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Vincent

Pitzer virial coefficients temperature dependency

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Hello,

 

I am currently creating a new database, based on the phrqpitz database. In the database, the virial coefficients (beta_0, beta_1, beta_2, C_Phi, theta, lambda and psi) temperature dependency is defined by a polynomial equation of the form:

 

X = X0 + c1*(T - T0) + c2*(1/T - 1/T0) + c3*ln(T/T0) + c4*(T2-T02) where T0 = 298.15K, T is the temperature in K and X0 is the value of the parameter at 25oC.

 

For the coefficients I am using I need more parameters since the coefficients are fitted by a general equation of the form:

 

X = X0 + c1*(T - T0) + c2*(1/T - 1/T0) + c3*ln(T/T0) + c4*(T2-T02) + c5*(T3-T03) + c6*(T4-T04) + C7*(1/T2-1/T02)

 

Is there any way I can modify the equation used in GWB to adapt it to my database, rather than recalculating all the parameters to find a temperature dependency fitted by the standard GWB equation? Although this is feasible, it is very time consuming and often I can't find a standard equation fitting as well my general equation.

 

Thank you very much in advance

 

Vincent

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Dear Vincent:

 

Thanks for your post. There is currently no provision for custom temperature dependency on Pitzer virial coefficients in GWB. I will add this to the list of feature requests- this has been requested at least one time by another user. However, implementing this would not be trivial, so I don't expect you'll see this feature anytime soon.

 

Regards,

 

Tom Meuzelaar

RockWare, Inc.

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Hello,

 

when reading the request to add such a complicated 7-term temperature dependence for Pitzer coefficients, I started to wonder whether this is justified in view of the availability of experimental data (measurements of mean acitivities etc.) that could constrain such parameters. In particular, some terms such as the high T powers (this is already a potential issue with T2 terms) might behave very unreasonably outside the calibrated T range where constrained by experiments. There could be inflection points and strong divergence appearing at temperatures well above the calibrated interval. Conversely, when terms with high temperature powers are avoided the extrapolation behavior is generally expected to be better. Finally, the more parameters are used in the fit procedure, the more they are highly correlated and are merely fit coefficients rather than robust values that have at least some physical meaning. These considerations should be taken into account when selecting an equation to fit Pitzer parameters to experimental data. Personally I would be very careful in using a function with so many fit coeficients, and rather settle for a more simple expression.

 

Technically, I cannot see yet why it would be so difficult to add a different expression for the temperature dependence in GWB. If this is programmed in a modular way with derivatives of the original T function propagating into activity coefficient (and osmotic coefficient) expressions, replacing the original T dependence and its derivatives by a new one should be no big deal actually. Admittedly reading the data in from database file and converting it to the right format might be more tricky (and could pose a compatibility problem with old database files, but perhaps one can just append the new coefficients after the existing ones and just read treat missing coefficients as zeroes).

 

Best regards,

 

Thomas

 

Thomas

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Thanks for both answers. I agree it may look a bit complicated to redesign the program, I was just wondering if there was a simple solution.

 

I also agree that 8 different terms can look a bit like over-complicating the situation. I realized I forgot to precise that not all of them are used. It is a general equation used by some author to fit the data. I think the highest number of parameters I have seen is 4. However, in some cases the T3 or the T4 or the 1/T2 were used.

 

Therefore, even if I did not necessarily need the complete equation, I needed a way to define them in GWB.

 

The whole idea is that I use compilations of parameters and their temperature dependency is based of this general equation. I could track down the original data, and do the fit with the GWB equation, but I preferred to save a lot of time and use these parameters.

 

In any case it would be useful to have custom defined virial coefficients, just in case, and especially because their temperature dependency is always based on empirical equations.

 

Best regards

 

Vincent

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"Admittedly reading the data in from database file and converting it to the right format might be more tricky (and could pose a compatibility problem with old database files, but perhaps one can just append the new coefficients after the existing ones and just read treat missing coefficients as zeroes)."

 

The GWB thermodynamic databases based on the Pitzer model (Phrqpitz) can be modified to add new Pitzer coefficients. I have been doing this for a while and it work pretty well.

 

"If this is programmed in a modular way with derivatives of the original T function propagating into activity coefficient (and osmotic coefficient) expressions, replacing the original T dependence and its derivatives by a new one should be no big deal actually."

 

Sorry but I am not sure I understand what you mean. The program is defined not to read various values of the coefficients at various temperatures (the way the solubility constants are defined) but to read the fit coefficients X0, c1, c2, c3 and c4 and recalculate the parameters from these and the equation. This is why I have difficulties defining the parameters if the temperature dependency does not follow the predefined fit equation.

 

Vincent

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