Molecular Insights into CO₂ Diffusion Behavior in Crude Oil

Abstract

CO₂ flooding plays a significant part in enhancing oil recovery and is essential to achieving CCUS (Carbon Capture, Utilization, and Storage). This study aims to understand the fundamental theory of CO₂ dissolving and diffusing into crude oil and how these processes vary under reasonable reservoir conditions. In this paper, we primarily use molecular dynamics simulation to construct a multi-component crude oil model with 17 hydrocarbons, which is on the basis of a component analysis of oil samples through laboratory experiments. Then, the CO₂ dissolving capacity of the multi-component crude was quantitatively characterized and the impacts of external conditions—including temperature and pressure—on the motion of the CO₂ dissolution and diffusion coefficients were systematically investigated. Finally, the swelling behavior of mixed CO₂–crude oil was analyzed and the diffusion coefficients were predicted; furthermore, the levels of CO₂ impacting the oil’s mobility were analyzed. Results showed that temperature stimulation intensified molecular thermal motion and increased the voids between the alkane molecules, promoting the rapid dissolution and diffusion of CO₂. This caused the crude oil to swell and reduced its viscosity, further improving the mobility of the crude oil. As the pressure increased, the voids between the internal and external potential energy of the crude oil models became wider, facilitating the dissolution of CO₂. However, when subjected to external compression, the CO₂ molecules’ diffusing progress within the oil samples was significantly limited, even diverging to zero, which inhabited the improvement in oil mobility. This study provides some meaningful insights into the effect of CO₂ on improving molecular-scale mobility, providing theoretical guidance for subsequent investigations into CO₂–crude oil mixtures’ complicated and detailed behavior.

1. Introduction

In recent decades, carbon dioxide (CO₂) has become the primary greenhouse gas (GHG) emission from human production and daily life, which is one of the leading causes of global warming. Global warming has affected the daily lives of all living beings [1]. To mitigate the adverse impact and achieve carbon neutrality, large-scale implementation of low-carbon and energy-saving measures has become a global consensus and future development trend [2]. According to the Global Carbon Capture and Storage Institute (GCCSI) report, CCUS-EOR represents a primary approach for reducing carbon emissions [3,4,5]. One of the most resultful approaches to enhance oil recovery (EOR) is injecting CO₂ into reservoirs, which not only improves oil recovery but also enables geological storage of CO₂ [6,7,8,9], thus enabling effective and efficient closed-loop utilization of CO₂. By dissolving and diffusing CO₂ into crude oil, it can be beneficial to decrease the viscosity and interfacial tension of crude oil, expand the crude oil’s volume, enhance the mobility of crude oil, and significantly increase oil recovery [10,11,12,13,14,15]. At the same time, a portion of CO₂ will be trapped in the reservoir to achieve the goal of carbon capture and storage. The displacement efficiency of CO₂ is largely influenced by the reservoir fluid’s properties and the CO₂–oil mixtures’ phase behavior. Therefore, the dissolution and diffusion of CO₂ in crude oil are two of the most critical parameters to quantify displacement efficiency.

Numerous experiments have been conducted in the past to investigate the enhanced oil recovery mechanisms of various gases, including CO₂ [16,17], N₂ [18], hydrocarbons [17,19,20], and others. These methods are typically categorized as direct or indirect. The direct method [21,22] calculates the diffusion coefficient by analyzing the components in the diffusion process. The indirect method [23] is primarily based on the PVT method, which determines the diffusion coefficient by monitoring the changes in vessel pressure or volume during the diffusion process. With the continuous advancements in testing methods, CT scanning [24], NMR [25], and other techniques have become widely utilized in the investigation of diffusion. Zhao et al. [26] realized in situ dynamic monitoring of procedures for diffusing CO₂ into crude oil using low-field magnetic resonance (NMR) technology, and calculated the CO₂ diffusion coefficient that changed with time and location. Li et al. [27] developed a new method that can be used under reservoir conditions for estimating the effective coefficient of CO₂ diffusion in oil-saturated porous media, and their results match the mathematical model. Song et al. [28] made use of X-ray Computer-Assisted Tomography (CAT) to evaluate the coefficient of carbon dioxide diffusion in heavy oil. Liu et al. [29] took advantage of online nuclear magnetic resonance (NMR) instruments to conduct CO₂-HNP experiments and found that the main controlling factor was driven by molecular diffusion-controlled dissolved CO₂. Widuramina et al. [30] used Schlieren imaging to visualize the dissolution rate of supercritical CO₂ in n-octane and n-decane.

However, there are still many challenges in investigating the microscopic mechanisms through experiments [31]. In recent years, the application of molecular dynamics (MD) simulation in the field of petroleum and gas engineering has significantly increased. MD simulation is based on classical Newtonian mechanics, and can help us to learn and comprehend the behaviors and mechanisms on a molecular scale inside a complex molecular system [32,33,34], including the analysis of microphysical, kinetic, and thermodynamic properties such as intermolecular forces and molecular trajectories [35]. Therefore, MD simulation is more effective than experiments in directly investigating microscopic mechanisms [31]. MD simulation is utilized in petroleum and gas engineering research to investigate the mobility characteristics of hydrocarbons [36] and the thermodynamic properties of displacement fluids and crude oil mixtures. Moh et al. [37] employed MD simulation to study the adsorption and oil displacement processes of CO₂ and CH₄ in calcite nanopores, while examining the impact of their diffusion coefficient differences on the displacement processes. Yuan et al. [38] revealed the adsorption and flow mechanisms of CO₂–decane miscible fluids in SiO₂ pores by the way of MD simulation, revealing that competitive adsorption between CO₂ and decane was a key factor for decane displacement. Zhang et al. [39] investigated the solubility of CO₂ in octane and its impact on the expansion behavior of octane. Li et al. [40] employed Monte Carlo (MC) and MD simulations to study the swelling reaction and viscosity reduction in n-alkanes by the influence of CO₂. By examining the interfacial interaction between Bakken crude oil and gas, Li et al. [41] calculated some key parameters, including the gas solubility, swelling coefficient, diffusion coefficient, and minimum miscibility pressure (MMP). Several researchers have conducted simulations to investigate the phase behavior and volume changes in CO₂–oil mixtures [41,42]. Recently, some scholars have utilized MD simulation to explore the viscosity changes and diffusing coefficients of nano-clusters in hydrocarbon fluids [43]. However, previous studies have predominantly focused on single-component crude oil, which could not accurately reflect the true nature of crude oil realistically. Therefore, the mutual effects between multi-component crude oil and CO₂ are particularly important.

To better understand the dissolution and diffusion mechanisms of CO₂ and multi-component crude oil as well as their influence on crude oil mobility, we utilize MD simulation to observe the process of CO₂ dissolution and diffusion. Additionally, we understand the swelling impact of CO₂ on crude, as well as the impact of conditions including temperature and pressure on the dissolution and diffusion. Finally, we predict the diffusion coefficient of multi-component crude oil and its impact on crude oil mobility. The included temperatures vary from 313 K to 323 K and the pressures range from 3 MPa to 10 MPa.

2. Methodology

2.1. Molecular Model

Figure 1 illustrates the molecular schematic diagram of the CO₂–oil simulation. The simulation system consisted of two parts: (1) A multi-component crude oil model (25.87 × 25.87 × 25.87 ų) before CO₂ dissolution, which included C1~C33+. Since C17+ accounts for a small proportion, we adopted the method of dividing pseudo-components to construct a reasonable crude oil model and facilitate simulation by dividing C18~C33+ into C17+. Therefore, the constructed crude oil model contained components ranging from C1 to C17+ with a density of 0.82 g/cm³ (

Table 1. Compositional analysis of the crude oil.

Component	Mole %	Plus Fraction Analysis	Mole %
C1	14.446
C2	6.487	C1–C4	37.793
C3	10.674	C5+	62.207
C4	6.186
C5	3.958
C6	3.223	C1–C8	57.605
C7	4.893	C9+	42.395
C8	7.738
C9	5.632
C10	5.162	C1–C16	84.856
C11	3.577	C17+	15.144
C12	3.109
C13	2.969
C14	2.527
C15	2.368
C16	1.907
C17+	15.144
Total	100

); (2) CO₂ molecules were added as adsorbents to the crude oil model and simulated under different reservoir pressures (3 to 10 MPa) and temperatures (313 K, 318 K, 323 K). This part is mainly the simulation of CO₂ dissolving within crude oil on the condition that reservoir statuses vary, without setting the reservoir structure. The simulated reservoir is a low-pressure one, and thus the pressure and temperature are based on actual reservoir conditions.

2.2. Simulation Details

We used the BIOVIA Material Studio 2019 software package [44] for the MD simulation, which mainly used Visualizer, Amorphous Cell, Sorption, and Forcite modules for the model construction, simulation, post-processing, and analysis. First, all alkanes and CO₂ molecules were constructed and geometrically optimized in the Visualizer module. Then, the construction of the crude oil model was completed in the Amorphous Cell module. Each component was set according to the composition of the crude oil sample so that the density of the crude oil model was consistent with that of the sample; this step ensures the authenticity and accuracy of the simulation model. To keep the model’s energy minimized, we used the steepest descent method; after that, we equilibrated for 1 ns in the NVT ensemble by the way of using a simulation timestep of 1 fs. In this article, we retained the temperature at 313 K, 318 K, and 323 K, respectively, by the Nosé–Hoover thermostat. In addition, simulations were performed using a timestep of 1 fs in the NPT ensemble, and the pressure was controlled at 3 to 10 MPa by the Berendsen barostat. After that, we used the Sorption module for the Monte Carlo simulation; CO₂ was added to the different crude oil systems as a diffused adsorption, and particle motion was sampled by the Metropolis method. In this work, the force fields for the CO₂ and crude oil were taken from the COMPASS force field, which was confirmed to have good applicability to alkane molecules. Simultaneously, this approach was adequately parameterized and strictly monitored using initial high-level calculations to obtain parameters and optimize them to match the experimental data. In this force field, the Lennard-Jones 9-6 potential and Coulomb’s electrostatic potential denote the non-bonded potentials. The former depicts the potential energy difference values between the weak repulsive and attractive forces of the van der Waals force. It is generally displayed as follows:

$$E={\displaystyle \sum _{i>j}\frac{q_i{q}_j}{r_{ij}}}+{\displaystyle \sum _{i>j}{E}_{ij}\left[2{\left(\frac{r_{ij}^0}{r_{ij}}\right)}^9-3{\left(\frac{r_{ij}^0}{r_{ij}}\right)}^6\right]}$$

(1)

$$r_{ij}^0={\left({\displaystyle \frac{{\left(r_i^0\right)}^6+{\left(r_j^0\right)}^6}{2}}\right)}^{{\displaystyle \frac{1}{6}}}$$

(2)

where ij represents an atom pair; E_ij is the potential well depth; r_ij⁰ denotes the zero potential distance for the atom pair; r is the distance between the two atoms.

We employed the particle mesh Ewald method to calculate the electrostatic interactions [45]. The cutoff length between the non-electrostatic interactions and electrostatic interactions was 1.25 nm [34,43]. Meanwhile, the Ewald method [34,43,46], having a precision of 0.01 kcal/mol, was applied. Periodic boundary conditions were used in the simulations. For the purpose of guaranteeing that the total energy of the simulation model was minimized and kept stable, we set 1 fs as a timestep for all the simulations in this article.

2.3. Diffusion Coefficient

Grounded on the definition of mean square displacement, the diffusion coefficient was calculated by Equation (3) [47,48]:

$$D={\displaystyle \frac{1}{6N_{\alpha }}}\underset{t\to \infty }{\lim }{\displaystyle \frac{d}{d_t}}{\displaystyle \sum _{i=1}^{N_{\alpha }}〈{\left[r_i(t)-r_i(0)\right]}^2〉}$$

(3)

where N_α represents the amount of diffused atoms in the system; r_i(t) represents the displacement vector of molecule i from time 0 to time t. The coefficient of diffusion is worked out by choosing and utilizing the best trendline (y = ax + b) of the MSD curves. The diffusion coefficient was obtained using Equation (4) [49]:

$$D={\displaystyle \frac{a}{6}}$$

(4)

According to the Stokes–Einstein (SE) equation, the coefficient of CO₂ diffusion affects the viscosity of crude oil, and they have an inverse relationship. The SE formula was listed in Equation (5) as follows [50],

$$\mu ={\displaystyle \frac{kT}{6\pi \alpha D}}$$

(5)

where T denotes the temperature; α is the CO₂ molecular radius in 1.65 × 10⁻⁸ cm [51]; k represents Boltzmann’s constant in 1.38 × 10⁻²³ J/K; D represents the diffusion coefficient and unit is cm²/s; and μ is the oil viscosity in Pa·s.

2.4. Model Validation

Under different pressure and temperature conditions, crude oil models exhibited different configurations and contact relations at the microscopic molecular level, resulting in different crude oil volumes, densities, and viscosity properties at the macroscopic level.

The density of individual oil molecules in the crude oil model, simulated for 1 ns under the NPT ensemble, was compared with the data provided by the National Institute of Standards and Technology (NIST) [52], as shown in Figure 2. The established single-component crude oil model was found to be reasonable. In addition, the density of the multi-component crude oil model was compared with the experimental test results of field oil samples, both of which were 0.82 g/cm³. Therefore, the model is considered reliable.

3. Results and Discussion

3.1. Density Distribution of CO₂

The distribution of CO₂ density dissolved into different systems is shown in Figure 3. The red portion represents the concentration distribution of CO₂ molecules dissolved in different systems. The location and approximate quantities of CO₂ molecules dissolved and diffused in different crude oil systems can be observed clearly. As shown in Figure 3, there were some large voids between different alkane molecules, and CO₂ dissolved and diffused into the voids. At the same temperature, with increasing pressure, the amount of CO₂ molecules dissolved in the different systems also increases, and the concentration distribution of CO₂ between the alkane molecular voids becomes more obvious. There were some differences in the behavior of temperature and pressure. Under the same pressure, with increasing temperature, the dissolution of CO₂ increased. High temperatures have a stronger effect on the CO₂ dissolving into different oil systems. The impact of temperature and pressure on the mechanism was later investigated in detail.

3.2. Model Swelling Rate

As the pressure increased, the crude oil systems were compressed and their volumes decreased. However, the temperature increase aggravated thermal motion between molecules, leading to an increase in system volume. CO₂ entered the alkane molecule voids through dissolution and diffusion, further increasing crude oil system volume. The volume swelling rate of the model was calculated by Equation (6):

$$\epsilon ={\displaystyle \frac{V_{fin}-V_{ini}}{V_{ini}}}$$

(6)

where V_fin represents the final model’s volume; V_ini represents the initial model’s volume; and ε defines the model swelling rate.

The variation trend in the volume swelling rates before and after dissolving CO₂ in the crude oil systems, at various temperatures and pressures, is revealed in Figure 4. It can be grasped that the models were compressed due to the decline in pressure, the volume of each model also decreased with the increase in pressure. The crude oil models exhibited fluctuations in volume before dissolving CO₂, mainly due to a large number of components in the crude oil model and differences in the chain length among alkane molecules, which affected the process of volume compression. However, the volume variation in the crude oil models decreased almost in a linear trend after dissolving the CO₂, and the rate of volume variation for each model was also similar and smaller than that of the undissolved CO₂ models. This indicates that, after filling the alkane molecular voids with CO₂ through dissolution and diffusion, the potential energy difference between the internal and external systems decreased. These systems had almost reached dynamic equilibrium and were less affected by external circumstances. The specific volume of the crude oil model before and after dissolving CO₂ and the calculated volume swelling rate at different pressures in the 323 K system are provided in

Table 2. Crude oil model volumes and swelling rates in the 323 K systems.

Pressure MPa	Final Model Volume Å3	Volumetric Strain Å3	Model Swelling Rate %
3	20,672.023	3356.741	19.39
4	20,329.764	3014.482	17.41
5	20,325.377	3010.095	17.38
6	20,218.541	2903.259	16.77
7	20,202.760	2887.478	16.68
8	20,070.536	2755.254	15.91
9	20,043.743	2728.461	15.76
10	19,804.000	2488.718	14.37

and

Table 3. CO₂–crude oil model volumes and swelling rates in the 323 K systems.

Pressure MPa	Final Model Volume Å3	Volumetric Strain Å3	Model Swelling Rate %
3	21,047.038	3731.756	21.55
4	20,948.019	3632.737	20.98
5	20,789.597	3474.315	20.07
6	20,588.867	3273.585	18.91
7	20,478.810	3163.528	18.27
8	20,393.628	3078.346	17.78
9	20,301.949	2986.667	17.25
10	20,082.561	2767.279	15.98

(Tables S1–S4).

As the temperature increased, these models swelled and their volume increased. From the simulation results of the systems at 313 K, 318 K, and 323 K, the average swelling rate of the crude oil models before dissolving the CO₂ molecules was 13.04% and the average swelling rate of the crude oil model after dissolving CO₂ molecules was 32.65% for every temperature increase of 5 K (Figure 5). The increase in temperature promoted both the dissolution and diffusion of CO₂ molecules and the swelling of the crude oil models. The reason is that as the temperature increases, the kinetic energy of all molecules increases, leading to increases in movement ability of the alkane molecules and the internal space of the crude oil system, resulting in system swelling. The movement ability of CO₂ molecules was also enhanced, increasing the probability of entering the intermolecular voids of alkanes and enhancing both dissolution and diffusion. As a result, the amount of dissolved CO₂ also increased.

3.3. Dissolution and Diffusion

The coefficients of the amount of CO₂ dissolving in different crude systems are shown in Figure 6. According to the curve analysis, at the same temperature, the dissolution of CO₂ in different systems increases with pressure. This indicates that an increase in pressure promoted the dissolution of CO₂ molecules. The reason is that there existed a potential energy difference between the internal voids of alkane molecules, and the external space was occupied by CO₂. At higher pressures, this potential energy difference increased, promoting the filling of CO₂ into the molecular voids of alkane and resulting in the stronger dissolution of CO₂.

In Figure 6, the dissolution coefficient of CO₂ increased rapidly at first and then gradually reached a relatively gentle growth with increasing pressure. In the early stage, when the pressure was low, there was a small potential energy difference between the internal area of the alkane molecules and the external area of the CO₂, resulting in limited dissolution of CO₂ in the voids. At this time, the attraction between the CO₂ and the alkane molecules was dominant, and the dissolution of CO₂ increased as pressure increased. Then, the dissolution gradually increased with pressure until it reached a plateau, indicating that as pressure increased, the distance between CO₂ and alkane molecules decreased and repulsive forces between them became dominant. The gradual increase in CO₂ dissolution continued until dynamic equilibrium was reached.

Under the same pressure, the dissolution of CO₂ in the 323 K system was always better than in other systems; the lowest amount was in the 313K system and there was a medium amount in the 318 K system. The dissolution behavior of molecules at different temperatures indicates that the movement of molecules was slower at lower temperatures, and the capacity for voids between alkane molecules to dissolve CO₂ was limited, which reduced the dissolution of CO₂. However, at higher temperatures, the kinetic energy of CO₂ increased, leading to increases in the free path of molecular motion and collision probability between CO₂ and alkane molecules. This affected the size of voids and resulted in a faster dissolution rate for CO₂. The dissolution rates of CO₂ were higher in the 323 K system than in the 318 K system but relatively higher in the initial 318 K system. This phenomenon indicates that, despite the positive promotion effect of high temperatures, pressure conditions still inhibited the dissolution of CO₂. The mechanism behind this pressure inhibition will be discussed at great length in the coming exposition.

The coefficient of CO₂ diffusion was determined at various pressure and temperature conditions (50). As shown in Figure 7, the pressure increased while the coefficient of CO₂ diffusion declined at the same temperature. However, with an increase in temperature at the same pressure, the diffusion coefficient of CO₂ increased. This is similar to the variation in the diffusion coefficient for multi-component crude oil, which is analyzed in the following sections.

3.4. Prediction of Diffusion Coefficient

To obtain the diffusion coefficient with the help of molecular dynamic simulation, the density distribution of the alkane molecules is supposed to be chiefly calculated. The density distribution of CO₂ in the crude oil systems under different conditions was obtained by simulation, as shown in Figure 3. Then, the specific amount of CO₂ dissolved in the oil systems was predicted, and with these numbers, we were able to calculate the diffusion coefficient of multi-component crude oil molecules. Figure 8 shows the Mean Square Displacement (MSD) vs. simulation time diagram for the 323 K system under varying pressure conditions.

As shown in Figure 8, the crude oil systems range widely between 0 and 2200 Ų before dissolving CO₂ in MSD, and the MSD range changed after dissolving the CO₂, which is between 0 and 2600 Ų. Then, the diffusion coefficient of the multi-component crude oil was calculated, as shown in Figure 9. With increasing pressure, the volume swelling rate of the crude oil system model decreased under the influence of external pressure due to the diffusion coefficient decrease before and after dissolving CO₂. For example, the diffusion coefficient in the 323 K system dropped from 0.3506 × 10⁻⁴ cm²/s at 3 MPa to 0.3015 × 10⁻⁴ cm²/s at 10 MPa and it declined from 0.4198 × 10⁻⁴ cm²/s at 3 MPa to 0.3694 × 10⁻⁴ cm²/s at 10 MPa before and after dissolving CO₂, respectively. With an increase in temperature, the kinetic energy of all molecules increased, resulting in a higher diffusion coefficient. For instance, the diffusion coefficient of the 3 MPa increased from 0.1224 × 10⁻⁴ cm²/s at 313 K to 0.3506 × 10⁻⁴ cm²/s at 323 K and from 0.1618 × 10⁻⁴ cm²/s at 313 K to 0.4198 × 10⁻⁴ cm²/s at 323 K before and after dissolving CO₂, respectively. From the analysis of these data and Figure 9, it can be concluded that the diffusion coefficient of the system was generally larger after dissolving CO₂ than before. This is because the dissolved CO₂ occupied alkane molecular voids, which reduced interaction forces between the alkane molecules.

The diffusion of multi-component crude oil and CO₂ was calculated, respectively. The diffusion coefficient of crude oil and its variation with temperature were analyzed before and after the dissolution of CO₂. It was found that both the dissolution of CO₂ and an increase in temperature can improve the mobility of crude oil. However, the viscosity reduction effect of temperature on multi-component crude oil was better than that of CO₂ dissolution. On the one hand, as pressure increased, the dissolution coefficient of CO₂ also increased; on the other hand, as pressure increased, the interaction between alkane molecules also increased and thus reduced the diffusion coefficient of both CO₂ and the alkane molecules. The mobility of crude oil generally showed a slight improvement.

4. Conclusions and Future Perspectives

In this study, molecular dynamics simulations were employed to investigate the dissolution and diffusion behavior of CO₂ in multi-component crude oil and its impact on oil mobility under varying temperature and pressure conditions. The results demonstrate that increasing temperature and pressure enhances the solubility of CO₂ in crude oil, promoting significant swelling and viscosity reduction, which in turn improves the mobility of the oil. The diffusion coefficients of CO₂ and crude oil were calculated, showing a temperature-dependent increase in diffusion, while higher pressures inhibited the diffusion process.

The findings from this study have important implications for enhanced oil recovery (EOR) and carbon sequestration. The improved understanding of CO₂ behavior in crude oil systems offers valuable insights for optimizing CO₂ injection processes in oil reservoirs, particularly in low-permeability and mature fields. By promoting crude oil flow and simultaneously storing CO₂ underground, this dual approach has the potential to increase oil recovery while contributing to global carbon capture and storage (CCS) efforts.

However, the model used in this research is subject to several limitations. While molecular dynamics simulations provide a detailed molecular-level perspective, they do not fully represent the complexities of actual reservoirs, including geological heterogeneity, broader hydrocarbon mixtures, and field-specific conditions. These limitations suggest the need for further research to bridge the gap between molecular simulations and real-world reservoir behavior.

Future studies should focus on incorporating more complex fluid compositions and geological factors into the model as well as validating these findings with experimental and field-scale data. Additionally, extending the application of CO₂ in EOR requires further exploration of optimal injection strategies that balance both oil recovery and CO₂ sequestration under various reservoir conditions. This study provides a theoretical foundation for such future research, with the goal of enhancing the efficiency and sustainability of CO₂-driven oil recovery processes.