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# Compressibility Factor Of Moist Air

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### #1 slmn

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Posted 16 April 2011 - 02:24 PM

Hi all,

I found many Excel sheets in the forum for calculating compressibility factor for different gases, but what about air? For dry air it is ok if you assume it as 21% O2 and 79% N2. You can get Z by any of the EOS - or by the compressibility chart using Kays Rule. But if I want to include moisture in air - say I have air with certain conditions P, T and relative humidity. Say 80%. How can I deal with that? Say with Kays Rule, how can I include the humidity ratio in my calculations? How do I manage the percentage of each constituent 21+79 = 100 and moisture? It will be more than 100%? Any idea?

### #2 Jiten_process

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Posted 16 April 2011 - 02:43 PM

I guess the effect of moisture is so low on 'Z' value that you can actually neglect it, however you have to consider humid volume for sizing purpose. As such you can use simulation tool to find accurate Z value. Take one stream as pure air (21% O2 and 79% N2) and define the second stream as pure water with flow rate same as total moisture that you have calculated. Add a mixture and connect these two stream as inlet. Take out the outlet stream as humid air and see the 'Z' value. I guess this is how you can do this.

Ask a compressor vendor what do they consider, i guess they might neglect this, however for inlet volume they do consider humid volume for the sizing purpose.

Neways, lets c what others have to say on this.

### #3 ankur2061

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Posted 17 April 2011 - 02:35 AM

slmn,

Jiten is absolutely right. The effect on Z for water saturated air or dry air is negligible. The dependency of Z is more on the pressure and temperature of the gas. While doing compression calculations for air, the effect of high relative humidity is more on the inlet volumetric flow also called as inlet cubic feet per minute or actual cubic feet per minute.

Air flow is normally represented as SCFM or Nm3/h where S represents "Standard" conditions of 14.7 psia (1 atma) pressure and 60 deg F (15.6 deg C) temp whereas N reperesnts "Normal" conditions of 1.013 bara (1 atma) and 0 deg C.

If you are required to perform inlet volume flow calculations for an air compressor you might like to have a look at the following link:

http://www.cheresour...2950#entry22950

Regards,
Ankur

### #4 slmn

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Posted 17 April 2011 - 09:24 AM

thank you very much for the valuable information
actually im trying to estimate the efficiency of the compressor of our gas turbine i have P,T,RH at inlet
and discharge ,i calculate the cp as indicated in ASME PTC 10 1997 from fig c1, and as i said i sticked in Z
now for estimating Z what do you suggest, using EOS, or the values in perry's handbook section two and interpolate for the required values.or the compressibility chart using kay's approach(it will be hard to transfer this chart to excel) , i need your advice.

finally if you please give more details about the two streams method , did you mean to estimate Z for air and Z for steam and take the mean or what.

thank you both again

### #5 ankur2061

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Posted 17 April 2011 - 10:49 AM

slmn,

Your response is confusing. Are you mixing air and steam? If it is just moist air then please provide the composition of the air in terms of air and water. Also provide the pressure and temperature at inlet and outlet. For compressor calculations the average compressibility needs to be considered i.e

Zavg = Z1+Z2 / 2

where Z1 is compressibility at the inlet conditions and Z2 is compressibility at theoutlet conditions.

Compressibility factors are best calculated using EOS such as Redlich-Kwong, Soave-Redlich-Kwong and Peng-Robinson. Among these Redlich-Kwong is easiest to program in an excel sheet because the solution of this EOS does not require an iterativeprocedure.

Hope this helps.

Regards,
Ankur.

### #6 slmn

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Posted 17 April 2011 - 11:50 AM

just moist air interning and leaving the compressor

inlet air pressure = 23 in HG , temp = 66 F , relative humidity = 80% ===> Z = ?

discharge press.=129 psig , temp = 663 F , relative humidity = 80% ====> Z = ?

### #7 Zauberberg

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Posted 17 April 2011 - 12:09 PM

This resource lists the compressibility values for Air at different pressures and temperatures. You can use the interpolation formula for calculating intermediate values:

http://pipeng.com/in.../itddaflup00501

As said by Ankur and Jiten, you can neglect influence of water vapor, as far as compressibility is concerned.

### #8 Art Montemayor

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Posted 17 April 2011 - 04:04 PM

All:

This is an interesting subject because it brings up some important issues having to do with the retrieval and confirmation of data used in engineering decisions and calculations. And I would take this opportunity to bring up some experience for the benefit of some of our younger engineering Forum members.

For many years, I have divorced myself from resorting to Perry’s Chemical Engineering Handbook. In my early years as a young graduate I was disillusioned and dismayed by the absence and quality of data in that publication. My disenchantment later turned to indignation when some of the data I found there was either erroneous, lacking in detail, outdated or out of touch with practicality. As the years have progressed since I bought my copy of the 3rd Edition (for \$16.75 – a handsome price in 1957) the price of this publication has reached a level where a young student should receive the total worth of what he/she is paying for this book. I personally believe the present price to be outrageous.

Now I look at what Zauberberg has presented to us and I discover that it is a copy of what someone found in Perry’s latest edition. It is a reduced table of some Russian data obtained in 1966 by some guys named Vasserman, Kazavchinskii, and Rabinovich. Sounds like a Troika to me. This data is published by Perry’s (through McGraw-Hill) and simply states that the data is in “bar” and K. It fails to specifically identify the pressure as absolute and leaves the reader in the lurch as to whether these guys used absolute or not. They calculated this data, so we might assume they used absolute units – but once again, we are forced to guess, assume, or suppose that they did. We don't even know if this data is generated on an absolutely dry theoretical air mixture - or moist atmospheric air. This is another illustration of what Perry’s puts together in their compilation of someone else’s data. Perry’s has consistently failed to give the Chemical Engineer what he/she has dearly paid for in hard cash: specific data.

I realize that the data may be based on European SI units that call for only absolute bars. However, we have no hard basis for ensuring the pressure base of the data. Perry’s itself follows up with Table 2-185, “Compressibility Factor for Water Substance (FPS units)” and identifies the rows on that table as PSIG and the columns as oF. Therefore, we have proof that the Handbook does not respect a “standard” nomenclature of absolute pressure (or temperature) units. How then, can we “assume” that the bar employed in the Russian data is absolute? Do we have to find (and purchase) the original Russian calculations? This is a good example of Shabby and sloppy engineering reporting. I believe that the Russian data is probably in absolute pressure units – but that belief does not approach my belief in God.

My point here, after allowing myself a righteous rant, is that engineering information is very important because we engineers are held legally, economically, and morally liable for our calculations and results out in industrial practice. A lot of the basic scientific and physical information and data that we employ is based on scientific results and experimentation. Yet the scientist is not held liable to the same degree that we all are! We are the ones that are sued and/or thrown in jail if our results cause harm. The scientist is left to admit that he might have made a mistake – and that is all that society expects from him/her. We are left holding the blame.

That is why I consider it so important to DEMAND specific, detailed, identified information and data when using it on engineering projects. We owe to ourselves and to our profession to insist on that quality of data to be upheld.

And I still don’t trust Perry’s Handbook. I think it is grossly overpriced and it stinks compared to the GPSA, Campbell’s Books, Ernie Ludwig’s Books, and other publications.

I apologize to Zauberberg if I question the data he presented, but I know him long enough to know that he probably agrees with some of what I state and also identifies with the message of being careful about how and where one obtains engineering design data. Thank you all for reading this.

### #9 katmar

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Posted 18 April 2011 - 04:40 AM

slmn, you need to move away from "scientific" thinking towards "engineering" thinking. The scientific question to ask here is "What is the Z value for the gas at the inlet and at the outlet". The engineering question here is "What uncertainty value do I need to incorporate into my calculation to ensure the Z value does not compromise my design".

Or to put it another way - how accurately do I need to estimate the Z value?

Looking at your data for the inlet conditions we can see that the water content is around 1% by mass. Already my engineering senses are saying "water effect is probably negligible". It will be hard to find Z data for the your exact mixture of air and water vapour, so my initial effort would be based on looking at the individual components.

Using Peng-Robinson for 66F and 23 inch HG (assumed absolute, but makes little difference) I get
Nitrogen : Z=0.9996
Oxygen : Z=0.9992
And from my steam tables for steam saturated at 66F I get Z=0.9992

And at 663F and 129 psig I get
Nitrogen : Z=1.0027
Oxygen : Z=1.0015
Steam : Z= 0.9858 (NB superheated - not saturated at 663F)

These numbers tell me that any deviation from ideality will be << 1%, and since they are based on EOS predictions I would regard Z as being 1.00 under all these conditions.

Taking Z as 1.00 will be a more accurate assumption than most of your other data such as composition, flow rate, pressure and temperature.

And so with just a little bit of applied (engineering) thinking we jump right around the problem of trying to determine an accurate Z value.

### #10 breizh

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Posted 18 April 2011 - 11:48 PM

Hi ,

You may find some interest reading this paper .

Breizh

### #11 slmn

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Posted 19 April 2011 - 09:51 AM

thank you all for this great help
and i appreciate any ideas regarding this

### #12 Art Montemayor

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Posted 19 April 2011 - 10:56 AM

Breizh:

Thank you very much for the nice article on calculating the water content of atmospheric and compressed air. It is the result of an academic exercise using regression on the published data found in the Iranian National Oil Company's standard for compressed air supply. You continue to submit good and interesting information for our members and I am grateful for your continued contributions.

While it is a good contribution to interested members like myself, Ankur, Zauberberg, et.al., it still lacks a specific, confirmed basis for the data results. Note that the published Table A.2 found in the referenced IPS-E-PR-330 paper lists the kPa pressure in GAUGE values. I am sure that Messrs. Bahadori and Mokhatab corrected their input into the regression exercise and that the generated equations are valid as per the Iranian table. However, also note that the Iranian table has NO REFERENCE or basis for its data presentation. This is not even mentioned by Bahadori and Mokhatab - or by Chemical Engineering magazine. I am not challenging the data nor claiming that it is not correct. All I would ask, as a practicing professional engineer is that the data be identified and certified as correct and accurate to what degree. If we are to use this data and the nice regressed equations, we should be well advised that we really have no published basis for the result. Consequentely, as is the case in most of these cases, be wary of how you use the results. At best, I would identify the result as an estimate - but without any idea as to its possible accuracy. Additionally, also note that the authors compare their example calculation results to the same data that they used as the basis for their regression. Of course it compares well; all that proves is that the method of least squares works in a good fit for the data. It doesn't mean that the equations generated will necessarily yield an ACCURATE value for the amount of water contained in saturated compressed air. We still look for an accurate measurement of that in order to have an idea as to how good are our estimating design equations.

Nevertheless, it continues to be the best that we can come up with until someone does a more thorough and documented, accurate project on identifying the water content in saturated compressed gases. What the simulation programs such as Hysys use to come up with their result is open to conjecture since they (like the Iranian table) don't report their basis or algorithm. So this is as good as we can get - for now.

If anyone has further or more detailed and identified data on this subject, I would be very grateful if they would let us all know.

### #13 breizh

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Posted 19 April 2011 - 10:24 PM

Art ,
Breizh

### #14 katmar

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Posted 20 April 2011 - 08:26 AM

Art, I think you are being too diplomatic in your comments on the Bahadori and Mokhatab article. I'm sure that breizh was only trying to help by posting the article, and I second your thanks to beizh for all the good help he offers here, but this article is terrible.

In the text on the top right hand side of page 57 they say "Increasing the pressure reduces the ability of air to hold moisture." This is very much in line with my own experience and calculations.

But in Figure 2 their regressed curve for 40C shows that the water content increases as the pressure increases from 700 to 1200 kPa. This made me look more carefully at the Figure. Firstly, the discrepancy between the regression line and the data points is close to 100% (5 ml/m3 vs nearly 10 ml/m3 at 750 kPa and 40C) and not the nice close agreement in their cherry-picked example. Secondly, I wondered if maybe it does increase if the "ml/m3" were based on actual m3 and not Nm3 so I tried to find in the text what m3 they were using. I could not find any mention of whether these are actual or Normal. Did I miss it somewhere?

We all know and respect the people like Kern, Simpson, Fair, Eckert and Kister who have published many articles over the years. In their cases the fact that they have had many articles published is a good indication of their abilities. But when I see a young PhD candidate who has already published 40 articles I get worried. There are too many like this who churn out poor articles simply to have a large number on their CVs. It's easy to take somebody else's data and throw it into a stats package and generate a few curves that constitute an article. But they should at least put a bit of thought into what they are doing. I would be far too embarrassed to publish such poor correlations.

But the worst of it is that a journal like Chemical Engineering has become a magazine with little or no editorial input.

### #15 Art Montemayor

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Posted 20 April 2011 - 10:32 AM

Thank you Harvey.

I can always count on you for clarification, frank, and honest comments. You continue to enlighten us with your accurate and descriptive review of engineering topics of importance.

I am afraid that you did not miss any mention of whether the gas volumes are actual or Normal. The authors (and what is worse, the Editor, Gerald Ondrey) simply do not make any mention of it. Yes, it is a sad and depressing experience to see Chemical Engineering - a publication that brought us the works of Kern, Simpson, Fair, Eckert, Kister, and numerous other notables in the past – lower its standards to this level. You haven’t mentioned the fact that the water units of mL/m3 also do not make mention of what temperature the mL are calculated at. We need the mass water rate for engineering design and we can’t get the water density if we don’t know its temperature.

At this point allow me to make this statement to our Forum readers: Our intent is certainly not to slam and simply criticize engineering articles or to take “pot shots” at them for the sake of satisfying our personal egos. The subject matter and topics here are of prime engineering importance for all engineers: the water (or vapor) content of gases and the ability to calculate and quantify the effect are of great importance in the design and operation of thermodynamic cycles and Unit Operations. At this stage of engineering development we simply lack the ability to predict accurate and consistent values for the condensable content in gas streams – especially with regards to polar molecules. The fact that we are still having trouble quantifying water content in compressed air should raise our concern. If we can’t master that, how can we proceed on to such bad actors like CO2, SO3, H2S, - even natural gas?

Our main topic for this thread continues to be the Compressibility Factor. However, please note how the related topic of gas humidity raises a question that we have difficulty in specifically addressing and resolving. When we resolve the basic subject of condensable contents in a gas, we will be able to definitely answer the Compressibility Factor question. For now all we can say is that it doesn’t seem to make a difference – as witnessed by empirical air compressor performance.

Thank you again, Harvey, for your support and frank, experienced opinions regarding the generation and employment of basic engineering data in engineering calculations and decisions. Like you, I also clamor for increased detailed, accurate, and applicable reported engineering study and research.

### #16 Elizabeth_I

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Posted 21 April 2011 - 07:36 AM

Thanks so much for the posts. They are really informative!