Inventory of Cs-137 in Reactor Shutdown on 1/1/2009

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Discussion Overview

The discussion revolves around calculating the inventory of Cs-137 in a nuclear reactor that was shut down on January 1, 2009. Participants explore the theoretical and practical aspects of determining the amount of Cs-137 produced and its decay over time, considering various factors such as fission yield and isotopic composition.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant calculates the daily production of Cs-137 based on reactor power and fission rates, questioning if their approach is correct.
  • Another participant inquires about other fission products that may decay into Cs-137, suggesting a broader consideration of decay chains.
  • A third participant acknowledges the initial calculations but raises concerns about the assumptions made, such as the constant fission yield of Cs-137 and the neglect of decay during buildup.
  • Concerns are expressed regarding the origin of the conversion factor used in the calculations and the need for more detailed isotopic information for accurate results.
  • There is a suggestion that the activity equation presented may be incomplete and should include units for clarity.
  • A later reply humorously notes the original post's date, implying that the initial poster may have resolved their issue by now.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the calculations or assumptions regarding the production and decay of Cs-137. Multiple competing views and uncertainties remain regarding the methodology and factors influencing the results.

Contextual Notes

Limitations include the dependence on specific isotopic compositions and assumptions about fission yields and decay rates, which are not fully resolved in the discussion.

kirilrost
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Problem:
Reactor operating at 2300 MW with specific power of 24.42 MW/MT, was shutdown on 1 January 2009. The reactor was fueled with 93.3 MT of uranium with initial enrichment of 3.8% U-235. At shutdown, core burnup 23.3 GW-day/MT.
Question:
1.What was inventory of Cs-137 when the reactor was shutdown?
2.How much Cs-137 will be left on 4 March 2009?

Actions:
Honestly, i have hard time understanding what is going here.
1.I thought that this is how many moles of the fission product Cs-137 does this reactor produce per day?
2.How much left is N(t)=N0*(0.5)t/t0.5? I need to plug in t here 4 March 2009 - 1 January 2009. Right?
Steps:
1. 1 mole fissioned =223 MWD
2300/223= 10.31 moles of fissioned per day
6.19 atoms of Cs-137 per 100 fissions.
10.31*0.00619=.6384304 moles of Cs-137 produced per day.
A=λN=(ln2)(.60222*1024)*(1/(365*24*3600*30.07))
Am i on the right track?
Thanks in advance.
 
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Are there any other fission products that might decay into CS137?
 
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You are on the right path. However, I don't know what the application is so I can't tell you if your assumptions are correct (is this a HW problem, or a real application?). Some things to think about

1. You are assuming a constant fission yield of Cs-137. This may be appropriate, but a specific fuel enrichment was given. To calculate a better fission yield, you would need to know what isotopes were in the core (U-235, U-238, Pu-239, etc.) This would require a detailed burnup calculation.

2. You are assuming the Cs-137 was not decaying as it was built up. This may be appropriate with the longer half-life, but there is also a fairly simple equation to calculate the build-up of a radioactive nuclide from a constant source (which I'm not giving here)

3. I'm not sure where the "1 mole=223 MWD" is coming from. It may be an appropriate rule of thumb, but there are more detailed ways to calculate this. As with the first point, you may need a detailed burnup calculation to know the specific isotopes in the core.

4. Either your Cs-137 yield is off by a factor of 10, or you are missing a factor of 10 when converting to percentage.

5. Finally, your activity equation is not quite correct. You are missing a term, and I highly recommend including units.
 
I just noticed that the original post was from 2011. I assume he eventually figured it out :)
 

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