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# Calibrating Peng-Robinson's EOS

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## Calibrating Peng-Robinson's EOS

(OP)
Hello,

What would be the best method to calibrate / match the Peng-Robinson's EOS to experimental data for Z-Factor? Can I tweak the coefficients / constants to minimise the sum of residuals squared? Do I need to apply some kind of pressure or temperature dependency to the binary interaction parameters? I am doing this manually in Excel & Python.

### RE: Calibrating Peng-Robinson's EOS

I usually let Aspen+ handle all that. A lot of folks use HYSYS. Do you have access to a simulator? What is your system of components? Why the need to custom fit PR? PR was originally developed for natural gas systems.

Good Luck,
Latexman

### RE: Calibrating Peng-Robinson's EOS

I get the impression you are building this z factor predictor from the ground up on your own with Excel/Python using the PR EOS. PR is meant only for hydrocarbon components with weak binary interactions only.

### RE: Calibrating Peng-Robinson's EOS

(OP)
Thanks for the feedback. I have extracted the binary interaction parameters from HYSYS and am using those in the model. I am working with hydrocarbon gasses so Peng-Robinson should be suitable. It is my understanding that the binary parameters are determined empirically and change with temperature, however HYSYS has selected the parameters to be suitable over a wide range of conditions. I was hoping to improve the model via matching to experimental data. Thanks again.

### RE: Calibrating Peng-Robinson's EOS

Aspen+ has it's "Methods Assistant" to help select the method. Idk if HYSYS has similar. Are you using real components or psuedocomponents? Will vacuum conditions be used? Is there appreciable Hydrogen in the mix?

The Achilles Heel of these methods (not so accurate) seems to be the liquid molar volume. Aspen+ uses the Rackett Model for liquid molar volume for real components when PR is selected.

In Aspen+, you can also use their Data Regression System (DRS) to determine the binary parameters from experimental phase equilibrium data (usually binary VLE data). Again, idk if HYSYS has similar.

I hope this helps. What are your T, P, and MW ranges of interest?

Good Luck,
Latexman

### RE: Calibrating Peng-Robinson's EOS

Pro II also has an add on program REGRESS to get interaction parameters and other constants to tune model results to suit actual VLE data. I have not used this before.

### RE: Calibrating Peng-Robinson's EOS

in standard Peng Robinson EOS, BIPs (Binary Interaction Parameters) are included in van der Waals mixing rules as fixed values calculated by data regression of Vapor-Liquid experimental data values (see Dechema),
if you wish to fit VLE data (fugacity calculated by EOS) any data regeression procedure can do the work,
for Python I have Prode Properties, see

https://www.prode.com/en/ppp.htm

Prode includes a data regression procedure (as the other tools mentioned) capable to fit BIPs to experimental values provided by user,
in Python you can access the procedure from Editor or directly from code,
I mean you can access the methods in Prode from your Python code and create your own procedure if that is your scope...

### RE: Calibrating Peng-Robinson's EOS

Is this for single component data (like a new species not in the database of say HYSYS or similar) or is for a mix of unknowns such as an oil sample?

--- Best regards, Morten Andersen

### RE: Calibrating Peng-Robinson's EOS

How much error do you get at the moment with the HYSYS abstracted BIPs' with the more complicated PR EOS ?

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