Liquid pipelines through mountainous terrain often experience slack flow: the pressure at the high point drops to the fluid's vapor pressure and a bubble of vapor separates out of the liquid. The bubble grows and shrinks as conditions in the line change and as hydraulic transients move through. Accurately simulating this situation is necessary for leak detection or any other transient model application on such a system.
Physically, the start of the vapor bubble is usually "pinned" to the top of a hill with the bubble extending downhill and downstream. As hydraulic transients move through, the bubble grows longer and shorter at the downstream end. The movement of the bubble end over a model time step is typically much smaller than a model's distance step, so it is a challenge to model it accurately. Traditionally, slack models have approximated the movement of the bubble end by fudging the amount of liquid in the mesh intervals around the end so that mass was conserved. This work describes a new model that ties a moving mesh point to the downstream end of the vapor bubble, so as to exactly capture the transient variations of bubble size.
The paper will discuss the challenges in simulating this moving knot in a semi-explicit model; extension of this model to the complete draining and filling of a pipe; dealing with bad or limited knowledge of the pipe elevation profile, which is critical to the behavior of the two-phase region; and will also show comparisons between this simulation and slack-region draining and filling on a real pipeline.
Many liquid pipelines experience slack. Slack is combined vapor and liquid flow that occurs when the pressure in the pipeline drops to the vapor pressure of the liquid. It is also commonly called "slack-line flow", "column separation", and "vapor pockets".
Slack can be caused in several ways. It can happen in a flowing pipeline, even in steady conditions, when the pipe goes over a large mountain; it can happen in a shut-in pipeline as it cools (even in the absence of any large elevation changes); and it can happen downstream of a valve that is suddenly closed, due to pressure drop from the surge. All of these types of slack will be discussed in detail below.
