Method for treating a feed gas stream and associated installation

An installation for treating a feed gas, comprising:

• an natural gas liquids extractor;
• at least a pipe supplying a feed gas stream and conveying the feed gas stream into the extractor;
• the extractor comprising:
• a cooler of the feed gas stream, configured to produce a cooled feed stream;
• an expander and a separator configured to separate at least one stream obtained from the cooled feed gas stream, the separator comprising a separation column, the separator being configured to produce a treated gas stream and a natural gas liquid stream;
• at least one compressor configured to compress the treated gas stream, to form a compressed treated gas stream;
• a fractionator configured to fractionate the natural gas liquid stream into a plurality of hydrocarbon cuts;
• a recycle stream withdrawer configured to withdraw a recycle stream in the compressed treated gas stream;
• a recycle stream introducer configured to reintroduce, without cooling, the recycle stream into at least one of:
• the feed gas stream upstream of the extractor, or
• the cooled feed gas stream, or
• a stream obtained from the cooled feed gas stream, upstream of the expander.