DOCA - A MATHEMATICAL APPROACH OF THE SELF-DISINTEGRATION EXPERIMENTAL DATA.pdf

7/27/2019 DOCA - A MATHEMATICAL APPROACH OF THE SELF-DISINTEGRATION EXPERIMENTAL DATA.pdf

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NUCLEAR 2010, Pitesti, Romania

161

A MATHEMATICAL APPROACH OF

THE SELF-DISINTEGRATION EXPERIMENTAL DATA

Dr.Phys. CEZAR DOCA and Dipl.Phys. LIDIA DOCA

Institute for Nuclear Research Pitesti, Romania

[email protected]

ABSTRACT

In the frame of the SARNET/FIPRED project, the oxidation and degradation of UO2 pelletswere experimentally investigated at the Institute for Nuclear Research Pitesti, by measuring

the self-disintegration rates, the grain (fragment) size distribution and the micro-scalecharacteristics. The considered temperatures were 600-1300 K and the air concentration in

the oxidizing atmosphere ranged from 20 to 80 %. Based on these measurements, the

Romanian experimental team proposed an interpretation of the mechanisms involved in

UO2 self-disintegration by air oxidation. The authors of this paper, who didnt participated

at the mentioned tests, suggested a possible mathematical approach of the self-

disintegration experimental data using several independent variables fitting functions.

Key words: self-disintegration, mathematical approach, fitting functions

Introduction

During a severe accident in a Pressurized Water Reactor, the air ingress into a damaged reactor core

may lead to enhanced fuel oxidation, affecting some fission products release, especially increasing thatof ruthenium. A collaborative research dedicated to the ruthenium issue (ruthenium is of particular

interest because of its high radio-toxicity and due to its ability to form very volatile oxides) was

carried out in the frame of the SARNET project (Ref. [1]).

In the frame of the SARNET/FIPRED project, at the Institute for Nuclear Research Pitesti, Romania,

the oxidation and degradation of UO2 pellets were experimentally investigated by measuring: the self-

disintegration rates, the grain (fragment) size distribution and the micro-scale characteristics in thefollowing ranges: 600-1300 K for temperature, and 20-80 % for air concentration. Based on these

measurements, the Romanian experimental team proposed a particular interpretation of themechanisms involved in UO2 self-disintegration by air oxidation (Ref. [2]-[5]).

In 2009, the authors of this paper, who did not participated at the mentioned tests, analyzed the self-

disintegration experimental data using the least squares method and found a general fitting functions

( )Txtf ,, , where the three independent variables are: t = time, x = air concentration, and T =temperature (Ref. [6]-[7]).


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Achievements

Shortly: the next figures show, graphically, the self-disintegration experimental data obtained for theindicated seven domains of temperature (Figure 1) and also for the four domains of air concentration

(Figure 2).

Figure 1 Experimental data for seven domains of temperature

We only observe, above, the distinct behavior forT= 974 K.


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Figure 2 Experimental data for four domains of air concentration

Identifying, in the experimental data, the time evolution of the phenomena, and using the method ofleast squares, we found the best three independent variables fitting function:

( ) ( ) ( ) ( ) tTxTxtTxTxtf += ,,,,,

where the , and parameters are functions of the air concentrationx, and of the temperature T.

The next figures show the fitting functions adequacy with the analyzed experimental data:


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Figure 3 The fitting functions for the seven domains of temperature

Figure 4 The fitting functions for the four domains of air concentration

The most probable experimental values of, and parameters, obtained by using the method of

least squares, are presented in the next three tables.


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Applying, again, the same least squares method on the three lots of numbers, we found, as the best two

variables fitting functions, the next three expressions in the independent variablesx and T:

( ) ( ) ( )

+

++== TE

T

DxC

x

BATxTx Tx lnexplnexp,

( ) ( ) ( )

T

FTED

xCxBA

xTxTx Tx

++

++

==1

,

( ) ( ) ( )22

,TFE

TD

xCB

xATxTx Tx

+

+

+

+==

inclusive T= 974 K

and


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( ) ( ) ( )2

,TFE

TD

xCxBA

xTxTx Tx

+

+

++==

exclusive T= 974 K

Lets compare, now, the experimental values from the above three tables, and the theoretical

( )Tx, , ( )Tx, and ( )Tx, functions having the graphical representations in the next figures.

Experimental ( )Tx, Theoretical ( )Tx,

Experimental ( )Tx, Theoretical ( )Tx,

Experimental ( )Tx, - inclusive T= 974 K Theoretical ( )Tx, - inclusive T= 974 K


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Experimental ( )Tx, - exclusive T= 974 K Theoretical ( )Tx, - exclusive T= 974 K

Figure 5 Experimental,and parameters values (left), and

theoretical values for ( )Tx, , ( )Tx, and ( )Tx, functions (right)

More or less, there seems that we are near to a suggestive (analytically) retrieval of the indicatedexperimental data.

Conclusions

In the experimental data we observed a distinct behavior forT= 974 K.Rationem vero harum gravitatis proprietatum ex phnomenis nondum potui

deducere, & hypotheses non fingo. Sir Isaac Newton, Philosophi NaturalisPrincipia Mathematica*

Consequently, we searched ( )Txtf ,, , ( )Tx, , ( )Tx, and ( )Tx, functions in two cases:using all data, that is to say inclusive for T = 974 K, and using partial data, that is to say

exclusive forT= 974 K; and we found that the major differences in the functions aspect are

just for ( )Tx, function, more exactly for ( )xx function.

The ( )Txtf ,, , ( )Tx, , ( )Tx, and ( )Tx, above functions facilitate a suggestive retrieval(by calculation) of the experimental data. But:

- The ( )Txtf ,, , ( )Tx, , ( )Tx, and ( )Tx, functions dont arise from sometheoretical/phenomenological model explaining the oxidation and degradation of UO2

pellets. In fact:

- The ( )Txtf ,, , ( )Tx, , ( )Tx, and ( )Tx, expressions only are the best three/twoindependent variables fitting functions, obtained by applying the method of least squareson the indicated experimental data.

Therefore, in this moment, the ( )Txtf ,, , ( )Tx, , ( )Tx, and ( )Tx, functions must becarefully used, more in qualitative interpretations and less in quantitative extrapolations.

The more experimental data, the better fitting functions.


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References

[1] P. Giordano, A. Auvinen, G. Brillant, J. Colombani, N. Davidovich, R. Dickson, T. Haste, T.Krkel, J.S. Lamy, C. Mun, D. Ohai, Y. Pontillon, M. Steinbrck, and N. Vr, Ruthenium

Behaviour under Air Ingress Conditions: Main Achievements in the SARNET Project, The 3rd

European Review Meeting on Severe Accident Research (ERMSAR-2008), Nesseber, VigoHotel, Bulgaria, 23-25 September 2008

[2] D. Ohai, Fission Product Release from Debris Bed (FIPRED) Project Description, SARNET-STP53, INR Report No 7734/2006, 2007

[3] D. Ohai, I. Dumitrescu and T. Meleg, FIPRED: Preliminary Tests on UO2 Sintered Pellets

Disintegration, SARNET-ST-P56, 2007, INR Report No 7735/2007

[4] D. Ohai, I. Furtuna and T. Meleg,Advances in FIPRED Results at High Temperature, SARNET-

ST-P68, INR Report No 8048/2008

[5] D. Ohai, I. Furtuna, I. Dumitrescu, Mechanism of UO2 Self-disintegration by Oxidation,

International Conference Progress in Cryogenics and Isotopes Separation, Calimanesti,

Romania, October 29-31, 2008

[6] C. Doca and L. Doca,Mathematical Analyze of the Self-Disintegration Experimental Data for theUO2 Sintered Pellets by Air Oxidation, INR Report No 8412/2009 (in Romanian)

[7] D. Ohai, I. Dumitrescu, C. Doca, T. Meleg and D. Benga, FIPRED Project - Experiments andCalculations, NUCLEAR 2009, The 2nd International Conference on Sustainable Development

through Nuclear Research and Education, Pitesti, Romania, 27-29 May, 2009

*I have not as yet been able to discover the reason for these properties of gravity from phenomena,

and I do not feign hypotheses (Isaac Newton, "Philosophiae Naturalis Principia Mathematica, General

Scholium" - 1726, translation by I. Bernard Cohen and Anne Whitman, University of California Press,1999)

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DOCA - A MATHEMATICAL APPROACH OF THE SELF-DISINTEGRATION EXPERIMENTAL DATA.pdf