The selection of efficient deep eutectic solvents (DESs) for simultaneous extraction of carbon dioxide (CO2) and hydrogen sulfide (H2S) as well as purification of methane (CH4) from raw natural gas (NG), a multilevel screening method, is proposed. This method integrates Henry's law constant (H) and vapor-liquid equilibrium (VLE)-based thermodynamic models, critical property estimation, and process simulation. Initially, the H-absorption selectivity desorption index (H-ASDI) screens potential DESs under infinite dilution conditions by estimating the infinite dilution activity coefficient to assess their target properties. Subsequently, their performance is evaluated using the VLE of {DES + NG} systems at specific compositions (1:1, 2:1, 3:1, and 4:1). Shortlisted DESs, identified through the VLE-based ASDI ', are further assessed in a conceptual NG sweetening process flow sheet to determine the best DES. After validating shortlisted DESs through process simulation, key physical properties are analyzed and compared to deduce their suitability for CO2 and H2S removal for practical applications in industries. This multilevel approach ensures thorough assessment and selection of DESs with optimal CO2 and H2S extraction capabilities, which are crucial for efficient gas sweetening processes in industrial applications.