A novel gas separation process is described and analysed in the context of carbon capture. It involves a highly selective absorbent fluid below its saturation pressure pre-mixed with the gas to be separated and adsorbed into a porous solid. This fluid mixture simultaneously forms gas-like and liquid-like regions within the porous solid depending on the pore size. The gas component to be separated is selectively absorbed by the liquid-like regions, and a novel ‘pressure-swing wetting layer absorption’ process is used to recover the absorbed gas. This work examines the equilibrium behaviour of this process in the context of carbon capture using the density functional theory (DFT) of classical fluids. The DFT model employed represents the porous solid in terms of ideal graphitic slit-pores, and a ternary fluid model is calibrated to represent mixtures of tetrahydrofuran (the absorbent fluid), carbon dioxide and nitrogen. Under the conditions investigated here we find that the equilibrium behaviour of this system is superior to the analogous pressure-swing adsorption process without solvent. This result motivates further experimental and dynamical process modelling studies of this system.