I'll make some estimates for you, but understand that they will be crude.
The type of resin used is known as a graft polymer - it is ordinary polyethylene - functionalized so that little strands of molecules stick out from it: These are what we call amidoxime functionalized acrylates. This co-grafting is achieved energetically by irradiating polyethylene in the presence of polyethylene.
I will refer to a recent paper on the subject to give some idea about the energy investment: Ind. Eng. Chem. Res. 2000, 39, 2910-2915. This paper is by the Japanese teams that have been working on this project for several decades.
Here is a description of the synthesis of one of their graft polymer resins:
Preparation of Hydrophilic Amidoxime Adsorbents.
The preparation of hydrophilic amidoxime (AO) fibers based on PE fibers by radiation-induced cograft polymerization and subsequent chemical modifications is illustrated in Figure 1. First, a combination of MAA or HEMA with AN was cografted onto the PE fiber using a preirradiation technique:10,11 irradiation by an electron beam was performed at a dose of 200 kGy in a nitrogen
atmosphere at ambient temperature. The irradiated fiber was immersed in a monomer solution previously
deaerated with nitrogen. The total concentration of the two monomers was set at 50 (w/w)% in DMSO as a solvent, where the weight ratio of AN/MAA or AN/ HEMA in the monomer mixture ranged from 100/0 to 50/50. Cografting was performed at 313 K for a reaction time up to 7 h. The fiber, rinsed repeatedly with dimethylformamide and methanol, was dried under reduced pressure and then weighed.
Here is a website from the University of Cambridge that gives the energy content of polyethylene:
http://www.doitpoms.ac.uk/tlplib/recycling-polymers/end.phpWe see that the energy content of polyethylene is about 71 MJ/kg. We also note that it is necessary to irradiate the polymer. In this case they are using beams of electrons to deliver 200 gray to the polymer. A gray is a joule of energy absorbed by a kg, and allowing for any inefficiencies and energy losses, lets multiply the 200 joules by 50 to add another megajoule to the cost of making cografted amidoxime functionalized PE. We're up to 72 MJ. Now lets triple this cost (arbitrarily) to account for the fact that we are using solvents (which will be recovered in multiple runs) and nitrogen gas, and that we will have to repurify and pump these solvents. We're up to 216 MJ/kg of resin. They told us they put it in a cage device 6 km of the shore of Japan, where the flow rates of seawater are maintained by currents and wave action (this is your solar energy, which provides the flow around the uranium.) Let's say that their boat gets only 6 km/gallon (yeah a weird unit) and estimate that they have burned in this practice, about 2 gallons of gasoline, accounting for another 260 MJ. We are now up to 500 MJ roughly, allowing for an even less generous assessment of what we have done thus far - I'm looking at the worst possible case. They leave the system there in floats and come back after 20 days, burning another 260 MJ of gasoline to pick the stuff up. We're up to around 800 MJ/kg now.
Note that the performance of resins still is undergoing optimization, and many variables are being explored.
They find that the have recovered 0.9 grams of uranium per kg of resin. Note that this resin is reusable, one can use it as many as ten times, but we'll leave that out now.
I'm going to arbitrarily charge them, for their acid washes and other purification, to remove the uranium from the resin another 700 MJ meaning that they have paid at total of 1500 MJ for 0.9 grams of uranium.
Now we need to ask what is the energy value of this uranium? First of all, we need to recognize that if this scheme ever becomes commercial, it will do so in a recycling atmosphere, since uranium will be a valuable commodity. Thus we can assume the
whole energy content, and not just the U-235. How much energy is that? Using the atomic weight of uranium, and 190 MeV per fission we see that the total energy recoverable from this uranium is 70 billion joules, while the cost of acquiring the uranium using 1 kg of resin was 1.5
billion joules. Thus we have received 70 billion joules for the investment of 1.5 billion joules. This is because of the enormous energy density of uranium. Of course each recycle will require some energy investment as well, but given that I have been exceedingly ungenerous in the energy cost of this scheme, it cannot be likely that there won't be a return much greater than 10 or 20 fold for seawater recovered uranium.
Since we will be using reusable resin, since we will actually have much better efficiency of hauling the resins in and out from the sea, since we will be hauling in ton lots, etc, etc, we can see that the scheme becomes quite attractive from an energy investment standpoint. I'm sure there will be many further process improvements, such as using supercritical carbon dioxide to extract the uranium from the resin, reducing the need for solvents, etc, the use of fission products to induce grafting in the polyethylene, and other changes I cannot anticipate. Thus we can easily envision a return in the hundreds for the energy invested. But to be sure, the matter will be large scale. If the resin is used 10 times, about 100 kg of resin will be required for each kg of uranium obtained. We are talking of many hundreds of thousands of tons of resin, and large submerged structures in ocean currents. However we should also recognize that it will take many decades to burn completely each kg of uranium in reactors in a continuous actinide refueling scheme. Each cycle burns less than 5% of the fuel.
The likely environmental impact will not be zero, but that is true of
any energy scheme, nuclear or otherwise. Therefore no one should ever interpret the availability of this technology as an excuse to waste energy. We must always conserve. I hope that if humanity survives, it will have learned some lessons by the events surrounding oil and not ignore the limits of energy production.