Nuclear Power Externalities: Fatalities per TWh and Accident Risk

R. Scott Kemp discusses the external costs of nuclear power, specifically focusing on the number of fatalities caused by nuclear accidents. This calculation is crucial for a comprehensive understanding of nuclear energy's economic and societal impact, especially when compared to other energy sources like wind, solar, and natural gas.

The Challenge of Externalities

While the explicit internalized economics of nuclear power 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 where the necessary value to justify certain actions is estimated. 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.

Isotopes of Concern in Reactor Accidents

Reactor accidents release various isotopes with significant activity. Cesium-137 and Cesium-134 are of primary interest due to their long half-lives (hundreds of years for Cesium-137) and their tendency to persist in the environment, slowly increasing background radiation. Iodine-131, though not always shown on activity plots, is also critical due to its short half-life and immediate, high-dose impact through ingestion and inhalation.

Why Cesium and Strontium Matter

Cesium and Strontium are particularly problematic because their chemical properties mimic essential elements in the human body. Strontium-90, for instance, 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, which spurred a political movement to move testing underground. Cesium, on the other hand, mimics potassium and is readily absorbed throughout the body.

Major Nuclear Accidents: Chernobyl and Fukushima

The two most significant nuclear accidents, both classified as INES 7 (the highest level on the International Nuclear Event Scale), are Chernobyl and Fukushima. These events provide crucial data for estimating the externality of nuclear power.

Chernobyl (1986)

Chernobyl, an RBMK-type water-graphite reactor without containment, experienced a steam explosion that ejected and melted fuel, triggering fires. These fires volatilized a large amount of fission products. The accident released 85 petabecquerels of Cesium-137. A 1998 European Commission report estimated an average contamination of 7 kilobecquerels of Cesium-137 per square meter across Europe.

Fukushima (2011)

Fukushima, a BWR-type reactor with high-pressure containment, released 21 petabecquerels of Cesium-137. The accident was initiated by a tsunami, which led to cooling system failures and subsequent meltdowns. While containment helped limit releases, hydrogen explosions and venting events still led to significant environmental contamination. Fortunately, prevailing winds carried much of the plume over the Pacific Ocean, though North America received substantial contamination.

Estimating a "Typical" Major Accident

To calculate the externality, a "typical" major accident needs to be defined. This involves weighting the characteristics of Chernobyl (an older, less contained design) and Fukushima (a more modern design with containment). Considering the 450 reactors globally, with 11 RBMK-type reactors still operating, a weighted average is used.

The calculation considers: - Chernobyl-type accidents: 85 petabecquerels of Cesium-137. - Fukushima-type accidents: 21 petabecquerels of Cesium-137, divided by 3 to account for the three reactors involved in the Fukushima event.

This leads to an estimated 9 petabecquerels for a "typical" accident. Further adjustments are made to account for internal vs. site-wide accidents, resulting in an estimate of 18 petabecquerels, roughly one-fifth of the Chernobyl release.

Dose Calculation and the Linear No-Threshold Model (LNT)

The LNT model assumes that any radiation dose, no matter how small, carries a proportional risk of cancer. This simplifies dose-response calculations, allowing for the estimation of average population dose multiplied by average individual dose.

Pathways of Radiation Exposure

Radiation exposure can occur through: - Ground shine: Direct radiation from contaminated land. - Inhalation: Breathing in airborne radioactive particles. - Ingestion: Consuming contaminated food or water.

These pathways are influenced by the chemistry of the isotopes and environmental factors. Experimental data is used to determine the average impact of environmental chemistry on isotope availability.

Converting Contamination to Dose

A key conversion factor is used: 9 micrograys (or microsieverts, as beta and gamma radiation are roughly equivalent in biological effectiveness) per kilobecquerel per square meter per year. This factor, combined with the estimated contamination from a typical accident and the half-life of Cesium-137, allows for the calculation of dose over time.

To account for internal doses (inhalation and ingestion), a scaling factor derived from UN data is applied. For every 150 units of external dose, there are 220 units of total dose (150 external + 70 internal).

Population Exposure and Person-Sieverts

The calculation considers the stable population of Europe (approximately 750 million people) and integrates the dose over an infinite time horizon (though most decay occurs within a few half-lives). This results in a total exposure of 860,000 person-sieverts.

A "person-sievert" represents the collective dose received by a population. Under the LNT model, a given dose to one person is equivalent to the same total dose spread across multiple people in terms of overall health impact.

Converting Person-Sieverts to Cancers and Deaths

Using the excess relative risk of cancer (0.64 per sievert) and the baseline cancer risk (20%), the 860,000 person-sieverts translate to approximately 110,000 cancers. Assuming half of these are fatal, this equates to 55,000 deaths in Europe from Cesium-137 alone, per typical accident.

This result is corroborated by data from the National Academies' BEIR VII report, which estimates 610 deaths per 100,000 person-gray (equivalent to person-sievert for this type of radiation), yielding a similar figure of around 52,000 deaths.

Including Other Isotopes and Global Impact

Iodine-131, despite its short half-life, contributes significantly to the initial dose. UNSCEAR reports estimate approximately 3.4 million person-sieverts from Iodine-131 in Chernobyl. When all major isotopes are considered and scaled to a typical accident, the total dose increases to 2.3 million person-sieverts, about 2.7 times higher than the Cesium-137-only estimate.

UNSCEAR also provides a multiplier of 1.6 to account for global contamination compared to European contamination. Applying these factors, a typical major accident is estimated to cause approximately 230,000 deaths worldwide from all isotopes.

The Controversy of the Linear No-Threshold Model

The LNT model is often debated. Critics argue that it may overestimate risk at low doses, suggesting a threshold below which radiation has no harmful effects. However, the mechanistic argument against a threshold points to the possibility of a single photon causing a poorly repaired double-strand break in DNA, leading to cancer. Therefore, from a physics perspective, a threshold is unlikely.

The discrepancy in published death tolls for Chernobyl (ranging from 4,000 to 270,000) often stems from different assumptions about the contamination-to-dose conversion factor. Older reports used a factor of 0.2, while more recent, validated measurements (after Fukushima) suggest a factor closer to 0.86. This difference, along with the "washing away" effect where isotopes become less bioavailable over time, explains the varying estimates. Accounting for the washing away effect could reduce the estimated deaths by about 60%.

Accident Frequency and Probabilistic Risk Assessment (PRA)

Estimating the frequency of major nuclear accidents is challenging. Probabilistic Risk Assessment (PRA) uses bottom-up decision trees to model accident probabilities. However, PRA models are often criticized for: - Incompleteness: Historical accidents have followed paths not included in prior PRA models. - Epistemic uncertainty: Many branching probabilities are based on assumptions rather than observed data.

While useful for comparing the relative safety improvements of design changes, PRA results are often misused as absolute measures of safety. For example, PRA models for modern reactors like the AP-1000 and EPR predict extremely low accident frequencies (e.g., 10^-8 events per year), suggesting that even with widespread nuclear power, major accidents would be rare.

However, historical data contradicts these predictions. The observed accident rate for existing reactors is about 50 times higher than what PRA models predict, indicating that PRA only captures a fraction of the total risk.

Historical Accident Rate as a Basis

Given the limitations of PRA, using the historical accident rate for major events (INES 7) is considered the most defensible approach. There have been two INES 7 events in approximately 21,500 reactor-years of experience, leading to an accident rate of roughly 10^-4 per reactor-year.

If nuclear power were to provide 80% of global electricity, this historical rate would translate to about 40 INES 7 events every 50 years, or roughly one major accident per year. Such a frequency would likely be unsustainable for public acceptance.

Nuclear Power's Safety in Context

Converting the accident rate and estimated deaths into a per-terawatt-hour figure: - Accident rate: 10^-4 accidents per reactor-year. - Assuming 1 gigawatt per reactor, this is 10^-11 accidents per megawatt-hour. - This translates to 10^-5 accidents per terawatt-hour. - Multiplying by 230,000 deaths per accident yields 2.3 deaths per terawatt-hour.

If the washing away effect is considered, this figure drops to 1.4 deaths per terawatt-hour.

Comparing this to other energy sources, nuclear power is relatively safe, falling somewhere between hydropower and natural gas in terms of fatalities per terawatt-hour. While the number of deaths from a major nuclear accident is dramatic, it's important to compare it to the continuous, less visible fatalities caused by other energy sources, such as air pollution from coal. The inability to empirically "see" these radiation-induced deaths in the background noise of cancer rates does not negate their occurrence.