Pore-scale prediction of the effective mass diffusivity and apparent permeability of carbon gels with adjustable nanoporous characteristics

Abstract

To explore the structural effects on transport properties in carbon gels, an improved method has been introduced to regenerate their nanostructure and numerically illustrate the adjustability of their porous characteristics with the variation of synthesis parameters. Two lattice Boltzmann equations are applied to investigate the permeation and diffusion in the gel structures at the pore scale, and the apparent permeability is formulated to describe the total mass flux using the dusty gas model. The structural properties of the reconstructed models and calculated apparent permeabilities have been fully validated by various experiments. A decoupled analysis of the impact of structural parameters on transport properties demonstrates that increasing porosity and pore size, while decreasing geometric tortuosity, leads to more pronounced changes in intrinsic permeability compared to gas diffusivity. By utilizing a database that encompasses 240 reconstructed gels, a structural–functional relationship for transport properties in carbon gels could be proposed. Concerning the intrinsic permeability, a near quadratic relationship with the porosity and mean pore size, independent of particle size, could be concluded. For the nondimensional effective diffusivity, a power exponent of 1.85 associated with porosity is proposed, and its independence of pore size could be revealed. In addition, for gels with porosities under 0.65 and mean pore sizes less than 133 nm, diffusion supersedes permeation as the dominant term in total mass transfer, indicating that particle sizes have a more pronounced influence on the apparent permeability. The predictive model offers guidance for tailoring the transfer properties of carbon gels at the stage of preparation.