Gas pipeline packing/unpacking calculations

[Mafuta]

What is the best and accurate way of calculating the volume of gas in the pipeline to account for packing/unpacking changes in the line? The whole idea is to be able to reconciliate btn d/s and u/s volumes at any time t. I have dP over the lenght of the pipe.
I will apprciate having your approach in this case.

 

[BigInch]

Assume the average pressure between known pressure points

Pavg=P₁)+(2/3)*(P₂-P₁)
and use an equation of state of your choice to calculate density and total mass in that length. Sum the segments.


"We have a leadership style that is too directive and doesn't listen sufficiently well. The top of the organisation doesn't listen sufficiently to what the bottom is saying." Tony Hayward CEO BP
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http://www.youtube.com/watch?v=hpiIWMWWVco

http://virtualpipeline.spaces.liv

 

[Mafuta]

Thank you for your inputs.

 

[delittle]

BigInch I see that you suggest
Pavg=P1+(2/3)*(P2-P1)
instead of
Pavg=P1+(1/2)*(P2-P1)
or
Pavg = (P1+P2)/2
I am just curious about the reason

 

[BigInch]

Pressure drop of gas pipelines along length is nonlinear.

"We have a leadership style that is too directive and doesn't listen sufficiently well. The top of the organisation doesn't listen sufficiently to what the bottom is saying." Tony Hayward CEO BP
"Being GREEN isn't easy." Kermit

http://www.youtube.com/watch?v=hpiIWMWWVco

http://virtualpipeline.spaces.liv

 

[zdas04]

If you pick your segments sufficiently small, then any averaging method is pretty much the same for most practical uses (BigInch's 2/3 considers the non-linearity of the dP, but is it a universal constant or a rule of thumb--probably a rule of thumb and close enough). I like to pick the segment size such that downstream pressure (in absolute units) is no less than 90% of upstream pressure (also in absolute units).

What I don't see is what the OP is trying to accomplish. If he's looking for line pack doesn't he have to calculate it when the line isn't flowing so the upstream and downstream pressures are the same? I'm not sure of the value of a "line pack" number based on average flowing pressure. Guess I'm missing something.

David

 

[delittle]

thanks BigInch and zdas4, I did suppose something as nonlinear distribution of pressures (and related densities) along the pipe segment but I was unable to explain the origin of the 2/3 rule of thumb.

 

[BigInch]

Believe it, or not?

The 2/3 factor was derived by professor Weymouth at the same time he published his more famous gas flow formula.

"We have a leadership style that is too directive and doesn't listen sufficiently well. The top of the organisation doesn't listen sufficiently to what the bottom is saying." Tony Hayward CEO BP
"Being GREEN isn't easy." Kermit

http://www.youtube.com/watch?v=hpiIWMWWVco

http://virtualpipeline.spaces.liv

 

[vzeos]

For anyone who is interested the publication that Biginch referred to can be accessed at the attached link.

Weymouth introduces his flow equation on page 735 and his pipeline storage capacity analysis on page 741.

http://books.google.com/books?id=oU...v=onepage&q=Weymouth, gas engineering&f=false

 

[BigInch]

You can calculate and keep track of a dynamic line pack through pressure and flow changes at all your data points. A hot running hydraulic model picks up SCADA data and cross checks against the theoretical state the model predicts, any differences setting off leak alarms, recommending control adjustments to optimize compressor speeds, minimize fuel consumption and balancing takes with current or predicted sales.

"We have a leadership style that is too directive and doesn't listen sufficiently well. The top of the organisation doesn't listen sufficiently to what the bottom is saying." Tony Hayward CEO BP
"Being GREEN isn't easy." Kermit

http://www.youtube.com/watch?v=hpiIWMWWVco

http://virtualpipeline.spaces.liv

 

[zdas04]

BigInch,
That would be one seriously cool pipeline. My experience is more with lines that we're not really certain of pipe diameter on all of it because it was built be a dozen different engineers over 75 years and many of them didn't keep good records. A system like you describe would be novel for me.

David

 

[vzeos]

The operation of natural gas transmission systems, today as in the past, has everything to do with line pack management. Professor Weymouth gives a good account of this subject in his paper.

By the way, the 2/3 factor was not derived by professor Weymouth. It is the result of constants of integration in deriving the average pressure equation used today. It is important to note that the assumed pipeline conditions were pressures below 1000 psia and temperatures of 60° F or higher.

Below is the derivation of the average pressure equation per Uhl, A. E., et al., Steady Flow in Gas Pipelines, Technical Report No. 10, Institute of Gas Technology, Chicago, 1965, pages 85 and 86.
*****************
For the operating ranges usually encountered in transmission practice; i. e., pressures below 1000 psia and temperatures of 60° F or higher, the variation of z with P is nearly linear, so that the compressibility factor may be represented by a function of the form

Z=1/(1+aP)

where a is a Constant dependent on T. The mean pressure (Pm) which must be used can be determined as follows:
[tt]
_{P2 P2}
(1/Zavg)[∫] PdP = [∫] (P/Z)dP
^{P1 P1}
or
_{P2 P2}
(1+aPm)[∫]PdP = [∫]P(1+aP)dP
^{P1 P1}
[/tt]

Upon integration

(1+aPm)(P1² - P2²)/2 = (P1² - P2²)/2 + a(P1³ - P2³)/3

or

Pm = 2/3(P1³- P2³)/( P1² - P2²)

If full integration of the general energy balance is desired, however, for the sake of extreme accuracy or where a computer program is involved, the variation of P and T and the consequent variation of z along the line can be accounted for by graphical or numerical techniques. Graphical integration could be effected by plotting P/ZT against P, and subsequently determining the area under the curve between the initial and terminal values of P. An additional possibility would involve the use of an analytical or virial equation of state.

*****************

 

[zdas04]

Very interesting discussion. Just because I'm a geek, I took an example of P(1)=1,000 psia P(2)=900 psia.

Simple Average = 950 psia
BigInch Equation = 933.3 psia
vzeos' Equation = 950.9 psia

In virtually every case I've ever had to work on, the difference between a simple average and vzeos' equation is not material. BigInch's equation would probably not make material difference either.

I've done this stuff using the upstream pressure to calculate compressibility and Reynolds Number (for friction calcs). I've done it with the downstream pressure. I've done it with simple average pressure. There has not been a single case where the choice among these three pressures made a material difference in a decision. The numbers come out different, but not enough to change a decision.

Maybe if we were talking very low pressures like 10 psia and 9 psia. Nope, using the simple average as the denominator, BigInch's equation would still be 1.75% low and vzeos' equation would be 0.092% high for every pair of numbers that I put in where the downstream pressure was 90% of upstream pressure.

David

 

[BigInch]

For transmission pipelines, its SOP. There's a whole lot of cool pipelines out there. Most high pressure transmission operations have these systems installed, with all kinds of goodies, such as look ahead features to see the effects that would occur, if you shut a given compressor, or a whole station, or 2 stations down for 24 hours within the next 30 minutes with the air temperture in NYC dropping by 35F by tomorrow. Stoner Pipeline Simulator CD comes with all the RTU interfacing and network communication functions, so you can run one instance constantly cross-checking SCADA data with it's hydraulic calcs in realtime and another instance in hot-standby, in case the first terminal fails, and a third independent system model just to do operator training.

Take a 200 mile long 30" pipeline with 1000 psig upstream and 100 psig downstream, then multiply that by 10 (from Houston to New York City). Did that make a volume difference? If I have time tomorrow, I'll set up a Stoner simulation and we can compare results.

"We have a leadership style that is too directive and doesn't listen sufficiently well. The top of the organisation doesn't listen sufficiently to what the bottom is saying." Tony Hayward CEO BP
"Being GREEN isn't easy." Kermit

http://www.youtube.com/watch?v=hpiIWMWWVco

http://virtualpipeline.spaces.liv

 

[vzeos]

zdas04
You should not jump to conclusions based on only one data point. If you look at a range of data, you will see that by using the arithmetic average pressure leads to greater and greater error. As you can see from the table below, your example of a 10% pressure drop leads to a 0.09% error. But if you consider a 90% pressure drop then the error is 18.24% from the true mean pressure. This kind of error will lead to considerable difficulties in pipeline line pack management.

[tt]
P1 P2 Pm dP Pavg %diff
1000 900 950.88 100.00 950.00 0.09%
1000 800 903.70 200.00 900.00 0.41%
1000 700 858.82 300.00 850.00 1.03%
1000 600 816.67 400.00 800.00 2.04%
1000 500 777.78 500.00 750.00 3.57%
1000 400 742.86 600.00 700.00 5.77%
1000 300 712.82 700.00 650.00 8.81%
1000 200 688.89 800.00 600.00 12.90%
1000 100 672.73 900.00 550.00 18.24%
[/tt]

 

[zdas04]

You are right. The reason that I limited my calcs to a 10% dP was that more than that and the constant density assumption in the flow equations becomes progressively less useful and the equations stray from reality very quickly.

While a 90% pressure drop is an 18% difference between mean pressure and average pressure, anything you would do with the system would have a MUCH larger difference. I've seen people use data like you presented try of figure the compressibility and friction on a very large dP (as a percent of initial conditions) and take them to the AGA equation or Weymouth or Panhandle and try to make economic decisions on the data. When people build systems with that kind of fundamental error (and it happens all the time), the systems just don't perform per the models.

So, in the world I live in, P(avg) and P(mean) are the same number and I'll use P(avg).

BigInch,
I've never heard of a system where the pressure into a booster compressor station got that low as a percentage of upstream pressure. Getting back to 1,000 would be a 3- or 4-stage centriigal and while I've never worked on mainline stuff, I've always been told that they try to keep the pressure drop under 1.5-2.0 ratios and use single stage equipment. Was I misinformed?

I worked with Stoner output back in the day when you sent them your data on punch cards and they mailed you back a couple of boxes of printout. I knew they had advanced with technology, but a link to RTU's is pretty far advanced in 25 years.

David

 

[BigInch]

My first setup had an accoustic teletype link to some mainframe in Carlisle, Pennsylvania. We had 800 gas wells and 2000 miles of pipe. Most time was spent waiting for data transmission and figuring out what the reams of text output was trying to tell you. Graphic displays were a good addition. Could still be better in that department. I would like an overall network view, like in
EPANET, but their prime application is only one, or maybe two parallel pipelines, not networks, so they survive with primitive "define path" views.

"We have a leadership style that is too directive and doesn't listen sufficiently well. The top of the organisation doesn't listen sufficiently to what the bottom is saying." Tony Hayward CEO BP
"Being GREEN isn't easy." Kermit

http://www.youtube.com/watch?v=hpiIWMWWVco

http://virtualpipeline.spaces.liv

 

[dcasto]

for all you old timers, when you ran circular charts and sent them to integration, the integrator used the 1/3 2/3 rule for marking the DP. It all works out the same as vzeos posted.

In the early 1990's we programed our SCADA to do a mass balance every minute (we had 15 sec to 2 minute scan rates. At the block valves every 20 miles (7 miles class 2 and 3) we measured temp and press and we calculated density. the meters in and out were added and substracted. The system would show a great trend line of the mass balance. If a meter went out or a transmitter on the line went out, the Rate of change and absolute error alarms went off.

We even simulated a leak by turning off a mid section meter and not telling gas control. The alarms went off and the operators started reacting. The supervisor told them of what was happening only after they reacted. Then as they called the responce authorities, other managment people were there to monitor and not let the drill proceed until the people were made aware. We even had a person at the fire house nearest the incident and they took the call with our people present. They used the drill to help train their people.

 

[PaoloPemi]

interesting discussion, I use a simple direct integration (10 dp steps in Excel), possibly equivalent to zdas04 procedure, but (in normal conditions) I would expect reasonably accurate estimates with the suggested 2/3 rule