With the increasing demand for energy in China, coalbed methane (CBM) plays an important role as unconventional natural gas. By liquefying CBM and mixing with natural gas, it has outstanding advantages in environmental protection and energy saving, and could achieve the comprehensive energy utilization. Before the liquefaction of CBM, the decarburization treatment is required to meet the standard of pipeline transportation. This paper developed a two-dimensional mathematical model for decarburization from CBM using membrane absorption. The effects of four amine solutions (ethanolamine (MEA), diethanolamine (DEA), triethanolamine (TEA), and 1-(2-hydroxyethyl)pyrrolidine (1-(2-HE) PRLD)) on the CO2 capture efficiency under different gas-liquid flow rates, absorption fluid concentrations, membrane structure sizes, and membrane modules in series were studied. The simulation results were in good agreement with the experimental data. Numerical results showed that the concentration of the absorption liquid had a significant effect on the decarburization efficiency. In addition, it was noted that the 1-(2-HE) PRLD solution had the best decarburization performance among the absorption liquids. Lastly, the optimal operating conditions for membrane technology to separate acid gases were identified via a parametric optimization. Therefore, it is proved that the membrane absorption method has a good potential in CBM purification.