Electrochemical Process Simulation III

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Electrochemical Process Simulation III

WIT Press publishes leading books in Science and Technology. Visit our website for new and current list of titles. www.witpress.com

WITeLibrary Home of the Transactions of the Wessex Institute. Papers presented at ELECTROCOR 2009 are archived in the WIT eLibrary in volume 65 of WIT Transactions on Engineering Sciences (ISSN 1743-3533). The WIT eLibrary provides the international scientific community with immediate and permanent access to individual papers presented at WIT conferences. Visit the WIT eLibrary at www.witpress.com.

THIRD INTERNATIONAL CONFERENCE ON SIMULATION OF ELECTROCHEMICAL PROCESSES

ELECTROCOR 2009 CONFERENCE CHAIRMAN C. A. Brebbia Wessex Institute of Technology, UK

INTERNATIONAL SCIENTIFIC ADVISORY COMMITTEE K. Amaya S.G.R. Brown J. Deconinck R. Kelly E. Lemieux P. Mandin A. Peratta M. Pocock A. Powell D.A. Shifler A. Taleb

Organised by Wessex Institute of Technology, UK Sponsored by WIT Transactions on Engineering Sciences

WIT Transactions Transactions Editor Carlos Brebbia Wessex Institute of Technology Ashurst Lodge, Ashurst Southampton SO40 7AA, UK Email: [email protected]

Editorial Board B Abersek University of Maribor, Slovenia Y N Abousleiman University of Oklahoma, USA P L Aguilar University of Extremadura, Spain K S Al Jabri Sultan Qaboos University, Oman E Alarcon Universidad Politecnica de Madrid, Spain A Aldama IMTA, Mexico C Alessandri Universita di Ferrara, Italy D Almorza Gomar University of Cadiz, Spain B Alzahabi Kettering University, USA J A C Ambrosio IDMEC, Portugal A M Amer Cairo University, Egypt S A Anagnostopoulos University of Patras, Greece M Andretta Montecatini, Italy E Angelino A.R.P.A. Lombardia, Italy H Antes Technische Universitat Braunschweig, Germany M A Atherton South Bank University, UK A G Atkins University of Reading, UK D Aubry Ecole Centrale de Paris, France H Azegami Toyohashi University of Technology, Japan A F M Azevedo University of Porto, Portugal J Baish Bucknell University, USA J M Baldasano Universitat Politecnica de Catalunya, Spain J G Bartzis Institute of Nuclear Technology, Greece A Bejan Duke University, USA

M P Bekakos Democritus University of Thrace, Greece G Belingardi Politecnico di Torino, Italy R Belmans Katholieke Universiteit Leuven, Belgium C D Bertram The University of New South Wales, Australia D E Beskos University of Patras, Greece S K Bhattacharyya Indian Institute of Technology, India E Blums Latvian Academy of Sciences, Latvia J Boarder Cartref Consulting Systems, UK B Bobee Institut National de la Recherche Scientifique, Canada H Boileau ESIGEC, France J J Bommer Imperial College London, UK M Bonnet Ecole Polytechnique, France C A Borrego University of Aveiro, Portugal A R Bretones University of Granada, Spain J A Bryant University of Exeter, UK F-G Buchholz Universitat Gesanthochschule Paderborn, Germany M B Bush The University of Western Australia, Australia F Butera Politecnico di Milano, Italy J Byrne University of Portsmouth, UK W Cantwell Liverpool University, UK D J Cartwright Bucknell University, USA P G Carydis National Technical University of Athens, Greece J J Casares Long Universidad de Santiago de Compostela, Spain, M A Celia Princeton University, USA A Chakrabarti Indian Institute of Science, India

A H-D Cheng University of Mississippi, USA J Chilton University of Lincoln, UK C-L Chiu University of Pittsburgh, USA H Choi Kangnung National University, Korea A Cieslak Technical University of Lodz, Poland S Clement Transport System Centre, Australia M W Collins Brunel University, UK J J Connor Massachusetts Institute of Technology, USA M C Constantinou State University of New York at Buffalo, USA D E Cormack University of Toronto, Canada M Costantino Royal Bank of Scotland, UK D F Cutler Royal Botanic Gardens, UK W Czyczula Krakow University of Technology, Poland M da Conceicao Cunha University of Coimbra, Portugal A Davies University of Hertfordshire, UK M Davis Temple University, USA A B de Almeida Instituto Superior Tecnico, Portugal E R de Arantes e Oliveira Instituto Superior Tecnico, Portugal L De Biase University of Milan, Italy R de Borst Delft University of Technology, Netherlands G De Mey University of Ghent, Belgium A De Montis Universita di Cagliari, Italy A De Naeyer Universiteit Ghent, Belgium W P De Wilde Vrije Universiteit Brussel, Belgium L Debnath University of Texas-Pan American, USA N J Dedios Mimbela Universidad de Cordoba, Spain G Degrande Katholieke Universiteit Leuven, Belgium S del Giudice University of Udine, Italy G Deplano Universita di Cagliari, Italy I Doltsinis University of Stuttgart, Germany M Domaszewski Universite de Technologie de Belfort-Montbeliard, France J Dominguez University of Seville, Spain

K Dorow Pacific Northwest National Laboratory, USA W Dover University College London, UK C Dowlen South Bank University, UK J P du Plessis University of Stellenbosch, South Africa R Duffell University of Hertfordshire, UK A Ebel University of Cologne, Germany E E Edoutos Democritus University of Thrace, Greece G K Egan Monash University, Australia K M Elawadly Alexandria University, Egypt K-H Elmer Universitat Hannover, Germany D Elms University of Canterbury, New Zealand M E M El-Sayed Kettering University, USA D M Elsom Oxford Brookes University, UK A El-Zafrany Cranfield University, UK F Erdogan Lehigh University, USA F P Escrig University of Seville, Spain D J Evans Nottingham Trent University, UK J W Everett Rowan University, USA M Faghri University of Rhode Island, USA R A Falconer Cardiff University, UK M N Fardis University of Patras, Greece P Fedelinski Silesian Technical University, Poland H J S Fernando Arizona State University, USA S Finger Carnegie Mellon University, USA J I Frankel University of Tennessee, USA D M Fraser University of Cape Town, South Africa M J Fritzler University of Calgary, Canada U Gabbert Otto-von-Guericke Universitat Magdeburg, Germany G Gambolati Universita di Padova, Italy C J Gantes National Technical University of Athens, Greece L Gaul Universitat Stuttgart, Germany A Genco University of Palermo, Italy N Georgantzis Universitat Jaume I, Spain P Giudici Universita di Pavia, Italy F Gomez Universidad Politecnica de Valencia, Spain R Gomez Martin University of Granada, Spain D Goulias University of Maryland, USA

K G Goulias Pennsylvania State University, USA F Grandori Politecnico di Milano, Italy W E Grant Texas A & M University, USA S Grilli University of Rhode Island, USA R H J Grimshaw, Loughborough University, UK D Gross Technische Hochschule Darmstadt, Germany R Grundmann Technische Universitat Dresden, Germany A Gualtierotti IDHEAP, Switzerland R C Gupta National University of Singapore, Singapore J M Hale University of Newcastle, UK K Hameyer Katholieke Universiteit Leuven, Belgium C Hanke Danish Technical University, Denmark K Hayami National Institute of Informatics, Japan Y Hayashi Nagoya University, Japan L Haydock Newage International Limited, UK A H Hendrickx Free University of Brussels, Belgium C Herman John Hopkins University, USA S Heslop University of Bristol, UK I Hideaki Nagoya University, Japan D A Hills University of Oxford, UK W F Huebner Southwest Research Institute, USA J A C Humphrey Bucknell University, USA M Y Hussaini Florida State University, USA W Hutchinson Edith Cowan University, Australia T H Hyde University of Nottingham, UK M Iguchi Science University of Tokyo, Japan D B Ingham University of Leeds, UK L Int Panis VITO Expertisecentrum IMS, Belgium N Ishikawa National Defence Academy, Japan J Jaafar UiTm, Malaysia W Jager Technical University of Dresden, Germany Y Jaluria Rutgers University, USA C M Jefferson University of the West of England, UK P R Johnston Griffith University, Australia

D R H Jones University of Cambridge, UK N Jones University of Liverpool, UK D Kaliampakos National Technical University of Athens, Greece N Kamiya Nagoya University, Japan D L Karabalis University of Patras, Greece M Karlsson Linkoping University, Sweden T Katayama Doshisha University, Japan K L Katsifarakis Aristotle University of Thessaloniki, Greece J T Katsikadelis National Technical University of Athens, Greece E Kausel Massachusetts Institute of Technology, USA H Kawashima The University of Tokyo, Japan B A Kazimee Washington State University, USA S Kim University of Wisconsin-Madison, USA D Kirkland Nicholas Grimshaw & Partners Ltd, UK E Kita Nagoya University, Japan A S Kobayashi University of Washington, USA T Kobayashi University of Tokyo, Japan D Koga Saga University, Japan A Konrad University of Toronto, Canada S Kotake University of Tokyo, Japan A N Kounadis National Technical University of Athens, Greece W B Kratzig Ruhr Universitat Bochum, Germany T Krauthammer Penn State University, USA C-H Lai University of Greenwich, UK M Langseth Norwegian University of Science and Technology, Norway B S Larsen Technical University of Denmark, Denmark F Lattarulo, Politecnico di Bari, Italy A Lebedev Moscow State University, Russia L J Leon University of Montreal, Canada D Lewis Mississippi State University, USA S lghobashi University of California Irvine, USA K-C Lin University of New Brunswick, Canada A A Liolios Democritus University of Thrace, Greece

S Lomov Katholieke Universiteit Leuven, Belgium J W S Longhurst University of the West of England, UK G Loo The University of Auckland, New Zealand J Lourenco Universidade do Minho, Portugal J E Luco University of California at San Diego, USA H Lui State Seismological Bureau Harbin, China C J Lumsden University of Toronto, Canada L Lundqvist Division of Transport and Location Analysis, Sweden T Lyons Murdoch University, Australia Y-W Mai University of Sydney, Australia M Majowiecki University of Bologna, Italy D Malerba Università degli Studi di Bari, Italy G Manara University of Pisa, Italy B N Mandal Indian Statistical Institute, India Ü Mander University of Tartu, Estonia H A Mang Technische Universitat Wien, Austria, G D, Manolis, Aristotle University of Thessaloniki, Greece W J Mansur COPPE/UFRJ, Brazil N Marchettini University of Siena, Italy J D M Marsh Griffith University, Australia J F Martin-Duque Universidad Complutense, Spain T Matsui Nagoya University, Japan G Mattrisch DaimlerChrysler AG, Germany F M Mazzolani University of Naples “Federico II”, Italy K McManis University of New Orleans, USA A C Mendes Universidade de Beira Interior, Portugal, R A Meric Research Institute for Basic Sciences, Turkey J Mikielewicz Polish Academy of Sciences, Poland N Milic-Frayling Microsoft Research Ltd, UK R A W Mines University of Liverpool, UK C A Mitchell University of Sydney, Australia

K Miura Kajima Corporation, Japan A Miyamoto Yamaguchi University, Japan T Miyoshi Kobe University, Japan G Molinari University of Genoa, Italy T B Moodie University of Alberta, Canada D B Murray Trinity College Dublin, Ireland G Nakhaeizadeh DaimlerChrysler AG, Germany M B Neace Mercer University, USA D Necsulescu University of Ottawa, Canada F Neumann University of Vienna, Austria S-I Nishida Saga University, Japan H Nisitani Kyushu Sangyo University, Japan B Notaros University of Massachusetts, USA P O’Donoghue University College Dublin, Ireland R O O’Neill Oak Ridge National Laboratory, USA M Ohkusu Kyushu University, Japan G Oliveto Universitá di Catania, Italy R Olsen Camp Dresser & McKee Inc., USA E Oñate Universitat Politecnica de Catalunya, Spain K Onishi Ibaraki University, Japan P H Oosthuizen Queens University, Canada E L Ortiz Imperial College London, UK E Outa Waseda University, Japan A S Papageorgiou Rensselaer Polytechnic Institute, USA J Park Seoul National University, Korea G Passerini Universita delle Marche, Italy B C Patten, University of Georgia, USA G Pelosi University of Florence, Italy G G Penelis, Aristotle University of Thessaloniki, Greece W Perrie Bedford Institute of Oceanography, Canada R Pietrabissa Politecnico di Milano, Italy H Pina Instituto Superior Tecnico, Portugal M F Platzer Naval Postgraduate School, USA D Poljak University of Split, Croatia V Popov Wessex Institute of Technology, UK H Power University of Nottingham, UK D Prandle Proudman Oceanographic Laboratory, UK

M Predeleanu University Paris VI, France M R I Purvis University of Portsmouth, UK I S Putra Institute of Technology Bandung, Indonesia Y A Pykh Russian Academy of Sciences, Russia F Rachidi EMC Group, Switzerland M Rahman Dalhousie University, Canada K R Rajagopal Texas A & M University, USA T Rang Tallinn Technical University, Estonia J Rao Case Western Reserve University, USA A M Reinhorn State University of New York at Buffalo, USA A D Rey McGill University, Canada D N Riahi University of Illinois at UrbanaChampaign, USA B Ribas Spanish National Centre for Environmental Health, Spain K Richter Graz University of Technology, Austria S Rinaldi Politecnico di Milano, Italy F Robuste Universitat Politecnica de Catalunya, Spain J Roddick Flinders University, Australia A C Rodrigues Universidade Nova de Lisboa, Portugal F Rodrigues Poly Institute of Porto, Portugal C W Roeder University of Washington, USA J M Roesset Texas A & M University, USA W Roetzel Universitaet der Bundeswehr Hamburg, Germany V Roje University of Split, Croatia R Rosset Laboratoire d’Aerologie, France J L Rubio Centro de Investigaciones sobre Desertificacion, Spain T J Rudolphi Iowa State University, USA S Russenchuck Magnet Group, Switzerland H Ryssel Fraunhofer Institut Integrierte Schaltungen, Germany S G Saad American University in Cairo, Egypt M Saiidi University of Nevada-Reno, USA R San Jose Technical University of Madrid, Spain F J Sanchez-Sesma Instituto Mexicano del Petroleo, Mexico

B Sarler Nova Gorica Polytechnic, Slovenia S A Savidis Technische Universitat Berlin, Germany A Savini Universita de Pavia, Italy G Schmid Ruhr-Universitat Bochum, Germany R Schmidt RWTH Aachen, Germany B Scholtes Universitaet of Kassel, Germany W Schreiber University of Alabama, USA A P S Selvadurai McGill University, Canada J J Sendra University of Seville, Spain J J Sharp Memorial University of Newfoundland, Canada Q Shen Massachusetts Institute of Technology, USA X Shixiong Fudan University, China G C Sih Lehigh University, USA L C Simoes University of Coimbra, Portugal A C Singhal Arizona State University, USA P Skerget University of Maribor, Slovenia J Sladek Slovak Academy of Sciences, Slovakia V Sladek Slovak Academy of Sciences, Slovakia A C M Sousa University of New Brunswick, Canada H Sozer Illinois Institute of Technology, USA D B Spalding CHAM, UK P D Spanos Rice University, USA T Speck Albert-Ludwigs-Universitaet Freiburg, Germany C C Spyrakos National Technical University of Athens, Greece I V Stangeeva St Petersburg University, Russia J Stasiek Technical University of Gdansk, Poland G E Swaters University of Alberta, Canada S Syngellakis University of Southampton, UK J Szmyd University of Mining and Metallurgy, Poland S T Tadano Hokkaido University, Japan H Takemiya Okayama University, Japan I Takewaki Kyoto University, Japan C-L Tan Carleton University, Canada M Tanaka Shinshu University, Japan E Taniguchi Kyoto University, Japan

S Tanimura Aichi University of Technology, Japan J L Tassoulas University of Texas at Austin, USA M A P Taylor University of South Australia, Australia A Terranova Politecnico di Milano, Italy E Tiezzi University of Siena, Italy A G Tijhuis Technische Universiteit Eindhoven, Netherlands T Tirabassi Institute FISBAT-CNR, Italy S Tkachenko Otto-von-GuerickeUniversity, Germany N Tosaka Nihon University, Japan T Tran-Cong University of Southern Queensland, Australia R Tremblay Ecole Polytechnique, Canada I Tsukrov University of New Hampshire, USA R Turra CINECA Interuniversity Computing Centre, Italy S G Tushinski Moscow State University, Russia J-L Uso Universitat Jaume I, Spain E Van den Bulck Katholieke Universiteit Leuven, Belgium D Van den Poel Ghent University, Belgium R van der Heijden Radboud University, Netherlands R van Duin Delft University of Technology, Netherlands P Vas University of Aberdeen, UK W S Venturini University of Sao Paulo, Brazil

R Verhoeven Ghent University, Belgium A Viguri Universitat Jaume I, Spain Y Villacampa Esteve Universidad de Alicante, Spain F F V Vincent University of Bath, UK S Walker Imperial College, UK G Walters University of Exeter, UK B Weiss University of Vienna, Austria H Westphal University of Magdeburg, Germany J R Whiteman Brunel University, UK Z-Y Yan Peking University, China S Yanniotis Agricultural University of Athens, Greece A Yeh University of Hong Kong, China J Yoon Old Dominion University, USA K Yoshizato Hiroshima University, Japan T X Yu Hong Kong University of Science & Technology, Hong Kong M Zador Technical University of Budapest, Hungary K Zakrzewski Politechnika Lodzka, Poland M Zamir University of Western Ontario, Canada R Zarnic University of Ljubljana, Slovenia G Zharkova Institute of Theoretical and Applied Mechanics, Russia N Zhong Maebashi Institute of Technology, Japan H G Zimmermann Siemens AG, Germany

Electrochemical Process Simulation III

Editors C. A. Brebbia Wessex Institute of Technology, UK R. A. Adey Wessex Institute of Technology, UK

Editors: C. A. Brebbia Wessex Institute of Technology, UK R. A. Adey Wessex Institute of Technology, UK

Published by WIT Press Ashurst Lodge, Ashurst, Southampton, SO40 7AA, UK Tel: 44 (0) 238 029 3223; Fax: 44 (0) 238 029 2853 E-Mail: [email protected] http://www.witpress.com For USA, Canada and Mexico Computational Mechanics Inc 25 Bridge Street, Billerica, MA 01821, USA Tel: 978 667 5841; Fax: 978 667 7582 E-Mail: [email protected] http://www.witpress.com British Library Cataloguing-in-Publication Data A Catalogue record for this book is available from the British Library ISBN: 978-1-84564-192-4 ISSN: 1746-4471 (print) ISSN: 1743-3533 (on-line) The texts of the papers in this volume were set individually by the authors or under their supervision. Only minor corrections to the text may have been carried out by the publisher. No responsibility is assumed by the Publisher, the Editors and Authors for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. © WIT Press 2009 Printed in Great Britain by MPG Book Group. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the Publisher.

Preface

This book contains papers presented at the third international conference on the Simulation of Electrochemical Processes held in Bologna, Italy in 2009. The meeting was organised by the Wessex Institute of Technology. The conference objective was to bring together researchers, engineers and scientist to present and discuss the state of the art in the computer simulation of electrochemical processes and its application in the areas of corrosion, corrosion related fracture and fatigue and coating and deposition processes. The theme of the conference was to encourage papers describing the development of computational models and their application in practice, including the comparison with experimental measurements and case studies. The editors are indebted to the members of the International Scientific Advisory Committee for their help in reviewing the abstracts and papers. The Editors Bologna, 2009

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Contents Primary to ternary current distribution at a vertical electrode during two-phase electrolysis Ph. Mandin, H. Roustan, J. B. Le Graverend & R. Wüthrich .............................. 1 Hydrogen production by the Westinghouse cycle: modelling and optimization of the two-phase electrolysis cell S. Charton, P. Rivalier, D. Ode, J. Morandini & J. P. Caire ............................ 11 A hydraulic model to simulate the hydrodynamics of a fluorine electrolyser J. P. Caire, G. Espinasse, M. Dupoizat & M. Peyrard ...................................... 23 Computational modelling of cathodic protection systems for pipelines in multi-layer soil A. B. Peratta, J. M. W. Baynham & R. A. Adey ................................................. 35 Numerical modelling of cathodic protection systems for deep well casings A. B. Peratta, J. M. W. Baynham & R. A. Adey ................................................. 47 Functional relationship between cathodic protection current/potential and duration of system deployment in desert conditions A. Muharemovic, I. Turkovic & S. Bisanovic..................................................... 59 Optimization of a ship’s ICCP system to minimize electrical and magnetic signature by mathematical simulation S. Xing, J. Wu & Y. Yan ..................................................................................... 69 Numerical analysis assisted monitoring method for the coating condition on a ballast tank wall K. Amaya, A. Nakayama & N. Yamamoto ......................................................... 79

The influence of coating damage on the ICCP cathodic protection effect J. Wu, S. Xing & F. Yun ..................................................................................... 89 Field-based prediction of localized anodic dissolution events taking place on ZnAl alloy coatings in the presence of 5% NaCl solution S. G. R. Brown & N. C. Barnard ....................................................................... 97 Eulerian-Lagrangian model for gas-evolving processes based on supersaturation H. Van Parys, S. Van Damme, P. Maciel, T. Nierhaus, F. Tomasoni, A. Hubin, H. Deconinck & J. Deconinck ................................... 109 Simulation of gas pipeline leakage using the characteristics method E. Nourollahi ................................................................................................... 119 Two-dimensional numerical modelling of hydrogen diffusion assisted by stress and strain J. Toribio, D. Vergara, M. Lorenzo & V. Kharin ............................................ 131 Mathematical modelling of electrochemical reactions in aluminium reduction cells R. N. Kuzmin, O. G. Provorova, N. P. Savenkova & A. V. Shobukhov........................................................................................... 141 Atomistic simulation of the nano-structural evolution of Raney-type catalysts from spray-atomized NiAl precursor alloys during leaching with NaOH solution N. C. Barnard, S. G. R. Brown, F. Devred, B. E. Nieuwenhuys & J. W. Bakker................................................................................................. 151 Corrosion of mild steel and 316L austenitic stainless steel with different surface roughness in sodium chloride saline solutions L. Abosrra, A. F. Ashour, S. C. Mitchell & M. Youseffi................................... 161 Recovering current density from data on electric potential J. Irša, A. N. Galybin & A. Peratta.................................................................. 173 Author Index .................................................................................................. 185

Simulation of Electrochemical Processes III

1

Primary to ternary current distribution at a vertical electrode during two-phase electrolysis Ph. Mandin1, H. Roustan2, J. B. Le Graverend1,3 & R. Wüthrich3 1

LECIME UMR 7575 CNRS-ENSCP-Paris6, ENSCP, France Alcan – Centre de Recherche de Voreppe, France 3 Department of Mechanical & Industrial Engineering, Concordia University, Canada 2

Abstract During two-phase electrolysis for hydrogen or fluorine industrial production, there are bubbles that are created at vertical electrodes, which imply quite important electrical properties and electrochemical processes disturbance. Bubbles are motion sources for the electrolysis cell flow, and then hydrodynamic properties are strongly coupled with species transport and electrical performances. The presence of the bubbles modifies these global and local properties: the electrolysis cell and the primary to ternary current density distribution are modified. This disturbance leads to the modification of the local current density. The goal of this proposition is to present the electrochemical engineering study and modelling of two-phase electrolysis properties at electrode vicinity. This work is due to the necessity for a better knowledge of the actual interface condition during electrolysis, for example to have a better process optimisation or electrode consumption prevention. Keywords: two-phase electrolysis, modelling, electrochemical engineering.

1

Introduction

Gas release and induced fluid flow at electrodes are characteristic for several electrochemical processes, such as hydrogen or fluorine production. The twophase phenomena in gas evolving electrodes are in general neglected because of the major difficulty to be correctly taken into account. Nevertheless, nowadays, with the increasing interest in hydrogen production and clean, sustainable WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/ECOR090011

2 Simulation of Electrochemical Processes III fluorine production for the nuclear industry, these processes have to be revisited with modern experimental and numerical tools for further optimization. Many authors [1–20] have worked on this topic and some interesting experimental observations and numerical modelling are now available for engineering optimization and process intensification. Because of gas evolving in the gravity field, the industrial two-phase electrolysis processes generally use vertical electrodes to promote bubble detachment and avoid gas accumulation. This is the reason why the present work focuses upon vertical electrodes.

2

Experimental set-up

The electrochemical reactors for continuous production are opened. A pump ensures circulation through the cell and the mass flow rate is controlled. The electrodes, anode and cathode have a large surface to ensure massive production and large current intensity is applied. The average current density is from 0.1 to 1 A cm-2. The produced bubbles are accumulated at the top of the cell. The laboratory study of these processes has lead us to define an adapted geometry for the closed electrochemical cell presented in figure 1.

Figure 1:

Electrochemical cell with gas evolving at electrodes.

In accordance with in situ configuration and geometry, two vertical plane electrodes separated with distance d=4.2 cm have been considered. The height is H=10 cm whereas the width is l=2 cm. The anode is made with the usual nickel (on the left in figure 1) and the cathode is made with the usual copper (on the right in figure 1). An Autolab PGSTAT 302 N is used in combination with a 20 A current booster to ensure average current density from 0 to 1 A cm-2 on the 20 cm2 electro active surface configuration studied. WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)


3

The classical alkaline water electrolysis has been chosen as a representative two-phase electrolysis process: 2 H2O + 2 e-  H2 + 2 OH-aq 2 OH-aq  0.5 O2 + H2O + 2 e-

E° = -0.83 V/ENH (R1) E° = 0.40V/ENH (R2)

Various alkaline liquid electrolytes have been considered in the present study: NaOH and KOH with various molar concentrations.

3

Results and discussion

The experiments have been performed under imposed current conditions. The cell potential evolution with time was then measured for various imposed current values. After a time defined with induced hydrodynamic conditions, a steady potential is measured at the electrochemical cell. Table 1 gives the associated measured potential for different values for the imposed current, the electrolyte concentrations and nature. As can be seen, it is easier to obey a given imposed current with NaOH than with KOH for concentration 0.1 M. However, at 1 M, the voltage to apply to impose the current is smaller with KOH. The explanation is difficult to give and needs further modelling effort to take into account multi-physico-chemical coupled phenomena. These measurements are really important for electrochemical engineering. The smaller the voltage is, the cheaper the hydrogen production. The hydrogen volume flow rate is directly related to the current according with the Faraday law: QH2 = (Iimp/n.F)*(R.Tamb/Pamb) (1) with QH2 the volume flow rate in m3 s-1, n=2 the transferred electron number in the electrochemical reactions, F=96500 C mol-1 the Faraday constant, R=8.314 J mol-1 K-1 the ideal gas constant, and Tamb =300 K and Pamb =1.013 105 Pa the ambient temperature and pressure, respectively. Table 1:

Average voltage U (V) at the electrochemical cell for various conditions of imposed current Iimp, electrolyte ions and concentration.

Voltage U Iimp (A)

KOH 0.1 M

QH2 mm3/s

NaOH 1M

0.1 M

1M

0.05

2.6 V*

2.0 V

2.52 V

2.03 V

6.4

0.1

3.4 V

2.13 V

3.2 V

2.17 V

12.8

0.2

4.6 V

2.33 V

4.4 V

2.45 V

25.5

0.5

8.2 V*

2.83 V

7.9 V

3.05 V

63.8

WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)

4 Simulation of Electrochemical Processes III

8 7

NaOH 0.1 M 0.05 A NaOH 0.1 M 0.1 A NaOH 0.1 M 0.2 A NaOH 0.1 M 0.5 A

U (Volts)

6 5 4 3 2 1 0

1

2

3

4

5

6

7

8

9

10

t (sec)

Figure 2:

Evolution of the cell potential U (V) with time for NaOH concentration 0.1 M, for various imposed current Iimp values. y

Iimp

U

Figure 3:

jx(y)

Vertical gas-evolving electrode: left is the geometric configuration and right is a current distribution example (y: electrode height; jx(y): local current density).

Figure 2 shows the evolution necessary to impose potential at the electrochemical cell to obtain a given current for various NaOH concentration values. As has been observed in table 1, the more concentrated the electrolyte is, the easier and cheaper the hydrogen production. The goal of the study is now to understand and then model the reasons for such an evolution. This is the first step for optimization and process intensification. The numerical modelling is now presented.



5

Electrolyte Hydrodynamics

Velocity field V

Navier-Stokes relations

Void fraction ε

Newton law for discrete phase

Electrical conductivity κ

Current density field j

Bruggeman relation: κ = κ 0 (1-ε) 3/2 (2) Current balance : div j =0 (3)

Current density distribution

Bubble mass flow rate q

Figure 4:

4

Faraday relation: q = M jn / (n F) (4)

Calculation flow-sheet for the coupling effect in electrochemical cell due to the presence of bubble release.

the

Numerical modelling

A primary current distribution at the electrodes is first developed. The schematic mathematical configuration is presented in figure 3. Figure 4 shows the simplified calculation algorithm for primary current distribution at the working electrode (hydrogen production). A classical CFD software is used to solve the Navier-Stokes equations under laminar hypothesis with finite volume methods. Then, for a given injected gas mass flow rate with constant spherical shape and diameter (mono disperse bubbles), each particle’s trajectory is calculated according to local conditions. The bubble friction is associated to a liquid electrolyte local motion source term, which ensures strong coupling between the continuous liquid phase and the discrete bubbles phase. According to the bubble residence time, an average void fraction ε (-) is calculated and then the local electrical conductivity κ (S m-1), the value of which is smaller than the pure liquid value κ 0 because of the insulating character of the gas, according to Bruggeman’s law (2). Then, the local current density j (A m-2) balance equation (3) can be calculated and yields to a smaller current density value where the bubble concentration is large, at the top of the electrodes. According to Faraday’s law (4), the smaller the current density j, the smaller the local gas mass flow rate q (kg s-1 m-2). WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)

6 Simulation of Electrochemical Processes III The Navier-Stokes calculation leads to a proposition of hydrodynamic profile, but the resulting current is not in good accord with the experimental results shown in table 1 and figure 2. The main reason is the great difficulty in correctly modelling the hydrodynamic properties. Then, to validate the hydrodynamic model itself, it has been decided to perform some experimental local field velocity experiments using a PIV laser plane. The bubbles are supposed to perfectly follow the local flow direction and magnitude because they are small enough. A fast CCD camera is used, which registers 170 picture couples at a frequency of 15Hz (66.67 ms). Each couple of picture is measured with a delay of 8 ms. Then, the post-processing of the picture couple allows the definition of a local velocity vector according to the bubble’s displacements during the 8 ms between the two post-treated pictures. The experimental set-up is presented in figure 5.

Figure 5:

PIV measurements experimental set-up.

60

60

0

0.0 6

4

0

position(2)

0 0.02

0

0.12

0.02

0.04

0.0 2 0.0 4 2 0.0

0

0.0

2 0.0

0

position(2)

0.02

0

0.02

0.04

6

0

0.04

0

10

2

0

20

0.0

0.1 0.08

0

30

Vy 0.24 0.22 0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 -0.02

0.02

14 13 12 11 10 9 8 7 6 5 4 3 2 1

0

0.06

0.0

0

0

10

40 0

0

20

50

0

30

Vy 0.24 0.22 0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 -0.02

4

0

14 13 12 11 10 9 8 7 6 5 4 3 2 1

0.0

0.06

40

0.1 2 0.0

0.06

50

-10

-10

0

0

-40

Figure 6:

-20

0

position

20

40

-40

-20

0

position

20

40

Unsteady vertical velocity component contours and stream function at I=1A, after 220 s electrolysis (left) and 220s + 80 ms (right).



7

For each electrolysis condition, four times 170 couple of pictures (8 ms time difference) have been measured at 15Hz (66.7 ms) during the unsteady and steady regime. The post-processing of the results is in progress, but leads to interesting and difficult to understand results and consequences. The electrodes with bubbles evolving seem to lead in the confined electrochemical cell to a hydrodynamic “puffing phenomenon”, clearly three dimensional and unsteady in the cell. Then all the coupled phenomena, transports and reactions are affected and should actually be three dimensional and unsteady. The primary current distribution modelling described is to be completed with an accurate homogeneous and surface realistic chemistry modelling. This is called the ternary current distribution modelling. This modelling needs the knowledge of transport kinetic properties (diffusion coefficients), speciation and reactions, which occur in the cell, with the associated thermodynamic and/or kinetic reactive properties. An example of local speciation and chemistry is given in figure 7. C (mol m-3)

Distance from anode (m) Figure 7:

5

Speciation profiles in the anode vicinity in the case of aluminium production according to the Hall-Heroult process [12].

Conclusion and interest in zero gravity experiments

As shown previously, the hydrodynamic properties are really difficult to model: both electrodes are naturally induced motion sources with one or two phase flows; this flow can be from laminar to turbulent and really confined. This is the reason why many years researchers [7, 8] have tried to avoid this difficulty with zero gravity experiments. The Japanese team has performed its experiments in a drop tower, whereas we plane to perform zero gravity in an Airbus A300-0G aircraft. This is possible if the plane follows what is called a parabolic trajectory (see figure 8 left). Various electrolysis experiments are performed for different liquid electrolyte and electrode conditions and each time the electrical and video properties are measured. At the beginning of a parabole the gravity level is 1G (normal); first the plane is accelerated at 2G and after 20 seconds, the engines are turned off and the zero gravity experiment begins at 22 seconds. After this the WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)

8 Simulation of Electrochemical Processes III engines are turned on and the plane accelerates at 2G for 20 seconds to stabilize and access the normal horizontal trajectory. At 1G and 2G the bubbles are produced and evolve vertically; at zero gravity their motion is “frozen” and they stop almost immediately. They have no motion at 22 seconds (fig. 8 right). The experimental measurement treatments are in progress. These experiments then allow the study of the gas, bath and electrode material in perfect absence of any convective transport during this time, which is really interesting for the twophase electrolysis modelling effort in progress.

Figure 8:

Description of the parabolic trajectory (left) and presentation of the bubbles behaviour for 1G, 2G and 0G (right).

Acknowledgements The authors are grateful to Alcan, CEA and AREVA and the French project AMELHYFLAM (ANR 2007) for their financial support. (AMELHYFLAM is the French acronym for the programme to improve Hydrogen, Fluorine and Alumina industrial production processes by coupled modelling of two-phase and electrochemical phenomena).

References [1] [2] [3] [4]

F. Jomard, J.P. Feraud, J.P. Caire, International Journal of Hydrogen Energy 33 (2008) 1142-1152 H. Kellogg, Anode Effect in Aqueous Electrolysis, Journal of the Electrochemical Society, vol 97 N°4 (1950) Kazuhisa Azumi, Tadahiko Mizuno, Tadashi Akimoto, and Tadayoshi Ohmori, Light Emission from Pt during High-Voltage Cathodic Polarization J. Electrochem. Soc. 146 (1999) 3374 L.J.J. Janssen, J.G Hoogland, The effect of electrolytically evolved gas bubbles on the thickness of the diffusion layer, Electrochimica Acta, Vol. 15 ( 1970) 1020 WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)


[5]

[6] [7]

[8] [9] [10] [11] [12] [13]

[14]

[15]

[16] [17]

9

L.J.J Janssen, C.W.M.P Sillen, E. Barendrecht et S.J.D Van Stralen, Bubble behaviour during oxygen and hydrogen evolution at transparent electrodes in KOH solution, Electrochimica Acta, Vol. 29, No 5 (1984) pp633-642 S.M. Korobeinikov, A.V. Melekhov, Yu. N. Sinikh and Yu. G. Soloveichik, Effect of strong electric field on the behaviour of bubbles in water, in High Temperature, Vol. 39, No 3 (2001) pp368-372 H. Matsushima, T. Nishida, Y. Konishi, Y. Fukunaka, Y. Ito, K. Kuribayashi, Water electrolysis under microgravity: Part I. Experimental technique, Electrochimica Acta, Volume 48, Issue 28 (2003) pp41194125 H. Matsushima, Y. Fukunaka, K. Kuribayashi, Water electrolysis under microgravity: Part II. Description of gas bubble evolution phenomena, Electrochimica Acta, Volume 51, Issue 20 (2006) pp4190-4198 H. Vogt, Ö. Aras, R. J. Balzer, The limits of the analogy between boiling and gas evolution at electrodes, International Journal of Heat and Mass Transfer, Volume 47, Issue 4 (2004) pp787-795 H. Vogt, R.J. Balzer, The bubble coverage of gas-evolving electrodes in stagnant electrolytes, Electrochimica Acta, Volume 50, Issue 10 (2005) pp2073-2079 J. Eigeldinger, H. Vogt, The bubble coverage of gas-evolving electrodes in a flowing electrolyte, Electrochimica Acta, Volume 45, Issue 27 (2000) pp4449-4456 Ph. Mandin, J. Hamburger, S. Bessou, G. Picard, Calculation of the current density distribution at vertical gas-evolving electrodes, Electrochimica Acta, Volume 51, Issue 6 (2005) pp1140-1156 R Wüthrich, L.A. Hof, A. Lal, K. Fujisaki, H. Bleuler, Ph. Mandin, G. Picard, Physical principles and Miniaturization of Spark Assisted Chemical Engraving (SACE), J of Micromech. Microeng., 15 (2005) 268275 Ph. Mandin, H. Roustan, R. Wüthrich, J. Hamburger & G. Picard, Twophase electrolysis process modelling: from the bubble to the electrochemical cell scale Transactions on Engineering Sciences, 2007 WIT Press, Simulation of Electrochemical Processes II, p73 Ph. Mandin, A. Ait Aissa, H. Roustan, J. Hamburger, G. Picard, Twophase electrolysis process: from the bubble to the electrochemical cell properties, Chemical Engineering and Processing: Process intensification, 47 (2008) pp1926-1932 C. Gabrielli, F. Huet, R.P. Nogueira, Fluctuations of concentration overpotential generated at gas-evolving electrodes, Electrochimica Acta, Volume 50, Issue 18 ( 2005) pp3726-3736 Allen J. Bard and Larry R. Faulkner, Electrochemical MethodsFundamentals and Applications, John Wiley & Sons, 2nd. Edition, 2001, 243.


10 Simulation of Electrochemical Processes III [18] [19] [20]

F. Lapicque, Electrochemical Engineering: An Overview of its Contributions and Promising Features, Chemical Engineering Research and Design, Volume 82, Issue 12 (2004) pp1571-1574 I. Zaytsev, G. Aseyev: Properties of Aqueous Solution of Electrolytes, CRC Press, Boca Raton, Ann Arbor, London, Tokyo (1992) R. Wüthrich, Ch. Comninellis, H. Bleuler: Bubble evolution on a vertical electrode under extreme current densities, Electrochimica Acta 50 (2005) pp5242-5246



11

Hydrogen production by the Westinghouse cycle: modelling and optimization of the two-phase electrolysis cell S. Charton1, P. Rivalier1, D. Ode1, J. Morandini2 & J. P. Caire3 1

Commissariat à l’Énergie Atomique, Marcoule – DTEG/SGCS/LGCI, France 2 Astek Rhône-Alpes, France 3 LEPMI, Grenoble INP, France

Abstract Hydrogen is currently viewed as a promising energy carrier for transportation applications. In this context, mass production of hydrogen is a major issue for the coming decades. Among the viable production processes, the hybrid sulphur cycle, or Westinghouse cycle, is studied by the Nuclear Energy Division of the French CEA. In this work, the influence of H2 bubbles on the current distribution within the electrolyser is studied. Turbulent two-phase flow simulations are performed with Ansys-Fluent CFD code in the 3D calculation domain using an Euler-Euler model. The electrokinetic problem is solved in the same domain by a finite element code, Flux-Expert, which is able to compute the secondary current distribution by means of specific interfacial elements. Parameters including the cell orientation (vertical or horizontal electrode), flow regime and bubble size are investigated, and the current model development status and needs are discussed. Keywords: two-phase flow, numerical model, hydrogen, fluent, flux-expert.

1

General context

Hydrogen is a unique zero carbon content energy vector. Its conversion into power and electricity within fuel cells would allow various applications, especially for transportation. Together with fuel cell development and hydrogen storage, hydrogen production is a major issue for the coming decades. The obvious inexhaustible feedstock for hydrogen production is water. Among the WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/ECOR090021

12 Simulation of Electrochemical Processes III potential thermochemical cycles able to split water into hydrogen and oxygen, the Westinghouse process appears particularly attractive for its low theoretical energy requirement (in association with a solar or nuclear high temperature source) and its minimal reagent inventory. The hybrid sulphur cycle (HyS) was developed and patented in the 1970s by the Westinghouse Electric Corporation and, since 2000, has been the subject of renewed interest, especially in the USA and in France. It consists of two steps: an electrochemical step based on sulphur dioxide (SO2) electro-oxidation into H2SO4 (E0 = 0,17VSHE under normal conditions), accompanied by hydrogen gas (H2) production at the cathode, and a thermochemical step in which sulphuric acid is decomposed at high temperature to recover SO2, which is recycled to the electrolyser. Among the phenomena and parameters that must be controlled and optimized in order to meet the requirements of hydrogen mass production, this paper focuses on the issues and modelling of two-phase forced convection flow through the electrochemical cell.

2

Overview of electrolyser modelling approaches

Numerical models for electrochemical process performance assessment or dimensioning generally assume uniform properties or one-dimensional property variations. For example, plug flow with axial dispersion is usually assumed within filter-press electrolysers [1], whereas a Darcy flow model is commonly used within the gas diffusion layer of PEM electrolysers and fuel cells [2]. Industrial electrochemical cells, for which the local current distribution must be precisely determined, mainly involve multidimensional approaches. The electrokinetic problem is then solved using specific finite element codes such as COMSOL or Flux-Expert. Conversely, when hydrodynamic phenomena are predominant or limiting with regard to electrochemical reactions, the flow field is modelled by CDF and the electrokinetic problem is simplified. Focusing on gas-producing electrolysers, Mandin et al. [3] have adopted a Lagrangian approach using Fluent while Agranat et al. [4] have chosen a true two-phase approach using the Euler-Euler algorithm available in PHOENICS. The same model was also implemented by Mat et al. [5], who solved the ionic species transport as well in order to derive the tertiary current density distribution within the simulation domain. In ref. [3] the electrical potential is calculated as a user-defined scalar undergoing a diffusion-like transport equation using Dirichlet boundary conditions at electrodes to obtain a primary current distribution. Chemical species transport is modelled neither in ref. [4], where the current density is assumed to be constant at the electrode surfaces, nor in ref. [5]. The simulation domain is generally two-dimensional and often reduced to single fluid zone. Bubbles are assumed to behave as rigid spheres of constant and uniform size. A few models combine a refined description of both the electrokinetic and hydrodynamic processes. Multiphysics problems are solved by coupling specific codes, either indirectly [6] or by enabling data exchange during the iterative WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)


13

process by means of user-defined library routines. The latter formalism was employed by Jomard et al. [7] who coupled Flux-Expert and Fluent to account for the effect of H2 bubble release on the overall performance of the Westinghouse electrolysis process. The same methodology is employed here. Although gas-evolving electrodes are frequently used in industrial processes, the behaviour of electrogenerated bubbles remains difficult to predict and model. In industrial reactors, large gas release may however strongly influence the electrolyser performance due to hydrodynamic modifications [8] and decreases electrolyte conductivity. These phenomena are examined here, where the process sensitivity to either operating conditions or unknown parameters, such as H2 bubble size and departure angle, is investigated. More fundamental aspects, such as bubble nucleation, growth and departure, are currently being studied within the scope of the AMELHYFLAM (AMELHYFLAM is the French acronym for Hydrogen, Fluorine and Alumina industrial production processes improvement by coupled modelling of biphasic and electrochemical phenomena) project, supported by the National Research Agency (ANR) and dedicated to this theme.

3

Model description

Although the Fluent user-defined functions have been modified in order to optimize data collection and source allocation in the two-phase domain, both the modelling strategy and the simulation domain are similar to the ones developed by Jomard et al. [7]. Hence, only the relevant information and new results are reported here. The exchange data formalism between the two codes is therefore not described. H2SO4 H2SO4 + SO2

H2

    

z

+

x y

X = 0.04m

H2SO4 Y = 0.013m

Figure 1:

Z = 0.16m

H2SO4 + SO2

Filter-press electrolyser configuration ( cathode,  hydrogen release zone,  catholyte,  membrane,  anolyte,  anode).


14 Simulation of Electrochemical Processes III 3.1 Description of the electrochemical cell The three-dimensional simulation domain is described Figure 1 for a twocompartment filter-press electrolyser. The cathode and anode compartments are separated by a rigid impermeable membrane, to prevent SO2 crossover. The conductivity of a CMX Neocepta® membrane is assumed for simulation. Both Pt electrodes are flat and parallel. Counter-current fluid flow is maintained under steady-state conditions in the plane-parallel compartments. The dimensions are those of the FM01-LC model, manufactured by ICI Chemical & Polymer Company, and used in the Westinghouse pilot test facility implemented in the Marcoule Laboratory [9]. 3.2 Simplifying assumptions Fluid flow and local mass transport effects in the FM01-LC cell has been investigated by Brown et al. [10] in the case of cupric ions reduction to copper using copper-printed segmented electrodes in the longitudinal or transverse directions. Experiments were carried out under laminar inflow conditions, in the range 212 < Re < 855, in a single compartment cell. According to their experimental results, the authors concluded that it is essential to use a turbulent promoter in order to avoid large variations in the current distribution both along and across the flow direction, due to insufficient radial mixing and to the inlet distributor pattern. Moreover, tracer experiments performed by Trinidad et al. [1] in the range 900 < Re < 1900 exhibits plug flow with axial dispersion behaviour and no evidence of dead zone or fluid channelling when a turbulent promoter is used. In the process under study here, where SO2 oxidation is the limiting half reaction, the electrolyte flow rates are controlled by volumetric pumps to ensure forced convection. Moreover, both the anode and cathode compartments are provided with a plastic mesh turbulence promoter. The flow is therefore assumed fully turbulent and a uniform velocity profile is assumed at the inlet. However, for simplification, these devices are not represented in the simulation domain. Although the turbulence promoter should actually influence the bubble population, no reference has been found on its effects. Two additional simplifying assumptions result from the pilot facility operating conditions. First, a high recirculation rate is imposed in both compartments, leading to a low SO2 conversion rate per pass, typically 5%, as given by the mass balance calculation described in [9]. The anolyte composition, CSO2 = 0.24 mol/l, is therefore assumed to remain constant along the cell, in order to achieve nearly uniform current distribution along the electrode. Furthermore, the catholyte loop is provided with an efficient phase separation device. The gaseous H2 volume fraction can therefore be neglected at the cell inlet. 3.3 Governing equations Current density, eqn. (1), is calculated by the finite-element code Flux-Expert solving the Laplace equation for potential, eqn. (2) throughout the computational domain. WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)


15

  (1) j     (2)      0 where  is the electrical potential in V and  the electrical conductivity in S.m-1. The SO2 oxidation process is kinetically limited, inducing a non-negligible anodic overvoltage, given by a Tafel electrokinetic law [11]. In order to account for the secondary potential distribution prevailing in the domain, potential jumps are calculated at the anode/fluid interface thanks to the interfacial-type elements provided within the solver. These zero-width finite elements allow electrical potential discontinuities to be managed, as described in ref. [7]. The same formalism is used at the cathode/fluid interface as well to model the proton reduction overvoltage. The fluid electrical conductivity  is assumed to be linearly dependent on temperature in all fluid zones and in the membrane as well. The linear law coefficients were fitted on impedance spectroscopy measurements performed over a wide range of temperatures and H2SO4 concentrations. The catholyte conductivity is also dependent on the gas volume fraction 2 following the Bruggeman relation: (3)    1   1.5



T , 2 



T ,0

2

The materials conductivity values à 50°C are given in Table 1. Table 1:

Materials conductivity at 50°C. 30%wt H2SO4 98,5

CMX 17,5

-1

 (S.m )

50%wt H2SO4 78,5

Both the temperature field and gas volume fraction distribution are computed by Fluent during the hydrodynamic iteration process. The steady-state fluid mechanics problem is solved using the Fluent EulerEuler multiphase model in the fluid domains. Mass, momentum and energy balances, the general forms of which are given by eqn. (4), (5), and (6), are solved for both the liquid and the gas phases. In solid zones the energy equation reduces to the simple heat conduction problem with heat source. By convention, i=1 designates the H2SO4 continuous liquid phase whereas H2 bubbles constitute the dispersed phase (i=2).     i  i ui   S i

 

(4)

 i  i u i . ui   i P     i   i  i g   K ji u j  ui 











 





(5)

j

     i C Pi  i uiTi    eff i Ti     i .u i  S Qi 

 Q ji

(6)

j

The source term Si in eqn (4) is zero in the overall domain but in the H2 release zone. The source term SQi in eqn (6) stands for the heat dissipation rate inherent WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)

16 Simulation of Electrochemical Processes III in the electrokinetic processes. The last terms on the right-hand side of eqn. (5) and eqn. (6) represent the interphase interactions, where Kji is computed according to the Schiller and Naumann model for the drag coefficient, as in ref. [5], and Qji using the default FLUENT assumptions. The renormalized k- model of FLUENT is used to compute the Reynolds stress tensors i and the effective properties for each phase. A k- turbulence model is also used in [3] and [8]. A less CPU-consuming model based on mixture-lengths is used in [4]. 3.4 Interphase and source terms In the Westinghouse electrochemical step, hydrogen is released at the cathode interface. In the numerical study, bubble generation is assumed to be localized in the first row of fluid cells neighbouring the electrode. In this special zone analogue to a boundary layer, the rate of gas production is assumed equal to the rate of the reduction process. It is modelled by the source term S2 of the dispersed phase mass-balance equation, assuming a 100% Faradic yield. (7) M H2   S2  j  n int   S1 2eF where MH2 is the gas molar mass (2 10-3 kg·mol-1), F = 96485 C.mol-1 is the Faraday constant and e = 10-4 m the width of the H2 release zone. The interfacial current density is calculated by Flux-Expert. The assumption S1 = -S2 was first made by analogy with boiling, although no significant difference in the simulation results was observed by assuming S1 = 0. Also provided by the finite element solver is the source term SQ in the energy balance, eqn. (6). Except within the H2 release zone, the volumetric heat flux corresponds to heat losses by Joule effect in the conducting materials. In zone , the heat dissipated by the irreversible interfacial processes is computed instead.   (8) SQ    j  n y  e

 

 

3.5 Boundary conditions Material properties are assumed to be constant in the CFD simulation. Data representative of the operating conditions frequently described in the literature [9,11] are used: the cell is operated under atmospheric pressure conditions with sulphuric acid solutions at 30 wt% in the cathode compartment and 50 wt% in the anode compartment, as recommended by the Westinghouse cycle efficiency evaluations. The desired specific flow-rate is imposed at the fluid inlet, where the temperature is maintained at 323 K. Adiabatic conditions prevail at the domain boundaries. A monodisperse population of spherical H2 bubbles is assumed. The bubble diameter was not measured and was arbitrarily set. The gas flow rate was computed from the current density, but regarding bubble impulsion we had a degree of freedom. Thus a constant departure angle θ is imposed to help compute the initial velocity components in the three directions of space (fig. 2). We WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)


17

assume therefore that bubbles are ejected perpendicularly (y-direction) and that they are deviated from an angle θ in the flow direction by the convective flow. Since bubbles are not allowed to evolve along the surface (i.e. in the xz-plane), the x-component of the departure velocity is zero. Regarding the electrokinetic problem, an imposed current supply is assumed at the anode corresponding to a uniform current density of 2000 A.m-2. The cathode potential is set at 0 V. CFD simulations were performed in single precision while the electrokinetic problem was solved in double precision. Double precision is required since current density is post-processed from the potential distribution and careful meshing is necessary as shown by Caire and Chifflet [12].

4

Parameter study

From a purely electrokinetic point of view (i.e. for single-phase flow), the calculated cell voltage equal to 0.732 V is mainly attributed to SO2 oxidation kinetics which is responsible for the anodic overvoltage (fig. 3). catholyte

anolyte

catholyte

gz

 vy

x

x

y

vbubble

z

z

x

anolyte

gy

gx

z

Figure 2:

catholyte

anolyte

vz

y

y

Schematic representation of the cell orientations (left) and bubble departure from the electrode surface (right). 0,800 anoodic overpotential

0,700

Voltage (V)

0,600 0,500 ohmic drop membrane

0,400 0,300 cathodic overpotential

0,200 0,100 0,000 0

0,002

0,004

0,006

0,008

0,01

0,012

y coordinate (m)

Figure 3:

Cell potential distribution for single-phase flow (x = 0.02, z = 0.08).


18 Simulation of Electrochemical Processes III The model was used to study the process sensitivity to the major unknown parameters: the H2 bubble size (50−200 µm) and their departure angle (30−60°). The effect of cell orientation and electrolyte flow rate in the range of the pilot facility operating conditions (75−200 L.h-1) was also investigated. Process sensitivity is measured in term of cell voltage and gas fraction maximum and average values. Gaseous phase spatial distribution is also examined. Major simulation results are summarized in table 2. Three kinds of cell orientation were studied in reference with gravity (fig. 2): i) vertical gas-evolving electrode, like in prior work [3–5,7], ii) gravity vector oriented downward in x-direction, which is the configuration of the pilot facility, and iii) horizontal cathode facing upward. They are referred to as gz, gx and gy respectively. For each case the gas fraction distribution in yz-plane within the cathode compartment is shown in fig. 4. When the flow direction is parallel to gravity (gz), a gas curtain remains confined near the electrode. Bubbles progressively spread within the liquid (in the y-direction) with increasing z. The maximum penetration depth is closed to 20% of the gap width. Additional simulations indicate that increasing flow rate confines the bubbles at the neighbouring electrode, but decreases the overall gas amount since bubbles are conveyed by the liquid flow. The same effect is, to a lesser extent, achieved by increasing the departure angle (Table 2). In the second case (gx), the plume is still present but a second bubble layer develops in the y-direction, expanding in the x-direction according to the gravity field. The gas fraction is therefore increasing, outside the bubble curtain, with increasing distance from the electrode. Gas fraction and voltage distribution contours in the catholyte compartment are illustrated fig. 5. In the gz case (left), the gas fraction increases in the flow direction (z), whereas in the gx case (right) H2 is trapped at the top of the cell, under the effect of gravity. In this configuration, a slight asymmetry can be observed in the liquid flow direction. The voltage distribution reveals the corresponding local variations of the fluid conductivity. In the case of the horizontal cathode facing upward (gy), the plume along the flow direction vanishes and gas accumulates just below the rigid membrane, where the simulation predicts a phase segregation (2  1). Convergence 2

2

2

0.30 0.20 alpha 0.10 0.00 1,5 YY(m) 3,5

1.00

0.20

0,35

1,0

0,2

0,30 0,25

0,20

0,1

0,10 0,05

0,1 10

0,05

0,0035 0,0045 0,0055 0,0065

5,5

y (mm)

Figure 4:

alpha

0,15

0,00

0,0015 0,0025

0.50

0.10 alpha

0,15

0,00

0,00

Z(m) 0,10

z (m)

0,15

0.00 1,5Y (m) 3,5 0,0

0,0015 0,0025

0,10 0,05

0,0035 0,0045 0,0055 0,0065

5,5

0,00

0,00

Z (m) 0,10

z (m)

y (mm)

0,5

0.00 1,5

0,15

0,0

0,10

0,0015 , 0,0025 0 0025

0,05 0,0035 0,0045 0,0055 0,0065

Y (m) 3,5

5,5

0,00

0,00

Z (m) 0,10

z (m)

y (mm)

Gas distribution in the cathode compartment for gz at x = 0.02 (left), gx at x = 0.03 (middle) and gy at x = 0.01 (right) for  =30°, dbubble =100 µm, flow rate 75 L.h-1.


Simulation of Electrochemical Processes III H2 (Fluent) gz

0,770

0,060

0,768

0,050

0,766

Gx orientation Gz orientation

0,764

0,030

0,762

0,020

0,760

0,010

0,758 0,756

0,000 50

100

d_bubbles (µm)

Figure 6:

V (Flux-Expert)

Surface plots of gas volume fraction 2 and voltage  in the cathodic compartment for dbubbles =100µm,  30°, flow-rate 75 L· h-1 in the gz (near the cathode) and gx (near the membrane) configurations.

0,070

0,040

gx

200

flow Cell voltage (V)

Gas fraction (average)

Figure 5:

H2 (Fluent)

V (Flux-Expert)

19

x z

Bubble trajectory

Left: gas holdup (circles) and cell voltage (triangles) evolutions with bubble size ( 30°, flow-rate 75 L·h-1) in the gx (top) or gz (bottom) orientation. Right: illustration of the bubbles trajectories in the gx configuration for small (top), medium (middle) and large (bottom) bubbles.

troubles were encountered during the resolution process since the dispersed phase became predominant. The same difficulties were encountered for the same reason when simulating the gx - dbubble = 200 µm configuration. The variation of the average gas fraction and the cell voltage with the bubble size is depicted in the left part of fig. 6 for the gz and gx configurations. In the gz configuration, the gas holdup (and correlatively the cell voltage) decreases with the bubble diameter, according to the bubbles rising velocity evolution.


20 Simulation of Electrochemical Processes III In the gx configuration, the bubble free rising direction is perpendicular to the flow direction. Increasing the bubble size is first leading to an increase of the gas holdup. Indeed, the bigger bubbles trajectories are more deviating from the flow trajectory, thus increasing their residence time in the cathode compartment (fig. 6, right). If the bubble diameter is further increased, the reverse phenomenon is observed. In this case, bubbles are rapidly rising from the cathode to the top of the, finite-width, electrolyser, from which they are conveyed straightforwardly toward the cell outlet by the convective flow, with a reduced residence time. Table 2: monophasic gx gx gx gx gx gy gz gz gz gz gz

5

dbubbles / 50 µm 100 µm 200 µm 100 µm 100 µm 100 µm 50 µm 100 µm 200 µm 100 µm 100 µm

Parameter study assumptions and results. Flow rate 75 L·h-1 75 L·h-1 75 L·h-1 75 L·h-1 75 L·h-1 200 L·h-1 75 L·h-1 75 L·h-1 75 L·h-1 75 L·h-1 75 L·h-1 200 L·h-1



2,max

2,mean

/° 30° 30° 30° 60° 30° 30° 30° 30° 30° 60° 30°

/ 0.458 0.726 0.936 0.774 0.258 0.996 0.386 0.367 0.350 0.357 0.295

/ 0.057 0.062 0.046 0.064 0.018 0.044 0.021 0.019 0.018 0.015 0.014

 0.732 V 0.767 V 0.769 V 0.766 V 0.768 V 0.757 V 0.773 V 0.761 V 0.761 V 0.761 V 0.760 V 0.757 V

Conclusion

A parameter study of the two-phase filter-press electrolyser was carried out in the scope of optimizing the Westinghouse electrochemical step. The process sensitivity to biphasic phenomena was qualitatively assessed using a multiphysics model. As compared with the “monophasic” case (i.e. the purely electrokinetic problem solved by Flux-Expert, without CFD coupling) and in the range of conditions explored, hydrogen bubbles are responsible for an additional overvoltage ranging from 25 to 40 mV. Among the investigated parameters, the electrolyte flow rate appeared to have the greatest influence on the cell voltage, irrespective of the cell orientation. The model has demonstrated its versatility, allowing a detailed description of the various phenomena involved, but failed in predicting nearly segregated configurations for which numerical difficulties occurred. As the gas fraction approaches 1, the electrolyte conductivity tends towards 0. Moreover, from a fluid mechanics standpoint, the validity of the Euler-Euler model is questionable and a Volume of Fluid approach should be preferred. Available experimental data, measured under fixed cell voltage conditions, exhibit unexpectedly low current densities. Indeed, although an ideal impermeable membrane was considered for the simulation, non-negligible SO2 crossover occurred during the experiments, due to the poor selectivity of the available membrane. Therefore, an appreciable fraction of the expected current WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)


21

density was consumed by side reactions induced by the sulphur species. The occurring of the latter side reactions, not taken into account in the model, prevents us from validating the two-phase model assumptions, unless a more efficient separator is used. A detailed description of species transport, membrane exchanges and electrochemical processes is required as well to reach a sufficient degree of understanding of the electrolytic cell functioning, and therefore to complete the design and optimization of an industrial-scale process. Such a phenomenological model is currently being developed. Experiments have also been designed to improve the SO2 oxidation overvoltage model, which will be described in a future paper. A phenomenological description of H2 bubbles evolving at industrial electrodes is currently in progress within the scope of the AMELHYFLAM project, and the qualitative phenomena highlighted by this simulation study will be helpful in designing the future cell instrumentation.

Acknowledgements The authors are grateful to the ANR project AMELHYFLAM for financial support and to the LECNA team of the CEA Saclay laboratory for the supplied electrochemical properties.

References [1] [2] [3] [4]

[5] [6] [7]

Trinidad P, Ponce de León C. & Walsh F.C., The application of flow dispersion models to FM01-LC laboratory filter-press reactor. Electrochemica Acta, 52, pp. 604-613, 2006. Duerr M., Gair S., Cruden A. & McDonald J., Dynamic electrochemical model of an alkaline fuel cell stack. Proc. of 16th World Hydrogen Energy Conference, June 13-16, Lyon (France), 2006. Mandin P., Hamburger J., Bessou S. & Picard G., Modelling and calculation of the current density distribution evolution at vertical gasevolving electrodes. Electrochemica Acta, 51, pp.1140-1156, 2005. Agranat V., Zhubrin S., Maria A., Hinatsu J., Stemp M. & Kawaji M., CFD modelling of gas-liquid flow and heat transfer in a high pressure water electrolyser system. Proc. of FEDSM, July 17-20, Miami (Florida) 2006. Mat M., Aldas K. & Ilegbusi O., A two-phase model for hydrogen evolution in an electrochemical cell. Int. Jal of H2 Energy, 29, pp. 10151023, 2004. Roustan H., Caire J.P., Nicolas F. & Pham P., Modelling coupled transfers in an industrial fluorine electrolyser. Jal of Applied Electrochemistry, 28, pp. 237-243, 1998. Jomard J, Feraud J.P., Morandini J., Du Terrail Couvat Y. & Caire J.P., Hydrogen filter press electrolyser modelled by coupling Fluent and Flux Expert codes. Jal of Applied Electrochemistry, 38, pp. 297-308, 2008. WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)

22 Simulation of Electrochemical Processes III [8] [9]

[10] [11] [12]

Espinasse G., Peyrard M., Nicolas F. & Caire J.P., Effect of hydrodynamics on Faradaic current efficiency in a fluorine electrolyser, Jal of Applied Electrochemistry, 37, pp. 77–85, 2007. Rivalier P., Charton S., Ode D., Duhamet J., Boisset L., Pabion J.L., Gandi F. & Croze J.P., Design study of a pilot test plant for hydrogen production by a hybrid thermochemical process, Proc. of the16th Int. Conf. on Nuclear Engineering, May 11-15, Orlando (Florida), 2008. Brown C.J., Pletcher D., Walsh F.C., Hammond J.K. & Robinson D., Local mass transport effects in the FM01 laboratory electrolyser. Jal of Applied Electrochemistry, 22, pp. 613-619, 1992. Appleby A.J. & Pinchon B., The mechanisms of the electrochemical oxidation of sulphur dioxide in sulphuric acid solutions. Jal of Electroanalytical Chemistry, 95(1), pp. 59-71, 1979. Caire J.P. & Chifflet H., Meshing noise effect in design of experiments using computer experiments, Environmetrics, 13(1), pp. 1-8, 2002.



23

A hydraulic model to simulate the hydrodynamics of a fluorine electrolyser J. P. Caire1, G. Espinasse2, M. Dupoizat3 & M. Peyrard4 1

LEPMI, Grenoble INP, France BERTIN Technologies, France 3 AREVA Business Unit Chimie, Secteur Mines Chimie Enrichissement, France 4 ASTEK Rhône-Alpes, France 2

Abstract Fluorine electrolysis is characterized by very large overpotentials and bubble effects that are not yet fully understood. The two-phase free flows appearing in the fluorine reactor are complex and attributable mainly to hydrogen bubbles evolving at the cathode. However, large fluorine bubbles gliding along the anode help to drag the electrolyte up along the anode and in doing so also take part to the two-phase movement. The fluorine electrolyser has been modelled in the past but there has been no means of comparing hydraulic computations with measurements in such an aggressive environment. A hydraulic model is presented here to test the ability of the Estet-Astrid finite volume code to model the fluorine reactor. The two-phase free flow was modelled using an Euler-Euler scheme assuming bubbles of uniform diameter. Laser Particle Image Velocimetry was used to measure both gas and liquid velocities. This paper presents the experimental study and the model made to obtain the plume shape. Numerical and experimental results are compared and some discrepancies are explained. Improvements are suggested for future modelling Keywords: hydrogen, fluorine, electrolysis, two-phase flow, hydraulic model, free convection, Estet-Astrid.

1

Fluorine electrolysis

Fluorine electrolysis is characterized by very large overpotentials and bubble effects [1, 2]. The fluorine electrolyser has been extensively described in [3]. The WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/ECOR090031

24 Simulation of Electrochemical Processes III characteristics of fluorine bubble release are not yet completely understood [1, 4]. The two-phase free flow is mainly due to hydrogen bubbles evolving at the cathode, but large fluorine bubbles also take part in the two-phase movement, as seen in fig. 1a. H. Roustan [1] has shown that to some extent the large gliding fluorine bubbles drag the electrolyte up along the anode. A numerical model was gradually developed in France to account for all the strongly linked phenomena involved in fluorine electrolysis [2–6]. The final numerical model combined two commercial codes, Flux-Expert (FE) and Estet-Astrid (EA), both distributed by Astek [7, 8]. Estet-Astrid is a CFD finite volume code for computing the free convection of two-phase flows. In the present study it was used with an EulerEuler model. The Estet-Astrid code took into account the forces acting on individual bubbles, namely buoyancy, drag force, lift force and added mass. Thanks to EA, Espinasse et al. estimated the fraction of the hydrogen plume that recombines with fluorine and thereby decreases Faraday current efficiency in an industrial fluorine electrolyser [6].

Figure 1:

a) Fluorine and hydrogen bubbles. b) Equivalent scheme of hydrogen plume and fluorine bubbles.

Since the plume of hydrogen bubbles is so important in a fluorine electrolyser, experimental work was carried out to validate the accuracy of plume prediction by EA. KF-2HF molten salt electrolyte is so aggressive that it makes laser Particle Image Velocimetry (PIV) measurements difficult in a large fluorine cell. We therefore designed a hydraulic set-up using water (see fig. 3) in order to simulate the two-phase hydrodynamics of the fluorine electrolyser. We present the specific experimental study performed to determine the shape of the plume and the EA computations. The experimental and CFD results are then compared. Hydrogen bubbles generated in fluorine electrolysis are very small (diameter close to 250 µm). Fluorine behaves in an unusual way: fluorine bubbles slip along the anode instead of detaching from the electrode in the same way as hydrogen bubbles. Fig. 1b) shows a schematic representation of the plume of hydrogen and the bubbles of fluorine that slip along the electrode, partially coated with CFx [4]. The hydrodynamics of a fluorine electrolyser are completely atypical. Roustan [1] showed that free convection of KF-2HF electrolyte was induced by both the hydrogen plume and the slipping film of fluorine, as shown in fig. 2. Electrolyte velocity was measured in the vicinity of the anode by PIV thanks to small alumina beads placed in a laboratory cell. WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)


25

Fig. 2 shows that velocity increases with height in an almost linear way along the cylindrical anode at low current density. With an increase in current density, i.e. in the fluorine flow rate on the anode, the velocity increases up to a plateau [1].

Figure 2:

Fluid velocity in vicinity of a cylindrical anode in a laboratory fluorine cell.

This drag effect was interpreted as follows: the almost continuous film of fluorine bubbles adhering to the anode slips upwards increasingly quickly and moves the electrolyte in its vicinity. Because of the large gas cover rate on the anode, the local current density is extremely high and the bubbles interact with the electrolyte, according to us, when small liquid jets exchange mass between the electrode and the bulk in a way similar to that described in Higbie’s penetration model [9]. Thus, the film of fluorine bubbles acts as a mobile wall that moves the liquid roughly at its speed (fig. 2). This idea of a moving wall was used in the hydraulic model. The hydrogen bubbles evolving at the cathode are driven by the molten salt and in the absence of a separator between the anode and cathode compartments (no diaphragm is resistant enough for use in a fluorine electrolyser) they can come in contact with fluorine and recombine spontaneously into hydrofluoric acid. Espinasse et al. [6] showed that when the intensity of the cell increases, Faraday efficiency decreases because of this recombination. It is thus particularly important to accurately simulate the hydrodynamics of the fluorine cell so as to predict its operation correctly. KF-2HF molten salt at 95 °C is very corrosive and extremely delicate to handle. It was thus decided to build a hydraulic model using water and nitrogen bubbles, which is easier to study and presents fewer hazards, the final objective being to validate the EA numerical model used previously for the fluorine cell.

2

Hydraulic model

The 60x60x10 cm scale model made out of Plexiglas is shown in fig. 3. Nitrogen flowing through a gas sparger fitted with a circular sintered-glass filter created a fairly realistic plume of nitrogen bubbles, probably similar to the hydrogen WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)


Figure 3:

Scheme of the hydraulic model with the 3 axis directions used in this study.

plume in the fluorine cell. The behaviour of the fluorine in the linear part of fig. 2 was simulated by a notched belt moving at constant speed which sweeps water along in the tank just as fluorine drags the electrolyte in the fluorine cell. The belt was covered with a partially opened casing to simulate an equivalent anode; the flow was therefore channelled only in the vertical direction. The belt casing and its associated electric motor could be moved along the x-axis to visualize the influence of the spacing between the two pseudo-electrodes. The model is not very thick for two reasons: i) PIV cannot be used to measure velocity along the y-axis, ii) free convection movements in the vertical plane are favoured, though Fig. 6 shows that some small parasitic movements appear in the y-direction. Thus it can be estimated that the fluorine film creeping along the anode surface is conveniently represented by the moving belt.

3 Measurements Particle Image Velocimetry (PIV) was used to determine the velocity vectors in the tank. The method is based on the image processing of a laser light sheet created in the vertical z-x plane which allows measurement of the displacement of 14 µm metallised hollow glass beads carried by the flow. Nitrogen flow was injected between 0 and 100 l/h through a circular sintered-glass filter. Ethylene glycol was added to modify the viscosity of the fluid from 1 to 3.4 mPa.s and decrease the diameter of the nitrogen bubbles from 5 to 1 mm, value close to the estimated hydrogen bubbles diameter in the fluorine reactor [13]. The uniform linear speed of the belt could be varied between 0 and 0.3 m/s to simulate in some extent the fluorine behaviour. 3.1 Study of bubble plume alone Since the PIV system could retrieve only one signal at a time for each phase it was not possible to obtain simultaneous measurements of both liquid and WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)


27

nitrogen bubble velocities in the plume. Thus, the velocity vectors were obtained successively through the left window of fig. 4 for the nitrogen bubbles in the plume and through the right window for the liquid.

Figure 4:

The two windows used for measuring gas and liquid velocity vectors in z-x plane.

Figure 5:

Plume of nitrogen bubbles and schematic movements of fluids in the y-z and z-x directions (bubble diameter 5 mm – gas flow rate 50 l/h).

Fig. 5 shows the bubble plume in front view (y-z plane) and profile (z-x plane). In both cases the photo is accompanied by a drawing schematizing the observed flows. For a constant gas input, the total gas/liquid contact surface is greater for small bubbles than for larger bubbles and the gas-liquid interactions are also greater. It was observed that the smaller the bubbles, the greater the liquid velocity, the more agitated and more turbulent the bubble plume, and the more spread out the plume at the air/liquid interface. 3.2 Study of the notched belt alone The speed of the notched belt could be changed to visualize its convective effect on the liquid initially at rest. Fig. 6 shows a photo of the liquid, with the moving WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)

28 Simulation of Electrochemical Processes III belt seen at left. The velocity vectors computed from PIV measurements were superimposed on the photo. The picture is of the upper part of the tank taken when the movement of the liquid was instigated by the belt alone.

Figure 6:

Figure 7:

Photo of liquid circulated by the notched with the reference points A, B, C.

PIV velocity of liquid circulated by the notched belt alone.

Fig. 7 presents the liquid velocities measured at A, B, C (see fig. 6) when the belt alone is actuated. A laminar/turbulent transition appears at a belt speed of 0.1 m/s. For speeds higher than 0.1 m/s, the flow becomes turbulent, and the liquid also moves in the third dimension i.e. along y-axis, as seen in fig. 5-left. In turbulent conditions, water is no longer dragged at the belt speed, and the slip velocity becomes significant. A Reynolds number could be assigned to the belt: Reb =

LV ν

(1)

where L is the belt width in m, V the velocity of the belt in m/s and ν the kinematic viscosity in m²/s. With this definition, the laminar-turbulent transition was observed at a Reb value of 2000, i.e. for V equal to 0.1m/s. In laminar conditions, the maximum velocities observed in the liquid (see fig. 7) are very WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)


29

close to the belt speed. At large distances from the belt and particularly at points A, B, and C the influence of the belt is less marked and the liquid velocities are lower. In turbulent conditions, maximum velocity is lower since belt-liquid coupling is lessened and the slip velocity becomes significant. Similar behaviour was observed for a fluorine film in a small laboratory cell when current density was increased i.e. when the velocity of the fluorine film on the anode was increased [1]. This confirms that the moving belt is a convenient method for simulating the fluorine film.

4

3D Numerical modelling

The Estet-Astrid commercial CFD code was used to simulate the hydraulic model. This finite volume code was used with a two-phase Euler-Euler K-ε turbulence model [6]. In this case the code solved a mass balance equation and a momentum balance equation both for the liquid and the gas. In this model, the liquid is regarded as the continuous phase, while the gas constitutes the minority phase, i.e. the dispersed phase. Compared with a Euler-Lagrange two-phase model, strong coupling between phases is easily treated and transients are more easily computed. The model did not take into account bubble diameter distribution (Log-Normal distributions are often observed in this case). However, Antal et al. [10] have shown that distribution of bubble diameters is the most significant parameter for a good description of plumes. The bubbles are regarded as rigid spheres. The two-phase model took into account as in [6] the following forces exerted on bubbles: 1 – gravity, 2 – buoyancy (Archimedes’ force), 3 – the force exerted by the flow on the bubble which results from two terms: the pressure effect, strongly related to the existence of a wake for poorly shaped particles; and the effect of the viscous term that dominates in well shaped bodies, which is the case for a spherical gas bubble. These effects can be split into two forces: a drag force in the direction of incidental flow and a lift force in the direction perpendicular to incidental flow, 4 – added mass, i.e. the force on the liquid related to the particle acceleration. It can be observed that the bubble diameter comes into play in all these forces at power 2 or 3, making the computation very sensitive to this parameter. There are many other forces which could be considered (compressive force due to the liquid, surface tension forces, wake-related forces exerted by neighbouring bubbles, electrostatic repulsion forces between bubbles, etc.). However, these forces were not taken into account in this numerical model. The physical data used for the two phases are shown in Table 1. Table 1:

Physical properties of the continuous and disperse phases.

Pressure Density Kinematic viscosity Inlet mass flow rate Bubbles diameter

H2O 101300 Pa 998 kg m-3 10-6 m2 s-1 0,0124 kg m-2 s-1


N2 101300 Pa 1.12 kg m-3 2.18.10-5 m2 s-1 0.001-0.005 m

30 Simulation of Electrochemical Processes III 4.1

Initial conditions

Initially the water was assumed to be at rest and the gas fraction null at any point of the system. At initial time, the gas (made up of bubbles of diameter d) was introduced at a constant mass flow rate with a given speed. The problem was thus time-dependent, and therefore solved in non-stationary conditions until stationary conditions were reached. The solution then perfectly described the transient evolution of the gas plume.

Figure 8: 4.2

Boundary conditions and curvilinear structured meshing.

Boundary conditions

Fig. 8 describes the boundary conditions used here for a plume of nitrogen composed of 1 millimetre-diameter bubbles. At gas output, the free surface of the water was assumed to be constantly at rest and the normal liquid velocity vectors null: ∂V = 0 ∂n

(2)

On this symmetry plane, the boundary condition for pressure is as follows: ∂ 2P =0 ∂τ∂n

(3)

This classical condition of EA [8] describes the ideal free liquid surface and let the gas pass freely through it. At walls of the tank the velocities were assumed to be null for the two phases. At gas input, a uniform velocity profile was imposed for the dispersed phase. It was assumed here that the input velocity vectors were tilted at 45° upwards from the horizontal in order to obtain realistic hydraulic WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)


31

conditions. This arbitrary condition was required since convergence problems appeared when the bubbles were injected perpendicularly to the sintered-glass filter. 4.3 Grid mesh Fig. 8 shows the structured curvilinear grid used in these calculations. The grid related to the hydraulic model is made of 18 planes in x-direction, 59 in ydirection, 45 in z-direction and 47790 nodes. No special meshing law was required at tank wall since a no slip condition was imposed in EA [8]. To describe the formation of plume which fully develops in 2 seconds it was necessary to use a time step close to 10-5 second, requiring a computing time of approximately 70 hours on an INTEL bi Xeon 2.5 GHz PC. Fig. 9 presents the velocities calculated by EA for gas bubbles and liquid along AB. The bubble velocity and liquid velocity increase with height. Both velocities have a similar profile on AB, but the bubble velocity is much higher than that of the liquid. The difference, close to 0.38 m/s, is attributed to the slip velocity between bubbles and liquid. This value is much more realistic than the 1.3 m/s free rising velocity of bubbles calculated from the Stokes formula.

5

Comparison of experimental and numerical results

The comparison between measurements and numerical results of fig. 10 shows some disparities. Three zones can be distinguished. In zone 1, close to the sparger at the plume bottom, the diameter of the bubbles is gauged at less than 1 mm. Along the plume, the diameter of the rising bubbles increases, probably by coalescence. Since all the forces acting on the bubbles depend on their diameter, the numerical model overestimates the size of the bubbles in the bottom of the plume. In the second zone, computed and measured velocities are practically identical. It is thought that the bubble diameters have their nominal value in this zone.

Figure 9:

Velocity computed on path AB situated at 2 cm from the left wall.

The third zone is at the top of tank where the plume spreads out. The numerical model again overestimates the gas velocity, probably because the WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)

32 Simulation of Electrochemical Processes III effect of the interface on escaping bubbles was not taken into account in this model. Closer examination of the bubble plume in fig. 11-left reveals that the bubble plume widens along the air-water interface whereas the computed plume seen in fig. 11-right is very narrow in this area.

Figure 10:

Comparison between numerical model and measurements for gas velocity on AB.

The difference between model and calculation undoubtedly comes from the effect of the free interface, which was not taken into account here. This model also lacks the interactions between bubbles: in reality, the rising bubbles collide with each other and then lose kinetic energy. The numerous collisions between quasi-rigid bubbles probably explain the widening of the plume seen in fig. 11. Moreover, the numerical model did not take into account the interactions that might exist between the bubbles in the plume and those at the sparger outlet. Nor did the model take into account bubble diameter distribution. This poor description of a plume is not related to EA.

Figure 11:

Photo of nitrogen plume and computed volume fraction of gas.

None of the usual commercial codes satisfactorily describes this type of plume, as underlined by Antal et al. [10] when comparing the three commercial codes CFX, FLUENT and NPHASE with the same plume benchmark. The main WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)


33

issues are probably related to the lack of interactions between bubbles and their environment (other bubbles, wakes of other bubbles, walls, air-liquid interface). Antal et al. [10] have also pointed out that it is not realistic to assume uniform diameters since diameter distributions of bubbles usually follow a Log-Normal law [13]. These problems are encountered in many fields [11], and particularly in the modelling of electrochemical reactors [11–12]. It is thus necessary to take account of these observations in order to improve models of two-phase fluids and obtain more realistic bubble plumes.

6

Conclusions

A hydraulic model giving a vertical two-phase flow similar to that of a fluorine cell was designed and investigated. Experimental results confirmed the similarities in behaviour between the hydraulic model and the fluorine cell. The comparison of numerical and PIV results for the hydraulic model showed that gas and liquid velocity vectors were realistic and of the same order of magnitude. The results were in good agreement for the nominal diameter of the bubbles and discrepancies occurred when coalescence was visible. The belt used as a moving wall behaved in a similar way to the gliding film of fluorine bubbles on an anode. However, the discrepancies observed - particularly for the gas plume reflected the lack of interactions between bubbles in this model. Moreover, the model required a long computing time due to the very small time step necessary to properly describe the transient flows in the tank and attain the stationary state. Further modelling work is in progress within the framework of the AMELHYFLAM project to improve the hydrodynamics of fluorine reactors.

Acknowledgements The authors are grateful to AREVA and the French project AMELHYFLAM (ANR 2007) for their financial support.

References [1] [2] [3] [4] [5]

Roustan H., Modélisation des transferts couplés de charge et de chaleur dans un électrolyseur industriel de production de fluor, INPG thesis, Grenoble, 1998. Roustan H., Caire J.P., Nicolas F. & Pham P., Modelling coupled transfers in an industrial fluorine electrolyser. Jal of Applied Electrochemistry, 28, pp. 237-243, 1998. Nicolas F., Techniques de l’Ingénieur, J 6 325, Editions T.I., Paris. Groult H., Devilliers D., Lantelme F. & Caire J.P., Combel M., Nicolas F., Origin of the anodic overvoltage observed during fluorine evolution in KF-2HF, J. of Elelectrochem. Soc., 149, E485-E492, 2002. Roustan H., Caire J.P., Nicolas F. & Pham P., in J.W. Van Zee, T.F. Fuller, P.C. Foller and F. Hine (Eds), ‘Advances in Mathematical WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)


[6] [7] [8] [9] [10]

[11] [12] [13]

Modeling and Simulation of Electrochemical Processes’, Electrochem. Soc. Proc. USA 98-10, 202, 1998. Espinasse G., Peyrard M., Nicolas F., Caire J.P., Effect of hydrodynamics on Faradaic current efficiency in a fluorine electrolyser, Jal of Applied Electrochemistry 37, 77–85, 2007. Flux-Expert, Guide de l'Utilisateur, ASTEK, Paris, 2001. Estet-Astrid, Guide de l'Utilisateur, ASTEK, Paris, 2001. Higbie R., The rate of absorption of pure gas into a still liquid during short periods of exposure. Transactions of A.I.Ch.E. 31 365, 1935. Antal, S.P., Ettorre, S.M., Kunz, R.F., Podowski, M.Z., Development of a next generation computer code for the prediction of multicomponent multiphase flows. In: proceeding of the International Meeting on Trends in Numerical and Physical Modeling for Industrial Multiphase Flow, Cargese, France, 2000. Mandin P., Hamburger J., Bessou S. & Picard G., Modelling and calculation of the current density distribution evolution at vertical gasevolving electrodes, Electrochemica Acta, 51, pp.1140-1156, 2005. Jomard J., Feraud J.P., Morandini J., Du Terrail Couvat Y. & Caire J.P., Hydrogen filter press electrolyser modelled by coupling Fluent and Flux Expert codes, Jal of Applied Electrochemistry, 38, pp. 297-308, 2008. Caire J.P., unpublished results.



35

Computational modelling of cathodic protection systems for pipelines in multi-layer soil A. B. Peratta, J. M. W. Baynham & R. A. Adey CM BEASY Ltd, UK

Abstract Computational modelling of cathodic protection (CP) systems involving thin multi-layer media represents a real challenge in terms of accuracy and efficiency required in the numerical calculation. In the case of CP for transmission pipelines, these long metallic structures are usually buried a distance H (approximately a metre or so) below ground level and extend horizontally typically more than ten thousand times H. A number of impressed current anode beds are distributed along the pipeline, providing protection against corrosion of the structure. In addition, the vertically stratified nature of the soil needs to be considered in the model, in order to obtain more accurate representation of the environment. This is particularly relevant when considering the effect of different types of rocks, soil porosity, or water saturation, at different depths. This type of scenario requires three dimensional modelling involving a thin multi layered electrolyte, with a typical aspect ratio (lateral extension to thickness) of the order 1E4 to 1E6. The paper presents an efficient and accurate computational approach based on the Boundary Element Method for simulating the level of protection against corrosion of the pipeline as well as current densities and electric potential in different points of the soil. The resulting modelling approach is then applied to assessing real case scenarios. The simulation approach considers the non linear electrode kinetics on the metal surfaces in the form of polarisation data and also the internal resistance of the pipeline and other electrical connections involved in the CP system. Example applications are presented showing how the model can be used to predict the “signatures” associated with different defect types in the pipe coating. Keywords: cathodic protection, multi-layer, Boundary Element Method, transmission pipelines. WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/ECOR090041


1

Introduction

One of the most effective ways to control corrosion in metallic structures embedded in an electrolyte, such as the case of underground or undersea transmission pipelines, is by means of a combination of coating and impressed current cathodic protection (ICCP) systems. Field surveys such as the Direct Current Voltage Gradient (DCVG), and monitoring systems are aimed at different aspects of the assessment of the corrosion control system. Field measurements require skilled technicians, are often expensive and difficult to obtain. In addition, different sections of the pipeline are not always accessible for the surveyors, and in most cases the noise in the potential measurements can mask developing defects in the pipeline coating. Moreover, the interpretation of field data and its correlation to the performance level of the corrosion control system is not always straightforward. The direct computational modelling of CP systems offers a variety of tools for processing the information collected from the field and complementing it, allowing better interpretation of field measurements, as well as enabling the correlation against the CP design parameters and their impact on the observable magnitudes. By direct CP simulation we mean the process of predicting field results such as: • ON and OFF potentials, • potential gradients and currents fields in the soil, as well as • over potential and current density along the pipeline, Provided that the ICCP design parameters such as for example: • geometrical arrangement and material properties of pipelines and anodes, • electrical resistivity distribution of the soil, • type and location of the electrical connections between rectifiers, anodes and structure • Coating breakdown factor along the pipeline are given as input data. The direct simulation of ICCP systems by computational modelling has achieved in the past few years quite a mature state producing reliable results for industrial environments. This type of simulation is particularly useful at the design stage for the analysis of “what-if” case scenarios including the problems of interference with foreign CP systems or metallic structures. The purpose of this work is to present an efficient 3D direct simulation tool based on the Boundary Element Method, applied to two case scenarios involving transmission pipelines. The paper is focused on the effects in the potential measurements introduced by variable breakdown factors associated with the coating. This document is organised in the following way. Section 2 describes modelling approach and provides pointers to the relevant literature involved in the method. Section 3 introduces a simple case for study where the effects of localised damages in the coating along the pipeline can be detected. Section 4 WIT Transactions on Engineering Sciences, Vol 65, © 2009 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)


37

shows a more realistic case scenario involving three parallel pipelines running along the same corridor. Finally Section 5 establishes the conclusions.

2

Direct modelling

The direct modelling consists of obtaining results of electric potential and current density any point in the electrolyte and at surfaces of electrodes. Under most common situations, this requires solving the steady state charge conservation equation in the electrolyte in 3D space given by: ∇⋅ j= 0 , x∈Ω (1) where j = −σ (x) ∇u (x) (2) represents current density, σ is the electrolyte conductivity, u(x) is the potential field, ∇ is the 3D Laplace operator, and Ω represents the integration domain (electrolyte). Eqs. (1)-(2) can be solved together with the corresponding boundary conditions which are usually prescribed by imposing polarisation curves at the electrode surfaces, isolating conditions at ground level, and/or fixed potentials at any known equipotential surfaces in the electrolyte (if any). The Boundary Element Method (BEM) [1] has been widely used to solve Laplacian equations and in particular simulate cathodic protection systems for underground and offshore structures [2–4]. The most significant advantages of the method are first that the formulation is based on the fundamental solution of the leading partial differential operator in the governing equation, and second that it requires only mesh discretisation on the boundaries of the problem. The former aspect confers high accuracy, while the latter substantially simplifies the pre-processing stage of the model, since volume discretisation is not needed. The forward modelling of long transmission pipelines involves considering the soil as a thin film electrolyte (see Figure 2), since the pipeline span (L) is much bigger than the soil depth relevant for the modelling (h). In addition, the soil is generally stratified in one or many layers along the vertical (z) direction. This thin film stratified integration domain is very difficult to solve with standard modelling techniques such as FEM or BEM. Therefore, in order to be able to solve this type of integration domains without the need for extraordinarily high computational resources, a “multi-layer” BEM has been developed (MLBEM). The idea behind the ML-BEM is that the stratified nature of the medium is packaged into the corresponding Green’s function. In other words, the BEM is applied in the same way as in the case of the homogeneous electrolyte, except that the Green’s function for the homogeneous Laplace equation given by 1 / (4π r ) is replaced by the multi-layer Green’s function given by:

G (x i , x j , m, n) =

1 4πσ m

N exp

α ijml

k =1

x i − x j + g ij

∑


(3)

38 Simulation of Electrochemical Processes III where x denotes the 3D coordinates, the sub indices i and j stand for the source and field point, respectively; m and l indicate the layer of the source and field points, respectively; α ijml is a weight coefficient and g ijml denotes a displacement vector. The Green’s function written in this way can be regarded as the one produced by a weighted method of images. The calculation of the weight and displacement vectors goes beyond the scope of this paper and can be derived from references [5] and references therein. Finally, the Green’s function (3) replaces the 1/r kernel used for homogeneous regions, and the same BEM strategy can be employed. Layered non-homogeneous soil CP and Pipeline Network

Typical pipeline network configuration In particular, the condition h

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