Nuclear Accident in Japan - Asiaa

Nuclear Accident in Japan The earthquake and tsunami in Japan are a terrible disaster. The suffering of the Japanese people has been exacerbated by the crisis unfolding in the nuclear power plant of Fukushima prefecture. Nuclear power remains a mystery to many people, which adds to the sense of fear and powerlessness when something has gone as wrong as it has at Fukushima (Fig. 1). This note is written to reach an understanding of the unfolding events, and to help assess corrective action, both for the near term and for the distant future. Figure 1. Map and timeline of events at Fukushima nuclear complex.

Frank H. Shu 7:45 pm 17 March 2011

Light Water Reactors The kind of nuclear power used in most parts of the world, including Japan, the United States, and Taiwan is generated when the nucleus of an atom of uranium-‐235 absorbs a neutron and splits into two smaller pieces called fission products. The process of absorption is enhanced if the neutron moves slowly. Two to three neutrons are released in the fission process, which are initially moving quite fast when they first come out of the uranium nucleus or are subsequently emitted by the fission products. If enough uranium-‐235 is packed closely together in the fuel rods of a nuclear reactor, one and only one of these neutrons will be absorbed by a neighboring uranium-‐235 nucleus, causing it to fission and release an additional two to three neutrons. The process of one uranium nucleus’s fissioning to induce another uranium nucleus to fission is called a chain reaction. The excess neutrons that are not absorbed by uranium are either absorbed by other nuclei, or are lost from the surface of the assemblage of fuel rods. To help a nearby uranium-‐235 atom to absorb one of these extra neutrons, a flow of water molecules circulate as a hot liquid under high pressure or as steam between the fuel rods, with the hydrogen in the water slowing down the fast neutrons when they collide with the water molecules. In light water reactors (LWRs), the hydrogen is of the normal kind, and water is said to be the moderating agent for the reactor. When one and only one neutron from a fissioning nucleus creates another fission reaction, the reactor is said to have a critical mass. In properly designed reactors (the only ones that can pass the licensing process today), natural processes that require no operator intervention guarantee that the reactor is exactly critical. Insertion or withdrawal of control rods to increase or decrease the amount of neutron absorption, can help to change the power level in the reactor or to adjust for the changing fuel composition as the fuel assemblage ages, but the fundamental job of guaranteeing that reactors do not go supercritical (which results in an exponential increase in the rate of reaction) nor go subcritical (which results in an exponential decrease in the rate of reaction) is left to these natural processes in the same way that the Sun, which is a fusion reactor, can be counted on to give a steady output of power, day after day. Figure 2. Layout of electricity generation by GE Boiling Water Reactor (BWR) plant


In light water reactors, water serves an additional purpose: it helps to carry away the energy of the fission chain reaction, ultimately to drive turbines that generate electricity (Fig. 2). In this capacity, water is spoken of as a coolant for the nuclear fuel. This cooling is required even if the reactor is shut down (for example, by the insertion of neutron-‐absorbing control rods). Some of the fission products generated by the splitting of uranium are radioactive, meaning that they emit electrons, or alpha particles, or gamma rays until they decay to stable forms by such emission. The radioactivity of these unstable fission products is an additional source of energy in nuclear reactors, and they are present whether the nuclear reactor is on or off. Immediately after shutdown, this so-‐called decay heat is about 6.5% of the previous power of the nuclear reactor. After two and a half minutes, it has declined to about 3% of the on-‐power. It declines more slowly after that; for example, 5 days after shutdown, the decay heat is still about 0.3% of the on-‐power. For the reactors in Fukyshima prefecture, this means that after shutdown on March 11 (the day that the earthquake and tsunami struck) each reactor on March 16 was still putting out 3.5 megawatts, which is enough to cause 2,500 tonnes of reinforced concrete to fail in about a week if the reactor core they enclose is left uncooled. This, as we shall see, is the basic dilemma that underlies the nuclear crisis in Japan. Given the disaster that has overtaken Fukushima, we are led to ask: Why are LWRs sited in earthquake-‐prone countries near seashores where they are subject to tsunamis? The answer is that LWRs depend on water for moderation and cooling. Large sources of water are used that are then discharged to an appropriate reservoir. LWRs must be located near large bodies of water: rivers, lakes, or oceans. Civilization often chooses the same sites to build its cities. The resulting co-‐location of nuclear power plants and population centers exacerbates the threats to human health and safety when improbable, but eventful, nuclear accidents occur. The confluence arises from the choice to use LWRs as our source of nuclear power. There are other choices possible. Earthquake and tsunami An earthquake measuring 9.0 on the Richter scale rocked Japan at 2:46 pm March 11, 2011. The earthquake was more powerful than the limit of 8.2 assumed by the designers of the Fukushima nuclear facility. As soon as the tremors were sensed, control rods descended into the reactor core and shut down the chain reactions in each of the four LWRs of the so-‐called “boiling water” type. Many power lines went down, but all the emergency generators designed to run on diesel fuel turned on and continued to pump water to carry away the decay heat. Unfortunately, the subsequent tsunami, carrying a wave of water 10 m tall, washed away the remaining power lines as well as the reserves of diesel fuel. After an hour of operation, the emergency diesel pumps also were without electrical power. The system then switched to a less powerful system that runs on batteries. The batteries operate only the valves in a pump system that uses the power of Frank H. Shu 7:45 pm 17 March 2011

evaporating water that comes into contact with the fuel rods still hot with decay heat. After cooling, the condensed steam is fed back into the cooling system to replace the evaporated water. Unfortunately water that comes into contact with the hot Zircaloy cladding of the fuel rods will thermal-‐chemically dissociate into hydrogen and oxygen, with the oxygen combining with the metal, leaving the hydrogen as a separated gas. Eventually, in reactor 1, the batteries also went dead, creating a period without any pump power. To relieve the steady build-‐up of pressure in the containment vessel, the workers vented the hydrogen into the containment building. When fresh batteries arrived, the pressure continued to build, and a decision was made to have a partial release to the atmosphere. Exposure of the hydrogen to air caused an explosion in reactor 1, which wrecked the outside walls, but left the steel containment structure around the reactor intact. A decision was then made to pump seawater into the reactor pressure vessel. This decision means that the Japanese sacrificed any attempt to salvage the reactor for the greater good of public safety. The explosion affecting reactor 1 occurred about 28 hours after the earthquake struck. Subsequent hydrogen explosions also destroyed the outer containment building in reactor 3 (accompanied by fire in reactor 4) and in reactor 2. Of these, the explosion involving reactor 2 may be the most serious because it apparently damaged not only the outer containment building, but also the pressure suppression “pool” (actually a torus; see Figs. 2 -‐ 4). The torus increases the effective volume of the reactor pressure vessel, thereby helping to suppress unplanned large changes of pressure therein. This strategy allows the reactor pressure vessel to be constructed with thinner steel walls than many of the critics of the GE BWR design feel comfortable with. For 5 days workers have bravely battled setback after setback in an attempt to keep the fuel rods cool. The last 50 workers were evacuated on March 16 after experiencing radiation exposure as much as 5 times the maximum safe dosage allowed for nuclear plant operators in the United States. Figure 3. Schematic of boiling water reactor in the Fukushima nuclear complex.

(Barry Brooks)


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Dimensions and physical properties of structures Technical details on the GE Mark I Boiling Water Reactors (BWRs) are difficult to obtain. We shall start with the assumption that the graphic in Figure 4 from the New York Times is to scale. From the safety document on BWRs we deduce that the outer diameter of the cylindrically shaped reactor vessel is about 5 m. We then approximate the containment vessel as a sphere surrounding the reactor vessel containing the fuel rods. The modeled spherical containment vessel has inner diameter 10 m and outer diameter of 14 m, with the thickness of 2 m made of reinforced concrete that is by volume 10% steel. We take this construction material to have a mean density of ρ = 2,700 kg m-‐3, a mean specific heat capacity of c v = 600 J kg-‐1 C-‐1, and a mean thermal conductivity of K = 2 W m-‐1 C-‐1. Finally, we assume that the containment building has volume V = (30 m)3. € Figure 4. New York Times graphic of GE Mark I BWR

Hydrogen explosion Suppose the volume of the building into which hydrogen is vented is V = (30 m)3. If this hydrogen is at a pressure of 1 atm and a temperature of 25 C, then there are 27,000 m3/0.0224 m3 = 1.2 x 106 moles of H2 = 2,400 kg of hydrogen. The complete combustion of this amount of hydrogen releases energy E = 3.4 x 1011 Joules, which is the energy equivalent of 81 tonnes of TNT. By bomb standards, the hydrogen explosion is reasonably impressive, but it is difficult to believe that it was felt “40 km away” as reported in some news accounts. The pressure change induced by the release of energy E in volume V,


E = 8.5 MPa = 84 atm , 3V /2 would have produced a strong shock wave (pressure jump by factor of 85). But it would not have come close to harming the steel containment vessel of reactor 1, € which has a compressive strength in excess of 400 MPa. Notice that the computed value of ΔP is independent of the assumed V because E is proportional to V if the explosion took place in the containment building at one atmosphere of pressure. In reactor 2, a valve failure occurred that prevented the venting of hydrogen from € the containment vessel. Somehow oxygen leaked into the system, perhaps because of the valve problems, and an explosion probably occurred inside the reactor containment vessel. This would be very bad, because then the explosion would have happened under pressurized conditions and in a confined volume (500 m3 instead of 27,000 m3). Instead of the 8.5 MPa over-‐pressure computed above for the containment building, the over-‐pressure of an explosion within the steel containment vessel could be well over a hundred MPa. BWRs are designed to operate at about 7 MPa. An explosion that generated over a hundred MPa could well damage the pressure suppression pool. Because radioactive elements unique to the fission process have been detected in the cooling water, it is likely that the reactor pressure vessel itself has been breached. As Paul Ho points out, a plausible scenario is that the welds, perhaps in the entrance and exit pipes, gave way (see Fig. 3). If so, the breach would make it harder to keep the fuel rods covered with water. Insufficiently cooled, the fuel rods are then in danger of melting and pooling on the floor of the pressure vessel or on the floor of the containment vessel. Fear that such a more compact configuration could lead to a supercritical assemblage of uranium is apparently what motivated the plant workers to flood the reactor with borated seawater. Boron is a highly efficient absorber of neutrons and would prevent any runaway chain reaction. Nevertheless, one must ask whether just the decay heat will suffice to initiate a complete meltdown of the confinement vessel, with a resulting release of the radioactivity of the fuel rods into the surrounding environment. Complete meltdown? With R1 = 5 m, R2 = 7 m, and ρ = 2,700 kg m-‐3, the mass of the containment vessel made of reinforced concrete is 4π M= ρs R2 3 − R13 = 2.47 × 10 6 kg. 3 The heat capacity of this much material is Mcv = 1.48 x 109 J C-‐1 . The amount of energy needed to raise the containment vessel from 25 C to 500 C (the point when € loses its elastic strength) is therefore 7.03 x1011 J. At time t reinforced concrete after the shutdown of a reactor operating at power ℘0 , the rate of release of decay ΔP =

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Frank H. Shu € 7:45 pm 17 March 2011

heat from radioactive fission products and the cumulative decay heat released since shutdown are approximately given in LWRs, within about 6% accuracy, by the formulae −0.2962 ⎛ t ⎞ ℘decay (t) = 0.137℘0 ⎜ ⎟ for t > 150 s. ⎝ s ⎠ ⎡ ⎤ ⎛ t ⎞ 0.7038 E decay = ⎢0.195⎜ ⎟ + 3.12 ⎥(℘0s) for t > 150 s. ⎝ s ⎠ ⎣ ⎦ The thermal power of the Fukushima Daiichi reactor is of order ℘0 = 1.2 x 109 W. Without any cooling, it would have taken t = 8.67 x 104 s, or 1 day, for the € containment vessel to fail. If we include the thermal inertial of the water in the system and the fact that the emergency cooling equipment switched on almost € immediately, there was no immediate danger of the containment failing. The first explosion occurred 28 hr after shutdown, or at t = 1 x 105 s, when the release rate of decay heat was ℘decay = 5.4 MW. To dissipate 5.4 MW of heat by evaporating water, whose latent heat for vaporization is 2.26 MJ/kg, would require that pumps bring 2.4 kg/s of water inside € to cool the fuel rods. To get 2,400 kg of hydrogen at a the containment structure dissociation efficiency of η would require contact with 21,600 η−1 kg of water, i.e., at this stage the time scale needed to vent the hydrogen was 9,000 η−1 s = 2.5 η−1 hr. Reasonable values of η explain why the Japanese operators were forced to vent the hydrogen inside the containment vessel into the containment building. € € € at, say, € t = 4.32 x 105 s. If All workers were evacuated on the fifth day of the accident € they cannot return, the subsequent rate of release of decay heat will have to be absorbed by the existing system: ⎛ t ⎞ −0.2962 ℘decay = 3.52 MW ⎜ ⎟ for t ≥ 5 d. ⎝ 5 d ⎠ Since the reactors were still being actively cooled up to t = 5d, the reinforced concrete should have had a temperature of 100 C, that of boiling water at near atmospheric €pressure. Suppose the amount of seawater left behind the containment vessel to be 400 tonnes. To evaporate it takes an amount of energy 9.04 x 1011 J. With a rate of decay heat given by the above formula, this will take 3.22 d. Beyond that time the rate of decrease of decay heat will follow the formula: ⎛ t ⎞ −0.2962 ℘decay = 3.04 MW ⎜ for t ≥ 8.22 d. ⎟ ⎝ 8.22 d ⎠

Frank H. S€hu 7:45 pm 17 March 2011

With the water boiled away, it will take an input equal to 5.92 x 1011 J to heat the reinforced concrete from 100 C to 500 C. With a decay-‐heat release-‐rate given by the above formula, this would take 2.34 d. Without any intervention, we can expect the containment structure to collapse at t = 10.6 d, i.e., in the early morning of March 22 given the assumptions made to do the calculation. One can enquire whether natural cooling can prevent this catastrophe through the outer surface of the containment vessel driving natural convection in the air. Newton’s law of cooling gives its temperature T2: 4 πR2 2κ a (T2 − Ta ) =℘decay , where the air inside the damaged containment building might have a temperature of Ta = 25 C and a heat-‐transfer coefficient κ a = 15 W m−2 C −1 . With the decay heat € given by ⎛ t ⎞ −0.2962 ℘decay = 2.82€MW ⎜ for t ≥10.6 d, ⎟ ⎝10.6 d ⎠ the solution for T2 reads € ⎛ t ⎞ −0.2962 T2 = Ta + 305 C ⎜ for t ≥10.6 d. ⎟ ⎝10.6 d ⎠ With a more pessimistic choice κ a = 5 W m−2 C −1, the coefficient 305 C in the above equation would be three times larger, and there would be no hope. Even with the € more optimistic scenario, the containment vessel still has to carry the heat flux by thermal conduction from the interior surface to the exterior: € ℘decay dT F= . 2 = −K 4 πr dr We approximate the thermal conductivity of the reinforced concrete K as a constant, and we get that the temperature T1 at the inner surface has to be higher than at the outer surface value T2 b€y ℘decay ⎛ 1 1 ⎞ ΔT = ⎜ − ⎟. 4 πK ⎝ R1 R2 ⎠ -‐1 -‐1, With K = 2 W m C , we have the requirement ΔT = 6,410 C (t/10.6 d) −0.2962 , a passive cooling requirement that is impossible to meet anytime in the near future. The shell € of reinforced concrete is too non-‐conductive and too thick to have a physical solution where it can remain intact once active cooling of the fuel rods stops. € Frank H. Shu 7:45 pm 17 March 2011

Thus, left unattended, the reinforced concrete containment structures will collapse on a time scale of order a week from March 16. Active cooling, preferably supplied automatically rather than by human operators, should be able to maintain the integrity of the containment structure. News analysis by the New York Times seems to suggest that the plant owners wish to clean up and reuse the site. Thus, they would prefer not to seal a damaged reactor with a concrete sarcophagus, as was done at Chernobyl. An attempt is being made to bring in a new power line to supply grid electricity to drive pumps that can do a better job of active cooling. The next few days will be crucial for the success or failure of this strategy. Updates 5:31 pm March 17, 2011: The Japanese government has enlarged the circle of evacuation to a radius of 30 km (largest circle in top-‐left of map in Fig. 1). 5:45 pm March 17, 2011: Engineers have laid a power line that can connect Reactor 2 to the electric grid after they complete spraying water into Reactor 3 to help cool the spent-‐fuel storage pool. The backup generator at Reactor 6 is working and supplying power to Reactor 5 and 6 for their spent-‐fuel storage pools. They are preparing to add water to these pools. 7:55 pm March 17, 2011: TEPCO hopes to reactivate the cooling system to Reactor 2 by Friday evening (Japan time). Helicopter flights earlier in the day refute the public claims of Nuclear Regulatory Commission Chairman Gregory Jaczko that a spent-‐fuel storage pool in the Fukushima complex had run dry.
