Acid gas absorption by ionic liquids (ILs) has arisen as a promising alternative technique for biogas or natural gas upgrading. In the present work, IL-based blends are evaluated for potential thermodynamic/kinetic synergistic effects on hydrogen sulfide (H2S) capture through physical and/or chemical absorption. First, a molecular simulation analysis by means of COSMO-RS was used to select IL-based blends with enhanced H2S absorbent thermodynamic properties. Physical absorption parameters of reference (KHenry) for H2S in several IL-based blends were calculated at 298 K, involving both IL mixtures and conventional industrial absorbents (tetraglyme (TGM)) with ILs at different compositions. A Henry’s constant deviation parameter (ΔHKHenryH2S) was employed to analyze the nonideal effects of the mixture on H2S gas solubility in IL-based blends. In addition, the viscosities and diffusivities of the IL-based blends were estimated as key parameters controlling H2S diffusion and absorbent uptake rates. From this analysis, a sample of IL-based blends with promising thermodynamic and kinetic properties was selected for H2S physical absorption. A process simulation analysis using the COSMO-based/Aspen Plus methodology was then carried out and the selected absorbents were evaluated by modeling H2S capture in an industrial-scale commercial packed column. One IL, 1-butyl-3-methylimidazoium acetate ([Bmim][OAc]), presenting high H2S chemical absorption and a low viscous industrial solvent (TGM) were also included. The strong kinetic control of H2S capture by physical absorption indicated the limited potential performance of IL-based blends or neat ILs in industrial equipment. In contrast, the COSMO/Aspen analysis revealed that adequate formulations based on [Bmim][OAc] and TGM present enhanced H2S absorbent properties compared to the neat compounds. These computational results may be used to guide future experimental research to design new H2S absorbents, reducing the highly demanding experimental input.