Ugo Bardi first calculation is for "evaporating the ocean", which no one is proposing and he unsurprisingly finds that has very poor energy return.
We need to process at least 2 × 10^13 tons of water per year to produce enough uranium for the current park of nuclear reactors in the world. To process this amount of water, we must rely on oceanic currents to move water through the membranes. In marine science, current strength is sometimes measured in “Sverdrups”, a unit that corresponds to one million tons of water per second, or 3 × 10^13 tons of water per year. Ugo looks at the Strait of Gibraltar which carries a current of about 1 Sverdrup.
Japan has proposed various scaling up plans for uranium from seawater They look at the Black Current (42 Sverdrup, 42 times stronger than the current Ugo looked at) in the ocean off of Japan and how much materials it is moving. They would put uranium extraction materials in its path and collect uranium and other resources as they are moved past the materials that would trap the resources.
Kuroshio which has 42 Sverdrups.
The Agulhas Current is the Western Boundary Current of the southwest Indian Ocean. It flows down the east coast of Africa from 27°S to 40°S. It is narrow, swift and strong. It is even suggested that the Agulhas is the largest western boundary current in the world ocean, as comparable western boundary currents transport less, ranging from the Brazil Current, 16.2 Sverdrups), to the Kuroshio, 42 Sverdrups
The sources of the Agulhas Current are the East Madagascar Current (25 Sverdrups), the Mozambique Current (5 Sverdrups) and a reticulated part of the Agulhas Current itself (35 Sverdrups). The net transport of the Agulhas Current is estimated as 100 Sv.
* Ugo considers a process where membranes for uranium extraction are carried at sea, submerged for a while, raised, brought back to land for processing, and then the cycle is repeated.
* Ugo assumes recovering one kilogram of uranium, therefore, would require processing at least 3 tons of membranes per year.
* Ugo calculates using the ratio of 5 kWh/kg for energy expenditure in fishing, and assuming the yield and the conditions reported by Seko , we can calculate a total energy expenditure of about 1000 TWh/year for processing the membranes to give sufficient amounts to fuel the present needs of the nuclear industry. This is close to the total energy that could be produced by the extracted uranium, ca. 2600 TWh/year. An energy gain (EROEI) of 2.6 is larger than unity, but it is too low for the process to be of practical interest.
Japan is looking at offshore processing, which would save the fuel costs of bringing the absorbent from the ocean to a land based facility.
Japan has lab scale work for extraction of uranium from seawater that is about twice the current cost of traditionally mined uranium using cotton dipped in juice with a lot of tannins.
Japan has proposed various scaling up plans for uranium from seawater Japan is also looking at genetically engineering seaweed to be the absorbent which will produce biofuel and extract uranium and vanadium by having high levels of tannin. By using organic materials absorbent there would not be the issue of using oil to create the capture material. By using genetically altered seaweed, there would be the energy gain from the biofuel and the uranium.
Ugo also bases his calculations on once through reactors. Switching to advanced breeder reactors or extensive reprocessing can increase the efficiency of uranium usage by 60 times.
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