Molecular dynamics simulation of surfactant reducing MMP between CH₄ and n-decane

Abstract

Reinjecting produced methane offers cost-efficiency and environmental benefits for enhances oil recovery. High minimum miscibility pressure (MMP) in methane-oil systems poses a challenge. To overcome this, researchers are increasingly focusing on using surfactants to reduce MMP, thus enhancing the effectiveness of methane injections for oil recovery. This study investigated the impact of pressure and temperature on the equilibrium interfacial tension of the CH4+n-decane system using molecular dynamics simulations and the vanishing interfacial tension technique. The primary goal was to assess the potential of surfactants in lowering MMP. Among four tested surfactants, ME-6 exhibited the most promise by reducing MMP by 14.10% at 373 K. Key findings include that the addition of ME-6 enriching CH4 at the interface, enhancing its solubility in n-decane, improving n-decane diffusion capacity, CH4 weakens n-decane interactions and strengthens its own interaction with n-decane. As the difference in interactions of n-decane with ME-6's ends decreases, the system trends towards a mixed phase. This research sets the stage for broader applications of mixed-phase methane injection in reservoirs, with the potential for reduced gas flaring and environmental benefits.

1. Introduction

Petroleum fuels continue to serve as essential resources across various industrial sectors and remain pivotal to global energy demands [1,2]. In the current stage, after primary and secondary oil recovery, only one-third of the original oil in place (OOIP) has been extracted from oil fields, leaving 70% of OOIP still within reservoirs [3,4]. Furthermore, the challenges associated with petroleum exploration and development are escalating. Particularly, low-permeability reservoirs pose unique difficulties due to their naturally low productivity, unfavorable reservoir properties, low permeability, and challenging development processes. Consequently, gas injection enhanced oil recovery (EOR) has become the most extensively utilized method for extracting light and intermediate crude oil reservoirs, potentially elevating oil recovery rates by 10%–25% [[5], [6], [7]]. Among the injected gas agent, CO₂ has demonstrated the most effective oil-enhancing capabilities. However, practical oilfield conditions often present challenges such as insufficient gas sources, high costs, and susceptibility to corrosion [8]. In contrast, using hydrocarbon gases as injection media can circumvent these drawbacks and remain unaffected by low reservoir permeability and formation water salinity [9]. For hydrocarbon gases, utilizing naturally produced gas as an injection medium not only mitigates the environmental impact of gas combustion but also supports sustainable development. If further achieving phase mixing with crude oil, the detrimental influence of interfacial tension (IFT) can be eliminated, optimizing the displacement of remaining oil within reservoirs, and thereby enhancing crude oil recovery rates.

However, for certain high-temperature reservoirs and shallow oil reservoirs, reaching the minimum miscibility pressure (MMP) between the gas and oil phases can sometimes lead to pressures exceeding the reservoir fracture pressure. Consequently, achieving phase mixing becomes challenging for such reservoirs [10]. Furthermore, the majority of miscible hydrocarbon gas injection methods are implemented within particular reservoir parameters. These parameters encompass reservoir temperatures (308 K–344 K), reservoir depths (128m–2045 m), and light crude oil (34–44 API) [11]. In such scenarios, the introduction of surfactants into the hydrocarbon-oil system can serve to reduce interfacial tension (IFT), consequently lowering the MMP between gas and oil. The change in the system's behavior, as it shifts from immiscible to partially miscible or nearly miscible injection conditions, widens the scope of applicability for miscible hydrocarbon gas injection techniques across various types of reservoirs. Hence, the reduction of MMP through the addition of surfactants to the gas-liquid biphasic system holds significant importance. This approach has the potential to enhance crude oil recovery and is crucial for expanding the scope of miscible hydrocarbon gas injection techniques to various reservoir types.

Because of its enhanced solvency and the quadrupole-quadrupole interactions occurring between carbon dioxide molecules, as opposed to the dipole interactions between methane molecules, carbon dioxide can achieve phase mixing at lower pressure [12]. This is primarily due to the shorter operating distances involved in CO₂ interactions. In contrast, the MMP between natural gas (CH₄) and crude oil is considerably higher. In the study of Hawthorne et al. [13], a comparison was made between the minimum miscibility pressures (MMP) of CH₄+oil systems and CO₂+oil systems, utilizing various crude oil compositions. The results indicated that the MMP of CH₄ is 2–3 times greater than that of CO₂. Dong et al. [14] conducted to study on the interfacial tension (IFT) of CH₄+n-decane systems and CH₄+CO₂+n-decane systems by molecular dynamics simulations. Their research indicated that the interaction between n-decane and CO₂ is notably stronger than that between n-decane and CH₄. The disparity in intermolecular forces between the two phases gives rise to interfacial tension. Crude oil molecules possess higher intermolecular forces due to the presence of permanent dipole forces and hydrogen bonding, while CH₄ molecules exhibit weaker van der Waals forces [15]. As a result, there exists a significant difference in the interaction forces between CH₄ and crude oil molecules, leading to higher interfacial tension. When there is a substantial difference in molecular forces between two substances, their interfacial tension increases, subsequently resulting in higher MMP. However, the elevated MMP levels pose challenges in achieving phase mixing between gas and liquid phases under in-situ reservoir conditions, leading to higher interfacial tension and increased residual oil saturation. Consequently, research on reducing the MMP of the CH₄-oil system is limited and inherently more challenging.

Many researchers have investigated the reduction of the MMP of the CO₂-oil system by surfactants. Guo et al. [16] synthesized a surfactant known as CAE and investigated its effect on reducing MMP through capillary tube experiments conducted at a constant temperature of 358 K while varying the pressure from 18 to 30 MPa. Their findings revealed that the addition of 0.2 wt% CAE before gas injection resulted in a 6.1 MPa reduction in MMP (a 22% decrease). Luo et al. [15] employed the Vanishing Interfacial Tension (VIT) technique was utilized to explore how nonionic surfactants impact the reduction of IFT and MMP within the CO₂-oil system. Their study demonstrated that the incorporation of 0.6 wt% propoxylated surfactant into CO₂ could lower MMP from 19.1 MPa to 13.8 MPa, representing a 27.75% reduction. Zhang et al. [17] employed ethanol as a co-solvent and utilized the VIT technique to study the effects of four distinct surfactants (2 EH-PO5-EO9, AOT, NP-9, TXIB) on reducing IFT and MMP in the CO₂-oil system. Their research indicated that in synergy with ethanol, AOT and TXIB surfactants exhibited more pronounced MMP reduction effects, achieving reductions of 7.02% and 11.85%, respectively. The above results collectively highlight that the addition of surfactants can lead to varying degrees of MMP reduction in the CO₂-oil system. Reducing the MMP in the methane and crude oil system, Mohamed Almobarak et al. [18] investigated the reduction of MMP using chemical agents in the CH₄-oil system, aiming to facilitate the injection of miscible hydrocarbon gas into high-temperature reservoirs through the use of chemical agents. They tested four different chemical additives (SOLOTERRA ME-1, SOLOTERRA ME-6, ISOFOL 16, and MARLIPAL O13) to assess their impact on lowering the Minimum Miscible Pressure. Their findings indicated that at 373 K, the utilization of a 5 wt% surfactant-based chemical, specifically SOLOTERRA ME-6, demonstrated the potential to reduce MMP by approximately 9%. Subsequently, building upon the previous study, Mohamed Almobarak et al. [19] introduced 20 mol% CO₂ into the system, resulting in a 13% reduction in MMP.

Based on the comprehensive study, it's clear that the MMP in the natural gas/CH₄-oil system is notably higher than in the CO₂-oil system. Furthermore, when compared to CH₄, adding surfactants to lower MMP in the CO₂-oil system has a more significant impact. In certain reservoirs, the pressure needed to reach the minimum MMP between gas and oil phases may exceed the formation's fracturing pressure. Therefore, there is an urgent need to explore feasible surfactants that can substantially decrease the MMP in the natural gas-oil system, thus expanding the applicability of miscible natural gas injection techniques to a wider range of potential reservoirs. Natural gas is usually a blend of different hydrocarbon gases, and the inclusion of ethane or propane tends to decrease the MMP between gas and liquid phase. Additionally, crude oil is a complex mixture with diverse components and varying proportions [13,20]. Hence, a strategy involving the use of pure CH₄ as a substitute for natural gas is viable, followed by the establishment of a CH₄-n-decane system molecular dynamics model. In contrast to experimental studies, molecular simulation methods offer advantages such as lower costs and fewer limitations, enabling the direct provision of microscopic insights into interfacial phenomena.

This study aims to explore the effectiveness of various surfactants in reducing the interfacial tension (IFT) between gas and liquid phases within the methane-n-decane system. This reduction in IFT is intended to facilitate the achievement of a miscible gas-liquid phase and, consequently, decrease the system's Minimum Miscibility Pressure (MMP). Through molecular simulations, this research aims to uncover the underlying microscopic mechanisms behind the reduction of MMP. Section 2 introduces the molecular models established in this study, as well as the setup of the force field and parameters. In Section 3, a comparison and explanation of interfacial properties and MMP among four distinct surfactants are presented to identify the most effective one. In Section 4, an analysis of the density profile, diffusion properties, and intermolecular forces of the chosen surfactant at different pressures and temperatures is conducted to elucidate the microscale mechanisms through which the surfactant reduces MMP. Section 5 provides the concluding remarks for this study.

2. Model and simulation method

2.1. Model building

The molecular dynamics simulations in this study were conducted using the open-source software LAMMPS [21], employing different models to represent the molecules involved.

The n-decane molecule was modeled using the NERD model [22], where individual atoms were used to represent CH₃ and CH₂ groups. This model yielded gas-liquid equilibrium curves that closely matched experimental data.

CH₄ molecules were modeled using the TraPPE-UA model [23], which utilizes a single atom to represent CH₄.

Small-molecule compounds typically consist of fewer atoms, with weaker bonds and relatively smaller intermolecular forces. Such compounds often possess multiple functional groups, such as hydroxyl, acyl, amino, carbonyl, etc. These functional groups can introduce a degree of polarity to the compound, facilitating both polar and non-polar interactions during gas dissolution, thereby enhancing the gas solubility. In light of this, this study chose four chemicals to decrease the IFT in the CH₄-n-decane system. These include two non-ionic alkoxylate surfactants (SOLOTERRA ME-1 and ME-6) and two lipophilic alcohols (Fatty alcohol polyoxypropylene ether (SPO₅), and 2-Butoxy ethanol). The molecular structures of these selected surfactants are schematically shown in Fig. 1(a–d). The OPLS-UA model [24] was employed for all four chemical compounds, using individual atoms to represent CH₃ and CH₂ groups in both alkanes and ethers.

Fig. 1.

Schematic molecular structures of surfactants.

represents C atoms, represents H atoms, represents O atoms.

The periodic boundary molecular models established in this study consist of a gas-liquid system composed of a central liquid alkane phase flanked by gas phases on both sides. An equal number of surfactant molecules are added at the gas-liquid interface on both sides. The simulation cell dimensions are 50 Å × 50 Å × 300 Å. The basic system models established include a binary system of CH₄+n-decane, as well as a ternary system of CH₄+surfactant + n-decane, as shown in Fig. 2(a–e). In this figure, region A represents methane, region B represents n-decane, and region C represents the surfactant. The system's pressure is regulated by varying the amount of CH₄ molecules added. The model contains over 10,000 atoms, with a constant number of 800 n-decane molecules (consisting of 8000 atoms) and a base number of 30 surfactant molecules (15 in each left and right region). The remaining molecules are CH₄. The visualization of the system is created using the OVITO software [25].

Fig. 2.

Molecular Dynamics Model Diagrams: (a) CH₄+n-decane system model, (b) CH₄+SOLOTERRA ME-1+n-decane system model, (c) CH₄+SOLOTERRA ME-6+n-decane system model, (d) CH₄+SPO₅+n-decane system model, (e) CH₄+2-Butoxy ethanol + n-decane system model.

In this study, to keep a consistent temperature during the entire MD simulation, the Nosé-Hoover thermostat was employed for temperature control [26,27]. Utilizing the particle-particle-particle-mesh (PPPM) summation method, the long-range electrostatic interactions were computed with a precision of 1.0 × 10⁻⁴ [28]. To reduce truncation and system size influences in interface property calculations, a unit cell of 5 × 5 nm² was selected parallel to the interface direction and a cutoff radius of 2 nm (Approx.6σ) was set for non-bonded interactions [[29], [30], [31]]. The simulation time step was set to 1 fs. The entire simulation duration included a 500 ps equilibration period, a 10 ns relaxation period, and a 20 ns production period. Statistical analysis was performed every 10 ps to calculate the system's IFT.

The formula for calculating IFT is given by equation (1) [[32], [33], [34]].

$$\mathrm{\gamma }=\frac{1}{2}{\int }_0^{L_z}\left(P_N\left(z\right)-P_T\left(z\right)\right)\text{dz}=\frac{1}{2}\left[P_{zz}-\frac{P_{xx}+P_{yy}}{2}\right]L_z$$ (1)

where $\mathrm{\gamma }$ represents the IFT, $P_N\left(z\right)$ and $P_T\left(z\right)$ denote the normal and tangential pressures, $P_{\alpha \alpha }\left(\alpha =x,y,z\right)$ signifies the diagonal elements of the pressure tensor, and $L_{\mathrm{z}}$ represents the length of the simulated system along the z-direction.

Atomic diffusion behavior is characterized by the time-dependent change in mean square displacement (MSD) [35].There is the MSD calculation formula (2):

$$\text{MSD}\left(\mathrm{t}\right)=⟨{\left|r_i\left(t\right)-r_i\left(0\right)\right|}^2⟩$$ (2)

Here, $r_i\left(0\right)$ denotes the initial position of atom $i$, and $r_i\left(t\right)$ denotes the position of atom $i$ at time t.

To examine fluid molecule aggregation and analyze fluid microstructure, use the radial distribution function. This function reflects the likelihood of locating another atom at a specific distance from a given atom and can be seen as the ratio of local density to the system's overall density within a defined region [36]. The expression is given by the following equation (3):

$$g\left(r\right)=\frac{dN}{\rho 4\pi r^{2}dr}$$ (3)

In which, $N$ represents the number of atoms, $r$ stands for the distance between two atoms, and $\rho$ denotes the system density.

2.2. Force field and parameters

One of the purposes of conducting molecular dynamics simulations is to obtain the potential energy functions for different systems. The potential energy function that describes the interatomic interactions within a system is referred to as a force field. In general, a molecular force field can be considered as a sum of various potentials, primarily including molecular interaction potentials such as bond stretching, bond angle bending, and dihedral angle torsional potentials, along with van der Waals and Coulombic electrostatic potentials, all of which are detailed in equations (4), (5), (6), (7), (8), (9), (10), (11).

$$U_{total}=U_{stretch}+U_{bend}+U_{torsion}+U_{coul}+U_{vdw}$$ (4)

In this study, bond stretching and bond angle bending potentials are represented using harmonic terms, while the dihedral angle torsional potential employs the OPLS (Optimized Potentials for Liquid Simulations) functional form. The bond stretching potential is defined as follows:

$$U_{stretch}=K_r{\left(r-r_0\right)}^2$$ (5)

The bond angle bending potential is defined as follows:

$$U_{bend}=K_{\theta }{\left(\theta -{\theta }_0\right)}^2$$ (6)

The torsional potential energy is expressed by the following formula:

$$U_{torsion}=V_0+V_1\left(1+\cos \phi \right)+V_2\left[1-\cos \left(2\phi \right)\right]+V_3\left[1-\cos \left(3\phi \right)\right]$$ (7)

where $r$, $r_0$ denote the equilibrium bond length and known bond length, ${\theta }_0$, $\theta$ stand for the known bond angle and equilibrium bond angle, $K_{\theta }$, $K_r$, and $V_n\left(n=0,1,2,3\right)$ represent the bond angle bending potential, constants for bond stretch potential, and dihedral angle torsion potential.

The Coulomb potential energy can be derived from Coulomb's law, as shown in the following formula:

$$U_{coul}=\frac{q_i{q}_j}{4\pi {\epsilon }_0{r}_{ij}}$$ (8)

where $q_i$ ($q_j$) represents the charge of atom i (j), ${\epsilon }_0$ is the dielectric constant, and $r_{ij}$ is the distance between atom i and atom j.

The van der Waals potential energy can be obtained from the 12-6 Lennard-Jones potential function, as shown in the following formula:

$$U_{vdw}=4{\epsilon }_{ij}\left[{\left(\frac{{\sigma }_{ij}}{r_{ij}}\right)}^{12}-{\left(\frac{{\sigma }_{ij}}{r_{ij}}\right)}^6\right]$$ (9)

where, the short-range interactions are characterized by ${\epsilon }_{ij}$, representing the well depth, and ${\sigma }_{ij}$, which denotes the core diameter of the Lennard-Jones potential.

Mixing rules are employed to calculate the Lennard-Jones (L-J) parameters for various pairs of atoms, with the commonly used Lorentz-Berthelot mixing rules [37], as shown in the following formula:

$${\epsilon }_{ij}=\sqrt{{\epsilon }_i{\epsilon }_j}$$ (10)

$${\sigma }_{ij}=\frac{{\sigma }_i+{\sigma }_j}{2}$$ (11)

Table 1 presents the parameters of each force field utilized in this study.

Table 1.

Force field parameters for each molecule.

Molecular	Atom	(nm)	(KJ·mol−1)	(e)	Model
n-decane	CH3	0.3910	0.8647	0	NERD [22]
	CH2	0.3930	0.3808	0
CH4	CH4	0.3730	1.2300	0	TraPPE-UA [23]
SOLOTERRA ME-6	CH3 (in C–C bond)	0.3910	0.6694	0	OPLS-UA [24]
	CH2 (in C–C bond)	0.3905	0.4937	0
	CH2 (in O–C bond)	0.3800	0.4937	0.250
	CH2 (in C–OH bond)	0.3905	0.4937	0.265
	C (in O–C bond)	0.3500	0.2761	0.170
	O (in O–C bond)	0.3000	0.7112	−0.500
	O (in O–H bond)	0.3120	0.7112	−0.683
	H (in C–C–H bond)	0.2500	0.1255	0.030
	H (in O–H bond)	0	0	0.418
SOLOTERRA ME-1	CH3 (in C–C bond)	0.3910	0.6694	0
	CH2 (in C–C bond)	0.3905	0.4937	0
	CH2 (in O–C bond)	0.3800	0.4937	0.250
	CH2 (in C–OH bond)	0.3905	0.4937	0.265
	C (in O–C bond)	0.3500	0.2761	0.170
	O (in O–C bond)	0.3000	0.7112	−0.500
	O (in O–H bond)	0.3120	0.7112	−0.683
	H (in C–C–H bond)	0.2500	0.1255	0.030
	H (in O–H bond)	0	0	0.418
Fatty alcohol polyoxypropylene ether （SPO5）	CH3 (in C–C bond)	0.3910	0.6694	0
	CH2 (in C–C bond)	0.3905	0.4937	0
	CH2 (in O–C bond)	0.3800	0.4937	0.250
	C (in C–OH bond)	0.3500	0.2761	0.205
	C (in O–C bond)	0.3500	0.2761	0.170
	O (in O–C bond)	0.3000	0.7112	−0.500
	O (in O–H bond)	0.3120	0.7112	−0.683
	H (in C–C–H bond)	0.2500	0.1255	0.030
	H (in O–C–H bond)	0.2500	0.1255	0.040
	H (in O–H bond)	0	0	0.418
2-Butoxy ethanol	CH3 (in C–C bond)	0.3910	0.6694	0
	CH2 (in C–C bond)	0.3905	0.4937	0
	CH2 (in O–C bond)	0.3800	0.4937	0.250
	CH2 (in C–OH bond)	0.3905	0.4937	0.265
	O (in O–H bond)	0.3120	0.7112	−0.683
	H (in O–H bond)	0	0	0.418

3. Surfactants preferred

3.1. Force field verification

For assessing the Minimum Miscibility Pressure (MMP) in the CH₄-n-decane system, this study utilized the well-established Vanishing Interfacial Tension (VIT) method, which is commonly employed for MMP determination [[38], [39], [40]]. In the VIT method, a constant temperature is maintained while measuring the equilibrium Interfacial Tension (IFT) between the gas and crude oil at different pressure levels. For estimating bulk properties, the study uses the Volume Translated Predictive Peng-Robinson 1978 (VT-PPR78) [41,42] equation of state (EoS) in conjunction with standard van der Waals one-fluid mixing rules and a linear mixing rule for volume correction [43]. Supplementing the simulated data and calculating interfacial properties, the study employs theoretical modeling that combines the VT-PPR78 equation of state (EoS) with density gradient theory (DGT). The Minimum Miscibility Pressure (MMP), denoting the minimum pressure needed to attain phase miscibility, is represented by the point where the estimated curve intersects with the pressure axis [44]. The Vapor-Liquid Equilibrium Interfacial Tension (VIT) is rooted in the concept that miscibility is achieved when the interfacial tension (IFT) between two distinct phases is eradicated.

In our previous work [14], Molecular Dynamics (MD) simulations were utilized to investigate the IFT of the CH₄+n-decane mixture system at various temperatures. The MD simulation results, as depicted in Fig. 3, closely matched the experimental data presented by Pereira [45] and the MD simulation outcomes by Choudhary et al. [43]. Therefore, utilizing the same MD model and molecular force field, we conducted simulations to estimate the IFT at 373.0 K. Additionally, estimations obtained through the Diffuse Gradient Theory (DGT) and the Volume-Translated Peng-Robinson 1978 Equation of State (VTPPR78 EoS) are depicted as lines in the graph. From Fig. 3, it can be observed that at a temperature of 373.0 K, the Interfacial Tension (IFT) measured using MD aligns with the results obtained from previous studies. Consistent with findings in the literature, the IFT in the CH₄+n-decane system diminishes with an increase in system pressure [41,43]. Under low pressures, increasing temperature results in a more significant decrease in the system's IFT, whereas at high pressures, the IFT remains stable. This study utilized a molecular force field that is suitable for the investigated system, along with the specified parameters and settings.

Fig. 3.

Interfacial tension (IFT) of CH₄+n-decane at different temperatures.

represents the results from MD simulations ( 313.3 K, 343.2 K, 373.0 K, 392.6 K) and the estimates obtained using the DGT with VT-PPR78 EoS are shown as lines ( 313.3 K, x 343.2 K, 373.0 K, 392.6 K). Experimental results by Pereira [45] are depicted as ( 313.3 K, 343.2 K, 392.6 K). Displays the MD simulation results by Choudhary et al. [43] ( 313.3 K, 343.2 K, 392.6 K).

3.2. Density profile

Fig. 4 depicts the density distribution of n-decane and methane along the vertical interface direction in the n-decane + methane system at 373.0 K and 11.09 MPa after reaching equilibrium with the addition of different surfactants. The dashed lines represent the density distribution without surfactants, while the solid lines represent the density distribution with surfactants. Figure 4a shows the density distribution of n-decane, Fig. 4(b) shows the density distribution of CH₄. The graph clearly illustrates that the introduction of surfactants causes a reduction in the density of n-decane, leading to an expansion of the volume occupied by the liquid phase. The CH₄ phase experiences an increase in density, resulting in a thicker phase interface. This indicates that the incorporation of surfactants facilitates better diffusion of CH₄ molecules into the n-decane phase, enhancing the degree of mixing and increasing the mixed phase volume. Notably, surfactant ME-6 demonstrates a more pronounced effect in reducing n-decane phase density and increasing CH₄ phase density.

Fig. 4.

Number density distribution of CH₄/n-decane with different surfactants added (373.0 K, 11.09 MPa).

Fig. 5(a–e) illustrates the impact of four types of surfactants (2-Butoxy ethanol, SPO₅, ME-1, and ME-6) on the phase behavior of the CH₄ + n-decane system. From the graph, it is evident that under the conditions of 373.0 K and 27.51 MPa, without the addition of surfactants, there is a distinct interface on both sides of the CH₄ + n-decane system. The CH₄ and n-decane components are separated into two distinct phases and have not reached complete mixing. Upon the addition of these four different surfactants, the volume of the mixed phase in the system increases, and the degree of mixing improves to varying extents. Particularly, with the inclusion of surfactant ME-6, the interface between CH₄ and n-decane is no longer discernible in the system, essentially achieving a fully mixed state for the CH₄ + n-decane system under the influence of ME-6.

Fig. 5.

Effect of Four Surfactants on the Phase Behavior of CH₄ + n-decane System at 373.0 K, 27.51 MPa.

The density distribution curves in Fig. 6(a and b) also support this observation. After the addition of surfactant ME-6, the density of the n-decane phase decreases, while the density of the CH₄ phase increases. Furthermore, both the n-decane and CH₄ phases are uniformly distributed throughout the system's container, approaching an average density. This indicates a significant increase in the degree of mixing between the n-decane and CH₄ phases, thus confirming the achievement of a mixed phase state in the system.

Fig. 6.

Effect of Surfactant ME-6 on the Density Distribution Curve of CH₄ + n-decane System at 373.0 K, 27.51 MPa.

3.3. Diffusion properties

To examine the diffusion characteristics of n-decane and CH₄ under various surfactant conditions as well as without surfactants, the mean square displacement (MSD) of these substances was determined at 373.0 K and 22.84 MPa. As shown in Figure 7a, it is noticeable that the diffusion rate of n-decane increases to varying degrees in the presence of different surfactants. As the diffusion rate of n-decane increases, a greater number of n-decane molecules occupy the adsorption sites initially held by methane molecules. This restriction limits the free movement space of methane molecules, resulting in increased steric hindrance for CH₄ molecules. Therefore, the diffusion rate of CH₄ decreases after the addition of surfactants (as shown in Fig. 7(b)). Among these four surfactants (2-Butoxy ethanol, SPO₅, ME-1, and ME-6), surfactant ME-6 is particularly noteworthy for significantly enhancing the diffusion rate of n-decane while diminishing the diffusion rate of CH₄.

Fig. 7.

MSD of n-decane/CH₄ at different surfactants at 373.0 K, 22.84 MPa.

3.4. Intermolecular forces

To systematically identify the most effective surfactant on a microscopic level after adding different surfactants, the radial distribution functions (g(r)) between different molecules were investigated for various surfactant conditions (2-Butoxy ethanol, SPO₅, ME-1, and ME-6). Figure 8a presents the radial distribution function depicts the interactions among n-decane molecules, while Fig. 8(b) illustrates the radial distribution function depicts the interactions between n-decane and methane molecules.

Fig. 8.

Radial distribution function of n-decane/CH₄ before and after the addition of ME-6 (373.0 K，11.09 MPa).

From Figure 8a, it can be observed that under the same conditions (373.0 K, 11.09 MPa), the peak values of g(r) for different surfactants are lower than that of the system without surfactant, indicating a reduction in the interaction force between n-decane molecules. Among these conditions, the addition of surfactant ME-6 exhibits the most significant decrease in peak value, indicating the strongest reduction in interaction force between n-decane molecules. Fig. 8(b) demonstrates that under the same conditions (373.0 K, 11.09 MPa), the peak values of g(r) with different surfactants are higher than that of the system without surfactant. This suggests that the addition of surfactants enhances the interaction forces between methane and n-decane molecules. Among these conditions, surfactant ME-6 shows the highest increase in peak value, indicating the most pronounced enhancement in the interaction force between methane and n-decane molecules.

After the introduction of surfactants, the distance between n-decane molecules increases, while the separation between methane and n-decane molecules decreases. This is attributed to the distribution of surfactants at the oil-gas interface, causing n-decane to be surrounded by methane molecules. As a result, the quantity of dissolved methane in n-decane increases, leading to improved mixing between methane and n-decane molecules, thus enhancing the phase mixing effect between them.

3.5. Interfacial tension and miscibility pressure

During the force field validation, the IFT of the CH₄ + n-decane system at 373.0 K was determined. Additionally, utilizing estimates obtained from the DGT and VTPPR78 EoS methods, the MMP for the system at that temperature was derived in the absence of surfactants. In this system, various surfactant molecules (ME-1, ME-6, SPO₅, and 2-Butoxy ethanol) were separately introduced, as depicted in Fig. 9. The IFT reduction results for the CH₄ + n-decane system with these four surfactants at 373.0 K were obtained, and the corresponding MMP values for different surfactant systems were calculated (as shown in Table 2). From the figures and tables, it can be observed that at 373.0 K, the introduction of these four surfactants into the CH₄ + n-decane system results in a decrease in the MMP of the CH₄-n-decane system. The surfactants 2-Butoxy ethanol, SPO₅, ME-1, and ME-6 lead to reductions in the system's MMP by 3.08%, 7.13%, 11.24%, and 14.10%, respectively. While the effect of 2-Butoxy ethanol on reducing the system's IFT is not significant, the addition of ME-6 surfactant results in a notable decrease in the IFT of the CH₄ + n-decane system. As a result, the system's MMP is lowered from 32.12 MPa to 27.59 MPa, marking a reduction of 14.10%.

Fig. 9.

Interfacial Tension (IFT) of CH₄ + Surfactant + n-decane System at 373.0 K. The symbols represent the results from the MD simulations, and the estimates obtained using the DGT with VTPPR78 EoS are depicted as lines.

Table 2.

MMP of CH₄ + different surfactants + n-decane system at 373.0 K.

Chemical	MMP (MPa)	MMP reduction
Base case	32.12	–
2-Butoxy ethanol	31.12	3.08%
SPO5	29.83	7.13%
ME-1	28.51	11.24%
ME-6	27.59	14.10%

Comparing ME-1, ME-6, SPO₅, and 2-Butoxy ethanol surfactants at 373.0 K across various aspects such as Density Profiles, Diffusion Properties, Intermolecular Forces, Interfacial Tension, and Miscibility Pressure, the results indicate that ME-6 surfactant has more favorable effects. It reduces the density of the n-decane phase while increasing the density of the CH₄ phase. It effectively enhances the n-decane diffusion rate while diminishing the CH₄ diffusion rate. The addition of ME-6 surfactant diminishes intermolecular forces between n-decane molecules and significantly augments forces between CH₄ and n-decane molecules. Furthermore, ME-6 surfactant notably reduces the Interfacial Tension (IFT) of the CH₄ + n-decane system, leading to a 14.10% reduction in the system's Minimum Miscibility Pressure (MMP). In summary, ME-6 surfactant shows potential in decreasing the IFT of the gas-liquid phases in the methane-n-decane system, facilitating phase mixing and ultimately lowering the MMP of the system. The subsequent section will delve into an analysis of the interfacial properties of ME-6 surfactant in the CH₄ + n-decane system across different pressures and temperatures. It will also explore the microscopic mechanism behind the reduction in interfacial tension caused by ME-6 surfactant.

4. Microscopic mechanisms at different temperatures and pressures

4.1. Interfacial properties of CH₄+ME-6+n-decane system under different pressure

4.1.1. Density profile

Under different pressure conditions, Fig. 10(a–e) illustrates the equilibrium state of CH₄ + ME-6 + n-decane at 373.0 K. Initially, methane molecules congregate at the interface between the two phases. As pressure increases, the number of molecules at the interface grows, with methane molecules entering the n-decane phase. The mass density distribution curves clearly showcase the interface structure between n-alkanes and methane. Once the system attains its ultimate equilibrium at 373.0 K, Fig. 11(a and b) depicts the distribution of density along the vertical interface direction of n-decane and CH₄. Dashed lines represent density distribution in a system without surfactants, while solid lines depict density distribution in the system with the addition of ME-6 surfactant. As system pressure rises, a portion of CH₄ dissolves into the n-decane phase, leading to a reduction in n-decane density and gradual expansion of the liquid phase. Simultaneously, certain n-decane molecules evaporate into the gas phase, increasing gas phase density and causing the phase interface to gradually thicken. Particularly in systems with added surfactants, the density of methane at the interface decreases, further enhancing the thickness of the phase interface.

Fig. 10.

Equilibrium State of the CH₄ + ME-6 + n-decane System at 373.0 K.

Fig. 11.

Number density distribution of CH₄/n-decane at different pressures (373.0 K).

4.1.2. Diffusion properties

In order to investigate the diffusion characteristics of n-decane and CH₄ with or without the addition of ME-6 surfactant, the Mean Square Displacement (MSD) of n-decane and CH₄ was calculated under different pressures. As shown in Fig. 12(a and b), it can be observed that regardless of whether ME-6 surfactant is added, the diffusion rate of n-decane increases with pressure, while the diffusion rate of CH₄ decreases with pressure. This is due to the increase in n-decane's diffusion rate as CH₄ solubility increases. Simultaneously, as pressure rises, the influence of intermolecular forces between n-decane and CH₄ becomes more pronounced, causing a higher number of n-decane molecules taking up the adsorption sites previously occupied by CH₄ molecules. Consequently, the space for CH₄ molecule free movement diminishes, leading to more collisions among CH₄ molecules in a smaller space. This increases resistance at the spatial points, ultimately resulting in a rapid decline in diffusion rate.

Fig. 12.

MSD of n-decane/CH₄ at different pressures at 373.0 K.

The addition of ME-6 surfactant significantly boosts the diffusion rate of n-decane, especially at high-pressure conditions where the increase in n-decane diffusion rate is more pronounced compared to cases without surfactant. Moreover, the introduction of ME-6 greatly enhances the intermolecular forces between n-decane and CH₄, leading to an increased occupation of adsorption sites by n-decane molecules, which were originally occupied by CH₄ molecules. This further diminishes the space for CH₄ molecule free movement, leading to increased resistance at spatial points. Particularly, at low-pressure conditions, the diffusion rate of CH₄ decreases faster when ME-6 surfactant is added compared to cases without surfactant.

4.1.3. Intermolecular forces

To gain further insight into the microstructural impact of adding ME-6 surfactant on the diffusion of CH₄ in relation to n-decane diffusion, the radial distribution functions (g(r)) of CH₄ and n-decane were analyzed in the CH₄ + ME-6 + n-decane system under various pressures, as depicted in Fig. 13. In Figure 13a, as the system pressure increases, the peak of g(r) for n-decane with n-decane decreases, indicating a reduction in the surrounding n-decane molecules. When combined with Fig. 13(b), the peak of g(r) for CH₄ and n-decane increases as the system pressure rises, implying an increase in the surrounding CH₄ molecules. These observations collectively suggest that with an increase in system pressure, an increasing number of CH₄ molecules are dissolved into the n-decane phase. Since CH₄ possesses a higher intrinsic diffusion coefficient compared to n-decane, this enhances the diffusion capacity of n-decane, leading to improved diffusion ability.

Fig. 13.

Radial distribution function of n-decane/CH₄ in the CH₄+ME-6+n-decane system at different pressures (373.0 K).

SOLOTERRA ME-6 is a non-ionic surfactant and a propoxylated alcohol. The SOLOTERRA ME-6 molecule consists of a hydrophobic hydrocarbon chain and a hydrophilic propoxylated group, exhibiting amphiphilic properties. Therefore, in this study, the amphiphilicity of the surfactant is thought to stem from the contrast between the oleophobic propoxylated head group and the oleophilic hydrocarbon chain of the alcohol. Upon the introduction of ME-6 surfactant into a CH₄ displacement system, surfactant molecules adhere to the interface between the gas and oil phases, facilitating the formation of a miscible region. This process takes place when the surfactant's head unit engages with CH₄ molecules, while the oleophilic tail (hydrocarbon chain) attaches to the crude oil, forming a stable molecular layer.

In this context, the oleophilic end of the surfactant interacts with the crude oil, while the oleophobic end interacts with CH₄. When the forces associated with these interactions are essentially balanced, the arrangement of molecules at the oil-gas interface is altered, reducing the repulsion between the oil and gas phases. Consequently, this lowers the interfacial tension between the two phases, facilitating miscibility. As shown in Fig. 14(a), with increasing pressure, the peak of the g(r) function between n-decane molecules and the oleophilic end of ME-6 gradually decreases, while in Fig. 14(b), the peak of the g(r) function between CH₄ and the oleophobic end of ME-6 exhibits an opposite trend. This reflects that as the disparity between the forces of interaction between n-decane molecules and the oleophilic end of ME-6, and the forces between CH₄ and the oleophobic end of ME-6 diminishes, the system approaches a mixed-phase state.

Fig. 14.

Radial distribution functions between different components at various pressures (373.0 K).

4.2. Interfacial properties of CH₄+ME-6+n-decane system at different temperatures

4.2.1. Density profile

Fig. 15(a–c) depicts the equilibrium states of CH₄+ME-6+n-decane at different temperatures under 22.84 MPa pressure. In comparison between 373.2 K and 343.2 K temperatures, at 373.2 K, the CH₄+ME-6+n-decane system exhibits a thicker phase interface, with more methane molecules entering the n-decane phase and an increased number of n-decane molecules evaporating into the gas phase. When comparing 373.2 K and 392.6 K temperatures, the differences in phase interface for the CH₄+ME-6+n-decane system at these two temperatures are relatively small. It's evident that the presence of ME-6 surfactant is more conducive to reducing the interfacial tension in the CH₄+n-decane system at higher temperatures, thereby promoting miscibility.

Fig. 15.

Equilibrium states of the CH₄+ME-6+n-decane system at different temperatures (22.84 MPa).

Fig. 16. Number density distribution of CH₄ and n-decane at the gas-liquid interface under 22.84 MPa conditions and various temperatures. In Fig. 16(a), at high-pressure conditions in the CH₄+n-decane system, the number density distribution of n-decane in the liquid phase decreases slightly with increasing temperature, while the number density of CH₄ also decreases as the temperature rises. In Fig. 16(b), with the addition of the surfactant ME-6 in the CH₄+n-decane system, there is a significant increase in the mixed-phase volume and a decrease in n-decane phase density, accompanied by an increase in CH₄ phase density. Surfactant ME-6 at temperatures of 373.0 K and 392.6 K promotes the evaporation of n-decane molecules into the gas phase and the dissolution of CH₄ molecules into n-decane. Overall, the surfactant performs better in reducing n-decane phase density and increasing CH₄ phase density, resulting in a thicker mixed-phase interface and larger mixed-phase volume, especially at higher temperatures.

Fig. 16.

Mass density distribution of CH₄/n-decane at different temperatures under 22.84 MPa.

To further understand the trend of interfacial tension (IFT) in the system with the addition of surfactant at different temperatures, the solubility of gases in oil, i.e., the gas density in the oil phase divided by the oil density in the oil phase, was evaluated using density distributions (Fig. 16). Fig. 17 illustrates the change in CH₄ solubility in n-decane at different temperatures. From the graph, it can be observed that without the surfactant, increasing the temperature decreases the solubility of CH₄ in oil, but the reduction is relatively small, indicating that temperature has a minor influence on CH₄ solubility in n-decane. After the addition of surfactant ME-6, the solubility of CH₄ in n-decane is increased to some extent, with a noticeable enhancement in CH₄ solubility in n-decane at higher temperatures.

Fig. 17.

Relationship between the Solubility of CH₄ in n-decane and Temperature (22.84 MPa).

4.2.2. Diffusion properties

Fig. 18(a and b) investigates the diffusion characteristics of n-decane and CH₄ at 22.84 MPa with the addition of the surfactant ME-6, under different temperatures. The calculation involved determining the Mean Square Displacement (MSD) for both n-decane and CH₄. As depicted in Fig. 18(a and b), it can be observed that the diffusion rates of both n-decane and CH₄ increase with rising temperatures. This phenomenon is attributed to the elevation of molecular thermal energy with increasing temperature, resulting in greater kinetic energy. As n-decane molecules are in the liquid state, higher temperatures weaken the interactions among them, enabling freer diffusion and movement due to increased thermal energy. Consequently, the MSD increases as a consequence. CH₄ molecules, existing in a gaseous state, exhibit high dynamism influenced by thermal energy. As temperature rises, CH₄ molecules gain more kinetic energy, leading to enhanced speed and energy. The relatively weak interactions between CH₄ molecules facilitate their free propagation and diffusion within the system. This implies that CH₄ molecules cover a longer distance at the same time, subsequently increasing the MSD value. As a result, the MSD trend exhibits an upward trajectory with increasing temperature, reflecting the more active diffusion behavior of gas molecules at higher temperatures.

Fig. 18.

MSD of n-decane/CH₄ at different temperatures at 22.84 MPa.

4.2.3. Intermolecular forces

To provide a microscale explanation for the effect of temperature on the reduction of interfacial tension (IFT) between CH₄ and n-decane in the presence of the surfactant ME-6, radial distribution functions (g(r)) are examined for different components before and after adding ME-6 under the same pressure but varying temperatures in the CH₄+n-decane system.

In the absence of the surfactant ME-6 (as illustrated in the left graphs of Fig. 19 (a) and (b)), elevated temperatures were found to decrease the g(r) peak values for n-decane-n-decane and n-decane-CH₄ interactions. This is predominantly due to the fact that interactions between n-decane molecules and between n-decane and CH₄ are primarily governed by van der Waals forces. As temperature increases, molecular thermal motion intensifies, leading to higher collision frequency between molecules. This results in enhanced repulsive components of van der Waals forces and weakened attractive components, causing an increase in molecular distances and subsequently diminishing the intermolecular forces.

Fig. 19.

Radial distribution function of n-decane/CH₄ in CH₄+ME-6+n-decane system at different temperatures (22.84 MPa).

Upon the introduction of the surfactant ME-6 into the system, as depicted in Fig. 19 (a) and (b) on the right, the peak of the radial distribution function (g(r)) between n-decane molecules decreases, while the peak of the g(r) between n-decane and CH₄ increases under the same temperature and pressure conditions. This phenomenon is attributed to the amphiphilic nature of the surfactant ME-6, leading to the formation of a molecular layer at the liquid interface.In the liquid phase, the hydrophobic end of the surfactant interacts with n-decane molecules, causing n-decane to accumulate at the oleophilic end of the surfactant layer. As a result, the intermolecular forces between n-decane molecules are reduced, leading to a decrease in their interaction forces, while the interaction forces between n-decane and CH₄ are enhanced.

At elevated temperatures, the intermolecular forces between n-decane molecules are augmented. This is due to the heightened molecular thermal motion at higher temperatures, causing the arrangement and orientation of surfactant molecules at the interface to change. This effect enhances the interaction between the oleophilic end of the surfactant and n-decane molecules, particularly as they approach each other more closely and form denser arrangements, thereby strengthening their interaction forces (as depicted in Figure 20a).

Fig. 20.

Radial distribution functions (g(r)) between different components at various temperatures (22.84 MPa).

In the gas phase, as the temperature rises, CH₄ molecules exhibit more vigorous thermal motion, resulting in an increased repulsive component of the van der Waals forces. Thus, whether or not surfactant is added, the elevated temperature leads to an escalation in the repulsion between n-decane and CH₄ molecules, resulting in a reduction of their mutual interaction forces. The same trend applies to the interaction between CH₄ and the oleophobic end of the surfactant ME-6 (as shown in Fig. 20(b)).

4.2.4. Interfacial tension and miscibility pressure

In general, temperature has a significant impact on the Minimum Miscibility Pressure (MMP) of CO₂-n-decane systems [46]. However, as observed from the data in Fig. 21 and Table 3, for the CH₄-n-decane system, the influence of temperature on MMP values is relatively small, even though there is still an increasing trend with rising temperature. This suggests that methane injection still favorable at higher temperatures. Moreover, at temperatures of 343.2 K, 373.0 K, and 392.6 K, the ME-6 surfactant shows a trend of reducing the Interfacial Tension (IFT) in the CH₄ + n-decane system. Among these, ME-6 demonstrates a better IFT reduction effect at 373.0 K compared to 343.2 K. Particularly, at 373.0 K, the interface tension reduction by ME-6 is more effective, with a decrease of 14.10% in MMP, while at 343.2 K, the decrease is 7.82%. This implies that ME-6 contributes to lowering the MMP under high-temperature reservoir conditions. The higher reduction in MMP could be attributed to the increased solubility of chemicals at higher temperatures, which enhances the miscibility between methane and n-decane. Therefore, the potential for further improving miscibility is relatively limited at lower temperatures. Based on the above analysis, the MMP values between methane and n-decane do not exhibit significant changes with an increase in temperature. Furthermore, under high-temperature conditions, the addition of a surfactant during methane injection provides the greater benefits.

Fig. 21.

Interfacial Tension (IFT) of CH₄ + ME-6 + n-decane system at different temperatures. The symbols represent the results from the MD simulations, and the estimates obtained using the DGT with VTPPR78 EoS are depicted as lines.

Table 3.

MMP of CH₄ + ME-6 + n-decane system at different temperatures.

Temperature	MMP (MPa)	MMP reduction
343.2K	31.72	7.82%
	29.24
373.0K	32.12	14.10%
	27.59
392.6K	34.82	13.58%
	30.09

5. Conclusions

In this study, we employed Molecular Dynamics (MD) simulations and the Vanishing Interfacial Tension (VIT) technique to investigate the effects of pressure and temperature on the equilibrium Interfacial Tension (IFT) of the CH₄+n-decane system. The goal was to explore the potential of chemically assisted methods to lower the Minimum Miscibility Pressure (MMP) in the CH₄+n-decane system. We tested four different surfactants for their effectiveness in reducing MMP and identified the surfactant that achieved the best IFT reduction. Additionally, we conducted simulations to study the effect of this surfactant on MMP reduction in the CH₄+n-decane system at different temperatures. The results obtained are as follows:

• 1.The addition of surfactants can lower the IFT of the CH₄+n-decane system. Among them, the surfactant SOLOTERRA ME-6 exhibited the most effective reduction in MMP, showing a potential MMP decrease of 14.10% at 373 K.
• 2.Upon the addition of the surfactant ME-6 to the CH₄+n-decane system, an increase in pressure and temperature leads to a greater enrichment of CH₄ at the interface. This results in an enhanced solubility of CH₄ in n-decane.
• 3.After the addition of a surfactant, it was observed through the study of diffusion characteristics that CH₄ can more easily weaken the interactions between n-decane molecules, thereby enhancing the diffusion capacity of n-decane. Additionally, the interaction forces between CH₄ and n-decane are increased, facilitating the mixing of CH₄ and n-decane to achieve phase miscibility.
• 4.As the pressure increases, the peak of the interaction force between n-decane molecules and the oleophilic end of ME-6 gradually decreases, while the interaction force between CH₄ and the oleophobic end of ME-6 gradually increases. When the difference between these two forces decreases, the system approaches a mixed-phase state.
• 5.The MMP value between CH₄ and n-decane doesn't show significant changes with the increase in temperature. Under high-temperature conditions, the greatest benefits of adding the surfactant ME-6 during methane injection are observed.

Additional information

No additional information is available for this paper.

CRediT authorship contribution statement

Zhenzhen Dong: Conceptualization. Shihao Qian: Writing – original draft, Software, Methodology. Weirong Li: Writing – review & editing, Funding acquisition. Xinle Ma: Validation. Tong Hou: Investigation, Formal analysis. Tianyang Zhang: Validation, Formal analysis. Zhanrong Yang: Methodology. Keze Lin: Visualization. Hongliang Yi: Supervision, Data curation.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.