A method for removing acidity and/or moisture from a hydrocarbon gas, in particular from a natural gas or a refinery gas fraction or a syngas, by absorption into a sweetening liquid and into a dehydration liquid, that are adapted to extract acid compounds or water from the gas, respectively. The method provides a step of prearranging a vertical elongated container (150) comprising at least one inner partition wall (168) that defines at least two treatment chambers within said container (151,152), a step of feeding a treatment liquid from the above into at least one of the two chambers (251,252) and feeding the gas to be treated from below into at least one same treatment chamber. It is also provided a step of selecting a treatment mode, wherein the gas flows along the two treatment chambers in a parallel or in a series arrangement, or one chamber being excluded; in particular the series-mode or the exclusion mode is actuated when the flowrate of the gas decreases below a minimum threshold value, while the parallel-mode is actuated when the flowrate of the gas rises above a maximum threshold value. An apparatus comprising at least such a container and a gas convey selective convey means (44′,44″), for actuating said treatment modes, in particular responsive to a flowrate of the gas. The apparatus and the method according to the invention allow to maintain the sweetening and/or dehydration efficiency, in particular in the case of a progressive reduction of the flowrate of natural gas that can be obtained from a well or gasfield.