Alkaline solutions resulting from extracting sulfide from hydrocarbon fluids can be treated in a combination of one or more electrodialysis cells and a bioreactor. The electrodialysis cell (2) includes an anode (4), a cathode (5), an electric power supply (7) and a first (12) and a second (11) compartment separated from each other by an anion exchange membrane (9). The alkaline solution is fed into the first compartment at the cathode side and the diluate (sulfide-depleted stream) leaving the first compartment has a lowered sulfide content and can be reused as the alkaline extractant solution. The concentrate (sulfide-enriched stream) leaving the second compartment is treated in the bioreactor (3) for removing sulfide and is then returned.