Text

Analysis of Hydrogen Bubble Concerns in TMI-2 Reactor Vessel
	ML19323F864
Person / Time
Site:	Crane
Issue date:	05/28/1980
From:	Gordon S, Honekamp J, Malloy D, Schmidt K; Metropolitan Edison Co
To:	;
References
	TASK-TF, TASK-TMR NUDOCS 8005290560
	Download: ML19323F864 (65)
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AN ANALYSIS OF THE ETDROGIN SU33LI CONCIRNS IN THE TEPII-MILI ISI.AND CNIT-2 RIACTOR V"SSI~

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J.R. Eonekamp, S. Gc :ica, K.H. Schmidt, and D.J. Malley e

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A$STRACT (1) After identifying and analyzing all sources of non-condensible gases in the " bubble", we determined that a continuing growth of the " bubble" during the period Friday, March 30 through Sunday, April 1 as reported in the press was not possible.

(2) During the first sixteen hours after reactor shut down, boiling of the primary coolant water took place and therefore in the worst case stoichiometric amounts of l

hydrogen and oxygen were produced by radiolysis of the primary coolant water.

At the end of the sixteen hour period, the maximum amount -of oxygen in the non-condensable bubble, including 0 introduced from addition 2

of air saturated water, was.7% of the hydrogen which I

is well below the explosion limit.

(.31. Af ter this sixteen hour period when boiling had ceased, no further oxygen was produced by radiolysis of the reactor coolant water.

On the contrary oxygen was recombined with hydrogen due to radiation at such a rate that the oxygen dissolved in the water was completely removed in less than five minutes.

The subsequent removal rate of oxygen from the bubble by dissolution and radiolysis in the water depended essentially on the rate of dissolution.

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. -. - - -. _ _ - -.,. - - - -, - - - -. - -,. _ -, _ - -,. - -, _ _, ~,, - ~.

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2 Introduction at the On Friday, March 30, two days after the accident Three-Mile Island Unit-2 Station, reports of a hydrogen bubble i

inside the reactor vessel began to appear in the news media.

The following excerpts taken from a series of articles in the Washington Post give some indication of the nature of the information that was being provided to the general public.

"This bubble had appeared late Thursday or early Friday.

At first, the Metropolitan Idison people believed thit it was a steam-bubble.

Then the experts from Sabcock and

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Wilcox which built the plant and the Nuclear Regulat* cry Commission agreed that, with pressures up to 1000 psi in the reactor, it couldn't possibly be 'a steam bubble.

A steam bubble would have collapsed.

That left only one possibility; a gas bubble containing hydrogen, temperamental volatile hydrogen.

The bubble, a thousand cubic feet and growing would make Saturday the worst day of the crisis".

1 "The second alarming development was the gas bubble centaining hydrogen, 1000 cubic feet l

in si::e at the top of the reacter.

The reactor i

had beccme so hot that the coolant water 1

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had decc= posed to its primary elements, oxygen and hydrogen.

The biggest danger was that the bubble would con,tinue to grow forcing all the ecolant out of the reactor, allcwing the te=perature of the fuel rods to build up until they reached 5000*.

At that heat, the uranium,would begin to melt.

Short of the meltdown, there was a possibility of an explosion either in the containment building or in. the reactor core.

On the first day of the accident, there had been a small hyd:cgen explosion in the containment -

i an event Met Id officials didn't tell state or federal officials gbout.

When NRC experts

,,i found out, they launched an immediate effort to analyze the physical chemistry of the bubble.

Thornburgh was told that the NRC's analysis showed that the hydrogen could become flammable or explosive in a matter of days.

A Princeton University scientist calculated that the energy in the bubble was enough to set off an explosion equal to three tons of TNT.

Such

e. force could rip the tcp of the reactor dome right off, flooding the containment with radioactive debris.

There were also fears that the hydrogen would escape to the

ntainmen:

and explode there.

One engineer calculated that a hydrogen explosien three times the force of Wednesday's blast might break

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t the four foot thick walls of the containneh:

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releasing radioactive =aterials into the ai.".

"Just before 3:30 p.s.

(Saturda'y, March 31) case the final straw.

Associated Press sent out an urgent story warning that the bubble situation had become extremely dangerous.

In fact, the story warned, the unnamed experts were warning that the bubble might explode at any minute".

"By 10:00 a.m. on Monday, they were readying bulletin material that would take the werd across the country.

Minutes later the dispatch j

was torn from the wire machine at a Harrisburg radio station.

An announcer read the news at 10:30:

'the hydrogen' bubble was nearly gone and cooling of the reactor was continuing'".

While the details of the hydrogen bubble story varf in the different media accounts, they all contain the basic elements; that is, there was a hydrogen bubble inside the vessel and it was growing and about to explode at any =cment.

In this paper, we attempt to address both of these points; that is, could.he bubble have been still grcwing during the period Friday through Sunday and was there any possibility of the bubble exploding.

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Th.:: cughout the period of concern, the water-inside the reactor vessel was being maintained at an average ta=perature of about 290*F and a pressure of 1000 to 1100 psi.

Circulation was being 1

maintained by operation of one rhactor coolant pump in the.(

loop and heat was being removed through the A steam generator.

The primary system flow as indicated by the flow meter in the hot leg of loop A was about 40% of full flow.

The heat generation ra.te inside the reactor vessel was in the order of 27 MW from i

fission product decay plus 6.7 MW due to the operation of j

the. one reactor coolant pump for a total of 1.2% of full power.

A1.1 but one of the outlet thermoccuples locate 3 directly above tbse core appear to have been working normally.

Most of these thermocouples indicated temperatures within a few degrees of 280*F although, a few were as much as 100 to 200*F higher.

Howevtr, none were reading-in excess of the saturation temperature carresponding to the pressure range of 1000 to 1100 psi- (550*F).

To address these two questions, it is necessary to start by identifying all the possible sources of gas which could have contributed to the bubble inside the reactor vessel.

The first anzi most obvious source of gas in the bubble wculd be water vapor.

However, at 280*? the vapor pressure of water is only 49.2 psi absolute.

Since the total system pressure was at the or:1er of 1000 to 1100 psi, it can readily be seen that water vapor could only have contributed about 5% of the total volume of the bubble.

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6 ource of gas to be' considered are the stable The next isotopes of Krypton and Xenon which are formed as a result of radioacti're decay of the fission p cducts inside the fuel ele =ent.

During nornal operation, almost all of this gas

.s retained within the uranium dioxide fuel pellet.

The r= minder, of the order of a few percent, is released f cm the ceramic fuel pellets to the void spaces inside the ircaloy cladding of the fuel element.

During the overheating of the core which occurred on the first dry, the sircaloy cladding on most of the fuel elements was heavily oxidized and cracked.

In addition, as the cer= 4c pellets themselves heated up, some of the gas retained in the UO was released.

It is therefore reasonable 2

to assume that some substantial fraction of the stable Krypton and Xenon isotopes in the fuel was released to the gas bubble i

inside the vessel.

'f one assumes that all of the Krypton and Xenon stable isotopes that were present in the core were released to the reactor vessel during the overheating, and that none escaped through the stuck open relief valve, the following si=ple calculation shows that this source of gas could have contributed only a few tenths of one percent of the total volume of the bubble:

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P 7

4 POWEREIS]RY:

95 Effective Full Power Days 95 EF?D x 2772 MW = 2.63 x 105' MWD 1. W D = 0.'9 6 g r a U 35 fissioned Total Fission yield of stable Kr and Xe I}

0.25 Moles of Gas Mole of 044s dissicted

@ 235 Fiss.

gle Gas _

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5 x

235 x 0.25 2.63 x 10 (MWD) x 0.96 MWD 235 gU Molts,,232 iss.

w Mola 3

liters ST?

t 3

x 22.4 x 0.035

= 211 ft 33 37p Mole Gas later P

3 1

^2 V1 = 211 ft V2=V1 7y 2

1 I

1 = 492*R (32*?)

T P1 = 14.7 psia 2 = 740*R (280*F)

T P2 = 1000 psia 14 7 740 3

2 = 211 x g x g = 4.7 ft at 280*F and 1000 psi v

3 Bubble volume measurements (2) made on the 31st indicate abouf 1500 ft at 970 psig and 280*?.

Therefore the contribution of Krypton and Xenon was 0.3%.

(1) D. R. Olander " Fundamental Aspects of Nuclear Reactor Fuel Elements" TID-26711-?1, EROA, 1976, pp. 201-2.

(2) 230th General Meeting - Advisory Committee on Reactor Safeguarfs.

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3 A second possible source of gas that ec=es f cm the fuel

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pins is the he'4 - - at is loaded into the circaloy cubing along with the uranium dicxide pellets during fabrication.

Discussions with the Babcock and Wilcox Cc=pany have indicated cha: the total a=ount of helium loaded into all of the fuel pins at fabrication amounted to 1,092 standard cubic feet.

This helium fill gas also contained s=all a=ounts of oxygen and nitrogen impurities.

The amount of nitrogen was 32 standard. cubic feet and the amount of oxygen was 8.5 standard cubic feet.

If it is assumed that all of the pins in the core failed and released all of the fill gas then l

the volume of this fill gas at the conditions of the bubble, i

280*? and a 1000 psi, would have been 25 cubic feet.

Again, it is apparent that the fill gas itself is a rather small fraction of the total volume of the bubble.

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Another source of gas which has been considered is the nitrogen and oxygen dissolved in the water that was injected inuo the plant during the accid.:.t.

The following calculation i

shows that this source of gas could have contributed at most 1%

of the volume of the bubble.

Inforsation received from the Babcock and Wilcox Company indicates that 284,000 gallons of barated water was pumped into the primary system.

Assume that this water was saturated with j

l air at about 1 atmosphere pressure and 10*C (50*F).

Au these i

3 conditions about 23 c s of al: will dissolve in a liter of water.

1 The ecmposition of the dissolved gas will be ahcut 3.;.5% c:cygen.

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3 Amoun of Air in Water Added to the System 3

5 lit *#

cm 2.47 x 10' cm' Air 2.34 x 10 (gall x 3.79 x 23

=

gs e-7 3

2.47 x 10 (cm Air) 273 3

= 1.07 x 10 gram Moles Air 2.24 x 10 (c=3/ Mole) 283 3

3 1.07 x 10 (cram Moles) 2.3s pound moles a :

=

4s4 (grams /pounc-)

Amount of Air Dissolved in the Water in the Primarv S/ stem From the TMI safety analysis report, it can be determined that 3

the water volume in the reactor coolant system is about 11,500 ft 3

3 Subtracting 1500 ft for the bubble leaves 10,000 ft or 74,800 gallons of water in the reactor coolant system. Thus, the amount of' water pumped into the reactor coolant system was almost four times the amount present in the system, the remainder escaping through the stuck open relief valve.

To provide an estimate of the mari=um amount of air that could have.been present in the bubble, assume that the water escaping through the relief valve 1

contained no air.

With this assumption, all the air from this 284,000 gallons of water pumped in remains in the reactor coolant l

l system either dissolved in the 74,800 gallen of water in the system or in the gas bubble.

The distribution of the air between the water and the gas bubble can be calculated frcm Henry's Law:

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-----,-r,.m.e-----

-s-m

10 (1)

Pair = K Xa4r Where:

P^~4. = partial pressure of Air in the gas bubble

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X,r = Mole fraction of Air'in the water a-X

= Henry's Law constant for Air (1.3 x 106 psia / mole fraction at 290*F)

J plus the material balance shown in equation (2).

M

= M'4:

(2)

X.

M1+Yni:

g a-an:

Where:

= Total moles in liquid phase M

= Total moles in gas phase j

g al_. = Total moles of air M

Y,

= Mole fraction of air in the bubble a

and Raoult's Law:

P.4: =P Y :.

(3) c.

a a.:

Where:

P

= Total pressure From equations (1) and (3)

=

v air = K X :.:

3 a.

t as:

K or YaLr = Xair y t

Substituting into equation (2)

'M a ~4 -

(4)

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X :.a.:

=

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M

. K 1

y. M9

.o As calculated oreviousiv M,r = 2.35 pound moles a-

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4 11 Asst =ning that the total =c1es in the liquid phase is essentially equa]. to the moles of water:

3 3

4 10,000 (ft ) x 57 (#/f t ) = 3.11 x 10 pound moles of water M

=

y 18 ( 4/ mole) 3 PV = 1000 usia x 1500 ft - = 189 pound moles c:, gas M

=

g 10.73 x 740 Therefore_:

2.35

=

6 2

Xair 4 + 1.3 x 10 x 1.89 x 10 3.11 x 10 3

10 8.7 x 10-6 X

=

a.4 From equation. (1) g = 1.3 x 10 x 8.7 x 10-6 6

P J

P,g = 11 psia From equation (3)

Y,g = 11 psia 1000 psia Yair = 0.011 3

Thus, the maximum amount of air in the bubble is 1.1% or 16.5 ft 3

based on a 1500 ft bubble at 280*? and 1000 psia.

The amount of air dissolved in the water would be (X x M.) = 0.26 pound moles, a.4.,.

a Approximately eight hours after the beginning of the accident the reactor coolant system pressure was reduced to approximately 400 psi.

Under hese conditions, some fraction of the borated water contained within the core flood tanks would have been injected into the reactor coolant syste=,

During no_ al operations,

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the core flood tanks are maintained at a pressure of 600 psi y

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a nitrogen gas blanket.

The water level in the tanks is maintained coolant 1

by a series of check valves which open as the reactc:

pressure falls below 600 psi.

The following analysis shows that the amount of dissolved nitrogen brought into the primary system from the core flood tanks amounts to only a fraction of 1%

of the total volume of the gas hubble.

3 Each of the two core flood tanks normally contain 1040 ft 3

of berated water (2270 ppm Soron) and 270 ft of nitrogen at 600 1 25 psig.

The mir.imum pressure indicated during the accident was 440 psig.

Under these conditions the nitrogen would have expanded discharging about 1000 gallons of water from each tank.

6 i

p unds x 454 grams

= 7.8 x 10 grams of water 2000 (gal) x 8.6 gaA pounc i

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PN " K 'h P,J = 585 psia 3

1.4 x 10 psia cc-STP/g of water at 50*C K

=

585

'y = 1.4 x 104_

= 0.42 cc-STP/g of. water' x

6

-STo 6

(gfwater x 7.8 x 10 g of water = 3.2 x 10 cc-STP 0.42 o

3 3

6 1

x 0.035

= 114 ft

- STP 3.2 x 10 (cc) x 0u_0 (cc/4) 1 1

At the conditions of the bubble, 1000 psi and 230*F, this ni:rogen would have contributed 2.5 f t3

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L3 The total' volume of all the gas sources identified :hus far is of the order of 125 cubic feet at 280*F and 1000 psi or 7% of the gas bubble.

The two sources of gas which have not

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yet been considered are hydrogen from Ehe corrosien of the ircaloy by water according to the reaction:

Zr + 2H O + ZrC

+ 2H 2

2 2

and the hydrogen and oxygen formed by the radiolysis of water.

The core of the Three-Mile Island reactor contains approximately 21 tons of =ircaloy cladding not including fuel pin and fittings",

instrument tubes, or other zircaloy components in the reactor.

From the above reaction, it can be seen that one pound male of zirconium reacting with water will produce two pound moles of hydrogen gas.

The 21 tons of zircaloy cladding corresponds to 460 pound moles of zirconium which if completely reacted would produce 920 pound moles of hydrogen.

It was shown earlier that the l500 cubic foot bubble at 280*? at a 1000 psi would contain of the order of 200 pound moles of gas..

It is therefore apparent that hydrogen from the =irconium water corrosion reaction is more than sufficient to contribute the other 92% of. the observed gas bubble volume, l

The final potential sources of gas, hydrogen and oxygen from radiolytic deccmposition of water, will be considered in t

detail later.

However, it is appropriate at this point to consider whether any of the sources of gas which have been identified thus f ar could have contributed to the impression that the gas bubble was still growing.

To address this cuestion,

we will =ake the arbitrary ass = prion that a 10% per day increase in the gas bubble sics, that is, 150 cubic feet per day will be

- considered as significant.

Wh4'a " 's is admittedly a purely arbitrary choice, it see=s unreasonable that a much smaller growth rate (e.g. 1% per day) would have been reported by the news media as the i= mediate danger indicated by the excerpts from the Washington Pos:..

It should be remembered that the bubble measurements over the period in question exhibited a downward

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trend, albeit with considerable scatter in the results, and that the bubble growth "* eat" disappeared quickly from the media.

However, it is appropriate to ask if the information at hand was sufficient to preclude an'i=2ediate threat due to growth of the bubble, s

All the sources of non-condensable gas, except for hydrogen

. J from corrosion of the Zircaloy and radiolytic decomposition which has not yet been discussed, amount.to at most 50 ft3 Since of these gases would have been released early in the sequence, most and their total volume was small, they could not have contributed

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to the impression that the bubble was growing.

As will be shown later, radiolytic decomposition of water in the presence of a substantial over pressure af hydrogen could not have produced more gas.

In fact the reactor was normally operated with an i

overpressure of hydrogen to prevent radiolytic deccmposition of the water.

Thus steam formation and additional corrosion of the Zircaloy are the only possible sources of gas which need to be add essed with respect to the question of concinued bubble crew:h.

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7 Given that the reactor coolant was at average temperature f

of 280*?, a pressure of 1000 to 1100 psi, and under forced circulation corresponding to about 20% of full flow (40% in one loop), continued bubble growth due to steam for=ation was not possible.

While some local boiling or even steam blanketing in damaged regions was possible, the steam leaving such a region would tend to condense in the surrounding subcooled water.

If steam did manage to reach the gas liquid interface and enter the bubble it would condense on the cold walls of the primary system which by this time would have been in equilibriumwith the reactor coolant at 2'80*F.

l The possibility of additional corrosion generated hydrogen giving rise to significant bubble growth during the period in

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question is somewhat more complex.

However, it is quite reasonable,

-i given a general knowledge of the Zircalor cor csion rate as a function of temperature and the existing plant conditions, to conclude that it was very unlikely that significant corrosion of the Zircaloy could still have been taking place.

Figure 1 shows the corrosion of Zircaloy in terms of oxygen pickup as a function 2

of time and temperature (3'4)

An. oxygen pickup of 0.15 grams /cm corresponds to the complete corrosion of the 0.026" thickness of 2

the fuel pin cladding.

The vertical line at 0.15 gram /cm indicates that cladding regions at temperatures above N ll50*C would have been completely oxidized during the first day and thus could not have been centributing additional hydrogen.

For a clad region to contribute hydrogen throughout the period between the first i

and fifth fay its temperature would have to be below s 1000*C.

(3) O2NL/NOREG - 17 (4) Lustman and Kenzie "The Metallurgy of Zir:enium" t

1

...o Using :.:e sa=e 10% per day rate as the definition of significant the 1500 f:3 bubble Ocn:ained bubble growth, and recalling tha:

139 pound oles of gas, significant growth would be 19 pound ~

i moles of hydrogen generated or about 9 pcund moles of Circalcy exidized per day.

Nine pound moles of~Zircaloy corresponds to all of the cladding on about 750 fuel pins.

The oxidation of 9 pound moles of Zircaloy would consume 1.3 x 10 grams of oxygen per day.

From Figure 1, the average 5

corrosion rate during the five day period at 1000*C (complete 2

oxidation of the clad thickness) is 3 x 10-2 grams /cm per day.

5 Therefore, to consume 1.3 x 10 grams of oxygen per day would 6

2 require that 4.3 x 10 cm or N 10% of the total clad surface

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area in the core be at 1000*C.

Lower clad tempeNatures would require a larger area with a temperature of 300*C corresponding to the involvement of half of the total c1' adding area in the core.

Such high temperatures in large regions of the core which were essentially intact at this point (i.e. regions which have enough unexidized Zircaloy left to represent a possible source of corrosion) is not plausible given the plant conditions of 280*F, 1000 psi and forced circulation.

These regions would have to be steam blanketed since the saturation temperature at 1000 co j

1100 psi is only 550*F.

Steam b'lanketing at decay heat pcwer levels and 20% full flow could only occur within er downstream of a flow bloWage (i.e. heavily damaged region).

Since the ccrs uncoverine, vould have proceeded generally from the top of the core downward, cladding in the upper regions of the ccre (i.e.

downstream of a flow blocka'ge) would have been heavily exidi:ed during the accident.

Therefore, even if significant flew bl:cha es were present during the time in cu. estion. lead' t ;, c ce=reratures i

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17 of the order of 1000*C (1332*F), the clad in these regi,ns could not have been centributing much hydrogen since ic would have already 'seen heavily oxidi::ed.

Hydrocen Exulosive Limits Based on the previous discussion the composition of the bubble at tihe end of the first day, excluding the effects of radiolyuic decomposition, is indicated in Table 1.

From the information in Figure 2 of reference 5, the lower limit'of flamability for a hydrogen, 54 steam mixture occurs at 5%

oxygen and the lower limit for detonation occurs at 12%

As can be seen from Table 1, the maximum concentration oxygen.

of oxygen in the bubble, excluding any contribution.from radiolysis, is 0.44.

Thus the key question becomes, could

'"l radiolytic decomposition of the water have contributed enough oxygen to reach levels of the order of 5 to 12% in the bubble?

w (5) NRC Memorandum e

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s Table 1 Volume at 1000 osi Co=conent and 280*F (f 3)

Mole i Steam -

74 5

Kr + Xe 4.7 0.3 N

from Air 10.8 0.7 2

Ne' from Core Flood Tanks 2.5 0.2 N

from Helium 2

Fill Gas 0. 7, 0.05 Helium 23 1.6 0

from Air

.S.7 0.4-3 0

from Helium 2

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Fill Gas 0.2 0.01~

w J

Eydrogen 1349 (balance) 91.7 TOTAL 1471

'100 t

+w

19 Analysis of 09 Evolution by Radiolysis The absorption of radiation in pure water in a light water reactor results in deco = position of the water through a complex series of reactions resulting initially in the production of reactive species such as:

OE radical, hydrogen atoms (E) and and H 0 hydrated electron (e~ q) as well as the products E2 22*

These species then react in a variety of ways.

These reactions are listed in Table 2 (see for example reference 1).

Table 2 Reaction k(25*C), (L mol~1

-1)

Ea (kcal 2o171) s 10 (1) E+E+H 1 x 10 3.0 2

9 (2) OE + OH + H 0 5.0 x 10 3.0 22 10 (3) e

+ OH - OE 3 x 10 3.5

~

aq m

10 (4) e

+E+H

+ OH~

2.5 x 10 3.5 2

9

~

-- e,q + H2+2OE 5 x 10 5.2

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(5) e 7

(6) OE + H2-E+HO 4 x 10 3.2 2

7 (7) CE+H0

302+30 2.25 x 10 1.95 22 2

7 (8) E+E0

+OE+HO 9 x 10 3.0 22 2

1.9 x 10'0 3.0 1

(9) E + 0,

EO 4

2 10 2 x 10 3.0 (10) E + E02*3022 0

(11) OE + E0

30+O 1 x 10 3.0 2

2 2

0 1.6 x 10 2.1 (12) E02 + HO2*3022+O2 10 (13) e

+EO

+ OE + OE 1.3 x 10 3.5

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aq 22 1.9.z 10 3.5 (14) e

+ 02+02 sq 0

H+ - E 2.3 x 10 2.8 (15) e

+

ag

~

(16) e

+ E 0 - E ' OE 16 6.7

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2 1.5 x 10'O 3.0 (17) E + OE - E 0 2

1.5 x 10 4.0

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(18) E + OE - e aq + E O 2

^

^'

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m. p

s

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initial yields of the primary species, E, CE, e,q, The H0 and H are.each expressed in terms of a nenber called G 22 2

which is the ac=ber of the species for=ed per 100 ev cf radiacica energy absorbed by the water.

These iditial yields depend principally on the nature of the radiation being absorbed by the water.

This is a reflection of the density of ionization produced by the radiation along the track in which it is l

absorbed.

In general particles which result in a high density of radiation along the track (high LET) favor a high initial yield of E and E 0 Such particles area 4 particles, protons, 2

22 deuterons and high energy neutrons (the effect of the neu* ens in E 0 is due to the high energy prouon recoils produced 2

by elastic collisions with the neutrons).. The particles t

producing a lower density of ions along the track (low LIT)

. _3 such as [ rays and S particles favor the prcducticn of E atoms, (2'3)

OE radicals and e aq Therefore, if water is subjected to high LET radiation 21one, the result would be a high' initial yield of E2 72 and E 0 and, as the concentration of E 0 builds up, reactions with E, 22 OE and e~

will decampose th'a E 0 to water and oxygen.

22 A stage is eventually reached when a stoichicmetric amount of would continuously form as the high LET radiation E2 and 02 is absorbed.

i 9

21 In a mixe'd field of radiation, e.g., [ rays and protons (or proton recoils frem fast neutrons), we have a situation where the E and H 0 resulting principally from the high LET 2

22 4

radiation undergo reaction with E at==s' and OH radicals i

produced principally by the low LET radiation.

These reactions i

are illustrated by reactions 6 and 8 in Table 2:

OE + E2-E*E0 (6) 2 E+E022-CE+E0 (8) 2 It can be seen from these reactions that the OE and E atoms, produced principally by the low LET radiation (e.g. 7 rays)

. recombine the hydrogen and hydrogen peroxide to form' water in a chain reaction.

Reaction (6) consumes an OE radical destroying

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a molecule of E while producing an E atom; reaction (8) 2 consumes an E atcm destroying a molecule of peroxide and producing an OE radical which.then can react by reaction 6 again resulting in an effective recombination of the hydrogen and hydrogen peroxide formed.

Thus the fc.= nation of E and 2

0 is prevented.

2 Reactions listed in Table 2 which compete with this chain recombination of hydrogen and hydrogen peroxide to form water are for example reaction (7), (10), (11) and (12) which lead to the formation of oxygen.

However, reaction (9) is a fast.

reaction with E atoms leading to the formation of the EO2 radical which by reacticn (13) for=s hydrogen peroxide again.

s It can be seen that anything which leads to the increased formati6n of E atoms and CH radicals will promote the recom-bination of hydrogen peroxide and hydrogen.

One of the most effective additives is hydrogen gas which promotes the chain sequence of reactions (6) and (8) by increasing the case of reaction (6) as well as (9).

Another effective method is to increase the ratio of Y radiation (low ET) to fast neutrens (high MT).

Other factors which must be considered are:

the impurities such as Cl".

These tend to recombine the radicals E and OH and prevent their availability in recombining the hydrogen and hydrogen percride I3'4I.

Eigh temperature has'little effecu on the reaction rates producing the hydrogen and hydroge=.

peroxide but do have an appreciable effect on the reaction 3

recombining these products.

Hence high temperature tends to decrease the formation of hydrogen and oxygen.

If hydrogen and oxygen are allowed to escape the aqueous phase by boiling or by being swept out with an inert gas, decomposition to E2 and 0 will be enhanced due to suppressing the back reaction 2

' (recombination)S With these considerations, the data one needs to calculate the rate of 0 and hydrogen peroxide formation during full power 2

operation,' at shut down, and during the cooling period are :

(

)

1 23

)

l.

Yrayflux 2.

Fast neutron fluxes 3.

S activity in the moderator 4.

Thermal neutron f'.cxes 5.

Initial conditions for any period including the concentration of the fellowing materials in the moderator i

a) 0 2 b) H2 c) Cl, F- (major probable impurities on*

the moderator of importance) d) Boric acid e) NaOE

~

6)

Rate constants dor elementa "f-reactions' (Table 2) 7)

Temperature

~

s a

8)

Boiling The following data were used in the computer calculation of 0 formation.

2 Q (total neutron flux at full power)

~

=

14 a g 2,,,-l 2.790 x 10 E

(average initial energy f neutrons,

=2Mev n

fa (flux weighted macroscopic cross section of core)

=

-2

-1 2.28773 x 10 cm 7

3 Volume of core = 3.08 x 10 m

4 volume of coolant in core = (3.08 x 10 x.58 L = 17,858 L)

Above data were taken from Appendix A.

(

l

Since the rate constant for OE + hslide ion is less.han 106 L mol-1sec-1, a simple calculation shows that at the low halide ion concentration present in the reactor coclant C.1 ppm), this reaction need not be considered.

I l

,~

The neutron dose than is:

14

-2 7

5 2.79 x 10 x 2.238 x 10 x 3.08 x 10 x 2 x 10 E

Li,358 2.2 x 10 2 eV/L sec 7

The photon dose at full power at shut down 21 2.2 x 10 eV/L sec Calculated from data

=

in Appendix A 16 Energy absorbed due to total ob., Li recoils. from 3 (n, ol. )

7 6

f Li reaction :

hh (eV/sec mole boren) = E;f 5' N[3]

6 Z. = 2.33 x 10 eV = total el-, Li recoil energy, 13 2

f = 4.74 x 10

.n/en sec (thermal) (Appendix A)

~3

[B] = 1.66 x 10~5 mal en (ref. 7)

- ~ 3

-22 (T = 7.5 x 10

\\

~

dE 6

13

-2*

g- = 2.33 x 10 x 4.74 x 10 x 7.55 x 10 23 x 1.66 x 10-5 x 6.02 x 10 i

17

= 8.33 x 10 eV/L sec This is small ccmpared to the proton recoil dose rate and is neglected.

Total activity due to fission products in 1

11 the primary coolanu is s x 10 disintegrations L see If we estimate 1 MeV average energy per disintegration and total absorption ene would arrive at a dose rate of 1

4 6 x 10'7 eVL 1 'sec

, a facter of about 3 x 10 less than the 7 dose rate at shut down.

Even after 30 days folicwing shu:

down the J dose rate from the fuel is abou: 500 cires tha v

contributed by the fission products found in the prinary eccian:.

Therefore, we neglect this centribution to the icw ET dese.

i e

u

.,,y

The G values we s calculated in the follcwing way.

The average logarithmic decrement of energy loss per fast neutron collision with a targe of a:o=le wt A is in l =

_3

( A-1) 2 A-1

_a 2a, in ( Avu s2 for A = 1(proton) :

ft = 2.71 5 2

Et = average energy of neutron before collision 22 = average energy of neutron after collision Proton recoil energy = ft-52 The energies of the proton recoils from the first three neutron collisions are tabulated in Table 3.

After 3

(

collisions, the proton recoils make only a small contribution

a. 3 to the dese compared to the 51:st three collisions and their contribution to the dose is therefore neglected.

The LIT values in Table 3 were determined by interpolation I

and extrapolation from data in reference'9 The G (e,q)

~

values in Table 3 are taken from reference.10.

The values for G(H),

GLE 0 ) and G(CEl were calculated f cm a diffusion kinetic 22 l1 model i

O W

e

_3 -o

-Table 3 Collision 4 5 (MeV) 5,(Mev) LET(

)

G(E)

G (E.30)

G(CE)

G(e,,)

3

-m n

y 2

1.27 238

.49

.91

.46

.21 3

.73

.458 562

.30

.99

.24

.05

.272

.172 2000

.12 1.15

.09 0

3

.100 Energy weighted G values for above three groups of proton

.855 and energy are 5(E) =.41, 5.(H 0 ) =.95, 5 (OH) =.37, 5 (H )

=

22 2

.15,all in units of particles per 100 eV absorbed.

5(e

)

=

We performed two groups c'f calculations using.our ccmpute:

code WR122 which is a modified version of code WR2012, Since there is some ambiguity of the actual pH of the water we made the calculations for 2 pH's namely 6 and S (measured i

at room temperature), ass"md ng in the first case that pH 6 was achieved by addition of boric acid and in the second case by addition of the same amount of boric acid and the required amount of NaOE.

The calculations were carried out for a temperatce of 280*F under non-boiling conditions and the a

actual E' and OH concentrations at that temperature were calculated for the above =ixcure and used.

As confirmed by our later calculations, we found that the results were not very sensitive to the pH in this range.

(

O

~,

27 L.

The first calculation ~ served to verify that during norr.al full power operation (with mixed neutron and T radiation), the and 02 are small.

steady state concentrations of 52, E 02z We used the dose rates cited in the text.

For the [ yields, we used the following G values:

G(CE = 2.7, G(E) = 0.45, 0. 7, G (e ",q) = 2. 81, G (H ) = 0.45.

GCE 0 )

u 2

22 The neutron G value have been described in the text.

The ratio of dose rate to neutron dose rate was about ten to one and weighted average G values were accordingly calculated.

We assumed an initial 0 concentration'of 2

0.1 ppm = 3.12 x 10-6 31-1 (marimum permissible 0 concentration, 2

table 5.2-1213).

The initial' hydrogen concentration used

-1 was.1 x 10-3 31

, a value in the middle range of values specified in the above cited table.

For the calculations to be realistic, we had to take into account the water 6

. circulation in the core, We used a value of 137.5 x 10 lbs.

water hr~1 for the circulation rate and a total coolant volume 5

u of 2.14 x 10 n

From these datia and the water volume in the core we calculate that the total water volume circulates once every 23.6 seconds.

As an approximation, we assumed that during this time, the difference in concentration of a species in the core water and the outside loop is reduced by a factor of 1/e.

The results for the first group of calculations can be j

summarized as follows:

i l

l i

i e

s.

sa A.

Oxygen concentration,in the core water drops down to essentially ::ero within 14 milliseconds (Fig. 2).

-o i

3.

A steady stata c oncentration of about 9 :c 10

=oi L of H 0 in the e is reached after 50-100 milliseconds 22 (Fig. 3 and 4).

C.

The oxygen concentration in the circulat:,ng loop after 100 seconds has di=inished to 1.446 of the initial value (Fig. 5).

D.

At the same H me, the H 0 concentration in the 22 circulating loop has essentially reached a

~1 steadystateof9x10[6 mol L Tig.'6 and 7).

The second group of calculations was carried out'for the time 16 hours1.851852e-4 days 0.00444 hours 2.645503e-5 weeks 6.088e-6 months after shut' down when boiling of. the water had stopped.

For the dose rate we used 3.4 x 1020,y 3-1

-1 sec

- -J which was calculated frem the data in Appendix A, and zero neutron dose since the asymptotic total neutron dose (Table VII, Appendix A) was negligible compared to the 'l dose.

Actually this asymptotic neutron dose is higher than quoted in the table by a factor of 10 due to the contribution of the 15 lf -n reaction on the deuterium in the coolant water but this value is still negligible and is neglected.

The calculation for the initial condition (H and 0 2

2 concentrations in the water) was based on a bubble size

/

(H2, 0; and steam) of 1471 ft at 180*C and 970 psi.

l We assumed that during the boiling stoichiometric amounts of

(

t l

-- -~

29

~

were produced with a,G value for C; of.225 molecules 02 and H2 per 100 ev energy absorbed in the water (one-half of G(H )).

2 We also assumed that no gas production took place in uncovered i

portions of the core.

We further assumed that the fraction of

]

1 0

vented out during the boiling period was equal to the 2

fraction of hydrogen and steam (added together) vented during this period.

We arrive at a ratio of oxygen to hydrogen in the bubble at the end of the boiling period (16 hrs. after shut down) of 0.7%.

For the 02 concentration in the water, we obtained a value of 2.G x 10-4 mol/1.

We calculate the hydrogen concentration to be 5.7 x 10-2 mol/1.

~

The details of these calculations are given in Appendix 3.

The flow of cooling water in the core was taken into account as described for the first group of calculations,

with the following modification:

1.

The flow rate was reduced by a factor of 5 since only one pump in one 14 cooling leg was in operation 2.

The total water volume was reduced by the volume of the bubble

(

t

~

30 i

Using these ir.icial conditions and assu=ptions and Obe r

computer code described abcve, we obtained results : hat ca'n be O

summarized as follows:

1.

~dichin about 230 seconds after boiling ceased, the 0 in the core water is ec: ally 2

removed if during this time no further oxygen is dissolved from the bubble (Fig. 8).

2.

The 0 removal curve for the cooling loop 2

(not shown) is essentially the same except for s slight delay due to the finite circulation rate.

3.

The rate of : emoval of oxygen is approximately

~~

~

linear with time and therefore independent of t

0 concentration within a. wide range.

From 2

J the rate of removal at the dose rate used, we calculated an approximate G value for oxygen removal, G (-0 ),

of about 1.4 molecules /100 ev.

2 4.

The behavior of the H 0 and H concentration 22 2

in the core water is shown in Figs. 9 and 10, respectively.

The corresponding curves for the cooling loop (not shown) are very similar.

5.

Similar calculations for lower dose rates which prevail at longer times after shut down yielded analogous results and approximately the same value for G (-O ).

2 i

p

~

31 The value of G (-0 ) cuoted'above was estimated in the 2

following way:

the curve in Fig. 8 shows a slope of about

-4

-1 ~1), the irradiated water volume is 2.2 x 10

/280"(mol L s

17853 L.

Therefore, the otal energy deposited per second is 20 24 1

3.4 x 10 x 17858 = 6.07 x 10 eVs -

The total circulating water volume is 177400 L.

Therefore, the total amount of 0 removed in 280 s is 2

2.2 x 10~4 x 177400 = 39 mol 02 Thus 39(mol) x 6.02 x 1023 (molec. per mol) x 100 (ev)

G (-0 )

=

3 24 (evs-l) 280 (s) x 6.'07 x 10 l

= 1.4 molecules O'2/100 eV

(

These results show that the only time oxygen was produced was under boiling conditions during the first 16 hrs, af ter shut down.

After this period.our calculations show that in the worst case only about 0.7% of 02 ccald have been contained in the bubble.

After this period, no further production of oxygen could have occurred.

In fact, the calculations indicate tha't oxygen would be continually consEned, the rate being.ssentially determined by the rate of dissolution of oxygen from the bubble.

Even under full power with mixed'Yand neutron fluxes and a very small a

hydrogen overpressure of about 1 atmosphere, oxygen would not be produced but actually consumed until a non-measurably low steady state concentration of oxygen is reached.

1

32 se References

~

1.

j. H. Sch=ide,,*. ?.hys. Cham. 31, 1257 (1977).

2.

A. C. Allen, "The Radiation Chemistry of Water and Acuecus

~

Solution", Chapter 1, Van Nostrand (1961).

3.

I.G. Dragonic' and Z. D. Dragonic', "The Radiation Chemistry of Water", Chapter 5, Academic Press (1971).

4.

J. W. T. Spinks and R. J. Wood, "An Introduction to Radiation Chemistry", pp. 309, John Wiley (1976).

5.

Sheffield Gordon and E. J. Hart, United Nations Peaceful Uses of Atomic Energy, Proceedings of the Second

}

International Conference, Geneva, vol. 29, pp. 13-17 (1958).

6.* E. J. Hart, W. R. McDonell and Sheffield Gordon, Argonne National Laboratory Report AN-4939, December 3, 1952.

~

7.

J. R. Honekamp, Personal Communication (from actual

._i water analysis).

8.

S. Glasstone, M, C. Edlund, "The Elements of Nuclear Reactor Theory", Van Nostrand (1952).

9.

E. J, Hart, W.

J. Ramler and S. R. Rocklin, Radiction Resecrch 4, pp. 378 (1956).

10. -

C. D. Naleway, M. C. Sauer, C. D. Jonah and K. E.

Schmidt, 3= diction Research

~7, pp. 47 (1979).

11.

C. D. Naleway, M. C. Sauer, C. D. Jonah, Personal Co==tnication.

12.

K. H. Schmidt, Argonne National Laboratory Reports, ANL-7199, April (1966) and ANL-7693 (1970).

e

33 13.

Metropolitan Edison Company, First-Safety Analysis Report, vol.

4, Docket No. 50-320.

14.

Nuclear Safety.V.alysis Co..ter Report NSAC-1 (July 1979).

~

15.

Y. 2. Chang and D. J. Malloy, Private Communication.

e e

m M

i l

I 1

l l

APPENDIX A

. J e

t l

l

l 5

34 l

l INERGY KI'IASE RA~IS Iro '~dI CORI C00LAZ he energy deposi: ion in the coolant as 1: flows drough de 'D'.I-I :::e is prinarily due :o :vo sources:

ga==a (Y) emissions and be:a (S) decay.

A and

ertiary source resul:s f:c= che neu::en flux in:erac:Lon vi:h :he va:s soluble boren, however, af:e shutdown 1: is rela:ively nico: in ec=parison vi d

he y and 3 sources.

A descrip:1on of :he calcula:icnal procedure whi d was employed to produce the y and S release races follows in See:1on I.

See:Lon II describes the approxination by which :he energy release ra:e is =ansfor=ed in:o an energy absorp: ion rate.

For comple:eness, an as:1=a:e of de neu::en flux level following neu:ronic shutdown is presen:ed in See: ion III.

I.

Y and S Inargy Release Rates A simplified calcula:ional model for IXI-2 was created for :he required calculations.

Releven: details concerning such quantities as the heavy se:al loading of the inicial core, power densi:1es and rod design were ob:ained from the F_inal Safe:y _ Analysis Report.

When cartain secondary de: ails could no: be obtained from the TSAR, typical values were u:111:ed from similar plan:s.

A summary of de calcula:1onal parameters which were u:d'* zed in the TMI-2 model is presented in Table I.

The y and S release rates were calculsted with the ORIGIN 1 code. CRIGEN is a point depletion code which solves the first order differential equa:1ons which describe.he produe:1on and decay of the various nuclides.

In this analysis, the cross sec:1on library contained 821 fission produe nur'

des, 146 ligh

-a elements and sacerials of construc:1on, and 99 heavy nuclides plus their daughters.

The code plus cross sections were benchmarked against.he ANS decay hea: s:andard and shown to produce reasonably accu are PW1 spent fuel decay hes: infor=a:Lon.

The ORIGIN inpu: was created to na:ch the information of Table I:

the key quanti ies were the heavy metal loading, power level and burnup.

The ou:pu: yields direc:17 the total release rate (y + S) and de y release rate.

The con::1bu: ion from the S particles is, therefore, inferred from these :vo values. The accuracy of dis i=ferred value is 11 sited due to the fac: :ha:

the ORI G ou:put yields only 3 significan digits.

Table II lists de pho:ou energy release rate (MeV/sec for the en: ire core) as a fune icn of time af:e:

neutronic shutdown and Table III presents the corresponding values for :he S energy release race.

II.

Y and S Inergy Absorption Ra:e in :he Coolan:

The energy release rate values of See:1on I can be ::ansf ormed in:o whole core energy absorption ra:es by urd'd wing the fallowing apprordm:Lons.

Firs:,

i: is assumed tha: the en:1:a photon popula: Lou is absorbed vichin :he core boundaries.

This, of course, is a conservative assumption.

Secondly, the frac:Lon of pho: ens which are absorbed in :he coolan: is assured to be equal to :ha: fraction of de homogenized (whole core) nacroscopi: pho:en renoval 1

cross section which is due :o :he coolan: alone.

0 35 C4==a :::enuation (or nass a ':enua: ion) coefficien:s are dependen: upou

.he energy :f :he photon; :his dependency will be ::aglected tu dis approxina:a analysis so as to render the probles canageable.

Instead, at:enua: ion coeffi-cients are selec:ed a: the energy near which :he grea: najori:7 of phocons are released:

1 MeV.*

To further si=plify :he analysis, :he Circ-4 and s: rue: ural s: eel in de core is assumed :o absorb photons it the same race as :he elenent iron (Fe) does.

Likewise, de heavy natal fuel absorp:ica is nedeled by lead's

(?b) T-absorp: ion properties (this assu=ption, in fac:, is u:ili:ed by 3&W in their analysis of TMI-2.) Wi:h :hese assumptions, che core photon absorption properties.are modeled as in Table IV.

Thus, :o a firs: approx 1=a:1on, 1: can be assumed tha: the coolan: absorbs about 12.6% of the total photons released by -J2e core.

U'41*-4 r a s11gh:17 differen: apprbach, the coolan: absorption frac =1on is arrived at via mass attenuation coefficients as shown in Table V.

37 using an average water densi:7 of 1.0 (a conservative assumption) the fraccion of phocons absorbed within che coolanc is coincidentally equal to 12.6% again.

As the wo models agree so closely, this value seems :o be an excellent approx 1=a:1on withd-the context of dis analysis.

1 The TMI-2 FSAR (Appendiz 6A) contains a shor: dese 1pcion of a calculation

, concar=ing gamma absorption in the coolas: following a LOCA and a-MEA (= W "=

hypothe:1 cal accident).

[The lat:er includes the release of 1%'of the solids and 50% of the halogen inventory and therafore has greater activi:y than would e expected for IMI-l's curren: situation.] The LOCA analysis will serve as a setter reference poin:.

The 3&W (FSAR) analysis uses an unspecified.propriacary code:

salient differences are as follows.

The ORIGEN code has over 800 explici: fission produe:

nuclides and hundreds of heavy metal and strue: ural isococes. The 3&W code has

~

only 200 fission produe:s modeled along with 23 %p and 23 %. The neglect of the re==4*4"r isotopes could lead :o non-conservative results, however, details are too sparse :o allow such a prediction. The 3&W code also allows S penetration through the cladding and energy deposition in:o the water outside :he core boundary.

The cumula:1ve effects are to increase. the total absorption race by 5*7%.

Finally, ths FSAR analysis was for a core a: 620 FPD as opposed to our calculations at 60 FPD.

The impac: of the burnup differential will be discussed below.

Figure 1 reproduces the LOCA energy deposition curve ** versus -J.me.

Also depicted is the energy deposi:1on into the coolanc as predicted vich.he ORIGIN code in conjunction with the assumptions describes above, i.e.12.6% of the total will be absorbed in the coolant.

(The cumula:ive energy deposition was found by applying piecewise continuous ::apazoidal and Si=pson integration to the values of Table II.

"The neglec: of the energy dependency of the attenua:1on coefficients should be a second-order effec:.

- THI-2 FSAR, Vol. 5, Chap. 6, Fig. 6A-3.

n

i 36

!: can be seen da: :he CRIGIN values agree wi:h :he ?SAR values :: within a fac:or of 1.A.

CR GIN, no: su.prisingly, produces the nore cocserva:ive

~

values between tha :vo.

~he effect of burnup upon this curre was established by comparing ins:snes-neous Y-release s:es (as opposed :o the eunula:1ve energy deposi:1on curte a:

Fig. 1) fron the poin: of shu:down :o 30 days after shu:down.

Ihe ra:io of Y-release ra:es for 3U = 20,000 W d/: (392 ??D) :o the ra:e a: 2,000 $ d/:

(60 ??D) ranged monoconically from 0.97 at shutdown :o 1.94 a: 30 days.

he effect of increased burnup would shif: the slope of the ORIGIN curre in a direction which is more consistent quali:azively wi:h ha shape of the 3&W c.urve; quanti:atively the ORIGIN values would : hen be vi:his a fac:or of 2 of the LOCA values.

I: is concluded tha: che CRIGIN values, in conbina:1on with a coolant absorption fraction of 0.126, will yield acceptably accurate values for the Y snergy deposition.

The S-energy deposition values musn be created from the values of Iable III by accounting for S penetra: ion of the cladding and the possible release of (primarily) fission products directly into the coolant. Penatration of the 6 =dddng should contribute only 2+3 percent to the total energy deposition.

An estimate of :he amount of heavy metal and fission products which were released into -de coolant must be made in order to account for the second

$ source.

l III. Neutron Flux Levels

(

The neutron fluz level after reac:or scram is composed of several parts.

First, the full power flux level decays avsy, normally within the period of about 100 milliseconds.

Secondly, the eqt librium precursor concen:ra: ion from full power decays, which produces a s.guificant neutron source over a cima period of ~30 minutes. Lastly, the flux will reach an asymptotic level which represents the multiplication of the residual sources (spontaneous fission, n-n and the startup sources) which remain af ter :he first evo fluz components have decayed to negliable values.

1.

Flux Level Calculational Procedure The neutron fluz level from the first two con:ribu: ors is calculated via standard poin: kinetics with 6 delayed neu:ron groups; 6

o-3

n=n

+ I A, C,,

(1) eff i=1 and 3,

n.

(2)

C, = -1, Cg+3

~

eff t

s

.a

37 l

~he conpuce: code RICi32 was u:111:ed :o solve Iqs. 2 snd diree:1y yield

he flux level from this source.

The :: ansi: ion :o :he asy=p:o:ic flux invol was approxi=a:ed by si= ply superi= posing :he above solu:Lon upon :he flux level which resul:s from :he sul:1 plica:1on af :he spon:aneous fission, c source and :he star:up sources as described below.

The asy=pto:1c s:eady-s:2:e source nultiplica:ics :er= of :he poin:

kine:1cs equa: ion reduces to S

(3) mult - lpl>

vich s represen:ing the centron release ra:e (n/sec) of :he individual source.

Equa:1on 3 yields the steady-state seu::en produe:1on (n/sec).

When this value is mul:1 plied by the effec:1ve neu:ron lifetime, i.fs, che :otal average neu=on population (# of neu : ens) a:.any point in cime is reali:ed.

.l The neutron densi:7 is then formed:

3

^

(4) a=S 1,,/Volumecore (n/cm ).

sult e_

)

The classic neu =on fluz can now beidefined as 2

9 5 a v (n/cm -sec),.

(Sa) s J

s 3

1o 1 eff s

1 v=

(5b)

Volume lp I Volume core a

vig I representing the average velocity of the nautron (approximated as I =

' elf a

and I being a fluz and core averaged sacroscopic abosrp:1on cross section.

a The promp: neu: en lifa:ime (30L) for tiI-2 is reported :o be 2.71 x 10-5 seconds.

[Two differant approximations for the eifac:1.ve neu: on lifa:ime u:d-ing the calcula:1onal node.l. of this study yiel.ted values of 3.1 x 10-5 and 1.2 x 10-5 seconds.} For purposes of -J:is approximate calculation, :he FSAR value of 2.71 1 10-5 seconds will be ue*1*-ed as approxima:ely equal 0 leff-t s

33 e

l 2.

Source Ra:e Defini: ions

~he =eu:ron release races (s) in the core regions ara es:isa:ed fron 3 separa:e compones:s:

spos:a:eous fission of de actinides, c-reac: ions (i.e. :he produe: Loc of c particles via s-day is ::assura:ics and : heir 13 ) and :he s:artup sources.

OR* GIN subsequen: is:erac:1on wi:h l'0 and 0

provides :he spon:aseous fissics infor=a: ion via de followi:g approx:=a: ion for v:

v = 2.84 + 0.1225 (A - 244),

(6) with A representing the a:omic weight of each spontaneously fission 1=g nuclide.

The energy dependence of these neu:rons is not explicitly given; however,1:

235U fission spec =um.

nerefore, the is adequately approx 1=a:ed w1:h the fission neutrons will have a. mean energy in the range of 1 2 Mev. The validity of this approximation has been checked against selec:ed :nv des and has been Ca, '44Ca, 252 242 Cf

~

shown to be reasonable (see, e.g., DP-984 and DP-939 for and 238Pu).

During startup, external sources (Am-Cm-Be),are u:111:ed co ini:iate the chain reaction.

Our information, as of this date, is that 2 fixed sources

^

were in place at the ime of the accident.

Each source has a' strength of 1.4 x 109 n/sec. Since :he reported strength has only 2 significan digits, varia-

1ons in the strength over time are neglected as second-order effects.

The exae:

location of :he startup sources is not specified and must be assumed.

A conserva-cive assumption is to place the sources far enough into the cora so : hat all of

,a the released neutrons are effec:1vely multiplied and exhibi: :he characteristic fluz shape / spectrum in :he core:

dis is equivalent :o assum1=g a homogeneous dis:ribution of the ex:ernal scurces throughou: the core.

(I: addi:1on to being conservative, :his assumptf on is consistent vi:h :he methodology utilized pre-viously.) The fluz level is then calculated via s:andard source mul:1 plica:1on.

The n-u source is predic:ed by ORIGZN via che following:

neutrons / alpha disintegration =.10-10 g2.65, (7) 3 where E represen:c :he alpha particle energy in Me?. Equation 7 is based n

23 8 upon experimen al results from

?uog, yet is applied :o all alpha emi::ars.

The validi:7.af this approxima: Lou is not knavn; however, the impact v4i' be insignificant as the startup source demisates the total source term.

"he =ean energy of these seutrons, for several particular isotopes, was in :he range of

~2.5+3.0 MeV. Thus, he au:ron spec::a appear to be similar :o the spontaneous fission spectra, bu: vith a slightly higher mean energy.

Table VI lis:s :he fixed (s:artup), c-and spon a eous fission neutron secrees as a function of :1=a after shu:down.

The values are rela:ively con-stant due to the ex=amely long half-lives associa:ed w1:h mos: of :he de:arnining reac:Lons and decay chains.

t e

,,_.-..--._..,,.w

39 a

3.

Neu:ron Flux *.evel Resul:s Tables 7!!a and 7!Ib lis: :he neu =on flux levels which resul: from i

Iq ::s. 1, 2 and 3.

ne shutdown k,ff value is no: accura:ely k=own; there-fore, :wo representative values were chosen (0.99 and 0.98) to illus nace che effect upon :he caucron fluz levels which can resul: from varying this quan:1:y.

During the solu: ion of :he poin: kinetics equa:1ons (Eq=s.1 and 2), :he shu:dowr.

=echanism was a linear reactivi:y ramp i= posed over 1.5 seconds (dis corresponds approxt=ately to the :ime required to SCLAM).

Vary 1:s :he ramp ra:e had 11::la perceptable effect upon the values, thus the approxima: Lou was deemed adequa:e.

I: should be s:ressed da: flux levels of Table VII are based upon :he assumption thac there is no flux shape change during :he =ansies:.

na: is, the spec =al shif t which resul:s from :he shu:down mechanism is neglec:ed and does not ancer ei: hor the analysis or the spec: rum discussion of the f allowing subsee:1on.

Additionally, :he sou=a multiplication term is based upon an approximate value of T (Eq:n. 5).

As such, the flux values are approximate.

a 4

Neutron Flux Ener2v Soectrum De energy spec==m of :he combined neucon sources will be primarily dependen upon the lactice parameters and slowing down properties of :he core.

The components of the neu =on fluz are-all created vi:hin the fuel, and v'1'

hus form thei represen ative energy spectrum in the same fashion as the fission neu =ons did during full power opera:1on. De only difference is in

he neutrons' initial energy. The fixed startup and spontaneous fission source neutrous have ini:ial energy spectrums which are very s***'e :o che

..s

.35U fission source, therefore, the resultant co'.1 averaged spectrum will be virtually identical to the spectrum presen: duriag normal opera:1on. The e-n source has initial energy spec :uns which are similar in shape to the fission spec::um, but with mean energies which are higher by ~1 to 1.5 Me7. These neutrons would, of course, lead to a harder resul:an: spec =um :han :he fission neu=ons would.

However, :he difference between it and the spontaneous fission neu=on con:1rbution should be relatively small. That is, in a light wa:er moderator environment, de differene between a spec =um which resul:s from fission neutrons at 1*2 Me7 and the spec =um from a n reactions with emergies nominally near 2*3.5 MeV vould be virtually =14 * = red by the dom *nanc slowing down properties of water. High energy (i.e. ~1 MeV) neutron reactions would increase significan:1, however, this should be a second order effect (glo-7 bally).

nus, :he neucron spec =um which results from the o-n, the spontaneous fission neutrons and the fixed startup source should be approximately equal :o the spec =um which was present during full power operation.

The delayed neu=ons, which were created during the full power operacion phase, :ypically have energies in the range of 250-560 kev.

These energies are smaller dan : hose of the previously described sources, bu: not considerably so.

More importantly, these energies are above. the resonance range, and :horefore, :he delayed neutrons will be affec:ed by nearly all of

he impor:an:. slowing dow processes:

the only relevant spec =al effec: which La missing is, of course, :he high energy effect.

The effec: is nitiga:ed :o a considerable exte:: due :o :he su'1:1 plication of de delayed neu =ons by the t

~

,. 0 i

0.98, de sys:e= ul:1pli:a

ore.

ycr exa=ple, in :he case where kshu:do-T.

ionis}sl~1=-9.

S.us, only 1 of every 50 neu:: ens will be : delayed neu::en and :he spec::a1 i= pac: is negliable.

""ae energy spec::um of :he cell averaged neu::en flux is, theref0:2 approx 1=a:ed vi:h de full power spec::n=.

A :ypical 5 group spec:: = is lis:ed in Table VI~I for full power and 13 =inu:es af:er shu:down.

Addi:icnally, the inferred neu:ron densi:y values are also lis:ed.

5.

Accori= ate Neutron Energy Decosition During '"her ali:a:1on ? ocess l

An estimate of de energy deposi:Lon in de modera:or which resul:s from the neu::en flux was made vi:h -de following assumptions.

yirst, de energy deposition sechanism in the coolan is assumed :o be sca :ering:

energy release due :o absorptions 1.: neglected.

Secondly, :he -Aer.:aliza:1on process is ypified as occurring exclusively in the moderator region (e conserva:ive

)

assumption) and : hat each neu::en losses 2 MeV during the procesac '"his las:

criteria resul:s from the fac: tha: the average fission neu:ron energ is i

~2 MeV and tha: -99.87. of all neu ens slow down :o a: less: group 3 of de 5 j

group s::ue:ure (I.mx of group 3 = 553 eV).

Therafore, :he energy loss per neu::en is approx 1=a:aly 2 MeV.

The neu:ron source rate which proa.tcas :he fluz levels in Table VII ran be inierred by res::anging Eq:n. 5:

1 2

9=Smul: 3 Volume (n/cm -sec),

(Ba) a Core-Or

$5 Volumecore (n/sec).

(8b)

S

=

3 m:

a By inserting a fluz value into Eq:n. 8b (along with the core average nacroscopic cross sec:1on and core volume from Table I), :he neu:ron source race is found.

Since 2 MeV are deposi:ad per =au:ron, the energy depositicu ra:e is D, = 2 9 I,* Volume,, (MeV/see-core),

(9a) or 6

M' eV

{9b) 1.40878 x 10 o

D

=

n sec-core I

e

,. ?.

s'

o :he conserva:ive assu=p: ice tha. all of :he energy is deposi:ed in o

.4

.ne coolan:, :he uni:s of Iq::. 95 are also P.eV/sec-: colas:.

Of cours'e, :he

colan: refers only :o :ha: volu=e of va:e which is vi:hi: :he core boundaries:

energy-deposi: ion densi:1es should be based upon :his volume, no: :he core volu=e.

RIyIRINCIS 1.

Bell, M.

J.,

"0RIGEN

~he ORNL Isotope Genera:Lon and Deple:1on Code,"

OR3L-4623, May, 1973.

2.

Glass:ece, Samuel and Sesenska, Alazander, " Nuclear Reactor Engineering,"

7an Nos::and Reinehold Company, 1967.

3.

311 ard, E. P. and Abbo, L.

S., edi: ors, "Reac:or Handbcok," Volume III Par: 3 - Shielding, In:erscisnes Publishing,1962.

4 Rhodes, D. J.

A., "Reac:or. Kine:1cs Calcula:1ons for Enriched NRU,"

PE-63, Chalk River, On:ario, Sep: ember,1963.

5.

E:harington, E. ed., " Nuclear I gineering Handbook," McGraw-Hil.L Sook Company, New York (1958).

l 1

1 I

)

l

)

~

D

MD *"Dl'3' [f m

,e, A

+

MJL

-m_

. _ _ _...~

_,_w

_. _._ m.-

+...n.

m.... _,

i

_.- a w.--.....-

n

.n.,.a..

e' cc _-(- w=,.

. w i...,,., r. w m._w.,

c 2.-.-ww, y.c, w, m_+ m.c - :

. r 3.-

=_w.,_=_._._..

f

.- = :- - ---.;

w-

~. _

...... =.~=~- ~ __-

.c:.

1..- _ =. - _..

e.

6 M- ::- _~~.M,5_2.9 =gh. j_.1_ = -E - __ -_' ___~-' J ~ + ' _.1 r.3 % -~

. f '=' = r

+* -

~- - -.__._-_

.= __.;. a__ =_ :=. :::._ -- - __- - --

= _ - - -

.=~_u=.__

~-- -

d6. _

v. q, a-,

w.. %,.,_.. v_ + g

_ _ g3m ame.; -*-- - m,p, c - - _r. _ _3 f.a -

e

_ _.E. _,..__.,. w.. '.n

._e.r. m _m.u.-e. "_ _. : = = - - _

L.; -

_ - _. _. _ _ ___-:---=.

- ~ 1 - -'~ ~. _3 :. 5_:.hT= 7- :_j.. = _...; - _ __ _ _ _ _ _ _ _. __ _ N p.- ::-L..:5b =. =_ _-,=a. s

"- ~ ~ ~ -

--u-i_-_

__. __ _.. _. __..g

_.--.---=.:_

_- n i

. ~..

. _ C.

3_*

- N

._-m m_=.ge Z.-

g.

.,..-,b,-s 3. m.n

..ep,.+, _

a w e.=.L*W*.=

M, t

.. _~. %.e. em. /

p e.-

em

_. -. = -

. + g -.a_.J."~_.

2

......- -..m.

.e..

.=.,

a c.

.=...,.,.,

.r._.--

_m % _

r.

4

-u_-

p.

g a

m

,e._

.,ma x

~ VN_ : _N_M__

-Y~---_^__5

-M_ -_-

.,3 g

-5_N _ _ __ N _5-. _ _,P

[_i _ - C ^t -__'L.-

~

9 a..

.=.

3..

ag M

C a-.

1-m

-,e.

as a

.e.

,. - -... __ - -,-g:

7 p_

2u*

._a___

1 7

-r---r-----

J ad se am

==

en m

.us C,m a

ese

.' _=""_.,..._s.:.a,.s.L._*_.

ed

^

no.oooooo 9

.=%..

4's

.a..

w-. e

9 s

,

a t,

-.m.

--,. p..

u TW"c,

M,.

M, g

,i _. a_

- =__. _ _ _ _,-

-.__.m.

_--.7

._m r

__ _ + - -

=

l*

._-=-=..==-_------_--___-.-------s-__--:__=b-.._-z._._---.__- _ = = _ = _ = - _ _ _ = --a.

s.- : - =-=

=--_h--_--

--? _--.E 3

r_

1

..-=._-_r=---__,w-m O

a "J

A -+

s.

A is a

e..

==.

m-r

, '.- i-

-.=

. - - * '= -

' =

x.

A

^

- *- ^

.A

]

y

. m

^

_r-h.,,,)n me.1

__y-5

.. - ^ :. -...c_-.-

1 a

my..

=.r GI a

w t

se -=

.J CD

=w he

=

C W

s a.

C 1

ll n

i

~

I I

I m.e e

4 re

C 4

ao e

C

,,.".2..,_::.._._*_~-..2- --.'..

e_,"*'...-._.V..,_.'..' hind._.M,,,.J'_29,U, _

^

g

.r

.e,...

-p _.._ '* ' _ar a - *.. +.....,. -.

g

_ -.. _ e 2

7-m.=

r

-- - 1 a [d JM r q"_ame met

=_ E /

2

--. _ p T"

-==-- 7 =rc ---"----o_)a--==._-

; - - _ = --

.-.-.-~r_--.---r_:-___-v_.,=.-

_=E-=---::=---=--

_=

a.

.3

_ _ mas.__,. _

_ _ _ _._.t

=-

1 I

e -

""**ee=",'

aB ['* >* a

H_+~.-

7 - ---

7 e

3 e== 3 A e

e

e o

33% & D s OO S % O O Q

e O

p

he e

e

%e 8

I 43

.A3LI ~.

3.ree Mi' a Island '.':1: 2 Calcula:icnal Fara:e:ars for Initial Leading Power, MW:

2772 Power 3ensi:y, kW/1 core 90.0 Core Volc=e, 1 30,790 Fuel Assembly Volu=e Trac:1ons Fuel 0.303 Moderator 0.580 Zircaloy 0.102 S:aisless 5: eel 0.003 7 aid 0.011 Initial Leading kg U 82064 kg 135U 2111 l

Average Enrichment wt%

2.57

.4 Power Denst:y MW/MIHM 33.78 Sursup mwd /MIEh' 2000 Effective Full lower Days 59.2 0.00691 3,fs 1, sec (~ = 1.,)

2.71 x 10-5 y

er.

Ad (longes: lived precursor), see-1 0.0124 Ia (9 veigh:ed) 2.28773 x 10' 1

h

\\%

TA3LI ::.

?he::n Releasa 7.2:as sf:a: ::au:::ni:

Shu:d:vn. "a'lisec, In: ira Oc:a

?ar:an: Of

i;h: Ilanen:,

Tissi:n Actinidas and

!::s1 ?::=

! L=a Ciad and 5:: ::ure

?: due:s Oaugh:ars Tissi:n ? du::s 7::2 i

2:d:vn S.68 els 3.04 -20 1.34

+i9 95.3 3.175 - 20

12.

7.90 -16 1.69 -20 1.20

+19 93.3 1.511 - 20 hou 7.37 +16 1.13

+20 1.03 +19 91.4 1.204 - 20 hours2.314815e-4 days 0.00556 hours 3.306878e-5 weeks 7.61e-6 months 7.33 +16 3.47

+19 9.64 +13 89.7 9.442 ' 19 hours2.199074e-4 days 0.00528 hours 3.141534e-5 weeks 7.2295e-6 months 7.72 +16 4.94

+19 S.64

+18 35.0 5.312 - 19

. hours 7.69 +16 3.73 'L9 7.23

+18 S3.5 4.466 ' 19 days 7.64 '16 2.51 +L9 4.05

+13 85.9 2.923 -19 in* ~

7.58 +16 2.06

+L9 2.25

+18 39.9 2.293 - 19 t

. d'cys 7.44

+16 1,46

'19 5.28

+17 96.0 1.520 '19 s

days 7.13 416 9.16

+18 3.35 416 98.9 9.265 +13 days 6.77

+16 6.48

'LS 3.37 415 98.9 6.552 13 r

\\

\\%

-n,

e 45 4

TA31I ~~~..

3e:s Release Ra:e4 af: : Neu:reni:

Shu: dot..,.MeV/sec, In: ire Core 1

Percen: of 113h: Ileses:,

Fission Ac:isides and To:21 f :=

Ti:o Clad and 3::ve:ure

?:odcen taugh:ers Fission ?:odue:s

!c :a!.

hu:desu 9.55 +16 5.41 +20 3.40 +19 93.9 5.759 -20

.5 =is.

8.99 +16 1.34 +20 2.61 -19 83.6 1.602 -20 hour 8.99 +16 S.49 -19 1.47 +19 85.2 9.969 -19 hours 8.92 +16 6.62 +19 1.11 +19 85.5 7.739 +19 1

.3 hcurs 8.68 +16 3.56 +19 9.46 +18 78.8 4.515 -19

.~. hcurs 8.49 +16 2..i5

+19-7.96 +18 74.5

~'

3.154

+19-i days 7.93 +16 1.47

+19, 4.42 +18 76.6 1.920 +19 i dav5 7.49 vi6 1.22 +19 2.46 +18 82.8 1.473 +19

/

i

0( 4 6.62 -16 9.17 +18 5.79 +17 93.4 9.815 +18 20 days 5.43 +16 6.30 +18 3.84 +16 98.5 6.393 +13 30 days 4.56 -16 4.87 +18 5.90 +15 99.0 4.922 +18 LIqual :o the difference be:veen :he :ozal release ra:e (rd) sinus :he Y release since only 3 digi:s are yielded from ORIGIN for :hese quantities, the ra:o:

eccuracy of the above numbers is less than :he number of digits presented.

e s

3 93 e

e

==

>e t

I O

J 2

3 w ;.

OM e

.g

=

4 4

7 g

e e

N

N N

.m

==

.e 3

= 3 I

U ::

V e

.* =l t

w e

.

s 4

l

5 3

N 4

m A

!N

=*

-e

=e e

N 2

e m

e C

D 4

m 4

N MA, m

C D O.

N.

O.

3 3 d

e s

C C

C C'

C =*

w

= a sua e

s 43 w

w 3

0 i

U w

J 30

^

Z C

1

=

w

.=*

U a

e 2 m

e C

b w 0

C

s m.

e.

e ;a.

a 3

u U

C C

C u

X S

.l 3

=

3 0

4 3

w ao E

C D

== 2

==

.d =

U O^

lal 3 ed N m

A C

=0

.=

J 4

4:

2 as u 4

S C

H k 2 N

4 N

3 o>u N

w C

=

w g w e

e e

UE 3 C

C C

w

.me =d G

S E

> ww C 3 Iw 1

==

O "J

h w

3 M

=

"J I

s w

a me z

8 ne w

^

U "J

O l

t t

N a

8 I

4 w

=

i z

l w

w t

w m

b s

I h

S T

S a.

=

w 1

j M

w 3

l

=

-2

J I'

X

J 3

7

=

0 t

W "J

Z 4

I h

s i

TABl.E V.

I'liuton Attenuation - Hodel 2 Hasu Attenuation Coefficienta Assumed Density l'roduc t l'e s ce n t of Region (Haterial)

(Ref. 3)

(g/cc) 1'roduc t Averaged llumugentred Tut.it Fuel (l't.)

0.0684 10.4 0.7114 0.2155 11.6 Clad usul Structure (Fe) 0.0595 6.5 0.3868 0.0406 1 1. '>

HuderaLor (110) 0.0706 0.7+1.0 Q.0635 0.0369

12. se, 2

'(using)=1.0) 0.2930 I

llomogeis t red Total 2

(cm /3) ~

81 HeV Y'u i

/

de we i

4

,s 7A3 *J '/..

eu:::n Sour:es Af:e: ::au:::st: Shu:devn, Neu:: ens /sec Ti: ed Neu::en Spen:aneous Oise 3ource 2a Fission 70 :a '.

1 i

Shu:down 2.8

-9 1.22

-7 5.40

+6 2.818

-9 15 nin.

2.8 w9 1.22 v7 5.40 %

2.818

-9 I hour 2.8

+9 1.22 v7 5.40

-6 2.818

-9 2 hours2.314815e-5 days 5.555556e-4 hours 3.306878e-6 weeks 7.61e-7 months 2.8

-9 1.22

-7 5.40 v6 2.818

+9 10 hours1.157407e-4 days 0.00278 hours 1.653439e-5 weeks 3.805e-6 months 2.8 4 1.23

-7 5.41

+6 2.818

-9 24 hours2.777778e-4 days 0.00667 hours 3.968254e-5 weeks 9.132e-6 months 2.8

+9 1.24

+7 5.42 4 2.318

-9 3 days 2.8

-9 1.26

+7 5.43

-6 2.818

-9 5 days 2.8 e 1.27

+7 5.43

+6 2.818 4 10 days 2.8

-9 1.29

+7 5.42

-6 2.813

-9 1

20 days 2.8

+9 1.29

+7 5.40 e 2.818

-9 30 day-;

2.8 v9 1.29

+7 5.38

+6 2.818 4 80 m a + 7" te e n.

Fu ; 236U, and su.oseques:

a 240 e.g.

f

49 s

t 2

TA3:.I ";2a.

To:21 Neu: en Flux *evels (nicm -sec) kshutdown " 0 99 Scar up, Spon:aneous Fission Residual Full Power a Time Plus s-n Sources

?lus Delayed Neu: ens To:ala Shutdown 3.960

+5 2.790 +14 2.790 -la 0.5 sec 3.960 v5 1.826 +14 1.826

-14 1 sac 3.960

+5 1.292 +14 1.292 +16 5 sec 3.960 v5 6.836 +13 6.836 +13 30 sec 3.960

+5 2.430 +13 2.430 +13 1 min 3.960

+5 1.175,13 1.175 +13 2 min 3.960

+5 3.467 +12 3.467 +12 5 min 3.960

+5 2.253 +11 2.253 +11 10 min 3.960

+5 5.630 4 5.630

-9 15 min 3.960

+5 1.495

+8 1.499

8 20 min 3.960

+5 3.975

+6 4.371

+6 25 min 3.960 v5 1.057 v5 5.017

+5 30 min 3.960

+5 2.809

+3 3.988

+5 35 min 3.960

+5 74.683 3.961 v5 40 min 3.960

+5 1.985 3.960

+5 45 min 3.960

+5 0.053 3.960

+5 3.960

+5

-2 1 hour1.157407e-5 days 2.777778e-4 hours 1.653439e-6 weeks 3.805e-7 months 3.960

+5 3.960

+5 2 hours2.314815e-5 days 5.555556e-4 hours 3.306878e-6 weeks 7.61e-7 months 3.960

+5 3.960

+5 10 hours1.157407e-4 days 0.00278 hours 1.653439e-5 weeks 3.805e-6 months 3.960

+5 3.960

+5 1 day 3.960

+5 3.961

+5 3 days 3.961

+5 3.961

+5 5 days 3.961

-5 3.961 v5 10 days 3.961

+5 3.961

+5 20 days 3.961

+5 3.961

+5 30 days 3.961

+5

Approximate : hor =al (E < 0.625 eV) flux can be obtained by :aking 17lll of this :otal value:

see Table 7 and section III.~

I I

s' e

~

..%.. eve.s,sO!O2 -Sec) k g.g.f;.gn

J.3

.0 g.

....-e....

"A.

.itu*:00

_u

. 3=a *-

0.

.o g

5:ar:up, 5pon:aneous 71ssie:

Residual 7u11 ?cwer :

Ti:e Plus :-: Source

?lus Oeiayed Neu:: ens To:a;a 1

i l

Shu:down 7.600

-4 2.790

-14 2.790

-11 0.5 sec 7.600

-4 1.348 +14 1.344

-11 1 sec 7.600

-4 8.250 v13 S.260 -13 5 sec 7.600

+4 3.745 +13 3.745 -13 30 sec 7.600

+4 1.173 -13 1.173 +13 1 =in 7.600

+4 5.365 +12 5.365 +12 2 min 7.600

+4 1.469 +12 1.469 +12 5 sin 7.600 v4 9.225 +10 9.225 v10 10 mis 7.600 v4

2. 223

+9

2. 23 3

+9 15 sin 7.600

-4 5.648

+7 5.656

-7 20 mi:

7.600

+4 1.429

+7 1.437

-7 25 =i:

7.600 v4 3.617

-4 1.122

-5 30 =in 7.600

+4 915.5 7.692

-4 35 =is 7.600

+4 23.167 7.602 e4 40 si:

7.600 v4 0.586 7.600

-4 45 =i=

7.500

+4 0.015 7.600

+4 7.600

+4 1 hour1.157407e-5 days 2.777778e-4 hours 1.653439e-6 weeks 3.805e-7 months 7.600

+4 7.600

-4 2 hours2.314815e-5 days 5.555556e-4 hours 3.306878e-6 weeks 7.61e-7 months 7.600

-4 7.600

-4 10 hours1.157407e-4 days 0.00278 hours 1.653439e-5 weeks 3.805e-6 months 7.600

+4 7.600

-4 1 day 7.600

+4 7.601

-4 3 days 7.601 e4 7.601 5 days 7.601

+4 7.602

+4 10 days 7.602

+4 7.602

-4 20 days 7.602

+4 7.602

+4 30 days 7.602

+4

' Approximate :her=al (I < 0.625 ev) flux can be ob:ained 'my :aking 17% of :his :otal value:

see Table V and see: ion III.

w

1 A:p cxina:e Neu::en Energy Spec::us

..m i

i Neu:ren 71um Spec::a (Neu::cas/c=,-sec)

.l l

7c11 15 Minu:es Inergy Inergy Nor=ali:ed Power Ai er Shu:down Group Range

o 100 Values (ks = 0.98) 1 0.821+10 MeV 23.6 6.58 +13 1.33 97 2

5.53 421 kev 32.7 9.14 +13 1.85

-7 3

1.855+553 ev 23.9 6.68 +13 1.35

+7 4

0.625-1.855 eV 2.8 7.70 +12 1.58

-6 5

10-54.625 eV 17.0 4.74 +13 9.60 %

Totals 100 2.79

+14-5.65'

+7

.(

Neutron Densi:7 Spectra

.,_i 7u11 Power Density Le:hargy n

Energy Range v (E(u)}

nE E Normalized 3

Group

[u I in(10 MeV/I)]

u E (u)

(cm/sec)

(Neutron /cm )

o 100 1

2.54 1.25 2.865 MeV 2.370

+9 2.776 M 0.012 2

9.803+2.5 6.152 21.303 kev 2.043

+8 4.474

+5 0.195 3

15.5-9.803' 12.652 32.L',7 eV 7.923

+6 S.431 M 3.671 4

16.388-15.5 16.044 1.077 eV 1.433' 4 5.299

-6 2.308 8

5

.27.631-16.588 22.120 0.025 ev^

2.20

+5" 2.154

-8*

93.814 (19.81)*

7 ( weightad) = 1.2153 x 106 cm/sec

% ssu=ing a Maxwellian dis:ribucica fa the :he =al group.

A

1 I

g 11 APPENDIX 3

O sp 9

8 9

6

~

s~..n.,=,.-

e nA..

~.!~_ S n=.

m. u._- St.33- =

=.. _.6,s. _-

m --. u._--

w

.v

1) TO:11 0:cigen production

1) Radiolysis under partial boiling conditions Table 1 Time Interval Avg. Dose Total Effective After Shu: Down Rate Dose Efficiency Dose (Ecurs)

(10 ev L s -)

10 eV L Facecra 1020 ey a '

20

-1 1

24

-1 0-1 12.48 4.49 0.8 3.59 l-2 7.42 2.67 0.7 1.87 2-3 6.24 2.25 0.35 0.79

~

0.61 3-4 5.62 2.02 0.3 4-8

-4.71 6 78

-1 6.78 8-14 3.81 8.23 1

8.23 14-16 3.46 2.49 0.8 1.99

...k TOTAL 23.86

" Reflects partial covering of core and/or incomplete boiling.

Values are considered conservative.

. Maximum 02 produced by radiolysis:

25 2.386 x 10 x 0.225 = 0.089 mol,. l 23 100 x 6.02 x 10 or 0.089 x 17900

= 15 93 mol 0- (total) s l

l t

w.

t t

53 b) 0 added with feed water 2

Air saturation assumed (2.33 x 10 mol L 0)*

2 6

234,000 gal = 1.075 x 10 3

3 0 contain 250.5 mol 0

~

2 2

Total 02 produced or added (worst case) : 1943 mol 0 2 (2) Toual hydrogen production:

4 burned in Containment:

226 lb. mol = 10.25 x 10 mol 4

I Still in Containment:

80 lb. mol =

3.63 x 10 mol 4

~

in Bubble and Solution

8.87 x 10 mol 4

Total E Produced 22.75 x 10 mol 2

c) Steam produced 6

284,000 gal. E 0 produce 1.075 x 10 kg 2

4

= 5.97 x 10 mol steam (3) Steam and E in bubble 2

~

3 Volume of Subble:

1471 ft

= 41,630 L Temperature:

250*F = 138*C = 411 K Pressure:

790 psig

= 67 atm Partial pressure of steam and bubble:

= 3.3 atm' Partial Pressure of E

= 63.7 ats 2

(O neglected) 2 6 3. 7 x 416 30 x 27 3 = 7. 86 x 104 mol H

in Bubble:

2 22.4 4L1 Steam in Subble 4135 mol

( '

See calculation belov

[

(4; Contants of solution Volume of H 0:

219,000 L - 41,630 L = 177,400 L 2

Distribution of gas between bubble and solution:

H (bubble)

,. 3, o. 3 0

_3 3 * -

3 e

~

H tsol)

_77,400 x 0.02 4ff 3

O (bubble) 41,630 273 2

= ~12*0

=

0 (s 1) 177,400 x 0.013 411 2

Therefore H in solution:

2 4

4 7.86 x 10 /7.79

= 1.01 x 10 mol 32 (5) Fraction of H and steam not vented 2

J Table 2 Amount Amount.

in Bubble

)

Produced (and solution)

(mol)

(mol) 5 2.27 x 10 8.87 x 10 E 2 3

4 Steam 0.60 x 10 0.41 x 10 4

. 87 x 10 9.28 x 10 1

I Fraction of 32 + steam retained in RCS:

0.323.

Assuming that the same fraction of 0 was retained, 2

this amounts to 0.323 x 1843 = 595 mol 02 Therefore 0

in bubble:

549 sol 2

0 in solution:

46 mol 2

0 /H in DCbblS:

0.7%

9 9

Concentrations in solution 10-2 =c; ;-l 1.01 x 10 /177,400 = 5.7 x H2:

46

/177,400

= 2;6 x 10-4 ::1 L O2:

(

l l

Temperature CC)

oo 200 300 400 500 600 700 800 000 1000 1200 100 1300 5

1400

=

S Days l

1500 l

105 l

8 g _.__

1 Day C

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104 l Comploie oxidation

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4 TIGURE 7

(*d,0 ) in Zore ~4a er Vs. Time 3_?ull Power Conditions

~

c. d = 8

_a ___________________________________ _____ _______.

u o

i, n.

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E

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