Analyzing the Key Factors Affecting Transient Pressures Occurring During Pipe Filling Using a Numerical Approach

It is common in practice to partially drain the pipelines for inspection and repair. If not properly controlled, refilling of the pipeline may expose them to significant transient pressures which can compromise the integrity of the pipeline and associated joints. Implementing a safe filling protocol requires that the location and size of hydro-mechanical equipment are calculated. Such information can be obtained through analysis of different filling scenarios, but unfortunately, such a detailed analysis is usually ignored in the design stage, not surprising why pipe incidents usually happen during operation.With the aid of numerical explorations, this paper aims to shed some light on the key factors affecting the filling hydraulics. To this end, a numerical model is proposed to calculate the filling hydraulics. The model uses the method of characteristics to solve the water hammer equations and employs the Discrete Gas Cavity Model (DGCM) to treat column separation. The model is validated with the experiments. Extensive numerical explorations reveal that lack of a safe filling protocol as well as lack or inadequate sizing of the required hydro-mechanical equipment can result in water hammer pressures. The results also show that without a properly sized bypass and air valve, it is impossible to control transient pressures during filling.

Extensive numerical explorations are conducted with a hypothetical water pipeline to analyze the key factors affecting the transient pressures which occur during filling. The pipeline has an undulating profile with the diameter, length, and acoustic wave speed of 0.9 m, 15900 m, and 1000 m/s respectively. The pipeline is supplied by a reservoir with a constant water depth of 5 m which is located at the upstream end of the pipeline. It is assumed that the last 1600 m of the pipelined is drained and an air valve at the end of the pipeline allows air management during the filling. A bypass line located at the upstream end of the empty zone is also equipped with a flow control valve to control the filling flow rates. Several numerical solutions are conducted with the different sizes of the air valve, bypass line and different opening times of the flow control valve, and the maximum and minimum pressure heads induced during filling are recorded.

Analyzing the results obtained from the numerical explorations show that when the flow control valve opens, the empty pipeline starts being filled with a filing flow rate which depends on the size of the bypass and the rate of opening of the flow rate. A large bypass line and rapid opening of the flow control valve result in the rapid filling of the empty pipeline and a significant down surge on the upstream side of the bypass line. The progressing water column in the empty pipe serves as a piston and pushes the air out of the system through the air valve. If the outlet orifice of the air valve is large enough, the air pressure in the empty pipeline does not increase significantly otherwise higher air pressures are built up which can slow down the filling water column. When the last air is eventually released from the system, the water column comes to rest and significant water hammer pressures result. The magnitude of the resulting water hammer pressure depends on the velocity at which the water column hits the pipe’s end as well as the acoustic wave speed of the pipe. Numerical exploration shows that the maximum and minimum pressures induced during filling depend on the diameters of both the outlet orifice of the air valve and the bypass line as well as the opening time of the flow control valve. For this particular case study, it is found that the bypass line diameter = 0.2 m, the outlet orifice diameter = 1.5 cm, and the flow control valve opening time = 40 s can control maximum and minimum pressure head within the acceptable range without unreasonably prolonging the filling time.

• The proposed model can be successfully assisted in analyzing the hydraulics of filling and in designing a safe filling protocol• Without a proper filling protocol, the resulting transited pressures can be strong enough to rupture the pipeline • Without a proposedly sized bypass, it is impossible to control negative pressures in the pipeline • The rate of opening of the flow control valve might play an important role in controlling the induced maximum and minimum pressures during filling• Reducing the diameter of the outlet orifice of the air valve significantly reduces the resulting transient pressures but at the same time prolongs the filling. • An optimum filling protocol can be obtained through an iterative procedure in which the bypass and air valve diameters, as well as the opening time of the flow control valve, are determined in such a way that the induced maximum and minimum transient pressures remain within the acceptable level and the filling is performed as fast as possible