Nuclear Power Deaths per TWh: 2.3 from a Typical Accident

R. Scott Kemp discusses the externalities of nuclear power, specifically focusing on the number of deaths caused by nuclear accidents. This calculation is part of a broader effort to compare nuclear power with other energy sources like wind, solar, and natural gas, especially in the context of decarbonization.

The Challenge of Externalities

While the explicit economics of energy sources are often calculated, externalities like climate change and safety are harder to quantify. For climate change, the difficulty lies in assigning a definitive monetary value, leading to an approach of estimating the necessary value to justify certain actions. However, even with equal decarbonization efforts, wind and solar often outcompete nuclear, except in thermal markets. This raises the question of whether additional safety externalities from nuclear, or other externalities from wind, solar, or natural gas, could alter this competitive landscape.

The initial focus is on calculating the externality for nuclear power, specifically the number of fatalities from accidents.

Isotopes and Their Impact

Reactor accidents release various isotopes with significant activity. Key isotopes include:

• Cesium-137 and Cesium-134: These dominate for hundreds of years. Cesium-137 has a half-life of 30.2 years. Cesium behaves similarly to potassium in the body, filtering through organs and remaining for extended periods.
• Iodine-131: Not shown on some plots due to its very short half-life (a few months to a couple of years). It delivers a large immediate dose, primarily through ingestion and inhalation shortly after an accident.
• Strontium-90: Behaves like calcium and can be incorporated into bones and teeth. Historically, above-ground nuclear weapons testing led to strontium-90 being found in the teeth of babies, causing a political movement that pushed testing underground. While not a major external emitter, ingestion is problematic.

The calculation will primarily focus on cesium, with iodine and other isotopes added later to account for their contributions.

Major Nuclear Accidents: Chernobyl and Fukushima

The two major INES (International Nuclear Event Scale) Level 7 events, Chernobyl and Fukushima, are used as primary data points for source terms.

Chernobyl

• Reactor Type: RBMK-type water-graphite reactor, lacking containment.
• Accident: A steam explosion ejected fuel, melted it, and triggered fires. These fires volatilized many fission products.
• Release: 85 petabecquerels of Cesium-137. The total non-noble gas activity was 4,000 petabecquerels.
• Contamination: 75% of the total release is estimated to have been deposited on land. A 1998 European Commission report estimated an average European spatial contamination of 7 kilobecquerels of Cesium-137 per square meter.
• Considerations: Ukraine, a major grain producer, uptakes cesium into its crops, which are then consumed. This suggests the European spatial average might be an underestimate for human exposure. The estimate is rounded up to 10 kilobecquerels per square meter to account for this.

Fukushima

• Reactor Type: BWR (Boiling Water Reactor) with high-pressure containment, similar to many modern reactors.
• Release: 21 petabecquerels of Cesium-137.
• Accident: Initiated by a tsunami following an earthquake. Cooling systems failed, leading to fuel melting and fission product release. Hydrogen explosions occurred, but a catastrophic spent fuel pool fire (which could have been 100 times worse than Chernobyl) was avoided. Venting of containment led to significant releases.
• Contamination: Winds primarily blew the plumes into the Pacific Ocean, limiting land contamination in Japan. However, North America received significant contamination. The average contamination was about 1% of Chernobyl's, but over a much larger land area.
• Global Factor: UNSCEAR (United Nations Scientific Committee on the Effects of Atomic Radiation) found a factor of 1.6 to convert European contamination to global contamination for Chernobyl. This factor is used to estimate global impact.

Estimating a "Typical" Major Accident

To estimate a typical accident, a weighted average of Chernobyl and Fukushima is used:

• Chernobyl-type: 11 RBMK reactors still operate. A small weighting is given to this type.

• Fukushima-type: Represents most reactors. The 21 petabecquerels from Fukushima are divided by 3, as it involved three reactor accidents at one site.

• Calculation: (85 PBq

• 11/450) + (21 PBq / 3
• (450-11)/450) ≈ 9 petabecquerels for a "typical" single reactor accident.
• Site Accidents: Considering that roughly half of accidents are internal to a single reactor and half are site accidents involving multiple reactors, the calculation is adjusted to 18 petabecquerels (roughly 1/5th of a Chernobyl event). This is the baseline for a "typical" accident.

Dose Pathways and Conversion to Deaths

Radiation exposure occurs through:

1. Ground Shine: Direct external irradiation from deposited material.
2. Inhalation: Breathing airborne particles (immediately after accident or from re-suspended dust).
3. Ingestion: Consuming contaminated food or water.

Data from a 1982 UN report provides conversion factors. For Cesium-137, 9 microsieverts per year per kilobecquerel per square meter is used for external irradiation. This factor is then adjusted to include inhalation and ingestion, which contribute an additional 69% to the total dose (scaling factor of 220/150 from external only to total).

Linear No-Threshold (LNT) Model

The LNT model is applied, which assumes that any dose of radiation, no matter how small, carries a proportional risk of cancer. This simplifies calculations, as 10 millisieverts to one person is equivalent to 1 millisievert to 10 people in terms of total person-sieverts.

Calculation Steps

1. Average Contamination: 10 kilobecquerels per square meter (for Europe, adjusted for grain production).
2. Dose Rate: 9 microsieverts per year per kilobecquerel per square meter.
3. Decay: Accounts for the 30.2-year half-life of Cesium-137.
4. Population: 750 million people in Europe, assumed stable over 100 years.
5. Integration: The dose is integrated from 0 to infinity (effectively over several half-lives).
6. Person-Sieverts: The calculation yields 860,000 person-sieverts of exposure from Cesium-137 in Europe.

Converting Person-Sieverts to Cancers and Deaths

• Cancer Risk: Using an excess relative risk of 0.64 per sievert and a baseline cancer risk of 20%, the calculation results in 110,000 cancers.
• Fatal Cancers: Assuming half of cancers are fatal, this leads to 55,000 deaths in Europe from Cesium-137 alone.
• BEIR VII Report: The National Academies' BEIR VII report provides similar figures for solid cancer mortality (610 deaths per 100,000 person-gray), which, when applied to the calculated person-gray, yields approximately 52,000 deaths, confirming the initial calculation.

Including Other Isotopes and Global Impact

• Iodine: UNSCEAR reports for Chernobyl indicate about 3.4 million person-sieverts from iodine, primarily affecting the thyroid.
• Total Dose: Including iodine and other minor isotopes, the total dose for a typical accident is estimated at 2.3 million person-sieverts, about 2.7 times higher than from Cesium-137 alone.
• Global Factor: Applying UNSCEAR's global multiplier of 1.6 (Europe to global) to the total dose.
• Final Estimate: 230,000 deaths per typical major accident worldwide, considering all isotopes. This figure represents cancer deaths only, excluding other health effects like teratogenic effects, inheritable defects, or deterministic diseases.

Discrepancies in Published Estimates

Published estimates for Chernobyl deaths vary widely (4,000 to 270,000). The lower estimates (e.g., 4,000) often come from studies that focus on only the most exposed cohorts or specific regions. The higher estimates, like the 270,000 from Greenpeace, are closer to the presented calculation.

The primary reason for this discrepancy lies in the contamination-to-dose conversion factor. Older reports used a factor of 0.2, while more recent scientific validation (after Fukushima, using high-purity germanium detectors) suggests a factor of 0.86. This newer factor is used in the presented calculation.

A caveat is that the Fukushima measurement was taken four months after the accident. It's possible that a "washing away" effect, where contaminants settle into the ground and become less available, could reduce the dose over time. If an exponential decay model is applied based on a six-year post-Chernobyl datum, the cesium contribution could be about one-fifth of the calculated value, leading to a total dose change of about 60% (since iodine is not affected by this). This would reduce the death estimate to between 138,000 and 230,000. The 230,000 figure is considered the more robust estimate.

Accident Frequency

Estimating accident frequency is challenging. Probabilistic Risk Assessment (PRA) uses bottom-up decision trees, but these models can be incomplete and rely on uncertain inputs. Historical data often shows that major accidents follow paths not anticipated by PRA models.

• PRA Limitations: While useful for relative safety changes (e.g., comparing hardware modifications), PRA is not ideal for absolute risk assessment, as it often underestimates actual accident rates.
• Historical Data: With 21,500 reactor-years of experience, there have been two INES 7 events (Chernobyl and Fukushima). This suggests a historical rate of roughly 10^-4 INES 7 events per reactor-year.
• Comparison with PRA: The historical rate of INES 7 events is about 50 times higher than what PRA models predict for the existing fleet. This indicates that PRA models are only capturing a small fraction of the total risk.
• Focus on INES 7: Only INES 7 events (beyond design basis accidents) are considered significant enough to cause widespread fatalities. Smaller accidents (INES 5 or below) have negligible releases.
• Accident Rate: Using the historical INES 7 rate of 10^-4 per reactor-year, and assuming each reactor is roughly 1 gigawatt, this translates to 10^-11 accidents per megawatt-hour, or 10^-5 accidents per terawatt-hour.

Deaths per Terawatt-Hour

Multiplying the accident rate by the estimated deaths per accident:

10^-5 accidents/TWh * 230,000 deaths/accident = 2.3 deaths per terawatt-hour.

If the washing-away effect is considered, this number could drop to 1.4 deaths per terawatt-hour.

Conclusion

Nuclear power, while not as safe as some models predict, is a relatively safe form of energy. The calculated 2.3 deaths per terawatt-hour places it between hydropower and natural gas in terms of safety. This number is crucial for comparing nuclear power with other energy sources, rather than dismissing it outright due to the seemingly large number of deaths per accident. The deaths, though significant, are often spread over a long period and are statistically difficult to attribute directly to an accident due to the high background rate of cancer.