Chasing Your Tails (Assay), Part One

Enrichment is often a black box, but understanding it is key to fine-tuning any model of global uranium requirements. Here’s part one of an overview of enrichment technology.

[Edited 6/15/20: added clarification between operational and contractual tails assay. Thanks, Dale!]

Summary (TL;DR)

  • Reactors require fuel with a higher-than-naturally-occurring concentration of the uranium-235 isotope. U-235 concentration is increased via enrichment.
  • The balance between uranium requirements and enrichment work (SWU) is moderated by the residual U-235 in enrichment waste material (the “tails assay”).
  • Predictions (or knowledge) of the future price of uranium and enrichment determine a utility’s choice of tails assay. If a guess is not precise, it can add additional cost and increase or decrease the amount of uranium they buy.

Introduction to Enrichment

Long before Chicago Pile-1 went critical in 1942, atomic scientists knew that the ratio of uranium isotopes from in nature would make nuclear chain reactions difficult. Uranium-238 forms the 99.3% majority of all uranium on Earth, but its atomic properties make it difficult to split in a nuclear reactor (or in a bomb). Uranium-235, 0.7% of all natural uranium, is chemically identical to uranium-238 (same number of protons, different number of neutrons), but its atomic structure makes it easier to fission (split) when hit by a neutron. [There are reactors that can use natural/unenriched uranium to make power, including both the current generation of CANDU reactors and future “fast” reactors, but these make up a small percentage of global demand and I don’t want to spend a ton of time discussing them (sorry, Canadian readers!)]

To build an atomic bomb (power reactors came later), uranium had to be “enriched” in uranium-235 content, that is, the relative proportion of U-235 to U-238 must be increased. Uranium concentrates (U3O8, as it is sold), is converted into uranium hexafluoride gas (UF6), and fed into centrifuges to perform enrichment.

There’s a microscopic amount of U-234 out there in nature, but this is the short summary, after all.

The general theory is simple: by using energy in the form of centrifuges spinning, natural uranium is divided into product (with more U-235) and tails (with less U-235). Product goes on to become reactor fuel, while tails are treated as waste. The tails assay, as it is called, is the U-235 content in the tails (e.g. 0.22%). Product material is generally produced between 3% and 5% U-235.

At 0.22% U-235 tails assay: 8.5 kilograms of natural UF6 at 0.7% U-235 go into the centrifuge cascade, 1 kilogram of EUP at 4.95% U-235 and 7.5 kilograms of tails at 0.22% U-235 come out.

It’s worth noting that any uranium can be fed into centrifuges, including material that is already enriched to enrich it more, or depleted tails material to capture more of its U-235 content (so-called “SWU for U”). Just as natural uranium can be enriched to 5%, depleted uranium can be enriched back to 0.7% (such that it mimics natural uranium).

Measuring Enrichment Work

Enrichment is measured in separative work units, known by its acronym, SWU [“swoo”]. The exact SWU calculation for enrichment is tedious, but it depends on two factors:

  • The quantity of enriched uranium to be produced (mass)
  • The difference in U-235 content between the product and tails

The number of uranium-235 atoms are conserved in the enrichment process; it’s just a question of how they are divided between product and tails. The greater the difference (i.e. the lower the tails assay), the more enrichment work (SWU) is required. There are two options, then, for how to produce the same amount of enriched uranium:

  1. Use more SWU. Less uranium is needed, and tails have less U-235.
  2. Use fewer SWU. More uranium is needed and tails have more U-235.
1 kgU of UF6 contains 2.61286 pounds of uranium

Calculating Reactor Uranium Requirements

If a nuclear reactor needs 30,000 kgU of uranium at 4.4% U-235 enrichment to make its next batch of fuel, how much uranium (in pounds of U3O8) does it need? The tails assay of the enrichment process is a critical input to this calculation.

The choice of tails can end up making a significant difference. A 0.04% tails difference can introduce a 6% difference into uranium requirements calculations. At the macro level, this could be tens of millions of pounds.

So how might a utility determine tails assay?

The short answer is: very carefully.

The long answer is that the optimal tails assay is a function of the UF6 price (uranium plus conversion) and the enrichment price. For a pair of UF6 and SWU prices, there is an optimal tails assay. When you see an “optimal tails assay” on a broker’s price sheet, they’re just putting the day’s uranium, conversion, and SWU prices into a formula and posting the result.

But it’s not an exact science. A tails assay in an enrichment contract might be chosen based on projections for these prices, many years in advance. These projections might be based on the projected rate of inflation, sentiment about the uranium price in a future year, or other more esoteric factors. In practice, guessing wrong introduces some inefficiency into the buying of enriched uranium.

For three U-SWU price pairs, the optimal tail assay bounces around. For the orange sequence, optimal tails assay might be at 0.18% or below. For grey and blue, the cost of EUP across the chosen tails assays is U-shaped [pun intended] and optimal tails lies somewhere in the middle of the graph.

Generally, the more relatively expensive SWU is to U, the higher the optimal tails assay. In other words, when enrichment is expensive, there is a tendency to use more uranium. When enrichment is cheap, there is a tendency to use less.

Graph borrowed from T.L. Neff of MIT

In the long-term, enrichment and uranium price projections are interdependent variables. And tails assay (while sometimes flexible within a contract) is guided by real and projected costs for both uranium and SWU, many years in advance. So when market watchers and price reports predict long-term uranium requirements, their own predictions for uranium and enrichment costs (and therefore, optimal tails assay) are baked into the model.

So, if there is a modeling error in uranium or enrichment costs, especially if enrichment costs become more expensive [*cough cough* substantial changes to the Russian Suspension Agreement *cough cough*], then there could be a significant delta between projected vs. actual uranium requirements. And if requirements go up in an undersupplied market…

Final Words

Doing calculations and making graphs is “fun,” but there are still two significant gaps in our understanding of enrichment:

  • For a given reactor, what tails assay are their enrichment contracts at? This governs how much uranium they actually buy.
  • For a given enricher, what tails assay do they operate their facilities at? This governs how much uranium they need to use to fill a contract.

Contractual tails assay, which is set by the contract between a utility and an enricher, governs the amount of uranium a utility sends to an enricher and how many SWU they pay for per kilogram of enriched product. This is distinct from the operational tails assay, which is how an enricher chooses to run their facility.

A gap between contractual and operational tails assay, in either direction, means that a different amount of uranium is being sent to enrichment facilities than is being used. Properly estimating the material balance through the enrichment step is critical to understanding secondary supply, which will be discussed in part two of this post.

Footnotes and Technicalities

  • After a certain point, global nuclear powers moved from uranium to plutonium as the preferred fuel for their weapons of mass destruction. Many legacy weapons ended up being turned into submarine and commercial power reactor fuel, as they were in the Megatons to Megawatts program where Russia shipped a lot (50% of annual U requirements for a decade) of EUP to the United States.
  • Canada’s CANDU reactor doesn’t require enrichment. The story of how this design came about is too long for a footnote.
  • Many “Generation 4” reactors of the future don’t require enriched uranium, or can even use other fuels to make power. Some designs require significantly more enrichment than the current fleet. In theory, many current-gen reactors could be fueled with plutonium recovered from weapons or nuclear waste. I have approximately 0% interest in trying to referee this topic.

Feel free to leave a comment on Twitter (@808sandU3O8) or at 808sandU3O8 at Thanks for reading!

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