Installation for the treatment by membrane permeation of a feed gas stream comprising at least methane and carbon dioxide, comprising: - a compressor A making it possible to compress the feed gas stream, - a first membrane separation unit able to receive the gas flow coming from the compressor and to provide a first permeate and a first retentate, - a second membrane separation unit able to receive the first retentate and to provide a second permeate and a second retentate, - a third unit of membrane separation capable of receiving the first permeate and of providing a third permeate and a third retentate, - at least one means for measuring the pressure of the feed gas flow at the inlet of the first membrane separation unit, - at least one means for measuring the methane concentration CH4 in the second retentate, and at least one compressor B making it possible to adjust the suction pressure of the third permeate as a function of the measured pressure of the feed gas flow and the methane concentration measured in the second retentate, with each membrane separation unit comprising at least one membrane more permeable to carbon dioxide than to methane.
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