The comparison between the novel M-H EOS and other EOSs.
The result of molar volume can be calculated when pressure is given. In
order to avoid imaginary
root,
the
corresponding values of molar volume are calculated by dichotomy using
Matlab. In this work, we mainly focus on the
volume
calculated in liquid-phase state because the precision of volume
calculated in gas-phase state is high enough by using the previous M-H
EOS9,12.
Besides
Hou’s modified M-H EOS, we select two general EOS as comparisons. Among
the large number of general EOSs, the Soave-Redlich-Kwong EOS (S-R-K
EOS) and the Peng-Robinson EOS (P-R EOS) are most representative
and
specially used for the comparison41-43. The S-R-K EOS
is expressed as follows:
\(P=\frac{\mathrm{\text{RT}}}{\mathrm{V}\mathrm{-}\mathrm{\delta}}\mathrm{-}\frac{\mathrm{a}\left(\mathrm{T}\right)}{\mathrm{V}\left(\mathrm{V}\mathrm{+}\mathrm{\delta}\right)}\text{\ \ }\)(22)
where
\(\mathrm{\text{\ \ }}\mathrm{a}\mathrm{(}\mathrm{T}\mathrm{)=}\mathrm{0.42748}\frac{\mathrm{R}^{\mathrm{2}}\mathrm{T}_{\mathrm{c}}^{\mathrm{2}}}{\mathrm{P}_{\mathrm{c}}}\left[\mathrm{1+(0.48+1.534}\mathrm{\omega}\mathrm{-}{\mathrm{0.176}\mathrm{\omega}}^{\mathrm{2}}\mathrm{)(1-}\mathrm{T}_{\mathrm{r}}^{\mathrm{0.5}})\right]^{\mathrm{2}}\ \mathrm{\ }\)(23)
\(\mathrm{\delta}\mathrm{=0.08664}\frac{\mathrm{R}\mathrm{T}_{\mathrm{c}}}{\mathrm{P}_{\mathrm{c}}}\)(24)
The P-R EOS is expressed as follows:
\(\mathrm{P}\mathrm{=}\frac{\mathrm{\text{RT}}}{\mathrm{V}\mathrm{-}\mathrm{\delta}}\mathrm{-}\frac{\mathrm{a}\left(\mathrm{T}\right)}{\mathrm{V}\left(\mathrm{V}\mathrm{+}\mathrm{\delta}\right)+\delta(V-\delta)}\text{\ \ }\)(25)
where
\(\ \mathrm{a}\mathrm{(}\mathrm{T}\mathrm{)}\mathrm{=}\ \mathrm{0.45724}\frac{\mathrm{R}^{\mathrm{2}}\mathrm{T}_{\mathrm{c}}^{\mathrm{2}}}{\mathrm{P}_{\mathrm{c}}}\left[\mathrm{1+(0.37464+1.54226}\mathrm{\omega}\mathrm{-}{\mathrm{0.26992}\mathrm{\omega}}^{\mathrm{2}}\mathrm{)(1-}\mathrm{T}_{\mathrm{r}}^{\mathrm{0.5}})\right]^{\mathrm{2}}\ \)(26)
\(\mathrm{\delta}\mathrm{=0.07780}\frac{\mathrm{R}\mathrm{T}_{\mathrm{c}}}{\mathrm{P}_{\mathrm{c}}}\)(27)
The
deviation of volume between
the
calculated data (VCal ) and
the
experiment data in literatures (VExp ) is defined
as:
\(\mathrm{Dev.=}\)\(\left|\frac{\mathrm{V}_{\mathrm{\text{Exp}}}\mathrm{-}\mathrm{V}_{\mathrm{\text{cal}}}}{\mathrm{V}_{\mathrm{\text{Exp}}}}\right|\mathrm{\times}\mathrm{100\%}\mathrm{\text{\ \ }}\)(29)
Table 3 The
maximum
and average deviation in liquid-phase state