Fluctuating elevation in pipeline

[eng180]

I am trying to simulate a long pipeline for the transport of liquids, e.g. water. The flow rate will be constant and equal to a specific value. The internal diameter will be the same for the entire pipeline. There are elevation fluctuations in the pipeline, the pipeline contains a number of high points and none of them is located near the end of the pipeline. To move the liquid, a number of centrifugal pumps connected in series may be used. The pumps may differ from each other, the distance between them may be very long and the wall thickness of the pipes should be as thin as possible.
If I understand correctly, I should use Bernoulli equation between every two pumps at key points to find the point where the elevation at that specific point minus the elevation of the first pump plus the friction head loss (for the specific flow rate and until that specific point) is maximum. This will be the minimum head that the first pump must provide (minus the head at the inlet of the pump) with the condition that the head at the inlet of the second pump is at least equal to the NPSH required. By checking different pump characteristic curves, I must then select each pump to provide the specific flow rate for its calculated head with the operating point being as close as possible to the best efficiency point. However, if I add the head of all the pumps, the sum may be higher than the total head calculated with Bernoulli equation between the beginning and the end of the pipeline (for the specific flow rate) due to the high points. The system will operate where the added pump characteristic curve intersects with the system curve. So, how can each pump operate at the specific flow rate and also provide enough head for the liquid to reach the high points, by adding a valve just before the end of the pipeline to increase friction loss?

Thank you in advance.

 

[BigInch]

A method that yields better and faster results,
Pick a design pressure. Let each pump discharge at maximum design pressure. Draw the elevation profile with the first pump station's discharge head equivalent of pipeline design pressure. Calculate friction loss in the pipeline per km, or per mile, using a friction loss equation, D'arcy, Manning, Colebrook, Fanning, whatever. From that first pump station's discharge head, run the pipeline friction drop line (HGL) to the next pump station. The next pump station will be where the line just about intersects the elevation profile. If there is any point on the pipeline between stations where pressure is higher than design pressure, you will have to reduce the discharge head of the first pump station and decrease the distance to the next pump station accordingly. Keep doing that until pipe design pressure at all points between stations is not exceeded. Then do the same at pump station 2 to 3. 3 to 4 ...

 

[brpillai]

Eng180, Adding to what Big inch said above, I would like to add the following:
long distance transmission lines do haveundulating ground profile. pressure at any point is the sum of the static head, minus friction and correction with respect to the profile/ elevation. You have to add pressure if the elevation is negative and minus if the elevation is higher.

Intermediate pump stations are selected based on minimum suction pressure required for the main line pumps or boosetr pumps. Normally it is kept at about 50m of liquid column. Pressure is raised further at the pump station so the liquid can reach the next point where the head falls to about 50m and this is repeated till reching the terminal location.

If due to elevation difference the pressure reaches a value higher than what the selected pipe wall thickneess/ grade can withstand, either go for higher grade or thickness. Similarly, due to peaks, if the pressure reduces such that a negative( vacuum )below atmosphere, pipe has to be desined for that condition.

I suggest to consult a pipeline design engineer for details, as improper design will lead in to difficult situations during operation.