## 2 The ZMS EOS
### The Ternary CO\({}_{2}\)-CH\({}_{4}\)-N\({}_{2}\) Mixture  
Combining binary interaction parameters of the CH\({}_{4}\)-CO\({}_{2}\), CO\({}_{2}\)-N\({}_{2}\) and CH\({}_{4}\)-N\({}_{2}\) systems, the EOS can also predict the thermodynamic properties of the CO\({}_{2}\)-CH\({}_{4}\)-N\({}_{2}\) mixture. Here, the experimental _PVTx_ and vapor-liquid equilibrium data are used to verify the accuracy of this EOS for the ternary mixture.  
The calculated _PVTx_ deviations for the ternary CO\({}_{2}\)-CH\({}_{4}\)-N\({}_{2}\) mixture from each experimental data set [1; 64; 69; 70; 71] are given in Table 4, where the temperature and pressure of the _PVTx_ data are up to 573.15 K and 1000 bar, and the composition almost covers the full range. The average absolute deviation of all _PVTx_ data from this EOS is 0.40% for the CO\({}_{2}\)-CH\({}_{4}\)-N\({}_{2}\) fluid mixture. Figure 4 shows the comparison between experimental data [71] and calculated densities for the CO\({}_{2}\)-CH\({}_{4}\)-N\({}_{2}\) mixture at different temperatures. It can be seen from Figure 4 that calculated densities from this EOS are in good agreement with experiment data, indicating that this EOS has a good predictive ability for the CO\({}_{2}\)-CH\({}_{4}\)-N\({}_{2}\) mixture.  
The vapor-liquid phase equilibrium properties of the ternary CO\({}_{2}\)-CH\({}_{4}\)-N\({}_{2}\) system are shown in Figure 5, where the curves are calculated from this EOS, and the experimental data are from the literature of [72; 73; 74]. As can be seen from Figure 5, all the experimental data points in the non-critical region agree well with this EOS, but in the near-critical region (Figure 5c), the calculated values deviate largely from experimental data [72; 73; 74].  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**References**} & \multirow{2}{*}{**\(\mathbf{N}\)**} & \multicolumn{5}{c}{**_T-P-x Range for xCO\({}_{2}\)-yCH\({}_{4}\)-(1-x-y) N\({}_{2}\)**} & \multirow{2}{*}{**AAD\%**} \\ \cline{3-6}  & & \(\mathbf{T}\) **(K)** & \(\mathbf{P}\) **(bar)** & \(\mathbf{x}\) & \(\mathbf{y}\) \\ \hline [PERSON] et al. [59] & 242 & 303–333 & 6–126 & 0–0.9998 & 0–0.999 & 0.45 \\ [PERSON] et al. [60] & 42 & 474.15 & 1000 & 0.0–1.0 & 0.0–1.0 & 0.28 \\ [PERSON] et al. [55] & 271 & 323–573 & 199–999 & 0.1–0.8 & 0.1–0.8 & 0.28 \\ [PERSON] et al. [61] & 200 & 293.15–353.25 & 5–180 & 0.098–0.9949 & 0.02–0.6525 & 0.52 \\ [PERSON] et al. [1] & 84 & 305.15 & 5–600 & 0.499–0.899 & 0.0505–0.331 & 0.82 \\ \hline \hline \end{tabular} Note: Deviations of the _PVTx_ data are the density deviations. \(N\) is the Number of data points, AAD is the abbreviation of average absolute deviation.  
\end{table}
Table 4: Calculated _PVTx_ deviations for the ternary CO\({}_{2}\)-CH\({}_{4}\)-N\({}_{2}\) mixture.  
Figure 5: Vapor-liquid phase equilibria for the CO\({}_{2}\)-CH\({}_{4}\)-N\({}_{2}\) system at different temperatures and pressures, (**a**) \(T=220\) K, \(P=60.8\) bar; (**b**) \(T=230\) K, \(P=62.05\) bar; (**c**) \(T=230\) K, \(P=86.19\) bar; (**d**) \(T=270\) K, \(P=45.6\) bar. Experimental data (squares [73], rounds [72], triangles [74]), this work (solid lines).