Compositional Modeling to Analyze the E ﬀ ect of CH 4 on Coupled Carbon Storage and Enhanced Oil Recovery Process

: The present study is aimed at the development of compositional simulation models of the co-injection of CO 2 and CH 4 during the water-alternating-gas (WAG) process in order to assess the e ﬃ ciency of carbon capture and storage in combination with enhanced oil recovery (CCS-EOR). The co-injection of CO 2 and CH 4 occupies more reservoir pore volume and causes higher reservoir pressure than CO 2 WAG, thus leading to an enhanced early EOR performance. However, the overall EOR performance of the co-injection method becomes lower than that of CO 2 WAG due to the reduced miscibility and sweep e ﬃ ciency upon further CH 4 addition. The decrease in gas displacement and sweep e ﬃ ciency weaken the hysteresis e ﬀ ects upon the residual trapping mechanism. However, the solubility trapping mechanism takes e ﬀ ect because the co-injection generates higher average reservoir pressure than does the CO 2 WAG. The index of global warming potential (GWP) in a mole unit is employed to quantify the carbon storage e ﬀ ects of CO 2 and co-injection WAG cases. According to the index, 1 mole of CH 4 sequestration has the same e ﬀ ects as that of 10 moles of CO 2 for global warming mitigation. In conclusion, the carbon storage e ﬀ ects are enhanced as CH 4 concentration in the WAG increases. developed model demonstrates that CH 4 has the combined e ﬀ ect of reducing EOR performance but increasing CCS performance. The above results indicate the signiﬁcance of the integrated analysis for accurate CO 2 sequestration in depleted or depleting hydrocarbon reservoirs under EOR.


Introduction
Carbon capture and storage (CCS) has become well-known as a technology for reducing the emission of greenhouse gases from fossil fuels during power generation and industrial processes [1]. Projects involving the injection of carbon dioxide (CO 2 ) for enhanced oil recovery (EOR) have been operating worldwide since the early 1970s [2] and EOR is expected to be a major driver for CCS by providing an additional revenue stream. Hence, combining the CO 2 -EOR and CCS into a coupled CCS-EOR approach provides a synergistic effect towards business and environmental protection by offering commercial opportunities to oilfield operators. Consequently, almost 80 million tons (Mt) of CO 2 are already being used for CCS-EOR each year [3,4].
Methane (CH 4 ) is generated as a by-product of oil extraction during primary and secondary oil production and EOR. As CH 4 is a potent greenhouse gas (GHG), the operator often chooses to flare this by-product instead of releasing it directly to the atmosphere if there is little commercial opportunity or sufficient regulatory incentive to bring it to market [5]. Also, CH 4 has been used as a re-injection gas for EOR [6,7]. Previous studies have examined the impacts of impurities in the CO 2 stream upon the minimum miscibility pressure (MMP) to find that the presence of CH 4 increases the MMP compared to that of CO 2 , thus negatively impacting upon EOR performance [8][9][10][11][12][13][14]. Moreover, since the global warming potential (GWP) of CH 4 over 100 years is 28 times that of CO 2 [15], it is worth considering the use of CH 4 for CCS projects aimed at mitigating global warming and climate change. Although some studies on the geological storage of CO 2 and CH 4 in an aquifer have been conducted, there are insufficient studies examining the impact of CH 4 on CCS-EOR [16][17][18][19]. Hence, it is necessary to store CH 4 in reservoirs in order to mitigate gas flaring and release into the atmosphere by using a CCS-EOR approach that can consider energy security and climate change simultaneously. However, CH 4 affects the miscibility as well as the hysteresis and solubility effects for residual and solubility trapping mechanisms and the ultimate EOR performance during CCS-EOR.
For this reason, compositional simulation models are developed in the present study in order to investigate the effects of CO 2 -CH 4 co-injection upon the CCS-EOR mechanisms and performance. The multiple-mixing-cell method is applied to calculate the MMP of the injected gases (i.e., a mixture of CO 2 and CH 4 ) and the reservoir oil. Of the four main CO 2 trapping mechanisms (namely: structural, residual, solubility, and mineral trapping), structural and mineral trapping are excluded from the scope of the present study due to their negligible effects upon CCS-EOR in a relatively short period [20]. Here, CO 2 can be stored in the reservoir by hysteresis and dissolution in water during the water-alternating-gas (WAG) process, thus indicating residual and solubility trapping mechanisms. A three-phase hysteresis model and Henry's law are applied for the residual trapping and solubility trapping, respectively.

Calculation of Minimum Miscibility Pressure (MMP)
Carbon dioxide (CO 2 ) is the most common type of gas used in gas injection and has been widely used in the EOR method for light oils. Injected CO 2 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 CO 2 -EOR can be achieved via multiple contact processes that make use of condensing and vaporizing gas drives. At the injected CO 2 front, intermediate molecular weight hydrocarbons evaporate from the reservoir oil into the CO 2 , where they equilibrate with the CO 2 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 CO 2 close to the injector is continuously mixed with fresh CO 2 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 CO 2 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: 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.

3.
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 . 4.
The tie-line length is computed for the pressure and the minimum tie-line length (TL) is saved. 5.
The pressure is increased and Steps 2-4 are repeated. 6.
A multiple-parameter TL regression is performed to determine the exponent n, the slope m, and the constant b in the equation TL n = mp + b (power-law extrapolation), and the resulting function is plotted. 7.
The MMP is determined when the power-law extrapolation gives zero to within the desired accuracy of 20 psia at the latest three pressures.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 16 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. 3.
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 . 4. The tie-line length is computed for the pressure and the minimum tie-line length (TL) is saved. 5. The pressure is increased and Steps 2-4 are repeated. 6. A multiple-parameter TL regression is performed to determine the exponent , the slope , and the constant in the equation TL = + (power-law extrapolation), and the resulting function is plotted. 7. The MMP is determined when the power-law extrapolation gives zero to within the desired accuracy of 20 psia at the latest three pressures.

The Three-Phase Hysteresis Model for Residual Trapping
Although conventional two-phase hysteresis models assume the reversibility of permeability during the drainage process following the previous imbibition cycle, this assumption is invalid for three-phase fluid flow because the relative permeability of gas is lower when displacing a water-oil mixture than when displacing oil only [29]. The three-phase hysteresis model proposed by Larsen and Skauge [30] is adopted in the present study and has shown better matching to experimental data than the two-phase model [31,32].
The gas permeability during the drainage process is calculated using Equation (1): We clarify that a list of symbols is given in the Nomenclature. The relative permeability of the gas with decreasing gas saturation (i.e., non-wetting phase in the imbibition process) is denoted by and is estimated by Equations (2) and (3):

The Three-Phase Hysteresis Model for Residual Trapping
Although conventional two-phase hysteresis models assume the reversibility of permeability during the drainage process following the previous imbibition cycle, this assumption is invalid for three-phase fluid flow because the relative permeability of gas is lower when displacing a water-oil mixture than when displacing oil only [29]. The three-phase hysteresis model proposed by Larsen and Skauge [30] is adopted in the present study and has shown better matching to experimental data than the two-phase model [31,32].
The gas permeability during the drainage process is calculated using Equation (1): We clarify that a list of symbols is given in the Nomenclature. The relative permeability of the gas with decreasing gas saturation (i.e., non-wetting phase in the imbibition process) is denoted by S g f and is estimated by Equations (2) and (3): where the trapped gas saturation, S gr , and Land's parameter [33], C, are estimated from Equations (4) and (5), respectively: S gr,max is the maximum trapped gas saturation and can be approximated using an empirical correlation with the porosity, φ [34], in accordance with Equation (6): To determine the relative permeability of the oil, the Stone's first model modified by Aziz and Settari [35] is applied. The minimum residual oil saturation, designated S om , is modified to reflect the effect of trapped gas on oil relative permeability, as shown in Equation (7): where S g and S g f are the total and free gas saturations respectively, and a is input parameter of 0.68 for mimicking a strongly water-wet condition [36].

Solubility Model
Carbon dioxide (CO 2 ) is also trapped by the solubility trapping mechanism due to contact with water. The mole fraction of CO 2 in each phase is determined from the thermodynamic equilibrium condition according to Equation (8): where f i,o , f i,g , and f i,w denote the fugacity of the i-th component in the oil, gas, and water phase, respectively. f i,o and f i,g are calculated using Peng-Robinson EOS [37,38]. By contrast, f i,w is given by Henry's law [39] in accordance with Equation (9): where H i and y i,w are Henry's constant and the mole fraction of the i-th component in the water phase, respectively. Henry's constant is calculated using Equations (10) and (11) under isothermal conditions [40,41]: where R is the gas constant and T is the temperature in Kelvin. Then, where D, E, and F are constants with values of −9.4234, 4.0087, and 10.3199, respectively, for CO 2 , and v i is the partial molar volume of the i-th component at infinite dilution (cm 3 ·mol −1 ), which is computed using Equation (12) [42]: where T is the reservoir temperature in K.

Fluid Modeling
Weyburn W3 fluid data [43,44] is used as the experimental data for fluid modeling in the present study. Since the Weyburn Field in Saskatchewan, Canada, reached the economic limit of waterflooding and became a target for CO 2 -EOR, extensive experiments have been conducted to investigate the interactions between oil and CO 2 for CO 2 -EOR and CCS purposes [43,45].
The fluid composition of W3 experimental data and corresponding input EOS parameters used for fluid modeling are summarized in Table 1, while Table 2 presents the oil properties calculated via a regression method using the Peng-Robinson Equation of State (PR-EOS) and matched against the experimental data to increase the reliability of the compositional reservoir simulation [37,38]. The MMP is then estimated using the multiple-mixing-cell method [28]. An examination of the bottom row of Table 2 indicates that the MMP datum associated with CO 2 in W3 fluid at a reservoir temperature of 63 ºC is 14,196 kPa (second column, Table 2), while the calculated value is 13,872 kPa (third column, Table 2), thus indicating a 2.3% error against the W3 data. The MMPs calculated using the multiple-mixing-cell method with varying mole fraction ratios of CO 2 to CH 4 are presented in Table 3. Here, it can be seen that the MMP increases with increasing mole fraction of CH 4 in the CO 2 injection stream, thus indicating that CH 4 reduces the displacement efficiency compared to that of pure CO 2 injection, in agreement with previous experimental studies [13,14].

Effects of CH 4 Injection on EOR Efficiency
A two-dimensional (2D) homogeneous model based on the work of Cho et al. [19] is designed to focus on investigating the miscibility and sweep efficiency without gravity override during WAG simulations. This reservoir model is discretized into 33 × 33 × 1 grid blocks of volume 3 × 3 × 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.

Effects of CH4 Injection on EOR Efficiency
A two-dimensional (2D) homogeneous model based on the work of Cho et al. [19] is designed to focus on investigating the miscibility and sweep efficiency without gravity override during WAG simulations. This reservoir model is discretized into 33 × 33 × 1 grid blocks of volume 3 × 3 × 3 m 3 each. A quarter of a 10-acre five-spot well pattern (i.e., CO2 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% CO2 + 0% CH4 (Case 1), 90% CO2 + 10% CH4 (Case 2), 80% CO2 + 20% CH4 (Case 3), and 70% CO2 + 30% CH4 (Case 4). The gas injection rate for each case is a constant 2265 m 3 /day under surface conditions to determine the effects of CO2 and CH4 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.  The decrease in displacement efficiency due to CO2-CH4 co-injection is described in terms of the IFT between the displacing and displaced fluids in the middle of the reservoir (grid block coordinates (17, 17, 1)) during the 13-year WAG in Figure 3. Due to the lower molecular weight of CH4 compared to CO2, the addition of CH4 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 CO2 and reservoir oil, while Cases 2, 3, and 4  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 CO2-CH4 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. When 20% mole fraction of CH4 is added into the CO2 injection stream (Case 3), the deep blue region of Figure 4a changes to the light blue area of Figure 4b, indicating a 23.9% increase in the oil viscosity from 0.46 mPa·s to 0.57 mPa·s.
The injected gas displaces the light and intermediate oil components from the initial oil, thereby increasing the oil viscosity after the multiple contact. For Case 1, the oil viscosity near the gas injector is zero because the oil is displaced by the high injection pressure and is miscible with the CO2. In addition, Figure 4 shows that the injection gas front in Case 3 is more convex than that in Case 1. This is because less gas is acting as a solvent to reduce the oil viscosity, while the fraction of injected gas that does not come into contact with the oil creates a gas channel that leads to early breakthrough of produced gas, as indicated in Figure 5.    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. When 20% mole fraction of CH 4 is added into the CO 2 injection stream (Case 3), the deep blue region of Figure 4a changes to the light blue area of Figure 4b, indicating a 23.9% increase in the oil viscosity from 0.46 mPa·s to 0.57 mPa·s. The injected gas displaces the light and intermediate oil components from the initial oil, thereby increasing the oil viscosity after the multiple contact. For Case 1, the oil viscosity near the gas injector is zero because the oil is displaced by the high injection pressure and is miscible with the CO 2 . In addition, Figure 4 shows that the injection gas front in Case 3 is more convex than that in Case 1. This is because less gas is acting as a solvent to reduce the oil viscosity, while the fraction of injected gas that does not come into contact with the oil creates a gas channel that leads to early breakthrough of produced gas, as indicated in Figure 5.   The cumulative gas injection under the reservoir condition obtained from the four CO2-CH4 WAG cases is indicated in Figure 6. Note that although the gas injection rate at the surface is constant, the volume occupied by gas differs in each case because CH4 is less compressible than CO2; hence, the more CH4 is added, the higher the gas injection rate at the reservoir (Jin et al., 2017). In addition, the average gas saturation in each of the four cases for the ten-year WAG period is indicated in Figure   7. In the first WAG cycle (2010-2012), Case 1 displays the lowest average gas saturation, while Cases 2 to 4 indicate that the average gas saturation increases with increasing addition of CH4 to the gas stream as CH4 occupies more reservoir pore volume than does CO2. Interestingly, this trend is reversed in the subsequent WAG cycles due to the poor sweep efficiency resulting from the CH4 addition, so that the average gas saturation eventually becomes the lowest for Case 4 by the end of the final WAG cycle (2019). Meanwhile, the average reservoir pressure obtained from the four CO2-CH4 WAG cases is indicated in Figure 8, where the greater pore occupation by CH4 is seen to increase the average reservoir pressure due to the lower compressibility of CH4 relative to CO2. As a result, the co-injection of CO2-CH4 generates higher oil recovery than the pure CO2 WAG during the early stages of WAG (2010-2012), but reduces the overall oil recovery at the end of the WAG process, as The cumulative gas injection under the reservoir condition obtained from the four CO 2 -CH 4 WAG cases is indicated in Figure 6. Note that although the gas injection rate at the surface is constant, the volume occupied by gas differs in each case because CH 4 is less compressible than CO 2 ; hence, the more CH 4 is added, the higher the gas injection rate at the reservoir (Jin et al., 2017). In addition, the average gas saturation in each of the four cases for the ten-year WAG period is indicated in Figure 7. In the first WAG cycle (2010-2012), Case 1 displays the lowest average gas saturation, while Cases 2 to 4 indicate that the average gas saturation increases with increasing addition of CH 4 to the gas stream as CH 4 occupies more reservoir pore volume than does CO 2 . Interestingly, this trend is reversed in the subsequent WAG cycles due to the poor sweep efficiency resulting from the CH 4 addition, so that the average gas saturation eventually becomes the lowest for Case 4 by the end of the final WAG cycle (2019). Meanwhile, the average reservoir pressure obtained from the four CO 2 -CH 4 WAG cases is indicated in Figure 8, where the greater pore occupation by CH 4 is seen to increase the average reservoir pressure due to the lower compressibility of CH 4 relative to CO 2 . As a result, the co-injection of CO 2 -CH 4 generates higher oil recovery than the pure CO 2 WAG during the early stages of WAG (2010-2012), but reduces the overall oil recovery at the end of the WAG process, as indicated in Figure 9. This is because the effects of displacement and reduction in sweep efficiency become more dominant than that of compressibility as the WAG proceeds. addition, so that the average gas saturation eventually becomes the lowest for Case 4 by the end of the final WAG cycle (2019). Meanwhile, the average reservoir pressure obtained from the four CO2-CH4 WAG cases is indicated in Figure 8, where the greater pore occupation by CH4 is seen to increase the average reservoir pressure due to the lower compressibility of CH4 relative to CO2. As a result, the co-injection of CO2-CH4 generates higher oil recovery than the pure CO2 WAG during the early stages of WAG (2010-2012), but reduces the overall oil recovery at the end of the WAG process, as indicated in Figure 9. This is because the effects of displacement and reduction in sweep efficiency become more dominant than that of compressibility as the WAG proceeds.      Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 16 Figure 9. Oil recovery factor obtained from the four CO2-CH4 WAG cases.

Effects of CH4 Injection on Carbon Storage Efficiency
As indicated in Figure 7, the addition of CH4 to the CO2 stream reduces the WAG sweep efficiency and gas saturation, thus decreasing the (Equation (4)) to lower the trapped gas saturation, . As a result, the residual trapped CO2 by hysteresis ( Figure 10) is seen to decrease as the ratio of CH4 to CO2 in the gas stream increases. In addition, the amount of solubility-trapped CO2 decreases as the concentration of CH4 increases, as indicated in Figure 11. However, this decrease is primarily due to the reduced volume of injected CO2 and does not mean that the addition of CH4 lowers the performance of solubility trapping. As mentioned in Section 3.2., the injected total gas rate is set to a constant of 2,265 m 3 /day, so that the amount of injected CO2 decreases with increasing CH4 addition.

Effects of CH 4 Injection on Carbon Storage Efficiency
As indicated in Figure 7, the addition of CH 4 to the CO 2 stream reduces the WAG sweep efficiency and gas saturation, thus decreasing the S gm (Equation (4)) to lower the trapped gas saturation, S gr . As a result, the residual trapped CO 2 by hysteresis ( Figure 10) is seen to decrease as the ratio of CH 4 to CO 2 in the gas stream increases. In addition, the amount of solubility-trapped CO 2 decreases as the concentration of CH 4 increases, as indicated in Figure 11. However, this decrease is primarily due to the reduced volume of injected CO 2 and does not mean that the addition of CH 4 lowers the performance of solubility trapping. As mentioned in Section 3.2., the injected total gas rate is set to a constant of 2,265 m 3 /day, so that the amount of injected CO 2 decreases with increasing CH 4 addition. ratio of CH4 to CO2 in the gas stream increases. In addition, the amount of solubility-trapped CO2 decreases as the concentration of CH4 increases, as indicated in Figure 11. However, this decrease is primarily due to the reduced volume of injected CO2 and does not mean that the addition of CH4 lowers the performance of solubility trapping. As mentioned in Section 3.2., the injected total gas rate is set to a constant of 2,265 m 3 /day, so that the amount of injected CO2 decreases with increasing CH4 addition.  The contributions of the residual trapping and solubility trapping mechanisms to geological carbon sequestration is examined in Figure 12 by comparing the mole proportions of injected and remaining CO2. Note that movable CO2 also has the potential to be trapped over time. Thus, compared to Case 1, the residual trapping performances of Cases 2, 3, and 4 are seen to decrease by 13.2%, 20.5%, and 27.4% respectively, due to the lower hysteresis effect and gas saturation. By contrast, the solubility trapping efficiencies remain relatively constant as the amount of injected CO2 is reduced with CH4 addition. This is because the CO2 solubility trapping is affected not only by gas saturation but also by reservoir pressure. Since the added CH4 increases the reservoir pressure, as indicated in Figure 8, this balances out the negative effect of the reduced CO2 injection, thereby resulting in the similar CO2 solubility trapping performance. Meanwhile, the amount of movable CO2 remaining in the reservoir decreases with increasing concentration of CH4 due to the gas breakthrough effect.
Although the above results elucidate the aspect of CO2 sequestration, it is also necessary to Figure 11. Solubility-trapped CO 2 obtained from the four CO 2 -CH 4 WAG cases.
The contributions of the residual trapping and solubility trapping mechanisms to geological carbon sequestration is examined in Figure 12 by comparing the mole proportions of injected and remaining CO 2 . Note that movable CO 2 also has the potential to be trapped over time. Thus, compared to Case 1, the residual trapping performances of Cases 2, 3, and 4 are seen to decrease by 13.2%, 20.5%, and 27.4% respectively, due to the lower hysteresis effect and gas saturation. By contrast, the solubility trapping efficiencies remain relatively constant as the amount of injected CO 2 is reduced with CH 4 addition. This is because the CO 2 solubility trapping is affected not only by gas saturation but also by reservoir pressure. Since the added CH 4 increases the reservoir pressure, as indicated in Figure 8, this balances out the negative effect of the reduced CO 2 injection, thereby resulting in the similar CO 2 solubility trapping performance. Meanwhile, the amount of movable CO 2 remaining in the reservoir decreases with increasing concentration of CH 4 due to the gas breakthrough effect. Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 16

Discussions
This study investigated the effects of CO2-CH4 co-injection on CCS-EOR performance and mechanisms using the compositional 2D reservoir simulation. The 2D homogeneous plane model was designed in order to focus on the miscibility and sweep efficiency without gravity override during WAG simulations. We anticipate that the proposed compositional model can be extended to a three-dimensional (3D) heterogeneous model for real field applications. Adding CH4 into the CO2 stream may affect the vertical sweep efficiency, resulting in the change of the CCS-EOR performance because the density of CH4 is much lighter than that of CO2. Also, reservoirs are heterogeneous in reality. The effects of heterogeneity on the performance are under investigation as future works.
Moreover, it is essential for the technically, economically, and environmentally sustainable development of CO2-EOR fields to analyze both oil recovery and carbon storage efficiencies in an integrated way. For an actual field application, the optimal CO2-CH4 injection design should be developed with consideration for economic factors, such as the volatile oil price, CO2 and CH4 purchase and recycle prices, operating costs, and tax credits for CCS. Ettehadtavakkol et al. [46]  Although the above results elucidate the aspect of CO 2 sequestration, it is also necessary to consider the contribution of CH 4 storage because the GWP of CH 4 is about 28 times that of CO 2 . The GWP is an index of the relative amount of heat trapped by a unit mass of other GHGs compared to CO 2 . In the present study, the GWP is transformed into the index per 10 7 moles of GHG. GWP of CH 4 per 10 7 moles is ten times higher than that of CO 2 with consideration for the molecular weight of each gas. In other words, the effect of 1 mole of CH 4 sequestration upon the prevention of global warming is the same as that of 10 moles of CO 2 sequestration. Thus, the relative amounts of trapped GHGs are presented in Figure 13, where 10 7 moles of trapped CO 2 and CH 4 are quantified as 1 and 10, respectively. For Case 1, the net GWP of trapped gases is 3.94 − 2.13 = 1.81, under the assumption that CH 4 is only produced without re-injection into the reservoir. As the CH 4 concentration increases, the trapped GWPs for the co-injection cases are increased by 123%, 230%, and 313% respectively, compared with Case 1 due to the CH 4 sequestration effect in spite of the reduction in CH 4 storage.

Discussions
This study investigated the effects of CO2-CH4 co-injection on CCS-EOR performance and mechanisms using the compositional 2D reservoir simulation. The 2D homogeneous plane model

Discussions
This study investigated the effects of CO 2 -CH 4 co-injection on CCS-EOR performance and mechanisms using the compositional 2D reservoir simulation. The 2D homogeneous plane model was designed in order to focus on the miscibility and sweep efficiency without gravity override during WAG simulations. We anticipate that the proposed compositional model can be extended to a three-dimensional (3D) heterogeneous model for real field applications. Adding CH 4 into the CO 2 stream may affect the vertical sweep efficiency, resulting in the change of the CCS-EOR performance because the density of CH 4 is much lighter than that of CO 2 . Also, reservoirs are heterogeneous in reality. The effects of heterogeneity on the performance are under investigation as future works.
Moreover, it is essential for the technically, economically, and environmentally sustainable development of CO 2 -EOR fields to analyze both oil recovery and carbon storage efficiencies in an integrated way. For an actual field application, the optimal CO 2 -CH 4 injection design should be developed with consideration for economic factors, such as the volatile oil price, CO 2 and CH 4 purchase and recycle prices, operating costs, and tax credits for CCS. Ettehadtavakkol et al. [46] focused on the sensitivity of economic parameters with various WAG ratios during CCS-EOR, but no study has been conducted in the CO 2 -CH 4 co-injection system to the best of our knowledge. Since the optimum operating conditions enhancing the performance of CCS-EOR depend on reservoir characteristics, it is necessary to develop a site-specific design based on economic analysis for the field application.
Gas injection changes the stability of asphaltene precipitation and deposition, and formation damages by asphaltene deposition affect CCS-EOR performance. The effects of asphaltene deposition on CCS-EOR in the CO 2 WAG process have been investigated in Cho et al. [19], while the effect of CH 4 addition has not been studied yet. We clarify that the CO 2 -CH 4 co-injection model considering asphaltene deposition is being developed as our on-going work.

Conclusions
A compositional numerical simulation was conducted to investigate the effects of CH 4 additions upon the coupled CO 2 -enhanced oil recovery (EOR) and carbon storage process. The oil properties were matched to the reference data from Weyburn W3 via the equation of state (EOS) parameter tuning. The minimum miscibility pressure (MMP) between the CO 2 /CH 4 mixture and the reservoir oil was estimated using the multiple-mixing-cell method. Based on the fluid model, the three-phase hysteresis model and Henry's law were applied for accurate simulation of WAG injection under dynamic conditions. The following conclusions were drawn from this study.
Because adding CH 4 to the CO 2 stream increased the MMP, the interfacial tension (IFT) between the co-injected gases and the reservoir oil had a higher value than that of CO 2 alone. Further, the addition of CH 4 resulted in a less pronounced reduction in oil viscosity after multiple contacts with the gas stream, thus indicating the lower displacement efficiency. Since CH 4 is less compressible than CO 2 , the CO 2 /CH 4 mixture occupied more pore volume than CO 2 in the first WAG cycle, but the reduction in sweep efficiency due to CH 4 addition reversed this tendency in subsequent cycles. Hence, although the CH 4 addition resulted in a higher EOR performance in the early stages due to the compressibility effect, the EOR performance was subsequently reduced due to the lower displacement and sweep efficiencies. The diminished sweep efficiency due to CH 4 addition led, in turn, to a reduction in the residual trapping performance of CO 2 . By contrast, the increased reservoir pressure acted to offset the lower sweep efficiency for CO 2 solubility trapping, thus maintaining the performance even with increasing amounts of CH 4 addition. Taking the global warming potentials (GWPs) of the respective gases into consideration, the overall carbon capture and storage (CCS) effects were improved by 123%, 230%, and 313% by the use of CH 4 to CO 2 ratios of 0.1, 0.2, and 0.3 respectively, compared to the use of CO 2 alone. In conclusion, the developed model demonstrates that CH 4 has the combined effect of reducing EOR performance but increasing CCS performance. The above results indicate the significance of the integrated analysis for accurate CO 2 sequestration in depleted or depleting hydrocarbon reservoirs under EOR.