Estimating Radioactive Contamination from the Accident at Fukushima Daiichi Nuclear Plant
Fukushima Daiichi is one of Japan’s largest power plants, and one of the fifteen largest nuclear power plants in the world. It is also one of the older plants in operation, encompassing both first-generation and more recent reactor designs among its six units. The newest unit is almost three times the size of Unit 1. As of this writing, April 1 2011, all six units are shut down amidst an emergency unique in history.
Very little information has so far emerged in the public domain that addresses the immediate need of the wider population. How severe is the accident? Will there be public health or long term environmental consequences? When will the emergency be over?
At public websites like www.zerohedge.com the user community has been attempting to provide relevant information as well as wider contextual and color commentary. The answer to the first question, severity, has been well demonstrated to be extremely severe, with all six reactors likely irreparably damaged, several partial meltdowns, loss of primary containment, loss of primary and backup cooling, and large scale radioactive releases. The last question, length of the emergency, has also been addressed and is at a minimum several years, as the reactors and spent fuel pools must be cooled while decay heat remains high enough to cause further damage. The remains of the plant will need to be looked after forever.
The central question, however, has only been addressed in broad terms. Clearly there is a lot of radioactive material at the plant site; clearly large releases are continuing. But there is no real quantification, little precise measurement, and little air dispersion modeling to inform the public. Here we attempt to address this part of the accident, three weeks into the developing and very dynamic situation.
Types and Amounts of Materials at the Site
There are five loaded reactor cores, six spent fuel storage pools and one large common fuel storage pool on site. Tokyo Electric Power Company (TEPCO) stores 11,125 fuel rod assemblies in the pools, with each assembly holding either 64 or 81 fuel rods for a total of approximately 800,000 fuel rods. 1,479 assemblies are at the Unit 4 pool, of which 548 are from the ‘core load’ removed for maintenance in December. At Unit 3, 32 assemblies in the pool are made of mixed plutonium-uranium or MOX fuel, as is the entire core load.
The cores themselves contain various numbers of fuel assemblies depending on the size of the units. Units 2, 3 and 4 are each 784 MW in rated electrical capacity, and each holds 548 fuel rod assemblies. So for perspective, each spent fuel pool holds about two core loads’ worth of fuel rods, while the common fuel pool on site holds about 1.5 times again as many as Units 1-6 combined.
Setting aside the common fuel pool, then, there are roughly 18 core loads in the reactor buildings, counting both the reactor cores and the spent fuel pools. If we assume that Units 5 and 6 are stable, we can deduct six loads and discuss 12 loads in the badly damaged Units 1-4. Note, however, that the common pool and Units 5 and 6 remain dependent on timely cooling, which could be in question if an event forces workers to evacuate again for an extended period.
We can be more precise about the nuclear materials in the reactor buildings for Units 1-4. According to TEPCO, the total number of fuel rods in those buildings’ spent fuel pools is 2,060 plus the core load from Unit 4, or 2,508 assemblies, or roughly 180,000 rods.
At 0.127 tons per assembly, this implies 431 tons of uranium within the damaged buildings’ pools. There should be another 534 assemblies in the cores of Units 2 and 3 which are the same size as Unit 4, and about half that number in Unit 1. Adding these 1,335 assemblies brings the total to 3,843 assemblies, 280,000 rods, and 488 tons of uranium in the damaged units. The MOX fuel rods are about 3% plutonium which does not materially alter the analysis of fission products, our main concern here.
While there are several dozen substances that can be of concern in a nuclear accident, this analysis will focus on cesium-134 and cesium-137. Cesium has a long half-life, is easily incorporated into living organisms, and results in full body radiation exposure. It has been the major legacy of contamination from Chernobyl, and is the basis for the exclusion zones enforced in Eastern European countries today and for the foreseeable future.
Cesium is a fission product, produced by the splitting or decay of larger atoms of uranium (or plutonium, whether from MOX fuel blending or from plutonium produced in normal nuclear fuel reactions). Together with strontium, cesium produces most of the decay heat over a long period after a core is shut down.
Oak Ridge National Laboratory analyzed the core constituents at the Brown’s Ferry nuclear plant as a ‘reference unit’ for boiling water reactors. In a 1,065 MW core, cesium was estimated at 429 kg given an extended period of fuel irradiation. For the slightly smaller 1,000 MW Chernobyl core the comparable figure would be 402 kg if the fuel was fully irradiated, but Chernobyl Unit 4 was only three years old. For the Fukushima Daiichi Units 2, 3 and 4 rated at 784 MW, 315 kg of cesium should be present in each core load of fuel. For the 460 MW Unit 1 185 kg of cesium would be present.
Thus, in the cores of Units 1-4, some 1,130 kg of cesium was in place when the accident occurred. Adding the spent fuel pools (net of the offloaded Unit 4 core) gives an additional 1,245 kg for a total of 2,375 kg of cesium in the damaged buildings.
Fraction Of On-Site Material Emitted Into the Atmosphere
According to the UN, only 22 kg of cesium was released into the atmosphere as a result of the Chernobyl accident. The amount of cesium at the Fukushima Daiichi site, then, represents over 100 Chernobyl releases. The next question is, what fraction of the total cesium may be released into the atmosphere from Fukushima Daiichi?
Release mechanisms for nuclear fission products are varied and complex. For cesium, an initial ‘burst release’ occurs when rod cladding fails at fairly low temperatures around 500 degrees. After that the major mechanism up to roughly 2,000 degrees is release of the ‘gap inventory’ held through condensation on free surfaces of the fuel, with diffusion of fission gas bubbles from deeper within the fuel becoming more important with increasing temperature and instability in the fuel rods (accident conditions, sudden changes in temperature etc.).
From experiments and simulations of reactor accidents, it is observed that cesium release approaches 100% at extended (more than 20 minute) heating over about 2,000 degrees.
Fission product release is enhanced by even minor amounts of oxidized uranium, so release rates would be greater, for example, if water was flashing into steam on exposed rods or in the presence of an air-fed fire.
At Fukushima Daiichi, each of the eight ‘hot spots’ in Units 1-4 has undergone a unique sequence of damage, including loss of coolant and resulting heating. Partial meltdowns, steam releases, and hydrogen buildups demonstrate that high temperatures were experienced. But without more detail on each reactor core and spent fuel pond, a full accounting and estimate for cesium (or any other radionuclide) release is impossible. Furthermore, the release rate of cesium varies with the extent of fuel irradiation, or burnup, further complicating any particular fuel assembly’s emission potential.
However, comparing possible release mechanisms, resulting emission rates, and circumstantial evidence from observed air contamination can provide a reasonable range estimate. For example, experiments on the initial burst emissions show a typical rate of 1 mg cesium per square centimeter of damaged fuel rod cladding for burst or gap release.
Because the accident at Fukushima is likely to be a long one, the burst or gap emissions are of less interest than the diffusion of fission products out of the deeper levels of the fuel. A design basis fuel rod may have 30% of its cesium inventory already condensed into the cladding gaps and other channels, primed for burst release. Over time, the fraction of cesium that is emitted if temperatures do not rise over 2,000 degrees is estimated at 50%. This means that 20% of the cesium is subject to release in the current status quo at Fukushima, along with any cesium in rods that have not failed yet. On the other hand, rods that have already been exposed to temperatures exceeding 2,000 degrees may have already expelled most or all of their cesium.
The Austrian Center for Weather and Climate Data estimated cesium release rates for the period of March 14-17. They used measurements on both sides of the Pacific Ocean to calibrate a source estimate. This estimate is in the range of 4*1015 to 5*1016 Bequerels (Bq) per day. This equates to 0.14-1.35 megacuries (MCi).
To assess the reasonableness of this estimate, the nuclear activity of cesium-137, 88 curies per gram, is used to translate the ZAMG estimate into cesium mass, and this mass into a fraction of the available cesium at the plant site. 0.14-1.35 MCi/day would require 1.5-12.3 kg of cesium, or just 0.1-0.5% of the inventory in the damaged buildings. This emission rate would ultimately result in 20% of the total cesium being emitted in 11-85 years, clearly a reasonable time frame for spent fuel to emit fission products.
Neither Chernobyl or Three Mile Island emitted cesium in anything like the quantities that have likely already been emitted at Fukushima Daiichi. Chernobyl likely emitted about 2.5 MCi, and Three Mile Island perhaps a hundredth of that amount. So we may be witnessing a Chernobyl every 2-20 days, perhaps every ten days as a midpoint.
Air Dispersal of Emitted Fission Products (in progress)