## 2 The ZMS EOS
### The Binary CH\({}_{4}\)-N\({}_{2}\) Mixture
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**References**} & \multicolumn{2}{c}{**Number of Data Points**} & \multicolumn{2}{c}{**_T-P-x Range for xCH\({}_{4}\)-(1-x) N\({}_{2}\)**} & \multirow{2}{*}{**AAD\%**} \\ \cline{2-2} \cline{5-6}  & **Styles** & **Total (Used)** & & & & \\ \hline Liu and Miller [45] & _PVTx_ & 7 (0) & 91–115 & 3–12 & 0.5 & 0.57 \\ Rodosevich and Miller [46] & _PVTx_ & 8 (0) & 91–115 & 43–454 & 0.8–0.95 & 3.83 \\ [PERSON] et al. [47] & _PVTx_ & 7 (0) & 91–115 & 1–11 & 0.5–0.86 & 0.11 \\ [PERSON] et al. [48] & _PVTx_ & 21 (0) & 95–140 & 1–21 & 0.5–0.95 & 0.10 \\ [PERSON] et al. [49] & _PVTx_ & 182 (50) & 110–120 & 15–1380 & 0.3–0.68 & 0.12 \\ Straty and Diller [65] & _PVTx_ & 578 (0) & 82–320 & 6–356 & 0.32–0.7 & 0.24 \\ [PERSON] and McCarty [56] & _PVTx_ & 85 (85) & 140–320 & 10–164 & 0.3–0.71 & 0.09 \\ [PERSON] et al. [64] & _PVTx_ & 190 (90) & 323–573 & 99–999 & 0.1–0.9 & 0.28 \\ Seitz and Blencoe [63] & _PVTx_ & 43 (0) & 673.15 & 199–999 & 0.1–0.9 & 5.36 \\ [PERSON] et al. [50] & _PVTx_ & 83 (83) & 308–333 & 9–120 & 0.5–0.78 & 0.12 \\ [PERSON] et al. [52] & _PVTx_ & 242 (56) & 230–400 & 9–192 & 0.8–0.9 & 0.23 \\ [PERSON] et al. [57] & _PVTx_ & 17 (0) & 129–180 & 15–50 & 0.4–0.9 & 2.10 \\ [PERSON] et al. [60] & _PVTx_ & 27 (27) & 17–270 & 1–16 & 0.9 & 0.06 \\ [PERSON] et al. [54] & _PVTx_ & 142 (42) & 304–470 & 100–1379 & 0.25–0.75 & 0.07 \\ [PERSON] and [PERSON] [51] & VLE & 23 (0) & 128–179 & 34 & 0.05–0.98 & 1.48 \\ [PERSON] and [PERSON] [53] & VLE & 20 (0) & 92–124 & 0.2–6 & 0.85–1.0 & 5.02 \\ [PERSON] et al. [47] & VLE & 60 (60) & 95–120 & 0.2–25 & 0.05–1 & 5.05 \\ [PERSON] et al. [62] & VLE & 11 (0) & 112 & 2–13 & 0.2–0.97 & 3.30 \\ [PERSON] et al. [59] & VLE & 83 (83) & 112–180 & 2–49 & 0.1–0.99 & 1.31 \\ [PERSON] et al. [61] & VLE & 8 (8) & 91 & 1–3 & 0.1–0.8 & 5.60 \\ [PERSON] et al. [58] & VLE & 10 (10) & 123 & 4–26 & 0.1–0.95 & 2.96 \\ [PERSON] and [PERSON] [66] & VLE & 48 (43) & 95–120 & 2–20 & 0.1–0.9 & 3.14 \\ [PERSON] et al. [57] & VLE & 16 (6) & 130–180 & 0.5–5 & 0.4–0.96 & 1.14 \\ [PERSON] et al. [55] & VLE & 77 (60) & 110–123 & 4–13 & 0.7–1.0 & 2.49 \\ \hline \hline \end{tabular} Note: Deviations of the PVTx data are the density deviations, and the deviations of VLE data are the equilibrium composition deviations. AAD is the abbreviation of average absolute deviation.  
\end{table} 
Table 3: Calculated _PVTx_ and VLE deviations for the CH\({}_{4}\)-N\({}_{2}\) mixture. Figure 1: Density deviations for the CH\({}_{4}\)-N\({}_{2}\) system at different pressures. Experimental data(triangles [64], stars [52], rounds [54], squares [49]): \(P\) is the pressure, \(\rho_{\rm cal}\) is the calculated density, and \(\rho_{\rm exp}\) is the experimental density. Figure 2: Experimental and calculated densities for the 0.8 mole CH\({}_{4}\) + 0.2 mole N\({}_{2}\) mixture at different temperatures. The experimental density data (rounds) [68], the PR (green dash lines) and SRK (blue dash lines) EOSs [67], this work (red lines): \(P\) is the pressure, \(\rho\) is the density, and \(T\) is temperature. Figure 3: Vapor-liquid phase equilibria of the CH\({}_{4}\)-N\({}_{2}\) system at different temperatures, (**a**) \(P\)-\(x_{\rm N_{2}}/y_{\rm N_{2}}\) figure at 170 K; (**b**) \(P\)-\(x_{\rm CH_{4}}/y_{\rm CH_{4}}\) figure for 170 K; (**c**) \(P\)-\(x_{\rm N_{2}}/y_{\rm N_{2}}\) figure for 115 K; (**d**) \(P\)-\(x_{\rm CH_{4}}/y_{\rm CH_{4}}\) figure for 115 K; (**e**) \(P\)-\(x_{\rm N_{2}}/y_{\rm N_{2}}\) figure for 110 K; (**f**) \(P\)-\(x_{\rm CH_{4}}/y_{\rm CH_{4}}\) figure for 110 K. Experimental data (rounds [55], triangles [57], squares [59]), this work (solid lines): \(x_{\rm N_{2}}\) and \(y_{\rm N_{2}}\) are the mole fractions of N\({}_{2}\) in the liquid and vapor phases, respectively \(x_{\rm CH_{4}}\) and \(y_{\rm CH_{4}}\) are the mole fractions of CH\({}_{4}\) in the liquid and vapor phases, respectively.