The analysis of transient phenomena during water filling operations in pipelines of irregular profiles has been studied much more compared to emptying maneuvers. In the literature, there is a lack of knowledge about mathematical models of emptying operations. This research starts with the analysis of a transient phenomenon during emptying maneuvers in single pipelines, which is a previous stage to understand the emptying operation in pipelines of irregular profiles. Analysis are conducted under two typical situations: (i) one corresponding to either the situation where there are no air valves installed or when they have failed due to operational and maintenance problems which represents the worse condition due to causing the lowest troughs of subatmospheric pressure, and (ii) the other one corresponding to the situation where air valves have been installed at the highest point of hydraulic installations to give reliability by admitting air into the pipelines for preventing troughs of subatmospheric pressure. Particularly, this research developed a mathematical model to predict the behavior of the emptying operations. The mathematical model is proposed for the two aforementioned situations. The liquid phase (water) is simulated using a rigid water column model (RWCM), which neglects the pipe and water elasticity given that the elasticity of the entrapped air pockets is much higher than the one from the pipe and the water. The air-water interface is simulated with a piston flow model assuming that the water column is perpendicular with the main direction of the flow. Gas phase is modeled using three formulations: (a) a polytropic model based on its energetic behavior, which considers an expansion of air pockets; (b) an air valve characterization to quantify the magnitude of admitted air flow; and (c) a continuity equation of the air. An ordinary differential equations system is solved using the Simulink tool of Matlab. The proposed model has been validated using experimental facilities at the hydraulic laboratories of the Universitat Politecnica de Valencia, Valencia, Spain, and the Instituto Superior Tecnico, University of Lisbon, Lisbon, Portugal. The results show how the mathematical model adequately predicts the experimental data, including the pressure oscillation patterns, the water velocities, and the lengths of the water columns. Finally, the mathematical model is applied to a case study to show a practical application, which can be used for engineers to study the phenomenon in real pipelines to make decisions about performing of the emptying operation.
The different versions of the original document can be found in: