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Carbon dioxide flooding is an Enhanced Oil Recovery (EOR) method to increase the amount of oil that can be extracted from oil reservoirs, which along with the process of carbon capture can play an important role to reduce greenhouse gas emission [1]. CO₂ flooding is largely controlled by adsorption and interfacial properties among CO₂, oil, and formation water [2]. A proper understanding of the interfacial behavior is therefore necessary for improving CO₂ EOR method [3]. Extensive experimental studies on the effect of interfacial tension on CO₂/brine relative permeability shows that a decrease in interfacial tension leads to increase in relative permeability [4]. Due to the low viscosity of CO₂, a significant quantity of injected CO₂ is trapped in the reservoir rocks by capillary forces [5]. Krevor et al. (2012) further showed in their experimental work that capillary heterogeneity is an important factor influencing the maximum CO₂ saturation and less areal sweep efficiency of reservoir fluids [6].

Experimental work on CO₂-oil-brine-rock interactions in a water– wet sandstone reservoir indicated that CO₂-rich fluid was the main factor causing dissolution and precipitation of rock minerals; feldspar and calcite [7]. Precipitation of kaolinite clays and other solid phases comprising O, Si, Al, Na, and C was also observed. However, the rate of mineral dissolution and precipitation was greatly reduced in areas where the reservoir was oil-wet (Miao Yu, 2016). A significant drop in permeability due to fines migration during CO₂ injection in the Pembina Cardium sandstone reservoir has been earlier reported [8].

The interfacial tension (IFT) has an effect on capillary pressure and relative permeability, and thus affects the flow through capillary tubes of porous medium [9]. Moreover, CO₂ and oil become completely miscible when the reservoir or injection pressure is above the minimum miscibility pressure (MMP), leading to the reduction of their IFT to zero [10]. Therefore, the IFT of the system of CO₂, water, and oil should be determined between the two phases of water and CO₂/oil. Laboratory experiments have shown that IFT decreases as the composition of CO₂ increases in the mixture [11, 12]. In addition, the interfacial behavior of water-oil has consistently shown changes due to variations in the solubility of CO₂ in oil. However, the effect of CO₂ on water-oil interface still poses challenges because the interaction mechanisms at the water – CO₂/oil interface cannot be fully understood from experiments. So, this work uses molecular dynamics simulation to fully study the interaction mechanism of super critical carbon dioxide, water and oil interfacial phenomena.

Molecular Dynamic (MD) simulations have been widely used to study the interfacial behavior in binary and ternary systems [13]. MD simulations of water/oil interfacial tension using model asphaltenes showed that IFT could be reduced by the surface concentration of asphaltene molecules [14]. Asphaltene molecules assemble from initial nanoaggregates to formation of thin films at the oil-water interface [15]. Kunieda et al. [2012] investigated the oil–fluid interface and found that the aromatic molecules in light oil accumulate at the interface. This accumulation phenomenon at oil–water interface was ascribed to the weak hydrogen bond interaction between water and aromatic hydrocarbons. Special molecular orientation of hydrocarbon molecules at the miscible hydrocarbon-fluid interface was reported [16]. For the CO₂–water, interface system, the molecular dynamics studies show that CO₂ molecules exhibit hydrophilicity and interact closely with water molecules at the interface [17]. However, there exist limited studies for the ternary water–CO₂–oil system, especially the microscopic behavior of CO2 distributing at water-oil interface. Most of the previous simulations use oil as a single component such as hexane, heptane, and octane, which do not represent the bulk oil composition usually produced from the reservoir.

In this work, the main objective is to study the influence of supercritical CO₂ (scCO₂) on water–oil interface in a typical mixture of Bakken fluid. In addition, the effect of CO₂ on the contact angle of water when wetting a kerogen-like surface will be investigated. The results from this work may help better understand the mechanism of scCO₂ impact on water–oil interface, which is of great interest in the design of CO₂- EOR in tight shale plays.

Methodology

The composition of Bakken oil sample for our simulation is taken from literature [18].The oil composition proposed by Nojabae et al (2016) was used to construct a model for the oil phase in the molecular dynamics simulations. The alkanes are modeled with linear structure, namely n-alkanes. The number of each component (pure hydrocarbon) and their corresponding composition in the oil phase is shown in Table 1.1, and the phase envelope of the fluid sample is also shown in Figure 1.1. The TRAPPE force field in GROMACS was used to determine the interfacial tension between water and oil. To check if the interfacial tension of the water/oil mixture can be accurately calculated by the chosen force field, the interfacial tension between the liquid and vapor phase for pure hydrocarbons in the oil mixture was calculated. Molecules of each pure component are placed in a simulation box and the system is equilibrated in the NVT ensemble, at a temperature of 293K for 4ns. The initial box size is calculated from PACKMOL’s volume guesser utility. The NVT equilibration run is followed by another 4ns NPT run under a pressure of 1 bar. The Ewald summation (PME) was used for electrostatic interactions, and the cut-off distance was set at 1.2 nm. The Modified Velocity rescale thermostat with a stochastic term (Bussi et al., 2007) and Berendsen barostat where used for temperature and pressure coupling respectively. The leapfrog integration method with a time step of 2 fs was implemented, and all bonds were constrained by the SHAKE algorithm. The electrostatic interactions are calculated using the Particle Mesh Ewald (PME) while the van der Waals interactions are represented by 12-6 Lennard-Jones function.

Figure 1.1: Phase envelope of bakken fluid sample.

Table 1.1: The composition of Bakken oil sample used in the simulations.

D₀ is the depth of potential well, R₀ is the Lennard-Jones radius, and R is the distance between two atoms. Modified Lorentz–Berthelot combining rules [19] were used for the well depth D₀ and the size parameter σ to describe non-bonded LJ interactions between sites of different type i and j according to the expressions:

After the NPT run, the box was then extended along the direction to add the vapor phase, equilibrated for another 4ns followed by NVT MD simulation for 5 ns.

For the interface model, we first created separate simulation boxes for the oil phase and the water phase with each having a dimension of 5nm by 5nm by 5nm. Energy minimization is carried out in both boxes to reduce the potential energy of the system and to ensure the stability of the system during simulation. For the box containing the oil phase, pressure and temperature are applied using the isobaric-isothermal ensemble (NPT) simulation [20]. The isobaric-isothermal-isointerface area ensemble (NPnAT) simulation is used to create a steady surface area for the water cell into the have the same dimension with the oil phase in the X and Y directions [21]. The SPE/E (single point charge extended) water model was used for water [22]. Lastly, the interface system was made by combining the two cells and performed in NPnAT ensemble simulation. For the NPnAT ensemble, the pressure on only one direction is controlled, and the box length on that direction (i.e. z in this case) is changed. The area, which is tangential to the controlled pressure, is fixed during MD simulation. Temperature was coupled in the system using the velocity rescale thermostat, and pressure using the Parrinello-Rahman barostat. All Equilibration steps, both for NVT, NPT, NPnAT was ran for 8 ns and a production run for 10ns in the NPnAT ensemble using the GROMACS molecular dynamics simulation package. The workflow given in Figure 1.2 shows the steps to create an interfacial system. The results are much more accurate when the interface is set on the plane of fixed areas like in our simulation case.

Figure 1.2: Workflow of modeling oil-water interface.

Figure 1.3 shows our initial oil-water interface and oil- CO₂ –water interface respectively. The same procedures were done when placing CO₂ molecules into the oil cell and calculating the water-oil+CO₂ interface system.

As depicted in Fig 1.3, there is a constant interfacial area between water and oil at all times in the simulation. Addition of supercritical CO₂ into the water-oil mixture causes changes in the interfacial region due to its miscibility in the oil and changes in the oil/water IFT. (Figure 1.3b and 1.3c). Since IFT is an equilibrium property the system was equilibrated for 5ns after the addition of scCO₂ followed by a 10 ns production run.

Figure 1.3: Initial model for oil-water interface and oil-water- CO₂ interface, brown color (oil), blue color (water) and green color (scCO₂).

The interfacial tension can be calculated based on our molecular dynamic simulation results (Lopez-Lemus et al., 2008)

where n is the axis normal to the interface, and hence P_nn and P_tt are normal and tangential components respectively of the pressure tensor P. Note that in the simulation the Z-axis is normal to the interface, and therefore the interfacial tension can be calculated by averaging the instantaneous interfacial tension

over the simulation time given [23]. The simulation was run for 10 ns so that the pressure tensors can converge in order to get a correct average of the interfacial tension.

Generally, in MD simulations, the instantaneous pressure, P_i (i=x, y, z), for each direction can be expressed [24]:

Where L_z is the box length in the Z-direction, which is perpendicular to the interface. Eq 3 can be written as:

Finding the average interfacial tension over the simulation run gives:

Since our system, have two interfaces, Eq 6. is divided by 2;

To validate our bulk oil model, IFT simulations for pure hydrocarbons and water were also carried out. Methane-water, hexane-water, heptane-water and octane-water IFT measurements at standard conditions were all simulated and as seen in Figure 1.5, they are exceptionally in good agreement with experimental results [25]. These pure hydrocarbons were selected to validate our simulation method because their experimental results are available. Furthermore, the densities of water and hydrocarbons were properly simulated. Figure 1.4 shows the partial densities of heptane and water across the z-direction of the simulation box. The densities of the methyl group (CH2) and ethyl group (CH3) in heptane are also included in Figure 1.4. From Figure 1.4, the density of water is 1000kg/m3 and for heptane 684 kg/m³ which directly agrees with the experimental density of water and heptane at standard conditions. These results show that oilwater interfacial system can be effectively studied through molecular dynamics simulations.

Figure 1.4: Heptane-water interfacial tension; densities from simulation (heptane and water) matches density of water and heptane derived from experiments.

Figure 1.5: Interfacial tension as a function of hydrocarbon number at 76.73⁰F and 14.7 psi for both experimental and molecular simulation.

Results and Discussion

The results in Table 1.2 give the agreement between our results and other experimental studies. Figure 1.6 shows our simulation surface tension and density values for liquid-vapor interface of propane, butane, pentane, hexane, heptane, and octane. Comparing with experimental results from literature, it shows the force field used in this study can correctly calculate interfacial tension between water and oil.

Figure 1.6: Densities of pure hydrocarbon from simulation at 68⁰F and 14.7 psi a) Propane b) Butane c) Pentane d) Hexane e) Heptane f) Octane.

a* surface-tension. c* Froba et al, 2003
Table 1.2: Interfacial tension between liquid and vapor phases of pure hydrocarbons at 68⁰F and 14.7 psi.

Figure 1.7 shows how the increase in the concentration of CO₂ decreases the oil-water interfacial tension. It is also clear that interfacial tension Table 1.3 generally increases with pressure increase at the reservoir temperature 220 °F. Interfacial tension for oil-water is as high as 44.25 mN/m at 6800 psi, which will then reduce to 40mN/m at pressures around 2000psi. It has also been proven experimentally that interfacial tension of oil-water increases with pressure increase [26]. As reported by Makimura et al. (2013), IFT decreases with increase in temperatures and reservoir pressures for hydrocarbons in the gaseous phase, such as methane and ethane.

Figure 1.7: Interfacial tension as a function of pressure and CO₂ concentration. The blue line shows oil-water interfacial tension, which takes a positive linear slope with pressure. The red line shows oil/water and 16.6 mol % of CO₂. The green line represents oil-water and 29.6 mol % of CO2; there is significant IFT reduction as pressure decreases.

b* engineering toolbox/ density/ alkanes
Table 1.3: Interfacial tension between liquid and vapor phases of pure hydrocarbons at 68⁰F and 14.7 psi.

Furthermore, the injection of CO₂ into oil reduces the interfacial tension because of the miscibility of CO2 in its supercritical state in both the oil phase and the water phase [27]. An addition of 0.166 mole fraction of CO₂ has minimal effect on IFT reduction, but an increase in CO₂ concentration to 0.30 mole fraction can significantly reduce the oil-water IFT from 44.5 mN/m to 35mN/m. From Figure 1.3 most of the CO₂ molecules move to the oil-water interface. We consider the accumulation of CO₂ molecules at the interface as being driven by the IFT differences between water-oil and CO₂-water. The interface produces an excess free energy, which is compensated by adsorbing CO₂. Once this occurs, the excess free energy per area decreases, reducing the IFT as γ = (dG/dA) _{T, P}

The interfacial region increases as the CO₂ mole fraction increases which implies that deeper molecular interactions occur at the coexistent region of water and oil. Looking at the trend of interfacial tension reduction, it is linear due to differences in the molar concentrations of hydrocarbons in the oil. This accumulation phenomenon at the oil-water interface is similar to results showing asphaltene molecules assembling from nano-aggregation to thin-film formation at the oilwater interface [27]; enhanced accumulation of scCO₂ at the interface as CO₂ mole fraction increases, leading to a reduction in IFT.

Interfacial tension of methane and water was also calculated using molecular dynamics simulation at different pressures and at two temperatures (76 °F and 220°F). Methane–water interfacial behavior is in an inverse relationship to that of oil-water because the solubility of methane in water increases as pressure and temperature increases. As shown in Figure 1.8a, the interfacial tension decreases as the pressure increases at 76 °F. Further decrease in the interfacial tension from 72.4 mN/m to 44.28mN/m is observed as the concentration of CO2 increases to 40mol percent. At a higher temperature, 220°F as depicted in Figure 1.8b, even more reduction in interfacial tension can be observed. For pure methane-water, interfacial tension reduces from 59mN/m to about 47.5 mN/m at 220°F, as compared to a decrease from 72.3 mN/m to 52.4 mN/m at 76 °F. With the increase in the concentration of CO₂ to up to 40mol percent, the interfacial tension reduces to 35.85 mN/m.

Figure 1.8a: Methane-water interfacial tension as a function of pressure at T=76⁰F.

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