The jungle of Specific Heat Capacities and how to get it right

[hirschaplin]

The importance of a correct K/gamma-value for you inlet gas when selecting a compressor is of the utmost importance as you can read here

http://www.jmcampbell.com/tip-of-th...tivity-of-k-values-on-compressor-performance/

Hence the question how to navigate this jungle and get it right.

First of all, I understand the Cp and Cv is expressed at different pressures, temperatures and even various units of measurement.

A simple googling of "K value Specific Heat Capacities" or similar yield several tables with suggestions for various gases.

Here is a link to one of the results

https://ceimusb.files.wordpress.com/2015/09/calor_especifico_de_gases.pdf

The table provides Cp and Cv values both kJ/kg K and Btu/lbmoF and at approx. 20 deg C and 1 atm:

The first confusion. Since the values are given at approx. 20 deg C and 1 atm, does this mean that if my actual gas composition is at a higher or lower pressure/temperature, the Cp and Cv values from this table will be incorrect for my particular case and discrepancies may occur?

Now the second confusion. Let us use Acetone from the table above as an example.

Cp/Cv in kJ/kg K yields: 1.47/1.32=1.11363636
Cp/Cv in Btu/lbmoF yields: 0.35/0.32=1.09375

Depending on which UoM I use, I will get different K values?!?! That can't be right?

My excel gas database does now consist of the following components:

Methane
Ethane
Propane
n-Butane
n-Pentane
n-Hexane
n-Heptane
n-Octane
n-Nonane
n-Decane
n-Undecane
n-Dodecane
n-Tridecane
n-Tetradecane
n-Pentadecane
n-Hexadecane
n-Heptadecane
n-Octadecane
n-Nonadecane
n-Eicosane
2-Methylpropane
2-Methylbutane
2,3-Dimethylbutane
2-Methylpentane
2,3-Dimethylpentane
2,3,3-Trimethylpentane
2,2,4-Trimethylpentane
Ethylene
Propylene
1-Butene
cis-2-Butene
trans-2-Butene
1-Pentene
1-Hexene
1-Heptene
1-Octene
1-Nonene
1-Decene
2-Methylpropene
2-Methyl-1-butene
2-Methyl-2-butene
1,2-Butadiene
1,3-Butadiene
2-Methyl-1,3-butadiene
Acetylene
Methylacetylene
Dimethylacetylene
3-Methyl-1-butyne
1-Pentyne
2-Pentyne
1-Hexyne
2-Hexyne
3-Hexyne
1-Heptyne
1-Octyne
Vinylacetylene
Cyclopentane
Methylcyclopentane
Ethylcyclopentane
Cyclohexane
Methylcyclohexane
1,1-Dimethylcyclohexane
Ethylcyclohexane
Cyclopentene
1-Methylcyclopentene
Cyclohexene
Benzene
Toluene
o-Xylene
m-Xylene
p-Xylene
Ethylbenzene
Propylbenzene
1,2,4-Trimethylbenzene
Isopropylbenzene
1,3,5-Trimethylbenzene
p-Isopropyltoluene
Naphthalene
Biphenyl
Styrene
m-Terphenyl
Methanol
Ethanol
1-Propanol
1-Butanol
2-Butanol
2-Propanol
2-Methyl-2-propanol
1-Pentanol
2-Methyl-1-butanol
3-Methyl-1-butanol
1-Hexanol
1-Heptanol
Cyclohexanol
Ethylene
1,2-Propylene
Phenol
o-Cresol
m-Cresol
p-Cresol
Dimethyl
Methyl
Methyl
Methyl
Methyl
Methyl
Methyl
Diethyl
Ethyl
Ethyl
Methyl
Diphenyl
Formaldehyde
Acetaldehyde
1-Propanal
1-Butanal
1-Pentanal
1-Hexanal
1-Heptanal
1-Octanal
1-Nonanal
1-Decanal
Acetone
Methyl
2-Pentanone
Methyl
2-Hexanone
Methyl
3-Methyl-2-pentanone
3-Pentanone
Ethyl
Diisopropyl
Cyclohexanone
Methyl
Formic
Acetic
Propionic
n-Butyric
Isobutyric
Benzoic
Acetic
Methyl
Methyl
Methyl
Methyl
Ethyl
Ethyl
Ethyl
Ethyl
n-Propyl
n-Propyl
n-Butyl
Methyl
Ethyl
Vinyl
Methylamine
Dimethylamine
Trimethylamine
Ethylamine
Diethylamine
Triethylamine
n-Propylamine
di-n-Propylamine
Isopropylamine
Diisopropylamine
Aniline
N-Methylaniline
N,N-Dimethylaniline
Ethylene
Furan
Thiophene
Pyridine
Formamide
N,N-Dimethylformamide
Acetamide
N-Methylacetamide
Acetonitrile
Propionitrile
n-Butyronitrile
Benzonitrile
Methyl
Ethyl
n-Propyl
n-Butyl
Isobutyl
sec-Butyl
Dimethyl
Methyl
Diethyl
Fluoromethane
Chloromethane
Trichloromethane
Tetrachloromethane
Bromomethane
Fluoroethane
Chloroethane
Bromoethane
1-Chloropropane
2-Chloropropane
1,1-Dichloropropane
1,2-Dichloropropane
Vinyl
Fluorobenzene
Chlorobenzene
Bromobenzene
Air
Hydrogen
Helium-4
Neon
Argon
Fluorine
Chlorine
Bromine
Oxygen
Nitrogen
Ammonia
Hydrazine
Nitrous
Nitric
Cyanogen
Carbon
Carbon
Carbon
Hydrogen
Hydrogen
Hydrogen
Hydrogen
Hydrogen
Sulfur
Sulfur
Water

This list originates from table 2-164 in this PDF

https://terpconnect.umd.edu/~nsw/chbe301/chap02.pdf

The third confusion is that it seems nearly impossible to find simple table values for Cp/Cv for all components in this list, especially at approx. 20 deg C and 1 atm.

Or maybe not because the same PDF has table "2-196 Heat Capacities of Inorganic and Organic Liquids" which indeed seems to provide at least the Cp value for all items in the list but you need to be a Chemical Professor to understand how to extract the proper value at approx. 20 deg C and 1 atm since they only provide it at min and max temp...:

Here again I think it is interesting to go back to the first confusion. As they provide a range, does it mean that the Cp value should be extracted by means of interpolation (?) at the actual gas operating temperature or shall I stick with approx. 20 deg C and 1 atm...?

Finally, as table 2-196 only provides the Cp value I understand that I can use the Cp value to get my Cv value by Cp-R=Cv but now I am confused again. Because by looking at this it seems like the R constant in this case is not 8.314... instead each entry in the list has it's own R.....(?):

If I can't obtain R then I guess I need to find Cv for each component in the list and get R by Cp-Cv=R...

Sorry but this is soooo confusing and tedious to solve. There must be a better way to find Cp and Cv for these components in a simple way that make sense.

 

[hirschaplin]

@Pierreick

I have a parameter to adjust the temperature, T is a variable in the equation I use.

I can't adjust the pressure with my current equation. When you say 1 bar is that 1 bar absolute pressure? How or why do you know it is at 1 bar?

I made this comparison of Methane between ChemCAD and my excel sheet:

The difference between ChemCAD and Excel now is very small, the biggest discrepancy is 0,29% as you can see.

If we consider that this is the gas composition on compressor suction side, I think this is reliable enough considering that 99% of all past projects has a compressor inlet temperature between 0 to 60 deg C and pressure between 0 and 3 barg.

As you can see above, ChemCAD provide Ideal Cp/Cv and just Cp/Cv which I assume is the "real Cp/Cv" that you refer to. However, when I notice the minor difference between them, it seems like it might not be worth the effort.

Cp and Cv is only interesting for me in order to determine the K value as correct as possible. Since deviations in the K value has a big effect of several compressor performance parameters:

What do you think, is my current method reliable enough to calculate the K-value which will feed my compressor performance calculation? Can you see a scenario where the K value of a suction gas mixture at temp. 0 to 60 deg C / 0 to 3 barg using this method will always be within a few percent of reality? Or to increase the stakes a bit, if you were the buyer of the compressor and you knew that the K value was calculated this way instead of using a trusted source like HYSYS, would you have confidence in that the result is good enough to be the basis of the compressor performance?

The reality is that I typically receive a gas specification from the customer that already includes most of this data. That means there is always a reference point where my calculated results can be validated against.

 

[pierreick]

Hi,
AS I said your calculations are made based on a few assumptions, Perfect gas law, for a single pressure and temperature (1 bar A and 20 C), is that acceptable? Cp and Cv will change with T, and P change.
Attached an example (methane at t= 20 C and 60C; P at 1 bar A and 4 bar A)
Good luck
Pierre

 

[hirschaplin]

@Pierreick you are wearing me down

I have understood that my calculations are based on the ideal gas law. Is 1 bar A and 20 C the definition of all ideal gases or why are you saying that this is the assumption of my calculations?

I am confused because of this T in the Cp equation:

I thought this T was the gas operating temperature and that it adjusts the Cp/Cv values to align with my actual operating temperature.

Can you describe why a compressor selection should be based on real gas instead of ideal gas? Why shall I consider real gas calculations?

 

[pierreick]

Hi,
You should acknowledge that Cp is a function of T and P. For ideal gas, cp is only a function of T. Is this valid for your study?
For real gas vs ideal gas, there is a compressibility factor Z, which could be obtained from EOS or graphically for the most common. It's up to you to select what is the most appropriate.

Resources to dig into them:

https://www.e-education.psu.edu/png520/m16_p6.html

https://cheguide.com/cubic_eos.html

Textbook: Themis Matsoukas fundamentals of chemical engineering thermodynamics


Good luck
Pierre

 

[hirschaplin]

Good morning,

This is becoming to abstract for my level of understanding.

Mainly I need K-value, Molecular weight and Z compressibility factor as input variables to my other calculations.

As I already have the Z compressibility factor in my volume/mass flow calculations, I am unsure of if/why I should implement here again, to what purpose or gain?

I also have some information stating that compressibility factor may be assumed at 1.0 for pressures below 3,4 barg. Which is the case for my suction side in 99% of all cases.

As of now, I am able to get values in my excel for K and MW that are matching with ChemCAD, HYSYS and customer gas specification sheets. That was basically what I was trying to achieve from the beginning. The things that you are talking about now is indeed very interesting, because if it enhances the correctness or overall result ofc I want to implement it. But otherwise or right now I don't have a context for why I should go further into what you are referencing.

I am willing to reimburse you to pick your brain in a private chat with various stupid questions. If you or anyone else with an extended understanding of these issues are interested, please share your contact details.

 

[hirschaplin]

@pierreick I couldn't resist to start look into

https://cheguide.com/cubic_eos.html

Very good link.

A question, can I use this method to find Z for a mix gas?

If yes, how can I determine the critical temperature, critical pressure and accentric factor of the mix gas? Is it in a similar way as for how I would determine the molecular weight of my mix gas, meaning:

I take the value for each component and property * % of composition and then I sum it up and divide it by 100?

Example for accentric factor (O2 50%, N2 30% and Argon 20%):

O2 0,02
N2 0,037
Ar 0

0,02 * 50 = 1
0,037 * 30 = 1,11
0 * 20 = 0

Sum = 1+1,11+0 = 2,11

Accentric factor of mix gas = 2,11 / 100 = 0,0211

Can I apply this method to determine critical temperature, critical pressure and accentric factor of the mix gas?

 

[shvet]

@pierreick
Looks like we are witnessing an origin of a new Prausnitz's Properties of Gases and Liquids where a professional explains the very basics to a newcomer. ))) Keep it up, and eventually a new good tutorial will be issued!

 

[hirschaplin]

Where do I find pseudo components and what is that?

 

[pierreick]

Hi Shvet,
For me thermo classes were 45 years ago!
Hirshaplin,
Consider the document attached to illustrate my previous replies.

Good luck
Pierre

 

[hirschaplin]

Yeah rocket science.

You don't have a paper to determine the critical temperature, critical pressure and acentric factor for a gas mixture?

 

[georgeverghese]

Pls note that the semi ideal Cp/Cv approximation to k gives some acceptably reasonable values for compressor power only for many gas streams, but not for discharge temp. Process simulators use the real k value (isentropic exponent) to estimate discharge temp.

 

[pierreick]

hi,
Pc =sum (Pci*xi)
Tc= sum (Tci*xi)
w=sum (wi*xi)
sum(xi)=1
with xi: molar fraction.

http://yrsp.elliott-turbo.com/public/comp_perf/index.jsp

http://www.jmcampbell.com/tip-of-the-month/2015/07/how-to-estimate-compressor-efficiency/

Let you close this thread.
Good luck
Pierre

 

[shvet]

@hirschaplin

for info

You should acknowledge that Cp is a function of T and P. For ideal gas, cp is only a function of T.

source: Energy Institute "Guidelines for the Avoidance of Vibration Induced Fatigue Failure Process Pipework" 2008