NOVELTY - Removing hydrogen sulfide and carbon dioxide from gas mixture (100) involves providing gas mixture having methane, carbon monoxide, hydrogen, hydrogen sulfide and carbon dioxide; contacting with first absorber under first set of operating conditions to form hydrogen sulfide-depleted gas stream and hydrogen sulfide-laden absorber stream; recovering the stream; contacting with a second absorber under a second set of operating conditions to produce a carbon dioxide-depleted gas stream and a carbon dioxide-laden absorber stream; and recovering carbon-dioxide laden absorber stream.    USE - For removing hydrogen sulfide and carbon dioxide from a gas mixture (claimed); for selective removal and recovery of acid gases from gas source such as gas source produced from catalytic gasification of carbonaceous material, combustion of carbonaceous material or oxy-blown gasification of carbonaceous material; in integrated gasification process for converting carbonaceous feedstock such as petroleum coke, liquid petroleum residue and/or coal to combustible gases such as methane.    ADVANTAGE - The method allows selective removal and recovery of acid gases from a gas source comprising at least hydrogen sulfide and carbon dioxide. The method enables selective removal of hydrogen sulfide with decreased carbon dioxide extraction from gasification product stream.    DETAILED DESCRIPTION - Removing hydrogen sulfide and carbon dioxide from a gas mixture (100) involves providing a gas mixture comprising methane, carbon monoxide, hydrogen, hydrogen sulfide and carbon dioxide; contacting the gas mixture with a first absorber under a first set of operating conditions to produce a hydrogen sulfide-depleted gas stream and a hydrogen sulfide-laden absorber stream, where the hydrogen sulfide-depleted gas stream comprises less than or equal to 5 ppm hydrogen sulfide; recovering the hydrogen sulfide-laden absorber stream; contacting the hydrogen sulfide-depleted gas stream with a second absorber under a second set of operating conditions to produce a carbon dioxide-depleted gas stream and a carbon dioxide-laden absorber stream, where the carbon dioxide-depleted gas stream comprises less than or equal to 50 ppm of carbon dioxide; and recovering the carbon dioxide-laden absorber stream, where the first operating conditions include a first operating temperature and a first operating pressure, the second operating conditions includes a second operating temperature and a second operating pressure, the first operating temperature is greater than the second operating temperature and the first and second absorbers comprise methanol. The process further involves recovering carbon dioxide from the carbon dioxide-laden at a pressure of 350-450 psia. INDEPENDENT CLAIMS are included for the following:    (1) converting carbonaceous composition into several gaseous products involving supplying carbonaceous composition to gasification reactor; reacting the carbonaceous composition in the gasifying reactor in the presence of steam and a gasification catalyst under temperature and pressure to form gaseous products comprising methane, hydrogen, carbon monoxide, carbon dioxide and hydrogen sulfide, where the gasification catalyst comprises an alkali metal; removing portion of the hydrogen sulfide and carbon dioxide from the gaseous products to produce a hydrogen sulfide and carbon dioxide-depleted product gas stream; and at least partially separating the hydrogen sulfide and carbon dioxide-depleted product gas stream to produce a stream comprising a predominant amount of one of the remaining gaseous products; and    (2) an apparatus for the purification of a gaseous mixture comprising: a first unit (102) containing a first unit top portion, a first unit bottom portion, a first gaseous mixture feed line (101), a first liquid feed line (111), a first condenser (106) in fluid communication with the first unit top portion, where the first condenser comprises a first condenser overhead portion, a first condenser bottom portion, and a first gaseous product line in fluid communication with the first condenser overhead portion, a first reboiler (103) in fluid communication with the first unit bottom portion, and a first bottoms line in fluid communication with the first unit bottom portion; and a second unit (202) containing a second unit top portion, a second unit bottom portion, a second gaseous mixture feed line in fluid communication with the first gaseous product line, a second liquid feed line, second condenser (206) in fluid communication with the second unit top portion, where the second condenser comprises a second condenser overhead portion, a second condenser bottom portion, and a second gaseous product line in fluid communication with the second condenser overhead portion, a second reboiler (203) having a second reboiler top portion and a second reboiler bottom portion, in fluid communication with the second unit bottom portion, and a second bottoms line in fluid communication with the second unit bottom portion or the second reboiler bottom portion.    DESCRIPTION OF DRAWING(S) - The figure shows schematic view of a process for sequentially and selectively removing hydrogen sulfide and carbon dioxide from a gas source.    Gas mixture (100)    First gaseous mixture feed line (101)    First unit (102)    First reboiler (103)    First condenser (106)    First liquid feed line (111)    Second unit (202)    Second reboiler (203)    Second condenser (206)    First liquid-gas separation unit (302)    Third reboiler (303)    Third condenser (306)    Holding tank (500)