The application results and analysis above have validated and confirmed the applicability and accuracy of the proposed method and application procedure for pipe leak detection in the single branched and simple looped pipeline systems considered in this study. These successful validations provide the possibility of the extension of the TFR-based method for leak detection to relatively more complex pipe systems consisting of multiple branched and looped junctions. From this perspective, and based on the similar procedures of this study, the TFR results can also be derived and applied for such pipeline systems with multiple junctions (branched and looped), which actually results in a similar form of leak-induced patterns given in this study, but with different expressions of the known-system based coefficients (e.g. C, R, S, T, and ϕ). For demonstration in this study, a typical pipeline system with two branched pipe junctions shown in Figure 5 is adopted for investigation. The information of system configurations and parameters are plotted in Figure 5, with different leakage test cases (no. 8 to no. 12) listed in Table 3.
Table 3
Leakage detection results for the system with two branched pipe junctions
| Test no. | Real leakage information | Results of leakage detection | |||||
|---|---|---|---|---|---|---|---|
| xLn (m) | KL (10–5 m2/s) | AL* (10–3) | xLnP (m) | ε (%) | KLP (10–5 m2/s) | ε (%) | |
| 8 | 300 (n = 1) | 2.0 | 8.13 | 346 | 15.3 | 1.36 | –32.0 |
| 9 | 150 (n = 2) | 1.2 | 1.22 | 141 | –6.0 | 0.78 | –35.0 |
| 10 | 210 (n = 3) | 0.5 | 2.26 | 216 | 2.9 | 0.43 | –14.0 |
| 11 | 140 (n = 4) | 5.0 | 12.20 | 157 | 12.1 | 4.65 | –7.0 |
| 12 | 80 (n = 5) | 3.0 | 2.03 | 84 | 5.0 | 2.49 | –17.0 |
| Test no. | Real leakage information | Results of leakage detection | |||||
|---|---|---|---|---|---|---|---|
| xLn (m) | KL (10–5 m2/s) | AL* (10–3) | xLnP (m) | ε (%) | KLP (10–5 m2/s) | ε (%) | |
| 8 | 300 (n = 1) | 2.0 | 8.13 | 346 | 15.3 | 1.36 | –32.0 |
| 9 | 150 (n = 2) | 1.2 | 1.22 | 141 | –6.0 | 0.78 | –35.0 |
| 10 | 210 (n = 3) | 0.5 | 2.26 | 216 | 2.9 | 0.43 | –14.0 |
| 11 | 140 (n = 4) | 5.0 | 12.20 | 157 | 12.1 | 4.65 | –7.0 |
| 12 | 80 (n = 5) | 3.0 | 2.03 | 84 | 5.0 | 2.49 | –17.0 |
Figure 5
Test pipeline system with two branched junctions.