natural gas compressibility factor question 4

[mod231]

Hello all, I am sizing a small natural gas line with a starting pressure of 40psi for an industrial application. It will need to flow 8300cfh, the pipe run is 3500'. I was going to use the Renouard equation, then I read in a piping design handbook that the compressibility factor "Z" doesn't really need to be accounted for on this short of a run, and with pressures this low. Is this correct? Is there a more appropriate formula for this situation?

Best regards.

 

[SNORGY]

In my opinion, I would apply Darcy Weisbach to the situation at an initial friction factor f=0.02 (or from Moody or Colebrook-White) to see if you calculate a line loss in excess of 10% x 40 psi (i.e., max dP = 4 psi). If you do, then you should account for compressibility in your pressure drop calculation. You might be able to use Isothermal, Weymouth, or Spitzglass (see Crane TP-410 / 410M).

Or, break it up into smaller sections (say 10 sections of 350 feet) and apply Darcy-Weisbach successively with different States 1 and 2 for each section, and add dP1 + dP2 + ... dP10.

Regards,

SNORGY.

 

[BigInch]

You don't need to consider NG compressibility until you are at the very least up to 250 psi, maybe not even then.

Let your acquaintances be many, but your advisors one in a thousand’ ... Book of Ecclesiasticus

 

[katmar]

I totally agree with SNORGY in that I would rather use the Darcy Weisbach equation, and with BigInch in that the compressibility is not an issue at this low pressure. But I would like to comment on your quotation of "compressibility factor 'Z' doesn't really need to be accounted for on this short of a run, and with pressures this low".

There are two considerations regarding Z. The first is that it determines the actual density of the gas at the start of the pipeline. The second is that Z may change over the length of the pipeline, thus complicating the prediction of the density at each point along the pipeline.

The first point applies to all pipelines - whether they are short, long or intermediate. In all cases you need to know the actual density at the start of the run (either as a density or as a compressibility, depending on the pressure drop equation you use). This knowledge may be as simple as in this case where you know Z=1, or it may be very complex.

The second point (Z changing along the pipeline) is more a function of the physical changes in the gas (pressure and temperature) than in the actual length of the pipe. A very short pipe going from very high pressure to a vent or flare may well still require consideration of the compressibility changes. On the other hand a very long line at relatively low pressure may not need compressibility to be considered.

So overall I would say the first part of that quotation (regarding pipeline length) is misleading, but the second part (regarding low pressures) is correct.

Just an aside - many experienced pipeline engineers will never have heard of the Renouard equation. I had to Google it myself, and as usual found the answer right here on Eng-Tips. It is apparently an empirical equation in the same mould as Panhandle or Weymouth and used mainly in Spanish and Portuguese speaking countries. These empirical equations are great for specialists in a particular industry who come to learn their strengths and weaknesses, and to know where and when they can be applied. For non-specialists it is better to use Darcy Weisbach which has a much more general applicability, and requires less industry knowledge in order to get to the "right" answer.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[mod231]

Thanks to all.

Regards.

 

[zdas04]

I generally limit the use of Darcy Weisbach to liquid flows. Gas flows are a touch more complex and I get results that match measured conditions much better with one of the equations derived from the Isothermal Gas Flow Equation (as it is called in the GPSA Field Data Book). Panhandle A, Weymouth, and the AGA Fully Turbulent equations all derived from the Isothermal equation (each is just a different way to solve for Fanning friction factor without iterating).

At high pressures (I defing "high pressure" as above 150 psia) I find that it doesn't matter so much which equation you use, they all give acceptable results consisten with their underlying assumptions. Below 50 psig, the "incompressible" assumption in all the equations becomes a big problem. The 10% pressure drop mentioned above is a response to people trying to ensure that they satisfy that assumption. I've found that if I ignore compressibility, breaking up a long pipe into sections does not change the answer and is a waste of time. If I recalculate compressibility (based on average pressure) for each section then I get very different answers for the sum of short sections. I find that ignoring compressibility creates a very large error at low pressures. Even though the change from 40 psia to 36 psia seems to be really small, the cumulative effects are large.

For example, let's assume that I start at 40 psia and predict that I'll end at 20 psia (50% pressure drop) using a single step. This violates the incompressible flow assumption so I break the line up so that no segment has more than 10% pressure drop. For one set of conditions I found that the pressure at the tail really worked out to 10 psia instead of 20 psia which is a huge operational difference (vacuum operations vs. positive pressure).

If you are talking about a flow line going from 2,000 psia to 1,850 psia (7.5% drop), then calculating a compressibility for the average pressure gives you an excellent match to field data. Going from 175 psia to 25 psia (still 150 psi drop, but now 86% drop) gives you a meaningless answer in one step.

We need to pay attention to the underlying assumptions of the arithmetic we use, and a low pressure it is disturbingly easy to violate the incompressible flow assumption inherent in all of the mainstream flow equations, including especially Darcy Weisbach.

I never ignore compressibility, but at low pressures I pay very special attention to it.

David

 

[katmar]

David, what you have written here makes me realize that I have made a major (but probably not justified) assumption in the terminology I use. When I speak of the Darcy Weisbach equation I include, in my own understanding, the isothermal and adiabatic equations for compressible flow as well as the simple liquid/incompressible version.

The isothermal and adiabatic equations are simply the DW equation integrated for the change of gas density using either an isothermal or adiabatic model.

Another very loose use of language in my post above was the failure to distinguish properly between "compressible flow" and the "compressibility factor - Z". I agree with you absolutely that in gas flow you should always include the compressibility (but not necessarily the compressibility factor).

Because I have the compressible versions of DW built into a computer program it is no extra work for me to always use the compressible equations when dealing with gases, so I never treat a gas as incompressible unless it is for some specific purpose. On the other hand it is relatively rare for me to have to worry about the compressibility factor Z in the industries where I usually work.

Thank you very much for prodding me into this realization. I hope mod231 is still following the thread and re-reads my earlier post in this (hopefully) clearer light.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[zdas04]

Katmar,
Again, language can be tough. All of the equations mentioned above are incompressible. The math for compressible flow is a LOT tougher. Most liquids are inherently incompressible to a large extent (nothing is truly incompressible, but most liquids are close enough) and if you drop pressure a significant percentage, density will change very slightly--generally the density change in a liquid is far outside the accuracy of the equations used and can be safely ignored.

Incompressible flow of an intrinsically compressible flow is a different kettle of fish. When you say "use the compressible equations" I think you mean "use the incompressible equations that have been tailored for compressible fluids". The compressibility factor goes into the calculation of density, Reynolds Number, friction factor, and it is explicit in several of the incompressible flow equations.

I work with compressible flows in ejectors pretty often and I wouldn't wish those calculations on anyone.

David

 

[SEP87]

Please can somebody explain why compressibility of NG need not be considered below 250 psi?

Thanks

 

[zdas04]

That will have to be someone else since I just spent an hour explaining that while compressiblity changes in magnitude slowly at low pressures, its importantance to the ability of an equation to match field data increases rapidly at low pressures.

David

 

[katmar]

David, I do not have the GPSA Field Data Book so I cannot be sure about their isothermal gas flow equation. However, I would guess that it is the same as either Equation 1-6 or 1-7 from the Crane 410 manual. Although Crane says equation 1-6 is for situations that fall outside the limitations of the Darcy equation, it is shown in Coulson and Richardson Volume 1 that this equation is simply the Darcy equation integrated for the isothermal gas model which describes how the density changes with pressure.

Equation 1-6 assumes the perfect gas law, which allows for the gas density changing along the length of the pipe as the pressure drops (temperature assumed constant). Thus it definitely takes into account the compressible nature of the gas (i.e. density changes significantly with a change in pressure).

In Eq 1-6 one of the input values is the specific volume of the gas at upstream conditions. This value could (actually should) be calculated using the compressibility factor Z and as long as Z does not change along the pipeline then it will give the correct result. Just to make this absolutely clear I will state explicitly - it allows the density of the gas to change along the length of the pipe (i.e. compressible flow) but does not allow the compressibility factor Z to change.

The difference in complexity between Crane Equations 1-6 and 1-7 is so small that there is no point in making the additional simplifying assumption required (i.e. neglect acceleration) for 1-7 if you are using a spreadsheet or a program.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[katmar]

SEP87, Note that it is the compressibility factor Z, and not the compressibility in terms of density changes, that can be neglected. As zdas04 has pointed out, at lower pressures the pressure drop along the line is often a higher fraction of the inlet pressure and this usually makes it important to treat NG as compressible below 250 psi. As I stated earlier, once you have the equations programmed or in a spreadsheet, it makes no sense not to do the calculation properly and always take the compressible flow into account

For NG the compressibility factor Z can be neglected below 250 psi because for temperatures between about -20 deg C and 400 deg C the compressibility factor Z does not vary from 1.00 by more than 1%.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[SEP87]

Thank you for clearing that up.
I misunderstood what people meant when they said compressibility is not an issue.
Thank you

 

[zdas04]

Katmar,
Equation 1.7a in Crane is almost the SCF/hour version of the GPSA equation 17.15 (which is in SCF/day). The three differences are (1) the GPSA equation includes an "effeciency" term; (2) GPSA has "compressibility based on average pressure"; and (3) GPSA includes a T(b)/P(b) to allow for base conditions other than 60F and 14.696 psia. The effeciency term magically reappears in Crane's version of Panhandle A (eq 1.9), but not in Weymouth (eq 1.8). In GPSA it is in both Weymouth and Panhandle A.

The assumptions for eq 1.6 in Crane include

4. Gas obeys the perfect gas laws

GPSA doesn't have that assumption.

The tenth section of Chapter One of Crane is titled "Principles of Compressible Flow in Pipe". That is a source of incredible confusion in the industry. They further confuse the issue by saying that equation 1.6 is appropriate for pressure drops greater than 40% of inlet pressure, but the assumptions for eq 1.6 includes

6. The friction factor is constant along the pipe"

The only way the friction factor can be constant is if the Reynolds Number is constant which is only true if the density is constant. If I halve the pressure, I approximately halve the density, which just about halves the Reynolds Number, so if I have an [ε]/D of 10^-8 (smooth pipe) and a Reynolds Number of 10^6 at the head of the pipe, a 50% reduction in pressure would change the friction factor by 13% which violates the assumptions of eq 1.7 (and by extension 1.7 and 1.7a).

The equations for incompressible flow of compressible fluids all came from the Bernoulli Equation. They are very useful and allow us to do many things that we couldn't have done without them, but they need to stay withing their limitations.

I'm starting to feel like I've moved a useful conversation way too far into the weeds and I apologise. In my defence, I work with a lot of engineers in a lot of companies who feel that it is reasonable to use Panhandle A in 2-inch pipe or pipe with a Reynolds Number < 5X10^6 or use Weymouth for a line with pressure dropping from 900 psig to 500 psig (Weymouth was developed for pressures under 130 psig, and none of the equations work for a dP much greater than 10%). I keep trying to get people to acknowledge the underlying assumptions in the math they use.

David

 

[katmar]

David, thanks for the clarifications on the differences between GPSA and Crane.

I must admit that when I wrote in my first post in this thread that Panhandle etc are best left to the experts in the field it was people like you and BigInch that I had in mind. You know what efficiencies to use and when to use which equation. But for generalists like me it is best to stick to Darcy Weisbach (or at least my expanded definition of DW, which includes the compressible versions).

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[mod231]

Wow, this turned into a really informative thread, great stuff! Thanks very much everyone.

 

[zdas04]

Katmar is far too nice a person to call me an idiot in an open forum, so he sent me an e-mail saying that I had made an error above. Of course, he was right so I wanted to clear up one point.

When I said

The only way the friction factor can be constant is if the Reynolds Number is constant which is only true if the density is constant. If I halve the pressure, I approximately halve the density, which just about halves the Reynolds Number, so if I have an ?/D of 10^-8 (smooth pipe) and a Reynolds Number of 10^6 at the head of the pipe, a 50% reduction in pressure would change the friction factor by 13% which violates the assumptions of eq 1.7 (and by extension 1.7 and 1.7a).

I was just plain wrong.

Reynolds number is usually stated as:
Re= Dv[&rho;]/[&mu;]

[&rho;] does change as I said, but velocity changes in the other direction by the same amount. Reynolds number is constant down a pipe. That is easy to see if you rearrange the Reynolds Number equation as:
Re=k*W/(d*[&mu;]) (where "k" is a constant for unit conversion and to include [&pi;])

Since "W" (mass flow rate) is constant everywhere in the pipe as long as flow is not added or removed, then except for minor changes in viscosity with pressure changes Reynolds Number is constant.

I really hate the taste of crow, but I dislike having wrong information associated with my handle even more.

David

 

[BigInch]

Gases are compressible, but the compressibility factor of a gas is simply the measure of how much that gas will differ from an ideal gas when both are compressed to a given PT; the compressibility factor of an ideal gas always being 1.00.

http://iptibm1.ipt.ntnu.no/~jsg/undervisning/naturgass/parlaktuna/Chap3.pdf

Let your acquaintances be many, but your advisors one in a thousand’ ... Book of Ecclesiasticus

 

[ione]

Very interesting discussion.


mod231,

Give a shot to the calculator at the link below (it relies on the isothermal gas flow assumption).

http://www.pipeflowcalculations.com/gasflow/

I would also give a read to this article, to better undestand limitations of the assumptions on which eqautions are based.

http://www.aft.com/news/pdf/CE Gasflow Reprint.pdf

 

[ione]

Katmar,

I’m a bit puzzled by your statement “For NG the compressibility factor Z can be neglected below 250 psi because for temperatures between about -20 deg C and 400 deg C the compressibility factor Z does not vary from 1.00 by more than 1%” from your post (4 May 11 10:04).

I’ve run your Uconeer to calculate compressibility factor for methane and played with pressures and temperatures in the ranges you’ve mentioned and got results which exceeds the 1% threshold.

Just to quote an example:

T1 = 0 °C
P1 = 200 psia
Z1 = 0.9598

Could it be that this difference is due the fact I used methane instead of NG?