Quote of the Day
The cave you fear to enter holds the treasure you seek.
— Joseph Campbell
Introduction
Figure 1: Dry Storage of Spent Fuel (Wikipedia).
A coworker was telling me about a relative of his who is an engineer at a nuclear power plant. One of his relative's many jobs is to babysit nuclear waste casks (Figure 1) – a task which includes monitoring their temperature. These casks are warmed from the inside by the radioactive decay of the waste they hold. As I understand it, this job has good long-term security because these casks are going to be a safety hazard for tens of thousands of years.
I thought it would be an interesting exercise to estimate the amount of spent fuel generated by nuclear plants in the US each year. My analysis is rough, but I will be able to compare my estimate with the reported waste generation rates as a check on my math.
Background
Definitions
- Gigawatt (GW)
- 109 W or 1000 Mega-Watts (MW).
- tonne
- I use this term for a metric ton or 1000 kg. A US ton is 2000 pounds or 907 kg. Both of these units are built-in Mathcad.
Nuclear Plant Sites in the US
The US has 99 active power reactors (Figure 2), with five units under construction and eighteen more planned.
Figure 2: Map of Nuclear Power Plants in the USA (Source).
The Energy Information Administration (EIA) publishes information on all these plants. This information, coupled with some basic physics, will allow us to estimate the amount of spent fuel generated per year in the US.
Analysis
Amount of Waste Generated Per GW Per Year
Figure 3 shows my estimate for the amount of nuclear waste generate per GW per year. This estimate of 27.9 tonne/GW-year is rough because it assumes that 100% of the fuel is burned, which is very unlikely. However, we are just looking to generate an estimate.
Figure 3: Uranium Fuel Burn Rate Per Year Per GW.
Estimate Comparison with Reality
The EIA reports that 39.7 GW-days of energy are generated per metric tonne of fuel, which is the reciprocal of what I estimated. Let's compare this value to my calculation (Figure 4).
Figure 4: Comparing My Estimate to EIA Estimate.
Annual US Spent Fuel Generation Rate
Figure 5 shows the amount of MW-hours per month of energy generated in the US. We can use this chart to estimate the amount of spent fuel generated each year.
Figure 5: US Electrical Energy Generation Per Month (Source).
Figure 6 shows my estimate for the amount of spent fuel generated annual in the US.
Figure 6: My Estimate for the US Annual Spent Fuel Generation Rate.
The EIA published annual spent fuel data, which I show in Figure 7. Note how our rate of accumulated spent fuel has linear growth – you would expect that because we have not been building new plants.
Figure 7: EIA Data on Annual Spent Fuel Generation Rate (Source).
While Figure 7 is a bit hard to read exactly, it appears to show ~2450 tonnes of spent fuel are generated annually, which agrees very well with my estimate.
Conclusion
This was a quick calculation that had surprisingly good agreement with reality. I am floored by the magnitude of the spent fuel storage problem – we are talking about thousands of tonnes of dangerous stuff that will be around for thousands of years.
I have enjoyed working through your analysis. I found it thorough and agree with the conclusions. As a little perspective, coal-fired generation at 65 000 000 MWhr per month would generate approximately 20 000 000 tonnes of ash per year compared with spent fuel of 2500 tonnes. A problem either way, but spent fuel is managed. Its on-site storage at power plants is licensed, regulated, and safely maintained. Hopefully, we will develop a permanent storage solution (e.g. Yucca Mountain). Little is done with ash except to pump it to ash ponds. It is permanent and does not decay over time.