It's about an order of magnitude more expensive than mining uranium. But the cost of fuel extraction is negligible in the context of the rest of nuclear's cost.
The author of the article linked in the top-level comment mentioned seawater extraction:
"as uranium is extracted, the uranium concentration of seawater decreases, so that greater and greater quantities of water are needed to be processed in order to extract the same amount of uranium. Abbott calculates that the volume of seawater that would need to be processed would become economically impractical in much less than 30 years."
> However, seawater concentrations of uranium are controlled by steady-state, or pseudo-equilibrium, chemical reactions between waters and rocks on the Earth, both in the ocean and on land. And those rocks contain 100 trillion tons of uranium. So whenever uranium is extracted from seawater, more is leached from rocks to replace it, to the same concentration. It is impossible for humans to extract enough uranium over the next billion years to lower the overall seawater concentrations of uranium, even if nuclear provided 100% of our energy and our species lasted a billion years.
That's in the Forbes article rather than the Phys.org article.
And there's a billion dollar/watt question in there. "Equilibrium" is doing a lot of work in that paragraph. In order for the claim to matter practically, the reactions he's talking about have to replenish uranium to extraction-viable concentration at the same rate it's extracted. It sounds like our Forbes writer is suggesting the process accelerates at least linearly with the extraction rate, and that'd be cool, but forgive me if I don't take it for granted without further focus on why that's a reasonable expectation.
That doesn't sound right. The oceans contain several billion tons of uranium. A 1 GW(e) reactor uses the equivalent of about 100 tons of natural uranium per year. So, he's claiming the world would have ~1 million reactors.
It's about an order of magnitude more expensive than mining uranium. But the cost of fuel extraction is negligible in the context of the rest of nuclear's cost.