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Modeling Transmission line priming starting from Empty conditions?


How can we model priming/filling a transmission pipeline, starting from an empty pipeline? The issue I am facing is that the pipeline has a dominant high point in the middle.  Transmission line is 10km long, starting elevation at pumps is +3.4m, high point in the middle is  at elevation +12.5m, and discharge point is at elevation of +1.4m. This means that while the pipe is priming/filling starting from empty pipe, the pipeline segment after the high point will be running as channel for short time until the pipeline is fully primed and required pressure is reached. My question is how to model this and ensure sufficient protection or priming sequence/starting flow and pattern to remain within the required pressure profile.