Membrane absorption is a novel method for acid gas removal compared to conventional separation techniques. The current study presents the simulation results using a computational fluid dynamics (CFD) method for biogas purification. A comprehensive two-dimensional (2D) mass-transfer model was developed and solved in a hollow fiber membrane contactor (HFMC) under a non-wetted condition. H2O, triethanolamine (TEA), diethanolamine (DEA), monoethamolamine (MEA), and potassium argininate (PA) were used as the absorbent liquids. The effects of gas liquid parameters and membrane characteristics on the CO2 removal efficiency and absorption flux and CH4 recovery were systematically examined and evaluated. The comparisons between model predictions and experimental data with various gas liquid parameters were in good agreement. An increase of gas velocity and CO2 content caused an increase of CO2 flux and a decrease of CO2 removal efficiency and CH4 recovery; however, an increase of absorbent velocity and concentration caused an increase in the above three values. In addition, a smaller fiber inner diameter and membrane thickness and a longer module were good for the biogas upgrading process. It should be noted that the highest CO2 flux coincided with the original module dimensions. The simulation predictions also showed that PA provided better membrane module performance than other absorbents. The order for CO2 absorption efficiency and CH4 recovery was PA > MEA > DEA > TEA > H2O. Overall, the developed model provides the guidelines for selecting the optimum module properties and fluid conditions. The membrane gas absorption technique has shown great potential in biogas upgrading.