Nuclear accident dynamics

There’s been a lot of wild speculation about the nuclear situation in Japan. Reporters were quick to start a “countdown to meltdown” based on only the sketchiest information about problems at plants, and then were quick to wonder if our troubles were over because the destruction of the containment structure at Fukushima I-1 didn’t breach the reactor vessel, based on equally sketchy information. Now the cycle repeats for reactor 3. Here’s my take on the fundamentals of the situation.

Boiling water reactors (BWRs), like those at Fukushima, are not inherently stable in all states. For a system analogy, think of a pendulum. It’s stable when it’s hanging, as in a grandfather clock. If you disturb it, it will oscillate for a while, but eventually return to hanging quietly. On the other hand, an inverted pendulum, where the arm stands above the pivot, like a broom balanced on your palm, is unstable – a small disturbance that starts it tipping is reinforced by gravity, and it quickly falls over.

Still, it is possible to balance a broom on your palm for a long time, if you’re diligent about it. The system of an inverted broomstick plus a careful person controlling it is stable, at least over a reasonable range of disturbances. Similarly, a BWR is at times dependent on a functional control system to maintain stability. Damage the control system (or tickle the broom-balancer), and the system may spiral out of control.

An inverted broom is, of course, an imperfect analogy for a nuclear power plant. A broom can be described by just a few variables – its angular and translational position and momentum. Those are all readily observable within a tenth of a second or so. A BWR, on the other hand, has hundreds of relevant state variables – pressure and temperature at various points, the open or closed states of valves, etc. Presumably someĀ  have a lot of inertial – implying long delays in changing them. Many states are not directly observable – they have to be inferred from measurements at other points in the system. Unfortunately, those measurements are sometimes unreliable, leaving operators wondering whether the water in area A is rising because valve B failed to close, or if it’s just a faulty sensor.

No one can manage a 10th or 100th order differential equation with uncertain measurements in their head – yet that is essentially the task facing the Fukushima operators now. Their epic challenge is compounded by a number of reinforcing feedbacks.

  • First, there’s collateral damage, which creates a vicious cycle: part A breaks down, causing part B to overheat, causing part C to blow up, which ignites adjacent (but unrelated) part D, and so on. The destruction of the containment building around reactor 1 has to be the ultimate example of this. It’s hard to imagine that much of the control system remains functional after such a violent event – and that makes escalation of problems all the more likely.
  • Second, there are people in the loop. Managing a BWR in routine conditions is essentially boring. Long periods of boredom, punctuated by brief periods of panic, do not create conditions for good management decisions. Mistakes cause irreversible damage, worsening the circumstances under which further decisions must be made – another vicious cycle.
  • Third, there’s contamination. If things get bad enough, you can’t even safely approach the system to measure or fix it.

It appears that the main fallback for the out-of-control reactors is to exploit the most basic balancing feedback loop: pump a lot of water in to carry off heat, while you figure out what to do next. I hope it works.

Meanwhile, on the outside, some observers seem inexplicably optimistic – they cheerfully conclude that, because the reactor vessel itself remains intact (hopefully), the system works due to its redundant safety measures. Commentators on past accidents have said much the same thing. The problem was that, when the dust settled, the situation often proved much worse than thought at the time, and safety systems sometimes contributed as much to problems as they solved – not a huge surprise in a very complex system.

We seem to be learning the wrong lessons from such events:

The presidential commission investigating the Three Mile Island accident learned that the problems rested with people, not technology.

This strikes me as absurd. No technology exists in a vacuum; they must be appropriate to people. A technology that requires perfect controllers for safe operation is a problem, because there’s no such thing.

If there’s a future for nuclear, I think it’ll have to lie with designs that incorporate many more passive safety features – the reactor system, absent control inputs, has to look a lot more like a hanging pendulum than a balanced broom, so that when the unlikely happens, it reacts benignly.

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.