Background

In a recent dinner conversation, the subject of nuclear power came up. I made the claim that coal produces more radioactive material than nuclear power per unit of energy produced.

My friend called bullshit. I like to try and validate my claims when someone calls bullshit. Not to prove I’m right, mind you, but to make sure that I am shaking off any falsely held beliefs. So, a few days later, I googled it, and found a Wikipedia article on the Environmental impact of nuclear power, which, in the ‘Comparison to coal-fired power generation’ section, claims:

Nuclear power plants in normal operation emit less radioactivity than coal power plants.[70][71]

Case closed, I thought. Not so. My friend checked the sources. These are Coal Combustion – ORNL Review Vol. 26, No. 3&4, 1993 and The EPA. Calculate Your Radiation Dose which is actually a dead link. That ORNL article is actually an archived Scientific American article, and it doesn’t actually talk about radiation per KWh. It talks about radioactive exposure in the chimney stack shadow of coal vs nuclear power plants.

Ok, so this one merited a bit more digging.

Literature Review (ha ha)

I found a University of Notre Dame lecture slide deck titled Radioactivity in Natural Resources (backup here) that did a lot of math, but didn’t do Bq/kWh. It also broke things down per radioactive element, life cycle step (smokestack emissions, different kinds of waste etc), and covered other sources as well (oil, natural gas etc).

I learned two things from the slide deck:

The standard unit of radioactivity is Bq, the Becquerel, ‘defined as the activity of a quantity of radioactive material in which one nucleus decays per second’ (thanks again, Wikipedia).
A lot of reports have been written around this subject, but one stands out for its comprehensiveness. A 1982 UNSCEAR Report titled Ionising Radiation: Sources and Biological Effects (backup here - it’s big!).

The UNSCEAR report looks fascinating, and it’s probably worth a holiday read. But time is money, and I need to get my answer and then get back to my day job. So, a bit of CTRL+F finessing brings me to page 108: Radiation Exposures Due To Coal-Fired Power Plants. There are many places you can measure radioactivity - in the actual rock, what comes out the chimney, what is in the ash. For the purposes of my back of the napkin, I’ll focus on what’s in the ash, and, if it’s easy, what comes out of the chimney. In particular, I am avoiding any calculation of doses to the population. That is, the radioactivity exposure to populations due to energy generation. That question seems to be the most common one addressed in these reports, but it’s not what I am trying to figure out.

Math

To recap, the question is:

What is the radioactivity per KWh of electricity generated for coal, and is it higher than nuclear?

We will try to answer this question for 1982.

It might be somewhere else in the report, but I found that the standard measurement is Bq/kg, rather than Bq/kWh. So we need to do a bit of math.

Coal Math

I’m sorry, but I haven’t set up math notation for my blog yet, so you’ll have to follow along as best you can with regular typesetting. I’ll render the math in code blocks to make it a little more readable.

Here’s how it breaks down. All figures are from the UNSCEAR report.

Ash content of coal burned in the USA in power plants with a capacity of more than 25MW ranged from 4% to 25% (pg 108 par 7). Let’s take coal -> ash as 8%, which I think is generous.

3x10^9 kg of coal is necessary to generate 1 GW annum of energy (pg112, par29)

So we have 3x10^9 kg coal * 0.08 ash factor = 2.4x10^8kg of ash per 1 GW annum of energy

When coal is burnt, there are several classes of waste. These seem to be the same actual substance, but at various levels of compaction. These are vitrified ash, slag, and fly-ash. Fly ash can be captured or escape.

There seems to be a approximately order of magnitude increase in concentration of radioactive material between ash and coal (pg 109, par11).

Most of the math int he report cares about escaping ash, because that is what drives population exposure, but there is a set of charts that show the specific activity in Bq/kg for a typical coal plant on page 110. A bit of eyeballing of that chart (which is hard, it is log scale) gives me the following values:

Lignite:
18 for Th
40 for U
17 for Ra
22 for Pb
23 for Po
120 Total Bq/kg

Ash (all types):
100 for Th
220 for U
200 for Ra
2000 for Pb
2000 for Po
4520 Total Bq/kg

Lignite, it seems, can be used to generate electricity as well, so I am going to move that out of scope.

We can now calculate the total radioactivity per GW annum energy generation using coal

4520 Bq/kg * 2.4x10^8 kg ash/GW annum energy

Which gives 1.0848e+12 Bq/GW annum energy.

1.0848e+12 Bq/GW annum energy / 365 days / 24 hours / 1000000 kW per GW
= 123.835616438 Bq/kWh

So, answer 1 for coal: 123.83 Bq/kWh.

Let’s try validate it by working backwards from escaped ash.

pg 111, par18 states that average atmospheric discharges per unit of energy generated (MBq/GWannum) are, assuming a 10% ash content with 97.5% ash retention:

4000 for K
1500 for U to Ra
5000 for Pb and Po
1500 for Th to Ra 
12000 Total MBq/GW annum

There are 1000 mega in a giga, so we can just knock 1000000 off both the mega and giga, and come to

12000 Bq/kW annum

To get to hours:

12000 / 365 / 24 = 1.37Bq/kWh in escaped ash

That’s for 2.5% of the ash. So, total ash content is 1.37 / 0.0275 = 49.81 Bq/kWh

Ok, final answer, then is between, say, 40 Bq/kWh and 125 Bq/kWh, and I’m inclined towards the higher end of that calculation.

Nuclear Math

Ok, I’m pretty tired by now, and my 30 minute foray has become a 2 hour foray. So let’s wrap this up.

Annex F (pg 249) deals with Nuclear Power Production. Good god, it’s categorized into mining, milling, fuel fabrication, and reprocessing.

I want to focus on high level waste. That’s the bad stuff and it accounts for about 95% of the radioactivity in nuclear waste. world-nuclear.org states that a 1000Mw nuclear plant produces about 3m^2 of high level nuclear waste.

3m^2 / 365 / 24 = 0.00034246575 m^2 per kWh or 342 cubic millimeters

The International Atomic Energy Agency classifies High Level Waste (backup here) as typically having levels of activity concentration in the range of 10^4-10^6 TBq/m^3 (page 15).

So, how many Bq per kWh? Well, we know how many cubic meters per kWh, so it’s pretty simple.


10^4 * 0.00034246575 = 3.42
10^5 * 0.00034246575 = 34.246575
10^6 * 0.00034246575 = 342.46575

So our final answer here is, frustratingly, between 3.4 and 340 Bq/kWh.

Final Answer

It’s not a slam dunk, AKA, order of magnitude difference.

Coal might produce more radioactive waste than nuclear power. But it’s going to come down to the actual specific activity of the high level waste.

Personally, I am inclined to take the midpoint of 10^5, which gives us 34.2 Bq/kWh, and marginally pips the lower bound for coal.