A natural-gas purification apparatus includes: a plurality of carbon-dioxide separation units that are arranged in series and separate carbon dioxide, through carbon-dioxide separation membranes, from natural gas pressurized by a compressor, cooled by a cooling unit to liquefy and separate a high-boiling-point hydrocarbon component, and heated by a heating unit; a gas supply pipe that is provided between the plurality of carbon-dioxide separation units through on-off valves and that supplies the natural gas; a compressor that is provided to the gas supply pipe; a cooling unit that liquefies and separates a high-boiling-point hydrocarbon component by cooling the natural gas pressurized by this compressor; and a heating unit that heats the natural gas after the separation of the high-boiling-point hydrocarbon component by this cooling unit.
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