A filtration apparatus that separates a liquid feedstock mixed with a gas into filtrate and retentate, the apparatus including at least one filtration device comprised of at least one monolith segment of porous material that defines a plurality of passageways extending longitudinally from a feed face of the structure to a retentate end face. The filtration device contains at least one filtrate conduit within it for carrying filtrate toward a filtrate collection zone, the filtrate conduit providing a path of lower flow resistance than that of alternative flow paths through the porous material of the device. The filtration device can also be utilized as a membrane support for a device for microfiltration, ultrafiltration, nanofiltration, reverse osmosis, or pervaporation. Also disclosed is a method for using such a filtration apparatus.