Effect of Sealing Greases on Inhibiting the Leakage of Supercritical CO₂: A Molecular Dynamics Study

Abstract

This work investigates the effect of sealing grease on inhibiting the leakage of supercritical carbon dioxide (CO₂) using molecular dynamics simulation. Consideration is given to the effects of temperature, pressure, and leakage channel height. It is found that CO₂ primarily leaks by diffusing into the interface between the grease and the channel at low temperatures, but the leakage is dominated by interfacial diffusion and the bulk penetration of CO₂ across the greases at high temperatures. Moreover, the presence of a large amount of supercritical CO₂ at the interface weakens the interactions between the grease and the channel, resulting in the extrusion of greases at high temperatures. For the pressure effect, the leakage always happens through interfacial diffusion with a low or high pressure. The high pressure can cause the extrusion of greases, as CO₂ distributed in both the interface and the grease can enhance its fluidity and make it more likely to be extruded from the channel under high pressure. Finally, leakage primarily involves interfacial diffusion for a small channel height, but it is also dominated by such diffusion and bulk penetrations with a large height, which is due to the boundary effect on the fluidity of greases.

1. Introduction

Supercritical carbon dioxide (scCO₂) has low viscosity and high density and diffusivity, and it has thus been applied in various engineering domains. Its supercritical state requires a temperature exceeding 31.1 °C and pressures above 7.38 MPa, thereby demanding good sealing performance of high-pressure vessels.

Sealing grease is capable of improving the sealing performance of high-pressure vessels without modifying their existing sealing surfaces, and it has been widely used to inhibit the leakage of gases or liquids under high pressure. However, the application of greases in inhibiting the leakage of scCO₂ may be challenged by its high diffusivity within organic matter and the inherent flow characteristics of the greases [1,2]. Moreover, because the leakage of fluids happens through micro- or even nano-scale leakage channels [3,4], the size effect on the flowing behaviors of both scCO₂ and greases as well as the leakage process becomes pronounced. These issues greatly complicate the understanding of the leakage mechanism.

Previous studies regarding greases have mainly focused on their tribological properties [5,6], life prediction [7], and applications in diverse mechanical systems [8,9]. Moreover, regarding the flowing behaviors of nanofluids in confined conditions, previous studies have mainly focused on their thermal and viscous properties [10,11,12,13]. However, few studies have investigated the sealing effect of greases on supercritical CO₂ and the corresponding leakage mechanisms, such that the optimization strategy of greases for sealing supercritical CO₂ is unclear.

Molecular dynamics (MD) simulation is a useful approach to mimic the phenomenon at small scales, and it has thus been widely employed to investigate the complicated mechanisms governing the behaviors of nanofluids under different conditions [3,14,15,16,17,18,19]. Therefore, this study employs MD simulations to systematically investigate the effect of sealing grease on inhibiting the leakage of supercritical CO₂. Consideration is given to the influence of various factors, such as pressure, temperature, and leakage channel height. The analysis will comprehensively account for the molecular diffusions, interfacial interactions, and molecular movement of sealing greases, all of which collectively influence the leakage performance of CO₂. We hope that this research may shed light on the leakage mechanisms of supercritical CO₂ under the influence of sealing grease and offer valuable insights and guidance for the development of next-generation, high-performance sealing greases.

2. Modeling

The model consisted of a large high-pressure box connected with a channel, as given in Figure 1. The box and the channel are filled with CO₂ and sealing grease, respectively. Inside of the box, a plane is set as a piston at the left side to apply external forces to the CO₂, thus maintaining a constant pressure during the sealing simulation. The initial internal dimensions of the box are about 164, 73, and 95 Å along the x-, y-, and z-directions, respectively. The amount of CO₂ molecules in the systems is kept at 1056 in all cases. The box, the channel, and the piston plane are set as rigid bodies during the simulation to avoid any deformations. On the left and right edges of the channel, rigid valves are set to confine the grease and isolate it with CO₂ before the sealing process. The non-periodic boundary conditions are set along all three directions.

The simulation is conducted in different steps. Firstly, the systems are relaxed at a low temperature for about 10 ps under the NVT ensemble to decrease the potential of the system and increase its stability. Afterwards, it is warmed up to the target temperature, followed by another relaxation period under this temperature. Furthermore, an external force is applied to the piston plane to reduce the volume of CO₂ and thus increase its pressure to the targeted value. This external force is realized by adding average forces to each atom in the piston plane. After the pressure becomes stable, the left valve is removed to make the grease contact the CO₂, and the system is stabilized for about 20 ps to allow for sufficient interactions between CO₂ and grease molecules. Finally, the right valve is removed to release the leakage of CO₂ through the channel. All of the temperature adjustments are realized by using the Nose–Hoover thermostat. The time steps in all simulations are set as 1 fs.

The atomic interactions between CO₂ molecules are described by the EPM2 force field [20], which is capable of accurately predicting the behaviors of CO₂ with different states. The sealing grease consisted of PAO, which is the typical composition of common sealing and lubricating grease [21,22]. The density of the grease was set to about 0.6 g/cm³, which is the common value for commercial products. The bond and angle parameters for the grease are governed by the CVFF force field [23], and the interactions between different grease molecules are described by the LJ potential with the addition of Coulombic pairwise interactions [24], which have been widely used for organic matter and small molecules. The same type is also employed to describe the interactions between CO₂ molecules and the grease molecules, with the potential parameters obtained according to the Lorentz–Berthelot mixing rule [25].

All of the simulations were conducted using open-sourced LAMMPS coding [26] and visualized using OVITO software [27]. Consideration was given to the effect of various parameters, including temperature T, pressure of CO₂ P_CO2, height of the channel h_c, and its surface roughness λ_s. The roughness is obtained by tailoring the channel surface according to a sine function y = λ_ssin(0.5z), in which λ_s is the amplitude and z is the position of atoms along the z direction. A base case is set with T = 310 K, P_CO2 = 50 MPa, h_c = 45.6 Å, and λ_s = 10 Å. One of these parameters will be changed when considering its effect on the sealing performance of greases.

The leakage quantity Q_L is evaluated by calculating the number of CO₂ molecules leaving the channel and crossing its right boundary in the model. Moreover, the number of CO₂ molecules N_CO2 diffused into the channel is calculated in the simulation to show the activities of these molecules under the influence of pressure. The mean-squared displacements of greases, MSD, are obtained to demonstrate their diffusions inside of the channel under the influence of CO₂. Their position of mass center along the x-direction X_m is evaluated to show their movement under high pressure, and their interactions with the channel E_c are also investigated to demonstrate their adhesion strengths with the channel under the influence of interfacial diffusions of CO₂.

3. Results and Discussions

3.1. Temperature Effect

To determine the effect of T on the performances of greases, T = 310, 330, 350, 380, and 400 K are employed in the simulations, all of which are above the critical temperature of sCO₂. The leakage quantity Q_L, shown in Figure 2a, demonstrates several different stages. When the simulation time t ≤ 1000 ps, the cases with different T almost show the same Q_L. With t > 1000 ps, the cases with T > 330 K show an increased Q_L, followed by its sharp increase to a stable value. However, for those with T ≤ 330 K, their Q_L increases slowly with t.

The different Q_L under various T can be further examined by analyzing the number of CO₂ molecules diffused into the channel N_CO2, as shown in Figure 1b. The N_CO2 increases largely at the very start of the simulation because the high pressure of CO₂ can easily induce their diffusion into the greases. With t > 250 ps, the increase in N_CO2 is almost linear for all cases under different T, but with different slopes. It is evident that a high T can cause a large slope, indicating that the high T can largely promote the diffusions of CO₂. Moreover, it should be noted that the increase in N_CO2 for the cases with T > 330 K has a maximum value after a certain simulation time, followed by a sharp decrease. However, the cases with T ≤ 330 K still have an increased N_CO2 until the end of the simulation.

The presence of these different Q_L and N_CO2 under various T can be explained by examining the atomic snapshot of the simulation, as given in Figure 3. It can be seen that at T = 310 K, the CO₂ molecules diffuse into the grease and can pass through it, resulting in their leakage. Moreover, the grease stably stays in the channel during the whole simulation and exhibits blockage effects [28], and thus the CO₂ molecules are accumulated inside of the grease, resulting in a gradually increased N_CO2. This increased N_CO2 further accelerates CO₂ molecules passing through the grease, resulting in a slight increase in the increased trend of Q_L. The above phenomenon is similar for the case at T = 330 K. However, for the cases with T > 330 K, with the increased N_CO2 in the channel, the grease molecules are gradually extruded from the channel; that is, a decrease is induced in the quantity of effective greases hindering CO₂ leakage. As a result, more CO₂ molecules can pass through the grease and increase the Q_L observed in Figure 1a. However, it should be noted that the CO₂ molecules can still be accumulated inside of the channel under the hindering effect of the grease. When the grease molecules are totally extruded from the channel, the CO₂ molecules rapidly pass through the channel, thus causing a sharp increase in Q_L in this case and an evident decrease in N_CO2. Because of the absence of grease inside of the channel, all of the CO₂ molecules in the chamber quickly leak under the pressure, causing the Q_L to reach a stable value, which is indeed the total amount of CO₂ molecules in the system.

The leakage path of high-pressure CO₂ molecules through the grease is quite important to understand the sealing performance of greases. The atomic visualizations show that at low temperature (e.g., T = 330 K), the CO₂ molecules inside of the channel are mainly distributed on the interface between the grease and the channel in a disordered manner, which is different from the literature [29,30]. These CO₂ molecules diffuse along the interface, and part of them is finally released by passing through the whole interface, as shown in Figure 4. With the T further increasing (e.g., T = 330 K), besides the interface as leakage paths, CO₂ molecules distributed inside of the grease can also continue to penetrate into the grease and are finally released. This can be verified by tracking the movement of certain CO₂ molecules, as in the configurations given in Figure 5. These configurations are captured by slicing the grease in its middle part, and the targeted CO₂ molecule is labeled in red. It is evident that this molecule can move toward the outlet, and its position is always inside of the grease, thus validating that the diffusion of CO₂ molecules inside of the grease contributes to their leakage at high T. Therefore, it is evident that the leakage paths at a low T are dominated by the interface between the grease and the channel, but they consist of both the interface and the bulk penetration through the grease at a high T.

The performance of grease molecules can be further examined by evaluating their MSD, the x-directional position of the mass center X_m, and their interaction energy E_c with the channel, as given in Figure 6. Both the MSD and X_m show a gradual increase with T = 310 and 330 K but a sharp increase with a higher T, which is consistent with the changes in Q_L with T in Figure 2. This is because the diffusion or movement indicated by the high MSD corresponds to the fact that the grease molecules can hardly stay stable in the channel, and thus it is difficult to inhibit the leakage of CO₂. Moreover, with T > 330 K, both the MSD and X_m show a large drop following the peak. This because when the grease molecules are extruded from the channel, they tend to attach to the outer surface of the channel under the effect of atomic interactions, thus showing a decreased X_m as well as the MSD.

The interaction energy E_c between the grease molecules and the channel (Figure 6c) shows that E_c increases with the T in the very beginning stage of the simulation. This change in E_c is because at a high T, the CO₂ molecules can easily diffuse into the interface between the greases and the channel and thus increase the distance between them. This indicates that the greases at a high T are easily moved under the function of high pressure from CO₂. With the simulation ongoing, the E_c shows a gradual increase under the low T but a sharp increase under T > 330 K. Such changes are induced by the combined influence of the interfacial diffusions of CO₂ and the extrusion of greases from the channel.

From the simulation, it is observed that the CO₂ can also diffuse into the spaces between grease molecules, which can be demonstrated by the analysis of their density, ρ_g, as given in Figure 7. It is clear that the ρ_g decreases with the T. Because a small density of organic matter commonly represents high fluidity, this decreased ρ_g indicates that the grease molecules easily flow under the function of extruding forces, which may be another factor contributing to the increased MSD, as well as the decreased ability of greases to inhibit leakages. Moreover, the outline of the left boundary of greases becomes quite irregular, which is attributed to the dissolution of greases by supercritial CO₂, which further enhances their diffusion.

From the analysis above, the leakage mechanisms of CO₂ through the greases can be briefly summarized as follows. At the beginning of the contact between the CO₂ and the greases, the grease molecules are closely attached to the channel surface and thus inhibit the leakage of CO₂ molecules. Afterwards, the CO₂ molecules diffuse into the interface between the greases and the channel, and part of these molecules can cross the whole interface and leave from the channel, which is the dominant mechanism at low T. Meanwhile, the CO₂ molecules can also diffuse into the interior of the greases, and such a diffusion trend is highly activated by a high T, finally causing CO₂ leakage by penetrating the whole of the grease. Moreover, at a high T, a large amount of CO₂ molecules diffuses into the greases to lower their density and increase their fluidity, making them easily extruded under pressure.

3.2. Pressure Effect

The sealing performance of greases greatly depends on the pressure (P), as given in Figure 8. It can be seen that the Q_L shows a gradual increase with t for P ≤ 50 MPa, but it demonstrates a dramatic increase with P > 50 MPa. A similar change trend is also observed for the amount of CO₂ molecules, N_CO2, staying in the channel. The changes in both the Q_L and the N_CO2 indicate that the cases with a small P have an increased leakage rate of CO₂, but the ones with a large P might indicate that the greases are extruded from the channel.

Activities of grease molecules can be further examined from their MSD and X_m, as shown in Figure 9. Both the MSD and the X_m have a nearly linear increase with t for the cases with P ≤ 50 MPa, but they show a dramatic increase followed by a sudden drop for the cases with P > 50 MPa. Such a dramatic increase verifies that the greases have been extruded from the channel, while the sudden drop is due to their movement after extrusions. Their interaction energy E_c with the channel also demonstrates a dramatic increase for the cases with P > 50 MPa and a clear difference between the cases with P ≤ 50 MPa. Comparing the changes of X_m and E_c, such a difference in E_c begins at the very beginning of the simulation, which has a small difference in X_m. This fact indicates that a high P might greatly promote the diffusion of CO₂ molecules into the interface between the greases and the channel and thus cause the increase in Q_L.

The leakage process of CO₂ molecules under different P can be clearly seen from the atomic visualizations, as given in Figure 10. With P = 10 MPa, the grease molecules are hardly extruded by pressures and thus maintained well in the channel, while the CO₂ molecules are mainly distributed at the interface between the greases and the channel. As a result, this interface becomes the dominant path for the CO₂ leakage. With the P increasing to a middle value (e.g., 30 or 50 MPa), it can be seen that the CO₂ molecules have the ability to penetrate into the greases, and the amount of those staying at the grease/channel interface also greatly increases. This agrees well with the change in E_c in Figure 9c. However, until end of the simulation, few CO₂ molecules penetrate through the greases, and the leakage path is still dominated by the grease/channel interface. For a high P (e.g., 80 or 100 MPa), the CO₂ molecules quickly diffuse into the grease/channel interface, and the greases are simultaneously extruded from the channel. In this case, few CO₂ molecules diffuse into the greases until their extrusions.

From the analysis above, it can be seen that a high P can accelerate the leakage of CO₂ molecules through the interface between the greases and the channel. Moreover, the leakage caused by the penetration of CO₂ through the grease is absent, as the high P that may cause this leakage can easily extrude the greases from the channel. Compared with the leakage enhanced by a high T, this absence of leakage may be because the solubility of CO₂ into the greases is hardly increased by a high P but it can be improved by a high T. This can be verified by the density of greases in Figure 11, where the greases with a high P exhibit greater density than those with a high T in Figure 7. This indicates that few CO₂ molecules were distributed inside of the greases.

3.3. Effect of Channel Height

The leakage behaviors of CO₂ can be highly influenced by channel heights h_c, given in Figure 12a, which is due to the size effect. For a small h_c, the Q_L almost linearly increases with the simulation time, thus showing the stable sealing performance of greases. However, for a high h_c, the Q_L first has a linear increase, but this is followed by a dramatic increase, which shows that the greases are extruded from the channel.

The effect of h_c on the Q_L can also be verified by the changes in N_CO2, as given in Figure 12b. For a small h_c, the N_CO2 shows a gradual increase, indicating the aggregation of CO₂ molecules in the channel due to their diffusion, and the N_CO2 increases with the h_c at any appointed time. For the largest h_c, the N_CO2 exhibits a sudden drop after the maximum point, showing that the greases are extruded from the channel at this moment. Hence, it is evident that their leakage effect can be generally decreased by a high h_c.

The effect of h_c can be further investigated by examining the MSD of grease molecules, the x-directional position of their mass center X_m, and their interaction energy with channel E_c, as given in Figure 13. For a large h_c, both the MSD and X_m show a dramatic increase, which indicates the sudden acceleration of the greases and their extrusion from the channel. Moreover, X_m increases with the h_c, showing that the fluidity of greases increases with a high h_c, which is because the channel hardly confines the greases with the increases in h_c. This can be proved by the fact that E_c greatly increases with the h_c, which indicates a decrease in the forces between greases and the channel.

The atomic visualization in Figure 14 shows that with a small h_c, the leakage of CO₂ molecules is mainly realized by their diffusion through the interface between the greases and the channel. This is because, in this case, there are little voids or free volumes in the y–z plane formed by the distribution of grease molecules, which hinder the diffusion of CO₂ into the greases. Moreover, the small leakage rate of CO₂ in this case is because of spatial crossover as the small amount of grease becomes suppressed in the channel and thus becomes well-attached to the channel to hinder the diffusion of CO₂ through the interface. With the h_c increasing, both the voids formed by greases and their molecular crossover become enhanced, and thus the CO₂ can easily diffuse into the greases and their interface with channels, resulting in an increased leakage rate.

4. Conclusions

This work investigates the effect of sealing grease on inhibiting the leakage of supercritical carbon dioxide (CO₂) using molecular dynamics simulation. The effects of temperature, pressure, and leakage channel height are systematically examined. The findings indicate that at low temperatures, supercritical CO₂ primarily leaks through the interface between the grease and the leakage channel. However, at higher temperatures, CO₂ significantly penetrates both the grease and the interface, becoming the dominant factor for leakage. Regarding the effect of pressure, the study shows that at low or high pressures, leakage mainly occurs through the interface between the grease and the leakage channel. A high pressure can enhance the fluidity of greases and make them more likely to be extruded from the leakage channel. Moreover, for a small leakage channel height, leakage primarily involves the interfacial penetration of supercritical CO₂. When the height is moderate, the amount of CO₂ penetrating into the grease increases, further raising the leakage rate. With a very large height, the fluidity of the grease becomes more pronounced, primarily because the influence of the leakage channel on the fluidity of greases weakens with increasing height. This makes it easier for the grease to be extruded from the leakage channel.