# Compositional Modeling of Dimethyl Ether-CO2 Mixed Solvent for Enhanced Oil Recovery
## 2 Materials and Methods  
### Fluid Modeling  
Fluid modeling was performed using the properties of Weyburn W3 fluid. The components of the Weyburn W3 fluid and the parameters of the equation of state (EOS) for fluid modeling are listed in Table 1[27]. The acentric factor was proposed by [PERSON] [28] as a comprehensive expression of the boiling point, molecular weight and polarity characteristics of pure ingredients. Parachor is a material-specific value that relates surface tension to chemical structure. Regression matching is promoted using the experimental data of the Weyburn W3 fluid. Results from the fluid model adequately matched the experimental data and confirmed the reliability for composition simulation. The data values compared with the modeling fluid are shown in Table 2. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Component**} & \multirow{2}{*}{**Composition**} & \multirow{2}{*}{**Critical Pressure**} & \multicolumn{2}{c}{**Critical**} & \multirow{2}{*}{**Parachor**} & \multirow{2}{*}{**Acentric Factor**} & \multirow{2}{*}{**Molecular Weight**} \\  & & **(kPa)** & & & & **(K)** & \\ \hline N\({}_{2}\) & 0.0207 & 3394.4 & 126.2 & 41 & 0.04 & 28.01 \\ CO\({}_{2}\) & 0.0074 & 7376.5 & 304.2 & 78 & 0.225 & 44.01 \\ H\({}_{2}\)S & 0.0012 & 8936.9 & 373.2 & 80 & 0.1 & 34.08 \\ C\({}_{1}\) & 0.0749 & 4600.2 & 190.6 & 77 & 0.008 & 16.04 \\ C\({}_{2}\) & 0.0422 & 4883.9 & 305.4 & 108 & 0.098 & 30.07 \\ C\({}_{3}\) & 0.0785 & 4245.5 & 369.8 & 150 & 0.152 & 44.09 \\ DME & 0.0001 & 5442.2 & 400.3 & 132 & 0.2 & 46.07 \\ C\({}_{4}\) & 0.0655 & 3722.7 & 416.5 & 185 & 0.1845 & 58.12 \\ C\({}_{5}\) & 0.0459 & 3379.4 & 464.9 & 228 & 0.239 & 72.15 \\ C\({}_{6-9}\) & 0.2155 & 3019.6 & 556.4 & 296 & 0.331 & 102.5 \\ C\({}_{10-17}\) & 0.2202 & 2017.5 & 692.3 & 505 & 0.584 & 184 \\ C\({}_{18-27}\) & 0.1027 & 1327.0 & 808.4 & 768 & 0.893 & 306.2 \\ C\({}_{28+}\) & 0.1252 & 1155.1 & 915.5 & 1001 & 1.1 & 585.61 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Oil components and properties of each component for equation of state (EOS) calculation. The Winprop software, developed by the Computer Modeling Group (CMG), was used for fluid modeling. The Peng-Robinson EOS (PR EOS) [29; 30] was used to calculate the fugacity of a component in the oil and gas phases. The concept of fugacity is usually used for multi-component equilibrium involving solid, liquid and gas phases. It is used to determine the amount of ingredients in each stage of a multi-component mixture at various temperatures and pressures [31]. Therefore, the Peng-Robinson equation was used to predict the phase behavior of the mixed fluid and to tune the experimental values. The PR EOS is as follows:  
\[p=\frac{RT}{v-b}-\frac{a}{v(v+b)+b(v-b)} \tag{1}\]  
or, in terms of the \(Z\) factor:  
\[Z^{3}-(1-B)Z^{2}+\Big{(}A-3B^{2}-2B\Big{)}Z-\Big{(}AB-B^{2}-B^{3}\Big{)}=0 \tag{2}\]  
where \(a\) is the attraction parameter, \(b\) is the repulsion parameter, \(p\) is the pressure (Pa), \(T\) is the temperature (K), \(v\) is the volume (\(\frac{m^{3}}{mol}\)), and \(R\) is the universal gas constant (\(\frac{m^{3}\cdot Pa}{K\cdot mol}\)). The EOS constants for pure components are given by:  
\[A=a\frac{p}{(RT)^{2}} \tag{3}\]  
\[B=b\frac{p}{RT} \tag{4}\]  
\[a=\Omega_{a}^{0}\frac{R^{2}T_{c}^{2}}{p_{c}}\alpha \tag{5}\]  
\[b=\Omega_{b}^{0}\frac{RT_{c}}{p_{c}} \tag{6}\]  
\[\alpha=\Big{[}1+m\Big{(}1-\sqrt{T_{r}}\Big{)}\Big{]}^{2} \tag{7}\]  
where \(\alpha\) is a parameter for temperature, \(p_{c}\) is the critical pressure, \(T_{c}\) is the critical temperature, and \(T_{r}\) is the reduced temperature.