2.1

Model systems

All-atom molecular dynamics (MD) simulations were conducted on the SiO₂ nanofluid–CO₂ system, which initially consisted of two independent phases. The first phase consisted of 500 CO₂ molecules as the bulk system, while the second phase consisted of 2000 water molecules, 4 SiO₂ nanoparticles, 1 PVP molecule (as the dispersant), and 20 Na+ and 20 Cl- ions. The selection of these components was based on experimental studies. The initial dimensions of the binary systems were 40 Å in the x and y directions, and the z dimension was determined by the densities of the SiO₂ nanofluid and CO₂. 3D periodic boundary conditions were applied to ensure system integrity. Figure 1 illustrates the original configuration of the SiO₂ nanofluid–CO₂ system.

Figure. 1

Initial configuration of SiO₂ nanofluid–CO₂ system.

2.2

Simulation details

The MD simulations in this study were performed using the Materials Studio software package, which utilized the COMPASS force field for describing all atoms. Each system underwent three simulation steps: initial energy minimization using the steepest descent algorithm to obtain a stable configuration, followed by a 500 ps run of the constant isothermal- isobaric ensemble (NPT) to achieve the desired temperature and pressure, and concluding with a 1500 ns simulation in the canonical ensemble (NVT) to collect the data. Temperature in NPT ensembles was regulated by the Andersen thermostat, while pressure was controlled by the Berendsen barostat. NVT ensembles employed the Nosé thermostat [9] for temperature control. All simulations utilized a 13 Å cutoff for vdW interactions, Ewald summation for electrostatic interactions, a timestep of 1 fs, and saved the full trajectory with frames outputted every 5 ps for later analysis.

2.3

CO₂ diffusion coefficient calculation

To describe the dissolution behavior of CO₂ to nanofluid, the diffusion coefficient of CO₂ is calculated based on the Einstein relation as follows [10]:

where D represents the diffusion coefficient of CO₂; N represents the number of CO₂ molecules; t is the simulation time; r(0) and r(t) are the position vectors of each molecule at time 0 and t, respectively.

3.1

Pressure effect on the diffusion coefficient of CO₂

In order to investigate the impact of pressure on the effectiveness of CO₂ mass transfer, simulations were conducted at pressure levels of 6 MPa, 12 MPa, 18 MPa, and 24 MPa, while maintaining a temperature of 313 K.

As shown in Figure 1, when pressure is increased from 6 MPa to 24 MPa, the diffusion coefficient of CO₂ increases by 69.9 % from 7.31×10⁻⁹ m²/s to 12.42×10⁻⁹ m²/s. The findings present compelling evidence that with the increase of initial pressure, CO₂ continues to diffuse into the nanofluid, leading to an enhanced solubility in the nanofluid. The increase in pressure strengthens the driving force for the absorption of CO₂, thereby augmenting the absorption of CO₂ in the aqueous phase.

To investigate the factors influencing the diffusion behavior of CO₂ to SiO₂ nanofluid, we conducted individual RDF analyses for each case. The RDF of O(CO₂) – H(H₂O) and Na – O(H₂O) in pressure from 6 MPa to 24 MPa are shown in Figs. 2 and 3, respectively.

Figure. 2

D of CO2 in SiO2 nanofluid at various pressures and 313 K

Figure. 3

RDF of O(CO2)- H(H2O) in SiO2 nanofluid at various pressures

The RDF curves for O(CO₂) and H(H₂O) exhibit two peaks at 2 Å and 4 Å, respectively. The magnitudes of these peaks represent the affinity between CO₂ and water molecules, with the first peak being related to hydrogen bonding.

The RDF curves of O(CO₂) and H(H₂O) at varying pressures is depicted in Figure 2. The curve demonstrates an upward trend in peak amplitude as pressure increases, implying intensified interactions between CO₂ and water molecules. Higher pressure facilitates the enhanced dissolution of CO₂ molecules, while simultaneously reducing the intermolecular distance. Consequently, it promotes closer contact between water and CO₂ molecules.

The RDF curves for Na and O(H₂O) both exhibit two peaks. The first peak occurs at approximately 2.3 Å, while the second peak occurs at around 4.6 Å. These two peaks represent the initial hydration shell and the second hydration shell of the Na ion, respectively, with the impact of the second peak being negligible for all relevant factors.

As shown in Figure 3, a decrease in the peak amplitude of the first peak is observed as pressure increases. This can be attributed to the increase in pressure, which reduces molecular motion, making it challenging for Na ions to associate with water molecules and resulting in a decrease in the quantity of the hydration shell.

3.2

Temperature effect on the diffusion coefficient of CO₂

As illustrated in Figure 4, the diffusion coefficient of CO₂ exhibits a thermally-induced increment with rising temperature, attributed to the heightened thermal motion of CO₂ molecules. Nevertheless, the temperature elevation results in the destabilization of the nanofluid, causing a reduction in the particle surface area. Consequently, this unfavorable effect hampers the enhancement of solubility in the nanofluid and impedes CO₂ dissolution.

Figure4

RDF of Na - O(H2O) in SiO2 nanofluid at various pressure

As shown in Figure 5, as temperature increase, the peak amplitude of the curve decreases, suggesting a reduction in water and CO₂ molecule affinity. Elevated temperatures disrupt hydrogen bonds between the two species, while simultaneously intensifying molecular motion and reducing their contact.

Figure. 5

D of CO2 in SiO₂ nanofluid at various temperatures and 12 MPa

Figure 6 illustrates that elevated temperatures lead to a decrease in the number of the hydration shells. This decrease can be attributed to the increased temperature, which enhances intermolecular repulsion among water molecules and promotes the diffusion of Na ions. As a consequence, the probability of intermolecular interaction between Na ions and water molecules rises, creating an unfavorable environment for CO₂ diffusion into the nanofluid.

Figure.6

RDFs of O(CO₂)- H(H₂O) in SiO₂ nanofluid at different temperatures

Figure. 7

RDFs of Na - O(H₂O) in SiO₂ nanofluid at different temperatures