## 3 The Applications of the ZMS EOS
### Calculating Excess Enthalpies
Therefore, to simplify the model, \(\mu_{i}^{V(0)}\) is assumed to be zero. Equation (16) can be simplified as  
\[ \begin{array}{rl}lnm_{i}=&lny_{i}P+ln\varphi_{i}-\frac{\mu_{i}^{L(0)}}{RT}- \sum\limits_{c}2\lambda_{i-c}m_{c}\\ &&-\sum\limits_{a}2\lambda_{i-a}m_{a}-\sum\limits_{c}\zeta_{i-c-a}m_{c}m_{a} \end{array}  \tag{17}\]  
where \(\frac{\mu_{i}^{L(0)}}{RT}\), \(\lambda\) and \(\zeta\) are the function of temperature and pressure, and the parameters can be determined by the solubility model of pure gases (CO\({}_{2}\), CH\({}_{4}\), N\({}_{2}\)). Since the 1980s, many solubility models for CO\({}_{2}\), CH\({}_{4}\) and N\({}_{2}\) gases in pure water and brine have been developed [79; 90; 91], most of which do not exceed 473 K and 1000 bar. Among them, the solubility models of CH\({}_{4}\), CO\({}_{2}\) and N\({}_{2}\) established by [PERSON] and co-workers [83; 86; 91] are applicable to a wider range of temperature, pressure, and salinity with higher accuracy. They have been chosen as the solubility models of pure CH\({}_{4}\), CO\({}_{2}\) and N\({}_{2}\) gases in this work. Table 5 lists the applicable temperature, pressure, and salinity ranges of these solubility models for pure gases. To verify the accuracy of the predictions, the experimental data for the solubility of the CO\({}_{2}\)-CH\({}_{4}\)-N\({}_{2}\) gas mixtures are compared with the calculated results. Figure 9 compares the experimental data on the solubility of the CH\({}_{4}\)-CO\({}_{2}\) mixture in pure water [92; 93] for the temperature range of 324.5-375.5 K and the pressure range of 100-750 bar, and it can be seen that the agreement is very good. The solubility experimental data of the CO\({}_{2}\)-N\({}_{2}\) gas mixture in pure water [94] and the calculated results are compared in Figure 10, where the temperature range is 308.15-318.15 K and the pressure range is 80-160 bar. As can be seen from Figure 10 the predictive results are in good agreement with the experimental data. The average absolute deviations between the calculated N\({}_{2}\) and CO\({}_{2}\) solubility of this model and the experimental data are 6.04% and 1.52%, respectively. Figure 11 compares the solubility \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Pure Gas** & \(T\) & \(P\) & **Salinity (\(m_{NaCl}\))** & **References** \\ \hline CH\({}_{4}\) & 273–523 K & 1–2000 bar & 0–6 mol/kg & [PERSON] and [PERSON] [83] \\ CO\({}_{2}\) & 273.15–723.15 K & 1–1500 bar & 0–4.5 mol/kg & [PERSON] et al. [91] \\ N\({}_{2}\) & 273–590 K & 1–600 bar & 0–6 mol/kg & [PERSON] and [PERSON] [86] \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Ranges of pure gas solubility models. experimental data of the CO\({}_{2}\)-N\({}_{2}\) gas mixture in saline water. The average absolute deviations between the calculated N\({}_{2}\) and CO\({}_{2}\) solubility and the experimental data are 2.04% and 2.49%, respectively. Figure 9: Comparisons between experimental and calculated solubilities for the CH\({}_{4}\)-CO\({}_{2}\) mixture in water. (**a**) \(m_{CH_{4}}\)-\(y_{CH_{4}}\) figure at 344.15 K; (**b**) \(m_{CO_{2}}\) - \(y_{CH_{4}}\) figure at 344.15 K; (**c**) \(m_{CH_{4}}\) -\(y_{CH_{4}}\) figure at 373.5 K; (**d**) \(m_{CO_{2}}\) - \(y_{CH_{4}}\) figure at 375.5 K; (**e**) \(m_{CH_{4}}\) -\(y_{CH_{4}}\) figure at 324.5 K. Experimental data (rounds [92], squares [93]), this work (solid curves): \(m_{CO_{2}}\) is the solubility of CO\({}_{2}\), \(m_{CH_{4}}\) is the solubility of CH\({}_{4}\). Figure 11: Comparisons between experimental and calculated solubilities for the CO\({}_{2}\)-N\({}_{2}\) mixture in saline water. (**a**) \(m_{N_{2}}\) - \(y_{N_{2}}\) figure; (**b**) \(m_{\text{CO}_{2}}\) - \(y_{N_{2}}\) figure. Experimental data (black squares [94]), this work (solid curves). Figure 10: Comparisons between experimental and calculated solubilities for the CO\({}_{2}\)-N\({}_{2}\) mixture in water.