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For the numerical study, a metallic pipeline system with two short deteriorated sections and one relatively long section with a change of pipe class is considered. The layout of the numerical pipeline system is given in Figure 2. The physical details of the pipe sections are summarised in Table 1. The length of each reach is carefully designed to satisfy the Courant condition for method of characteristics (MOC) simulations (with a time step of 0.05 ms). The system is a reservoir-pipeline-reservoir (R-P-R) system. Reservoir 1 has a constant head of 60 m, and the constant head for Reservoir 2 is 57 m. The total length of the pipeline is 1 km. The steady-state flow is calculated as 0.264 m3/s, corresponding to a velocity of 1.34 m/s. For the normal pipe sections, the internal diameter is 500 mm, the wall thickness is 8 mm, the Reynolds number is (indicating turbulent flow) and the wave speed is 1,154 m/s. Two pipe sections L2 and L9 which have thinner wall thicknesses (6 and 5 mm), larger internal pipe diameters (504 and 506 mm) and smaller wave speeds (1,083 and 1,036 m/s) are placed in the system to simulate the deteriorated sections (e.g. extended internal corrosion). Pipe section L7 with a length of approximately 150 m, the same internal diameter as the majority of the pipe, but a thinner wall thickness (7 mm) and thus a lower wave speed (1,123 m/s), is placed in the system to simulate a section of a lesser pipe class. A significantly higher Darcy–Weisbach friction factor (0.03) has been assigned to sections L2 and L9 to represent the effect of a much higher wall surface roughness as would result from a pipe that has experienced corrosion. The dual sensor (with a sensor spacing of 0.9809 m) is placed in the middle of the pipeline system at T1 and T2, respectively. A side-discharge valve which is located at 0.9809 m upstream from T1 is used as the transient generator. The steady-state discharge through the side-discharge valve is set as 0.01 m3/s. The length of each pipe section has been selected to satisfy the Courant condition for the time domain MOC simulations so that no interpolation scheme is required (Chaudhry 2014).
Table 1

Physical details of the pipe sections used in the numerical simulations

LinkLength (m)Internal diameter (mm)Wall thickness (mm)Wave speed (m/s)Friction factor (–)
L1 415.9593 500 1,154 0.017 
L2 12.0213 504 1,083 0.030 
L3 72.0096 500 1,154 0.017 
L4 0.9809 500 1,154 0.017 
L5 0.9809 500 1,154 0.017 
L6 69.9901 500 1,154 0.017 
L7 150.1451 500 1,123 0.017 
L8 60.0080 500 1,154 0.017 
L9 11.9944 506 1,036 0.030 
L10 205.9890 500 1,154 0.017 
LinkLength (m)Internal diameter (mm)Wall thickness (mm)Wave speed (m/s)Friction factor (–)
L1 415.9593 500 1,154 0.017 
L2 12.0213 504 1,083 0.030 
L3 72.0096 500 1,154 0.017 
L4 0.9809 500 1,154 0.017 
L5 0.9809 500 1,154 0.017 
L6 69.9901 500 1,154 0.017 
L7 150.1451 500 1,123 0.017 
L8 60.0080 500 1,154 0.017 
L9 11.9944 506 1,036 0.030 
L10 205.9890 500 1,154 0.017 
Figure 2

Layout of the pipeline system used in the numerical simulations (not to scale). See Table 1 for physical details.

Figure 2

Layout of the pipeline system used in the numerical simulations (not to scale). See Table 1 for physical details.

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