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How radioactive is nuclear reactor waste?

  1. Sep 14, 2011 #1
    I want to know how much radioactivity in Becquerels is produced by a typical light water reactor in one year of operation.

    I don't know how one would go about estimating this number. I found one reference that said 27 tons of spent fuel are generated by a typical reactor per year. But I don't really know how radioactive spent fuel is per kg.
  2. jcsd
  3. Sep 14, 2011 #2
    Well, there are many different radionuclides present in spent fuel, and with each with a different half life, the activity will vary depending upon when you refer. There are numerous codes that model reactor dynamics and give predicted waste based upon the different parameters (reactor type, fuel enrichment, etc.), but these cost money unless you are a nuclear engineering student. http://rsicc.ornl.gov/Default.aspx" [Broken] might be a good site to look at.
    Last edited by a moderator: May 5, 2017
  4. Sep 14, 2011 #3


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    I don't know the answer either, but I'll bet it varies depending on the output of the reactor.

  5. Sep 14, 2011 #4


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    Staff: Mentor

    If one is referring to spent fuel, then that depends on the batch size, power density, capacity factor and time of operation.

    There is not typical light water reactor, although there are relatively common types, such as BWR/4's with 764 assemblies and 4-loop PWRs with core of 193 assemblies of 17x17. However, not all plants operate with the same fuel cycle management, e.g., cycle length, batch size, capacity factor, etc. Cycle lengths in the US are either 18 months or 24 months, although at least one plant uses a unique schedule in between. Batch sizes vary from 30% to nearly 50%. Some plants have uprated a little or a lot from the initial commissioned power rating.

    Each plant has to do an estimate of radioactive products just in case. Some may use a so-called standard for the particular class of plant.

    I'll see if I can find some representative numbers.
  6. Sep 14, 2011 #5
    It's fairly easy to get a rough estimate from publicly available data.

    For example, http://en.wikipedia.org/wiki/Decay_heat says "After one year, typical spent nuclear fuel generates about 10 kW of decay heat per tonne, decreasing to about 1 kW/t after ten years."

    So, let's consider ten year old spent fuel. One 1 kW/t is 1 W/kg = 1 J/(s*kg). Since all this heat is produced solely by radioactive decay, it means that radiation inside spent fuel pellets is 1 Gray/s. (In other words, it's still insanely radioactive).

    Since after 10 years most short-lived isotopes have decayed, most of this radioactivity is caused by 30-year half-life isotopes Cs-137 and Sr-90 (see http://en.wikipedia.org/wiki/Fission_product_yield). Sr-90 is pure beta emitter, so if fuel is intact, it goes not give off much gammas. Gammas are mostly from Cs-137.

    Very roughly, we can assume that about half of the radiation is produced by gamma-active Cs-137. Decay energy of Cs-137 is 1.176 MeV. 1 MeV is 1.602*10^-13 J. Thus decay energy of one decay is 1.884*10^-13 J. In order to generate 0.5 J/s (0.5 W), how many decays of Cs-137 do we need? About 2.5*10^12.

    That's the answer you seek: the gamma activity of intact spent fuel after 10 years cool down is about 2.5 Terabecquerels per kg.
  7. Sep 14, 2011 #6
    In http://jol.liljenzin.se/KAPITEL/CONTENT.HTM" [Broken] I found the following graph:


    It shows the radioactivity of fission products per kg of initially present heavy metal (IHM) in spent PWR fuel at 33 MWd/kg burnup. It seems that after roughly a day we have 1015 Bq/kg in the fission products of the spent fuel. But I don't know what 33 MWd/kg burnup means (MWd = megawatt days?), nor do I know how much IHM a "typical" reactor would use in a year.
    Last edited by a moderator: May 5, 2017
  8. Sep 14, 2011 #7
    That estimate is not too far off the graph I found. At 10 years, the graph shows 10 Terabecquerels per kg.
  9. Sep 14, 2011 #8


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    That is a deceptively simple question. The complete answer takes more that counting discharged fuel bundles and multiplying it by the activity per kg.

    There are multiple ways that radioactivity is generated in a nuclear plant. The posters above have focused on the fission product source term. Most of that is discharged as spent fuel based on the replacement batch size during refueling. This also includes transuranics (such as plutonium) that are generated in the core during operation, but are not fission products.

    An additional production of radioactivity is due to activation products of coolant (such as tritium, Na-24, etc. ), and neutron activation of structures and components.
    One of the largest production of activation products is activation of coolanbt oxygen into N-16 which is a very strong beta/gamma decay source. However it is such a short lived product that it is gone when the plant reaches shutdown. But if you are strictly interested in how much rwadioactivity is produced you should consider it.

    In addition there may be production of solid radwaste including used cleaning supplies, anti-contamination clothing, ion exchange resins and so on. There may also be minor liquid and or gaseous releases to the environment. These sources are there and separate from the spent fuel bundles in the fuel pool or dry storage.
  10. Apr 15, 2012 #9
    Check out.

    This website has two Java programs that may interest you.
    Right side of page about 1/3 of the way down.
    They present information, that relates to your question, interactively in graphical form.

    1. Spent Nuclear Fuel
    2. Decay Chains.

    1. Shows various aspects of spent fuel (radioactivity, decay heat, etc) as they change over
    2. Shows the decay products of fission over time.
  11. Apr 16, 2012 #10
    Lamarsh gives an equation:

    A(t) = 1.4e6 P (t-0.2 - (t+T)-0.2) ) Ci

    P is power produced in MegaWatts (I'm assuming he means average power)
    T is time in days in the core
    t is time in days since removal

    To calculate per kilogram, take Mega-Watt days per ton, and divide by about 1000 days active (3 years), then divide by 1000 kg/ton. the result will be P, and T will be 1000.

    1 Ci = 3.7e10 Bq
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