Natural Gas Pressure Increase with Elevation 4

[katiefaz]

Hello,

There are 2 points on a gas network with a height difference of 103metres - I have worked out that the elevation correction should be around 2.5mBar between the points. My question is, does it make a difference if the pressure in the pipe at these points is at a high or low pressure. What I'm trying to ask is; is an elevation correction of 2.5mBar correct whether the pressure in the pipe is 50mBar or 50 Bar?

Thanks!

 

[LittleInch]

NO, as the difference uses density - higher pressure = higher density.

however the difference in a higher pressure pipe is usually negligible

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[katiefaz]

Thanks for the quick reply LittleInch

I worked out the pressure correction using:

h = K x (1-G) x H
where,
K = 0.123 (dimensionless)
h = pressure change due to altitude (mbar)
H = altitude change (metres)
G = density of the gas relative to air (dimensionless)

Is this the correct formula and if not, could you point me in the direction of the right one. Sorry if this is a silly question!!

Thanks Again

 

[LittleInch]

I would just stick to P (pressure in kPa) = metres x density (kg/m^3) x 9.81

Your calculation doesn't make sense as the pressure difference for the same height should increase with a higher density fluid, not decrease.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[zdas04]

The equation we use in gas is

P_lower=P_upper*exp(Cons*SG*h/(T*Z))

The cons=0.01875 for ft, and R or 0.03418 for m, and K. The height has to be really large for this to be material. I'm working on a project this morning that has a 2000 m elevation change of 0.7 SG gas and the multiplier is 1.22. In your case with that gas the multiplier is around 1.01.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[MortenA]

I once did a project "Medgas" where the pipline goes across the sea close to Gibraltar. Its dips around 2200 m and the upstream pressure was 200 barg with an arrival pressure of 80 barg - here elevation did matter. But normally i wouldnt cosider it at all.

 

[katmar]

Another situation where the elevation does make a difference is in highrise buildings. In this case the gas distribution network would be at a very low pressure and the small change in pressure due to height becomes a higher fraction of the supply pressure. It is also complicated by the fact that the gas is usually lighter than air and you can get the strange situation that as you go up the building the gauge pressure in the gas system actually increases because the decrease in absolute pressure is less for the gas in the pipe than it is for the surrounding air.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[PEDARRIN2]

This is confusing to me, so I tried putting into a "real" situation.

I have a high rise at 1500 ft above sea level, which is ~457.2 meters. At the base, I have a natural gas pipe with 7 in w.c. gauge pressure which would be equivalent to 1.72 kPa (gauge). Atmospheric pressure is assumed to be 101.33 kPa. So the P(abs) of the system would be 101.33 + 1.72 = 103.058 kPa (absolute).

At the top of the building, the atmospheric pressure is 95.91 kPa. According to LittleInch, the pressure (assuming this is absolute) of the natural gas in the pipe at 457.2 meters would be 0.8 kg/m3 x 457 m x 9.81, which equals(?) = 3,586.5 kPa, which does not make sense. So please help me know where I am missing the boat.

Using the equation provided by zdas04, assuming T=60C, Z=1, SG = 0.6, I get a factor of 1.03, which means the gauge pressure of the gas at the top would be 1.67 kPa. Since the atmospheric pressure at the top would be 95.91 kPa, that makes the absolute pressure of the gas at the top to be 97.58 kPa.

Am I in the ball park?

 

[LittleInch]

Sorry,

my formulae was really for liquids and should be Pa, not KPa. As the density of the gas will change with height, then you need to take the average value for this calculation.

I'm actually trying to work out if 7 in water column would actually deliver any gas to the top floor or not and I can't figure it out. 1.72 kpA equates to a column of only 220m of gas??

Remember guage pressure is in essence the difference between the inside and the outside. So using your figures inside your pipe at the top you have exactly 103kPa. Outside pressure is 95.91. Therefore guage pressure would be 7.09 kPa at the top instead of 1.72 at the bottom

I still think there is an issue here that the pressure at the bottom is not enough, but I've probably missed something here.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[PEDARRIN2]

So, in reality, the change in pressure is 3.5 kPa using the P=density * g * h.

I understand the quandary about whether there is sufficient pressure to get to the top. I have never designed a gas system for such a tall building. 7" w.c. may not be realistic. I chose the Willis (Sears) Tower as the example. It is 108 stories tall. The highest I have designed is a 13 story (still high rise) hotel and we had 5 psig inside the building, due to gas flow requirements

I have 103 kPa at the bottom, not the top. 1.72 kPa (gauge) + 101.33 kPa (atmospheric) = 103 kPa (absolute).

At the top, I have 1.57 kPa (gauge, using zdas04 formula) + 95.91 kPa (atmospheric)= 97.48 kPa (absolute).

What I don't understand is where the 3.5 kPa from Little Inch formula comes into play.

And I applied zdas04 formula to the gauge pressure (gas inside the pipe) - which I do not know if I used it correctly.

 

[zdas04]

Don't even try to use ρgh for a fluid whose density is absolutely dependent on pressure.

Atmospheric pressure at 1500 ft elevation is 96.187 kPaa (13.951 psia). 7 in_h20 is 1.744 kPag (0.253 psig) so the delivery pressure is 97.93 kPaa (14.204 psia). You didn't say how tall your building is, but to get an atmospheric pressure of 95.91 kPaa I need an elevation of 1580 ft ASL (or 80 ft above ground level).

Pressure at the top becomes:

P_top=97.93kPaa*exp(-0.03418(K/m)*0.59*24.38m/288.15K/1.0)=97.76kPaa.

(the negative in the exponent is to solve the equation for the bottom pressure being known instead of the top). With a atmospheric pressure at the top equal to 95.91 kPaa, if you open the valve you should get gas (but all your pipe sizes would be too small for this dP since they are designed for 7 inH20 dP and less than 2 inH20) would starve the appliances.)

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[katmar]

Using the rho x g x h formula (which I believe will apply to any fluid and not just liquids) we can calculate the pressures at the top of the building. We have to also assume that the gas and the air each have a constant density all the way up. For the heights we are working with this assumption is good enough. I know that David doesn't like this assumption, and it would not hold for the sort of work he is doing, but it is fine here.

I have also assumed that the base of the building is at sea level and that it is 457 m high.

Assuming a density of 0.761 kg/m³ for the gas we can calculate the static head in the gas pipe as
0.761 x 9.8 x 457 = 3408 Pa = 3.41 kPa differential.
The absolute pressure of the gas in the pipe at the top of the building is therefore
103.05 - 3.41 = 99.64 kPaa

Assuming an air density of 1.205 kg/m³ makes the static head outside the pipe
1.205 x 9.8 x 457 = 5.4 kPa differential
and the absolute pressure of the air at the top of the building is
101.33 - 5.4 = 95.93 kPaa

The gauge pressure of the gas at the top of the building is now
99.64 - 95.93 = 3.71 kPa or 14.9 "WC.

This would certainly allow the gas to flow up the building and out to the appliances, but might surprise someone expecting to find gas at 7 " WC. The very low pressures might also make the risers quite large and it might be better to supply the building at a higher pressure and create sub-networks at 7 " WC to supply groups of 5 to 10 floors. I don't have hands-on experience of how this is done in practice - hopefully someone who has earned the T-shirt can tell us how it is really done.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[LittleInch]

That's it - because the density of the gas is lower than air then it will always "rise". If the gas density was > air at the same initial pressure then it would be less than atmospheric pressure at the top and air would flow in when you turned on the tap...

Daves point is valid though as the density is dependant on pressure and when you're talking about such small numbers it will make a difference. dave - his post is a bit confusing, but I think the example is a 1500 ft high building with the base at sea level.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[zdas04]

Katmar,
I'm working on a project this morning where the density at the top of a column of gas is 70% of the density at the bottom of the column. Which rho do you use in that case? Compressibility at the top is 0.86 and at the bottom is 0.78. Which one do you use?

At pressures this close to atmospheric you can assume that the two densities are close enough to call incompressible, but that is a really terrible habit to get into if you regularly work with gas. Sooner or later you find yourself in a situation where compressibility matters (like it always does with gaseous CO2) and you have trained yourself to ignore that bit of esoterica. It can lead to bad decisions.

I know I come across as pedantic on this (and many other) points, but I get to clean up messes caused by sloppy engineering every day. It is a rare week that someone doesn't call and say "the system isn't performing like the design said it would" (followed either by "how do I fix it" or "can I sue the engineer"). When I dig into it I find that the pipe was sized using the (vile) Modified Bernoulli equation ignoring elevation change for a multiphase system with 3000 ft of elevation change over 20 miles, or using the AGA Fully Turbulent equation outside of the horizontal portion of the Moody Diagram, or ignoring compressibility when it is material, etc. This is all well and good for salesmen or environmentalists, but we're engineers for goodness sake. Bad habits have a way of sneaking up on you.

LittleInch,
I wondered about that, but a 1500 ft tall building seemed less likely than their just assuming that atmospheric pressure is ALWAYS 101.35 kPaa (which I see all the time). Wikipedia only lists 3 buildings which might have gas service at or above 1,500 ft (the observation deck on the Empire State Building is at 1250 ft AGL, Hancock Building in Chicago observation restaurant is at 1030 ft).

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[PEDARRIN2]

Katmar,

I liked how you calculated the atmospheric pressure at the different elevations - instead of using a table like I did. I agree that if 7" w.c. is what is being distributed, the pipe risers would be very large. It is interesting, however, that the system actually "gained" pressure, going from 7" w.c. (gauge) to 15" w.c. (gauge) due to the change in the atmospheric pressure at the elevated height.

The way I look at it, the density of the gas does change as it rises, proportional to the pressure change in P=rho*g*h. It only comes to about 3.3%, so should not be an issue.

 

[PEDARRIN2]

zdas04,

Your point is exactly why I always read your posts and try to learn from them, because you have to fix what other's got wrong from assumptions or just plain laziness.

I know what I know (which isn't much), but I also know when I am getting into areas where I don't know.

I don't like tables, unless I understand the math behind them, just so I know when it can be used and when it cannot.

Be as pedantic as you want.