I am currently doing solubility modelling for supercritical fluid extraction processes with Peng Robinson EOS and Soave-Redlich-Kwong EOS. In my model, I've observed that all my binary interaction parameters changes with respect to pressure and temperature.The binary interaction parameters are key constants used to predict the solubility of solute in supercritical fluid solvent.
There are research papers out there showing single Kij and Lij values at isothermal conditions at increasing operating pressure. However, there are also papers, albeit a few, papers showing different values at different temperature and pressure.
So I was wondering if there is a right or wrong thing in this basis. Hope someone can help clarify my doubts.
Many thanks,
Chai
Yes you can have temperature dependent kij (linear or quadratic), see the enclosed example for a group contribution method with temperature dependency:Article Predicting the Phase Equilibria of CO2 + Hydrocarbon Systems...
You need to correct your eos parameters and deriviatives to take this into account.
I would not introduce a pressure dependence in the kij. This would require substantial modifications.
Dear Antonin Chapoy,
First of all thank you for the answer. As I'm unfamiliar with the entire concept, can you please elaborate more?
For example in my case, at isothermal conditions, I extracted my compounds at 15, 25 and 35 MPa to obtain yield Y1, Y2 and Y3.
At different pressures, i back-calculated the EOS and optimize using excel solver to obtain global optimum solutions K1, K2 and K3 at 15, 25 and 35 MPa to obtain AARD% = 0.
All values of Kij solution obtained at different pressure isothermally are different.
If you solve each equilibrium data point separately for kij, you would have different kij at different temperature and pressure.
you need to solve all those data point in a single run. To do so, I recommend to write a matlab code which enjoys an optimization algorithem for finding Kij.
Also you can use equation 4 in the article attached by professor Antoin Chaopy and by doing so you don't need to use optimization algorithms.
Dear Abbas Fallah,
I see. I am currently doing my global optimization using Excel Solver, however as you have mentioned, I have been doing it separately at different temperature and pressure. Previously I have done regression analysis from Excel to obtain a single value for Chrastil equations. I am wondering if you might have guides to carry out data solving in a single run using Excel.
I've looked through Eq. 4 and from the 12 groups defined, it lacks the COOH group which is my targeted substance compound which may render the data predicted inaccurate.
Again, thank you for your excellent advice.
I would definitively not recommend adjusting for single P&T points, what parameters are you going to use when you are working with ternary or multicomponent systems or at different pressure and temperature. You can adjust for different T and find a simple correlation kij =a+b*T or kij = a+bT+cT2.
Dear Chai Yee Ho,
Unfortunately, I have not used Excel for such purposes so far. If you write a matlab code for your system, I can give you an optimization algorithm to find Kij. Usually i use this algorithm for my phase equilibria studies.
Good luck.
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