Pressure swing adsorption (PSA) is an excellent way for separation and purification of gas mixtures. The mass and energy equations are derived from thermodynamics conservation laws. A multicomponent adsorption model is developed for simulating the breakthrough curves of the mixtures of H2/CO/CO2/CH4 and of H2/CO2 in the activated carbon (AC) bed of hydrogen purification system. The one-dimensional model is developed and implemented on Comsol platform. The model simulates molar fraction evolutions of four components and temperature profiles of the bed and the wall at the axial locations of 20 cm, 70 cm and 110 cm. The model is validated by experimental data and improved by considering a piping system. Parametric studies are made to investigate the influence of the system pressure, gas filling velocity and gas mixture composition on the performance of hydrogen purification system, and to propose guidelines for optimal design of PSA system for hydrogen purification.