TECHNOLOGY FOCUS - INSTRUMENTATION AND TESTING - Preferred Apparatus: The apparatus has two or more adsorber vessels, arranged for cyclic alternating and repetitive operation in which one or more of the adsorber vessels is adsorbing carbon dioxide from the gas mixture, while the other of the adsorber vessels is desorbing previously adsorbed carbon dioxide from the carbon pyrolyzate adsorbent bed, or in a pressure balancing or standby operation mode awaiting resumption of adsorbing operation. Each of the at least one adsorber vessels is arranged for pressure or vacuum swing operation, temperature swing operation, pressure/vacuum swing operation, or temperature/pressure swing operation. Each of at least one adsorbent bed(s) is disposed in an adsorber vessel through which the gas mixture is arranged to flow during the first period of time, and which is arranged for desorption of carbon dioxide from the carbon pyrolyzate adsorbent in the bed during the second period of time.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Components: The adsorbent material has (a) total ash content of less than 1%, as measured by ASTM D2866, (b) bulk density of 0.55-1.25 g/cc as measured by ASTM D2854, (c) carbon dioxide heats of adsorption and desorption each of which is 5-50 kJ/mole, and (d) single pellet radial crush strength for nominal 3 mm pellet of greater than 7 kilopound (kP) as measured by ASTM D4179. The adsorbent material comprises monolith, block, brick, bar, disc, honeycomb, channeled block, fibrous wool, felt, fabric, sponge, mat, particulate, tablet, pellet, extrudate, bead, particulate or tablet, preferably pellet, bead, or extrudate. The particulate form comprises adsorbent particles of size 0.1-7 mm. The adsorbent material comprises carbon pyrolyzate of organic material comprising non-graphitizing hard carbon having narrow slit-shaped micropores. The carbon pyrolyzate of organic material is pyrolyzate of polyvinylidene fluoride, polyvinylidene chloride, or copolymer of polyvinylidene fluoride or polyvinylidene chloride with acrylonitrile, styrene, methyl acrylate, vinyl fluoride, vinyl chloride, or methyl methacrylate. The carbon pyrolyzate has micropores that are tunable through an activation process of controlled environment, pressure, temperature, and time to improve selectivity of carbon dioxide adsorption in preference to methane adsorption. The adsorbent material is derived from polymer or copolymer comprising more than 50 wt.% polyvinylidene chloride, where starting polymer or copolymer has density of 0.75-1.75 g/cc and melting point of 125-265 degrees C. EXAMPLE - No suitable example given.