Instant pressure change gas in pipeline
Instant pressure change gas in pipeline
(OP)
Hi All,
This question is a bit frustrating since I am thinking about it all day!
The problem: I have a pipeline of 5000 meter, on one side I have a compressor and on the other side I have a consumer. In one scenario I have an equilibrium and for instance the pressure at the consumer is 4,7 bar(g) and pressure at compressor is 5,5 bar(g) (Pressure of compressor is controlled by pressure controller at consumer).
If the consumer consumes more, the pressure at the consumer will decrease, to speak in numbers, for instance to 4,5 bar(g). The compressor will need to correct this and will compress more kg/s, which will result in an pressure increase by the consumer till it will reach the 4,7 bar(g) again (New equilibrium).
My question: How fast will this pressure change be?
Is is the speed of sound of the gas? For instance speed of sound is 300 m/s pressure change will take 5000/300 = 17 seconds?
Hope someone can give me an answer with good formula's or text!
Thanks in advance,
sincerely,
Eltjo
This question is a bit frustrating since I am thinking about it all day!
The problem: I have a pipeline of 5000 meter, on one side I have a compressor and on the other side I have a consumer. In one scenario I have an equilibrium and for instance the pressure at the consumer is 4,7 bar(g) and pressure at compressor is 5,5 bar(g) (Pressure of compressor is controlled by pressure controller at consumer).
If the consumer consumes more, the pressure at the consumer will decrease, to speak in numbers, for instance to 4,5 bar(g). The compressor will need to correct this and will compress more kg/s, which will result in an pressure increase by the consumer till it will reach the 4,7 bar(g) again (New equilibrium).
My question: How fast will this pressure change be?
Is is the speed of sound of the gas? For instance speed of sound is 300 m/s pressure change will take 5000/300 = 17 seconds?
Hope someone can give me an answer with good formula's or text!
Thanks in advance,
sincerely,
Eltjo





RE: Instant pressure change gas in pipeline
Say, your air compressor capacity is 100 cfm and initially you are consuming at the rate of 60 cfm and then your consumption increased to 80 cfm. So, it should take 20*60/100 = 12 seconds.
RE: Instant pressure change gas in pipeline
Thanks for the fast response.
I understand your explanation, but you don't give an answer of the speed of pressure change over the 5000 meter pipeline. Maybe, I did not made my question correct.
What is the time, when at one end of a 5000 meter gas pipeline the pressure instantly increases, for the change is noticeable at the other end of the pipeline?
RE: Instant pressure change gas in pipeline
RE: Instant pressure change gas in pipeline
My feeling says this is not correct, since it is a gas and not a liquid. I think it takes some time for the pressure change to be seen at the end of the pipe.
If the pressure increase for instance is in a sphere I think you are correct, but this is a 5000 meter pipeline.
RE: Instant pressure change gas in pipeline
It would be a difficult calculation to do exactly by hand because you have a varying pressure profile all the way along the pipeline and you would need to perform a finite element analysis with many iterations to get an accurate answer. Depending on why you want this information, it might be more expensive to do the calculation than the value it gives. Self tuning PID controllers are so cheap now it is probably the most practical answer to just install one and let it sort itself out. But it is an interesting question and I can see why it has troubled you all day.
Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com
RE: Instant pressure change gas in pipeline
The procedure I gave seems to give much lesser time than that based upon sonic flow calculation (because of my example). However, it takes much more time. If I consider a 1" sch40 pipe for this application, which has an ID of 0.0266m, the total volume will be 5000*0.00056 = 2.8 cu.mtr.
If we have a difference of 36 cfm, which is about 0.0168cu.mtr/s(corresponding to 30m/s velocity), the time would be 2.8/0.0168 = 166 sec.
My approach and velocity approach, both are same. I said it as Q/V (where Q is difference between rate of generation and rate of consumption) and V is pipe volume.
Q = 3.142xd2xv/4 and V = 3.142xd2xL/4, where v is velocity and L is pipe length.
So, Q/V = v/L (which speaks of dividing the pipe velocity with pipe length)
RE: Instant pressure change gas in pipeline
Harvey
RE: Instant pressure change gas in pipeline
Thanks for your answer.
I think however there is a flaw in your answer. Let us say that we have a 5000 meter pipeline without any flow and just a static pressure. If in one end we put some more gas molecules, i.e. the pressure will get higher, there is no gas velocity (dynamic pressure), but the pressure will level out in the whole pipe. My colleagues think the pressure increase at the end of the pipe will be seen calculated with the average speed of gas molecules (approx. 350 m/s) in 15 seconds.
Your 30 m/s of the gas velocity is the actual gas speed through the pipe? (Pipe size dependent?) I ask this because this value will change significantly since consumers consummation will change significantly? Velocity will be around 0 - 15 m/s and with little to none consuming your answer will become very large.
Background info:
I am designing a network where a compressor needs to maintain the pressure at the end of the pipe. If the consumer at the end of the pipe consumes more, the pressure there will decrease and the compressor needs to do some more work and needs to put some more kg/s into the pipeline. In order to let it work I need to know this value so I can estimate the ramp up/down of the consumer (=ramp up/down compressor + "answer of this question" + safety margin)
RE: Instant pressure change gas in pipeline
Pipe length is approx. 5000 meter with internal diameter of approx. 250 mm --> Volume will be around 230 m3
RE: Instant pressure change gas in pipeline
Where do you put the gas molecules from? If the gas molecules don't flow then how will they enter the pipe?
What I am trying to reiterate is that the approach you considered gives the minimum time possible (based on sonic velocity) to get the pressure to an equilibrium state.
When there is no consumption, the entire compressor capacity is used to fill the pipe (i.e pressurise it) and so time taken would be less.
RE: Instant pressure change gas in pipeline
And since the compressor will rise the pressure in one end of the pipe, even when there is no consummation, there will be a pressure wave to stabilize the pressure in the whole pipeline.
ramp up/down of the consumer =ramp up/down compressor + "answer of this question" + safety margin
RE: Instant pressure change gas in pipeline
Probably, you can install a pressure transmitter at the end and use the pressure signal to control the VFD. The inbuilt PID controller can check the rate of pressure drop (with respect to the set value) and run the compressor accordingly. Life becomes easy if you have auto tuning type PID controller.
Harvey,
I think FEA is useful if you have to calculate the time with respect to the pressure build up at various points along the length of a pipeline, at any instant of time. It may be redundant, to check at the end.
RE: Instant pressure change gas in pipeline
If this is the velocity under these steady state conditions then I think this is the scenario you should be considering as your base case. The scenario of somehow injecting moelcules into one end while there is no flow is an artificial one and I cannot see how it adds to the solution.
If your consumer is an on-off application you will be controlling the supply end down to 4,7 barg during the no flow periods and there will be little capacity for the pipeline to suddenly deliver when the consumer requires flow. You should consider putting an air accumulator tank at the consumer end and controlling its pressure to a value a bit above that required by the consumer. You could then regulate the pressure to the consumer while controlling the accumulator pressure independently.
Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com
RE: Instant pressure change gas in pipeline
This pipeline storage/dampening effect is very well known in pipeline operations, and the pressure changes at both ends are so cyclical that you often see pressure at the delivery point increasing while consumption is increasing due to the position of the spring in its oscillation cycle.
In real flows of real gases you never see steady state conditions for more than a few milliseconds at a time, and the time lag between a change in consumption and a change in the average pressure at the supply can vary widely (I've seen it appear to be faster than the speed of sound and I've seen it to be slower than the mean velocity in the line). FEA will give you an average of averages and can be pretty close on 900 tests out of 1,000, but no particular data set will necessarily match any particular FEA run on the scale that this discussion covers.
David
RE: Instant pressure change gas in pipeline
RE: Instant pressure change gas in pipeline
If not use the rough estimates given here and then tune the system.
Best regards
Morten
RE: Instant pressure change gas in pipeline
I did a little workaround for my problem:
- I know now that the ramp up/down for the compressor unit is 5 minutes (0 --> 100%).
- I have calculated the time the molecules will stay in the pipeline @ maximum consummation. (Which is also around 5 minutes)
As a safety margin I will set the maximum ramp up/down of the consumers @ 10 minutes. (The sum of both) Of course this is conservative and the real number is lower, but for me this safety measure is fine.
Again thanks for your responses!