## 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
[91] thought that when the \(\alpha\) function of the PR equation was replaced with an exponential function, more accurate prediction results of the saturated vapor pressure and liquid density of a pure substance could be obtained compared with the original PR equation under low pressure conditions (1\(\sim\)101.325 kPa). Six types of exponential functions were compared by [PERSON] et al. [91], and it was found that the Heyen-type \(\alpha\) function (shown in Equation (12)) had the best predictive ability. By fitting for the experimental data of vapor pressure and saturated liquid density of 71 pure substances, the parameters _MA1_ and _MA2_ in a Heyen-type \(\alpha\) function were expressed as a function of the eccentric factor \(\omega\), as shown in Equations (13) and (14) (hereinafter referred to as MAPR2):  
\[\alpha=\exp(MA_{1}(1\ -\ T_{r}^{MA_{2}})) \tag{12}\]  
\[MA_{2}=\frac{-\ 0.3327\omega^{2}-\ 1.8678\omega\ -\ 0.2626}{1.3642\omega\ +\ 0.3788}+1.3642\omega\ +\ 1.3788 \tag{13}\]  
\[MA_{1}=\frac{1.3642\omega+0.3788}{MA_{2}} \tag{14}\]  
2 **Specific volume translation modification method**  
Usually, for the PR equation, the accuracy of the predicted saturated vapor pressure is high, while that of the predicted liquid density is low. In response to this phenomenon, the introduction of specific volume translation can directly improve the accuracy of the predicted liquid density, as shown in Equations (15) and (16) [88; 96]:  
\[p=\frac{RT}{(V+\Delta V)\ -\ b}\ -\ \frac{a}{(V+\Delta V)\ (V+\Delta V+b)+b(V+ \Delta V\ -\ b)} \tag{15}\]  
\[V=V_{\rm PR}-\Delta V \tag{16}\]  
where \(V_{\rm PR}\) is the liquid specific volume calculated by the PR equation, m\({}^{3}\)/kg, and \(\Delta V\) is the specific volume translation, m\({}^{3}\)/kg. Another specific volume translation modification model proposed by [PERSON] et al. [88] is shown in Equations (17)-(19):  
\[\Delta V=\Delta V_{c}\cdot\Delta VT \tag{17}\]  
\[\Delta V_{c}=(0.3074\ -\ Z_{c})RT_{c}\ /\ p_{c} \tag{18}\]\[VT=VT_{1}+(1\ -\ V{T}_{1})\exp[VT_{2}(1\ -\ T_{r})] \tag{19}\]  
where \(\Delta V_{c}\) is the specific volume translation at the critical point, m\({}^{3}\)/kg; \(Z_{c}\) is the critical compression factor; \(VT\) is a temperature-dependent parameter; and \(VT_{1}\) and \(VT_{2}\) are the required parameters for \(VT\). \(VT_{1}\) and \(VT_{2}\) were obtained by correlating 198 polar and non-polar working fluids and the expressions are shown in Equations (20) and (21). According to [PERSON]'s study [88], when the saturated liquid density was predicted by Equations (17)-(21) (hereinafter referred to as VTPR1), the average relative deviation (ARD) between the predicted and reference values was 1.83%, which showed a strong versatility. \[m=0.3919+1.4996\omega\ -\ 0.2721\omega^{2}\ +\ 0.1063\omega^{3} \tag{11}\]0  
\[m=0.3919+1.4996\omega\ -\ 0.2721\omega^{2}\ +\ 0.1063\omega^{3} \tag{11}\]1  
For the parameter \(VT\) in Equation (17), [PERSON] et al. [87] proposed another model (hereinafter referred to as VTPR2), as shown in Equation (22):  
\[m=0.3919+1.4996\omega\ -\ 0.2721\omega^{2}\ +\ 0.1063\omega^{3} \tag{11}\]2  
where \(VT_{3}\), \(VT_{4}\), and \(VT_{5}\) are the required parameters for \(VT\) in the VTPR2 model, whose expressions are shown in Equations (23)-(25), respectively. The ARD between the predicted and reference values of the densities of 25 halogenated hydrocarbons when using VTPR2 model is within 2.0% [87]. \[m=0.3919+1.4996\omega\ -\ 0.2721\omega^{2}\ +\ 0.1063\omega^{3} \tag{11}\]3  
\[m=0.3919+1.4996\omega\ -\ 0.2721\omega^{2}\ +\ 0.1063\omega^{3} \tag{11}\]4  
\[m=0.3919+1.4996\omega\ -\ 0.2721\omega^{2}\ +\ 0.1063\omega^{3} \tag{11}\]5  
The specific volume translation modification model proposed by [PERSON] et al.