In natural gas processing plants, acid gas enrichment (AGE) units play a vital role in increasing H2S purity in the acid gas feed of sulfur recovery units (SRUs). Moreover, AGE units also produce a CO2-rich gas stream that is often vented to atmosphere. If CO2 purity is sufficiently high, this stream can be used as an injection gas for enhanced oil recovery (EOR) or for sequestration. In hot climates, AGE units operate at significantly low efficiencies owing to the exothermic nature of their operation. Any enhancement in the efficiency can reap significant benefits. In this work, we study the economic and environmental impact of a process scheme wherein a Ranque–Hilsch vortex tube (RHVT) is used as a cooling system for a lean solvent in an AGE unit located in a hot region of the United Arab Emirates. A simulation model is built using the process simulator ProMax® and is validated using plant design data. It is found that reducing the lean solvent temperature increased the purity of H2S and CO2 product streams. At temperatures lower than 25 °C, the inverse occurs as CO2 absorption becomes favorable thermodynamically. Consequently, a lean solvent temperature of 25 °C is identified to be optimal, thus achieving the lowest energy consumption and carbon footprint, while maintaining high purities of the product gases. At the optimal temperature, the proposed scheme results in steam savings of 13 kg/s (equivalent to 40% reduction in total steam rate). This reduced energy consumption leads to an annual CO2 footprint reduction of 83.7 million kg (equivalent to 40% reduction in total CO2 footprint). The optimal lean solvent temperature increases the purity of the H2S-rich gas stream (acid gas) to 67.3 mol% compared to its base case value of 45.7 mol%. Further, the purity of CO2-rich gas stream increases to 97 mol% compared to its base case value of 89 mol%, thus making it suitable for EOR or sequestration. Economically, the evaluated annual energy savings translate to 11.2 million USD, at a crude oil price of 50 USD. The computed payback period is 1.3 years, thus showing the potential of the proposed process. The process scheme proved to be superior to other commercial alternatives from economic and environmental perspectives.