Disclosed are a facility and a method using the facility for treating a feed gas stream comprising at least methane and carbon dioxide by membrane permeation, the facility comprising: —a first membrane separation unit capable of receiving the feed gas stream and providing a first permeate and a first retentate, —a second membrane separation unit capable of receiving the first retentate and providing a second permeate and a second retentate, —a compressor for compressing the first permeate to a pressure of between 17 bar and 25 bar, —a means for cooling the first compressed permeate to a temperature lower than −40° C., —a distillation column for separating the first cooled permeate into a gas stream and a liquid stream, —at least one means for recycling the gas stream exiting the distillation column to the inlet of the first membrane separation unit, —a means for measuring the concentration of methane and/or carbon dioxide in the gas stream exiting the distillation column, —a means for comparing the concentration of methane and/or carbon dioxide measured by the measurement means with a target value, and —a means for adjusting the pressure and/or the temperature of the first permeate depending on the comparison carried out by the comparison means.

Disclosed are a facility and a method using the facility for treating a feed gas stream comprising at least methane and carbon dioxide by membrane permeation, the facility comprising: —a first membrane separation unit capable of receiving the feed gas stream and providing a first permeate and a first retentate, —a second membrane separation unit capable of receiving the first retentate and providing a second permeate and a second retentate, —a compressor for compressing the first permeate to a pressure of between 17 bar and 25 bar, —a means for cooling the first compressed permeate to a temperature lower than −40° C., —a distillation column for separating the first cooled permeate into a gas stream and a liquid stream, —at least one means for recycling the gas stream exiting the distillation column to the inlet of the first membrane separation unit, —a means for measuring the concentration of methane and/or carbon dioxide in the gas stream exiting the distillation column, —a means for comparing the concentration of methane and/or carbon dioxide measured by the measurement means with a target value, and —a means for adjusting the pressure and/or the temperature of the first permeate depending on the comparison carried out by the comparison means.

Selective removal of non-aromatic hydrocarbons from a xylene isomerization process for para-xylene production is accomplished using a membrane unit positioned within a xylene recovery loop. The membrane unit may include a one-stage or multi-stage (e.g., two-stage) membrane system and may be configured to separate a membrane unit product stream from a non-aromatics rich stream, which can be removed from the xylene recovery loop. The membrane unit may have a xylene permeance of about 60 gm/m2/hr/psi and a xylene to non-aromatic permeance ratio of about 15.

Selective removal of non-aromatic hydrocarbons from a xylene isomerization process for para-xylene production is accomplished using a membrane unit positioned within a xylene recovery loop. The membrane unit may include a one-stage or multi-stage (e.g., two-stage) membrane system and may be configured to separate a membrane unit product stream from a non-aromatics rich stream, which can be removed from the xylene recovery loop. The membrane unit may have a xylene permeance of about 60 gm/m2/hr/psi and a xylene to non-aromatic permeance ratio of about 15.

One variation of a method includes: ingesting an air sample captured during an air capture period at a target location for collection of a first mixture including carbon dioxide and a first concentration of impurities; conveying the first mixture through a liquefaction unit to generate a second mixture including carbon dioxide and a second concentration of impurities less than the first concentration of impurities; in a methanation reactor, mixing the second mixture with hydrogen to generate a first hydrocarbon mixture comprising a third concentration of impurities comprising nitrogen, carbon dioxide, and hydrogen; conveying the first hydrocarbon mixture through a separation unit configured to remove impurities from the first hydrocarbon mixture to generate a second hydrocarbon a fourth concentration of impurities less than the third concentration of impurities; and depositing the second hydrocarbon mixture in a diamond reactor containing a set of diamond seeds to generate a first set of diamonds.

One variation of a method includes: ingesting an air sample captured during an air capture period at a target location for collection of a first mixture including carbon dioxide and a first concentration of impurities; conveying the first mixture through a liquefaction unit to generate a second mixture including carbon dioxide and a second concentration of impurities less than the first concentration of impurities; in a methanation reactor, mixing the second mixture with hydrogen to generate a first hydrocarbon mixture comprising a third concentration of impurities comprising nitrogen, carbon dioxide, and hydrogen; conveying the first hydrocarbon mixture through a separation unit configured to remove impurities from the first hydrocarbon mixture to generate a second hydrocarbon a fourth concentration of impurities less than the third concentration of impurities; and depositing the second hydrocarbon mixture in a diamond reactor containing a set of diamond seeds to generate a first set of diamonds.

One variation of a method includes: ingesting an air sample captured during an air capture period at a target location for collection of a first mixture including carbon dioxide and a first concentration of impurities; conveying the first mixture through a liquefaction unit to generate a second mixture including carbon dioxide and a second concentration of impurities less than the first concentration of impurities; in a methanation reactor, mixing the second mixture with hydrogen to generate a first hydrocarbon mixture comprising a third concentration of impurities comprising nitrogen, carbon dioxide, and hydrogen; conveying the first hydrocarbon mixture through a separation unit configured to remove impurities from the first hydrocarbon mixture to generate a second hydrocarbon a fourth concentration of impurities less than the third concentration of impurities; and depositing the second hydrocarbon mixture in a diamond reactor containing a set of diamond seeds to generate a first set of diamonds.

One variation of a method includes: ingesting an air sample captured during an air capture period at a target location for collection of a first mixture including carbon dioxide and a first concentration of impurities; conveying the first mixture through a liquefaction unit to generate a second mixture including carbon dioxide and a second concentration of impurities less than the first concentration of impurities; in a methanation reactor, mixing the second mixture with hydrogen to generate a first hydrocarbon mixture comprising a third concentration of impurities comprising nitrogen, carbon dioxide, and hydrogen; conveying the first hydrocarbon mixture through a separation unit configured to remove impurities from the first hydrocarbon mixture to generate a second hydrocarbon a fourth concentration of impurities less than the third concentration of impurities; and depositing the second hydrocarbon mixture in a diamond reactor containing a set of diamond seeds to generate a first set of diamonds.

One variation of a method includes: ingesting an air sample captured during an air capture period at a target location for collection of a first mixture including carbon dioxide and a first concentration of impurities; conveying the first mixture through a liquefaction unit to generate a second mixture including carbon dioxide and a second concentration of impurities less than the first concentration of impurities; in a methanation reactor, mixing the second mixture with hydrogen to generate a first hydrocarbon mixture comprising a third concentration of impurities comprising nitrogen, carbon dioxide, and hydrogen; conveying the first hydrocarbon mixture through a separation unit configured to remove impurities from the first hydrocarbon mixture to generate a second hydrocarbon a fourth concentration of impurities less than the third concentration of impurities; and depositing the second hydrocarbon mixture in a diamond reactor containing a set of diamond seeds to generate a first set of diamonds.

One variation of a method includes: ingesting an air sample captured during an air capture period at a target location for collection of a first mixture including carbon dioxide and a first concentration of impurities; conveying the first mixture through a liquefaction unit to generate a second mixture including carbon dioxide and a second concentration of impurities less than the first concentration of impurities; in a methanation reactor, mixing the second mixture with hydrogen to generate a first hydrocarbon mixture comprising a third concentration of impurities comprising nitrogen, carbon dioxide, and hydrogen; conveying the first hydrocarbon mixture through a separation unit configured to remove impurities from the first hydrocarbon mixture to generate a second hydrocarbon a fourth concentration of impurities less than the third concentration of impurities; and depositing the second hydrocarbon mixture in a diamond reactor containing a set of diamond seeds to generate a first set of diamonds.