**1. Introduction**

Polymers, surfactants, and alkalis are the main repellents in current chemical flooding, but a single chemical can only improve the oil displacement efficiency or sweep efficiency. Combination flooding [1] has synergistic effects, with surfactants significantly reducing the interfacial tension at the oil–water interface and increasing the number of capillary numbers. Alkalis injected into the reservoir can chemically react with organic acids in the reservoir, thereby reducing adsorption losses. However, the traditional tertiary oil recovery chemical agents, which can improve the level of recovery, are limited, The nanoparticles are uniform in size and can form compact, well-structured monolayers at the water/non-aqueous phase interface. The emulsions are very stable under high temperatures and high-salt reservoir conditions [2]. Nanoparticle-stabilized emulsions have a high viscosity, which can help manage migration rates during oil transport and provides a viable method of pushing highly viscous oil out of the subsurface, relative to surfactants with a high retention on reservoir rocks [3]. Some oil fields in the geological reserves still constitute 50% of the unswept region, and people are in urgent need of a breakthrough in conventional chemical agents to significantly improve recovery factors [4].

**Citation:** Wang, J.; Tian, S.; Liu, X.; Wang, X.; Huang, Y.; Fu, Y.; Xu, Q. Molecular Dynamics Simulation of the Oil–Water Interface Behavior of Modified Graphene Oxide and Its Effect on Interfacial Phenomena. *Energies* **2022**, *15*, 4443. https:// doi.org/10.3390/en15124443

Academic Editors: Ioannis F. Gonos, Eleftheria C. Pyrgioti and Diaa-Eldin A. Mansour

Received: 20 May 2022 Accepted: 15 June 2022 Published: 18 June 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Nanoparticles have the advantages of a large specific surface area and small size and have some special properties different from those of conventional chemical agents. A large number of scholars in China and abroad have carried out a series of theoretical, experimental, and simulation work on the influence of the concentration, size, and charge of nanoparticles on the oil recovery factor [5–7]. Wang et al. [8] found that oil droplets could be spontaneously detached from the solid surface when the charge of the nanofluid composed of charged nanoparticles reached a certain critical value. The modified nanoparticles can effectively reduce the interfacial tension and improve the carrying capacity of water relative to the oil phase. Luo et al. [9] used molecular dynamics to study the self-assembly behavior of SiO2 nanoparticles at the oil–water interface and found that the modified nanoparticles could effectively reduce the interfacial tension and improve the carrying capacity of water relative to the oil phase. Jia et al. [10] used experimental methods and found that amphiphilic graphene flake nanofluids could form a solid interfacial film, which reduced the interfacial tension at the oil–water interface. Through this mechanism, the oil droplets on the rock surface were desorbed. Compared with conventional chemical flooding, in this agent, the oil displacement efficiency of nanofluids was increased by two times.

At present, the research on nanoparticles is mainly focused on experimental aspects [11–13]. The simulation means for modified nanoparticles are still at the stage of exploration and realization [14,15]. This study selected alkyl-modified graphene oxide as the research object and used the all-atom molecular dynamics simulation method [16] to study the diffusion of modified nanoparticles (NGOs) in the aqueous phase and the self-aggregation phenomenon at the oil–water interface. We also established two different models through the visualization software Materials Studio. Model I analyzed the dispersion nature of nanoparticles in the aqueous phase, Model I analyzed the dispersion properties of nanoparticles in the water phase, while Model II observed the molecular configuration of nanoparticles at the oil–water interface and the self-aggregation phenomenon of nanoparticles at the oil–water interface. The interaction of modified nano molecules on the oil–water phase at three temperatures was investigated according to the constructed models, and finally, the effect of modified graphene oxide on the interfacial tension at different temperatures was revealed.

#### **2. Models and Methods**

Molecular dynamics simulation is commonly used method for the software, Material Studio, Lammps, Amber, etc. This visualization software, with built-in rich algorithms, a powerful interactive interface, and multi-scale and multi-functional modules, is widely used in the field of molecular property simulation. The properties of the oil–water interface [17], the aggregation pattern of the solution [18], and the wettability of oil droplets on the solid surface [19] were investigated by domestic and foreign scholars under the action of chemical flooding systems. The simulation process is chosen from all-atom molecular dynamics simulation, which has the advantage of a high accuracy compared to dissipative molecular dynamics simulation [20].

## *2.1. Model Construction*

The simulations were completed with Materials Studio (MS) software, and the simulation process was carried out using the COMPASS force field [21]. Firstly, the simulations established three crude oil systems with different molecular compositions of hexane, heptane, and isooctane, as shown in Figure 1.

The binding energies required for the reaction of the three different coupling agents with graphene oxide were obtained according to the first principle [22], and the parameters are shown in Table 1. The binding energy of haloalkane with graphene oxide was +0.47, which means that the reaction of haloalkane with graphene oxide was not easy to carry out; the reaction conditions were harsh, and the resulting structures were unstable. However, the binding energies of −1.96 and −1.68, for alkylamines and silane coupling agents with graphene oxide, respectively, indicate that the reaction process of alkylamines and silane

coupling agents with graphene oxide is easier; the reaction conditions are milder and the resulting products have a good structural stability.

**Figure 1.** Molecular configuration of oil droplet composition (grey—carbon, white—hydrogen): (**a**) oil phase box; (**b**) oil phase composition.



To investigate the effect of graft length on the properties of graphene oxide, the binding energies of thirteen, sixteen, and nineteen alkylamines were separately investigated. As shown in Table 2, the binding energies gradually decreased with increasing alkylamine carbon chain length, indicating that, as the alkylamine carbon chain length increased, the reaction proceeded with more ease, and the structure of the resulting modified graphene oxide products became more stable.

**Table 2.** The binding energy of different graft chain lengths.


To investigate the interaction between water molecules, the reservoir surface, and modified graphene oxide, the adsorption energy of water molecules on the surface of the modified graphene oxide was simulated.

As shown in Table 3, with 13 alkylamines, the adsorption energy of the modified water molecule is −1.06; with 16 alkylamines, the modified graphene oxide adsorption energy is −0.94; and with 19 alkyls, the modified graphene oxide adsorption energy is −0.76. The adsorption of water molecules on both types of modified graphene oxide is an exothermic process, and the surface of the modified product is strongly chemisorbed. Additionally, the octadecylamine-modified graphene oxide had the weakest interaction with water compared to the other chain lengths.

**Table 3.** The adsorption energy of water molecules with modified graphene oxide.


An analysis of the change in binding energy and adsorption energy shows that as the graft chain length increases, the exothermic reaction is enhanced and the binding energy increases. As the graft chain length increases, the adsorption is a spontaneous process and the adsorption energy decreases. On balance, the final choice was to choose s with a relatively smooth reaction process, a high adsorption energy of the modified molecules with water, and a better reduction in interfacial tension.

By oxidizing a thin layer of graphene, structures containing -COOH and -OH on the surface could be obtained. In this study, alkyl long-chain groups were grafted onto the surface of graphene oxide using the azide chemical reaction of cetylamine, as shown in Figure 2.

**Figure 2.** Azide chemical reaction process.

A thin-layer, graphene oxide model with a diameter of 1.8 nm was constructed, and seven cetylamine long chains were grafted on the unilateral side of the graphene oxide model to obtain partially alkyl-modified graphene oxide nanoparticles (NGOs). The NGOs before and after modification are shown in Figure 3.

**Figure 3.** Modified graphene oxide conformation (gray—carbon atoms; red—oxygen atoms; white —hydrogen atoms; blue—nitrogen atoms): (**a**) Thin layer of carbon; (**b**) GO; (**c**) NGOs.

To investigate the dispersion properties of nanoparticles in water, a water–NGO miscible system was built. A square simulation box with a size of 21.92 Å × 21.92 Å × 21.92 Å was created by "amorphous cells tools". The mixed solution system contained 56.4% water and 42.6% NGOs. The initial constructed model is shown in Figure 4a. To investigate the self-aggregation of nanoparticles at the oil–water interface, a columnar simulation box of 26.25 Å × 26.25 Å × 777.61 Å was constructed by the "build layer" tool. To eliminate the influence of periodic boundaries, a thickness of 10 was added above the oil model. The initial model of the vacuum layer is shown in Figure 4b, the molecular dynamics simulation was performed using the "forcite tools", and the simulation parameters are shown in Table 4.

**Figure 4.** Schematic diagram of the initial model: (**a**) Model I (**b**) Model II.

**Table 4.** Model II force field parameters.

