Pressure drop of gas in a pipe line 9

[enrjdean]

Hi Guys

I'm currently looking at sizing a pipe to carry 6.55m^3/s of exhaust gas over 1609m @ 40 psig in a 12" pipe. I've gone through these set of equations to look at the pressure drop over the line:

http://www.engineersedge.com/fluid_flow/pressure_drop/pressure_drop.htm

But the answer I'm getting back (4036Pa) seems extremely low? I'm recently graduated, so perhaps its my lack of feel for this sort of problem.

Would this be a reasonable figure, are the equations I'm using appropriate or not?

I'd appreciate any help or comments you guys have

Jim

 

[Latexman]

Jim,

Please give us some feedback when you can; we've got a fair amount invested in this problem.

Good luck,
Latexman

 

[enrjdean]

Hi Guys

I've managed to get hold of the composition of the gas, so I've uploaded an excel sheet, my calculation for density is in red.

What is a good text/reference book that would guide me through such compressible problems and help me understand the theory a bit better. I've trawled through some of my fluid mechanics/thermo books and tried to apply examples from there to this problem, but I'm getting even more rubbish out.

Jim

 

[BigInch]

Not bad for starters,

http://www.pdhengineer.com/Course F...Files/Oil and Gas/Gas Pipeline Hydraulics.pdf

**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies)

http://virtualpipeline.spaces.live.com/

 

[enrjdean]

Thanks BigInch, exactly the type of literature I was looking for! Clear, concise explanations followed by examples and no mumbo jumbo, thanks!

Jim

 

[katmar]

The procedure you have used in this spreadsheet will give you the density at 0 deg C and 101.325 kPa (the "old" normal conditions). For flow calculations you need the density at the upstream conditions. It seems to me that you are applying recipes for which you perhaps do not know the theory that underpins them. If you do know this theory then forgive me for rehashing the basics below.

It would be better to use the procedure that you used in your second post (13 Apr 09 15:02). This is based on the ideal gas law, which is a good approximation of the truth under your conditions. Note that it is wrong to call 287 J/kg*K the "universal gas constant for air". It is more accurately called the "gas constant for air". The universal gas constant has a value of 8.31447 kJ/(kgmol.K) and calculations using it must be done on a molar basis, but it applies to all (ideal) gases.

The ideal gas law is

PV = nRT where P is in kPa absolute, V is in m³, n is the number of kg moles, R is as above and T is in Kelvin

Using n = 1.0 kgmol and re-arranging we get V = RT/P (which is the basic form you used before, but now in molar terms)

I am confused as to what your actual flow temperature and pressure are, but we can pick any numbers to illustrate the method. Using "old" normal conditions gives

V = 8.31447 x 273.15 / 101.325 = 22.414 m³/kgmol

This is the well known value that you have used in cell E22. The SUM(E7:E21) gives the average molecular weight of your gas as 19.86 kg/kgmol and dividing it by the volume calculated above gives the density as 19.86/22.414 = 0.886 kg/m³. You got this answer correctly in your spreadsheet, but seemingly without knowing why - as I said above, forgive me if I am wrong on this.

We can now use this same procedure to give the density at 65 psig and 89 F (549.4 kPa abs and 304.8 Kelvin). Now

V = 8.31447 x 304.8 / 549.4 = 4.613 m³/kgmol and applying the average molecular weight we get the density as 19.86/4.613 = 4.31 kg/m³.

Once you have understood this procedure you can download a free units conversion program called Uconeer from my web site (see signature below) which has a calculator for converting between mass flow and volumetric flow for gases. This calculator will calculate the gas density for you, based on the molecular weight, temperature and pressure.

For calculating your pressure drop you should look up isothermal, compressible, turbulent flow. Perry's "Chemical Engineers Handbook" is a good starting point, or the Crane 410 "Flow of Fluids through valves, fittings and pipe". In a long pipe isothermal conditions are most likely to apply, but if your flow is adiabatic then using the isothermal assumption will most likely slightly over estimate the pressure drop, which is usually the conservative scenario.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[enrjdean]

Thanks Katmar, much appreciated!

Jim

 

[quark]

I agree with Isothermal, compressible and turbulent air flow model. Adiabatic conditions are least likely to prevail in this case.

My final remark is that I would be careful about being conservative in pressure drop calculation if choked flow is the least thing what I want.

 

[FOURe]

efunda.com has a calculator for pressure drop.

My suggestion is to try and plug your input numbers and see what the output is so you can compare it with your numbers:

http://www.efunda.com/formulae/fluids/calc_pipe_friction.cfm

The more reference output numbers you get, the better you are ...

http://www.engineering-4e.com

 

[Latexman]

FOURe,

That calculator is for incompressible flow. While the flow rate in this post is somewhat in question, the velocity is probably high enough for the diameter and length of line that good engineering judgement calls for compressible flow methods. That could be accomplished several different ways. One way is by using the density of the gas at the average of the inlet and outlet conditions. This would be iterative, but one could use the calculator you posted to crunch the numbers. Another way is by using compressible flow methods like the closed form, isothermal compressible flow equation. Yet another way is use a numerically integrated form of the differential isothermal compressible flow equation in a spreadsheet. Of course at the end of the day, the final solution and the method chosen must be evaluated for appropriateness.

Good luck,
Latexman

 

[FOURe]

Latexman:

I agree with you more than 100 [%].

I do know that the stated problem has been going on for quite some time.

My idea was just to provide another quick way of coming up with some output values ...

I do know that the provided source is for incompressible flow. In this case, we are dealing with compressible flow. Therefore, two different cases. However, if the compressible flow gas velocity is "small", the provided eFunda.com calculator could be used to get some preliminary output values.

In the end, no matter what gets used for the purpose of engineering calculations, "the final solution and the method chosen must be evaluated for appropriateness".

In my opinion, there is no doubt about your words and piece of advice -- you and other participants in this problem are "good" ...

http://www.engineering-4e.com

 

[Montemayor]

At the risk of being reprimanded for adding yet another post to this lengthy (but interesting) thread, I will just add one of my favorite, old spreadsheets for calculating compressible flow problems. It has served me well and it responds to what Jim Dean requested. I hope it helps complement what Katmar and Latex have so ably explained.

 

[FOURe]

Mr. Montemayor:

It is always good to hear from you and to get your input on the subject matter.

http://www.engineering-4e.com

 

[BigInch]

Montemayor,

Your advice is always appreciated, as is the spreadsheet.
Thank You.

**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies)

http://virtualpipeline.spaces.live.com/

 

[vzeos]

You can also use the attached spread sheet.

 

[enrjdean]

Mr. Montemayor

Thanks for the spreadsheet, much appreciated! Rather than blindly plug my values into it, I'm trying to work through the sheet so I can gain a better understanding of whats going on with the calculations. However, theres a few constants croping up, that I can only guess at what they are.

CELL G25 =C7+((C17^2)/C24*(2*C22*C11/(C9/12)+LN((C26+14.7)/(C7+14.7))))/144/32.2

In this equation for finding P2, I'm assuming that the value of 14.7 is in psig i.e 1atm? However what are the values of 144 & 32.2 refering to, are these simply for converting the units?

Jim

 

[JohnGP]

Montemayor will be able to give you a more detailed explanation of the maths, but very quickly, they're conversion factors for those nasty non-SI units - 144 converts from in² to ft², because there are "feet" in the flow, density, and length units and "inches" in the diameter and pressure units. The number 32.2 is the gravitational constant (I think it's called that, because I haven't used it for more years than I can remember) to handle the mix of "pounds mass" in the flow and density values, and "pounds force" in the pressure numbers.

The pressures are given in "psig", so to convert to "psia" 14.7 is added (which is I atm as you have noted).

 

[WoodyPE]

On the roughness factor (which is important), you might want to consider the fact that the surface smoothness could degrade over time.

 

[racookpe1978]

But, would surface roughness inside a flare line be increasing that much over time?

I'd expect much worse for, say, seawater or condensate water in a pipe in continuous service, but is nat. gas in a flare that corrosive?

Or is it much more corrosive than "simple" raw water?

 

[BigInch]

Natural gas by itself is not corrosive, but when combined with trace amounts of water, CO2, H2S, fostering chemical reactions that yield carbonic and sulfuric acids, which as you probably already know or guessed, can make short work of a piece of pipe.

As for friction factors changing during the life of a pipeline, I've actually seen one gas gathering systems with rather high gas velocities where the pipe in some areas actually appeared to decrease in roughness over the years. As sand production was also increasing in conjunction with the wells in that same area, I supposed at the time it was due to a sand blasting effect on the pipe walls.

**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies)

http://virtualpipeline.spaces.live.com/

 

[enrjdean]

BigInch

I've been reading through the PDF that you posted which shows different examples and equations that are used for calculating the pressure drops/flow rates ect of a compressible fluid. These examples use a effiency factor of a pipe (E) and also a compressibility factor (Z). The spreadsheet Mr. Montemayor posted uses a roughness factor. Which is the more accurate of the two for predicting the pressure drop?

Have I missed something in the math or are the two, two different ways of calculating the pressure drop/flow rate which achieve the same goal?

I know that this thread has turned into a bit of an animal, but I would just like to understand how the two different equations differ - if in fact they do?

Jim