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