دانلود رایگان مقاله برخی از خواص معادله GHC حالت

Abstract

The composition functionality of the mixture energy parameter, aM, used in the Gibbs-Helmholtz Constrained (GHC) equation of state is studied. An analysis is presented that shows that aM for liquid mixtures is approximately quadratic in composition. All non-quadratic behavior is due solely to ln(TcM) in the GHC up-scaling equation. If a mean value approximation of this term is used, then aML is quadratic, but non-symmetric, in composition. For vapors, non-quadratic behavior is coupled to the molar volume of the mixture through the term βM = (VM + bM)/VM. It is shown that the difference between βM and some average βM is very small and aMV is quadratic in composition. Sensitivity analyses of aM and resulting molar density to these approximations are also presented. Finally, the non-symmetric composition functionality of aM is discussed along with GHC predictions of mixture second virial coefficients. Numerical examples are presented to support all claims.

5. Conclusions and discussion

The composition functionality of liquid and vapor mixture energy parameters given by the GHC equation of state were rigorously analyzed. It was shown that both expressions for the mixture energy parameter are quadratic, but non-symmetric, in composition under very reasonable approximations. For liquid mixtures, when ln(TcM) was replaced byC i=1 xiln(Tci), the resulting difference was small (<4%) and the corresponding sensitivity of aL M and L M over the entire binary composition range were <2% and <1% respectively for all mixtures studied. The maximum differences in aL M and L M were 3.15% and 1.79% for mixtures of CO2-water at 100 ◦C and 400 bar. In contrast, for vapor mixtures, the approximation of ˇM = (VM + bM)/VM by an average value, ˇ¯ M, provided rigorous, but weak, quadratic composition functionality of aV M. Moreover, this vapor approximation, ˇ¯ M, resulted in AAD% differences inaV M and V M of <10−3 and <10−4 respectively for all mixtures studied. Finally, although second virial coefficients predicted by the GHC equation exhibited weak quadratic composition functionality, this did not have an impact of vapor density predictions.