Specific heat ratio in gas compression 2

[Meshry]

In gas compressor; what is the specific heat ration? How could it affect the compressor performance?
in compressor's data sheet; I can see Cp/Cv varying with the temperature. is this the only parameter which could affect it?

thanks

 

[rotw]

quote from K. Ludtke, "Process Centrifugal Compressors".

"Although the pertinent formulae for the compressibility factor, the polytropic volume and temperature exponent were published in the 1940s, the message has, even today, not reached all engineering contractors that different exponents for calculating
head and temperature have to replace the traditional "ratio of specific heats", which is irrelevant for real process gases..."

"...But even today the message has not got around to all engineering companies that different exponents for head and temperature replaced the (perfect gas) values K= cp/cv , which have become irrelevant for process gases."

 

[zdas04]

I have to say that K. Ludtke is only speaking for dynamic compressors. For positive displacement compressors his statement is nearly perfectly incorrect.

[bold]David Simpson, PE[/bold]
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[rotw]

Zdas, thanks for this precision.

I take the occasion to ask you a question, just to better my understanding of positive displacement (PD) machines.

So for PD compressors, I understand the head is calculated based on the adiabatic exponent (k=Cp/Cv).
But we know that when the gas behavior departs from ideal gas, isentropic exponent "split" into an "isentropic volume exponent kv" and an "isentropic temperature exponent kt". Why don't we pick these two exponents (instead of the adiabatic exponent) for the purpose of performance calculation?

In other words, this would be equivalent of assuming PD compression process as subset case of a polytropic path, that is to say polytropic efficiency set equal to one, subsequently we would use kv for calculation of head and kt for temperature
e.g. T2/T1 = (P2/P1)^[(kt-1)/kt] (Indices 1,2 referring to inlet, respectively outlet.)

Would this be more accurate or am I completely off the mark, in which case please excuse my ignorance.

 

[zdas04]

I don't know that you are completely off the mark, but you would be limiting some calculations unnecessarily. If you can assume an adiabatic process (and I've done some very detailed work that convinced me that the departures from adiabatic performance are outside the uncertainty of the rest of the calculations, so I'm comfortable with PD machines being adiabatic), then you have access to some effective simplifying assumptions that make life in the PD world easier than in the dynamic compression world. For example, I can calculate a performance envelope for a PD machine with just knowledge of the frame MAWP, available HP, interstage cooler capacity for a multi-stage machine, and maximum acceptable temperature. It ends up a lot simpler than we see for dynamic machines.

[bold]David Simpson, PE[/bold]
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[georgeverghese]

This is new to me, that the polytropic exponent n used for compressor poly head and power calcs is not the same as the value of n to be used for actual discharge temp calcs for centrifugals. Does this Ludtke book give us an idea of how different these two values of n are for some typical gas and operating pressure range?
I've done so many of these calcs for projects in the past, and I dont recall any significant discrepancies with compressor vendor predictions, so I suspect these two values must be nearly the same?

 

[Meshry]

Gents,
Please excuse my ignorance, would you please give a simplified answer for my thread? or advise a good book/paper to read.

appreciated.

 

[rotw]

georgeoverghese,

Does this Ludtke book give us an idea of how different these two values of n are for some typical gas and operating pressure range?
Absolutely. Don't know about pressure ranges, guess accuracy is purpose driven.

I've done so many of these calcs for projects in the past, and I dont recall any significant discrepancies with compressor vendor predictions, so I suspect these two values must be nearly the same?

Not always, for example low temperature and/or high pressure could result in a huge difference between Cp0/Cv0 (ideal), Cp/Cv, kv and kt. They would also depart from each other, thus resulting in inaccuracies (from discrepancies to serious deviations) in compression process calculations.
In addition and that is my opinion, if your compressor conditions fall "slightly" in the liquid-vapor envelop / non homogeneous phase (that can happen), expect also deviations.
Example: -> I computed via GERG EOS an hypothetic cas composition 81%Methane, 13.5%CO2, 2.7%Ethane, 1.8%n-Hexane, 0.9%n-Heptane (approx. and in mol. weight%).
at Pressure 50 MPa, Temperature 420K: Kt=1.21, Kv=2.52, Cp/Cv=1.47
at Pressure 0.5 MPa, Temperature 420K: Kt=1.22, Kv=1.22, Cp/Cv=1.22

Zdas, agree with your statement, makes full sense.

 

[apetri]

Meshry,
the short answer is yes, specific heat ratio ( cp / cv ) has influence on gas compressor's operations,
with ideal gas law for adiabatic compression you obtain

PV=RT
P1*V1^cpcv=P2*V2^cpcv
T2=T1*(P2/P1)^(1-1/cpcv)

a basic example :

P1=1 Bar.a
P2=2 Bar.a
T1=300 K
cp/cv=1.3

T2 = 300*2^0.23
T2 = 352 K

take care that for real fluids and operations these correlations (based on ideal gas law, adiabatic compression) may not be suitable (see the comments on previous posts)

 

[georgeverghese]

@rotw,

Strange, your earlier post said that these kt and kv are polytropic exponents, and not isentropic exponent k. Polytropic exponent n is influenced by compression polytropic eff also, so how does this GERG program compute these values without polytropic eff input? I'll do a google search on this in any case - would be good to find thermodynamic differential expressions that show the difference between these.

@meshry,
To add to @petri's response, Cp/Cv is influenced by pressure, temp and gas properties. For natural gas mixes, Cp/Cv values go higher with increasing mol.wt. For a fixed P2 and P1,T1, compression head developed is lower for higher Cp/Cv. But for most gases, since Cp/Cv increases with mol. wt, you'll find the compression power is thus not affected by changes in Cp/Cv - this is definitely the case for most natural gas and refinery gas streams. But discharge temp increases with increasing Cp/Cv.

Note that there are various values for the Cp/Cv of a gas: ideal gas Cp/Cv, semi ideal gas Cp/Cv, and real gas Cp/Cv. Semi ideal gas Cp/Cv values approach real values only when P/Pc is very low. Use only real gas Cp/Cv values for compression calcs.

 

[rotw]

georgeverghese,

No, i did not refer to polytropic exponents in my earlier posts but to "isentropic exponents" (in plural...). And yes, if you would like to understand better about polytropic exponents in particular, K. Ludtke is an excellent reference too.

In short, the point raised here is that isentropic volume exponent kv, isentropic temperature exponent kt and heat ratio depart one another when real gas applications come into play. An example was given to illustrate the concept. I used GERG which is practical for deriving selected thermodynamic properties, but it could have been another equation of state. The polytropic exponents (volume and temperature) are derived based on kv, kt and polytropic efficiency, that is to say via simple mathematical formulas. Hope this clarifies.

 

[georgeverghese]

Must say there is obviously no need for these factors kt and kv if one were to be working with the real gas Cp/Cv value, as there wouldnt be any deviations. Though I dont have this book at hand, must say this Cp/Cv value Mr. Ludtke refers to here is possibly not the actual thermodynamically derived isentropic exponent published (by Pro/ II say in their compressor output sheet), but some other inexact value derived through some semi empirical route. One should only use the real gas thermo dynamically derived value for Cp/Cv = k value for the gas when doing compressor calcs, especially for high pressures or for gases with polar-nonpolar components interactions. Hence I suspect the Cp/Cv value produced by GERG is semi empically derived, and not thermodynamically derived. This also probably explains why the GPSA procedure for compressor calcs remains unchanged all these years as it requires thermodynamically derived isentropic exponent values.

Does look like there are many flavours of Cp/Cv being produced by process simulators. I must say that I have developed a reasonable level of confidence with the results produced through the GPSA route for discharge temp and compressor head / power, as I take care to use only thermodynamically correct values for Cp/Cv.

 

[apetri]

George,
maybe rotw is comparing cp/cv of ideal vs. real gas,
cp/cv values for real fluids can be calculated with a EOS, there are different versions of GERG (GERG 2004 and GERG 2008) the latter being more accurate, don't know which version has rotw, my version of Prode Properties includes the last GERG 2008 / AGA 2017 version and the calculated values for mixture C1 0.81 CO2 0.135 C2 0.027 C6 0.019 C7 0.009 at 500 Bar.a 420 K are cp = 2.70668 cv = 1.83998
cp/cv = 1.4710
Peng Robinson gives cp = 2.7031 cv = 1.88027 cp/cv = 1.437 close to the value calculated with GERG 2008
Peng Robinson Extended (Prode PRX) gives cp/cv = 1.4525 (a bit more accurate than PR) and so on...

 

[georgeverghese]

@petri,
Thanks for the comparisons within Aspen simulator (?) for the GERG / PR / PR Ex EOS options.
Would be good if we could get real gas Cp/Cv values off Pro/ II and Hysis simulators for comparison - for this gas with 13.5% CO2 at 500bar, Pro/ II recommends using the SRK Kabadi Danner option for the EOS for gases containing more than 5% v/v of H2S + CO2.

 

[rotw]

Must say there is obviously no need for these factors kt and kv if one were to be working with the real gas Cp/Cv value, as there wouldnt be any deviations.

I don't think I succeeded to pass the point, sorry my communication failure...

The GERG (I used the 2008 version, that is to answer to Apetri) is an equation of state which include an ideal part and a residual/departure part (at this occasion is based on the Helmholtz free energy equation), the later part accounts for the real gas effects. In this respect Cp/Cv for ideal gas is simply a subset or a "limit case". Depending on the combination of conditions, the parameters Cp/Cv, kv, kt which were to be quite equal in the ideal case, will respectively deviate and to a certain extent. Other equation of state will demonstrate the same behavior, the departure effect will be captured mathematically in a different manner and to a lower accuracy (with the GERG setting the benchmark). But this is accessory to the topic raised. As far as we are concerned with compressor calculations (and dynamic machines like Zdas pointed out), Cp/Cv is not relevant for performance prediction. For centrifugals, calculations are based on polytropic exponents, which themselves are derived from isentropic exponents with polytropic efficiency defined. If you are dealing with an injection machine compressing CO2 at high pressure, you better pay a great deal of attention to what K. Ludtke pointed out and which I quoted in my first post.

 

[apetri]

@georgeverghese
the values have been calculated with Prode Properties thermodynamic library, here there is a free (limited) version for Microsoft Excel,

http://www.prode.com/en/properties.htm

Prode Properties includes a rigorous method (based on Maxwell equations) to model polytropic stages (compressors, expanders, pumps etc.) for both single phase and two phase flows, these models allow to specify any polytropic efficiency (and setting polytropic efficiency to 1.0 you obtain the isentropic model), fluid properties are calculated with selected EOS (GERG 2008, Peng Robinson, Lee Kesler, MBWR etc..), errors should be limited mainly by accuracy provided by EOS...

you may find several threads at Eng-Tips discussing Prode Properties models for compressors / expanders ...

 

[georgeverghese]

At the moment, it is not clear to me what Mr. Ludtke's perception of the Cp/Cv value is. If it is some semi empirical value that does not replicate actual thermodynamic behaviour at high pressures, then I can understand the need for some correction factors to account for this departure. That appears to be case from @rotw's latest response (ideal component for Cp/Cv and some additional factors to account for residual departure).

One of the industry standard procedures that most process and mechanical engineers use is the widely referenced GPSA for getting reasonable values of compression power, polytropic head and Td, but this procedure requires real gas thermodynamically correct isentropic exponents in the compression operating range. Until the authors of the GPSA assigned to be custodians of this procedure update this routine, I will have to assume this procedure remains correct for all operating pressure ranges. As @rotw says, Mr. Ludtke's contention is that this approach is not current practice for many in this industry - and it isnt going to get clarified in this awkward public forum setting - too many questions to ask. Even till as late as 2010, I can confirm that the Simsci - Pro II process simulator uses only real gas Cp/Cv = k and either poly or isentropic eff (and no other fudge factors) in their compressor simulation unit operation.

 

[apetri]

I do not know the exact meaning of "As far as we are concerned with compressor calculations ... Cp/Cv is not relevant for performance prediction" reported by rotw,
maybe the author considers different aspects which can influence discharge conditions,
however for compressible fluids (adiabatic or polytropic process) given p1, p2 and t1 different values of cp/cv will result in different t2,
as said, one can speculate how cp/cv , mw or other parameters can affect the compression cycle and possible simplifications (which maybe can explain the initial statement)

anyway the above is the basis for the correlations given by GPSA (similar to ideal gas law but averaged values)

Hp = (Zavg * R * T1 / (Mw*(n-1)/n) ) * ((P2/P1) ^ (n-1)/n -1 )

and the Shultz method (ASME PTC10) which adopts calculated averaged values,

cp/cv is not required in methods which integrate (P1,T1->P2,T2) based on Maxwell equation

dH = T*dS + V*dP

which is the case for example of Prode Properties,
these methods are more accurate being based on analytical or numerical integration of Maxwell formula,
also they can can work with both vapor and liquid phases (you can model compressors, expanders with condensation, pumps, etc.),
however the results are about the same (i.e. for gas compression values calculated with GPSA are close to the values calculated with Prode Properties) and since cp/cv has influence on results from GPSA I would say it's the same for other methods (with the above mentioned exceptions).

 

[rotw]

Lets continue with the hypothetical gas stated above, P=50 MPa, T=420K.
Say I would like to compress that gas to 55 MPa, and the compressor has a polytropic efficiency - say 80%.
By assuming a small compression ratio here, the properties - each taken individually - would not change too much along the compression path. Just for simplicity, otherwise we could integrate or use Shutlz method, it wont change the outcome.

If I assume perfect gas (which is NOT correct as demonstrated above via EOS), but say for argue sake here.
With a k=Cp/Cv, the discharge temperature is T2 = T1 * (P2/P1) * [(k-1) / (k * Eta_P)] and would be approx. T2 = 436K.

If I assume real gas and use the CORRECT and RELEVANT methodology (again see K. Ludtke):
T2 = T1 * (P2/P1)^m with m= (ZR/Cp) * (1/Etap -1) + (kt-1)/kt
I could use average, Shultz method (or better), it would get me to approx T2 = 428.6 K

See the difference ?

 

[georgeverghese]

Error in my last posting: There are 2 procedures available in Simsci - Pro II for compressor simulations as explained in the Pro II reference manuals

(a)A default GPSA procedure which derives k from thermodynamically derived isentropic head
(b)An ASME procedure which derives k directly from the thermodynamically correct expression.

In this ASME procedure, there IS a fudge factor f involved in the calcs to get to polytropic head. This f value derivation requires additional information on gas thermodynamic properties in Pro II, and I presume this is what Mr. Lutdke's book talks about (the Schultz X and Y factors which then possibly lead on to kt and kv values?). But in Pro II, this fudge factor is calculated from actual gas properties, while I believe it is predicted in the Schultz method. I seem to have ignored the effect of f in my spreadsheet calcs. The manual does not explain how actual discharge temperature is derived / implemented through the ASME method.

This Pro - II flavour on the GPSA procedure would derive a value of k which would be much better than run of the mill semi empirically derived values. But it is still not the true isentropic exponent which is obtained in Pro II through the ASME method - beats me why this is the case - am still trying to get my head around this!

The manual recommends the ASME procedure as it covers a wider range of gas compositions and compression ratios.