An apparatus and corresponding method of use extracts, cools, and transports effluents from subterranean, sub-sea oil formations to distant shore based processing facilities. The effluents, mostly crude oil, are conveyed rapidly to a cold flow generator near the oil wellhead on the sea bottom using the cold seawater to chill the effluents to a dispersed mixture including generated solids. The mixture is transported close to sea bottom temperatures, slowly, with small pressure drops, in low-cost submerged bare pipes over long distances to on or near shore processing facilities that can produce useful hydrocarbon products more cost effectively than at sea processing facilities. The apparatus eliminates or minimizes the need for heated or insulated pipe, the need for large floating processing structures, the need for sub-sea processing equipment, and/or the need for chemical additions to production flow.