Coupled thermo-hydro-chemical-mechanical models for … · place within the bentonite as well as...

Coupled thermo-hydro-chemical-

mechanical models for the bentonite

barrier in a radioactive waste

repository

Author: Alba Mon López

Doctoral Thesis UDC 2017

Advisor: Francisco Javier Samper Calvete

Civil Engineering Ph.D. Program

Civil Engineering School

Modelos acoplados termo-hidro-

químico-mecánicos de la barrera de

bentonita de un almacenamiento de

residuos radiactivos

Autora: Alba Mon López

Tesis Doctoral UDC 2017

Director: Francisco Javier Samper Calvete

Programa de doctorado de Ingeniería Civil

E.T.S. Ingenieros de Caminos, Canales y Puertos

Dr. Francisco Javier Samper Calvete, Ph.D. from University of Arizona (USA) and the

Polytechnical University of Madrid (Spain), Full Professor, certifies that this doctoral thesis,

entitled Coupled thermo-hydro-chemical-mechanical models for the bentonite barrier in

a radioactive waste repository, has been performed by Alba Mon López under his

supervision in order to obtain the Doctor of Philosophy degree with the International Mention

by the University of A Coruña

Dr. Francisco Javier Samper Calvete, Doctor por la Universidad de Arizona (EEUU) y

por la Universidad Politécnica de Madrid (España), Catedrático de Universidad, certifica que

la tesis doctoral con título, Coupled thermo-hydro-chemical-mechanical models for the

bentonite barrier in a radioactive waste repository, ha sido desarrollada por Alba Mon

López bajo su supervisión para obtener el grado de Doctor y con Mención Internacional por la

Universidad de A Coruña.

A Coruña, April 2017

A Coruña, Abril 2017

Alba Mon López Dr. F. Javier Samper Calvete

PhD. Student Advisor

Doctorando Director

Acknowledgements

I would like to thank Professor Javier Samper for the opportunity to join his research

group and performing this dissertation under his supervision. It would have been impossible to

complete this dissertation without his inspiration, encouragement, patience and support

throughout my graduate research.

Most of the research presented in this dissertation has been performed within the

framework of the PEBS Project funded by the European Atomic Energy Community's Seventh

Framework Programme (FP7/2007-2011) under grant agreement #232598; the CEBAMA

Project funded by the European Atomic Energy Community's (Euratom) Horizon 2020

Programme (NFRP-2014/2015) under grant agreement #662147; and the FEBEX-DP Project

(Grimsel Phase VI) funded by the FEBEX-DP Consortium. This work has been also supported

by ENRESA (Spain), the Spanish Ministry of Economy and Competitiveness (Projects

CGL2012-36560 and CGL2016-78281), FEDER funds and the Galician Regional Government

(Project 10MDS118028PR and Fund 2012/181 from “Consolidación e estruturación de

unidades de investigación competitivas”, Grupos de referencia competitiva). I have also

enjoyed a research pre-doctoral contract from the University of A Coruña.

I would like to recognize Peter Eriksson from SKB (Sweden) and Georg Kosakowski

from PSI (Switzerland) who gave me the opportunity to spend 1 and 3 months, respectively,

and brought me the chance to enjoy their research institutions and had very enriching

experiences. The stay at SKB was funded by a training scholarship from the LUCOEX project.

The research stay at PSI was funded by an INDITEX-UDC scholarship.

The models that I performed in my dissertation have relied on measured data from the

FEEBX in situ test and the experiments carried out by CIEMAT and UAM. I would like to thank

Pedro Luis Martín, Mariví Villar, Ana María Fernández, María Jesús Turrero and Elena Torres

from CIEMAT and Jaime Cuevas from UAM for providing these data.

I would like to thank also all my colleagues of the research group Agua y Suelo,

especially to Luis Montenegro who encouraged and supported me during my research work,

Bruno Pisani, Jesús Fernández, Acacia Naves and Yanmei Li.

Finally, I would like to dedicate this dissertation to my friends, to my parents and to my

husband, Abel, without his confidence and support it would not have been possible to achieve

it.

Agradecimientos

Me gustaría agradecer a Javier Samper la oportunidad de trabajar en su grupo de

investigación y poder realizar la tesis doctoral bajo su supervisión. Habría sido imposible

realizarla sin su inspiración, paciencia y apoyo durante la etapa de realización de la tesis.

La mayor parte de este trabajo ha sido desarrollado dentro del marco de proyecto

europeo PEBS Project financiado por el “European Atomic Energy Community's Seventh

Framework Programme” (FP7/2007-2011) bajo el contrato Nº 232598; el proyecto CEBAMA

financiado por “European Atomic Energy Community's (Euratom) Horizon 2020 Programme

(NFRP-2014/2015)” bajo el contrato Nº 662147; y el proyecto FEBEX-DP (Grimsel Fase VI)

financiado por el Consorcio del Proyecto FEBEX-DP. Este trabajo también ha sido apoyado

por ENRESA (España), Ministerio de Economía y Competencia (Proyecto CGL2012-36560 y

CGL2016-78281), fondeos FEDER y fondos de la Xunta de Galicia (Proyecto

10MDS118028PR y fondos: 2012/181 de “Consolidación e estructuración de unidades de

investigación competitivas”, Grupos de referencia competitiva). También he disfrutado de una

un contrato pre-doctoral financiado por la Universidad de A Coruña.

Me gustaría agradecerle a Peter Eriksson de SKB (Suecia) y a Georg Kosakowski de

PSI (Suiza) la oportunidad de pasar 1 y 3 meses con ellos respectivamente, de participar en

sus centros de investigación y llevarme experiencias enriquecedoras. La estancia en SKB fue

financiada por una beca del Proyecto LUCOEX, y la estancia en PSI fue financiada por la beca

INDITEX-UDC.

Los modelos llevados a cabo durante esta tesis han dependido de los datos medidos

en el ensayo in situ del proyecto FEBEX y de experimentos de laboratorio de CIEMAT y UAM.

Me gustaría agradecerles la aportación de los datos que he necesitado a Pedro Luis Martín,

Mariví Villar, Ana María Fernández, María Jesús Turrero, Elena Torres de CIEMAT y a Jaime

Cuevas de la UAM.

Me gustaría también agradecer la colaboración de mis compañeros del grupo de Agua

y Suelo, especialmente a Luis Montenegro quien me ha alentado y apoyado durante el trabajo

de investigación, Bruno Pisani, Jesús Fernández, Acacia Naves y Yanmei Li.

Finalmente, me gustaría dedicar la tesis a mis amigas, mi padres y a mi marido, Abel,

sin su confianza y su apoyo esto no habría sido posible.

Coupled THCM models of the bentonite barrier in a HLW repository

i

Coupled thermo-hydro-chemical-mechanical models for the

bentonite barrier in a radioactive waste repository

Abstract

Compacted bentonite is foreseen in several countries as a backfill and sealing material

for high-level radioactive waste (HLW) disposal. The long-term performance assessment and

the evaluation of the safety of a HLW repository requires the use of numerical models dealing

with the thermal (T), hydrodynamic (H), chemical (C) and mechanical (M) processes and their

interplays. This dissertation presents coupled THCM models of the bentonite barrier of HLW

repositories in clay and granite. The models account for the geochemical processes taking

place within the bentonite as well as the interactions of the bentonite with the concrete liner

and the corrosion products of the metallic canister. The THCM code INVERSE-FADES-CORE

has been updated, extended to deal with reactive gaseous phases, verified and benchmarked

against other codes. Coupled THCM numerical models have been applied to: 1) Small-scale

heating and hydration laboratory tests performed by CIEMAT on compacted FEBEX (Full-scale

Engineer Barrier Experiment) bentonite and its interactions with corrosion products and

concrete; 2) FEBEX mock-up and in situ tests; 3) Long-term reactive transport model

predictions of HLW repositories in granite and clay rocks. The results of the numerical models

of the lab and in situ tests show a good agreement with the measured data.

.


iii

Modelos acoplados termo-hidro-químico-mecánicos de la barrera

de bentonita de un almacenamiento de residuos radiactivos

Resumen

La bentonita compactada es el material previsto para el relleno y sellado de los

residuos radioactivos de alta actividad (RAA) en un almacenamiento geológico profundo

(AGP). La evaluación del comportamiento y de la seguridad de un AGP requiere utilizar

modelos numéricos acoplados térmicos (T), hidrodinámicos (H), químicos (Q) y mecánicos

(M). En esta tesis se han desarrollado modelos acoplados THQM de la barrera de bentonita

para el AGP en granito y en arcilla. Los modelos tienen en cuenta los procesos geoquímicos

que tienen lugar en la bentonita y sus interacciones con el hormigón y con los productos de

corrosión del contenedor metálico. Los modelos se han realizado con una versión del código

THQM INVERSE-FADES-CORE que se ha mejorado para tener en cuenta el transporte

reactivo de gases en la fase gaseosa y se ha verificado y comparado con otros códigos. Se

han realizado modelos numéricos THQM de: 1) Ensayos de laboratorio; 2) Ensayos FEBEX

(Full-scale Engineer Barrier Experiment) en maqueta e in situ; 3) Predicciones de la evolución

geoquímica a largo plazo de la barrera de bentonita en un AGP en granito y en arcilla. Los

resultados de los modelos numéricos muestran un buen ajuste a los datos medidos.


v

Modelos acoplados termo-hidro-químico-mecánicos da barreira de

bentonita dun almacenamento de residuos radioactivos

Resumo

A bentonita compactada é o material previsto para o recheo e selado dos residuos

radioactivos de alta actividade (RAA) nun almacenamento xeolóxico profundo (AXP). A

avaliación do comportamento e da seguridade dun AXP precisa de modelos numéricos

acoplados térmicos (T), hidrodinámicos (H), químicos (Q) e mecánicos (M). Nesta tese

desenroláronse modelos acoplados THQM da barreira de bentonita para o AXP en granito e

arxila. Os modelos teñen en conta os procesos xeoquímicos que teñen lugar na bentonita e a

súas interaccións co formigón e cos produtos de corrosión do contenedor metálico. Os

modelos fixéronse con unha versión do código THQM INVERSE-FADES-CORE que se

mellorou para ter en conta o transporte reactivo de gases na fase gaseosa e que se verificou

e comparou con outros códigos. Fixéronse modelos numéricos THQM de: 1) Ensaios de

laboratorio de hidratación e quecemento de mostras de bentonita FEBEX (Full-scale Engineer

Barrier Experiment) compactada e a súas interaccións con produtos de corrosión e formigón;

2) Ensaios FEBEX en maqueta e in situ; 3) Predicións da evolución xeoquímica a longo prazo

da barreira de bentonita nun AXP en granito e arxila. Os resultados dos modelos numéricos

amosan un bo axuste aos datos medidos.


vii

Preface

The storage of high-level radioactive waste (HLW) in deep geological repositories

(DGR) is based on a multibarrier concept, which includes natural and engineered barriers. The

natural barrier is the host rock while the engineered barriers include the waste form, the

canister, and the bentonite buffer. Significant research has been performed during the last

decades to improve the knowledge, characterize the key parameters and constitutive

equations and develop numerical models for the HLW repository barriers. FEBEX (Full-scale

Engineered Barrier Experiment) is a demonstration and research project for the engineered

bentonite barrier of a HLW repository. FEBEX is based on the Spanish reference concept for

radioactive waste disposal in crystalline rock, which consists on the disposal of spent fuel in

carbon steel canisters in long horizontal disposal drifts excavated in granite. The main physical,

thermal, hydrodynamic, mechanical and geochemical properties of the bentonite were

extensively studied during the project. This research has been tackled within the framework of

projects funded by the EURATOM Program of the European Commission. Significant parts of

this dissertation have been developed within the PEBS (Long-term Performance of Engineered

Barrier Systems), CEBAMA (Cement-based materials, properties, evolution, barrier functions)

and FEBEX-DP Projects (Full-scale Engineered Barrier Experiment Dismantling Project).

The main objective of this dissertation is the updating and the testing of coupled

thermal, hydrodynamic, chemical and mechanical (THCM) models for the compacted bentonite

barrier in a high-level radioactive waste repository including the following activities: 1) Updating

and improving the conceptual and numerical THCM model ; 2) Improving the THCM code

INVERSE-FADES-CORE; 3) Modeling laboratory tests; 4) Testing THCM models with data

from the FEBEX mock-up and in situ tests; and 5) Evaluation of the long-term geochemical

evolution of HLW repositories in granite and clay with reactive transport models.

Coupled THCM models of the bentonite barrier in a radioactive waste repository

ix

Contents

Coupled thermo-hydro-chemical-mechanical models for the bentonite barrier in a

radioactive waste repository .................................................................................................. i

Modelos acoplados termo-hidro-químico-mecánicos de la barrera de bentonita de un

almacenamiento de residuos radiactivos ........................................................................... iii

Modelos acoplados termo-hidro-químico-mecánicos da barreira de bentonita dun

almacenamento de residuos radioactivos ........................................................................... v

Preface .................................................................................................................................. vii

Contents ................................................................................................................................. ix

List of Figures .................................................................................................................... xviii

List of Tables ................................................................................................................... xxxiii

List of terms and abbreviations .................................................................................... xxxvii

Chapter 1. Introduction .......................................................................................................... 1

1.1. Motivation and objectives ............................................................................................ 1

1.2. State-of-the-art ............................................................................................................ 2

1.2.1. Bentonite barrier in a radioactive waste repository ...................................................... 2

1.2.2. Bentonite and iron interactions ..................................................................................... 3

1.2.3. Bentonite and concrete interactions ............................................................................. 4

1.2.4. Coupled THCM processes, codes and models ............................................................ 6

1.3. Scope .......................................................................................................................... 7

Chapter 2. Mathematical formulation of THCM models ...................................................... 9

2.1. Introduction ................................................................................................................. 9

2.2. Coupled THCM processes in a bentonite barrier in a HLW repository ....................... 9

2.3. Mathematical formulation .......................................................................................... 11

2.3.1. Reactive gas transport mathematical formulation ...................................................... 15

Chapter 3. THCM code INVERSE-FADES-CORE ............................................................... 17

3.1. Introduction ............................................................................................................... 17

Contents

x

3.2. Main features of INVERSE-FADES-CORE ............................................................... 17

3.3. Update of INVERSE-FADES-CORE ......................................................................... 18

3.4. Benchmarking of INVERSE-FADES-CORE V2 ........................................................ 20

Chapter 4. Integrated analysis of thermal, hydrodynamic and chemical data of

compacted FEBEX bentonite .............................................................................................. 21

4.1. Introduction ............................................................................................................... 21

4.2. Green-Ampt analytical solutions for water intake ...................................................... 22

4.3. Dimensionless variables ........................................................................................... 23

4.4. Integrated analysis of cumulative water intake data ................................................. 24

4.5. Integrated analysis of water content data ................................................................. 25

4.6. Integrated analysis of temperature data .................................................................... 25

4.7. Integrated analysis of chemical data ......................................................................... 26

4.8. Conclusions ............................................................................................................... 26

Chapter 5. Coupled THCM model of the heating and hydration tests on 60 cm long cells

............................................................................................................................................... 29

5.1. Introduction ............................................................................................................... 29

5.2. Test description ......................................................................................................... 29

5.3. Model calibration and results .................................................................................... 31

5.4. Conclusions ............................................................................................................... 35

Chapter 6. Coupled THCM models of heating and hydration tests to study the

interactions of Fe corrosion products and bentonite ....................................................... 37

6.1. Introduction ............................................................................................................... 37

6.2. Tests description ....................................................................................................... 37

6.3. Model results ............................................................................................................. 38

6.4. Sensitivity analysis .................................................................................................... 41

6.5. Conclusions ............................................................................................................... 41

Chapter 7. Coupled THCM model of the heating and hydration concrete-bentonite

interactions in the HB4 cell ................................................................................................. 43

7.1. Introduction ............................................................................................................... 43


xi


7.3. Model results ............................................................................................................. 44

7.4. Conclusions ............................................................................................................... 46

Chapter 8. Coupled THCM model of the mortar-bentonite interactions in the double

interface cells ....................................................................................................................... 49

8.1. Introduction ............................................................................................................... 49


8.3. Model description ...................................................................................................... 50

8.4. Model results ............................................................................................................. 50

8.5. Sensitivity analysis .................................................................................................... 52

8.6. Conclusions ............................................................................................................... 53

Chapter 9. THCM models of the FEBEX mock-up and in situ test ................................... 55

9.1. Introduction ............................................................................................................... 55

9.2. Model testing with data from the FEBEX mock-up test ............................................. 56

9.3. THCM models of the FEBEX in situ test ................................................................... 58

9.3.1. Introduction ................................................................................................................. 58

9.3.2. Testing and updating of the THCM model of the FEBEX in situ test ......................... 59

9.3.3. Pre-dismantling THCM model predictions of the geochemical conditions of the FEBEX

in situ test .................................................................................................................................... 62

9.3.4. Predictions of the tracers migration in the FEBEX in situ test .................................... 64

9.3.5. Predictions of the interactions of the bentonite with the concrete plug of the FEBEX in

situ test ........................................................................................................................................ 65

9.4. Conclusions ............................................................................................................... 66

Chapter 10. Reactive transport modelling of the long-term interactions of corrosion

products and compacted bentonite in a HLW repository in granite ............................... 69

10.1. Introduction ............................................................................................................. 69

10.2. Conceptual and numerical model ............................................................................ 69

10.3. Model results ........................................................................................................... 70

10.4. Sensitivity analysis .................................................................................................. 71

10.5. Conclusions ............................................................................................................. 72

Contents

xii

Chapter 11. Long-term non-isothermal reactive transport model of compacted

bentonite, concrete and corrosion products in a HLW repository in clay ...................... 73

11.1. Introduction ............................................................................................................. 73

11.2. Conceptual and numerical model ............................................................................ 74

11.3. Model results ........................................................................................................... 75

11.4. Sensitivity analysis .................................................................................................. 75

11.5. Conclusions ............................................................................................................. 76

Chapter 12. Conclusions and future work ......................................................................... 77

12.1. Improvements in the THCM model and the THCM code ........................................ 77

12.2. Integrated analysis of thermal, hydrodynamic and chemical data of compacted

FEBEX bentonite .................................................................................................................... 77

12.3. Coupled THCM models of laboratory test ............................................................... 79

12.4. THCM models the FEBEX mock-up and in situ tests .............................................. 81

12.5. Long-term reactive transport models of the geochemical interactions of the

compacted bentonite with concrete and corrosion products in HLW repositories .................. 83

12.5.1. Reactive transport modelling of the long-term interactions of corrosion products and

compacted bentonite in a HLW repository in granite .................................................................. 83

12.5.2. Long-term non-isothermal reactive transport model of compacted bentonite, concrete

and corrosion products in a HLW repository in clay .................................................................... 83

12.6. Recommendation for future work ............................................................................ 84

Chapter 13. References ....................................................................................................... 87

APPENDIX 1. INVERSE-FADES-CORE code improvements, verification and

benchmarking ....................................................................................................................... 97

A1.1. Main capabilities of INVERSE-FADES-CORE ........................................................... 98

A1.2. Code improvements ................................................................................................... 99

A1.3. Implementation of the reactive gas transport ........................................................ 100

A1.3.1. Mathematical description of the gas transport equation .................................... 100

A1.3.2. Chemical reactions involving the gaseous and liquid phases ............................ 103

A1.3.3. Code verification ................................................................................................ 104


xiii

A1.4. Benchmark cases ..................................................................................................... 111

A1.4.1. Non-isothermal geochemical interactions of concrete, bentonite and clay ........ 111

A1.4.2. Atmospheric concrete carbonation .................................................................... 113

A1.5. Description of the changes in the input files ......................................................... 115

A1.6. References ................................................................................................................ 116

APPENDIX 2. Integrated analysis of thermal, hydrodynamic and chemical data of

compacted FEBEX bentonite ............................................................................................ 119

A2.1. Introduction ............................................................................................................... 120

A2.2. Heating and hydration experiments on FEBEX bentonite .................................... 122

A2.2.1. FEBEX in situ test .............................................................................................. 122

A2.2.2. FEBEX mock-up test ......................................................................................... 123

A2.2.3. Laboratory experiments ..................................................................................... 123

A2.2.4. Water content data ............................................................................................ 125

A2.2.5. Chemical data .................................................................................................... 126

A2.3. Dimensional analysis ............................................................................................... 127

A2.3.1. Dimensionless variables .................................................................................... 127

A2.3.2. Green-Ampt analytical solutions for water inflow ............................................... 128

A2.4. Results of the dimensional analysis ....................................................................... 131

A2.4.1. Integrated analysis of temperature data ............................................................ 131

A2.4.2. Integrated analysis of cumulative water intake data .......................................... 132

A2.4.3. Integrated analysis of water content data .......................................................... 134

A2.4.4. Integrated analysis of chemical data ................................................................. 137

A2.5. Discussion of results ............................................................................................... 138

A2.6. Conclusions .............................................................................................................. 140

A2.7. References ................................................................................................................ 141

APPENDIX 3. Coupled THCM model of the heating and hydration tests on 60 cm long

cells ..................................................................................................................................... 145

A3.1. Introduction ............................................................................................................... 146

A3.2. Test description ........................................................................................................ 146

Contents

xiv

A3.3. Available data ............................................................................................................ 147

A3.4. Model description ..................................................................................................... 150

A3.5. Model calibration ...................................................................................................... 155

A3.6. Model results ............................................................................................................. 159

A3.6.1. Thermo-hydro-mechanical results ..................................................................... 159

A3.6.2. Chemical results ................................................................................................ 169

A3.7. Discussion and conclusions ................................................................................... 183

A3.8. References ................................................................................................................ 187

APPENDIX 4. Coupled THCM models of heating and hydration tests to study the

interactions of Fe corrosion products and bentonite ..................................................... 189

A4.1. Introduction ............................................................................................................... 190

A4.2. Corrosion tests on small cells ................................................................................. 191

A4.2.1. Introduction ........................................................................................................ 191

A4.2.2. Test description ................................................................................................. 191

A4.2.3. Analysis of available data .................................................................................. 192

A4.2.4. Model description ............................................................................................... 193

A4.2.5. Model results ..................................................................................................... 199

A4.3. Corrosion tests on medium-size cells .................................................................... 217

A4.3.1. Introduction ........................................................................................................ 217

A4.3.2. Test description ................................................................................................. 217

A4.3.3. Available data .................................................................................................... 219


A4.3.5. Model results ..................................................................................................... 220

A4.4. Summary and discussion of results ....................................................................... 229

A4.5. Conclusions .............................................................................................................. 232

A4.6. References ................................................................................................................ 233

APPENDIX 5. Coupled THCM model of the heating and hydration concrete-bentonite

interactions in the HB4 cell ............................................................................................... 237

A5.1. Introduction ............................................................................................................... 239


xv

A5.2. Test description and available data ........................................................................ 241

A5.3. Numerical model ....................................................................................................... 243

A5.3.1. Conceptual model .............................................................................................. 243

A5.3.2. Numerical model ................................................................................................ 247

A5.4. Model results ............................................................................................................. 250




A5.6. Conclusions and future works ................................................................................ 263

A5.7. References ................................................................................................................ 265

APPENDIX 6. Coupled THCM model of the mortar-bentonite interactions in the double

interface cells ..................................................................................................................... 273

A6.1. Introduction ............................................................................................................... 274

A6.2. Test description ........................................................................................................ 274

A6.3. Model description ..................................................................................................... 277

A6.4. Model results ............................................................................................................. 284



A6.4.3. Comparison of the results of the double interface test on 2I 3 and 2I 4 cell ...... 298


A6.6. Conclusions .............................................................................................................. 302

A6.7. References ................................................................................................................ 303

APPENDIX 7. Testing and updating of the THCM model of the FEBEX in situ test ..... 307

A7.1. Introduction ............................................................................................................... 308

A7.2. Sensitivity analyses and solute back diffusion analysis ...................................... 310

A7.2.1. Sensitivity analyses ........................................................................................... 311

A7.2.2. Solute back diffusion from the bentonite into the granite ................................... 317

A7.3. 2-D axisymmetric model .......................................................................................... 320


Contents

xvi

A7.3.2. Thermal and hydrodynamic results .................................................................... 321

A7.3.3. Cl- concentration results .................................................................................... 338

A7.3.4. Comparison of the results of the 2-D and 1-D axisymmetric models ................. 339

A7.3.5. Sensitivity runs ................................................................................................... 343

A7.4. Updated THCM model .............................................................................................. 347

A7.4.1. Improvements and updates of the THCM model ............................................... 347

A7.4.2. Updated model calculations in a hot section ..................................................... 348

A7.4.3. Sensitivity analyses of the updated THCM model ............................................. 352

A7.5. Model testing with measured thermal and hydraulic data collected from 2002 to

2015 ..................................................................................................................................... 355

A7.5.1. Temperatures .................................................................................................... 355

A7.5.2. Relative humidity and water content .................................................................. 359

A7.5.3. Pore water pressures ......................................................................................... 363

A7.5.4. Water content and dry density after dismantling ................................................ 364

A7.6. Conclusions .............................................................................................................. 367

A7.7. References ................................................................................................................ 371

APPENDIX 8. Pre-dismantling THCM model predictions of the geochemical conditions

of the FEBEX in situ test .................................................................................................... 373

A8.1. Introduction ............................................................................................................... 374

A8.2. Geochemical predictions for the hot section ......................................................... 374

A8.3. Geochemical predictions for the cold section ....................................................... 380

A8.4. Sensitivity of the predictions to the diffusion coefficients ................................... 385

A8.4.2. Hot section ......................................................................................................... 386

A8.4.3. Cold section ....................................................................................................... 386

A8.5. Transport of conservative species from the granite into the bentonite .............. 389

A8.6. Conclusions .............................................................................................................. 390

A8.7. References ................................................................................................................ 392

APPENDIX 9. Predictions of the tracer migration of the FEBEX in situ test................. 393

A9.1. Introduction ............................................................................................................... 394


xvii

A9.2. Tracers used in the FEBEX in situ test ................................................................... 394

A9.2.1. Types of tracers ................................................................................................. 394

A9.2.2. Tracer location ................................................................................................... 395

A9.2.3. Tracer sampling plans ....................................................................................... 397

A9.3. Predictions of iodide migration ............................................................................... 401

A9.3.1. Previous iodide migration modelling .................................................................. 401

A9.3.2. Updated iodide migration ................................................................................... 401

A9.3.3. Sensitivity analyses ........................................................................................... 403

A9.4. Predictions of the migration of point tracers ......................................................... 406

A9.4.1. Numerical model ................................................................................................ 406

A9.4.2. Tracer parameters ............................................................................................. 408

A9.4.3. Numerical model results .................................................................................... 408

A9.5. Summary and conclusions ...................................................................................... 414

A9.6. References ................................................................................................................ 416

APENDIX 10. Predictions of the interactions of the bentonite with the concrete plug of

the FEBEX in situ test ........................................................................................................ 419

A10.1. Introduction ............................................................................................................. 420

A10.2. Methodology ........................................................................................................... 420

A10.3. Detailed 2-D axisymmetric model ......................................................................... 422

A10.4. 1-D model of the geochemical interactions ......................................................... 425

A10.4.1. 1-D model description ...................................................................................... 425

A10.4.2. 1-D THCM model results ................................................................................. 427

A10.5. Conclusions ............................................................................................................ 439

A10.6. References .............................................................................................................. 441

APPENDIX 11. Reactive transport modelling of the long-term interactions of corrosion

products and compacted bentonite in a HLW repository in granite ............................. 443

APPENDIX 12. Long-term non-isothermal reactive transport model of compacted

bentonite, concrete and corrosion products in a HLW repository in clay .................... 455

APPENDIX 13. Resumen .................................................................................................... 473

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List of Figures

Figure 2.1. Scheme of the couplings between thermal (T), hydrodynamic (H), chemical (C) and mechanical (M) processes. .................................................................................................................... 11 Figure 3.1. Computed partial pressure (bar) of CO2(g) at 1 day with INVERSE-FADES-CORE (line) and TOUGHREACT (symbols) for the Case 1. ..................................................................................... 19 Figure 3.2. Calcite volume fractions computed with INVERSE-FADES-CORE (line) and TOUGHREACT (symbols) for the verification Case 4. .......................................................................... 19 Figure 4.1. Schematic design of the in situ test (ENRESA, 2000) (top left), the mock-up test (Martín et al., 2006) (top right), the CT cells (Fernández et al., 1999) (bottom left), and the CG cells (Villar et al., 2008a) (bottom right). ............................................................................................................................ 22 Figure 4.2. Time evolution of the dimensionless cumulative water intake versus dimensionless time for the CT (Fernández et al., 1999) and the CG cells (Fernández and Villar, 2010) and the mock-up test (ENRESA, 2006a). .......................................................................................................................... 24 Figure 5.1. Experimental setup of the CG tests (Villar et al., 2008a). .................................................. 30 Figure 5.2. Spatial distribution of the measured (symbols) and computed (line) gravimetric water content at the end of the CG0.5, CG0.5b, CG1, CG1b, CG2, CG2b and CG7.6 tests. ........................ 33 Figure 5.3. Spatial distribution of the measured aqueous extract (symbols) and the computed (lines) Cl- concentrations at the end of the CG0.5, CG0.5b, CG1, CG1b, CG2 and CG2b tests. And comparison of the Cl- concentrations reported by Fernández and Villar (2010) (symbols) and the computed (lines) Cl- concentrations at the end of the CG7.6 test. ........................................................ 33 Figure 6.1. Scheme of the corrosion tests on small cells (left) (Torres et al., 2008) and of the corrosion tests on medium-size cells (right) (Turrero et al., 2011). ....................................................................... 38 Figure 6.2. Spatial distribution of the computed cumulative magnetite precipitation at selected times in the corrosion test on small cell at 100ºC (left) and in the medium-size corrosion test on FB3 cell (right). ............................................................................................................................................................... 40 Figure 6.3. Measured (symbol) and computed (line) weight of precipitated iron hydroxide at the end of in the corrosion test on small cell at 100ºC (t = 180 days) and after cooling. ....................................... 40 Figure 7.1. Scheme of the concrete-bentonite test on HB4 cell (Turrero et al., 2011). ........................ 44 Figure 7.2. Spatial distribution of the computed pH in the HB4 cell at selected times. ........................ 46 Figure 8.1. Scheme of the six double interface tests (Cuevas et al., 2016). ........................................ 50 Figure 8.2. Spatial distribution the computed pH in the double interface 2I3 test at selected times. ... 52 Figure 9.1. Computed (line) and measured (symbols) water intake for the FEBEX mock-up test. ...... 57 Figure 9.2. Computed (line) and measured (symbols) relative humidity in the sensors located at 0.22 m from the heater for the FEBEX mock-up test. ........................................................................... 57 Figure 9.3. Computed (lines) and measured (symbols) relative humidity in the sensors located at 0.37 m from the heater for the FEBEX mock-up test. ........................................................................... 57 Figure 9.4. Computed (lines) and measured (symbols) relative humidity in the sensors located at 0.55 m from the heater for the FEBEX mock-up test. ........................................................................... 58 Figure 9.5. Computed (lines) and measured (symbols) relative humidity in the sensors located at 0.70 m from the heater for the FEBEX mock-up test. ........................................................................... 58 Figure 9.6. Comparison of the predicted gravimetric water content (lines) in a hot section (left) and a cold section (right) and the measured gravimetric water content data (symbols) in sections S22, S27, S45, S49, S52, S9, S15 and S58 at the times of dismantling of heater 1 (year 2002) and heater 2 (year 2015). The plots at the bottom show the location of the sections where water contents were measured. .............................................................................................................................................. 62 Figure 9.7. Pre-dismantling predictions of Cl- and Ca2+ concentrations (lines) in 2002 and 2015 in a hot section. The graph also shows the inferred Cl- concentrations in sections 19 and 29 in 2002 (symbols). .............................................................................................................................................. 63 Figure 9.8. Pre-dismantling predictions of Cl- and Ca2+concentrations (lines) in 2002 and 2015 in a cold section. The graph also shows the inferred Cl- concentrations in section 12 in 2002 (symbols). . 63


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Figure 9.9. Computed concentrations of dissolved borate (top left), selenate (top right), europium (bottom left) and cesium (bottom right) (mol/L) at 18 years with the 2-D numerical model in a vertical plane normal to the axis of the gallery. .................................................................................................. 65 Figure 9.10. Predicted pH (left) and changes in porosity caused by dissolution/precipitation reactions (right) in the bentonite and the concrete at selected times. .................................................................. 66 Figure 10.1. Scheme of the engineered barrier system and 1-D finite element grid of the axisymmetric model (Samper et al., 2016). ................................................................................................................. 70 Figure 10.2. Radial distribution of the computed bentonite porosity which changes due to mineral dissolution/precipitation at selected times (Samper et al., 2016). ......................................................... 71 Figure 11.1. 1-D finite element grid which accounts for the canister, the bentonite barrier, the concrete liner and the clay formation (Mon et al., 2017). ..................................................................................... 74 Figure 11.2. Radial distribution of the computed porosity which changes due to mineral dissolution/precipitation at selected times. ............................................................................................ 75

Figure A1.1. 1-D finite element grid used for Case 1 and prescribed partial gas pressures at the boundaries. .......................................................................................................................................... 104 Figure A1.2. Computed partial pressure (bar) of CO2(g) at 1 day with INVERSE-FADES-CORE (line) and TOUGHREACT (symbols). ........................................................................................................... 105 Figure A1.3. Computed time evolution of the partial pressure (bar) of CO2(g) with INVERSE-FADES-CORE (line) and TOUGHREACT (symbols) at x = 0.19 dm. .............................................................. 105 Figure A1.4. 1-D finite element grid used for Case 2 and fixed pressure at the left boundary. ......... 106 Figure A1.5. Computed partial pressure (bar) of CO2(g) at t = 0.1 and 1 days with INVERSE-FADES-CORE (line) and TOUGHREACT (symbols). ...................................................................................... 106 Figure A1.6. Computed time evolution of the partial pressure (bar) of CO2(g) with INVERSE-FADES-CORE (line) and TOUGHREACT (symbols) at x = 0.19 dm. .............................................................. 106 Figure A1.7. 1-D finite element grid used in Case 3 and prescribed pressure profile. ...................... 107 Figure A1.8. Computed calcite volume fraction with INVERSE-FADES-CORE (line) and TOUGHREACT (symbols). .................................................................................................................. 108 Figure A1.9. Computed pH with INVERSE-FADES-CORE (line) and TOUGHREACT (symbols). ... 108 Figure A1.10. Computed Ca2+ concentration with INVERSE-FADES-CORE (line) and TOUGHREACT (symbols). ............................................................................................................................................ 108 Figure A1.11. Computed partial pressure with INVERSE-FADES-CORE (line) and TOUGHREACT (symbols) at t = 0.1 and 1 days. .......................................................................................................... 109 Figure A1.12. Computed calcite volume fraction with INVERSE-FADES-CORE (line) and TOUGHREACT (symbols) at t = 0.1 and 1 days. ................................................................................ 110 Figure A1.13. Computed pH with INVERSE-FADES-CORE (line) and TOUGHREACT (symbols) at t = 0.1 and 1 days. .................................................................................................................................... 110 Figure A1.14. Computed Ca2+ concentration with INVERSE-FADES-CORE (line) and TOUGHREACT (symbols) at t = 0.1 and 1 days. .......................................................................................................... 110 Figure A1.15. Scheme of the near-field geometry and the 1-D axisymmetric conceptual model for the benchmark of the interactions of concrete, bentonite and clay (Berner et al., 2013). ......................... 111 Figure A1.16. Comparison of the mineral volumetric fractions computed with OpenGeos-GEMS and CORE2DV5 at 1 year for the isothermal benchmark case at 25ºC. ..................................................... 112 Figure A1.17. Evolution of liquid saturation during concrete drying computed with TOUGH2 (line), HYTEC (triangles) and INVERSE-FADES-CORE (circles) at selected times. .................................... 114 Figure A1.18. Dissolved tracer concentration profiles computed with TOUGHREACT (lines), CRUNCHFLOW (solid squares), MIN3P (crosses), HYTEC (triangles) and INVERSE-FADES-CORE (circles) at selected times. ................................................................................................................... 114 Figure A2.1. Scheme of FEBEX in situ test (ENRESA, 2006a). Vertical lines show the location of the sampling sections (dimensions in meters). ......................................................................................... 121 Figure A2.2. Scheme of the FEBEX mock-up test (Martín et al., 2006). ........................................... 121 Figure A2.3. Scheme of the CG cells (Villar et al., 2008a). ................................................................ 124 Figure A2.4. Scheme of the CT cells (Fernández et al., 1999). ......................................................... 124 Figure A2.5. Scheme for parallel flow (left) and radial flow (right). .................................................... 129 Figure A2.6. Comparison of the Green-Ampt analytical solution and the measured cumulative water intake for the mock-up test (Samper et al., 2011b). ............................................................................ 130

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Figure A2.7. Dimensionless cumulative water intake versus dimensionless time for radial and parallel flow calculated for the same volume and thickness, hydration surface and thickness, volume and hydration surface and calibrated volume, thickness and hydration surface. ....................................... 131 Figure A2.8. Steady-state dimensionless temperatures versus dimensionless distance for the CT and CG cells and the mock-up and the in situ tests. The error bars show the maximum and minimum temperature fluctuations. ..................................................................................................................... 132 Figure A2.9. Cumulative water intake data for the CT (Fernández et al., 1999) and CG cells (Fernández and Villar, 2010) and the mock-up test (ENRESA, 2006a). ............................................. 134 Figure A2.10. Time evolution of the dimensionless cumulative water intake versus dimensionless time for the CT (Fernández et al., 1999) and CG cells (Fernández and Villar, 2010) and the mock-up test (ENRESA, 2006a). .............................................................................................................................. 134 Figure A2.11. Dimensionless gravimetric water content versus dimensionless distance for the CT and CG cells and the mock-up and the in situ tests for dimensionless times ranging from 0.0064 to 0.095. The dimensionless times, tD, are arranged in four figures, a) tD = 0.005, b) tD = 0.01, c) tD = 0.025 and d) tD from 0.071 to 0.095. .................................................................................................................... 136 Figure A2.12. Time evolution of the dimensionless average gravimetric water content for the CT and the CG cells and the mock-up and the in situ tests. ............................................................................ 136 Figure A2.13. Dimensionless Cl- concentration data versus dimensionless distance from the CT and CG cells and the in situ test for selected dimensionless times. .......................................................... 137 Figure A2.14. Minimum, maximum and average pH of the aqueous extracts of the bentonite samples taken from the dismantled of the CT and CG cells and the in situ test versus dimensionless time. ... 138 Figure A3.1. Experimental setup of CG tests (Villar et al., 2008a)..................................................... 147 Figure A3.2. Raw data (symbols) and corrected data (discontinuous lines) of cumulative water intake for CG cells. ......................................................................................................................................... 148 Figure A3.3. One dimensional finite element mesh used for the numerical model of the 60 cm long CG cells. .............................................................................................................................................. 151 Figure A3.4. Spatial distribution of the mean measured (symbols) and the computed (lines) temperatures at the end of the CG1 and CG1b tests with the previous and the revised models. ...... 156 Figure A3.5. Spatial distribution of the measured (symbols) and the computed (line) saturation degree at the end of the CG1 and CG1b tests with the previous and the revised models. ............................ 156 Figure A3.6. Spatial distribution of the measured (symbols) and the computed (lines) concentrations of the exchanged Na+, K+, Ca2+ and Mg2+ at the end of the CG0.5b test with the previous and the revised model. ..................................................................................................................................... 158 Figure A3.7. Time evolution of the measured water intake (symbols) for the CG7.6 test and the computed cumulative water intake (lines) for the previous and the revised models. .......................... 159 Figure A3.8. Comparison of the Cl- concentrations of the GMFV reported by Fernández and Villar (2010) (symbols) and the Cl- concentrations at the end of the CG7.6 test computed with the previous and the revised models (lines). ........................................................................................................... 159 Figure A3.9. Spatial distribution of the measured (symbols) and the computed (line) porosity at the end of the CG0.5 and CG0.5b tests. ................................................................................................... 160 Figure A3.10. Spatial distribution of the measured (symbols) and the computed (line) gravimetric water content at the end of the CG0.5 and CG0.5b tests. .................................................................. 160 Figure A3.11. Spatial distribution of the measured (symbols) and the computed (line) saturation degree at the end of the CG0.5 and CG0.5b tests. ............................................................................. 161 Figure A3.12. Time evolution of the measured (symbols) and the computed (line) cumulative water intake of the CG0.5 and CG0.5b tests. ............................................................................................... 161 Figure A3.13. Spatial distribution of the mean measured (symbols) and the computed (lines) temperatures at the end of the CG0.5 and CG0.5b tests. ................................................................... 162 Figure A3.14. Time evolution of the measured (discontinuous lines) and the computed (continuous lines) temperatures at the sensors located at x = 0.1, 0.2, 0.3, 0.4 and 0.5 m (from the heaters) of the CG0.5 and CG0.5b tests. .................................................................................................................... 162 Figure A3.15. Spatial distribution of the measured (symbols) and the computed (line) porosity at the end of the CG1 and CG1b tests. ......................................................................................................... 163 Figure A3.16. Spatial distribution of the measured (symbols) and the computed (line) gravimetric water content at the end of the CG1 and CG1b tests. ........................................................................ 163 Figure A3.17. Spatial distribution of the measured (symbols) and the computed (line) saturation degree at the end of the CG1 and CG1b tests. ................................................................................... 164 Figure A3.18. Time evolution of the measured (symbols) cumulative water intake for the CG0.5 test and the computed (lines) water intake of the CG0.5, CG1 and CG1b tests. ...................................... 164


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Figure A3.19. Spatial distribution of the maximum, the minimum and the mean measured (symbols) and computed (lines) temperatures at the end of the CG1 and CG1b tests. ...................................... 164 Figure A3.20. Time evolution of the measured (discontinuous lines) and the computed (continuous lines) temperatures at the sensors located at x = 0.1, 0.2, 0.3, 0.4 and 0.5 m (from the heaters) of the CG1 and CG1b tests. .......................................................................................................................... 165 Figure A3.21. Spatial distribution of the measured (symbols) and the computed (line) porosity at the end of the CG2 and CG2b tests. ......................................................................................................... 165 Figure A3.22. Spatial distribution of the measured (symbols) and the computed (line) gravimetric water content at the end of the CG2 and CG2b tests. ........................................................................ 166 Figure A3.23. Spatial distribution of the measured (symbols) and the computed (line) saturation degree at the end of the CG2 and CG2b tests. ................................................................................... 166 Figure A3.24. Time evolution of the measured water intake (symbols) for the CG0.5 and CG2 tests and the computed water intake (lines) for the CG0.5, CG1 and CG2 tests. ....................................... 166 Figure A3.25. Spatial distribution of the maximum, the minimum and the mean measured (symbols) and the computed (lines) temperatures at the end of the CG2 and CG2b tests. ................................ 167 Figure A3.26. Time evolution of the measured (discontinuous lines) and the computed (continuous lines) temperatures at the sensors located at x = 0.1, 0.2, 0.3, 0.4 and 0.5 m (from the heaters) of the CG2 and CG2b tests. .......................................................................................................................... 167 Figure A3.27. Spatial distribution of the measured (symbols) and the computed (line) porosity at the end of the CG7.6 test. ......................................................................................................................... 168 Figure A3.28. Spatial distribution of the measured (symbols) and the computed (line) gravimetric water content at the end of the CG7.6 test. ......................................................................................... 168 Figure A3.29. Spatial distribution of the measured (symbols) and the computed (line) saturation degree at the end of the CG7.6 test. ................................................................................................... 168 Figure A3.30. Time evolution of the measured water intake (symbols) for the CG0.5, CG2 and CG7.6 tests and the computed cumulative water intake (lines) of the CG0.5, CG1, CG2 and CG7.6 tests. . 169 Figure A3.31. Spatial distribution of the computed temperature at the end of the CG7.6 test. ......... 169 Figure A3.32. Spatial distribution of the measured (symbols) and the computed (lines) Cl- concentrations at the end of the CG0.5 and CG0.5b tests. Measured data include aqueous extract and squeezing data (logarithmic scale, top, and natural scale, bottom, for Cl- concentrations). ............... 170 Figure A3.33. Spatial distribution of the measured (symbols) and the computed (line) concentrations of the exchanged Na+, K+, Ca2+ and Mg2+ at the end of the CG0.5b test. ........................................... 171 Figure A3.34. Spatial distribution of the measured (symbols) and the computed (lines) Cl- concentrations at the end of the CG1 and CG1b tests. Measured data include aqueous extract and squeezing data (logarithmic scale, top, and natural scale, bottom, for Cl- concentrations). ............... 172 Figure A3.35. Spatial distribution of the measured (symbols) and the computed (line) concentrations of the exchanged Na+, K+, Ca2+ and Mg2+ at the end of the CG1b test. .............................................. 173 Figure A3.36. Spatial distribution of the measured (symbols) and the computed (lines) Cl- concentrations at the end of the CG2 and CG2b tests. Measured data include aqueous extract and squeezing data (logarithmic scale, top, and natural scale, bottom, for Cl- concentrations). ............... 174 Figure A3.37. Spatial distribution of the measured (symbols) and the computed (line) concentrations of the exchanged Na+, K+, Ca2+ and Mg2+ at the end of the CG2 and CG2b test. .............................. 175 Figure A3.38. Comparison of the Cl- concentrations of the GMFV reported by Fernández and Villar (2010) (symbols) and the computed (lines) Cl- concentrations at the end of the CG7.6 test (logarithmic scale, top, and natural scale, bottom, for Cl- concentrations). ............................................................ 176 Figure A3.39. Comparison of the Ca2+ concentrations of the GMFV reported by Fernández and Villar (2010) (symbols) and the computed (line) Ca2+ concentrations at the end of the CG7.6 test. .......... 177 Figure A3.40. Comparison of the Mg2+ concentrations of the GMFV reported by Fernández and Villar (2010) (symbols) and the computed (line) Mg2+ concentrations at the end of the CG7.6 test. ........... 177 Figure A3.41. Comparison of the Na+ concentrations of the GMFV reported by Fernández and Villar (2010) (symbols) and the computed (line) Na+ concentrations at the end of the CG7.6 test. ............ 177 Figure A3.42. Comparison of the K+ concentrations of the GMFV reported by Fernández and Villar (2010) (symbols) and the computed (line) K+ concentrations at the end of the CG7.6 test. .............. 178 Figure A3.43. Comparison of the SO4

2- concentrations of the GMFV reported by Fernández and Villar (2010) (symbols) and the computed (line) SO4

2- concentrations at the end of the CG7.6 test. ......... 178 Figure A3.44. Comparison of the HCO3

- concentrations of the GMFV reported by Fernández and Villar (2010) (symbols) and the computed (line) HCO3

- concentrations at the end of the CG7.6 test. ......... 178 Figure A3.45. Spatial distribution of the computed SiO2(aq) concentrations at the end of the CG7.6 test. ...................................................................................................................................................... 179

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Figure A3.46. Comparison of the pH of the GMFV reported by Fernández and Villar (2010) (symbols) and the computed (line) pH at the end of the CG7.6 test. ................................................................... 179 Figure A3.47. Spatial distribution of the cumulative dissolution/precipitation of calcite for the CG7.6 test at selected times (positive values for precipitation and negative for dissolution). ........................ 180 Figure A3.48. Spatial distribution of the cumulative dissolution/precipitation of gypsum for the CG7.6 test at selected times (positive values for precipitation and negative for dissolution). ........................ 181 Figure A3.49. Spatial distribution of the cumulative dissolution/precipitation of anhydrite for the CG7.6 test at selected times (positive values for precipitation and negative for dissolution). A zoom of the anhydrite precipitation near the heater is shown on the right. ............................................................. 181 Figure A3.50. Spatial distribution of the cumulative dissolution/precipitation of chalcedony for the CG7.6 test at selected times (positive values for precipitation and negative for dissolution). ............ 182 Figure A3.51. Spatial distribution of the measured (symbols) and the computed (line) concentrations of the exchanged Na+, K+, Ca2+ and Mg2+ at the end of the CG7.6 test. ............................................. 182 Figure A3.52. Spatial distribution of the concentrations of the sorbed species on the strong, weak #1 and weak #2 sites at the end of the CG7.6 test. ................................................................................. 183 Figure A4.1. Sketch of the corrosion tests on small cells (Torres et al., 2008). ................................. 192 Figure A4.2. Finite element mesh and boundary conditions of the numerical model of the corrosion tests in small cells. ............................................................................................................................... 194 Figure A4.3. Spatial distribution of the computed (lines) and the measured (symbol) volumetric water content at selected times in the corrosion test on small cell a3 at 100ºC. .......................................... 199 Figure A4.4. Spatial distribution of the computed (lines) and the measured (symbol) saturation degree at selected times in the corrosion test on small cell a3 at 100ºC. ....................................................... 200 Figure A4.5. Spatial distribution of the computed (lines) and the measured (symbol) porosity at selected times in the corrosion test on small cell a3 at 100ºC. ........................................................... 200 Figure A4.6. Spatial distribution of the computed temperature in the corrosion test on small cells at temperatures 25ºC, 50ºC and 100ºC. ................................................................................................. 200 Figure A4.7. Spatial distribution of the computed concentration of dissolved Cl- at selected times in the corrosion test on small cell a3 at 100ºC. ....................................................................................... 201 Figure A4.8. Spatial distribution of the computed concentration of dissolved Na+, K+, Ca2+, Mg2+, HCO3

-, SO42- and SiO2(aq) at selected times in the corrosion test on small cell a3 at 100ºC. ........... 203

Figure A4.9. Spatial distribution of the computed concentration of dissolved Fe2+ for 0 < t < 30 days in the corrosion test on small cell a3 at 100ºC. ....................................................................................... 204 Figure A4.10. Spatial distribution of the computed concentration of dissolved Fe2+ for 60 < t < 180 days in the corrosion test on small cell a3 at 100ºC between 60 and 180 days. ................................ 204 Figure A4.11. Spatial distribution of the computed cumulative iron corrosion at selected times in the corrosion test on small cell a3 at 100ºC. (Negative for dissolution and positive for precipitation). ..... 204 Figure A4.12. Spatial distribution of the computed cumulative precipitation/dissolution of magnetite at selected times in the corrosion test on small cell a3 at 100ºC. (Negative for dissolution and positive for precipitation). ....................................................................................................................................... 205 Figure A4.13. Spatial distribution of the computed cumulative precipitation/dissolution of Fe(OH)2(s) at selected times in the corrosion test on small cell a3 at 100ºC. (Negative for dissolution and positive for precipitation). ....................................................................................................................................... 205 Figure A4.14. Measured (symbol) and computed (line) weight of precipitated iron hydroxide at the end of in the corrosion test on small cell a3 at 100ºC (t = 180 days) and after cooling. ............................ 205 Figure A4.15. Spatial distribution of the computed cumulative precipitation/dissolution of goethite at selected times in the corrosion test on small cell a3 at 100ºC. (Negative for dissolution and positive for precipitation). ....................................................................................................................................... 206 Figure A4.16. Spatial distribution the computed cumulative precipitation/dissolution of calcite at selected times in the corrosion test on small cell a3 at 100ºC. (Negative for dissolution and positive for precipitation). ....................................................................................................................................... 206 Figure A4.17. Spatial distribution the computed cumulative precipitation/dissolution of gypsum at selected times in the corrosion test on small cell a3 at 100ºC. (Negative for dissolution and positive for precipitation). ....................................................................................................................................... 206 Figure A4.18. Spatial distribution the computed cumulative precipitation/dissolution of anhydrite at selected times in the corrosion test on small cell a3 at 100ºC. (Negative for dissolution and positive for precipitation). ....................................................................................................................................... 207 Figure A4.19. Spatial distribution the computed cumulative precipitation/dissolution of quartz at selected times in the corrosion test on small cell a3 at 100ºC. (Negative for dissolution and positive for precipitation). ....................................................................................................................................... 207


xxiii

Figure A4.20. Spatial distribution of the computed pH at selected times in the corrosion test on small cell a3 at 100ºC. .................................................................................................................................. 207 Figure A4.21. Spatial distribution of the computed Eh at selected times in the corrosion test on small cell a3 at 100ºC. .................................................................................................................................. 208 Figure A4.22. Spatial distribution of the computed (lines) and measured (symbols) concentrations of the exchanged cations after cooling of the corrosion test on small cell a3 at 100ºC. ......................... 208 Figure A4.23. Computed (line) and measured (symbol) concentrations of the exchanged Fe2+ after the cooling of the corrosion test on small cell a3 at 100ºC........................................................................ 208 Figure A4.24. Spatial distribution of the computed concentrations of sorbed species on strong, weak #1 and weak #2 sorption sites at the end of the corrosion test on small cell a3 at 100ºC. ................. 209 Figure A4.25. Spatial distribution of the measured (symbol) and the computed (lines) saturation degree at the end of the corrosion test on small cell a3 at 100ºC for the base run and sensitivity run to the liquid permeability. ......................................................................................................................... 210 Figure A4.26. Sensitivity of the computed cumulative precipitation of magnetite at the end of the corrosion test on small cell a3 at 100ºC to changes in the liquid permeability. .................................. 210 Figure A4.27. Measured (symbol) and computed (line) weight of iron at the end of the corrosion test on small cell a3 at 100ºC for the base run and the sensitivity run to the liquid permeability. ............. 210 Figure A4.28. Spatial distribution of the measured (symbol) and the computed (lines) saturation degree at the end of the corrosion test on small cell a3 at 100ºC for the base run and the sensitivity run to vapor tortuosity. ......................................................................................................................... 211 Figure A4.29. Sensitivity of the computed cumulative precipitation of magnetite at the end of the corrosion test on small cell a3 at 100ºC to the vapor tortuosity. ......................................................... 211 Figure A4.30. Measured (symbol) and computed (line) weight of iron at the end of the corrosion test on small cell a3 at 100ºC for the base run and the sensitivity run to the vapor tortuosity. .................. 212 Figure A4.31. Sensitivity of the computed cumulative precipitation of magnetite at the end of the corrosion test on small cell a3 at 100ºC to the magnetite precipitation at equilibrium (sensitivity run) and kinetically controlled (base run). ................................................................................................... 212 Figure A4.32. Measured (symbol) and computed (line) weight of iron at the end of the corrosion test on small cell a3 at 100ºC for the base run and the sensitivity run to magnetite precipitation. ............ 213 Figure A4.33. Sensitivity of the computed cumulative precipitation of magnetite at the end of the corrosion test on small cell a3 at 100ºC to changes in the corrosion rate. ......................................... 213 Figure A4.34. Measured (symbol) and computed (line) weight of iron at the end of the corrosion test on small cell a3 at 100ºC for the base run and the sensitivity run with a smaller corrosion rate. ....... 214 Figure A4.35. Spatial distribution of the computed concentration of dissolved Fe2+ at the end of the corrosion tests (after cooling) in the small cells at 25, 50 and 100ºC. ................................................ 215 Figure A4.36. Spatial distribution of the computed pH at the end of the corrosion tests (after cooling) in the small cells at 25, 50 and 100ºC. ................................................................................................ 215 Figure A4.37. Spatial distribution the computed cumulative dissolution for iron at the end of the corrosion tests (after cooling) in the small cells at 25, 50 and 100ºC. ................................................ 216 Figure A4.38. Spatial distribution of the computed magnetite cumulative precipitation at the end of the corrosion tests (after cooling) in the small cells at 25, 50 and 100ºC. ................................................ 216 Figure A4.39. Spatial distribution of the computed Fe(OH)2(s) cumulative precipitation at the end of the corrosion tests (after cooling) in the small cells at 25, 50 and 100ºC. .......................................... 216 Figure A4.40. Spatial distribution of the computed (lines) and the measured (symbols) iron weight at the end of the corrosion tests (after cooling) in the small cells at 25, 50 and 100ºC. ......................... 217 Figure A4.41. Scheme of the corrosion tests on medium-size cells (Turrero et al., 2011). ............... 218 Figure A4.42. One dimensional finite element mesh for the numerical model of the corrosion test on the FB3 cell. ......................................................................................................................................... 219 Figure A4.43. Spatial distribution of the measured (symbols) and the computed (line) volumetric water content at the end of the medium-size corrosion test on FB3 cell. ..................................................... 221 Figure A4.44. Spatial distribution of the measured (symbols) and the computed (line) porosity at the end of the medium-size corrosion test on FB3 cell. ............................................................................ 221 Figure A4.45. Spatial distribution of the measured (symbols) and the computed (line) temperature at the end of the medium-size corrosion test on FB3 cell. ...................................................................... 221 Figure A4.46. Spatial distribution of the measured (symbols) and the computed (line) relative humidity at the end of the medium-size corrosion test on FB3 cell. .................................................................. 222 Figure A4.47. Time evolution of the computed (lines) and the measured (symbols) temperature in the sensors T2 (18 mm from the heater) and T1 (74 mm from the heater) of the medium-size corrosion test on FB3 cell. ................................................................................................................................... 222

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Figure A4.48. Time evolution of the computed (lines) and the measured (symbols) relative humidity in the sensors RH2 (18 mm from the heater) and RH1 (74 mm from the heater) of the medium-size corrosion test on FB3 cell. ................................................................................................................... 222 Figure A4.49. Spatial distribution of the computed concentration of dissolved Cl- at selected times in the medium-size corrosion test on FB3 cell. ....................................................................................... 223 Figure A4.50. Spatial distribution of the computed concentration of dissolved Na+, K+, Mg2+, Ca2+, SO4

2-, HCO3-, and SiO2(aq) at selected times in the medium-size corrosion test on FB3 cell. ........... 224

Figure A4.51. Spatial distribution of the computed concentration of dissolved Fe2+ at selected times in the medium-size corrosion test on FB3 cell. ....................................................................................... 225 Figure A4.52. Spatial distribution of the computed cumulative Fe(s) corrosion at selected times in the medium-size corrosion test on FB3 cell (negative for dissolution and positive for precipitation). ....... 226 Figure A4.53. Spatial distribution of the computed cumulative magnetite precipitation at selected times in the medium-size corrosion test on FB3 cell (negative for dissolution and positive for precipitation). ....................................................................................................................................... 226 Figure A4.54. Spatial distribution of the computed cumulative calcite precipitation/dissolution at selected times in the medium-size corrosion test on FB3 cell (negative for dissolution and positive for precipitation). ....................................................................................................................................... 226 Figure A4.55. Spatial distribution of the computed cumulative gypsum precipitation/dissolution at selected times in the medium-size corrosion test on FB3 cell (negative for dissolution and positive for precipitation). ....................................................................................................................................... 227 Figure A4.56. Spatial distribution of the computed cumulative anhydrite precipitation/dissolution at selected times in the medium-size corrosion test on FB3 cell (negative for dissolution and positive for precipitation). ....................................................................................................................................... 227 Figure A4.57. Spatial distribution of the computed cumulative quartz precipitation/dissolution at selected times in the medium-size corrosion test on FB3 cell (negative for dissolution and positive for precipitation). ....................................................................................................................................... 227 Figure A4.58. Spatial distribution of the computed pH at selected times in the medium-size corrosion test on FB3 cell. ................................................................................................................................... 228 Figure A4.59. Spatial distribution of the computed Eh at selected times in the medium-size corrosion test on FB3 cell. ................................................................................................................................... 228 Figure A4.60. Spatial distribution of the computed (lines) and measured (symbols) concentrations of the exchanged cations at the end of the medium-size corrosion test on FB3 cell. ............................. 228 Figure A4.61. Spatial distribution of the computed concentration of exchanged Fe2+ at the end of the test of the medium-size corrosion test on FB3 cell. ............................................................................ 229 Figure A4.62. Spatial distribution of the computed concentration of sorbed species on strong, weak #1 and weak #2 sorption sites at the end of the test of the medium-size corrosion test on FB3 cell. ..... 229 Figure A5.1. Sketch of the concrete-bentonite test on HB4 cell (Turrero et al., 2011). ..................... 242 Figure A5.2. One dimensional finite element mesh and boundary conditions for the numerical model of the HB4 test. .................................................................................................................................... 244 Figure A5.3. Computed (lines) and measured (symbols) volumetric water content and porosity of the HB4 cell. .............................................................................................................................................. 251 Figure A5.4. Time evolution of the computed (lines) and the measured (symbols) temperature and relative humidity in the sensor 1 (50 mm from hydration) and sensor 2 (94 mm from hydration) of the HB4 cell. .............................................................................................................................................. 251 Figure A5.5. Computed (lines) and the measured (symbols) temperature and relative humidity of the HB4 cell at the end of the test. ............................................................................................................ 252 Figure A5.6. Spatial distribution of the computed pH in the HB4 cell at selected times. ................... 253 Figure A5.7. Time evolution of the computed concentration of dissolved Na+, Cl-, SO4

2-, Ca2+ and K+ (up), SiO2(aq), HCO3

-, Al3+ and Mg2+ (bottom) at x = 0.025 m (concrete). .......................................... 254 Figure A5.8. Time evolution of the computed concentration of dissolved Na+, Cl-, SO4

2-, Ca2+ and K+ (up), SiO2(aq), HCO3

-, Al3+ and Mg2+ (bottom) at x = 0.035 m (bentonite). ......................................... 255 Figure A5.9. Cumulative precipitation/dissolution of calcite, brucite and cristobalite and ettringite at 1610 days after the cooling phase. ..................................................................................................... 256 Figure A5.10. Cumulative precipitation/dissolution of sepiolite, anhydrite, gypsum, portlandite and CSH1.8; and CSH0.8 and quartz at 1610 day after the cooling phase. .............................................. 256 Figure A5.11. Time evolution of the cumulative precipitation/dissolution of brucite, calcite, CSH1.8 and portlandite and ettringite x = 0.025 m (concrete). ......................................................................... 257 Figure A5.12. Time evolution of the cumulative precipitation/dissolution of calcite, gypsum and sepiolite at x = 0.035 m (bentonite). .................................................................................................... 257


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Figure A5.13. Spatial distribution of the mineral volume fraction in the HB4 cell at t = 0 (top) and at the end of the test (bottom). ...................................................................................................................... 259 Figure A5.14. Spatial distribution of the porosity in the HB4 cell at the end of the test. .................... 261 Figure A5.15. Spatial distribution of the computed (lines) and measured (symbols) concentrations of exchanged K+, Ca2+, Na+ and Mg2+ in the HB4 test at 1610 days after the cooling. ......................... 261 Figure A5.16. Spatial distribution of the computed concentration of sorbed species in strong sorption site and weak #1 and #2 sites at the end of the test. .......................................................................... 261 Figure A6.1. Scheme of the six double interface small cells (Cuevas et al., 2016). .......................... 276 Figure A6.2. Double interface cell #3 (Cuevas et al., 2013), one dimensional finite element mesh, and boundary conditions used in the numerical model. ............................................................................. 278 Figure A6.3. Spatial distribution of the computed (lines) and measured (symbols) volumetric water content at the beginning and at the end of the double interface 2I3 test. ........................................... 284 Figure A6.4. Spatial distribution of the computed saturation degree at the beginning and at the end of the double interface 2I3 test. ............................................................................................................... 285 Figure A6.5. Time evolution of the computed (line) and measured (symbols) cumulative water intake in the double interface 2I3 test. ........................................................................................................... 285 Figure A6.6. Spatial distribution of the computed (lines) and measured (symbols) concentrations of dissolved Cl- at selected times in the double interface 2I3 test. .......................................................... 286 Figure A6.7. Spatial distribution of the computed concentrations of dissolved Ca2+, Mg2+, Na+ and K+ in the double interface 2I3 test at selected times. ............................................................................... 287 Figure A6.8. Spatial distribution of the computed concentrations of dissolved SO4

2-, HCO3-, SiO2(aq)

and Al3+ in the double interface 2I3 test at selected times. ................................................................. 288 Figure A6.9. Spatial distribution the computed pH in the double interface 2I3 test at selected times. ............................................................................................................................................................. 289 Figure A6.10. Computed concentrations versus measured data in the water tank at the end of the double interface 2I3 test (t = 18 months). ............................................................................................ 289 Figure A6.11. Spatial distribution of the computed cumulative precipitation/dissolution of calcite in the double interface 2I3 test. Positive values for precipitation and negative values for dissolution. ......... 291 Figure A6.12. Spatial distribution of the computed cumulative precipitation/dissolution of portlandite in the double interface 2I3 test. Positive values for precipitation and negative values for dissolution.... 291 Figure A6.13. Spatial distribution of the computed cumulative precipitation/dissolution of brucite in the double interface 2I3 test. Positive values for precipitation and negative values for dissolution. ......... 292 Figure A6.14. Spatial distribution of the computed cumulative precipitation/dissolution of gypsum in the double interface 2I3 test. Positive values for precipitation and negative values for dissolution.... 292 Figure A6.15. Spatial distribution of the computed cumulative precipitation/dissolution of anhydrite in the double interface 2I3 test. Positive values for precipitation and negative values for dissolution.... 292 Figure A6.16. Spatial distribution of the computed cumulative precipitation/dissolution of ettringite in the double interface 2I3 test. Positive values for precipitation and negative values for dissolution.... 293 Figure A6.17. Spatial distribution of the computed cumulative precipitation/dissolution of C1.6SH in the double interface 2I3 test. Positive values for precipitation and negative values for dissolution.... 293 Figure A6.18. Spatial distribution of the computed cumulative precipitation/dissolution of C1.2SH in the double interface 2I3 test. Positive values for precipitation and negative values for dissolution.... 293 Figure A6.19. Spatial distribution of the computed cumulative precipitation/dissolution of sepiolite in the double interface 2I3 test. Positive values for precipitation and negative values for dissolution.... 294 Figure A6.20. Spatial distribution of the mineral volume fraction and pH in the double interface 2I3 test. Initial mineral volume (top) and at t = 20 months (bottom). ......................................................... 295 Figure A6.21. Spatial distribution of the porosity in the double interface 2I3 test at the end of the test (t = 20 months). ....................................................................................................................................... 296 Figure A6.22. Spatial distribution of the computed (lines) and measured (symbols) concentrations of the exchanged Na+, K+, Ca2+ and Mg2+ in the double interface 2I3 test at selected times. The vertical lines show the error bars of the measured data. ................................................................................. 297 Figure A6.23. Spatial distribution of the computed concentrations of sorbed species in strong, weak #1 and weak #2 sorption sites at the end of the double interface 2I3 test (t = 20 months). ................ 297 Figure A6.24. Spatial distribution of the computed (lines) and the measured (symbols) concentrations of the exchanged Na+, K+, Ca2+ and Mg2+ in the double interface test on 2I3 and 2I4 cells at t = 20 months. The vertical lines show the error bars of the measured data. ............................................... 299 Figure A6.25. Spatial distribution of the computed dissolved concentrations of Na+, K+, Ca2+ and Mg2+ in the double interface tests on 2I 3 and 2I 4 cells at t = 20 months. .................................................. 299

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Figure A6.26. Spatial distribution of the computed cumulative precipitation/dissolution of calcite, gypsum, brucite, sepiolite, C1.6SH and C1.2SH in the double interface test 2I 3 and 2I 4 cells t = 20 months. Positive values for precipitation and negative values for dissolution. ................................... 300 Figure A7.1. General scheme of the FEBEX in situ test in the following periods: a) 1997 to 2002 and b) 2002 to 2015. .................................................................................................................................. 308 Figure A7.2. Schemes of the 1-D axisymmetric models used for the hot and the cold sections (Zheng et al, 2011). .......................................................................................................................................... 309 Figure A7.3. Layout and location of the sections 7,12, 19, 28, 29 and 31 in which water content data and pore water chemical data were collected during the dismantling of the heater 1 of the FEBEX in situ test in 2002 (Samper et al., 2008). ............................................................................................... 309 Figure A7.4. Sensitivity of the computed (lines) concentrations of dissolved Cl-, Ca2+, Mg2+ and SO4

2-, in a hot section in 2002 after cooling and dismantling of the heater 1 to a change in the retention curve of the bentonite. Also shown the inferred concentrations in sections 19 and 29 (symbols). .............. 314 Figure A7.5. Sensitivity of the computed (lines) concentrations of dissolved Cl-, Ca2+, Mg2+ and SO4

2-, in a cold section in 2002 after cooling and dismantling of the heater 1 to a change in the retention curve of the bentonite. Also shown the inferred concentrations in sections 12 (symbols). ................. 314 Figure A7.6. Cumulative dissolution of smectite (left) and precipitation of analcime (right) in the bentonite in 2002 after cooling and dismantling of the heater 1. ........................................................ 315 Figure A7.7. Sensitivity of the computed (lines) concentrations of dissolved Ca2+, K+, Mg2+ and HCO3

-

in a hot section in 2002 after cooling and dismantling of the heater 1 to smectite dissolution. Also shown the inferred concentrations in sections 19 and 29 (symbols). ................................................. 315 Figure A7.8. Sensitivity of the computed (lines) concentrations of dissolved Cl-, Ca2+, Mg2+ and pH in a hot section in 2002 to cooling and changing the gas boundary condition. Also shown the inferred

concentrations in sections 19 and 29 (symbols). ................................................................................ 316 Figure A7.9. Sensitivity of the computed (lines) concentrations of dissolved Cl-, Ca2+, Mg2+ and pH in a hot section in 2002 to changes in the vapor tortuosity. Also shown the inferred concentrations in sections 19 and 29 (symbols). ............................................................................................................. 316 Figure A7.10. Sensitivity of the computed (lines) Cl- concentrations in the granite at a distance of 0.2 m from the bentonite-granite interface to changes in the effective diffusion coefficient in the granite. The measured concentrations were reported by Buil et al (2010). ..................................................... 318 Figure A7.11. Time evolution of the computed Cl- concentrations at several times (lines) with an effective diffusion coefficient of 1·10-12 m2/s in the granite and 1.4·10-10 m2/s in the bentonite and measured concentration of Cl- (symbol) in 2015. ................................................................................ 319 Figure A7.12. Time evolution of the computed SO4

2- concentrations at several times (lines) with an effective diffusion coefficient of 1·10-12 m2/s in the granite and 1.4·10-10 m2/s in the bentonite and measured concentration of SO4

2- (symbol) in 2015. ........................................................................... 319 Figure A7.13. Time evolution of the computed Na+ concentrations at several times (lines) with an effective diffusion coefficient of 1·10-12 m2/s in the granite and 1.4·10-10 m2/s in the bentonite and measured concentration of Na+ (symbol) in 2015. .............................................................................. 319 Figure A7.14. Time evolution of the computed Ca2+ concentrations at several times (lines) with an effective diffusion coefficient of 1·10-12 m2/s in the granite and 1.4·10-10 m2/s in the bentonite and measured concentration of Ca2+ (symbol) in 2015. ............................................................................. 320 Figure A7.15. Finite element mesh for the 2-D axisymmetric THCM model of the FEBEX in situ test and location of the relevant sections. .................................................................................................. 321 Figure A7.16. Contour plots of computed saturation degrees (%) at the dismantling times of heater 1 in 2002 (left) and heater 2 in 2015 (right). ........................................................................................... 323 Figure A7.17. Contour plots of the computed temperatures at the dismantling times of heater 1 in 2002 (left) and heater 2 in 2015 (right). ............................................................................................... 323 Figure A7.18. Time evolution of the calculated (lines) and measured (symbols) temperatures in section B2 at radial distances r = 0.27 m, r = 0.4 m and r = 1.13 m. Section B2 is located at the end of the FEBEX gallery. .............................................................................................................................. 324 Figure A7.19. Time evolution of the calculated (lines) and measured (symbols) temperatures in section D2 located at the edge of heater 2 at radial distances r = 0.48 m, r = 0.81 m and r = 1.14 m. ............................................................................................................................................................. 325 Figure A7.20. Time evolution of the calculated (lines) and measured (symbols) temperatures in hot section E2 located near the center of heater 2 at radial distances r = 0.48 m, r = 0.82 m and r = 1.10 m. ......................................................................................................................................................... 326


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Figure A7.21. Time evolution of the calculated (lines) and measured (symbols) temperatures in hot section F2 located at the mid-point of heater 2 at radial distances r = 0.48 m, r = 0.8 m and r = 1.05 m. ............................................................................................................................................................. 327 Figure A7.22. Time evolution of the calculated (lines) and measured (symbols) temperatures in section I located at the edge of heater 2 (near heater 1) at radial distances r = 0.48 m, r = 0.8 m and r = 1.14 m. .............................................................................................................................................. 328 Figure A7.23. Time evolution of the calculated (lines) and measured (symbols) temperatures in section G located at the edge of the dummy at radial distances r = 0.48 m, r = 0.81 m and r = 1.14 m. ............................................................................................................................................................. 329 Figure A7.24. Time evolution of the calculated (lines) and measured (symbols) temperatures in section H located between both heaters at radial distances r = 0.78 m and r = 1.07 m. .................... 330 Figure A7.25. Time evolution of the computed (line) and the measured (symbols) relative humidity in the hot section E2 at radial distance r = 1.1 m. ................................................................................... 331 Figure A7.26. Time evolution of the computed (lines) and the measured (symbols) relative humidity in the hot section F2 at radial distances r = 0.8 m and r = 1.05 m. ......................................................... 331 Figure A7.27. Time evolution of the computed (lines) and the measured (symbols) relative humidity in section G at several radial distances. This section is located at the edge of the dummy. .................. 333 Figure A7.28. Time evolution of the computed (lines) and the measured (symbols) relative humidity in section H at several radial distances. This section is located at the mid-point of between the two heaters. ................................................................................................................................................ 334 Figure A7.29. Time evolution of the computed (lines) and the measured (symbols) relative humidity in section I at several radial distances. This section is located at the edge of heater 2 (near heater 1). 335 Figure A7.30. Time evolution of the computed (lines) volumetric water content in section M2 and the measured TDR water content data (symbols). This section is located at the mid-point of heater 2. .. 336 Figure A7.31. Time evolution of the computed (lines) pore water pressures in a hot section (F2) and the measured pore water pressures (symbols) in several packed-off sections of boreholes drilled in the granitic rock surrounding the FEBEX gallery....................................................................................... 337 Figure A7.32. Contour plots of the computed Cl- concentrations in 2002 (left), in 2007 (intermediate) and in 2015 (right). .............................................................................................................................. 338 Figure A7.33. Time evolution of the temperatures (lines) calculated with the 1-D and 2-D axisymmetric models and the measured temperatures (symbols) in hot section F2 located at the mid-point of heater 2 at radial distances r = 0.48 m, r = 0.82 m and r = 1.05 m. ....................................... 340 Figure A7.34. Time evolution of the temperatures (lines) calculated with the 1-D and 2-D axisymmetric models and the measured temperatures (symbols) in cold section B2 located at the end of the gallery. ....................................................................................................................................... 340 Figure A7.35. Time evolution of the relative humidities (lines) calculated with the 1-D and 2-D axisymmetric models and the measured relative humidities (symbols) in hot section F2 located at the mid-point of heater 2. ........................................................................................................................... 341 Figure A7.36. Time evolution of the volumetric water content (lines) computed with the 1-D and 2-D axisymmetric models and measured data (symbols) in hot section M2. ............................................. 342 Figure A7.37. Spatial distribution of the concentrations of Cl- computed with the 1-D and 2-D axisymmetric models in a hot section in 2002 and 2015 and measured data in 2002 (symbols) in hot sections M2 and F2. ............................................................................................................................ 343 Figure A7.38. Spatial distribution of the concentrations of Cl- computed with the 1-D and 2-D axisymmetric models in a cold section in 2002 and 2015 and measured data (symbols) in cold section B2. ....................................................................................................................................................... 343 Figure A7.39. Sensitivity of the computed temperature with the 2-D axisymmetric model in a cold section to a 35% increase in the thermal conductivity of the bentonite. The figure shows also the temperatures calculated with the base run of the 2-D model and the measured temperatures in section B2. ....................................................................................................................................................... 344 Figure A7.40. Sensitivity of the computed temperature with the 2-D axisymmetric model in a hot section to a 35% increase in the thermal conductivity of the bentonite. The figure shows also the temperatures calculated with the base run of the 2-D model and the measured temperatures in section F2. ........................................................................................................................................................ 345 Figure A7.41. Sensitivity of the computed temperature with the 2-D axisymmetric model in a cold section to a 20% increase in the thermal conductivity of the granite. The figure shows also the temperatures calculated with the base run of the 2-D model and the measured temperatures in section B2. ....................................................................................................................................................... 346

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Figure A7.42. Sensitivity of the computed temperature with the 2-D axisymmetric model in a hot section to a 20% increase in the thermal conductivity of the granite. The figure shows also the temperatures calculated with the base run of the 2-D model and the measured temperatures in section F2. ........................................................................................................................................................ 346 Figure A7.43. Sensitivity of the relative humidities computed with the 2-D axisymmetric model in a hot section to a 26% increase in the permeability of the bentonite. The figure shows also the relative humidities calculated with the base run of the 2-D model and the measured relative humidities in section F2. ........................................................................................................................................... 347 Figure A7.44. Computed (lines) Cl-, Ca2+, K+, Mg2+, Na+, SO4

2-, HCO3- and pH with the previous (base

run) and the updated (updated run) models in a hot section in 2002 and inferred data (symbols) in sections 19 and 29 (symbols). ............................................................................................................. 350 Figure A7.45. Cumulative calcite (left) and gypsum (right) precipitation/dissolution computed with the previous (base run) and the updated (updated run) models in a hot section in 2002 (negative for dissolution and positive for precipitation). ........................................................................................... 351 Figure A7.46. Comparison of the gravimetric water content computed (lines) in a hot section in 2002 with the previous model (base run) and the updated model (updated run) and measured gravimetric water content data (symbols) in sections S22, S27, S45, S49 and S52 at the times of dismantling of heater 1 (year 2002). The plot at the bottom shows the location of the sections where water contents were measured .................................................................................................................................... 351 Figure A7.47. Sensitivity of the concentrations of Cl-, Ca2+, K+, Mg2+, Na+, SO4

2-, HCO3- and pH

computed (lines) with the updated model in a hot section in 2002 to changes in the diffusion coefficient of the bentonite. Also shown the inferred data in sections 19 and 29 (symbols). ............................... 353 Figure A7.48. Sensitivity of the concentrations of Cl-, Ca2+, K+, Mg2+, Na+, SO4

2-, HCO3- and pH

computed (lines) with the updated model in a cold section in 2002 to changes in the diffusion coefficient of the bentonite. Also shown the inferred data in section 12 (symbols).in a cold section in 2002. .................................................................................................................................................... 354 Figure A7.49. Time evolution of the computed (line) and measured temperature data (symbols) in hot sections E2 and F2 at a radial distance r = 0.48 m. ............................................................................ 357 Figure A7.50. Time evolution of the computed (line) and measured temperature data (symbols) in hot sections E2 and F2 at a radial distance r = 0.80 m. ............................................................................ 357 Figure A7.51. Time evolution of the computed (line) and measured temperature data (symbols) in hot sections E2 and F2 at a radial distance r = 1.10 m. ............................................................................ 357 Figure A7.52. Time evolution of the computed (line) and measured temperature data (symbols) in cold section C at a radial distance r = 0.6 m. ...................................................................................... 358 Figure A7.53. Time evolution of the computed (line) and measured temperature data (symbols) in cold section C at a radial distance r = 1.1 m. ...................................................................................... 358 Figure A7.54. Time evolution of the computed (line) and measured temperature data (symbols) in cold section B2 located at the end of the FEBEX gallery at a radial distance r = 0.6 m and r = 1.1 m. ............................................................................................................................................................. 358 Figure A7.55. Time evolution of the computed (line) and the measured relative humidity data (symbols) in hot section F2 at a radial distance r = 0.8 m. .................................................................. 360 Figure A7.56. Time evolution of the computed (line) and the measured relative humidity data (symbols) in hot sections E2 and F2 at a radial distance r = 1.05 m. ................................................. 360 Figure A7.57. Time evolution of the computed (line) and the measured relative humidity data (symbols) at the center (r = 0) of cold section C located between heater 1 and the original concrete plug. ..................................................................................................................................................... 360 Figure A7.58. Time evolution of the computed (line) and the measured relative humidity data (symbols) in cold section C located between heater 1 and the original concrete plug at a radial distance r = 0.6 m. ............................................................................................................................... 361 Figure A7.59. Time evolution of the computed (line) and the measured relative humidity data (symbols) in cold section C located between heater 1 and the original concrete plug at a radial distance r = 1.1 m. ............................................................................................................................... 361 Figure A7.60. Time evolution of the computed (line) and the measured TDR water content data (symbols) in hot section M2 at a radial distance r = 0.59 m. ............................................................... 361 Figure A7.61. Time evolution of the computed (line) and the measured TDR water content data (symbols) in hot section M2 at a radial distance r = 0.74 m. ............................................................... 362 Figure A7.62. Time evolution of the computed (line) and the measured TDR water content data (symbols) in hot section M2 at a radial distance r = 0.85 m. ............................................................... 362


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Figure A7.63. Time evolution of the computed (line) and the measured TDR water content data (symbols) in hot section M2 at a radial distance r = 1.04 m. ............................................................... 362 Figure A7.64. Time evolution of the computed (line) and the measured pore water pressure (symbols) in the granite rock at a radial distance of 3.03 m. ............................................................................... 363 Figure A7.65. Time evolution of the computed (line) and the measured pore water pressure (symbols) in the granite rock at a radial distance of 8.18 m. ............................................................................... 363 Figure A7.66. Time evolution of the computed (line) and the measured pore water pressure (symbols) in the granite rock at a radial distance of 16.58 m. ............................................................................. 364 Figure A7.67. Comparison of the predicted gravimetric water content (lines) in a hot section and the measured gravimetric water content data (symbols) in sections S22, S27, S45, S49 and S52 at the times of dismantling of heater 1 (year 2002) and heater 2 (year 2015). The plot at the bottom shows the location of the sections where water contents were measured..................................................... 365 Figure A7.68. Comparison of the predicted dry density (lines) in a hot section and the measured dry density data (symbols) in sections S22, S27, S45, S49 and S52 at the times of dismantling of heater 1 (year 2002) and heater 2 (year 2015). The plot at the bottom shows the location of the sections where dry densities were measured. ............................................................................................................. 365 Figure A7.69. Comparison of the predicted gravimetric water content (lines) in a cold section and the measured gravimetric water content data (symbols) in sections S9, S15 and S58 at the times of dismantling of heater 1 (year 2002) and heater 2 (year 2015). The plot at the bottom shows the location of the sections where water contents were measured........................................................... 366 Figure A7.70. Comparison of the predicted dry density (lines) in a cold section and the measured dry density data (symbols) in sections S9, S15 and S58 at the times of dismantling of heater 1 (year 2002) and heater 2 (year 2015). The plot at the bottom shows the location of the sections where dry densities were measured. .................................................................................................................... 366 Figure A8.1. Pre-dismantling predictions of Cl- concentrations (lines) in 2002 and 2015 in a hot section. The graph shows also the inferred Cl- concentrations in sections 19 and 29 (symbols) in 2002. ............................................................................................................................................................. 377 Figure A8.2. Pre-dismantling predictions of Ca2+ concentrations (lines) in 2002 and 2015 in a hot section. The graph shows also the inferred Ca2+ concentrations in sections 19 and 29 (symbols) in 2002. .................................................................................................................................................... 377 Figure A8.3. Pre-dismantling predictions of Mg2+ concentrations (lines) in 2002 and 2015 in a hot section. The graph shows also the inferred Mg2+ concentrations in sections 19 and 29 (symbols) in 2002. .................................................................................................................................................... 377 Figure A8.4. Pre-dismantling predictions of Na+ concentrations (lines) in 2002 and 2015 in a hot section. The graph shows also the inferred Na+ concentrations in sections 19 and 29 (symbols) in 2002. .................................................................................................................................................... 378 Figure A8.5. Pre-dismantling predictions of K+ concentrations (lines) in 2002 and 2015 in a hot section. The graph shows also the inferred K+ concentrations in sections 19 and 29 (symbols) in 2002. ............................................................................................................................................................. 378 Figure A8.6. Pre-dismantling predictions of SO4

2- concentrations (lines) in 2002 and 2015 in a hot section. The graph shows also the inferred SO4

2- concentrations in sections 19 and 29 (symbols) in 2002. .................................................................................................................................................... 378 Figure A8.7. Pre-dismantling predictions of HCO3

- concentrations (lines) in 2002 and 2015 in a hot section. The graph shows also the inferred HCO3

- concentrations in sections 19 and 29 (symbols) in 2002. .................................................................................................................................................... 379 Figure A8.8. Pre-dismantling predictions of pH (lines) in 2002 and 2015 in a hot section. The graph shows also the inferred pH in sections 19 and 29 (symbols) in 2002. ................................................ 379 Figure A8.9. Pre-dismantling predictions of cumulative calcite dissolution (negative)/precipitation (positive) (lines) in 2002 and 2015 in a hot section. ............................................................................ 379 Figure A8.10. Pre-dismantling predictions of cumulative gypsum (negative)/precipitation (positive) (lines) in 2002 and 2015 in a hot section. ............................................................................................ 380 Figure A8.11. Pre-dismantling predictions of cumulative anhydrite (negative)/precipitation (positive) (lines) in 2002 and 2015 in a hot section. ............................................................................................ 380 Figure A8.12. Pre-dismantling predictions of Cl- concentrations (lines) in 2002 and 2015 in a cold section. The graph shows also the inferred Cl- concentrations in section 12 (symbols) in 2002. ....... 382 Figure A8.13. Pre-dismantling predictions of Ca2+ concentrations (lines) in 2002 and 2015 in a cold section. The graph shows also the inferred Ca2+ concentrations in section 12 (symbols) in 2002. .... 382 Figure A8.14. Pre-dismantling predictions of K+ concentrations (lines) in 2002 and 2015 in a cold section. The graph shows also the inferred K+ concentrations in section 12 (symbols) in 2002. ....... 383

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Figure A8.15. Pre-dismantling predictions of Mg2+ concentrations (lines) in 2002 and 2015 in a cold section. The graph shows also the inferred Mg2+ concentrations in section 12 (symbols) in 2002. ... 383 Figure A8.16. Pre-dismantling predictions of Na+ concentrations (lines) in 2002 and 2015 in a cold section. The graph shows also the inferred Na+ concentrations in section 12 (symbols) in 2002. ..... 383 Figure A8.17. Pre-dismantling predictions of SO4

2- concentrations (lines) in 2002 and 2015 in a cold section. The graph shows also the inferred SO4

2- concentrations in section 12 (symbols) in 2002. .. 384 Figure A8.18. Pre-dismantling predictions of HCO3

- concentrations (lines) in 2002 and 2015 in a cold section. The graph shows also the inferred HCO3

- concentrations in section 12 (symbols) in 2002. . 384 Figure A8.19. Pre-dismantling predictions of pH (lines) in 2002 and 2015 in a cold section. The graph shows also the inferred pH in section 12 (symbols) in 2002. .............................................................. 384 Figure A8.20. Pre-dismantling predictions of cumulative calcite dissolution (negative)/precipitation (positive) (lines) in 2002 and 2015 in a cold section. .......................................................................... 385 Figure A8.21. Pre-dismantling predictions of cumulative gypsum dissolution (negative)/precipitation (positive) (lines) in 2002 and 2015 in a cold section. .......................................................................... 385 Figure A8.22. Sensitivity of the computed concentrations of dissolved Cl-, Ca2+, K+, Mg2+, Na+, SO4

2-, HCO3

- and pH in a hot section in 2015 to an increase of the diffusion coefficients. The diffusion coefficients of the sensitivity are 10 times larger than those of the reference prediction run. ............ 387 Figure A8.23. Sensitivity of the computed concentrations of dissolved Cl-, Ca2+, K+, Mg2+, Na+, SO4

2-, HCO3

- and pH in a cold section in 2015 to an increase of the diffusion coefficients. The diffusion coefficients of the sensitivity are 10 times larger than those of the reference prediction run. ............ 388 Figure A8.24. Radial distribution of the computed log-concentrations of F- in a hot section at selected times. ................................................................................................................................................... 389 Figure A8.25. Radial distribution of the computed concentrations of F- in a hot section at selected times (left). The plot at the right shows a zoom of the concentrations near the bentonite-granite interface. .............................................................................................................................................. 390 Figure A9.1. Traced sections in the FEBEX in situ test and sections containing point tracers (García-Gutiérrez, 1997). .................................................................................................................................. 396 Figure A9.2. Layout of the final dismantling sampling. The figure includes the number of the section of measurements of: tracers, THM and THG, water content and dry density, sensors, microbial and corrosion (see AITEMIN, 2015 for more details). ................................................................................ 398 Figure A9.3. Sampling section 37. This section contains iodide which was added in filter paper. The Sampling Plan considers radial profiles of iodide concentrations along the colored bentonite blocks 37-1 to 37-3 (see AITEMIN, 2015 for more details). ................................................................................ 398 Figure A9.4. Bentonite (colored blocks) selected for sampling the point tracers in section 46, which contains borate, europium, selenate and perrhenate (see AITEMIN, 2015 for more details). ............ 399 Figure A9.5. Bentonite blocks (colored blocks) selected for sampling the point tracers (borate and cesium) located in section 48 (see AITEMIN, 2015 for more details). ................................................ 399 Figure A9.6. Sampling section 50. This section contains iodide which was added in filter paper. The Sampling Plan considers radial profiles of iodide concentrations along 3 bentonite blocks (see AITEMIN, 2015 for more details). ........................................................................................................ 400 Figure A9.7. Sampling section 51. This section contains iodide which was added in filter paper. The Sampling Plan considers radial profiles of iodide concentrations along 3 bentonite blocks (modified from AITEMIN, 2015). This section contains also borate, europium, selenate and perrhenate in the colored bentonite blocks (see AITEMIN, 2015 for more details). ........................................................ 400 Figure A9.8. Inverse modelling results of inverse model 1 (a) and inverse model 2 (b) (from Zheng, 2006). ................................................................................................................................................... 402 Figure A9.9. Radial distribution of the calculated iodide concentrations at selected times and pre-dismantling prediction of iodide concentrations in 2015 (t = 18.5 years) for sections 50 and 51. Also shown the measured iodide data in 2002. ........................................................................................... 402 Figure A9.10. Radial distribution of the calculated iodide concentrations at selected times and pre-dismantling prediction of iodide concentrations in 2015 (t = 18.5 years) for section 37. Also shown the measured iodide data in 2002. ............................................................................................................ 403 Figure A9.11. Sensitivity of the computed iodide concentrations in section 37 after 5.5 years (2002) to changes in the accessible porosity of the bentonite. ........................................................................... 404 Figure A9.12. Sensitivity of the computed iodide concentrations in section 37 after 5.5 years (2002) to changes in the initial iodide concentration in the bentonite. ................................................................ 405 Figure A9.13. Sensitivity of the computed iodide concentrations in section 37 after 5.5 years (2002) to changes in the distribution coefficient of the bentonite. ...................................................................... 405


xxxi

Figure A9.14. Sensitivity of the computed iodide concentrations in section 37 after 5.5 years (2002) to changes in the diffusion coefficient of the bentonite. .......................................................................... 406 Figure A9.15. Scheme of the location of the 2-D numerical model in a vertical plane perpendicular to the axis of the gallery used for tracer migration. ................................................................................. 407 Figure A9.16. Finite element grid of the 2-D numerical model in a vertical plane perpendicular to the axis of the gallery used for tracer migration. Blue circles indicate the approximate location of the tracers when they were emplaced. ...................................................................................................... 407 Figure A9.17. Computed temperatures at t = 0, 5, 10 and 18 years with the 2-D numerical model in a vertical plane normal to the axis of the gallery. ................................................................................... 409 Figure A9.18. Computed water saturation at t = 0, 5, 10 and 18 years with the 2-D numerical model in a vertical plane normal to the axis of the gallery. ................................................................................ 410 Figure A9.19. Computed concentrations of dissolved borate (mol/L) at: 5 years (top left); 10 years (top right); 15 years (bottom left) and 18 years (bottom right) with the 2-D numerical model in a vertical plane normal to the axis of the gallery. ................................................................................................ 412 Figure A9.20. Computed concentrations of dissolved selenate (mol/L) at: 5 years (top left); 10 years (top right); 15 years (bottom left) and 18 years (bottom right) with the 2-D numerical model in a vertical plane normal to the axis of the gallery. ................................................................................................ 412 Figure A9.21. Computed concentrations of dissolved europium (mol/L) at: 5 years (top left); 10 years (top right); 15 years (bottom left) and 18 years (bottom right) with the 2-D numerical model in a vertical plane normal to the axis of the gallery. ................................................................................................ 413 Figure A9.22. Computed concentrations of dissolved cesium (mol/L) at: 5 years (top left); 10 years (top right); 15 years (bottom left) and 18 years (bottom right) with the 2-D numerical model in a vertical plane normal to the axis of the gallery. This tracer was emplaced in an outer block near the bentonite-granite interface. .................................................................................................................................. 413 Figure A9.23. Computed concentrations of dissolved borate (mol/L) at: 5 years (top left); 10 years (top right); 15 years (bottom left) and 18 years (bottom right) with the 2-D numerical model in a vertical plane normal to the axis of the gallery. This tracer was emplaced in an outer block near the bentonite-granite interface. .................................................................................................................................. 414 Figure A10.1. Layout and location of the new concrete plug (first and second stages, red square), the dummy canister and the monitoring sections after the dismantling of the heater 1 of the FEBEX in situ test. ...................................................................................................................................................... 421 Figure A10.2. Finite element mesh of the 2-D axisymmetric model of the entire test (left) and finite element grid for the detailed 2-D axisymmetric model selected for modelling the interactions of bentonite and concrete. ....................................................................................................................... 421 Figure A10.3. Detailed 2-D axisymmetric model selected for modelling the interactions of bentonite and concrete and location of the 1-D profiles normal to the bentonite-concrete interface at radial distances r = 0.55 m, 0.75 m and 1 m. ................................................................................................ 422 Figure A10.4. Finite element mesh of the 1-D numerical model used to simulate the geochemical interactions at the bentonite-concrete interface. ................................................................................. 422 Figure A10.5. Temperature computed with the detailed 2-D axisymmetric THM model of the bentonite-concrete interface along a horizontal line normal to the interface at a radial distance of r = 0.75 m. ........................................................................................................................................... 423 Figure A10.6. Measured temperatures along two boreholes drilled through the concrete plug before switching off the heater 2. (NAGRA, 2015) The lower x-axis shows the distance measured from the concrete-bentonite interface. ............................................................................................................... 424 Figure A10.7. Computed saturation degree in 2015 (top plot) and a zoom of the bentonite-concrete interface (below). ................................................................................................................................. 424 Figure A10.8. Saturation degree computed with the detailed 2-D axisymmetric THM model of the bentonite-concrete interface along horizontal lines normal to the interface at radial distances of r = 0.55 m, 0.75 m and 1 m. ...................................................................................................................... 425 Figure A10.9. Time evolution of the liquid pressure and bentonite saturation prescribed at all the nodal points within the bentonite in the 1-D model of the geochemical interactions. ......................... 427 Figure A10.10. Computed temperature at selected times. ................................................................. 427 Figure A10.11. Computed water content at selected times. .............................................................. 428 Figure A10.12. Computed saturation degree at selected times. ........................................................ 428 Figure A10.13. Predicted concentrations of dissolved Cl- along the bentonite-concrete interface at selected times (lines) and inferred aqueous extract data in the concrete (symbols). ......................... 429

Contents

xxxii

Figure A10.14. Predicted concentrations of dissolved Ca2+, Mg2+, Na+, K+, SO42-, HCO3

-, SiO2(aq) and Al3+ along the bentonite-concrete interface at selected times (lines) and approximate inferred aqueous extract data in the concrete (symbols). ............................................................................................... 431 Figure A10.15. Predicted pH along the bentonite-concrete interface (lines) and approximate inferred aqueous extract data in the concrete (symbols) at selected times. .................................................... 432 Figure A10.16. Zoom of the predicted pH in the bentonite and concrete the interface at selected times. ................................................................................................................................................... 432 Figure A10.17. Predicted concentrations of exchanged Na+ (top left), Ca2+ (top right), K+ (bottom left) and Mg2+ (bottom right) along the bentonite-concrete interface at selected times (values in meq/100g). ............................................................................................................................................................. 433 Figure A10.18. Zoom of the predicted concentrations of exchanged Na+, Ca2+, K+ and Mg2+ in the bentonite near the concrete interface in 2015 (values in meq/100g). ................................................. 433 Figure A10.19. Predicted volume fraction of quartz along the bentonite-concrete interface at selected times. ................................................................................................................................................... 435 Figure A10.20. Predicted volume fraction of cristobalite along the bentonite-concrete interface at selected times. ..................................................................................................................................... 435 Figure A10.21. Predicted volume fraction of calcite in the bentonite and concrete the interface at selected times. ..................................................................................................................................... 435 Figure A10.22. Zoom of the predicted volume fraction of calcite in the bentonite and concrete interface at selected times. .................................................................................................................. 436 Figure A10.23. Predicted volume fraction of portlandite along the bentonite-concrete interface at selected times. ..................................................................................................................................... 436 Figure A10.24. Zoom of the predicted volume fraction of portlandite in the bentonite and concrete interface at selected times. .................................................................................................................. 436 Figure A10.25. Predicted volume fraction of ettringite along the bentonite-concrete interface at selected times. ..................................................................................................................................... 437 Figure A10.26. Predicted volume fraction of CSH1.8 along the bentonite-concrete interface at selected times. ..................................................................................................................................... 437 Figure A10.27. Zoom of the predicted CSH1.8 volume fraction in the bentonite and concrete interface at selected times. ................................................................................................................................. 437 Figure A10.28. Predicted volume fraction of CSH0.8 along the bentonite-concrete interface at selected times. ..................................................................................................................................... 438 Figure A10.29. Predicted volume fraction of brucite along the bentonite-concrete interface at selected times. ................................................................................................................................................... 438 Figure A10.30. Zoom of the predicted volume fraction of brucite in the bentonite and concrete interface at selected times. .................................................................................................................. 438 Figure A10.31. Predicted volume fraction of sepiolite along the bentonite-concrete interface at selected times. ..................................................................................................................................... 439 Figure A10.32. Predicted changes in porosity caused by dissolution/precipitation reactions. ........... 439


xxxiii

List of Tables

Table A1.1. Initial concentration of the pore water for the Case 3. .................................................... 107 Table A2.1. Summary of the main features of the heating and hydration tests, including duration, bentonite thickness, total cumulative water intake, initial volumetric water content, average temperature and available data for CT cells (Fernández et al., 1999), CG cells (Villar et al., 2008a, 2008b; Fernández and Villar, 2010), mock-up test (ENRESA, 2006a) and in situ test (ENRESA, 2006a). ................................................................................................................................................. 125 Table A2.2. Boundary and heater temperatures, initial and saturated gravimeric water contents and intial and boundary pore water Cl- concentration of the CT and CG cells, and the mock-up and the in situ tests............................................................................................................................................... 132 Table A3.1. Main features of the 60 cm heating and hydration tests. ................................................ 147 Table A3.2. Water flow parameters used for the numerical model of the CG cells (ENRESA, 2006a; Zheng et al., 2010). ............................................................................................................................. 152 Table A3.3. Thermal parameters used for the numerical model of the CG cells (ENRESA, 2006a; Zheng et al., 2010). ............................................................................................................................. 152 Table A3.4. Solute transport parameters used for the numerical model of the CG cells (ENRESA, 2006a; Zheng et al., 2010). ................................................................................................................. 152 Table A3.5. Mechanical parameters used for the numerical model of the CG cells (ENRESA, 2006a; Zheng et al., 2010). ............................................................................................................................. 152 Table A3.6. Chemical composition of the initial bentonite porewater and the granitic hydration water. ............................................................................................................................................................. 153 Table A3.7. Initial concentrations of exchanged cations (in meq/100g) for FEBEX bentonite (Fernández et al., 2004). ..................................................................................................................... 153 Table A3.8. Site capacities for strong (s), weak # 1 (w1) and weak # 2 (w2) sites (mol/L) for FEBEX bentonite (Bradbury and Baeyens, 1997). ........................................................................................... 153 Table A3.9. Initial mineral volume fractions (%) of CG tests (ENRESA, 2006a). ............................... 154 Table A3.10. Chemical reactions and equilibrium constants for aqueous complexes and minerals (Wolery, 1992), protolysis constants for surface complexation reactions (Bradbury and Baeyens, 1997) and selectivity coefficients for cation exchange reactions of the original and revised model (ENRESA, 2006b) at 25ºC..................................................................................................................................... 154 Table A4.1. Main features of the corrosion tests on small cells (Torres et al., 2008). ....................... 192 Table A4.2. Water flow parameters (ENRESA, 2006a; Zheng et al., 2010). ...................................... 194 Table A4.3. Thermal parameters (ENRESA, 2006a; Zheng et al., 2010). ......................................... 194 Table A4.4. Solute transport parameters (ENRESA, 2006a; Zheng et al., 2010). ............................. 195 Table A4.5. Mechanical parameters (ENRESA, 2006a; Zheng et al., 2010). .................................... 195 Table A4.6. Chemical composition of the initial porewater in bentonite and the hydration boundary. 196 Table A4.7. Site capacities (mol/L) of strong sites and weak #1 and weak #2 for FEBEX bentonite (Bradbury and Bayens, 1997, 2003). .................................................................................................. 197 Table A4.8. Initial concentration of exchanged cations (in meq/100g) for FEBEX bentonite (Fernández et al., 2004). ......................................................................................................................................... 197 Table A4.9. Initial mineral volume fractions (%) considered in the THCM model of the corrosion test. ............................................................................................................................................................. 197 Table A4.10. Kinetic parameters of Fe(s) and magnetite used in the THCM model of the corrosion test (De Wint and Torres, 2009). ................................................................................................................ 197 Table A4.11. Chemical reactions and equilibrium constants for aqueous complexes and minerals (Wolery, 1992), protolysis constants for surface complexation reactions (Bradbury and Baeyens, 1997) and selectivity coefficients for cation exchange reactions (ENRESA, 2006b at 25ºC. ....................... 197 Table A4.12. Calibrated values of the kinetic parameters for magnetite precipitation in the models of the corrosion test on small cells at 25º, 50º and 100ºC. ..................................................................... 214 Table A5.1. Experimental observations of mineral precipitation at the end of the HB4 test. ............. 243 Table A5.2. Chemical reactions and equilibrium constants for aqueous complexes and minerals (Wolery, 1992), protolysis constants for surface complexation reactions (Bradbury and Baeyens, 1997)

Contents

xxxiv

and selectivity coefficients for cation exchange reactions (ENRESA, 2006c) at 25ºC of the THCM model of the HB4 column test. ............................................................................................................ 246 Table A5.3. Kinetic parameters for the mineral phases of the HB4 cell (Fernández et al., 2009; Palandri and Kharaka, 2004). .............................................................................................................. 247 Table A5.4. Water flow parameters for the THCM model of the HB4 column test (ENRESA, 2006a; Zheng et al., 2010, Villar et al., 2012; Villar, 2013). ............................................................................ 248 Table A5.5. Mechanical parameters for the THCM model of the HB4 column test (ENRESA, 2006a; Zheng et al., 2010). ............................................................................................................................. 248 Table A5.6. Thermal parameters for the THCM model of the HB4 column test (ENRESA, 2006a; Zheng et al., 2010). ............................................................................................................................. 248 Table A5.7. Solute transport parameters for the THCM model of the HB4 column test (ENRESA, 2006a; Zheng et al., 2010). ................................................................................................................. 249 Table A5.8. Chemical composition of the initial porewater in bentonite, concrete and the hydration boundary water. ................................................................................................................................... 250 Table A5.9. Experimental observations and THMC model results at the end of the HB4 test. .......... 260 Table A6.1. Experimental observations for the 2I3 test. ..................................................................... 277 Table A6.2. Water flow parameters for the THCM model of the mortar-bentonite interactions on the double interface cells (ENRESA, 2006a; Zheng et al., 2010, Villar et al., 2012; Villar, 2013). ........... 278 Table A6.3. Thermal parameters for the THCM model of the mortar-bentonite interactions on the double interface cells (ENRESA, 2006a; Zheng et al., 2010). ............................................................ 279 Table A6.4. Solute transport parameters for the THCM model of the mortar-bentonite interactions on the double interface cells (ENRESA, 2006a; Zheng et al., 2010). ...................................................... 279 Table A6.5. Mechanical parameters for the THCM model of the mortar-bentonite interactions on the double interface cells (ENRESA, 2006a; Zheng et al., 2010). ............................................................ 279 Table A6.6. Chemical composition of the initial porewater in the bentonite, the mortar, and the initial and final hydration water composition. ................................................................................................ 281 Table A6.7. Initial mineral volume fractions (%)for the THCM model of the mortar-bentonite interactions on the double interface cells. ........................................................................................... 281 Table A6.8. Mineral kinetic parameters for the THCM model of the mortar-bentonite interactions on the double interface cells (Fernández et al., 2009). ............................................................................ 282 Table A6.9. Initial concentration of exchanged cations (in meq/100g) of the double interface 2I tests (Cuevas et al., 2016). .......................................................................................................................... 282 Table A6.10. Chemical reactions and equilibrium constants for aqueous complexes and minerals (Wollery, 1992), protolysis constants for surface complexation reactions (Bradbury and Baeyens, 1997) and selectivity coefficients for cation exchange reactions of the natural FEBEX bentonite and pre-treated bentonite (ENRESA, 2006b) at 25ºC. ............................................................................... 282 Table A6.11. Experimental observations of mineral phases and THCM model results for the 2I3 test at t = 20 months. ...................................................................................................................................... 296 Table A7.1. Dissolution/precipitation reactions of smectite and analcime and equilibrium constants at 25ºC. .................................................................................................................................................... 312 Table A7.2. Diffusion coefficients in pure water for the base run (taken from Zheng et al., 2011) and the sensitivity run. ................................................................................................................................ 352 Table A8.1. Diffusion coefficients in pure water for the base run (taken from Zheng et al., 2011) and the sensitivity run. ................................................................................................................................ 386 Table A9.1. Tracers used in the FEBEX in situ experiment. .............................................................. 395 Table A9.2. Total masses of tracer compounds used in the FEBEX in situ experiment. More details can be found in García-Gutiérrez (1997). ............................................................................................ 395 Table A9.3. Parameter values used for the sensitivity runs of iodide migration in section 37 of the FEBEX in situ test. ............................................................................................................................... 403 Table A9.4. Main transport and sorption parameters of the tracers used in the FEBEX in situ test. Data for cesium and selenite were taken from Samper et al. (2006). Data for europium were derived from García-Gutiérrez et al. (2011) and Zhou et al (2013). Data for other tracers such as borate and perrhenate were taken from Samper et al. (1998). CP = Clay Plug; SSS = Sintered Stainless Steel408 Table A10.1. Initial chemical composition of the bentonite and concrete pore water taken from Zheng et al (2011) and Samper et al. (2013). ................................................................................................ 426 Table A10.2. List of primary species, aqueous complexes, minerals, exchanged cations and surface complexation sorption sites of the 1-D geochemical reactive transport model. .................................. 426 Table A10.3. Initial mineral volume fraction (%) in the bentonite and concrete. ................................ 426


xxxv

Table A10.4. Measured aqueous extract data and inferred concentrations in the concrete (NAGRA, 2015). Inferred concentrations have been derived by neglecting the role of chemical reactions ....... 429


xxxvii

List of terms and abbreviations

Greek Terms

α bentonite compressibility

thermal Cauchy coefficient (W/ºC)

∅ porosity

volumetric gas content (m3/m3)

volumetric water content (m3/m3)

dry density (kg/m3)

gas density (kg/m3)

water density (kg/m3)

solid density (kg/m3)

mean effective stress (Pa)

suction (kPa)

solute tortuosity in water phase

solute tortuosity in gas phase

vapor tortuosity

liquid viscosity (kg/m·s)

gas viscosity (kg/m·s)

Ω ratio between the ion activity product and the equilibrium constant

, η parameters of the kinetic law

activity coefficient of the i-th dissolved primary species

stoichiometric coefficient of the fith gas on the iith dissolved species

bulk thermal conductivity (W/mºC)

, , , thermal conductivities of water, vapor, air and solid particles

π osmotic pressure (Pa)

ε strain

Latin Terms

A, B, C, D empirical constants for the state-surface for the FEBEX compacted

bentonite

b1, b2, b3, b4, b5 coefficients derived by fitting the equation of logK values at 0, 25, 60, 100

and 300ºC

concentration of dissolved chemical species

concentration of aqueous extract


xxxviii

solute concentrations of the boundary water

dimensionless concentration of dissolved chemical species

concentration of conservative species in the clay pore water

concentration of the f-th gas species (mol/L) in the sink term

total dissolved concentration of the j-th species (mol/L) in the sink term

total concentration of the f-th gas species (mol/kg) in the gaseous phase

total concentration of the f-th gas species (mol/L) in the gaseous phase

total dissolved concentration of the j-th species (mol/L)

coefficient of the thermal expansion of the solid particles (1/ºC)

d molecular diameter of the f-th gas species (m)

Df dispersion coefficient in gaseous phase (m2/s)

diffusion coefficient of the f-th gas species (m2/s) in a pure and ideal

gaseous phase

Dj dispersion coefficient in the liquid phase (m2/s)

molecular diffusion in water (m2/s)

Dv dispersion coefficient for the vapor (m2/s)

effective molecular diffusion for the vapor (m2/s)

e void ratio

Ea apparent activation energy of the reaction (kJ/mol)

, , advection, molecular and dispersion mass flux vector (kg/m2/s)

F dilution factor

activity coefficient of the f-th gas species

average specific enthalpy of the soil (J/kg)

, , , specific enthalpies of free water, vapor, air and solid particles

dispersive mass flux of the vapor

KNa-cation selectivity coefficient for cation exchange with respect to Na+

thermodynamic equilibrium constant

intrinsic permeability of the liquid (m2)

relative permeability of the liquid

intrinsic permeability of the gas (m2)

relative permeability of the gas

kinetic rate constant at 25ºC (mol/m2/s)

thermo-osmotic permeability (m2/K/s)

L length of the experiment

M molecular weight of the f-th gaseous species (g/mol)

mass of gas per unit volume of medium (kg/m3)

mass of liquid water per unit volume of medium (kg/m3)

Ms mass of powdered clay sample in the aqueous extract method


xxxix

Mw molecular weight (g/mol)

Avogadro’s number

NC number of primary species

Ng number of gaseous species

P gas phase pressure (kPa)

atmospheric pressure (Pa)

partial pressure of the f-th gas species

total precipitated/dissolved mineral (mol/L)

liquid pressure (kPa)

gas pressure (kPa)

volumetric gas flux

volumetric liquid flux

heat flux

radial distance for radial-flow

R gas constant

corrosion rate (μm/year)

rc condensation rate (kg/m2/s)

dimensionless radial distance for radial-flow

external radio

re evaporation rate (kg/m2/s)

sink term in the gas transport equation (kg/m3/s)

Rf chemical reaction source/sink the gas transport equation (mol/m3/s)

relative humidity

internal radio

ri sink term in the transport equation (kg/m2/s)

rm dissolution/precipitation rate (mol/m2/s)

gas saturation degree

liquid saturation degree

time

T temperature (ºC)

T* external temperature (ºC)

boundary temperature

dimensionless time

dimensionless temperature

heater temperature

Tref reference temperature (ºC)

cumulative water intake

dimensionless cumulative volume intake


xl

bentonite pore volume

velocity of the particles (m/s)

gravimetric water content

gravimetric water content of the aqueous extract

dimensionless water content

gravimetric water content of the clay sample

total cation exchanged concentration (mol/L)

distance from the hydration boundary for parallel flow

dimensionless distance from the hydration boundary for parallel flow

mass fraction of water in the liquid phase

mass fraction of air in the gas phase

mass fraction of vapor in the gas phase

total sorbed concentration (mol/L)

advance of the saturation front in the Green-Ampt equation

Abbreviations

AET Aqueous extract test

AGP Almacenamiento geológico profundo

AXP Almacenamento xeolóxico profundo

CEBAMA Cement-based materials, properties, evolution, barrier functions Project

CEC Cation exchanged capacity

CG Hydrating and heating 60 cm-long bentonite test (“Celdas Grandes”)

CIEMAT Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas

CSH Calcium silicate hydrate mineral phase

CT Thermohydraulic cell of compacted bentonite test (“Celdas

Termohidrualicas”)

DGR Deep geological repository

EBS Engineered barrier system

ENRESA Empresa Nacional de Residuos Radiactivos S.A.

FB Medium-size corrosion experiment

FEBEX Full-scale Engineered Barrier Experiment

FEBEX-DP Full-scale Engineered Barrier Experiment Dismantling Project

GMFV Geochemical model reported by Fernández and Villar (2010)

HB Concrete and bentonite interactions experiments (“Hormigón bentonita”)

HLW High-level radioactive waste

NFPRO Near Field Processes Project

OPC Ordinary Portland Cement

PEBS Long-term Performance of Engineered Barrier Systems Project


xli

TDR Time Domain Reflectometry

THCM Thermo-hydro-chemical-mechanical

THQM Termo-hidro-químico-mecánico

RAA Residuos de alta actividad

SC Small corrosion (experiment)

URL Underground research laboratory

2I Double interface mortar-bentonite-magnetite interaction experiment


1

Chapter 1. Introduction

1.1. Motivation and objectives

The storage of high-level radioactive waste (HLW) in a deep geological repository



canister, and the bentonite buffer.

Significant research has been performed during the last decades to improve the

knowledge, characterize the key parameters and the constitutive equations and develop

numerical models for the HLW repository barriers. This research has been tackled within the

framework of projects funded by the EURATOM Program of the European Commission.

Significant parts of this dissertation have been developed within the PEBS (Long-term

Performance of Engineered Barrier Systems), CEBAMA (Cement-based materials, properties,

evolution, barrier functions) and FEBEX-DP Projects (Full-scale Engineered Barrier

Experiment Dismantling Project).

The main objective of this dissertation is the updating and the testing of coupled

thermal, hydrodynamic, chemical and mechanical (THCM) models for the compacted bentonite

barrier in a high-level radioactive waste repository. To achieve this objective, the following

activities were carried out:

Updating and improving the conceptual and numerical coupled thermo-hydro-chemical

and mechanical models (THCM) of the bentonite barrier of a HLW repository.

Implementing the improvements in the THCM code INVERSE-FADES-CORE and

producing an updated version (INVERSE-FADES-CORE V2).

Modeling laboratory tests.

Testing THCM models with data from the FEBEX (Full-scale Engineered Barrier

Experiment) mock-up and in situ tests.

Modelling the long-term geochemical evolution of HLW repositories in granite and clay.


2

The following methodology has been used:

Perform a survey and review of the scientific literature.

Review the conceptual and numerical model.

Update and improve the code INVERSE-FADES-CORE.

Model the laboratory experiments.

Test THCM models with data from the FEBEX mock-up and in situ tests.

Perform long-term geochemical simulations for repositories in granite and clay.

1.2. State-of-the-art

1.2.1. Bentonite barrier in a radioactive waste repository

The storage of high-level radioactive waste (HLW) in a deep geological repository



canister, and the bentonite buffer. FEBEX (Full-scale Engineered Barrier Experiment) is a

demonstration and research project for the engineered bentonite barrier of a HLW repository.

FEBEX is based on the Spanish reference concept for radioactive waste disposal in crystalline

rock, which consists on the disposal of spent fuel in carbon steel canisters in long horizontal

disposal drifts excavated in granite. The main physical, thermal, hydrodynamic, mechanical

and geochemical properties of the bentonite were extensively studied during the project

(ENRESA, 2000, 2006a). The FEBEX project includes the following two main large-scale

experiments which started in February of 1997: 1) The in situ full-scale test performed at the

Grimsel underground research laboratory (URL) in Switzerland; and 2) The mock-up test

operated at the CIEMAT facilities in Spain (ENRESA, 2006a; 2006b; 2006c; Martín et al.,

2006). These tests replicate a HLW repository in which the canisters with the spent fuel were

replaced by heaters. Laboratory tests were carried out with different sizes, durations, heating,

and wetting conditions (Villar et al., 2012). Some of them were performed in the so-called

thermohydraulic cells (CT), which are 13 cm-long, during 1 to 6 months (Fernández et al.,

1999; Cuevas et al., 1997; ENRESA, 2006a; 2006b; 2006c). Other heating and hydration (HH)

tests were performed in 60 cm-long cells (CG tests) with durations ranging from 0.5 to 7.6

years (Villar et al., 2008a).

Villar et al. (2012) presented a summary of the information gathered during 15 years

on the saturation of compacted FEBEX bentonite obtained from heating and hydration


3

laboratory tests, the mock-up test, and the in situ test. They analyzed the hydration rate, the

temperature and the water content data and their relevance for the rate of saturation and vapor

migration through the bentonite buffer.

Villar el at. (2008b) presented a coupled THM model of the CG cells performed with

CODE_BRIGHT (Olivella et al., 1996) by using a 1-D axis-symmetric finite element mesh. The

model reproduces the general trends observed THM data in the tests. Fernández and Villar

(2010) reported the geochemical data and presented a geochemical model of the CG7.6 test

(GMFV) to interpret and derive the pore water composition. The geochemical model was

performed with PHREEQC2 (Parkhust and Appelo, 1999).

Some geochemical reactions such as smectite dissolution are often ignored in short to

medium-term geochemical models because they can be disregarded in the short term. Savage

et al. (2010c) studied the potential contribution of the smectite hydrolysis to the long-term

geochemical processes in a KBS-3 bentonite buffer. They concluded that smectite dissolution

could be significant for the future geochemical state of a buffer, but the time scale of this

process is too long for experimental verification. Smectite dissolution has the beneficial effect

of leading to a slight decrease (1 cm) of the thickness of the altered bentonite zone (Johnson

et al., 2014; Samper et al., 2016).

1.2.2. Bentonite and iron interactions

Iron-bentonite interactions and the effects of corrosion products on the bentonite were

first identified by NAGRA in the mid 1980’s (Savage, 2012). Extensive experimental studies

and numerical models of the iron-bentonite interactions and the effects of corrosion products

on the bentonite have been performed in recent years (ENRESA, 2004; Montes-H et al., 2005;

Bildstein et al., 2006; De Wint and Torres, 2009; Wersin et al., 2007; Samper et al., 2008;

Savage et al., 2010a; Marty et al., 2010a, 2010b; Lu et al., 2011, Turrero et al., 2011; Torres

el al., 2013; Ngo et al., 2014, Samper et al., 2016). Corrosion tests were performed to ascertain

the effects of the corrosion products in the bentonite during the NFPRO project (ENRESA,

2005, Torres et al., 2008).

Some numerical models predict that magnetite will be the main corrosion product

(Samper et al., 2008; Lu et al., 2011, Samper et al., 2016) while others predict also the

formation of Fe-bearing aluminosilicates (Wersin et al., 2007; Savage et al., 2010a; Marty et

al., 2010a; Ngo et al., 2014) and ferrous hydroxide (De Windt and Torres, 2009). Bildstein et

al. (2006) modelled the interactions of a carbon-steel canister with the MX-80 bentonite and

the clay formation in the French reference system at 50 ºC over 10.000 years. They considered


4

the following corrosion products: iron oxides and hydroxides, iron carbonates, and iron-rich

smectite and Fe-phyllosilicates. Wersin et al. (2007) studied the impact of iron components

released from the canister corrosion on the bentonite buffer (MX-80) within the KBS-3H

concept using the Olkiluoto site in Finland. They accounted for iron corrosion, cation exchange,

protonation/deprotonation, Fe(II) surface complexation and thermodynamic and kinetic mineral

dissolution/precipitation. Samper et al. (2008) presented 1-D and 2-D multicomponent reactive

transport models to simulate the interactions of corrosion products with bentonite in the near

field of a repository in granite. Numerical simulations were performed at a constant

temperature of 25 ºC for 0.3 Ma. They found that magnetite is the main corrosion product.

Magnetite precipitation reduces the bentonite porosity. Lu et al. (2011) presented an updated

version of the model of Samper et al. (2008) which considers 3 types of sorption sites in the

bentonite, kinetically-controlled canister corrosion and magnetite precipitation, and the

competition of Ni2+ for sorbing sites. Savage et al. (2010a) reported a model of the iron-

bentonite interactions based on natural analogues. They claim that the sequence of the

alteration of the clay by Fe-rich fluids may proceed via an Ostwald step sequence. They

modelled iron corrosion and the alteration of the MX-80 bentonite. Savage et al. (2010b) found

that smectite dissolution may be significant for the future geochemical state of a buffer, but the

time scale of this process is too long for experimental verification. Marty et al. (2010a) modelled

the long-term alteration of the engineered bentonite barrier in an underground radioactive

waste repository. Their study focused on the feedback effects of geochemical reactions on the

transport properties of compacted MX-80 bentonite. Their calculations were performed at

100 ºC to estimate the maximum thermal effect on the mineralogy of the engineered barrier.

The model was run for 105 years. Ngo et al. (2014) presented a coupled transport-reaction

model for the long-term interactions of iron, bentonite and Callovo-Oxfordian (COX) claystone

which extended the work of Marty et al. (2010a) by investigating the influence of the reactive

surface area of the primary minerals on the bentonite and the COX claystone and the diffusion

coefficient on the evolution of the iron-bentonite system.

1.2.3. Bentonite and concrete interactions

The interactions of cement-claystone barriers have been studied by laboratory

experiments and industrial and natural analogues (Savage et al., 1992; Bauer and Berger,

1998; Steefel and Lichtner, 1998; Huertas el al., 2000; De Windt et al., 2004; Melkior et al.,

2004; Soler et al., 2004; Tinseau et al., 2006; Gaucher and Blanc, 2006; Yang et al., 2008;

Fernández et al., 2009b; Savage, 2011; Savage et al., 2011; Berner et al., 2013; Kosakowski

and Berner, 2013; Shao et al., 2013; Watson et al., 2013; 2016; Lalan at al., 2016; Cuevas at


5

al., 2016; Lothenbach et al., 2017). Cuevas et al. (2016) performed test on double interface

cells with mortar, bentonite and magnetite powder. Several sets of tests of concrete-bentonite

columns tests were performed to study the interactions of concrete and bentonite (Turrero et

al., 2011; Torres et al., 2013).Recently, Alonso et al. (2017) and Fernández at al. (2017)

presented the interactions of the concrete and bentonite interface of the concrete plug in the

FEBEX in situ test.

Extensive reactive transport modelling studies of the long-term cement-bentonite

interactions and the effects of the hyperalkaline plume have been performed during the last 25

years (Fritz and Madé, 1991; Savage et al., 2002; 2010b; Watson et al., 2007; 2009a; 2009b;

Ueda et al., 2007; Yamaguchi et al., 2007; Fernández et al., 2009a; Marty et al., 2009, 2010a;

Lehikoinen, 2009; Savage, 2012). Shao et al. (2013) performed reactive transport simulations

of the Maqarin marl rock natural analogue for 500 years with a 1-D model by using the

OpenGeoSys-GEM code. Their results show pore clogging with the precipitation of ettringite

and CSH phases in the marl rock exposed to the hyperalkaline plume in a band of 0.5 to 1 cm.

According to the numerical model, the pores of the clay rock formation become clogged after

2·104 years. Watson et al. (2016) presented reactive transport simulations of the mineral-fluid

interactions along the fractures of the Maqarin analogue and concluded that the fracture

sealing is likely to occur when hyperalkaline fluids derived from cement degradation come into

contact with rocks saturated with neutral pH and bicarbonate-rich groundwaters. Kosakowski

and Berner (2013) presented numerical reactive transport calculations to evaluate the

geochemical evolution at cement-clay interfaces for different transport scenarios through

several Opalinus clay rocks for a time span of 2·103 years. High pH, mineralogical and porosity

changes are restricted to narrow zones for all host rocks. The clogging of the pore space leads

to a strong reduction of diffusive fluxes across the interface, which stops the geochemical

alteration processes and significantly slows down mass transport across the interface. Berner

et al. (2013) presented the simulations of the interactions of a MX-bentonite buffer with a low-

pH concrete and the Opalinus Clay. Calculations were performed for 3·104 years with the

OpenGeoSys-GEM code. Their results show that the thickness of the zone containing

significant mineralogical alterations is at most a few cents of mm in both the bentonite and the

Opalinus Clay adjacent to the liner. The precipitation of minerals reduces the porosity near the

bentonite-concrete and concrete-Opalinus Clay interfaces. The effect is more pronounced and

faster at the concrete liner-Opalinus Clay interface. The simulations reveal that significant pH

changes (i.e. pH > 9) in the bentonite and the Opalinus Clay are limited to zones less than 10

cm thick after 3·104 years. Watson et al. (2013) performed a reactive transport modelling of a

cement-clay interface at the industrial analogue of Tournemire (France) by using QPAC, the

Quintessa's general-purpose modelling software. The sample overcoring and extraction in


6

boreholes filled with concrete and cement, which have had remained in contact with the natural

mudstone for 15-20 years, allowed the mineralogical characterization of the alterations

observed around the concrete-mudstone interface. In the concrete and in the mudstone there

is a general increase in porosity while there is a reduction in porosity at both sides of the

concrete-mudstone interface. Watson et al. (2013) concluded that the inclusion of the cation

exchange in the base model reduces the extent of the hyperalkaline plume in the mudstone.

However, the pH profile is almost unaffected when protonation/deprotonation reactions on the

montmorillonite surface are considered in the model. Yang et al. (2008) presented a numerical

model of water flow, heat transfer and multicomponent reactive solute transport to evaluate

the long-term geochemical evolution in the bentonite barrier, the concrete and the clay

formation for a potential geological radioactive waste repository in a clay formation.

Calculations were performed for 1 Ma by using the CORE2D V4 code. They concluded that:

1) The dissolution of the CSH minerals in the concrete causes an increase in pH to 13; 2) The

porosity of the bentonite buffer decreases from 0.4 to 0.3; and 3) The hyperalkaline plume from

the concrete migrates 70 cm into the clay formation over the time range of 1 Ma.

1.2.4. Coupled THCM processes, codes and models

The geochemical evolution of the bentonite barrier during the initial stages of the

hydration and heating of the repository depends on the thermal, hydrodynamic and mechanical

processes. The mathematical formulation of the coupled thermo-hydro-mechanical processes

has been reported by Cox and Pruess (1990), Olivella et al. (1996), Yu-Shu Wu and Pruess

(1999), Navarro and Alonso (2000) and Yu-Shu Wu et al. (2004). Existing THC codes includes:

TOUGHTREACT (Xu and Pruess, 2001); RETRASO (Saaltink et al., 2004); MULTIFLOW

(Lichtner, 1996); CRUNCH (Steefel, 2001); FRACON (Nguyen et al., 2005); and OpenGeoSys

(Kolditz et al., 2012). Heating and hydration experiments were interpreted using THM (Villar et

al., 2008b; Gens et al., 2009) and THC numerical models (Zheng and Samper, 2005, 2008;

Zheng et al., 2008, 2010 and 2011). Later, coupled THCM models were used to study the

coupled THCM processes for the repository performance assessment (Guimaraes et al., 2007;

Samper et al., 2008; Zheng et al., 2008; Zheng and Samper, 2008; Zheng et al., 2010; Zheng

et al., 2011;).


7

1.3. Scope

This dissertation includes 13 chapters, which describe the main contents of the

dissertation. The details of the contributions of the dissertation are described in 13 appendixes.

One of them is the Spanish version of the Extended Summary.

Chapter 2 describes the mathematical formulation of the coupled thermo-hydro-

chemical and mechanical processes which includes the formulation of the reactive gas

transport implemented in this dissertation

Chapter 3 presents the main features of the THCM code INVERSE-FADES-CORE as

well as the improvements, the updates, the verification and the benchmarking with other codes.

Chapter 4 deals with the integrated analysis of the available water intake, water

content, temperature, pH and chloride concentration data for the FEBEX bentonite from

laboratory tests and the mock-up and the in situ tests.

Chapter 5, 6, 7 and 8 are devoted to the THCM models of laboratory experiments.

Chapter 5 presents the THCM models of the heating and hydration tests performed by CIEMAT

on 60 cm long cells. The THCM models of the heating and hydration corrosion tests are

presented in Chapter 6. Chapter 7 describes the THCM model of the heating and hydration

test with concrete-bentonite interactions in the HB4 cell. Chapter 8 describes the THCM

models of the mortar-bentonite interactions in the double interface cells.

The models of the large-scale FEBEX mock-up and in situ tests are presented in

Chapter 9. This chapter includes the updating of the 1-D THCM model of the in situ test, the

updated geochemical predictions of the bentonite barrier in hot and cold sections at the

dismantling of the in situ test in 2015, the prediction of the tracer migration, and the prediction

of the geochemical interactions of the bentonite with the concrete plug.

The reactive transport modelling of the long-term interactions of corrosion products and

compacted bentonite in a HLW repository in granite is presented in Chapter 10. Chapter 11

presents the long-term non-isothermal reactive transport model of the compacted bentonite,

concrete and corrosion products in a HLW repository in clay.

Chapter 12 summarizes the main conclusions of the dissertation and lists the

recommendations for future work.


9

Chapter 2. Mathematical formulation of THCM models

2.1. Introduction

Modelling the geochemical evolution of the bentonite barrier during the early stages of

a HLW repository requires the use of models which account for the thermal gradients caused

by the heat released from the waste, the multiphase phase flow of air, vapor and liquid water,

bentonite swelling and the geochemical reactions involving aqueous, exchanged, sorbed and

mineral species. The mathematical formulation of the coupled thermo-hydro-mechanical

processes are presented by Cox and Pruess (1990), Olivella et al. (1996), Yu-Shu Wu and

Pruess (1999), Navarro and Alonso (2000), and Yu-Shu Wu et al. (2004). Zheng et al. (2010)

presented thermo-hydro-chemical models of the FEBEX bentonite.

This chapter presents the mathematical formulation of the coupled THCM model of the

bentonite barrier in a high-level radioactive waste repository. The formulation includes the

description of the reactive gas transport which has been implemented in INVERSE-FADES-

CORE V2 in this dissertation. The details of the reactive gas transport can be found in

Appendix 1.

2.2. Coupled THCM processes in a bentonite barrier in a HLW

repository

The Spanish reference concept of a high-level radioactive waste repository in granite

(ENRESA, 2000) consists on the disposal of spent fuel elements in cylindrical carbon steel

canisters placed in horizontal disposal drifts. The disposal drifts, having 500 m in length and

2.4 m in diameter, are located at a depth of 500 m in a granite formation. The distance between

disposal drifts is 35 m. The canisters are spaced 2 m. The canisters are 4.54 m long, 0.10 m

thick and have an external diameter of 0.90 m. The reference concept of a high-level

radioactive waste repository in clay, on the other hand, includes additionally, a 0.3 m thick

concrete sustainment located between the bentonite buffer and the clay formation. (ENRESA,

2004)

Chapter 2. Mathematical formulation

10

The bentonite buffer is the sealing material for the waste disposal. Bentonite has a very

low permeability and is able to retain radionuclides without large alterations. The bentonite in

the repository will be subject to high temperatures generated by the nuclear waste package

and to the hydration from the host rock. The corrosion of the carbon steel of the canister and

the concrete degradation may induce bentonite alterations, which could result in changes in

bentonite parameters such as porosity, permeability, sorption and swelling.

The unsaturated bentonite is as porous medium with three phases: solid, liquid and

gas. The main thermal and hydrodynamic processes include: 1) Advective flow in the liquid

and gaseous phases; 2) Diffusive flow in the liquid and gaseous phases; 3) Advective heat

transport in the liquid and gaseous phases; 4) Heat conduction through the three phase; and

5) Heat transfer between the phases.

The mechanical behaviour requires knowing the forces, strains, displacements and

stresses. The hydration and heating of the bentonite affect the saturation degree and the

suction pressure which in turn may induce changes in the strain and stress. The hydration and

the drying of the bentonite may induce swelling and shrinkage, respectively.

Chemical reactions in the bentonite include: 1) Homogeneous reactions such as

aqueous complexation, acid-base and redox reactions; and 2) Heterogeneous reactions such

as cation exchange, surface complexation, mineral dissolution/precipitation, and gas

dissolution/exsolution. Chemical reactions depend on temperature (T). In addition, the

transport of reactive chemical species depend on flow and hydrodynamic (H) processes and

mechanical (M) phenomena because the changes in porosity affect the dissolved

concentrations and the transport processes.

This dissertation deals with coupled THCM numerical models which account for the

interplays among thermal (T), hydrodynamic (H), chemical (C) and mechanical (M) processes

(Figure 2.1). The numerical model accounts for most of the interactions between then THCM

processes illustrated in Figure 2.1.


11

Figure 2.1. Scheme of the couplings between thermal (T), hydrodynamic (H), chemical (C) and mechanical (M) processes.

2.3. Mathematical formulation

Water mass balance is given by (Navarro and Alonso, 2000):

0 (2.1)

where is the material derivative with respect to the solid particles which move with a

velocity vector (m/s), ( ) is the divergence operator, and are the bulk densities of

the liquid and gaseous phases (kg/m3), respectively, is the mass fraction of water in the

liquid phase, the mass fraction of the vapor in the gas phase, is the vector of volumetric

liquid flux (m/s) which is given by Eq. (2.15), is the vector of volumetric gas flux (m/s) which

is given by Eq. (2.16), is the dispersive mass flux of vapor with respect to the mean gas

velocity (kg/m2/s) which is given by Eq. (2.17), and is the mass of water per unit volume of

porous medium (kg/m3) which is given by:

∅ 1 (2.2)

where ∅ is the porosity and is the liquid saturation degree.

The air mass balance equation is given by (Navarro and Alonso, 2000):

0 (2.3)

where is the mass fraction of air in the gaseous phase, is the mass fraction of air in the

liquid phase, and is the mass of air per unit volume of porous medium (kg/m3) which is

given by:

T

C

H

M


12

∅ 1 (2.4)

The solid mass balance is given by (Navarro and Alonso, 2000):

0 (2.5)

where is the dry density of the medium which is equal to 1 ∅ , where is the density

of the solid particles (kg/m3). If the coefficient of the thermal expansion of the solid particles

(1/ºC), , is considered and the mechanical compressibility of the particles is disregarded,

then Eq. (2.5) becomes:

∅1 ∅ (2.6)

where is the temperature (ºC).

The formulation assumes that all phases are at local thermal equilibrium and therefore

they are all at the same temperature. Hence, the energy balance is described in terms of an

equation of internal energy which is defined by the following balance of enthalpy:

0 (2.7)

where is the average specific enthalpy of the soil (J/kg) which in turn is given by:

∅ ∅ ∅ 1 ∅ 1

∅ 1 ∅ (2.8)

where , , and are the specific enthalpies of free water, vapor, air and solid particles

respectively, which are assumed to depend linearly on temperature and specific heat (Navarro

and Alonso, 2000) and is the vector of convective energy flux which is given by:

(2.9)

where is the vector of volumetric vapor flux (m/s) which is given by the last terms of

Eq. (2.1), that is, and is the bulk thermal conductivity tensor (W/mºC)

which for unsaturated bentonite is computed as a volume-weighted average of the

conductivities of the components according to:

∅ ∅ ∅ 1 1 ∅ (2.10)

where w, v, a and s are the thermal conductivities of water, vapor, air and solid,

respectively. This equation is inspired in the formulation of De Vries’s (1963) which according

to Tang et al. (2008) provides the best fit to measured thermal conductivity data for several

bentonites such as FEBEX bentonite. The formulation in Eq. (2.10), however, may not be the

appropriate for courser porous materials.


13

According to Soler (2001), the Dufour effect is negligible compared to thermal

conduction and therefore can be disregarded.

The following incremental formulation of the equilibrium equation of Navarro and

Alonso (2000) is used:

∆ ∆ ∆ 0 (2.11)

where ∆ is the increment of the average soil density, is the gravitational acceleration (m/s2),

is the unit vector in the gravity direction, is the vector expression of Kronecker’s delta,∆

is the increment in gas pressure (Pa) which for saturated conditions should be replaced by the

increment in the liquid pressure (Pa), ∆ , and ∆ is the vector of increments of effective stress

(Pa) which is related to the vector of increments of total stress ∆ (Pa) in unsaturated

conditions through:

∆ ∆ ∆ (2.12)

while for saturated conditions the previous equation is replaced by

∆ ∆ ∆ (Fredlund and Rahardjo, 1993).

Solute transport processes include advection, molecular diffusion, and mechanical

dispersion. Each of them produces a solute flux per unit surface and unit time. There are as

many transport equations as primary chemical species in the system. The mass balance

equation for the j-th primary species is given by (Zheng and Samper, 2008):

∗ 1,2, … , (2.13)

where is the total dissolved concentration of the of j-th species (mol/L), is the mass of

liquid water per unit volume of medium (kg/m3) which is equal to , where ∅ is the

volumetric watercontent (m3/m3), , and are the total precipitated, sorbed and exchanged

concentrations (mol/L), respectively, of the j-th primary species, is the sink term (kg/m2/s),

is the dissolved concentration of j-th species (mol/L) in the sink term , is the number of

primary species. ∗ is the following transport operator:

∗ (2.14)

where is the dispersion coefficient (m2/s), and and are the condensation and

evaporation rates (kg/m2/s), respectively.

Coupled transport phenomena such as thermal and chemical osmosis may be

important for compacted bentonites (Keijzeret al., 1999; Keijzer and Loch, 2001; Soler, 2001).

The volumetric liquid flux, , includes the classical Darcian term together with the chemical

and thermal osmotic terms:


14

(2.15)

where is the liquid pressure (Pa), is the intrinsic permeability tensor of the liquid (m2),

is the relative permeability of the liquid, is the viscosity of the liquid (kg/m/s), is the

elevation, is the thermal-osmotic permeability (m2/K/s), is the osmotic pressure (Pa), and

is a dimensionless reflection coefficient for chemical osmosis which measures the

non-ideality of a membrane and is defined as the ratio of the applied osmotic pressure to the

developed hydraulic pressure at equilibrium. An ideal membrane has a reflection coefficient of

1 whereas it varies between 0 and 1 for non-ideal membranes.

The volumetric gas flux, , is given by:

(2.16)

where is the intrinsic permeability tensor of the gas (m2), is the relative permeability of

gas, and is the viscosity of the gas phase (kg/m/s).

The dispersive mass flux of vapor, , is calculated by the Fick’s law:

(2.17)

where is the hydrodynamic dispersion tensor for vapor (m2/s) which includes the effects of

mechanical dispersion and molecular diffusion. The effective molecular diffusion coefficient for

the vapor, , (m2/s) is calculated from (Pollock, 1986):

5.9 10 273.15 .

(2.18)

where is the vapor tortuosity (dimensionless).

The mechanical law is given by:

(2.19)

where is the strain vector, is the elastic matrix (1/Pa), is a vector of coefficients (1/Pa)

which account for the deformation caused by changes in suction , , and is a

vector of thermal expansion coefficients (1/ºC). The standard sign convention used in Soil

Mechanics is adopted here according to which compressions are positive.

To overcome the difficulties of the different mechanical models, some researchers have

resorted to simpler models such as the state-surface approach to simulate bentonite swelling.

Nguyen et al. (2005) used successfully the state-surface approach to interpret a swelling

pressure test. The following state-surface expression of Lloret and Alonso (1995) has been

adopted in this dissertation to model bentonite swelling:


15

ln (2.20)

where is the void ratio which is equal to the volume of voids divided by the volume of the

solids; is the atmospheric pressure in Pa, is the mean effective stress in Pa; is suction

in Pa, and , , and are empirical constants which for FEBEX compacted bentonite are

A = 0.76, B = -0.052446, C = -0.0406413 and D = 0.00479977 (Nguyen et al., 2005).

The chemical model for compacted bentonite accounts for the following reactions:

aqueous complexation, acid/base, redox, cation exchange, surface complexation and mineral

dissolution/precipitation. The chemical system is defined in terms of the concentrations of the

primary species. The concentrations of the secondary species are computed from the

concentrations of the primary species through appropriate mass action laws (Xu et al., 1999).

The concentrations of the precipitated, exchanged and adsorbed species are computed using

similar equations. A detailed description of the calculations of the chemical reactions can be

found in Xu et al. (1999) and Zheng et al. (2011). The Gaines-Thomas convention is used for

cation exchange. Surface complexation is modelled using three types of

protonation/deprotonation sites, SS-OH, SW1-OH and SW2-OH, as proposed by Bradbury and

Baeyens (1997).

The equilibrium constants for aqueous complexes and minerals depend on temperature

under non-isothermal conditions. They are calculated with the following expression which is

valid for temperatures between 0 and 300 ºC:

(2.21)

where to are coefficients which are derived by fitting Eq. (2.21) to measured values

at 0, 25, 60, 100 and 300ºC (Wolery, 1992).The thermodynamic database of EQ3/6 (Wolery,

1992) is used for aqueous complexes and minerals.

2.3.1. Reactive gas transport mathematical formulation

The reactive transport of gases could be relevant in the geochemical evolution of a

HLW repository. H2(g) can be generated and accumulated in the backfilling of the waste

package by the corrosion of the steel canister (Xu et al., 2008), which may affect the long-term

repository safety. On the other hand, the ambient CO2(g) of the air can react with the calcium

hydroxide of the concrete and cause concrete carbonation. The carbonation could affect the

mechanical strength of the concrete and decrease the alkalinity of the bentonite in contact with

the concrete. The high temperature in the bentonite buffer may cause water evaporation and

CO2(g) degassing which could decrease pH and lead to calcite precipitation. The revised


16

version of INVERSE-FADES-CORE, INVERSE-FADES-CORE V2, which accounts for the gas

reactive transport in the gaseous phase, can deal with the previous gas-related chemical

processes.

The reactive transport of the f-th gas species was implemented in this dissertation as

an additional mass balance equation of the f-th gas species in the gaseous phase. The gas

mass balance accounts for: a) Advection; b) Molecular diffusion; and c) Mechanical dispersion.

Each one of these processes produces a gas flux per unit surface and per unit time. There are

as many transport equations as gaseous species in the system. The gas transport equation

for the f-th gas is given by:

1,2, … , (2.22)

where is the gas density; is the concentration of the of f-th gas species (mol/kg) in the

gaseous phase; is the volumetric gas content ( ∅); is the dispersion tensor of

the f-th gas species; is the number of gaseous species; and are the gas mass flux

entering or leaving the system (kg/m3/s), respectively; is the gas chemical reactions term

(mol/m3/s); and is the external concentration of the f-th gas species in the entering gas flux.

Reordering the Eq. (2.22) and applying the gas mass balance in the gas phase, the

reactive gas transport equation is given by:

1,2, … , (2.23)

where is the mass of gas per unit volume of medium (kg/m3) which is equal to . Similar

to the solute transport equation (Eq. 2.13), the gas transport equation as:

∗ 1,2, … , (2.24)

where ∗ is the following transport operator:

∗ (2.25)

The details of the reactive gas transport formulation are presented in Appendix 1.


17

Chapter 3. THCM code INVERSE-FADES-CORE

3.1. Introduction

The THCM models developed in this dissertation have been performed with INVERSE-

FADES-CORE. INVERSE-FADES-CORE is a finite element code for non-isothermal

multiphase flow and reactive transport in deformable media. The code is the result of

integrating the capabilities of FADES (Navarro, 1997), CORE2D (Samper et al., 2003), FADES-

CORE (ENRESA, 2000; Juncosa, 2001) and INVERSE-CORE (Dai and Samper, 2004). The

details of the formulation implemented in the code can be found in Navarro (1997), Juncosa

(2001) and Zheng (2006).

This chapter presents the main features of INVERSE-FADES-CORE as well as the

improvements, the updates, the verification and the benchmarking with other codes.

The details on code improvements, reactive gas transport, code verification and

benchmarking can be found in Appendix 1.

3.2. Main features of INVERSE-FADES-CORE

INVERSE-FADES-CORE is a finite element code for modelling non-isothemal

multiphase flow, heat transport and multicomponent reactive solute transport under both

chemical equilibrium and kinetics conditions. The code takes into account the mass balance

of water, air, solid and energy; the transport of solids; and mechanical equilibrium. The solute

transport accounts for advection, molecular diffusion and mechanical dispersion. The code

solves both forward and inverse multiphase flow and multicomponent reactive transport

problems in 1-, 2- and 3-D axis-symmetric porous and fractured media (Zheng and Samper,

2004, 2005). State variables of the forward model include liquid and gas pressures and

temperature, which are solved by a Newton–Raphson method. A sequential iteration method

is used to solve the reactive transport equations. The concentrations of secondary species are

computed from the concentrations of primary species through appropriate mass action laws


18

(Xu et al., 1999). A detailed description of the calculations of the chemical reactions can be

found in Xu et al. (1999). The Gaines-Thomas convention is used for cation exchange. Surface

complexation can be modelled by using up to three types of protonation/deprotonation sites,

SS-OH, SW1-OH and SW2-OH, as proposed by Bradbury and Baeyens (1997).

To overcome the difficulties of the different mechanical models, some researchers have

resorted to simpler models such as the state-surface approach to simulate bentonite swelling.

Nguyen et al. (2005) used successfully the state-surface approach to interpret a swelling

pressure test.

3.3. Update of INVERSE-FADES-CORE

The numerical simulations performed in this dissertation have been performed with the

updated version of INVERSE-FADES-CORE (INVERSE-FADES-CORE V2). The code has

been updated and reviewed to debug programming errors, improve the input and output files

and facilitate its use. The following corrections and improvements have been performed:

Correction of a bug when reading and writing sorption data.

Correction of the calculation of the kinetic rate of mineral dissolution/precipitation.

Improvements in the following output files: spx.out, int.out, mix.out, outiter.

Printing an output file with the calculated mineral volume fractions.

Printing out the condition number of the Jacobian matrix for the solution of the

chemical equations.

Making operational the use of triangular elements.

INVERSE-FADES-CORE V2 accounts for gas reactive transport in the gaseous phase.

The formulation of reactive gas transport implemented in INVERSE-FADES-CORE V2

includes additional mass balance equations for the reactive gaseous species in the gaseous

phase. The mass balance equation for a given gas accounts for: a) Advection; b) Molecular

diffusion; c) Mechanical dispersion; and d) Exchange with the liquid phase. The formulation of

gas reactive transport in the gaseous phase is described in Appendix 1.

The formulation of the gas reactive transport implemented in INVERSE-FADES-CORE

V2 was verified by comparing the numerical results of INVERSE-FADES-CORE V2 with the

results computed with TOUGHREACT (Xu et al., 2008) for the following verification 1-D cases:


19

Case 1. Prescribed gas partial pressures at the boundaries.

Case 2. Prescribed gas partial pressure at the left boundary.

Case 3. Prescribed partial pressure with a mineral.

Case 4. No prescribed partial pressure with a mineral.

The numerical results of TOUGHREACT and INVERSE-FADES-CORE V2 coincide in

most of the cases. However, there are some small differences especially near the boundaries.

These differences could be due to differences in the numerical implementation of the boundary

conditions and the numerical methods used by TOUGHREACT (integrated finite differences)

and INVERSE-FADES-CORE V2 (finite elements). The results in Cases 1 and 2 tend to a

constant value equal to the prescribed pressure at the boundaries (Figure 3.1). In Cases 3 and

4, calcite precipitates at x > 0.55 dm where the combination of the partial pressure of CO2(g)

(0.015 bar) and pH (7.1) leads to calcite precipitation (Figure 3.2). The calcite volume fraction

computed with TOUGHREACT and INVERSE-FADES-CORE V2 are similar.

Figure 3.1. Computed partial pressure (bar) of CO2(g) at 1 day with INVERSE-FADES-CORE (line)

and TOUGHREACT (symbols) for the Case 1.

Figure 3.2. Calcite volume fractions computed with INVERSE-FADES-CORE (line) and TOUGHREACT (symbols) for the verification Case 4.

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0 0.2 0.4 0.6 0.8 1

Pa

rtia

l pre

ssur

e C

O2(

g)

Distance (dm)

TOUGHREACT (1d)

INVERSE-FADES-CORE (1d)

0.0E+00

2.0E-06

4.0E-06

6.0E-06

8.0E-06

0 0.2 0.4 0.6 0.8 1

Ca

lcite

vo

lum

e f

ract

ion

Distance (dm)

TOUGHREACT

INVERSE-FADES-CORE


20

3.4. Benchmarking of INVERSE-FADES-CORE V2

Benchmark problems are indispensable to increase the confidence and the reliability

of the simulation tools. The objectives of the benchmarks are achieved by comparing the

numerical results of the same problem computed with different codes. INVERSE-FADES-

CORE V2 has been benchmarked against others codes by means of two benchmarking

problems which are presented in Appendix 1. The first benchmark deals with modeling the

chemical interactions of a concrete liner with the compacted bentonite of the engineered barrier

and the host clay rock under isothermal and non-isothermal conditions. The second bechmark

is focused on the carbonation of concrete in unsaturated conditions during the repository

operational stage. Benchmarking results are shown in Appendix 1.


21

Chapter 4. Integrated analysis of thermal, hydrodynamic

and chemical data of compacted FEBEX bentonite

4.1. Introduction

A large number of hydrodynamic, geochemical and thermal data have been collected

for compacted bentonites during the last 30 years to characterize their properties and evaluate

their suitability for the Engineered Barrier System (EBS) of a high-level radioactive waste

repository. Laboratory and in situ heating and hydration experiments on compacted bentonites

have been performed within European Projects such as FEBEX I, FEBEX II, NFPRO and

PEBS for various sizes (from 0.1 m to more than 10 m) and durations that range from a few

months to more than 14 years. Villar et al. (2012) presented a summary of the information

gathered during 15 years on the saturation of compacted FEBEX bentonite obtained from

heating and hydration laboratory tests, the mock-up test and the in situ test. They analyzed the

hydration rate, temperature and water content data and their relevance for the rate of saturation

and vapor migration through the bentonite buffer. The analysis of Villar et al. (2012) has been

extended and expanded in this dissertation by considering hydrochemical data and performing

a dimensional analysis of the data. The dimensional analysis is a mathematical tool to establish

relationships among physical quantities by using their dimensions. Dimensionless variables

were defined for cumulative water intake, water content, temperature, pH and concentration of

dissolved Cl- in terms of dimensionless space and time. Analytical solutions based on the

Green-Ampt method have been developed for bentonite hydration under parallel and radial

flow conditions to facilitate the integration of cumulative water intake.

The FEBEX project includes two main large-scale experiments, the in situ full-scale

(Figure 4.1a) test and the mock-up test (Figure 4.1b) operated by CIEMAT. Laboratory tests

were carried out on thermohydraulic cells (CT) (Figure 4.1c), which are 13 cm-long, during 1

to 6 months; and on 60 cm-long cells (CG) (Figure 4.1d) with durations ranging from 0.5 to 7.6

years. These tests have different geometries and experimental conditions. Water hydration in

CT and CG cells takes place at the bottom and the upper surfaces, respectively. Water flow in

Chapter 4. Integrated analysis of bentonite data

22

these cells is one dimensional and parallel to the axis of the cells. Hydration in the mock-up

and in situ tests occurs through the outer surface and exhibits axial symmetry.

Appendix 2 presents the main features of the FEBEX heating and hydration

experiments and the available data. The appendix describes the Green-Ampt analytical

solutions for bentonite hydration and presents the dimensionless expressions for the key

variables and the integrated dimensional analysis of cumulative water intake, water content,

temperature and chemical concentration data.

a) b)

c) d)

Figure 4.1. Schematic design of the in situ test (ENRESA, 2000) (top left), the mock-up test (Martín et al., 2006) (top right), the CT cells (Fernández et al., 1999) (bottom left), and the CG cells (Villar et al.,

2008a) (bottom right).

4.2. Green-Ampt analytical solutions for water intake

The analytical solutions for parallel and radial flow show significant differences. The

analysis of these differences was performed by comparing the equations of the depth of the

hydration front, z, the infiltration rate, q, and the cumulative intake, V, for both cases. The most

relevant parameters in these equations are the thickness of the sample, the volume of the

bentonite and the hydration surface. The Green-Ampt equations for radial flow have been


23

compared with the solution for parallel flow for the following cases: 1) The same thickness and

volume of the sample as radial conditions; 2) The same thickness and hydration surface of the

bentonite as radial conditions; 3) The same volume and hydration surface as radial conditions;

and 4) The optimized thickness, volume and hydration surface. The best fit to the radial flow

solution is obtained for the parallel flow solution by using the optimized values of the thickness,

the volume and the hydration surface of the bentonite. The second best approximation

corresponds to using the same volume and thickness of the bentonite for radial and parallel

flow. It can be concluded that the cumulative water intake for radial and parallel flow are

comparable when the volume and hydration surface of the tests are appropriately selected.

4.3. Dimensionless variables

The following dimensionless variables were defined:

(4.1)

2 (4.2)

∆ (4.3)

(4.4)

(4.5)

(4.6)

(4.7)

where , , , , , , are the dimensionless cumulative water intake, time, volumetric

water content, temperature, concentration of dissolved chemical species, and radial distance

for radial-flow and distance from the hydration boundary for parallel flow; is the cumulative

water intake; is the diameter of the cell; is the length of the experiment; and are the

saturated and initial volumetric water contents, respectively; ∆ , , and are the

bentonite permeability, density and compressibility, respectively; and are the boundary

and the heater temperatures, respectively; and are the solute concentrations of the

boundary water and the initial pore water, respectively; is the radial distance from the

hydration boundary, and are the external and internal radii for a radial-flow system,


24

respectively. is the distance from the hydration boundary and is the length of the sample

in a parallel-flow system.

PV is the bentonite pore volume. For parallel flow, PV is given by:

2

4∆ (4.8)

For radial flow, PV is given by:

2 2 ∆ (4.9)

4.4. Integrated analysis of cumulative water intake data

Measured cumulative water intake may contain measurement errors which in the CG

cells are equal to about 15%. There are differences in the initial water content of the tests. The

cumulative intake of the mock-up test is larger than the water intake of other tests because the

block joins and gaps of the bentonite barrier were flooded at the beginning of the mock-up test.

The dimensional analysis of the measured cumulative water intake data show that the

cumulative water intake data of the CT and CG cells and the mock-up test cannot be scaled

up. There are large differences at early times due to an electric shutdown and the filling of the

block joints. Such differences, however, decrease with time and become negligible for

dimensionless times, , greater than 0.04 (see Figure 4.2).

Figure 4.2. Time evolution of the dimensionless cumulative water intake versus dimensionless time for the CT (Fernández et al., 1999) and the CG cells (Fernández and Villar, 2010) and the mock-up

test (ENRESA, 2006a).

CT-22

CT-23

CG0.5 CG0.5b

CG2

CG7.6 MOCK UP

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E-08 1.0E-07 1.0E-06 1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E-01 1.0E+00

Dim

en

sio

nle

ss

cu

mu

lati

ve w

ate

r in

tak

e

Dimensionless time


25

4.5. Integrated analysis of water content data

The water content data for the mock-up test are larger than the water content data from

other tests. This could be due to the fact that the water content is calculated from the relative

humidity and the porosity is assumed to be constant. Water content data for the mock-up test

for dimensionless times smaller than 0.04 are the largest for all the tests. The curves of the

water content versus radial distance for the CG cells, the mock-up and in situ tests have similar

slopes for > 0.08. There are differences in water content data among the tests which could

be due to differences in:

The initial flooding. The joins and gaps of the mock-up test were flooded at the

beginning of the test. This explains why the water content data for the mock-up test are

always largest.

The geometric configuration of the water flow and heat transfer.

The thermal gradient. The temperatures at the boundaries are similar in most tests.

However, the thickness of the bentonite ranges from 12 cm (CT cells) to 65 cm (in situ

test). It should be taken into account that water evaporates near the heater. Vapor

diffuses away from the heater and condenses later some distance away. This process

retards the hydration of the bentonite buffer. This process is more relevant in the in situ

test, where the water content is lower than the initial water content until = 0.05.

The internal boundary condition at the heater-bentonite interface. The bentonite is

directly in contact with the heater in the CT and CG cells as well as in the mock-up test,

whereas in the in situ test there is a metallic liner with a gap between the heater and

the liner. The measured water content data in CT cells are smaller than those of the

other tests because the CT cell was subjected to a higher thermal gradient.

4.6. Integrated analysis of temperature data

The analysis of temperature focused on the spatial distribution along the bentonite

buffer. The temperature decreases from the heater to the hydration boundary. The curves of

temperature versus distance from the heater show a large thermal gradient near the heater.

The thermal gradient near the hydration boundary is smaller. The measured dimensionless

temperature profiles show a slope of 0.8 which is similar for all the tests in the bentonite blocks

near the heater and 0.35 in the half near to the hydration boundary. Boundary temperatures

are similar in most of the tests (100ºC at the heater and about 20ºC at the hydration boundary).


26

Heat dissipation is especially relevant in the CG cells which show the smallest dimensionless

temperatures, although the slopes are similar in all the tests. Heat dissipation through the top

and the bottom boundaries is largest in the CT cells, due to the porous stone and the metallic

heater plate.

4.7. Integrated analysis of chemical data

Chemical data were determined at the end of the heating and hydration tests. The

chemical composition of the bentonite pore water was derived from aqueous extract tests

which were interpreted numerically with inverse geochemical models. This added a difficulty

to the integrated analysis of chemical data. In general, Cl- concentrations are smallest near the

hydration boundary and increase near the heater. The concentration of Cl- in the central

sections of the bentonite buffer is constant for early and intermediate times. The analysis of

the dimensionless Cl- concentrations from several tests shows that: 1) The Cl- concentrations

in the CT23 cell are much smaller than those of other tests; 2) There are significant differences

in the Cl- concentrations measured at several sections of the in situ test; and 3) The Cl-

concentrations decrease with time near the hydration boundary.

pH data from the CG cells and the in situ test are consistent. However, the pH data

from the CT cells are markedly larger than the pH data for the CG cells and the in situ test.

Possible reasons for the differences in chemical data among the tests include: 1) The method

used to measure the chemical variables.; 2) The chemistry of the hydration water; 3) The

geometric configuration of the flow (radial/parallel); 4) The thermal gradient; and 5) The

differences in the experimental conditions such as heterogeneities in the barrier and the

granitic rock in the in situ test.

4.8. Conclusions

Green-Ampt analytical solutions have been derived and used to compare radial and

parallel flow through the bentonite. The comparison shows that the analytical solutions are

markedly different. Such analysis shows that the best fit to compare radial and parallel flow is

obtained by optimizing the parameters, especially the volume and the hydration surface. This

should be taken into account when translating the results obtained in the tests, where the

conditions are parallel, to radial flow conditions.


27

The integrated analysis of the cumulative water intake data shows an overall

consistency. The largest differences occur at early times due to the differences in the

experimental conditions, which decrease with time. Hydration data from most of the tests

converge for dimensionless time larger than 0.04.

Water content data of the mock-up test are larger than those of the CT cells. The slope

of the water content data are similar for the CG cell, and the in situ and mock-up tests for

dimensionless times larger than 0.04.

The slope of the dimensionless temperature is about 0.8 in most of the tests. The

integrated analysis of Cl- shows that the general behavior is similar in most tests, except for

the CT23 cell data. The pH data are consistent except for the CT cell.

The general THCM processes in the CT and CG cells, the mock-up and the in situ tests

are similar. The general behavior of the cumulative water intake, water content, temperature

and chemical concentration data are also similar in these tests. However, some differences

have been found in the integrated analysis of the data which are caused by differences in the

size, geometry and initial and boundary conditions in the tests.

The integrated analysis of measured THC data has shown that the data with different

space-time scales from lab cell and column tests and the mock-up and in situ tests cannot be

scaled up. The conclusions obtained from this integrated analysis are similar to those reported

by Villar el at. (2012).

The dimensional analysis of hydrodynamic, thermal and chemical data assume that the

density, the porosity and the hydraulic conductivity of the bentonite are constant. However,

these parameters change during the tests (Villar et al., 2008b). The integrated analysis could

be improved by: 1) Extending the Green-Ampt solution to account for water distribution, 2)

Developing analytical solutions for temperature and concentration, and 3) Performing the

integrated analysis of chemical data for reactive species.

The dimensional analysis has been useful to identify the role of experimental

conditions, but it failed to provide a framework to integrate all the experimental data. Such

integration is most likely to be achieved by means of coupled THCM numerical modelling.

Coupled THCM numerical models constructed with data from lab tests and the mock-up and

the in situ tests can be safely used for long-term predictions.


29

Chapter 5. Coupled THCM model of the heating and

hydration tests on 60 cm long cells

5.1. Introduction

Laboratory experiments were performed within European Projects such as FEBEX I,

FEBEX II, NFPRO and PEBS to characterize the thermal-hydrodynamic-chemical and

mechanical properties of the compacted bentonite and evaluate the suitability of the bentonite

barrier as a backfilling material for a HLW repository. Heating and hydration laboratory tests

were performed on compacted bentonite, which mimic the conditions of the repository

(ENRESA, 2000, 2006a).

This chapter presents a coupled THCM model of the heating and hydration tests

performed on 60 cm long cells. This model extends the THM model of Villar et al. (2008b) and

the geochemical model reported by Fernández and Villar (2010) (GMFV) because the THCM

model accounts for geochemical reactions in addition to thermal, hydrodynamic and

mechanical processes. The complex interplays among thermal, hydrodynamic, mechanical

and geochemical processes can be represented appropriately with a coupled THCM model. In

addition, this coupled THCM model provides a powerful tool for the analysis and understanding

of the performance of the bentonite barrier of a HLW repository.

The details of the THCM model of the heating and hydration tests on 60 cm long cells

are presented in Appendix 3.

5.2. Test description

CIEMAT performed a series of heating and hydration tests on cylindrical compacted

bentonite samples 60 cm long and 7 cm in diameter (see Figure 5.1). These tests lasted from

0.5 to 7.6 years (Villar et al., 2008a). They include: the CG0.5 test (lasted 0.5 years), the CG1

test (lasted 1 years), the CG2 test (lasted 2 years) and the CG7.6 test (lasted 7.6 years). The

Chapter 5. THMC models of heating and hydration test on 60 cm long cells

30

heating and hydration tests performed on 60 cm long cells (CG tests) provide a large amount

of measured THCM data including:

Temperature and water intake recorded during the tests.

Water content, dry density and saturation degree measured at the end of the tests.

Geochemical data such as dissolved species concentration, concentrations of

exchanged cations and mineralogical observations at the end of the tests.

Some measured water intake data may contain errors caused by experimental artifacts.

These errors were filtered and raw water intake data were corrected. The measured

concentrations of the exchanged cations may also contain experimental errors. The

concentrations of the exchanged cations were discarded whenever the total sum of the

concentrations of the exchanged cations was smaller than 90% of the CEC of the natural

FEBEX bentonite. The chemical composition of the bentonite pore water was estimated with

the squeezing and the aqueous extract methods (Fernández and Villar, 2010). The dilution

factor was calculated for each section by using the water content measured at the end of the

test. The concentration of the conservative species Cl- in the bentonite pore water samples

was calculated for the CG0.5, CG1 and CG2 tests by multiplying the measured aqueous

extract concentration by the dilution factor. The consistency between aqueous extract and

squeezing Cl- concentration data has been checked. Data showing large discrepancies were

discarded.

Figure 5.1. Experimental setup of the CG tests (Villar et al., 2008a).


31

5.3. Model calibration and results

The numerical model was performed with a 1-D finite element mesh with INVERSE-

FADES-CORE V2. The model was performed in two stages. The results of the original

(previous) model were compared to measured data in the testing stage. The comparison of

the model results and the measured data revealed the following discrepancies: 1) The

computed porosity is smaller than the measured data; 2) The computed water content and

saturation degree near the heater are larger than the measured data; 3) The computed

temperatures in the sensors are larger than the measured data; 4) The computed water intake

overestimates the measurements; 5) The computed concentrations for the CG7.6 test are

smaller than the concentrations of the geochemical model of Fernández and Villar (2010); and

6) The concentrations of the exchanged Ca2+ and Mg2+ do not fit the measured data.

The following improvements were performed in the revised model to overcome the

previous discrepancies: 1) Adjusting the vapor tortuosity; 2) Considering lateral heat

dissipation at the sensors; 3) Adjusting the selectivity coefficients; and 4) Updating the material

properties of the elements located in the boundaries.

A slight increase in the vapor tortuosity from 0.3 to 0.4 leads to an increase in vapor

diffusion, bentonite pore water evaporation near the heater and pore water concentrations.

The numerical results with a vapor tortuosity of 0.4 reproduce the measured water content and

Cl- concentration data near the heater better than the previous model which has a vapor

tortuosity of 0.3. This result confirms that the water content, relative humidity, water

evaporation, solute concentration and mineral precipitation near the heater are very sensitive

to small changes in the vapor tortuosity.

The blocks of compacted bentonite were installed inside Teflon cells, which had no

thermal isolation. Therefore, a large amount of heat dissipation took place in these tests

through the Teflon walls (Fernández and Villar, 2010). The revised or calibrated model

accounts for the heat loss by means of a thermal Cauchy condition at the sensors. The

computed temperatures with the revised model reproduce the measured temperatures at the

sensors. The implementation of the Cauchy condition to simulate the lateral heat loss improves

the representation of the temperatures. The thermal gradient decreases in the upper part of

the cells (0.1 m < x < 0.5 m) and increases sharply near the heater (0.5 m < x < 0.6 m) to

almost a value of 5ºC/cm. The large temperature gradient leads to an increase in the water

evaporation and a decrease of the gravimetric water content near the heater.


32

The selectivity coefficients were calibrated in order to reproduce the initial concentration

of the exchanged cations of the FEBEX bentonite. It should be taken into account that the

numerical method used in INVERSE-FADES-CORE V2 initializes the concentrations of the

dissolved species to achieve chemical equilibration with the minerals present in the system.

The equilibration of the bentonite pore water with the mineral phases may change slightly the

concentrations of some dissolved cations such as Ca2+. Such change leads in turn to changes

in the concentrations of the exchanged cations. The selectivity coefficients for cation exchange

were adjusted to fit the measured concentrations of the exchanged cations. The concentrations

of the exchanged cations computed with the revised model fit the measured exchanged cation

data, but some discrepancies remain for exchanged Ca2+ and Mg2+.

The definition of the material zone at the hydration interface has a strong impact in the

numerical solution. There are significant differences in the water intake when the porous stone

is considered. The differences in the treatment of the boundary condition increase with time.

Similarly, the definition of the material zone at the bentonite-heater interface can affect the

amount of water evaporation and the solute mass balance errors. It can be concluded that

model results are very sensitive to changes in the boundary conditions at the heater interface

and at the hydration boundary. Inappropriate conditions can lead to large changes in

evaporation rates, solute concentrations, mineral precipitation near the heater and large mass

balance errors.

The revised THCM model reproduces the general trends of the measured

temperatures, porosities, gravimetric water contents, saturation degrees and water intake.

Computed temperatures reach steady state in a few days. The computed temperatures in the

bentonite are smaller than 50ºC, except in a 10 cm band near the heater where the temperature

increases with a gradient of 5ºC/cm. The computed gravimetric water content near the

hydration boundary increases due to bentonite hydration and swelling. The computed

gravimetric water content near the heater, however, decreases from its initial value (0.14) to

0.05 in CG0.5, CG1 and CG2 tests and 0.085 in CG7.6 test due to pore water evaporation

(see Figure 5.2). For the most part, the thermal, hydrodynamic and mechanical results of the

THCM model agree with those reported by Villar et al. (2008b).

The concentration of dissolved Cl- near the hydration boundary decreases due to the

dilution caused by the hydration water. The concentration of Cl- near the heater increases due

to the water evaporation. In general, the computed Cl- concentrations fit the measured data,

but the computed results under predict the measured data near the hydration. The computed

Cl- concentrations of the CG2 test near the hydration boundary fit the measured data better


33

than those of the CG0.5 and CG1 tests. The computed Cl- concentrations in the CG7.6 test

are similar to those of the GMFV, except near the heater (see Figure 5.3).

Model results show that the calcite dissolves near the hydration boundary within the

interval 0 < x < 0.1 m. Calcite shows a precipitation front, which moves through the bentonite

with time from x = 0.05 m in t = 0.5 years to x = 0.3 m in t = 7.6 years. Calcite precipitates also

near the heater.

Figure 5.2. Spatial distribution of the measured (symbols) and computed (line) gravimetric water content at the end of the CG0.5, CG0.5b, CG1, CG1b, CG2, CG2b and CG7.6 tests.

Figure 5.3. Spatial distribution of the measured aqueous extract (symbols) and the computed (lines) Cl- concentrations at the end of the CG0.5, CG0.5b, CG1, CG1b, CG2 and CG2b tests. And

comparison of the Cl- concentrations reported by Fernández and Villar (2010) (symbols) and the computed (lines) Cl- concentrations at the end of the CG7.6 test.

0

10

20

30

40

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Gravim. w

ater content (%

)

Distance (m)

Initial (t=0)Model results (t=188d)CG0.5CG0.5bModel results (t=440d)CG1CG1bModel results (t=762d)CG2CG2bModel results (t=2775d)CG7.6

1.00E‐02

1.00E‐01

1.00E+00

1.00E+01

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Cl‐(m

ol/L)

Distance (m)

Initial (t=0)Model results (t=188d)Aqueous extract CG0.5Aqueous extract CG0.5bModel results (t=440d)Aqueous extract CG1Aqueous extract CG1bModel results (t=762d)Aqueous extract CG2Aqueous extract CG2bModel results (t=2775d)GMFV


34

The concentration of dissolved bicarbonate and exchanged Ca2+ increase when calcite

dissolves. On the other hand, the pH and the concentrations of dissolved Ca2+ and HCO3- and

exchanged Ca2+ near the heater decrease when calcite precipitates. The pH decreases slightly

in the CG7.6 test, except near the heater where the pH increases. The pH is about 7.5

throughout the bentonite and increases to 8.4 at the heater interface.

The computed concentration of gypsum shows a dissolution front which propagates

from the hydration boundary into the bentonite column. Gypsum precipitates near the heater

(0.5 m < x < 0.6 m) after the cooling stage in the CG7.6 test. Anhydrite shows an opposite

behavior to that of gypsum. Anhydrite precipitates near the heater (0.45 m < x < 0.6 m) when

the temperature is above 50ºC and dissolves after the cooling stage and precipitates as

gypsum. The concentration of the dissolved sulphate is similar to the initial concentration,

except near the heater where it increases sharply due to water evaporation.

The model predicts a small amount of chalcedony dissolution in the bentonite. The rate

of dissolution is largest near the heater. The concentration of dissolved silica increases from

its initial value due to chalcedony dissolution.

The computed concentrations of exchanged cations reproduce the general trend of the

measured data for the CG0.5, CG1 and CG2 tests, except for exchanged Ca2+. The model

predicts an increase in the concentration of exchanged Na+ and K+ near the heater and a

decrease of the concentration of the exchanged Ca2+ and Mg2+. The changes in the

concentration of exchanged Ca2+ are triggered by calcite precipitation/dissolution. The general

trends of the computed concentrations of the exchanged cations in the CG7.6 test are similar

to those of the CG0.5, CG1 and CG2 tests. However, the changes in the concentrations of

exchanged cations are more pronounced.

The computed concentrations of the dissolved Ca2+, Mg2+, Na+ and K+ show trends

similar to those of the GMFV. The THCM model reproduces the measured THM variables such

as water intake, temperatures, water contents and porosities. The lack of a full set of chemical

data has prevented a full calibration of the model with geochemical data. It should be taken

into account that the geochemical data from the GMFV assume that the geochemical porosity

is a very small part of the total porosity.


35

5.4. Conclusions

A coupled THCM model of the heating and hydration tests performed on 60 cm long

cells has been presented. The model has been performed in two stages. Model results in the

testing stage were compared to measured data. The comparison of the model results and the

measured data shows the following discrepancies: 1) The computed porosity is smaller than

the measured data; 2) The computed water content and saturation degree are larger than the

measured data near the heater; 3) The computed temperatures are larger than the measured

data in the sensors; 4) The computed water intake overestimates the measurements; 5) The

computed concentrations for the CG7.6 test are smaller than the concentrations of the

geochemical model of Fernández and Villar (2010); and 6) The concentration of the exchanged

Ca2+ and Mg2+ do not fit the data. The following improvements were performed in the calibration

stage: 1) Adjusting the vapor tortuosity; 2) Considering lateral heat dissipation at the sensors;

3) Adjusting the selectivity coefficients; and 4) Updating the material properties at the boundary

elements. The revised THCM model reproduces the observed temperatures, saturation

degrees, porosities. Moreover, model results fit the measured concentrations of the Cl- and

measured exchanged cations data for the CG0.5, CG1, CG2 tests. The computed

concentrations of Cl-, Na+, Ca2+, Mg2+, K+, HCO3-, SO4

2- and pH reproduce the general trends

of the results reported by Fernández and Villar (2010) for the CG7.6 test.


37

Chapter 6. Coupled THCM models of heating and hydration

tests to study the interactions of Fe corrosion products

and bentonite

6.1. Introduction

Corrosion tests are useful to ascertain the effects of the corrosion products in the

bentonite. CIEMAT performed corrosion tests during the NFPRO (Near Field Processes)

project to study the interactions of the bentonite and the corrosion products (ENRESA, 2005;

Torres et al., 2008).

This chapter presents the THCM numerical models of two types of heating and

hydration tests performed by CIEMAT to study the interactions of compacted bentonite and

corrosion products under the conditions of a HLW repository. The experiments were performed

at several temperatures on samples of different lengths. The 1-D THCM models performed

include: 1) The corrosion tests on 25 mm long small cells (SC) at 25, 50 and 100ºC and with a

duration of 180 days; and 2) The corrosion tests on 10 cm long medium-size cells (FB) at

100ºC and with a duration of 1593 days. The THCM models presented in this dissertation

extend the model of the corrosion tests of De Windt and Torres (2009).

The details of the THCM numerical models of the heating and hydration corrosion tests

can be found in Appendix 4.

6.2. Tests description

The corrosion tests on small cells, SC cells, were performed by CIEMAT. The cells

contained 21 mm of compacted FEBEX bentonite and 4 mm of carbon-steel powder. The tests

were performed at 25º, 50º and 100ºC. The durations of the tests were 6 and 12 months

(Figure 6.1a). The corrosion tests performed on medium-size cells, FB cells, were carried out

also at the CIEMAT facilities. They contain a 86.8 mm long sample of compacted FEBEX

Chapter 6. THCM models of the heating and hydration corrosion tests

38

bentonite and a layer of 13 mm of carbon-steel powder. The temperature was prescribed at

100ºC at the bottom of the cell (Figure 6.1b). The medium-size corrosion tests lasted from

6 months to 4.5 years.

The bentonite dry density, the water content and the saturation degree were measured

at the end of the corrosion tests on small and medium-size cells. In addition, the temperature

and the relative humidity were recorded at the sensors installed on the corrosion test on

medium-size cells. The iron weight were measured at the end of the corrosion tests on small

cells. Moreover, the concentration of the exchanged cations were measured at the end of the

corrosion tests. Mineralogical observations indicate that Fe(OH)2(s) precipitates. These data

were used to calibrate the kinetic parameters of the precipitation of the corrosion products.

a) b)

Figure 6.1. Scheme of the corrosion tests on small cells (left) (Torres et al., 2008) and of the corrosion tests on medium-size cells (right) (Turrero et al., 2011).

6.3. Model results

The numerical models were performed with INVERSE-FADES-CORE V2 by using a

1-D finite element mesh. The THCM numerical models include the bentonite and the Fe

powder. The models of the corrosion tests on small cells were performed for the tests at 25,

50 and 100ºC which lasted 6 months. The model of the corrosion test on the medium-size cell

was performed for the FB3 test which lasted 1593 days.


39

Fe(s) corrosion was assumed to occur at a constant corrosion rate according to Lu et

al. (2011) and Samper et al. (2016). The kinetic parameters of magnetite precipitation were

taken from De Windt and Torres (2009).

The computed water content and the porosity increase near the hydration boundary to

a value of 0.48 and decrease toward the Fe powder to values slightly larger than the initial

values in the corrosion tests on small and medium-size cells. The models predict that the

bentonite samples are almost saturated at the end of the tests, except near the Fe powder.

The computed temperatures reach steady state in a few minutes. The temperature is uniform

at 100ºC in the Fe powder because the specific heat and the thermal conductivity are larger

than those of the bentonite. The computed water content, porosity and saturation degree fit

the measured data at the end of the corrosion tests on small and medium-size cells. The

computed temperature and relative humidity in the medium-size cell reproduce the measured

data at the sensors, except the relative humidity near the heater where the measurements are

affected by vapor leakage through the sensors.

The Cl- concentration is affected by the hydration, the diffusion and the evaporation

near the heater. The computed concentration of Cl- near the hydration boundary decreases

because the pore water concentration of the hydration water in smaller than that of the initial

bentonite pore water. The computed Cl- concentration at the Fe power increases due to water

evaporation. Finally, Cl- diffuses from the Fe powder into the bentonite during the cooling

phase.

The computed concentrations of Na+, K+, Ca2+, Mg2+ and SO42- show trends similar to

those of Cl-. In addition, these species are subjected to mineral dissolution/precipitation and

cation exchange reactions. The changes in the computed concentrations of Cl-, Na+, K+, Ca2+,

Mg2+ and SO42- in the corrosion test on medium-size cell are larger than those in the small

corrosion tests because the test on the medium-size cell lasted longer than the tests on small

cells.

Model results show that gypsum dissolves initially in the bentonite and then it remains

constant. Anhydrite precipitates in the bentonite near the Fe power, but it dissolves soon after.

The behaviors of the sulfate minerals are similar in both corrosion tests. The computed

concentration of dissolved SO42- is affected slightly by gypsum and anhydrite

dissolution/precipitation.

The computed concentration of dissolved silica is controlled by quartz dissolution/

precipitation. The predicted dissolution of quartz in the bentonite, especially near the Fe

powder leads to the increase of dissolved SiO2(aq) in the bentonite near the Fe powder.


40

The model predicts calcite dissolution in the bentonite near the hydration boundary and

calcite precipitation near the Fe powder. A peak of calcite dissolution followed by calcite

precipitation is computed in the corrosion test on medium-size cells near the Fe powder at

large times. The computed concentration of HCO3- in the bentonite near the hydration

boundary is smaller than that in the Fe powder. This pattern of dissolved HCO3- is related to

calcite precipitation/dissolution.

The computed concentration of dissolved Fe2+ decreases in the bentonite and in the

Fe powder, especially at the interface bentonite-Fe powder due to the precipitation of corrosion

products and Fe2+ exchanged.

Magnetite and Fe(OH)2(s) precipitate in the Fe powder and at the bentonite-Fe powder

interface is predicted in the corrosion test on small cells. Goethite precipitates at early stages

and then it redissolves. Siderite does not precipitate. On the other hand, only magnetite

precipitates in the Fe powder in the model of the corrosion test on the medium-size cells (see

Figure 6.2). The predictions of the precipitation of corrosion products are consistent with the

laboratory observations. The computed results reproduce the iron weight data (Figure 6.3) and

the model results reported by De Windt and Torres (2009).

Figure 6.2. Spatial distribution of the computed cumulative magnetite precipitation at selected times in the corrosion test on small cell at 100ºC (left) and in the medium-size corrosion test on FB3 cell (right).

Figure 6.3. Measured (symbol) and computed (line) weight of precipitated iron hydroxide at the end of

in the corrosion test on small cell at 100ºC (t = 180 days) and after cooling.

0.00

0.25

0.50

0.75

1.00

0.000 0.005 0.010 0.015 0.020 0.025

Magnetite (m

ol/kg )

Distance from hydration side (m)

t=15 d

t=30 d

t=90 d

t=180 d + cooling

Fe powder

0.00

0.25

0.50

0.75

1.00

0.00 0.02 0.04 0.06 0.08 0.10

Magnetite (mol/kg)


t=10 d

t=100 d

t=1000 d

t=1593 d

Fe powder

0

2

4

6

8

10

0.000 0.005 0.010 0.015 0.020 0.025

wt(%)


Model results (t=180 d)

Measured wt(%)

Fe powder


41

The concentration of exchanged Ca2+ decreases in the bentonite near the Fe powder

where the calcite precipitates. The computed concentration of exchanged Mg2+ also increases

near the Fe powder. On the other hand, the concentrations of exchanged Fe2+, Na+ and K+

increase in bentonite near the Fe powder. Model results fit the measured cation exchange

data, except for exchanged Na+.

The computed pH in the bentonite decreases initially due to the thermal filed. The pH

increases in the bentonite-Fe powder interface due to the precipitation of the corrosion

products. The pH after the cooling phase is about 7.5 in the bentonite and 9 in the Fe powder.

The computed Eh decreases with time to -0.6V due to corrosion. The models predict that

Ss-OFe+ is the dominant sorbed species on the strong sites while Sw2-OH predominates on

weak #2 sites and Sw1-OH and Sw1-OFe+ are the main sorbed species on the weak #1 sites in

both corrosion tests.

6.4. Sensitivity analysis

The sensitivity analysis performed on the corrosion test on the small cells at 100ºC

indicates that: 1) The precipitation of magnetite at equilibrium is larger than that computed with

kinetically-controlled magnetite precipitation; 2) Fe(OH)2(s) does not precipitate when

magnetite precipitates at equilibrium; and 3) Fe(OH)2(s) does not precipitate when the

corrosion rate is decreased.

The general trends of the concentrations of the dissolved, exchanged and surface

complexation complexes are similar in the corrosion tests performed on small cells at 25, 50

and 100ºC. Iron corrosion at 100ºC is larger than that at 25ºC and 50ºC because the corrosion

rate increases with the temperature. The precipitation of magnetite is largest for the test at

100ºC and smallest for the test at 50ºC because the kinetic rate constant of magnetite is

smallest for 50ºC. The numerical results fit the measured iron weight data for the tests at 50

ºC and 100ºC.

6.5. Conclusions

The corrosion tests carried out by CIEMAT have been modelled with coupled THCM

models. The corrosion experiments include: 1) The small corrosion cells with a length of 25

mm and a duration of 180 days; and 2) The medium-size corrosion cells (10 cm long) with a


42

duration of 1593 days. The thermo-hydrodynamic model results fit the general trends of the

measured data in the bentonite in both corrosion tests. There are some discrepancies in the

computed time evolution of the temperature and relative humidity of the medium-size cells

which could be attributed to problems in the water injection system during the tests and vapor

leakage through the sensors.

The model results for the small corrosion cells indicate that: 1) Magnetite and

Fe(OH)2(s) are the main corrosion products which compete for Fe2+ precipitation; 2) The

corrosion products penetrate a few mm into the bentonite; 3) The numerical results fit the

measured iron weight data; 4) Fe2+ sorbes by surface complexation; and 5) Fe2+ exchange is

less relevant than Fe2+ sorption by surface complexation. Model results of the medium-size

cells show that magnetite precipitates in the Fe powder. The experimental observations

indicate that there is no magnetite precipitation in the bentonite. Some magnetite precipitation

was observed at the interface, which is consistent with the small amount of magnetite

precipitation computed at the interface.

The precipitation of magnetite at chemical equilibrium is larger than that computed with

a kinetically-controlled precipitation. Fe(OH)2(s) does not precipitate when magnetite

precipitates at equilibrium and when the corrosion rate is decreased.


43

Chapter 7. Coupled THCM model of the heating and

hydration concrete-bentonite interactions in the HB4 cell

7.1. Introduction

The concrete barrier will be the support of the galleries in the Spanish conceptual

reference for a HLW repository in clay rock (ENRESA, 2004). The concrete is a source of

alkaline solutions. The precipitation of mineral phases at the interfaces might reduce drastically

the porosity. Several laboratory experiments have been performed within NF-PRO (Near Field

Processes) and PEBS (Long-term performance of Engineered Barrier System) projects to

study this issue.

The concrete and bentonite tests (HB test) were carried out by CIEMAT on medium-

size cells containing a 7.15 cm long bentonite sample in contact with a 3 cm long piece of

concrete (see Figure 7.1). This chapter presents a 1-D coupled THCM model of the heating

and hydration laboratory test performed on bentonite and concrete. The details of the model



The concrete-bentonite column tests were performed at the CIEMAT facilities to study

the interactions of concrete and bentonite (Turrero et al., 2011; Torres et al., 2013). The tests

were carried out on medium-size cells containing a 7.15 cm thick bentonite sample in contact

with a 3 cm thick piece of concrete (see Figure 7.1) which were hydrated and heated at 100ºC.

The test duration ranged from 6 to 140 months.

Water content and dry density were measured along the cell at the end of the tests.

The sensor installed in the bentonite columns recorded the relative humidity and temperature.

The dissolved and exchanged concentrations were measured at the end of the tests. Mineral

observations were also performed at the dismantling of the tests.

Chapter 7. THCM model of the concrete-bentonite interactions in HB4 cell

44

Figure 7.1. Scheme of the concrete-bentonite test on HB4 cell (Turrero et al., 2011).

7.3. Model results

The numerical model of the HB4 test was performed with INVERSE-FADES-CORE V2

by using a 1-D finite element mesh. The HB4 test lasted 54 months. The model includes the

concrete (0 < x < 3 cm), and the bentonite (3 cm < x < 10.5 cm).

The bentonite hydrates through the concrete which gets fully saturated after 7 days.

The computed water content in the bentonite near the concrete interface increases to 0.5 due

to the hydration and decreases to 0.1 near the heater due to water evaporation. The computed

porosity of the bentonite near the hydration boundary increases 25% due to the bentonite

swelling and decreases 10% near the heater. The computed temperatures reach steady state

in a few minutes. The computed relative humidities increase and reach steady state after 250

days with RH = 100% at the sensor located near the hydration boundary and RH = 40% near

the heater. The computed relative humidity near the heater is smaller than that measured at

the sensor.

The concentration of Cl- in the bentonite decreases due to Cl- diffusion from the

bentonite into the concrete. The Cl- concentration becomes uniform after 100 days. The

concentrations of dissolved Na+, Ca2+, Mg2+ and SO42- are also affected by the diffusion from

the bentonite into the concrete. On the other hand, the concentration of the K+ and pH in the

bentonite increase due to the diffusion from the concrete into the bentonite. In addition, pH and

the concentrations of the dissolved Na+, Ca2+, Mg2+, K+ and SO42 are affected by cation

exchange and mineral dissolution/precipitation.


45

Cristobalite dissolves in the bentonite near the heater due to the increase in

temperature caused by the heater. The increase in temperature leads to an increase in the

concentration of dissolved silica. Quartz dissolution in the concrete is not relevant. Calcite

precipitates in the concrete near the hydration boundary and in the bentonite near the concrete

interface. Calcite dissolves in the bentonite downwards the precipitation front.

The model predicts the dissolution of portlandite and CSH1.8 and a small precipitation

of C0.8SH in the concrete. The concentration of dissolved calcium in the concrete increases

initially due to the dissolution of portlandite and CSH1.8. Later, the concentration decreases

due to calcite precipitation and the exchange of dissolved Ca2+ with exchanged magnesium.

Therefore, the computed concentration of exchanged Ca2+ increases and that of exchanged

Mg2+ decreases.

Similar to calcite, brucite precipitates in the concrete near the hydration boundary

because the hydration water has a large concentration of magnesium. Brucite precipitates also

at both sides of the concrete-bentonite interface. Sepiolite precipitates in the concrete near the

bentonite interface.

Ettringite precipitates in the concrete near the hydration boundary and dissolves in the

rest of the concrete. The dissolution rate is largest near the bentonite interface. Ettringite

dissolution/precipitation affects the concentration of dissolved aluminum and SO42-. The

increase in the concentration of dissolved SO42- in the bentonite is due to the large

concentration of SO42- in the hydration water, the dissolution of gypsum and anhydrite and the

diffusion of SO42- from the concrete into the bentonite.

The computed pH shows a sharp decrease at the concrete-bentonite interface which

coincides with the precipitation of brucite in the concrete and the precipitation of calcite and

sepiolite in the bentonite. The alkaline front penetrates and migrates through the bentonite.

The pH front (pH > 8.5) reaches 1 cm into the bentonite after the cooling phase (Figure 7.2).

The most important changes in the porosity in the HB4 cell occur in: 1) The hydration

boundary, 2) The concrete near the bentonite interface, and 3) The bentonite near the concrete

interface. The porosity in the hydration boundary decreases when brucite precipitates. Calcite,

ettringite, C1.8SH and C0.8SH precipitation also contribute to the decrease in the porosity.

Their contributions, however, are much smaller than that of brucite. The porosity in the

concrete near the bentonite interface reduces 51% due also to brucite precipitation. The

porosity in the bentonite near the concrete interface decreases 14% when brucite, calcite and

sepiolite precipitate. There is also a small decrease of the porosity (3%) near the heater due

to the precipitation of gypsum and anhydrite after the cooling phase.

Chapter 7. THCM model of the concrete-bentonite interactions in HB4 cell

46

Figure 7.2. Spatial distribution of the computed pH in the HB4 cell at selected times.

For the most part, the numerical model reproduce the measured water content,

porosity, temperature, relative humidity and captures the main trends of mineralogical

laboratory observations. However, there are some discrepancies, especially for ettringite and

CSH precipitation.

7.4. Conclusions

A coupled THCM model of the bentonite and the concrete test in the HB4 cell has been

performed. The model reproduces the measured temperature, relative humidity, water content

and porosity data. However, the model overestimates the relative humidity measured at the

sensor near the heater. Model results show that advection is relevant during the first months

of the test. Then, solute diffusion is the main transport process. The main mineralogical

alterations are predicted to occur at the hydration boundary, the concrete near the bentonite

interface, and the bentonite near the concrete interface.

Calcite and Mg phases precipitate at the hydration boundary due to the large

concentrations of bicarbonate and magnesium in the hydration water. The largest amount of

calcite and brucite precipitation take place at the bentonite and concrete near the interface.

Sepiolite also precipitates in the concrete near the bentonite interface. The model predicts the

dissolution of portlandite in the concrete and CSH1.8 and a small C0.8SH precipitation.

Ettringite precipitates in the concrete near the hydration boundary and dissolves in the rest of

the concrete. The porosity changes due to mineral precipitation/dissolution, especially at the

hydration boundary and in the bentonite and concrete near the interface. The porosity reduces

51% in the concrete at the bentonite interface when brucite precipitate.


47

The pH front (pH > 8.5) diffuses into the bentonite 1 cm at the end of the test.

Model results capture the main trends of the mineralogical observations. The model,

however, does not reproduce ettringite and CSH precipitation. The predicted precipitation for

these phases is smaller than the observed values.


49

Chapter 8. Coupled THCM model of the mortar-bentonite

interactions in the double interface cells

8.1. Introduction

The concrete barrier will be the support of the galleries in the Spanish reference

concept for a geological repository in clay host rock (ENRESA, 2004). The mortar is a source

of alkaline solutions resulting from the concrete degradation. The precipitation of mineral

phases at the interfaces might reduce drastically the porosity of the bentonite and the clay host

rock.

The so-called double interface tests were performed by CIEMAT during the PEBS

Project to study the interactions of corrosion products, bentonite, and mortar at the ambient

geochemical conditions of the repository expected to occur after 1,000 to 3,000 years. This

chapter describes the THCM models of the mortar-bentonite interactions in the double

interface cells. The details of the models are presented in Appendix 6.


The tests on double interface cells, 2I, were performed by CIEMAT on 25 mm long cells

which contain: mortar, bentonite and magnetite powder (Cuevas et al., 2013; 2016) (see Figure

8.1). The temperature in the cells was maintained constant at 60ºC for 540 days. The inner 2.5

cm length of this cell includes 0.5 cm of mortar, 1.8 cm of pre-treated FEBEX bentonite and

0.2 cm of magnetite powder.

Chapter 8. THCM model of mortar-bentonite interactions in double interface cells

50

Figure 8.1. Scheme of the six double interface tests (Cuevas et al., 2016).

The available measured data include:

The time evolution of the water intake.

The water content and the dry density at the end of the tests.

The concentrations of the aqueous species in the bentonite and the water of the tank,

which were measured at the end of the tests.

The mineralogical observations at the end of the tests.

8.3. Model description

The numerical model for the 2I3 cell was performed with a 1-D finite element mesh with

INVERSE-FADES-CORE V2. The model accounts for the hydration system (the water tank,

the water pipe and the filter), the lime mortar, the bentonite and the magnetite powder. The

model considers the hydration system to reproduce the water leakage in the water tank and

the backwards solution diffusion which occurred in some of the tests.

8.4. Model results

Model results show that the lime mortar, the bentonite and the magnetite powder are

fully saturated at the end of the test. The final computed water contents are 0.3, 0.41 and 0.60

in the mortar, the bentonite and the magnetite, respectively. The computed water content

corresponds to the total porosity because the system is saturated and the bentonite suffered

a very small deformation. The computed water content, saturation degree and water intake

reproduce the measured data at the end of the test.


51

The computed concentration of Cl- increases in the mortar and decreases in the

bentonite due to the diffusion from the bentonite into the mortar. The concentrations of Cl-

become uniform after a few days and equal to 0.058 mol/L. This concentration is ten times

larger than that measured in the bentonite and smaller than the measured in the mortar. These

discrepancies could be due to Cl- sorption in the mortar or to the precipitation of chloride

mineral phases.

The computed concentrations of dissolved Na+, K+, Ca2+ and Mg2+ show also the effect

of diffusion. However, they are subjected also to cation exchange reactions. SO42- and Al3+

diffuse from the mortar into the bentonite. These species are also subjected to mineral

dissolution/precipitation.

The computed concentration of dissolved Ca2+ at the end of the test increases from the

initial value. The dissolution of portlandite in the mortar and the diffusion of dissolved Ca2+ into

the bentonite lead to the precipitation of calcite, CSH1.2 and CSH1.6 in the bentonite and

mortar near the interface. The computed concentration of exchanged Ca2+ also increases in

the bentonite at the end of the test.

The computed concentrations of dissolved and exchanged Mg2+ decrease from their

initial values in the mortar near the hydration boundary and in the bentonite near the mortar

interface due to the precipitation of brucite and sepiolite. In addition, sepiolite shows some

precipitation peaks in the bentonite. Sepiolite, CSH1.6 and CSH1.2 precipitation lead to the

decrease of the concentration of dissolved SiO2(aq). The model predictions show a small

amount of quartz precipitation and no crisbolatite precipitation.

The model predicts that anhydrite precipitates in the mortar and in the bentonite, but

anhydrite is transformed into gypsum after the cooling phase. The computed dissolved

concentration of SO42- decreases when anhydrite and gypsum precipitate. The computed

ettringite precipitation shows a peak in the bentonite near the mortar interface at early times.

Later, it redissolves. Ettringite precipitation does not affect the concentrations of dissolved

SO42- and Al3+.

For the most part, the numerical model captures the main trends of the mineralogical

observations. However, there are some discrepancies, especially for ettringite precipitation in

the mortar which is not computed with the model, and brucite precipitation in the bentonite that

is not observed in the laboratory.

The porosity changes due to mineral dissolution/precipitation at the end of the test are

small and limited to the mortar and a few mm in the bentonite. The porosity increases 8% in

Chapter 8. THCM model of mortar-bentonite interactions in double interface cells

52

the mortar near the bentonite interface due to portlandite dissolution. On the other hand, the

porosity decreases 1.5% in the bentonite in a 0.2 mm thick zone near the mortar interface due

to calcite and brucite precipitation.

The pH shows a diffusive front from the mortar into bentonite. The computed pH at the

end of the test is about 10.5 in the mortar and the pH decreases from 10.5 at the interface to

8 in the first 10 mm of the bentonite (see Figure 8.2).

Figure 8.2. Spatial distribution the computed pH in the double interface 2I3 test at selected times.


The sensitivity analysis to the CEC and the initial composition of the exchange complex

has been analyzed by modelling the double interface test on 2I 4 cell which was performed on

a sample of natural FEBEX bentonite which has a CEC equal to 102 meq/100g. The computed

exchanged concentrations at the end of the tests show similar patterns in the tests performed

with natural and pre-treated FEBEX bentonite. The concentration of exchanged Ca2+ increases

while the concentrations of the exchanged Mg2+ and Na+ decrease. Cation exchange reactions

in the sample containing natural FEBEX bentonite are enhanced compared to the sample of

pre-treated FEBEX bentonite. The concentrations of dissolved of Mg2+ and Na+ in the test

containing natural FEBEX bentonite are larger than those of the pre-treated FEBEX bentonite

test while the concentrations of dissolved of Ca2+ and K+ in the natural FEBEX bentonite test

are smaller than in the test with pre-treated bentonite. Brucite and gypsum

dissolution/precipitation is slightly sensitive to the change in the composition of the exchange

complex.

7

8

9

10

11

12

0.000 0.005 0.010 0.015 0.020 0.025

pH


t=0t=7dt=6 monthst=1 montht=12 monthst=18 monthst=20 months

Mortar

Magnetite powder


53

8.6. Conclusions

A coupled THCM model of the mortar-bentonite interactions of the double interface

tests has been presented.

The model reproduce the measured water intake, water content and the dry density at

the end of the test. The mode predicts the portlandite dissolution in the mortar and calcite,

brucite, CSH1.2 and CSH1.6 precipitation in the mortar and in the bentonite near the interface.

Anhydrite precipitates in the mortar, but it is transformed into gypsum after the cooling phase.

The model predicts a small precipitation of ettringite and quartz and no cristobalite dissolution.

The porosity decreasing is maximum (1.5%) in the bentonite in a 0.2 mm thick zone near the

mortar interface due to calcite and brucite precipitation. The pH front (pH>8) penetrates into

bentonite 10 mm at the end of the test.

For the most part, the numerical model captures the main trends of the observed

mineral dissolution/precipitation patterns. However, there are some discrepancies, especially

for ettringite precipitation in the mortar which is not computed with the model, and brucite

precipitation in the bentonite which was not observed in the laboratory. Some of these

discrepancies could be due to the limitations of the model which does not account for CASH

phases because there are no thermodynamic data for such CASH phases.

The results of the sensitivity run to the initial composition of the exchange complex

show that: 1) Cation exchange reactions in the test containing natural FEBEX bentonite are

enhanced compared to the test of pre-treated FEBEX bentonite; 2) The concentrations of

dissolved of Mg2+ and Na+ in the test containing natural FEBEX bentonite are larger than those

of the test with pre-treated FEBEX bentonite while the concentrations of dissolved of Ca2+ and

K+ in the test with the natural FEBEX bentonite are smaller than in the test with pre-treated

bentonite; and 3) Brucite and gypsum dissolution/precipitation is slightly sensitive to the

change in the composition of the exchange complex.


55

Chapter 9. THCM models of the FEBEX mock-up

and in situ test

9.1. Introduction

FEBEX (Full-scale Engineered Barrier Experiment) is a demonstration and research

project for the engineered barrier of a high-level radioactive waste repository. FEBEX is based

on the Spanish reference concept for radioactive waste disposal in crystalline rock. The

canisters are emplaced in horizontal drifts and surrounded by a compacted bentonite clay

barrier made of a Spanish bentonite from Cortijo de Archidona which is known as FEBEX

bentonite. The project included two main large-scale tests: the FEBEX in situ full-scale test

performed at Grimsel, Switzerland, and the FEBEX mock-up test operating at the CIEMAT

facilities in Madrid, Spain (ENRESA, 2006a; 2006b). Both tests started in February 1997.

Coupled 1-D axisymmetric thermo-hydro-chemical and mechanical (THCM) models of

the FEBEX tests were developed within the FEBEX Project based on laboratory tests, online

data from the FEBEX mock-up test and on line and partial dismantling data from the FEBEX

in situ test (Zheng et al., 2011).

This chapter presents the models of the FEBEX mock-up and in situ tests. The chapter

starts with the testing of the previous 1-D THCM model of the mock-up test reported by Zheng

and Samper (2008) with the most recent water intake and relative humidity data. Then, the

models of the FEBEX in situ tests are presented, including:

The testing and updating of the previous THCM model of the FEBEX in situ test

reported by Zheng et al. (2011). The detailed account of the contributions in this task


The updated geochemical predictions of the bentonite barrier in hot and cold sections

at the dismantling of heater 2 of the in situ test in 2015. The details of this contribution


The model predictions of the tracer migration. The details of these predictions are

presented in Appendix 9.

Chapter 9. THCM models of the FEBEX mock-up and in situ tests

56

The predictions of the geochemical interactions of the bentonite with the concrete plug.

The details of these predictions can be found in Appendix 10.

9.2. Model testing with data from the FEBEX mock-up test

The mock-up test replicates at almost full-scale the Spanish reference concept for

radioactive waste disposal in granite (ENRESA, 2005). The components of the mock-up test

include: two electric heaters, a 0.64 m-thick clay barrier, instrumentation, automatic control of

heaters, and a data acquisition system. The bentonite buffer in the mock-up test is confined in

a steel structure which ensures a uniform temperature and water pressure around the external

surface of the buffer. Heating and hydration of the clay buffer started in February 1997 and

has continued uninterruptedly at the CIEMAT facilities in Madrid (Martín and Barcala, 2005;

Martín et al., 2006).

A THC model of the FEBEX mock-up test was performed within the FEBEX project

(see Zheng and Samper, 2008). This model was constructed with data from t = 0 until t = 3,000

days. In this dissertation, this model has been tested with data collected from t = 3,000 days

to t = 5,000 days. The computed cumulative water intake reproduces the measured water

intake data (Figure 9.1). Some deviations are observed at t = 5,000 days. The computed

volume is smaller than the measured volume. The computed relative humidities reproduce the

measured data at 0.22 m (Figure 9.2) until 1,500 days. However, the computed relative

humidities are smaller than the measured data after 1,500 days. Measured data at 5,000 days

are 10% larger than computed humidities at the sensors located 0.37 m from the heater (Figure

9.3). The computed relative humidities fit well the measured data at a distance of 0.55 m

(Figure 9.4). The computed relative humidities are slightly larger than the measured data at

0.70 m from the heater (Figure 9.5). In summary, the computed relative humidities reproduce

the measured data at the external sensors, but underestimate the measured data after 1,500

days at the internal sensors. A double porosity model could overcome these discrepancies.


57

Figure 9.1. Computed (line) and measured (symbols) water intake for the FEBEX mock-up test.

Figure 9.2. Computed (line) and measured (symbols) relative humidity in the sensors located at 0.22 m from the heater for the FEBEX mock-up test.

Figure 9.3. Computed (lines) and measured (symbols) relative humidity in the sensors located at 0.37 m from the heater for the FEBEX mock-up test.

0

500

1000

1500

2000

0 1000 2000 3000 4000 5000 6000

Water intake in

the m

ock‐up (L)

Time (days)

Measured water intake

Model results

0

20

40

60

80

100

0 1000 2000 3000 4000 5000 6000

Relative humudity (%

)

Time (days)

Sensor V_A3_1 Sensor V_A4_1


Sensor V_B3_1 Sensor V_B4_1

Sensor V_B6_1 Model results

0

20

40

60

80

100

0 1000 2000 3000 4000 5000 6000

Relative humidity (%

)

Time (days)





V_A4_1V_A7_1

A3

A4

A6

A7

B7

B6

B3

B4

V_A3_1V_A6_1

V_B3_1V_B6_1

V_B4_1V_B7_1

V_A4_2V_A7_2

A3

A4

A6

A7

B7

B6

B3

B4

V_A3_2V_A6_2

V_B3_2V_B6_2

V_B4_2V_B7_2


58



9.3. THCM models of the FEBEX in situ test

9.3.1. Introduction

The previous THCM model of the FEBEX in situ tests has been updated and improved

in this dissertation. The following activities were performed:

Reviewing and analysing some aspects of the previous 1-D THCM model of the FEBEX

in situ test such as: 1) Extending the 1-D axisymmetric THCM model to 2-D

axisymmetric conditions; 2) Quantifying the sensitivity of the chemical predictions to the

uncertainties in the retention curve of the bentonite, the vapor tortuosity, the dissolution

0

20

40

60

80

100

0 1000 2000 3000 4000 5000 6000

Relative humidity (%

)

Time (days)





10

30

50

70

90

110

0 1000 2000 3000 4000 5000 6000

Relative humidity (%)

Time (days)





V_A4_3V_A7_3

A3

A4

A6

A7

B7

B6

B3

B4

V_A3_3V_A6_3

V_B3_3V_B6_3

V_B4_3V_B7_3

V_A4_4V_A7_4

A3

A4

A6

A7

B7

B6

B3

B4

V_A3_4V_A6_4

V_B3_4V_B6_4

V_B4_4V_B7_4


59

of smectite, and the changes in the boundary conditions caused by the cooling and the

dismantling of the test; and 3) Studying the back diffusion of solutes from the bentonite

into the granite.

Updating the previous 1-D axisymmetric THCM model of the FEBEX in situ test by:

1) Improving the boundary condition at the heater-bentonite interface; 2) Refining the

spatial discretization of the finite element mesh; and 3) Revising the dispersivities of

the bentonite and the granite.

Comparing the updated model with on line temperature, relative humidity, water

content, and pore water pressure in the granitic rock data collected from 2002 to 2015,

with gravimetric water content data measured after the dismantling of heater 1 in 2002,

and with chemical data collected after the dismantling of heater 1.

Performing pre-dismantling THCM model predictions of the geochemical conditions for

the hot and cold sections after the dismantling of heater 2 in 2015.

Updating the predictions of the tracer migration.

Performing pre-dismantling predictions of the geochemical interactions of the bentonite

barrier with the concrete plug.

9.3.2. Testing and updating of the THCM model of the FEBEX in situ test

Several sensitivity runs were performed with the previous THCM model. The results of

the sensitivity runs show that the computed concentrations of dissolved species in a hot section

in 2002 are sensitive to an increase in the parameter α of the van Genuchten retention curve

of the bentonite. The increase in α leads to larger water evaporation rates and larger solute

concentrations near the heater. The pH and the concentration of HCO3- are not sensitive to

the change in α. The computed concentrations of most species in the cold section, however,

lack sensitivity to the change in α.

The computed concentrations are not sensitive to smectite dissolution and analcime

precipitation because the cumulative dissolution of smectite and precipitation of analcime in

2002 is very small. The computed concentrations in 2002 are not sensitive to the change in

the boundary condition of the gas during the dismantling stage. On the other hand, the

computed concentrations are sensitive to the cooling because the solubility of the minerals

and the chemical parameters depend on temperature.

The computed concentrations of dissolved Ca2+, K+, Mg2+, Na+ and Cl- near the heater

in 2002 increase when the vapor tortuosity increases. However, the concentrations away from

the heater decrease when the vapor tortuosity increases. The computed pH and the


60

concentrations of dissolved SO42- and HCO3

- are less sensitive to the changes in the vapor

tortuosity.

Solute diffusion from the bentonite into the granite is very sensitive to the effective

diffusion coefficients of the bentonite and the granite. The effective diffusion, De, in the granite

used in the previous model was too small. The computed concentrations of Cl-, SO42-, Na+ and

Ca2+ in the granite with De = 10-12 m2/s (in the granite) and De = 1.4·10-10 m2/s (in the bentonite)

are consistent with the Cl-, SO42-, Na+ and Ca2+ concentrations measured by Buil et al (2010)

in a borehole parallel to FEBEX galleries.

The 1-D axisymmetric THCM model of the FEBEX in situ test has been extended to

2-D axisymmetric conditions. The temperatures computed with the 2-D model in a hot section

are smaller than those calculated with the 1-D model. The temperatures computed with the

2-D model in a cold section are larger than those calculated with the 1-D model. The

temperatures computed with the 1-D model fit the measured data better than the temperatures

calculated with the 2-D model. The volumetric water contents computed with the 1-D model

are larger than the water contents calculated with the 2-D model at all radial distances. The

volumetric water contents computed with the 1-D model fit the measured data better than the

volumetric water contents calculated with the 2-D model. The 1-D axisymmetric model

outperforms the 2-D axisymmetric model because the model parameters used to perform the

comparison of both models are the parameters calibrated with the 1-D axisymmetric model. A

detailed calibration of the parameters of the 2-D axisymmetric model probably will lead to

model results at least as good as or better than the results of the 1-D axisymmetric model.

The concentrations of Cl- in 2002 computed with the 2-D model are large near the

heaters 1 and 2. The largest concentrations are located at the edge of heater 2. The contour

lines are approximately parallel to the axis of the gallery along heaters 1 and 2. In the edges

of the heaters, however, the contour lines are not parallel to the gallery axis. The computed

contour plots of Cl- concentrations illustrate that the edge effects extend approximately over a

distance of 0.5 to 1 m. The concentrations of Cl- in 2015 show a significant decrease compared

to the concentrations in 2002 around heater 2. Large concentrations of Cl- still remain in the

bentonite barrier between the dummy and heater 2 and between heater 2 and the end of the

gallery.

The previous 1-D axisymmetric THCM model of the FEBEX in situ test reported by

Zheng et al. (2011) has been updated by: 1) Improving the boundary condition at the heater-

bentonite interface; 2) Refining the spatial discretization of the finite element mesh; and

3) Modifying the solute dispersivities of the bentonite and the granite. The revised


61

implementation of the boundary condition leads to more water evaporation than the previous

model. The computed concentrations of Ca2+, K+, Mg2+, Cl- and Na+ near the heater with the

updated model are significantly larger than the concentrations calculated with the previous

model. The computed pH and the concentrations of SO42- and HCO3

- with the updated model

are similar to those of the previous model.

The improvement in the boundary condition at the heater-bentonite interface leads to

a significant decrease of the mass balance error. The mass balance errors in the model of the

cold section are generally smaller than 10%. The mass balance errors of the updated model

are deemed acceptable.

The computed concentrations of Ca2+, K+, Mg2+, Na+ and HCO3- become smoother

when the diffusion coefficients of the bentonite are increased by a factor of 10. The profiles of

Cl- and SO42- are less sensitive to the change in the diffusion coefficient because the diffusion

coefficients of these species are smaller than the diffusion coefficients of the rest of the

species. The computed pH is not sensitive to the change in the diffusion coefficients.

The updated 1-D axisymmetric THCM model of the FEBEX in situ test has been tested

with gravimetric water content and dry density measured data at the dismantling of heater 1 in

2002 and heater 2 in 2015 and on line temperature, relative humidity, water content and pore

water pressure in the granitic rock data collected from 2002 to 2015. The comparison of the

computed values with the measured data leads to the following conclusions:

The numerical model reproduces the main trends of the measured temperature data.

The computed temperatures near the bentonite-granite interface in hot sections are

smaller than the measured temperatures during the first 2,000 days and larger than the

measured temperatures after 2,000 days. The computed temperature in 2015 is 3ºC

larger than the measured temperature at the bentonite-granite interface.

The computed relative humidities reproduce the general trends of the measured

relative humidity data.

The computed time evolution of the water contents in a hot section reproduce the time

evolution of the measured TDR water content data, except at r = 0.59 m. The best fit of

computed values to measured data is achieved at r = 1.04 m, especially at the sensor

on the right side of the tunnel.

The computed pore water pressures at the granitic rock are smaller than the measured

values due to the heterogeneities of the granitic rock, which are not taken into account

in the model and the uncertainty in the prescribed pore water pressure at the external

boundary.


62

The predicted water contents in a hot section and a cold section at the times of

dismantling of heater 1 (in 2002) and heater 2 (in 2015) are within the band of measured

data and match the general trend of the measured data (see Figure 9.6).

The predicted dry density in a cold and hot section times of dismantling of heater 1 (in

2002) and heater 2 (in 2015) are for the most part within the band of measured data.

There are some discrepancies in the hot and cold sections in 2002. The computed dry

density overestimates the measured dry density near the heater (0.7 m < r < 1 m). This

discrepancy is not observed in 2015.

Figure 9.6. Comparison of the predicted gravimetric water content (lines) in a hot section (left) and a cold section (right) and the measured gravimetric water content data (symbols) in sections S22, S27,

S45, S49, S52, S9, S15 and S58 at the times of dismantling of heater 1 (year 2002) and heater 2 (year 2015). The plots at the bottom show the location of the sections where water contents were

measured.

9.3.3. Pre-dismantling THCM model predictions of the geochemical conditions

of the FEBEX in situ test

Pre-dismantling THCM model predictions of the geochemical conditions for the hot and

cold sections in June 2015 have been performed with the updated 1-D axisymmetric THCM

model (see the details in Appendix 8). Prediction uncertainties have been quantified by

sensitivity runs to the diffusion coefficients of the chemical species.

The predicted concentrations of Cl- in a hot section in 2015 are largest near the heater

due to the evaporation of the bentonite pore water and smallest at the granite-bentonite

interface due to the hydration of the buffer with granite pore water, which has a concentration

smaller than that of the bentonite. The predicted concentrations of Cl- in 2015 are much smaller

than the concentrations in 2002 (Figure 9.7). The predicted concentrations of dissolved cations

(Ca2+, Mg2+, Na+ and K+) in a hot section are also large near the heater (Figure 9.7). Moreover,


63

the predicted concentration of SO42- in a hot section in 2015 increases near the heater and

decreases in the rest of the bentonite barrier. The computed HCO3- near the bentonite-granite

interface in a hot section is large because the hydration of bentonite with granite water induces

the dissolution of calcite at the bentonite-granite interface. The predicted pH in the bentonite

near the heater in a hot section in 2015 is 7.5 and decreases slightly towards the granite

interface.

The predicted concentration of Cl- in a cold section in 2015 shows a diffusion profile

with low concentration in the bentonite near the granite interface and a concentration of about

0.16 mol/L in the center of the bentonite barrier (Figure 9.8). The predicted concentrations of

dissolved cations (Ca2+, Mg2+, Na+, K+ and SO42-) show diffusion profiles similar to the profile

of the concentration of Cl- (Figure 9.8). The predicted concentration of HCO3- in the bentonite

near the granite interface in 2015 is 10-2 mol/L and decreases to 10-3 mol/L at the center of the

barrier. The predicted pH in the bentonite remains stable around 7.5.

Figure 9.7. Pre-dismantling predictions of Cl- and Ca2+ concentrations (lines) in 2002 and 2015 in a hot section. The graph also shows the inferred Cl- concentrations in sections 19 and 29 in 2002

(symbols).

Figure 9.8. Pre-dismantling predictions of Cl- and Ca2+concentrations (lines) in 2002 and 2015 in a cold section. The graph also shows the inferred Cl- concentrations in section 12 in 2002 (symbols).


64

The predicted concentrations in the hot sections are very sensitive to an increase of

the diffusion coefficients by a factor of 10. In general, the profiles of the concentrations of most

of the chemical species become smoother when the diffusion coefficient is increased. The

concentrations decrease near the heater and increase in the rest of the bentonite barrier. The

concentration of dissolved Ca2+ increases everywhere in the bentonite because calcite

dissolution near the heater is enhanced when the diffusion coefficients of the bentonite are

multiplied by 10. Such increase in the concentration is Ca2+ is accompanied by a decrease in

the concentration of dissolved HCO3-.

The predicted radial profiles of the concentrations of Ca2+, K+, Mg2+, Na+ and HCO3- in

the cold sections become smoother when the diffusion coefficients are increased. The profiles

of Cl- and SO42- are also sensitive to the change in the diffusion coefficients. Their sensitivity,

however, is much smaller than the sensitivity of other species because the diffusion

coefficients of Cl- and SO42- are much smaller than the diffusion coefficients of the rest of the

species. The predicted pH is slightly sensitive to the change in the diffusion coefficients.

9.3.4. Predictions of the tracers migration in the FEBEX in situ test

Updated predictions of the tracer migration have been performed for: 1) Iodide along

several radii in sections 37, 50 and 51 (hot sections) by using a 1-D axisymmetric model; 2)

Borate, europium, perrhenate and selenate at the inner blocks of section 46 (hot sections) by

using 2-D models in vertical planes; and 3) Caesium and borate at the outer blocks of section

48 (hot sections) by using 2-D models in vertical planes. The details of the tracer predictions


The predictions of the migration of the tracers have been computed with the updated

version of the THCM model of the FEBEX in situ test. The predictions of tracer migration lead

to the following conclusions:

Large iodide concentrations are predicted near the heater 2. The iodide concentration

in section 37 near the heater 1 decreased after the heater was switched off in 2002 due

to the increase in water content caused by vapor condensation and bentonite hydration.

The predicted perrhenate concentrations in 2015 show that this tracer has diffused

entirely in the full section.

The plumes of the point tracers located in the inner blocks are (Figure 9.9):

o Almost circular with an approximate diameter of 8 cm for borate.

o Semicircular with an approximate diameter of 20 cm for selenite.

o Slightly anisotropic with an approximate length of 8 cm for europium.


65

The plumes of the point tracers located in the outer blocks are (Figure 9.9):

o Almost circular with an approximate diameter of 7 cm for cesium.

o Almost circular with a diameter of 10 cm for borate.

The comparison of the predicted tracer concentrations with the measured values will

provide the basis for the testing and partial validation of the current THCM models for

compacted bentonites.

Figure 9.9. Computed concentrations of dissolved borate (top left), selenate (top right), europium (bottom left) and cesium (bottom right) (mol/L) at 18 years with the 2-D numerical model in a vertical

plane normal to the axis of the gallery.

9.3.5. Predictions of the interactions of the bentonite with the concrete plug of

the FEBEX in situ test

The geochemical interactions of the bentonite and the concrete plug have been

modelled with a 1-D non-isothermal variably-saturated water flow and multicomponent reactive

transport model along a horizontal line normal to the interface at a radial distance of 0.75 m

from the axis of the gallery. The computed temperature in the bentonite in 2015 ranges from

24 ºC in the concrete to 34 ºC in the bentonite. These temperatures compare well with the

temperatures measured along a borehole drilled through the concrete plug before switching

off the heater 2.

0 - 0.0005

0.0005 - 0.0008

0.0008 - 0.0011

0.0011 - 0.0014

0.0014 - 0.0017

0.0017 - 0.002

0.002 - 0.0023

0.0023 - 0.0026

0.0026 - 0.0029

0.0029 - 0.0032

0 - 0.001

0.001 - 0.007

0.007 - 0.013

0.013 - 0.019

0.019 - 0.025

0.025 - 0.031

0.031 - 0.037

0.037 - 0.043

0.043 - 0.049

0.049 - 0.055

0 - 0.0005

0.0005 - 0.0013

0.0013 - 0.0022

0.0022 - 0.003

0.003 - 0.0039

0.0039 - 0.0047

0.0047 - 0.0056

0.0056 - 0.0064

0.0064 - 0.0073

0.0073 - 0.008

0 - 0.00001

0.00001 - 0.00005

0.00005 - 0.00009

0.00009 - 0.00013

0.00013 - 0.00017

0.00017 - 0.00021

0.00021 - 0.00025

0.00025 - 0.00029

0.00029 - 0.00033

0.00033 - 0.00037

B Se

CsEu


66

Model predictions show that calcite dissolves in the bentonite and precipitates near the

bentonite-concrete interface. The precipitation front propagates into the bentonite. Portlandite

dissolves in the concrete interface. Ettringite precipitation is very small and nonuniform. The

precipitation of this mineral phase is transient. It redissolves and is present in 2015 only in

small amounts. Neither gypsum nor anhydrite precipitate. CSH1.8 dissolves in the concrete

near the concrete-bentonite interface while CSH0.8 precipitation in the concrete is extremely

small. Brucite precipitates in the bentonite near the interface. The front of brucite precipitation

moves from the bentonite-concrete interface into the bentonite. Sepiolite shows a similar

precipitation front. The model does not predict the precipitation of the Friedel salt. The porosity

decreases slightly in the bentonite near the concrete-bentonite interface due to the

precipitation of brucite, calcite and sepiolite. The porosity in the concrete, on the other hand,

increases near the interface due mostly to the dissolution of portlandite. The changes in

porosity only affect 2 cm in the bentonite and concrete interface in both sides of the interface

(Figure 9.10b). The pH increases slightly in the concrete. The high pH front after 13 years

penetrates a few cm into the bentonite (Figure 9.10a).

a) b)

Figure 9.10. Predicted pH (left) and changes in porosity caused by dissolution/precipitation reactions (right) in the bentonite and the concrete at selected times.

9.4. Conclusions

The THC model of the FEBEX mock-up test was tested with data collected from

t = 3,000 days to t = 5,000 days. The computed water intake and the relative humidities at the

external sensors reproduce the measured data. However, the computed relative humidity

underestimates the measured data at the internal sensors after 1,500 days.

The previous 1-D axisymmetric model of the FEBEX in situ test has been extended to

2-D axisymmetric conditions. In general, the 1-D model results fit the temperature and water


67

content measured data better than the 2-D model. A detailed calibration of the parameters of

the 2-D axisymmetric model will lead to model results at least as good as or better than the

results of the 1-D axisymmetric model. The contour lines of the Cl- concentration are

approximately parallel to the axis of the gallery along heaters 1 and 2, but the edge effects

extend approximately over a distance of 0.5 to 1 m.

The previous 1-D THCM model of the FEBEX in situ test has been updated by

improving the boundary conditions, refining the mesh at the heater-bentonite interface and

updating the solute dispersivities in the bentonite and granite. These improvements on the

THCM 1-D model lead to an increase in the water evaporation near the heater and larger

concentrations near the heater.

The updated 1-D axisymmetric model has been used to compare the model results with

the thermal and hydraulic data from 2002 to 2015 and to perform the pre-dismantling

geochemical predictions at 2015. The numerical results reproduce the main trends of the

temperature, relative humidity, water content and dry density. The predicted concentrations in

the hot sections show large concentrations near the heater and small concentrations at the

bentonite-granite interface. The predicted concentrations in a hot section in 2015 are smaller

than those computed in 2002. The predicted concentrations in a cold section in 2015 show a

diffusion front.

Updated predictions of the tracer migration have been performed with the most updated








The plume of borate in the inner blocks is almost circular with a diameter of 8 cm, the

plume of selenite is semicircular with an approximate diameter of 20 cm and the plume

of europium is anisotropic with an approximate length of 8 cm.

The plume of cesium in the outer blocks is almost circular with an approximate diameter

of 7 cm and is almost circular with a diameter of 10 cm for borate.

A detailed 1-D non-isothermal variably-saturated water flow and multicomponent

reactive transport model normal to the bentonite-concrete interface has been performed to

study the geochemical interactions of the bentonite and the concrete plug. Model predictions


68

show that calcite dissolves in the bentonite and precipitates near the bentonite-concrete

interface. The precipitation front propagates into the bentonite. Portlandite dissolves in the

concrete interface. Ettringite precipitation is very small and nonuniform. Neither gypsum nor

anhydrite precipitate. CSH1.8 dissolves in the concrete near the concrete-bentonite interface

while CSH0.8 precipitation in the concrete is extremely small. Brucite precipitates in the

bentonite near the interface. The front of brucite precipitation moves from the bentonite-

concrete interface into the bentonite. Sepiolite shows a similar precipitation front. The porosity




porosity only affect 2 cm in the bentonite and concrete interface in both sides of the interface.

The pH increases slightly in the concrete. The high pH front after 13 years penetrates a few

cm into the bentonite.


69

Chapter 10. Reactive transport modelling of the long-term

interactions of corrosion products and compacted

bentonite in a HLW repository in granite

10.1. Introduction

Carbon steel and compacted bentonite have been proposed as candidate materials for

the overpack and buffer, respectively, in the multi-barrier system of deep geological

repositories for high-level radioactive waste (HLW). The corrosion of the carbon steel may

induce buffer alterations which could result in changes in parameters such as porosity,

permeability, sorption and swelling. The prediction of the long-term evolution of the engineered

barrier in a repository should not be a blind extension of the models developed for experiments

to different space and time scales. It requires a careful assessment of the key long-term

processes and their couplings as well as an evaluation of the resulting uncertainty and its

consequences. Contrary to thermal, hydrodynamic and mechanical transient processes which

will last for several hundreds to 1,000 years, the geochemical reactions induced by canister

corrosion will take place at all temporal scales.

This chapter presents a non-isothermal reactive transport model for the long-term

(1 Ma) interactions of the corrosion products and compacted bentonite in a HLW repository in

granite. The details can be found in Appendix 11.

10.2. Conceptual and numerical model

The geometry of the model corresponds with the Spanish reference concept of a high-

level radioactive waste repository in granite (ENRESA, 2000). It consists on the disposal of

spent fuel elements in cylindrical carbon steel canisters placed in horizontal disposal drifts.

The disposal drifts, having 500 m in length and 2.4 m in diameter, are located at a depth of

500 m in a granite formation. The canisters are 4.54 m long, 0.10 m thick and have an external

diameter of 0.90 m. They are surrounded by blocks of compacted bentonite.

Chapter 10. Long-term model of a HLW repository in granite

70

A 1-D axisymmetric numerical model of the canister and the bentonite has been used

to simulate the long-term interactions of the corrosion products and the bentonite (Figure 10.1).

Water flow and solute transport through the granite was simulated with a constant water flux

of 0.1 L/y parallel to the axis of the gallery at the bentonite-granite interface. A constant

corrosion rate of 2 μm/year was assumed in the reference run.

Figure 10.1. Scheme of the engineered barrier system and 1-D finite element grid of the axisymmetric model (Samper et al., 2016).

10.3. Model results

Canister corrosion causes an increase in the pH and the concentration of dissolved

Fe2+ of the bentonite porewater. Iron precipitates as magnetite and siderite and sorbs via cation

exchange and surface complexation on weak sites. The largest pH in the bentonite is almost

9.5 at 2·105 years. Several fronts are observed in the concentration of dissolved Fe2+, pH and

Eh which are related to sorption fronts. Magnetite is the main corrosion product and its

precipitation reduces significantly the porosity of the bentonite barrier near the canister and

could even clog the pores (Figure 10.2). The thickness of the bentonite zone affected by the

decrease of porosity increases with time and is equal to 7 cm at t = 1 Ma.


71

Figure 10.2. Radial distribution of the computed bentonite porosity which changes due to mineral

dissolution/precipitation at selected times (Samper et al., 2016).


A detailed sensitivity analysis has been performed to changes in model parameters and

conceptual model assumptions. The larger the corrosion rate, the larger the magnetite and

siderite concentration near the canister-bentonite interface but the smaller their penetration

into the bentonite. Therefore, the larger the corrosion rate, the faster the porosity reduction

near the canister but the smaller the thickness of affected bentonite. This thickness ranges

from < 5 cm for a corrosion rate of 5 μm/year to nearly 12 cm for 0.5 μm/year. The larger the

effective diffusion, De, the larger the thickness of the bentonite where magnetite, siderite and

calcite precipitate and the thicker the bentonite affected by pore clogging. This thickness varies

from 4 to 10 cm in the considered range of the De. The bentonite thickness affected by the

porosity reduction decreases when the ground water flow through the granite, Q, increases.

Such thickness decreases from 7 cm to 3 cm when Q increases by a factor of 10. The changes

in the bentonite cation exchange selectivities do not affect the computed pH, Eh and the

concentrations of other dissolved and precipitated species. The computed magnetite

concentration near the canister-bentonite interface is sensitive to changes in the initial

chemical composition of the bentonite porewater. The thickness of altered bentonite is doubled

when the dependence of the corrosion rate on the chemical conditions is considered. The

thermal transient and the effect of temperature on the corrosion rate do not have a very

significant influence on the geochemical evolution of the bentonite barrier. The thickness of

altered bentonite decreases when kinetic magnetite precipitation is considered. Such thickness

decreases 3 cm when smectite dissolution and analcime precipitation are taken into account.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

4.5 4.75 5 5.25 5.5 5.75 6

Porosity

r (dm)

102y

104 y

106 y

Chapter 10. Long-term model of a HLW repository in granite

72

However, it is similar to that of the reference run when cronstedtite is considered besides

smectite dissolution and analcime precipitation.

10.5. Conclusions

A non-isothermal reactive transport model of the long-term interactions of the corrosion

products and compacted bentonite in a HLW repository in granite has been presented.


Fe2+ of the bentonite pore water. The largest pH in the bentonite is almost 9.5 at 2·105 years.

Magnetite is the main corrosion product and its precipitation reduces significantly the porosity

of the bentonite barrier near the canister and could even clog the pores. The thickness of the

bentonite affected by the decrease of porosity increases with time and is equal to 7 cm at

t = 1 Ma. This thickness is doubled when the dependence of the corrosion rate on the chemical

conditions is considered and reduces 3 cm when smectite dissolution and analcime

precipitation are taken into account. Model results are not sensitive to the thermal transient

and the effect of temperature on the corrosion rate.

The conclusions of the simulations are consistent for the most part with those reported

by others for bentonite barriers. However, there are differences in the geochemical systems

and the hypotheses used by Savage et al. (2010a).


73

Chapter 11. Long-term non-isothermal reactive transport

model of compacted bentonite, concrete and corrosion

products in a HLW repository in clay

11.1. Introduction

Carbon steel and compacted bentonite have been proposed as candidate materials for

the overpack and buffer, respectively, in the multi-barrier system of deep geological

repositories for high-level radioactive waste (HLW). A concrete liner is required in tunnels

excavated in clay host rock. The addition of a concrete liner takes place as a support layer in

clay formations. Concrete and cement are used for mechanical support in shotcrete, tunnel

seals and plugs.

The corrosion of the carbon steel and the concrete degradation may induce bentonite

alterations which could result in changes in parameters such as porosity, permeability, sorption

and swelling. The interaction of cementitious materials with the clay host rock produces a

hyper-alkaline fluid (10 < pH < 13.5) which can interact with the initially unsaturated bentonite

surrounding the carbon steel canister (Yang et al., 2008). The physical and chemical properties

of the bentonite and the clay host rock could be affected by this hyper-alkaline fluid. This

interaction could produce high pH in the bentonite and in the clay, cause mineral dissolution

and precipitation of secondary minerals, and reduce the porosities of the bentonite buffer and

the host rock.

This chapter presents a non-isothermal reactive transport model to quantify the long-

term interactions of the corrosion products, concrete degradation, clay and bentonite in a HLW

repository in clay. The details of the model can be found in Appendix 12.

Chapter 11. Long-term model of a HLW repository in clay

74

11.2. Conceptual and numerical model

The model corresponds to a radioactive waste repository in clay according to the

Spanish Reference Concept (ENRESA, 2004). Cylindrical carbon steel canisters with 0.9 m

diameter are emplaced in horizontal galleries and embedded into a 0.75 m thick bentonite

buffer. A 0.3 m thick concrete sustainment is located between the bentonite buffer and the clay

formation.

The non-isothermal multicomponent reactive transport model aims at studying the long-

term geochemical interactions of compacted bentonite with the concrete liner and the corrosion

products in a HLW repository in a clay formation for 1 Ma. This non-isothermal reactive

transport extends the scope of the model of Yang et al. (2008) by accounting simultaneously

for canister corrosion and concrete degradation and incorporating additionally: 1) Surface

complexation on three types of sorption sites; 2) Iron sorption by surface complexation;

3) Kinetic smectite dissolution; and 4) Precipitation of secondary clay minerals.

A 1-D axisymmetric numerical model has been used to simulate the long-term

geochemical interactions of compacted bentonite with concrete and corrosion products in a

HLW repository in a clay formation with a total length of 25 m (Figure 11.1). The model

accounts for the canister, the bentonite, the concrete and the clay host rock. A constant

corrosion rate of 2 μm/year was assumed.

Figure 11.1. 1-D finite element grid which accounts for the canister, the bentonite barrier, the concrete liner and the clay formation (Mon et al., 2017).


75

11.3. Model results

Model results show that magnetite is the main corrosion similar to the model results of

the long-term model in granite (see Appendix 11). Its precipitation reduces the bentonite

porosity near the canister. Concrete degradation leads to the precipitation of secondary

minerals and the reduction of the porosity of the bentonite and the clay formation at their

interfaces with the concrete liner. The decrease of the porosities is especially important for

t > 104 years. The zones affected by pore clogging at the canister-bentonite, and concrete-clay

interfaces at 1 Ma are equal to 1, and 3.3 cm thick, respectively (see Figure 11.2). The pH in

the bentonite after 1 Ma is uniform and equal to 9.42. At that time, the hyperalkaline front

(pH > 8.5) migrates 2.5 cm into the clay formation.

Figure 11.2. Radial distribution of the computed porosity which changes due to mineral dissolution/precipitation at selected times.


Sensitivity runs were performed to analyse the uncertainties in cation exchange

selectivities and evaluate the relevance of surface complexation reactions, kinetic smectite

dissolution, and Mg-saponite precipitation. Only the concentrations of the exchanged Ca2+,

Mg2+, Na+ and K+ are sensitive to changes in the selectivity coefficients. The computed pH at

t = 1 Ma in the sensitivity run without surface complexation reactions is the same as that of the

base run.

Accounting for smectite dissolution leads to: 1) Slight changes in the computed pH in

the bentonite at t = 1 Ma; 2) A reduction in the breakthrough of the pH front into the clay

formation from 35 to 15 cm; 3) An increase in brucite precipitation in the bentonite near the

Chapter 11. Long-term model of a HLW repository in clay

76

concrete interface and in the concrete; and 4) A decrease of gypsum precipitation. The run

with Mg-saponite precipitation in the bentonite leads to slightly larger pH, slightly smaller

magnetite precipitation and smaller smectite dissolution at t = 1 Ma.

11.5. Conclusions

A non-isothermal reactive transport model of the interactions of the compacted

bentonite with the corrosion products of a carbon-steel canister and the concrete liner in a

HLW in clay has been presented

Canister corrosion and concrete degradation cause an increase in the pH. The largest

pH in the bentonite is 9.4 at 106 years. Magnetite is the main corrosion product and its


could even clog the pores. In addition, the concrete degradation in the repository in clay leads

to the precipitation of secondary minerals and the reduction of the porosity of the bentonite

and the clay formation at their interfaces with the concrete liner. The decrease of the porosity

is especially important for t > 104 years. The thickness of the zones affected by pore clogging

at the canister-bentonite, and concrete-clay interfaces at 1Ma are equal to 1, and 3.3 cm,

respectively.

The results show similarities with the results of the models reported by others for

engineered barrier systems at similar chemical conditions, including: 1) Pore clogging at the

canister-bentonite and concrete-clay interfaces; 2) Narrow alteration zones; and 3) Limited

smectite dissolution after 1 Ma.


77

Chapter 12. Conclusions and future work

12.1. Improvements in the THCM model and the THCM code

The numerical simulations performed in this dissertation have been performed with the

coupled THCM code INVERSE-FADES-CORE. The code has been updated and reviewed to

debug programming errors, improve the input and output files and facilitate its use.

Reactive gas transport has been implemented in INVERSE-FADES-CORE V2 by

including additional mass balance equations for the reactive gaseous species in the gaseous

phase. The implementation of the reactive gas transport has been verified by comparing the

numerical results of INVERSE-FADES-CORE V2 with the results computed with

TOUGHREACT (Xu et al., 2008) with four test cases.

In addition, INVERSE-FADES-CORE V2 has been benchmarked with other codes for

the following two benchmarking problems: 1) Modeling the chemical interactions of the

concrete liner with the compacted bentonite of the engineered barrier and the host clay rock;

and 2) Modelling the carbonation of concrete in unsaturated conditions during the operational

period of a repository.

12.2. Integrated analysis of thermal, hydrodynamic and

chemical data of compacted FEBEX bentonite

Green-Ampt analytical solutions have been derived and used to compare radial and

parallel flow through the bentonite. The comparison shows that the analytical solutions are

markedly different. Such analysis shows that the best fit to compare radial and parallel flow is

obtained by optimizing the parameters, especially the volume and the hydration surface. This

should be taken into account when translating the results obtained in the tests, where the

conditions are parallel, to radial flow conditions.

The integrated analysis of the cumulative water intake data shows an overall

consistency. The largest differences occur at early times due to the differences in the


78

experimental conditions, which decrease with time. Hydration data from most of the tests

converge for dimensionless time larger than 0.04.

Water content data of the mock-up test are larger than those of the CT cells. The slope

of the water content data are similar for the CG cell, and the in situ and mock-up tests for

dimensionless times larger than 0.04.

The slope of the dimensionless temperature is about 0.8 in most of the tests. The

integrated analysis of Cl- shows that the general behavior is similar in most tests, except for

the CT23 cell data. The pH data are consistent except for the CT cell.

The general THCM processes in the CT and CG cells, the mock-up and the in situ tests

are similar. The general behavior of the cumulative water intake, water content, temperature

and chemical concentration data are also similar in these tests. However, some differences

have been found in the integrated analysis of the data which are caused by differences in the

size, geometry and initial and boundary conditions in the tests.

The integrated analysis of measured THC data has shown that the data with different

space-time scales from lab cell and column tests and the mock-up and in situ tests cannot be

scaled up. The conclusions obtained from this integrated analysis are similar to those reported

by Villar el at. (2012).

The dimensional analysis of hydrodynamic, thermal and chemical data assume that the

density, the porosity and the hydraulic conductivity of the bentonite are constant. However,

these parameters change during the tests (Villar et al., 2008b). The integrated analysis could

be improved by: 1) Extending the Green-Ampt solution to account for water distribution,

2) Developing analytical solutions for temperature and concentration, and 3) Performing the

integrated analysis of chemical data for reactive species.

The dimensional analysis has been useful to identify the role of experimental

conditions, but it failed to provide a framework to integrate all the experimental data. Such

integration is most likely to be achieved by means of coupled THCM numerical models.

Coupled THCM numerical models constructed with data from lab tests and the mock-up and

the in situ tests can be used for long-term predictions.


79

12.3. Coupled THCM models of laboratory test

A coupled THCM model of the heating and hydration tests performed on 60 cm long

cells has been presented. The model has been performed in two stages. Model results in the

testing stage were compared to measured data. The comparison of the model results and the

measured data shows the following discrepancies: 1) The computed porosity is smaller than

the measured data; 2) The computed water content and saturation degree are larger than the

measured data near the heater; 3) The computed temperatures are larger than the measured

data in the sensors; 4) The computed water intake overestimates the measurements; 5) The

computed concentrations for the CG7.6 test are smaller than the concentrations of the

geochemical model of Fernández and Villar (2010); and 6) The concentration of the exchanged

Ca2+ and Mg2+ do not fit the data. The following improvements were performed in the calibration

stage: 1) Adjusting the vapor tortuosity; 2) Considering lateral heat dissipation at the sensors;

3) Adjusting the selectivity coefficients; and 4) Updating the material properties at the boundary

elements. The revised THCM model reproduces the observed temperatures, saturation

degrees, porosities. Moreover, model results fit the measured concentrations of the Cl- and

measured exchanged cations data for the CG0.5, CG1, CG2 tests. The computed

concentrations of Cl-, Na+, Ca2+, Mg2+, K+, HCO3-, SO4

2- and pH reproduce the general trends

of the results reported by Fernández and Villar (2010) for the CG7.6 test.

The corrosion tests carried out by CIEMAT have been modelled with coupled THCM

models. The corrosion experiments include: 1) The small corrosion cells with a length of 25

mm and a duration of 180 days; and 2) The medium-size corrosion cells (10 cm long) with a

duration of 1593 days. The thermo-hydrodynamic model results fit the general trends of the

measured data in the bentonite in both corrosion tests. There are some discrepancies in the

computed time evolution of the temperature and relative humidity of the medium-size cells

which could be attributed to problems in the water injection system during the tests and vapor

leakage through the sensors.

The model results for the small corrosion cells indicate that: 1) Magnetite and

Fe(OH)2(s) are the main corrosion products which compete for Fe2+ precipitation; 2) The

corrosion products penetrate a few mm into the bentonite; 3) The numerical results fit the

measured iron weight data; 4) Fe2+ sorbes by surface complexation; and 5) Fe2+ exchange is

less relevant than Fe2+ sorption by surface complexation. Model results of the medium-size

cells show that magnetite precipitates in the Fe powder. The experimental observations

indicate that there is no magnetite penetration in the bentonite. Some magnetite precipitation

was observed at the interface, which is consistent with the small amount of magnetite


80

precipitation computed at the interface. The precipitation of magnetite at chemical equilibrium

is larger than that computed with a kinetically-controlled precipitation. Fe(OH)2(s) does not

precipitate when magnetite precipitates at equilibrium and when the corrosion rate is

decreased.

A coupled THCM model of the bentonite and the concrete test in the HB4 cell has been

performed. The model reproduces the measured the temperature, the relative humidity, the

water content and the porosity data. However, the model overestimates the relative humidity

measured at the sensor near the heater. Model results show that advection is relevant during

the first months of the test. Then, solute diffusion is the main transport process. The main

mineralogical alterations are predicted to occur at the hydration boundary, the concrete near

the bentonite interface, and the bentonite near the concrete interface. Calcite and Mg phases

precipitate at the hydration boundary due to the large concentrations of bicarbonate and

magnesium in the hydration water. The largest amount of calcite and brucite precipitation take

place at the bentonite and concrete near the interface. Sepiolite also precipitates in the

concrete near the bentonite interface. The model predicts the dissolution of portlandite in the

concrete and CSH1.8 and a small C0.8SH precipitation. Ettringite precipitates in the concrete

near the hydration boundary and dissolves in the rest of the concrete. The porosity changes

due to mineral precipitation/dissolution, especially at the hydration boundary and in the

bentonite and concrete near the interface. The porosity reduces 51% in the concrete at the

bentonite interface when brucite precipitate. The pH front (pH > 8.5) diffuses into the bentonite

1 cm at the end of the test. Model results capture the main trends of the mineralogical

observations. The model, however, does not reproduce ettringite and CSH precipitation. The

predicted precipitation for these phases is smaller than the observed values.

A coupled THCM model of the mortar-bentonite interactions of the double interface

tests has been presented. The model reproduce the measured water intake, water content and

the dry density at the end of the test. The mode predicts the portlandite dissolution in the mortar

and calcite, brucite, CSH1.2 and CSH1.6 precipitation in the mortar and in the bentonite near

the interface. Anhydrite precipitates in the mortar, but it is transformed into gypsum after the

cooling phase. The model predicts a small precipitation of ettringite and quartz and no

cristobalite dissolution. The porosity decreasing is maximum (1.5%) in the bentonite in a 0.2

mm thick zone near the mortar interface due to calcite and brucite precipitation. The pH front

(pH>8) penetrates into bentonite 10 mm at the end of the test. For the most part, the numerical

model captures the main trends of the observed mineral dissolution/precipitation patterns.

However, there are some discrepancies, especially for ettringite precipitation in the mortar

which is not computed with the model, and brucite precipitation in the bentonite which was not


81

observed in the laboratory. Some of these discrepancies could be due to the limitations of the

model which does not account for CASH phases because there are no thermodynamic data

for such CASH phases. The results of the sensitivity run to the initial composition of the

exchange complex show that: 1) Cation exchange reactions in the test containing natural

FEBEX bentonite are enhanced compared to the test of pre-treated FEBEX bentonite; 2) The

concentrations of dissolved of Mg2+ and Na+ in the test containing natural FEBEX bentonite

are larger than those of the test with pre-treated FEBEX bentonite while the concentrations of

dissolved of Ca2+ and K+ in the test with the natural FEBEX bentonite are smaller than in the

test with pre-treated bentonite; and 3) Brucite and gypsum dissolution/precipitation is slightly

sensitive to the change in the composition of the exchange complex.

12.4. THCM models the FEBEX mock-up and in situ tests

The THC model of the FEBEX mock-up test was tested with data collected from

t = 3,000 days to t = 5,000 days. The computed water intake and the relative humidities at the

external sensors reproduce the measured data. However, the computed relative humidity

underestimates the measured data at the internal sensors after 1,500 days.

The previous 1-D axisymmetric model of the FEBEX in situ test has been extended to

2-D axisymmetric conditions. In general, the 1-D model results fit the temperature and water

content measured data better than the 2-D model. A detailed calibration of the parameters of

the 2-D axisymmetric model will lead to model results at least as good as or better than the

results of the 1-D axisymmetric model. The contour lines of the Cl- concentration are

approximately parallel to the axis of the gallery along heaters 1 and 2, but the edge effects

extend approximately over a distance of 0.5 to 1 m.

The previous 1-D THCM model of the FEBEX in situ test has been updated by

improving the boundary conditions, refining the mesh at the heater-bentonite interface and

updating the solute dispersivities in the bentonite and granite. These improvements on the

THCM 1-D model lead to an increase in the water evaporation near the heater and larger

concentrations near the heater.

The updated 1-D axisymmetric model has been used to compare the model results with

the thermal and hydraulic data from 2002 to 2015 and to perform the pre-dismantling

geochemical predictions at 2015. The numerical results reproduce the main trends of the

temperature, relative humidity, water content and dry density. The predicted concentrations in

the hot sections show large concentrations near the heater and small concentrations at the


82

bentonite-granite interface. The predicted concentrations in a hot section in 2015 are smaller

than those computed in 2002. The predicted concentrations in a cold section in 2015 show a

diffusion front.

Updated predictions of the tracer migration have been performed with the most updated








The plume of borate in the inner blocks is almost circular with a diameter of 8 cm, the

plume of selenite is semicircular with an approximate diameter of 20 cm and the plume

of europium is anisotropic with an approximate length of 8 cm.

The plume of cesium in the outer blocks is almost circular with an approximate diameter

of 7 cm and is almost circular with a diameter of 10 cm for borate.

A detailed 1-D non-isothermal variably-saturated water flow and multicomponent

reactive transport model normal to the bentonite-concrete interface has been performed to

study the geochemical interactions of the bentonite and the concrete plug. Model predictions

show that calcite dissolves in the bentonite and precipitates near the bentonite-concrete

interface. The precipitation front propagates into the bentonite. Portlandite dissolves in the

concrete interface. Ettringite precipitation is very small and nonuniform. Neither gypsum nor

anhydrite precipitate. CSH1.8 dissolves in the concrete near the concrete-bentonite interface

while CSH0.8 precipitation in the concrete is extremely small. Brucite precipitates in the

bentonite near the interface. The front of brucite precipitation moves from the bentonite-

concrete interface into the bentonite. Sepiolite shows a similar precipitation front. The porosity




porosity only affect 2 cm in the bentonite and concrete interface in both sides of the interface.

The pH increases slightly in the concrete. The high pH front penetrates a few cm into the

bentonite after 13 years.


83

12.5. Long-term reactive transport models of the geochemical

interactions of the compacted bentonite with concrete and corrosion

products in HLW repositories

Reactive transport models of the interactions of the bentonite with other components

of the engineered and geological barriers have been performed for HLW repositories in granite

and clay.

12.5.1. Reactive transport modelling of the long-term interactions of corrosion

products and compacted bentonite in a HLW repository in granite


Fe2+ of the bentonite pore water. The largest pH in the bentonite is almost 9.5 at 2·105 years.

Magnetite is the main corrosion product and its precipitation reduces significantly the porosity

of the bentonite barrier near the canister and could even clog the pores. The thickness of the

bentonite affected by the decrease of porosity increases with time and is equal to 7 cm at

t = 1 Ma. This thickness is doubled when the dependence of the corrosion rate on the chemical

conditions is considered and reduces 3 cm when smectite dissolution and analcime

precipitation are taken into account. Model results are not sensitive to the thermal transient

and the effect of temperature on the corrosion rate. The conclusions of the simulations are

consistent for the most part with those reported by others for bentonite barriers. However, there

are differences in the geochemical systems and the hypotheses used by Savage et al. (2010a).

12.5.2. Long-term non-isothermal reactive transport model of compacted

bentonite, concrete and corrosion products in a HLW repository in clay

Canister corrosion and concrete degradation cause an increase in the pH. The largest

pH in the bentonite is 9.4 at 106 years. Magnetite is the main corrosion product and its


could even clog the pores. In addition, the concrete degradation in the repository in clay leads

to the precipitation of secondary minerals and the reduction of the porosity of the bentonite

and the clay formation at their interfaces with the concrete liner. The decrease of the porosity

is especially important for t > 104 years. The thickness of the zones affected by pore clogging

at the canister-bentonite, and concrete-clay interfaces at 1Ma are equal to 1, and 3.3 cm,

respectively. The results show similarities with the results of the models reported by others for

engineered barrier systems at similar chemical conditions, including: 1) Pore clogging at the


84

canister-bentonite and concrete-clay interfaces; 2) Narrow alteration zones; and 3) Limited

smectite dissolution after 1 Ma.

12.6. Recommendation for future work

Future studies to improve the integrated analysis include:

Extending the Green-Ampt solution to account for water distribution.

Developing analytical solutions for temperature and concentration.

Performing the integrated analysis of chemical data for reactive species.

The THCM models of the laboratory tests could be improved by:

Calibrating the THCM model with hydrochemical data. This will require the numerical

inverse analysis of the aqueous extract data.

Taking into account the CO2(g) degassing The implementation in INVERSE-FADES-

CORE V2 of the gas reactive transport equation could be tested with the THCM

model of the CG tests.

Performing a detailed analysis of the discretization errors by refining the finite

element mesh in areas with large concentration gradients to reduce the mass

balance errors.

Evaluating the sensitivity of the model results to kinetic parameters.

Improving the THCM model of the interactions of mortar and bentonite by account

for Cl- sorption in the mortar.

The THCM models of the FEBEX in situ test could be improved by:

Calibrating the model parameters and boundary conditions of 2-D axisymmetric

model such as the thermal conductivity, the hydraulic conductivity, the retention

curve, the vapor tortuosity and the longitudinal dispersivity of the bentonite and the

thermal and hydraulic boundary conditions in the granitic rock.

Accounting for the inner-block solute diffusion during the time elapsed since block

extraction and water sampling for chemical analyses.

Modelling Cs sorption with a reactive transport model.

Testing the model results of the interactions of bentonite and the concrete plug with

the measured data which have been published just after completing this dissertation

(Alonso et al., 2017 and Fernández et al, 2017).


85

Model predictions of the long-term geochemical evolution of the bentonite barrier could

be improved by:

Considering adsorbed, interlayer and free water.

Allowing for different effective diffusion coefficients for each chemical species.

Allowing for the canister void space to have properties other than those of the

bentonite and simulating canister corrosion in a more realistic manner by adopting

a dynamic corrosion front.

Taking into account kinetic magnetite precipitation.

Accounting for other secondary minerals such as Fe-phylosilicates, Fe-rich

smectites and zeolites.

Accounting for the feedback on porosity and other transport and chemical

parameters caused by mineral dissolution/precipitation and allowing for the dynamic

update of the reactive surface areas of the minerals.


87

Chapter 13. References

Alonso, M.C., García, J. L., Cuevas, J., Turrero, M.J., Fernández, R., Torres, E., Ruiz, A.I.,

2017. Interaction processes at the concrete-bentonite interface after 13 years of FEBEX-

Plug operation. Part I: Concrete alteration, Physics and Chemistry of the Earth, Parts A/B/C

(In Press)

Bauer, A. and Berger, G., 1998. Kaolinite and smectite dissolution rate in high molar KOH

solutions at 35° and 80 °C. Appl. Geochem. 13, 905–916.

Berner, U., Kulik, D. A. and Kosakowski, G., 2013. Geochemical impact of a low-pH cement

liner on the near field of a repository for spent fuel and high-level radioactive waste. Physics

and Chemistry of the Earth 64, 46-56.

Bildstein, O., Trotignon, L., Perronnet, M. and Jullien, M., 2006. Modelling iron-clay interac-

tions in deep geological disposal. Phys. Chem. Earth 31, 618–625.

Bradbury, M.H. and Baeyens, B., 1997. A mechanistic description of Ni and Zn sorption on Na-

montmorillonite. Part II: modelling. J. Contam. Hydrol. 27, 223–248.

Buil, B, Gómez, P., Peña J., Garralón, A., Turrero, M.J., Escribano, A., Sánchez, L. and Durán,

J.M., 2010, Modelling of bentonite–granite solutes transfer from an in situ full-scale

experiment to simulate a deep geological repository (Grimsel Test Site, Switzerland),

Applied Geochemistry 25:1797–1804.

Cox, B.L. Pruess, K., 1990. Numerical experiments on convective heat transfer in water-

satured porous media at near-critical conditions. Transport in porous media, 5, 299-323.

Cuevas, J., Villar M., Fernández, A., Gómez, P. and Martín, P., 1997. Pore waters extracted

from compacted bentonite subjected to simultaneous heating and hydration. Applied

Geochemistry, 12, 473–481.

Cuevas, J., Turrero, M.J., Torres, E., Fernández, R., Ruiz, A.I. and Escribano, A., 2013.

Deliverable D2.3-3-2 of PEBS Project. Laboratory tests at the interfaces. Results of Small

Cells with mortar-bentonite-magnetite. CIEMAT.

Cuevas, J., Ruíz, A.I., Fernández, R., Torres, E., Escribano, A., Regadío, M., Turrero, M. J.,

2016. Lime mortar-compacted bentonite-magnetite interfaces: An experimental study

focused on the understanding of the EBS long-term performance for high-level nuclear

waste isolation DGR concept. Applied Clay Science 124-125, 79-93.


88

Dai, Z. and Samper, J., 2004. Inverse problem of multicomponent reactive chemical transport

in porous media: formulation and applications. Water Resour Res 40, W07407.

De Windt, L., Pellegrini, D. and Van der Lee, J., 2004. Coupled modeling of cement/claystone

interactions and radionuclide migration. J. Contam. Hydrol. 68, 165-182.

De Windt, L. and Torres, E., 2009. Modélisation d’expériences en cellule reproduisant les

conditions THC d’une alvéole de déchets HAVL. Rapport Technique R201009LDEWI.

Accord spécifique IRSN/ARMINES.

De Vries, D.A., 1963. Thermal properties of soils. In: Van Wijk, W.R. (Ed.), Physics of Plant

Environment. North-Holland Publishing Company, Amsterdam, pp. 210–235.

ENRESA, 2000. FEBEX Project. Full-scale engineered barriers experiment for a deep

geological repository for high level radioactive waste in crystalline host rock. Final Report.

Publicación Técnica ENRESA 1/2000, Madrid, 354 pp.

ENRESA, 2004. Evaluación del comportamiento y de la seguridad de un almacén geológico

profundo de residuos radiactivos en arcilla. PT 49-1PP-M-A1-01.

ENRESA, 2005, Phenomenological description. Reference Concept (Spent Fuel-Carbon Steel

Canister-Bentonite-Granite). NF-PRO Integrated Project. Deliverable D5.1.1. Part 1. Final

version.

ENRESA, 2006a. Full-Scale Engineered Barriers Experiment: Updated Final Report. ENRESA

Tech. Publ. PT 05-02/2006, 589 pp.

ENRESA, 2006b. FEBEX: Final report on thermo-hydro-mechanical modelling. ENRESA

Techn. Publ. PT 05-2/2006, 163 pp.

ENRESA, 2006c. FEBEX: Final THG modelling report. ENRESA Technical Publication. PT 05-

3/2006, 155 pp.

Fernández, A.M., Cuevas, J., Rivas, P. and Martín, P.L., 1999. THG tests in termohydraulic

cells. Technical Report 70-IMA-L-0-41, CIEMAT, Madrid.

Fernández, A., Cuevas, J. and Mäder, U.K., 2009a. Modelling concrete interaction with a

bentonite barrier. Eur. J. Mineral 21, 177-191.

Fernández, R., Mäder, U.K., Rodriguez, M., Vigil de la Villa, R. and Cuevas, J., 2009b.

Alteration of compacted bentonite by diffusion of highly alkaline solutions. European Journal

of Mineralogy 21, 725–735.

Fernández A. M. and Villar M.V., 2010. Geochemical behavior of bentonite barrier in the

laboratory after up to 8 years of heating and hydrating. Applied Geochemistry, 25, 809-824

Fernández, R., Torres, E., Ruiz, A. I., Cuevas, J., Alonso, M. C., García, J. L., Rodríguez, E.,

Turrero, M. J., 2017. Interaction processes at the concrete-bentonite interface after 13 years

of FEBEX-Plug operation. Part II: Bentonite contact. Physics and Chemistry of the Earth,

Parts A/B/C (In Press)


89

Fredlund, D.G. and Rahardjo, H., 1993. Soil Mechanics for Unsaturated Soils.Wiley-IEEE. 517

pp.

Fritz, B. and Madé, B., 1991. Geochemical modelling of bentonite-alkaline solutions

interactions in the near-field of a repository for spent nuclear fuel. SKB Technical Report

91-05. Swedish Nuclear Fuel and Waste Management Company, Stockholm, Sweden.

Gaucher, E. C. and Blanc P., 2006. Cement/clay interactions – A review: Experiments, natural

analogues, and modeling. Waste Management Volume 26, Issue 7, 776–788.

Gens, A., Sánchez, M., Guimarães, L., Alonso, E. E., Lloret, A., Olivella, S., Villar, M. V. and

Huertas F., 2009. A full-scale in situ heating test for high-level nuclear waste disposal:

observations, analysis and interpretation. Géotechnique, 59(4): 377-399.

Guimarães, L.D., Gens, A. and Olivella, S., 2007. Coupled thermo-hydro-mechanical and

chemical analysis of expansive clay subjected to heating and hydration. Transp. Porous

Med. 66 (3), 341–372.

Juncosa, R., 2001. Modelos de flujo multifásico no isotermo y de transporte reactivo

multicomponente en medios porosos. ENRESA, Publicación Técnica, Ph. D Dissertation,

Universidad Politécnica de Madrid. 287 pp.

Huertas, F., Farias, J., Griffault, L., Leguey, S., Cuevas, J., Ramírez, S., Vigil de la Villa, R.,

Cobeña, J., Andrade, C., Alonso, M.C., Hidalgo, A., Parneix, J.C., Rassineux, F., Bouchet,

A., Meunier, A., Decarreau A., Petit, S., Vieillard P., 2000. Effects of cement on clay barrier

performance: (Ecoclay Project).

Johnson, L., Gaus, I., Wieczorek, K., Mayor, J.-C., Sellin, P., Villar, M.V., Samper, J., Cuevas,

J.A., Gens, M., Velasco, M., Turrero, M.J., Montenegro, L., Martin, P.L. and Armand, G.,

2014. Integration of the Short-term Evolution of the Engineered Barrier System (EBS) with

the Long-term Safety Perspective. PEBS Deliverable D4.1.

Keijzer, T.J.S., Kleingeld, P.J. and Loch, J.P.G., 1999. Chemical osmosis in compacted clayey

material and the prediction of water transport. Eng. Geol. 53, 151–159.

Keijzer, T.J.S. and Loch, J.P.G., 2001. Chemical osmosis in compacted dredging sludge. Soil

Sci. Soc. Am. J. 65, 1045–1055.

Kolditz, O., Bauer, S., Bike, L., Böttcher, N., Delfs, J. O., Fischer, T., Görke, U. J., Kalache, T.,

Kosakowski, G., McDermott, C. I., Park, C. H., Radu, F., Rink, K., Shao, H., Shao, H. B.,

Sun, F., Sun, Y. Y., Singh, A. K., Taron, J., Walther, M., Wang, W., Watanabe, N., Wu, Y.,

Xie, M., Xu, W. and Zehner, B., 2012. OpenGeoSys: an open-source initiative for numerical

simulation of thermo-hydro-mechanical/chemical (THM/C) processes in porous media.

Environ Earth Science 67:589–599.


90

Kosakowski, G. and Berner, U., 2013. The evolution of clay rock/cement interfaces in a

cementitious repository for low- and intermediate level radioactive waste. Physics and

Chemistry of the Earth 64, 65-86.

Lalan, P., Dauzères, A., De Windt, L., Bartier, D., Sammaljärvi, J., Barnichon, J.D., Techer, I.,

Detilleux, V., 2016. Impact of a 70 °C temperature on an ordinary Portland cement

paste/claystone interface: An in situ experiment. Cement and Concrete Research 83, 164-

178.

Lehikoinen, J., 2009. Bentonite-cement interaction -– Preliminary results from model

calculations. Posiva Working Report WR 2009-37. Posiva Oy, Olkiluoto, Finland.

Lichtner, P.C., 1996. Continuum formulation of multicomponent–multiphase reactive transport.

In: Lichtner, P.C., Steefel, C.I., Oelkers, E.H. (Eds.), Reviews in Mineralogy. Reactive

Transport in Porous Media. Mineralogical Society of America, Washington, DC.

Lloret, A. and Alonso, E.E., 1995. State surfaces for partially saturated soils. In: Proceedings

of the International Conference on Soils Mechanics and Foundation Engineering, Balkema,

pp. 557–562.

Lothenbach, B., Bernard and E., Mäder, U., 2017. Zeolite formation in the presence of cement

hydrates and albite. Physics and Chemistry of the Earth.

Lu, C., Samper, J., Fritz, B., Clement, A. and Montenegro, L., 2011. Interactions of corrosion

products and bentonite: An extended multicomponent reactive transport model. Physics

and Chemistry of the Earth 36, 1661–1668, doi: 10.1016/j.pce.2011.07.013.

Martín, P.L., Barcala, J.M., 2005. Large scale buffer material test: mock-up experiment at

CIEMAT. Eng. Geol. 81, 298–316.

Martín, P.L., Barcala, J.M., and Huertas, F., 2006. Large-scale and long-term coupled thermo-

hydro-mechanic experiements with bentonite: the FEBEX mock up test. J. Iberian Geol. 32

(2), 259-282.

Marty, N.C.M., Tournassat, C., Burnol, A., Giffaut, E. and Gaucher, E. C., 2009. Influence of

reaction kinetics and mesh refinement on the numerical modelling of concrete/clay

interactions. Journal of Hydrology 364, 58-72.

Marty, N.C.M, Fritz, B., Clément, A. and Michau, N., 2010a. Modelling the long term alteration

of the engineered bentonite barrier in an underground radioactive waste repository. Applied

Clay Science 47, 82-90.

Marty, N., Claret, F., Gaboreau, S., Cochepin, B., Munier, I., Michau, N., Gaucher, E. C. and

Burnol, A., 2010b. Dual alteration of bentonite by iron corrosion and concrete interaction

under high temperature conditions. In Clays in Natural and Engineered Barriers for

Radioactive Waste Confinement, Nantes, France, pp. 473–474.


91

Melkior, T., Mourzagh, D., Yahiaoui, S., Thoby, D., Alberto, J.C., Brouard, C., Michau, N., 2004.

Diffusion of an alkaline fluid through clayey barriers and its effect on the diffusion properties

of some chemical species. Applied Clay Science, Volume 26, 99–107.

Mon, A., Samper, J., Montenegro, L., Naves, A., Fernández, J., 2017. Reactive transport

model of compacted bentonite, concrete and corrosion products in a HLW repository in clay.

Journal of Contaminant Hydrology 197, 1-16.

Montes-H, G., Marty, N., Fritz, B., Clement, A. and Michau, N., 2005. Modelling of long-term

diffusion-reaction in a bentonite barrier for radioactive waste confinement. Appl. Clay Sci.

30, 181–198.

Navarro, V., 1997. Modelo de comportamiento mecánico e hidráulico de suelos nosaturados

en condiciones no isotermas. Ph.D. Dissertation, Universidad Politécnica de Cataluña, 329

pp.

Navarro, V. and Alonso, E.E., 2000. Modelling swelling soils for disposal barriers. Compt.

Geotech. 27,19-43.

Ngo, V. V., Delalande, M., Clément A., Michau, N. and Fritz, B., 2014. Coupled transport

reaction modelling of the long-term interaction between iron, bentonite and Callovo-

Oxfordian claystone in radioactive waste confinement systems. Applied Clay Science, 101,

430-443.

Nguyen, T.S., Selvadurai, A.P.S. and Armand, G., 2005. Modelling the FEBEX THM

experiment using a state surface approach. Int. J. Rock Mech. Min. Sci. 42 (5–6), 639–651.

Olivella, S., Gens, A., Carrera, J. and Alonso, E.E., 1996. Numerical formulation for a simulator

(CODE_BRIGHT) for the coupled analysis of saline media. Eng. Comput. 13 (7), 87–112.

Parkhust, D. L., and Appelo, C. A. J., 1999. User’s guide to PHREEQC (version 2) – a computer

program for speciation, batch-reaction, one-dimensional transport, and inverse

geochemical calculations. US, Geol. Surv. Water-Resour. Invest. Rep., 99-4259.

Pollock, D.W., 1986. Simulation of fluid flow and energy transport processes associated with

high-level radioactive waste disposal in unsaturated alluvium. Water Resour. Res. 22 (5),

765–775.

Saaltink, M.W., Batlle, F., Ayora, C., Carrera, J. and Olivella, S., 2004. RETRASO, a code for

modelling reactive transport in saturated and unsaturated porous media. Geol. Acta 2 (3),

235–251.

Samper, J., Yang, C. and Montenegro, L., 2003. CORE2D version 4: a code for non-isothermal

water flow and reactive solute transport. User’s Manual. University of La Coruña, Spain.

Samper, J., Lu, C. and Montenegro, L., 2008. Coupled hydrogeochemical calculations of the

interactions of corrosion products and bentonite. Physics and Chemistry of the Earth 33,

S306–S316, doi:10.1016/j.pce.2008.10.009.


92

Samper, J., Naves, A., Montenegro, L. and Mon., A., 2016. Reactive transport modelling of the

long-term interactions of corrosion products and compacted bentonite in a HLW repository

in granite: Uncertainties and relevance for performance assessment, Applied

Geochemistry. Vol 67, 42-51.

Savage, D., Bateman, K., Hill, P., Hughes, C., Milodowski, A., Pearce, J., Rae, E. and

Rochelle, C., 1992. Rate and mechanism of the reaction of silicates with cement pore fluids.

Appl. Clay Sci. 7, 33-45.

Savage, D., Noy, D. J. and Mihara, M., 2002. Modelling the interaction of bentonite with

hyperalkaline fluids. Applied Geochemistry 17, 207-223.

Savage, D., Watson, C., Benbow, S. and Wilson, J., 2010a. Modelling iron/bentonite

interactions. Applied Clay Science 47, 91-98.

Savage, D., Benbow, S., Watson, C., Takase, H., Ono, K., Oda, C. and Honda, A., 2010b.

Natural systems evidence for the alteration of clay under alkaline conditions: an example

from Searles Lake, California. Applied Clay Science 47, 72–81.

Savage, D., Arthur, R., Watson, C. and Wilson, J., 2010c. An evaluation of models of bentonite

pore water evolution. SSM Technical Report 2010:12. Swedish Radiation Safety Authority,

Stockholm, Sweden.

Savage, D., 2011. A review of analogues of alkaline alteration with regard to long-term barrier

performance. Mineral. Mag. 75, 2401–2418.

Savage, D., Soler, J.M., Yamaguchi, K., Walker, C., Honda, A., Inagaki, M., Watson, C.,

Wilson, J., Benbow, S., Gaus, I. and Rueedi, J., 2011. A comparative study of the modelling

of cement hydration and cement-rock laboratory experiments. Applied Geochemistry 26,

11381152.

Savage, D., 2012. Prospects for coupled modelling. STUK-TR 13. Radiation and Nuclear

Safety Authority.

Shao, H., Kosakowski, G., Berner, U., Kulik, D.A., Mäder, U. and Kolditz, O., 2013. Reactive

transport modeling of the clogging process at Maqarin natural analogue site. Physics and

Chemistry of the Earth 64, 21-31.

Soler, J.M., 2001. The effect of coupled transport phenomena in the Opalinus clay and

implications for radionuclide transport. J. Contam. Hydrol. 53, 63–84.

Soler, J.M., Paris, B., Pfingsten, W. and Mäder, U., 2004. Flow and reactive transport modeling

in the framework of GTS-HPF. Water–Rock Interaction XI. Balkema, Rotterdam, The

Netherlands, pp. 983–987.

Steefel, C.I., 2001. GIMRT, Version 1.2: software for modelling multicomponent,

multidimensional reactive transport. Users guide. Technical report UCRL-MA-143182,

Lawrence Livermore National Laboratory, Livermore, California.


93

Steefel, C.I. and Lichtner, P.C., 1998. Multicomponent reactive transport in discrete fractures

II. Infiltration of hyperalkaline groundwater at Maqarin, Jordan, a natural analogue site. J.

Hydrol. 209, 200-224.

Tang, A.M., Cui, Y.J. and Le, T.T., 2008. A study on the thermal conductivity of compacted

bentonites. Appl. Clay Sci. 41 (3–4), 181–189.

Tinseau, E., Bartier, D., Hassouta, L., Devol-Brown, I. and Stammose, D., 2006. Mineralogical

characterization of the Tournemire argillite after in situ reaction with concretes. Waste

Manag. 26, 789-800.

Torres, E., Turrero, M. J., Peña, J., Martín, P.L., Escribano, A., Alonso, U., Villar, M.V., 2008.

Deliverable 2.3.2 of component 2 NF-PRO project. Interaction iron-compacted bentonite:

corrosion products and changes in the properties of the bentonite, CIEMAT.

Torres, E., Turrero, M.J. and Escribano, A., 2013. Synthesis of corrosion phenomena at the

iron/bentonite interface under unsaturated condictions. Technical Note

CIEMAT/DMA/2G210/02/2013. PEBS Project.

Turrero, M. J., Villar, M. V., Torres, E., Escribano, A., Cuevas, J., Fernández, R., Ruiz, A. I.,

Vigil de la Villa, R., del Soto, I., 2011. Deliverable 2.3-3-1 of PEBS Project. Laboratory tests

at the interfaces, Final results of the dismantling of the tests FB3 and HB4, 2011. CIEMAT.

Ueda, H., Hyodo, H., Takase, H., Savage, D., Benbow, S. and Noda, M., 2007. Evaluation of

the kinetics of cement-bentonite interaction in a HLW repository using the reactive solute

transport simulator. In 15th International Conference on Nuclear Engineering, Nagoya,

Japan, pp. ICONE15-10566.

Villar, M.V, Fernández, A.M., Martín, P.L., Barcala, J.M., Gómez-Espina, R. and Rivas, P.,

2008a. Effect of heating/hydration on compacted bentonite: test in 60 cm long cells.

Colección Documentos CIEMAT.

Villar, M.V., Sánchez, M., Gens, A., 2008b. Behaviour of a bentonite barrier in the laboratory:

experimental results up to 8 years and numerical simulation. Physics and Chemistry of the

Earth, Vol. 33, Supplement 1, pp. S476-S485.

Villar M.V., Martín P. L., Bárcena I., García-Sinériz J. L., Gómes-Espina R. and Lloret A., 2012.

Long-term experimental evidences of saturation of bentonite under repository conditions.

Engineering Geology, 149-150, 57-69.

Watson, C., Benbow, S. and Savage, D., 2007. Modelling the interaction of low pH cements

and bentonite. Issues affecting the geochemical evolution of repositories for radioactive

waste. SKI Report 2007:30. Swedish Nuclear Power Inspectorate, Stockholm, Sweden.

Watson, C., Hane, K., Savage, D., Benbow, S., Cuevas, J. and Fernández, R., 2009a.

Reaction and diffusion of cementitious water in bentonite: results of ‘blind’ modelling.

Applied Clay Science 45, 54–69.


94

Watson, C., Hane, K., Savage, D., Benbow, S., Cuevas, J., Fernández, R., Norris and S.,

Amme, M., 2009b. Modelling diffusion and reaction of cementitious water in bentonite. In

The Scientific Basis for Nuclear Waste Management XXXIII, 413–420. Burakov and A.S.

Aloy, Eds.

Watson, C., Savage, D., Wilson, J., Benbow, S., Walker, C. and Norris, S., 2013. The

Tournemire industrial analogue: reactive transport modelling of a cement-clay interface.

Clay Minerals 48, 167-184.

Watson, C., Wilson, J., Savage, D., Benbow, S. and Norris, S., 2016. Modelling reactions

between alkaline fluids and fractured rock: The Maqarin natural analogue. Applied Clay

Science 121-122, 46–56.

Wersin, P., Birgersson, M., Olsson, S., Karnland, O. and Snellman, M., 2007. Impact of

corrosion-derived iron on the bentonite buffer within the KBS-3H disposal concept – The

Olkiluoto site as case study. Posiva Report 2007/11. Posiva Oy, Olkiluoto, Finland.

Wollery, T.J., 1992. EQ3/3. A software package for geochemical modeling of aqueous system:

package overview and installation guide version 7.0. UCRL-MA-110662-PT-I, Lawrence

Livermore National Laboratory, Livermore, California.

Xu, T., Samper, J., Ayora, C., Manzano and M., Custodio, E., 1999. Modeling of non-

isothermal multi-component reactive transport in field scale porous media flow systems. J.

Hydrol. 214 (1–4), 144–164.

Xu, T. and Pruess, K., 2001. Modeling multiphase non-isothermal fluid flow and reactive

geochemical transport in variably saturated fractured rocks: 1. Methodology. Am. J. Sci.

301, 16–33.

Xu, T., Senger, R. and Finsterle, S., 2008. Corrosion-induced gas generation in a nuclear

waste repository: Reactive geochemistry and multiphase flow effects Applied Geochemistry

23 3423–3433.

Yamaguchi, T., Sakamoto, Y., Akai, M., Takazawa, M., Iida, Y., Tanaka, T. and Nakayama, S.,

2007. Experimental and modeling study on long-term alteration of compacted bentonite with

alkaline groundwater. Physics and Chemistry of the Earth 32, 298-310.

Yang, C., Samper, J. and Montenegro, L., 2008. A coupled non-isothermal reactive trans-port

model for long-term geochemical evolution of a HLW repository in clay. Environmental

Geology 53, 1627–1638, doi: 10.1007/s00254-007-0770-2.

Yu-Shu, W. and Pruess, K., 1999. Integral solution for transient fluid flow through a porous

medium pressure-dependent permeability. International Journal of Rock Mechanics and

Mining Sciences, 37, 51-61.


95

Yu-Shu, W., Liu, H.H. and Bodvarsson, G.S., 2004. A triple-continuum approach for modeling

flow and transport process in fractured rocks. Journal of Contaminant Hydrology, 73, 145-

179.

Zheng, L. and Samper, J., 2004. Formulation of the inverse problem of non-isothermal

multiphase flow and reactive transport in porous media. Comput. Meth. Water Resour. XV,

1317–1327.

Zheng, L. and Samper, J., 2005. A dual continuum coupled multiphase flow model with mixed

second order water transfer term for structured soils. Jornadas de la Zona no Saturada

2005, VII, 301-306.

Zheng, 2006. Coupled thermo-hydro-mechanical-geochemical models for structurated

deformable porous media. Ph.D. Dissertation, Universidade de A Coruña.

Zheng, L. and Samper, J., 2008. Coupled THMC model of FEBEX mock-up test. Physics and

Chemistry of the Earth 33, S486–S498, doi:10.1016/j.pce.2008.10.023.

Zheng, L., Samper, J., Montenegro, L. and Mayor, J.C., 2008. Flow and reactive transport

model of a ventilation experiment in Opallinus clay, Physics and Chemistry of the Earth,

Vol. 33, S486–S498. doi:10.1016/j.pce.2008.05.012.

Zheng, L., Samper, J., Montenegro, L. and Fernández, A.M., 2010. A coupled THMC model of

a heating and hydration laboratory experiment in unsaturated compacted FEBEX bentonite.

Journal of Hydrology 386, 80-94, doi: 10.1016/j.jhydrol.2010.03.009.

Zheng, L., Samper, J. and Montenegro, L., 2011. A coupled THC model of the FEBEX in situ

test with bentonite swelling and chemical and thermal osmosis. Journal of Contaminant

Hydrology 126, 45-60.

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