is defined as

Zi =ρicisi

with i = 1, 2 (6.10)

with respect to the density of air ρi and the speed of sound ci in the ith section of the

pipe, and in the same environment, there is no difference between the air density and

the speed of sound, i.e. ρ1 = ρ2 and c1 = c2, we have

r1,2 =Z2 − Z1

Z2 + Z1

=

ρ2c2S2− ρ1c1

S1

ρ2c2S2

+ ρ1c1S1

=1S2− 1

S1

1S2

+ 1S1

=S1 − S2

S1 + S2

. (6.11)

Similarly, a series of reflection and transmission coefficients between two adjacent


segments of pipe are given in [84]:

r1,2 =S1 − S2

S1 + S2

(6.12)

r2,1 =S2 − S1

S1 + S2

= −r1,2 (6.13)

t1,2 =2× s1S1 + S2

= 1 + r1,2 (6.14)

t2,1 =2× s2S1 + S2

= 1− r1,2 (6.15)

where S1 and S2 are the cross section areas of segments 1 and 2 respectively; r1,2 is the

reflection coefficient from segment 1 to 2 and t1,2 is the transmission coefficient from

segment 1 to 2; similarly r2,1 is the reflection coefficient from segment 2 to 1 while t2,1

is the transmission coefficient from segment 2 to 1.

6.2.2 Digital waveguides

Digital waveguides [106] are digital filter designs that model the acoustic wave propa-

gation inside of the pipe in a lossless way throughout the whole length; with the losses

and dispersion described using filters. They offer filter-like structures to simulate the

modified physical systems [94,107]. Digital waveguides were widely used in the musical

field for musical sound synthesis and computational models [108–110].

A simplified digital waveguide structure is shown in Figure 6.4.

Figure 6.4: Waveguide Filter Structure


The excitation signal U corresponds to the energy supplied to the whole system at the

beginning of the system. The output Y represents the travelling wave component at

the end of the selected point. D0 is the minimum digital time delay in the system over

a round-trip distance. F is the filter that describes the remaining losses in the system

over the round-trip.

The method of using digital waveguides will not be discussed in depth in this thesis.

However, there is a comprehensive review of this topic in the literature [111]. It offers

a basic model for the simulator models. In Section 6.2.2 and Section 6.3.2 of this

chapter, more detail for the modelling is provided.

6.2.3 The cylindrical model to build pipeline

A tubular object, i.e. pipe, whose cross-sectional area varies with axial distance can

be modelled by a series of i discontinuously joined cylindrical segments. The length

of each segment is l and it has a corresponding one-way travel time T , that is defined

as:

T =l

c(6.16)

where c is the speed of sound. Figure 6.5 shows the division of one section of a pipeline

into several segments, each with different cross section areas.

With reference to Figure 6.6, the generalised scattering equation is presented to process

how the signal propagates and is reflected when the signal hits the barrier between

two adjacent segments [61]:p+i+1,i(nT )

p−i+1,i(nT )

=1

(1− ri,i+1)

1 −ri,i+1

−ri,i+1 1

p+i,o(nT )

p−i,o(nT )

(6.17)

with i = 1, 2, ...,M and n = 1, 2, ..., N , where M is the number of all the segments

and N is the number of samples recorded.


SOURCE TUBE

TEST OBJECT

Segment 1 2 3 4 5 … i-7 i-6 i-5 i-4 i-3 i-2 i-1 i

l

Figure 6.5: Discretizing a Pipeline

p+1,i p+

1,o

p+2,i

...

p+i,op+

i,i

p-1,i

p-2,i

p-1,o

p-i,i p-

i,o

Segment 1 Segment i

Figure 6.6: Signal Propagating Along the Pipe

A space-time diagram is displayed in Figure 6.7. The arrows indicate the direction of

the signal propagation (forwards and backwards) at different times in each segment.

The pressures at the left and right sides of each segment are also displayed. For


example, when signal p+1,o[T ] hits the barrier between segment 1 and segment 2 at

time T, signal p+2,i[T ] and signal p−1,o[T ] are generated according to the transmission

and reflection coefficients. There is an assumption that no backward travelling wave

is present in a segment before a forward travelling wave has reached that segment.

0 1 2 3 4 5

0

T

2T

3T

4T

5T

6T

p+0,i[0T]

p-0,o[0T]

Segment i

Time t

p-1,o[T] p+

2,i[T]

p+2,o[2T]

p+3,i[2T]

p+3,o[3T]

p+4,i[3T]

p+4,o[4T]

p+5,i[4T]

p+5,o[5T]

p+1,i[0T]

p+1,o[T]

p+1,i[2T]

p+1,o[3T]

p+2,i[3T]

p+2,o[4T]

p+3,i[4T]

p+3,o[5T]

p+4,i[5T]

p+4,o[6T]

p+1,i[4T]

p+1,o[5T]

p+2,i[5T]

p+2,o[6T]

p+5,i[6T]p+

3,i[6T]p+1,i[6T]

p-1,i[2T]

p-2,o[2T]

p-2,i[3T]

p-3,o[3T]

p-3,i[4T]

p-4,o[4T]

p-4,i[5T]

p-5,i[6T]

p-1,o[3T]

p-1,i[4T]

p-2,o[4T]

p-2,i[5T]

p-3,o[5T]

p-3,i[6T]

p-4,o[6T]p-

2,o[6T]

p-1,o[5T]

p-1,i[6T]

p-0,o[2T]

p-0,o[4T]

p-0,o[6T]

Figure 6.7: Space-time Diagram [61,112]

To include attenuation losses along the pipeline, discrete time filters are applied as the

acoustic signal is passed through each segment [61]:

p+i,o(nT ) = p+i,i((n− 1)T ) ∗ xi(nT ) (6.18)

p−i,i(nT ) = p−i,o((n− 1)T ) ∗ xi(nT ) (6.19)

where ∗ represents convolution. Sequence xi(nT ) is the loss filter x(nT ) inside the ith


segment, as described in Section 6.2.4.

6.2.4 Attenuation filter

To produce an algorithm capable of simulating the behaviour of an acoustic pres-

sure wave travelling in a cylindrical void requires a suitable means of accounting for

attenuation. The initial Keefe’s model was introduced in 3.2.4.

As validated in Chapter 4, Kirchhoff’s attenuation equation matched the experimental

attenuation with an error of less than 5 %. The comparison between Kirchhoff’s

equation and Keefe’s equation is shown in Figure 6.8. It is clearly illustrated that

both of the attenuation equations match each other closely after 20 Hz. The main

frequency of the wave for testing industrial pipe was between 20 Hz and 100 Hz. The

absorption value mainly relies on the temperature and the sampling frequency.

100

101

102

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Frequency (Hz)

Att

enu

atio

n (

dB

/m)

Kefee

Kirchhoff

Figure 6.8: Attenuation Comparison Between Kirchhoff’s And Keefe’s Equation

The proposed simulator is a causal time-stepping solver; therefore, (3.35) must be

transformed into discrete time. To perform this transform, (3.35) is discretized and

inverted using the inverse Fast Fourier algorithm as per Amir [6] and Sharp [51]. The


resulting discrete time filter x(nT )is typically beset by ripple due to phase disconti-

nuities in the frequency domain filter. To remove the ripple, the rotating phase [113]

was applied to the filter X(ejω). To diminish the time delay caused by the rotating

phase model, an all pole model [6] was used by performing a M pole transfer function

on filter x′(nT ). M is normally adjusted according to the length of the attenuation

filter.

1. To remove the discontinuity, the rotating phase method works by forcing the

phase to be zero at f = 12F (applied to equation (3.35)).

X ′(jω) = e−γ(ω)lejωl

ϑp(2π12F ) (6.20)

After discretizing X ′(jω) and applying IFFT to equation (6.20), a new discrete

time domain filter x′(nT ) is achieved.

2. The autocorrelation of filter x′(nT ) was calculated, where m = 0, 1, ..., N − 1.

R(m) =N−1−m∑n=0

x′(nT )x′((n+m)T ) (6.21)

3. The predictor coefficients ak for the all-pole model were calculated using Durbins

recursive method [6], where k = 1, 2, ...,M . The gain G was calculated using ak

and R(m).

G =

√√√√R(0) +M∑k=1

akR(k) (6.22)

4. The frequency domain filter X ′(ejω) is evaluated on the unit circle, where f =

0, 1N, 2N, ..., N−1

N.

X ′(ejω) =G

1 +40∑k=1

ake−jωk(6.23)

5. A ripple-free filter approximation x′′(nT ) was calculated by applying IFFT to

X ′(ejω).

The combined model is a minimum phase model, which means that the delay caused

by the tube is missing. The missing delay could be expressed explicitly by adding a

delay to the forward signals and subtracting it from the backward signals.


6.3 The pipeline network simulator

To expand the current study for single pipes, research into pipe networks was con-

ducted. Pipe network systems are used widely in natural gas transportation, particu-

larly in domestic gas distribution systems. A pipe network simulator provides a way to

help the interpretation of the measurements obtained when APR is applied to pipeline

networks. The pipe network simulator was based on the single pipe simulator, how-

ever, special processing was introduced for the branch joints. To speed up the single

pipe simulator, a non-equal segment model based on the feature location was used to

build the pipe network simulator.

The division of one pipeline with different acoustic impedance changes is shown in

Figure 6.9.

The model presented here is a discrete time model, which discretizes the tubular

pipeline by concatenating cylindrical segments. Different from the previous work

in [114], which divided a tube into segments of the same length, the pipe is divided

into a set of segments with different lengths separated by known features of the pipe,

which improved simulation speed. The length of the ith segment is

li = Ni ×c

fs(6.24)

Ni = [lpic/fs

] (6.25)

where the speed of sound and the sampling frequency are represented by c and fs

respectively; lpi is the practical length of the ith segment and [a] means the nearest

integer to a.

6.3.1 Reflection and transmission coefficients at joints

A generic Y-piece is shown in Figure 6.10. The junction is modelled as a point in a

lossless scenario and does not include any losses. A forward transmitting signal in +x

direction is considered to split into three parts at the junction. The resulting signals

are reflected signal in -x direction and transmitted signals in +y and +z directions.


Segment SX1 SX2 SX3 SX4

SOURCE TUBE MAIN PIPE

BRANCH 1

BRANCH 2

SOURCE TUBE MAIN PIPE

BRANCH 1

BRANCH 2

Segment SZ

1

Seg

men

t S

Y1

Figure 6.9: Pipeline with Branches Discretization

0

x

y

z

Figure 6.10: A Generic Y-piece-branch


Given x, y, z as the unit distance in each direction as shown in Figure 6.10, in the main

pipe shown on the left in the x direction. pi is the acoustic pressure inside of the pipe

and Ui is the volume velocity.

p0 = Aej(ωt−kx) +Bej(ωt+kx),

U0 = Aej(ωt−kx)+Bej(ωt+kx)

ρ0c0S0.

(6.26)

where A is the amplitude of the input signal and B is the amplitude of the reflection

signal at the reflection point. In the first branch in the y direction, A1 is the amplitude

of the signal transmitting in the +y direction.p1 = A1ej(ωt−ky),

U1 = A1ej(ωt−ky)

ρ1c1S1.

(6.27)

Similarly, in the second branch in the z direction, A2 is the amplitude of the signal

transmitting in the +z direction.p2 = A2ej(ωt−kz),

U2 = A2ej(ωt−kz)

ρ2c2S2.

(6.28)

At the location x = y = z = 0, the diameter of the pipe is far smaller than the

wave length. Because of the continuity of pressure and volume velocity, there exist

continuity conditions on acoustic pressure and the flow [84], such that:

p0 = p1 = p2 (6.29)

U0 = U1 + U2 (6.30)

Dividing (6.30) by (6.29) gives:

U0

p0=U1

p1+U2

p2(6.31)

Evaluating this and (6.4)1

Z0

=1

Z1

+1

Z2

(6.32)


S0

ρ0c0(A−B) =

S1

ρ1c1A1 +

S2

ρ2c2A2 (6.33)

Given

Yi =Siρici

(6.34)

with i = 0, 1, 2,

Y0A−BA+B

= Y1 + Y2 (6.35)

and thenA

B=

1− Y1+Y2Y0

1 + Y1+Y2Y0

=Y0 − (Y1 + Y2)

Y0 + (Y1 + Y2). (6.36)

Again, in the same environment, there is no difference between the air density and the

speed of sound, i.e. ρ0 = ρ1 = ρ2 and c0 = c1 = c2, we have

r+0 =A

B=Y0 − (Y1 + Y2)

Y0 + (Y1 + Y2)=S0 − (S1 + S2)

S0 + (S1 + S2). (6.37)

Similarly, all the reflection coefficient ri for different pipes at the joint are

r+0 =S0 − (S1 + S2)

S0 + (S1 + S2)(6.38)

r+1 =S1 − (S0 + S2)

S1 + (S0 + S2)(6.39)

r+2 =S2 − (S0 + S2)

S2 + (S0 + S2)(6.40)

according to [84], where the same gas propagates in all pipe branches in this study, S0,

S1 and S2 are the cross section areas of segments in the x, y, z direction respectively;

The subscript ’+’ means a signal is transmitting in the x+ direction.

The transmission coefficient ti = 1 + ri is still applicable to the branch pipelines.

6.3.2 The network model

A generic pipeline network is shown in Figure 6.11. Each branch in this network can

be modelled by a series of n cylindrical segments, similar to the way the single pipe

simulator was modelled in Section 6.2. For the joints between the branches, such as

joint A, B, C and D in Figure 6.11, the following approach was used.

Each junction causes three major changes in acoustic propagation, shown in Fig-

ure 6.12. If a subscript ′+′ is used to designate a wave travelling in the forward


B

CA D

Figure 6.11: A Generic Pipeline Network

direction and a subscript ′−′ for a wave travelling in the backward direction, then in

reference to Figure 6.12

p−0 (nT ) = p+0 (nT ) · r+0 + p−1 (nT ) · t−1 + p−2 (nT ) · t−2 (6.41)

p+1 (nT ) = p+0 (nT ) · t+0 + p−1 (nT ) · r−1 + p−2 (nT ) · r−2 (6.42)

p+2 (nT ) = p+0 (nT ) · t+0 + p−1 (nT ) · t−1 + p−2 (nT ) · r−2 (6.43)

p0+ p2

+

p1+

p0-

p1-

p2+ p0

-

p1+

p2-

(a) (b) (c)

Figure 6.12: Signals Change at the Junction

To deal with the branch joints, a dimension is added to label different branches in the

pipe network in the network model with one dimension for time and one for segments.

The way to deal with the branch dimension is to set designated connection locations at

the beginning of the simulator. Every branch can be considered as a window with their

own time-space diagrams, which is the same as Figure 6.7. In each window, the signal

propagates in the same way as a single pipe simulator except for the junctions between


branches. The connections between the windows contribute to the third dimension,

which is the branch dimension. The pressure values at the connections are updated

every cycle during the simulation.

6.3.3 Summary of the pipe simulators

Both the single pipe simulator and pipe network simulator use the time domain signals

to describe the acoustic signal transmitting inside the pipeline. When a layout of the

pipeline system is known, the impulse response can be generated by the simulator.

The pipeline system can be numerically modelled using the step-by-step method. Any

signal at each segment is available by initiating the output in the simulator. This helps

to interpret signals which are recorded at any accessible points of the pipeline system.

The network simulator uses a nodal model to discretise the pipeline. Compared to

the equally discretized model, this saves computing time for convolution inside each

segment. For a certain length of the pipe without any significant features, the output

signal can be calculated immediately by the convolution of input signal of this segment

and the attenuation filter when it is modelled in the nodal mode. This improves the

calculation efficiency compared the the equal step model.

The minimum step of calculation l is determined by the sampling frequency fs and

speed of sound c. This has been discussed earlier in this chapter to define the step of

discretisation. In the actual test, sampling frequency of 1 kHz is used very often. For

a long pipeline with hundreds of kilometers, the minimum step effect is less compared

to the whole length of the pipe. However, if the pipe is short within a few meters,

the minimum step has to be defined small enough and this requires high sampling

frequency. Otherwise, some key features will be interpreted in the wrong location.

In summary, the simulator developed in this chapter is efficient and applicable to the

long pipes, especially the nodal model in network simulator. Mentioning hundreds of

kilometers, low sampling frequency device can also provide a way to record the signals

which reflect the features/defects of the pipeline.


6.4 Laboratory validation of the single pipeline sim-

ulator

6.4.1 Experimental setup for single pipeline simulator

To validate the accuracy of the simulator, a series of experimental tests were carried

out. The apparatus used in these tests is shown schematically in Figure 6.13. The pipes

used in the lab tests were new polyethylene pipes with an outer diameter of 50 mm and

internal diameter of 39.8 mm. A Fostex FF105WK loudspeaker was connected to the

beginning of the test tube via a plastic adaptor, which had the same diameter as the

test tube. Two 1/4-inch Bruel and Kjaer DeltaTron pressure-field microphones were

inserted in the test pipe via two 7 mm holes so that the diaphragm of the microphones

was flush inside the pipe wall at the either end of the test tube. Signal output and

acquisition were handled by NI-9263 and NI-9234 modules; sampling was performed

simultaneously across all channels at 51.2 kHz.

MIC1

LOUDSPEAKER TEST TUBE

AMPLIFIER

COMPUTER

A/DD/A

MIC2

DISSIPATION TUBE

COMPACT DAQ

BOARD

Figure 6.13: Experimental Setup

The distance between the loudspeaker and MIC1 was 0.2 m. The tube length between

the two microphones was 100 m while the second part of the pipe (dissipation pipe) was

50 m. As the excitation signal used in the test was ≈ 0.25 s (that is 0.25×340 = 85 m),

both the test pipe and the dissipation pipe were long enough to make sure that the

transmitted signal and the reflected signal from the end of the pipe did not interfere

with each other in the microphone recordings.


6.4.2 Results and analysis

A series of digitally generated short burst sinusoidal waves with different frequencies

were used as input signals. The frequencies of the input signals ran from 50 Hz to

1000 Hz in 10 Hz increments. For each test, the signals recorded by both microphones

were time windowed so that only the section of either signal containing the sine burst

was present. The RMS value of the time windowed data was then calculated. Testing

was repeated 5 times at each frequency and results were averaged to reduce the effects

of any environmental noise. Attenuation between the two microphones was calculated

as per [2]:

αp = −8.686× ln(p2p1

)/l (6.44)

where l is the length between the two microphones, p1 and p2 are the RMS values of

time windowed pressure signals recorded by the two microphones and αp is experimen-

tal attenuation in dB/m (1Np = 20 log10 e = 8.686 dB).

The simulator was configured so that the pipe dimensions, such as diameter and length,

and gas properties, such as pressure and temperature, matched the experimental set-

up. The same series of input signals were sent through the simulator to generate the

simulated response. In Figure 6.14 the attenuation, according to (6.44), attenuation is

plotted against frequency for both the experimental and the simulated response. The

error between the two data sets is presented in Figure 6.15. The simulated response

was also compared to the direct use of (6.44) and found to give very similar results;

slight deviation is to be expected due to numerical errors. Figures 6.14 and 6.15 show

that the experimental results are very similar to those gained via simulation, thus

validating the pipe simulation algorithm.

In the results from the tests, the maximum error between the simulation and exper-

imental results was 3.02%. It was observed that higher errors were recorded at the

higher frequencies. This was most likely caused by the lower signal to noise ratio(SNR)

achieved at high frequency due to the greater attenuation. It was noticeable that for

frequencies between 460 Hz to 860 Hz, the experimental attenuation was consistently

lower when compared with simulation results. The reason for this was unclear, but

may have been caused by background noise during the test.


0 200 400 600 800 1000 0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Frequency (Hz)

Att

enu

atio

n (

dB

/m)

Simulation Attenuation

RMS attenuation

Figure 6.14: Attenuation Results for Pipe with ID = 39.8 mm

0 200 400 600 800 1000 -4

-3

-2

-1

0

1

2

X: 910

Y: -3.023

Frequency (Hz)

Err

or

(%)

Figure 6.15: Error Between the Simulation And Experiment Results


6.4.3 Further demonstration of experimental tests

To further test the capabilities of APR for surveying pipeline networks, prototype

hardware consisting of a speaker-microphone system that could be connected to a gas

main, using a 1” BSP threaded connection was developed. A schematic showing the

hardware layout is presented in Figure 6.16. The microphone is inserted 200-500 mm

into the gas main while the speaker is located outside the main but is in direct contact

with air in the main. The hardware is connected to a laptop via a ’Peli’ case that

contains all the necessary amplification and data acquisition equipment. Figure 6.17

is a photograph of the system including the Peli case.

Figure 6.16: Layout of the Prototype Hardware

To evaluate the prototype system and the mathematical model a series of tests were

first performed in the laboratory using 50 mm MPDE pipe, Figure 6.18 shows the

layout used for testing. Table 6.1 lists the features present in the pipe and their

location for each of the six tests. For each test two measurements were taken, first

with the microphone installed in the pipe to the right of the prototype hardware

facing L4 (as shown in Figure 6.18) and second with the microphone installed in the

pipe to the left of the prototype hardware, facing L1. Taking readings at two different

microphone locations gives directionality, allowing us to determine if a given feature is


in the pipe section to the left of the prototype hardware or in the section to the right.

Plastic box

Wiring

Speaker

Gas main Guide tubeConnection tube

Microphone

Figure 6.17: Diagram of the Prototype System Used for Testing Air Filled Pipes

Prototype

hardware

Microphone

Ball valveL1

L2L3 L4 L5

48.896.2

122.9 98.750.1

0.2

Figure 6.18: Layout of the 50 mm Pipework Used in Laboratory Testing; L1, L2 and

L4 Represent Pipe Feature Locations While L3 And L5 Are Open Ends, All Lengths

Are in meters

Table 6.1: Test Rig Feature Table

Pipe feature LocationTest 1 Clear pipe n/aTest 2 Partially closed ball valve L1Test 3 Fully closed ball valve L1Test 4 300 ml water pool L2Test 5 25 � 200 mm long solid cylinder inside pipe L4Test 6 32 � 200 mm long solid cylinder inside pipe L2

Figure 6.19 shows the simulated and measured responses of the pipe system shown in

Figure 6.18 when it was free from features, as per test 1 in Table 6.1. Figures 6.20-6.24

present the results from Tests 2-6 (Table 6.1) where additional features are present in


the pipe. In Tests 2-6 the results were analysed in a way that mimics the proposed

analysis method of real pipe systems. The top plot in Figures 6.20-6.24 shows a

simulation of the clear pipe that was generated using knowledge of the pipe layout.

The second plot is the measured response. By comparing the expected response with

the actual response it is possible to identify and locate any unexpected signal features

and provide information on the geometry of what is causing these signal features.

The bottom plot in Figures 6.20-6.24. shows a simulation of the pipe that includes

the physical item(s) that are suspected to be causing the unexpected signal features.

This simulation can be used to confirm the presence of expected and unexpected pipe

features (water pools, misbehaving valves, unknown services), and provide details of

their location and size.

In Figure 6.19, the top plot shows the expected response from a clear pipe while the

bottom plot shows the measured response. The two plots are similar and there are no

unexpected features in the measured response. It is evident in the measured response

that the signal feature at ≈ 100 m results from a feature that lies to the right of the

prototype hardware at L5 because the signal recorded with the microphone in the

right position (in red) arrives before the signal recorded with the microphone in the

left position (blue) and as such the feature is clearly associated with the open end at

L5, vice versa is true of the signal feature at ≈ 125 m and therefore this feature is

clearly associated with the open end at L3.

Simulation of clear pipe


Imp

uls

e re

spo

nse

Imp

uls

e re

spo

nse

Microphone left

Microphone right

Measured response of clear pipe


Figure 6.19: Comparison Results Between Simulation Results And Experimental Re-

sults in Test 1






Imp

uls

e re

spon

seIm

pu

lse

resp

on

seIm

pu

lse

resp

on

se

Microphone left

Microphone right

Measured response of pipe with partially closed ball valve

Simulation of pipe with partially closed ball valve


sults in Test 2

In Figure 6.20, comparing the simulation of a clean pipe with the measured response

(top and middle plots) gives a clear indication of a partial blockage at L1 (Figure 6.18).

The shape of the measured signal at ≈ 50 m indicates a blockage (rise followed by fall),

because the signal features from both open ends of the pipe are present it is apparent

that the blockage is only partial and from the order of arrivals of the microphone left

and microphone right signals it is ascertained that the partial blockage is to the left

of the prototype Hardware. The simulation result in the bottom plot confirms that a

partial blockage L1 is congruent with the results obtained in the measured response

(middle plot).


(top and middle plots) indicates a full blockage at L2 (Figure 6.18). The shape of the

measured signal at ≈ 50 m is indicative of a blockage (rise followed by fall), because

the signal features from the open end at L3 (Figure 6.18) is not present it is inferred

that there is a complete blockage. The order of arrivals of the microphone left and

microphone right signals suggest that the blockage is to the left of the prototype

hardware. The simulation result in the bottom plot closely resembles the measured

response and so confirms the diagnosis.


Imp

uls

e re

spon

seIm

pu

lse

resp

on

seIm

pu

lse

resp

on

se

Microphone left

Microphone right





Measured response of pipe with fully closed ball valve

Simulation of pipe with fully closed ball valve

Figure 6.21: Comparison Results between Simulation Results And Experimental Re-

sults in Test 3

Imp

uls

e re

spon

seIm

pu

lse

resp

on

seIm

pu

lse

resp

on

se

Microphone left

Microphone right





Measured response of pipe with 300 ml water pool at L2

Simulation of pipe with 300 ml water pool at L2


sults in Test 4


(top and middle plots) indicates a partial blockage at L2 (Figure 6.18). Although the


signal feature at ≈ 97 m overlaps with the signal feature from the open end at L5 it is

possible to ascertain from the order of arrival of the microphone left and microphone

right signals that the small signal feature at ≈ 97 m comes from the left section of the

pipe while the bigger feature caused by the open end at L5 comes from the right section.

The simulation result in the bottom plot confirms the location and characteristics of

the unexpected feature and is used to provide further sizing information.


(top and middle plots) gives a clear indication of a partial blockage at L4 (Figure 6.18).

The shape of the measured signal at ≈ 52 m is indicative of a blockage (rise followed

by fall), because the signal features from both open ends of the pipe are present it

is apparent that the blockage is only partial and from the order of arrivals of the

microphone left and microphone right signals it is ascertained that the blockage is to

the right of the prototype hardware. The simulation result in the bottom plot confirms

that a partial blockage at L4 is congruent with the measured results and can be used

to improve locational accuracy and give sizing information.

Imp

uls

e re

spon

seIm

pu

lse

resp

on

seIm

pu

lse

resp

on

se

Microphone left

Microphone right





Measured response of pipe with cylindrical blockage at L4

Simulation of pipe with cylindrical blockage at L4


sults in Test 5



(top and middle plots) indicates a partial blockages at both L2 and L4 (Figure 6.18).

The shape of the unexpected features suggest they are caused by blockages and as the

signal from both open ends of the pipe are present, this suggests that both blockages

are only partial and from the order of arrivals of the microphone left and microphone

right signals the direction of each blockage relative to the prototype hardware can be

ascertained. The simulation result in the bottom plot confirms that partial blockages

at L2 and L4 match the measured results. The simulation result also reveals that

the partial blockage at L2 causes a greater restriction than the partial blockage at L4

despite the signal feature at ≈ 50 m being larger than the signal feature at ≈ 97 m.

This anomaly is caused by losses in acoustic energy as sound travels along the pipe.

Imp

uls

e re

spon

seIm

pu

lse

resp

on

seIm

pu

lse

resp

on

se

Microphone left

Microphone right





Measured response of pipe with cylindrical blockage at L4 and L2

Simulation of pipe with cylindrical blockage at L4 and L2


sults in Test 6


6.5 Laboratory validation of the network pipeline

simulator

To validate the proposed network pipeline simulator, a series of tests were conducted

in the laboratory.

6.5.1 Experimental setup for the network pipeline simulator

The pipes used in these tests were new polyethylene pipes (MDPE pipe). Details of

the test equipment are listed in Table 6.2. Sampling was performed simultaneously

across all channels at 96 kHz, the highest rate for the analogue output channel, to

minimize the discretization error.

Table 6.2: Equipment Used in the Tests

Equipment Model

Amplifier YAMAHA A-S300

Loudspeaker SEAS H1208-08 L22RN4X/P

Microphone Bruel & Kjaer DeltaTron 1/4-inch 4944-A

Data Acquisition Board National Instruments USB-4431

6.5.2 Reflection and transmission coefficients validation tests

Two different layouts of the pipes, shown in Figure 6.25 and 6.26, were used to validate

the model used within the simulator. All the pipes used in this test had an internal

diameter (ID) of 39.8 mm and an outer diameter (OD) of 50 mm. The capped ends

are marked as E1 and E2. The main test points, where the microphone was attached,

were the locations marked L1, L2 and L3. The distance between L1 and J1 was 24 m

while L1 was 25 m from the loudspeaker. The length between J1 and L2 was 50 m and

it was 50 m from J1 and L3. To ensure the accuracy of the test, the same microphone

was inserted into the pipe where it was flush inside the pipe during each test.


The excitation signal was a logarithmic sine sweep with 221 samples ranging from

20 Hz to 1 kHz and was played five times back to back so that a complete cyclic signal

could be achieved in the middle of the data sequence. The resulting pressure signal

was recorded by the microphone inserted in the pipe.

The averaged periodic response signal of the second to the fourth sequences was de-

convolved with the periodic input signal to determine the impulse response of the

pipe. This impulse response included the acoustic response of the pipe, the acous-

tic response of the speaker system and enclosure and the electrical response of the

laptop/DAQ/amplifier.

MIC

LOUDSPEAKER MAIN PIPE

AMPLIFIER

COMPUTER

A/DD/A

BRANCH

DAQ BOARD

J1 E2

E1

L3

L2L1

Figure 6.25: Pipe Layout A

6.5.3 Results and analytics

The equivalent pipeline network was simulated using parameters to match those used

in the experiment. The comparison results are shown in Table 6.3. As the attenuation

for a tubular pipe has already been validated in previous work [114,115], the reflection


MIC

LOUDSPEAKER MAIN PIPE

AMPLIFIER

COMPUTER

A/DD/A

BRANCH 1

DAQ BOARD

J1

BRANCH 2

E1

E2

L3

L1

L2

Figure 6.26: Pipe Layout B

and transmission coefficients were calculated as

r1,23 =p

psim(6.45)

and

t1,2 = t1,3 =p

psim(6.46)

where p is the peak value of the reflected or transmitted wave in the experiment; psim

is the peak value of idealised signals when there is no T-piece branch. From Table 6.4,

it is clear that the maximum error for the reflection and transmission coefficients that

was measured in this experiment was 5.697%.

Table 6.3: Peak Values at Each Location

L1 (×10−5) L2 (×10−5) L3 (×10−5)

Layout ASimulation(without branch) psim 7.227 4.703 4.695

Experiment p -2.393 2.956 2.978

Layout BSimulation(without branch) psim 10.683 7.206 7.192

Experiment p -3.530 4.622 4.597


Table 6.4: Errors Between the Simulation And Experiment Results

r t1,2 t1,3

Layout ASimulation -0.333 0.667 0.667Experiment -0.331 0.629 0.634

Error(%) 0.601 5.697 4.948

Layout BSimulation -0.333 0.667 0.667Experiment -0.330 0.641 0.639

Error(%) 0.901 3.898 4.198

6.5.4 Network Pipeline simulator validation tests

Pipeline tests for setups with different numbers of branches

0.9

50

.95

0.9

5

7

3

LOUDSPEAKER

MIC

14

7550

1 2

100

J1E1 E2

E3

(a)

4

125

1

50

E1 E2

36

E4

50

5

(b)

7

4

14

7550

1 2

50

J1E1 E2

E3

(c)

36

E4

50

6

MIC

MIC

0.3

0.3

0.3

6

6

5

J3

J3

LOUDSPEAKER

LOUDSPEAKER

Figure 6.27: Layouts of the Pipe Network Setup


Figure 6.27, shows the layout of the experimental setups for pipeline networks with

two and three branches separately. In this figure all distances are labeled in meters.

All the ends of the pipes were capped to simulate a closed system. The ID of the

main pipe was 39.8 mm while the ID of the 14 m branch pipe was 25.4 mm. The

pipe system was excited by a loudspeaker using a logarithmic sine sweep as with the

previous tests.

All the simulator parameters were specified to match the experimental setup in Fig-

ure 6.27. The pipe used in the main section had a ID of 39.8 mm and the branches had

IDs of 25 mm. If not specified otherwise, all the experimental set-ups had the same

pipe diameters in this section. In the simulation, the input signal was set to be a clean

short burst of an impulse. However, the input signal in actual situation, will not be the

idealised burst, which caused the slight differences between the simulated signal and

experimental signal at each feature. The simulation results are plotted and compared

with the experimental results in Figure 6.28 - Figure 6.30. This figure shows that a

number of features can be identified in the trends and that each feature is associated

with reflections that result from a change in cross sectional area. For example, the

first feature F1 in Figure 6.28 is caused by the reflection from J1 in Figure 6.27 (a).

The locations that caused the relative reflections are listed in Table 6.5.

The differences in amplitudes between the simulated and experimental results were

caused by small errors in the calculation of the attenuation of the acoustic signal

along the pipe and from errors associated with the T-piece reflection and transmission

coefficients, which are not known precisely. However, given that in an industrial set-

ting, there will be debris and other features in the pipelines, the results show that the

network simulator can simulate a pipeline network and generate an acoustic response

that is similar to that obtained from the real system, and it can therefore be used to

help identify and locate unexpected defects in a pipeline system.



Imp

uls

e re

spo

nse

SimulationExperiment

0 20 40 60 80 100 120 140 160-1

0

1

210

-4

Figure 6.28: Comparison Between Simulation And Experiment Results for Layout (a)

Distance from microphone (m)0 20 40 60 80 100 120 140 160-1

Imp

uls

e re

spon

se

0

1

210

-4


Figure 6.29: Comparison Between Simulation And Experiment Results for Layout (b)


Distance from the microphone (m)

Imp

uls

e re

spo

nse

0

-10 20 40 60 80 100 120 140 160

1

2 10-4


Figure 6.30: Comparison Between Simulation And Experiment Results for Layout (c)

Referring back to a previous example in Section 6.1, that used the same layout, a hole

was inserted in the pipe. Assuming that the precise location of the hole was unknown,

the acoustic response of the pipe was determined and analysed. By comparing the

experimental result with the simulation results in Figure 6.31, the location of the

7 mm hole was identified as the point in the expanded section of the plot where

the experimental and simulated results begin to differ. This location was manually

confirmed to be the correct location of the hole.

All the features in different layouts are summarised and lised in Table 6.5. For example,

in Layout (a), feature F1 represents the feature of J1, F2 is the reflection from E3

and features F3 and F4 represents E2 and E1, respectively as labeled in Figure 6.27.

Feature 5 is the combination from both E3 and E1. Similarly, the rest of features in

Layout (b) and (b) can be explained by the features in the table.

Table 6.5: Locations That Caused Each Feature in Different Layouts

Layouts F1 F2 F3 F4 F5(a) J1 E3 E2 E1 E3+E1(b) J3 E4 E2 E1 E4+E2(c) J3 J1 E3+E4 E2 E1


Figure 6.31: Comparison Between the Simulation And Experiment Results for a Three-

branches Pipeline

A pipeline test with a loop and branch

The pipe layout when a loop was located in the network is shown in Figure 6.32. This

network was also simulated in the simulator. It was noted that because of the limited

space in the laboratory, all the pipes that were used in the experiment were coiled up.

This explains how a 14 m loop was able to connect two pipe sections that were 25 m

apart in the pipe main.

MIC

1005050 25

30

14

Figure 6.32: Layout of a Pipe Main Containing a Loop And a Branch

The experimental and simulated acoustic response of the pipe is shown in Figure 6.33.

This figure shows that the simulator was able to generate an acoustic response for the


pipe network containing a loop with a high degree of accuracy, once again confirming

the suitability of the simulator for estimating pipeline behaviour.

Figure 6.33: Comparison Between the Simulation And Experiment Results for the

Layout in Figure 6.32

A pipeline test for detecting a defect in a branch

A further pipeline layout was set up as shown in Figure 6.34. The pipe main for

this set up contained with four branches of varying length. A cylindrical object with

dimensions 155 mm × 8.15 mm was inserted in the pipe as a partial blockage. APR

testing revealed that there was something located approximate 86 m from the end

of the pipe. By conducting a APR second test from the branch as shown in Figure

6.36 and triangulating the results, it was clear that the partial blockage was correctly

located along branch 1 where it is marked with a circle in Figure 6.34. This result

confirmed that the simulator could be used to help identify partial blockages in pipe

networks. However, with pipeline networks it may be necessary to determine the APR

from multiple locations in the network. Separate tests were conducted to determine

the exact location of the blockage, from pipe main and pipe branch. By a single result

recorded from pipe main as shown in Figure 6.35, it is difficult to identify the location


of the blockage. However, with another set of result from pipe branch as shown in

Figure 6.36, it is confirmed that the blockage is located in the pipe branch.

MIC50505050 25

Defect 20

30

14

36

MIC

Figure 6.34: Layout of a Pipe Main with 4 Branches

Figure 6.35: Comparison Between the Simulation and Experiment Results for the Pipe

Main with the Layout Depicted in Figure 6.34


Figure 6.36: Comparison Between the Simulation and Experiment Results When a

Partial Blockage Was Located in a Pipeline Branch, as per the Layout in Figure 6.34

6.6 Summary

A series of validation tests demonstrated that the experimental attenuation is consis-

tent with those that were estimated using the simulator; the maximum experimental

error was found to be 3.02% in the pipeline containing no branches. A pipe network

simulator has been designed to model the propagation of acoustic waves in a pipe

network containing branches and loops. To model the signal propagation at branch

joints, reflection and transmission coefficients were considered and the resulting simu-

lator validated using a number of experimental scenarios. Comparison of the simulated

and experimental results were very consistent and believed to be suitable to help in the

interpretation of APR data collected from real gas pipelines. The following Chapter

shows results that were obtained when the APR equipment and simulator was applied

to industrial gas pipelines.

Chapter 7

Industrial Case Studies

7.1 A case study for an industrial pipeline - Case 1

This section describes how the single pipeline simulator was used to support the sur-

veying of a live industrial pipeline. In the experiment, approximate details of the

pipeline, such as changes in cross section and valve locations were known. Using the

simulator it was possible to compare the acoustic response of the pipe with the sim-

ulated response and identify any inconsistencies. The overall aim of this study was

to identify and locate a pig that had become stuck in the pipe. The pipeline was

approximately 12 km long and was pressurised to approximately 5 MPa.

7.1.1 Description of the test

To generate an excitation signal with sufficient energy and the appropriate frequency

content to travel the required distance, a pulse of pressurised gas was injected into the

pipeline using the Echometer Remote Fire Gas Gun.

The resulting reflection sequence was recorded by a pressure transducer housed in the

same assembly used to inject the pressure pulse. The pressure of the gas in the pipeline

was 6.1 MPa and the temperature was approximately 8.9◦C. The pressure pulse was

injected in to the pipeline 10 times and the acoustic response recorded for each test

154

CHAPTER 7. INDUSTRIAL CASE STUDIES 155

was averaged to increase the SNR. The composition of the compressed gas used in the

industrial test, which affects the speed of sound in the gas, is listed in Table 7.1.

Table 7.1: Gas Composition

Gas Component Formula Gas Composition (% Mole)

Methane CH4 81.35

Nitrogen N2 6.59

Carbon Dioxide CO2 0.04

Ethane C2H6 6.64

Propane C3H8 3.56

I-Butane C4H10 0.56

N-Butane C4H10 0.95

I-Pentane C5H12 0.14

N-Pentane C5H12 0.01

Helium He 0.16

Figure 7.1 shows the recorded reflections as the excitation pulse propagated along

the test pipeline. The excitation pulse was introduced at time 0 s, but unfortunately

it was not possible determine the precise pulse that was injected as the microphone

located within the equipment saturated. Without the precise input signal it is not

possible to use the simulator and therefore a method was developed to obtain an

estimate of the injected signal. This method involved analysing the signal produced

by a known feature in the pipeline, in this case a change in internal diameter from 186

mm to 216 mm. Deconvolution with an appropriate time domain propagation filer, as

presented in Section 6.2.4, of the reflected signal from this feature was then used to

determine the approximate signal that was injected into the pipe.

The injected signal was relatively complex because the single pulse that was injected

into the pipe was reflected from various pipe fittings that were within approximately

20 m of the injection point. The method of recovering the actual input signal was the

inverse of how the attenuation filter was used to implement wave propagation. The

excitation signal was achieved by applying (7.1) - (7.3). The feature lying between


9.97 s and 10.4 s (zoomed section of Figure 7.1) was used as p−i,o, the output backward

signal at ith segment. xi(nT ) was the time domain attenuation filter obtained if

the segment length was taken to be equivalent to the spacing between the pressure

transducer and where the reference signal p−i,o was reflected. The recovered input signal

at the first segment p+1,i, that was used as the input signal for the simulator, is shown

in Figure 7.2.

p−i,o(nT ) = p−i,i(nT ) ∗−1 xi(nT ) (7.1)

p+i,o(nT ) = p−i,o(nT )/ri,i+1 (7.2)

p+i,i(nT ) = p+i,o(nT ) ∗−1 xi(nT ) (7.3)

0 10 20 30 40 50 60 70 80

-0.01

-0.005

0

0.005

0.01

0.015

Time (s)

Imp

uls

e R

esp

on

se

10 10.2 10.4-5

0

5x 10

-3

Figure 7.1: Raw Data with the First Distinguished Feature

7.1.2 Results of the industrial testing

By comparing the simulated signal with the recorded experimental signal, any un-

expected features in the pipeline can be revealed. There were altogether 12 major

reflections that were identified in Figure 7.3. The first reflection occurred after 9.97 s,


which corresponded to a known bore reduction (the pipe bore changed whenever the

pipe went under a road). It was followed by several reflections corresponding to the

location and size of other known features. Each of these features corresponded to

changes in internal pipe diameter of approximately 10 mm, corresponding to a change

in cross sectional area of 10%, (2002 − (200 − 10)2)/2002 = 9.75% . The only obvi-

ous difference between the expected and measured signals lay at 18.53 s, as shown in

Figure 7.4. Using the simulator, the feature was investigated and interpreted to be a

short unexpected blockage of approximately 50%. The pipe was later inspected using

a radiographic camera which located the blockage to within 3 m of that estimated

using APR. The blockage was confirmed to be a cleaning pig that had become stuck

in the pipe.

Figure 7.2: Recovered Input Excitation Signal

The reflection at 65.8 s resulted from the end of the pipe as shown in Figure 7.5. The

results from this test and relevant validation tests by the simulator, together with

knowledge of SNR, suggest that the APR technique, utilising the Echometer Remote

Fire Gas gun to deliver the acoustic signal, could detect a full blockage at up to 32 km

under similar conditions as with this test. In generating this distance it is assumed

that a feature is only detectable when the amplitude of the feature signal is at least


twice that of the noise. This detection length could be extended if the gas inside the

pipeline was at higher pressure or the input impulse amplitude was increased.

Impuls

e R

esponse

Time (s)

Simulation

Experiment

Figure 7.3: Reflection Signals from the Pipeline

0 20 40 60 80 100 120

-0.01

-0.005

0

0.005

0.01

Time (s)

Impuls

e R

esponse

Simulation

Experiment

18.5 19 19.5-0.01

0

0.01

Figure 7.4: A 50% Blockage Interpreted by the Simulator

The maximum distances for different blockage percentages detected by the present

APR equipment for this particular pipeline condition (eg. pressure and temperature,


etc.) are listed for a variety of pipelines in Table 7.2. For example, if a 1 m pipe is

to be surveyed under the same conditions, then it should be possible to detect a full

blockage at 17.1 km and a 50% blockage at 13 km, etc. As many sub-sea pipelines

operate at approximately 100 bar and have diameters of approximately 1 m, the table

provides an indication of the maximum length that the current APR technique could

be applied to.

0 10 20 30 40 50 60 70

-4

-2

0

2

4

x 10-3

Time (s)

Impuls

e R

esponse

Simulation

Experiment

65.5 66 66.5-5

0

5x 10

-3

Figure 7.5: Reflection From the End of the Pipe

Table 7.2: Maximum Detected Distances When Pressure = 6.1 MPa And Temperature= 8.9◦C, with the Distances Measured in Meter

Percentage

Distances D(mm)

20 50 100 200 500 1000

10% 1200 3100 6000 12500 31000 6000020% 1700 4300 8500 17500 43500 8500030% 2050 5100 10000 20500 52000 10000040% 2300 5700 11500 23000 59000 11500050% 2550 6300 12500 26000 64000 13000060% 2800 6900 14000 28000 69500 13500070% 3050 7500 14500 29500 78500 14500080% 3150 7500 15000 31000 80500 15000090% 3250 8100 15500 32000 81500 170000100% 3300 8150 15700 32400 82000 171000



In a further test APR, using the Echometer Gas gun was used to detect a subsea

valve opening and closing. The layout of the field test was shown in Figure 7.6.

Unfortunately the composition of gas was unknown to us. Topsides pressure during the

tests was 25 Mpa, and ambient (surface) temperature was 16 ◦C. Sea bed temperature

would have been significantly lower and estimated to be 6 ◦C. Sampling frequency was

1 kHz for all the tests; this was limited by equipment. In total, 10 acoustic tests were

performed and the average response determined to improve the SNR. The speed of

sound was estimated to be 366 m/s for this on-site test after calibration, which was

calculated based on the known feature reflection location l and the time it took to

travel t, c = l/t .

The acoustic pulse was injected after 1.5 s and as with an earlier test which caused

the first 1.5 s empty in the signal, it was not possible to correctly ascertain the precise

pulse that was injected because the microphone saturated. A similar method to that

applied in Section 7.1 was applied to estimate the input signal.

A comparison of the experimental and simulator results are shown in Figure 7.7.

A reflection was identified at the location of ’Spool Item 14’ in the layout diagram

(Figure 7.6). Through consultation with plant operators, this reflection was believed

to be from the bottom of the riser or a 90◦ bend. The simulator helped to simulate

the response of Figure 7.6 and the feature was identified based on the difference at the

zoom in area n Figure 7.7. A 70 % closed (cross section percentage) at Valve 16 was

also simulated to offer the difference when the opening size of the valve changed. The

difference was shown between the red (fully closed) and green color (70% closed) in

Figure 7.7.


Figure 7.6: Layout of the Testing at Alba

1.5 2 2.5 3 3.5 4 4.5 5 5.5 6-0.1

-0.05

0

0.05

0.1

Time (s)

Impuls

e re

sponse

Original closed record

70% closed simulation

Fully closed simulation

2.7 2.8 2.9 3

-0.01

0

0.01

0.02

Figure 7.7: Comparison Between the Simulation And Experiment Results


As part of the on going commercialisation of the Acoustek R© APR technique at the

University of Manchester, several live trials were performed on live gas distribution

pipeline networks. The results of these trials are analysed in this Section to further

validate the developed simulator. Among the various trials that were conducted, the

trial at ”Haylie Gardens” could be used to test the single pipeline simulator. Further

trials will be introduced in Case 4 to Case 6 to validate the network simulator. In


each of the trials the experimental equipment that was used is imaged in Figure 7.8.

The aluminum ’box’ contains a 150 mm loudspeaker which was connected to the pipe.

The small yellow cable houses two microphones, which were inserted into the pipe.

Figure 7.8: Test Equipment

The pipe main was 76.2 mm spun iron with the condition clean and free of debris.

Live trial Haylie Gardens demonstrated that the system was capable of detecting and

locating features over a range of 100 m. Figure 7.9 gives the site layout. The distances

of each part are shown in the figure.

Figure 7.10 shows plots from the Acoustek R© software (top plot) and the simulator

(bottom plot) and Table 7.3 presents the table of features detected by the Acoustek R©

equipment. The simulation results used the same set up as the layout shown in Fig-

ure 7.9. The reflections at direction Dir 2 was considered in the simulation. However,

compared to the recorded signal, feature 25F1 was not obvious in the recording from

on-site staff. if observed at distance 10.8 m, the reflected signal from 25F1 is shown

in the simulation while because of the original input signal with long ringing, the first

reflection was difficult to identify in the original signal. The simulator generated the

response of the pipeline when it is under the idealised situation with clean and smooth

inside of the pipeline. It is also shown that, the amplitude of the reflections are higher


in the simulation than those in the recording. One reason might be that the inside

surface of the pipe was not idealised clean and the coarse surface caused energy loss

inside of the pipe.

Speaker location

and mic direction

Gas main

Excavation

Ex1

Ex2

Dir 1

Dir 2 25F1

25F2

25F3

76.2

Cast

Stand pipe

62.4

103.1

Hayli

e G

ard

ens

Figure 7.9: Layout of Trial Haylie Gardens


Table 7.3: Features in Layout of Trial Haylie Gardens

Feature code Features detected Direction Distance Confirmed

25F1 Blockage/reduction Dir 2 10.8m No

25F2 branch/expansion Dir 1 63.1m Stand pipe at 62.4 m

25F3 Large blockage/reduction or cap Dir 1 103.2m Capped end visible at 103.1m



Simulation results

Field test results

Imp

uls

e re

spon

seIm

pu

lse

resp

on

se

Figure 7.10: Impulse Response of Trial Haylie Gardens


In addition to the Haylie Gardens trial, there were a number of trials conducted on

pipeline networks. For each trial, the simulator was used to estimate the response of

the network, with parameters set to correspond to the layouts provided and measured

by the on-site staff.

In case 4, the investigated test was conducted at Newmains Rd, Renfrew. The pipe

main was 152.4 mm ductile iron with extremely dirty condition filled with gravel like

substances. The main contained two abandoned sections (the two branches at the

top of Figure 7.11. These abandoned mains were capped. This trial result has been

included to show the performance of the system in conditions when the pipe is not


clean.

Speaker location

and mic direction

Gas main

Excavation

New

Main

Road

Ex1

Abandoned

Abandoned

20F1

N

Du

ctil

e Ir

on

Dir 1

61

63

Figure 7.11: Layout of Trial Newmains Rd

The standard approach for inspecting gas distribution pipeline is to insert small cam-

eras on long tethers (up to 50 m). However, for this study the pipe was so dirty that a

camera could not be inserted and attempts were being made to pump the main clear

of debris prior to replacement. The debris in the main caused a high noise level on the

signal obtained from the Acoustek R© equipment but still some information could be

obtained: at the suspected location of the two abandoned mains, there is a clear fea-

ture in the signal resulting from the capped ends. Figure 7.11 gives the site layout and


Table 7.4: Features in Layout of Trial Newmains Rd, Renfrew


20F1 Raise in signal level Dir 1 61.1 Abandoned mains on maps at 61m and 63m

Figure 7.12 shows plots from the Acoustek R© software and the pipe network simulator

and presents the table of features in Table 7.4 detected by the Acoustek R© equipment.

This plot shows the response of the simulator when it modeled the pipeline using the

same layout as in Figure 7.11. From the observation, at distance 60-70 m the second

abandoned main is estimated to be further than 63 m based on the difference in the

plots.



Simulation results

Field test results

Imp

uls

e re

spon

seIm

pu

lse

resp

on

se

Figure 7.12: Impulse Response of Trial Newmains Rd


The pipe main was 101.6 mm spun iron with clean condition and free of debris. Live

trial Crocus Grove was performed at Location Ex1. Figure 7.13 gives the site layout

while Figures 7.14 shows the plots from the Acoustek R© software and the pipe network

simulator and presents the table of features detected by the Acoustek R© equipment.


Speaker location

and mic direction

Gas main

Excavation

Cro

cus

Gro

ve

63 mm PE

Ex3

Ex2

Ex1

11

9.8

95.2

72.1 11.3

90 mm PE

Siphon

49.6

N

23F1

23F2

23F3

23F5

22.2

Figure 7.13: Layout of Trial Crocus Grove

Prior to the arrival most of the site had been inspected using a camera, however,

the siphon (23F3) was unknown and was not present on any maps. The APR test

revealed a significant and unexpected feature at 93.8 m; due to an equal tee this signal

feature could relate to one of two sections in the 101.6 mm main. To confirm which

stretch of pipe the feature was in, another trial was performed at Excavation Ex3. This

second test confirmed that the feature was directly in front of the test location and

that the feature was large enough to stop any signal passing it. Following discussion

with operators and a subsequent camera inspection, a siphon was later confirmed as

the cause of this reflection. As well as finding the unexpected siphon the Acoustek R©




Simulation results

Field test results

Imp

uls

e re

spon

seIm

pu

lse

resp

on

se

Figure 7.14: Impulse Response of Trial Crocus Grove

system correctly located all other large features present in the network. The size

of siphon was also evaluated by the simulator and the simulated results are shown

in Figure 7.14. A siphon refers to a tube in an inverted ’U’ shape, which causes a

liquid to flow upward without help of pump. In the simulator, a 30% expansion was

modeled at the location 23F3 in Figure 7.13 as an equivalent feature of a siphon. The

reflection at location 95.2 m in the plot underneath was from the simulated siphon,

which matched the recorded signal.


This trial was conducted at Harburn Ave, Livingston. The pipe main was 200 mm

ductile iron with clean condition. Operatives requested the use of the Acoustek R©

system to test an area for blockages following a water ingress problem. From a single

location the Acoustek R© system was able to confirm that approximately 500 m of gas

main was clear of obstructions. Figure 7.15 gives the site layout and Figure 7.16 shows

plots from the Acoustek R© software and the pipe network simulator and presents the


table of features detected by the Acoustek R© equipment. The Acoustek R© system

detected a pipe feature (31F3 in Figures 7.15 and 7.16) at 354.2 m. Unfortunately this

feature could not be fully confirmed: gas maps show a branch nearby but the distance

estimated from the map is ≈390 m. The detected features are shown in Table 7.5.

The simulator was built based on the layout in Figure 7.15. Because of the complexity

of the pipe layout, not all the features can be reflected in the recorded signal of the

actual equipment because of the low signal to noise ratio. The simulator can quickly

generate the response of the system based on the drawing from the test site. For

example, at distance around 140 m, there is no obvious reflections from the original

recording. However, based on the simulation results, the reflection should be shown

in the plot. The reason might be, in reality, there was no cross section change instead

of what is described in the drawing or the reflection was too weak to be identified. In

general, the simulator offered an accurate view to get the response of a known layout

of the tested object.

Table 7.5: Features in Layout of Trial Harburn Ave


31F1 tee/expansion Dir 2 47.2m Found with camera at 46.8m

31F2 blockage/reduction Dir 1 98.4m Reduction from 200mm to 6” present on maps

31F3 tee/expansion/siphon Dir 1 354.2m reduction to 125mm and tee nearby on maps

Speaker location

and mic direction

Gas main

Excavation

NDir 1

Dir 2Ex1

152.4

D

I

180 PE 125

PE

125 PE

200 DI200 DI

200 PE

250 DI

125 PE

150 D

I

Approx 390

31F1

Ap

pro

x 9

0

46.8

Approx 100

Figure 7.15: Layout of Trial 31




Simulation results

Field test results

Imp

uls

e re

spo

nse

Imp

uls

e re

spon

se

Figure 7.16: Impulse Response of Trial 31

7.7 Summary

A number of field tests were described in this chapter. The results from these field

tests were used to validate both the single pipeline and network pipeline simulators.

The capabilities and accuracy of the simulator was demonstrated by applying it to

results obtained from an active industrial pipeline, approximately 10 km in length. In

this case, the simulator accurately generated the reflections along the pipeline and

revealed all of the known pipe features. Using the simulator it was possible to detect

and characterise cross-sectional changes of 10% in the pipeline. In the first case study,

Case 1, a blockage was successfully identified in a pipeline with length of more than

12 km. In Case 2, a suspicious defect was identified and located by the simulator. In

Cases 3 to 6, simulated results matched what was obtained from field tests. From the

results of the field testing, it was ascertained that both simulators provided very useful

information that can be utilised to help identify defects along the pipeline system.

Chapter 8

Discussions, Conclusions and

Future Work

The work presented in this thesis has expanded the functional range of existing APR

simulation tools and as a consequence improved the practical application of the tech-

nology. The assumptions of previous researchers have been experimentally validated in

long range applications and new simulation methods have been introduced to improve

simulation accuracy and execution time in pipelines with the long lengths associated

with gas distribution networks. Thorough validation of the new simulation tools was

performed, both in the laboratory and in extensive field trials.

8.1 Discussions

(1) Application of APR

APR offers considerable benefits in the monitoring of industrial pipelines. The reason

for this is that the impulse response of a pipe, which is determined when applying APR

technology, contains significant information regarding features and conditions within

the pipe. APR operates by injecting an acoustic impulse into the gas within the tested

object (pipelines being the test subject of this work) and measuring the reflections

that are produced, whenever this signal encounters a change in acoustic impedance

171

CHAPTER 8. DISCUSSIONS, CONCLUSIONS AND FUTURE WORK 172

as it propagates along the length of the pipeline. There are many applications of

APR in that have been reported in the literatures, such as its application to detect

seismic layers, reconstruct medical airways, reconstruction and defect characterisation

of musical instruments and the detection of abnormal conditions within pipelines. A

review of relevant research was provided in Chapter 3.

The focus of the work described in this thesis has been the application of APR tech-

nology for the detection and location of holes, blockages and erosion in pipelines. To

illustrate the capabilities of APR in this field, an extensive set of experiments have

been performed in the laboratory at the University of Manchester. Larger sized pipes

have also been studied in field trials. The field tests were conducted in different lo-

cations across the UK to demonstrate the capabilities of APR for the inspection of

gas pipeline systems. Major defects were identified from the acoustic response of the

tested pipelines. The acoustic response of the pipes was also able to reveal the location

of the defect, through knowledge of the speed of sound in the gas and the transmission

time of the acoustic signal.

(2) Attenuation validation

Although several research studies have attempted to validate Kirchhoff’s acoustic at-

tenuation theory previously, these studies have produced variable results with errors of

up to 15% being reported, as explained in Chapter 4. To gain a better understanding

of the attenuation of acoustic signals in long lengths of pipelines, a comprehensive set

of experiments was conducted to analyse the behaviour of acoustic signals in pipes.

The results of this work was able to validate the use of Kirchoff’s theory within a

pipeline simulator that was able to estimate the acoustic response of pipelines and

pipeline networks.

The results of the experimental studies demonstrated that Kirchhoff’s equation un-

derestimated the acoustic attenuation measured in the experiments by up to 5%. 5%

is believed to be within the noise that would be measured in real environments where

the internal wall of the pipeline can contain debris and corrosion which will affect the

acoustic attenuation. This result validated the choice of using Kirchoff’s equation as

the basis for the pipeline simulators that were developed.


Analysis of the experimental results showed that the higher frequencies had attenuated

faster than the lower frequencies and the acoustic signals attenuated faster in small

bore pipes compared with pipes with larger diameters.

(3) Feature characterisation

There are different categories of features/defects that may exist along a pipeline, such

as expansion/contraction of the inner diameter. To help develop a model that was

able to simulate the reflections produced by these features a series of experiments was

conducted to characterise 15 pipes that had a variety of features, such as holes and

blockages introduced within them.

For these pipes, the presented models were able to approximate the acoustic response

of features such as holes and blockages with very good accuracy. For example a change

in the cross sectional area within a pipeline could be estimated with an accuracy of

approximately 7 %, suggesting that if there is a 0.25 mm change in pipeline diameter

then the models would estimate the size of this reduction as 0.23 mm, which in most

practical applications of APR technology would be insignificant.

(4) Pipeline simulators building methods

In practice, even for a simple pipeline, the response can be complex and difficult to

interpret directly from the reflected signal. To help identify whether there is a defect

inside the pipe, a reference signal, indicating the expected response of the pipe if there

are no defects within it, can be highly beneficial. By comparing the actual acoustic

response of the pipe with that expected, any defects or other abnormalities can be

identified.

Theoretically, when a pipeline system is in its initial state, which means the piping is

new and only just commissioned, the reference signal is achieved by performing tests

using APR. However, in practice, it is not easy to obtain the initial response of a

pipeline. In this way, a simulator is required to generate the idealised response of a

system, which provides the reference signal from the initial state.

To develop a simulator to estimate the acoustic response of a pipe, a loss filter, based on


Keefe’s approximation was introduced in Chapter 6. This filter defined the attenuation

and losses inside a number of segments that the pipe was divided into. Both the

transmission and reflection coefficients for changes in cross sectional area were derived

based on the continuity of pressure and particle velocity. These coefficients were

included in the scattering which helped describe how the signal propagates along the

pipeline system.

For pipeline networks, a corresponding simulator was built using a network model

that included all branches in the system. In addition to considering attenuation on

the straight lengths of pipe, transmission and reflection coefficients at the joints were

also introduced into the scattering equations.

Both the single pipeline and network simulators were validated using tests conducted

in the laboratory and through comprehensive field tests. These tests demonstrated

that the developed simulators provided an accurate estimate of the acoustic response

of the pipelines.

(5) Experimental validations in the laboratory

A series of laboratory experiments were conducted to validate the developed sim-

ulators. Different pipe layouts were used with different sizes of pipe main and pipe

branches under different lengths. Defects, such as holes and blockages, were introduced

into the pipeline. The recorded response of the experimental pipelines were compared

with the responses estimated using the simulators (single pipeline and pipeline net-

work simulators). In one experiment a water blockage, a common and difficult to

locate problem in gas distribution pipelines, was introduced into the pipe. A model

developed to simulate water pooling inside a pipe was successfully used to estimate

the real response of a water pool.

For the network simulator, transmission and reflection coefficients were validated in

the laboratory using a comprehensive set of tests. In these tests, different sizes of

branches at various locations were introduced. Thorough testing the network simulator

was found to accurately approximate the acoustic response of all the tested pipeline

networks. Furthermore, the simulator was able to locate and estimate the size of a


partial blockage that was introduced in the network.

(6) Field tests validations

A series of field tests were conducted at a variety of locations around the UK to test

the capability and accuracy of the simulators. All these tests used live pipelines which

contained debris and many other features and were therefore provided a thorough test

of the capabilities of the ability of the simulators to aid in the interpretation of APR

data. In the tests, the pipe sizes ranged from 25 mm to 250 mm with pipe lengths of

up to 12 km. The owners of the pipelines provided details of the composition of the

gas within the pipelines (which was necessary to estimate the speed of sound) and the

layout of the pipeline networks.

The pipelines contained numerous changes in cross sectional area, particularly in the

test involving the 12 km pipeline, as discussed in Chapter 7. The measured acoustic

response of this pipeline was particularly difficult. However, the pipeline simulator

was able to aid in the interpretation of this response and using it, a cleaning pig that

had become stuck in the pipe was detected and located to within 3 m of its actual

position.

For the field test results analysed in Chapter 7, the gas composition inside of the pipe

was unavailable. However, it was still possible to estimate the speed of sound in the gas

through calibration using known obstructions in the pipeline. All the results obtained

using the pipeline simulators were consistent with the results obtained from the field

tests and in some of the trials the simulator was able to detect and locate unexpected

features in the pipelines.

8.2 Conclusions

Kirchhoff’s equation was demonstrated to be applicable to long lengths of pipelines

with large diameters. The difference between experimental and theoretical results was

consistently less than 5%.


The simulation tools developed in this thesis were shown to provide an accurate method

for estimating the acoustic response of pipelines and pipeline networks.

Through industrial testing, it was shown that APR could detect a blockage in a pipeline

at a distance of up to 12 km, with the limitation of the technique, using the same

equipment and pipeline in this case, being approximately 35 km.

Both simulators developed in this thesis generated idealised responses of pipeline sys-

tems, which have been validated both in the laboratory and in field tests.

The developed simulators can help interpret APR measurements of complex pipelines

and pipeline networks.

8.3 Future work

The following future works are recommended.

• Setting up experimental conditions with adjustable pressures and temperatures

Currently all the tests conducted in the laboratory were within a certain range

of temperature from 20 to 27◦C and the pressure was atmospheric. In the future,

it would be recommended that greater variation in temperature and pressure be

introduced.

• Adding the estimation of the size correctly and efficiently in the simulator

It is recommended that the simulators have an auto-sizing function embedded

within them. With the information of the correct size of the defect, the operator

can decide what actions should be taken instantly. Although there has been a

considerable amount of work undertaken in this area by Kemp et al., applications

have been restricted to small and short bore tubular objects, with the main

application being musical instruments. Unlike musical instruments with clean

internal walls, industrial pipelines are usually very dirty. Furthermore, industrial

pipelines are considerably longer than musical instruments, which can introduce

scale-up problems.


• Monitoring pipelines in real-time

The ideal situation for pipeline systems is that they can be monitored and ab-

normalities detected in real-time. Extending the research reported in this thesis

to real-time application would be highly beneficial.

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