13 replies to this topic

[bernath]

Dear All,

I have just learned to use compressible flow on my recent incoming project. Using an incompressible flow (Darcy Weibach) is not an option for me since we have to divide the pipe to many small segments. Therefore I'm now looking for compressible flow articles or books whose content are simple and have been acknowledged globally by many process engineers.

My current reference is Crane TP410 and Shashi Menon's Piping Calculation Manual. The problem is they give quite different formula for isothermal compressible flow equation (Menon gives correlation for elevation that made the equation far more complicated). I'm kind of confused of what to choose. When it comes to isothermal compressible flow calculation, which form of equation you refer to? Is it Crane TP410, Menon's Piping Calculation Manual, or anything else?

I'm still quite confuse whether to employ isothermal or adiabatic equation. The conditions and terms for each equation still not clear for me. Need some help here..

Please kindly advise.

The attached file is the isothermal compressible flow equation in Menon's book. For Crane TP410, I believe everyone has already had it.

many thanks
regards
bernath

Attached Files

•  Menon - Piping Calculations Manual - isothermal compressible flow.pdf   37.02KB   407 downloads

[ankur2061]

Bernath,

Flow in piping (short lengths of pipe) is generally considered isothermal. Essentially this means that there is no temperature change from the source (start point) to the destination (end point). Also for short lengths of pipe any cooling due to Joule-Thomson expansion (isentropic process) of the gas can be neglected.

The case you have encountered is similar to what I have encountered and resolved many times.

The method is as follows:

1. Split the piping into number of short designated length segments

2. Calculate the pressure drop (delta P) using the Darcy-Weisbach equation for the first segment for the volume flow (V) at the start point, mass flow (W), temperature (T) and pressure (P) at the start point. Arrive at the new pressure value (P1) at the end of the segment 1 as (P-deltaP)

3. Arrive at a new density value (rho1) for the new pressure (P1) at the end of the first segment using rho1 = P1*M / R*T*Z

4. Calculate the new volume flow (V1) with the new density (rho1) at the start of the segment 2 as V1 = W / rho1

5. Calculate the pressure drop for the segment 2 with the new volume flow (V1) and arrive at the new pressure value P2 at the start of the segment 3.

6. Repeat the above steps till you have the final pressure value at the end of the entire pipe.

It is important to note that in the above procedure the value of T and Z are assumed constant for the entire pipe length and that is what I have mentioned in the opening paragraph of my response.

The above method is recommended to be used when the pressure drop for the entire piping system is more than 10% of the initial pressure value but less than 40% of the initial pressure value. For calculating pressure drop in vacuum pipes it is recommended to be used for all cases regardless of the pressure drop value as a percentage of the absolute pressure.

Hope this helps.

Regards

[Zauberberg]

The method described by Ankur is commonly used in compressible flow calculations, and it gives good results. You can find references in Crane TP410 and GPSA Databook.

What I would add with respect to isothermal and adiabatic flow, is that for low pressure drop applications we normally consider isothermal flow whereas for high pressure drop cases the effects of gas expansion should not be neglected, and flow is calculated as adiabatic. I have also found this reference in a couple of engineering standards and practices.

[katmar]

It is commonly quoted that if the overall pressure drop is less than 10% of the upstream pressure of the gas in absolute terms then you can safely assume incompressible behaviour and use the average conditions in the Darcy-Weisbach equation. In my experience this is true, but not really relevant. It comes from the days when people did not have computers on their desks and to do a proper compressible flow calculation could take you an hour or more using a slide rule or log tables.

If you are doing this sort of calculation on any sort of regular basis then you will either have access to software that will do it properly, or you will write your own spreadsheet to do it. Once you have the software then it is as easy to do the compressible flow calculation as it is to do the incompressible calculation and there is no longer any reason to take a short cut.

I see no advantage in dividing the pipeline into segments and using incompressible flow equations. This is much more work than just putting the correct equation into a spreadsheet. It is true that for gases you need to take the expansion of the gas into account as the pressure decreases along the line. The isothermal and the adiabatic equations will do this for you. The only difference is that the isothermal equation assumes that the expansion occurs only because of the drop in pressure and not because of any change in temperature (hence isothermal) while the adiabatic equation takes the temperature change into account as well.

Generally adiabatic means that the temperature decreases along the pipeline and the gas does not expand as much as it would under constant temperature conditions. This makes the exit velocity lower (gas is more dense) under adiabatic conditions than under isothermal. Thus the pressure drop you would calculate with the adiabatic assumption would be less than with the isothermal assumption. For a long gas line it is usually very slightly conservative to assume isothermal rather than adiabatic behaviour - i.e. isothermal gives higher pressure drops or lower flows.

Generally it is important to use the adiabatic equation for short, high pressure drop lines such as relief valve vents where the advantage you get due to cooling is significant. Otherwise I always assume isothermal.

The difference between the Menon and Crane isothermal formulas is well described on page 1-8 of the Crane manual. Crane makes a whole bunch of simplifying assumptions, while Menon treats the general case. If the Crane assumptions hold then use their simplified form. If not, bite the bullet and use Menon.

[bernath]

@Ankur: What a great step by step explanation.. thank you for putting much effort to give us such a detail sum up.. It would be very helpful for junior engineer like me.

Yet I'm still wondering (for isothermal assumption) if we assume that Z is constant along the pipeline, then would the result still be acceptable in terms of accuracy? How to calculate Z in every segment of the pipe? I think it would be very complicated if it's performed by hand calculations or spreadsheets.


Quote:

"I see no advantage in dividing the pipeline into segments and using incompressible flow equations. This is much more work than just putting the correct equation into a spreadsheet. It is true that for gases you need to take the expansion of the gas into account as the pressure decreases along the line. The isothermal and the adiabatic equations will do this for you"

@Katmar: I agree with your statement. A very well explanation of adiabatic vs isothermal compressible flow. Many thanks

regards,
bernath

[katmar]

It is difficult to imagine a real-world situation where you would have a significant change in Z along the pipeline, but if you did you could combine Ankur's and my advice and break the pipeline into segments and then use either an isothermal or adiabatic compressible flow equation for each segment, while adjusting the Z value for each segment according to the actual conditions. But I suspect this would be a very rare situation. It is especially difficult to imagine Z changing much under isothermal conditions.

[bernath]

It is difficult to imagine a real-world situation where you would have a significant change in Z along the pipeline, but if you did you could combine Ankur's and my advice and break the pipeline into segments and then use either an isothermal or adiabatic compressible flow equation for each segment, while adjusting the Z value for each segment according to the actual conditions. But I suspect this would be a very rare situation. It is especially difficult to imagine Z changing much under isothermal conditions.

Dear Katmar,

Okay, I agree. I think it's not necessary to update Z for every segment of pipe in real world situation.

Yet I still have one question left.

If we use compressible flow for pipeline, suppose that Z is constant along the pipeline, is it still necessary to divide the pipe into several pipe segment?

If I'm not wrong, we use the inlet density for isothermal compressible flow equation. We all know density will change accordingly as the gas moves forward. I don't see any term in the equation that compensate the effect of density change. Has the isothermal flow equation already take into account the changes in density along the pipeline? or we just have to use average pressure density for the equation? Please advice

Sorry if my question is indeed very basic.

thank you
regards,
bernath

[katmar]

Applying the isothermal (or adiabatic) model to the energy balance (=Bernoulli equation plus friction) before it is integrated takes the density change into account. The way the density changes is a function of whether the flow is isothermal or adiabatic.

For isothermal flow, the friction factor is virtually constant as well because it is a function of Reynolds number which includes the product of velocity and density, and the product of these is constant (under isothermal conditions). Re is also a function of viscosity, but that will not change much. And because Re is usually very high for gases the friction factor is a fairly weak function of Re.

One of the better discussions of all this is in Volume 1 of Coulson and Richardson's series on chemical engineering (Page 159 in my sixth edition).

[chemsac2]

As excellently put by Katmar, isothermal compressible flow equation in Crane is derived from integrating differential form of Bernoulli equation and law of conservation of mass.

Since Bernoulli equation is for incompressible flow, it can not be used as it is for compressible fluids for entire range of sonic velocities. Refer wikipedia page on Bernoulli equation.

Since isothermal equation is derived by integrating all pressure dependent terms in equation like velocity and density, dividing pipe in small segments is not necessary if change in Z is not significant which would in fact be the case for small pressure drops.

Once I tried reducing number of segments in a simulator and did not find any change in sink pressure.

Refer attached file for derivation of isothermal equation.

Regards,

Sachin

Attached Files

•  20. Compressible_Flow_Hydraulics2.pdf   1.74MB   385 downloads

[sheiko]

Attached is another interesting article (also available here http://www.aft.com/news/view.php?ID=97). I suggest you to take a look at the paragraph "Simplification error: How big?".

Attached Files

•  CE_Gasflow_Reprint.pdf   1021KB   329 downloads

Edited by sheiko, 24 February 2011 - 09:15 PM.

[bernath]

thanks all.. what a great article from AFT..

[sheiko]

Another article on the subject. More practical than theoretical, but quite informative.

Attached Files

•  HP 1999-May Compressible fluid pressure drop.pdf   2.88MB   356 downloads

[bernath]

Another article on the subject. More practical than theoretical, but quite informative.

many thanks sheiko.. I've been looking everywhere to get this article..

how gracious you are..

God bless you

regards,
bernath

[breizh]

For those interested and who can get access to Chemical engineering (1996/1997):

2 good papers :
-Calculate pipeline flow of compressible fluid : CE Feb 1996 by TW Cochran
-Critical length helps calculate compressible flow :CE Feb 1997 Italo H Farina

Breizh