Uranium fuels

Malik takes Hana to the fuel laboratory, where a technician is examining a cross-section of a high-burnup PWR fuel rod under a microscope. The pellet is no longer a clean cylinder: a pattern of radial cracks runs out from the center, the center has a different grain structure, a porous rim has formed at the edge, and the gap to the cladding has closed. "Low-enriched uranium dioxide, about 60 megawatt-days per kilogram after three cycles," Malik says. "The pellet has been completely reshaped by heat and fission."

Why uranium dioxide

Almost all power reactors burn uranium dioxide (UO₂) fuel. Metallic uranium, used in some early reactors, has a much higher density of uranium atoms and higher thermal conductivity, but it changes phase at modest temperatures, swells badly under irradiation and reacts with water. UO₂ is a ceramic with the fluorite crystal structure. It melts at about 2850 °C, is chemically compatible with water and zirconium alloys, keeps its crystal structure up to melting, and can hold large amounts of fission products in its lattice. Its main drawbacks are low thermal conductivity, which makes the pellet center run hot, and brittleness, which means pellets crack during the first power rise.

Natural and enriched fuel

Uranium in nature contains about 0.711 percent uranium-235 by mass, the rest being almost all uranium-238. CANDU reactors can use natural uranium because heavy water absorbs so few neutrons. Light water reactors need fuel enriched in uranium-235, typically 3 to 5 percent, with some recent fuel programs moving toward slightly higher levels within the low-enriched range. Enrichment itself is a separate industrial process and is not covered in this materials course; what matters here is that enrichment and burnup together set how long fuel stays in the core and how much it is changed by irradiation.

A 17 × 17 PWR fuel assembly is about 4 m long and holds 264 fuel rods. Each rod holds a stack of enriched UO₂ pellets inside a zirconium alloy cladding tube filled with pressurized helium. Assemblies stay in the core for three or four cycles of 18 to 24 months each, so a third or so of the core is replaced at each refueling outage.

Burnup

Burnup measures how much energy the fuel has produced per unit mass of initial heavy metal, usually in megawatt-days per kilogram of uranium (MWd/kgU). About 200 MeV is released per fission, so 1 MWd of energy corresponds to roughly 1 gram of heavy metal fissioned. A burnup of 10 MWd/kgU, which is typical of CANDU discharge, means about 1 percent of the heavy atoms have fissioned. Light water reactor fuel reaches 40 to 60 MWd/kgU, so roughly 4 to 6 percent of the atoms have fissioned, and in the United States the burnup of a rod is limited by its licensing basis, commonly a rod-average burnup of about 62 MWd/kgU.

Each fission replaces one heavy atom with two lighter fission product atoms, so the number of atoms in the fuel grows with burnup. Some fission products, such as cesium and strontium, form oxides or compounds; others, such as zirconium and the rare earths, dissolve in the UO₂ lattice; others form metallic precipitates; and the noble gases xenon and krypton, about 15 percent of fission products, are almost insoluble.

The temperature profile and pellet cracking

Because UO₂ conducts heat poorly, the center of a pellet is much hotter than its surface. For a pellet with uniform heat generation and constant conductivity, the temperature difference between center and surface depends only on the linear heat rate q' and the conductivity:

With q' = 40 kW/m and k = 3 W/m·K, the difference is about 1060 K. Because k falls as temperature rises, real calculations use the conductivity integral, the area under the k(T) curve, rather than a single value. The steep gradient means the hot center expands more than the cooler rim, and the resulting tensile hoop stress at the rim cracks the pellet during the first power rise, into a handful of radial wedges. The fragments move outward toward the cladding, an effect called relocation, which narrows the gap.

Changes with burnup

Conductivity degradation and fission gas release interact in a way that matters for safety. As burnup rises, the fuel conducts heat less well, so for the same linear heat rate the center runs hotter. Fission gas release rises steeply once the center exceeds about 1200 to 1300 °C, because diffusion of gas atoms is thermally activated. Released xenon and krypton conduct heat far worse than the helium fill gas, so gap conductance falls and the fuel runs hotter still. Fuel performance codes follow this coupled behavior step by step through the fuel's life, and design limits on linear heat rate fall with burnup to keep it in check.

# UO2 fuel: conductivity degradation with burnup and the fuel centerline temperature.
import math
def k_uo2(T_K, bu_MWd_kgU):
    # Illustrative fit of a widely used form: phonon term with a burnup penalty plus an electronic term.
    t = T_K / 1000.0
    phonon = 1.0 / (0.0375 + 2.165e-4 * T_K + 0.0035 * bu_MWd_kgU)
    elec = 4715e6 / t**2.5 * math.exp(-16361.0 / T_K) / 1e9 * 1e3
    return phonon + elec
def center_temp(q_lin, T_surf_K, bu):
    # Integrate dT = q'/(4 pi k(T)) in small steps of conductivity integral.
    target = q_lin / (4 * math.pi)          # W/m, conductivity integral required
    T, acc, dT = T_surf_K, 0.0, 1.0
    while acc < target:
        acc += k_uo2(T, bu) * dT
        T += dT
    return T
T_s = 773.0     # pellet surface temperature, K (about 500 C)
for q in (20e3, 30e3, 40e3):
    for bu in (0.0, 30.0, 60.0):
        Tc = center_temp(q, T_s, bu)
        print(f"q' = {q/1e3:4.0f} kW/m, burnup {bu:4.0f} MWd/kgU: centerline {Tc-273.15:6.0f} C")
# Fission gas release, a simplified threshold view (illustrative)
for Tc in (1100, 1300, 1500, 1700):
    frac = 0.01 if Tc < 1250 else min(0.5, 0.01 + 0.0012 * (Tc - 1250))
    print(f"centerline {Tc} C -> fission gas release roughly {100*frac:.0f} percent")

q' =   20 kW/m, burnup    0 MWd/kgU: centerline    889 C
q' =   20 kW/m, burnup   30 MWd/kgU: centerline   1088 C
q' =   20 kW/m, burnup   60 MWd/kgU: centerline   1285 C
q' =   30 kW/m, burnup    0 MWd/kgU: centerline   1140 C
q' =   30 kW/m, burnup   30 MWd/kgU: centerline   1459 C
q' =   30 kW/m, burnup   60 MWd/kgU: centerline   1751 C
q' =   40 kW/m, burnup    0 MWd/kgU: centerline   1432 C
q' =   40 kW/m, burnup   30 MWd/kgU: centerline   1860 C
q' =   40 kW/m, burnup   60 MWd/kgU: centerline   2194 C
centerline 1100 C -> fission gas release roughly 1 percent
centerline 1300 C -> fission gas release roughly 7 percent
centerline 1500 C -> fission gas release roughly 31 percent
centerline 1700 C -> fission gas release roughly 50 percent

Pellet-cladding interaction

When reactor power rises quickly, pellets heat and expand faster than the cladding, and if the gap has closed the pellet pushes the cladding outward. Stress concentrates where pellet cracks meet the cladding. If corrosive fission products such as iodine are present, the cladding can crack from the inside by stress corrosion cracking, a failure mode called pellet-cladding interaction (PCI). Defenses include limits on how fast power can be raised after a period at low power, barrier liners of pure zirconium on the inside of some BWR cladding, chamfered pellets and, in CANDU fuel, the graphite-based coating inside the sheath. CANDU on-power refueling also moves bundles into higher-power positions, so fuel management rules limit the power increase a bundle may experience as it is shuffled.

Other fuel forms

Several other fuel forms are in use or under development. Mixed oxide fuel combines uranium and plutonium oxides and is used in some light water reactors overseas. Uranium silicide and uranium nitride have higher uranium density and conductivity and are studied for accident-tolerant fuel, as Lesson 10 explains. TRISO particle fuel, used in high-temperature gas reactors, packs a small kernel inside layers of carbon and silicon carbide that retain fission products to very high temperatures, as Lesson 11 describes. Metallic fuels of uranium alloyed with zirconium are used in some fast reactor designs. Each has its own behavior under irradiation, but the questions are always the same: how hot it runs, how it swells, how it releases gas and how it interacts with its cladding.

Fabrication and quality

Fuel behavior in the reactor begins with fabrication. UO₂ powder is pressed into green pellets and sintered at about 1700 °C in a hydrogen atmosphere to reach the specified density. The grain size, pore size distribution and oxygen-to-metal ratio all affect later behavior: larger grains, for example, slow fission gas release because gas atoms must travel farther to reach a grain boundary, and some vendors add small amounts of chromium or aluminum oxides to grow larger grains. Pellets are ground to a precise diameter, inspected, and loaded into tubes, which are then filled with helium and sealed by welding end caps.

Moisture control deserves special mention. Early experience with zirconium alloy fuel showed that small amounts of moisture or hydrogenous contamination inside a rod could cause local hydriding of the cladding from the inside, producing sunbursts of hydride and eventually defects. Strict drying of pellets and control of fill gas now make such failures rare. Debris is another common cause of fuel defects in light water reactors: small pieces of metal carried by the coolant can fret through cladding, so plants use debris filters at the bottom of each assembly and strict foreign-material exclusion during outages.

Fuel after the reactor

Used fuel continues to be a materials problem after it leaves the core. It is first cooled in water-filled pools, where the cladding must resist corrosion for years or decades. Later it may be transferred to dry storage casks or containers, where it is held in an inert gas. In dry storage, the main concerns are the cladding temperature during drying and early storage, which limits hydride reorientation and creep, and the long-term integrity of the container and its welds. In Canada, used CANDU bundles are stored in pools and then in dry storage containers at the stations, pending a deep geological repository. In the United States, used fuel is likewise stored in pools and dry casks at reactor sites. In both cases, the fuel's materials history in the reactor affects how it behaves in storage.