The gaseous effluent flowing in through line 1 is contacted in absorption zone ZA with the liquid absorbent solution flowing in through line 9. The gaseous effluent depleted in acid compounds is discharged through line 2. The absorbent solution laden with acid compounds is discharged through line 3. The absorbent solution once laden with acid compounds comprises two phases: a first phase poor in acid compounds and a second phase rich in acid compounds. The two phases are separated in zone ZS. The first phase is recycled through lines 5 and 9 to absorption zone ZA. The second phase is fed through line 4 into regeneration zone ZR. In zone ZR, the acid compounds are separated from the absorbent solution. The acid compounds are discharged through line 7. The regenerated absorbent solution is recycled through lines 6 and 9 to zone ZA.