Molecular Modeling of CO₂ and n-Octane in Solubility Process and α-Quartz Nanoslit

Abstract

After primary and secondary oil recovery, CO₂-enhanced oil recovery (EOR) has become one of the most mentioned technologies in tertiary oil recovery. Since the oil is confined in an unconventional reservoir, the interfacial properties of CO₂ and oil are different from in conventional reservoirs, and play a key role in CO₂ EOR. In this study, molecular dynamics simulations are performed to investigate the interfacial properties, such as interfacial tension, minimum miscibility pressure (MMP), and CO₂ solubility. The vanishing interfacial tension method is used to get the MMP (~10.8 MPa at 343.15 K) which is in agreement with the reported experimental data, quantitatively. Meanwhile, the diffusion coefficients of CO₂ and n-octane under different pressures are calculated to show that the diffusion is mainly improved at the interface. Furthermore, the displacement efficiency and molecular orientation in α-quartz nanoslit under different CO₂ injection ratios have been evaluated. After CO₂ injection, the adsorbed n-octane molecules are found to be displaced from surface by the injected CO₂ and, then, the orientation of n-octane becomes more random, which indicates that and CO₂ can enhance the oil recovery and weaken the interaction between n-octane and α-quartz surface. The injection ratio of CO₂ to n-octane is around 3:1, which could achieve the optimal displacement efficiency.

1. Introduction

Most of the giant oil fields around the world are categorized as mature fields [1]. After primary and secondary recovery, more than 50% of the original oil-in-place still stays in a trapped state in the reservoir [1,2,3]. To extract the remaining oil, numerous technologies for enhanced oil recovery (EOR) have been developed, such as CO₂ injection [4,5], surfactant [6], polymer [7], and microbial EOR [8]. Among these technologies, CO₂ EOR has received widespread attention, due to its easy accessibility, low price, and excellent properties [4,5]. For example, the low viscosity and high dissolving capability make supercritical CO₂ a promising candidate for EOR [9].

In CO₂ EOR, the changes of interfacial properties in solubility process are the key to understanding the underlying mechanisms. Gallegos et al. [10] measured the solubility of CO₂ in n-octane and n-decane, and correlated these data using the Peng-Robinson equation of state [11], which could be used to predict the solubility at other temperatures. Nagarajan et al. [12] and Shaver et al. [13] obtained the interfacial tensions and phase compositions of CO₂ and n-decane. Rommerskirchen et al. [14] used a sapphire cell to measure the minimum miscibility pressure (MMP), which is quicker and lower-cost than the slim tube experiment. These fundamental data in bulk state are the basis for better understanding of CO₂ EOR. However, the characteristic features of unconventional reservoir are widely distributed in nanopores and exhibit ultra-low permeability [3]. Under such conditions, Darcy’s law is not applicable, and fluid properties change greatly compared with the conventional reservoir. Pathak et al. [15] found the bubble point pressure of hydrocarbon fluids in nanopores is lower than in the bulk. Alfarge et al. observed the most dominant flow in shale nanopores is diffusion flow [16]. Majumder et al. [17] and Whitby et al. [18] measured the flow of hexane and decane through multiwalled carbon nanotube. They observed that flow velocity is 4~5 orders of magnitude faster than the prediction by conventional theory. For further examining the effects of nano-confinement, molecular dynamics (MD) simulation has been used in recent years. Wang et al. [19] also observed the fast transport of CO₂ and n-octane in organic nanopore separately, which are 1~3 orders of magnitude faster than the prediction of the no-slip Poiseuille equation. Santos et al. [20] and previous work [21] observed that alkanes are displaced by CO₂ from calcite and quartz surface, due to the stronger adsorption of CO₂. Numerous studies [21,22,23] found that CO₂ can enhance the diffusion coefficient of alkanes in nanoslit, which helps oil flow through nanoslit and nanopore throat easier.

Although previous works considerably deepened the understanding of the adsorption of oil and the mechanism of CO₂ EOR, there are still some problems to be solved. (1) How to predict interfacial properties of CO₂ and oil accurately by MD simulation? Compared with experiments, it is more efficient and economical to get the properties from MD simulation. In previous works, Mejia et al. [24] predicted the vapor–liquid interfacial properties by experiment and complemented these predictions using MD simulation and the statistical associating fluid theory (SAFT) equation of state. They pointed out that the accuracy of the MD results relies on the used force fields. Previous work [21] showed using suitable combination rules could couple the different force fields better, which will be further validated in this work. The accurate simulation prediction could also enable us to better understand the solubility process of CO₂ and oil. (2) How about the efficiency of CO₂ EOR? Most existing research focuses on whether CO₂ can displace oil in nanoslits. The displacement efficiency and optimal injection ratio are not considered, but they are essential for cost and production forecasts. To investigate the displacement efficiency, the microstructure in nanoslit still needs to be studied, such as molecular orientation and distribution.

In this work, the interfacial properties of CO₂ and n-octane in solubility process and α-quartz nanoslit are investigated by MD simulations. Firstly, the interfacial properties of CO₂ and n-octane, such as interfacial tension, minimum miscibility pressure and CO₂ solubility, are predicted accurately. Secondly, in order to further understand the solubility process and the change of flow characteristics, detailed diffusion coefficient distribution and radial number density are calculated. Then, the density profiles of CO₂ and n-octane are divided into adsorbed layers and bulk, to investigate the CO₂ displacement efficiency. Finally, the interaction energy and orientation change of both CO₂ and n-octane, under different injection ratios, are evaluated to clarify the adsorption behavior.

2. Method

The schematic configuration of the simulation unit cell is shown in Figure 1. Figure 1a shows the simulation cell for the CO₂ and n-octane binary system. The cell is set as a rectangular box with dimensions Lx = Ly = 6 nm, and Lz = 35 nm, which is large enough to eliminate the system size effects for phase equilibrium and interfacial properties calculation [24,25]. The initial configuration is composed of 1000 n-octane molecules in the middle, and various numbers of CO₂ molecules on both sides. The various numbers of CO₂ in the cell ranges from 1000 to 4000 at intervals of 500, to represent different pressures. The force fields are taken from the work of Zhu et al. [26] for CO₂ and the NERD force field [27] for n-octane. Simulations are performed in the NVT ensemble using the GROMACS 4.6.7 package [28], with periodic boundary conditions imposed in all directions. The leapfrog algorithm [29] with time step of 2 fs is implemented. A cut-off radius of 2 nm is used in the calculation of van der Waals interactions and electrostatic interactions in the real space. The electrostatic interactions are obtained using the particle mesh Ewald (PME) method [30]. According to the experimental data that will be compared later [31], the ensemble temperature is maintained at 343.15 K using the Nosé-Hoover thermostat [32]. To reach equilibrium, each simulation is first run for 20 ns and, then, a 20 ns production run is performed.

Figure 1b shows the simulation cell for CO₂ and n-octane binary mixture confined in an α-quartz nanoslit. The CO₂ and n-octane are confined between two α-quartz surfaces with a size of 5.89 × 5.95 nm². The thickness of α-quartz is 2.16 nm, which is larger than the cut-off distance. All the non-bridging oxygen atoms on the surface are fully protonated, and the surface has no net charge. Considering abundant nanopores in the size range of 3–8 nm in unconventional reservoir [33], the width of nanoslit is 5 nm. The CLAYFF force field [34] is implemented for α-quartz surfaces, which has been widely used to investigate the fluid confinement properties in rock nanopores [20,22]. The α-quartz substrate is fixed, and the hydrogen atoms can move during the simulation, which is constrained by the H–O bond and H–O–Si angle. Due to the fact that about 50% of original oil in place is still trapped in the nanopores [1,3], the number of n-octane in the nanoslit is fixed at 250, which is about 50% of the n-octane fully filling the nanoslit. To investigate the effect of different CO₂ loading on the structure changes and displacement efficiency, the ratios of CO₂ to n-octane change from 0 to 5 at intervals of 1. The various numbers of CO₂ in the nanoslit are 0, 250, 500, 750, and 1000. The long-range Coulomb interactions are calculated by the PME method with a correction for slab-geometry [35]. An 18.68 nm vacuum is introduced in the Z-direction, which is larger than two times length of the nanoslit.

The Lennard-Jones potential [36] is used to describe the van der Waals interactions:

$$V_{LJ}\left(r_{ij}\right)=4{\epsilon }_{ij}\left[{\left(\frac{{\sigma }_{ij}}{r_{ij}}\right)}^{12}-{\left(\frac{{\sigma }_{ij}}{r_{ij}}\right)}^6\right],$$

(1)

where $V_{LJ}$ (kJ/mol) is the Lennard-Jones potential, $r_{ij}$ (nm) is the distance, ${\epsilon }_{ij}$ (kJ/mol) is the potential well describing the interaction intensity between atom i and atom j, and ${\sigma }_{ij}$ (nm) is the distance between the atoms when the interaction potential is zero. The interaction parameters between CO₂ and n-octane are calculated by a modified Lorentz-Berthelot rule (a = 0.9 in Equation (2)), as follows, which is similar to previous work [19]. The parameters of CO₂, n-octane, and α-quartz are listed in Supplementary Information Table S1.

$${\sigma }_{ij}=\frac{{\sigma }_{ii}+{\sigma }_{jj}}{2},\hspace{1em}{\epsilon }_{ij}=a\sqrt{{\epsilon }_{ii}{\epsilon }_{jj}}$$

(2)

3. Results and Discussions

3.1. Solubility Process of CO₂ and n-Octane System

The number density profiles of the CO₂ and n-octane system under different pressure are shown in Figure 2, respectively. Since the pressures are lower than the MMP, two obvious CO₂/n-octane interfaces are formed on both sides of oil phase. The width of interfaces became wider from 3 nm (2.3 MPa) to 6 nm (8.2 MPa) and the ratio of peak density to bulk density (no matter the gas phase or the liquid phase) decreases with pressure, which indicates the interfaces tend to disappear. For clearly showing the intensity of the interfaces, the interfacial tensions (IFT) are calculated by the formulation of Gibbs, as follows [37]:

$$\gamma =\frac{1}{2}\left[P_{zz}-\frac{P_{xx}+P_{yy}}{2}\right]L_z,$$

(3)

where $\gamma$ (N/m) is the IFT, $P_{\alpha \alpha }\left(\alpha =x,y,z\right)$ (Pa) are the diagonal elements of the pressure tensor, and $L_z$ (m) is the length of the simulation box in the Z-direction.

As shown in Figure 3, the IFT decreases with the pressure, and presents a good linear relationship. On the one hand, this trend shows that the intensity of the interface becomes weak. On the other hand, the good linear relationship can be used to predict the MMP. Vanishing interfacial tension method is widely used for predicting the MMP, and the MMP are obtained by linearly extrapolating the IFT decreasing to zero, as shown in Figure 3 [38]. A linear function is used to fit these points. The results show that IFT = −1.369P + 14.786, where P is the pressure. According to the zero value of IFT, the predicted MMP is 10.8 MPa, which is close to the experimental data 11.2 MPa of Liu et al. [39]. Similarly, the predicted MMP (8.63 MPa and 11.0 MPa) at 323.15 K and 348.25 K are also consistent with the experimental value 8.57 MPa (323.15 K) of Yang et al. [40] and 11.5 MPa (348.25 K) of Gallegos et al. [10], as shown in Supplementary Information Figure S1. Therefore, calculating IFT by MD simulations is an efficient and low-cost method to predict the MMP. The MMP prediction for multicomponent oil and the real crude oil still needs further verification.

The solubility of CO₂ in n-octane is also an important property for the mixing process. Figure 4a shows the data of the mole fraction of CO₂ in the n-octane, which is calculated by the number of molecules in the liquid phase (not including the interfaces). It can be seen that the solubility of CO₂ in the n-octane increases as the pressure of the system increases, which agrees well with the experimental data and predicted solubility by equations of state [29]. As shown in Figure 2, n-octane molecules are always concentrated in the liquid phase, and almost no n-octane is dissolved in CO₂. It shows that a large amount of CO₂ dissolved in oil is the main process of mixing, which causes the volume of oil to expand. The volume expansion coefficients (V/V₀) of liquid phase are shown in Figure 4b, which is close to the experimental data [31].

The increase of CO₂ solubility also improves the flow characteristics of oil. Therefore, the diffusion coefficient distribution of CO₂ and n-octane are calculated to observe the change of flow characteristics, using Einstein relation [41] to fit the mean square displacement as follows:

$$D=\underset{t\to \infty }{\mathit{lim}}\frac{\langle {\left|R_i\left(t\right)-R_i\left(0\right)\right|}^2\rangle }{6t},$$

(4)

where D is the diffusion coefficient (m²/s), $R_i\left(t\right)-R_i\left(0\right)$ (m) is the center of mass displacement of the molecules, and t (s) is the simulation time.

As shown in Figure 5a, the diffusion coefficients of CO₂ in the gas phase are an order of magnitude larger than CO₂ in the liquid phase, and have a significant drop at the interfaces. The diffusion coefficients of gas phase decrease with the increase of pressure. In liquid phase, CO₂ is affected by the strong interaction of n-octane, and the diffusion coefficients are slightly larger than n-octane at around 1.6 × 10⁻⁸ m²/s and have no obvious change. For n-octane (Figure 5b), due to the increasing solubility of CO₂, the diffusion coefficients of n-octane increase. Especially in the interface zone, the effect is more obvious. Although there is a little change in the middle of the liquid phase, as the proportion of interface zone increases gradually, the total diffusion coefficient of n-octane increases more obviously.

To further understand the influence of structure changes to diffusion after CO₂ dissolved, the radial number density is calculated, as shown in Figure 6. For CO₂ (Figure 6a,b), the number density only has one peak in the gas phase under low pressure. Beyond the supercritical pressure, the second peak appears in number density, and shows the supercritical properties. In liquid phase, the second peak is more obvious, and the value is larger due to the interaction of n-octane, even at low pressure. Therefore, CO₂ is denser in the liquid phase, and the diffusion coefficient is lower. For n-octane (Figure 6c,d), as the system pressure increases, the surrounding n-octane decreases, and the surrounding CO₂ increases, which is of benefit to weaken the interaction between n-octane molecules. At the same time, the increased diffusion of CO₂ facilitates improved diffusion of n-octane.

3.2. Microstructure of CO₂ and n-Octane in α-Quartz Nanoslit

After exploring the solubility process, the adsorption structure changes of n-octane and CO₂ are investigated, when different mole ratios of CO₂ molecules are injected into the α-quartz nanoslit. Figure 7a shows that the pure n-octane exhibits a strong adsorption on the surface, and almost no n-octane in the middle of the slit. This means most n-octane molecules are in a state of adsorption and low diffusion, which is not conducive to the exploitation. By injecting CO₂, this situation could be changed. After adding CO₂ into the nanoslit, CO₂ adsorbs on the α-quartz surface, which is closer than n-octane. The adsorbed n-octane molecules are displaced to the middle of the slit by the CO₂ (the detailed interaction energy of n-octane and CO₂ on α-quartz surface are shown in Supplementary Information Figure S2). For the ratio of 1:1, the adsorbed n-octane molecules decrease slightly. Meanwhile, the multilayer adsorbed layers still exist, and 54% of n-octane molecules are in the bulk (not adsorbed) state in the zone from −1.65 nm to 1.65 nm. When increasing the ratio to 3:1, the second adsorbed layer almost disappears. Seventy-three percent of n-octane molecules are in bulk state within the same zone. However, when the ratio goes up to 4:1, the adsorption state has no obvious change, except the CO₂ increase. The molecules in bulk state are 77% in the same zone. Although a lot of CO₂ molecules are added, the n-octane molecules in bulk state only increase 4%. According to the density profile, if only the displacement efficiency is considered, the optimal injection ratio is around 3:1 under this condition. Therefore, although high CO₂ injection is of benefit to oil recovery, the economic efficiency still needs to be considered.

Under nano-confinement, molecules always have a preferential orientation at the adsorption interfaces (i.e., two obvious adsorbed layers) due to asymmetric forces. To analyze the effect of α-quartz nanoslit on the orientation of CO₂ and n-octane, the orientation distribution of them in first and second adsorbed layers (Figure 7) are examined respectively, as shown in Figure 8, by calculating the angle θ between molecular vector (O–O vector for CO₂ and CH₃–CH₃ vector for n-octane) and a reference vector perpendicular to the α-quartz surface. When the molecule is parallel to the α-quartz surface, θ will be close to 90°, and when the molecule is perpendicular to the surface, θ will tend to 0° or 180°. An orange dash line is shown in every picture to present the orientation distribution in bulk state. In the first adsorbed layer, both CO₂ and n-octane prefer to be parallel to the α-quartz surface, due to the attraction of α-quartz surface. This behavior is little affected by CO₂ injection, which is similar to the behavior on the calcite surface [18]. Although most n-octane molecules maintain their original adsorption orientation, most of the area of the α-quartz surface is occupied by CO₂, according to the density profile (Figure 7). The n-octane in the first layer is displaced to the second layer or the middle of nanoslit. In the second adsorbed layer, the orientation distribution of CO₂ is almost the same as the bulk state, which implies that CO₂ is weakly affected by the surface. For n-octane, when CO₂ is not injected, the orientation is mainly around 45° and 135°. After injection of CO₂, the orientation of n-octane tends to be random, which suggests that CO₂ weakens the interaction between n-octane and the α-quartz surface, and more n-octane molecules become bulk state. This phenomenon is also consistent with the gradual disappearance of the second adsorption layer in the density profile (Figure 7). Therefore, CO₂ injection can help to displace the oil in adsorbed state and enhance the oil recovery.

4. Conclusions

CO₂ EOR plays an important role in tertiary oil recovery and has attracted growing research interest due to its excellent properties, such as low viscosity and easy accessibility. Owing to the wide distribution of nanopores in unconventional reservoirs, confinement effects must be considered, and have significant impact on the interfacial properties. In this work, a series of MD simulations have been performed to investigate the interfacial properties of CO₂ and n-octane in solubility process and α-quartz nanoslit. In the solubility process, CO₂ dissolves into n-octane and causes the volumetric expansion of n-octane and the fading of interfaces, which leads to the interfacial tension decreasing linearly with pressure. A linear function is used to fit the interfacial tension and obtain the MMP by vanishing interfacial tension method. The MD-predicted MMP and CO₂ solubility are in agreement with the experimental data, quantitatively. To further understand the improvement of flow characteristics, the diffusion coefficient distribution of n-octane shows that the diffusion is mainly improved at the interface. Although there is a little improvement in the middle of the liquid phase, the total diffusion coefficient increases more obviously as the proportion of interface zone increases gradually. The number density of n-octane indicates that the improvement of its diffusion is due to the increase in surrounding CO₂, which weakens the interaction between n-octane molecules. After understanding the solubility process, the adsorption structure changes of n-octane and CO₂ in α-quartz nanoslit, and the optimal injected ratio, have been investigated. The adsorbed n-octane molecules are displaced from the surface by injected CO₂, which is beneficial to enhancing oil recovery. Considering the displacement efficiency, the optimal injection ratio is around 3:1 under this condition. Then, the orientation distributions of CO₂ and n-octane have been observed to determine the adsorption state. The orientation of both CO₂ and n-octane is concentrated on 90° in the adsorbed layer closest to the surface. In the second layer, the orientation of n-octane tends to be random after injection of CO₂. All observed phenomena, such as increased diffusion, displacement of oil, and more random orientation of oil, are propitious to CO₂ EOR. Therefore, this work has systematically studied the whole process, from solubility process to oil displacement, in nanoslit, and is helpful to understanding the mechanism of CO₂ EOR at microscales. In future work, other types of oil, such as naphthenic hydrocarbon, aromatic hydrocarbon, and real crude oil, need to be further studied. (1) The applicability of predicted interface properties through MD simulation still needs to be verified for different kinds of oil. Especially, use of the vanishing interfacial tension method to predict MMP in MD simulations. (2) The different interactions between crude oil and rock surface lead to significantly different adsorption situations. For various adsorption states, the optimal CO₂ injection ratio still needs to be explored.