Prediction and Correlations of Residual Entropy of Superheated Vapor for Pure Compounds

Abstract

Prediction of accurate values of residual entropy (SR) is necessary step for the
calculation of the entropy. In this paper, different equations of state were tested for the
available 2791 experimental data points of 20 pure superheated vapor compounds (14
pure nonpolar compounds + 6 pure polar compounds). The Average Absolute
Deviation (AAD) for SR of 2791 experimental data points of the all 20 pure
compounds (nonpolar and polar) when using equations of Lee-Kesler, Peng-
Robinson, Virial truncated to second and to third terms, and Soave-Redlich-Kwong
were 4.0591, 4.5849, 4.9686, 5.0350, and 4.3084 J/mol.K respectively. It was found
from these results that the Lee-Kesler equation was the best (more accurate) one
compared with the others, but this equation is sometimes not very preferable. It was
noted that SRK equation was the closest one in its accuracy to that of the Lee-Kesler
equation in calculating the residual entropy SR of superheated vapor, but it was
developed primarily for calculating vapor-liquid equilibrium and to overcome this
problem, efforts were directed toward the possibility of modifying SRK equation to
increase its accuracy in predicting the residual entropy as much as possible. The
modification was made by redefining the parameter α in SRK equation to be a
function of reduced pressure, acentric factor, and polarity factor for polar compounds
in addition to be originally function of reduced temperature and n parameter –which is
also function of acentric factor– by using statistical methods. This correlation is as
follows:

α =[1+n(γ)]²  , γ=-0.920338Pr^-0.34091 +0.064049Tr⁴ ω +0.370002ω-Pr^0.996932 Tr^-4x
This new modified correlation decreases the deviations in the results obtained by
using SRK equation in calculating SR when comparing with the experimental data.
The AAD for 2791 experimental data points of 20 pure compounds is 4.3084 J/mol.K
while it becomes 2.4621 J/mol.K after modification. Thus SRK equation after this
modification gives more accurate results for residual entropy of superheated vapor of
pure 20 compounds than the rest of the equations mentioned above.