Thermodynamic factors for diffusion connect the Fick and Maxwell-Stefan diffusion coefficients used to quantify mass transfer. Activity coefficient models or equations of state can be fitted to experimental or simulation data, from which thermodynamic factors can be obtained by differentiation. The accuracy of thermodynamic factors determined using indirect routes is dictated by the specific choice of an activity coefficient model or an equation of state. The Permuted Widom’s Test Particle Insertion (PWTPI) method developed by Balaji et al. enables direct determination of thermodynamic factors in binary and multicomponent systems. For highly dense systems, for example, typical liquids, it is well known that molecular test insertion methods fail. In this article, we use the Continuous Fractional Component Monte Carlo (CFCMC) method to directly calculate thermodynamic factors by adopting the PWTPI method. The CFCMC method uses fractional molecules whose interactions with their surrounding molecules are modulated by a coupling parameter. Even in highly dense systems, the CFCMC method efficiently handles molecule insertions and removals, overcoming the limitations of the PWTPI method. We show excellent agreement between the results of the PWTPI and CFCMC methods for the calculation of thermodynamic factors in binary systems of Lennard-Jones molecules and ternary systems of Weeks-Chandler-Andersen molecules. The CFCMC method applied to calculate the thermodynamic factors of realistic molecular systems consisting of binary mixtures of carbon dioxide and hydrogen agrees well with the NIST REFPROP database. Our study highlights the effectiveness of the CFCMC method in determining thermodynamic factors for diffusion, even in densely packed systems, using relatively small numbers of molecules.

H₂-CO₂ mixtures find wide-ranging applications, including their growing significance as synthetic fuels in the transportation industry, relevance in capture technologies for carbon capture and storage, occurrence in subsurface storage of hydrogen, and hydrogenation of carbon dioxide to form hydrocarbons and alcohols. Here, we focus on the thermodynamic properties of H₂-CO₂ mixtures pertinent to underground hydrogen storage in depleted gas reservoirs. Molecular dynamics simulations are used to compute mutual (Fick) diffusivities for a wide range of pressures (5 to 50 MPa), temperatures (323.15 to 423.15 K), and mixture compositions (hydrogen mole fraction from 0 to 1). At 5 MPa, the computed mutual diffusivities agree within 5% with the kinetic theory of Chapman and Enskog at 423.15 K, albeit exhibiting deviations of up to 25% between 323.15 and 373.15 K. Even at 50 MPa, kinetic theory predictions match computed diffusivities within 15% for mixtures comprising over 80% H₂ due to the ideal-gas-like behavior. In mixtures with higher concentrations of CO₂, the Moggridge correlation emerges as a dependable substitute for the kinetic theory. Specifically, when the CO₂ content reaches 50%, the Moggridge correlation achieves predictions within 10% of the computed Fick diffusivities. Phase equilibria of ternary mixtures involving CO₂-H₂-NaCl were explored using Gibbs Ensemble (GE) simulations with the Continuous Fractional Component Monte Carlo (CFCMC) technique. The computed solubilities of CO₂ and H₂ in NaCl brine increased with the fugacity of the respective component but decreased with NaCl concentration (salting out effect). While the solubility of CO₂ in NaCl brine decreased in the ternary system compared to the binary CO₂-NaCl brine system, the solubility of H₂ in NaCl brine increased less in the ternary system compared to the binary H₂-NaCl brine system. The cooperative effect of H₂-CO₂ enhances the H₂ solubility while suppressing the CO₂ solubility. The water content in the gas phase was found to be intermediate between H₂-NaCl brine and CO₂-NaCl brine systems. Our findings have implications for hydrogen storage and chemical technologies dealing with CO₂-H₂ mixtures, particularly where experimental data are lacking, emphasizing the need for reliable thermodynamic data on H₂-CO₂ mixtures.

Underground hydrogen (H₂) storage in saline aquifers is a viable solution for large-scale H₂ storage. Due to its remarkably low viscosity and density, the flow of H₂ within saline aquifers exhibits strong instability, which needs to be thoroughly investigated to ensure safe operations at the storage site. For the first time, we develop a lattice Boltzmann model tailored for pore-scale simulations of the H₂-brine system under typical subsurface storage conditions. The model captures the significant contrast of fluid properties between H₂ and brine, and it offers the flexibility to adjust the contact angle to suit varying wetting conditions. We show that the snap-off is enhanced in a system with a high capillary number and a small contact angle. These conditions lead to a low recovery factor, which is unfavorable for H₂ production from the aquifer. Moreover, the relative permeability curves, computed from the simulation results, exhibit distinct behaviors for H₂ and brine. In the case of the wetting phase, the relative permeability can be quantified using the quadratic expression, whereas for the non-wetting phase, the relative permeability exhibits a nearly linear behavior, and saturation alone appears insufficient to characterize the relative permeability at large saturations of non-wetting phase. This implies that different formula for liquid and gas phases may be employed for continuum-scale simulations.