First determine what amine you need. Different amines are selected for different levels of H2S and CO2 content. For information look at vendor websites (BASF, INEOS, etc). The basic sweetening system is a contactor (absorption) tower, a rich amine flash drum, rich/lean amine heat exchanger and an amine regenerator (stripper) tower. There are numerous references online to the basic design of these systems. An example is:

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