Author’s
Translation
The Cause and the effects of
Hajime Nishimura Prof.
Fumito Kotari
Godfoot Research http://homepage1.nifty.com/gfk
Contents
1. The daily release of the radioactive matter to the
atmosphere
2. The daily release of the radioactive matter to the
marine sphere
3. Comparison with the cases of Chernobyl and Three Mile
Island
4. The complete sequence of events leading to the
hydrogen explosion
5. The capital cause of the disaster concluded from the
theoretical analysis
Estimation of the Daily Release of Radioactive Matter
into the Atmosphere
Purpose The estimation of the daily discharge of the
radioactive matter from the Fukushima Atomic Power Plant No.1 to the
atmosphere.
Method Our method is the reverse application of
the atmospheric pollution model which is normally
to predict the pollutant concentration of any given place under the given
discharge rate of the pollutant from a stack. By the reverse application, we
mean to estimate the rate of the pollutant discharge from the given
concentration of some place. Here we apply the method for the radio active
matter taking it as the pollutant. In actual application, the intensity of the
effect of the radioactive matter to human body measured at monitoring stations
and expressed by μSv/h was used as
the input data to the whole model by converting it to the radioactive matter
concentration Bq/m3 before applying it to the atmospheric pollution
model.
Environmental
data as input Fig. 1 shows the
intensities of the bodily effect of the radio active matter expressed inμSv/h measured at the seven monitoring stations
placed at about 40 kms from the plant site on 22 and 23 March. The figure does
not show any uniform distribution but characterized by the appearance of a
singular point at Iidate Mura. The non-uniform distribution reveals that the
radioactive matter does not disperse by the simple diffusion from the source
but is mainly carried away leeward by the wind with some lateral diffusion
which expand the lateral distribution of the pollutant along the path of the wind.
The resultant form of the distribution is called a plume. Iidate Mura seems to
located exactly under the plume or in the plume. As the bodily effect
intensities of the neighboring stations at Minami Soma and Tamura separated
less then 10 kms from the line connecting the plant site with Iidate Mura are
drastically lower than that of Iidate Mura, the plume width seems to be
considerably smaller than 10 km at around 40 km from the source, the power
plant.
Plume
Model Two
types of diffusion model are usually applied to the atmospheric dispersion of
the pollutant: the puff model and the plume model. Judging from the
distribution of the radioactive matter shown in Fig 1, we have applied the
plume model In the plume Model, the concentration in
the plume is assumed to vary primarily with the distance from the source and
secondarily from the vertical and horizontal distances from the center of the
plume. The concentration distribution in the plume at a given leeward distance
from the source is assumed to obey the normal Gaussian distribution described
by exp－（y/σｙ)２ exp－（z/σz)２. Therefore the
average concentration of the plume at the section of the given point x appears at y=0 and z=σz. If we approximate the plume as having a
rectangular cross section with 2σｙas its width and 2σz. as
its height, the average concentration appears where the rectangular plume
touches on the ground.
Application
to the present case In
order to apply the plume model to the present case, the primary importance lies
on the determination of the height of the origin of the plume. We determined it
from the photograph of the white smoke of vapor rising from the site, which is
estimated 5 or 6 times as high as the height of the power plant building of 50
m high. Therefore the height of the plume source was found as high as 300 m.
The next task
is the determination of the atmosphere stability from the weather on Mar 24 and
25. As it was cloudy with drizzles of rain under the wind of 2~3 m/s, the stability was found as D.
The consequent
task is to find the leeward distance for whichσz reaches 200~300m from the D curve in Fig. 2. We know the distance is
around 30~40 km from the plant site. From Fig. 1 we know Iidate Mura satisfies
the condition and it means so the concentration at the site represent the
average concentration in the plume
at this cross section.
The width
2σｙ and
the height 2σz
of the plume at Iidate Mura is respectively estimated as 2000m and 200m. Therefore
when the wind velocity was 2 m/s, the total daily volume of the air Q passing over Iidate Mura as a plume is
Q = U 2σｙ2σz = 4 x 2 x 105 m/d x 103
x 102 = 8 x 1010
Estimation
of atmospheric radioactive emission
Once the air volume Q is known, the daily discharge of the radioactive
matter to the atmosphere G can be estimated as
G = Q Cav
when the average concentration of the plume Cav at the point
is known.
We
have determined Cav , the concentration of radioactive matter in the
air Bq/m3 from the amount of the radioactive matter in bodily tissue
expressed by μSv/h. In the case of the constant daily uptake
of the radioactive matter Bq/d, the
amount of the internal effective radioactive matter expressed by Sv/h depends
on the mean residence time of the radio active matter. This principle applies not only for the
bodily intake of the radioactively tainted milk and water but also for the inhalation of the
tainted air, which means we can estimate the concentration of the radioactive
matter in the air Bq/d from the
internal amount of the radioactive matter Sv/h once we know the amount of air
inhaled in day.
The relation between Bq and
Sv/h has been established for Iodine 131 exp
experimentally as 1Bq = 7.4 x 10--3μSv/h or
1μSv/h＝130 Bq
The radioactive matter concentration Bq/ m3 at the site of
internal concentration of 1μSv/h
can be determined by knowing the amount the air inhaled by an adult man . As it
is about 10 m3 the
radioactive concentration in the
air corresponding to 1μSv/h is
13 Bq/ m3
As the internal concentration at Iidate Mura was 10 μSv/h , the atmospheric
concentration is supposed to be 130
Bq/ m3
Therefore
the daily emission of the radioactive matter from the
130 Bq/ m3 x 8 x 10 10 =
1013 Bq / d = 10 T Bq / d
The daily discharge to the atmosphere was found as
10 Tera Becquerel per day
Estimation of the Daily
Discharge of Radioactive Matter to the Coastal Area
Purpose Estimation of the daily
discharge of the radioactive material from
Method Two methods are available for the
purpose. One is the estimation using the data on the overflow water from the
unit, the amount of overflow for a day G kg /day and its concentration C Bq/kg.
The other
method is to utilize the diffusion equation for the coastal area together with the
radioactive concentration data Bq/kg of the offshore seawater measured by the
monitoring boat.
Daily
discharge from direct method The radioactive
material concentration in the effluent water from the plant site measured on
March 21 at 800 m downstream of the end of the effluent duct was 3 x 104 Bq/kg while the total
amount of the water sprayed on the plant on Mar. 21 and 22 is reported as about 200 tons for each
day.
Therefore the total amount
of radio active material Q discharged on March 21 is estimated as
Q = 3 x 104 Bq/kg x 200
x 103 kg/ d = 6 GBq/d
The daily discharge of the radioactive material
to the coastal area is estimated as about
6 GBq/d
Empirical coastal diffusion
equation Any material
continuously discharged from a sewage to the coastal area is dispersed by the
turbulent diffusion, which actually consist of the horizontal as well as
vertical diffusion. Both diffusions depends on the tidal current and wind and
therefore the theoretical prediction is totally impossible. Only the empirical
approach based on the numerous measurements of pollutant concentrations in the
coastal area is the way for practical solution.
In 1970s,
Nishimura took such approach in the Seto Inland Sea, which is not an inland sea
but a channel of 150 km x 40 km with the both ends connected to the
An empirical diffusion equation derived from such effort is
C = ( 10-3 ~ 10-4 ) ( L / S )
where C and L are the concentration and the daily discharge (kg/day),
while S is the surface area of the sea encircled with the contour that
connected the the same concentration C.
The coefficient 10-3 ~ 10-4 corresponds to the
reciprocal of the diffusion coefficient that include both the horizontal as
well as the vertical diffusion. In the outer ocean the coefficient approaches
to 10-4.
Daily discharge estimated from
diffusion model A boat is daily monitoring
the concentration of the sea water at 30km off coast of the power plant, the
result of which is shown in Fig. 3
If we assume a rectangle of 30km x 60 km as the area encircled by the
contour of the same concentration, the corresponding concentration was about 44
Bq/ l in Iodine 131 and 16 Bq/ l
Cesium 137 and 60 Bq / l in total.
Therefore
the daily discharge of the radioactive material estimated from the offshore
data using the empirical diffusion equation is
L = 104 C S = 104 x 60 x 30 x 60
= 10９ Bq/ d
= 1 GBq/ d
The daily discharge of the radioactive material from the
Comparison
with
A worthwhile comparison with the present case would be the comparison
with the cases at
On the
For the
case at Chernobyl, as it was an total explosion of the atomic pile rather than
an accident, the estimation is easy when we assume about a half of the
radioactive material contained in the reactor was released to the environment.
According to a report of OECD, that assumes 50 % of Iodine 131is released, the
total amount of discharge is estimated as 1760 PBq, where PBq is a million GBq.
Theoretical Realization of the
First Stage Process induced by
the First Impact that finally
lead to the Hydrogen Explosion
Any disaster resembles
avalanche Even if the first impact may
have caused
the first accident, it cannot cause a disaster unless it started the
first stage of
process which lead to the second accident which, by starting the second
stage
of process, triggered the final disaster.
Hydrogen explosion in every
reactor in operation As shown in Fig. 4,
hydrogen explosions occurred in reactor N0.1,No.2 and No 3, each of
which is
accompanied by a burst of the radioactivity level 8 hours after the explosion.
Each explosion was a huge one blowing off the most part of building.
Most
experts of explosion I interviewed by telephone agreed to liken the
explosion
as powerful as 100 kg of TNT. The explosion did not only destroyed the
building but would have severely damaged the machines and appliances in
the building which would have been useful in evacuation and restoration.
An accurate disclosure of the
fist stage of process is the aim of the paper
The most important lesson everyone can learn from this disaster would be
the reproduction of the first stage that ultimately lead to a disaster
in this
case but would have not been inevitable otherwise managed. For useful
lesson, a very accurate knowledge is necessary. Inaccurate supposition
might
cause a disadvantage to pupil. Japanese proverb goes akago wo nagasu
drain
a baby with bathwater and atsumono nj korjte namasu wo fuku a very hot
pudding makes one very cautious of cold pudding.
Rumored cause of the
accident Rumor goes as
"Tsunami washed away everything including important machines and
equipments of the
"The nuclear reactor could not stand the earthquake and severely
damaged"
"
that should have avoided the cut of the coolant supply to the
reactor"
"The used fuel rods cooled in the fuel rod pool the placed at the
upper floor
of the reactor produced hydrogen when dried up because of the absence of
cooling water"
How to get an accurate
knowledge of the first stage process
As the sophisticated measurement systems temporally failed immediately
after the earthquake and were not restored a while, only measurement
data
available is the water level in Unit 1, though the data for the first 10
hours is
still unavailable.
Under this
condition, only method to infer the actual process of the first
stage is a genuine theoretical reproduction of the whole process fully
utilizing whole laws of physics. Such inference leaves a limited freedom
to
the initial condition and the circumstantial condition. Therefore the
theoretical reproduction is justified only when the estimated situation
made
a complete agreement with the limited available data. When the agreement
is complete by tuning the initial and circumstantial conditions, the
assumed
conditions are true and actual.
That was the reason
for us to have started with the theoretical reproduction of the water level.
Theoretical Reproduction of
the Water Level in the Reactor
For the water in the reactor No.1, the change of temperature before
boiling and the change of the liquid level after boiling were rigorously
estimated using the heat balance equations.
For the change of the
temperature T before boiling
ρC S h0 dT/ dt =
For the change of the water
level h after boiling
⊿HρS dh/ dt = Q
where S is the
cross sectional area of the reactor, h0 the initial water level and
⊿H is the heat of
vaporization of water.
All
parameters used in the calculation is shown in Table 2 and the result of estimation is shown in
Fig. 5 together with the measured data of the observed water level. The
agreement seems to be excellent. It means that the initial condition and the
circumstantial condition assumed in the calculation are justified. Its meaning
is unexpectedly crucial and vital and will be discussed in the conclusion.
Theoretical Estimate of the
Temperature Rise of a Fuel Rod when dried up
When the upper part of the fuel rod is dried up, residual heat
generation will cause a harsh temperature rise until the radiation heat release
balances with the heat generation. The time course of the temperature rise can
be estimated by
ρC v dT/ dt = q －ｓσＴ４
where v, s and q
respectively stand for the volume, surface area and residual heat generation
per unit length of a fuel rod. All parameters used in calculation is shown in
Fig. 6. The graph shows the
temperature rises very quickly and within 2 minutes, it almost approaches to
the equilibrium temperature that is 779 degree Centigrade.
At high
temperature, the casing of the fuel rod made of zircaloy reacts with water
vapor and produces hydrogen. The rate of this reaction steeply depends on
temperature as shown in Fig. 7. An
appreciable reaction occurs in the temperature range between 750 C and 800 C.
The found temperature exactly falls in this range.
Important
Conclusions drawn from the Analysis
1)
The emissions of the
radioactive materials into the atmosphere is about a thousand times greater
than the emission to the coastal area.
2) When
compared with the case of the Chernobyl accident , the daily amount of the atmospheric
emission is about a hundred thousandth 1/100,000 of the total emission from the
Chernobyl explosion. So it means the total emission from the
3) From the exact agreement of the purely
theoretical estimation and measured data on the water level, we can infer that
the earthquake gave no damage to the reactor itself but gave a leaking failure
to the pipe line to or from the steam turbine.
4) The whole disaster is
a sequence of accidents triggered by the foregoing one. The accident was the
stop of the coolant water to the reactor which resulted in the dry up of the
reactor and the complete exposure of the fuel rods followed by an instant
temperature rise to 800 degree centigrade, which produced a large amount of
hydrogen that eventually explode and destroyed the building and the important
appliances.
5) The primary cause of
the whole series of the accidents is obviously the stoppage of the coolant
water supply to the reactor. The reactor was equipped with the emergency
electricity supply driven by diesel engine which was designed to start 10
seconds after the stoppage of the whole electricity supply. Therefore the
capital cause of the disaster is the failure of functioning of the emergency
electricity supply system.
6) From a detailed
analysis of the theoretical calculation, it was discovered the initial water
temperature of the reactor was 40 degree centigrade while the temperature under
the normal operation is about 140 degree centigrade. This means emergency
electric supply system including the Diesel engine worked properly after the
earthquake for some duration enough
to cool down the reactor. Its stoppage after a few minutes is a mystery.
All the
Figures and Tables are attached.