TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The adsorption column is constituted of at least four adsorbent beds, and in a preferred way at least ten adsorbent beds. The adsorbent has a dynamic capacity of carbon dioxide by at least 4 mmol/g, preferably 2mmol/g between an adsorption pressure (Pads) of 5 MPa, preferably 3 MPa and a desorption pressure (Pdes) of 0.4 MPa. The adsorbent has a pore size of 5-50 Angstrom , preferably 7-25 Angstrom and a porous volume of 0.5-5 ml/g, preferably 0.8-3 ml/g. The adsorbent is formed by the metal-organic frameworks (MOFs), mesoporous silica and activated carbon having a specific surface area of more than 2000 m2/g. The adsorbent is breathing MOFs, i.e. flexible structures of which the pores are open and have sizes of greater than 5 Angstrom at the Pads. The adsorbent is IRMOF-1, IRMOF-3, IRMOF-6, IRMOF-11, MOF-177, (tri)copper-bis(4,4',4"-triazine-2,4,6-triyl-tribenzoate), MIL-100, M1L-101 and MIL 53. The operating temperature is 10-250 degrees C, preferably 10-50 degrees C. Preferred Process: The process is done by: implementation of pressure swing adsorption, when the impurities other than carbon dioxide (CO2) has an affinity for the adsorbent similar to that of CO2; and implementation of PSA, when the impurities other than CO2 present an affinity for the adsorbent significantly lower than CO2, at least one adsorbent bed has two different types of adsorbents, the first with a dynamic capacity of at least 2 mmol/g between Pads of 5 MPa and a desorption pressure Pdes of 0.4 MPa and a second adsorbent for adsorption of impurities other than CO2. The pressurization is carried out several times and depressurization comprises partial co-current depressurization and counter flow depressurization. The two different adsorbents are distributed in at least two specific successive layers of beds. The desorption step comprises a counter flow desorption, with the desorption pressure of CO2 (2-0.4 MPa) and the step of desorption at low pressure comprising 0.4 MPa and atmospheric pressure and, with co- or counterflow. The step of adsorption in the first high-pressure bed is done in series with the second bed, and the desorption of the first bed is carried out at high pressure with counter flow. The high pressure adsorption of the second bed is carried out in series with the first bed. The process operated by implementation of simulated moving bed includes implementing conditions of adequate adsorption (including a pressure Pads) of the charge containing hydrogen and impurities with a solid adsorbent content in beds to preferentially adsorb impurities. The process is coupled with another process separation as the separation membrane or process solvent extraction. A polar impurity is added to the burden to increase the capacity dynamics of the adsorbent. EXAMPLE - No suitable example given.