Method and system for gas purification with first direct absorption step and second absorption step by means of membrane contactor

Method for purification of a pressurized gas stream comprising acidic gases, wherein the method comprises -in a first absorption step bringing the pressurized gas stream in direct contact with a first absorption solution absorbing at least part of the acidic gases, obtaining a gas liquid mixture, -separating the gas liquid mixture in a partly purified pressurized gas stream and a first rich absorption solution, -in a second downstream absorption step bringing the partly purified pressurized gas in contact with a second absorption solution through a membrane contactor, obtaining a second rich absorption solution and a purified pressurized gas stream, and -wherein the first absorption solution is a partially lean absorption solution.