Collective Adsorption of Carbon Dioxide and Hydrocarbons Mixtures in Nanopores: A DFT Study

In recent years, the properties of carbon dioxide and hydrocarbons mixtures have attracted considerable interest due to the carbon dioxide emissions. Carbon dioxide capture, utilization, and storage (CCUS) is one of the most essential research areas nowadays. In the oil and gas industry, CO₂can be utilized for enhanced oil recovery (EOR) and shale gas production stimulation [1-3]. Shale rocks contain pores ranging in size, predominantly up to 10 nm [4]. On such a scale, the contribution of surface-fluid molecular interactions to fluid behavior is significant. Therefore, bulk and confined fluid equilibrium properties are different. An alteration of equilibrium mixture composition was obtained by Gibbs Ensemble Monte Carlo simulations (GEMC) [5]. However, this approach has high computational requirements comparing with Density Functional Theory (DFT).

DFT is widely used to predict processes of one component fluids on nanoscale, such as adsorption, capillarity condensation, and others [6-9]. In the 1990s, it was also used to describe mixture properties but was recognized as not accurate enough [10,11]. We have no information about any research on Lennard-Jones fluid mixture with classical molecular DFT since then. The inaccuracy of density profiles for mixture components in pore and mixture adsorption isotherms was explained by the application of mean filed approximation (MFA) for attractive interactions treatment [10,11]. According to the MFA framework, molecules interact with 12-6 Lennard Jones potential that depends on intermolecular interaction parameters σ_ij and ε_ij . In previous works on fluid mixture DFT study [10,11], Lorentz – Berthelot mixing rule was used to obtain parameters σ_ij and ε_ij for different types of molecules. We suggest that the MFA work better with appropriate intermolecular interaction parameters definition. Another mixing rule that is empirically fitted to the experimental data was applied in DFT study of binary mixtures [12]. However, here local density approximation (LDA) was used to account for hard sphere interactions, which is insufficient for fluid structure description near a wall.

To accurately describe fluid mixture behavior in pores, we use fundamental measure theory (FMT) to calculate hard sphere interactions. We also fit DFT equation of state (DFT EoS) to the mixture isotherm experimental data to select parameters σ_ij and ε_ij for the mixture. We use mixture data available in literature [13,14,15]. We show that DFT EoS with parameters found by Lorentz – Berthelot mixing rule poorly represents fluid mixture properties in the bulk.

In our work, we investigate fluid mixture properties in pores using DFT. At first, DFT EoS is fitted to mixtures isotherms available in literature [12,13,14] and calculated by molecular dynamics at the desired conditions. Then parameters σ_ij and ε_ij are known, and we study fluid mixtures in pores. Structural properties, composition, and adsorption of hydrocarbon and CO₂ mixtures with different pore sizes and different concentrations of CO₂ are investigated. We consider mixtures of methane, ethane, and butane with carbon dioxide in slit-shaped carbon pores, where solid-fluid interactions are described by Steel 10-4-3 potential. Simulations are carried at the temperature T = 320 K, and carbon dioxide mole fraction is in the range from 1% to 50% within pores 0.6 – 10 nm wide.We obtain equilibrium density profiles of mixtures for various pore widths, pressures, and component concentrations in the bulk. Then equilibrium density profiles are integrated, and composition change in pores is analyzed. We also obtain adsorption isotherms for different mixture compositions.

The figure demonstrates carbon dioxide equilibrium concentration x(CO₂) in slit-like carbon pore H_CC = 1nm depending on its concentration in the bulk mixture at T = 320 K and ρ_mixture = 1.2*10^-4 Ã…^-3. Despite the low CO₂ concentration in the bulk mixture, it is adsorbed in the pores more in particular cases. The CO₂ presence changes the adsorption behavior to the preferential adsorption of carbon dioxide over hydrocarbons, and this effect becomes stronger in smaller pores. It is concluded that pore sizes and fluid-fluid and solid-fluid component parameters relationship controls the mixture adsorption behavior.

These results are essential for simulations and predictions of CO₂ behavior for CCUS technological applications. The proposed framework of DFT with FMT and MFA for molecular interaction description and definition of intermolecular interaction parameters by fitting experimental data predicts fluid-solid interfacial behavior accurately. This framework can extend DFT application for fluid mixtures behavior investigations in different industry fields. Further, we will extend our DFT calculations for designing a shale gas simulation.

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