In a process for filtering water containing solids using filtering membranes (24) in an open tank (120), feed water (14) is introduced into the tank to replace permeate removed (36) from the tank to keep the membranes preferably immersed in water while permeate is withdrawn. From time to time the concentration of solids in the water in the tank is reduced through deconcentration steps in which a volume of water having an increased concentration of solids compared to the initial concentration of solids is drained from the tank and a similar volume of feed water is introduced into the tank. The membranes may remain immersed in water during the deconcentrations by adding feed water to the tank while retentate is withdrawn from the tank.