REFPROP Equimolar Mixture Accuracy

[Evan577101]

Hello, I am a researcher developing a calorimeter to measure the properties of supercritical zeotropic CO2 and refrigerant mixtures. In our work, we utilize REFPROP as a real-time check and to analyze our experimental results against its Equations of State (EOS) and mixing rules. Currently, we are testing a CO2/R134a mixture at molar ratios of 0.9/0.1 and 0.5/0.5. For the 0.9/0.1 molar ratio, our experimental data aligns very well with REFPROP’s calculated enthalpy. However, when testing the equimolar (0.5/0.5) mixture, we have observed significant deviations, sometimes exceeding 20-30% near the critical point, between our measured enthalpy across the calorimeter and the values calculated by REFPROP.

Could you please clarify the limitations of REFPROP’s calculations for mixtures at varying molar ratios? Furthermore, is this magnitude of deviation expected for an equimolar ratio, particularly near the critical point?

Thank you for your time, and I appreciate any insights you can provide.

[nist-aharvey]

The first thing is to be sure you are computing the right things. Enthalpy as a standalone number is meaningless because it is always relative to a reference state. So the meaningful quantity would be the change in enthalpy between two points (which for an isobaric change is proportional to the isobaric heat capacity). Related, mixture enthalpy calculations can give results that look strange because of reference states -- whether it applies the reference state convention to a mixture or separately to each of the components in a mixture. To keep from getting inconsistent results if you are doing things like computing an enthalpy of mixing, you should choose the latter: go under Options, Reference State, and select "Apply reference state to Each pure component".

If you are doing all those things right, then the question becomes how accurate you can expect REFPROP to be, and there is no universal answer there. It depends in part on whether REFPROP has mixture-specific mixing parameters fitted, as opposed to just REFPROP'S default mixing. In this case, there are mixture parameters, but it looks like they were fitted to VLE data and maybe gas-phase densities, not to any data related to heat capacity. In cases like that, as a rough estimate I might trust the mixture heat capacity to within 10% for the liquid and 5% for the supercritical vapor, at least at most conditions. Near the critical point you start getting divergence of the heat capacity and potential errors get larger. [You can see if you are in that region if your heat capacities are getting larger quickly -- and one might see larger errors if REFPROP was predicting the critical point with some error so that the divergence in REFPROP was not happening in quite the right place] Errors could be expected to be larger for a 50-50 mixture than for 90-10 just because the pure-component endpoints are known with good accuracy, so it would not be surprising to see something like a 5% error for a 50-50 mixture but only 2% for 90-10. For any single-phase mixture property (density, heat capacity, sound speed), the uncertainties are smaller as you approach the better-known pure-component endpoints.

IF your difference across the calorimeter involves a two-phase state, then correct predictions become more difficult and errors in enthalpy changes can be introduced by errors in the modeling of the VLE. The VLE becomes more difficult to model near the critical point. Also, if you are modeling across phase changes you absolutely need to use the "Apply reference state to Each pure component" reference state convention to get meaningful enthalpy differences.

No enthalpy data were available when REFPROP's binary parameters were fitted, but there has been one study published more recently. It has heat capacities for liquid mixtures near 50-50 composition. So these data could be a good test for REFPROP and/or your calorimetry apparatus:
Arami-Niya, A.; Xiao, X.; Al Ghafri, S. Z.S.; Jiao, F.; Khamphasith, M.; Pouya, E. S.; Sadaghiani, M. S.; Yang, X.; Tsuji, T.; Tanaka, Y.; Seiki, Y.; May, E. F., Measurement and modelling of the thermodynamic properties of carbon dioxide mixtures with HFO-1234yf, HFC-125, HFC-134a, and HFC-32: vapour-liquid equilibrium, density, and heat capacity, Int. J. Refrig., 2020, 118, 514-528