## 2 Materials and Methods
### Minimum Miscibility Pressure (MMP)  
CO\({}_{2}\) is widely used in EOR through injection into an oil reservoir to increase oil recovery. CO\({}_{2}\) is used as a solvent, reducing oil viscosity and expanding the volume of oil in the reservoir. These phenomena can be expected to be more prominent if the oil and gas are more miscible. If the injected gas and fluid are not completely miscible, some of the gas does not dissolve into the oil and moves faster than the fluid, forming a separate phase. This causes an early breakthrough at the production well and lowers the productivity of the oil reservoir. To avoid this circumstance, determining whether the gas and fluid are under miscible conditions at the reservoir pressure is of significant interest. The lowest pressure to achieve miscibility by a multiple contact process under the given pressure and temperature is called the minimum miscibility pressure (MMP). Below the MMP, immiscible displacement occurs and consequently the oil recovery is reduced. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Component** & **Composition** & **Critical Pressure (kPa)** & **Critical Temperature (kPa)** & **Molecular Weight (g/gmol)** & **Accentric Factor** & **Parachor** \\ \hline N\({}_{2}\) & 0.0207 & 3394.4 & 126.2 & 28.0 & 0.04 & 41 \\ CO\({}_{2}\) & 0.0074 & 7376.5 & 304.2 & 44.0 & 0.23 & 78 \\ H\({}_{2}\)S & 0.0012 & 8936.9 & 373.2 & 34.1 & 0.1 & 80 \\ Methane, C\({}_{1}\) & 0.0749 & 4600.2 & 190.6 & 16.0 & 0.01 & 77 \\ Ethane, C\({}_{2}\) & 0.0422 & 4883.9 & 305.4 & 30.1 & 0.1 & 108 \\ Propane, C\({}_{3}\) & 0.0785 & 4245.5 & 369.8 & 44.1 & 0.15 & 150 \\ Butane, C\({}_{4}\) & 0.0655 & 3722.7 & 416.5 & 58.1 & 0.19 & 186 \\ Pentane, C\({}_{5}\) & 0.0459 & 3379.4 & 464.9 & 72.1 & 0.24 & 228 \\ C\({}_{6-9}\) & 0.2156 & 3019.6 & 556.3 & 102.5 & 0.33 & 297 \\ C\({}_{10-17}\) & 0.2202 & 2017.5 & 692.2 & 184.0 & 0.58 & 508 \\ C\({}_{18-27}\) & 0.1027 & 1327.0 & 808.4 & 306.2 & 0.89 & 771 \\ C\({}_{28+}\) & 0.1252 & 1155.1 & 915.5 & 566 & 1.1 & 1112 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Oil composition and properties for equation of state (EOS) calculations. \begin{table}
\begin{tabular}{c c c c c} \hline
**Dissolved Gas** & **Saturation Pressure (MPa)** & **GOR (sm3/m3)** & **Gas Solubility (sm3/m3)** & **FVF (m3/m3)** & **SF (m3/m3)** \\ \hline
0.0058 & 2.9 & 19 & 0 & 1.087 & 1.074 \\
0.158 & 4.5 & 42 & 23 & 1.143 & 1.13 \\
0.412 & 8 & 113 & 94 & 1.308 & 1.292 \\
0.439 & 8.4 & 125 & 106 & 1.336 & 1.32 \\
0.521 & 9.9 & 158 & 139 & 1.409 & 1.392 \\
0.595 & 11.4 & 221 & 202 & 1.546 & 1.527 \\
0.641 & 12.6 & 263 & 244 & 1.634 & 1.614 \\
0.826 & 19.7 & 875 & 856 & 2.694 & 2.668 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: PVT properties of the reservoir fluid and CO\({}_{2}\) mixtures at 140 \({}^{\circ}\)F. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **W3** & **Fluid Model** & **Difference (\%)** \\ \hline Oil density at saturation pressure (kg/m\({}^{3}\)) & 806.4 & 805.7 & 0.09 \\ Saturation pressure (kPa) & 4920 & 4916 & 0.08 \\ Viscosity at saturation pressure (mPa-s) & 1.76 & 1.76 & 0.0 \\ Formation volume factor (m\({}^{3}\)/m\({}^{3}\)) & 1.12 & 1.108 & 1.07 \\ API (\({}^{\circ}\)) & 31 & 34.48 & \(-\)11.23 \\ MMP with CO\({}_{2}\) (kPa) & 14,196 & 13,900 & 2.09 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of the data for Weyburn fluid and the fluid model. Methods for measuring MMP include the slim-tube test, the rising-bubble method, and the vanishing interfacial tension (VIT) test [29; 30; 31; 32; 33]. The slim-tube test has been widely used to measure MMP and is the most used method [34]. Since these methods are time-consuming, expensive, and sometimes less accurate, it is better to use the simulation method to determine the MMP. A slim-tube simulation model is conducted to measure the MMP. The slim tube is saturated with oil, and gas is subsequently injected to displace the oil in the slim tube. The amount of gas and oil is determined, and the recovery is defined.