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Excessive CO2 content will reduce the natural gas calorific value and increase the energy consumption of the regenerator in natural gas desulfurization and decarbonization. This paper uses Aspen HYSYS to model a novel two-stage flash process of acid gas removal process from natural gas. According to the results from the simulation, as well as running experiences in a natural gas processing plant in the middle east, it can be demonstrated that this new process, which has been used in the field of natural gas desulfurization and decarbonization, can meet the requirement of product specifications. Based on the steady state simulation, Aspen HYSYS sensitivity function is used to evaluate influence of key operating parameters, such as the second flash pressure and temperature, on the energy consumption. Compared to the traditional acid gas removal process and acid gas enrichment process, the new two-stage flash acid gas removal process has less energy consumption (2.2 × 109 kJ·h−1). In addition, two-stage flash acid gas removal process also improves the efficiency of acid gas enrichment, while the overall energy consumption is less than combination process of traditional process and acid gas enrichment process.