EngineerHub.orgWhat this calculator does
Fuel burnup measures the thermal energy extracted from a specified initial heavy-metal mass. The calculation itself is an energy balance and is valid for any reactor when the thermal power, irradiation history, heavy-metal inventory and assigned fission-power share describe the same physical scope. The reactor and fuel-system selector adds interpretation: it explains which burnup measure is most useful, provides broad reference context, identifies special limitations and enables an optional enrichment or fissile-inventory estimate. It does not convert those reference values into a design or regulatory limit.
Fuel and reactor basis
Burnup is normally reported in GWd/MTU or GWd/tHM. Enrichment helps establish cycle capability but does not change historical burnup.
These assumptions affect only the energy-equivalent fission, mass and FIMA estimates. They do not alter energy-based burnup.
Calculated burnup
FIMA, equivalent mass fissioned and fissile-utilization values are derived from final average burnup and simplified atomic assumptions. They are not isotope inventories: neutron capture, breeding, leakage and isotope-specific fission contributions require a depletion calculation.
Target burnup planner
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The planner uses the same heavy-metal mass and assigned power share.
Each segment contributes rated thermal power × power level × availability × calendar duration. Use availability for the fraction of the segment during which the unit actually operated. An outage can be represented by a zero power level.
Cumulative average burnup
Theory and engineering background
What burnup means
Burnup is the cumulative thermal energy released by a defined fuel inventory divided by that inventory’s initial heavy-metal mass. The common unit is GWd/tHM. For uranium-only fuel, GWd/MTU is numerically equivalent when the tonne basis is the initial uranium mass. MWd/kgHM has the same numerical value as GWd/tHM.
A result of 45 GWd/tHM means that every initial tonne of heavy metal assigned to the calculation has produced 45 gigawatt-days of thermal energy on average. It says nothing by itself about where that energy was produced inside an assembly, rod or fuel pellet.
Energy-balance equation
Ei = Prated · Li · Ai · ti
BU = BU0 + Σ(Ei · s)/(1000 · MHM)
L is fractional thermal-power level, A is availability during the segment, t is calendar days, s is the fraction of core fission power assigned to the selected fuel scope, and MHM is initial heavy-metal mass in tonnes. The factor 1000 converts MWd to GWd.
EFPD is the equivalent duration at rated reactor thermal power. It is a reactor operating-history measure; a batch or assembly can have a different specific exposure because its power share changes with time.
Why reactor type matters
The burnup equation does not depend on moderator, coolant or neutron spectrum. Interpretation does. A natural-uranium PHWR bundle, enriched LWR assembly, TRISO particle population and fast-reactor subassembly have different fuel-performance mechanisms, refuelling strategies, enrichment ranges and preferred exposure metrics.
Solid-fuel reactors normally retain a defined heavy-metal inventory during irradiation. Online-refuelled PHWRs require bundle- or channel-resolved histories. Liquid-fuel systems may add, remove or process heavy metal continuously, so a fixed initial-mass burnup can become ambiguous.
Enrichment and fissile inventory
Enrichment does not enter the historical burnup equation. Once thermal energy and initial heavy-metal mass are known, burnup is fixed. Enrichment matters when assessing cycle length, reactivity capability, fresh-fuel handling, criticality, fuel-management strategy and whether a proposed target is plausible.
The optional fissile input estimates initial fissile mass and compares it with the energy-equivalent mass fissioned. That ratio is not actual U-235 or plutonium depletion. In thermal uranium fuel, fission of bred plutonium can make the energy-equivalent ratio approach or exceed 100% of the initial U-235 mass.
Burnup limits are not universal
A burnup number is not automatically an operating limit. Applicable limits may be rod-average, assembly-average or local and can be controlled by cladding corrosion and hydrogen pickup, fission-gas release, rod internal pressure, fuel swelling, pellet–cladding interaction, fast fluence, linear heat generation rate, power ramps, transient response and accident behavior.
Back-end systems also matter. Higher burnup or enrichment may require revised spent-fuel-pool criticality evaluations, decay-heat and source-term analyses, transportation packages, dry-storage demonstrations and handling controls. Enter a comparison value only when it comes from the applicable design and licensing basis.
Reference context by fuel family
- Conventional U.S. LWR fuel: NRC material describes current vendor rod-average limits as roughly 62 GWd/MTU, with 75–80 GWd/MTU being pursued for higher-burnup concepts. These are not universal core-average limits.
- Natural-uranium PHWR fuel: IAEA material describes average burnup near 7 GWd/tU; modest enrichment can raise achievable discharge burnup.
- Fast-reactor fuel: IAEA reviews report demonstrations above 130 GWd/tHM and, in some programmes, beyond 200 GWd/tHM. Materials and cladding exposure are often decisive.
- HTGR/TRISO: FIMA and particle performance envelopes are often more informative than GWd/tHM alone.
Average, peak and local burnup
Core-average, batch-average, assembly-average, rod-average and local pellet burnup are different quantities. A core average can remain moderate while individual rods or axial zones are substantially higher. The selected heavy-metal mass and assigned energy must refer to exactly the same region.
For an assembly or batch, its share of integrated fission power is not generally equal to its fraction of core heavy-metal mass. Power peaking, enrichment zoning, burnable absorbers, control history, leakage and fuel shuffling all affect exposure.
What FIMA can and cannot show
FIMA means fissions per initial heavy-metal atom. It is especially useful when comparing fuel systems with different heavy-metal compositions. This calculator converts thermal energy to an approximate number of fissions using the selected MeV per fission, then divides by the estimated initial heavy-metal atom count.
A true depletion calculation tracks U-235, U-238, plutonium isotopes, thorium/U-233, minor actinides, fission products and neutron captures. The simplified FIMA output cannot predict isotopic composition, reactivity, decay heat, radiotoxicity or criticality.
Good power-history practice
- Use thermal power, not net or gross electrical output.
- Split the history when power, availability or fuel power share changes materially.
- Use zero power for shutdown periods; use availability only when it represents operating time within the segment.
- For online refuelling, follow each bundle or defined cohort from insertion to discharge.
- Document whether the reported result is core, batch, assembly, bundle, rod or local burnup.
Model boundaries
- No neutron transport, depletion, core-follow or fuel-shuffling model.
- No fuel temperature, gap conductance, fission-gas release or cladding-stress calculation.
- No criticality, shutdown-margin, decay-heat or source-term prediction.
- No automatic allowable-burnup determination.
- No correction for changing heavy-metal inventory in continuously processed liquid fuel.
Primary references
How to use the result
Use the calculated burnup as an auditable energy-accounting result. Then compare it with the correct plant, fuel-vendor or licensing document for the same averaging scope. The profile text and reference warnings are educational prompts, not acceptance criteria.
For design or safety work, transfer the power history to validated neutronic depletion and fuel-performance methods and reconcile the resulting assembly, rod and local exposure distributions.
Frequently asked questions
Does enrichment change the calculated burnup?
No. Historical burnup is thermal energy divided by initial heavy-metal mass. Enrichment affects neutron economy, excess reactivity, cycle length and the feasible fuel-management strategy, but it does not change burnup that has already been produced.
Is there a universal maximum fuel burnup?
No. The applicable value depends on reactor type, fuel and cladding design, whether the limit is local, rod-average or assembly-average, operating history, safety analyses and the licensing basis. Use the optional comparison field only with a value applicable to the exact calculation scope.
Why does the tool ask for reactor type if the equation is universal?
The selection provides interpretation. It changes the explanatory context, default fissile-field wording and reference warnings. It does not alter the integrated energy or burnup calculation.
Should I enter thermal or electrical power?
Enter reactor thermal power. Electrical power excludes rejected heat. Using electrical output directly will understate burnup unless it is first converted with a justified thermal-efficiency model.
What heavy-metal mass should I use?
Use the initial mass of uranium, plutonium, thorium or other actinide heavy metal in the selected scope. Exclude oxygen, carbide carbon, nitride nitrogen, graphite matrix, cladding and structural material. The energy assigned must refer to the same scope.
Can I calculate burnup for one assembly or CANDU bundle?
Yes, as an average, when you know the assembly or bundle initial heavy-metal mass and its integrated fraction of core fission power. For a CANDU bundle, follow the actual channel/bundle history from insertion to discharge. A simple mass fraction is not generally an adequate substitute for power share.
Why can equivalent fissile utilization exceed 100%?
The value compares energy-equivalent mass fissioned with initial fissile mass. In uranium fuel, U-238 captures neutrons and breeds plutonium that later fissions. The simplified ratio therefore is not actual U-235 depletion and can approach or exceed 100% without violating mass conservation.
What is the difference between GWd/tHM and MWd/kgHM?
They are numerically identical because one gigawatt-day per tonne equals one megawatt-day per kilogram. The heavy-metal basis must still be stated clearly.
Does FIMA depend on enrichment?
The energy-equivalent FIMA estimate depends primarily on burnup, assumed energy per fission and average initial heavy-metal atomic mass. Enrichment changes isotope composition and actual depletion behavior, which this simplified estimate does not resolve.
Can the tool predict remaining reactivity or cycle length from enrichment?
No. Remaining reactivity depends on neutron spectrum, geometry, leakage, burnable absorbers, moderator and coolant conditions, control history, breeding and fission-product poisoning. The target planner is only an energy/time calculation.
Can it be used for MOX, fast-reactor or TRISO fuel?
The energy-based burnup and FIMA estimates can be used when the heavy-metal inventory and assigned power are defined. The optional fissile percentage must be interpreted according to the fuel composition, and all design limits must come from fuel-specific analyses.
Can it be used for liquid-fuel molten-salt reactors?
Only for a defined fixed inventory over a stated interval. Online feed, cleanup, fission-product removal and actinide withdrawal require a material-flow and depletion model. A single initial-mass discharge burnup may not be physically meaningful.