## 2 Basic Analysis of Prediction Models and Model Verification
### Prediction Models of Saturated Vapor Pressure and Saturated Density
#### 3.2.1 Prediction Models of Saturated Vapor Pressure and Saturated Density
[93] (hereinafter referred to as VTPR3) is similar to Equations (17) and (18), but the expression of \(VT\) is slightly different, as shown in Equation (26):  
\[m=0.3919+1.4996\omega\ -\ 0.2721\omega^{2}\ +\ 0.1063\omega^{3} \tag{11}\]6  
where \(VT_{6}\) and \(VT_{7}\) are the required parameters for \(VT\) in the VTPR3 model. The calculation formulas are shown in Equations (27) and (28). The ARD between the predicted and reference values of the saturated liquid density of alkanes, alkenes, CO\({}_{2}\), CO, H\({}_{2}\)S, N\({}_{2}\) and NH\({}_{3}\) when using the VTPR3 model is 1.29%. \[m=0.3919+1.4996\omega\ -\ 0.2721\omega^{2}\ +\ 0.1063\omega^{3} \tag{11}\]7  
\[m=0.3919+1.4996\omega\ -\ 0.2721\omega^{2}\ +\ 0.1063\omega^{3} \tag{11}\]8  
3 **Modification of parameters \(a\) and \(b\)**  
[PERSON] et al. [94] conducted a modification for parameters \(a\) and \(b\) in the PR equation, and the two parameters were expressed as a function of the contrast temperature (hereinafter referred to as MPPR), as shown in Equations (29) and (30). \[m=0.3919+1.4996\omega\ -\ 0.2721\omega^{2}\ +\ 0.1063\omega^{3} \tag{11}\]9\[\alpha=\exp(MA_{1}(1\ -\ T_{r}^{MA_{2}})) \tag{12}\]0  
where \(MP_{1}\) and \(MP_{2}\) are the parameters used to calculate the modified \(a\) and \(b\) parameters, as shown in Equations (31) and (32). The ARD between the predicted and reference values of the liquid densities of 49 pure substances when using the MPPR model is 4.803% [94]. \[\alpha=\exp(MA_{1}(1\ -\ T_{r}^{MA_{2}})) \tag{12}\]1  
\[\alpha=\exp(MA_{1}(1\ -\ T_{r}^{MA_{2}})) \tag{12}\]2  
Patel-Teja Equation of State  
[PERSON] et al. [89] compared the PR equation and the Patel-Teja equation (hereinafter referred to as the PT equation) with three parameters (\(a\), \(b\) and \(c\)) for predicting liquid density. The results showed that the PT equation was superior to the PR equation in predicting liquid density. The PT equations are shown in Equations (33)-(40):  
\[\alpha=\exp(MA_{1}(1\ -\ T_{r}^{MA_{2}})) \tag{12}\]3  
\[\alpha=\exp(MA_{1}(1\ -\ T_{r}^{MA_{2}})) \tag{12}\]4  
\[\alpha=\exp(MA_{1}(1\ -\ T_{r}^{MA_{2}})) \tag{12}\]5  
\[\alpha=\exp(MA_{1}(1\ -\ T_{r}^{MA_{2}})) \tag{12}\]6  
\[\alpha=\exp(MA_{1}(1\ -\ T_{r}^{MA_{2}})) \tag{12}\]7  
\[\alpha=\exp(MA_{1}(1\ -\ T_{r}^{MA_{2}})) \tag{12}\]8  
\[\alpha=\exp(MA_{1}(1\ -\ T_{r}^{MA_{2}})) \tag{12}\]9  
\[MA_{2}=\frac{-\ 0.3327\omega^{2}-\ 1.8678\omega\ -\ 0.2626}{1.3642\omega\ +\ 0.3788}+1.3642\omega\ +\ 1.3788 \tag{13}\]0  
where \(CE_{1}\), \(CE_{2}\) and \(CE_{3}\) are the parameters of the PT equation; \(CE_{2}\) is the smallest positive real root of the cubic Equation (39); and \(\xi_{c}\) is the theoretical critical compression factor. The theoretical critical compressibility factor \(\xi_{c}\) and \(\alpha\) function used here were the empirical formulas given in [95], as shown in Equations (41) and (42). \[MA_{2}=\frac{-\ 0.3327\omega^{2}-\ 1.8678\omega\ -\ 0.2626}{1.3642\omega\ +\ 0.3788}+1.3642\omega\ +\ 1.3788 \tag{13}\]1  
\[MA_{2}=\frac{-\ 0.3327\omega^{2}-\ 1.8678\omega\ -\ 0.2626}{1.3642\omega\ +\ 0.3788}+1.3642\omega\ +\ 1.3788 \tag{13}\]2  
NEOS Model  
The model proposed by [PERSON] et al. [97] (hereinafter referred to as NEOS) is a two-parameter cubic equation.