Elevation correction for pressure 2

[DrCaddy]

Dear Friends,

In NFPA regulations, I have seen elevation correction in the calculation of pressure for pipes carrying CO2(Reason stated: Density of CO2 varies with height especially if the change in elevation is as high as 50 feet). Is such a correction necessary for my system also which has a high pressure cylinderical pipe of constant CSA? If so, is there a formula to calculate the pressure loss due to elevation given that only the inlet pressure and the temperature of the gas are known.

I have tried the following method as a work-around sacrificing some accuracy in the result: I took another pipe of similar dimensions (length equivalent to the height of the original pipe) and I calculated the terminal pressure for this pipe which I assumed to be horizontal to the ground. With the inlet and outlet pressure in hand for the horizontal pipe, I calculated the average density of the gas. Then I applied the formula,

delta P = 9.81 * Density of the gas * Height
where,
delta P = Outlet pressure - Inlet pressure

Do you think that this method is sufficient enough or is there some other better solution? I am a beginner in this area. Please help.

TIA,
Caddy

 

[zdas04]

In liquids the change in head due to elevation change is significant. The static gradient of pure water is 0.43 psi/ft so a 50 ft elevation change is 51.5 psi which could easily be significant in a lot of flow problems.

You get to a non-compressible static gradient by converting the density (in say lbm/ft^3) to force per area (say psi/ft). In imperial units it is simply density divided by 144.

Gases are much more complex. The static head of a compressible fluid is impacted by the gas stacked up above it and the equation is

P(bottom) = P(top)* exp(0.01875*SG*height/(temp*Z))

At 2,000 psig at the top, 50 ft elevation change would see 2002.5 psig. Is that significant? Sometimes, ususally not. If you started at 50 psig, the bottom would be 50.078 psig. If you started at 25,000 psig you'd pick up 31 psig.

The bottom line is that if your CO2 is acting like a liquid it matters, if it is acting like a gas then it probably doesn't unless your pressures are pretty high.

David Simpson, PE
MuleShoe Engineering

http://www.muleshoe-eng.com

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

The harder I work, the luckier I seem

 

[vzeos]

DrCaddy:

There are several methods to approach the pressure correction due to elevation. In the general gas flow equation for pipelines, the pressure drop term including the elevation correction is:

(P₁²-P₂²)- 0.0375 G dX P_avg²/(Z_avgT_avg)


Where:
P₁ and P₂ = inlet and outlet pressure, psia
G= gravity relative to air
dX=elevation change, feet
P_avg=average pressure, psia
Z_avg=average compressibility
T_avg=average temperature, deg R

If you want more detail I suggest you obtain:
1. Smith, R. V., Miller, J. S. and Ferguson, J. W., Flow of Natural Gas through Experimental Pipelines and Transmission Lines, U. S. Bureau of Mines Monograph No 9, American Gas Association, New York, 1956.

2. Uhl, A. E., et al., Steady Flow in Gas Pipelines, Technical Report No. 10, Institute of Gas Technology, Chicago, 1965.

 

[DrCaddy]

Thank you zdas04 and RGasEng. I am sorry I left a few rather important details of the system in my post => that my system is a nitrogen system and that in the calculation the effect of temperature change is neglected completely and the flow rate through the pipe is assumed to be constant. These assumptions make the calculation of the system a lot simpler. I should add that the inlet pressure of the system is usually around 3000 psia.

RGasEng:

Since I am not quite familiar with this area, I find it difficult to comprehend the equation you have written. Should there be an equal to sign in the place of minus sign in your equation, otherwise what is it equated to?


I saw an iterative technique to solve the problem in a book and I thought it would be a good idea to share it with you all. It is as follows:

First, the average density of the gas is calculated by assuming an initial exit pressure. Then, the actual exit pressure of the pipe is calculated using the Bernoulli's equation. If the exit pressure is close to the initial assumption then that value is taken as the exit pressure of the pipe. Otherwise the iteration is repeated with the calculation of the new average density with the exit pressure from the previous iteration. Then the actual exit pressure is computed using the new density. Iterations are repeated until the exit pressure from the previous iteration and the current iteration are close enough.

This technique has made my life easier, since I have written a code to let the computer do the iterations for me

 

[vzeos]

DrCaddy:

That 3000 psi could make a big difference. Anyway the expression I wrote is not an equation. It is the pressure drop term that goes into the general gas flow equation.

The general gas flow equation, with the elev correction, is:

Q_b= 117.4 (T_b /P_b )([√]1/f){(P₁²- P₂² - 0.0375 G dX (P_avg²/Z_avgT_avg))/( G L Z_avgT_avg)}^1/2 D^2.5

Where:
Q_b=scfh
T_b=base temp, deg R
P_b=base pressure, psia
[√]1/f = transmission factor (f = fanning friction factor)
P₁ and P₂ = inlet and outlet pressure, psia
D=diameter, inches
G= gravity relative to air
dX=elevation change, feet
P_avg=average pressure, psia
T_avg=average temperature, deg R
L=Length, feet
Z_avg=average compressibility

Let me know if you have any additional questions on this.

 

[DrCaddy]

RGasEng:
Is there a formula to compute the average compressibility?

 

[vzeos]

Yes, there are quite a few compressibility equations with varying degrees of complexity and accuracy. I would suggest Googling “compressibility equation” or “virial equation of state.” But first…………..

There is a free thermodynamic properties program available on the University of Idaho’s website (link attached.) Download ALLPROPS for Windows (v1.0). This program is deceptively sophisticated. You can calculate a number of thermodynamic properties including compressibility.

After you start the program, access the Options menu to select the properties to display and to select your units. Then access the Fluids menu to select your fluid. You can calculate properties at a point by supplying your state variables and pressing Enter or, from the Tools menu, you can define Tables or Graph to be generated.

What I have done in the past is to generate a table of properties, then copy the table into an Excel file. Once you have the table in Excel you can graph it and try fitting an equation to the portion of data that is in your range of interest.

http://www.webpages.uidaho.edu/~cats/software.htm

 

[athomas236]

I tried the web link RGasEng but it said acces forbidden.

Regards

athomas236

 

[vzeos]

athomas236,

See thread391-135120.