filtering fuel through a fuel filter located in a filter housing;

collecting water contaminated with residual amounts of fuel separated from a fuel by the fuel filter in a collecting space in the filter housing;

introducing contaminated water from the collecting space through a water discharge inlet into a water discharge device containing a water-permeable membrane;

passing water molecules through the water-permeable membrane due to a pressure difference across the membrane, whereby the water is freed of residual fuel, and

collecting water freed from residual fuel after passage through the membrane and discharging the water freed from residual fuel to the environment,

wherein said water-permeable membrane has channel structures which are closed in a sealed manner at their upper ends and open at their lower ends, the channel structures receiving water molecules which pass through the water-permeable membrane and combine to form water droplets, wherein the open lower ends of the channel structures open into a separated water receiving area of the discharge device housing which receives the water discharged from the open lower ends of the channel structures.