Japan Earthquake: Nuclear Plants at Fukushima Daiichi

[Yamanote]

Some further information from Tepco on this issue:

http://www.tepco.co.jp/en/nu/fukushima-np/images/handouts_120212_07-e.pdf

 

[duccio]

The problems arise from the Mark I containment, which is certainly non-optimal for the scenario that evolved at Fukushima. The accident was 'beyond design basis' ... the plant staff had so little time to respond, and the response was muted with complete loss of both off-site AND on-site power

Astronuc, you got my point. More modern designs are better, but BWR + Mark I is still the most common. The actual best practice is to contain the core as much as possible, which works fine when there's nothing else to do as it limits the damages. But I don't remember on which report, I read that one hour after the tsunami there were already 400 people on the plant, including operators, firefighters, contractors... that's an enourmous amount of very flexible power.

If I understand it correctly, after SCRAM, as long as the fuel is submerged under water AND the cladding is intact, there's no major release of radiation, and it's still possible for humans to go inside of the reactor building (and around it).

Right on top of the reactor there's a pool with at least 700 tonnes of water (10 meter diameter times 10 meter of depth, without considering the spent fuel pool side which must remain filled, and the tools pool which on the contrary could also be used for cooling).

Once it is clear that there's no electrical power but there's enough "man power", the RPV could be brought to outside pressure, and then the top plug of PCV and RPV could be pulled so that the pool water would flood the fuel, heat up and evaporate naturally at 100 degrees. 700+ tonnes of water, along with the initial venting of steam, would be enough for a few hours of flooded and cooled fuel (but that's just my guess, I didn't do the math).

Human force would just need to fill the pool with water, but with freedom to go inside and outside the reactor building, that wouldn't be an impossible task.

Your idea is a core element in the design of the newer AP1000 reactors just approved by the US NRC.

(so, it wasn't really "my idea", I shouldn't claim fathership of it ;)

The problem was that the reactors at Fukushima were difficult to depressurize because the valves needed power to be opened. So a bad accident was made much worse.

I believe they are already required to fix it as soon as possible, along with hardened venting pipes. As I do believe that there're ways to make earthquake/tsunami/power-loss resisting valves, and cranes to lift the cover of the reactor (or any other action required by emergency response).

One factor that made me think of this, is that fire hoses, small portable diesel pumps, and even buckets, are really common and cheap, so it should be economically viable for operators to store many of them here and there on the plant. Much cheaper than many other changes they are now forced to do to the plants.

I thought you might be interested in this tidbit from the Washington Post...

Thanks Jim, that material was tremendous, it took me two days to read all the emails but it was worth it. Garwin had to think about it after the accident happened and the core already melted, and as he noted, one of the biggest challenge was the radiation level inside of the building and the debris scattered around (that's why the idea of the charges)

 

[nikkkom]

Once it is clear that there's no electrical power but there's enough "man power", the RPV could be brought to outside pressure, and then the top plug of PCV and RPV could be pulled so that the pool water would flood the fuel

Is this really possible to do w/o electricity? Look at the bolts which keep reactor cover closed:

http://science.soup.io/post/115911576/Nuclear-reactor-core-and-Cherenkov-radiation

They are numerous, and huge. I have hard time imagining how they can be quickly unbolted by hand.

 

[Rive]

They are numerous, and huge. I have hard time imagining how they can be quickly unbolted by hand.

With preinstalled directed explosives it's easy, fast. The steam separator would protect the fuel from the worst of the blast.

However I would be more happy with safety equipments which has more moderate side effects if they goes off accidentally. If the core is already at ambient pressure then any fire truck would be able to refill the RPV without so much risks involved.

Ps.: all this is matter of spare pneumatics control- and feedwater line connections outside the main building. For example. And then no explosives involved.

 

[Yamanote]

I presume that some solutions for proper venting and passive cooling are already available, but at Fukuichi all systems relied on electricity. So it seems that in all considerations a total loss of electric power was never taken into account (or ignored for some reason).

Solutions are there, at least on paper, but they are either not built-in in (old?) plants, or doesn't work under real emergency conditions. So every accident means a new learning cycle (hopefully?).

In the past the containment was designed to contain the radioactive stuff inside under any circumstances, there wasn't even a vent. Now we have seen that this is not an easy job to do, especially when Hydrogen from a core meltdown is involved. In particular cases it might be better or even necessary to release the gases (scrubbed please!) to effectively depressurize the containment and to enable water injection into the reactor core avoiding further damage.

 

[duccio]

I presume that some solutions for proper venting and passive cooling are already available, but at Fukuichi all systems relied on electricity. So it seems that in all considerations a total loss of electric power was never taken into account (or ignored for some reason).

Solutions are there, at least on paper, but they are either not built-in in (old?) plants, or doesn't work under real emergency conditions. So every accident means a new learning cycle (hopefully?).

Indeed. But the more we add, the more there is to mantain and to take into account in case of failure.

I'm not sure that those bolts could be unbolted by hand, or that putting explosive inside a reactor is a good idea (even if it is impressive the degree of control they can achieve on controlled explosions). On that point, maybe feedwater line with standard connections here and there could be a good solution, and maybe some feedwater line connecting the pool to the RPV as well, but there should also be a way for water to evaporate and for steam to go out.

However, I'm not really after a solution, I'm more after some reverse problem solving. Going from the "what should have been there to avoid the emergency" to the "what actually WAS available on the field, once a real emergency started, and how could have we used it better". We don't know what could fail next time, and it's extremely hard to predict and to prevent.

We know we had a heating core, pressure, hydrogen, a pool full of water, and a lot of man power. It was extremely hard for vehicles to get close to the plant because of the hearthquake and the tsunami, but somehow firetrucks managed to reach the plant. Everything else failed, sometimes in unpredictable ways (like DC control panels flooded).

 

[tsutsuji]

http://www3.nhk.or.jp/news/genpatsu-fukushima/20120213/index.html :

13 February 10:00 91.2°C

The other two thermometers at the same height indicate 33°C. The other three thermometers located 150 cm lower are in a declining trend. This is giving strength to Tepco's view that the thermometer is broken. But there is no conclusive evidence that it is broken. Tepco maintains the same injection rate while carefully watching the situation.

 

[etudiant]

http://www3.nhk.or.jp/news/genpatsu-fukushima/20120213/index.html :

13 February 10:00 91.2°C

The other two thermometers at the same height indicate 33°C. The other three thermometers located 150 cm lower are in a declining trend. This is giving strength to Tepco's view that the thermometer is broken. But there is no conclusive evidence that it is broken. Tepco maintains the same injection rate while carefully watching the situation.

Is it not equally probable that the sensor is simple near a hot spot, an area of stagnating water flow where fuel may also have accumulated? Given that the interior of the reactor has been seriously damaged, some such development seems more than likely, imho.
TEPCO claims the residual decay heat from the fuel in the reactor is down to about 0.6 megawatts. That will boil a lot of water unless there is really efficient heat transfer, which may be absent given the debris within the trashed reactor.

 

[Shinjukusam]

Is it not equally probable that the sensor is simple near a hot spot, an area of stagnating water flow where fuel may also have accumulated? Given that the interior of the reactor has been seriously damaged, some such development seems more than likely, imho.
TEPCO claims the residual decay heat from the fuel in the reactor is down to about 0.6 megawatts. That will boil a lot of water unless there is really efficient heat transfer, which may be absent given the debris within the trashed reactor.

Yeah, is there a simple to understand diagram showing where on the bottom of the vessel this sensor is located?

might be nice to have a general idea of what is above/beside it.

 

[nikkkom]

So it seems that in all considerations a total loss of electric power was never taken into account (or ignored for some reason).

This is not "seems", it's a fact. TEPCO admitted as much.

Solutions are there, at least on paper, but they are either not built-in in (old?) plants, or doesn't work under real emergency conditions. So every accident means a new learning cycle (hopefully?).

The problem is, TEPCO (and all other operators) was not ignorant about the consequences of the meltdown. They just, at some level(s) of managerial maze, decided to take the risk and not spend money on additional protection.

IOW: we know how to make reactors safer. We also have "lessons learned" from past accidents.
What we do not know is how to make plant owners stop cutting corners and lying to us (and probably to themselves) that their plants are safe.
We do not know how to make them analyze "lessons learned" from past accidents. 25 years after Chernobyl and workers again have no adequate dosimeters? How stupid is that?

 

[elektrownik]

Unit 2 sensor is damaged because it is 250+ C now, and it is impossible

 

[nikkkom]

Is it not equally probable that the sensor is simple near a hot spot, an area of stagnating water flow where fuel may also have accumulated?

The temperature difference of about 30 degrees in two spots of a steamy hot metal enclosure? That's unlikely.

 

[Shinjukusam]

Unit 2 sensor is damaged because it is 250+ C now, and it is impossible

If you're going to fail, fail big.

Where was that announced?

 

[elektrownik]

If you're going to fail, fail big.

Where was that announced?

Here: http://www.tepco.co.jp/nu/fukushima-np/f1/images/2u_temp2.pdf

 

[Shinjukusam]

Here: http://www.tepco.co.jp/nu/fukushima-np/f1/images/2u_temp2.pdf

Got it. Either that's a failure or something really bad just happened. Going by the decrease in every other sensor, I sure hope it's the former.

 

[Rive]

Unit 2 sensor is damaged because it is 250+ C now, and it is impossible

I don't think so. We know nothing about the position of the fuel debris inside the RPV. Some pars of it can be still melted (or just hot).

 

[zapperzero]

Unit 2 sensor is damaged because it is 250+ C now, and it is impossible

Ok, let's take this ball and run with it. What happened? Is a wire or some sort of contact corroding rapidly? That's what it sounds like. Why is this happening? Will it happen to the other two sensors and if so, what then?

 

[elektrownik]

Ok, let's take this ball and run with it. What happened? Is a wire or some sort of contact corroding rapidly? That's what it sounds like. Why is this happening? Will it happen to the other two sensors and if so, what then?

Here is explanation:

In the press conference of 2/13 PM, Tepco announced they lost the heating gauge of reactor 2.
Reactor 2 marked 93.7℃ at 2/13/2012 11:00, but it went to 276.4℃ at 17:00.
Tepco is asserting the heating gauge is broken.

The heating gauge is thermocouple, Tepco tried to check resistance but immediately after the test, the heating gauge indicating 276.4℃. The resistance was about 500Ω. Tepco is asserting the wire is nearly broken.

It is also good to look at this plot: http://www.tepco.co.jp/nu/fukushima-np/f1/images/12021312_temp_data_2u-j.pdf
It is interesting that another sensor plot which was damaged is almost the same like this sensor which is damaged now. Around 2/13 date.

 

[Astronuc]

AFP - Japan's Fukushima [Unit 2] reactor may be reheating: operator
http://news.yahoo.com/japans-fukushima-reactor-may-reheating-operator-234153498.html

Tokyo Electric Power said one of three thermometers on the number-two reactor at the Fukushima Daiichi nuclear plant indicated gradual heating this month and reached 82 degrees Celsius (179.6 degrees Fahrenheit) Sunday.

The temperature was above the 80-degree safety standard newly employed by Japan's nuclear safety authority, prompting the utility to publicise the reading and notify public agencies.

But it remains below the 100 degree level that the government says is needed to maintain the safe state of "cold shutdown".

The utility said it will check the accuracy of the thermometer in question, as two others on the same reactor have been measuring its temperature at around 35 degrees.

As a precaution, TEPCO has increased the volume of water and boric acid solution being poured on the reactor to cool it down.

In a steady-state heat transfer situation, there is a balance between the heat generated (source) and heat transfer (removal). If the temperature in the system is rising, it either means that the heat source is increasing, or the transfer mechanism is reducing such that the heat arrival (at the location of temperature measurement) is greater than the heat leaving. This may happen due to a reduction in flow in the heat transfer method. It could also mean a fault in the thermometer.

 

[Borek]

I have not followed the situation for a long time, so I am not sure about details. What pressures are we talking about? Temperature shouldn't go above boiling point, 276℃ means boiling unless pressure is over 60 atm.

 

[Samy24]

Is it plausible, that 3 sensors fail at the same time.
I have attached a list of temperatures from Tepco reports and marked the three sensors in doubt.

No 1 (the "failed sensor") has nearly the same temperature as No 2. So No 1 and No 2 are correct or both failed in the same way.
No 3 is now at 3.6 °C. It's going downwards since the same time No 1 did rise. Is this temperature possible at that location?

I can think of two possibilities:
1. All three sensors faild at the same time. Reason?
2. There is a new hole in the buttom of the RPV. Injected water flows directly to sensor no 3 without taking heat form the fuel. What is the fresh water temperature being injected?

 

[tsutsuji]

Yeah, is there a simple to understand diagram showing where on the bottom of the vessel this sensor is located?

might be nice to have a general idea of what is above/beside it.

There is a diagram on http://www.tepco.co.jp/en/nu/fukushima-np/images/handouts_120212_07-e.pdf page 2

The company says an inspection showed that a cable inside the thermometer is probably cut, resulting in a false reading.
Monday, February 13, 2012 21:17 +0900 (JST)
http://www3.nhk.or.jp/daily/english/20120213_28.html

http://mainichi.jp/select/wadai/news/20120214k0000m040062000c.html The thermometer temporarily read 400°C after 3 PM and around 275°C in the evening on 13 February. Tepco said "we have a nearly definitive judgement that it is broken" (...) "The atmosphere inside the PCV has a high humidity. We suspect that as time goes, the circuit line connected to the thermometer is cut or has an insulation defect" (...) "We will check when the thermometer started being broken, bring together conclusions and explain those to the NISA". If other thermometers break down like this one in the future, knowing the reactor status might become extremely difficult.

http://www.tepco.co.jp/en/nu/fukushima-np/images/handouts_120213_10-e.pdf latest temperature plot

 

[etudiant]

There is a diagram on http://www.tepco.co.jp/en/nu/fukushima-np/images/handouts_120212_07-e.pdf page 2


If I interpret the diagram correctly, the high readings come from a location that is higher than the fuel would be, unless there was enough water circulating to wash fuel particles upward. That seems to support TEPCOs thesis of instrument failure as the most probable cause.
Of course, this also suggests that the remaining sensors may fail fairly soon as well, certainly well before the reactor cools down enough to end the cooling flow.
Is it sensible to insert additional temperature sensors using the port set up for the fiber optics camera or does that not help?

 

[tsutsuji]

http://www3.nhk.or.jp/news/genpatsu-fukushima/20120213/index.html Tepco measured a thermometer resistance 1.7 times greater than normal. As this phenomenon occurs when part of a thermometer cable is cut, Tepco says that the probability that the thermometer has broken down is high. Tepco will use another method to find out if the cable is broken, and will reach a final conclusion. For the time being, the injection rate is kept stable, and the situation is carefully watched.

 

[zapperzero]

If I interpret the diagram correctly, the high readings come from a location that is higher than the fuel would be.

I know I'm nitpicking here but I just can't help it. We have no information about where the fuel is - just some educated guesses, which we dignify with the moniker "models". Some of the corium may have stuck to a wall and then inched downwards, for all we know.

 

[elektrownik]

http://www.reuters.com/article/2012/02/13/us-japan-nuclear-idUSTRE81C0FN20120213

Matsumoto said there was little sign of steam, which would be produced when water is at such a high temperature

So maybe readings from sensor were correct ?

 

[Gaffney]

The sensor might be broken but they aren't testing to make sure if the others are also broken? They have put in a lot of risk for just a broken sensor. Pumping in the max amount of water from 3.1t/h to 17.1t/h within two weeks, injecting boron, doing tests for a nuclear reaction quickly.

This might just be following protocol and the sensor could be broken, the worst case could be that the fuel has shifted and a small nuclear reaction is starting to build. It could lead to hydrogen being produced, causing another explosion/large radioactive release.

There have been indications that the plant has been releasing more radiation in February because of rises in radiation over japan. Could possibly be linked with the steam that was seen on the tepco cam in February which was coming from building three or four.

What we do know is that Tepco is using a lot of water with reactor two and there isn't a massive amount of space to store it left.

 

[jim hardy]

i'm no industry apologist, just an old instrument guy.

If i recall these sensors are thermocouples.
If thermocouples have one weakness it's this - moisture in their connecting wires.

A thermocouple is just two wires of dissimilar metals joined together at the end.
The dissimilar metals when heated produce tens of microvolts per degree , and one reads that miniscule voltage to infer temperature at the business end.

So in effect you have a microvolt source that's a function of(temperature) in series with the resistance of the wires . Most thermocouple wire has resistance that is substantially higher than copper. Make a thevenin equivalent out of that and measure it with instrument of your choice.

Now should the insulation of those wires get damaged and allow moisture to ingress,
you no longer have just a thermocouple, you also have dissimilar metals in an electrolyte which make a galvanic cell.
That places a galvanic cell electrically in parallel with your thermocouple junction.
Galvanic cells make thousands of microvolts not tens.
If there's enough wetted area on the moist part of the wires the galvanic cell will deliver enough current to overwhelm the thermocouple's meager voltage.
If you're lucky the polarity of the galvanic cell will cause a voltage indicating temperatures below freezing so you know immediately it's haywire.
If you're unlucky it makes a voltage that indicates high temperature and everybody wrings their hands until reading becomes impossibly high.

SO-- my point is this - they changed injection flow and one thermocouple departed from its neighbors. It bears watching but is suspect. I think they have a water leak above that thermocouple.

In my plant i checked for such things with a simple analog multimeter, which you don't ordinarily use on thermocouples.
The way you tell is read resistance, switch the polarity and read again. If the reading changes by more than about 1/4 inch needle deflection it's likely wet. (Modern digital meters don't have that reversing switch you have to swap the leads and infer from the numbers, which is much less intuitive)
Then you read the current it'll deliver into your multimeter on current scale and if it's more than a few microamps you know there's a substantial galvanic cell out there. If the thermocouple is the ungrounded type a simple resistance to Earth confirms insulation damage..

It is sometimes difficult to explain these details to people who aren't mildly autistic like me.
And you understand why those details aren't in the press release - they infer uncertainty which is not acceptable public image.

And while a lowly instrument technician like me might firmly believe in his results, there's no such thing as absolute certainty.
I'm sure they have better technnicians than me over there and that's why they are saying they think the sensor has failed. It'll probably come back when it dries out. I saw a report of resistance measurement "1.5X normal" and would love to know what it read with polarity reversed - 2/3 normal would be a telling answer. (Just as would "1.5X normal with no sign of wetness".)

Dont know why i rambled so - just want to help those guys over there but cannot.

Anyhow don't bet a lot of money or invest much worry on a lone thermocouple that's suffered the abuse those have. But keep an eye on it.

please advise if this post is out of line.

 

[Yamanote]

If there is no re-criticality or Hydrogen built-up and increased water injection dosn't lead to a temperature decrease, what more can be done than assuming this particular sensor is broken?

Btw, it's not the only temperature sensor in unit two showing this behaviour and some temperatures in unit one are rising as well, only unit three seems to be stable:

http://www.houseoffoust.com/reactors/graphs.html

It is likely that more and more sensors will fade away as time passes by.

 

[Yamanote]

Thanks a lot for your explanation Jim, I fully agree with you!

It also makes me wonder, why Tepco pays so much attention to this temperature sensor, perhaps they have some other signs that something might go on inside reactor number two.

Regarding the radiation releases - could it be, that higher release is just related to lower outside temperature?

 

[Gaffney]

One thing I don't understand is how the amount of water has been multiplied 6x over February but there has been no change in the reactor water level. Is the gauge broken, is the water evaporating quicker or is the water escaping the reactor?

 

[elektrownik]

One thing I don't understand is how the amount of water has been multiplied 6x over February but there has been no change in the reactor water level. Is the gauge broken, is the water evaporating quicker or is the water escaping the reactor?

I think that this is the case.

 

[Yamanote]

Yes, there is absolutely no change. Either the gauge is broken, or there is a leak at this level, letting escape even the big amount of water they are adding now.

 

[Borek]

It also makes me wonder, why Tepco pays so much attention to this temperature sensor

Regardless of what is happening, imagine the wave of criticism they would face if they ignore it.

 

[rmattila]

The main circulation pump seals have certainly leaked since mid-March, and if there's any hole in the shroud, water from the core region will escape that way. In addition, there most probably are holes in the RPV bottom penetrations caused either by molten core material or corrosion.

But as far as I know, we still haven't been told which pressure measurement locations the reported level measurement is actually based on.

 

[Yamanote]

Regardless of what is happening, imagine the wave of criticism they would face if they ignore it.

You are right Borek and I really appreciate their precaution this time. So let's hope for the best.

 

[etudiant]

One thing I don't understand is how the amount of water has been multiplied 6x over February but there has been no change in the reactor water level. Is the gauge broken, is the water evaporating quicker or is the water escaping the reactor?

Seen that the water level in the reactor was too low to be seen by the borescope, one can assume the RPV has some leaks, maybe large ones and that any reported reactor water level may be invalid. Obviously the increased injections will gradually raise the water level in the plant basement, but with 80,000 cubic meters there already, it will take some time to make a substantial increase.
The JAIF used to publish daily, then weekly situation reports that included the water levels in the various parts of the facility, but that stopped about a month ago when a more generic summary was substituted. TEPCO was the source of their data, so it may still be available there if one knows where to look.

 

[Yamanote]

TEPCO was the source of their data, so it may still be available there if one knows where to look.

If this is what you mean:

-> http://www.tepco.co.jp/en/nu/fukushima-np/index-e.html

-> Scroll down to "Situation of water level, transfer and treatment of the accumulated water"

This information is also provided with the daily press conference report and every now and then there is a more detailed report:

http://www.tepco.co.jp/en/press/corp-com/release/betu12_e/images/120201e3.pdf

 

[mheslep]

Unit 2 sensor is damaged because it is 250+ C now, and it is impossible

is it possible that the water boiled/drained away?

 

[etudiant]

If this is what you mean:

-> http://www.tepco.co.jp/en/nu/fukushima-np/index-e.html

-> Scroll down to "Situation of water level, transfer and treatment of the accumulated water"

This information is also provided with the daily press conference report and every now and then there is a more detailed report:

http://www.tepco.co.jp/en/press/corp-com/release/betu12_e/images/120201e3.pdf

Thank you, that is exactly what I was thinking of.
A very helpful reference that also gives some insight into the functioning of the water decontamination effort.

 

[zapperzero]

Anyhow don't bet a lot of money or invest much worry on a lone thermocouple that's suffered the abuse those have. But keep an eye on it.

It's great info from you as usual, jim. But it makes it sound to me as if the other thermocouples failing too is pretty much a given.

 

[elektrownik]

Strange temps in unit 2 (data from today):

 

[zapperzero]

Strange temps in unit 2 (data from today):

More sensors on the fritz? Maybe because of the extra water?

 

[gbettanini]

Strange temps in unit 2 (data from today):

Is a melt-through possible?

 

[elektrownik]

Interesting that all strange temperature data are from bottom of RPV or close to this part of RPV so it is possible that something bad is in progress.

 

[jim hardy]

Multiple sensors trending together is worrisome.

But do i see readings of 118, 251 and 4 ?
Those need to be cross checked against other indications such as visible steam, temperature and particulate analysis of air exiting building.

and ask the technnicians whether those tc's are wet.

 

[swl]

I have not followed the situation for a long time, so I am not sure about details. What pressures are we talking about? Temperature shouldn't go above boiling point, 276℃ means boiling unless pressure is over 60 atm.

I'm guessing it will be difficult to pressurize that RPV much above one atmosphere. And if the TC is away from water, there need not be any pressure.

 

[Borek]

I'm guessing it will be difficult to pressurize that RPV much above one atmosphere.

That's what I was aiming at - as the pressure is unlikely to be that high, if the sensor is under water it must be wrong.

And if the TC is away from water, there need not be any pressure.

Yes, but what is the water level and is the TC under water or above? Or do we simply not know?

 

[tsutsuji]

http://www3.nhk.or.jp/news/genpatsu-fukushima/20120214/1350_ondokei.html The NISA instructed Tepco to write a report by 15 February, on such things as the cause of the high thermometer values and the way to measure temperatures by other methods.

http://www.mbs.jp/news/jnn_4953273_zen.shtml Tepco tested 15 of the 41 thermometers installed inside unit 2's PCV, and found that two more thermometers were broken. Nothing abnormal was found with the two thermometers located at the same height as the one that had abnormal values.

http://www.47news.jp/CN/201202/CN2012021401002271.html 8 thermometers are broken out of a total of 41 at unit 2's RPV. Adding to the thermometer that momentarily reached 400°C, two other thermometers were found with an abnormal electric resistance. Tepco had judged that 5 other thermometers were broken. Tepco is judging the RPV's temperature trend with the remaining 33 thermometers.

 

[elektrownik]

Xenon detected in unit 2: http://enenews.com/tepco-press-handout-xenon-detected-reactor-2-containment-vessel-9-hour-half-life
http://www.tepco.co.jp/en/nu/fukushima-np/images/handouts_120214_07-e.pdf