Did Seismic Ground Motion Cause a Flux Spike Big Enough to Trip North Anna?

Over the last two weeks there has been considerable discussion over: "What specifically caused the dual unit reactor trips at Dominion's North Anna Station during the Earthquake in Mineral Virginia?" Some of the possible likely causes discussed include:

• Sensed power imbalance in the unit auxiliary transformers?

• "Relay chatter" (which is actually caused by the seismic ground motions shaking mechanical relay contacts apart) that gives the appearance of de-energize to trip logic actuating?

On of the more exotic modes hypothesized was that horizontal ground motions that lasted about 3 seconds had caused a neutron power disturbance that generated a reactor trip on high local neutron flux. The New York Times reported the following:

"Because the earthquake moved the water in the reactors, the sensors indicated that the neutron population there was no longer distributed properly, and the system called for the automatic shutdown, Dominion officials say."

Reference: http://green.blogs.nytimes.com/2011/09/08/when-an-earthquake-shuts-a-reactor/

This gives the possible impression that shaking a nuclear reactor will make the power spike to the point where the neutron flux goes from its nominal full output power (e.g. 100%) to greater than 110%. It sounds fishy to me based upon basic physics principles. One of the youngster engineers in our engineering department asked me about this and I asked him if he remembers his Reactor Engineering 101 courses from college? Could a nuclear reactor actually physically respond to the ground motions? He didn't remember so I spent a couple of hours the other afternoon with him. [I actually get paid to mentor the young folks - its more enjoyable than going to project meetings...] This is what I walked him through.

A Nuclear Reactor is a heavily damped system which physically behaves according to natural time constants - some of which are a minute or more in magnitude. When you try to change the output power rapidly in won't immediately react because of all those time constants. A very long time ago early nuclear engineers measured the dynamic response of different types of reactors (fast reactors, water cooled reactors, and graphite reactors) and they found that the effective neutron lifetime and delayed neutron precursors played a huge role in controlling the time behavior and safety of reactors. 

The figure below is taken from p.487 of Bell & Glasstone's "Nuclear Reactor Theory"[Reference 1]. It shows a comparison of the Gain and Phase shift to an oscillatory (sine wave-type) disturbance to reactivity - either by control rod motions or any other thing that tries to change the neutron balance in a critical reactor. The frequency scale is in units of Radians/second. To convert to more typical units recall that: 

       1 Cycle/second = 360 Degrees/sec = 2*Pi Radians/sec = 6.283 Radians/sec.

Thus: 1Radian/sec = 0.159 Cycles/sec, 10 Radians/sec = 1.59 Cycles/sec, 100 Radians/sec = 15.9 Cycles/sec.

What the curves show:

1. The top curve is the Gain (like in a stereo amplifier as a function of frequency).
2. The second curve shows the phase angle shift. This is a delay in reaching a peak value given that there are 360 degrees in a cycle.
3. If a very low frequency oscillation in the core reactivity (less than say one cycle every ten seconds) is made the reactor amplifies this. Thus a 1% perturnation in reactivity results in a several percent perturbation in neutron flux.
4. If the oscillation is about one cycle per second - there is no amplification. Thus a "one-for-one" effect -- a 1% change in core reactivity results in about a 1% change in power
5. If the oscillation is greater than one cycle per second and higher - there is an attenuation or damping of the neutron flux response because the inherent time constants within the nuclear reactor system are incapable of responding to such fast changing input events.

There are several curves represented for different reactor types. The key difference is the Effective Neutron Lifetime Parameter - larger effective neutron lifetimes (such as for a graphite reactor) are less responsive and thus damp the response even more.

What Kind of Frequency Input Did the Earthquake Present?

I don't have seismograph records for the recent earthquake so I will rely on a recent USGS projection [Reference 2] which shows the likely acceleration magnitude vs. ground motion period for 30km away from an Eastern US fault.

To understand where the greatest acceleration content is one must convert the period (expressed in seconds) to cycles per second. A period of 0.01 seconds equates to 100 Cycles/sec. A period of 0.1 seconds equates to 10 Cycles per second. A period of 1 second would be 1 cycle/sec. Thus one would expect the highest accelerations would be with a frequency of: 10-100 Cycles/sec.

Putting It All Together

I do not have the exact effective neutron lifetime parameter for the reactor cores at North Anna. I do have them for a set of PWRs and they range from 2.53E-5 sec to 3.14E-5 sec. If I overlay the region of earthquake accelerations on top of the Gain curve I get a figure like the one below.

The frequency range of the seismic events occurs in a frequency range that is too fast for the reactor to respond to -- so the reactor core and neutron population effectively ignores the shaking. My conclusion is that a horizontal seismic acceleration which might shake fuel rods and thus cause a reactivity oscillation is not in a frequency range where anything would happen. Ruling this out, more likely causes of a neutron flux trip would more likely be effects of the shaking on excore neutron detectors and their cabling.

References
1. George I. Bell,  Samuel Glasstone, "Nuclear Reactor Theory", Copyright 1970 Van Nostrand Reinhold.
2. P. Somerville, et al, "Ground Motion Attenuation Relations for the Central and Eastern United States", Final Report to the USGS, Contract 99HQGR0098, June 2001.