In this work, a series of K2CO3-containing composite materials based on alumina supports with different porous structure were synthesized and studied in a direct air capture process. Alumina supports with the modified porous structure were obtained as a result of the thermal treatment of porous gamma-Al2O3 at elevated temperatures. Composite materials were synthesized by impregnating the porous support (unmodified or modified alumina) with an aqueous solution of potassium carbonate. All the K2CO3/Al2O3 sorbents were tested in the process of CO2 absorption from the air with a relative humidity of 25% followed by thermal desorption as a result of heating the material to 200 degrees C. The composite materials were characterized by X-ray diffraction and temperature-programmed desorption methods. Among the materials studied, the composite sorbent based on the porous alumina thermally modified at T = 750 degrees C demonstrated the highest dynamic CO2 absorption capacity. This composite material was later tested in a direct air capture/methanation process combining CO2 capture from ambient air and methanation via the catalytic Sabatier reaction. The process was implicated using an adsorber and a catalytic reactor connected in series. To regenerate the composite sorbent after the step of CO2 absorption from ambient air, the adsorber was heated to 200 degrees C in an H-2 flow. The desorbed CO2 was converted into methane in the preheated catalytic reactor containing the Ru/Al2O3 methanation catalyst. The optimization of the operating conditions (namely, the catalytic reactor temperature and the inlet H-2 flow rate) allowed for obtaining CH4 from carbon dioxide with a yield of 98%. The thermal energy required for heating the new CO2 sorbent from 25 to 200 degrees C at the desorption/methanation step of the direct air capture/methanation process was estimated to be 9 MJ per 1 m(3) (STP) of produced CH4.