An improved contactor/separator process is presented where one or more stages of contact and separation is achieved by providing one or more shroud and disengagement device combinations within a vessel, where the disengagement device is connected to the top of the shroud that contains vertically hanging fibers. A liquid admixture of immiscible fluids is directed co-currently upward through the shroud at flooding velocity or greater, where all of the admixture exits the disengagement device through a coalescing material. Tray supports are used to stack additional shroud and disengagement combinations vertically within the vessel. Each tray allows less dense liquids exiting one disengagement device from a lower shroud and disengagement device combination to enter the bottom of a shroud of a shroud and disengagement device combination position vertically above the lower shroud and disengagement device combination.