Gas pipeline packing/unpacking calculations
Gas pipeline packing/unpacking calculations
(OP)
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.
I will apprciate having your approach in this case.





RE: Gas pipeline packing/unpacking calculations
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
http://www.youtube.com/watch?v=hpiIWMWWVco
"Being GREEN isn't easy." Kermit
http://virtualpipeline.spaces.liv
RE: Gas pipeline packing/unpacking calculations
RE: Gas pipeline packing/unpacking calculations
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
RE: Gas pipeline packing/unpacking calculations
"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
http://www.youtube.com/watch?v=hpiIWMWWVco
"Being GREEN isn't easy." Kermit
http://virtualpipeline.spaces.liv
RE: Gas pipeline packing/unpacking calculations
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
RE: Gas pipeline packing/unpacking calculations
RE: Gas pipeline packing/unpacking calculations
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
http://www.youtube.com/watch?v=hpiIWMWWVco
"Being GREEN isn't easy." Kermit
http://virtualpipeline.spaces.liv
RE: Gas pipeline packing/unpacking calculations
Weymouth introduces his flow equation on page 735 and his pipeline storage capacity analysis on page 741.
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RE: Gas pipeline packing/unpacking calculations
"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
http://www.youtube.com/watch?v=hpiIWMWWVco
"Being GREEN isn't easy." Kermit
http://virtualpipeline.spaces.liv
RE: Gas pipeline packing/unpacking calculations
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
RE: Gas pipeline packing/unpacking calculations
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:
P2 P2
(1/Zavg)∫ PdP = ∫ (P/Z)dP
P1 P1
or
P2 P2
(1+aPm)∫PdP = ∫P(1+aP)dP
P1 P1
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.
*****************
RE: Gas pipeline packing/unpacking calculations
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
RE: Gas pipeline packing/unpacking calculations
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
http://www.youtube.com/watch?v=hpiIWMWWVco
"Being GREEN isn't easy." Kermit
http://virtualpipeline.spaces.liv
RE: Gas pipeline packing/unpacking calculations
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.
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%
RE: Gas pipeline packing/unpacking calculations
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
RE: Gas pipeline packing/unpacking calculations
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
http://www.youtube.com/watch?v=hpiIWMWWVco
"Being GREEN isn't easy." Kermit
http://virtualpipeline.spaces.liv
RE: Gas pipeline packing/unpacking calculations
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.
RE: Gas pipeline packing/unpacking calculations