A system and method for efficiently removing hydrogen sulfide from a natural gas feed stream to produce a Stinson Process feed stream and an acid gas stream. A first solvent separates the majority of the carbon dioxide and hydrocarbons from the hydrogen sulfide in the natural gas feed to produce the Stinson feed stream. By removing the majority of the hydrogen sulfide prior to feeding the Stinson Process, a carbon dioxide stream suitable for use in flooding operations may be produced with the Stinson Process. The system and method also increase the concentration of hydrogen sulfide in the acid gas stream, making it suitable for sulfur recovery operations. The system and method are particularly suitable for natural gas feed streams containing 0.5%-20% hydrogen sulfide and at least 20% carbon dioxide. Operation in an anhydrous mode with the addition of nitrogen aids in solvent recovery for recycling.