Nuclear Fuel in the Destroyed 4th Unit of Chernobyl NPP
Volodymyr M. PAVLOVYCHInstitute for Nuclear Research of the National Academy of Science of Ukraine,
01028, Pr.Nauki, 47, Kyiv, Ukraine, e-mail: pavlovich@kinr.kiev.ua

Abstract
The main question, which determines the nuclear safety of the 4th destroyed unit of theChernobyl NPP, as well as the question about the amount and distribution of nuclear fuel inside the“Sarcofagus” is discussed in the paper. The methods of determination of nuclear fuel quantity inside
the “Sarcofagus” and the quantity thrown out of its boundaries are considered in detail. Special
attention was paid to the quantity and distribution of the fuel in the under-reactor premise 305/2,
which is looked as the most nuclear dangerous. On the base of such investigation and also taking into
account the results of fuel containing material sample analysis, it is possible to make some calculationof the fuel containing material criticality and scenario of self-sustaining chain reaction development in
the hypothetical situation of nuclear danger. Some of the results of such calculation are also presented
in the paper.

1. The general description
One of the basic problems of the destroyed 4-th unit of Chernobyl NPP (somebody began to call it as"Shelter" or "Sarcophagus") which substantially defines the nuclear and radiation safety of the object, isthe problem of nuclear fuel inside the Shelter. In order to estimate the nuclear and radiation safety ofvarious premises of the Shelter, the knowledge is necessary about the nuclear fuel amount in each premise,the degrees of its primary enrichment and burnup at the moment of accident, the physical properties of thefuel containing materials (FCM), and opportunity of water incoming into each premise of the Shelter.
It is well known (see for example [1]) that at the moment of the accident there were approximately
214,600 kg of nuclear fuel in the fourth unit of ChNPP. The basic amount (190.2 ton) of this fuel was
loaded into the reactor core, the part of the spent fuel was placed in the south cooling pond (14.8 ton), at
the stand in the central hall (CH) there were the assemblies of fresh fuel (5.5 ton) prepared to loading to
the core, and, at last, there was 4.1 ton of fresh nuclear fuel in a room of fresh fuel preparation.
At the moment of the accident, there were 1,659 fuel assemblies in the reactor core, and each
assembly contained 0.1147 ton of uranium. The fresh fuel of the reactor RBMK-1000 before the accident
at Chernobyl NPP contained 2 % of uranium-235. By the moment of the accident the majority of fuelassemblies were the first fueling assembly with fuel burnup from 11 up to 15 MWt⋅day/kg U. There wereTable 1. Burnup distribution of fuel assembly (FA).
Average burnup
Group
Number of FA
MWt⋅day/kg U
1
721
13.7
2
392
12.3
3
154
10.5
4
101
8.8
5
35
7.0
6
43
5.4
7
41
3.5
8
172
1.2
FA total number
1659
Average burnup
10.9

45

also fresh fuels in the reactor core. The distribution of fuel assemblies by the burnup level of 8-group
approximation is given in Table 1.
A rough estimation shows that the burnup of 10 MWt⋅day/kg U approximately corresponds to a
reduction of uranium-235 concentration by 1 % and an increase of plutonium-239 concentration (at theinitial stage of campaign) by 0.4 %. Thus, if assuming an average burnup of 10.5 MWt-day/kg U, there
were approximately 1,900 kg of uranium-235 and 760 kg of plutonium-239 in the reactor core at the
moment of the accident.
Already in 1986 first estimations [2] have shown that as a result of the accident 3 - 5 % of nuclear
fuel originally concentrated in the reactor core was thrown out of the 4-th unit boundary. The researches,
which have been carried out during the subsequent 15 years, have confirmed these estimations as a whole.
Now it is considered [1] that more then 96 % of fuel of the core + fuel in the pool of endurance + fresh
fuel of the central hall remain inside the Shelter. 4.1 ton of fresh fuel was removed in 1986 from the fresh
fuel preparation room after the accident.
In order to understand the physical properties of the fuel containing materials of the Shelter it isexpedient to remind the basic stages of the accident scenario. As a result of reactor runaway with prompt
neutrons there was a destruction of pin claddings, and the heated fuel has entered contact to the coolant(water). The explosive formation of water vapors has caused a sharp increase of pressure inside the reactor.
This first explosion has resulted that the reactor cover (scheme “Е”, see Fig. 1 [1]) was thrown out in thecentral hall at the height about 14 m, and the reactor bottom plate (scheme “ОР”) was lowered
approximately by 4 meter into the under-reactor premise 305/2, and the southeast quadrant of the scheme“ОР” was completely destroyed. During the flight of the scheme “Е” there was the second explosion
which has destroyed the reactor building and particularly a drum-separator premise a part of wall of which
has appeared inside the reactor vault. After that explosion the reactor cover was lowered in the position
shown in Fig. 1.
As a result of the explosions a part of the fuel was thrown out of the limits of the reactor building,and the residual fuel in reactor began to be heated up due to heat release of fission products and burning ofgraphite. This process proceeded approximately within 10 days. During this time about 14 thousand tonsof various materials: lead, dolomite, marble powder, sand, zeolite sorbent, and absorbers of neutronscontaining boron were dropped from helicopters to the central hall and the reactor vault.
A part of these materials which has got into the reactor vault was melted together with fuel, pincladdings, walls of technological channel pipes, and material of the scheme “OP” backfilling (serpentinite).
These melted materials have penetrated into the under-reactor rooms, whence then they have spread on

Fig.1
46

Fig.2numerous premises of the lower floors of the reactor building (Fig. 2 [1]). In these premises the solidified
melt has formed so-called lava-like fuel containing masses (LFCM).
The lava-like FCM of the Shelter represent heterogeneous ceramics of brown or black color withinclusions of various natures. For example, only black ceramics is located in the premise 304/3, and there
are both black and brown ceramics in the premise 305/2. The color of black ceramics is caused mainly byradiation defects, and after annealing it gets the bottle-green color which is the characteristics of silicabase glasses. The oxides of iron cause the color of brown ceramics, basically. The average content ofdifferent nuclides in ceramics of the premises 304/3 and 305/2 with exception of actinides is submitted inTable 2. A special attention should be given to the boron contents in LFCM. As it is known, boron is "aburning-out absorber", i.e. the quantity of an isotope B-10, which absorbs neutrons, decreases in the media
with non-zero neutrons flux. In addition, boron is well-dissolved in water and can be washed away fromthe porous LFCM. We can not make the exact estimations of the amount of "burnt out" and moreover ofthe "washed up" boron. Therefore, it is necessary to make criticality calculations with content of boron
taken from 10 years old LFCM sample analysis, and also without boron.
Table 2. Chemical composition of the FCMin premises 304/3 and 305/2 and concrete in wt. %.
MixtureChemical element
FCM, 304/3
FCM, 305/2
Concrete
B
0.06*
0.07*
O
43.4
37.1
55.26
Na
4.20
3.34
0.55
Mg
2.40
3.34
0.79
Al
4.80
2.90
2.90
Si
29.8
24.7
26.44
K
1.25
1.05
0.61
Ca
5.50
3.90
8.64
Fe
1.40
0.70
3.64
Zr
3.20
4.00
3.20
C
0.40
H
0.77
47

Let us consider now the LFCM macroscopic properties. According to the data of numerous
investigations of samples taken from various under-reactor premises, the density of the LFCM changes
over a wide range depending on porosity of the material. In this connection it is necessary to note that the
LFCM are a strongly porous material with the sizes of pores and cavities of which change frommicroscopic dimensions up to the sizes about 1000 - 2000 cc. The LFCM are also a strongly non-uniform
material whose density varies depending on the depth within the LFCM: for example, (0.9 - 1.8) g/cc in
the premise 304/3 and (1.8 - 3.5) g/cc in 305/2.
At the present time the nuclear fuel in the Shelter is in several modifications. First of all, there are the
kept fuel assemblies (the southern cooling pond and the central hall). The fragments of fuel pins andassemblies (core fragments) are found out also in various places. In some places of the under-reactor
rooms, non-melted pellets of uranium dioxide were found out. In the LFCM, fuel exists as various
inclusions in a silica-base matrix with the sizes from several up to 300 micrometers of various chemical
structures [3]. Besides, uranium is also dissolved in a silicate matrix of the LFCM [4]. The concentrationof uranium dissolved and included in the LFCM matrix changes from 4 % up to 10 % in various premisesof the Shelter, and the mass portion of uranium-235 mainly corresponds to the burnup rate [5,6], though insome samples the portion of uranium-235 was much higher than the average [7,8].
Practically in each premise of the Shelter, the finely dispersed fuel particles (fuel dust) are observedwith the sizes of particles from parts of micrometer up to hundreds of micrometers. This dust can represent
the main radiation danger in conditions of hypothetical caving of the Shelter structures.
At last, it was revealed in 1990 that in water, which accumulates in some places of the bottom floorsof the Shelter, salts of uranium, plutonium and americium are dissolved. The estimations show that up to
4,000 cubic meter of water per one year [7] can penetrate through the holes of the roofing of the Shelter
and at the process of moisture condensation from the air. Percolating through fuel containing materials,
this water dissolves some salts of uranium and transfers them to the bottom premises of the Shelter.
The nuclear safety of each premise of the Shelter is determined by the amount of fuel in this premise,
the geometrical arrangement of this fuel, the opportunity of water ingress in this premise and its
penetrations inside the fuel containing materials.
2. Estimation of fuel quantity in the Shelter premises and thrown out of its boundaries.
An estimation of the thrown out fuel quantity (3 ± 1.5) % offered in 1986 in the report of the Soviet
delegation at IAEA meeting [2] has caused the large doubts. These doubts, which bound up basically withplentiful release of radioactive iodine-131 and caesium-137, were expressed as a rule by thenonprofessionals who did not take into account volatility of some components of the spent nuclear fuel.
It is possible basically to estimate the emission of nuclear fuel by three different ways [9]:1. Measuring the quantity and the content of activity thrown out into the environment directly during theactive stage of the accident;
2. Measuring the density of radionuclide pollution of the territory both directly adjacent to the Shelter
and in the remote areas;
3. Determination of the fuel quantity in various premises of the Shelter. Then the knowledge of the total
fuel load of reactor make it possible to estimate the quantity of the thrown out fuel by the difference.
It is natural that the most exact estimation of the thrown out fuel amount can be obtained combining
all three methods.
The measurement of activity and contents of emission directly during the active stage of the accident
was connected to the large methodical difficulties of aerosol sampling above the damaged reactor. Thesedifficulties have resulted in the large enough errors (50 %) in determination of radioactive aerosol
concentration in emission. Therefore, the first estimations of the thrown out activity were rather
approached. Table 3 contains the results of researches published in work [2].
48Table 3. Radioactivity ejection from the 4-th unit (in % to the activity accumulated
in reactor to the moment of the accident).
IsotopeEjection,%
IsotopeEjection,%
133
141
Xe
~100
Ce
2.3
85m
144
Kr
~100
Ce
2.8
85
89
Kr
~100
Sr
4.0
131
90
I
20
Sr
4.0
132
239
Te
15
Np
3.2
134
238
Cs
10
Pu
3.0
137
239
Cs
13
Pu
3.0
99
240
Mo
2.3
Pu
3.0
95
241
Zr
3.2
Pu
3.0
103
242
Ru
2.9
Pu
3.0
106
242
Ru
2.9
Cm
3.0
140
Ba
5.6
The second way requires an estimation of the radioactive pollution of the large territories in the
different countries and is very labour consuming. However, since the remote territories became polluted
mainly by the volatile radionuclides (iodine, tellurium, caesium), and finely dispersed fuel particles
containing heavy transuranium elements accumulated in the majority within the limits of a 30-kilometerzone around the Shelter, then it is possible to make an exact enough estimation of fuel emission by having
carefully performed pollution investigations of the zone of alienation. In addition to this, undoubtedly, it isnecessary to estimate a degree of reduction of the pollution by transuranium elements with increase of
distance from a source of emission.
Such estimations were executed in 1986 by the group of researchers of Kurchatov Institute, and they
were continuously became more precise during all 15 years past after the accident [10,11,12]. Theseestimations once again confirm a conclusion of work [1]: more than 95 % of fuel from the destroyed
reactor core is concentrated in the Shelter.
3. The distribution of nuclear fuel on the Shelter rooms.
It seems that the third way of determination of the nuclear fuel amount which has been thrown out
from the Shelter, i.e. the determination of the amount of fuel located in various premises of the Shelter, isexactest and accessible. However, a plenty enough of reasons exist obstructing to the detailed inspectionof the Shelter. It is possible to attribute such handicaps to the followings: high radiation fields in the
Shelter premises, the blockages of various materials dropped from helicopters to the central hall, theoverflows of stiffened "fresh" concrete (1986) on the LFCM congestion and the large thickness of the
LFCM layer in the premise 305/2, where the basic LFCM congestion is located.
The determination of the nuclear fuel quantity inside the Shelter and its distribution on premises isvery important also from the point of view of nuclear safety of the Shelter and its radiation influence on
the ChNPP personnel and the environment in the case of possible emergencies. Therefore below, we shallconsider in detail the items of information about the distribution of nuclear fuel in the Shelter premises
obtained up to the present time.
Let's begin from the central hall (CH) - one of the most complex places of the Shelter premises for an
estimation of fuel quantity. Let's remind that in the CH before the accident, there were 5.5 ton of fresh fuelprepared for loading into the reactor core and 14.8 ton of the spent fuel in the southern cooling pond. The
fuel pins are also in so-called “Helen hair” – the rests of technological channels which are hanging downfrom the scheme “Е”. Besides, in various places of the CH there can be fuel dispersed by the second
explosion. It is possible only to use the indirect methods to estimate the quantity of the dispersed fuel,since the materials dropped from helicopters during the active stage of the accident cover the CH. The
estimation of fuel quantity in “Helen hair” also can be carried out by indirect methods in connection with49

high radiation fields in the CH.
Scientific groups from Khlopin Radium Institute and Kurchatov Institute carried out such estimations
on the basis of measurement of radiation dose rate and localization of its sources in 1992. The estimationsof such type can be only qualitative in connection with impossibility of exact localization of radiation
sources. The results of calculations based on measurements of such type give that the quantity of fuel on
the scheme “Е” can be in limits from 10 up to 30 ton. There was found also up to 1 ton of fuel on the wallsof the CH and other structures. Totally together with the spent fuel of cooling pond (the periscope
inspection of which have shown the absence of water and the presence of all nondestroyed fuelassemblies) there can be from 31 up to 51 ton of fuel in the CH.
On the basis of video and periscope inspections of the reactor vault, it is possible to make aconclusion that there are no ordered structures of the former reactor in the shaft and now it iscommunicated with the under-reactor premise 305/2. Therefore, it is meaningful to estimate the quantityof fuel in the reactor shaft together with a premise 305/2.
Already in 1986 – 89, the first thermometric measurements of fuel quantity in the under-reactor
premises were performed. These measurements were based on the fact that the integrated thermal flow
outgoing from these premises completely should be determined by the thermal source power, andconsequently by the complete mass of the fuel [13]. The specified estimations of 1990 [14] taking into
account an error of measurements give for fuel mass in the premise 305/2 the value of 75±25 ton.
It is possible also to estimate the fuel quantity in lavas of the under-reactor premises by balance of
caesium and magnesium [3]. The last specified data [11,12] show that the complete emission of caesium137 has made an activity about 2 MCi that forms about 28 % from the value of 7 MCi initiallyaccumulated in the reactor core at the moment of the accident (compare with initial assessments of works[2], Table 3). This caesium took off only from the fuel, which has melted during the active stage of theaccident and has formed the lava-like FCM.
On the other hand, the data of the numerous analyses show that no more than 40 % of caesium-137
remained in lava. It means that about 60 % of caesium-137 from its initial quantity in fuel, which hasformed lava, has taken off, and these 60 % of caesium-137 have given the activity of 2 MCi. Therefore theinitial activity of the caesium-137, which contained in the fuel forming a lava, is equal to (2/0.6) =3.3 MCi.
It makes (3.3/7) =47 % from the amount originally accumulated in reactor, so 47 % of reactor fuel loading(190.2×0.47) =89.39 ton has come in a lava. Taking into account an error of estimations, we have 90±27
ton.
The similar estimations can be made by the amount of magnesium whose average concentration inlava is equal to 3 % (compare with Table 2). The magnesium enters only into the structure of serprntinite,by which the scheme “OP” was filled up and its contents in serpentinite are 25.1 %. During the formationof lava, about 140 ton of serpentinite were melted [3]. Taking into account the percentage of magnesium
in serpentinite and in the samples of a lava, it is possible to say that during the melting in the process of alava dilution by other materials its weight has increased in (25.1/3) =8.5 times and has reachedapproximately 1200 ton. The average content of uranium in lava samples is about 7 % [3]. Therefore thelower estimation of its weight in lava of the under-reactor premises makes about (1200×0.07) =84 ton.
Taking into account the possible error, we have 80±24 ton. All three estimations are in good coincidence
among themselves.
It is necessary to note that at these estimations the presence of reactor core fragments is not taken into
account, i.e. the fragments of pins and fuel assemblies and also non-melted fuel pellets which wereobserved in the under-reactor premises, and also can be under the melt in connection with their large
densities. Therefore, and also with other reasons, it is necessary to consider the estimation of fuel quantity
by the amount of caesium and magnesium to be underestimated.
Nevertheless, there was a work [15] in 1992 in which these estimations are put under doubt. The
50

Fig.3 Computer model of the premise 305/2 and the reactor shaft.
authors of the paper [15] used for the estimations only the data of visual inspection and principle ofcommunicated vessels. In their opinion, the under-reactor premises contain no more than 25±5 ton of
uranium.
This work was fairly criticized by many authors. However, it has served as a certain stimulus for new
careful auditing of all data on the fuel quantity in the premise 305/2 [16]. For this auditing, the authors
used the results of the analysis of more than hundred samples taken from the premise 305/2 in 1986-1997,
the measurements of dose rate of γ - radiation, the results of all video- and photography of the premise
305/2 and the reactor shaft.
Then the whole space of the premise 305/2 was separated by the squares with a cross section 2×2 m.
The estimation of the fuel quantity was performed in the LFCM volume over every square taking into
account all data mentioned above. The square which data were absent or even partly was considered as
empty that certainly underestimated the results. The computer model of the premise 305/2 and the reactor
shaft was composed on the base of such detailed analysis of all materials which are located in this premise(Fig.3).
The precise consideration of all data concerning the premise 305/2 and the reactor shaft allows to
make the following conclusion: there are not less than 60 ton of fuel in these premises. The LFCM passed
from the premise 305/2 through the concrete wall destroyed by the explosion (or burns by the LFCM?)
into the room 304/3 and then to steam distribution corridors (see Fig.2). The second flow of the heatedlava passed through the steam outlet valves of different floors even to the first floor of the pool bubbler.
The estimations of fuel quantity in all these premises raise no doubts. They are presented in Table 4 where
the data of all measurements and estimations of fuel amount in the Shelter are summarized [1].
As we can see from this Table, the premise 305/2 and the central hall are the most “suspicious” fromthe point of view of nuclear safety. At the steam distribution corridors with marks 9 and 6 m, the lava
layers are thin (the maximum value of 0.6 m in the premise 304/3), and in spite of sufficiently large fuelamount the probability of self sustaining chain reaction (SCR) ignition in these premises is negligible
according to some evaluation.
In the southern cooling pond of the spent fuel where the water is absent at the present time thesituation is safe until the pitch of the assembly suspension is conserved. The danger can arise only in thecase of assembly caving to the bottom of the pond and its affluxion by water.
The water in the lowest premises of the Shelter has no nuclear danger at the present time. However,51

Table 4. FCM distribution inside the Shelter.
Premises (mark)- The central hall (35.50)- Other upper floor premises- The south cooling pond
(18.00-35.50)- The under-reactor premises:
305/2 (9.00) + 307/2 + the"OR" system + the reactor
vault- 304/3, 303/3, 301/5, 301/6, the"elephant's foot " and others- Stream-distribution corridor(SDC) (6.00), including FCM
in the valves.
- Pool bubbler, 2d floor (PB-2)- Pool bubbler, 1st floor (PB-1)- Lower premises of the reactor
unit,

Estimated fuel in
FCM (on uranium basis in
metric tons)

FCM type and state- Core fragments (most of them areburied under materials dropped at
the active stage of the accident.
Under them LFCM can be found)- Fuel dust.
- Fresh fuel assemblies- In the area of the scheme "E"- Fuel assemblies with the spentfuel- Lava-like FCM, core fragments

?

30?
5.5
10-30
~14.8
75 (+25,-35) was proved
to be >60 t.

- LFCM

11±5- LFCM

25±11- LFCM- LFCM- Water with dissolved salts ofuranium8±3
1.5±0.7~3000 m3 of water <3 kg U

as far as the concentration of uranium salts will increase in the future the risk of the SCR ignition can also
increase.
In order to estimate the nuclear safety of various premises of the Shelter two different ways exist. The
first way is calculation of the neutron multiplication factor in these premises in different conditions
including the most unfavorable condition of FCM water affluxion. The criticality calculation should be
supplemented with calculation of SCR scenario development in the case if the criticality calculation showsa possibility of the multiplication factor exceeding of unity.
The second way consists in direct measurements of the neutron multiplication factor in the Shelter
premises, and possible organization at this base of the continual monitoring of the FCM reactivity. The
most expedient way is a creation of the mutual experimental and calculational method due to the absenceof the full data to both precise criticality calculation and interpretation of experimental measurements.
4. The evaluation of the nuclear safety of different Shelter premises and possible scenario of SCR
development.
The nuclear safety of the “Shelter”, which is actually the question of criticality of the fuel-containing
masses, has been considered by several groups of researchers [17-19]. Most of these calculations used themodels whose properties are rather far from that of the real LFCM.
A model of the LFCM, closest to reality, was used in [18]. The LFCM in this paper were simulated
by a multilayer system with variation of the LFCM density by layers in a rectangular geometry
approximately corresponding to the layout of the rooms 304/3 and 305/2. The neutron reflection fromconcrete walls and floor was also taken into account. The nuclide composition of the LFCM and fuelconcentration was chosen closest to the experimental data that were obtained during a study of the LFCM
composition. The calculations show a deep subcriticality of both dry LFCM and LFCM filled by water.
Nevertheless, the question of LFCM criticality remains open because in this work the existence of the core52

Fig. 4. Vertical cross section of rectangularparallelepiped of FCM with fuel pellets
randomly distributed over its volume(model 1d).

Fig. 5. Vertical cross section of rectangularparallelepiped of FCM: three layer model of
FCM, limited by a layer of concrete frombelow with nonmelted part of fuel in bottom
sublayer as a cubic lattice of pellets (model
3b).

fragments in the premise 305/2 did not take into account.
What is it necessary to know for realization of criticality calculations?
1. Nuclide composition of the FCM and concrete, on which the FCM are located and also which covers
the FCM in some places. This concrete can play a role of a reflector of neutrons.
2. Macroscopic properties of the FCM, such as density and porosity.
3. Geometrical parameters of the FCM – the size and shape of FCM accumulations.
4. Quantity and spatial distribution of fuel – this is the main question.
Nuclide composition of the FCM and concrete and also macroscopic properties of the FCM are
known rather well from the results of the numerous analyses of the FCM samples. The geometricalparameters of the FCM in the under-reactor premises are known at the present time with sufficientaccuracy due to investigation [16]. However, the question on quantity and spatial distribution of fuel in the
FCM remains open in many details, especially in distribution of non-melted core fragment and fuel pellets,and for realization of real calculations it is required to involve the additional assumption about fueldistribution.
To determine the greatest possible value of the effective multiplication factor the various models of
the FCM in the premise 305/2 were considered [20]. The schematic image of some of these models is
given in Figures 4 and 5.
The enrichment of fuel was determined on the basis of the average fuel burnup of the order of 11.5
МWt⋅day/kgU [3]. As there was also the fresh fuel in the reactor before the accident, some models of the
FCM were calculated with enrichment of fresh fuel. The total amount of fuel in the FCM was defined byboth the average and the top values given by thermal measurements. The results of calculations are given
at Figures 6-7 and in Table 5. All values were calculated depending on the contents of water in the FCM.
In Figure 6, the neutron flux density spatial distribution is presented taking into account the presence of
upper concrete reflector (ceiling). The analysis of such figures can help to determine the places of neutron
detector installation in the FCM accumulations. In Figure 7, the neutron energy spectrum inside the FCM
is given depending on a degree of FCM filling by water. In Table 5 the dependencies of the effective
multiplication factor on a degree of FCM filling by water are given.
As it is evident from Table 5, the account of FCM heterogeneity not always results in increase of theeffective multiplication factor. The effect depends on water concentration that is influencing on slowing-53

down properties of the medium. The results of calculations show that the value of the effective
multiplication factor weakly depends on the accepted model of an arrangement of non-melted inclusions,which allows to use for the majority of calculations the lattice models. For all models with the averageamount of fuel (Model 3-5), the effective multiplication factor quickly increases from values 0.25-0.35 fordry FCM up to 0.65-0.70 at 20 % filling by water. At the further filling FCM by water, the effective
multiplication factor decreases up to 0.60-0.65 for first two models of the FCM (Model 3, 4) and slowly
increases up to value 0.8 for the last model of the FCM with non-melted inclusions in the bottom sublayer(Model 5). For infinite medium with a maximum quantity of fuel and the average burnup with a cubic
lattice of pellets (Model 1f), the multiplication factor reaches 0.87 at 20 %-filling by water. The samemodel with fresh fuel (Model 1g) gives k ∞ ≈ 0.99 at 20 %-filling by water, which is increased till 1.07 at
40 %-filling by water.
Thus, some models of fuel containing masses of the “Shelter” give the FCM multiplication factor
exceeding unity. Our recent calculations show that there can be other models with the multiplication factor
exceeding unity even with the spent fuel but with the bigger thickness of the layers. However, these valuesof the multiplication factor are reached only when enough quantity of water is contained in FCM volume.
It means that during affluxion of the FCM by water from any external sources (rains, the condensation) the
self-sustaining chain reaction of fuel nucleuses can arise inside the FCM.
The dynamics of ignition and development of SCR in FCM in various conditions of filling FCM bywater and at various values of greatest possible reactivity, i.e. maximal effective multiplication factor,
taking into account the Doppler-effect, is analyzed below. It is shown that, depending on the speed of
FCM filling by water, the various modes of SCR development can be realized.
We shall assume that the heterogeneous composition with greatest possible effective multiplication
factor exceeding unity is realized in the FCM (both the presence of such composition and an opportunityof its affluxion by water up to achievement of maximal reactivity are rather problematic), and we shallconsider a qualitative picture of SCR development.

Neutron flux spatial distribution

14
12

FAST, DRY FCMDRYFCM

25

THERM., DRY FCM

10

5%H2O
20

FAST, 20%H2O
8

20%H2OTHERM., 20%H2O

Neutron Flux, rel.un

Neutron Flux, rel.un

Energy spectra

30

15

6

10

4
2
0
0

50

100

150

200

250

300

5

0

350

-2

10

Height, cm

-1

10

0

10

1

10

2

10

3

10

4

10

5

10

6

10

EnergyFig. 6. A fast and thermal part of a neutron
flux in a premise 305/2 in dependence onheight for model 2a taking into account thepresence of a concrete ceiling at height 1м
from a FCM surface.
(0-100 cm – concrete, 100-180cm – FCM,
180-280 cm – air, >280cm – concrete)

Fig. 7. A neutron energy spectrum in a
premise 305/2.

54

7

10

8

10

Table 5. Results of the effective multiplication factor calculations for different models of the FCM
in the room 305/2
Effective multiplication
factorModel of the FCM
SubmodelDry FCM+ FCM+
FCM
20%
40%
H2O
H2O
Completely homogenized fuel
0.26
0.76
0.70
1a. cubic lattice of pellets in the uniform FCM 0.28
0.75
0.68
1b. square lattice of pins in the uniform FCM
0.29
0.75
0.67
1. Model of the FCM in the form 1c. repeating cubes of the FCM,
0.28
0.65
0.70
of infinite medium
containing lattice of pellets
1d. random distribution of pellets
0.28
0.65
0.70
1е. cubic lattice of pellets in the uniform FCM
0.32
0.81
0.73
– fresh fuelCompletely homogenized fuel
0.30
0.85
0.90
1. Model of the FCM in the form
1f. cubic lattice of pellets in the uniform FCM 0.32
0.87
0.96
of infinite medium (maximal
1g.
cubic
latticeofpellets
intheuniform
quantity of the fuel)0.40
0.99 1.073
FCM –fresh fuelCompletely homogenized fuel
0.11
0.64
0.64
2. Model of the FCM in the form
2a. cubic lattice of pellets in the uniform FCM 0.11
0.63
0.62
of the uniform layer with2b.
squarelattice
of
pins
in
the
uniform
FCM
0.12
0.63
0.62
vacuum boundary conditions
0.11
0.63
0.61
2c. random distribution of pellets
3. Model of the FCM in the form Completely homogenized fuel
0.25
0.66
0.65
of the uniform along height
3a. cubic lattice of pellets in the uniform FCM 0.25
0.65
0.63
layer, located over the concrete
3b. square lattice of pins in the uniform FCM
0.26
0.65
0.62
layer
Completely homogenized fuel of sublayers
0.25
0.66
0.66
4. Three-layer model of the FCM
4b.
cubic
latticeofpellets
intheuniformwith sublayer density
0.26
0.65
0.63
FCM of sublayers
dependence on the height,
located over the concrete layer 4c. square lattice of pins in the uniform FCM 0.25
0.65
0.62
of sublayers
Completely homogenized fuel of sublayers
0.32
0.73
0.78
5. Three-layer model of the
5b.
cubic
latticeofpellets
intheuniform
FCM, located over the concrete
0.33
0.67
0.76
layer with nonmelted part of the FCM of sublayers
5c. square lattice of pins in the uniform FCM
fuel in the lower sublayer
0.34
0.68
0.74
of sublayers
In order to analyze the FCM behavior in conditions of its reactivity changing due to filling FCM bywater, it is necessary to solve the system of kinetic equations describing the situation. First of all, this is
the equation of neutron transfer in the FCM medium, which should take into account the change in mean
neutron lifetime due to the presence of delayed neutrons and dependence of reactivity on water quantity
into the FCM and its temperature. The steady state calculations show that the dependence of reactivity on
water quantity seems to be quadratic, which represents the moderating and absorbing properties of thewater.
The second equation actually is the law of energy conservation, which takes into account fission
energy release, the heating of the FCM, heat removing from the FCM surface and water evaporation. The
third equation represents the law of water mass conservation, which takes into account the water incomingfrom the external source and its evaporation due to fission heating.
These equations in the frame of point model were investigated by qualitative stability methods andwere solved by numerical methods [20]. The mentioned above different modes of SCR development
depending on the parameter values were found. These modes are: the single neutron burst both insubcritical and overcritical regimes, the damped and stable neutron oscillations. The realization of one of55

Neutron Flux

6

10

5

10

4

10

3

10

time, c

2

10

0.0

6

5.0x107

1.0x107

7

1.5x102.0x1077

7

7

2.5x100100

Temperature, C

80
60
40

time, c

20
0.0
0.20

6

5.0x101.0x10

Water Mass, g/cm

0.15

1.5x107

2.0x102.5x10

3

0.20

0.10

0.19

0.05
0.18
2.0x10

0.00
0.0
0.0

6

7

5.0x107

2.2x107

1.0x10time, c7

1.5x107

7

2.0x102.5x10

Reactivity
0

-0.1
-0.2

-1x10

-3

-2x10

-3

2.0x10

-0.3
0.0

6

5.0x107

1.0x107

2.2x10time, c77

1.5x107

2.0x107

2.5x10Fig. 8. Mode of an aperiodic subcritical burst.
these modes depends on the value of the neutron multiplication factor, on the velocity of FCM filling by
the water, on the rate of heat removing etc. One of the most probable regimes of the subcritical neutron
burst is presented in Fig. 8.
It is necessary to note that in 1990 and 1996 there were two neutron bursts registered by the neutron
detectors located in the premises 304/3 and 305/2. There were a lot of discussions on the causes of thesebursts, but it is evident that in both cases they occurred after the intensive rains in Chernobyl region. The
pictures of burst development were very similar to that presented in Fig. 8.
5. The measurement of the FCM reactivity in the Shelter premises
Let us emphasize once more that the nuclear safety of the Shelter is defined first of all by the value ofthe neutron multiplication factor in the FCM of premises 305/2, 304/3, 210/6, the central hall, the reactor
shaft and the southern cooling pond. Since the space distribution of the fuel in those places and thegeometry of the FCM also are known inaccurately, the neutron calculation in those premises could be
performed with the help of not very realistic models giving only not exact evaluations of the multiplication
factor. In order to make the well-founded decision to increase the nuclear safety of the Shelter, thoseevaluations were inadequate. Therefore, a necessity arisen to measure the multiplication factor in thosepremises.
It is necessary to note that the attempts of such measurements in the Shelter were made in 1991 [21].
Those measurements were performed on the base of neutron pulse method, and authors have used the56standard geophysical equipment of neutron logging of the bores. They have no possibility to vary thefrequency of neutron pulse emission, and they have small time of registration (2 ms) of the system
response. Therefore, they could not detect the delayed neutrons and determine the multiplication factor
with a sufficient precision.
One can conditionally divide the experimental methods of reactivity measurement on two classes:
active and passive methods. The active methods assume some impact to multiplying system andsubsequent measurement of the system response. One can realize the active methods both by the
introduction into the system of the subsidiary reactivity (positive or negative) or with the influence by theexternal neutron source.
The methods connected with the introduction of additional reactivity are not suitable to measure theneutron multiplication factor in the FCM of the Shelter. This is, first of all, due to impossibility to estimate
the value of injected reactivity even with known physical parameters of the injected materials. The causeof such situation is the same that leads to impossibility of exact calculation of the neutron multiplication
factor. The pulse neutron method is the most widely distributed among the methods of external neutron
source influence. But it is necessary to insert the pulse neutron source inside the FCM and to have a goodelectronic equipment in order to obtain the precise result. This method needs the boring of cavities inside
the LFCM that is impossible at the present time.
Contrarily, the passive methods of reactivity determination are based on the measurement andanalysis of the fluctuations of steady neutron background which is caused by the buildup of transuranium
elements during the reactor operation or by the stationary external neutron source. By now in the FCM of
the Shelter, the steady neutron background is determined by the spontaneous fission of some transuranicsand (α,n)-reactions, and it's fluctuations are due to statistical (probabilistic) nature of those processes.
By now there are several monitoring systems of the FCM neutron characteristics in operation at theShelter («Finish», «Pilot», «KSFCM»). The current measurements of neutron flux density in the locationsof neutron detectors are carried out with the help of these systems. The indications of neutron detectors areaveraged over some intervals of time, considerably larger than the neutron lifetime. So there aremeasurements of the average on-time neutron flux density.
The indications of existing FCM monitoring systems can give the information only about thetendencies of neutron flux density changes, nothing speaking about the real value of such importantcharacteristic of nuclear material accumulations as the effective multiplication factor keff. The knowledgeof keff and keeping it at the certain level is one of the requirements of regulating bodies to organization
maintaining, storing or supervising of the nuclear material accumulations.
It should be noted that the measurement of the neutron statistical characteristics can give much more
information on nuclear material accumulation parameters than simple establishment of the tendency to
reduction or growth of the neutron flux density. The methods of the analysis of the neutron flux density
fluctuations and definition on their basis of the nuclear critical characteristics are conditionally divided
into two parts: statistical discrete methods and methods of the neutron noise analysis. Both methods arebasically possible to use for the subcriticality control of nuclear material congestion in the Shelter. The
condition of modern electronics allows joining practically all methods in one experimental device
executed on the basis of personal computer, which provides processing of the information according toalgorithms determined by theoretical approaches. By now, such device is manufactured, and it is planned
to use it in the near future to measure the effective multiplication factor in FCM of the Shelter.
6.Conclusion
As it is evident from the above that the Shelter at the present time is the nuclear dangerous object, itis necessary to make the significant efforts in order to define the degree of the danger and then to make theShelter ecologically safe.
57

References
1.
2.

The Shelter Current Safety Analysis and Situation Development Forecasts (Updated Version). Tacis, 1998.
USSR State Committee on the Utilization of Atomic Energy - The Accident at the Chernobyl NPP and its
Consequences, IAEA Post Accident Meeting, Vienna, 25-29 August, 1986.
3. Pazukhin E.M. Lavalike Fuel Containing Masses of the 4th Unit of the Chernobyl NPP: Topography, Physicaland Chemical Properties, Scenario of Formation. Radiochamistry. 1994, v.36, No.2., p.97-142. (In Russian)
4. Zhidkov A.V. Fuel Containing Materials of the Shelter Today: Actual Physical Properties and the Possibility of
Their State Forecasts. The Problems of Chernobyl. No.7, p.23-40, Chernobyl 2001.(In Russian)
5. Pazukhin E.M. The Burnup and Isotope Content of the Nuclear Fuel in the lava of the 4th Unit of Chernobyl
NPP. Preprint of the ISTC “Shelter” No.00-8 Chernobyl 2001,12p. (In Russian)
6. Pazukhin E.M. Some Nuclear Physical Properties of the Fuel of the 4th Unit of Chernobyl NPP. The Problemsof Chernobyl. No.7, p.149-158, Chernobyl 2001.(In Russian)
7. Bogatov S.A., Korneev A.A., Krinitsin A.P. et al. The problem of water in the Shelter Preprint of the ISTC
“Shelter” No.99-5 Chernobyl 2001,27p. (In Russian).
8. Olkhovik Yu.A., Bondarenko G.N. Regional and Geochemical Evaluations of the radionuclide release of
ChNPP including “Hot” Particles. In “Chernobyl Accident”. Kiev, Naukova Dumka, 1995,p.203. (In Russian)
9. Borovoi A.A. Nuclear Fuel and Fission Products Release from reactor of the 4th Unit of ChNPP during theaccident. The Problems of Chernobyl. No.7, p.130-140, Chernobyl 2001.(In Russian)
10. Borovoi A.A. Fission products and Transuranic Release during Chernobyl Accident. International Conference“The fission of Nuclei – 50 Years”, Leningrad, 1989.
11. Sich A.R. The Chernobyl Accident Revisited, Part 3: Chernobyl Source Term Release Dynamics…// Nuclear
Safety. – 1995. V.36, No2.
12. Devel I., Guntay S., Powers D.A. The Chernobyl Reactor Accident Source term. OCDE/GD(96)12.- Paris, 1996.
13. Grinchenko G.P., Ogorodnik S.S., Popov V.D. et al. Thermometric measurement at the Shelter. The Questionsof the Atomic Science and Technology. Ser.Nuc.Phys.Res.1990, No.11(19), p.32-35.(In Russian)
14. Borovoi A.A., Ogorodnik S.S., Popov V.D. et al. The Evaluation of the Fuel Amount in the FCM
Accumulation of Under-Reactor Premise: (Intermidiate Report/ KE of Kurchatov Institute. .№ 11.07/26 –Chernobyl, 1990. (In Russian)
15. Kiselev A.N., Nenagliadov A.N., Surin A.I. et al. Experimental Study of the Lavalike Fuel Containing Masses(FCM) at the 4th Unit of ChNPP. М. 1992, 120 p. (Preprint of the Kurchatov IAE, №5533/3). (In Russian)
16. Borovoi А.А., Lagunenko А.S., Pazukhin E.M. Under-Apparatus Premise 305/2 of the 4th Unit of Chernobyl
NPP: Its State, Fuel Quantity Evaluation. Chernobyl 1997, 12 p. (Preprint of the ISTC “Shelter” №97-7). (InRussian)
17. Nuclear and Radiation Safety during the Operations at the “Shelter”: (Report)/ ISTC “Shelter” of the National
Academy of Sciences of Ukraine.- Archive No. 3173 - Chornobyl, 1993. (In Russian)
18. The Elaboration of Suggestions and Recommendations on Monitoring and Diagnostics of Multiplying
Properties of the LFCM of the “Shelter” of Chernobyl NPP: (Report)/ISTC “Shelter” of the National Academy of
Sciences of Ukraine. Archive No. 3234 - Chernobyl, 1993. (In Russian)
19. The Technical Justification of Nuclear Safety of the “Shelter”: (Report)/ I.I.Kurchatov Institute.-Moscow, 1990.
(In Russian)
20. V. A. Babenko, L.L. Jenkovszky, V.N. Pavlovych, et al, Fuel-Containing Masses of the Destroyed 4-th Unit of
the Chernobyl NPP: Multiplying Properties and Neutron Characteristics. Nucl.Sc.&Eng. November 1999.
21. Lebedev G.V., Shikalov V.F. The Subcriticality Measurement of the Fuel Containing Masses of theShelter. Moscow, 1995, 24 p. (Preprint of the Kurchatov IAE,No.5876/5)

58