## 3 Results
### Effects of CH\({}_{4}\) Injection on EOR Efficiency  
A two-dimensional (2D) homogeneous model based on the work of [PERSON] et al. (2019) is designed to focus on investigating the miscibility and sweep efficiency without gravity override during WAG simulations. This reservoir model is discretized into \(33\times 33\times 1\) grid blocks of volume \(3\times 3\times 3\) m\({}^{3}\) each. A quarter of a 10-acre five-spot well pattern (i.e., CO\({}_{2}\) injector and oil producer) is set up for the reservoir model. Thus, the EOR and CCS performances are mainly governed by the displacement and sweep efficiencies. The total simulation period is 13 years (2007-2020), beginning with 3 years of waterflooding followed by 10 years of WAG, as shown schematically in Figure 2. The WAG consists of five cycles, in each of which water and gas are injected sequentially. Four WAG model simulation cases are analyzed, namely: 100% CO\({}_{2}\) + 0% CH\({}_{4}\) (Case 1), 90% CO\({}_{2}\) + 10% CH\({}_{4}\) (Case 2), 80% CO\({}_{2}\) + 20% CH\({}_{4}\) (Case 3), and 70% CO\({}_{2}\) + 30% CH\({}_{4}\) (Case 4). The gas injection rate for each case is a constant 2265 m\({}^{3}\)/day under surface conditions to determine the effects of CO\({}_{2}\) and CH\({}_{4}\) compressibility upon EOR performance while excluding the effect of any difference in injection rate. The initial conditions for the reservoir model are presented in Table 4. Thus, the producing bottom hole pressure is fixed at 13,789 kPa, while the initial reservoir pressure and temperature are computed on the basis of hydrostatic and geothermal gradients. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Depth (m) & 2811 \\ Initial reservoir pressure (kPa) & 27,579 \\ Reservoir temperature (\({}^{\circ}\)C) & 63 \\ Permeability (m\({}^{2}\)) & \(1.0\times 10^{-13}\) \\ Porosity (\%) & 0.25 \\ Initial oil saturation, \(S_{\rm o}\) (fraction) & 0.7 \\ Connate water saturation, \(S_{\rm w}\) (fraction) & 0.3 \\ Producing bottom hole pressure (kPa) & 13,789 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Initial and operating conditions used for the reservoir simulation. \begin{table}
\begin{tabular}{c c} \hline \hline
**Components** & **MMP (kPa)** \\ \hline CO\({}_{2}\) 100\% & 13,872 \\ CO\({}_{2}\) 90\% + CH\({}_{4}\) 10\% & 21,346 \\ CO\({}_{2}\) 80\% + CH\({}_{4}\) 20\% & 22,015 \\ CO\({}_{2}\) 70\% + CH\({}_{4}\) 30\% & 22,622 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Minimum miscibility pressures (MMPs) calculated using the multiple mixing cell method with various mole fraction ratios of CO\({}_{2}\) to CH\({}_{4}\). Figure 2: Schematic diagram of the water alternating gas (WAG) injection model. The decrease in displacement efficiency due to CO\({}_{2}\)-CH\({}_{4}\) co-injection is described in terms of the IFT between the displacing and displaced fluids in the middle of the reservoir (grid block co-ordinates (17, 17, 1)) during the 13-year WAG in Figure 3. Due to the lower molecular weight of CH\({}_{4}\) compared to CO\({}_{2}\), the addition of CH\({}_{4}\) makes the displacing fluid lighter and the IFT of the gas mixture higher compared to that of Case 1, as indicated in Figure 3a. In addition, the IFT after the multiple contact with the initial oil (2010-2011) is examined more closely in Figure 3b. Here, Case 1 gives the lowest IFT value of 0.08 mN/m between the CO\({}_{2}\) and reservoir oil, while Cases 2, 3, and 4 give 225%, 588%, and 1000% higher values of 0.26, 0.55, and 0.88 mN/m, respectively. Meanwhile, the decrease in displacement efficiency due to CO\({}_{2}\)-CH\({}_{4}\) co-injection is described in terms of the 2D change in oil viscosity when 0.15 PV of gas is injected in Figure 4. The blue swept area in Figure 4a indicates that the injected fluids make maximum contact with the reservoir oil in Case 1, and that the minimum oil viscosity in this Case is 0.46 mPa-s.