A method for purifying a stream comprising hydrogen, nitrogen, methane and argon to produce a hydrogen and nitrogen containing synthesis gas, a methane rich fuel gas, and at least one nitrogen product, the method comprising the steps of: conditioning the pre-purified feed stream to a temperature near saturation at a pressure greater than 2068 kPa (300 psia); directing the conditioned feed stream to a synthesis gas rectification column configured to produce an hydrogen and nitrogen enriched overhead vapor stream and a methane-rich condensed phase stream at the bottom of the synthesis gas rectification column; subcooling a portion of the methane-rich condensed phase stream via indirect heat exchange with a diverted first portion of a hydrogen free methane bottom stream from a hydrogen stripping column to produce a warmed first portion of the hydrogen free methane bottom stream and a subcooled methane-rich condensed phase stream; reintroducing the warmed first portion of the hydrogen free methane bottom stream from the hydrogen stripping column into the hydrogen stripping column; expanding the subcooled methane-rich condensed phase stream in an expansion valve to a pressure less than or equal to 689 kPa (100 psia); introducing the subcooled and expanded methane-rich condensed phase stream into the hydrogen stripping column proximate the top of the hydrogen stripping column, wherein the hydrogen stripping column is configured to strip hydrogen from the methane rich condensed phase stream and produce the hydrogen free methane bottom stream and a hydrogen enriched gaseous overhead, recycling the hydrogen enriched gaseous overhead from the hydrogen stripping column back to the feed stream; vaporizing a second portion of the hydrogen free methane bottom stream, after expansion in a valve, against the hydrogen and nitrogen enriched overhead vapor stream in a condenser-reboiler disposed within the synthesis gas rectification column to produce a vaporized methane-rich stream or a partially vaporized methane-rich stream; directing the vaporized methane-rich stream or the partially vaporized methane-rich stream and a nitrogen reflux stream to a nitrogen rectification column configured to produce a nitrogen containing overhead vapor stream substantially free of methane, and a methane enriched liquid bottoms stream; warming at least a portion of the nitrogen containing overhead vapor stream via indirect heat exchange with the feed stream to produce a warm gaseous nitrogen stream and directing the warm gaseous nitrogen stream to a nitrogen recovery system to produce the at least one nitrogen product; warming the hydrogen and nitrogen enriched overhead vapor stream via indirect heat exchange with the feed stream to produce the hydrogen and nitrogen containing synthesis gas; and warming the methane enriched liquid bottoms stream via indirect heat exchange with the feed stream to produce the methane rich fuel gas. conditioning the pre-purified feed stream to a temperature near saturation at a pressure greater than 2068 kPa (300 psia); directing the conditioned feed stream to a synthesis gas rectification column configured to produce an hydrogen and nitrogen enriched overhead vapor stream and a methane-rich condensed phase stream at the bottom of the synthesis gas rectification column; subcooling a portion of the methane-rich condensed phase stream via indirect heat exchange with a diverted first portion of a hydrogen free methane bottom stream from a hydrogen stripping column to produce a warmed first portion of the hydrogen free methane bottom stream and a subcooled methane-rich condensed phase stream; reintroducing the warmed first portion of the hydrogen free methane bottom stream from the hydrogen stripping column into the hydrogen stripping column; expanding the subcooled methane-rich condensed phase stream in an expansion valve to a pressure less than or equal to 689 kPa (100 psia); introducing the subcooled and expanded methane-rich condensed phase stream into the hydrogen stripping column proximate the top of the hydrogen stripping column, wherein the hydrogen stripping column is configured to strip hydrogen from the methane rich condensed phase stream and produce the hydrogen free methane bottom stream and a hydrogen enriched gaseous overhead, recycling the hydrogen enriched gaseous overhead from the hydrogen stripping column back to the feed stream; vaporizing a second portion of the hydrogen free methane bottom stream, after expansion in a valve, against the hydrogen and nitrogen enriched overhead vapor stream in a condenser-reboiler disposed within the synthesis gas rectification column to produce a vaporized methane-rich stream or a partially vaporized methane-rich stream; directing the vaporized methane-rich stream or the partially vaporized methane-rich stream and a nitrogen reflux stream to a nitrogen rectification column configured to produce a nitrogen containing overhead vapor stream substantially free of methane, and a methane enriched liquid bottoms stream; warming at least a portion of the nitrogen containing overhead vapor stream via indirect heat exchange with the feed stream to produce a warm gaseous nitrogen stream and directing the warm gaseous nitrogen stream to a nitrogen recovery system to produce the at least one nitrogen product; warming the hydrogen and nitrogen enriched overhead vapor stream via indirect heat exchange with the feed stream to produce the hydrogen and nitrogen containing synthesis gas; and warming the methane enriched liquid bottoms stream via indirect heat exchange with the feed stream to produce the methane rich fuel gas.