The fuel cycle

Hana's next assignment takes her away from the reactor itself. Marcus Lee, who leads Meridian's fuel and waste group, is preparing a summary for TVA of where the Clinch River reactor's fuel will come from and where it will go. He asks Hana to work through the numbers with him. The journey of uranium from the ground to the reactor and on to final disposal is called the nuclear fuel cycle, and it is the subject of this lesson.

An overview of the cycle

The front end of the fuel cycle prepares fuel: uranium is mined and milled, converted to a chemical form suitable for processing, enriched in uranium-235 if the reactor requires it, and fabricated into fuel assemblies. The fuel then spends several years in the reactor. The back end deals with what comes out: used fuel is cooled in pools, moved to dry storage and eventually placed in a deep geological repository. Some countries reprocess used fuel to recover uranium and plutonium for reuse. Each step is regulated, and international safeguards account for the nuclear material at every stage.

Mining and milling

Uranium is a fairly common element, about as abundant in the Earth's crust as tin. Economic deposits contain from about 0.1 percent uranium oxide to, in exceptional cases, more than 15 percent. Kazakhstan, Canada and Namibia are the largest producers. Canada's mines are in the Athabasca Basin of northern Saskatchewan, which holds the world's highest grade deposits. Uranium is mined in open pits, underground mines or, increasingly, by in-situ recovery, in which a solution pumped through the ore body dissolves the uranium and is brought back to the surface without excavation.

At the mill, ore is crushed and leached with acid or alkali to dissolve the uranium, which is then recovered as a uranium oxide concentrate, \(\text{U}_3\text{O}_8\), a yellow or brown powder called yellowcake. The leftover crushed rock, the tailings, still contains the radium and other decay products of uranium, as Lesson 3 explained, and must be managed for the long term to prevent radon release and water contamination. Modern tailings facilities in Saskatchewan place them in mined-out pits engineered to isolate them from groundwater.

Conversion, enrichment and fabrication

Conversion purifies the concentrate and turns it into the chemical form needed next. For CANDU reactors, the uranium is converted directly to uranium dioxide powder. For enrichment, it is converted to uranium hexafluoride, \(\text{UF}_6\), which becomes a gas at modest temperatures. Conversion in the United States takes place at a facility in Metropolis, Illinois.

Enrichment raises the proportion of uranium-235 from 0.72 percent to the 3 to 5 percent needed by light water reactors. Because the two isotopes are chemically identical, enrichment exploits their tiny difference in mass. Today, essentially all commercial enrichment uses gas centrifuges, in which the slightly heavier uranium-238 molecules concentrate toward the outer wall of a spinning cylinder. The separation in one machine is small, so many are connected in cascades. Commercial enrichment plants operate in a handful of countries under international safeguards, and their output for power reactors is limited to low-enriched uranium, below 20 percent and usually below 5. Some advanced reactors are designed to use fuel between 5 and 20 percent, called HALEU, and its supply is a current challenge for those designs.

Enrichment splits the feed into two streams: the product, enriched in uranium-235, and the tails, or depleted uranium, with about 0.2 to 0.3 percent uranium-235. A simple mass balance on uranium-235 relates the amounts of feed, product and tails. Fuel fabrication then converts the enriched hexafluoride back to uranium dioxide, presses and sinters pellets, loads them into zirconium alloy tubes and assembles them into fuel assemblies, in each case to very tight tolerances and with careful quality control.

Here \(F\) and \(P\) are the masses of feed and product, and \(x_F\), \(x_P\) and \(x_T\) are the uranium-235 fractions in the feed, product and tails. The program applies it to the reference plant's annual fuel need from Lesson 5.

# Uranium needed for one year of fuel: the mass balance at the start of the
# fuel cycle and the volume of used fuel at the end (rounded values).
x_feed, x_tails = 0.00711, 0.0025     # U-235 fraction in natural uranium and in tails
def feed_per_product(x_prod):
    return (x_prod - x_tails) / (x_feed - x_tails)

product = 5.9                          # t of enriched uranium loaded per year (Lesson 5)
for x in (0.035, 0.045, 0.0495):
    f = feed_per_product(x)
    print(f"Fuel at {x:.2%} U-235: {f:4.1f} t natural U per t of fuel, {f*product:5.1f} t per year, tails {f*product-product:5.1f} t")

# Natural-uranium CANDU fuel skips enrichment: feed equals fuel
print(f"Natural uranium fuel (CANDU) for the same heat: 39.4 t per year, no tails")

# Mining: ore needed at two ore grades (fraction of U3O8 in ore)
u_per_u3o8 = 0.848
need_u3o8 = feed_per_product(0.0495) * product / u_per_u3o8
for grade in (0.001, 0.15):
    print(f"Ore at {grade:.1%} U3O8: about {need_u3o8/grade:,.0f} t of ore")

# Used fuel: uranium dioxide at about 10.4 t per cubic meter of pellets
vol = product * 1.134 / 10.4         # UO2 is 1.134 times the uranium mass
print(f"\nUsed fuel pellets per year: about {vol:.2f} m3")

Fuel at 3.50% U-235:  7.0 t natural U per t of fuel,  41.6 t per year, tails  35.7 t
Fuel at 4.50% U-235:  9.2 t natural U per t of fuel,  54.4 t per year, tails  48.5 t
Fuel at 4.95% U-235: 10.2 t natural U per t of fuel,  60.2 t per year, tails  54.3 t
Natural uranium fuel (CANDU) for the same heat: 39.4 t per year, no tails
Ore at 0.1% U3O8: about 70,934 t of ore
Ore at 15.0% U3O8: about 473 t of ore

Used fuel pellets per year: about 0.64 m3

Fuel in the reactor

Fuel stays in a light water reactor for three to six years, moved between core positions at each refueling outage. During that time, about two thirds of the uranium-235 fissions, some uranium-238 becomes plutonium, part of which fissions in turn, and fission products build up. At discharge, used light water fuel is still about 95 percent uranium, mostly uranium-238, with about 1 percent plutonium and 4 to 5 percent fission products and minor actinides. CANDU fuel stays in the reactor for about a year and a half and has a lower burn-up, so it discharges more fuel per unit of energy but with less uranium-235 left in it.

Used fuel storage

Freshly discharged fuel is intensely radioactive and produces substantial decay heat, so it first goes into a deep pool of water next to the reactor. The water cools the fuel and shields workers: a few meters of water is enough to make it safe to stand at the poolside. After several years, when the heat has fallen, fuel can be moved to dry storage, in steel and concrete containers that are cooled by natural air flow and need no power or water. Dry storage is used at most nuclear sites in North America and is designed to last for decades.

The volume is small. All the used fuel produced by Canada's reactors since the 1960s would fit in an area the size of about seven hockey rinks stacked to the height of the boards. The program shows that the reference plant discharges well under a cubic meter of pellets a year. Fuel assemblies take more room than the pellets alone, and containers more still, but the total is still small compared with wastes from other energy sources, because, as Lesson 1 showed, nuclear fuel is so energy-dense.

Reprocessing and recycling

Used fuel can be dissolved and separated chemically into uranium, plutonium and the remaining waste. France, Russia and a few other countries do this, using recovered plutonium in mixed oxide fuel and storing separated uranium for reuse. Reprocessing reduces the volume of high-level waste and recovers energy, but it is more expensive than buying fresh uranium at current prices, and it creates separated plutonium, which needs strict security and safeguards. Canada and the United States do not reprocess commercial fuel and plan to dispose of used fuel directly. Future fast reactors could change the economics by consuming plutonium and long-lived actinides.

Waste categories

Most radioactive waste by volume is low-level, with little activity. High-level waste is a small volume but contains almost all the radioactivity. Lesson 3 showed that the activity of used fuel falls by about 99 percent within a few decades. After about 1000 years, the remaining activity is dominated by long-lived actinides, and after several hundred thousand years, the radiotoxicity of used fuel falls to about that of the natural uranium ore it came from. That long tail is why disposal is designed for very long periods.

Deep geological repositories

The international consensus is that high-level waste should be placed hundreds of meters underground in stable rock, inside engineered barriers. Used fuel is sealed in corrosion-resistant containers, often copper or steel, surrounded by compacted bentonite clay that swells when wet and blocks water movement, and placed in a rock formation that has been stable for millions of years. Each barrier slows any escape of radioactive material, so that even in the very long term the dose to people at the surface stays far below natural background. Finland's repository at Onkalo, in granite about 430 meters deep, is the first to be completed, with disposal expected to begin in the mid-2020s, and Sweden and France are following.

In the United States, federal law made the Department of Energy responsible for disposing of commercial used fuel, and Yucca Mountain in Nevada was designated as the repository site in 1987, but the project stalled amid political opposition and no license has been issued. Used fuel therefore remains in pools and dry storage at reactor sites, and the government pays utilities for storage costs. The Waste Isolation Pilot Plant in New Mexico, a deep repository in salt, has operated since 1999 for long-lived waste from defense programs, showing that deep disposal works, but it does not accept commercial used fuel.

Marcus's summary for TVA also covers transport. Used fuel and other radioactive materials are shipped in packages designed to survive severe accidents, including drops, fire and immersion, and tested to international standards. Decades of shipments worldwide have not caused a release harmful to people.

Costs and responsibility

Fuel is a small part of the cost of nuclear electricity, usually around 10 to 20 percent of the total generating cost, and uranium itself is only part of that, with conversion, enrichment and fabrication making up the rest. That is a sharp contrast with gas plants, where fuel is most of the cost. Doubling the price of uranium raises the cost of nuclear electricity by only a few percent. Waste management costs are also included in the price of electricity: plant owners pay into dedicated funds that will cover storage, transport and disposal, and the decommissioning of the plants themselves. Marcus calls this one of the least appreciated features of nuclear energy: the cost of dealing with its waste is collected while the electricity is sold, rather than left for future generations.