Application of Lee-Kesler EoS Mixing Rules

[Sirius P.Eng.]

I'm currently applying the Lee-Kesler EoS to calculate enthalpy departure but I have run into problems applying the mixing rules mostly because different approaches are used in literature.

All the other formulas (Zci, vci and w and Pc) are straightforward except the critical molar volume (Vc) and critical temperature (Tc).

I'm having challenges simplifying this formula for a single has natural gas composition. How do I simplify the equations for a natural gas stream with no liquid phase. I will be glad if anyone with experience with applying the Lee-Kesler EoS mixing rules can shed some light on this.

I have attached screenshots of the mixing rules from theAll the other formulas are straightforward.

 

[Sirius P.Eng.]

The Original Lee-Kesler Mixing Rules.

 

[pmover]

no simplification of the equations, just follow the math rules.

xi - mole fraction of the ith component
xj - mole fraction of the jth component
Vcj - critical molar volume of the jth component
Vci - critical molar volume of the ith component
Tci - critical temperature of the ith component
Tcj - critical temperature of the jth component

so, the gas composition is known, so are xi and xj.
- Vc and Tc for each component are known
- if you write code, best done using loops for n-components, where n is the number of components in gas composition.
- if using excel, can write formula in rows (down) and columns (across).

see the attached image file for an example using 4 components of a gas composition.

hope this helps and good luck.

 

[Sirius P.Eng.]

Hello @pmover,

I can't thank you enough for your clarification.

Just so we can put this matter to rest please find some time to go through the attached excel file.

It is an attempt to calculate the molar volume Vc for a hypothetical three-component mixture of methane, ethane and propane using the LK EoS mixing rule.

I have taken the critical properties from ASPEN HYSYS.

Once it is okayed, I will write a MatLab code for the calculations.

Please let me know if I pulled it off as advised. Thank you.

 

[pmover]

using your values, i obtained a different value; see below for what i obtained.

https://files.engineering.com/getfi...Application_of_Lee-Kesler_Mixing_Rules-1.xlsx

 

[apetri]

Sirius,
in addition to pmover notes and comments,
Lee-Kesler is a old and well documented method,
you can find application examples in many books (my copy of Thermophysical Properties of Fluids includes the FORTRAN codes as in other books...),
note that Kay's rule works well for rather similar molecules,
a better approach would be the van der Waals one-fluid method which takes explicit account of the interactions between molecules,
another approach was the method proposed by Plocker, see the Lee-Kesler-Plocker model for details...

 

[Sirius P.Eng.]

@pmover
I can't thank you enough for all your help.

I really appreciate it. Realized I was executing the math wrongly in excel.
I have since corrected it and the result is the same as yours.

Thank you so once again.

@apetri
Thank you very much for the additions. Indeed, I had initially calculated the pseudo critical properties with Kay's mixing rule and found the results to be the same as in HYSYS critical properties view for the mixture. I was wondering if HYSYS uses Kay's mixing rule for hydrocarbon mixtures even though i had specified Peng-Robinson as the Thermodynamic EoS Package.

Also, I am trying to calculate the enthalpy change for a heating process and found from literature that the Lee-Kesler Enthalpy Departure calculation method is the most accurate within the applicability limits. That's why I am using that method.

Once my Matlab code runs, I will be sure to compare the results with other EoS.

 

[apetri]

Sirius,
are you a student ? You can find a good discussion about the different methods for estimating the critical properties of mixtures in The Properties of Gases and Liquids (Poling, Prausnitz, Connel) which I recommend, as general rule there could be large differences comparing pseudocritical properties with (true) critical properties,
I am not familiar with Aspen, I utilize Prode Properties, with Prode you can select different models for the different states (vapor,liquid,solid...) and properties (fugacity, enthalpy..), for example Peng-Robinson for fugacity and Lee-Kesler for Enthalpy or Entropy, from your description I suppose Aspen does the same and you should obtain different values selecting different models, yes the Lee-Kesler model is reasonably accurate with Enthalpies, Entropies of hydrocarbon mixtures, but it is less accurate for phase equilibria, do not forget that Lee Kesler model has been proposed in 1975 and nowadays we have many models giving accurate results for both properties and phase equilibria.

 

[Sirius P.Eng.]

@apetri

I work in the gas processing industry actually. But I am building a mathematical model of a natural gas heater with Matlab.

Thank you for the great insights provided. I can tell you have a solid background in Thermodynamics. I will check out "The Properties of Gases and Liquids (Poling, Prausnitz, Connel)" that recommend. As you mentioned also, there may be newer models and much more accurate models for enthalpy calculation - Could please advise if you know any that are specifically more accurate for predicting enthalpy departure for natural gases than the Lee-Kesler EoS.

 

[apetri]

probably, for hydrocarbons properties, the first accurate model was the AGA8-DC92 equation of state of Starling and Savidge (1992), limited to gas phase,
at present (for hydrocarbons) the internationally accepted standards are the GERG 2008 (Europe) and the equivalent AGA 2017 (USA),
there are several other models, you can find the description in The Properties of Gases and Liquids