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Nuclear Engineering

Nuclear Fuel Burnup & Reactivity Simulator

Compute the burnup, U-235 depletion, Pu production, fission-product build-up and end-of-cycle reactivity margin of a reactor fuel load in real time. Sweep enrichment, thermal power, operating days and reactor type for first-pass fuel-cycle design.

Parameters
U-235 enrichment
%
Natural U 0.7%, PWR fuel 3-5%, research reactors <20%
Fuel mass (UO₂ basis)
kg
PWR core load is typically 80-100 t
Thermal power
MW
Electric / thermal efficiency (33%). 1000 MWe ≈ 3000 MWth
Target burnup
GWd/MTU
Standard PWR 40-50, high-burnup 55-65
Full-power operating days
day
A PWR cycle is roughly 540 days (18-month operation)
Reactor type
Affects neutron spectrum and conversion ratio
Results
—
Achieved burnup (GWd/MTU)
—
U-235 depletion (%)
—
Pu production (kg)
—
Fission products (kg)
—
Reactivity loss (pcm)
—
End-of-cycle margin (pcm)
—
Fuel assembly lattice — burnup map

Each pin colour shows local burnup (green = fresh, yellow = mid, red = highly burnt). White flashes mark fission events, purple flashes mark U-238 → Pu-239 conversion.

Reactivity ρ vs burnup (cycle history)
Mass balance — U-235, Pu, fission products
Theory & Key Formulas

$$BU = \frac{P_{th}\,\cdot\,t_{full}}{M_{HM}},\qquad \rho_{EOC} = \rho_{BOC} - \alpha_{BU}\,\cdot\,BU$$

BU: burnup (MWd/MTU), P_th: thermal power (MW), t_full: full-power days, M_HM: heavy-metal mass (MTU). ρ: reactivity (pcm), α_BU: burnup reactivity coefficient (~200 pcm/GWd for LWR).

$$N_{fission} = \frac{BU \cdot 86400}{E_{fission}},\qquad E_{fission} \approx 200\,\mathrm{MeV} = 3.2\times10^{-11}\,\mathrm{J}$$

Each fission releases about 200 MeV, so cumulative fission count N_fission can be derived from burnup. Multiply by 0.85 to estimate the U-235 fission count (the remaining 15% is neutron capture).

$$m_{Pu} \approx C_{R}\,\cdot\,M_{HM}\,\cdot\,BU,\qquad m_{FP} \approx 1.05\,\mathrm{g/MWd}\,\cdot\,BU\,\cdot\,M_{HM}$$

Pu production scales with the conversion factor C_R (~0.4 g/MWd for LWR) and burnup. Fission products accumulate at about 1.05 g per MWd by mass conservation (the fissioned uranium mass essentially becomes the FP mass).

Fuel Burnup and Fission-Product Build-up

🙋
People talk about "reactor fuel burnup", but nothing actually burns in a chemical sense, right? What is being "burnt"?
🎓
Great question. In nuclear fuel, "burning" means U-235 undergoing fission when it captures a neutron. Each fission releases roughly 200 MeV — millions of times what a chemical bond breaking releases. Burnup is the indicator of "how much energy was extracted per ton of fuel", in units of GWd/MTU. For a PWR, 1 GWd/MTU corresponds to taking 1 GW · day = 86,400 GJ out of a single ton.
🙋
So can we keep raising burnup forever and never refuel? When I set "target burnup" to 80 on the left, the "end-of-cycle margin" keeps shrinking…
🎓
That is exactly the heart of fuel-cycle design. As burnup grows, U-235 is steadily consumed, fission products — especially Xe-135 and Sm-149 — start poisoning the chain reaction by absorbing neutrons, and reactivity drops by roughly 200 pcm per GWd. When the "initial reactivity" can no longer cover the "burnup reactivity loss", the core cannot sustain criticality. That moment is end-of-cycle, the time to discharge the fuel.
🙋
So if we just load more U-235 by raising enrichment, we can run longer?
🎓
Exactly. Commercial LWRs use 3-5% enrichment to reach about 45 GWd/MTU over an 18-month (540-day) continuous run. To improve economics, "high-burnup" operation pushes 55-65 GWd/MTU and needs enrichment closer to 5%. Advanced Accident Tolerant Fuel (ATF) targets 6-8%. NRC rules generally cap commercial fuel below 5%, so anything higher is the realm of SMRs and research reactors.
🙋
A lot of Pu is produced too. Is it thrown away as waste, or reused?
🎓
Here is the twist: Pu-239 is itself fissile, so in the second half of fuel life 30-40% of power actually comes from bred Pu-239. "U-238 captures a neutron, becomes Pu-239, that Pu-239 then fissions" is happening continuously even in LWRs. Recovering Pu from spent fuel as MOX is "once-through reprocessing"; multiplying it in breeders is the "closed cycle". Japan's Monju and France's Phénix / Superphénix aimed at the latter. The US, partly for cost reasons, has gone with direct disposal (once-through).
🙋
About 1 g of fission products per MWd is a lot. What problems do they actually cause?
🎓
Three categories. First, "reactivity poisons" — Xe-135 with a 9.2-hour half-life builds up after a shutdown and causes the "xenon override" that delays restart. Second, "decay heat" — even after fission stops, FP decay keeps generating heat, and at Fukushima this is what caused the meltdowns once cooling failed. Third, "long-lived nuclides" — Cs-137 (30 yr), Sr-90 (28 yr), Tc-99 (210,000 yr), I-129 (15.7 million yr) need management on geological timescales. Integrating all this is the core of nuclear fuel-cycle engineering, and a central topic in UQ (uncertainty quantification) and PRA (probabilistic risk assessment).

Frequently Asked Questions

Burnup is the cumulative thermal energy extracted per metric ton of uranium (MTU), expressed in MWd/MTU or GWd/MTU. For example, operating a 3000 MW PWR for 540 days with 90 MTU of fuel gives 3000·540/90 = 18,000 MWd/MTU = 18 GWd/MTU. Standard PWR discharge burnup is 40-50 GWd/MTU, and modern high-burnup cores reach 55-65 GWd/MTU to lower fuel-cycle cost and waste volume.
Each fission releases about 200 MeV, so burnup directly translates to a cumulative fission count. This tool assumes 85% of U-235 reactions are fissions and 15% are captures (forming U-236). For 4.5% enrichment at 18 GWd/MTU, roughly 36% of U-235 is consumed. At 45 GWd/MTU more than 80% of U-235 is depleted, and bred Pu-239 supplies 30-40% of the power near end-of-cycle.
U-238 captures a neutron to form U-239, which beta-decays through Np-239 to Pu-239 (half-lives 23 min and 2.4 days). This is called conversion. A typical LWR produces about 0.4 g Pu per MWd, so a 90-ton PWR core at 18 GWd/MTU builds up roughly 648 kg of plutonium. Fast breeder reactors (FBRs) can reach conversion ratio > 1 (true breeding), making more Pu-239 than they burn. Plutonium can be recovered by PUREX reprocessing and reused as MOX fuel.
Three causes: (1) fissile inventory loss as U-235 is burned, (2) neutron poisons such as Xe-135 and Sm-149 building up among the fission products, and (3) the gradual change in the actinide chain. This tool uses roughly 200 pcm of reactivity loss per GWd/MTU and subtracts it from the beginning-of-cycle (BOC) reactivity to give the EOC margin. Once EOC reactivity goes negative the core becomes sub-critical. In real PWRs, soluble boron concentration is decreased over the cycle to compensate, and refuelling happens when boron approaches 0 ppm.

Real-World Applications

Commercial reactor fuel-cycle design: Most PWRs and BWRs use a "three-batch" core: each refuelling replaces a third of the fuel with fresh assemblies and shuffles the rest. Over three 18-month cycles, each assembly accumulates roughly 15 GWd/MTU per cycle for a discharge burnup near 45 GWd/MTU. Fresh fuel enrichments are spread over 4.0-4.95% to balance leakage against burnup. This tool gives a first-pass single-assembly check before running detailed core-follow codes.

SMR and advanced reactor evaluation: SMRs such as NuScale and BWRX-300 extend the cycle to 24-60 months to cut maintenance. Sodium-cooled or high-temperature gas reactors such as Natrium and XE-100 target ultra-high burnup > 100 GWd/MTU to shrink waste volume by an order of magnitude. Sweeping enrichment and operating days here gives a feel for the design space these advanced systems are aiming at.

Spent fuel management and reprocessing: Burnup sets decay heat, dose rate and criticality safety of spent fuel. Dry-cask storage designs (boron loading, cooling-channel layout) are built around burnup-binned decay heat curves, and PUREX reprocessing plants size Pu and U recovery from burnup. The Pu / FP outputs of this tool match what is needed for high-level reprocessing process design.

Regulatory safety analysis and UQ: Submittals to NRC or the Nuclear Regulation Authority demand detailed burnup-dependent reactivity, decay heat and radionuclide inventories from codes such as SCALE/ORIGEN or Serpent. Simple estimates like this tool support V&V of those detailed analyses and let UQ studies pre-screen sensitive input parameters before launching a full-core run.

Common Misconceptions and Pitfalls

The biggest pitfall is treating burnup as a synonym for "fuel lifetime". Burnup is an integrated thermal energy figure, while fuel life is set by a combination of reactivity (criticality), cladding integrity, FP-gas internal pressure, PCI (pellet-cladding interaction) and several other limits. Even when reactivity would allow more operation, cladding corrosion or hydrogen uptake hitting their limits can force end-of-cycle. The US currently caps commercial fuel near 62 GWd/MTU largely because of cladding, and ATF programmes are targeting > 75 GWd/MTU. This tool only models the thermal-energy side, so cladding and FP-gas behaviour must be checked separately.

Next, the assumption that "Pu produced equals proliferation risk". The Pu produced in LWRs has a complex isotopic mix — Pu-239 is only ~60%, the rest is Pu-240/241/242. Once Pu-240 is above 7%, the material is "reactor-grade Pu", widely considered unsuitable for weapons. Conversely, Pu discharged at very low burnup (< 5 GWd/MTU) can be "weapons-grade" with Pu-239 > 93%, which is why IAEA safeguards closely track burnup histories. This tool reports total Pu mass only, so proliferation studies require an isotopic code such as ORIGEN.

Finally, do not assume that "200 pcm/GWd reactivity loss is universal". That coefficient is a representative LWR value and shifts strongly with reactor type, enrichment and the presence of burnable poisons (gadolinia, integral boron). Gd₂O₃-bearing fuel intentionally lowers initial reactivity to spare soluble boron, giving an inverted-U reactivity curve. Graphite-moderated RBMK cores combine a positive temperature/void coefficient with this picture and were a root cause of Chernobyl. The simple linear model here is for first-pass sizing only; serious design requires a time-dependent depletion calculation.

How to Use

  1. Enter initial U-235 enrichment (3.0–5.0 wt%) in the enrichNum field to define fuel composition.
  2. Set fuel assembly mass (400–600 kg/assembly) using massNum to specify heavy metal loading.
  3. Input reactor thermal power (2500–3500 MWth) via powerNum to establish fission rate and burnup progression.
  4. Define target burnup (30–60 GWd/MTU) in targetNum to calculate required residence time and isotopic evolution.
  5. Click Calculate to simulate U-235 depletion, plutonium buildup, fission-product accumulation, and reactivity margin loss over the fuel cycle.

Worked Example

A pressurized water reactor loads 193 fuel assemblies at 4.2 wt% U-235 enrichment, 500 kg/assembly HM, operating at 3000 MWth nominal power with a target burnup of 45 GWd/MTU. The simulator calculates: U-235 depletion reaches 68%, Pu-239 production accumulates to 8.2 kg/assembly, fission-product inventory reaches 12.4 kg/assembly, and reactivity loss totals −4200 pcm over the cycle. End-of-cycle control-rod reactivity margin of +850 pcm ensures shutdown capability margin meets Technical Specification requirements.

Practical Notes

  1. Higher initial enrichment (5.0 wt%) extends cycle length but increases fresh-fuel cost; 3.5–4.2 wt% is typical for 18–24 month cycles in PWRs.
  2. Fission-product poisoning (Xe-135, Sm-149) causes ~2800 pcm reactivity penalty; simulator accounts for equilibrium xenon and samarium concentrations.
  3. Plutonium production provides ~1000–1200 pcm reactivity feedback, reducing net cycle reactivity loss and extending cycle length naturally.
  4. Verify end-of-cycle margin exceeds +300 pcm for boron letdown capability and xenon-transient recovery in low-power operation.