The back of the envelope
Continuing analysis of the Fukushima crisis
CORRECTION TO THIS ARTICLE: Due to editorial deadlines, this column about the nuclear reactors at Fukushima includes a timeline of events only through March 15. Developments between March 15 and the date of publication are not reflected in the column.
In the last issue of The Tech, I tried to explain the events at the Fukushima Nuclear Power Plant and gave my opinion, as someone with two nuclear engineering degrees from MIT, as to what I thought the situation on the ground was and the likely course of events. In particular, I made three important claims:
1) Looking back, we will reflect on the events at Fukushima Daiichi as a success, not a failure, of nuclear safety engineering.
2) The risk to the public from radiological releases from Fukushima Daiichi has been and will be effectively zero.
3) It is likely that the none of the fuel at Fukushima Daiichi has been or will become melted.
As an opinion columnist with some 80 or so articles to my name, I’ve had to eat crow before. I don’t like the taste, but I’d rather dine on my words than live the rest of my life making only those predictions that are too vague or distant to ever come back to haunt the predictor. Whether it was speculation on the legislative chances of ObamaCare, the weapons program of Iran, or the suitability of Sarah Palin as a vice presidential candidate, I’ve managed to make a fool of myself in this paper even when I had days to prepare my thoughts. In trying to assess Fukushima Daiichi, a technically complex, ongoing event with limited information, I had mere hours to analyze the problem, and my article did not appear until two days after it was written — an eternity where crises are concerned.
I still stand by two out of three of my claims. A 40-year-old nuclear power plant was just subjected to the fifth largest recorded earthquake in history. It had not been designed to remain operational in the aftermath of that event, only to fail in a manner that protected the public from harm. It is doing just that, and in my book, that counts as a powerful demonstration of reliability.
The public faces virtually zero risk from radioactivity. The most exposed individual so far has been a worker who received a measured 10.63 mrem of dose — this is against a background yearly dose of roughly 350 mrem for the average individual. And the public is at significantly less risk than those working on-site.
Unfortunately, the third claim, that the uranium at Fukushima 1, 2, and 3 is and will remain unmelted, has not stood up as well. As I look over the reports from Units 1 and 3, I still see windows of time in which clad melting might be possible, though not many where fuel melting is a concern. However, new events at Unit 2 (which occurred after I had written my article) do appear to have resulted in partial fuel melting.
There is plenty of non-technical opinion to be written on nuclear power in the aftermath of the earthquake — predictions on the future of the nuclear renaissance, commentary on the performance of the government and the media, philosophical discussions about risk and societal trade-offs, etc. But there will always be time for those topics. Right now, the best use of my column inches is to share what I have scribbled on the back of my envelope so that fellow engineers can critique my mental model of events, build their own calculations of what is happening at Fukushima, and better explain to their friends and family what is going on. With that goal in mind, here is my current understanding of the thermodynamics of the Fukushima reactors, and my own timeline of events.
Friday, March 11
14:46 — A 9.0 earthquake occurs off the northeast coast of Japan. Shortly afterward, Units 1, 2, and 3 of the Fukushima Daiichi power plant trip, control rods are fully inserted, and the reactors enter hot shutdown. Off-site power is lost. Backup generators successfully start at Units 1, 2, and 3 and core cooling begins. Core power output falls to at 91 MW in Unit 1, and 155 in Units 2 and 3. The earthquake causes a very small LOCA (loss-of-coolant-accident) in the primary loops of Units 1, 2, and 3 due to broken pump seals (on the order of 125 to 175 kg/hr).
15:41 — Tsunami strikes the Fukushima Daiichi plant, disabling all backup power generators. Battery power kicks in for Units 1, 2, and 3. At moment of impact, core power output in Unit 1 is 21 MW, and output in Units 2 and 3 is 36 MW.
Unit 1 — Thermal Characteristics
Unit 1’s reactor vessel is approximately a cylinder with a height of 19.7 m and a radius of 2.4 m, giving it a volume of 356 cubic meters, with the top of the fuel rods positioned at roughly 4 m above the bottom of the vessel. At the time of shutdown, the reactor contained 68,000 kg of UO2 fuel, and its primary coolant system contained 148,000 kg of H2O. At the time of shutdown, the maximum clad temperature in the reactor was 310°C, the peak (centerline) fuel temperature was 1690°C, and the average coolant temperature was 234°C. Operating core power output was 1380 MWth. At full capacity, the coolant pumps can move 21,800,000 kg of coolant through the primary loop.
Friday, March 11
~19:15 — A pump or valve failure at Unit 1 ceases or reduces coolant flow at Unit 1. Power output at Unit 1 is currently at ~7 MW.
21:34 — TEPCO reports falling coolant levels at Unit 1 and begins work to restore power to Unit 1’s emergency core coolant pumps, either because of a mechanical failure of normal pumps or a pressure situation within the core that prevents low-pressure coolant injection.
Saturday, March 12
~01:15 — TEPCO restores full or partial coolant flow in Unit 1. By the time cooling is re-established, the fuel rods have been uncovered and the fuel clad is damaged due to overheating.
~03:00 — Conditions in Unit 1 compel TEPCO to consider venting steam to relieve pressure. They notify the government and evacuation occurs.
10:07 — TEPCO begins venting steam from Unit 1.
15:40 — Hydrogen generated from damage to the fuel cladding explodes, destroying the outer containment building of Unit 1. The inner containment building and reactor vessel are undamaged.
20:43 — TEPCO begins injecting seawater into the reactor vessel of Unit 1.
Sunday, March 13
11:55 — TEPCO begins injecting seawater into the Unit 1 containment building.
Monday, March 14
01:10 — Injection of seawater into the reactor vessel of Unit 1 ceases, due to lack of seawater in the source pit.
03:20 — Injection of seawater resumes. Degree of core damage remains unchanged.
Units 2 and 3 — Thermal Characteristics
The reactor vessels of units two and three are approximate cylinders with heights of 21.9 m and radii of 2.75 m, giving them each a volume of 356 cubic meters, with the top of the fuel rods positioned a roughly 4 m above the bottom of the vessel. At the time of shutdown, each reactor contained 94,000 kg of UO2 fuel, and their primary coolant systems contained 207,000 kg of H2O. At the time of shutdown, the maximum clad temperature in the reactor was 310°C, the peak (centerline) fuel temperature was 1740°C, and the average coolant temperature was 242°C. Operating core power output was 2380 MW–. At full capacity, the coolant pumps can move 33,300,000 kg of coolant through the primary loop.
UNIT 2
Saturday, March 12
~04:45 — Battery power is replaced with power from mobile generators, and cooling continues.
Monday, March 14
~07:00 — A safety relief valve is stuck in the closed position. Operators are unaware of the problem, and pressure builds.
~13:10 — High pressure (7 MPa) in Unit 2 ceases flow of coolant water. The water level in Unit 2 is reported to be decreasing.
19:20 — As the water level reaches the top of the fuel rods, TEPCO attempts injection of seawater into the Unit 2 reactor and fails due to pressure. The rods become uncovered.
~19:55 — TEPCO discovers the stuck safety valve and opens it, relieving pressure.
20:10 — TEPCO begins seawater injection into the reactor vessel of Unit 2.
20:50 — TEPCO reports that it presumes damage to fuel elements in Unit 2 based on radiation readings.
22:14 — TEPCO estimates fuel damage in Unit 2 as less than 5 percent.
Tuesday, March 15
06:10 — A hydrogen explosion at Unit 2 damages the Unit’s suppression tanks. The containment building remains intact, but there is partial damage to Unit 2’s reactor vessel, initiating a small LOCA (loss-of-coolant). Cooling is sufficient to compensate for the LOCA.
Saturday, March 12
~02:45 — Battery power in Unit 3 fails. Coolant flow stops.
~04:45 — Mobile generators are hooked up and coolant flow resumes. No core damage occurs.
Sunday, March 13
~09:00 — TEPCO observes unusual conditions in Unit 3, particularly its emergency core coolant system. They are unsure whether it is a problem with the system or the instrumentation.
~12:00 — TEPCO begins injection of seawater into the Unit 3 core as a precaution.
Monday, March 14
01:10 — Seawater injection into the reactor vessel of Unit 3 is interrupted due to lack of seawater in the source pit.
03:20 — Seawater injection into the reactor vessel of Unit 3 resumes. No core damage occurs.
11:01 — A hydrogen explosion destroys the outer containment building of Unit 3.
Tuesday, March 15
09:38 — Oil from a water pump at Unit 4 ignites.
~11:00 — The oil fire is extinguished.
~18:00 — The spent fuel pool at Unit 4 begins boiling.
20:54 — The water level of Unit 4’s spent fuel pool is deemed low enough to represent a health risk to workers. Workers are re-located away from the vicinity of the pool.
21:11 — TEPCO begins work to pump coolant into Unit 4’s spent fuel pool.