Predict VLE and LLE from TC
lines.Definition of the TC
lineIt is shown [refs. 1 and 2] that VLE data converge to a line, if the following Y and Z are plotted versus X defined as follows: X=(p _{s1}+p_{s2})/(P_{c1}+p_{s2})
Y=(G _{1}^{inf}p_{s1}-p_{s2})/(P_{c1}-p_{s2})Z=(p _{s1}-G_{2}^{inf}p_{s2})/(P_{c1}-p_{s2})where p _{s1} and
p_{s2} are vapor pressures of components 1 and 2,
respectively; P_{c1} is the critical pressure of component 1.
Furthermore, G_{1}^{inf} and G_{2}^{inf}
are the infinite dilution activity coefficients (IDAC) of components 1 and
2, respectively.Examples of the TC
lineIn Fig. 1, Y and Z are plotted versus X for the benzene (1) + ethanol (2) binary. Figure 1 shows that all of the experimental data can be satisfactorily represented by the lines passing through the origin. The following two equations are useful for representing the VLE data: Y, Z = aX^{b}Y, Z = aX
+bX^{2} +cln(1+X)where a, b and
c are constants. Figure 1 includes both of the constant-temperature
data and constant-pressure data. It is important to use appropriate
infinite dilution activity coefficient equations satisfactorily representing
P, x data. Fig. 1 Y and Z versus X for the benzene (1) + ethanol (2) binary, (solid line) XY TC line (, , x) Y from experimental data, (-----) XZ TC line and (, , +) Z from experimental data. Examples of T, x, y prediction from the TC line In Fig. 2, T/T _{b2} and y_{1} are plotted
versus x_{1} for the benzene (1) + ethanol (2) binary system at
101.3 kPa, where T and T_{b2} denote the system temperature and
the boiling point of component 2, respectively, and where x_{1}
and y_{1} denote the mole fractions of component 1 in the liquid
and vapor phases, respectively. As shown in Fig. 2, the experimental
y_{1} data, denoted by the (+) symbols, are fluctuating.
Unfortunately, there is no method for identifying accurate data, as noted
at BeAware.htm. However,
Fig. 2 clearly shows that the green solid line predicted using the TC
lines in Fig. 1 at 101.3 kPa is accurate, as it represents the (+)
data.Fig. 2 T/T _{b2} and y_{1
}versus x_{1} for the benzene (1) + ethanol (2) binary at
101.3 kPa, (red solid line) T/T_{b2}predicted from TC lines, (x) T/T _{b2 }from experiments, (green solid line) y_{1}
predicted from TC lines and (+) y_{1} from
experiments.References1) Satoru Kato(Tokyo Metropolitan Univ.), Juergen P. Schmelzer (Univ. of Applied Sci., Germany), Peter Gostomski (Univ. of Canterbury, NZ), Kenneth N. Marsh (Univ. of Canterbury, NZ), J. Chem. Eng. Data, 56 (2011) 4927-4934. 2) Satoru Kato (Tokyo Metropolitan Univ., TC Lines), Peter Gostomski (Univ. of Canterbury, NZ), Akiyoshi Oda (Nippon Refine, Japan), Joerg Freitag (Nippon Refine, Japan), Seiya Hirohama (Invensys, Japan), David Bluck (Invensys, U.S.A.), Fluid Phase Equilibria, 357 (2013) 36-42. |