The present study investigates the hydrodynamics and mass transfer of the liquid–gas ejector using three-dimensional (air–water) and two-dimensional (CO2/air-MEA (Monoethanolamine) solution) computational fluid dynamics (CFD) modeling. For 3D simulation, validation of the CFD results of this ejector with experimental data (error less than 5%) showed high simulation accuracy. The effects of motive liquid flow rate and outlet pressure parameters on the air entrainment rate and air hold-up are also investigated. It was found that by increasing the outlet pressure by about 70% (from 3587 to 6127 Pag), the rate of gas entrainment and gas hold up decreased by about 37% and 20%, respectively. On the contrary, these parameters showed increasing behavior of about 74% and 15%, respectively, when the mass flow rate of liquid increased by about 21%. In addition, three-dimensional phenomena such as mixing shock and the location of its occurrence are examined, which is the reason for recirculation and vortex in the ejector. Next, by simulating a two-dimensional simulation and changing the inlet fluids to CO2/air-methanol amine, the ejector was designed to simultaneously increase the gas pressure and absorb carbon dioxide. A user-defined function code was used to express the mass transfer from the gas to the liquid phase. The results, in this case, showed that with increasing the outlet pressure of the ejector (from 0 to 2000 Pag), and enhancing the concentration of MEA solution (from 10% to 30%), the CO2 removal boosted from 83% to 95%. A similar behavior was shown when the L/G ratio increased from 3.5 to 5.5. This study serves as a showcase on how to do an exact design and analysis for liquid–gas ejectors in flare gas recovery systems.