# Chasing Your Tails (Assay), Part Two

### Armed with a basic understand of enrichment, let’s dig deeper into enrichment math and the vagaries of secondary uranium supply.

New to the blog? Part one of this post on enrichment can be found here.

#### Summary (TL;DR)

• It’s not the only source of secondary supply, but excess enrichment capacity can artificially reduce the demand for mined uranium supply.
• The opposite can also be true: a shortage in enrichment capacity can create secondary demand.
• Uranium and enrichment are substitute goods. More SWU can be substituted for U and vice versa, so their prices are interconnected via secondary supply. An increase or decrease in one price often has the same impact on the other.

#### Introduction to Secondary Supply

In part one of this enrichment overview, I talked about how tails assay (i.e. the uranium-235 content of enrichment’s depleted uranium waste product) links uranium and enrichment requirements. In part two, I will discuss how mismatches between enrichment capacity and demand make exact calculations for global uranium requirements more difficult.

The most in-depth fuel cycle modelers can leverage obscure resources and proprietary data to put hard numbers on the impacts of secondary supply on the uranium market. For more casual market watchers, however, it’s hard to gain literacy on the fuel cycle without examples on what might be going on behind the curtain. The examples below are simplified, but they should get you started.

#### Case #1: 10 Reactors and One Enrichment Plant

Welcome to Nucleria

Let’s imagine a small nation (we’ll call it “Nucleria”) with ten identical nuclear reactors. One day, the King of Nucleria decides that his country is too dependent on foreign nuclear fuel imports, so he proposes a self-sufficiency program to produce all of Nucleria’s nuclear fuel domestically, headed by four nobles from his court:

• The Duke of Yu, who will oversee uranium mining
• The Fluorine Count, who will design the conversion facility
• The Earl of Swoo, who will build the enrichment division
• Baron Zirconium, will oversee the fabrication of fuel

The four nobles return to their castles, keeps, and above average-sized houses to map out Nucleria’s nuclear future. The Fluorine Count predicts a conversion cost of \$15 per kilogram of UF6, and the Duke of Yu thinks that the sustaining cost of his uranium mine will be \$46 per pound of U3O8. Because there are 2.613 pounds of yellowcake uranium per kilogram of UF6, the predicted cost per kilogram of UF6 is \$135.

Calculating Optimal Tails Assay and SWU Requirements

The Earl of Swoo estimates an enrichment cost of \$125 per SWU at her facility, so she calculates the most optimal way to produce enriched uranium at these prices (\$135/kgU of UF6 and \$125/SWU). The optimal tails assay at these prices is approximately 0.22%.

Nucleria’s 10 reactors operate on the following principles:

• 157 assemblies per core, containing 420 kilograms of enriched uranium each
• An average of 68 assemblies are replaced on an 18-month cycle
• The average enrichment of reload assemblies is 4.4% U-235

So, Nucleria’s uranium fleet requires 190,400 kilograms of enriched uranium each year. [68 assemblies * 420 kgU/assembly * (2 reloads/3 years)]

To produce 190,400 kilograms of 4.4%-enriched uranium each year at 0.22% tails, this requires 1.36 million SWU, 1.62 million kgU of UF6, and 4.2 million pounds of uranium as U3O8. [These prices come out to about \$2,039/kgU EUP, or \$850k per assembly.]

After confirming with Duke Yu and the Fluorine Count that their facilities could support these annual production rates, Swoo commissions her centrifuge facility. After a few years, the four nobles finish construction, with Swoo shipping exactly enough enriched uranium to Baron Zirconium’s fabrication factory to make fuel for Nucleria’s fleet. Perfectly balanced, as all things should be.

#### Case #2: 10 Reactors and One Failed Build

With the perfectly balanced case out of the way, let’s put some rain clouds over Nucleria, our self-contained nuclear nation.

Nucleria’s fleet was actually destined to contain 11 nuclear reactors, not 10, and construction on the 11th reactor broke ground a few years before the King of Nucleria embarked on his nuclear self-sufficiency initiative. When Yu, FC, Swoo, and Baron Zirconium were designing their facilities, they planned to supply this reactor, too. For 11 reactors, Swoo built a centrifuge facility with 1.5 million SWU per year capacity.

But things did’t go as planned. Delay after delay, and redesign after redesign, construction was finally halted on the 11th reactor with no plans to finish. [Frankly, this was a huge bummer.] The most direct effect to our four nobles, however, was that each of their facilities were built just a little too big for the Nuclerian reactor fleet.

“That’s fine,” said Yu, “our sales book is full so we will keep selling our U!”

“Unexpected,” mumbled the Fluorine Count, “but I can make my maintenance outages longer and produce less UF6 to compensate.”

“Redundant capacity is never a bad thing,” added Baron Zirconium, eyeing the new fuel designs he wanted to try and the untapped export markets in nearby countries.

But for the Earl of Swoo, all was not well. Once built, those centrifuges keep on spinning (stopping an operating centrifuge can break it). What to do, with an extra 150,000 SWU?

Option #1: Stockpile UF6 (Underfeeding)

The Earl of Swoo, burdened with extra SWU, evaluates her options to deal with the oversupply. The first option that came to mind was decreasing her facility’s tails assay. At 0.18% tails, she could produce the same amount of enriched uranium by using more SWU and less U.

Swoo saves about 100,000 kilograms of UF6 per year, or about ~250,000 pounds of uranium. This is approximately 6% of Nucleria’s annual requirements. Using less UF6 and lower tails assay is known as underfeeding.

We can see very quickly that Nucleria now has more uranium than it needs, assuming that the Duke of Yu’s mine doesn’t cut production. But Yu makes money for each pound of uranium he produces, and his province needs the cash, so he has no immediate incentive to cut supply. But eventually, with Swoo’s excess U on the market, Yu will have a harder and harder time getting the \$46 per pound he needs to keep his mine running. In a market where the different players aren’t all cooperating, it can take a while for the market to sort these inefficiencies out.

It’s worth mentioning here that, instead of marketing the excess supply as natural UF6, an enricher can split the difference and create more enriched uranium than is under contract and sell the excess directly to end users. This is the origin of some “spot” EUP.

Option #2: Tails Re-Enrichment (SWU for U)

Decades before our story, Nucleria built dozens of nuclear weapons, ostensibly to protect itself from foreign invasion. They were never used, but the process of enriching uranium to make these weapons left a large environmental legacy in some isolated Nuclerian communities. In addition to pollution, these programs left behind huge quantities of “high-assay tails.” This is tails material from enrichment, just like the current centrifuge facility produces, except that this legacy material has much larger residual U-235 content because the older technology wasn’t as efficient as the modern centrifuges.

Keeping the 0.22% operational tails assay of the initial design, Swoo uses 1.35 million SWU to produce enriched uranium for Nucleria’s reactors and the excess 150,000 SWU to “re-enrich” the legacy tails material from a starting assay of 0.30% to the 0.711% of natural uranium.

At 0.22% tails assay, 150,000 SWU can transform 0.30% tails material into 204,000 kgU of 0.711%-enriched (i.e. “natural” uranium). This is the equivalent of 530,000 pounds U3O8, or about 13% of Nucleria’s annual requirements. Quite literally, this is “SWU for U.”

Case #2 Summary

Because centrifuges keep spinning, extra SWU capacity can quickly cause an imbalance on the uranium side. However, this imbalance is often hidden from view because utilities continue to procure the amount of uranium required by their contracts. Eventually, extra uranium created via enrichment excess will be sold back to utilities, decreasing uranium demand and (all other things equal) lowering the price of uranium. And as the price of uranium goes down, the optimal tails assay goes up and SWU demand goes down.

The key takeaway here is that a small SWU excess – perhaps caused by a premature reactor closure or overly optimistic planning on the part of an enricher – can cause a significant drop in uranium demand. This isn’t “fake” supply as some like to call it, but it’s often hard to sort out how much secondary supply is in the market at any one time because so many necessary inputs to that calculation are secret.

#### Case #3: Secondary…Demand? (Overfeeding)

It’s hard to conceive now, but in the heady days of the “Nuclear Renaissance” there was potentially going to be a global shortage of enrichment capacity. In Case #2, we saw how excess SWU can reduce uranium demand. If the situation were reversed, we can imagine the opposite to be true: a SWU shortage can actually increase uranium demand.

There are a few conceivable ways that a SWU shortage could happen:

• An enrichment facility doesn’t meet its projected capacity
• Uranium prices skyrocket, decreasing the optimal tails assay and creating greater SWU demand than capacity
• Structural changes in demand, such as new reactors or increased fuel demand at existing reactors

To continue the saga of Nucleria, let’s build off of Case #1 (ten reactors, perfectly balanced U and SWU). Several years after Nucleria got their supply chain off the ground, the King of Nucleria decided to use the royal treasury to fund two additional reactors. For simplicity’s sake, let’s assume that the new reactors are of the same design as the original ten. This brings Nucleria’s annual requirements to:

• 228,440 kgU of 4.4%-enriched uranium per year, which requires:
• 5.04 million pounds of uranium
• 1.95 million kgU of conversion
• 1.63 million SWU

The Earl of Swoo, whose enrichment facility is designed for 1.36 million SWU per year, decides to build some extra centrifuges to increase the capacity of the facility by 270,000 SWU per year. Swoo decides to deploy a new centrifuge design, but with one year to go before the new reactors need fuel, it’s clear that the new centrifuges won’t be ready in time.

The Earl of Swoo has a problem: her centrifuge facility has 1.63 million SWUs under contract next year, but only 1.36 million SWU capacity online. Nucleria officially has a SWU shortage.

Swoo has an idea. Although the utilities have their SWU under contract at 0.22% tails assay, the centrifuge facility can be reconfigured to operate at a higher tails assay. By operating the facility at 0.30% tails assay, 1.36 million SWU can produce the required amount of enriched uranium. However, the higher operational tails assay means that the facility needs more uranium: 2.28 million kgU of UF6 as feed. This requires 330,000 kgU of extra UF6 (860,000 pounds of U3O8) – a 17% increase in demand. Using more uranium and a higher tails assay is known as overfeeding.

In the worst case scenario, Swoo is actively bidding against nuclear utilities to secure the uranium supply she needs to fuel her enrichment facility. If the market can’t supply enough uranium, the price will go through the roof. And if the uranium price increases, the optimal tails assay decreases and the demand for SWU goes up. Just like how an excess supply of SWU can drag the uranium price down, a shortage of U can drive the SWU price up.

#### Summary: why do we care about all of this?

To be blunt, the world has way too much enrichment capacity right now. This contributed to a reduction in uranium demand, which in turn contributed to the cratering of the uranium price due to oversupply. And when the U price goes down, the SWU price drops with it (although both U and SWU were oversupplied in their right without this dysergy).

And unlike uranium mines, which can be shut off when they start bleeding money, most of the investment in a centrifuge plant is up front and centrifuges can stay in service for 25 years or more. So, sure, eventually the overcapacity can be cured by simply waiting for the retirement of centrifuges, but this isn’t a quick process. And because utilities contract for enrichment much less frequently than uranium, it can take a long time for the imbalances discussed above to be discovered and/or quantified.

Anyway, if you’ve made it this far, thanks for reading. I’m hoping to tackle other sources of secondary supply in my next post. Feel free to leave a comment on Twitter (@808sandU3O8) or at 808sandU3O8 at gmail.com. Thanks for reading!

## One thought on “Chasing Your Tails (Assay), Part Two”

1. Michael Roberts says:

Brilliant, thanks for explaining this process in a way I understand. Very kind of you to go to all this effort

Cheers

Mike

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