# Burnup Vs. Consumption Rate

by terryphi
Tags: burnup, consumption, rate
 P: 52 So, In Lamarsh, when he talks about the burnup , he's talking about the fission energy released per unit mass of fuel where as when he talks about consumption rate, he's talking about the amount of fissile matter consumed per unit energy produced?
P: 21,585
 Quote by terryphi So, In Lamarsh, when he talks about the burnup , he's talking about the fission energy released per unit mass of fuel where as when he talks about consumption rate, he's talking about the amount of fissile matter consumed per unit energy produced?
The consumption rate is simply the mass of fuel consumed per unit time, which would be derived from the power level or fission rate divided by the energy produced per fission (and using various conversion factors).

Burnup is often expressed as energy produced (power integrated over time) per unit mass of initial fuel. It is also expressed, by some, as FIMA, fissioned initial metal atoms.

Roughly 1% FIMA or 0.01 fissioned atoms corresponds to ~950 GWd/tU, based on 200 MeV of recoverable energy per fission. The conversion varies based on what is assumed as recoverable energy. The energy per fission is less for U-235 than for Pu-239/-241, so the relationship between FIMA and GWd/tU changes with cycle exposure, or fissile content. MOX (U,PuO2) would have a higher energy per fission at BOL.
 P: 52 In class we were taught that (CR) = (1+alpha)BR Is it just me, or is there no uniformly agreed upon definition?
P: 21,585

## Burnup Vs. Consumption Rate

 Quote by terryphi In class we were taught that (CR) = (1+alpha)BR Is it just me, or is there no uniformly agreed upon definition?
Which Lamarsh book is one using?

I assume CR = conversion ratio, and BR is breeding ratio? Breeding means beyond that which is used in the reactor. LWR convert U-238 to Pu-239, but they consume some of the Pu-239, and produce less fissile material than consumed, so they are not considered breeders.
 P: 52 We're using "Introduction to Nuclear Engineering" CR -> consumption rate BR -> Burnup Rate.
P: 21,585
 Quote by terryphi We're using "Introduction to Nuclear Engineering" CR -> consumption rate BR -> Burnup Rate.
I have the third edition.

Consumption rate as used in the text refers to consumption of U-235 (or rather depletion = loss of U-235). Then they use burnup rate for grams (of U-235) fissioned per day. IMO, this muddies the water, since not all fission occur in U-235.

The burnup rate is based on fissions, while the consumption rate is based on fission + neutron absorption by U-235. In addition to fissioning, the U-235 may absorb a neutron and become U-236, which has a low fission cross-section. In fact, U-236 will absorb a neutron and become U-237, which decays to Np-237.

In reality, about 8 to 10% of fissions occur in U-238 as a result of fast fissions. Some U-238 is converted to Pu-239, -240 and -241, and at high burnups, ~40 GWd/tU, most thermal fissions occur in Pu-239/-241 in high enrichment (> 4%) fuel.
See chapter 2 in http://www.nap.edu/catalog.php?record_id=9263 - particularly page 18 and Fig. 2-5.

Most of the time, burnup is calculated using the thermal energy, which does not distinguish among fast fissions and thermal fissions or the isotopes producing fission.

Another factor to consider is that large nuclear reactor have fuel of different vintage, which are divided into batches. At the beginning of a cycle, there is fresh fuel (no exposure), which may be one quarter to almost one half of the core. There is an almost equal amount of fuel (once-burned) being reinserted for a second cycle. There is some smaller fraction of twice-burned fuel in for a third cycle, if the core loads between one-third and one-half of the core. In plants using more than three batches, there may be some thrice-burned assemblies in for a fourth cycle. The third and fourth cycle assemblies are loaded on the periphery of the core, and they function more as a reflector since the power density is generally less than one-third of core average power.

High burnup fuel, with exposures (burnups) > 40 GWd/tU will have most fissions in Pu-239/-241, as well as some portions of fissions in U-238.

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