HALEU is frightfully expensive (calcs)

HALEU is basically 20% enriched uranium, and I have watched with disbelief as it has gone from an obscure fuel option to the central fuel form for the US Department of Energy’s Advanced Reactor Development Program (ARDP).

But boy oh boy, is this stuff expensive. And other people are starting to notice and realize that this crazy-expensive fuel is not going to be compatible with a broad expansion of nuclear energy. One of the groups that is showing some courage is the Nuclear Innovation Alliance. They published a report on December 15th where they stepped forward and talked about just how expensive HALEU is going to be.

Nuclear Innovation Alliance: Summary for Policymakers: Characterizing an Emerging Market for High-Assay, Low-Enriched Uranium Production

Calculated HALEU production cost for uranium enriched to 19.75% is $23,725/kgU for HALEU in an oxide form and $25,725 for HALEU in a metallic form under baseline economic assumptions but could be higher.

I’ve written uranium-fuel-cycle calculators, so I thought it would be fun to check their calculations. The really bold claim that they made was that a separative work unit (SWU) is going to cost a lot more in a HALEU enrichment cascade than in an LEU enrichment cascade. And that lines up with what everyone in the enrichment industry has been telling me. The assumption that “a SWU is a SWU is a SWU” is just flat-out wrong, they have been telling me. There are a lot more considerations for a HALEU cascade than for an LEU cascade, and that’s going to dramatically change the price. NIA goes so far as to put numbers on that assertion, saying that an LEU SWU will cost $150 but that a HALEU SWU will cost $1000. I’m not sure anyone knows for sure right now, but that is a reasonable estimate. And when you plug those value into the financial equations things start to look very different. Here’s the governing equation for the price of an enriched material:

(1)    \begin{equation*} \frac{\$}{m_p} = \left(\frac{m_f}{m_p}\right) \left(\frac{\$}{m_f}\right) + \left(\frac{SWU}{m_p}\right) \left(\frac{\$}{SWU}\right) + \left(\frac{m_f}{m_p} - 1\right) \left(\frac{\$}{m_t}\right) \end{equation*}

NIA says that to save money, you’d make low-enrichment uranium first. Then you’ll use that LEU as the feed for a HALEU enrichment cascade. Click on this thumbnail to view a graphic from their report depicting that idea:

And that strategy also lines right up with what I’m hearing from a lot of other people. Following the guideline of the NIA document, here’s the calculation around an LEU at 4.95% enrichment, using natural uranium feed at 0.711% and removing a depleted stream at 0.23%. This gives you a ratio of feed to product of about 9.8:

     \begin{displaymath} \frac{m_f}{m_p} = \frac{0.0495 - 0.0023}{0.0071 - 0.0023} = 9.8129 \end{displaymath}

I used $187.50 per kilo of uranium (not per kilo of UF6) as the assumed cost of the natural uranium hexafluoride (NUF6) feed. That’s based on watching market prices and also on conversations with trusted sources in the industry, rather than on the numbers in the NIA paper, which introduces differences in the final calculated costs. I used their estimates for a separative work unit cost of $150 in LEU because that lined right up with what I was hearing from others. I also modeled a putative disposal of depleted uranium hexafluoride (DUF6) is $5.00 per kilo of uranium.

     \begin{displaymath} \frac{\$}{m_p} = (9.81)\left(\frac{\$187.50}{\text{kg}}\right) + \left(\frac{8.16\text{ SWU}}{\text{kg}}\right)\left(\frac{\$150.00}{\text{SWU}}\right) + (8.81)\left(\frac{\$5.00}{\text{kg}}\right) \end{displaymath}

     \begin{displaymath} \frac{\$}{m_p} = \left(\frac{\$1839.92}{\text{kg}}\right)+ \left(\frac{\$1223.27}{\text{kg}}\right)+ \left(\frac{\$44.06}{\text{kg}}\right) = \$3107.25\text{/kg} \end{displaymath}

Now you use that expensive LEU (4.95%) as the “feed” for the even-more expensive HALEU (19.75%). You can assume that you will discharge a depleted stream at the natural uranium enrichment level (0.711%). The feed to product ratio is this case is about 4.5.

     \begin{displaymath} \frac{m_f}{m_p} = \frac{0.1975 - 0.0071}{0.0495 - 0.0071} = 4.4914 \end{displaymath}

The “feed” cost at this stage is the LEU cost. You can assume that the discharge from this cascade has the same value as NUF6 feed. So you get your money back on that, which is why it’s negative in this equation. But the SWU cost for the HALEU system is much higher to account for the technology challenge of this level of enrichment. The NIA report modeled it at $1000/SWU, versus only $150/SWU for the LEU case. It’s more expensive because you have to worry about accidental criticality in the enrichment cascade, and you don’t have to worry about that in the LEU system.

     \begin{displaymath} \frac{\$}{m_p} = (4.49)\left(\frac{\$3107.25}{\text{kg}}\right) + \left(\frac{5.89\text{ SWU}}{\text{kg}}\right)\left(\frac{\$1000.00}{\text{SWU}}\right) - (3.49)\left(\frac{\$187.50}{\text{kg}}\right) \end{displaymath}

     \begin{displaymath} \frac{\$}{m_p} = \left(\frac{\$13955.88}{\text{kg}}\right)+ \left(\frac{\$5889.19}{\text{kg}}\right)- \left(\frac{\$654.64}{\text{kg}}\right) = \$19190.43\text{/kg} \end{displaymath}

So there’s a prediction of $19,190/kgU for HALEUF6…a “product” that is pushing twenty grand per kilo. And you haven’t even made it into anything yet. If you want to make it into an oxide powder or into metal that’s going to cost you a lot more money. NIA thinks that it might cost as much as $2000/kgU to make HALEUF6 into HALEUO2. They think it might cost as much as $4000/kgU to make HALEUF6 into HALEU-metal. And that’s even before you attempt to fabricate this material into actual fuel elements, like pellets or rods or pebbles. And if you want to make it into TRISO fuel, that’s going to cost you even more money on top of that. No one will tell you exactly, but it’s not a bad guess that you’re looking at about thirty grand a kilo by the time you get to a HALEU TRISO fuel form.

Now you might say, well, it’s ok that it costs so much more money because it has so much more uranium-235 in it. Yeah, 20% HALEU has about four times more uranium than 5% LEU. So, theoretically, that’s four times more energy you can extract from the fuel. But that’s four times the energy at over six times the cost. Those economics are going in the wrong direction!

It’s even worse when you compare it to a reactor like a CANDU, that runs on natural uranium. HALEU has about 28 times the fissile content of natural uranium at over 100 times the price. The conclusion is pretty inescapable: the more you enrich the fuel, the worse your economics get.

What’s the per-megawatt-hour cost of this fuel? Well first we figure out how much energy we can get from fissile material.

     \begin{displaymath} E = \frac{(180.0\text{ MeV/fission})(160.219\times 10^{-15}\text{ J/MeV})}{(235.0\text{ amu/fission})(1.661\times 10^{-27}\text{ kg/amu})} = 73.90 \times 10^{12}\text{ J/kg} \end{displaymath}

     \begin{displaymath} E = \frac{28.8\times 10^{-12}\text{ J/fission}}{390.2\times 10^{-27}\text{ kg/fission}} = 73.90 \times 10^{12}\text{ J/kg} \end{displaymath}

That’s a lot of energy, basically 74 terajoules per kilogram. But that’s “heat” energy, what about electricity? We’ll be very generous and assume that this fissile material is being used in a reactor that can produce electricity at 45% efficiency.

     \begin{displaymath} E = (73.90 \times 10^{12}\text{ J/kg})\left(\frac{0.45\text{ MW-hr}}{3.6\times 10^9\text{ J}}\right) = 9237.9\text{ MWh/kg} \end{displaymath}

But only 1/5th of the HALEU is fissile so we need to knock this value down by a factor of five, and that gives us:

     \begin{displaymath} \text{cost} = \frac{\$19190.43\text{/kg}}{(0.20)(9237.9\text{ MWh/kg})} = \$10.35/\text{MWh} \end{displaymath}

So you’re spending $10 on fuel for each megawatt-hour of electricity you make, and that’s assuming that you extracted every last speck of energy out of the HALEU, and that’s just on the HALEUF6. If you form it into an expensive fuel like TRISO it’s going to go higher, probably to more like $15/MWh. If you assume some degree of limited burnup in the fuel it’s going to go higher, more like $20/MWh. These are not the sorts of numbers you expect in nuclear power, where traditionally fuel costs have been a rather tiny overall part of the electricity bill. This is looking more like coal or natural gas, where fuel costs are a sizeable part of the overall electricity bill.

Today DOE issued an RFP to make HALEU that seems to have left everyone in the uranium enrichment industry with a bad taste in their mouth. DOE shouldn’t be too surprised if none of them “jump” on this opportunity.

Now if you had a reactor that could accept UF6 directly as a fuel feed, you could skip all these “deconversion” and “fabrication” steps and save yourself a lot of money, whether you were using LEUF6 feed or HALEUF6 feed. Hmmm, what kind of reactor could accept UF6 directly as a fuel feed? It would probably have to be some kind of fluid-fueled reactor that was based on fluorides. Hmmm, I guess I’ll have to keep thinking about that….what could it be?

Anyway, here’s a lighter take on the whole problem if you want a bit of a chuckle:

One thought on “HALEU is frightfully expensive (calcs)

  1. The utilities oppose cheaper energy because they fear reduced revenues and profits. The contractors love HALEU because they can make lots of money. Thorium is too cheap. Anyone can get it. It’s ubiquitous in the environment like lead but you only need a tiny amount.
    So the only way we can get cheaper energy is if we promise to buy more.
    Like at costco. Want high quality and low price? Buy a big package. Volume discount.
    We can get 10 times cheaper than fossil fuel energy from fission, if we update from the 1960’s designs. Many ways to do it including this one.
    But we have to promise to buy 20x more energy!
    Yet the environmental movement is trying to make us use LESS energy.
    If we use less at a lower price that KILLS the utilities and contractors.
    Don’t expect the politicians to let that happen.
    Capitalism is great at making more money– not less.
    However if we make our hydrocarbon fuels synthetically, cheaper that drilling, using Hydrogen from Uranium/Thorium+Water, and Carbon from the environment, that takes a lot of energy. Which is good because we have to use a lot.
    And if we heat our homes electrically (cheap and easy if electricity is 10x cheaper)..
    Then we safe the environment and everyone makes money!

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