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 m
3/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 L
2 and L
9 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 L
7 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 L
2 and L
9 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 m
3/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 1Physical details of the pipe sections used in the numerical simulations
Link
. | Length (m)
. | Internal diameter (mm)
. | Wall thickness (mm)
. | Wave speed (m/s)
. | Friction factor (–)
. |
---|
L1 | 415.9593 | 500 | 8 | 1,154 | 0.017 |
L2 | 12.0213 | 504 | 6 | 1,083 | 0.030 |
L3 | 72.0096 | 500 | 8 | 1,154 | 0.017 |
L4 | 0.9809 | 500 | 8 | 1,154 | 0.017 |
L5 | 0.9809 | 500 | 8 | 1,154 | 0.017 |
L6 | 69.9901 | 500 | 8 | 1,154 | 0.017 |
L7 | 150.1451 | 500 | 7 | 1,123 | 0.017 |
L8 | 60.0080 | 500 | 8 | 1,154 | 0.017 |
L9 | 11.9944 | 506 | 5 | 1,036 | 0.030 |
L10 | 205.9890 | 500 | 8 | 1,154 | 0.017 |
Link
. | Length (m)
. | Internal diameter (mm)
. | Wall thickness (mm)
. | Wave speed (m/s)
. | Friction factor (–)
. |
---|
L1 | 415.9593 | 500 | 8 | 1,154 | 0.017 |
L2 | 12.0213 | 504 | 6 | 1,083 | 0.030 |
L3 | 72.0096 | 500 | 8 | 1,154 | 0.017 |
L4 | 0.9809 | 500 | 8 | 1,154 | 0.017 |
L5 | 0.9809 | 500 | 8 | 1,154 | 0.017 |
L6 | 69.9901 | 500 | 8 | 1,154 | 0.017 |
L7 | 150.1451 | 500 | 7 | 1,123 | 0.017 |
L8 | 60.0080 | 500 | 8 | 1,154 | 0.017 |
L9 | 11.9944 | 506 | 5 | 1,036 | 0.030 |
L10 | 205.9890 | 500 | 8 | 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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