TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Components: The methane feed gas is at least one of landfill gas, natural gas, enteric fermentation gas, gob gas, manure management gas, or wastewater treatment gas. The methane feed gas comprises (%) methane (45-60), carbon dioxide (20-40), nitrogen (5-15), oxygen (0.5-5), and water vapor (0.1-3). Preferred Method: The feed gas is pre-treated prior to the first PSA stage to remove at least one of volatile organic compounds (VOCs), siloxanes, hydrogen sulfide, and water. The methods utilize an adsorbent which is at least one of a zeolite, an activated alumina, a silica gel, or activated carbon. The first PSA stage adsorbent comprises a silica gel. The first PSA stage comprises at least three parallel adsorption columns, A, B, and C. The first PSA stage columns operate synchronously, such that while first adsorption column A is being fed, second adsorption column B undergoes pressure equalization with third adsorption column C, followed by countercurrent blowdown, evacuation, and purge; and simultaneously, third adsorption column, C, undergoes pressure equalization with second adsorption column B, followed by pressurization with purified product, and at the end of column A feed step, first adsorption column A commences pressure equalization along with second adsorption column B, and third adsorption column C commences its feed step. The second TSA stage comprises at least three parallel adsorption columns, A, B, and C. The second TSA stage columns operate synchronously, such that while first adsorption column A is being fed, second adsorption column B is cooled by the effluent of column A; simultaneously, the third adsorption column C undergoes countercurrent blowdown and heating, purge, cooling via purge, followed by pressurization with purified product; at the end of column A feed step (state 50), first adsorption column A commences countercurrent blowdown and heating, while adsorption column B commences its feed step, and third adsorption column C commences cooling by the effluent of column B. The third PSA stage comprises at least four parallel adsorption columns, A, B, C, and D. The third PSA stage columns operate synchronously, such that while first adsorption column A is being fed, second adsorption column B undergoes rinse, being fed with a recycled part of the enriched methane, and producing as effluent having a composition similar to that of the feed; the net enriched methane product is withdrawn; the pressure in column B is incrementally higher than that in column A, allowing the effluent from column B to be combined with the feed without further compression; simultaneously, third adsorption column C undergoes countercurrent blowdown and evacuation; simultaneously, fourth adsorption column, D, undergoes purge; followed by pressurization with purified product; at the end of column A feed step, first adsorption column A commences rinse; adsorption column B commences countercurrent blowdown; third adsorption column C commences purge; and fourth adsorption column D commences its feed step. In the method (m2) the first PSA stage and the second PSA stage, each comprise at least three parallel adsorption columns, A, B, and C. In the method (m2), the third PSA stage and second PSA stage comprises at least four parallel adsorption columns, A, B, C, and D. In the method (m3) the third PSA stage columns operate synchronously, such that while first adsorption column A is being fed, second adsorption column B undergoes rinse, being fed with the recycled part of the enriched methane, and producing as effluent having a composition similar to that of the feed; the net enriched methane product is withdrawn; the pressure in column B is incrementally higher than that in column A, allowing the effluent from column B to be combined with the feed without further compression; simultaneously, third adsorption column C undergoes countercurrent blowdown and evacuation; simultaneously, fourth adsorption column, D, undergoes purge; followed by pressurization with purified product; at the end of column A feed step, first adsorption column A commences rinse; adsorption column B commences countercurrent blowdown; third adsorption column C commences purge; and fourth adsorption column D commences its feed step. EXAMPLE - No suitable example is given.