Fuel Burnup Simulator: Isotope Evolution in Nuclear Fuel

simulator advanced ~14 min
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Burnup ≈ 42 GWd/tHM — 18-month cycle depletes ~65% of initial U-235

At 4% enrichment and 25 kW/m power density with 90% capacity factor, an 18-month fuel cycle achieves approximately 42 GWd/tHM burnup, consuming 65% of initial U-235 while breeding about 6 kg of Pu-239 per tonne.

Formula

Burnup = Power_density × time × capacity_factor / fuel_mass
dN_U235/dt = -σ_f235 · φ · N_U235 (U-235 depletion)
dN_Pu239/dt = σ_c238 · φ · N_U238 - σ_a239 · φ · N_Pu239 (Pu-239 buildup)

The Life of a Fuel Assembly

A nuclear fuel assembly enters the reactor as a precisely engineered array of ceramic UO₂ pellets sealed in zirconium alloy tubes. Over 3–5 years, it undergoes a profound transformation: U-235 atoms split, releasing energy and fission products; U-238 atoms transmute into plutonium; and the crystal structure of the ceramic degrades under relentless neutron and fission fragment bombardment. Tracking this evolution is essential for reactor operation, safety analysis, and spent fuel management.

U-235 Depletion and Pu-239 Breeding

Fresh 4% enriched fuel contains about 40 kg of U-235 per tonne. As the reactor operates, U-235 is consumed by fission at a rate proportional to neutron flux. Simultaneously, the abundant U-238 captures neutrons and transmutes through neptunium-239 into fissile plutonium-239. By mid-cycle, Pu-239 fission contributes a significant fraction of reactor power — the fuel effectively breeds its own replacement fissile material, extending the useful cycle length.

Fission Product Buildup

Each fission event creates two highly radioactive fission product nuclei from a library of over 800 possible isotopes. Some, like Xe-135, have enormous neutron absorption cross-sections that poison the chain reaction. Others, like Cs-137 and Sr-90, define the long-term radioactivity of spent fuel. The accumulation of fission products is the primary reason fuel must eventually be replaced — not because fissile material is exhausted, but because the neutron economy can no longer overcome the poison load.

Burnup and Cycle Optimization

This simulation tracks U-235 depletion, Pu-239 buildup, and integrated burnup over a fuel cycle. Adjust enrichment, power density, cycle length, and capacity factor to explore the tradeoffs between fuel utilization, cycle economics, and reactivity management. Higher enrichment enables longer cycles and deeper burnup, but increases fuel fabrication costs and the reactivity swing that must be managed with burnable absorbers or control rods.

FAQ

What is fuel burnup in nuclear engineering?

Burnup measures the total energy extracted from nuclear fuel, expressed in gigawatt-days per metric tonne of initial heavy metal (GWd/tHM). Modern PWR fuel achieves 40–60 GWd/tHM, meaning each tonne of uranium produces as much energy as burning about 15,000 tonnes of coal.

How does Pu-239 form in a reactor?

U-238 (which makes up 95%+ of fuel) captures a neutron to become U-239, which beta-decays to Np-239, then to Pu-239 with a half-life of 2.3 days. Pu-239 is itself fissile — by end of a typical fuel cycle, 30–40% of fission energy comes from Pu-239 bred in-situ, effectively extending the fuel's useful life.

What is xenon poisoning?

Xe-135 is a fission product with the highest known neutron absorption cross-section (2.6 million barns). It builds up during operation and peaks about 11 hours after shutdown, potentially making restart impossible for 24–48 hours. This 'xenon deadtime' was a factor in the Chernobyl accident when operators tried to override it.

Why does burnup matter for spent fuel management?

Higher burnup means more fission products (more radioactive, more heat-generating spent fuel) but fewer total assemblies to store. It also changes the isotopic mix of plutonium, affecting reprocessing value and proliferation resistance. Burnup is the single most important parameter for spent fuel characterization.

Sources

Embed

<iframe src="https://homo-deus.com/lab/nuclear-engineering/fuel-burnup/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub