## 2 Methodology  
### Calculation of Minimum Miscibility Pressure (MMP)  
Carbon dioxide (CO2) is the most common type of gas used in gas injection and has been widely used in the EOR method for light oils. Injected CO2 acts as a solvent to reduce oil viscosity and expand oil volume in reservoirs. These phenomena occur more frequently under miscible conditions than they do under immiscible conditions [21]. As shown schematically in Figure 1, miscibility conditions during CO2-EOR can be achieved via multiple contact processes that make use of condensing and vaporizing gas drives. At the injected CO2 front, intermediate molecular weight hydrocarbons evaporate from the reservoir oil into the CO2, where they equilibrate with the CO2 to take part in the next contact with the reservoir oil in a phenomenon called the vaporizing gas drive or the forward multiple contact process. After each contact, however, the equilibrated reservoir oil behind the injected CO2 close to the injector is continuously mixed with fresh CO2 in a process called the condensing gas drive or the backward multiple contact process [22; 23]. Due to the mass transfer of intermediate hydrocarbons between CO2 and oil, the composition and properties, such as the density and viscosity, of the reservoir oil and injected gases are changed. This, in turn, leads to a difference in the interfacial tension (IFT) between the equilibrated oil and gas at each location. As the reservoir approaches the miscible condition, the oil viscosity and IFT decrease, such that the IFT tends towards zero and the miscible condition is reached with a reservoir pressure higher than the MMP [24].  
A variety of methods, such as the slim-tube, vanishing interfacial tension, and rising bubble technique, have been conventionally employed to estimate the MMP [25; 26; 27]. However, since these methods are time-consuming, expensive, and occasionally less accurate, it is often beneficial to implement computational methods for calculating the MMP. For this purpose, the multiple-mixing-cell method using the cubic equation of state (EOS) is one of the most prevalent methods [28]. In the present study, this method is applied according to the following steps:  
1. The system temperature is defined and the starting pressure for the process is estimated.
2. A calculation is performed for the displacing gas and the displaced oil to obtain the new equilibrium compositions of liquid and vapor after the first contact.  
Step 2 is repeated for each contact using the previous and new equilibrium compositions, injected gas, and reservoir oil to obtain the updated compositions until the lengths of all key tie-lines converge to a tolerance of \(10^{-8}\).  
The tie-line length is computed for the pressure and the minimum tie-line length (TL) is saved.  
The pressure is increased and Steps 2-4 are repeated.  
A multiple-parameter TL regression is performed to determine the exponent \(n\), the slope \(m\), and the constant \(b\) in the equation \(\text{TL}^{n}=mp+b\) (power-law extrapolation), and the resulting function is plotted.  
The MMP is determined when the power-law extrapolation gives zero to within the desired accuracy of 20 psia at the latest three pressures.