NOVELTY - Producing methane product gas from feed gas (12) comprising mixture of methane, carbon dioxide, nitrogen, oxygen, and water vapor involves first pressure swing adsorption (PSA) stage where carbon dioxide and water vapor are removed from the feed gas; second temperature swing adsorption (TSA) stage, where carbon dioxide and water are removed from the first intermediate product stream (20); and optionally third PSA stage where nitrogen and oxygen are removed from the second intermediate product to produce the methane product gas.    USE - For producing methane product gas from feed gas comprising mixture of methane, carbon dioxide, nitrogen, oxygen, and water vapor (claimed).    ADVANTAGE - The method produces methane product gas, which has less than 50 ppm carbon dioxide, less than 0.5 ppm water vapor, less than 5% nitrogen, and less than 1% oxygen. The process produces enriched methane suitable for liquefaction or pipeline distribution, which avoids the problems associated with conventional process. The process treats at least 10 scfm but less than 20000 scfm of feed gas; enables production to be safer and more cost effective than conventional process, by using sequence of cyclic adsorption stages in one system; and provides control delivery and quality of gas from each stage of the system, such that the final quality of the product gas is acceptable for liquefaction or pipeline distribution. The method is simple in the construction of the separation system, this eliminates the requirement for separate vessels, valves, fittings, and interconnecting plumbing, which are required in other conventional processes, each handling the removal of one component, thus reduction in physical components and interconnections, greatly reducing the cost of the completed system.    DETAILED DESCRIPTION - Producing a methane product gas from a feed gas (12) comprising a mixture of methane, carbon dioxide, nitrogen, oxygen, and water vapor, where the methane product gas is enriched in methane compared to the feed gas involves a first pressure swing adsorption (PSA) stage where carbon dioxide and water vapor are removed from the feed gas to produce a first intermediate product stream (20) enriched in methane, oxygen, and nitrogen, compared to the feed gas; a second temperature swing adsorption (TSA) stage, where carbon dioxide and water are removed from the first intermediate product stream to produce a second intermediate product containing less than 35 ppm carbon dioxide and less than 35 ppm water vapor; and optionally a third PSA stage where nitrogen and oxygen are removed from the second intermediate product to produce the methane product gas having less than 50 ppm carbon dioxide, less than 0.5 ppm water vapor, less than 5% nitrogen, and less than 1% oxygen.    DESCRIPTION OF DRAWING(S) - The figure shows view of block-diagram of multistage adsorption system.    Feed Gas (12)    Feed compressor (14)    Pressurized feed gas (16)    Water (18)    Waste stream (20)