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Imbibition in a Model Open Fracture

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Imbibition in a Model Open Fracture Imbibition in a model open fracture Capillary rise, kinetic roughening, and intermittent avalanche dynamics Xavier Clotet i Fons Aquesta tesi doctoral està subjecta a la llicència Reconeixement- NoComercial 3.0. Espanya de Creative Commons. Esta tesis doctoral está sujeta a la licencia Reconocimiento - NoComercial 3.0. España de Creative Commons. This doctoral thesis is licensed under the Creative Commons Attribution-NonCommercial 3.0. Spain License. Imbibition in a model open fracture Capillary rise, kinetic roughening, and intermittent avalanche dynamics Ph.D. Thesis Xavier Clotet i Fons Ph.D. advisors: Dr. Jordi Ort´ın Rull Dr. Stephane´ Santucci Agra¨ıments Primer de tot vull donar les gr`aciesalsmeusdirectorsdetesi,elJordiOrt´ın i l’St´ephane Santucci. Les discussions que hem tingut sobre f´ısica i sobre la ci`encia en general m’han encomanat la seva passi´o per fer recerca. Al Jordi li vull agrair haver confiat en mi des del principi. Durant la supervisi´odel treball desenvolupat aquests anys, els seus consells sempre han estat molt valuosos: des dels experiments, on m’ha fet veure la import`ancia de ser cur´os, a la redacci´o d’aquesta tesi, que ha revisat amb detall. Tamb´e vull agrair-li haver-me animat sempre a posar-hi la banya, especialment en els moments dif´ıcils. I want to thank St´ephane first for offering to be the coadvisor of my Thesis. It has been a great opportunity to work at Laboratoire de Physique with him. He passes his endless energy and motivation for physics on, making easier to solve any problem. He also makes you look on the bright side always. I also want to thank him his warm welcome in Lyon from the very first day. Tamb´e vull agrair als companys de laboratori tantes hores, problemes, discussions i solucions (i taques d’oli) compartides. El Ramon Planet em va ensenyar com funcionava el sistema experimental, em va explicar els trucs de funcionament i em va presentar les eines b`asiques d’an`alisi de dades. Fora del laboratori tamb´e hem compartit un munt d’estones agradables, especialment a Li´o on m’ha acollit en totes les visites. He tingut la sort de compartir la major part d’aquests anys al laboratori amb la Laura Casanellas. Que necess`aries algunes pauses a mitja tarda entre el soroll d’un experiment i l’oli de l’altre! El Jordi Soriano tamb´e ha tingut sempre un moment per donar-me un cop de m`a al laboratori, o en l’an`alisi de dades, o en el que fos necessari. Gr`acies als companys de despatx, Carles Blanch, David Palau i Guillermo Rodr´ıguez pel bon ambient que hi hem mantingut; especialment al Guillermo, amb qui ens hem suportat (tamb´e) durant la redacci´o de les tesis respectives. Tamb´e als companys de departament amb qui hem compartit deliciosos dinars i caf`es: Pau Bitlloch, Claudia Trejo, Xavier Fontan´e, Marta Manzanares, Oriol Rios, i perdoneu que no us mencioni a tots. Il a ´et´e un plaisir aussi de partager mon s´ejour `a Lyon avec des gens de l’ENS et La Doua. Merci beaucoup Osvanny Ramos, Marie-Julie Dalbe, S´ebastien Lherminier, i ii Chapter 0. Agra¨ıments Ania Modliska et, sp´ecialement, Baptiste Blanc pour me faire sentir chez moi. La Clara Picallo es mereix una menci´o a part per tants sopars, excursions i consells. Aquesta tesi no hagu´es estat possible sense el suport t`ecnic del Taller mec`anic dels CCITUB amb el Manel Quevedo al capdavant, a qui li agraeixo la seva dedicaci´oper trobar sempre la millor soluci´ot`ecnica. Tamb´e a l’Albert Comerma per les visites al laboratori, els consells i els muntatges electr`onics. Als meus pares, el Llu´ısilaPilar,amagermana,laMaria,iatotalafam´ılia vull agrair-los el suport incondicional durant aquests anys (i per preguntar de tant en tant si l’oli avan¸cava b´e) i per tots els anteriors que han fet que arrib´es fins aqu´ı. Finalment voldria agra¨ır als f´ısics pel m´on que durant i despr´es de la carrera ens hem dispersat des de Dunedin a Santa Cruz, passant per Par´ıs, Granada, Edimburg, Amsterdam, Copenhaguen o Londres, o quedat al pa´ıs, de Barcelona a Albesa, de Cam- brils a Olot. Els caf`es, els dinars, els skypes i les cerveses tamb´e han contribu¨ıt a fer cr´eixer aquesta tesi i, encara m´es important, no nom´es la tesi. Tamb´ehihacontribu¨ıt aquella gent de Manresa, amb menci´o especial per l’Aura, amb qui fa anys i panys que compartim penes i alegries. Tamb´e els companys del quinto. Malgrat no poder men- cionar tothom amb qui he passat part d’aquests anys i m’han donat un cop de m`a(iem disculpo per aix`o), no em voldria oblidar de la gent de muntanya, de l’Ararat al Punta Alta, amb qui hem compartit cims i aventures que sempre ajuden a veure-ho tot plegat m´es clar. Aquesta tesi ha estat possible gr`acies a la beca de Formaci´o del Professorat Universi- tari que em va ser concedida pel Ministeri d’Educaci´o, a un Ajut de Personal Investigador predoctoral en Formaci´o que em va ser concedit per la Universitat de Barcelona, als programes Enveloppe attractivit´e i Accueil Doc que em van ser concedits per la R´egion Rhˆone-Alpes i al finan¸cament rebut de la Generalitat de Catalunya (2009SGR00014) i del Ministeri d’Educaci´o (FIS2010-21924-C02-02) al Grup de Recerca en F´ısica no Lineal. Xavier Clotet i Fons Manresa, 27 d’abril de 2014 Contents Agra¨ıments i I Thesis 1 Outline of the Thesis 3 1 Introduction 5 1.1 Flow in disordered media ........................... 5 1.1.1 Disordered media ............................ 6 1.1.2 Characterization of the flow ...................... 8 1.2 Capillary rise .................................. 12 1.2.1 Equilibrium height ........................... 14 1.2.2 Capillary Rise Dynamics ........................ 15 1.3 Interfacial fluctuations ............................. 18 1.4 Rough interfaces ................................ 21 1.4.1 Kinetic roughening ........................... 22 1.4.2 Kinetic roughening in imbibition ................... 24 1.5 Avalanche dynamics .............................. 25 1.5.1 Local avalanches ............................ 26 1.5.2 Global spatio-temporal dynamics ................... 30 1.5.3 Intermittency .............................. 34 2 Experimental setup, protocol, and preliminary data analysis 37 2.1 Overview of the setup configurations used .................. 38 2.2 Models of disordered media .......................... 40 2.3 Fluids ...................................... 44 2.4 Driving protocol ................................ 45 2.5 Image acquisition systems ........................... 46 2.6 Methods of analysis .............................. 47 2.7 Experimental protocol ............................. 52 3 Capillary rise in Hele-Shaw models of disordered media 55 3.1 Experimental procedure ............................ 56 3.2 Pressure balance equation ........................... 57 iii iv CONTENTS 3.2.1 Pressure balance formulation in HS models of porous media .... 58 3.2.2 Analytical solutions .......................... 60 3.3 Results ...................................... 61 3.3.1 Capillary rise experiments ....................... 61 3.3.2 Imbibition displacements in a horizontal cell ............. 64 3.4 Analysis and discussion ............................ 64 3.4.1 Contributions to the pressure balance equation ........... 64 3.4.2 Generalized capillary pressure Y ................... 65 3.5 Conclusions ................................... 68 4 Kinetic roughening in forced-flow imbibition 71 4.1 Morphological analysis: base-line correction ................. 72 4.2 Scaling exponents ................................ 76 4.3 Discussion .................................... 77 4.4 Conclusions ................................... 80 5 Local spatio-temporal dynamics 81 5.1 Fluctuations of v(x, y) ............................. 82 5.1.1 Statistical distributions of local velocities .............. 84 5.1.2 Spatial and temporal correlations of v(x, h(x, t)) .......... 87 5.2 Local avalanches ................................ 92 5.2.1 Statistical characterization of local avalanches ............ 94 5.2.2 Scaling relations ............................101 5.2.3 Effect of the disorder on the dynamics of the interface .......103 5.3 Conclusions ...................................105 6 Global spatio-temporal dynamics 107 6.1 Fluctuations of V(t) ..............................108 6.1.1 Statistical analysis of V(t) ......................109 6.1.2 Controlling parameter /c ......................111 6.1.3 Temporal correlation of V(t) .....................112 6.2 Global avalanches ................................115 6.2.1 Effect of the experimental conditions on the statistics of avalanches117 6.2.2 Effect of /c on the distributions of sizes and durations ......120 6.2.3 Collapse of the distributions ......................122 6.2.4 Joint distribution P (S, T ) .......................125 6.2.5 Shape of avalanches ..........................126 6.3 Conclusions ...................................131 7 Experimental evidence of intermittency in slow imbibition 133 7.1 Velocity increments ...............................134 7.2 Characterization of intermittency .......................137 7.3 Controlling parameters of intermittent dynamics ..............140 7.4 Conclusions ...................................144 CONTENTS v 8 Conclusions and future perspectives 147 8.1 Conclusions ...................................147 8.2 Future perspectives ...............................152 II Summaries 155 9 Resum en catal`a 157 9.1 Introducci´o ...................................157 9.2 Sistema experimental ..............................159 9.3 Resultats principals ..............................161 10
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