Ruptured crude pipeline

[ScottL]

I'm struggling to determine the right equations for calculating the flow through a ruptured pipeline to determine the total amount of time before a 20-mile long section will completely empty following a shutdown of the pumps. The goal is to provide a safety plan that includes an estimate of the time available for repair of a pipe before the entire section empties out. The pipeline I'm evaluating runs downhill about 100 ft/ mile and I'm assuming the rupture happens near the end of the pipe, just before the receiving facility, to simulate a worst case scenario.

The point is to calculate the maximum time available to respond and repair the rupture before the pipe is emptied out. The pipe is a 6" ID with an average pipe pressure around 800 psi and flow rate vary from 1-10 barrels per minute. Any guidance on how to calculate this (assuming the pressure changes over time as the head pressure of the remaining liquid column in the pipeline decreases). I have found some information in the forums on leaks from holes, but my goal is to determine the flow rate through a 6-12" long rupture, such as what might happen following mechanical damage or if the pipe is otherwise embrittled and then ruptures.


I have a few specific questions, too:
1. Does the pressure in the pipe drop rapidly following shutdown of the pumps, and if so, how can I calculate or estimate the remaining pressure after the pump is off and the leak starts to dissipate the pressure?
2. Does the location of the leak on the pipe affect the flow rate? The pipe is buried under a few feet of typical rocky or porous soil conditions.
3. Are there any other considerations I need to consider?

[admin]

There is no specific fluid dynamics easy solution that can handle flow through non regular cavities in pipes. Numerical simulation should be used and that is not an easy process.
When you shut down pumps only gravity is forcing fluid to flow out from pipe, so depending on the actual pump head the pressure difference is significant and will influence on flow rate very much.
Location of cavity will for sure influence, as flow will be bigger if cavity is on lower part of pipe line, making fluid column bigger.