Steam as a representative fluid in API 581- 2016 EDITION

[alkhiat]

I faced a problem during the application of API 581-2016 edition and I hope you could help me in this issue.

I am trying to apply RBI for a steam vessel , when I chose the representative fluid as steam , no release rate was calculated , this is because of the huge value of Cp that was calaculated for steam refer to note 3 in table 4.2 in API 581 -2016 , when using this huge value to calculate k k=Cp/(Cp-R) ,where R=8.314 the result equal to 1.

If you use k=1 in gas release rate equation (equation 3.6 or 3.7- API 581-2016) there will be no result so there will be no consequence . , temperature used is 773 K

 

[cavbilly]

Maybe you are not using consistent units of measure between Cp and R. Make sure you have these in the same units, and try again.

 

[Chumpes]

hi
only details :
1/ k = Cp/(Cp-R) cannot be equal to 1 because R is different from zero
for very high Cp, k is getting closer to 1 but k never reaches 1 unless Cp becomes infinite.

2/ in API 581, equations (3.6) and (3.7) have a term (k-1) at the denominator of fractions, thus k = 1 gives a division by zero, which is not possible.

Why not considering actual values of variables instead of roughly rounded figures ? would it change your results ?

 

[alkhiat]

Greetings
If you use note 3 equation in API 581 and took steam ideal gas constant values from table 4.2 you will obtain a value of Cp equal to 4.2185E+14 Where R = 8.314 , so the value k will be 1.000000000000020 which is not applicable to be used in equation 3.6 or 3.7
Also the actual value of k for steam from some references is around 1.32 so it seems to be there are some mistakes in code or in my understanding to code .

 

[cavbilly]

I do not have a copy of API 581 or API 581 RPI(risk protocol inspection?)
I am not going to spend $900 to have it.

In performing these calculations, one must have familiarity with the units of measure involved.

R= 8.31447, refers to the value of the ideal gas constant with units of kPa-L/mol-°K, where mol is gram moles. If one were to use Kilogram moles, then the
value of R = 8314.47 kPa-L/Kgmol-°K. Note that R= 8.31447 J/mol-°K, such that R= 8314.47 J/Kgmol-°K.

Link
see this link for R in all systems of units, including energy units system, and P, V units systems

Cp of steam from steam tables: T specified = 773 °K, P= 100 bar gauge (equivalent to 10,000 kPa.) Cp= 2590.22 J/Kg-K units, Cv= 1848.18 J/Kg-K
values of Cp and Cv converted to your unit system of kPa-L/mol-°K are as follows: Cp= 2.59022 J/g-K, Cv= 1.84818 J/g-K.


Link
see this link for Spirax-Sarco Steam Tables where steam is superheated to your specified temperature and whatever bar gauge pressure you choose, and you can change
the pressure units to kPa if you wish.

Linksee this link for clarification of heat capacity ratio γ=Cp/Cv (used by engineers)represents that for ideal gas, but for real gas, we use κ=Cp/Cv for the actual gas properties at P,T.

from the same steam tables, isentropic coefficient k=1.28183, whereas the ratio of heat capacties from the steam tables is 1.401497

Since you want Cp/(Cp-R), you must phrase R in mass units, not mol units. R=8314.47 J/Kgmol-°K, and water is 18.0152 Kg/Kgmol, thus the value of R you need is 461.525 J/Kg-°K (steam).
Thus Cp/(Cp-R)becomes 2590.22/(2590.22-461.525)=1.21681. compare to the isentropic coefficient k of 1.28183.
In this manner, your k-1 in API 581 becomes 0.28183, or 0.21681, depending on how you arrive at a value of k. I hope you find this helpful.

 

[Chumpes]

RBI = risk based inspection
the use of international units helps a lot (i never use kgmol because kg is a mass unit and kgmol should probably stand for kmol (1 kilo-moles = 1000 moles), and i wonder what a gram mole is... a mole ??)

 

[cavbilly]

@Chumpes
Yes, if the SI units are employed, then everything is based upon second, meter, kilogram (not gram). Moles are Avogadro's number of atom or molecule, represents that mass in grams, i.e. carbon is exactly 12 g/mole,if all the atoms were ¹²C.

Yes, gram mole is a mole. Yes 1000 moles is the same as a 1 Kg-mole mass. Once again, the units have to be consistent in order to obtain anything other than garbage results.

I am just now learning about the protocol of RBI. Please excuse my lack of acumen on this particular topic. I do not even have a copy of the standard.