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                                Development
                         of a Matrix Alteration
                                Model (MAM)




                                     enresa
                                      publicación técnica 01/2005
       Development
of a Matrix Alteration
       Model (MAM)


               A. Martínez Esparza, M. A. Cuñado, J. A. Gago
                                                     ENRESA
  J. Quiñones, E. Iglesias, J. Cobos, A. González de la Huebra
                                                       CIEMAT
                                  E. Cera, J. Merino, J, Bruno
                                                     ENVIROS
                 J. de Pablo, I. Casas, F. Clarens, J. Giménez
                                                          UPC
ENRESA
Dirección de Ciencia y Tecnología
Emilio Vargas nº 7
28043 Madrid - España
Tfno.: 915 668 100
Fax: 915 668 169
www.enresa.es
Diseño y producción: TransEdit
Imprime: GRAFISTAFF, S.L.
ISSN: 1134-380X
D.L.: M-15427-2005
Abril de 2005
This report has been drawn up on behalf of ENRESA.
It represents the opinion of the contractor wich need not
necessarily coincide with that of ENRESA in every respect.
The authors of the documents would like to remark their acknowledgement to the European
Commission for supporting the “SFS – project” (Contract nº: FIKW-CT-2001-20192 SFS).
This work had been done under this agreement.
To the SFS colleagues and their companies for their constructive comments and critics that al-
lowed to obtain a more robust model.
Contents




           Contents
Contents
                                                                                                           Contents




RESUMEN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5

FOREWORD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9

LIST OF ACRONYMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

0. EXECUTIVE SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15

1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19
   1.1. Review of the available model and development of a conceptual approach based
        on the major processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
         1.1.1. Process 1. Generation of oxidants and reductants by water radiolysis . . . . . . . . . . . . . 22
         1.1.2. Process 2. Oxidation of the spent fuel matrix and other redox sensitive radionuclides . . . . . . 22
         1.1.3. Process 3. Reduction of the oxidants present in the system . . . . . . . . . . . . . . . . . . 22
         1.1.4. Process 4. Dissolution of the spent fuel matrix and radionuclides release . . . . . . . . . . . . 22
         1.1.5. Process 5. Precipitation of secondary solid phases (developed in WP5) . . . . . . . . . . . . 23
         1.1.6. Code Intercomparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2. MATHEMATICAL MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25
   2.1. Oxygen promoted mechanismfor the oxidation of the matrix. . . . . . . . . . . . . . . . . . . . . 27
   2.2. Hydrogen peroxide promoted mechanism for the oxidation of the matrix . . . . . . . . . . . . . . . 27
   2.3. Hydrogen promoted mechanism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
   2.4. Mechanisms accounting for the dissolution of the oxidised UO2 co-ordinates sites. . . . . . . . . . . . 28

3. MODEL VALIDATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31
   3.1. Non irradiated UO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
         3.1.1. Flow through experiments with non irradiated UO2 in a oxygen atmosphere . . . . . . . . . . 34



                                                                                                                 III
Development of a Matrix Alteration Model (MAM)



                                                 3.1.1.1. Experimental results and semi-empirical models . . . . . . . . . . . . . . . . . . 34
                                                 3.1.1.2. Model calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
                                        3.1.2. Flow through experiments of non-irradiated UO2 with hydrogen peroxide. . . . . . . . . . . . 37
                                                 3.1.2.1. Experimental results and fitting of the data . . . . . . . . . . . . . . . . . . . . 37
                                                 3.1.2.2. Model calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
                                   3.2. Alpha doped material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
                                        3.2.1. Flow through experiments with alpha doped UO2 powder. . . . . . . . . . . . . . . . . . . 42
                                                 3.2.1.1. Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
                                        3.2.2. Batch experiments with alpha doped UO2 pellets . . . . . . . . . . . . . . . . . . . . . . 44
                                                 3.2.2.1. Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
                                                 3.2.2.2. Model validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
                                        3.2.3. Batch experiments at high hydrogen pressures with alpha doped UO2 pellets . . . . . . . . . . 46
                                                 3.2.3.1. Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
                                   3.3. Spent fuel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
                                        3.3.1. Flow through experiments in carbonated waters under oxidising conditions. . . . . . . . . . . 49
                                                 3.3.1.1. Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
                                                 3.3.1.2. Model validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
                                        3.3.2. MOX fuel static leaching at high H2 pressure. . . . . . . . . . . . . . . . . . . . . . . . . 51
                                        3.3.3. Fuel pellet static corrosion in brine at 3.2 bar H2 overpressure. . . . . . . . . . . . . . . . . 53
                                   3.4. SIMFUEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
                                        3.4.1. Experimental details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
                                        3.4.2. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

                               4. BASE CASE CALCULATIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59
                                   4.1. General parameters for the base case calculations. . . . . . . . . . . . . . . . . . . . . . . . . . 61
                                   4.2. Boundary conditions and parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
                                   4.3. Granite reference case calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
                                   4.4. Base case calculation in salt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
                                        4.4.1. Base case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
                                        4.4.2. Base case with the new Cl2- reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
                                        4.4.3. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
                                   4.5. Comparison of results in different media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
                                   4.6. Comparison with published rates and rate laws . . . . . . . . . . . . . . . . . . . . . . . . . . 70
                                   4.7. Base case calculation in clays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
                                        4.7.1. General parameters used for the clay reference case . . . . . . . . . . . . . . . . . . . . . 73
                                        4.7.2. Clay reference calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
                                        4.7.3. Comparison between granite and clay reference case . . . . . . . . . . . . . . . . . . . . 74
                                   4.8. Matrix alteration rates of the reference cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
                                   4.9. Sensitivity analysis of MAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77



IV
                                                                                                          Contents



         4.9.1. Influence of the specific surface area of the pellet . . . . . . . . . . . . . . . . . . . . . . 80
         4.9.2. Influence of carbonate concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
         4.9.3. a range and pellet burnup influence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
         4.9.4. Canister resistance and the hydrogen influence . . . . . . . . . . . . . . . . . . . . . . . 85

5. APPLICABILITY OF THE MAM AND CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
   5.1. Spent fuel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
   5.2. Processes affecting spent fuel matrix alteration . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
   5.3. Boundary conditions and geometrical parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 94
   5.4. Specific a-activity threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
   5.5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

6. REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .97




                                                                                                                 V
Resumen




          Resumen
Resumen
                                                                                                         Resumen



El presente documento recoge las principales tareas       simplificado de oxidación del UO2 por H2O2 a tra-
llevadas a cabo por ENRESA y colaboradores en el          vés del radical hidroxil ha sido clave para
marco del proyecto SFS (Spent Fuel Stability) del 5º      reproducir la interacción observada experimental-
Programa Marco de la Comisión Europea. Dicha              mente entre el H2O2 y el carbonato presente en so-
participación se ha centrado en el desarrollo del         lución.
Modelo de Alteración de la Matriz (MAM), un mo-
delo para estudiar la alteración/disolución oxidante      Una vez desarrollado el modelo, se ha aplicado a
a largo plazo del combustible nuclear gastado en          ejercicios genéricos de Evaluación del Comporta-
condiciones de repositorio.                               miento según un caso base definido en dos medios
                                                          geológicos, granito y arcilla. Dicho caso base con-
Dentro del objetivo general de desarrollo del mode-       sidera una concentración inicial de hidrógeno que
lo, se han llevado a cabo las siguientes actividades:     se mantiene constante durante todo el tiempo de
desarrollo del modelo conceptual, integración del         evaluación y que se corresponde con la atmósfera
mecanismo de alteración de la matriz en el modelo         de hidrógeno generada por la corrosión de las par-
radiolítico, calibración y prueba del modelo, cálcu-      tes metálicas del sistema de repositorio. Los resulta-
los para el caso base en ejercicios de evaluación         dos de la modelación indican una disminución de
del comportamiento, análisis de sensibilidad y eva-       las velocidades de disolución a medida que trans-
luación de la aplicabilidad del MAM.                      curre el tiempo en ambos medios geológicos. Di-
                                                          cha disminución es debida a la disminución de la
El modelo conceptual de la disolución oxidante del        tasa de dosis alfa. Por otra parte, las velocidades
UO2 se basa en los procesos que se espera tengan          de alteración de la matriz en arcilla son ligeramente
lugar a largo plazo en condiciones de repositorio.        inferiores a las velocidades calculadas en granito.
Cuando el agua subterránea penetre en las proxi-          Esta diferencia es atribuible a las diferentes concen-
midades del combustible nuclear gastado, el primer        traciones de carbonatos y diferentes pH de las
proceso que ocurrirá será la radiólisis del agua. Di-     aguas subterráneas.
cha radiólisis generará oxidantes y reductores, dan-
do lugar a condiciones localmente oxidantes que           Las velocidades de disolución obtenidas en los cál-
provocarán la oxidación de la superficie del com-         culos del caso base se han comparado con el ran-
bustible. La presencia de agentes complejantes en         go de velocidades de disolución calculadas con
solución favorecerá la disolución de las especies del     modelos empíricos o semi-empíricos publicados en
componente mayoritario de la matriz, el uranio, que       la literatura. El análisis comparativo indica que la
se encuentre oxidado en la superficie.                    extrapolación de los modelos empíricos y semi-em-
                                                          píricos que incluyen una dependencia explícita del
La integración del mecanismo de alteración de la          oxígeno o del peróxido de hidrógeno predicen unas
matriz (oxidación y disolución) en el modelo radiolíti-   velocidades de disolución en buen acuerdo con las
co por medio de reacciones elementales se ha lleva-       calculadas en el caso base. Por el contrario, aque-
do a cabo a partir de modelos mecanísticos desarro-       llos modelos sin dependencia explícita respecto al
llados para interpretar experimentos de disolución        oxígeno o al peróxido de hidrógeno predicen velo-
con UO2 no irradiado. Las constantes cinéticas del        cidades mayores a las calculadas en el caso base.
mecanismo de disolución oxidativa han sido calibra-
das a partir de experimentos de disolución de UO2         Para el caso base en granito se ha llevado a cabo
en continuo. El modelo desarrollado ha sido capaz         un análisis de sensibilidad. De este análisis se des-
de reproducir las velocidades de disolución experi-       prende que la presencia de la radiación alfa es el
mentales para un rango de pH > 5 y [HCO3-] <              principal parámetro para producir la alteración de
10-2 M cuando el oxidante es O2 a presiones parcia-       la pastilla de UO2 en ausencia de oxidantes. Otros
les inferiores al 21 %, y para un rango 3 < pH < 9        parámetros clave para obtener extrapolaciones rea-
y [HCO3-]=2·10-3 M y cuando el oxidante es H2O2           listas son la proporción área/volumen (densidad de
a concentraciones inferiores a 10-4 M. Estas condi-       puntos de coordinación, superficie específica de la
ciones cubren el rango de condiciones geoquímicas         pastilla), concentración de carbonatos y la presen-
esperadas en un repositorio, con independencia del        cia de hidrógeno en el sistema.
medio geológico considerado. Por otra parte, el pro-
ceso de calibración ha permitido obtener una visión       Por último, cabe destacar que el modelo MAM tie-
más detallada del mecanismo de alteración del UO2         ne un gran rango de aplicabilidad con independen-
en presencia de agua. En particular, el mecanismo         cia de las condiciones ambientales del repositorio



                                                                                                              3
Development of a Matrix Alteration Model (MAM)



(geometría, tipo de tasa de dosis, química de las      continuo con combustible gastado y reactores está-
aguas subterráneas, etc.), y ha dado resultados fia-   ticos con análogos químico-físicos del combustible
bles al aplicarlo en experimentos con sistemas en      irradiado a largo plazo (UO2 con emisores alfa).




4
Abstract




           Abstract
Abstract
                                                                                                           Abstract



The present report is a summary of the main tasks         UO2 oxidation by H2O2 involving hydroxyl radicals
carried out within the WP4 of the SFS project (5th        has been useful in reproducing the observed inter-
Framework Programme of the European Commis-               action between H2O2 and carbonate present in
sion) by ENRESA and collaborators, mainly focused         solution.
on the development of the so-called Matrix Alter-
ation Model (MAM), a model to study the long-term         Base case calculations for PA exercises have been
oxidant dissolution of the spent fuel matrix under        done in two different media, granite and clay. The
repository conditions.                                    base case considers an initial hydrogen concentra-
                                                          tion that is kept constant during all the evaluation
A variety of issues have been addressed: develop-         time corresponding to the expected hydrogen atmo-
ment of the MAM conceptual model, integration of          sphere due to the corrosion of metallic parts in the
a new matrix alteration mechanism in the radiolytic       repository system. Modelling results indicate a de-
model, calibration and testing of the model, calcu-       crease of the dissolution rates with time in both me-
lations for base case in Performance Assessment ex-       dia. This decrease is related to the a dose rate de-
ercises, sensitivity analysis and an assessment of        crease. In addition, matrix alteration rates in clay
applicability of the MAM.                                 are slightly lower than the ones calculated in gran-
The conceptual model for the UO2 oxidant dissolu-         ite. This difference is mainly explained by the differ-
tion is based on the processes expected to occur in       ent carbonate concentrations and/or pH of both
the long term under repository conditions. Briefly,       groundwater’s.
when water will enter in contact with the fuel sur-       Dissolution rates obtained in the base case calcula-
face, the first process we may expect is the radiolysis   tions have been compared to the range of dissolution
of water. Water radiolysis will generate reductants       rates calculated by using empirical or semi-empirical
and oxidants and we may expect local oxidising            models from the literature. The comparative analysis
conditions. Because of these local conditions, the        indicates that the extrapolation of empirical and
surface of the fuel will be oxidized. The oxidation of    semi-empirical models with some oxygen or hydro-
the matrix and the attachment of aqueous ligands          gen peroxide dependence predict dissolution rates in
able to form strong complexes with its major com-         quite good agreement with the ones calculated in the
ponent will favour the dissolution of the matrix.         base cases. On the contrary, those models without
The integration of the matrix alteration (oxidation       oxygen or hydrogen peroxide dependence overesti-
and dissolution) mechanism in the radiolytic model        mate those dissolution rates calculated for the base
by means of elemental reactions has been mainly           cases.
elucidated from the mechanistic models developed          A sensitivity analysis has been carried out for the
for non-irradiated UO2 dissolution experiments.           granite reference case and for the evaluation range.
Moreover, flow-through dissolution experiments with       This analysis points out that for this model the pres-
unirradiated UO2 have been used to calibrate the          ence of a radiation field is the main parameter for
oxidative dissolution mechanism of UO2. The model         producing the alteration of the pellet in absence of
developed has been able to reproduce experimental         the oxidants. There are other key parameters that
dissolution rates for pH > 5 and [HCO3-] < 10-2 M         are necessary to establish in order to obtain a real-
when the oxidant is O2 at partial pressures lower         istic extrapolation, i.e., S/V ratio (co-ordination site
than 21%, and 3 < pH < 9 and [HCO3-] = 2·10-3             density, specific surface area of the pellet), carbon-
M and when the oxidant is H2O2 at concentrations          ate concentration, presence of hydrogen in the sys-
below 10-4 M. These ranges cover the geochemical          tem.
conditions we may expect in the repository with no
dependence on the geological medium studied.              Finally, MAM has proved a large applicability with
Furthermore, the calibration process has provided         independence of the environmental repository con-
some insight into the detailed mechanisms taking          ditions (geometry, type of dose rate, groundwater
place in the alteration of UO2 in the presence of         chemistry, etc.). The MAM model has given reliable
water. In particular, the simplified mechanism of         results using flow-through and batch reactors.




                                                                                                                 7
Foreword




           Foreword
Foreword
                                                                                                        Foreword



The present work has been developed in the scope         dinella), SKB (P. Carbol), SCK.CEN (K. Lemmens), FzK
of the 5th Framework Programme (2001-2004) of            (A. Loida), EMN (B. Grambow)
the European Commission into SFS (Spent Fuel Sta-
bility) Project which objective was the development      To WP1 co-ordinated by CEA (C. Poinssot) thus the
of a reliable and robust model as a function of time     total project, by supply the selection and data of
for prediction of long term spent fuel behaviour in      spent fuel to be study and discussions on dose rate
repository conditions, based in experimental tests       to use in radiolytic models (B. Grambow).
carried out in the present and afore projects.           To WP2 FzK (M. Kelm) for supply the reactions and
                                                         constants to be used in the radiolytic model, and in-
In the framework of the SFS project, ENRESA has
                                                         puts and discussions on saline base case.
co-ordinated the Work Package 4 in charge of de-
veloping the Matrix Alteration Model, a model fo-        And finally to Nagra (L. Johnson) by integration of
cused on the long-term alteration/dissolution of         the Instant release Model developed by WP1, fo-
UO2, the main constituent of the spent fuel matrix       cused on defining, the fraction of inventory of labile
(95-97%). The present report is a summary of the         safety relevant nuclides that may be rapidly released
main tasks carried out and results obtained within       from the gap fuel and fuel assembly materials and
this work package by ENRESA and its collaborators:       the Matrix Alteration Model WP4 and their contribu-
CIEMAT, Enviros and UPC. Their close collabora-          tion to define the boundary conditions and supply of
tion has been crucial to succeed in achieving the        the Opalinus clay water for clay base case.
project goals.
                                                         The authors gratefully acknowledge every one of the
The authors wants to thanks, especially to WP·3.Ex-      WP4 participants, their national institutions and aut-
perimental work, co-ordinated by K.Spahiu of SKB,        horities and the European commission, the collabo-
which close cooperation has been possible the inte-      ration in the development of the work committed:
gration of the experimental results on time, for cali-   ANDRA (Z. Andriambolona), CEA (C. Jegou), EMN
bration and validation of the model. Experiments         (B. Grambow), FzK (V. Metz, A. Loida) and SKC (K.
carried out by ITU (D. Wegen, D. Serrano, V. V. Ron-     Spahiu).




                                                                                                             11
                    List of Acronyms

AP:        Activation Product
BCW:       Boom Clay Water
CEA:       Commissariat Energie Atomique (France)
CIEMAT:    Centro de Investigaciones Mediambientales y Tecnológicas (SPAIN)
CW:        Carbonated Water
EMN:       École des Mines de Nantes (France)
ENRESA:    Empresa Nacional de Residuos Radiactivos, SA (SPAIN)
GB:        Granite Groundwater
GBW:       Granitic Bentonite Groundwater
INE-FzK:   Institute für Nucleare Entsorgung. Forschungszentrum Karlsruhe (Germay)
IRF:       Instant Release Fraction
ITU-JRC:   Institute for Transuranic Elements: Karlsruhe
MAM:       Matrix Alteration Model
MQ:        Deionised Water
NAGRA:     NAtionale Genossenchaft für die lagerung Radioaktive Abfalle (Swizerland)
PA:        Performance Assessment
RN:        Radionuclide
SCK·CEN: StudieCentrum voor Kernernergie - Centre d’ Etude de l’Énergie Nucléaire (Belgium)
SF:        Spent Fuel
SFS:       Spent Fuel Stability
SHE:       Standard Hydrogen Electrode
SKB:       Svensk Kärnbränslehantering AB (Sweden)
0. Executive Summary




           0. Executive Summary
0. Executive Summary
                                                                                                     0. Executive Summary



This work reports on the mathematical development             been included. Following is a summary with some
of the conceptual Matrix Alteration Model (MAM)               conclusions extracted from the modelling work car-
with three main items:                                        ried out by using the experimental data generated by
                                                              the different laboratories.
  o   The integration of the matrix alteration mecha-
      nism in the radiolytic model                            Dissolution data obtained from alpha-doped material
  o   The calibration and testing of the model and            in Boom clay waters by SCK-CEN is quite controver-
                                                              sial when comparing to the general behaviour we
  o   The base case calculations                              might expect under their experimental conditions.
The integration of the matrix alteration (oxidation and       Flow-through experiments were performed in order to
dissolution) mechanism in the radiolytic model by             study the alteration behaviour of the spent fuel matrix
means of elemental reactions has been mainly eluci-           by avoiding precipitation of secondary solid phases.
dated from the mechanistic models developed for               However, the complexity of the groundwater compo-
non-irradiated UO2 dissolution experiments with oxy-          sition used in the dissolution tests leads to a difficult
gen (de Pablo et al., 2003; de Pablo et al., 2004; de         interpretation of the results The authors attribute the
Pablo et al., 1999; Giménez et al., 2001) as well as          dissolution behaviour to the presence of humic sub-
from the work performed by Ekeroth et al. (Ekeroth            stances acting as H2O2 scavenger and/or surface
and Jonsson, 2003) with hydrogen peroxide.                    passivators. In addition, the complexing capacity of
                                                              these substances cannot be neglected and conse-
Flow-through dissolution experiments with unirradia-          quently surface complexation processes might have
ted UO2 have been used to calibrate the oxidant dis-          an important role in such systems. The presence of
solution mechanism of UO2. The model developed                humic substances prevents a straightforward way of
has been able to reproduce experimental dissolution           interpreting the experimental results from a model-
rates for pH > 5 and [HCO3-] < 10-2 M when the                ling point of view. On the other hand, the high con-
oxidant is O2 at partial pressures lower than 21%,            tent of uranium in the water is an additional prob-
and 3 < pH < 9 and [HCO3-] = 2·10-3 M when the                lem in the quantification of very low uranium
oxidant is H2O2 at concentrations below 10-4 M.               concentrations.
These ranges cover the geochemical conditions we
may expect in the repository with no dependence on            ITU carried out static dissolution experiments in three
the geological medium studied. Moreover, the cali-            environmental conditions by using alpha doped with
                                                              233
bration process has provided some insight into the               U material. The results reveal that there is an im-
detailed mechanism taking place in the alteration of          portant influence of the pre-oxidation of the surface
UO2 in the presence of water. In particular, the sim-         sample on the dissolution data masking in some
plified mechanism of UO2 oxidation by H2O2 involv-            cases the proper dissolution process given by the test
ing hydroxyl radicals has been useful in reproducing          conditions. The authors suggest that this pre-oxida-
the observed interaction between H2O2 and carbon-             tion should depend on the alpha activity of the sam-
ate present in solution.                                      ples. There is no correlation between the initial re-
                                                              lease due to this pre-oxidation and the environmental
Model testing has been done with data generated
                                                              conditions. Modelling dissolution data with the MAM
within WP3. SCK-CEN and ITU worked with alpha
                                                              has been done by taking several hypotheses in
doped materials at different environmental condi-
                                                              agreement with the experimental observations. That
tions, i.e. reducing, anoxic and oxidising. In addition,
                                                              is, most of the results have been predicted by the
FzK-INE and ITU performed dissolution experiments
                                                              model when considering a pre-oxidation of the sur-
with spent fuel in brines and reducing conditions and
                                                              face sample and in some cases the modelling work
in carbonated water and oxidising conditions respec-
                                                              has been performed assuming a oxygen concentra-
tively. It is important to highlight that this testing pro-
                                                              tion in agreement with the one expected in the
cess has been based on the information available
                                                              glove-box according to the quality assurance system.
from the different experimental groups, that is, envi-
                                                              Based on these assumptions, the fitting of the model
ronmental conditions, experimental results and data
                                                              to the experimental data has been possible in most of
interpretation given the delay in the reports including
                                                              the studied cases.
all this information (D9 (Grambow et al., 2004) and
D10 (Spahiu et al., 2004)). Further information re-           In addition, different experimental series were car-
lated to new experimental evidences, changes in the           ried out at different hydrogen pressures in order to
environmental conditions etc. given by the authors            study the hydrogen effect on the matrix alteration.
during the revision process of this report have not           Dissolution data reveal that there is no dissolution



                                                                                                                      17
Development of a Matrix Alteration Model (MAM)



with time indicating probably a solubility control.         termining the influence of the ( radiation on the
However, the D9 (Grambow et al., 2004) -D10                 spent fuel matrix alteration rate under simulated re-
(Spahiu et al., 2004) reports should give some evi-         pository conditions. The results obtained in this study
dences or new findings about the processes imply-           show different behaviour as a function of both the
ing some interaction between the hydrogen and the           solution composition and the initial atmosphere. As
fuel matrix, i.e. surface passivation by the hydrogen       a preliminary conclusion, we may say that under
molecule and/or formation of the radical ·H with            reductants conditions (H2=1 bar), gamma radiation
the consequent reduction of the oxidised uranium. It        has a beneficial effect at short contact times since U
is well known based on experimental evidences               concentrations determined in solution are very low
((Loida et al., 2004; Quiñones et al., 2004; Röllin         indicating that the overall alteration rate is mini-
et al., 2001; Sunder et al., 1990), among others)           mised in the presence of the gamma source. For
that there is some interaction between the hydrogen         times longer than one day, there is a clear increase
and the fuel matrix that leads to lower matrix alter-       of the U concentrations in solution.
ation rates. However, the mechanisms taking place
are not still well described and further experimental
                                                            At this stage of the project, base case calculations
work is necessary. In this context, the NF-PRO Pro-
                                                            have been done in two different media, granite and
ject includes more experimental effort directly ad-
                                                            salt and based on the D12 report (Martínez Esparza
dressed to elucidate these processes. The interpreta-
                                                            et al., 2004b). The base case considers an initial hy-
tion of new experimental data based on some of
                                                            drogen concentration that is kept constant during all
these mechanisms as well as the determination of
                                                            the evaluation time corresponding to the expected
their parameters will allow including these processes
                                                            hydrogen atmosphere due to the corrosion of metal-
in a matrix alteration model in the next future.
                                                            lic parts in the repository system. Modelling results in-
Dissolution data obtained from alpha doped sam-             dicate a decrease of the dissolution rates with time in
ples are important since this type of material is able      both media. This decrease is related to the alpha
to give us relevant information on the spent fuel be-       dose rate decrease. There is a difference between
haviour in the midterm under repository conditions.         both dissolution rates of roughly two orders of mag-
Flow-through tests should continue in the future with       nitude, being higher in the granite base case. This
doped material in order to determine dissolution            difference is mainly attributed to both the presence of
rates by avoiding parallel processes. These studies         a significant amount of carbonate in the granitic wa-
should be focused on determining the alteration (ox-        ter enhancing the matrix dissolution rate as well as
idation and dissolution) of the matrix as a function        the different radiolytic yields in brines with respect to
of the main environmental parameters such as, pH,           the ones in pure water that produce a less oxidant
carbonate and chloride concentrations and under             environment. This comparative analysis highlights the
anoxic and reducing conditions in order to quantify         determinant role of carbonates on predicting long-
the radiolysis effects.                                     term dissolution rates.
Spent fuel data are also very valuable since they
give us information on the expected dissolution be-         Finally, dissolution rates obtained in the base case
haviour at short term in time, that is, after closure of    calculations have been compared to the range of
the repository. In addition, this material gives addi-      dissolution rates calculated by using empirical or
tional and very valuable information on the release         semi-empirical models from the literature, when ap-
behaviour of the radionuclides embedded in the              plying the same environmental conditions as the ones
spent fuel matrix. Dissolution data obtained from           used in the base case calculations. The comparative
spent fuel powdered samples in flow-through tests           analysis indicates that the extrapolation of empirical
carried out in the hot cell laboratories at ITU have        and semi-empirical models with some oxygen or
been used as a testing exercise with a quite good           hydrogen peroxide dependence predict dissolution
result in the modelling work.                               rates in quite good agreement with the ones calcula-
                                                            ted in the base case. On the contrary, those models
Much work should be focused on studying different
                                                            without oxygen or hydrogen peroxide dependence
spent fuel samples (for instance in size, in burn up) un-
                                                            overestimate those dissolution rates calculated for the
der anoxic and reducing conditions in order to study
                                                            base cases, both in granite and in salt. This analysis
the radiolysis effects on the spent fuel alteration.
                                                            highlights once again these oxidant compounds as
Dissolution studies of SIMFUEL solid samples irradi-        one of the main variables of the system when predic-
ated with a (-radiation source were focussed on de-         ting long-term matrix alteration/dissolution rates.



18
1. Introduction




                  1. Introduction
1. Introduction
                                                                                                         1. Introduction



Assessing the performance for spent nuclear fuel in        of spent fuel (Bruno et al., 1996; Bruno et al., 1998;
a potential future geological disposal system re-          Cera et al., 2000; Quiñones et al., 2000).
quires an understanding of the important time-de-
                                                           The workpackage activities started, with a workshop
pendent phenomena influencing its behaviour on a
                                                           held in Avila, for presentation and discussion of the
time-scale up to millions of years. Such a demand-
                                                           different models approaches and on understanding
ing goal requires the development and qualification
                                                           of the alteration/dissolution processes, based on
of models predicting the long-term release rate of
                                                           these experiences, to allow the system to be cor-
radionuclides. Such models are usually referred to
                                                           rectly formulated in terms of oxidants consumption
as ”Source term models”. The aim of the Spent Fuel
                                                           and uranium and radionuclide release, assuming
Stability project is to develop a reliable and robust
                                                           that the radionuclides embedded in the matrix will
model for the spent fuel source term which could
                                                           dissolve with the same rate that the UO2 matrix.
then be used with confidence in the performance
assessment exercise, whatever the countries and dis-       The review of these different models, radiolytic, ther-
posal system designs are applied.                          modynamic and electro-geochemical models were
                                                           published, thus of the proceedings (Martínez Espar-
Radionuclide source terms for spent nuclear fuel are       za et al., 2002).
schematically composed of two contributions:
                                                           These documents and Discussions with WP2, WP3
  i. the so-called Instant Release Fraction (IRF)          and WP5 participants have constituted the basis to
     which to be instantaneously released when wa-         build the conceptual model. This basis and the con-
     ter arrives into the waste package and which          ceptual model are described in detail in the D12 of
     corresponds to the radionuclides located either       the project “Conceptual Model of the Matrix Alter-
     at the interface between the cladding and the         ation Model (MAM)” (Martínez Esparza et al.,
     pellet (gap), or in the grain boundaries, fracture    2004b). The final objective is to give a tool, for
     and voids.                                            WP5, capable of predicting the spent fuel matrix al-
                                                           teration with independence of environmental condi-
  ii. the release of the radionuclides located within      tions.
      the grains as a consequence of the alteration
      of the matrix.                                       The stability of the spent fuel will depend on a few
                                                           variables of the system: Groundwater (pe, pH and
The objective in this WP4, as was redefined in the         its composition, i.e, the carbonate and Chloride
kick-off meeting of the project, it was focused on the     contents as the main aqueous ligands, constitute the
development of the matrix alteration model (MAM),          master variables of this chemical system), tempera-
specially oxidant dissolution, based in experimental       ture, pressure. Among these, the pe is the most criti-
data developed in the present project, mainly in WP3       cal one.
and something in WP2 and in WP4, as support of             The main processes affecting the oxidation and dis-
the radiolysis scheme and reactions constants.             solution of the spent fuel matrix and consequently
                                                           affecting radionuclide release are depicted sche-
The instant release fraction and the release model
                                                           matically in the Figure 1-1.
have been developed by the WP1 and WP5 respec-
tively. The synthesis is developed within the WP5          When water enters in contact with the surface of the
with the support of the rest of WPS.                       fuel, the first process we may expect is the radiolysis of
                                                           water. This radiolysis generate oxidants and reductants
                                                           and, in spite of nominally anoxic or reductant condi-
1.1. Review of the available model                         tions we can expect local oxidizing conditions.
     and development                                       Due to these local oxidant conditions, the surface of
                                                           the fuel will oxidize as well as other redox sensitive
     of a conceptual approach based                        radionuclides with the destabilization of the matrix
     on the major processes                                (*). The attachment of aqueous ligands available to
                                                           form strong complexes with its major component will
There are a large work carried out on the develop-
                                                           favour the dissolution of the matrix and the conse-
ment and testing of source term models developed in
                                                           quent release of Rn’s embedded in it.
the former EU framework program (1994-1998) and
on the development of a simplified kinetic model based     Finally, the precipitation of pure or mixed secondary
on mass balance equations for the radiolytic dissolution   solid phases is expected if solubility limits are



                                                                                                                    21
Development of a Matrix Alteration Model (MAM)




                                                       a, b,g                   H2O
                                                                                                              Water radiolysis
                                                                        Generation of oxidants
                                                                          (H2O2, O2, H2…)
                      UO2

                                   UO2+x                  e
                                                           -
                                                                                                   Oxidation of the fuel matrix

                                                               Attachment aqueous ligands
                                                                      (H2O, HCO3-)
                                                                                                      Dissolution of the matrix
                                                         Detachment
                                                          U(VI)(aq)



                                                                                                 Precipitation of 2i solid phases
                                                 “UO3·2H2O(s)”
                                                 “UO4·4H2O(s)”




                                                                                                  Figure 1-1. Conceptual model scheme.




reached. The main processes to take into consider-                    1.1.3. Process 3. Reduction of
ation as well as the approaches to be used are de-
scribed hereafter:
                                                                             the oxidants present in the system
                                                                      Reduction processes will occur according to the fol-
1.1.1. Process 1. Generation of oxidants                              lowing reactions
       and reductants by water radiolysis
                                                                                         O 2 + 2H 2O + 4e - Þ 4OH-                       (1.2)
H2O + radiolysis ® oxidants + reductants. The
main oxidants generated by radiolysis or recombi-                                           H 2O 2 + 2e - Þ 2OH-                         (1.3)
nation reactions are O2, H2O2 and radicals like
·
  OH, ·CO3 etc. The main reductant generated
                                                                                      (U, Rn' s) O 2( s) Þ Rn+ n + U( VI )(aq )          (1.4)
radiolytically is H2.


1.1.2. Process 2. Oxidation of the spent                              1.1.4. Process 4. Dissolution
       fuel matrix and other redox                                           of the spent fuel matrix
       sensitive radionuclides                                               and radionuclides release
                        U(IV) ® U(VI)                 (1.1)           U(VI) speciation in the aqueous phase will depend
                                                                      on the groundwater composition contacting the fuel.
In groundwater systems with chloride concentrations                   The radionuclides embedded in the matrix are as-
above 2 mol/dm3, other oxidants such as OH-, Cl-,                     sumed to be congruently dissolved although this
ClO3- radicals and HClO are relevant.                                 work is done in WP5.



22
                                                                                                                                         1. Introduction



1.1.5. Process 5. Precipitation                                              culty to handle heterogeneous systems, and a lack
                                                                             of model validation.
       of secondary solid phases
       (developed in WP5)                                                    In order to gain confidence in the uses of this kind
                                                                             of models, an Intercomparison exercise between two
There is a limited knowledge about the precipitation
                                                                             kinetics codes, ”Chemsimul” (Kirkegaard and Bjerg-
kinetics and solid phases in repository conditions.
                                                                             bakke, 1999) and “Maksima” (Carver et al., 1979)
The lack of information on precipitation kinetics has
                                                                             has been carried out (Quiñones et al., 2003a).
made necessary to simplify the system and consider
a thermodynamic approach.                                                    The kinetics reactions related to the matrix alteration
This is the main difference with the three first pro-                        rate are a simplified version of the reactions sup-
cesses which are studied kinetically.                                        plied by the WP2 (Kelm and Bohnert, 2004). Figure
                                                                             1-2 shows a comparison of the output data ob-
Like the dissolution process, precipitation of second-
                                                                             tained by both codes. The differences in the worst
ary phases will depend on water chemistry inside the
                                                                             case are lower than 1%. They are linked to the dif-
canister: pH, pe and concentration of complexing
                                                                             ferent integration method used for solving the differ-
anions. Radiation Source strength has showed the
                                                                             ential equations, numerical precision used in each
formation of different phases. Formation of scho-
                                                                             code, whether the G-values, kinetics constants have
epite UO3·XH2O and studtite UO4·4H2O or ura-
                                                                             more or less digits.
nium peroxides at lower and higher alpha radiation
fields (Clarens et al., 2003b; Díaz Arocas et al.,                           The boundary conditions as well as the parameters
1995; Grambow et al., 2004; McNamara et al.,                                 needed for the development of the mathematical
2003; Spahiu et al., 2004).                                                  and numerical model have been also summarized
                                                                             and discussed in the D12 (Martínez Esparza et al.,
1.1.6. Code Intercomparison                                                  2004b).

Radiolytic models do not have a wider acceptance                             Boundary conditions include characterization of the
due to limited availability of kinetic data, the diffi-                      spent fuel, groundwater compositions, and canister




                                                                             time / s
                                        0               2x106                      4x106                    6x106

                                                                                                                       UO3
                                                                                                                       H2O2
                                0.8 %
                                                                                                                       H2
                                                                                                                       H2(g)
                                                                                                                       O2
                                0.6 %                                                                                  O2(g)
                   Diference




                                0.4 %



                                0.2 %



                                0.0 %



                               -0.2 %




           Figure 1-2. Differences obtained in the output data as a function of the code used (Maksima or Chemsimul (Quiñones et al., 2003a)).



                                                                                                                                                    23
Development of a Matrix Alteration Model (MAM)



and cladding characteristics relevant for the MAM,      radiolysis processes and alteration of the matrix.
temperature and evaluation time.                        This main parameters and assumptions are summa-
                                                        rized in Table.4-1.
Parameters of relevance for the model development
are the geometry of the system and associated pa-       Main discussion were about the calculation of maxi-
rameters as radiation field, hydraulic parameters for   mum or mean dose rate and depth of the irradiated
considering a water turnover, and kinetic reactions     water layer, that as can be seen in the sensitivity
for considering generation and recombination by         analysis have a great influence on alteration rate.




24
2. Mathematical Model




       2. Mathematical Model
2. Mathematical Model
                                                                                              2. Mathematical Model



The development of the Matrix Alteration Model is             >UO2-O2 + >UO2 Y 2>UO3               Fast   (eq. 3)
summarized in D13. ”Mathematical Model Develop-
ment and Experiments Integration in the MAM”             The rate determining step will be the first reaction,
(Martínez Esparza et al., 2004c).                        that is, the adsorption of the oxygen molecule to the
                                                         first co-ordination site. Consequently, the rate con-
Processes as well as kinetic data derived from the       stant of equation 3 will be an arbitrary value much
mechanistic models developed for non-irradiated          higher than the rate constant of the first reaction
UO2 dissolution experiments with oxygen in concen-       (eq. 2).
trations simulating oxygen radiolytically generated
(de Pablo et al., 2001; de Pablo et al., 2003; de        By developing this mechanism (Merino et al., 2004)
Pablo et al., 2004) as well as from the work per-        in agreement with the one reported in de Pablo et
formed with hydrogen peroxide by Ekeroth /Johnson        al. (de Pablo et al., 1999) it was obtained:
(Ekeroth and Jonsson, 2003) and Clarens (Clarens,
2004).                                                          k(O2exp) = 0.0025 M-1 · s-1 = 2×kO2

After the integration of the mechanism in the radio-     and therefore,
lytic model, this is calibrated with experimental data
                                                                          kO2 = 0.0013 M-1 · s-1
and tested with the experiments developed in WP3
with alpha doped pellets and with real spent fuel.
Finally the model is applied to base case calcula-       2.2. Hydrogen peroxide promoted
tions in different media as Granite and Clay.
                                                              mechanism for the oxidation
                                                              of the matrix
2.1. Oxygen promoted mechanism                           Hydrogen peroxide is one of the primary molecular
     for the oxidation of the matrix                     species generated by alpha radiolysis in water that
                                                         may act as oxidant of the UO2 surface. There is also
Kinetic parameters as well as the reaction mecha-        evidence that this compound may be one of the
nisms accounting for oxygen-mediated processes           main oxidants of the spent fuel matrix (Shoesmith,
have been elucidated based on the semi-empirical         2000). Corrosion potential (Ecorr) measurements in-
models developed by de Pablo and his group (de           dicate that the oxidation by H2O2 is faster than by
Pablo et al., 2004; Giménez et al., 2001).               O2. However, the mechanistic information concern-
The oxidation of the UO2 surface by oxygen is ex-        ing hydrogen peroxide oxidation is still quite limited.
pressed by these authors as follows:                     There are several interpretations of the processes and
                                                         mechanisms taking place during hydrogen peroxide
            > UO 2 + 1 / 2 O 2 Û > UO 3        (eq. 1)
                                                         oxidation. However, most of the authors agree that
                                                         hydrogen peroxide oxidation occurs by radical for-
with a kinetic constant k(O2exp) = 0.7 M-1·s-1 at 25
                                                         mation with very high oxidation potentials, and with
ºC (Giménez et al., 2001). This value was fitted by
                                                         the radical hydroxyl (·OH) as one of the main species
fixing the total density of surface sites to 10-8
                                                         generated in this process (Andreozzi et al., 1999; Ed-
mol·dm-2. Consequently, the kinetic constant has
                                                         wards and Curci, 1992; Salem et al., 2000). In ad-
been recalculated by taking the density of surface
                                                         dition, H2O2 auto-decomposition is also known to be
sites selected for this work ((Clarens et al., 2003a),
                                                         catalysed on oxide surfaces containing mixed oxida-
as explained in D12 (Martínez Esparza et al.,
                                                         tion states (Abbot and Brown, 1990). When hydro-
2004b)), that is, 2.74·10-6 mol·dm-2, obtaining an
                                                         gen peroxide concentration ranges 10-4 M < [H2O2]
oxidation rate constant of:
                                                         < 10-2 M, the oxidant dissolution and hydrogen per-
            k(O2exp) = 0.0025 M-1 · s-1                  oxide decomposition should occur simultaneously
                                                         (Shoesmith and Sunder, 1992). On the other hand,
This process has been incorporated into the MAM          most of the authors also highlight that bicarbonate
model based on the mechanism of Schortmann and           may act as scavenger of the ·OH to form the radical
DeSesa (Schortmann and DeSesa, 1958) as two el-          ·CO3- (Andreozzi et al., 1999). The radical carbon-
emental processes as follows:                            ate has a lower oxidation potential than the radical
                                                         hydroxyl, and therefore this species is less reactive
     >UO2 +O2 Y >UO2-O2                kO2     (eq. 2)   than its precursor. Experiments carried out with non



                                                                                                                27
Development of a Matrix Alteration Model (MAM)



irradiated UO2 with an initial H2O2 concentration                  The constant associated to the second reaction (eq.
with and without carbonates in the system respec-                  5), was derived from the work of Ekeroth et al.
tively (de Pablo et al., 2001) gave a lower dissolu-               (Ekeroth and Jonsson, 2003). The authors report a
tion rate for uranium and a higher rate of consump-                second order rate constant for the oxidation of UO2
tion of hydrogen peroxide when carbonate was                       by the radical hydroxyl of 0.428 m/min. Thus, recal-
present in the system. The authors argued this be-                 culating this rate constant we obtained kOH =
haviour to the radical scavenging. Dissolution tests               2.6·104 M-1·s-1. This value is the one used for equa-
performed with spent nuclear fuel at several carbon-               tion 5. Once the intermediate species >UO2OH is
ate concentrations (Bruno et al., 2004) showed dif-                formed, another radical oxidises this intermediate to
ferent steady state concentrations of hydrogen per-                give a U(VI) species and water. This process will be
oxide depending on the solution composition,                       faster than the previous one. The rate limiting step will
specifically the bicarbonate content. In fact, steady              be the decomposition of H2O2, as this reaction has
state concentrations decreased when increasing the                 the lowest kinetic constant.
carbonate content, confirming once again the effect
                                                                   The proposed mechanism is a simplified form of the
of this compound acting as radical scavenging.
                                                                   overall oxidation process by H2O2. This approach
The mechanism proposed by Ekeroth and Jonsson                      has the advantage of involving the OH radicals,
(Ekeroth and Jonsson, 2003) for the reaction be-                   and this will be a key point when calibrating the
tween UO2 and H2O2 is based on a slow one-elec-                    model in the presence of bicarbonate, as will be
tron transfer step accounting for the oxidation of                 shown in section 4.1.2.
UO2 by ·OH, with a primary step analogous to the
Fenton reaction. Most of the authors agree in simi-
lar reaction sequences for the oxidation of metallic               2.3. Hydrogen promoted
oxides by H2O2 based on Fenton-like or Haber                            mechanism
Weiss-like mechanisms (Andreozzi et al., 1999; Mil-
ler and Valentine, 1999).                                          Based on experimental evidences (Loida et al., 2004;
                                                                   Quiñones et al., 2004; Röllin et al., 2001; Sunder et
In the present work, the proposed mechanism is
                                                                   al., 1990), there is a clear effect on decreasing the
quite similar to the one proposed by the other au-
                                                                   uranium concentration in solution when hydrogen is
thors but avoiding the formation of a U(V) surface
                                                                   present in the system. The processes involved are not
species as intermediate (that is, the assumption of a
                                                                   well known but it is expected some interaction be-
dismutation between U(IV) and U(VI)). Therefore,
                                                                   tween the hydrogen and the fuel matrix, i.e. surface
auto-decomposition catalysed by the uranium oxide
                                                                   passivated by the hydrogen molecule, that is the hy-
is considered in a simplified form. In such case, the
                                                                   drogen acting as scavenger and/or formation of the
mechanism proposed for the oxidation of the spent
                                                                   radical ·H and reduction of the oxidised uranium.
fuel matrix by hydrogen peroxide is:
                                                                   These mechanisms of interaction between H2 and
  >UO2+H2O2 Y >UO2+2·OH                          kH2O2   (eq. 4)   uranium have not been yet described, however, the
                                                                   D9 (Grambow et al., 2004) - D10 (Spahiu et al.,
                                                                   2004) reports should give some evidences or new
  >UO2+· OH Y >UO2OH                             kOH     (eq. 5)
                                                                   findings about them.
  >UO2OH+·OH Y >UO3+H2O                          Fast    (eq. 6)   The interpretation of new experimental data based
                                                                   on some of these mechanisms as well as the deter-
The overall mechanism accounts for the general ox-                 mination of their parameters will allow including
idation reaction by H2O2, that is:                                 these processes in a matrix alteration model in the
                                                                   next future.
        >UO2 + H2O2 Y >UO3 + H2O                         (eq. 7)

The kinetic constant associated to the first mechanis-
tic reaction (eq. 4), that is kH2O2, was calibrated by             2.4. Mechanisms accounting for
using the data generated from the dissolution of                        the dissolution of the oxidised
non irradiated UO2 at different hydrogen peroxide
concentrations in a flow-through system (de Pablo et
                                                                        UO2 co-ordinates sites
al., 2003). The results of this calibration are pre-               The kinetic constants associated to the dissolution
sented in Section 4.1.2, and the resulting kinetic                 processes once the surface sites have been oxidised
constant is 2.2 M-1·s-1.                                           are also derived from the oxidation/dissolution



28
                                                                                         2. Mathematical Model



mechanisms proposed by de Pablo and his group           al., 2004c; Merino et al., 2004). Therefore, the
(de Pablo et al., 2003; Giménez et al., 2001). Their    processes included in the reaction scheme for the
mechanisms are based on two dissolution steps:          dissolution of the oxidised UO2 are:

  1. Surface co-ordination of U(VI) by the aqueous        >UO3+H+ Y UO2(OH)+             kH          (eq. 8)
     ligands (H+, H2O or HCO3-)
  2. Detachment (dissolution) of the product species      >UO3+H2O Y UO2(OH)2(aq)        kH2O        (eq. 9)
For H+ and H2O the rate determining step will be
the detachment of the product species (de Pablo et        >UO3+HCO3- Y
al., 2003), while for bicarbonate, the limiting pro-         Y UO2CO3(aq) + OH-         kHCO3 (eq. 10)
cess will be the surface co-ordination step (de Pablo
et al., 1999).
                                                          UO2CO3(aq)+HCO3- Y
These processes have been included in the reaction           Y UO2(CO3)22-+H+            Fast       (eq. 11)
scheme by means of a simplified mechanism as a
function of the rate determining step but corre-        The kinetic constants have been taken from the
sponding in all cases to the overall dissolution        semi-empirical models developed by de Pablo and
mechanisms (Martínez Esparza et al., 2004a;             co-workers, namely kH = 2 M-1 · s-1, kH2O = 10-5
Martínez Esparza et al., 2004b; Martínez Esparza et     M·s-1 and kHCO3 = 5 · 10-2 M-1 · s-1.




                                                                                                           29
3. Model Validation




                      3. Model Validation
3. Model Validation
                                                                                                                          3. Model Validation



The MAM has been applied to the leaching tests of                 experiments carried out by using non irradiated
alpha doped pellets and spent fuel carried out in the             UO2 in an oxygen atmosphere in presence and ab-
scope of SFS project WP3 (Spahiu et al., 2004), un-               sence of carbonate in the system (de Pablo et al.,
der the ENRESA-ITU collaboration agreement. The                   2004; de Pablo et al., 1999). The second one re-
results are given in the Figures and Tables of the re-            fers to the flow through experiments also by using
spective sections (3.1, 3.2 and 3.3).                             UO2 samples at several hydrogen peroxide concen-
This calibration exercise is presented in this para-              trations. Some tests were also carried out with car-
graph separated as a function of the conditions of                bonate in solution (de Pablo et al., 2003). Dissolu-
the experiment, i.e., type of tests carried out by us-            tion rates were determined by using a thin-film flow
ing non-irradiated UO2, a-doped material or spent                 through reactor as described in Casas et al. (Casas
fuel. The information given in each section presents              et al., 1994). The next figure (Figure 3-1) depicts the
a summary of the experimental setup, the results                  experimental device used in these experiments.
and the data obtained using MAM considering each
specific environmental condition.                                 The leachant is introduced in the column containing
Finally, a summary of the application of the MAM to               the UO2 sample by means of a peristaltic pump, the
Base case in granite and clay environments is pre-                pH is continuously monitored with an on-line com-
sented as well as a sensitivity analysis of the main              bined glass electrode and the uranium concentration
parameters: surface area, presence or not of hydro-               is analysed by using the SCINTREX UA-3 uranium
gen in the system, container life time, reaction                  analyser (Robbins, 1978) or ICP-MS. Hydrogen per-
scheme, dose rate, water irradiated depth and fuel                oxide is analysed by a chemiluminiscence method
burn-up (Martínez Esparza et al., 2004c).                         with luminol and cobalt as reagents. Experimental
                                                                  details are reported in their publications (D13).

3.1. Non irradiated UO2                                           The next sub-sections show the experimental results
Two sets of experiments were used for the model                   plotted as uranium dissolution rates versus the dif-
calibration. The first set refers to the flow through             ferent environmental parameters considered in the




                                                                      Column


                pH-meter


                                                                                         Gas outflow
                                                                                                             Gas inflow



                Sample


                                                                  Peristaltic pump
                           SCINTREX



                                         Figure 3-1. Experimental setup used in the flow-through experiments carried out at DIQ-UPC.



                                                                                                                                         33
Development of a Matrix Alteration Model (MAM)



experimental series as well as the semi-empirical            where U(VI)(aq) is any of the four species of uranium
models elucidated to interpret the data obtained.            in solution. Therefore, the evolution of uranium in
                                                             solution will be the balance of two processes, disso-
                                                             lution of the oxidised uranium (by the three mecha-
3.1.1. Flow through experiments                              nisms explained before) in the surface and advective
       with non irradiated UO2 in                            transport out of the system. The output of the model
       a oxygen atmosphere                                   will give the concentration of uranium, and when
                                                             the system reaches the steady state, the concentra-
                                                             tion of uranium will remain constant. From this con-
3.1.1.1. Experimental results                                centration, dissolution rates can be derived using
         and semi-empirical models                           the same formula used in the experimental determi-
The kinetics of dissolution of the unirradiated ura-         nation of dissolution rates:
nium dioxide were investigated as a function of pH,
oxygen partial pressure and carbonate content (de                  r (mol · m-2 · s-1) = U(VI)(aq) Q/S      (eq. 13)
Pablo et al., 2004; de Pablo et al., 1999). As previ-
ously reported, the authors interpreted the experi-          where S is the total surface area of the sample un-
mental results as a surface mediated dissolution             der study. To achieve steady state, however, it has
mechanism differentiated into three steps.                   been necessary to impose that the concentration of
  1. Initial oxidation of the uranium dioxide solid          the species >UO3, representing oxidised sites, must
     surface.                                                be much lower than the concentration of the species
                                                             >UO2, the reactive sites.
  2. Surface co-ordination of H+ (favoured at acid-
     ic pH), H2O (favoured at neutral-alkaline pH)
                                                             The computer code used to solve the resulting differ-
     and HCO3- (favoured in the presence of car-
                                                             ential equations from all the kinetic reactions has been
     bonate in the system).
                                                             Chemsimul (Kirkegaard and Bjergbakke, 2002). The
  3. Detachment of the surface complexes.                    results of applying the model to the experiments at
                                                             different oxygen partial pressures and at variable pH
From this mechanism, and by modelling the experi-
                                                             are shown in Figure 3-4. The calibration process
mental results, the authors derived two general rate
                                                             has led to a good fit for pH > 5 and for oxygen
equations, the first one as a function of the carbon-
                                                             partial pressures of 0.05 and 0.21 bar. The differ-
ate content (de Pablo et al., 1999) and the other
                                                             ence between our model and the semi-empirical
one as a function of pH (de Pablo et al., 2004).
                                                             model can be due to the uncertainty in determining
Both expressions include the dependence on both
                                                             the reactive volume, the thin layer where the pow-
the oxygen concentration in the aqueous phase and
                                                             dered UO2 is located in the column.
the concentration of sites available to be oxidised.
By fitting the general expressions to the experimental
                                                             The next series of experiments, with carbonate in-
results, the authors quantified the kinetic constants
                                                             cluded in the leachant, was modelled by adding the
associated to the different processes. The experi-
                                                             carbonate system in the reaction scheme. The re-
mental data as well as the fitting of the semi-empiri-
                                                             sults (Figure 3-5) show a good agreement between
cal models developed by the same authors are de-
                                                             our model and the semi-empirical model in the car-
picted in Figure 3-2 and Figure 3-3.
                                                             bonate concentration range of 10-4 – 10-2 M. The
                                                             divergence of the two models at the low carbonate
3.1.1.2. Model calibration                                   content is due to the inclusion of the protonation
In order to apply the model to the continuous                and water molecule complexation in our model.
flow-through experiments, it has been necessary to           These processes were not included in the semi-em-
add a series of reactions simulating the transport of        pirical model developed by de Pablo et al. (de
uranium in solution out of the system. This process,         Pablo et al., 2004) and they are predominant in the
the water turnover, can be represented by a linear,          dissolution step at low CO3- concentration. At high
first order reaction with the kinetic constant given by      carbonate content, however, the semi-empirical
the quotient between the flow rate (Q) and the               model includes the phenomenon of site saturation,
volume of reaction (V):                                      not included in the MAM, a process that should be
                                                             implemented in future developments of our kinetic
     U(VI)(aq) Y U(VI)(out)         k = Q/V (s-1) (eq. 12)   model.



34
                                                                                                                                    3. Model Validation




                                                 -10
                                                                                                              5% O2
                                                                                                              5% O2
                                                                                                              21% O2
                                                                                                              21% O2
                                                                                                              100 % O2
                                                                                                              100% O2
                       log r (mol · m-2 · s-1)




                                                 -11




                                                 -12
                                                       5    6        7        8                 9        10              11   12
                                                                                     pH


Figure 3-2. Dissolution rates vs. pH at different O2 partial pressures (de Pablo et al., 2004). Data points represent measured values and lines
                                                                                represent semi-empirical model developed by the same authors.




                                                  -9




                                                 -10
                   log r (mole · m-2 · s-1)




                                                 -11




                                                 -12
                                                       -5       -4       -3                         -2            -1           0
                                                                                            -
                                                                                  log ([HCO ])
                                                                                           3




  Figure 3-3. Dissolution rates vs. [HCO3-] at 25 ºC (de Pablo et al., 1999). Data points represent measured values and solid line represents
                                                                                       semi-empirical model developed by the same authors.



                                                                                                                                                   35
Development of a Matrix Alteration Model (MAM)




                                                       -10
                                                                                                    MAM model
                                                                                                    Semi-empirical model
                             log r (mol · m-2 · s-1)                                                Experimental values



                                                       -11




                                                                  pO2 = 5 %

                                                       -12
                                                             5         6           7   8        9          10              11      12
                                                                                           pH


                                                       -10

                                                                                                            MAM model
                                                                                                            Semi-empirical model
                                                                                                            Experimental values
                             log r (mol · m-2 · s-1)




                                                       -11




                                                                 pO2 = 21 %
                                                       -12
                                                             5                 6           7                    8                   9
                                                                                           pH


                                                       -10
                                                                                                            MAM model
                                                                                                            Semi-empirical model
                                                                                                            Experimental values
                             log r (mol · m-2 · s-1)




                                                       -11




                                                                 pO2 = 100 %

                                                       -12
                                                             5          6          7   8        9          10              11      12
                                                                                           pH



              Figure 3-4. Results of the MAM model applied to flow-through experiments with unirradiated UO2 in the presence of O2 at different pH.



36
                                                                                                                                       3. Model Validation




                                                    -7
                                                              MAM model
                                                              Semi-empirical model
                                                    -8
                                                              Experimental values


                                                    -9
                         log r (mol · m-2 · s-1)




                                                   -10


                                                   -11


                                                   -12


                                                   -13
                                                         -5         -4                  -3                   -2              -1
                                                                                              -
                                                                                     log[HCO ]
                                                                                             3




          Figure 3-5. Results of the MAM model applied to flow through experiments with unirradiated UO2 in carbonated water under atmospheric
                                                                                                                                    conditions.




It must be noted that the semi-empirical models de-                                    tailed in Table 3-1. All this work is reported in de
veloped by de Pablo and co-workers were different                                      Pablo et al. (de Pablo et al., 2003).
for the two separate series of experiments. Our
model has been able to reproduce both series with                                      For the first two series, the kinetic laws were calcu-
a unique set of reactions and kinetic constants, rep-                                  lated from a linear regression of a log rate – log
resenting an integrated approach to the kinetic                                        [species] plot.
modelling of this type of experiments.
                                                                                       Experimental results as well as the linear regressions
                                                                                       are depicted in the next figures (Figure 3-6, Figure
                                                                                       3-7, and Figure 3-8).
3.1.2. Flow through experiments
       of non-irradiated UO2                                                           In the first series the authors observed a linear de-
       with hydrogen peroxide                                                          pendence of the dissolution rate with the hydrogen
                                                                                       peroxide concentration with a reaction order close
                                                                                       to one (Figure 3-6). This linear dependence was ob-
3.1.2.1. Experimental results and fitting                                              served for hydrogen peroxide concentrations rang-
         of the data                                                                   ing from 5·10-6 to 10-4 M. At higher concentrations
                                                                                       the dissolution rate does not depend on H2O2 con-
Several experiments were conducted to study the ef-
                                                                                       centration, in accordance with other experimental
fect of H2O2 on the dissolution of unirradiated UO2.
                                                                                       evidence (de Pablo et al., 2001; Shoesmith and
The work focused on studying the effect of hydrogen
                                                                                       Sunder, 1992).
peroxide concentration as well as the effect of bicar-
bonates and pH. Hydrogen peroxide was assumed                                          The authors derived the following dissolution rate
to remain constant in each experiment and only                                         from this data:
uranium concentration in solution was determined.
Different experimental series were carried out as de-                                             r (mol · m-2 · s-1) = 10-5 · [H2O2]0.90      (eq. 14)



                                                                                                                                                      37
Development of a Matrix Alteration Model (MAM)



         Table 3-1
         Experimental conditions.

                      Series                                          [H2O2]                            [HCO3-]                      pH

                         I                                          5 · 10-6-10-4                          0                         5.8

                         II                                         10-6-5 · 10-4                       2 · 10-3                     8.1

                        III                                             10-5                               0                     3.5-10.5



A linear dependence was also found for the series                                            master variable are depicted in Figure 3-8. The au-
carried out as a function of the hydrogen peroxide                                           thors interpreted the increase at acidic pH by the
in presence of carbonate in the system (Figure 3-7).                                         complexing effect of protons as found in oxygen
However, a fractional reaction order of 0.59 was                                             media. On the other hand, at basic pH they sug-
determined. The authors interpreted this reaction or-                                        gested the decomposition of H2O2 to give HO2-, a
der by the fact that there may exist parallel reactions                                      more active species that could be responsible for
between H2O2 and bicarbonates.                                                               the increase in the dissolution rate. Neither regres-
                                                                                             sion analysis nor semi-empirical model was carried
The authors derived the following dissolution rate
                                                                                             out, due to the lack of a detailed mechanism.
from this data:

        r (mol·m-2·s-1) = 10-6.2·[H2O2]0.59                                (eq. 15)          3.1.2.2. Model calibration
The last series was carried out at a fixed hydrogen                                          The same reactions simulating transport out of the
peroxide concentration but varying the pH of the so-                                         system in the oxygen experimental series were taken
lution. The dissolution rates as a function of this                                          here. Previous attempts to model the experimental




                                                          -9
                               log r (mol · m-2 · s-1)




                                                         -10




                                                         -11
                                                               -6                   -5                         -4               -3
                                                                                         log ([H2O2])



          Figure 3-6. Dissolution rates vs. H2O2 concentration in flow-through experiments (de Pablo et al., 2003). Data points are measured values,
                                                                     and solid line is the empirical model (linear regression) developed by the authors.



38
                                                                                                                                                      3. Model Validation




                                                                 -8

                                  log r (mol · m-2 · s-1)




                                                                 -9




                                                                -10
                                                                      -7           -6       -5                      -4       -3             -2
                                                                                                 log ([H2O2])



Figure 3-7. Dissolution rates vs. H2O2 concentration in flow-through experiments at a constant HCO3- of 2·10 -3 M (de Pablo et al., 2003).




                                       -8




                                       -9
        log r (mol · m-2 · s-1)




                                  -10




                                  -11
                                                            3              4   5        6        7              8        9        10   11        12
                                                                                                     pH




     Figure 3-8. Dissolution rates vs. pH in flow through experiments at a constant H2O2 concentration of 10 -5 M (de Pablo et al., 2003).



                                                                                                                                                                     39
Development of a Matrix Alteration Model (MAM)



data with a one-step mechanism failed, and there-                                of the parallel reactions taking place in the system.
fore we have proposed the simple mechanism in-                                   The main oxidising species, the ·OH radical, is con-
volving the OH radicals explained earlier on.                                    sumed not only by UO2, but also by other species in
                                                                                 the recombination reactions.
It should be pointed out that the formation of OH
radicals by decomposition of H2O2 has forced us to                               The flow experiments with different concentrations of
introduce the recombination reactions scheme when                                H2O2 and a constant concentration of bicarbonate
applying the model to non-irradiated UO2, that is, a                             (Series II, Figure 3-10) are discussed in the following
system without radiolysis. In this respect, the recom-                           paragraph. The empirical model developed by de
bination reactions lead to the formation of O2,                                  Pablo et al. (de Pablo et al., 2003), already gave a
which adds to the overall oxidation of the sample                                fractional order for the dependency of the dissolu-
under study. On the other hand, to reproduce the                                 tion rate versus H2O2 concentration in the presence
experiments with carbonate in the leachant the car-                              of carbonate. Previous attempts to model these ex-
bonate system has been also included in the reac-                                periments without the decomposition of H2O2 in
tion scheme. All these reactions, the radical recom-                             ·OH failed as there was no mechanism of interac-
bination and carbonate system schemes, have been                                 tion between hydrogen peroxide and carbonate. As
taken from WP2 and described in D4 for a closed                                  previously said, our model takes into account all the
system (Kelm and Bohnert, 2004).                                                 reactions of the carbonate system, including a reac-
                                                                                 tion between ·OH and HCO3-. It appears that this
For the experiments with varying concentrations of                               simple reaction is essential to explain the behaviour
H2O2 (Series I, Figure 3-9), the empirical model de-                             of the system. Moreover, the corresponding kinetic
veloped by de Pablo et al. (de Pablo et al., 2003),                              constant has been taken from the literature, without
namely a regression analysis for the points with                                 the need of further calibration.
H2O2 < 10-4 M, gave a reaction order close to
one, whereas our model gives a slope less than 1.                                Finally we have obtained a good fit for the experi-
This indicates a fractional order as a consequence                               ments in series III with variable pH (Figure 3-11).




                                                     -9




                                                    -10
                          log r (mol · m-2 · s-1)




                                                    -11


                                                                                                         MAM model
                                                                                                         Empirical model
                                                                                                         Experimental values

                                                    -12
                                                          -6        -5                           -4                            -3
                                                                              log ([H2O2])


              Figure 3-9. Results of the MAM model applied to flow-through experiments with unirradiated UO2 in anoxic conditions at different H2O2
                                                                                                                                    concentrations.



40
                                                                                                                                                         3. Model Validation




                                                  -8
                                                                                                                             MAM model
                                                                                                                             Empirical model
                                                                                                                             Experimental values



                                                                    log r = 0.59 log[H2O2]-6.2
                 log r (mol · m-2 · s-1)




                                                  -9




                                                 -10
                                                       -7                -6                           -5                -4                          -3
                                                                                                 log ([H2O2])



    Figure 3-10. Results of the MAM model applied to flow-through experiments with unirradiated UO2 in anoxic conditions at different H2O2
                                                                                                concentrations with [HCO3-] = 2·10 -3 M.




                                                       -8
                                                                                                                             MAM model
                                                                                                                             Experimental values



                                                       -9
                       log r (mol · m-2 · s-1)




                                                   -10




                                                   -11
                                                            3   4         5         6             7             8   9        10         11         12
                                                                                                       pH



Figure 3-11. Results of the MAM model applied to flow-through experiments with unirradiated UO2 in anoxic conditions at different pH values
                                                                                                                with [H2O2] = 1·10 -5 M.



                                                                                                                                                                        41
Development of a Matrix Alteration Model (MAM)



The agreement is also good at even lower pH than          2003) and the Midterm report of SFS (Poinssot,
in the experiments with O2. At alkaline conditions        2003).
the model predicts a constant dissolution rate, as
                                                          Oxidised layers of the a-doped UO2 were removed
was the case for the experiments with O2, due to the
                                                          by a combination of annealing and washing (predis-
predominance of the complexation with the water
                                                          solution). Afterwards, the doped UO2 was leached
molecule in the dissolution step. This contrasts with
                                                          with Real Boom Clay groundwater (RCW) in the dy-
the experimental evidence of a higher dissolution
                                                          namic leach cells for several weeks at 25 - 30EC.
rate at high pH. As de Pablo et al. (de Pablo et al.,
                                                          The test medium was Real Boom Clay water (RCW).
2003), pointed out, this higher dissolution rate is
                                                          RCW is characterised by its high carbonate concen-
probably due to the decomposition of H2O2 into
                                                          tration, its high content of organic material, mainly
HO2-, a more reactive species not included in our
                                                          humic acids, and its reducing capacity.
model. The relevance of this process, however, is
not high at the pH conditions expected in the repos-      U and Pu concentrations were measured by ICP-MS
itory, which are less alkaline.                           or a-spectrometry. O2 and H2 were measured by
                                                          mass spectrometry. Hydrogen peroxide was mea-
                                                          sured by means of the chemiluminescence’s tech-
3.2. Alpha doped material                                 nique and the chlorate ion was determined by ion
                                                          chromatography.
Three sets of experiments were used. The first one re-
                                                          The dissolution data obtained in the different experi-
fers to the flow through experiments carried out with
                                                          ments are depicted in the following figures (Figure
Boom clay waters and with alpha doped UO2 simulat-
                                                          13-12).
ing two different fuel ages. These experiments were
carried out at SCK-CEN. The second one refers to the      The first figure shows uranium concentrations mea-
batch experiments carried out with alpha doped pel-       sured in solution as a function of time. The results in-
lets with 233U at several percentages and under differ-   dicate that uranium dissolution decreases when in-
ent gas atmospheres: hydrogen, oxygen and argon.          creasing the activity of the solid sample (see Figure
These experiments were performed at ITU in the frame      3-12, F1-Q1 and F6-Q1 for comparison). These re-
of collaboration agreements between ITU, ENRESA           sults are quite controversial since we might expect the
and CIEMAT (Quiñones et al., 2005). The third one         contrary behaviour. The authors attribute this trend to
refers to a set of experiments carried out under reduc-   the effect of the humic acids (HA) present in Boom
ing conditions (high hydrogen pressures) by using one     clay waters (120 < TOC (mg C·dm-3) < 390). These
alpha-doped pellet with 233U 10%. This set of experi-     organics might act as hydrogen peroxide scavenger
ments was also carried out at ITU in agreement with       due to the oxidation of HA by the H2O2 generated by
SKB.                                                      water radiolysis, or they could also give place to a
                                                          passivation effect in the UO2 surface (Lemmens,
                                                          2004). In addition, these substances may form
3.2.1.Flow through experiments                            macromolecules having a larger complexation capac-
                                                          ity, so, surface complexation processes may be of rel-
      with alpha doped UO2 powder                         evance in such systems. In any case, the presence of
                                                          humic substances in the leachant prevents a straight-
3.2.1.1. Experimental results                             forward way of interpreting the experimental results, at
                                                          least from a modelling point of view. In addition, the
SCK-CEN carried out several flow-through dissolu-         relatively high uranium concentration of the water
tion tests installed in an Ar/0.4% CO2 glove box          used as leaching solution may also mask the results as
with alpha-doped UO2 powder simulating fuel ages          well as the aliquot analyses. On the other hand, the
of <500 years (F1) and ~100 000 years (F6), in            concentration of uranium increases when decreasing
order to study both the influence of alpha activity in    the flow rate (Q1<Q2<Q3) as expected given that
the UO2 dissolution rate and the influence of the re-     the contact time will be higher.
ducing Boom clay groundwater used as solution.
233                                                       The authors report a maximal uranium dissolution rate
    U and 238Pu isotopes were added to the UO2 pel-
                                                          ranging from 2 to 0.77 Fg.m-2.d-1 when the a-activity
lets by using the “sol-gel” process to generate low
                                                          increases from 1.6x106 to 2.5x108 Bq/g UO2.
and high alpha doses respectively. The materials
used as well as the experimental procedure are de-        Figure 3-12 also shows hydrogen peroxide evolution
tailed in Cachoir et al. (Cachoir and Lemmens,            with time. In this case the results indicate a different



42
                                                                                                                                     3. Model Validation




                                             1.E-07
                                                                                                               F1-Q1
                                                                                                               F6-Q1
                                                                                                               F6-Q2
                                                                                                               F6-Q3
                            Conc. U (M)




                                             1.E-08




                                             1.E-09
                                                      0    10    20        30        40        50        60    70      80
                                                                                Time (days)

                                             1.E-04
                                                                                                               F1-Q1
                                                                                                               F6-Q1
                                                                                                               F6-Q2
                                             1.E-05                                                            F6-Q3
                            Conc. H2O2 (M)




                                             1.E-06




                                             1.E-07
                                                      0   10    20    30        40        50        60    70   80      90
                                                                                Time (days)


         Figure 3-12. Experimental uranium and hydrogen peroxide concentrations in solution in flow-through experiments with alpha-doped pellets
                                                                                                               in Boom Clay waters (SCK-CEN).




trend to the one expected since there is no difference                            to higher H2O2 concentrations but lower U concen-
on H2O2 concentrations as a function of the sample                                trations.
activity. The authors argue that the H2O2 production
should be independent on flow rate. However, the                                  Table 3-2 shows the oxygen and hydrogen concentra-
concentration of this oxidant increases when increas-                             tions measured at the end of the experiments. Oxygen
ing the flow rate, contrariwise to the uranium trend.                             concentrations are quite high in comparison to hydro-
The authors state that at high flow rate, the H2O2                                gen concentrations indicating a possible oxygen intru-
should has less time to react with the UO2 surface,                               sion into the system. Measured oxygen concentrations
due to a faster removing by the water flow; leading                               correspond to oxygen partial pressures of 6% approxi-



                                                                                                                                                    43
Development of a Matrix Alteration Model (MAM)



mately. The authors do not consider the gas results as                       Three experimental series were carried out, the first
reliable. Oxygen concentrations in the clay water in                         one in unaerated conditions by flowing N2 in the ex-
contact with the UO2 were most probably much lower                           perimental system before starting the leaching tests,
than the measured concentrations. In addition, the ac-                       the second one in a continuous 6% hydrogen atmo-
tual H2 concentrations were probably higher than the                         sphere and the third series in anoxic conditions by
measured ones.                                                               bubbling a gas mixture of Ar with 0.02% CO2. Ura-
                                                                             nium concentrations measured as a function of time
Given the uncertainties in the interpretation of the
                                                                             are depicted in Figure 3-13. The experimental de-
experimental results as well as the relevance of par-
                                                                             tails and results will be extensively described in the
allel processes not included in the model, there is
                                                                             D9 report (Grambow et al., 2004).
not a direct application of the model to these sets of
experiments.                                                                 Solutions were analysed for the concentration of dif-
                                                                             ferent uranium isotopes using a high resolution in-
This group in the frame of the D9 (Grambow et al.,                           ductively coupled plasma-mass spectroscopy (HR-
2004) and D10 (Spahiu et al., 2004) reports when                             ICP-MS) as described in the D9 report (Grambow et
published will give more insight in the interpretation                       al., 2004).
of their results.
                                                                             In unaerated conditions there is an increase of U con-
                                                                             centrations in solution for UO2 doped with 10% 233U
3.2.2. Batch experiments with alpha                                          compared to the other two sample types (a-doped
       doped UO2 pellets                                                     UO2 with 1% 233UO2 and non irradiated UO2). The
                                                                             values for UO2 with 1% 233U are indistinguishable
                                                                             from those for undoped UO2 within the timeframe of
3.2.2.1. Experimental results                                                these tests. The release in CW is slightly higher than in
Three materials were used in the frame of the present                        MQ, although for the low activity and for the undoped
project: UO2 containing 10 % and 1 % of 233UO2,                              UO2 this difference is very small.
and undoped UO2. Alpha-doped materials were also                             In the experiments carried out in a hydrogen atmo-
fabricated using the sol-gel technique. Before the                           sphere, experimental data indicate initial 238U con-
leaching tests, all samples were annealed for several                        centrations in solution higher for the alpha doped
hours at 1000EC in Ar/(6%)H2. Two S/V ratios were                            material than that for undoped UO2. The authors
used for the tests as described in the contribution to                       attribute this initial release to the pre-oxidised sur-
the D9 report(Grambow et al., 2004; Rondinella et                            face occurring before sample immersion. No addi-
al., 2004).                                                                  tional dissolution is observed after the initial release.
Static tests were performed at room temperature, us-                         For those experiments performed in anoxic condi-
ing borosilicate (Pyrex) glass or quartz vessels in                          tions, the results show no significant uranium disso-
glove boxes with N2 atmosphere and a nominal oxy-                            lution as a function of time under these conditions.
gen content of 8% provided by the glove box ventila-                         The authors interpret the different concentration at
tion service. Deionised water (MQ) and/or carbon-                            the beginning of the leaching experiments as a func-
ated water (CW) were used for the leaching tests. The                        tion of the solid sample by a slightly higher oxida-
carbonated water composition is reported in the ITU-                         tion of the doped samples in the storage period
ENRESA-CIEMAT contribution to the D9 (Grambow                                prior to the leaching test, indicating that the oxida-
et al., 2004) report (Rondinella et al., 2004).                              tion process should be faster for samples with higher



         Table 3-2
         Experimental O2 and H2 concentrations in the different flow-through experiments (SCK-CEN).

                        Experiment                                 O2 aq (M)                            H2 aq (M)

                           F6-Q1                                    7.6 · 10-5                         < 3.2 · 10-7

                           F6-Q2                                    1.0 · 10-5                           5.7 · 10-7

                           F6-Q3                                    7.7 · 10-6                           3.2 · 10-7



44
                                                                                                                                   3. Model Validation




                                              1.E-06


                                              1.E-07


                                              1.E-08
                                U conc. (M)




                                                                                              undoped, MQ
                                238




                                              1.E-09
                                                                                              1 % doped, MQ
                                                                                              10 % doped, MQ
                                                                                              undoped, CW
                                              1.E-10
                                                                                              1 % doped, CW
                                                                                              10 % doped, CW
                                              1.E-11
                                                       0      100             200             300               400
                                                                             Time (d)


                                              1.E-06
                                                                                               Undoped, Ar
                                                                                               1 % doped, Ar
                                              1.E-07                                           10 % doped, Ar
                                                                                               undoped, H2
                                                                                               10 % doped, H2
                                U conc. (M)




                                              1.E-08
                                238




                                              1.E-09



                                              1.E-10
                                                       0      100             200             300               400
                                                                             Time (d)


           Figure 3-13. Experimental 238U concentrations in unaerated (above), anoxic (below) and reducing (below) conditions in MQ water and
                                                                                              carbonated water (CW). CW used if no indicated.



alpha-activity. The authors derived a dissolution rate                       such conditions. Moreover, SEM examination of the
of 0.6 mg/m2/d approximately for the UO2 sample                              surface samples after the dissolution period re-
with 10% 233U.                                                               vealed little changes on the surface, with some pre-
                                                                             cipitation associated to Si, however, according to
                                                                             the authors, with a very limited effect.
3.2.2.2. Model validation
The series of experiments under unaerated condi-                             On the other hand, the experiments under anoxic/
tions were carried out in presence of oxygen in the                          reducing conditions gave place to hardly detectable
system, and therefore the possible effects of radio-                         dissolution rates, with observed effects related to ini-
lytically generated oxygen cannot be distinguished in                        tial oxidation of the samples.



                                                                                                                                                  45
Development of a Matrix Alteration Model (MAM)



These experimental features make difficult the vali-                             their experimental results. However, the main differ-
dation of the MAM model using these experimental                                 ence is that in order to reproduce the experimental
data. However, under several assumptions, some                                   data, we had to consider for modelling the results in
modelling exercises have been carried out, and they                              this set of experiments an unrealistic initial oxidation
are explained in the following paragraphs. The                                   of the surface, implying oxidation of other internal
computer code used in these simulations has been                                 layer besides the external one.
the Macksima-Chemist (Carver et al., 1979).
                                                                                 Finally, the experiments under a H2 atmosphere
The experiments with deionised water in the presence                             have been modelled (Figure 3-17) assuming an ini-
of oxygen have been modelled assuming a constant                                 tial content of O2 corresponding to the one mea-
concentration of O2 corresponding to a partial pres-                             sured in the glove box in the reactor that subse-
sure of 8 % (Figure 3-14).                                                       quently is consumed. Again, it has been necessary
                                                                                 to assume an initially oxidised surface with the same
On the other hand, the modelling results of the experi-
                                                                                 U(VI)/U(IV) ratio as the one taken for the experi-
ments in carbonated water are shown in Figure 3-15.
                                                                                 ments carried out under oxidising conditions.
In the case of the 10% doped pellet, an initial oxidised
surface has been assumed (UVI)/U(IV) = 0.096),
leading to a better fit of the experimental results.                             3.2.3. Batch experiments at high
In the case of the experiments under an Ar atmo-                                        hydrogen pressures with alpha
sphere (Figure 3-16), it has been necessary to as-                                      doped UO2 pellets
sume that there is an initial content of O2 in the
glove box in agreement with the oxygen concentra-
tions measured in the glove box and reported by the
                                                                                 3.2.3.1. Experimental results
authors. The other hypotheses considered are once                                Batch experiments were performed in a Ti-autoclave
again that the surface is also partially oxidised at the                         at different hydrogen pressures by using an al-
beginning of the experiments. The pre-oxidation of                               pha-doped UO2 pellet with 10 % 233U. 233U was
the surface is also argued by the authors to explain                             measured by alpha spectrometry (P. Carbol as is ref-




                                                        -6
                                                  10



                                                        -7
                                                  10
                    U conc. / mol · kg-1 of H2O




                                                        -8
                                                  10



                                                                                            exp. model
                                                        -9
                                                  10                                                        UO2
                                                                                                             238     233
                                                                                                            ( U - 1 % U)O2
                                                                                                             238       233
                                                                                                            ( U - 10 % U)O2
                                                       -10
                                                  10
                                                             0   20    40                  60                 80                100
                                                                               time / d


         Figure 3-14. Comparison of the model and experimental uranium concentrations for the experiments under unaerated conditions in deionised
                                                                                                                 water (Quiñones et al., 2005).



46
                                                                                                                                                3. Model Validation




                                        -5
                                  10



                                        -6
                                  10
  U conc. / mol · kg-1 of H2O




                                        -7
                                  10



                                  10-8

                                                                                exp. model
                                                                                                     UO2
                                        -9
                                  10                                                          (238U - 1 % 233U)O2
                                                                                              (238U - 10 % 233U)O2
                                                                                              100% (238U - 10 % 233U)O2 cord. p. oxd
                                       -10
                                  10
                                             0   50        100        150    200             250           300                  350       400

                                                                            time / d



Figure 3-15. Comparison of the model and experimental uranium concentrations for the experiments under unaerated conditions
                                                                              in carbonated water (Quiñones et al., 2005).




                                  10-6



                                        -7
                                  10
    U conc. / mol · kg-1 of H2O




                                        -8
                                  10



                                        -9
                                  10


                                                                                              exp. model
                                  10-10                                                                             UO2
                                                                                                                    238           233
                                                                                                                    ( U - 1 % U)O2
                                                                                                                    238             233
                                                                                                                    ( U - 10 % U)O2

                                  10-11
                                             0        20         40           60                   80                     100             120

                                                                            time / d



Figure 3-16. Comparison of the model and experimental uranium concentrations for the experiments under anoxic conditions (Ar
                                                                                      atmosphere) (Quiñones et al., 2005).



                                                                                                                                                               47
Development of a Matrix Alteration Model (MAM)




                                                   10-7
                                                                                             exp. model
                                                                                                             UO2
                                                                                                             (238U - 10 % 233U)O2


                                                   10-8
                     U conc. / mol · kg-1 of H2O




                                                   10-9




                                                   10-10
                                                           0          100              200                   300
                                                                                  time / d


                  Figure 3-17. Comparison of the model and experimental uranium concentrations for the experiments under reducing conditions (H2
                                                                                                          atmosphere) (Quiñones et al., 2005).




erence on Spahiu et al., 2004). Alpha specific activ-                              Uranium concentrations measured in solution are
ity has been converted to molar concentration of                                   very low and there is no difference on the uranium
233
    U taking into account its specific activity and to                             release as a function of the experimental conditions.
total uranium concentration by assuming congruent                                  Uranium concentrations do not seem to vary neither
dissolution with the major uranium isotope.                                        as a function of the hydrogen pressure applied to
                                                                                   the system nor depend on the presence of carbon-
Solution composition and hydrogen pressure changed
                                                                                   ates in the solution composition. These results
at different time intervals but by using the same sam-
                                                                                   should indicate an initial and rapid dissolution and
ple and the same device. Table 3-3 shows the differ-
                                                                                   afterwards no dissolution with time.
ent experimental conditions at the different time inter-
vals and Figure 3-18 shows the measured uranium                                    Application of the model to this series of experiments
concentrations as a function of time.                                              is not straightforward by several reasons. Looking at


         Table 3-3
         Experimental conditions imposed to the dissolution tests at different time intervals.

                                                               Contact time / d                  Experimental conditions

                          Period 1                                   113                            10mM Cl-, 16 bar H2

                          Period 2                                   140                     10mM Cl-, 2mM HCO3-, 16 bar H2

                          Period 3                                   322                     10mM Cl-, 2mM HCO3-, 1.6 bar H2

                          Period 4                                   462                     10mM Cl-, 2mM HCO3-, 0.16 bar H2




48
                                                                                                                                                  3. Model Validation




                        1.E-09

                                                                                                      Period 1      Period 2     Period 3

                                                                                                      Period 4      Period 5
                        1.E-10
       [U] (mol·dm-3)




                        1.E-11




                        1.E-12




                        1.E-13
                                 0              100               200                300               400                500               600
                                                                                   Time (d)



                         Figure 3-18. Uranium concentrations measured in Ti-autoclave experiments carried out with alpha-doped pellets at different hydrogen
                                                                                                                                                   pressures.




the experimental results, there is not a clear evidence                                       been possible to use them for validating the MAM
of uranium dissolution with time indicating that the                                          model. Nevertheless, they are included here for
uranium concentrations in solution may be exerted by                                          their intrinsic value.
a thermodynamic control, according also to the au-
thor suggestions. In addition, the mechanisms of in-                                          3.3.1. Flow through experiments
teraction between H2 and U(VI) have not been de-
scribed and characterised in sufficient detail in the                                                in carbonated waters under
frame of this project to be included in the model. The                                               oxidising conditions
D9 (Grambow et al., 2004) - D10 (Spahiu et al.,
2004) reports should give some evidences or new                                               3.3.1.1. Experimental results
findings about the processes implying some interac-                                           Two irradiated UO2 fuel samples from pins with aver-
tion between the hydrogen and the fuel matrix, i.e.                                           age burn-ups of 53 and 29 MWd/Kg U were used.
surface passivation by the hydrogen molecule and/or                                           For both samples a slice of rod fuel (including clad-
formation of the radical ·H with the consequent re-                                           ding material) was cut in disks directly from the pin.
duction of the oxidised uranium.                                                              The samples weighted 2.07 g and 2.57 g for the
                                                                                              spent fuels with a burn-up of 29 and 53 MWd·kg-1
                                                                                              U, respectively. The geometric surface area taken
3.3. Spent fuel                                                                               into account was 1.3 cm2 approximately. A commer-
                                                                                              cial granitic groundwater was used in these experi-
Spent fuel data were generated in two hot cell labo-
                                                                                              ments. More details are given by Serrano et al.
ratories, ITU and FzK-INE (Spahiu et al., 2004).
                                                                                              (Serrano and Wegen, 2004) to D9 (Grambow et al.,
Several dissolution experiments were carried out, as
                                                                                              2004) contribution.
explained in the following sections. These experi-
ments provide valuable insight on the processes go-                                           In addition to fuel fragments, one milled has been
ing on in the system, although it has not always                                              selected for the application of the model. The burn-



                                                                                                                                                                 49
Development of a Matrix Alteration Model (MAM)



up was 53 MWd·kg-1 U, and the cladding was cut                                    Both pH and redox potential were monitored during
off before milling. Particle size ranged between 150                              all the experimental time. The pH obtained from
and 250 µm. A surface area of 120 cm2 was calcu-                                  pellets and milled samples did not alter significantly
lated by means of an empirical relation. Serrano et                               during the experiment time, and stabilised after a
al. (Serrano and Wegen, 2004) also give more de-                                  few days in both samples. For the redox potential,
tails on the sample preparation as well as on the                                 the values of the solution in contact with the fuel
physical parameters to the D9 (Grambow et al.,                                    with higher burn-up showed a rapid increase during
2004) contribution.                                                               the first 10 days followed by stabilisation.
Dynamic leaching experiments under oxidising con-
ditions by equilibrating the leachant solution with air                           The calculated uranium dissolution rates for the dif-
were performed in a hot cell at room temperature                                  ferent samples are given in Table 3-4 (Serrano and
(25 ± 2E C). The solution used was a carbonated                                   Wegen, 2004).
water containing 1mM NaHCO3 and 19 mM NaCl.
The flow rate of the solution was kept within the                                 Dissolution rates indicate a faster dissolution of the
range of 0.001-0.1 ml/min for ensuring steady                                     sample with a larger burn-up. This behaviour is con-
state. Aliquots were taken at regular time intervals                              sistent with the assumption that radiolysis of the wa-
until a steady-state concentration of all measurable                              ter, caused by radioactive decay of fission and acti-
radionuclides was reached. Radionuclide concentra-                                vation products present in the spent fuel and in the
tions were measured with a High Resolution Induc-                                 fuel surface, constitute a constant source of oxidis-
tively Coupled Mass Spectrometer (HR-ICP-MS).                                     ing agents, much higher as higher the activity is.
The experimental device used in these experiments
is depicted in Figure 3-19. A detailed explanation of                             Uranium concentrations as a function of time deter-
the experimental setup is reported in the SFS Mid-                                mined in the dissolution tests of the milled sample
term report (Poinssot, 2003).                                                     are shown in Figure 3-20.




                        COLD LAB                                                                                      HOT CELL
                                                          a
                        Feed solution




                                                                                  b     c          d
                                        pH, T and Eh
                                          control

                                          Flow rate
                                        pump control
                                                                                                       e
                                        Stirring system
                                             control                                             g
                                                                                                                  f




                Figure 3-19. Schematic diagram of the mixed flow reactor used in the experiments reported here. a) Feed pump, b) redox electrode,
                                                               c) pH electrode, d) sample holder, e) leachate sampler, f) waste, g) stirring system.



50
                                                                                                                                                     3. Model Validation




                          1.E-04

                                                                                                                    1 Accidental stop of flow-rate
                                                                                                 3                  2 Increase of flow-rate
                                                                                  2
                                                                                                                    3 Progressive readjustment to
                                                                         1
                                                                                                       4               original flow-rate
                          1.E-05                                                                                    4 Original flow-rate
            U conc. (M)




                          1.E-06




                          1.E-07
                                   0          20         40         60          80               100       120         140             160           180
                                                                                      Time (d)



                           Figure 3-20. Experimental U concentrations in dynamic leaching experiments at oxidising conditions in carbonated water (ITU)
                                                                                                                          (Serrano and Wegen, 2004).




3.3.1.2. Model validation                                                              From the modelled uranium concentration a disso-
                                                                                       lution rate can be calculated applying equation 13.
The model has been applied to the leaching tests of                                    A very similar result is obtained (see Table 3-5 and
the milled sample, and the result is shown in Figure                                   Figure 3-22), giving confidence in the application of
3-21. The concentration of uranium in solution is                                      the model to real spent fuel.
correctly described when the steady state is reached.
The initial release experimentally observed probably
due to a pre-oxidation of the spent fuel sample can-                                   3.3.2. MOX fuel static leaching at high H2
not be reproduced as this process is not included in                                          pressure
the model. It should be noted that the oxidation of
the spent fuel is driven by atmospheric oxygen, as                                     As stated in the SFS Midterm report, a new experi-
radiolytically produced oxidants do not reach high                                     mental set-up for leaching experiments on irradiated
enough concentrations to influence the overall oxi-                                    spent MOX fuel was designed at ITU facilities. The
dation process, as shown in the previous figure.                                       MOX-fuel used in the leaching experiment has a


       Table 3-4
       Dissolution rates for the different samples.

                                       Sample (type, burnup)                                           Dissolution rate (mol m-2 s-1)

                                   UO2 LWR fuel 29 MWd·kg-1 U                                                (6.8 ± 2.9) 10-11

                                   UO2 LWR fuel 53 MWd·kg-1 U                                                (2.7 ± 1.3) 10-10

                             UO2 LWR fuel 53 MWd·kg-1 U, milled                                              (3.2 ± 0.2)·10-11



                                                                                                                                                                    51
Development of a Matrix Alteration Model (MAM)




                                                    1.E-04
                                                                                                 MAM model
                                                                                                 Experimental values


                                                    1.E-05
                                     Conc. U (M)




                                                    1.E-06




                                                    1.E-07
                                                             0          50           100            150                200
                                                                                    Time (d)

                                                    1.E-12
                                     Conc. (M)




                                                                                                              H2
                                                                                                              H2O2
                                                    1.E-13
                                                             0           50          100            150                200
                                                                                    Time (d)


            Figure 3-21. Application of the MAM model to spent fuel dynamic leaching experiments at oxidising conditions in carbonated water (ITU).
                                                                                            Experimental data corrected with respect the flow rate.




         Table 3-5
         Comparison of dissolution rates obtained from the experiments and derived from the model for the powdered spent fuel sample.

                                                                                                          r (mol·m-2·s-1)

                                             Experimental                                               (3.2 ± 0.2)·10-11

                                                   Model                                               (4.6 ± 1.8*)·10-11

         *Estimated uncertainty based on experimental errors in parameter values.




52
                                                                                                                                                               3. Model Validation




                                       1.E-10

                                                                                                                                                MAM model

                                                                                                                                                Experimental values
        Diss. rate (mol · m-2 · s-1)




                                       1.E-11
                                                                                                        Powder 53


                                Figure 3-22. Graphical comparison of dissolution rates obtained from the experiments and derived from the model for the powdered spent
                                                                                                                           fuel sample. Uncertainties are also indicated.




burn-up of 48 MWd·kg-1 U. The MOX-fuel was cut                                                         to the scarcity of data and the fact that these experi-
from a fresh fuel rod and the cladding was re-                                                         ments were run under a high H2 pressure, they have
moved. The MOX-fuel pieces were selected so that                                                       not been included in the validation of the model in
it gave a S/V-ratio of 0.28 m-1, similar to the ratio                                                  the SFS project.
used in the 233U-experiment (see section 3.2.3). The
surface area of the fuel (fuel pieces A+B) is 50.8
mm2 and the weight is 0.399 g.                                                                         3.3.3. Fuel pellet static corrosion in brine
The MOX-autoclave was loaded with irradiated MOX-                                                             at 3.2 bar H2 overpressure
fuel on 18.12.2002. Prior to the start of the leaching
the fuel was submerged in a H2-saturated solution                                                      Static dissolution experiments with a pellet sample
(containing 10 mM NaCl + 2 mM HCO3-), for half                                                         from a 50 MWd·kg-1 U spent fuel has been carried
an hour, in order to remove the oxidised surface                                                       out at FzK-INE facilities. The spent fuel pellet, coded
layer. The composition of the leaching solution was                                                    K8, has suffered pre-oxidation at a certain extent
the same as in the 233U-experiment (10 mM NaCl +                                                       during 7 years of storage. The pellet was pre-treated
2 mM HCO3-). Immediately after the loading of the                                                      by several wash cycles under anoxic conditions in
fuel the autoclave was pressurised to 54 bar pure H2.                                                  5M NaCl brine (200 ml brine).
The stirring of the solution was set to 60 rpm. So far
only a few samplings were made mostly to the fact                                                      To study the impact of H2 overpressure, spent fuel
that the autoclave only contains in total 180 ml solu-                                                 pellet was corroded under static conditions in anoxic
tion and do not exist possibility of refilling. The results                                            carbonate free 5 M NaCl solution using a high
are given in Figure 3-23.                                                                              pressure autoclave (500 ml) over totally 3 years. An
                                                                                                       external H2 overpressure of 3.2 bar (40 bar Ar-8
The analysis of the leachate indicates a very small                                                    H2) was applied. The pH was freely evolving. The
release of both actinides and fission products. Due                                                    amount of O2 in the gas phase was always below



                                                                                                                                                                              53
Development of a Matrix Alteration Model (MAM)




                              1.E-07
               U conc · (M)




                              1.E-08
               238




                              1.E-09
                                           S1 (0.1 d)                         S2 (26 d)                          S4 (206 d)


                                       Figure 3-23. Concentration of 238U in MOX fuel fragments dissolution experiments under high H2 pressure.




the detection limit of the mass spectrometer (ca.                             configuration has attempted to emulate the possible
0.04%).                                                                       environmental conditions in the repository when the
                                                                              engineering barriers are corroded, and calibrate the
Results of the uranium concentrations and measured
                                                                              effects on spent fuel short term tests..
pH at different sampling intervals are given in Figure
3-24. The observed variation of the U concentration
with time is coupled with a fluctuation in the mea-
sured pH. Since there is no increase in the uranium
                                                                              3.4.1.Experimental details
concentration, it is suggested that the observed U                            The leaching experiments were done in a pool-type
concentration is controlled by a thermodynamic equi-                          (-irradiation facility, “Nayade”, located at CIEMAT.
librium with an U solid phase.                                                This radioactive facility allows irradiating materials
In Loida et al. (Loida and Metz, 2004), there is a                            under water using a ( emitter (e.g., 60Co). The
complete description and a detailed discussion of                             leaching experiment samples were placed in a
the solubilities of U(IV) and U(VI) solid phases in                           tightly closed basket in the reactor and immersed in
comparison to the measured U concentrations.                                  the water pool. The basket was then surrounded by
                                                                              (-radiation sources (Serrano et al., 2000). Prior to
                                                                              starting the experiments, Fricke dosimetry was done
3.4. SIMFUEL                                                                  on the basket, with an initial dose absorbed by the
                                                                              leaching vessel of 14.2 mGy s-1. This ( dose rate is
A study of SIMFUEL leaching has been included in
                                                                              consistent with a spent fuel of 40 MWd kg-1 U after
this report to show other type of material that could
                                                                              50 years of cooling time (Loida et al., 2004;
be used in model calibration. In particular, the influ-
                                                                              Quiñones et al., 2004; Serrano et al., 2000).
ence of the ( radiation on the dissolution behaviour
of spent fuel matrix under initial reducing conditions                        SIMFUEL pellets used for these tests were supplied by
has been investigated at CIEMAT. The experimental                             AECL, Chalk River Research Laboratories. The con-



54
                                                                                                                                          3. Model Validation




                         1.E-06                                                                                                8

                                                                                                                               7.5

                         1.E-07                                                                                                7

                                                                                                                               6.5
               [U] (M)




                         1.E-08                                                                                                6




                                                                                                                                     pH
                                                                                                                               5.5

                         1.E-09                                                                                                5


                                                                                                 U              pH             4.5

                         1.E-10                                                                                                4
                                  0         200             400            600            800            1000           1200
                                                                        Time (days)



                                      Figure 3-24. Measured U concentrations and pH in solution in the static dissolution experiments of K8 pellet.




centrations of additives in SIMFUEL simulate the fis-                            3.4.2.Results
sion products representative of a burn up of 50 MWd
kg-1 U. The percent of each element in the UO2 ma-                               Figure 3-26 shows the evolution of U concentrations
trix and general characteristics of SIMFUEL are given                            obtained from the experiments done using GBW.
elsewhere (Lucuta et al., 1991). This material was                               Squares, triangles, and circles are data obtained in
used in powder form with a particle size that ranged                             an Ar atmosphere from several experiments (e.g., fil-
between a 32–50 µm (BET measured specific surface                                tered and ultrafiltered, etc., described in (Quiñones
area of 0.12 m2 g-1). The amount of solid added to                               et al., 2004)). Rhombus symbols represent the results
each of the experiments was approximately 20 mg                                  obtained at 1 bar of H2. Stars are the blank experi-
(2.4 cm3 leachant was used) in order to achieve a                                ments done in absence of ( radiation and inside a
sample to volume (S/V) ratio of 1000 m-1. Before                                 glove box (e.g., in an Ar atmosphere).
starting the experiments, all powder was cleaned in
order to avoid the superficial oxidation of the matrix.                          The presence of ( radiation produces an increase in
Preparation, sampling methodology, and chemical                                  the U content (more than one order of magnitude) in-
analysis of all leaching tests were done as described                            dependent of the atmosphere used in the experiments.
in (Quiñones et al., 1998; Serrano et al., 2001).                                The evolution of uranium in the initial experiments re-
Sequential batch-leaching experiments were done in                               veals a clear influence from the presence of H2 (lower
specially-designed heat-sealed vessels (Figure 3-25).                            U concentrations than with Ar).
Two types of leachants were used: synthetic ground-
water GBW (Martinez et al., 1996); and GW (Serra-                                Although, and focussed on the Ar experiments, a de-
no et al., 2001), (Table 3-6). In order to study the                             crease of U is observed when t > 20 days, probably
possible influence of the H2 atmosphere, two types of                            due to the precipitation of a solid phase. The final U
atmospheres, Ar (1 bar) and H2 (1 bar), were used in                             values from the Ar experiments are, however, always
the experiments.                                                                 higher than when H2 is used (e.g., a factor of 2).



                                                                                                                                                         55
Development of a Matrix Alteration Model (MAM)




                                          Figure 3-25. Reactor vessels before (transparent) and after irradiation (dark) (Quiñones et al., 2004).




         Table 3-6
         Composition of the synthetics Groundwater samples used.

                                         Granitic (GW) (Serrano et al., 2001) /          Granitic bentonitic (GBW) (Martinez et al., 1996) /
                  Species
                                                        mg l-1                                                 mg·l-1

                   Ca+2                                   9.8                                                     135

                  Mg+2                                     7                                                      600

                   Na+                                    11                                                     3750

                    K+                                    5.9                                                      20

                    Cl-                                   13                                                     6550

                   NO3-                                   8.1                                                     110

                   SO4-2                                  8.4                                                    1500

                   HCO3-                                 72.5                                                      27

                    Br-                                 < 0.1                                                      15

                   SiO2                                   30                                                      8.3

                    pH                                    7.8                                                     7.3

                 Eh / mV                                  239




56
                                                                                                                                                                   3. Model Validation




                                                        -4
                                                   10

                                                                                                                   Ar (1 atm)
                                                                                                                                             filtered
                                                                                                                                             ultrafiltered
                                                   10
                                                        -5                                                         H2 ( 1 atm)
                                                                                                                                 without g radiation
                   [U] / mol · (kg de H2O) -1




                                                        -6
                                                   10




                                                   10-7




                                                             0         20             40            60             80                 100                    120
                                                                                                    time / d


                                                Figure 3-26. Evolution of U in leaching experiments performed in GBW under ( radiation field (Quiñones et al., 2004).




The results obtained (Figure 3-26) reveal that in the                                               If a comparison between Figure 3-26 and Figure
presence of an external ( source, the presence of H2                                                3-27 is made, the following consequences are ob-
is not capable to inhibit the oxidation/dissolution pro-                                            tained. In the GW experiments, a decrease in the U
cess of UO2. This behaviour is opposite to what has                                                 content is not observed, whereas if GBW is used, a
been reported in previous spent fuel leaching experi-                                               decrease of more than one order of magnitude is
ments in presence of H2 (Röllin et al., 2001). One                                                  seen; the U value achieved is at less one order of
possible reason for this different behaviour is related to                                          magnitude higher using GW than using GBW. This
interaction with other radiolytic products and con-                                                 observation is related to the chemical composition
sumption of H2 since the H2 in spent fuel leaching                                                  of the leachant (Table 3-6) (e.g., ionic strength and
(Röllin et al., 2001) is continuously supplied whereas                                              carbonate concentration, (Quiñones et al., 1999)).
in our case it is not.                                                                              Using a H2 atmosphere in the leaching experiments
                                                                                                    done with GBW has a measured effect on the oxi-
                                                                                                    dation/dissolution rate of the matrix whereas in GW
Figure 3-27 shows a compilation of the evolution of
                                                                                                    it did not. However, this is not a negligible effect of
U in GW as a function of the atmosphere used in the
                                                                                                    the UO2 corrosion as would be expected from the
leaching experiments. The axis labels used are identi-
                                                                                                    literature (Röllin et al., 2001).
cal to those in Figure 3-26 to make understandable
the graphs to the reader. When the leachant used is
GW, in the first steps of the experiments, only a                                                   In conclusion, the experimental results suggest that
slightly different behaviour is observed as a function                                              the presence of H2 (1 bar) in leaching experiments
of the atmosphere used in the experiments. In the se-                                               performed using ( radiation has beneficial effect
rial done with H2 a lower dissolution rate than in                                                  only for short times. This effect could be explained
presence of Ar is revealed. At the end of the experi-                                               due to the consumption of H2 because of the inter-
ments, U achieves similar values independently of the                                               action with the radiolytic products generated by (
atmosphere used                                                                                     radiation in the system.



                                                                                                                                                                                  57
Development of a Matrix Alteration Model (MAM)




                                                    10-4




                                                    10-5
                      [U] / mol · (kg de H2O) -1




                                                         -6
                                                    10
                                                                                                                 Ar (1 atm)
                                                                                                                                           filtered
                                                                                                                                           ultrafiltered
                                                                                                                 H2 ( 1 atm)
                                                         -7
                                                                                                                               without g radiation
                                                    10


                                                              0        20              40             60             80                  100               120
                                                                                                   time / d


                                                   Figure 3-27. Evolution of the U in leaching experiments performed in GW under ( radiation (Quiñones et al., 2004).




Furthermore, and from experimental evidence obtai-                                                   presence of a H2 atmosphere is lower than in grani-
ned in this study, on synthetic bentonitic-granitic                                                  te groundwater as a consequence of the amount of
groundwater, the U concentration reached in the                                                      carbonate in the synthetic groundwater.




58
4. Base Case Calculations




                            4. Base Case
                             Calculations
4. Base Case Calculations
                                                                                                                               4. Base Case Calculations



                                                                             ary conditions, geometry, parameters and kinetic
4.1. General parameters for                                                  reactions see the conceptual model report D12
     the base case calculations                                              (Martínez-Esparza et al., 2004b).

In this section the results and discussion of the ex-
trapolation of the MAM model from 103 to 106                                 4.2. Boundary conditions
years are presented. This extrapolation was per-
formed considering that the waste container failed                                and parameters
at 1000 years and, therefore, this time was used as
                                                                             The boundary conditions and parameters used in
starting point until one million years from repository
                                                                             the different case base studies are summarised in
closure (end time). The reference spent fuel for the
                                                                             Table 4-1.
base case calculation has a burnup of 41.5
MWd·kg-1 U, with a geometry consisting of a fuel                             Most of the parameters and boundary conditions
pellet surrounded by a gap full of water. The geo-                           are similar with no dependence on the environmen-
chemical conditions vary with the repository con-                            tal conditions as depicted in Table 4-1. Slight differ-
cept, but it has been taken a constant pH of 7 for                           ences in the water layer and alpha dose rates used
the base case (see next sections for water composi-                          are not relevant in the results obtained.
tion in the different media). In addition, a constant
H2 content coming from container corrosion has                               Table 4-2 gives alpha dose rates used in the differ-
also been considered. For more details on bound-                             ent time-periods in the three media studied.


       Table 4-1
       Boundary conditions and parameters used in the base cases (Martínez Esparza et al., 2004b).

       Parameter                                  Granite                              Clay      Salt

        Spent Fuel                                 41.5 MWd·kg-1 U

        Geometry                                   Fuel Pellet surrounded by water (D12)

        Water Layer                                45 µm                                          40 µm

                                                   Specific, 70cm2/g (D12
        Surface Area                                                                              Geometric
                                                   (Martínez Esparza et al., 2004b))

        Alpha dose rate                            Table 4-2                                      Calculated (CEA inventory)

        G values                                   H2O                                            5 M NaCl

        Water composition                          Evolving with time                  Fixed with time

        H2 Partial Pressure                        3 bar constant                                 0 initial

        Canister Failure                           1.000 y

        Timing                                     1.000.000 y

        Temperature                                25ºC

                                                                                                  D4 (Kelm and Bohnert, 2004)
                                                   D4 (Kelm and Bohnert, 2004)
                                                                                                  Water system
        Radiolysis Scheme                          Water system
                                                                                                  Carbonate system
                                                   Carbonate system
                                                                                                  Chloride system

        UO2 alteration scheme                      New scheme (D13)                               “Christensen” scheme (D4)
                                                   (Martínez Esparza et al., 2004a)               (Kelm and Bohnert, 2004)




                                                                                                                                                    61
Development of a Matrix Alteration Model (MAM)



         Table 4-2
         Alpha dose rates (Gy/s).

                        time / year              Granite and Clay (Quiñones et al., 2000)   Salt (Kelm and Bohnert, 2004)

                           1.000                                3.46·10-2                             2.97·10-2

                           2.500                                1.63·10-2

                           5.000                                1.23·10-2                             9.43·10-3

                          10.000                                8.22·10-3                             7.04·10-3

                          25.000                                4.12·10-3

                          50.000                                1.82·10-3                             1.52·10-3

                          100.000                               6.69·10-4                             5.92·10-4

                          500.000                               3.08·10-4                             2.85·10-4




However, a direct comparison of the different matrix
alteration rates as a function of the environment is
                                                                         4.3. Granite reference case
not possible because some of the parameters and                               calculation
approaches used for their calculations are also dif-
ferent. In granite and clay, a specific surface area of                  In addition to the general parameters mentioned in
70 cm2·g-1, as stated in the D12 report (Martínez                        the conceptual model, alpha dose rate evolution
Esparza et al., 2004b), is used both to calculate the                    and chemistry of the groundwater are also needed
total number of reactive sites to be included in the                     for the base case in granite.
reaction scheme and to normalise the obtained cor-
rosion rate instead of the geometric surface area                        The alpha dose rate evolution is given in Table 4-2.
used to calculate the alpha dose rate. This is based                     It has been taken from Quiñones et al. (Quiñones et
on the fact that the majority of the oxidising species                   al., 2000), following the methodology of Rodríguez
will be generated in the ionised layer (geometric                        Almazán et al. (Rodríguez Almazán et al., 1998).
surface area) for calculating alpha dose rates, but                      This methodology takes into account the inventory of
these oxidising species will be able to penetrate in                     the reference fuel (alpha activity is dominated by the
the cracks and attack the exposed surface (total sur-                    isotopes of Pu, U, Cm and Am), the self-absorption
face area) for calculating matrix alteration rates.                      of alpha particles in the spent fuel itself and their
                                                                         range in water and the energy deposited in the gap
On the other hand, in the saline base case the geo-                      water. The G values for different species and water
metric area is used instead, in order to be consistent                   type compositions are given in Table 4-3.
with the calculated alpha dose rate. Moreover, both
models use different mechanisms for the UO2 sur-                         On the other hand, the geochemical evolution of
face alteration. Granite and clay base cases are                         the contacting granitic groundwater has been taken
calculated by using a new matrix alteration scheme                       from the Spanish performance assessment exercise
reported in the D13 (Martínez Esparza et al.,                            ENRESA-2000 (Quiñones et al., 2000). A calcula-
2004c), while the salt base case is calculated by us-                    tion was made to account for the interaction be-
ing the so-called “Christensen” scheme reported in                       tween granitic waters and the bentonite surrounding
the D4 (Kelm and Bohnert, 2004).                                         the disposed spent fuel. The result of this interaction
                                                                         is a progressive alkalinisation of the contacting wa-
Those parameters and boundary conditions related                         ter, leading to higher pH and higher bicarbonate
to the different environments are summarised in Ta-                      content. The evolution of the relevant species is
ble 4-3 and Table 4-4.                                                   given in Table 4-4.



62
                                                                                                            4. Base Case Calculations



Table 4-3
G" values (molec/100eV).

                 Species                                Granite and Clay                          Salt

                    OH                                        0.23                                0.06

                   e-aq                                       0.06                                0.06

                    H                                         0.20                                0.26

                    H2                                        1.25                                1.52

                   H2O2                                       0.95                                0.23

                   H+                                         0.06

                   OH-                                                                            1.01

                   HO2                                        0.21                                0.05

                    Cl-                                                                           -1.62

                   ClOH-                                                                          0.55

                   HClO                                                                           1.07

                   H2O                                       -2.56                                -3.25




Table 4-4
Water compositions used in the three media (Martínez Esparza et al., 2004c).

                          Granite                                      Clay                          Salt

     time (y)               pH           HCO3-(M)              pH              HCO3-(M)    pH                 Cl-(m)

      1.000                6.71          1.75·10-3

      2.500                6.74          2.09·10-3

      5.000                6.78          2.55·10-3

     10.000                6.82          3.21·10-3
                                                              7.24             1.35·10-3   7.00                5.60
                                                 -3
     25.000                7.29          4.48·10

     50.000                8.18          5.14·10-3

       105                 8.53          5.28·10-3

      5·105                8.56          5.28·10-3




                                                                                                                                 63
Development of a Matrix Alteration Model (MAM)



It is important to remark that in the reference case a                                                      pressure of hydrogen in the vault is controlled by the
new approach has been done in order to simulate                                                             iron and cladding corrosion. As can be observed
the decrease of the matrix surface as a function of                                                         (Figure 4-1), the H2O2 concentration in solution de-
leaching time. In this calculation it is considered that                                                    creases from 8·10-9 to 9·10-11 mol·dm-3 after one
specific surface area and the density of coordination                                                       million years. This trend may be explained by the
points remains constant, although for each time step                                                        lower hydrogen peroxide generation as a conse-
the reactivity of the solid is recalculated.                                                                quence of the alpha dose rate decrease with time as
                                                                                                            well as to its consumption by oxidation of the solid
The results obtained and plotted in the following fig-                                                      surface and recombination reactions.
ures were obtained using the Maksima Chemist
code (Carver et al., 1979). Calculations has been
                                                                                                            However, in the case of O2 concentration in solu-
also done in parallel for intercomparison with the
                                                                                                            tion the behaviour is the opposite to the one ob-
Chemsimul code (Kirkegaard and Bjergbakke,
                                                                                                            served for H2O2, i.e., an increase of concentration
1999) leading to the same results (Quiñones et al.,
                                                                                                            in solution with the decrease of alpha dose rate
2003b). Furthermore, the model considers the con-
                                                                                                            considered. This fact is associated to the interaction
centration and dose profile constants between peri-
                                                                                                            of the molecular species with the UO2 surface but
ods of time, as they are pointed out on Table 4-2.
                                                                                                            also coupled to the H2O2 decomposition in solution
The final results obtained for each species are
                                                                                                            and ulterior formation of O2.
linked and explained together which those data that
could make easier the understanding to the reader.
                                                                                                            The results obtained considering the hypothesis
Figure 4-1 compiles the evolution of the concentra-                                                         aforementioned allow to predict the matrix alter-
tion in solution of the molecular species, i.e., H2O2,                                                      ation rate as a function of the alpha dose rate and
H2 and O2 (square, circle and triangle, respectively).                                                      groundwater evolution. A decrease of the alteration
The H2 concentration is a constant during the com-                                                          rate as a function of time is obtained (Figure 4-2).
plete evaluation time “PpH2 = 3 bar”. This restric-                                                         This is related to the decrease of the alpha dose
tion of the reference case is justified as the partial                                                      rate. This phenomenon is clearly depicted in Figure




                                               2.0x10-3
                   conc. / mol · kg-1 of H2O




                                                   10-8



                                                        -9
                                                   10


                                                                      H2O2
                                                       -10            H2
                                                  10                  O2

                                                                  3                             4                                 5                                 6
                                                             10                            10                                10                                10
                                                                                                     cooling time / year


                                                                             Figure 4-1. Evolution of the molecular species concentration in solution in granite reference case.



64
                                                                                                                                                     4. Base Case Calculations



4-3, where the matrix alteration rate is plotted ver-                                           ferent UO2 alteration scheme, namely “Christensen
sus the alpha dose rate.                                                                        scheme”, including the UO2 alteration by chlorine
                                                                                                species (see D4 (Kelm and Bohnert, 2004)). In addi-
Table 4-5 compiles the matrix alteration rate calcu-
                                                                                                tion, the model accounts for 56 recombination re-
lated for granite reference case. The highest value
                                                                                                actions with chlorine species. As shown in the D4
(5.7·10-13 mol·m-2·s-1) is obtained at the beginning
                                                                                                report (Kelm and Bohnert, 2004), these reactions
of the run. On the other hand, for times in the
                                                                                                are relevant in systems with high chlorine contents.
range of 105 – 106 years the predicted average al-
                                                                                                All results and discussion obtained are compiled in
teration rate is 1.5·10-14 mol·m-2·s-1. This alteration
                                                                                                D13 (Martínez Esparza et al., 2004a)
value is in accordance with experimental values ob-
tained in presence of hydrogen by Quiñones et al.                                               However, MAM model has been not applied to the
(Quiñones et al., 1998).                                                                        saline medium (chloride concentrations above 2
                                                                                                mole·dm-3) given the lack of contrasted and vali-
                                                                                                dated kinetic information and mechanisms concern-
4.4. Base case calculation in salt                                                              ing the oxidation of UO2 by chlorine species like
In the framework of the SFS project and within the                                              HClO, ClO3- , Cl2- etc. that are of relevance on the
WP4 (Martínez Esparza et al., 2004a) it has been                                                overall matrix alteration in these systems.
developed a radiolytic model to be used in granite
                                                                                                As well as the different UO2 alteration mechanisms,
medium by using a UO2 alteration scheme based
                                                                                                different approaches and parameters have been
on empirical and semi-empirical models, namely
                                                                                                used in granite and saline cases leading to results
“new alteration scheme”. As agreed in the final
                                                                                                that were not comparable as reported in the D13
meeting, the model has been also applied to a
                                                                                                (Martínez Esparza et al., 2004a). In order to identify
clayed medium by obtaining the same good results.
                                                                                                the differences and to check the capabilities of both
On the other hand, the model used in saline media                                               models for calculating matrix alteration rates in all
has been developed within WP2 (with M. Kelm as                                                  the environments it was agreed in the final project
WP coordinator) and is based on a completely dif-                                               meeting held in Wettingen the first quarter of Sep-




                                                           10-12
                                                                                                                           Granite. Reference case
                pellet alteration rate /mol · m-2 · s -1




                                                                -13
                                                           10




                                                           10-14




                                                                      103      104                                105                                 106
                                                                                         cooling time / year


                                                                            Figure 4-2. Evolution of the pellet alteration rate in granite conditions. Reference case.



                                                                                                                                                                          65
Development of a Matrix Alteration Model (MAM)




                                                                -12
                                                           10
                      alteration rate /mol · m-2 · s -1                            Granite. Reference case




                                                           10-13




                                                                -14
                                                           10




                                                                           -4                                     -3                                   -2
                                                                      10                                     10                                   10
                                                                                                                          a dose rate / Gy · s
                                                                                                                                             -1




                                                                                Figure 4-3. Matrix alteration rate calculated versus the alpha dose rate considered for granite reference case.




         Table 4-5
         Evolution of the matrix alteration rate – Granite reference case.

                                                      time / year                                   Matrix alteration rate / mol·m-2·s-1                    a dose rate / Gy·s-1

                                                           1000                                                        5.697·10-13                               3.46·10-2

                                                           2500                                                        1.951·10-13                               1.63·10-2

                                                           5000                                                        1.187·10-13                               1.23·10-2

                                                          10000                                                        7.457·10-14                               8.22·10-3

                                                          25000                                                        4.045·10-14                               4.12·10-3

                                                          50000                                                        3.126·10-14                               1.82·10-3

                                                          100000                                                       1.526·10-14                               6.69·10-4

                                                          500000                                                       6.426·10-15                               3.08·10-4

                                                          1000000                                                      4.390·10-15                               2.22·10-4




66
                                                                                                                   4. Base Case Calculations



tember to apply both models to the other environ-                          experimental series were taken for modelling, one
ments of interest for comparison, that is to apply the                     for a spent fuel pellet (sample K9) and another one
Christensen scheme to the granite media and the                            for a spent fuel fragment (sample F3). There were
new alteration scheme to the salt.                                         also powder samples, but their specific surface had
                                                                           a very large uncertainty and it was decided not to
The results of applying MAM radiolytic model that is
                                                                           include them in the modelling analysis.
the “new alteration scheme” to the saline case base
are included hereafter. It also present an exploration                     The following approaches and assumptions have
of the capabilities and extensions needed to be done                       been taken:
in the model if we want to extend its application to a                        o    Recombination of radicals have been taken
saline medium.                                                                     from deliverable D4 (Kelm and Bohnert, 2004)
                                                                                   of the SFS project
4.4.1. Base case                                                              o    The chlorine system (recombination reactions,
Our calculations for the base case in granite have                                 only homogeneous) has also been taken from
previously been reported in the D13. In this section                               Kelm et al. (Kelm and Bohnert, 2004).
we present an attempt to calculate the base case in                           o    The oxidation-dissolution mechanism of the
salt for comparison purposes. Calculations in both                                 UO2 has been taken from the D13 report of the
cases have been done by using the same ap-                                         SFS project (Martínez Esparza et al., 2004a).
proaches and by considering the same input param-                                  Oxidation by chlorine species is not included in
eters. The result of these calculations are summa-                                 this reaction scheme.
rised in Table 4-6.                                                           o    pH has been kept constant during the simula-
The lower value obtained in the saline medium is at-                               tions.
tributed to the lack of a detailed mechanism involv-                          o    Concentration of active sites has been derived
ing the oxidation of the UO2 by the chlorine species                               from the density of sites (from (Clarens et al.,
present in the system.                                                             2003a)) multiplied by the total reactive surface
The new alteration scheme does not account for the                                 of the sample and divided by the volume of the
oxidation of UO2 by any chlorine species although it                               solution.
is well known these processes are of relevance in                             o    Only gamma radiation has been taken into
salt media. In order to quantify the importance of                                 consideration. Although alpha and beta radia-
these alteration mechanisms we have done an at-                                    tion are also present, their contribution to
tempt to model some experimental data obtained in                                  radiolytic gas generation is small, as evidenced
brines with our present mechanism, the results are                                 by the fact that no enhanced gas generation is
shown in the next section.                                                         present in powder samples (Grambow et al.,
                                                                                   1996). In addition, gamma dose rate has been
Radiolytic model applied to an experimental system                                 taken from a similar Swedish fuel, as given in
Carefully spent fuel dissolution experiments in brines                             the previous European project (Grambow et
carried out by A. Loida at INE-FzK (described in                                   al., 2000).
(Grambow et al., 1996)) were selected for this mod-                           o    G-values for a 5 M NaCl brine solution have
elling exercise. The spent fuel samples were intro-                                been taken, as given in Kelm et al. (experimen-
duced in an autoclave with a brine solution, and so-                               tal series were run with a 95 % saturated NaCl
lution and gas samples were taken periodically. Two                                solution (Kelm and Bohnert, 2004)).


       Table 4-6
       Parameters considering in the salt base case calculations.

                                                                                                UO2 alteration
             Medium            Water chemistry      Radiolytic yields      Surface area                          r (mol·m-2·s-1)
                                                                                                  scheme

               Salt            5 M Cl-,no CO3‘s           brines        Specific (70 cm2·g-1)     New (D13)        1.80·10-15

                               2·10-3 M HCO3-,
              Granite                                     water         Specific (70 cm2·g-1)     New (D13)        5.70·10-13
                                  0.01 M Cl-



                                                                                                                                        67
Development of a Matrix Alteration Model (MAM)



  o   Congruent dissolution of strontium has been                  UO2 matrix. As a first approach and to assess
      assumed, given by the authors as matrix disso-               semi-quantitatively relevant process or processes, we
      lution indicator, taking into account the mole               have added an overall reaction. This reaction ac-
      fraction of Sr related to U in the spent fuel.               counts for the alteration of UO2 by chlorine species
                                                                   and it has been added to the alteration mechanism
The simulations for the two experimental series have               for the fitting of the model to the experimental data:
given the results shown in Figure 4-4.

As expected, our model underestimates the dissolu-                    UO2 + Cl2- ® UO3 + Products                        k = 500 M-1s-1
tion of strontium (and therefore, the fuel alteration
rate). This is clearly due to the lack of an oxidation             We have selected the Cl2- anion as it is the most re-
mechanism between the chlorine species and the                     active species according to the alteration mecha-




                                                                    K9
                                1.E-06


                                1.E-07

                                1.E-08
                       Sr (M)




                                1.E-09


                                1.E-10


                                1.E-11                                                      Experimental values
                                                                                            Model

                                1.E-12
                                         0       200      400               600               800                 1000
                                                                 Time (d)

                                                                    F3
                                1.E-06

                                1.E-07


                                1.E-08
                       Sr (M)




                                1.E-09

                                1.E-10


                                1.E-11                                                      Experimental values
                                                                                            Model

                                1.E-12
                                         0       200       400              600                800                1000
                                                                 Time (d)


                                                       Figure 4-4. Simulations for the two experimental series under brine conditions.



68
                                                                                                                                  4. Base Case Calculations



nism of Christensen (Kelm and Bohnert, 2004). The                             case calculation for the saline medium we have cal-
kinetic constant has been “calibrated” to give the                            culated once again the base case by introducing
best fit to experimental data, as shown below:                                also this reaction in the new alteration scheme. The
                                                                              result of this simulation, together with the other two
Looking at these results, it seems quite clear the ne-
                                                                              already discussed, is given in the Table 4-7.
cessity of including an alteration mechanism ac-
counting for the chlorine species (Figure 4-5).
                                                                              As expected, the alteration rate when oxidation by
                                               -                              the Cl2- species is included in the system increases
4.4.2. Base case with the new Cl reaction     2
                                                                              giving an alteration rate slightly higher than the one
Finally, in order to check the effect of including a re-                      obtained in the granite medium. A higher alteration
action as the one previously “calibrated” in the base                         rate in saline medium than in granite is the one we




                                                                                K9
                            1.E-06


                            1.E-07


                            1.E-08
                   Sr (M)




                            1.E-09


                            1.E-10
                                                                                                         Experimental values
                            1.E-11                                                                       Model
                                                                                                         Model with Cl2[-]

                            1.E-12
                                     0              200                400               600               800                 1000
                                                                              Time (d)

                                                                                F3
                            1.E-06


                            1.E-07

                            1.E-08
                   Sr (M)




                            1.E-09

                            1.E-10
                                                                                                         Experimental values
                                                                                                         Model
                            1.E-11
                                                                                                         Model with Cl2[-]

                            1.E-12
                                     0               200               400                600              800                 1000
                                                                              Time (d)


                                     Figure 4-5. Simulations for the two experimental series under brine conditions considering chlorine species .



                                                                                                                                                       69
Development of a Matrix Alteration Model (MAM)



         Table 4-7
         Final alteration rates obtained for different reference case calculations.

                                        Water                                         Surface     UO2 alteration
                Medium                                   Radiolytic yields                                           r (mo·m-2·s-1)
                                      chemistry                                        area         scheme

                                   5 M Cl-,no CO3‘s                                 specific
                  Salt                                        Brines                                New (D13)         1.80·10-15
                                                                                  (70 cm2·g-1)

                                   2·10-3 M HCO3-,                                  specific
                 Granite                                       water                                New (D13)         5.70·10-13
                                      0.01 M Cl-                                  (70 cm2·g-1)

                                  5 M Cl-, no CO3‘s                                 specific     New (D13) with
                  Salt                                         brines                                                 7.70•10-13
                                                                                  (70 cm2•g-1)   the Cl2- reaction




should expect taking into account the more corro-                                more or less linear correlation between alteration
sive environment of brines.                                                      rate and dose rate.

                                                                                 On the other hand, there is a difference between
4.4.3. Conclusion                                                                both dissolution rates of roughly two orders of mag-
This exercise has to be taken as a first attempt to                              nitude, being higher in the granite base case. Al-
model dissolution data in brines. Obviously there is                             though, as stated before, these two corrosion rates
a need for a detailed mechanism for the alteration                               cannot be directly compared, this difference cannot
of UO2 by chlorine species. Therefore, further inves-                            be attributed to the different H2 pressures consid-
tigations are needed to elucidate this mechanism in                              ered. In fact, the granite base case considered a
order to be able to confidently predict alteration                               higher H2 concentration, which in principle would
rates in saline media with our model.                                            favour a lower dissolution rate. The difference is
                                                                                 more likely to be due to the presence of a significant
                                                                                 amount of carbonate in the granitic water, which is
4.5. Comparison of results                                                       known to enhance UO2 dissolution, and the differ-
                                                                                 ent radiolytic yields in brines that make a less oxidis-
     in different media                                                          ing environment in this medium. In addition, the fact
Matrix dissolution rates calculated in granite and sa-                           of considering different UO2 oxidation schemes may
line case bases are compared in Figure 4-6. It                                   also contribute to the differences found in both
should be pointed out that a direct comparison of                                cases. The sensitivity analysis will clarify these differ-
dissolution rates is hindered by the fact that different                         ences.
assumptions were made for the two different media
treated here. In the granite base case, a total sur-
face area of 70 cm2·g-1, as stated in the D12 report                             4.6. Comparison with published
(Martínez Esparza et al., 2004b), was used both to
calculate the total number of reactive sites to be in-
                                                                                      rates and rate laws
cluded in the reaction scheme and to normalize the                               A literature search of rate laws derived from experi-
obtained corrosion rate. On the other hand, in the                               mental data and reported in several environmental
saline base case the geometric area was used in-                                 conditions has been done in order to compare these
stead, in order to be consistent with the calculated                             dissolution rates with the ones calculated when ap-
alpha dose rate. Moreover, both models use differ-                               plying the MAM, both in granite and salt.
ent mechanisms for UO2 alteration. In spite of that,
some interesting comments can be drawn. Firstly,                                 Dissolution data calculated by using rate laws found
we can see that in both cases there is a decrease in                             in the literature are depicted in Figure 4-8 and Figure
the dissolution rate as a function of time, driven by                            4-9. Figure 4-8 accounts for the rate laws elucidated
the decrease in alpha dose rate. In fact, if we plot                             from experiments carried out in presence of carbon-
dissolution rates as a function of alpha dose rate                               ate while Figure 4-9 depicts the rate laws derived
(Figure 4-7) we can see that in both cases there is a                            from experiments in carbonate-free media. Both fig-



70
                                                                                                                                                                                    4. Base Case Calculations




                                                             1.E-12

                                                                                                                                                   Granite Base Case
                                                             1.E-13
Dissolution rate (mol · m-2 · s-1)




                                                             1.E-14



                                                             1.E-15



                                                             1.E-16                               Saline Base Case



                                                             1.E-17
                                                                 1.E+03                                 1.E+04                                  1.E+05                                     1.E+06
                                                                                                                            Time (y)



                                                                                          Figure 4-6. Comparison of dissolution rates obtained by the model in the two media: granite and salt.




                                                             1.E-12



                                                             1.E-13
                        Dissolution rate (mol · m-2 · s-1)




                                                             1.E-14



                                                             1.E-15



                                                             1.E-16                                                                                                    Granite Base Case
                                                                                                                                                                       Saline Base Case

                                                             1.E-17
                                                                1.E-04                                  1.E-03                                  1.E-02                                     1.E-01
                                                                                                                                          -1
                                                                                                                      alpha dose rate (Gy·s )



                                                                      Figure 4-7. Comparison of dissolution rates vs. alpha dose rates obtained by the model in the two media: granite and salt.



                                                                                                                                                                                                         71
Development of a Matrix Alteration Model (MAM)



ures also include the case base results in granite and                                                           lished rate laws with oxidant dependence overesti-
in salt respectively for comparison.                                                                             mate the calculated dissolution rates of the granite
                                                                                                                 case base. Most of these rate laws were derived
This comparative analysis indicates that the extrapo-                                                            from data obtained from spent fuel dissolution tests.
lation of empirical and semi-empirical models with                                                               These higher rate constants of the empirical and
some oxygen or hydrogen peroxide dependence                                                                      semi-empirical models, should be attributed to the
predict dissolution rates in quite good agreement                                                                nature of the solid sample probably due to the effect
with the ones calculated in the base cases. That is                                                              of a higher dose rate and a contribution from the b,
the case of the rate law of de Pablo et al. (de Pablo                                                            g field. In addition, the range of applicability of
et al., 1999) for UO2, when applying the conditions                                                              some of these rate laws is also quite limited.
given in the base case, the range of dissolution
rates agrees well with the long-term alteration rate                                                             In the absence of carbonates the predicted dissolu-
of the granite base case. On the other hand, the                                                                 tion rates in the saline case are in fair agreement with
granite base case predicts an even lower dissolution                                                             the rates published by de Pablo et al. (de Pablo et
rate at long times than the range dissolution rates                                                              al., 2001; de Pablo et al., 2003) for UO2 with O2
reported under reducing conditions, explained by                                                                 and H2O2 as oxidants respectively. It is important to
the assumption of an initial H2 content that remains                                                             highlight that although the rate laws were derived
constant during all the evaluation time. Those mod-                                                              from very different media, they may reproduce the
els without oxygen or hydrogen peroxide depend-                                                                  calculated dissolution rates in the saline case base.
ence overestimate those dissolution rates calculated
for the base case both in granite and in salt.                                                                   In general, there is a good agreement between the
                                                                                                                 dissolution rates calculated in both media with the
This is because all these rate laws were derived from                                                            range of dissolution rates calculated by using the
experimental systems with larger oxidant concentra-                                                              rate laws elucidated both in presence and absence
tions than the ones expected under repository condi-                                                             of carbonates in the system respectively. The ranges
tions. It is also important to highlight that other pub-                                                         of dissolution rates calculated by using the empirical




                                                1.E-08
                                                                                                                                         SF, 0.002<P(O2)<0.2atm
                                                                                                                                         r = f (Ctot, pH, T)
                                                1.E-09                SF, P(O2)=0.2atm                                                  (Gray et al., 1992)
                                                                      r = f (Ctot, pH)
                                                                      (Röllin et al., 2001)
                                                1.E-10                                                     SF
           Dissolution rate (mol · m-2 · s-1)




                                                                                                                                                       UO2, pH>10
                                                                                                           r = f (Ctot, pH, O2, T)
                                                                                                                                                       r = f (Ctot, H2O2)
                                                                                                           (Steward & Gray, 1994)
                                                1.E-11                                                                                                 (Hiskey, 1980)

                                                                   Granite Base Case
                                                1.E-12                                                                                         UO2, pH =7.5-8.5
                                                                                                                                               r = f (Ctot., O2)
                                                                                                                                               (de Pablo et al., 1999)
                                                1.E-13
                                                                     SF, H2
                                                1.E-14               exp. range
                                                                     (Röllin et al., 2001)

                                                1.E-15
                                                    1.E+03                                    1.E+04                                 1.E+05                                 1.E+06
                                                                                                               Time (y)



                                           Figure 4-8. Comparison of the result of the granite base case with published rate laws applied to conditions in the base case (carbonate
                                                                              content, O2 or H2O2 concentration) and experimental rates measured under a hydrogen atmosphere.



72
                                                                                                                                                          4. Base Case Calculations




                                                 1.E-11
                                                             SF, H2                                                        UO2, pH = 6
                                                             exp. range                                                    r = f (H2O2)
                                                 1.E-12      (Loida et al., 2003)                                          (de Pablo et al., 2000)
            Dissolution rate (mol · m-2 · s-1)




                                                 1.E-13


                                                 1.E-14
                                                                                                                                       Saline Base Case

                                                 1.E-15

                                                                                    UO2
                                                 1.E-16                             r = f (pH, O2)
                                                                                    (de Pablo et al., 2002)

                                                 1.E-17
                                                    1.E+03                              1.E+04                                1.E+05                       1.E+06
                                                                                                              Time (y)



                               Figure 4-9. Comparison of the result of the saline base case with published rate laws applied to conditions in the base case (absence
                                                         of carbonate, O2 or H2O2 concentration) and experimental rates measured under a hydrogen atmosphere.




and semi-empirical models differ in about one order                                                                 mation has been extensively reported in the D12
of magnitude depending on the presence or not of                                                                    (boundary conditions and parameters) (Martínez Es-
carbonate in the studies carried out for deriving                                                                   parza et al., 2004b) and the D13 (matrix alteration
such models.                                                                                                        scheme) (Martínez Esparza et al., 2004c) as well as
                                                                                                                    summarised in the above section.
This comparative analysis highlights that oxidant
compounds as well as carbonate concentration are                                                                    The main difference with respect the granite case
very important variables of the system when predict-                                                                base refers to the groundwater composition used for
ing long-term matrix alteration dissolution rates.                                                                  performing the calculations. Clay groundwater com-
                                                                                                                    position was supplied by WP5 and corresponds to
                                                                                                                    the Opalinus clay reference water composition that
4.7. Base case calculation in clays                                                                                 was obtained after equilibrating the bentonite refer-
                                                                                                                    ence water with the Opalinus clay porewater (John-
4.7.1.General parameters used for                                                                                   son, 2004). The resulting composition is given in
                                                                                                                    Table 4-8.
      the clay reference case
In the framework of the SFS and because as agreed
in the final project meeting held in Wettingen (Swit-
                                                                                                                    4.7.2.Clay reference calculation
zerland) 8-10 of September it was agreed to apply
                                                                                                                    The results of applying the MAM to the clay environ-
MAM model to the spent fuel behaviour in a clay en-
                                                                                                                    ment are presented below.
vironment in addition to the granite and salt. Case
base in clays was calculated by using the same ap-                                                                  Figure 4-10 compiles the evolution of the concen-
proaches as the ones applied in granite reference                                                                   tration in solution of the molecular species in the
case; that is the matrix alteration scheme, parameters                                                              fuel–cladding gap (square, circle and triangle repre-
and most of the boundary conditions. All this infor-                                                                sents the concentration of H2O2, H2 and O2, re-



                                                                                                                                                                               73
Development of a Matrix Alteration Model (MAM)



         Table 4-8
         Opalinus clay reference water composition (used for calculations the bentonite reference water) (Johnson, 2004).

                                                                                                  Maximum expected variation

                                         Opalinus Clay               Bentonite1               Bentonite1                    Bentonite1
                                        reference water           reference water              low pH                        high pH

                     pH                      7.24                      7.25                      6.90                         7.89
               log pCO2 [bar]                -2.2                      -2.2                      -1.5                         -3.5

            Ionic strength [eq/L]        2.28 × 10-1                3.23 × 10-1               3.65 × 10-1               2.63 × 10-1

                    CO3                  2.70 × 10-3                2.83 × 10-3               6.99 × 10-3               5.86 × 10-4

                     Na                  1.69 × 10-1                2.74 × 10-1               2.91 × 10-1               2.49 × 10-1

                     Ca                  1.05 × 10-2                1.32 × 10-2               1.33 × 10-2               1.34 × 10-2

                    Mg                   7.48 × 10-3                7.64 × 10-3               8.91 × 10-3               1.34 × 10-3

                     K                   5.65 × 10-3                1.55 × 10-3               1.67 × 10-3               1.38 × 10-3

                    SO4                  2.40 × 10-2                6.16 × 10-2               6.39 × 10-2               5.59 × 10-2

                     Cl                  1.60 × 10-1                1.66 × 10-1               2.06 × 10-1               8.61 × 10-2

                     Fe                  4.33 × 10-5                4.33 × 10-5               7.74 × 10-5               8.00 × 10-6

                     Al                  2.17 × 10-8                1.92 × 10-8               1.53 × 10-8               7.55 × 10-8

                     Si                  1.78 × 10-4                1.80 × 10-4               1.80 × 10-4               1.84 × 10-4




spectively). Hydrogen concentration is kept constant                          2004a) for the granite base case allow predicting the
during all the evaluation time with a partial pressure                        matrix alteration rate as a function of the alpha dose
of 3 bar as in the granite base case, D13 report.                             rate and cooling time. As is the other base cases
The H2O2 concentration in solution decreases from                             (granite and salt) a decrease of the alteration rate as
4.5·10-9 to 4.4·10-11 mol·dm-3 after one million                              a function of time is observed (Figure 4-11). This be-
years. The decrease on the hydrogen peroxide con-                             haviour relates to the decrease of alpha dose rate
centration is explained through the alpha dose rate                           due to the cooling time of the spent fuel. Figure 4-12
decrease with time, i.e., a lower hydrogen peroxide                           shows clearly the influence of the alpha dose rate.
generation and its consumption by oxidation of the
                                                                              Table 4-9 summarises the matrix alteration rates cal-
solid surface and recombination reactions.
                                                                              culated for the clay base case. Matrix alteration rates
As in the granite base case, the oxygen concentra-                            range between 3.10-13 and 4.10-15 mol·m-2·s-1, for
tion evolution shows a different behaviour than the                           cooling times of 1.000 and 1.000.000 years, re-
one calculated for the hydrogen peroxide concen-                              spectively.
tration. However, the trend is different to the one
observed in the granite base case. In the present
calculation, oxygen concentrations in solution keep                           4.7.3.Comparison between granite
quite constant during all the evaluation time with a                                and clay reference case
value around 8·10-9 mol·dm-3.
                                                                              In order to make easier the understanding to the
The results obtained considering the hypothesis pre-                          reader, a comparison between the results obtained
sented in the D13 report (Martínez Esparza et al.,                            for clay and granite reference cases has been done.



74
                                                                                                                                                                        4. Base Case Calculations




                                                     -3
                                            2.0x10
conc. / mol · kg-1 of H2O




                                                     -8
                                               10



                                                     -9
                                               10

                                                                   Clay Reference case
                                                                               H2O2
                                               10   -10                        H2
                                                                               O2

                                                               3                                       4                                 5                                   6
                                                          10                                      10                                10                                  10
                                                                                                            cooling time / year


                                                                                      Figure 4-10. Evolution of the molecular species concentration in solution in clay reference case.




                                                   -12
                                              10
                                                                                                                                                 Clay. Reference case
 pellet alteration rate /mol · m-2 · s -1




                                              10-13




                                                   -14
                                              10




                                                          103                                     104                               105                                  106
                                                                                                            cooling time / year



                                                                                                            Figure 4-11. Evolution of the pellet alteration rate in a clay environment.



                                                                                                                                                                                             75
Development of a Matrix Alteration Model (MAM)



         Table 4-9.
         Evolution of the matrix alteration rate – Clay base case.

                                                         time / year                          Matrix alteration rate / mol·m-2·s-1                   a dose rate / Gy·s-1

                                                            1000                                          3.308·10-13                                     3.46·10-2

                                                            2500                                          1.528·10-13                                     1.63·10-2

                                                            5000                                          1.135·10-13                                     1.23·10-2

                                                           10000                                          7.567·10-14                                     8.22·10-3

                                                           25000                                          3.786·10-14                                     4.12·10-3

                                                           50000                                          1.832·10-14                                     1.82·10-3

                                                          100000                                          8.803·10-15                                     6.69·10-4

                                                          500000                                          4.411·10-15                                     3.08·10-4

                                                          1000000                                         4.380·10-15                                     2.22·10-4




It is important to remember that the main difference                                                                 case evolved water is considered (Table VIII in (Martí-
between cases is the groundwater chemistry, i.e., the                                                                nez Esparza et al., 2004c)). This change has a direct
clay reference case has a constant groundwater com-                                                                  effect on the matrix alteration rate due mainly to the
position (Table 4-8) whereas in the granite reference                                                                different carbonate concentrations in solution.




                                                             10-12
                                                                               Clay. Reference case
                     alteration rate /mol · m-2 · s -1




                                                                  -13
                                                             10




                                                                  -14
                                                             10




                                                                        10-4                           10-3                              10-2
                                                                                                              a dose rate / Gy · s
                                                                                                                                 -1




                                                                                Figure 4-12. Matrix alteration rate calculated versus the alpha dose rate considered for clay base case.



76
                                                                                                                                               4. Base Case Calculations



The results of the base cases, granite and clay are                                        dant increases until 105 years where there is a slight
depicted in the next figures (Figure 4-13 and Figure                                       decrease to reach a constant level until the end of
4-14).                                                                                     the evaluation time. This effect may be explained by
                                                                                           the different chemical composition of both ground-
Matrix alteration rates as a function of time follow
                                                                                           waters coupled to the hydrogen peroxide decompo-
the same trend in both cases, a decrease of this pa-
                                                                                           sition and the mass reduction effect after 2500
rameter with time (Figure 4-13). However, matrix al-
                                                                                           years.
teration rates in clay are lower than the ones calcu-
lated in granite. The difference is explained by the
different carbonate concentrations and pH of both
groundwaters.
                                                                                           4.8. Matrix alteration rates
Figure 4-14 shows matrix alteration rates as a func-
                                                                                                of the reference cases
tion of the alpha dose rates. This plot depicts the                                        Table 4-10 and Figure 4-16 summarise the matrix
same trend in both cases, as expected enhancing the                                        alteration rates obtained for the three environments.
matrix alteration rates when increasing dose rates.                                        Matrix alteration rates in granite are extensively re-
                                                                                           ported in the D13, matrix alteration rates in clay are
However, the figure changes when looking at the
                                                                                           reported in the next chapter of the present deliver-
molecular species (Figure 4-15). Hydrogen peroxide
                                                                                           able and finally matrix alteration rates in salt are
concentrations show a similar trend although they
                                                                                           taken from a technical note that is included as An-
are slightly lower in clay than in granite at the be-
                                                                                           nex of this report (Kelm, 2004).
ginning and at the end of the calculated time-peri-
ods. On the other hand, oxygen concentrations
evolve completely different in both cases as a func-
tion of time. Oxygen concentrations are quite con-
                                                                                           4.9. Sensitivity analysis of MAM
stant during all the evaluation time in the clay water                                     The sensitivity analysis of the granite base case is
whereas in the granite groundwater there is a clear                                        presented in this section. The objective is to identify
evolution with time. The concentration of this oxi-                                        and to assess the influence of the main variables of




                                                          10
                                                               -12                                        Reference case comparison
                                                                                                                       Granite          Clay
               pellet alteration rate /mol · m-2 · s -1




                                                               -13
                                                          10




                                                          10-14




                                                                     103   104                               105                                106
                                                                                    cooling time / year


                                                                           Figure 4-13. Evolution of the pellet alteration rate for granite and clay base cases.



                                                                                                                                                                    77
Development of a Matrix Alteration Model (MAM)




                                                                         -12
                                                                    10
                                                                                         Reference case comparison
                                                                                              Granite      Clay
                           alteration rate /mol · m-2 · s -1




                                                                         -13
                                                                    10




                                                                    10-14




                                                                                    -4                                      -3                                         -2
                                                                               10                                      10                                         10
                                                                                                                                 a dose rate / Gy · s
                                                                                                                                                       -1




                                                                                                                 Figure 4-14. Calculated matrix alteration rates in granite and clay vs. alpha dose rates.




                                                               2.0x10-3
                   conc. / mol · kg-1 of H2O




                                                                   10-8


                                                                                                                                                                            Reference Case Comparison
                                                                        -9
                                                                                                                                                                            Granite Clay
                                                                   10                                                                                                                        H2O2
                                                                                                                                                                                             H2
                                                                                                                                                                                             O2


                                                                  10-10


                                                                             103                                     104                                    105                                         106
                                                                                                                                 cooling time / year


                                                                                                       Figure 4-15. Evolution of the concentration of molecular species in solution for granite and clay.



78
                                                                                                                                                          4. Base Case Calculations



Table 4-10
Matrix alteration rates in mol·m-2·s-1 calculated at the different time-periods in the three environments.

          Time / year                                                      Granite                                 Clay                               Salt

                                            1.000                         5.70·10-13                        3.31·10-13                             1.57·10-12

                                            2.500                         1.95·10-13                        1.53·10-13

                                            5.000                         1.19·10-13                        1.14·10-13                             5.01·10-13

                                    10.000                                7.46·10-14                        7.57·10-14                             3.72·10-13

                                    25.000                                4.05·10-14                        3.79·10-14

                                    50.000                                3.13·10-14                        1.83·10-14                             8.04·10-14

                             100.000                                      1.53·10-14                        8.80·10-15                             3.12·10-14

                             500.000                                      6.43·10-15                        4.41·10-15                             1.50·10-14

                 1.000.000                                                4.39·10-15                        4.38·10-15




                                                                                                                       Reference case comparison
                                                                                                                      Granite           Clay       Salt
                                                           -12
                                                      10
           pellet alteration rate /mol · m-2 · s -1




                                                           -13
                                                      10




                                                      10-14



                                                                      3
                                                                 10                    104                                105                                106
                                                                                             cooling time / year


        Figure 4-16. Comparison of the evolution of the matrix alteration rate as a function of the environment considered. Granite and Clay
                             reference case were performed with MAM model and salt with Christensen model (Kelm and Bohnert, 2004).



                                                                                                                                                                               79
Development of a Matrix Alteration Model (MAM)



the system; that is parameters and boundary condi-                            4.9.1.Influence of the specific surface
tions, on the matrix alteration rate.
                                                                                    area of the pellet
Table 4-11 summarises the variables and the range
                                                                              In this section we have summarised the variation in
of values used in the sensitivity analysis. This table is
                                                                              the model output (granite case) when different val-
the result of several meetings organised in the
                                                                              ues of the specific surface area of the pellet are
framework of this project (Madrid 2003, Cambrils
                                                                              considered. The influence of this parameter on the
2003 and Madrid 2004) with the participation of all
                                                                              matrix dissolution rate was extensively discussed in
the partners for selecting the main variables and the
                                                                              the previous reports D12 (Martínez Esparza et al.,
range of values of interest.
                                                                              2004b) and D13 (Martínez Esparza et al., 2004c).
                                                                              In the present report, the objective is to develop fur-
It is important to clarify that this exercise only allows                     ther the influence that this parameter has on the
to foresee the effect of each modification on the fi-                         MAM output and if it is in agreement with the exper-
nal results, that is, it is intended to gauge the sensi-                      imental observation coming from the different expe-
tivity of the model to variations in the selected pa-                         riences done during the project or published in the
rameters. When possible, the output will be                                   bibliography.
compared to experimental observations performed
in this project or published in the literature. None-                         Using the data obtained extrapolating with the MAM
theless, it is expected that in cases where model lim-                        model (developed in this project) it is observed that
itations are known (as is the case, for example, with                         when the pellet specific surface is higher than in the
the representation of H2 influence in the reaction                            granite reference case the fractional matrix dissolu-
scheme) the comparison with experimental data will                            tion rate (in terms of fraction of pellet altered per
not be straightforward.                                                       year) is higher too (as can be observed Figure 4-17).



         Table 4-11
         Summary of the MAM sensitivity analysis.


                            Case                                 Parameter                                Value

                                                                                                         7 cm2·g-1
                     Specific surface area                   Specific surface area
                                                                                                       1.000 cm2·g-1

                                                                                                         10 mbar

                     Carbonate in water                          Pp (CO2(g))                              3 mbar

                                                                                                         Absence

                           a L.E.T.                 Thickness of the irradiated water layer               30 µm

                                                                                                       33 MWd·kg-1

                                                                  UO2 pellet                           41 MWd·kg-1
                        Pellet burnup
                                                                                                       47 MWd·kg-1

                                                                 MOX pellet                            41 MWd·kg-1

                                                                                                          1 mM
                    Presence of Hydrogen                           [H2](aq)
                                                                                                         160 mM

                      Canister resistance                        Time failure                            10.000 y




80
                                                                                                                                          4. Base Case Calculations



In this figure, the extrapolation of the pellet alter-                           Regarding the effect of changing the specific surface
ation rate is drawn with lines. Continuous lines                                 on the concentration in solution of the molecular
mean that, according to the assumptions made in                                  species (O2 and H2O2 correspond to Figure 4-18
the model, some material is still present in the pel-                            and Figure 4-19, respectively) a clear effect on the
let. The line is changed to a dotted line when all the                           H2O2 is observed, i.e., the more surface is input in
initial amount is altered but an extrapolation is                                MAM, the less concentration in solution is obtained.
made considering a constant UO2 species. For ex-                                 This effect is clearly related to the surface oxidation
ample in the case of the extrapolation done for spe-                             process and in concordance to that observed in the
cific surface area of 1000 cm2·g-1 this change can                               laboratory (de Pablo et al., 2001). However, this
be observed in Figure 4-17.                                                      dependence is not so easy to infer in the case of the
                                                                                 O2 concentration in solution. Probably due to the
As stated, a clear effect of this parameter on the                               coupling to several phenomena, i.e., surface oxida-
output data is observed. As can be observed in Fig-                              tion process by O2, decomposition of H2O2 and its
ure 4-17 and in comparison to granite reference                                  recombination with the radiolytic products.
case, when the specific surface area value input is
lower or higher than the initial one the alteration
rate obtained is lower or higher than reference case.                            4.9.2.Influence of carbonate
                                                                                       concentration
It is important to remark that parameter changes of
orders of magnitude do not give modifications on                                 Following the same methodology, the next parame-
the pellet alteration rate of the same order. This be-                           ter evaluated is the influence of the CO2 partial
haviour is in concordance with the experimental evi-                             pressure on the MAM extrapolation. Three different
dences done and published in the bibliography                                    cases are assessed (as can be observed on Figure
(Quiñones et al., 1998; Quiñones et al., 1999; Se-                               4-20). During these evaluations, the partial pressure
rrano et al., 2001; Serrano et al., 1998).                                       was considered constant for all the evaluation time.




                                                                                                                                   2
                                                10
                                                     -4                                   Granite. Reference case (PelletSE = 70 cm /g)
                                                                                                          2
                                                                                          PelletSE = 7 cm /g
                                                                                                              2
                                                                                          PelletSE = 1000 cm /g
              pellet alteration rate / year-1




                                                10-5




                                                10-6




                                                               3
                                                          10       104                              105                                     106
                                                                         cooling time / year


             Figure 4-17. Influence of the specific surface area on the evolution of the pellet alteration rate under granite environment conditions.




                                                                                                                                                               81
Development of a Matrix Alteration Model (MAM)




                                                               -6
                                                         10




                                                               -7
                                                         10
                  O2(1) conc. / mol · kg-1 of H2O




                                                         10-8




                                                               -9
                                                         10                                                                                          Granite. Reference case
                                                                                                                                                                       2
                                                                                                                                                     PelletSE = 70 cm /g
                                                                                                                                                                     2
                                                                                                                                                     PelletSE = 7 cm /g
                                                                                                                                                                         2
                                                                                                                                                     PelletSE = 1000 cm /g

                                                         10-10
                                                                     103                               104                                105                                  106
                                                                                                                  cooling time / year



                                                                             Figure 4-18. Influence of the pellet specific surface area value considered on the evolution O2 concentration.




                                                                                                                                                     Granite. Reference case
                                                                                                                                                                       2
                                                                                                                                                     PelletSE = 70 cm /g
                                                                                                                                                                     2
                                                                                                                                                     PelletSE = 7 cm /g
                                                        10-8                                                                                                             2
                                                                                                                                                     PelletSE = 1000 cm /g
                    H2O2(1) conc. / mol · kg-1 of H2O




                                                        10-9




                                                        10-10




                                                             -11
                                                        10
                                                                   103                               104                                 105                                   106
                                                                                                                cooling time / year


                                                                           Figure 4-19. Influence of the pellet specific surface area value considered on the evolution H2O2 concentration.



82
                                                                                                                                                   4. Base Case Calculations



Figure 4-20 summarises the results obtained when                                                               4.9.3. a range and pellet burnup
these changes are performed. It is important to
point out that the granite reference case considers a
                                                                                                                      influence
geochemical evolution of the groundwater. Because
of that, the alternating behaviour of the new cases is                                                         One of the controversial issues raised during this
observed. As can be checked and in concordance                                                                 project was related to alpha LET and, more specifi-
to the experimental results (de Pablo et al., 2003),                                                           cally, the range in water of alpha particles escaping
an increase in the carbonate concentration in solu-                                                            from the pellet. For this reason two different ap-
tion makes the dissolution rate rise. This effect is not                                                       proaches were presented and discussed on the Ma-
so clear observed in the MAM output due to the                                                                 drid Meeting. One approach considers a range of
coupling with the mass effect, i.e., the more is al-                                                           50 µm, whereas the other gives a value of 30 µm.
tered in each step at the same dose rate, the less                                                             This topic is explained with more detail in D13
amount of pellet remains and therefore (as was                                                                 (Martínez Esparza et al., 2004c). These approaches
aforementioned) the lower matrix alteration rate is                                                            infer a different alpha dose on the surface of the
calculated.                                                                                                    pellet, which is the reason why the present study has
                                                                                                               been carried out.

In the case of the molecular species (Figure 4-21                                                              Figure 4-23 shows the data obtained with MAM for
and Figure 4-22, O2 and H2O2, respectively), the                                                               this sensitivity analysis (Table 4-11). First the influ-
higher carbonate concentration, the more concen-                                                               ence of different alpha ranges considered was eval-
tration in solution is obtained. On the other hand, a                                                          uated. In the granite reference case the input value
clear dependence with the alpha dose rate is ob-                                                               was 50 µm. If this line is compared to that labelled
served. Oxygen concentration in solution increases                                                             in Figure 4-23 as “30 µm irradiated layer” it can be
with the decrease of the dose rate, whereas in the                                                             observed that (when this is the only parameter
case of the hydrogen peroxide a decrease on the                                                                changed) a decrease on this value produces a lower
concentration is related to the decrease of the alpha                                                          radiolytic product generation and because of a
dose rate.                                                                                                     lower matrix alteration rate obtained. This effect is




                                                          10-12
               pellet alteration rate / mol · m-2 · s-1




                                                          10-13




                                                          10-14

                                                                        Granite. Reference case
                                                                        PpCO2(g) = 10 mbar
                                                                        PpCO2(g) = 0,3 mbar
                                                                        absence of carbonate

                                                          10-15
                                                                  103                             104                         105                    106
                                                                                                        cooling time / year



              Figure 4-20. Influence of the CO2 partial pressure on the evolution of the pellet alteration rate under granite environment conditions.



                                                                                                                                                                        83
Development of a Matrix Alteration Model (MAM)




                                                                        -7
                                                                  10


                                                                  10-8

                                                                        -9
                                                                  10
                           O2(1) conc. / mol · kg-1 of H2O




                                                                        -10
                                                                  10

                                                                        -11
                                                                  10

                                                                                                                                                      Granite. Reference case
                                                                        -12
                                                                  10                                                                                  PpCO2(g) = 10 mbar
                                                                                                                                                      PpCO2(g) = 0,3 mbar
                                                                                                                                                      absence of carbonate
                                                                        -13
                                                                  10

                                                                        -14
                                                                  10
                                                                              103                         104                              105                                    106
                                                                                                                    cooling time / year



                                                                                      Figure 4-21. Influence of the CO2 partial pressure value considered on the evolution O2 concentration.




                                                                                                                                                        Granite. Reference case
                                                                                                                                                        PpCO2(g) = 10 mbar
                                                                                                                                                        PpCO2(g) = 0,3 mbar
                                                             10-8
                                                                                                                                                        absence of carbonate
                  H2O2 conc. / mol · kg-1 of H2O




                                                             10-9




                                                                  -10
                                                             10




                                                                              3                              4                                  5                                       6
                                                                        10                              10                                 10                                      10
                                                                                                                   cooling time / year


                                                                                    Figure 4-22. Influence of the CO2 partial pressure value considered on the evolution H2O2 concentration.



84
                                                                                                                                                                        4. Base Case Calculations




                                                                  -11
                                                             10




                                                             10-12
               pellet alteration rate / mol · m-2 · s-1




                                                             10-13


                                                                                 Granite. Reference case
                                                                                 30 m irradiated layer
                                                                  -14
                                                             10                  33 MWd/kg U
                                                                                 41 MWd/kg U
                                                                                 47 MWd/kg U
                                                                                 41 MWd/kg U (MOX)

                                                             10-15
                                                                  103                                  104                             105                                106
                                                                                                               cooling time / year



                                                          Figure 4-23. Influence of the pellet burnup on the evolution of the pellet alteration rate under granite environment conditions.




related to the total amount of water irradiated, the                                                                  rameter. Moreover, the Figure 4-22 shows that in
more amount of water, the more oxidant generated.                                                                     the case of MOX fuel (higher a dose rate in the sur-
                                                                                                                      face of the pellet) the MAM predicts a higher alter-
Once observed this behaviour, the next step is to                                                                     ation of the pellet, i.e., the whole pellet will be al-
evaluate the influence of the different dose rate, i.e.,                                                              tered in less than 5000 y. However, it is necessary
different burnup of the pellet and the influence of                                                                   to remind that the MAM model does not include any
MAM extrapolations. For the study the radionuclide                                                                    passivation process due to a secondary phase for-
inventory for each fuel burnup was supplied by C.                                                                     mation, mineralization or ageing process.
Poinssot WP1 (Poinssot, 2002) and the a dose rate
extrapolation were done by B. Grambow (consider-                                                                      Figure 4-23 and Figure 4-24 present the burnup in-
ing ” range of 30 µm) (Grambow et al., 2004).                                                                         fluence on the molecular species in solution. In both
                                                                                                                      cases, the tendency of the results presents a clear de-
Using the hypothesis aforementioned input in the                                                                      pendence with the pellet burnup, i.e., the more
MAM model it is possible to extrapolate the matrix                                                                    burnup (a dose rate) the more concentration in solu-
alteration rate and study the influence of the alpha                                                                  tion is obtained. The evolution of the plots follows the
dose rate on the alteration process (Figure 4-22).                                                                    initial tendency showed by the granite reference case.
The data obtained and represented in the Figure
4-22 show an increase of the alteration rate with the
pellet burnup (a dose rate). The comparison of the                                                                    4.9.4.Canister resistance
rates extrapolated for the reference case and the                                                                           and the hydrogen influence
run labelled “41 MWd·kg-1 U” shows that it is lower
than a factor of two. This fact means that with inde-                                                                 In this case, the discussion is divided in two parts. In
pendence of the approach used for calculating the                                                                     the first one, the influence of the canister life will be
” range and the dose rate the values obtained are                                                                     discussed and in the second, the results obtained as
very close. The important point it is to have a con-                                                                  a function of the hydrogen partial pressure will be
sistency in the methodology for calculating this pa-                                                                  commented.



                                                                                                                                                                                             85
Development of a Matrix Alteration Model (MAM)



         Table 4-12
         Evolution of the a dose rate on the surface of the pellet for different burnup and type of fuels.

                                                                                                  Alpha dose rate on the pellet surface / Gy·s-1
          Spent fuel cooling time
                                                                                                          UO2                                               MOX
                  / year
                                                                  33 MWd·kg-1 U                       41 MWd·kg-1 U              47 MWd·kg-1 U       47.5 MWd·kg-1 U

                        1000                                        6.082E-02                           7.052E-02                  7.709E-02             4.457E-01

                        5000                                        2.054E-02                           2.310E-02                  2.495E-02             1.307E-01

                   10000                                            1.496E-02                           1.671E-02                  1.798E-02             8.907E-02

                   50000                                            3.250E-03                           3.580E-03                  3.830E-03             1.497E-02

                  100000                                            1.160E-03                           1.350E-03                  1.510E-03             6.350E-03

                  500000                                            5.124E-04                           6.314E-04                  7.253E-04             3.200E-03




Figure 4-25, Figure 4-26 and Figure 4-27 present                                                                 slightly higher than the granite reference case (lower
in comparison to the granite reference case the re-                                                              than a factor of two). This difference is due to the
sults extrapolated with MAM when a container life of                                                             mass effect associated to the methodology of the
10000 y is considered. The pellet alteration rate is                                                             calculation, i.e., the amount of solid in the refer-




                                                     10-6             Granite. Reference case
                                                                      30 m irradiated layer
                                                                      33 MWd/kg U
                                                                      41 MWd/kg U
                                                                      47 MWd/kg U
                                                     10-7             41 MWd/kg U (MOX)
                   O2(1) conc. / mol · kg-1 of H2O




                                                     10-8




                                                     10-9




                                                            103                                 104                               105                         106
                                                                                                           cooling time / year



                                                                              Figure 4-24. Influence of the pellet burnup value considered on the evolution O2 concentration.



86
                                                                                                                                                              4. Base Case Calculations




                                                       -8
                                                 10
       H2O2 conc. / mol · kg-1 of H2O




                                                 10-9


                                                                   Granite. Reference case
                                                                   30 m irradiated layer
                                                       -10         33 MWd/kg U
                                                 10                41 MWd/kg U
                                                                   47 MWd/kg U
                                                                   41 MWd/kg U (MOX)


                                                             103                             104                         105                                    106
                                                                                                   cooling time / year



                                                                        Figure 4-25. Influence of the pellet burnup value considered on the evolution H2O2 concentration.




                                                 10-12
                                                                                                                               Granite. Reference case
                                                                                                                               [H2(l)] = 1 mM
                                                                                                                               [H2(l)] = 160 mM
                                                                                                                               container failure at 10000 y
      pellet alteration rate / mol · m-2 · s-1




                                                      -13
                                                 10




                                                 10-14




                                                 10-15
                                                             103                             104                         105                                    106
                                                                                                   cooling time / year



Figure 4-26. Influence of the hydrogen partial pressure on the evolution of the pellet alteration rate under granite environment conditions.



                                                                                                                                                                                   87
Development of a Matrix Alteration Model (MAM)




                                                    10-7
                  O2(1) conc. / mol · kg-1 of H2O




                                                    10-8




                                                         -9
                                                    10
                                                                                                                                              Granite. Reference case
                                                                                                                                              [H2(l)] = 1 mM
                                                                                                                                              [H2(l)] = 160 mM
                                                                                                                                              container failure at 10000 y
                                                         -10
                                                    10
                                                                    3                                  4                                  5
                                                               10                                 10                                 10                                      106
                                                                                                             cooling time / year


                                                                          Figure 4-27. Influence of the hydrogen partial pressure value considered on the evolution O2 concentration.




                                                         -8
                                                    10                                                                                        Granite. Reference case
                                                                                                                                              [H2(l)] = 1 mM
                                                                                                                                              [H2(l)] = 160 mM
                                                                                                                                              container failure at 10000 y
                  H2O2 conc. / mol · kg-1 of H2O




                                                    10-9




                                                    10-10




                                                    10-11
                                                               103                                104                                105                                     106
                                                                                                             cooling time / year


                                                                        Figure 4-28. Influence of the hydrogen partial pressure value considered on the evolution H2O2 concentration.



88
                                                                                              4. Base Case Calculations



ence case is lower than in the run that considers a         of the oxidant species by recombination with the
canister life of 10000 y, which produces an increase        radiolysis species generated present in water.
in the dissolution rate. This fact is corroborated by
the evolution of the molecular species concentration        The effect of the hydrogen partial pressure and its
(Figure 4-26 and Figure 4-27), that follow the same         mechanism of recombination with the pellet surface
tendency.                                                   (reduction of the oxidized layer, sorption phenom-
                                                            ena, etc.) is one of the open questions that are nec-
In the case of the hydrogen sensitivity analysis, the       essary to resolve for performing more realistic PA
model does not include any mechanism of interac-            exercises. In order to elucidate the reaction mecha-
tion with the pellet surface; only the kinetics recom-      nism between the hydrogen and the spent fuel ma-
bination reactions. Therefore, the results obtained         trix new experiments need to be done.
may not be used for extrapolating the behaviour un-
der higher partial pressure of hydrogen, only just the      Those experiments will support development of new
effect produced by this change on the recombina-            reaction mechanism of hydrogen with the matrix.
tion of the radiolytic products.
                                                            Thus the MAM will be applicable in a great range of
The increase of the hydrogen partial pressure implies       repository environmental conditions and will explain
a reduction of the pellet alteration rate. This effect is   the matrix alteration by radiolytics oxidants (in ab-
associated to a similar decreasing behaviour of the         sence of other oxidants) and the competing effect
molecular species concentration with the increase of        on interaction with the matrix of reductants and
the partial pressure. Probably due to a consumption         radiolytics or environmental oxidants




                                                                                                                   89
5. Applicability of the MAM and Conclusions




                                                5. Applicability
                                                   of the MAM
                                              and Conclusions
5. Applicability of the MAM and Conclusions
                                                                           5. Applicability of the MAM and Conclusions



The MAM model, mainly based on a scheme of ki-              MAM has been validated for different oxygen
netic reactions most of them experimentally vali-           concentrations from 2.29·10-5 to 1.28·10-3
dated has been successfully applied to different            mol·dm-3. In the case of hydrogen peroxide,
cases to calibrate the model as well as to determine        the model was successfully applied at concen-
long-term dissolution rates.                                trations lower than 10-4 mol·dm-3. In dissolution
                                                            experiments using hydrogen peroxide in order
The applicability is discussed below in terms of the
                                                            to fit the model to experimental data it was
different possible cases.
                                                            necessary to include the effect of the radical
                                                            HO· on the heterogeneous reaction scheme.
5.1. Spent fuel                                             The effect of other oxidants on the spent fuel
                                                            oxidation such as ClO- has not been consid-
MAM model can be applied to any spent fuel
                                                            ered in this work. Therefore, dissolution exper-
burn-up. Burn-up is used to calculate the dose rate.
                                                            iments in brine can be only estimated since
Dose rate gives the oxidant/reductant production,
                                                            heterogeneous reactions between UO2 and
which is the base of the radiolytical model.
                                                            chlorine species are not included.
It is important to point out that unirradiated UO2,
                                                         c) Reduction of the oxidants present in the system
SIMFUEL, alpha-doped UO2 and spent fuel have
been successfully used during the validation/calibra-       We have considered the consumption of oxi-
tion of the MAM model.                                      dants in the homogeneous phase which have
                                                            already described in current radiolytic models:
Related to the solid, MAM model does not consider
the effect of the RIM structure on the alteration/dis-         H 2 + HO×Þ H 2O + H ×            k = 3.4 × 107
solution as well as changes in the morphology of
the spent fuel (formation of cracks, preferential           The increase of hydrogen pressure, taking into
grain boundary attacks, etc.)                               account the mentioned homogeneous reac-
                                                            tion, reduces drastically the number of moles
                                                            of uranium oxidized in the system. At 1.6 bar
5.2. Processes affecting spent fuel                         of hydrogen, the oxidized uranium moles are
                                                            more than two orders of magnitude lower than
     matrix alteration                                      at 0.01 bar of hydrogen.
In the D12 (Martínez Esparza et al., 2004b) and             Moreover, new homogeneous hydrogen reac-
D13 (Martínez Esparza et al., 2004c), a detailed            tions with species produced by the radiolysis of
description of the processes affecting the oxidation        brines have also taken into account in order to
and dissolution of the spent fuel matrix is given.          be able to explain experimental results; the
These processes are discussed below in terms of the         most important considered reaction is the fol-
applicability of the MAM.                                   lowing one:
  a) Generation of oxidants and reductants by wa-              H 2 + Cl- Þ H ×+ HCl + Cl-         k = 43 × 10 5
                                                                                                       .
                                                                       2
     ter radiolysis
     The generation and recombination reaction              described in Kelm et al. (Kelm and Bohnert,
     mechanisms as well as the selected kinetic con-        2004).
     stants accounting for water, carbonate and             Finally, no mathematical formulation (kinetic
     chloride systems (homogeneous reactions) were          equations) of the results obtained at high hy-
     supplied by the WP2(Kelm et al2004) and de-            drogen pressure (heterogeneous reactions)
     scribed in the D12 (Martínez Esparza et al.,           has been developed in D10. Results have
     2004b).                                                been mainly interpreted supposing a solubility
                                                            control of the UO2-matrix. Therefore, no inte-
  b) Oxidation of the spent fuel
                                                            gration into the MAM model related to the inhi-
     Spent fuel surface oxidation processes (hetero-        bition of matrix alteration/oxidation has been
     geneous reactions) have been included in the           possible to carry out.
     reaction scheme taking into account oxidants
                                                         d) Dissolution of the matrix
     consumption by the spent fuel surface in the
     overall balance of the species generated               Kinetic parameters as well as reaction mecha-
     radiolytically.                                        nisms have been elucidated partly from the



                                                                                                                  93
Development of a Matrix Alteration Model (MAM)



       models developed based on non-irradiated          In the sensitivity analysis commented in this deliver-
       uranium dioxide dissolution experiments (de       able long-term dissolution rates at different boundary
       Pablo et al., 2003; de Pablo et al., 2004; de     conditions have been determined. Related to the
       Pablo et al., 1999; Giménez et al., 2001).        groundwater composition, the model has also shown
                                                         its applicability in the clay case.
       Dissolution of the oxidised UO2-matrix is very
       dependent on water chemistry. MAM model           Due to the lack of kinetic data at different tempera-
       has been basically calibrated and validated       tures, 25 ºC is considered during all the evaluation
       from acid pH (~3) to basic pH (~10), some         time. No applicability of the MAM model has been
       deviations have been observed at alkaline         considered at different temperatures.
       pH’s higher than 10 in the presence of hydro-
                                                         MAM model can be applied to any evaluation time.
       gen peroxide which can be related to more
                                                         In fact, spent fuel dissolution experiments carried out
       oxidised species at high alkaline pH’s.
                                                         in flow through reactors (Martínez Esparza et al.,
       The influence of carbonate concentration vari-    2004c) has been used to validate the model.
       ation has also been studied. MAM can repro-
       duce experimental dissolution rate values in      Base case considers a uranium dioxide cylindrical (h
       the hydrogen carbonate concentration range        = 13.46 mm and N = 8.19 mm) pellet with a mass
       10-4 – 10-2 mol·dm-3.                             of 7.38 g. This pellet is encapsulated in the Zircaloy
                                                         cladding, and therefore the amount of water in con-
       It is important to point out which parameters     tact with the waste is limited. However, the MAM
       have not been included in the MAM model. In       model can be applied to other geometries such as
       this sense, the effect of organic matter (humic   pellets, particles, fragments, etc. In this project, dif-
       and fulvic acids) has not been included since     ferent geometries has been used during the model
       no reliable experiments are available. Phos-      validation.
       phate, calcium and silica, which seem to have
       influence on the spent fuel dissolution, have     Different geometries mean also different site densi-
       not been incorporated in MAM model due to         ties. Site density controls the spent fuel surface
       the scarce of experimental data.                  which could be oxidized thus this density is related
                                                         to the specific surface area of the solid. In the sensi-
  e) Precipitation of secondary solid phases             tivity analysis, the importance of this parameter is
       The precipitation of secondary solid phases       pointed out.
       on the spent fuel surface depends on the wa-      Only a radiation is considered in the reference case
       ter chemistry. Different phases have been         (1.000 y < t < 1.000.000 y). At this time interval,
       identified in spent fuel, non-irradiated UO2,     ( radiation is considered negligible in comparison
       SIMFUEL and alpha-doped UO2 pellets. The          with the a radiation. The applicability of the model
       formation of secondary phases in Perfor-          is not restricted to alpha radiation. The model has
       mance Assessment exercises has been con-          been applied with success to spent fuel experimental
       sidered that it is instantaneous; consequently    data where a, b and g are present.
       a thermodynamic approach has been nor-
       mally used in the radionuclide concentration      Determination of long-term spent fuel dissolution
       calculations.                                     rates has been performed taking into account a
                                                         quasi-closed system. This system can be considered
       These phenomena have not been included in         a mixing tank. During the MAM validation and cali-
       the MAM model, the output of the model is ba-     bration, other experimental devices different from
       sically dissolution rates. NF-PRO project in-     mixing tank have been used. MAM model has given
       cludes the study of the importance of second-     reliable results using flow-through and batch reac-
       ary phase formation on spent fuel experiments.    tors, using in this last case, different methodologies:
                                                         sequential, continuous, etc.
5.3. Boundary conditions and
     geometrical parameters                              5.4. Specific a-activity threshold
Boundary conditions and geometrical parameters ap-       One of the main conclusions from D9 (Grambow et
plied to the base case are described and discussed in    al., 2004) is that “it looks like there is a specific ac-
detail in D13 (Martínez Esparza et al., 2004a).          tivity threshold below which no effect of specific al-



94
                                                                                  5. Applicability of the MAM and Conclusions



pha activity is observed and above which an in-             (mainly carbonate concentration and pH) and their
crease of corrosion rates with alpha activity is ob-        evolutions.
served”. This threshold seems to depend on envi-
ronmental parameters but it is not clear how to             The sensitivity analysis, carried out with MAM for
correlate both.                                             granite reference case and for the evaluation range,
                                                            points out that for this model the presence of a dose
Therefore, it has not been possible at this stage to        field is the main parameter for producing the alter-
integrate these results into the model. More experi-        ation of the pellet in absence of the oxidants. There
ments should be necessary to understand perfectly           are other key parameters that are necessary to fix in
the relation of alpha activity and dissolution rates.       order to obtain a realistic extrapolation, i.e., S/V ra-
If this threshold is well established it would be the al-   tio (coordination site density, specific surface area of
pha activity value where the transition from the            the pellet), carbonate concentration, presence of hy-
radiolitycal model to the solubility control model          drogen in the system.
would take place.
                                                            MAM has proved a large applicability with indiffer-
                                                            ence of the environmental repository conditions (ge-
5.5. Conclusions                                            ometry, type of dose rate, groundwater chemistry,
                                                            etc.). MAM model has given reliable results using
This document presents the Matrix Alteration Model          flow-through and batch reactors, using in this last
developed in the WP4, the sensibility analysis per-         case, different methodologies: sequential, continu-
formed for several key parameters and the study of          ous, etc. The model shows a good fit with experi-
the applicability of the MAM.                               mental data in the pH range 3 - 12.
The MAM has been applied to granite and clay en-            Although there are some environmental conditions
vironments. This model allows to extrapolate and to         that the importance of the matrix radiolytic oxidation
predict the pellet alteration rate for the time range       process on the final alteration rate could decrease.
of 103 to 106 years. In the case of salt environment,       For example under very high oxygen contents or
the model can not give a realistic extrapolation due        reductants environments. The first one the contribu-
to the reaction mechanism between chloride species          tion of radiolysis is lower than environmental oxida-
(generated by radiolysis) and the UO2 matrix is             tion. Whereas, in the second case, there is a com-
unknown.                                                    peting effect on radiolytically induced by recom-
The matrix alteration rates obtained by MAM show a          bination of the environmental reductants and radio-
very good stability of the spent nuclear fuel under         lytic oxidants and/or U(VI) reduction to U(IV) and
repository conditions.                                      re-precipitation as UO2.

Focussed on the evolutions of the matrix alteration         Future developments of the MAM, need to be im-
rate calculated for granite and clay reference cases,       plemented for including these processes (or mecha-
the discrepancies observed are related to the               nisms) in the MAM based on experimental work
changes in the groundwater composition considered           done or will be done in future projects.




                                                                                                                         95
6. References




                6. References
6. References
                                                                                                             6. References



Abbot J. and Brown D. G. (1990) Kinetics of iron-cata-             ment XXIV, Vol. 663 (ed. K. P. Hart and G. R.
    lyzed decomposition of H2O2 in alkaline solution.              Lumpkin), pp. 409-416. The Materials Research So-
    Inter. Jour. Chem. Kinetics 22, 963-974.                       ciety.
Andreozzi R., Caprio V., Insola A., and Marotta R. (1999)     de Pablo J., Casas I., Clarens F., Giménez J., and Rovira
     Advanced oxidation processes for water purification           M. (2003) Contribución experimental y modeliza-
     and recovery. Catalysis Today 53, 51-59.                      ción de procesos básicos para el desarrollo del
Bruno J., Cera E., Duro L., Eriksen T. E., and Werme L.            modelo de alteración de la matriz del combustible
     O. (1996) A Kinetic Model for the Stability of Spent          irradiado. In Publicaciones técnicas, Vol. 01/2003.
     Nuclear Matrix under Oxic Conditions. J. of Nuclear           ENRESA.
     Materials Vol. 238, 110-120. J. Nucl. Mater. 238,        de Pablo J., Casas I., Giménez J., Clarens F., Duro L.,
     110-120.                                                      and Bruno J. (2004) The oxidative dissolution mech-
                                                                   anism of uranium dioxide. The effect of pH and oxy-
Bruno J., Cera E., and Merino J. (2004) On the applica-
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                                                                                                                       101
     Títulos publicados




                                                                                           PUBLICACIONES TÉCNICAS

                                  1991                                         Publicaciones no periódicas                                                                                                   1996
01    REVISIÓN SOBRE LOS MODELOS NUMÉRICOS RELACIONADOS                             SEGUNDO PLAN DE I+D. INFORME ANUAL 1992.                                            01   DESARROLLO DE UN PROGRAMA INFORMÁTICO PARA EL ASESORAMIENTO
      CON EL ALMACENAMIENTO DE RESIDUOS RADIACTIVOS.                                PRIMERAS JORNADAS DE I+D EN LA GESTIÓN DE RESIDUOS RADIACTIVOS.                          DE LA OPERACIÓN DE FOCOS EMISORES DE CONTAMINANTES GASEOSOS.
02    REVISIÓN SOBRE LOS MODELOS NUMÉRICOS RELACIONADO                              TOMOS I Y II.                                                                       02   FINAL REPORT OF PHYSICAL TEST PROGRAM CONCERNING SPANISH CLAYS
      CON EL ALMACENAMIENTO DE RESIDUOS RADIACTIVOS. ANEXO 1.                                                                                                                (SAPONITES AND BENTONITES).
      Guía de códigos aplicables.                                                                                                                                       03   APORTACIONES AL CONOCIMIENTO DE LA EVOLUCIÓN PALEOCLIMÁTICA
                                                                                                                    1994                                                     Y PALEOAMBIENTAL EN LA PENÍNSULA IBÉRICA DURANTE LOS DOS ÚLTIMOS
03    PRELIMINARY SOLUBILITY STUDIES OF URANIUM DIOXIDE UNDER
      THE CONDITIONS EXPECTED IN A SALINE REPOSITORY.                                                                                                                        MILLONES DE AÑOS A PARTIR DEL ESTUDIO DE TRAVERTINOS
                                                                               01   MODELO CONCEPTUAL DE FUNCIONAMIENTO DE LOS ECOSISTEMAS
04    GEOESTADÍSTICA PARA EL ANÁLISIS DE RIESGOS. Una introducción                                                                                                           Y ESPELEOTEMAS.
                                                                                    EN EL ENTORNO DE LA FÁBRICA DE URANIO DE ANDÚJAR.
      a la Geoestadística no paramétrica.                                                                                                                               04   MÉTODOS GEOESTADÍSTICOS PARA LA INTEGRACIÓN DE INFORMACIÓN.
                                                                               02   CORROSION OF CANDIDATE MATERIALS FOR CANISTER APPLICATIONS
05    SITUACIONES SINÓPTICAS Y CAMPOS DE VIENTOS ASOCIADOS                          IN ROCK SALT FORMATIONS.                                                            05   ESTUDIO DE LONGEVIDAD EN BENTONITAS: ESTABILIDAD HIDROTERMAL
      EN “EL CABRIL”.                                                                                                                                                        DE SAPONITAS.
                                                                               03   STOCHASTIC MODELING OF GROUNDWATER TRAVEL TIMES
06    PARAMETERS, METHODOLOGIES AND PRIORITIES OF SITE SELECTION                                                                                                        06   ALTERACIÓN HIDROTERMAL DE LAS BENTONITAS DE ALMERÍA.
                                                                               04   THE DISPOSAL OF HIGH LEVEL RADIOACTIVE WASTE IN ARGILLACEOUS HOST
      FOR RADIOACTIVE WASTE DISPOSAL IN ROCK SALT FORMATIONS.                                                                                                           07   MAYDAY. UN CÓDIGO PARA REALIZAR ANÁLISIS DE INCERTIDUMBRE
                                                                                    ROCKS. Identification of parameters, constraints and geological assessment
                                                                                    priorities.                                                                              Y SENSIBILIDAD. Manuales.

                                  1992                                         05   EL OESTE DE EUROPA Y LA PENÍNSULA IBÉRICA DESDE HACE -120.000 AÑOS
                                                                                                                                                                        Publicaciones no periódicas
                                                                                    HASTA EL PRESENTE. Isostasia glaciar, paleogeografías paleotemperaturas.
01    STATE OF THE ART REPORT: DISPOSAL OF RADIACTIVE WASTE IN DEEP            06   ECOLOGÍA EN LOS SISTEMAS ACUÁTICOS EN EL ENTORNO DE EL CABRIL.                           EL BERROCAL PROJECT. VOLUME I. GEOLOGICAL STUDIES.
      ARGILLACEOUS FORMATIONS.                                                                                                                                               EL BERROCAL PROJECT. VOLUME II. HYDROGEOCHEMISTRY.
                                                                               07   ALMACENAMIENTO GEOLÓGICO PROFUNDO DE RESIDUOS RADIACTIVOS
02    ESTUDIO DE LA INFILTRACIÓN A TRAVÉS DE LA COBERTERA DE LA FUA.                DE ALTA ACTIVIDAD (AGP). Conceptos preliminares de referencia.                           EL BERROCAL PROJECT. VOLUME III. LABORATORY MIGRATION TESTS AND IN
03    SPANISH PARTICIPATION IN THE INTERNATIONAL INTRAVAL PROJECT.             08   UNIDADES MÓVILES PARA CARACTERIZACIÓN HIDROGEOQUÍMICA                                    SITU TRACER TEST.
04    CARACTERIZACIÓN DE ESMECTITAS MAGNÉSICAS DE LA CUENCA DE MADRID          09   EXPERIENCIAS PRELIMINARES DE MIGRACIÓN DE RADIONUCLEIDOS                                 EL BERROCAL PROJECT. VOLUME IV. HYDROGEOLOGICAL MODELLING AND
      COMO MATERIALES DE SELLADO. Ensayos de alteración hidrotermal.                CON MATERIALES GRANÍTICOS. EL BERROCAL, ESPAÑA.                                          CODE DEVELOPMENT.
05    SOLUBILITY STUDIES OF URANIUM DIOXIDE UNDER THE CONDITIONS               10   ESTUDIOS DE DESEQUILIBRIOS ISOTÓPICOS DE SERIES RADIACTIVAS
      EXPECTED IN A SALINE REPOSITORY. Phase II                                     NATURALES EN UN AMBIENTE GRANÍTICO: PLUTÓN DE EL BERROCAL
06    REVISIÓN DE MÉTODOS GEOFÍSICOS APLICABLES AL ESTUDIO                          (TOLEDO).
                                                                                                                                                                                                             1997
      Y CARACTERIZACIÓN DE EMPLAZAMIENTOS PARA ALMACENAMIENTO                  11   RELACIÓN ENTRE PARÁMETROS GEOFÍSICOS E HIDROGEOLÓGICOS.                             01   CONSIDERACIÓN DEL CAMBIO MEDIOAMBIENTAL EN LA EVALUACIÓN
      DE RESIDUOS RADIACTIVOS DE ALTA ACTIVIDAD EN GRANITOS, SALES                  Una revisión de literatura.                                                              DE LA SEGURIDAD. ESCENARIOS CLIMÁTICOS A LARGO PLAZO EN LA PENÍNSULA
      Y ARCILLAS.
                                                                               12   DISEÑO Y CONSTRUCCIÓN DE LA COBERTURA MULTICAPA DEL DIQUE                                IBÉRICA.
07    COEFICIENTES DE DISTRIBUCIÓN ENTRE RADIONUCLEIDOS.                            DE ESTÉRILES DE LA FÁBRICA DE URANIO DE ANDÚJAR.                                    02   METODOLOGÍA DE EVALUACIÓN DE RIESGO SÍSMICO EN SEGMENTOS
08    CONTRIBUTION BY CTN-UPM TO THE PSACOIN LEVEL-S EXERCISE.                                                                                                               DE FALLA.
09    DESARROLLO DE UN MODELO DE RESUSPENSIÓN DE SUELOS                        Publicaciones no periódicas                                                              03   DETERMINACIÓN DE RADIONUCLEIDOS PRESENTES EN EL INVENTARIO
      CONTAMINADOS. APLICACIÓN AL ÁREA DE PALOMARES.                                                                                                                         DE REFERENCIA DEL CENTRO DE ALMACENAMIENTO DE EL CABRIL.
                                                                                    SEGUNDO PLAN I+D 1991-1995. INFORME ANUAL 1993.
10    ESTUDIO DEL CÓDIGO FFSM PARA CAMPO LEJANO. IMPLANTACIÓN EN VAX.                                                                                                   04   ALMACENAMIENTO DEFINITIVO DE RESIDUOS DE RADIACTIVIDAD ALTA.
11    LA EVALUACIÓN DE LA SEGURIDAD DE LOS SISTEMAS DE ALMACENAMIENTO                                                                                                        Caracterización y comportamiento a largo plazo de los combustibles nucleares
      DE RESIDUOS RADIACTIVOS. UTILIZACIÓN DE MÉTODOS PROBABILISTAS.                                                1995                                                     irradiados (I).
12    METODOLOGÍA CANADIENSE DE EVALUACIÓN DE LA SEGURIDAD DE LOS                                                                                                       05   METODOLOGÍA DE ANÁLISIS DE LA BIOSFERA EN LA EVALUACIÓN
      ALMACENAMIENTOS DE RESIDUOS RADIACTIVOS.                                 01   DETERMINACIÓN DEL MÓDULO DE ELASTICIDAD DE FORMACIONES                                   DE ALMACENAMIENTOS GEOLÓGICOS PROFUNDOS DE RESIDUOS
                                                                                    ARCILLOSAS PROFUNDAS.                                                                    RADIACTIVOS DE ALTA ACTIVIDAD ESPECÍFICA.
13    DESCRIPCIÓN DE LA BASE DE DATOS WALKER.
                                                                               02   UO LEACHING AND RADIONUCLIDE RELEASE MODELLING UNDER HIGH AND
                                                                                       2
                                                                                                                                                                        06   EVALUACIÓN DEL COMPORTAMIENTO Y DE LA SEGURIDAD DE UN
                                                                                    LOW IONIC STRENGTH SOLUTION AND OXIDATION CONDITIONS.                                    ALMACENAMIENTO GEOLÓGICO PROFUNDO EN GRANITO. Marzo 1997
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                                                                               03   THERMO-HYDRO-MECHANICAL CHARACTERIZATION OF THE SPANISH                             07   SÍNTESIS TECTOESTRATIGRÁFICA DEL MACIZO HESPÉRICO. VOLUMEN I.
      PONENCIAS E INFORMES, 1988-1991.
                                                                                    REFERENCE CLAY MATERIAL FOR ENGINEERED BARRIER FOR GRANITE AND                      08   III JORNADAS DE I+D Y TECNOLOGÍAS DE GESTIÓN DE RESIDUOS
                                                                                                                                                                               as




      SEGUNDO PLAN DE I+D, 1991-1995. TOMOS I, II Y III.
                                                                                    CLAY HLW REPOSITORY: LABORATORY AND SMALL MOCK UP TESTING.                               RADIACTIVOS. Pósters descriptivos de los proyectos de I+D y evaluación
      SECOND RESEARCH AND DEVELOPMENT PLAN, 1991-1995, VOLUME I.
                                                                               04   DOCUMENTO DE SÍNTESIS DE LA ASISTENCIA GEOTÉCNICA AL DISEÑO                              de la seguridad a largo plazo.
                                                                                    AGP-ARCILLA. Concepto de referencia.                                                09   FEBEX. ETAPA PREOPERACIONAL. INFORME DE SÍNTESIS.
                                  1993                                         05   DETERMINACIÓN DE LA ENERGÍA ACUMULADA EN LAS ROCAS SALINAS                          10   METODOLOGÍA DE GENERACIÓN DE ESCENARIOS PARA LA EVALUACIÓN
                                                                                    FUERTEMENTE IRRADIADAS MEDIANTE TÉCNICAS DE TERMOLUMINISCENCIA.                          DEL COMPORTAMIENTO DE LOS ALMACENAMIENTOS DE RESIDUOS
01    INVESTIGACIÓN DE BENTONITAS COMO MATERIALES DE SELLADO                        Aplicación al análisis de repositorios de residuos radiactivos de alta actividad.        RADIACTIVOS.
      PARA ALMACENAMIENTO DE RESIDUOS RADIACTIVOS DE ALTA ACTIVIDAD.
                                                                               06   PREDICCIÓN DE FENÓMENOS DE TRANSPORTE EN CAMPO PRÓXIMO                              11   MANUAL DE CESARR V.2. Código para la evaluación de seguridad de un
      ZONA DE CABO DE GATA, ALMERÍA.
                                                                                    Y LEJANO. Interacción en fases sólidas.                                                  almacenamiento superficial de residuos radiactivos de baja y media actividad.
02    TEMPERATURA DISTRIBUTION IN A HYPOTHETICAL SPENT NUCLEAR FUEL
                                                                               07   ASPECTOS RELACIONADOS CON LA PROTECCIÓN RADIOLÓGICA DURANTE EL
      REPOSITORY IN A SALT DOME.
                                                                                    DESMANTELAMIENTO Y CLAUSURA DE LA FÁBRICA DE ANDÚJAR.
03    ANÁLISIS DEL CONTENIDO EN AGUA EN FORMACIONES SALINAS. Su aplicación
                                                                               08   ANALYSIS OF GAS GENERATION MECHANISMS IN UNDERGROUND RADIACTIVE
                                                                                                                                                                                                             1998
      al almacenamiento de residuos radiactivos
                                                                                    WASTE REPOSITORIES. (Pegase Project).
                                                                                                                                                                        01   FEBEX. PRE-OPERATIONAL STAGE. SUMMARY REPORT.
04    SPANISH PARTICIPATION IN THE HAW PROJECT. Laboratory Investigations on
                                                                               09   ENSAYOS DE LIXIVIACIÓN DE EMISORES BETA PUROS DE LARGA VIDA.                        02   PERFORMANCE ASSESSMENT OF A DEEP GEOLOGICAL REPOSITORY
      Gamma Irradiation Effects in Rock Salt.
                                                                               10   2º PLAN DE I+D. DESARROLLOS METODOLÓGICOS, TECNOLÓGICOS,                                 IN GRANITE. March 1997.
05    CARACTERIZACIÓN Y VALIDACIÓN INDUSTRIAL DE MATERIALES ARCILLOSOS
                                                                                    INSTRUMENTALES Y NUMÉRICOS EN LA GESTIÓN DE RESIDUOS RADIACTIVOS.                   03   FEBEX. DISEÑO FINAL Y MONTAJE DEL ENSAYO “IN SITU” EN GRIMSEL.
      COMO BARRERA DE INGENIERÍA.
                                                                               11   PROYECTO AGP- ALMACENAMIENTO GEOLÓGICO PROFUNDO. FASE 2.                            04   FEBEX. BENTONITA: ORIGEN, PROPIEDADES Y FABRICACIÓN DE BLOQUES.
06    CHEMISTRY OF URANIUM IN BRINES RELATED TO THE SPENT FUEL DISPOSAL
      IN A SALT REPOSITORY (I).                                                12   IN SITU INVESTIGATION OF THE LONG-TERM SEALING SYSTEM                               05   FEBEX. BENTONITE: ORIGIN, PROPERTIES AND FABRICATION OF BLOCKS.
                                                                                    AS COMPONENT OF DAM CONSTRUCTION (DAM PROJECT).
07    SIMULACIÓN TÉRMICA DEL ALMACENAMIENTO EN GALERÍA-TSS.                                                                                                             06   TERCERAS JORNADAS DE I+D Y TECNOLOGÍAS DE GESTIÓN DE RESIDUOS
                                                                                    Numerical simulator: Code-Bright.
08    PROGRAMAS COMPLEMENTARIOS PARA EL ANÁLISIS ESTOCÁSTICO                                                                                                                 RADIACTIVOS. 24-29 Noviembre, 1997. Volumen I
      DEL TRANSPORTE DE RADIONUCLEIDOS.                                                                                                                                 07   TERCERAS JORNADAS DE I+D Y TECNOLOGÍAS DE GESTION DE RESIDUOS
                                                                               Publicaciones no periódicas                                                                   RADIACTIVOS. 24-29 Noviembre, 1997. Volumen II
09    PROGRAMAS PARA EL CÁLCULO DE PERMEABILIDADES DE BLOQUE.
10    METHODS AND RESULTS OF THE INVESTIGATION OF THE                               TERCER PLAN DE I+D 1995-1999.                                                       08   MODELIZACIÓN Y SIMULACIÓN DE BARRERAS CAPILARES.
      THERMOMECHANICAL BEAVIOUR OF ROCK SALT WITH REGARD TO THE FINAL               SEGUNDAS JORNADAS DE I+D. EN LA GESTIÓN DE RESIDUOS RADIACTIVOS.                    09   FEBEX. PREOPERATIONAL THERMO-HYDRO-MECHANICAL (THM) MODELLING
      DISPOSAL OF HIGH-LEVEL RADIOACTIVE WASTES.                                    TOMOS I Y II.                                                                            OF THE “IN SITU” TEST.
Development
of a Matrix Alteration
Model (MAM)


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