Japan Earthquake: nuclear plants

Dmytry

Math:
When the water is leaking from the pool and fresh water is being re-introduced at a rate of x litres per unit time, and the volume of pool is v , and amount of salts is c, the amount decreases as:
dc/dt=-c*x/v
Equation of concentration is then
c=c0*e^-t*x/v
(to doublecheck, differentiating both sides gives dc/dt=c0*e^-t*x/v *-x/v = -c*x/v)
so we have:
e^-t*x/v = 0.59
-t*x/v = log(0.59)
t*x/v=0.3 edit: actually, 0.53 , used Google calculator and there log is a base-10 logarithm.
meaning 0.53 of the spent fuel pool volume has leaked out in that time period where the concentration decreased to 0.59 of original value. That is ignoring any extra cs-137 that may have leached from the fuel during that time.

triumph61

A better Picture

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SteveElbows

I've been trying to make sense of pool water levels by doing some graphs showing the water level and the amount of spraying. Sometimes it seems to make sense but other times it does not. This makes me question the reported water level. Is it safe to assume that the Fuel Pool Cooling Skimmer Surge Tank levels are a good indication of water level in the actual pool?

On a related note I see that reactor 1's FPC Skimmer levels have started to drop in recent days. This reading was steady at 4500mm for the many days that this data has been published, but it went up to 4550mm on the 25th, dropped to 4200mm on the 27th, 3700mm on the 28th, 3000mm on the 29th and the figures for the 30th show it is down to 2600mm!

rowmag

Updated sub-drain isotope level measurements as of 4/30:

http://www.tepco.co.jp/cc/press/betu...es/110430l.pdf

fluutekies

Thank you for the fast math!

One correction:

e^-t*x/v = 0.59
-t*x/v = ln(0.59)
t*x/v=0.53

meaning 0.53 of the spent fuel pool volume has leaked out in that time period where the concentration decreased to 0.59 of original value. That is ignoring any extra cs-137 that may have leached from the fuel during that time.

Based on this model, assumptions & correction, the leak of SFP#4 could be

~ 42 m3/day or 1.8 m3/h or ~29 L/min

Azby

<But I am quite certain that he must have said "20 microsieverts per hour"...>

Actually, it's 20 millisieverts per year. As per this Gov't statement (sorry, in Japanese, and pretty impenetrable even in Japanese....):

http://www.mext.go.jp/b_menu/houdou/23/04/1305174.htm

And this protest by Greenpeace:

http://www.greenpeace.org/internatio...nese-children/

See this map for reference:

http://www.mext.go.jp/component/a_me...519_042618.pdf

(First page map shows levels measured on April 24 in microsieverts/hr; second page map shows predicted 1st year doses in mSv. This provides more detail for the NSSA/DOE map of April 18)

BEIR VII predicts that 20mSv/yr will give about 0.2% increased risk of cancer/yr (so about 2% in 10 yrs, 6% in 30 yrs). The Japanese gov't justifies their decision by assuming children will be indoors 16 hours per day. I'd prefer them to be more cautious. I'd have less problem with a similar policy for areas getting 10mSv/yr, as long as residents were clearly informed of the risk parameters and allowed to opt out with full compensation.

Dmytry

Ahhh... yea I meant natural logarithm of course. Used the Google to calculate, and in programming the ln is typically called 'log'
http://www.cplusplus.com/reference/clibrary/cmath/log/
The number did feel wrong. Should start always using wolframalpha instead, it shows how it understood you.
edit: interesting...
http://www.wolframalpha.com/input/?i=log%280.59%29

MadderDoc

I use Avidemux to extract frames from videos and can heartily recommend it. It allows you to easily skip forwards and backwards, frame to frame, or keyframe to keyframe, and pick a good target frame or a frame range. The selected frame(s) can be dumped to the disk as bmp or jpg, quality is good (but of course depends on your renderer.

I think perhaps this video has been shot with a camera slightly above the surface, with submersed lighting from the sides of the camera. The apparent visually disturbing thermal gradients may in fact be motion of the water surface, the camera is looking through.

I have attached the best frame I could find using Avidemux. After extraction of the frame, the color levels have been adjusted using Gimp. (The video wastes a lot of its color levels in the shade, where very little information is contained.

As criterium for 'best frame' I used the position digits stamped into the racks , in the best frames I found these are readable (but only barely), while in most frames you cannot see that there are digits at all. It is clear that some of the stuff moving about is debris, but just as clear that some of them are bubbles. This becomes particularly clear when skipping framewise backwards with Avidemux. in reverse you see the bubbles _dive_, in the wiggling fashion so typical for bubbles, to disappear into crevices below.
I think these 'bumps' must be for handling the racks. I am not sure that the bumps in rack no 2 and rack no 7 look different. They do look much alike to me.

This object becomes clearly visible from about frame 60 moving towards the upper left. By tracking its motion there's no clear indication of bubble behaviour, it could be a paint flake, or some other low density debris.

LOL

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Dmytry

on topic of the video, check the grid in topleft corner. Very visibly damaged. Looks like sagging of aluminium near the melting temperature.

edit: also the camera is clearly underwater... it is entirely off focus until it goes underwater, as you would expect from a camera that can only shoot underwater (needs correct index of refraction).
And in the end you can see so much waving, you wouldn't be able to see so clearly through such waving with camera above water.

MadderDoc

That's a very interesting observation, Steve. Do you have access to data for the sprayed amount to SFP1 over time? (I scanned the Tepco press releases, but could find reference to sprayings to SFP1 only on March 31st).

If I understand the arrangement with the skimmer surge tank, once water level in the pool goes below some level, the system becomes compartmentalized, and the level in the skimmer surge tank will no longer be an indication of the level in the pool.

MadderDoc

I am not sure the grid in topleft corner is actually a fuel assembly rack. Compared to what is clearly racks elsewhere, this one has other dimensions.

My interpretation of the waves seen at the end is they are produced as the camera arrangement is withdrawn, when the submersed lighting sources breaks through the water surface. Once the light sources are out of the water, the camera becomes unable to focus on anything inside the pool, so it tries to focus in stead on the reflections of light from the surface.

MadderDoc

Yes, of the Big Green Closet Jorge is talking about, this is a much better photo. It appears to me to be some sort of ladder arrangement, either meant for support of something above it, or for affixing wiring. It looks blue to me. The smaller green box-like object which may be at the foot of the wall is not visible in this photo, it is hidden behind the debris in the foreground.

rowmag

NUCENG has already told us that it is not:

http://physicsforums.com/showpost.ph...postcount=5370

Dmytry

the point is, it looks visibly damaged, the lines of grid are not straight and it is so in the video, not just some transient distortion.

edit: ahh, you meant the other grid with big holes? Ignore it. Definitely not a fuel rack. I mean, on the left side of the top of the video, near middle. There's another something on the topright, its not visibly damaged.
There's just too little waving in the video for the waves we see in the end. Does not look anything like look through waving water surface.

edit: also. This thing been cooled by salt water, and theres fresh water pouring in. Of course there will be a lot of 'shimmer' that is not from temperature differences, but from salinity differences

rowmag

Here are Asahi Shimbun's annotations:


Labels are, clockwise from the top:
--Spent fuel assemblies, etc.
--Control rods
--Debris
--Fresh fuel assemblies
--Metal rack

Dmytry

For purpose of disambiguation what is what when discussing it (or did someone do this already) :

I'm speaking of 1 which looks damaged, looks like aluminium sagging near the melting temperature.
5 looks obviously damaged, especially the upper portion. 4 looks intact except for upper portion.

6: I don't know what it is, it does not look good, but it may naturally look like crap without needing any damage.

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fluutekies

I learned that in general it's LGa or for special cases like LG10 = Log and LGe = LN. But still confused about 1,000 vs 1.000 and 1 000.

In order to complete the estimations, an estimate of the begin concentration can be calculated according to:

n(0) = n(t) / e ^(-t*x/v)

with t(0) = 15-Mar-2011 then 13-Apr-2011 is t = 29 days of leaking with x = 42 m3/day from a volume SFP#4 v =1200 m3. n(t) on 13_Apr was 93 Bq/cm3 -->

extrapolated ~ 257 Bq/cm3 Cs-137 on 15-Mar-2011,
which is ~ 3 E+11 Bq or 0.3 TBq Cs-137 total in SFP#4

To be continued (calculation of mol or g Cs-137 for that decay and comparison against mol or g Cs-137 in undamaged fuel rods)